The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 4500 pounds on Planet A, find the elephant's weight on Planet B.
Based on the ratio of the weights of objects in Planet A to Planet B, an elephants weighing 4,500 pounds on Planet A would weigh 135 pounds on Planet B
How to find the weight?The ratio of the weight of an object in Planet A is 100 to 3 on Planet B. This means that every 100 pounds on Planet A is 3 pounds on Planet B.
If an elephant on Planet A is 4,500 pounds, on Planet B it would weigh:
Weight on Planet B = (4,500 x 3) / 100
Weight on Planet B = 13,500 / 100
Weight on Planet B = 135 pounds
In conclusion, the weight of the elephant on Planet B would be 135 pounds.
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Logan is having his dog professionally groomed and wants to tip the groomer 15%. What equation can Logan use to calculate the tip, y, if his total bill is x dollars?
Answer:
y = 1.15x
Step-by-step explanation:
15% = 0.15
100% = total bill
Total bill + 15% = 115% or 1.15
x × 1.15 = y
One spring day, Grayson noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 58° F. For the next 5 hours, the temperature rose 1° per hour. For the next 3 hours, it rose 3° per hour. The temperature then stayed steady until 6 p.m. For the next 4 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 63° at midnight. On the set of axes below, graph Grayson's data.
On the graph that is included with the solution, the temperature fluctuations are depicted.
A graph is a representation of the relationship between two variables, often measured along one of two right-angled axes each.
It is 56° at 6 a.m.
It rises to 61° for the next 5 hours because it is increasing by 1° per hour, and after another 4 hours it will rise to 69° because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it fell for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.
It is 56° at 6 a.m. The temperature rises to 61° for the next 5 hours because it is increasing by 1° per hour, and then after 4 hours it will rise to 69° again because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it dropped for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.
The final graph is shown in the below attached figure.
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7 x - 7; x = 4!!!???
Answer: 21 x=4
Solve the system of equations
Steps:
Evaluate
{ 7x−7 x=4
Calculate
{ x=4 21
Solution
{ 21 x=4
Find the circumference of the circle. Use 3.14 for x
17 ft
The circumference of the circle with a radius of 7 ft is 106.76 ft
What is circumference?The circumference of a circle is the perimeter of the circle
How to calculate the circumference?The given parameters are
Radius = 17 ft
As a general rule, radius are represented by the variable r
So, we have the following representation equation
r = 17
The circumference of the circle is then calculated as
C = 2πr
Next, we substitute the value of the variable r in the above equation
i.e. r = 17
So, we have the following equation
C = 2π * 17
From the question, we have
π = 3.14
So, we have the following equation
C = 2 * 3.14 * 17
Evaluate the products
So, we have the following equation
C = 6.28 * 17
Evaluate the products
So, we have the following equation
C = 106.76
Hence, the circumference is 106.76 ft
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2. Write ONE algebraic rule that represents triangle JKL being translated to triangle J"K"L".
The original coordinates of JKL:
J(-3, -3), K(-4, 2) and L(2,1)
First, it is translated by the algebraic rule (x,y)->(x+2, y-3):
J(-3, -3)-> J'(-3+2, -3-3)=J'(-1, -6)
K(-4, 2) -> K'(-4+2, 2-3)= K'(-2, -1)
L(2,1) -> L'(2+2, 1-3)= L'(4, -2)
Then, this image is translated by (x,y)-> (x-2, y-1)
J'(-1, -6) -> J''(-1-2, -6-1) = J''(-3, -7)
K'(-2, -1) -> K''(-2-2, -1-1)= K''(-4, -2)
L'(4, -2) -> L''(4-2, -2-1)= L''( 2, -3)
Coordinates for triangle J''K''L'':
J''(-3, -7), K''(-4, -2) and L''( 2, -3)
2. To find algebraic rule that represents JKL to J''K''L'':
[tex]\begin{gathered} J^{\doubleprime}(-3,-7)\text{ and J(-3, -3)} \\ (x,y)\rightarrow(x,\text{ y+4)} \end{gathered}[/tex]Items 11-15. Lines a, b, c, and d
intersect as shown.
