(100 POINTS!)
Create a proportion using the form %/100= is/of to represent the following word problem:

15 is 1 1/2 % of what number?

Answer:

170 + 156.33 + 9.38 + 98.42 + 52.54= 486.67

1,445.26 - 486.67= 958.59

Faith has $958.59 left.

The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.

This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.

This happens when the rejection region is found to be around the area that is in the critical value.

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The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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Answer:

C. 4 × 10 × 2

Step-by-step explanation:

There are four walls that are ten feet on each side.

You would take 4 (number of walls) × 10 (number of feet in length), and because there are 2 sides of the walls, you would take that × 2.

Therefore, your answer is 4 × 10 ×2

The function among the given option is height of a building in feet, height of the building in inches , Option B is the correct answer.

A function is a law that relates a dependent and an independent variable.

The options mentioned below needs to be studied to determine which forms a function.

Option A , C and D doesn't really form a function ,

For two variables need to be a function then they have to be dependant on each other and have only one output for a given input.

height of a building in feet, height of the building in inches

Height of building in feet = (height of building in inches/12)

so this is a function

Therefore Option B is the right answer.

The missing options are

If the relationships below are given in the form (input, output), which pairing always describes a function?

A) (number of doors in a car, number of cup holders in the car)

B) (height of a building in feet, height of the building in inches)

C) (beverage charge on a bill, total meal charge on the bill)

D) (distance from home during a trip, time elapsed during the trip)

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To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.

Answer:

Step-by-step explanation:

Given;

Loan = $36,320 (Principal)

Rate R = 6% = 0.06

Time T = 1year

Required

Interest that will be charged on this loan at the end of the first year

Using the formula for calculating simple interest as;

SI = PRT/100

SI = 36,320 * 6 * 1/100

SI = 0.06 * 36,320

SI = $2,179.2

Hence the amount of interest that will be charged on this loan at the end of the first year is  $2,179.2

Answer:

4

Step-by-step explanation:

44 yeah yeah what about the other

Use the chain rule:

\(\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}\)

We have

\(y=8u-6\implies\dfrac{\mathrm dy}{\mathrm du}=8\)

\(u=3x-8\implies\dfrac{\mathrm du}{\mathrm dx}=3\)

so we get

\(\dfrac{\mathrm dy}{\mathrm dx}=8\cdot3=\boxed{24}\)

Alternatively, you can substitute u in the definition of y and differentiate with respect to x :

\(y=8u-6=8(3x-8)=24x-64\implies\dfrac{\mathrm dy}{\mathrm dx}=24\)

The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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Step-by-step explanation:

so, what's the problem ?

it's all there, we only need to take the calculator (or simply our heads) and do the calculation :

2×5 - 5×2 = 10 - 10 = 0

you see ? that was all that was needed.

put the given values for the variables into the places of these variables, and then calculate !

that is what variables are for : placeholders for actual values.

\(\boxed{\bold{Vertical,~(3,0)}}\)

- You can either graph this like this, OR graph this using desmos.com.

- So since we know \(x\) is, (Horizontal,) we have to graph \(y\), (Vertical.) So to sum this up, this just means whatever variable you don't know yet, that will be the one that you graph as an infinite.

Surface area is the sum of the area of faces of a figure. The ratio of their surface area is 2268 : 112

A prism is a solid shape with 6 faces

The formula for calculating the total surface area is expressed as:

TSA = 2(lw+wh+lh)

For the Red prism

Ar = 2(162 +324 + 648)
Ar = 2268 square units

For the blue prism

Ab = 2(8 + 16 + 32)
Ab = 112 square units

Take the ratio of the surface area

Ratio = 2268 : 112

Hence the ratio of their surface area is 2268 : 112

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Surface area is the sum of the area of faces of a figure. The ratio of their surface area is 4:81.

How to calculate the surface area of a prism?

A prism is a solid shape with 6 faces

The formula for calculating the total surface area is expressed as:

TSA = 2(LW+WH+LH)

For the Red prism

For the blue prism

Take the ratio of the surface area

Ratio = 4:81

Hence the ratio of their surface area is 4:81

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The correct proof of the equation is cos3θ =cos(2θ + θ) =  cos²θ - 3cosθsin²θ (Proved)

Given the trigonometry identity below:

cos3∅=cos²∅-3cos∅sin²∅

We are to prove that both sides of the equation are equal.

cos 3θ = cos(2θ + θ)

Using the double angle formula for cosine, we can expand the first term:

cos(2θ + θ) = cos2θ cos θ - sin2θ sinθ

Since cos2θ = cos²θ - sin²θ

cos(2θ + θ) =  cos²θ - sin²θ - 2cosθsinθsinθ

cos(2θ + θ) = cos²θ - sin²θ - 2cosθsin²θ

On simplifying, we can see that;

cos3θ =cos(2θ + θ) =  cos²θ - 3cosθsin²θ (Proved)

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Answer: 7a+3

Step-by-step explanation:

9a and 2a are two like terms that we can combine. Because there is a minus sign in front of the 2a, we should subtract 9a from 2a to get

7a. Then because the 3 has plus sign in front of it, we add 7a to 3. BUT because 3 a is NOT a like term, you don’t actually add it, so it looks like this: 7a+3. Hope this helped!

The statement about probability that is correct would be that the probability of landing on yellow is less than the probability of landing on blue. That is option B.

Probability is defined as the total number of possible outcome of an event.

The repeated colour which are numbered from 1 to 8 are as follows:

Therefore, the probability of landing on yellow is less than the probability of landing on blue because 1/4 is less than 3/8.

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Answer: B: The probability of landing on yellow is less than the probability of landing on blue.

Step-by-step explanation:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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Answer:

x = 13, y = 3

Step-by-step explanation:

3(5y - 2) - 4y = 27

15y - 6 - 4y = 27

11y = 33

y = 3

x = 15 - 2

x = 13

The zeros of g(x) = (x + 2)(x − 1)(x − 2) are x = -2, 1 and 2

From the question, we have the following parameters that can be used in our computation:

The 5 functions of g(x)

To determine the key features of the function g(x), we make use of the first

g(x) = (x + 2)(x − 1)(x − 2)

So, we have

Zeros

This is when the function equals 0

(x + 2)(x − 1)(x − 2) = 0

Evaluate

x = -2, 1 and 2

The y-intercept

This is when the value of x in the function equals 0

g(0) = (0 + 2)(0 − 1)(0 − 2)

Evaluate

g(0) = 4

End behaviour

This is the behavior of the graph of the function as it approaches the ends of the x-axis

So, we have

\(\mathrm{as}\:x\to \:+\infty \:,\:g\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:g\left(x\right)\to \:-\infty \:\)

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Answer:

325

Step-by-step explanation:

all other numbers are squares of natural numbers.

144 = 12²

169 = 13²

196 = 14²

225 = 15²

256 = 16²

289 = 17²

325 is no square. 324 would have been 18².

Answer:

I am not sure about the first 4 but the rest are in the pic

Answer:

so where does that line intersect the y axis? just plug in x=0 and you see y= -1. so (0, -1)

y = -x -1 is parallel because it has the same slope and goes through the right point

Answer:

9000

Step-by-step explanation:

Answer:

s=x(20)

Step-by-step explanation:

s= solution

x= # of weeks

4x2=8

4x3=12

12+8=20

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.

To find the wide variety of girl population, we will subtract the quantity of male population from the full population.

Total population = 88,51,84,692

Number of male = 45,40,34,570

Number of female = Total population - Number of male

= 88,51,84,692 - 45,40,34,570

= 43,11,50,122

Therefore, the number of female population is 43,11,50,122.

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The area of the circle to the nearest tenth is 81.7 square units to the nearest tenth

The formula for calculating the area of a circle is expressed as shown below;

A = πr²

where

r is the radius of the circle

Given the following parameters

diameter = 10.2

radius = 10.2/2 = 5.1

Substitute

Area = 3.14(5.1)²

Area =  81.6714

Hence the area of the circle to the nearest tenth is 81.7 square units to the nearest tenth

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