Write a rule for each graph below and explain it step by step

The measure of a from the triangle ATD is 27 units. Therefore, the option B is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

From the given triangle ADT, ∠A=46°, ∠D=84°, AT=37, AD=t and TD=a.

By angle sum property,

∠A+∠D+∠T=180°

46°+84°+∠T=180°

130°+∠T=180°

∠T=50°

sin46°/a=sin84°/37=sin50°/t

0.7193/a=0.9945/37=0.7660/t

0.7193/a=0.9945/37

0.9945a=0.7193×37

0.9945a=26.6141

a=26.6141/0.9945

a=26.76

≈27

0.9945/37=0.7660/t

0.9945t=0.7660×37

0.9945t=28.342

t=28.342/0.9945

t=28.5

Therefore, the option B is the correct answer.

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The null hypothesis H0 in this case would be that the standard deviation of the number of accidents per day is equal to 0.04, while the alternative hypothesis Ha would be that the standard deviation of the number of accidents per day is not equal to 0.04.

The null hypothesis represents the status quo or the default assumption, which is that there has been no change in the standard deviation of the number of accidents per day. The alternative hypothesis represents the claim made by the actuaries, which is that there has been a change in the standard deviation.

Mathematically, the null and alternative hypotheses can be expressed as follows:

H0: σ = 0.04

Ha: σ ≠ 0.04

where σ represents the standard deviation of the number of accidents per day.

The hypothesis test would be used to determine whether there is evidence to support the actuaries' claim that the standard deviation has changed, or whether there is not enough evidence to reject the null hypothesis that the standard deviation remains equal to 0.04.

300 people read neither​ of the papers.

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. It is a fundamental theory in mathematics and can be used as a foundation for all other areas of mathematics.

Total population n(ξ) = 5000

Number of people reading Concord, n(C) = 2800

Number of people reading Guardian, n(G) = 2300

Number of people reading both = n(C ∩ G)] = 400

Number of people reading any of the newspaper = n(C ∪ G)] = n(C) + n(G) - n(C ∩ G) = 2800 + 2300 - 400 = 4700.

Number of people reading none of them is equal to = Total population - Number of people reading any of the newspaper = 5000 - 4700 = 300

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Answer:

6)  x = 6

7) x = 4

8) x = 4

9) x = 6

10) x = 6

Step-by-step explanation:

This is based on Dr. Henry Borenson's method of using pawns to explain algebraic equations.  Frankl I find using variables more intuitive

Let each pawn represent an x in the equations

6.
x + 8 = 10 + 4

x = 10 + 4 - 8

x = 14 - 8 = 6

7.  

x + x = 4 + x
2x = 4 + x
2x - x = 4

x = 4

8.

x + x + x + 2 = 7 + 7
3x + 2 = 14

3x = 14 - 2

3x = 12

x = 12/3

x = 4

9.

2x + 4 = x + 10

2x - x = 10 - 4

x = 6

10

3x = x + 10 + 2

3x = x + 12

3x - x = 12

2x = 12

x = 6

Answer:

j1gru3hek3n

Step-by-step explanation:

bso2jw4usk8

The sum of the capitals would be $530400.

The formula to calculate the simple interest is -

I = PRT/100

Given is that a capitalist has two capitals that differ in $221,000. The largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces.

We can write the amount produced by largest as -

A = P(1 + rt)

A = 221000(1 + 0.2 x 3)

A = 221000 x 1.6

A = 353600

Amount generated by smallest -

a = 353600/2

a = 176800

Their sum would be -

A + a = 530400

Therefore, the sum of the capitals would be $530400.

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{Question in english -

A capitalist has two capitals that differ in S/. 221,000, the largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces. Find the sum of the capitals.}

The lateral surface area of the mailer is 234 In²

It is important to note that the formula for the lateral area of a triangular prism is expressed as;

A = (a + b+ c) h

Given that the parameters are enumerated as;

Now, substitute the values into the equation, we have;

Lateral area, A = (4 + 4 + 5) 18

Add the values

Lateral area = (13)(18)

Multiply the values

Lateral area = 234 In²

Hence, the value is 234 In²

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Answer: Janelle can fill 6 feeders.

Step-by-step explanation:

To find the number of feeders Janelle can fill, we need to divide the total amount of bird food she has by the amount of bird food each feeder can hold.

First, let's convert the total amount of bird food from cups to half-cups:

3 cups / 2 = 6 half-cups

So, Janelle has 6 half-cups of bird food, and each feeder can hold 1 half-cup.

Therefore, she can fill:

6 half-cups / 1 half-cup per feeder = 6 feeders.

So, Janelle can fill 6 feeders.

G is a linear function with a rate of change of -12 and an initial value of 100. Its equation is: g = -12x + 100.

Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.

As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.

Since f(x) = axe + b is the typical slope-intercept form of a linear function,

an is the slope (rate of change), and b is the y-intercept (initial value).

g = -12x + 100 is the necessary linear function, which is what has been presented.

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The volume of the composite figure is 12 cubic in.

How to calculate the Volume of Composite Shapes?

Composite shapes have a volume that is made up of basic shapes. We can calculate the volume of the composite shapes using the steps listed below:

Step 1: Break down the compound shape into different components.

Step 2: Determine the volume of each basic shape.

Step 3: Combine the volumes of all the basic shapes.

Step 4: Write the solution in cubic units.

Firstly we can divide the figure into two rectangular prisms A and B. Then add these two to total volume the volumes of each prism.

The volume of prism A = length × width × height

V = 4 * 2 * 1

V = 8 cubic in.

The volume of prism B = length × width × height

V  = 1 * 2 * 2

V = 4 cubic in.

Total volume = volume of prism A + volume of prism B

= 8 cubic in + 4 cubic in

= 12 cubic in

Hence, the volume of the composite figure is 12 cubic in.

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The statement that correctly defines continuous and discrete quantitative variables is:

"A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units."

A variable is a quantity that may assume any one of a set of values.

This means that a continuous variable can take on any value within a certain range, which could be infinite, and that it can have decimal values. In contrast, a discrete variable has specific values that are separate and countable, such as integers or categories. For example, the height of individuals is a continuous variable, while the number of siblings someone has is a discrete variable.

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Answer:

Step-by-step explanation:

Generally an equation which will be true for all values of x have some statement which can be simplified into another state which will always be true.

So for example: [tex]x+4=x+4[/tex], is kind of a bit obvious to tell it's going to be true for all values as the two expressions have the same exact terms, but we can subtract "x" from both sides leading us to the statement: [tex]4=4[/tex] which is always true.

One important thing to note is you must be cautious at times, for example: [tex]\frac{x-2}{x-2}=\frac{x-2}{x-2}[/tex] may seem to be true for all values, and x-2 over x-2 is the same thing, so it simplifies to one and same thing on the right side: [tex]1=1[/tex] thus the statement should be true for all values right? Not completely, it's true for most values, except for x=2, and this is because 1=1 isn't exactly the same expression. In the original fraction the denominator has an x-2, and if we plug in x=2, we get 2-2 resulting in division by one, which of course isn't definable. So that's just one important thing to note as simplifying expressions may result in expressions that look equal, but are slightly different in a way.

The measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangles; ∆ABC with hypotenuse = 45 and adjacent = BC, the triangle ∆ADC with hypotenuse = BC and adjacent = 9 with the angle C we can solve for BC as follows:

for ∆ABC;

cosC = 9/BC {adjacent/hypotenuse}

for ∆ADC;

cosC = BC/45 {adjacent/hypotenuse}

9/BC = BC/45

BC² = 9 × 45 {cross multiplication}

BC² = 405

BC = √405 {take square root of both sides}

BC = 20.1246

Therefore, the measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C

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Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

Answer: |-16| =x

- (-16)= x

x = 16

Step-by-step explanation:

thank you

The domain of the relation include the following: C. {-5, -2, 0, 1, 4}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:

Domain = {-5, -2, 0, 1, 4}.

In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {-5, -2, 0, 1, 4}.

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Explanation:

Spreadsheet software is strongly recommended. If you have excel, then it's best to use it since it's used practically everywhere. If you don't have excel, then there are tons of free alternatives such as OpenOffice or LibreOffice.

Enter the data as shown. Then form a third column labeled xy which represents multiplying each x and y pair for any given row. Eg: Tom = xy = 7*2 = 14. Use cell references to quickly compute this new column. I don't recommend manually multiplying each pair of items.

Once the xy column is formed, add up everything in it since [tex]\Sigma[/tex] represents summations. The command called "Sum" or "SUM" does this very quickly. In a cell off to the side type in [tex]=Sum(C2:C10)[/tex] which will add up the elements in cell C2, C3, ... all the way up to C10. Don't forget about the equal sign up front. That's needed to execute the command rather than print out text.

The result of the command should be 350

To verify you can manually add up the values to check the answer is correct.

Answer:

X = 7+2+5+9+6+10+9+8+4

X= 50

Y = 2+5+7+4+2+9+9+4+10

Y = 52

Now ,

Σ(xy)= 50×52

= 2600

Hope it helpful to you

The two smaller angles are 39 degrees each. The other angle is 106

The measure of the angles would be found using the formula

2*x + 24 = 180

This is because the sum of angles that are in a triangle is = 180

the two equal angles are x + x = 2x

the other angle is 24 greater than 2x

2x + 24 = 180

2x = 180 - 24

2x = 156

x = 78

eaxh of the two equal angles are 78 degrees

while the other angle is 78 + 24 = 106

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Answer:

Step-by-step explanation:

The y-intercept of a linear equation in slope-intercept form, y = mx + b, represents the point at which the line crosses the y-axis. In this form, "m" represents the slope of the line and "b" represents the y-intercept.

If we have a graph of y = -9x + 11, the y-intercept can be found by setting x equal to 0 and solving for y:

y = -9x + 11

y = -9 * 0 + 11

y = 11

So, the y-intercept of the original graph is (0, 11).

Now, if we have a graph of y = -9x + 14, the y-intercept can be found in the same way:

y = -9x + 14

y = -9 * 0 + 14

y = 14

So, the y-intercept of the new graph is (0, 14).

Comparing the y-intercepts of the two graphs, we can see that the y-intercept of the new graph has shifted up by 3 units, from (0, 11) to (0, 14).

Therefore, the correct answer is A: The y-intercept of the new graph would shift up 3 units.

Answer: 32

Step-by-step explanation: divide 8 into 4/100

Kcf

Keep change flip

Keep the 4/100 change the division sign to multiplication then flip the 8 to 8/1 then just multiply across.

According to the given statement Nevada's property prices have grown more rapidly , median home value 148,880 and median house values will be 15.6.

The selling price of the middle property in a list of properties listed by highest sale price through lowest over a predetermined time period is the median house price. Thus, if 71 homes were sold, the median home price would correspond to the sale price of the 36th home.

Rate of change for Pennsylvania  [tex]= (97000 - 42400) / (2000 - 1950) = 1092[/tex]

Rate of change for Nevada [tex]= (142000 - 53700) / (2000 - 1950) = 1816[/tex]

As a result, Nevada's property prices have grown more rapidly.

b) Median home value of Pennsylvania in 2010[tex]= 42400 + 1092 * (2010 - 1950) = $148,880[/tex]

c) Pennsylvania[tex]= 42400 + 1092x[/tex]

Nevada[tex]= 53700 + 1816x[/tex]

[tex]42400 + 1092x = 53700 + 1816x\\724x = 11300\\x = 15.6[/tex]

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Answer: 5.26

Step-by-step explanation:

Answer:

= 0.190

Solution:

Change the divisor 2.63 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.

We then have the equations:

50 ÷ 263 = 0.190

and therefore:

0.5 ÷ 2.63 = 0.190

Both calculated to 3 decimal places.

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The new list of rents, ordered from least to greatest, would be 865, 970, 985, 1005, 1015, 1035, 1055, 1080, 1045, 1095. The median rent would also be changed from $1095 to $1045.

In  linear equation, 2 miles per hour is the rate in miles per hour .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Divide the distance by the time.

(1/5 miles) / (1/10 hour)

= 10(1/5) miles per hour

= 2 miles per hour

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Answer:

[tex]6\pi[/tex]

Step-by-step explanation:

There's two things to note here, we're dealing with a semi-circle and also a semi-circle that has some area taken out of it.

The area of a circle can be calculated using the formula: [tex]A=\pi r^2[/tex] where "r" is the radius, equal to half the diameter.

Since we're dealing with the semi-circles, we can just divide this area by two to get: [tex]A=\frac{\pi r^2}{2}[/tex]

Now as noted, we have some of the area taken out, but fortunately it's just another semi-circle. We can simply calculate the area of the entire semi-circle, and then calculate the area of the semi-circle inside and subtract them.

So the diameter of the entire thing is just 8 ft, so the radius is half of this, equal to 8 ft. That means the area is: [tex]A=\frac{\pi (4)^2}{2}=A = \frac{\pi * 16}{2} = 8\pi[/tex]

One mistake that may be made here, is assuming the radius of the smaller semi-circle is just two, as provided in the image. It's actually the radius of the inner semi-circle plus two which gives us the radius of the outer circle, of 4 feet. Now luckily in this case, it actually still results in 2 ft (since 2 + 2 = 4), but in other examples, that may noe be the case.

So now let's calculate the area of the inner semi-circle: [tex]A=\frac{\pi (2)^2}{2}=2\pi[/tex]

Now let's just subtract the areas: [tex]8\pi - 2\pi = 6\pi[/tex], so the area is 6 pi

Answer:

y = 2/3x + 4

Step-by-step explanation:

y-intercept (b) is 4

Use points (-6, 0) and (0, 4) to find the slope (m) = (4-0)/(0--6) = 4/6 = 2/3

y = mx + b = 2/3x + 4

Answer:

126

Step-by-step explanation:

360-97-47-90=126

so 126

Answer: C) 126

Step-by-step explanation: first, you need to use this equation...

m∠A + m∠B + m∠C + m∠D = 360°

=> m∠A + 97° + 47° + 90° = 360°    add all of the numbers...

=> m∠A + 234° = 360°                  subtract both sides by 234

=> m∠A = 360°- 234°

=> m∠A = 126°

Hope you've understood...

The grades that Angie need to receive in her next test so that her average is 92 is 91.

The average is defined as the mean value a given data set. The formula to calculate the mean of a given data set is:

Average = Sum of the observations / Total number of observations

Assume the marks that Angie needs in her next test is represented by x.

Given that Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. Therefore, the grades she need to receive in her next test so her average is 92 is:

Average = Sum of the grades of all test / Total Number of test

92 = (88+96+92+93+x)/5

460 = 369+x

460 - 369 = x

x = 91

Hence, she needs 91 grades in her next test.

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The complete question is:

Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive in her next test so that her average of all test is 92?