11. Which pairs of lines are parallel?
(a) a and b
(b) a and c
(c) c and d
(d) b and d
12. What is x?
13. What is y?
(a) 37
(b) 84
(c) 88
(d) 92
14. What is z?
(a) 84
(b) 92
(c) 96
(d) 109
15. If the slope of line d is given, the slope of which other line is known?
LEFT SIDE OF PAPER!!
Answer:
11. (c) c and d
12. x = 109°
13. (b) 84
14. (c) 96
15. C
Step-by-step explanation:
11. Parallel means that if the lines continued on forever, the lines will never cross. They have the same slope.
12. x is an alternate exterior angle to the angle labeled 109°. this means that the angles are equivalent.
13. y is the last unknown angle in the triangle. The interior angles of a triangle always add up to 180°. So 180° = 55° + 41° + y.
y = 180° - 55° - 41° = 84°
14. z is a supplementary angle to y, meaning that y + z = 180°.
180° - 84° = 96° = z
15. Lines d and c are parallel meaning they have the same slope, therefore if you know the slope of one, you know the slope of the other.
Can someone answer this! Its due in 34 minutes!!!!
I WILL BE USING LAWSOF EXPONENTS.
[tex] = {3}^{3} \times (3^{2})^{3x} \\ = {3}^{3} \times 3^{2 \times3 x} \\ = {3}^{3} \times {3}^{6x} \\ = 3^{3 + 6x} [/tex]
IF IT SAID THAT K IS THE IS THE EXPRESSION IN TERMS OF K THEN THE EXPRESSION NOW IS
[tex]3 +6 x[/tex]
HOPE THIS HELPS
♾️ How is the infinite possible? Has anyone ever counted numbers their whole life?
Answer: False, not possible.
The human was never meant to calculate or go beyond their fingers in search of great numbers, taking count for themselves, giving them names, appropriating. If you wanted to go higher for a laugh, it was called guessing. "Give me ZERO of this, give me 14,739,628,837 of that" are words that nobody says and words that stand behind delusion.
The only "anyone" to be counting their whole life is a divine. Keep math, numbers, and geometry sacred.
The equation y = 9x represents the liters of water a baseball team drinks each practice. This equation shows that after four practices, the team will have consumed 36 liters of water.
Determine the constant of proportionality.
36
9
4
0.25
The constant of proportionality of y = 9x is 9.
i.e y ∝ x and y = 9x
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
y = 9x
y = liters of water the baseball team drinks each practice
x = number of practice
We have an equation that after four practices, the team will have consumed 36 liters of water.
y = 36
9x = 38
x = 4
The equation can be written with a constant of proportionality as:
y ∝ x
y = 9x
So,
9 is the constant of proportionality.
Thus,
The constant of proportionality of y = 9x is 9.
i.e
y ∝ x
y = 9x
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Answer: The constant of proportionality of y = 9x is 9
Simplify the complex rational expression. Type your answer in simplest form, multiplying any factors you may have in the numerator or denominator. When typing your answers, type your terms with variables in descending power and in alphabetical order without any spaces between your characters. If needed use the carrot key ^ (press shift and 6) to indicate an exponent.\frac{\left(\frac{2c}{c+2}+\frac{c-1}{c+1}\right)}{\frac{\left(2c+1\right)}{c+1}}
We will simplify the complex expression shown below:
[tex]\frac{\frac{2c}{c+2}+\frac{c-1}{c+1}}{\frac{2c+1}{c+1}}[/tex]The simplification process is shown below >>>>
[tex]\begin{gathered} \frac{\frac{2c}{c+2}+\frac{c-1}{c+1}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{2c(c+1)+(c-1)(c+2)}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{2c^2+2c+c^2+2c-c-2}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{3c^2+3c-2}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{3c^2+3c-2}{(c+2)(c+1)}\times\frac{c+1}{2c+1} \\ =\frac{3c^2+3c-2}{(c+2)\cancel{c+1}}\times\frac{\cancel{c+1}}{2c+1} \\ =\frac{3c^2+3c-2}{(c+2)(2c+1)} \end{gathered}[/tex]If we multiply out the denominator, we have:
[tex]\begin{gathered} \frac{3c^2+3c-2}{(c+2)(2c+1)} \\ =\frac{3c^2+3c-2}{2c^2+c+4c+2} \\ =\frac{3c^2+3c-2}{2c^2+5c+2} \end{gathered}[/tex]AnswerThe numerator is
[tex]3c^2+3c-2[/tex]The denominator is
[tex]2c^2+5c+2[/tex]Consider the following definite integral.sxex²+1d'dx0Identify the definite integral that will result after making a u-substitution.
The first choice is the correct result
Three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes. Which of the following statements is true regarding Rick's votes?
The statement that is true regarding Rick's votes is D. Rick has 32 more votes than Jami.
How to calculate the value?From the information, three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes
Rick = h + 10
Jami = h - 22
In this case, it's important to note that the difference between Jami and Rick will be:
= 10 - (-22)
= 10 + 22
= 32
Therefore, Rick will have 32 more votes.
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Three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes. Which of the following statements is true regarding Rick's votes?
A. Rick has 10 more votes that Jami
B. Rick has 22 more votes that Jami
C. Rick has 5 more votes than Helen
D. Rick has 32 more votes than Jami.
How long is the hypotenuse?
The sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse. The hypotenuse exists c = 50.
How to determine hypotenuse?To determine the hypotenuse from the sides of a right triangle, use the Pythagorean theorem. Sum of squares is squared as c = √(a² + b²).
The longest side of a right-angled triangle, or the side opposite the right angle, exists comprehended as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
a² + b² = c²
⇒ c = √(a² + b²)
Where, a = 30 and b = 40, then
substitute the values in the above equation, we get
30² + 40² = c²
900 + 1600 = c²
2500 = c²
50 = c
Therefore, the hypotenuse exists c = 50.
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Oscar
and maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles one entry in the table paired 152 km with 95 miles if k represents the number of kilometers and m represents the number of miles who wrote the correct equation that would relate kilometers to miles
The answer to the given question is Oscar wrote the correct equation that would relate kilometers to miles.
Calculation and Parameters1. Table
km miles
152 95
2. Set the proportion with / and solve for k
/ = 152 km / 95 miles
/ = 1.6 km / 1 miles
= 1.6 , where 1.6 / 1 represents kilometers per mile.
So, Oscar is right.
Maria is wrong because:
If we solve the proportionality:
/ = 152 km / 95 miles
/ = 95 miles / 152 km
= 0.625 , where 0.625 represents miles per kilometer
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The complete question is:
"Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired 152 km with 95 miles. If represents the number of kilometers and represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why.
Oscar wrote the equation = 1.6, and he said that the unit rate 1.6 / 1
represents kilometers per mile.
Maria wrote the equation = 0.625 as her equation, and she said that 0.625 represents kilometers per mile."
9t + 5(t + 3) = -(t + 13) + t
If we solve the given equation for t we get that t=-2
The equation given,
9t+5(t+3) = -(t+13) +t
⇒9t + 5t + 15 = -t -13 +t
⇒14t + 15 = -13 (∵-t+t=0)
⇒14t = -13-15 (bringing 15 from left hand side to right hand side the sign is flipped and 15 becomes -15)
⇒14t = -28
⇒[tex]t=\frac{-28}{14}[/tex] (dividing both sides by 14)
⇒t = -2
Thus on solving the equation we get t = -2
Your question was incomplete but most probably your full question was
Solve for t when this equation is given, 9t+5(t+3) = -(t+13) +t
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Calculate the pay for the following day of a
weekly time card given a wage of $12/hr.
Name
Week of:
Morning
Afternoon
In
Out
In
Out
Monday 08:15
12:15
13:00
17:30
pay = $[?]
Round your answer to the nearest hundredth.
The pay for the given weekly time is, $102.
What is the pay wage?
