The number of ways to choose the groups is given as follows:
20 ways.
The probability that both Juan and Maria are in the vaccine group is given as follows:
1/5.
La probabilidad de que Juan y María estén en el grupo de la vacuna de estudio es:
1/5.
What is the combination formula?The number of different combinations of x objects from a set of n elements, when the order of the elements is not important, is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that six people are divided into two groups of 3 people, hence the number of ways to choose the groups is given as follows:
C(6,3) = 6!/(3! x 3!) = 20 ways.
The number of outcomes in which Juan and Maria are in the vaccine group is given as follows:
1 x 1 x 4(the third member can be any of the remaining four people) = 4.
Hence the probability is given as follows:
4/20 = 1/5.
More can be learned about the combination formula at https://brainly.com/question/11732255
#SPJ1
Km = km/h÷km + h . find the consistency of the equation.
A fish tank is 50 cm long and 40 cm wide and 20 cm high how many millimeters of water does the tank hold
Answer:
The fish tank holds 40,000 ml of water.
Step-by-step explanation:
Volume = Length x Width x Height
Volume = 50 x 40 x 20
Volume = 40,000
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?
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.
For more such questions on height, click on:
https://brainly.com/question/28990670
#SPJ8
Parker has 12 blue marbles. Richard has 34
of the number of blue marbles that Parker has.
Part A
Explain how you know that Parker has more blue marbles than Richard without completing the multiplication.
Enter equal to, greater than, or less than in each box.
Multiplying a whole number by a fraction
less than
1 results in a product that is
the original whole number.
Part B
How many blue marbles does Richard have? Enter your answer in the box.
blue marbles
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
coordinate plane with points at negative 14 comma 1 labeled Woozy Wheel, negative 6 comma 2 labeled Bumper Boats, negative 2 comma negative 4 labeled Roller Rail, negative 2 comma negative 6 labeled Trolley Train, 2 comma negative 3 labeled Silly Slide, and 6 comma 11 labeled Parachute Plunge
Determine the distance between the Bumper Boats and the Parachute Plunge.
15 units
225 units
8 units
63 units
Answer:the answer is 15 units
Step-by-step explanation:
just took the test
What is the name of the Platonic solid below
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.
For more such information on: Platonic solid
https://brainly.com/question/32030513
#SPJ8
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
Question 4Multiple Choice Worth 5 points)
(Dilations MC)
Polygon ABCD with vertices at A(1,-1), B(3, -1), C(3, -2), and D(1, -2) is dilated to create polygon ABCD with vertices at A(4, -4), B(12,-4), C(12, -3), and D(4, -3). Determine the scale factor used to
create the image
0 1/4
0 1/2
0 2
0 4
The scale factor used to create the image of polygon ABCD is 4.
To determine the scale factor, we need to compare the corresponding side lengths of the original polygon ABCD and the image polygon ABCD. Let's denote the scale factor as k.
Original polygon ABCD:
Side AB: length = 3 - 1 = 2
Side BC: length = -2 - (-1) = -1
Side CD: length = 1 - 3 = -2
Side DA: length = -2 - (-1) = -1
Image polygon ABCD:
Side AB: length = 12 - 4 = 8
Side BC: length = -3 - (-4) = 1
Side CD: length = 4 - 12 = -8
Side DA: length = -3 - (-4) = 1
Comparing the corresponding side lengths, we can set up the following equations:
k * 2 = 8 (for side AB)
k * (-1) = 1 (for side BC)
k * (-2) = -8 (for side CD)
k * (-1) = 1 (for side DA)
From the equations, we can see that k = 4 satisfies all of them.
Therefore, the scale factor used to create the image of polygon ABCD is 4.
For more such questions on scale factor, click on:
https://brainly.com/question/29967135
#SPJ8
What is the equation in point slope form of the line that is perpendicular to the given line and passes through the point(2,5)?
Answer:
Step-by-step explanation:
To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:
Find the slope of the provided line.
The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.
Substituting the values, the equation of the perpendicular line becomes:
y - 5 = (-1/m)(x - 2)
Simplifying the equation further, we can rewrite it in point-slope form:
y - 5 = (-1/m)x + (2/m)
The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. How many subscribers are needed to bring a total profit of $123,525?
In order to achieve a profit of $123,525, the Vilas County News would require a subscriber base of 6,355,500 individuals.
Let's break down the problem step by step to find the number of subscribers needed to bring a total profit of $123,525.
First, we know that the Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. This means that the current profit from the 3,000 subscribers is $20 x 3,000 = $60,000.
Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. This means that for every additional subscriber, the profit increases by $0.01. Therefore, we need to find how many additional subscribers are required to reach a total profit of $123,525 - $60,000 = $63,525.
To find the number of additional subscribers needed, we divide the additional profit required by the increase in profit per subscriber: $63,525 / $0.01 = 6,352,500.
However, we need to remember that this number represents the total number of additional subscribers needed, not the final total number of subscribers. To find the final total number of subscribers, we add the additional subscribers to the current number of subscribers: 6,352,500 + 3,000 = 6,355,500.
Therefore, to bring a total profit of $123,525, the Vilas County News would need a total of 6,355,500 subscribers.
For more question on profit visit:
https://brainly.com/question/30495119
#SPJ8
HELP PLESSE
The total cost of a lunch is shared among 8 people. the total bill is 55 what is the cost
Answer: A,
Step-by-step explanation:
8 people, times whatever each person payed will equal to 55$ in total
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.
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.
For more such answers on linear regression
https://brainly.com/question/25987747
#SPJ8
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
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.
For similar question on diagonal distance.
https://brainly.com/question/31654603
#SPJ8
If all the values in the series are same, then
Select one:
a. A.M = G.M = H.M
b. A.M > G.M > H.M
c. A.M < G.M < H.M
d. None of these
e. A.M ? G.M ? H.M
Note: A.M means Arithmetic mean, H.M means Harmonic mean, while G.M means Geometric mean.
Any answer without justification will be rejected automatically.
If all the values in the series are the same, the A.M, G.M, and H.M are all equal and can be represented as A.M = G.M = H.M = x.
If all the values in the series are the same, the arithmetic mean (A.M), geometric mean (G.M), and harmonic mean (H.M) will all be equal.
Let's consider a series with the same value repeated n times, denoted as x:
Series: x, x, x, ..., x (n times)
Arithmetic Mean (A.M):
The arithmetic mean is calculated by summing all the values in the series and dividing by the total number of values. In this case, the sum of all the values is nx, and since there are n values, the arithmetic mean is (nx) / n = x. So, A.M = x.
Geometric Mean (G.M):
The geometric mean is calculated by taking the nth root of the product of all the values in the series. In this case, the product of all the values is x^n, and since there are n values, the nth root of x^n is x. So, G.M = x.
Harmonic Mean (H.M):
The harmonic mean is calculated by taking the reciprocal of the arithmetic mean of the reciprocals of all the values in the series. Since all the values are the same, the reciprocal of each value is 1/x. The arithmetic mean of the reciprocals is (1/x + 1/x + ... + 1/x) / n = (n/x) / n = 1/x. Taking the reciprocal of 1/x gives x. So, H.M = x.
For such more question on values:
https://brainly.com/question/26352252
#SPJ8
Margie's work for adding linear expressions is shown below. After checking her answer with the answer key, she solved it incorrectly.
Given (−2.67b + 11) − (5.38b − 15)
Step 1 −2.67b + 11 + (−5.38b) + 15
Step 2 −2.67b + 5.38b + 11 + 15
Step 3 (−2.67b + 5.38b) + (11 + 15)
Step 4 2.71b + 26
Part A: Identify and explain the first step where Margie made an error. (2 points)
Part B: Explain how to correctly write the expression in fewest terms by correcting the error in Part A. Show all work. (2 points)
Step-by-step explanation:
Part A: The first step where Margie made an error is Step 1:
−2.67b + 11 + (−5.38b) + 15
The error lies in the addition of the two terms: (−5.38b) + 15. Margie incorrectly added the two terms together instead of subtracting them.
Part B: To correctly write the expression in the fewest terms, we need to correct the error from Part A. The correct step-by-step process is as follows:
Given: (−2.67b + 11) − (5.38b − 15)
Step 1: Distribute the negative sign to the terms inside the second parentheses:
−2.67b + 11 − 5.38b + 15
Step 2: Combine like terms:
(−2.67b − 5.38b) + (11 + 15)
Step 3: Simplify:
−7.05b + 26
Therefore, the correct expression, written in the fewest terms, is −7.05b + 26.
6 + 9x^2 + 3x^3 + 2x^4 - 12x
how many positive, negative, and complex zeros are there?
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.
For similar question on complex zeros.
https://brainly.com/question/31011487
#SPJ8
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
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
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.
For more such questions on cos visit:
https://brainly.com/question/30339647
#SPJ8
Pls help I need help on this
Answer:
[tex]5a2b2/4[/tex]
Step-by-step explanation:
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!!
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.
For more questions on Circle
https://brainly.com/question/28162977
#SPJ8
Which statement correctly compares the centers of the distributions?
Frequency
10
8
6
Class Sizes at East Hills HS
24 26 28 30 32 34 36 38 40 42 44
Frequency
2864 NO
10
Class Sizes at Southview HS
0
24 26 28 30 32 34 36 38 40 42 44
OA. The median of Southview HS is greater than the median of East
Hills HS.
B. The range of East Hills HS is greater than the range of Southview
HS.
C. The mean of East Hills HS is greater than the mean of Southview
HS.
OD. The mean of Southview HS is greater than the mean of East Hills
HS.
The correct statement is C. The mean of East Hills HS is greater than the mean of Southview HS. So, option C is the correct answer.
To compare the centers of the distributions, we need to consider the measures of central tendency such as the median and the mean.
Looking at the given information about the class sizes at East Hills HS and Southview HS:
East Hills HS class sizes: 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44
Southview HS class sizes: 0, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44
Let's compare the measures of central tendency:
Median: The median is the middle value of a dataset when arranged in ascending or descending order. In this case, both datasets have an odd number of values, so the median is the middle value.
For East Hills HS: Median = 34
For Southview HS: Median = 34
Therefore, the medians of both distributions are the same.
Mean: The mean is calculated by summing all the values in the dataset and dividing by the total number of values.
For East Hills HS: Mean = (24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44) / 11 ≈ 35.727
For Southview HS: Mean = (0 + 24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44) / 12 ≈ 33.667
Therefore, the mean of East Hills HS is greater than the mean of Southview HS.
Based on the comparisons, the correct statement is:
C. The mean of East Hills HS is greater than the mean of Southview HS.
So, option C is the correct answer.
for such more question on distributions
https://brainly.com/question/25224028
#SPJ8
The question is asking for comparison of the centers and range of two data sets - the class sizes at two different high schools. Because no specific numeric data given for the mean and median of both school sizes, it's not possible to definitively choose an answer. Theoretically, if Southview has a higher concentration at larger class sizes, its median and mean might be larger.
Explanation:This question refers to comparing the statistical centers (mean and median) and range of two data sets, which are the class sizes at East Hills High School and Southview High School. The centers and range of a data distribution tell us about the typical values, variety, and spread in the data set.
Without actual numbers (i.e., mean and median) for both the East Hills HS and Southview HS distributions, we can't definitively answer this question. However, let's assume that the representations provided suggest that Southview HS has a higher concentration of students in larger class sizes. In that case, the mean and median for Southview HS could be greater than those for East Hills HS, which would suggest option A and D. With regards to the range, if the minimum and maximum values of class sizes are the same in both schools, then the range, which is the difference between the maximum and minimum, would be the same. Therefore, option B wouldn't be accurate. However, as previously mentioned, this can only be suggestive as actual numbers are required for a definite answer.
Learn more about Statistics here:https://brainly.com/question/31538429
#SPJ2
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?
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.
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?
pls pls pls help
Based on the graph of F(x) below, which of the following statements is true
about F(x)?
The correct statement regarding the relative extremas of F(x) is given as follows:
F(x) has a relative maximum at x = -1 and a relative minimum at x = -0.8.
What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing.Hence the extremas for this problem are given as follows:
Maximum: x = -1.Minimum: x = 0.8.More can be learned about relative minimums of a function at https://brainly.com/question/9839310
#SPJ1
Use basic inference rules to establish the validity of the argument: p ⟹ ¬q ,q V r ,p V u ,¬r├ u
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.
For more such questions on validity, click on:
https://brainly.com/question/16216589
#SPJ8
Need help on this!!! Pls help!!!
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.
More can be learned about the mean of a data-set at brainly.com/question/1156334
#SPJ1
Which of the following numbers is closest to 7? √51 50 46 st
Answer:
Step-by-step explanation:To determine which of the given numbers is closest to 7, we can calculate the absolute difference between each number and 7 and choose the number with the smallest absolute difference.
Let's calculate the absolute differences:
Absolute difference between √51 and 7:
|√51 - 7| ≈ 7.13 - 7 ≈ 0.13
Absolute difference between 50 and 7:
|50 - 7| = 43
Absolute difference between 46 and 7:
|46 - 7| = 39
Comparing the absolute differences, we can see that the number closest to 7 is √51. The absolute difference between √51 and 7 is the smallest among the given options.
Therefore, √51 is the number closest to 7.
"Valeria and her family play the board game Parrots and Pirates on game night. Players who land on a cannon space roll a 6-sided weighted penalty die to determine how many gold doubloons they will lose. To see how the die is weighted, Valeria rolls it 15 times and records the results. Based on the data, what is the probability of rolling a 6 with this die.
The probability of rolling a 6 with this die would be = 1/15.
How determine the outcome of the given event?To determine the possibility of the given event, the formula for probability should be used and it's given below as follows:
Probability= Possible outcome/sample space
where;
possible outcome= 1
sample space= 15
Probability = 1/15
Learn more about probability here:
https://brainly.com/question/31123570
#SPJ1
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
%.
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%.
For more such questions on percentile,click on
https://brainly.com/question/28839672
#SPJ8
Which point could not be part of a function that includes (3, -1), (4, 2), (5, 4), (-2, 0), and (8, -3)?
(6, -7)
(2,2)
(3, -2)
(7, 4)
Answer:
(3, -2) is the correct choice.
The ratio of males to females is 2:3. there are 12 boys in class. How many females are in the class
Answer:
Number of Females in Class = x Given: Ratio of Males to Females = 2:3 Given: Number of Males in Class = 12 Assume the total number of people in class = y 2/3 of y = x 2x = 3y 12 + x = y y - 12 = x y - 12 = 2x 3y - 36 = 2x 3y = 2x + 36 y = (2x + 36) / 3 y = (2(12) + 36)/3 y = 24 x = y - 12 x = 24 - 12 x = 12 Answer: There are 12 females in the class.
Step-by-step explanation: