A private high school advertised that last year their freshman students, on average, had a score of 80 on the high school entrance exam. Assuming that average refers to the mean, which of the following claims must be true based on this information?

Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.

Check the picture below.

so following the template below, a shift 2 units to the left, means C=2

[tex]G(x)=\sqrt{x+2}[/tex]

Answer:

data given

interest rate 12%

amount to be received 15ooo

time9years

Step-by-step explanation:

from

A=p[1+r/100]^n

where

A is amount

p is principal

r is rate interest

n number of interist period

now,

15000=p[1+12/100]^8

15000/1.12^8 =p×1.12^8/1.12^8

p=6058.24

p=6058)

: .you should invest 6,058

The amount to be invested initially if you want to have fifteen thousand dollars after nine years is $3947.18.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

We are given that:

A=15000

r=0.12

t=9

We need to find P. You can do this by rearranging the formula:

P=ertA​

Then plug in the given values and use a calculator:

P=e0.12×915000​

P≈3947.18

Therefore, by the given interest rate the answer will be $3947.18.

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To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.

A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.

This can be written in mathematical notation as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.

In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:

Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks

Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks

Now we can use the Pythagorean theorem to find the distance between their houses:

Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks

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To convert the expression, Y=x^2-64/16 into the polar form, we would have: r = 2 / √(sin^2θ + cos^2θ).

The polar form of a mathematical expression is a way of representing complex numbers using their magnitude and angle.

For a complex number z = a + bi, where a and b are real numbers, its polar form is given by z = r(cosθ + i sinθ), where r is the magnitude of z and θ is the angle that z makes with the positive real axis.  

So, for the given expression, the polar form can be converted this way:

r^2 sin^2θ = r cos^2θ - 4

r^2(sin^2θ + cos^2θ) = 4

r = 2 / √(sin^2θ + cos^2θ)

Therefore, the polar form is r = 2 / √(sin^2θ + cos^2θ).

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Answer:

We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:

x^2 + 12^2 = 16^2

Simplifying:

x^2 + 144 = 256

x^2 = 112

Taking the square root of both sides:

x ≈ 10.6 feet

Therefore, Brenda is approximately 10.6 feet away from the fish.

Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.

The standard deviation of statistics is a measurement of how much a group of data values deviate from their mean (average) value. While a significant standard deviation suggests that the pieces of information are dispersed throughout a broader range of values, a low standard deviation suggests that the data points are generally close to the mean.

given

a) If the sample's standard deviation is 3 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:

z = (30 - 15) / 3 = 5

b) The context of the data and the standard deviation will determine whether 30 inches is distant from a mean of 15 inches.

A departure of 15 inches from the mean, meanwhile, can be viewed as being significantly off the mean if the standard deviation is minimal.

c) If the underlying data's standard deviation is 10 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:

z = (30 - 15) / 10 = 1.5

Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.

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Answer:

We can simplify the expression -8(2.5g-4.25)+5.25 by distributing the -8:

-8(2.5g-4.25)+5.25 = -20g + 34 + 5.25

Simplifying further, we can combine the constant terms:

-8(2.5g-4.25)+5.25 = -20g + 39.25

So the value of the constant term is 39.25.

Thus, the height of flagpole from the ground is found as 23.34 feet.

The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.

The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.

Given data:

Using the trigonometric ratios in the right triangle ABE.

tan 35 = h / 30

h = 30* tan(35)

h = 18.34

Height of flagpole = 18.34 + 5 = 23.34 feet

Thus, the height of the flagpole from the ground is found as 23.34 feet.

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To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). See explanation below and attached graph.

To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). For example:

So, we have the following points for the graph: (-3, -4), (-2, -2 1/3), (-1, -1 2/3), (0, -1), (1, -1/3), (2, 1/3), (3, 1).

We can now plot these points on a graph, with x-values on the horizontal axis and f(x) values on the vertical axis. We can label the horizontal axis as "x" and the vertical axis as "f(x)" or "y".

Note that the graph of f(x) = (2/3)x - 1 is a straight line with slope 2/3 and y-intercept -1.

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Answer:

y=9 (3x/9-2) + 18=3x

Step-by-step explanation:

Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]

f(x)=2x+7

domain: x = {2, 3, 5, 9}

Replace each x value and solve for y

x=2

f(2)= 2(2) + 7 = 4 + 7 = 11

x=3

f(3)= 2(3) + 7 = 6 + 7 = 13

x=5

f(5)= 2(5) + 7 = 10 + 7 = 17

x=9

f(9)= 2(9) + 7 = 18 + 7 = 25

We can find the range of the function by plugging in each value in the domain into the function and listing the output values:

When x = 2, f(2) = 2(2) + 7 = 11

When x = 3, f(3) = 2(3) + 7 = 13

When x = 5, f(5) = 2(5) + 7 = 17

When x = 9, f(9) = 2(9) + 7 = 25

Therefore, the range of the function for the given domain is y = {11, 13, 17, 25}.

Hence, the correct answer is B. y = {11, 13, 17, 25}.

Required algebraic expression is (t+30).

What is algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. It may also contain brackets or parentheses to indicate the order of operations.

Algebraic expressions can be written using letters or symbols to represent variables, and they are used to represent mathematical relationships or formulas. For example, the expression "3x + 4" represents the sum of three times a variable x and the constant 4.