The key distinction between a salary and wages is that wage earners are compensated by the hour, whereas salaried employees receive set payments every pay period.
In the given example the total time for the morning and the afternoon is given.
The total time for the morning is 4 hours and the total time for the afternoon is 4.5 hours.
So, the total number of hours are 4 + 4.5 = 8.5 hours.
The wage of each hour is $12.
So, the wage of 8.5 hours is,
8.5 x $12 = $102.
Therefore, the pay for the given day of a weekly time card given a wage of $12/hr is $102.
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a geneticist is interested in the proportion of african males who have a certain minor blood disorder. in a random sample of 100 african males, 24 were found to be afflicted. (a) compute a 99% confidence interval for the proportion of african males who have this blood disorder. (b) what sample size (i.e., the number of african males) is needed if we wish to construct the 99% confidence interval of the proportion of african males with this blood disorder to be 0.20?
a) The confidence interval is (0.13, 0.35) for the males who have this blood disorder.
b) The number of African males or the sample size is 88 for the value of P to be 0.20
It is mentioned that a geneticist is interested in the proportion of the African males who have a certain minor blood disorder. In a random sample of 100 males, 24 were found to be afflicted.
So we have,
n (total males) = 100
X (afflicted males)= 24
Let P be the sample porportion,
P = X/ n
∴ P = 24 / 100 = 0.24
a) Here it is given to find the confidence interval if the proportion of males is 99% who have this blood disorder so,
c = 99 % = 0.99
∴ α = [tex]1 -[/tex] c = 1 - 0.99 = 0.01
⇒ α/2 = 0.01/2 = 0.005
Using Z table,
Z of α/2 = [tex]Z_{0.005}[/tex] = 2.576
Margin of error E = [tex]Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }[/tex]
= 2.576 x [tex]\sqrt{\frac{0.24(1-0.24)}{100} }[/tex]
= 0.11
Now, 99 % confidence interval is P ± E
P-E < P < P +E
0.24 - 0.11 < P' < 0.24 + 0.11
P' = (0.13, 0.35) is the required confidence interval.
b) It is given to find the the number of African males when
P = 0.20
Z = 2.576
E = 0.11
Now E = [tex]Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }[/tex]
⇒ 0.11 = 2.576 x [tex]\sqrt[2]{\frac{0.20(1-0.20)}{n} }[/tex]
⇒ 0.0427 = [tex]\frac{0.4}{\sqrt{n} }[/tex]
⇒ [tex]\sqrt{n}[/tex] = 9.37
⇒ n = [tex](9.37)^{2}[/tex]
⇒ n = 87.7969
Hence the approximate number of males is 88 for the proportion of males with this blood disorder to be 0.20
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Please help me with this math problem!! Will give brainliest!! :)
Answer: 1/2
Step-by-step explanation:
Answer:
The correct answer seems to be 1/2
3) Identify the following by using the given figure
a) Two pairs of adjacent angles
b) Two pairs of supplementary angles
c) Linear pairs
Step-by-step explanation:
a) angles that share 1 side and are next to each other
<DBA, <ABE
<ABE, <EBC
b) two angles whose measures add to 180°
<ABE, <EBC
<ABD, <DBC
c) two adjacent angles whose noncommon sides lie on a line
<ABE, <EBC
<ABD, <DBC
What is the equation in slope-intercept form of the line that passes through the point (−3,0) and is parallel to the line represented by y=3.2x+7.3
The equation in slope intercept form of the line passes through the point (-3,0) and is parallel to the line represented by y = 3.2x+7.3 is y = 3.2x+9.6
The equation of the line that parallel to the line
y = 3.2x+7.3
Slope intercept form of the line
y = mx+b
y is the y coordinate
x is the x coordinate
m is the slope of the line
b is the y intercept
Compare it with the equation
The slope of the line m = 3.2
Point slope form of the line passing through the points (-3,0) with the slope of the line 3.2
[tex]y-y_{1}=m(x-x_{1} )[/tex]
Substitute the values in the equation
y-0 = 3.2(x-(-3)
y = 3.2(x+3)
y = 3.2x+9.6
Hence, the equation in slope intercept form of the line passes through the point (-3,0) and is parallel to the line represented by y = 3.2x+7.3 is y = 3.2x+9.6
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a magician charges a $30 fee to cover travel and expenses, plus $19.99 per hour. write an equation to represent the relationship between h, the number of hours, and t, the total charge for the magician.
Answer:
t = 19.99h + 30
Step-by-step explanation:
t is the total cost and h is the hourly charge. The 30 is a one time fee.
3. (02.02)
Angle ABC is formed by segments AB and BC on the coordinate grid:
90 degree
m/ABC 180 degrees
Angle ABC is rotated 90 degrees counterclockwise about the origin to form angle AB'C'. Which statement shows the measure of angle A'B'C' (4 points)
OmzABC 90
m/ABC= mzABC
5-
OmzABC-2 m/ABC
8
The statement that shows the correct measure of ∠A'B'C' is
m∠ABC = m∠A'B'C'.
What type of transformation does rotation do?
Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point. A rotation produces a new figure known as the image. The picture matches the original figure exactly.
The rotation will typically be at a similar angle, even if a figure can be rotated by any number of degrees. Positive degrees will cause the figure to revolve counterclockwise. The graphic will turn clockwise if the degree value is negative. Any point on the figure can be rotated.
Given, ΔABC with co-ordinates (3, 4), (5, 3) and (3, 2); also ∠ABC = 53.13°
Again, ΔABC is rotated counter-clockwise by 90° to make the ΔA'B'C'.
Thus, new triangle having co-ordinates (-4, 3), (-3, 5) and (-2, 3) is obtained.
Rotation retains congruence since it is a transformation that does not alter side length or angle measure.
Thus, we have ∠A'B'C' = 53.13°
Therefore, ∠ABC = ∠A'B'C' = 53.13° i.e. m∠ABC = m∠A'B'C'.
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write 2 quadratic equations (of any form) that are not equivalent, each with a vertex of (4,5)
Answer:
[tex]g(x)=-x^2+8x-11\\\\f(x)=x^2-8x+21[/tex]
Step-by-step explanation:
Generally when you're given the vertex of a quadratic, you can express it in vertex form: [tex]f(x)=a(x-h)^2+k[/tex], where (h, k) is the vertex, and "a" is some constant value that determines the stretch/compression and the direction (up or down)
So we know that: (h, k) = (4, 5), meaning we can plug those values into the equation: [tex]f(x)=a(x-4)^2+5[/tex]
we can change the function by changing the value of the constant "a".
we can use two arbitrary values, but in this example I'll use -1 and 1.
this gives us the following functions: [tex]f(x)=(x-4)^2+5\\g(x)=-(x-4)^2+5[/tex]
these two functions are actually very similar, the only different is they're reflected across the x-axis (and some vertical shift) since the y-value is being negated, or at least part of it.
In your question it states (of any form), so I'm assuming we can leave it in vertex form, but just in case I'll expand them further into standard form
[tex]f(x)=(x-4)^2+5\\\\f(x)=(x-4)(x-4)+5\\\\f(x)=x(x-4)-4(x-4)+5\\\\f(x)=x^2-4x-4x+16+5\\\\f(x)=x^2-8x+21[/tex]
We can also expand the other function similarly.
[tex]g(x)=-(x-4)^2+5\\\\g(x)=-[(x-4)(x-4)]+5\\\\g(x)=-[x(x-4)-4(x-4)]+5\\\\g(x)=-[x^2-4x-4x+16]+5\\\\g(x)=-[x^2-8x+16]+5\\\\g(x)=-x^2+8x-16+5\\\\g(x)=-x^2+8x-11[/tex]
I need help asap!!!!
The answer is -1 and 5
Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per
gigabyte. She wants to keep her bill under $60 per month. Write and solve an
inequality which can be used to determine g, the number of gigabytes Ella
can use while staying within her budget.
> ≤ >
Inequality: 5g +37.5 < 59
9 4.3
Submit Answer
attempt 2 out of 2
The gigabyte needed will be g<2.2 as per the given condition that is- " Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per gigabyte. She wants to keep her bill under $60 per month."
What is inequality?A mathematical statement of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things. The five inequality symbols in Maths are greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).
How to solve inequality?Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the numbers on the other by adding or subtracting quantities.
Here,
Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per gigabyte. She wants to keep her bill under $60 per month.
So the inequality will be,
49+5g<60
5g<11
g<2.2
The required gigabyte will be g<2.2 under the following circumstances: "Ella's cell phone plan has a fixed monthly fee of $49 and a per-gigabyte charge of $5. She wants to keep her monthly bill under $60."
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The midpoint of AB is M(1, 1). If the coordinates of A are (-2,5), what are the
coordinates of B?
The coordinates of B are (4 , -3) .
A cartesian coordinate system, which uses signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length, uniquely identifies any point in a plane by a pair of numerical coordinates.
The origin of each reference coordinate line, known as an axis of the system or simply an axis (plural axes), is the intersection of the ordered pairs (0, 0). The coordinates can also be determined by looking at the locations of the perpendicular projections of the point onto the two axes, which are shown as signed distances from the origin.Let the coordinates of B be (x, y)
As M is the mid point of AB , we know from the distance formula that the coordinates of M will be:
abscissae of M = (-2 + x) /2
or, 1 = (-2 + x) /2
or, x = 4
Ordinate of M = (5 + y)/2
or , 1 = (5 + y)/2
or, y = -3
Therefore the coordinates of B are (4 , -3)
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a laboratory worker finds that 3% of his blood samples test positive for the hiv virus. in a random sample of 70 blood tests, what is the mean number that test positive for the hiv virus? (round your answer to 1 decimal place)
In linear equation ,The mean number that the test positive for the HIV virus is 2.1 .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Let x be the number of blood samples test positive for the HIV virus in a sample of 70 blood test.
Here X ~ Binom( n = 70, p = 0.03)
Using binomial distribution property , the mean of X is
μ = ηp
= 70 * 0.03 = 2.1
The mean number that the test positive for the HIV virus is 2.1 .
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simplify the following: [tex]\frac{(7^2.3^-1)^4.7^5}{(3^2.7^-6)^3}[/tex]
(. means multiply)
The simplification of the equation [tex]\frac{(7^{2}.3-1 )^{4} }{(3^{2}.7-6)^{3} }[/tex] is 2453.5.
How to simplify the equation?
Consider the equation [tex]\frac{(7^{2}.3-1 )^{4} }{(3^{2}.7-6)^{3} }[/tex]
Solve for Numarator [tex](7^{2} .3-1)^{4}[/tex]= [tex](7^{2} .3-1)^{2} (7^{2} .3-1)^{2}[/tex]
= [tex](147-1)^{2}[/tex][tex](147-1)^{2}[/tex]
= (21316) (21316)
Solve for Denominator [tex](3^{2}.7-1)^{3\\}[/tex]
= [tex](63-6)^{3}[/tex]
= 57³
Solve both, and simplify the equation.
= [tex]\frac{(21316) (21316)}{185193}[/tex]
= 2453.5
∴ Simplification is 2453.5
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Identify the vertex of the quadratic function given by the equation f(x) = -x² + 8x - 14.
Answer: (4, 2)
Step-by-step explanation:
1) Identify the values of a, b, and c.
a = -1
b = 8
c = -14
2) Use the vertex formula to find the x-value of the vertex.
[tex]{\displaystyle x={\frac {-b}{2a}}}[/tex]
[tex]{\displaystyle x={\frac {-8}{2(-1)}}}[/tex]
[tex]{\displaystyle x={\frac {-8}{-2}}}[/tex]
[tex]{\displaystyle x=4[/tex]
3) Plug the value into the original equation to get the y value.
f(x) = -x² + 8x - 14
f(x) = -(4)² + 8(4) - 14
f(x) = -(16) + 32 - 14
f(x) = 2
3) Put it in an ordered pair
(4, 2)