Answers
Answer:
Step-by-step explanation:
Let the centre be C.
Since TR is a straight line,
∠SCT + ∠SCR = 180
∠SCT = 180 - 53
∠SCT = 127
The angle of a semicircle is 180°. Minor arcs are arcs less than a semicircle i.e. less than 180° and major arcs are arcs greator than a semicircle i.e. greater than 180°.
a) arc(SPT) has measure of 90 + 65 + 25 + 53 = 233° > 180° and hence a major arc
Also 1° = π/180 radians
233° = 233 * π/180 = 1.29π radians
b) arc(ST) has measure of 127° < 180° and hence a minor arc
127° = 127 * π/180 = 0.71π radians
c) arc(RST) has a measure of 53 + 127 = 180° which is a semicircle
180° = 180* π/180 = π radians
d) arc(SP) has a measure of 53 + 25 + 65 = 143° < 180° and hence a minor arc
143° = 143* π/180 = 0.79π radians
e) arc(QST) has a measure of 25 + 53 + 127 = 205° > 180° and hence a major arc
205° = 205 * π/180 = 1.14π radians
f) arc(TQ) has a measure of 90 + 65 = 155° < 180° and hence a minor arc
155° = 155 * π/180 = 0.86π radians
Answer:
[tex]\text{a.} \quad \text{Major arc}:\;\;\overset{\frown}{SPT}=233^{\circ}[/tex]
[tex]\text{b.} \quad \text{Minor arc}:\;\;\overset{\frown}{ST}=127^{\circ}[/tex]
[tex]\text{c.} \quad \text{Semicircle}:\;\;\overset{\frown}{RST}=180^{\circ}[/tex]
[tex]\text{d.} \quad \text{Minor arc}:\;\;\overset{\frown}{SP}=143^{\circ}[/tex]
[tex]\text{e.} \quad \text{Major arc}:\;\;\overset{\frown}{QST}=205^{\circ}[/tex]
[tex]\text{F.} \quad \text{Minor arc}:\;\;\overset{\frown}{TQ}=155^{\circ}[/tex]
Step-by-step explanation:
Major ArcA major arc is an arc in a circle that measures more than 180°.
It is named with three letters: two endpoints and a third point on the arc.
Minor ArcA minor arc is an arc in a circle that measures less than 180°.
It is named with two letters: its two endpoints.
SemicircleA semicircle is a special case of an arc that measures exactly 180°.
The endpoints of the semicircle are located on the diameter, and the semicircle divides the circle into two equal parts.
Arc of a circleThe measure of an arc of a circle is equal to the measure of its corresponding central angle.
[tex]\hrulefill[/tex]
a) Arc SPT is a major arc since it is named with three letters.
It begins at point S, passes through point P, and ends at point T.
[tex]\begin{aligned}\overset{\frown}{SPT}&=\overset{\frown}{SR}+\overset{\frown}{RQ}+\overset{\frown}{QP}+\overset{\frown}{PT}\\&=53^{\circ}+25^{\circ}+65^{\circ}+90^{\circ}\\&=233^{\circ}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
b) Arc ST is a minor arc since it is named with two letters.
It is measured in a counterclockwise direction from point S to point T.
[tex]\begin{aligned}\overset{\frown}{ST}&=360^{\circ}-\overset{\frown}{SPT}\\&=360^{\circ}-233^{\circ}\\&=127^{\circ}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
c) Arc RST is a semicircle.
Arc RST is a semicircle since its endpoints are located on the diameter of the circle, RT.
[tex]\overset{\frown}{RST}=180^{\circ}[/tex]
[tex]\hrulefill[/tex]
d) Arc SP is a minor arc since it is named with two letters.
It is measured in a clockwise direction from point S to point P.
(If it was measured in a counterclockwise direction, it would be a major arc, as it would be more than 180°, and therefore would be named using three letters).
[tex]\begin{aligned}\overset{\frown}{SP}&=\overset{\frown}{SR}+\overset{\frown}{RQ}+\overset{\frown}{QP}\\&=53^{\circ}+25^{\circ}+65^{\circ}\\&=143^{\circ}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
e) Arc QST is a major arc since it is named with three letters.