Let's represent the amount of time that Jill spends watching television as the variable j. We know that she watches 30 minutes more than Bill, so we can write:

j = t + 30

This algebraic expression says that Jill's time j is equal to Bill's time t, plus 30 additional minutes.

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Answer:

167.6190 approximately 167.62 inches

Step-by-step explanation:

formula for surface area of a cone is 1/3πr×r×slant height. How this helps.

Answer:

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

This null hypothesis prompt is actually straight forward. Note that where the above conditions exist, we must NOT reject the null hypothesis due to the values of the z-statistics and the significance level.

The idea that there is no influence on the population is known as the null hypothesis. We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no impact in the population (p≤α ).

So to determine whether or not to accept or reject the null hypothesis, we must determine dthe z-score.

To find the the critial value for a left-tailoed test, where the signifiance level is 0.01, note that we must find the z-score that leaves 1% of the area in the left tail.

Using the standard distribution table, the z-score for 0.01 left tail is about -2.33.

Since

z-satistics which  is equal to -1.95 (as given) is greater than the z-score, we must NOT reject the null hypothesis.

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Answer:

Whats the question?

Step-by-step explanation:

Answer: q= -2/35

Step-by-step explanation:

Rearrange terms 2 Subtract  from both sides 3.Simplify the expression Subtract the numbers Subtract the numbers 4 Divide both sides by the same factor 5 Simplify the expression Divide the numbers Cancel terms that are in both the numerator and denominator Move the variable to the left

Answer:

q = -2/35

Step-by-step explanation:

2/7 = 4/5 + 9q

(2/7) - (4/5) = 9q

(10/35) - (28/35) = 9q

-18/35 = 9q

(-18/35) / 9 = q

(-18/(35*9)) = q

-18/315  = q

q = -2/35

Check:

2/7 = 4/5 - 9*2/35

2/7 = 4/5 - 18/35

10/35 = 28/35 -18/35

10 = 28 -18

To cover a 2000 sq ft wall, we will need 5 gallons of paint.

what is area?

Area is the measure of the size of a two-dimensional surface or region, expressed in square units. It is a fundamental concept in geometry and is used to quantify the amount of space inside a shape, such as a square, rectangle, triangle, or circle. The unit of measurement for area varies depending on the system used, but in the International System of Units (SI), the standard unit of area is the square meter (m²). In everyday life, we often use other units of area such as square feet, square inches, or square centimeters.

To find the conversion factor, we need to divide the number of square feet by the number of square feet covered by one gallon of paint:

Conversion factor = 1 gallon / (400 sq ft/gallon)

So, for a wall that is 2000 sq ft, we can use this conversion factor to find the number of gallons of paint needed:

Number of gallons = (2000 sq ft) / (400 sq ft/gallon) = 5 gallons

Therefore, to cover a 2000 sq ft wall, we will need 5 gallons of paint.

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Answer:

40 cm²

Step-by-step explanation:

you have to multiply the top of the triangle by the base(40) which is 80 then you divide by two since it's a triangle then you get 40 again since your finding the area you have to put the 2 above the cm

I hope this helps you.

you can check your ans. by sub. in the value of x and y into both the equation which must give you the same answer.

Answer:

Step-by-step explanation:

We need to find a number which increased by 3.5 of itself equals 621.

Let that number be x.

x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.

x(1+3.5) = 621

x(4.5) = 621

x = 621/4.5

x = 138

Therefore the required number is 138.

Answer: 138

Step-by-step explanation:

We need to find a number which increased by 3.5 of itself equals 621.

Let that number be x.

x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.

x(1+3.5) = 621

x(4.5) = 621

x = 621/4.5

x = 138

Therefore the required number is 138.

Answer:

Step-by-step explanation:

We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.

The mean number of bedrooms in a house in this neighborhood will be: 3.824.

In order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.

Next, we will add the products, and then divide by the total frequency. So we can start as follows:

(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478

Total frequency = 7 + 35 + 56 + 27 = 125

Therefore, the mean number of bedrooms = 478 / 125  approximately 3.824

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Answer:

Step-by-step explanation:

Okay so when a smaller number is divided by a larger number, the quotient is less than 1.  Hope this helps Bye sisters slay.

The expression 10m‾‾√ is an expanded form of the mathematical term ln10.

Step-by-step explanation:

5 cos (307)  = 3

5 sin (307) = -4  

just plot the point   ( 3, -4 )     Done.

Answer:

The point is (3, -4) because 5 cos [307] = 3 and 5 sin [307] = -4

The new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).

A shape is translated when it is moved up, down, left or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To perform the given translation (x, y) → (x − 3, y - 4) on the triangle ABC with vertices A(0, 7), B(7, 3), and C(1, 4), we need to apply the same transformation to each vertex of the triangle and obtain their new coordinates.

For vertex A(0, 7), the transformation gives:

(x, y) → (x − 3, y - 4)

(0, 7) → (0 - 3, 7 - 4)

The new coordinates of A are (-3, 3).

For vertex B(7, 3), the transformation gives:

(x, y) → (x − 3, y - 4)

(7, 3) → (7 - 3, 3 - 4)

The new coordinates of B are (4, -1).

For vertex C(1, 4), the transformation gives:

(x, y) → (x − 3, y - 4)

(1, 4) → (1 - 3, 4 - 4)

The new coordinates of C are (-2, 0).

Therefore, the new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).

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