It begins at point Q, passes through point S, and ends at point T.
[tex]\begin{aligned}\overset{\frown}{QST}&=\overset{\frown}{QR}+\overset{\frown}{RS}+\overset{\frown}{ST}\\&=25^{\circ}+53^{\circ}+127^{\circ}\\&=205^{\circ}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
f) Arc TQ is a minor arc since it is named with two letters.
It is measured in a counterclockwise direction from point T to point Q.
(If it was measured in a clockwise direction, it would be a major arc, as it would be more than 180°, and therefore would be named using three letters).
[tex]\begin{aligned}\overset{\frown}{TQ}&=\overset{\frown}{TP}+\overset{\frown}{PQ}\\&=90^{\circ}+65^{\circ}\\&=155^{\circ}\end{aligned}[/tex]
Related Questions
Ian took out a $19,000 personal loan to pay for his home renovations. He will not make a payment for 5 years and there is a 15% interest rate. How much will be owed in 5 years with monthly compounding?
Round your answer to the nearest cent.
Do NOT round until your final answer.
Answers
The amount owed in 5 years with monthly compounding, considering a $19,000 personal loan with a 15% interest rate, will be $34,558.52.
1. Convert the interest rate to a decimal: 15% = 0.15.
2. Determine the number of compounding periods: Since the loan compounds monthly, multiply the number of years by 12. In this case, 5 years * 12 months/year = 60 months.
3. Calculate the monthly interest rate: Divide the annual interest rate by 12. In this case, 0.15 / 12 = 0.0125.
4. Use the compound interest formula to calculate the future value:
Future Value = Principal * (1 + Monthly Interest Rate)^(Number of Compounding Periods)
Future Value = $19,000 * (1 + 0.0[tex]125)^{(60[/tex])
5. Evaluate the expression inside the parentheses: (1 + 0.0[tex]125)^{(60[/tex]) ≈ 1.954503.
6. Multiply the principal by the evaluated expression: $19,000 * 1.954503 = $37,133.57 (unrounded).
7. Round the final answer to the nearest cent: $34,558.52.
Therefore, in 5 years with monthly compounding, the amount owed on the $19,000 personal loan will be approximately $34,558.52.
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What is the name of the Platonic solid below
Answers
The name of the Platonic solid that resembles a cuboid is the hexahedron, or more commonly known as a cube.
The correct answer is option C.
The name of the Platonic solid that resembles a cuboid is the hexahedron, also known as a cube. The hexahedron is one of the five Platonic solids, which are regular, convex polyhedra with identical faces, angles, and edge lengths. The hexahedron is characterized by its six square faces, twelve edges, and eight vertices.
The term "cuboid" is often used in general geometry to describe a rectangular prism with six rectangular faces. However, in the context of Platonic solids, the specific name for the solid resembling a cuboid is the hexahedron.
The hexahedron is a highly symmetrical three-dimensional shape. All of its faces are congruent squares, and each vertex is formed by three edges meeting at right angles. The hexahedron exhibits symmetry under several transformations, including rotations and reflections.
Its regularity and symmetry make the hexahedron an important geometric shape in mathematics and design. It has numerous applications in architecture, engineering, and computer graphics. The cube, as a special case of the hexahedron, is particularly well-known and widely used in everyday life, from dice and building blocks to cubic containers and architectural structures.
Therefore, the option which is the correct is C.
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The question probable may be:
What is the name of the Platonic solid which resembles a cuboid?
A. Dodecaheron
B. Tetrahedron
C. Hexahedron
D. Octahedron
The time (in minutes) between volcanic eruptions was measured along with the duration (in minutes) of the eruption.
Use the data to answer the following question.
Time Between Eruptions 12.17 11.63 12.03 12.15 11.30 11.70 12.27 11.60 11.72
Duration of Eruption 2.01 1.93 1.97 1.99 1.87 1.99 2.11 1.96 2.03
Your answers should be numerical values. If necessary, round to four decimal places. Use rounded
answers for subsequent questions parts.
The value of the linear correlation coefficient is
The value of the coefficient of determination is
The regression line is y =
The predicted duration of an eruption is
The residual for x = 12.03 is
x+
minutes if the time between eruptions is 12.03 minutes.
Answers
The actual duration of eruption for x = 12.03 is 1.97 minutes, so the residual is 1.97 - 3.8431 = -1.8731 minutes.
The value of the linear correlation coefficient, also known as the Pearson correlation coefficient, measures the strength and direction of the linear relationship between two variables.
In this case, it represents the correlation between the time between eruptions and the duration of the eruption. To calculate the linear correlation coefficient, we can use the given data. The linear correlation coefficient is 0.8404.
The coefficient of determination, denoted as R-squared, represents the proportion of the variance in the dependent variable (duration of eruption) that can be explained by the independent variable (time between eruptions).
It is calculated by squaring the linear correlation coefficient. In this case, the coefficient of determination is 0.7055.
The regression line represents the best-fit line that approximates the relationship between the independent and dependent variables.
It can be expressed in the form of y = mx + b, where y represents the predicted duration of the eruption, x represents the time between eruptions, m represents the slope of the line, and b represents the y-intercept.
To determine the regression line, we can perform linear regression analysis using the given data. The regression line is y = 0.1608x + 1.8305.
The predicted duration of an eruption can be calculated by substituting the given time between eruptions value into the regression line equation. For x = 12.03 minutes, the predicted duration of an eruption is y = 0.1608 x 12.03 + 1.8305 = 3.8431 minutes.
The residual for x = 12.03 is the difference between the actual duration of eruption and the predicted duration. It can be calculated by subtracting the predicted value from the actual value. The actual duration of eruption for x = 12.03 is 1.97 minutes, so the residual is 1.97 - 3.8431 = -1.8731 minutes.
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There are 6 horses in a race. How many ways can the first three positions of the order of the finish occur assume there are no ties
Answers
Since there are 6 horses competing for the first position, there are 6 possibilities for the first place.
Once the first place is determined, there are 5 remaining horses for the second place, and then 4 remaining horses for the third place.
Therefore, the total number of ways is calculated as follows:
6 (possibilities for first place) × 5 (possibilities for second place) × 4 (possibilities for third place) = 120 ways.
So, there are 120 different ways the first three positions can occur in the race.
A person observes the top of a radio antenna at an angle of elevation of 5 degrees after getting 1 mile closer to the antenna the angle of elevation is 10 degrees how tall is the antenna to the nearest tenth of a foot?
Answers
The height of the antenna is approximately 5.1 feet.
1. Let's assume the height of the antenna as 'h' feet.
2. We have two angles of elevation: 5 degrees and 10 degrees.
3. When the person is 1 mile closer to the antenna, the change in the angle of elevation is 10 - 5 = 5 degrees.
4. We can use the tangent function to find the height of the antenna. The tangent of an angle is equal to the opposite side divided by the adjacent side.
5. The opposite side is the change in height, which is h feet (since the person moved closer by 1 mile, the change in height is equal to the height of the antenna).
6. The adjacent side is the horizontal distance from the person to the antenna. We can use trigonometry to find this distance.
7. In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
tan(5 degrees) = h / x (where x is the horizontal distance in miles)
8. Similarly, after moving closer, the tangent of the angle becomes:
tan(10 degrees) = h / (x - 1)
9. We can solve these two equations simultaneously to find the value of h.
10. Rearranging the equations, we get:
h = x * tan(5 degrees)
h = (x - 1) * tan(10 degrees)
11. Setting the two expressions for h equal to each other, we have:
x * tan(5 degrees) = (x - 1) * tan(10 degrees)
12. Solving this equation for x, we find:
x = tan(10 degrees) / (tan(10 degrees) - tan(5 degrees))
13. Substitute the value of x back into one of the earlier equations to find h:
h = x * tan(5 degrees)
14. Calculate the value of h using a calculator:
h ≈ 1 * tan(5 degrees) ≈ 0.0875 miles ≈ 0.0875 * 5280 feet ≈ 461.4 feet
15. Rounded to the nearest tenth of a foot, the height of the antenna is approximately 5.1 feet.
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6 + 9x^2 + 3x^3 + 2x^4 - 12x
how many positive, negative, and complex zeros are there?
Answers
There are no positive or negative zeros, and the number of complex zeros cannot be determined without further information.
To determine the number of positive, negative, and complex zeros of the given polynomial [tex]6 + 9x^2 + 3x^3 + 2x^4 - 12x,[/tex] we need to analyze its behavior and apply the properties of polynomial functions.
Positive Zeros:
Positive zeros are the values of x for which the polynomial evaluates to zero.
To find positive zeros, we set the polynomial equal to zero and solve for x.
However, in this case, we can see that all the coefficients of the terms in the polynomial are positive.
Therefore, there are no positive zeros.
Negative Zeros:
Negative zeros are the values of x for which the polynomial evaluates to zero.
Similar to positive zeros, we set the polynomial equal to zero and solve for x.
However, in this case, we can see that all the coefficients of the terms in the polynomial are positive.
Therefore, there are no negative zeros.
Complex Zeros:
Complex zeros occur when the polynomial has complex roots. Since the given polynomial has only real coefficients, complex zeros will occur in conjugate pairs.
To determine the number of complex zeros, we need to examine the degree of the polynomial.
In this case, the highest power of x is [tex]4 (x^4),[/tex] indicating a fourth-degree polynomial.
A fourth-degree polynomial can have at most four complex zeros. However, we cannot determine the exact number of complex zeros without further information or solving the polynomial explicitly.
In conclusion, the given polynomial has no positive or negative zeros due to all coefficients being positive.
The number of complex zeros cannot be determined without additional information.
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In 2010, the population of Houston, Texas, was 2,099,451. In 2017, Houston's population was estimated to be 2,312,717. What is the estimated annual growth rate of Houston's population?
Answers
Answer:
it 10:579
Step-by-step explanation:
it is the anser
Question 9(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
A fair, 6-sided die is rolled 50 times. Predict how many times it will land on a number greater than 3.
1/2
5
25
50
Answers
Answer:
A 1/2
Step-by-step explanation:
was on my test trust me on this one
On the dice there are six outcome (1,2,3,4,5,6)
1.3.5 - odd
2,4,6 - even
Therefore half of them are even outcomes
Even chance = 1/2
Hope this helps!
please help i’m confused
Answers
The regression equation is y = 17.1643X - 2.47977
What is the equation of regression?To solve this problem, we have to calculate the equation of regression.
Sum of X = 2.97
Sum of Y = 28.66
Mean X = 0.33
Mean Y = 3.1844
Sum of squares (SSX) = 0.3552
Sum of products (SP) = 6.0959
Regression Equation = y = bX + a
b = SP/SSX = 6.1/0.36 = 17.1643
a = MY - bMX = 3.18 - (17.16*0.33) = -2.47977
y = 17.1643X - 2.47977
The line of best fit is y = 17.1643X - 2.47977
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Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is
%.
Answers
The percentile of 6.2 in the given dataset is 30%. This means that 30% of the values in the dataset are lower than or equal to 6.2.
To determine the percentile of 6.2 in the given dataset, we need to calculate the percentage of values in the dataset that are lower than or equal to 6.2.
First, we arrange the dataset in ascending order: 4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2.
Next, we count the number of values that are lower than or equal to 6.2. In this case, there are three values: 4.2, 4.6, and 5.1.
The next step is to calculate the percentage. We divide the count (3) by the total number of values in the dataset (10) and multiply by 100.
(3/10) * 100 = 0.3 * 100 = 30%
Percentiles are used to understand the relative position of a particular value within a dataset. In this case, 6.2 is higher than 30% of the values in the dataset and lower than the remaining 70%.
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Solve the system of equations. 8 � + 5 � = 24 � = − 4 � 8x+5y=24 y=−4x
Answers
The solution to the system of equations is x = 2 and y = -8.
To solve the system of equations, we'll use the substitution method. The given equations are:
Equation 1: 8x + 5y = 24
Equation 2: y = -4x
We'll substitute Equation 2 into Equation 1 to eliminate one variable:
8x + 5(-4x) = 24
8x - 20x = 24 [Distribute the -4]
-12x = 24 [Combine like terms]
x = 24 / -12 [Divide both sides by -12]
x = -2
Now that we have the value of x, we can substitute it back into Equation 2 to find the value of y:
y = -4(-2)
y = 8
Therefore, the solution to the system of equations is x = -2 and y = 8.
However, let's double-check the solution by substituting these values into the original equations:
Equation 1: 8(-2) + 5(8) = 24
-16 + 40 = 24
24 = 24 [LHS = RHS, equation is satisfied]
Equation 2: 8 = -4(-2)
8 = 8 [LHS = RHS, equation is satisfied]
Both equations are satisfied, confirming that x = -2 and y = 8 is indeed the solution to the given system of equations.
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NO LINKS!! URGENT HELP PLEASE!!!
4. What is a regular polygon?
5. For a regular pentagon, (NOT MULTIPLE CHOICE),
a. Find the measure of a single interior angle.
b. Find the measure of a single exterior angle.
6. The measure of the interior angle of a regular polygon is 162°. How many sides does it have?
Answers
5. For a regular pentagon:
a. The measure of a single interior angle can be found using the formula: (n - 2) * 180° / n, where n represents the number of sides of the polygon. For a pentagon, n = 5. Plugging the values into the formula:
Single interior angle = (5 - 2) * 180° / 5 = 3 * 180° / 5 = 540° / 5 = 108°
b. The measure of a single exterior angle in a regular polygon can be found by subtracting the measure of the corresponding interior angle from 180°.
Single exterior angle = 180° - Single interior angle = 180° - 108° = 72°
6. If the measure of the interior angle of a regular polygon is 162°, we can use the formula for the measure of a single interior angle: (n - 2) * 180° / n = 162°, where n represents the number of sides of the polygon.
Solving for n:
(n - 2) * 180° / n = 162°
Multiplying both sides by n:
(n - 2) * 180° = 162° * n
Distributing:
180°n - 360° = 162°n
Subtracting 180°n from both sides:
-360° = -18°n
Dividing both sides by -18°:
n = 20
Therefore, the regular polygon with an interior angle of 162° has 20 sides.
Star answer please ?
Answer:
4.
A regular polygon is a polygon in which all sides are equal in length and all angles are equal in measure.
5.
a. The measure of a single interior angle in a regular pentagon is:
[(n – 2)*180°]/n = 540°/5 = 108°.
b. The measure of a single exterior angle in a regular pentagon is:
360°/n = 360°/5 = 72°.
6.
This can be found using the following formula:
[(n – 2)*180°]/n = Interior angle
(n-2)*180=162°*n
180n-360=162n
180n-162n=360
18n=360
n=360/18
n=20
where n is the number of sides in the regular polygon.
A regular polygon with an interior angle of 162° has 20 sides.
Use a Calculator to evaluate The following. Round the answer to the nearest hundredths
1. Cos 10
2. Sin 30
3. Sin 20
4. Tan 25
5. Tan 48.5
Answers
1. Using a calculator, we find that cos 10 ≈ 0.98.
2. Using a calculator, we find that sin 30 ≈ 0.50.
3. Using a calculator, we find that sin 20 ≈ 0.34.
4. Using a calculator, we find that tan 25 ≈ 0.47.
5. Using a calculator, we find that tan 48.5 ≈ 1.14.
Using a calculator to evaluate the given trigonometric functions, rounded to the nearest hundredth, we have:
Cos 10:
Using a calculator, we find that cos 10 ≈ 0.98.
Sin 30:
Using a calculator, we find that sin 30 ≈ 0.50.
Sin 20:
Using a calculator, we find that sin 20 ≈ 0.34.
Tan 25:
Using a calculator, we find that tan 25 ≈ 0.47.
Tan 48.5:
Using a calculator, we find that tan 48.5 ≈ 1.14.
These values represent the approximate decimal values of the trigonometric functions at the given angles, rounded to the nearest hundredth.
Just a reminder, when using a calculator, make sure it is set to the correct angle mode (degrees or radians) as per the given problem.
It's important to note that these values are approximate since they are rounded to the nearest hundredth. If you need more precise values, you can use a calculator that allows for a greater number of decimal places or use trigonometric tables.
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PLS HELPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
The correct option is the 3rd one
angle 1 = angle 4 = angle 5 = angle 8 = 60 degrees,
angle 2 = angle 3 = angle 6 = angle 7 = 120 degrees
Step-by-step explanation:
To solve this, we only need to look at the top two angles, 1 and 2
Since line l is a line, angle 1 and 2 must sum to 180,
Since angle 1 = 60 degrees, then,
angle 1 + angle 2 = 180
60 + angle 2 = 180
angle 2 = 120 degrees
the only option that corresponds to this is the third option,
angle 1 = angle 4 = angle 5 = angle 8 = 60 degrees,
angle 2 = angle 3 =
Given the piecewise functions shown below, select all of the statements that are true.
Answers
The true statements are:
a. f(-1) = 2
c. f(1) = 0
Let's evaluate each statement using the given piecewise function f(x):
a. f(-1) = -(-1) + 1 = 2
b. f(-2) = -(-2) + 1 = 3 (Not 0, so this statement is false)
c. f(1) = (1)^2 - 1 = 0
d. f(4) = (4)^2 - 1 = 16 - 1 = 15 (Not 7, so this statement is false)
Therefore, the correct statements are:
a. f(-1) = 2
c. f(1) = 0
Statement a is true because when x = -1, we use the first piece of the piecewise function, which gives us -(-1) + 1 = 2.
Statement c is true because when x = 1, we use the third piece of the piecewise function, which gives us (1)^2 - 1 = 0.
Statements b and d are false because they do not match the corresponding values obtained from evaluating the piecewise function at the given inputs.
Therefore, the true statements are:
a. f(-1) = 2
c. f(1) = 0
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Circle 1 has center (-6, 2) and a radius of 8 cm. Circle 2 has center (-1,-4) and a radius 6 cm.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter your answers in the boxes. URGENT PLEASE!!
Answers
Circle 1 (-6, 2) with a radius of 8 cm can be transformed into Circle 2 (-1, -4) with a radius of 6 cm through translation, scaling, and translation, proving their similarity.
To prove that two circles are similar, we need to find a sequence of transformations that maps one circle to another circle. In this case, we need to find a sequence of transformations that map Circle 1 to Circle 2. Circle 1 has a center (-6, 2) and a radius of 8 cm. Circle 2 has a center (-1,-4) and a radius of 6 cm.
Let's write the equations of the two circles:C1: (x + 6)² + (y - 2)² = 64C2: (x + 1)² + (y + 4)² = 36Step 1: TranslationWe can translate Circle 1 by (-5,-6) to obtain a new circle with center at the origin. The equation of the translated circle is C1': (x + 11)² + (y - 4)² = 64Step 2: Scale
We can scale the translated Circle 1' by a factor of 3/4 to obtain a circle with a radius of 6.
The equation of the scaled circle is C1'': (x + 11)² + (y - 4)² = 36Step 3: TranslationWe can translate the scaled Circle 1'' by (2,-4) to obtain a new circle with center at (-1,-4). The equation of the translated circle is C1''': (x - 1)² + (y + 4)² = 36The transformations applied to Circle 1 to obtain Circle 2 are:
Translation by (-5,-6)
Scale by 3/4
Translation by (2,-4)
Therefore, we can say that Circle 1 and Circle 2 are similar. Circle 1 can be transformed into Circle 2 by translation, scale, and translation.
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Evaluate the expression. −3[−4(3−10)−12] over −2(−1) What is the value of the expression?
Answers
Answer: -24
Step-by-step explanation:
To evaluate the expression, I guess we need to break it down into steps:
Expression: -3[-4(3-10)-12] / -2(-1)
Step1: Simplify the innermost parentheses Inside the square brackets: 3 - 10 = -7 Expression becomes: -3[-4(-7) - 12] / -2(-1)
Step2: Simplify the multiplication in square brackets: -4 * (-7) = 28. Expression becomes: -3[28 - 12] / -2(-1)
Step3: Simplify the subtraction inside the square brackets: 28 - 12 = 16. Expression becomes: -3[16] / -2(-1)
Step4: Simplify the multiplication outside the square brackets: -3 * 16 = -48. Expression becomes: -48 / -2(-1)
Step5: Simplify the multiplication inside the denominator: -2 * (-1) = 2 Expression becomes: -48 / 2
Step 6: Perform the division -48 divided by 2 is equal to -24
Therefore, the value of the expression -3[-4(3-10)-12] / -2(-1) is -24.
taber invested money in an account where interest is compounded every year. he made no withdrawals or deposits. the function A(t) = 525(1+0.05) represents the amount of money in the account after t years. how much money did taber originally invest?
Answers
witch of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it
a. length(time)
b.Time(race)
c.time(length)
d.cost(time)
Answers
The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".
When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.
In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.
a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.
b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.
c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.
d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.
Therefore, "time(length)" is the most suitable and appropriate name for the function.
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Need help on this!!! Pls help!!!
Answers
a) The mean of the data-set is of 2.
b) The range of the data-set is of 4 units, which is of around 4.3 MADs.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.
The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:
Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)
Mean = 2.
The range is the difference between the largest observation and the smallest, hence:
4 - 0 = 4.
4/0.93 = 4.3 MADs.
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Select all the correct answers.
Third
B.
90 feet
A. 16, 200 feet
√180 feet
C. √16, 200 feet
180 feet
D.
The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first base throws the ball to a
player at third base, what is the distance the player has to throw?
First
90 feet
Home
Reset
Next
Answers
The diagonal distance from home plate to third base is approximately √16,200 feet.
The correct answers are:
B. 90 feet
C. √16,200 feet
D. 180 feet.
In baseball, the bases are arranged in a square shape.
The distance between each base is 90 feet.
Therefore, the correct answer for the distance a player at first base has to throw to a player at third base is 90 feet (option B).
To find the diagonal distance from home plate to third base, we can use the Pythagorean theorem.
Since the area of the baseball field is a square, the diagonal distance represents the hypotenuse of a right triangles.
The two legs of the right triangle are the sides of the square, which are 90 feet each.
Using the Pythagorean theorem [tex](a^2 + b^2 = c^2),[/tex] we can calculate the diagonal distance:
a = b = 90 feet
[tex]c^2 = 90^2 + 90^2[/tex]
[tex]c^2 = 8,100 + 8,100[/tex]
[tex]c^2 = 16,200[/tex]
c = √16,200 feet (option C)
Therefore, the diagonal distance from home plate to third base is approximately √16,200 feet.
The options A, √180 feet, and 180 feet are incorrect because they do not represent the correct distances in the given scenario.
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50 points. Will give brainliest.
Write a polynomial equation that has roots: 3, √2 and -4i.
Answers
Answer:
Step-by-step explanation:
Given x=3, [tex]\sqrt{2}[/tex], and -4i
y= (x-3)([tex]x^{2}[/tex]-2)([tex]x^{2}[/tex]+16)
Answer:
x^4 - 3x^3 - 16√2x^2 + (16√2 + 16)x - 48 = 0
Step-by-step explanation:
If the roots of a polynomial equation are 3, √2 and -4i, then the factors of that polynomial are (x - 3), (x - √2) and (x + 4i), since each factor represents one of the roots.
However, since -4i is a complex number, its conjugate 4i is also a root of the polynomial. So we also need the factor (x - 4i).
Thus, the polynomial equation is:
(x - 3) (x - √2) (x + 4i) (x - 4i) = 0
To simplify this equation, we can use the fact that (a + bi)(a - bi) = a^2 - b^2i^2 = a^2 + b^2:
(x - 3) (x - √2) (x^2 + 16) = 0
Expanding this equation yields:
x^4 - 3x^3 + 16x - 16√2x^2 + 48√2x - 48 = 0
So the polynomial equation with roots 3, √2, and -4i is:
x^4 - 3x^3 - 16√2x^2 + (16√2 + 16)x - 48 = 0
What 2 numbers can multiply to -40 and add up to 6
Answers
Answer: 10 and -4
Step-by-step explanation: 10 + - 4 = 6 and 10 x -4 = -40
Which expression is equivalent to a18a6
Answers
Answer:
[tex]\textsf{B.} \quad a^{12}[/tex]
Step-by-step explanation:
To simplify the given rational expression, we can apply the rule of exponents, which states that when dividing two powers with the same base, we subtract the exponents.
Using this rule:
[tex]\dfrac{a^{18}}{a^{6}}= a^{18-6} = a^{12}[/tex]
Therefore, the given rational expression is equivalent to a¹².
Use basic inference rules to establish the validity of the argument: p ⟹ ¬q ,q V r ,p V u ,¬r├ u
Answers
Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.
1. We are given the following premises:
- p ⟹ ¬q (Premise 1)
- q V r (Premise 2)
- p V u (Premise 3)
- ¬r (Premise 4)
2. To prove the conclusion, u, we need to use the premises and apply inference rules.
3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.
4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.
5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.
6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.
7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.
8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.
9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.
10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.
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Algebra Question
68% Oppose year round school
32% Favor year round school
Error +/- 5%
The error given in the graph represents the actual percent could be 5% more or 5% less than the percent reported by the survey.
A. Write and solve an absolute value equation to determine the least and greatest percent of students who could be in favor of year-round school.
B. A classmate claims that ⅓ of the student body is actually in favor of year-round school. Does this conflict with the survey data? Explain.
*can't add graph for some reason
Answers
A. To determine the least and greatest percentage of students who could be in favor of year-round school, we can use the error given in the survey, which is +/5%. Let's denote the actual percentage of students in favor of year-round school as x.
The least percentage can be found by subtracting 5% from the reported percentage of 32%:
32% - 5% = 27%
So, the least percentage of students in favor of year-round school is 27%.
The greatest percentage can be found by adding 5% to the reported percentage of 32%:
32% + 5% = 37%
Therefore, the greatest percentage of students in favor of year-round school is 37%.
Hence, the least percentage is 27% and the greatest percentage is 37%.
B. A classmate claiming that ⅓ of the student body is actually in favor of year-round school conflicts with the survey data. According to the survey, the reported percentage in favor of year-round school is 32%, which is not equal to 33.3% (⅓). Therefore, the classmate's claim contradicts the survey results.
It's important to note that the survey provides specific data regarding the percentages of students in favor and opposed to year-round school. The claim of ⅓ being in favor does not align with the survey's findings and should be evaluated separately from the survey data.
B
E
7
4
3
1
-2 -1 0
D
Determine the line of reflection.
O Reflection across x = 4
Reflection across y = 4
Reflection across the x-axis
Reflection across the y-axis
3
4
C
D'
8
E'
9
10
B'
A'
11
Answers
Answer: 10
Step-by-step explanation: it is a 5+ 5 =
Jenny is watching her favorite soccer team playing a match. The odds against her favorite team winning are 7/10. What is the probability of her favorite team winning?
Answers
Answer:
70%
Step-by-step explanation:
Find the 15th term of the geometric sequence 8,32,128
Answers
Answer:
2147483648
Step-by-step explanation:
Write the geometric sequence as an explicit formula
[tex]8,\,32,\,128\rightarrow8(4)^0,8(4)^1,8(4)^2\rightarrow a_n=a_1r^{n-1}\rightarrow a_n=8(4)^{n-1}[/tex]
Find the n=15th term
[tex]a_{15}=8(4)^{15-1}=8(4)^{14}=8(268435456)=2147483648[/tex]
Which graph represents a function
Answers
Answer:
The one at the bottom right above the next button
Step-by-step explanation: