Dana's survey showed that 3 out of 8 students preferred pepperoni pizza and
1 out of 8 preferred cheese pizza. How many more of the 72 students surveyed by
Dana preferred pepperoni pizza than preferred cheese pizza?

Answer:

Step-by-step explanation:

Setting up a diagram would be helpful here, so we should have the vertical leg representing the 84-ft. tree and the horizontal leg representing the 120 ft. shadow.  With the two measurements we are given, we should use the tangent ratio, opp/adj,  to set up an equation to solve for the angle of elevation. So the equation will be:

tan θ = 84/120.  Using the tan inverse function on the calculator, we have tan-1( 84/120) = θ and, rounding our decimal value to the nearest 10th, we have θ =35°.  

The value of the car will be £2,621 after 5 years.

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Given that, The value of a second-hand car is £8,000. Each year it loses 20% of its value, we are asked to find its value after 5 years.

This is a situation of exponential decay.

Hence, using the exponential decay formula =

A = P(1-r)ⁿ

Where A is final value, P is principal value, r is rate of decrease and n is the number of years.

Here, we will find A, and we have,

P = £8,000.

r = 20% = 0.20

t = 5

Therefore,

A = 8000(1-0.20)⁵

A = 8000(0.80)⁵

A = 8000(0.32768)

A ≈ 2,621

Hence, the value of the car will be £2,621 after 5 years.

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Answer:

1.) x = 50 2.) x = 70

Step-by-step explanation:

These angles are complementary angles meaning the angles add up to 90°. Therefore, we can set up equations to solve for the variables.

1.)

x + 40 = 90

x = 50

2.)

x + 20 = 90

x = 70

Answer:

x = 50°

x = 70°

Step-by-step explanation:

90° - 40° = 50°

x = 50°

90° - 20° = 70°

x = 70°

Answer:

3x ^2 + 5x - 7 = 0

5x ^2+ 15x = 0

x ^2 - 4x = 4x + 7

Step-by-step explanation:

Just find a equation with a degree of 2 and boosh

Answer: -6P - 10

Step-by-step explanation:

STEP 1.   -12 - 6P + 2

STEP 2.   -6P + ( -12 + 2 )

STEP 3.   -6P - 10

9514 1404 393

Answer:

  (C)  SAS

Step-by-step explanation:

The obtuse angles in each triangle are "corresponding" with respect to the segments marked parallel and the horizontal transversal.

Those angles are between pairs of proportional sides:

  60/42 = 40/28 = 10/7

so, the applicable theorem is SAS. The triangles can be proven similar using the SAS theorem.

Answer:

(0,-4),(1,1)(2,6)

Step-by-step explanation:

The possible radius and height for Cone B are 3 units and 16 units respectively

The formula for calculating the volume of a cone is expressed mathematically;

Volume = 1/3 πr²h

Given that;

From the information given, we have that;

Now, let the height of cone B be 16 units

Substitute the value into the formula, we have;

48π = 1/ 3 × π × r² × 16

multiply the values, we have

48 = 16r²/3

cross multiply

16r² = 144

Divide both sides by 16

r² = 144/16

r² =9

Find the square root of both sides

r = 3units

Hence, the values are 3 units and 16 units

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Answer:

Yes, Anna and Sharon both created triangles that are congruent. Their triangles are congruent because they have 2 corresponding, congruent side-lengths and an included angle that is congruent. Therefore, their triangles are congruent by SAS (Side-Angle-Side).

Exterior angle of triangle x has a value of 135 in this sentence.

A protractor can be used to measure angles precisely. Angles are measured in degrees, hence the term "degree measure." Since one full revolution is equivalent to 360 degrees, it is divided into 360 segments.

According to the "sides of a triangle rule," any two sides of a triangle must add up to be longer than the third side.

By extending one side of the triangle, an external angle is formed. An exterior angle is the angle formed by the stretched side and the side that is immediately adjacent.

Practice. Triangle Angle Measurement

via the triangle's external angle characteristic, x = 105 + 30 = 135.

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Answer:

Since the apparent height h of the tower varies inversely with Corin's distance d from the tower, we know that h and d are inversely proportional. This means that the product of h and d is constant. We can write this relationship as:

hd = k

where k is a constant.

We can find the value of k by substituting the known values of h and d:

9 inches * 800 feet = k

Solving for k, we find that k = 7200 inches * feet.

Since h and d are inversely proportional, we can write the inverse relationship as:

d = k / h

Substituting the value of k that we found earlier, we have:

d = 7200 inches * feet / h

To find the apparent height of the tower if Corin is standing 2000 feet away, we can substitute 2000 for d in the equation above:

h = 7200 inches * feet / 2000 feet = 3.6 inches

Therefore, the apparent height of the tower would be 3.6 inches if Corin is standing 2000 feet away.

Step-by-step explanation:

Answer: To find the factor pairs for -240, we can use the following steps:

Find the prime factorization of -240: -240 = (-2) * (-2) * (-2) * (-3) * (-5)

For each prime factor, there are two possible factor pairs: (-1) and (1), and (-n) and (n). For example, for the factor -2, the possible factor pairs are (-1) and (1), and (-2) and (2).

The factor pairs for -240 are: (-1) and (1), (-2) and (2), (-3) and (3), (-5) and (5), (-6) and (6), (-10) and (10), (-15) and (15), (-30) and (30).

Thus, the factor pairs for -240 are: (-1, 1), (-2, 2), (-3, 3), (-5, 5), (-6, 6), (-10, 10), (-15, 15), and (-30, 30).

Step-by-step explanation:

The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here, graph 1 varies 4 times the x value every time there is an increase of 1 in the x-axis and in graph 2 it is a linear equation with intercept at 4 and thus the graph increases with +4 and   A proportional relationship exists between two values x and y when they can be expressed in the general form y = kx,

Hence, The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.

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Answer:

Rotation

Step-by-step explanation:

Answer:

M<1 is 43 degrees and M<2 is 137

Step-by-step explanation:

This is a case of supplementary angles. M<1 and M<2 are supplementary, which means that their angle degrees added together will be equal to 180. The same is for M<2 and M<3, and M<3 and M<4, and M<1 and M<4. Basically, two angles are supplementary when they form a straight line, or 180 degrees

First, we know that M<1 and M<2 added together is 180. We know M<1 is 7x+1, so then, we have:

(7x+1) + (M<2) = 180

Therefore, we have 180-(7x+1) = M<2. We can't solve the equation further on from there, so we move on.

Next, we know that M<2 and M<3 added together is 180. We know that M<3 is 12x-29, so then, we have:

(12x-29) + (M<2) = 180

Therefore, we have 180-(12x-29) = M<2. Now, we have two equations to solve x:

180-(7x+1) = M<2 and 180-(12x-29) = M<2. As both equations equal M<2, they equal each other. Thus, we have:

180-(7x+1) = 180-(12x-29)

We can cancel out 180, so:

-(7x+1) = -(12x-29)

-7x-1 = -12x+29

-30 = -5x

x = 6.

Now that we have x, we can find M<1, M<3, and M<2. M<1 is (7x+1), so we use substitution, putting 6 for x, and M<1 is evaluated to 43 degrees.

Now that we have M<1, we can find M<2 easily. M<1 + M<2 = 180, so 43 + M<2 must be 180. Therefore, M<2 is 137 degrees.

We can do the same for M<3, but the problem does not require it.

The population change for each period is given as follows:

Hence the average annual change for the period between 1970 and 1995 is given as follows:

7,932,000 people a year.

The population change over a period is given by the subtraction of the population at the end of the period by the population at the beginning of the period.

The population data for each year is given by the table on the image presented at the end of the answer.

Hence the changes are obtained as follows:

The change between 1970 and 1995 is of:

5.691 - 3.708 = 1.983 billion.

This period is composed by 25 years, hence the average annual change is of:

1.983/25 = 0.07932 billion people a year = 7,932,000 people a year.

The chart is given by the image presented at the end of the answer.

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The value of the tan(α) is -0.2624.

In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.

Given that, the angle α intersects the unit circle at point (-0.2538, 0.9673). We need to find the value of tan(α),

We know that, the tangent of the angle is the ratio of the perpendicular and the base,

So,

tan(α) = -0.2538 / 0.9673

= -0.2624

Hence, the value of the tan(α) is -0.2624.

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Answer:

10.8 g

Step-by-step explanation:

Exponential decay equation:  [tex]A=A_0e^{-rt}[/tex]

[tex]A_0[/tex] is the initial amount (at time t = 0, "noon")

r is the decay rate

You have two pieces of information:

Noon   t = 0  [tex]A_0=50[/tex]

3:00 pm  t = 3  [tex]A=30[/tex]

Plug those in to get  [tex]30=50e^{-r(3)}[/tex]

Divide by 50.

[tex]0.6=e^{-3r}[/tex]

Take the natural log of both sides.

[tex]\ln(0.6)=-3r[/tex]

Divide by -3.

[tex]\frac{\ln{(0.6)}}{-3}=r\\\\r \approx .17027[/tex]

Now, for 9:00 pm, use this value of r and  t = 9.

[tex]A=50e^{-.17027(9)} \approx 10.8[/tex]

Answer:

In the account that paid 3% Ramon put $800

In the account that paid 6% Ramon put $1,600

Step-by-step explanation:

Answer:

x+y= 9700 & 0.06x + 0.04y=466

Step-by-step explanation:

let X & Y be each account.  Together, they are $9,700.

So, x+y=9700

thus, account 1 (x) earns 6 %. which converted to decimal is 0.06

account 2 (y) earns 4 % which converted is 0.04

It also said that both accounts were $466, after 1 year.

0.06x+0.04y=466

Using the concept of proportion to find the value of x in the similar triangle, x is equal to 6.67

Similar triangle theorem states that if two triangles have corresponding angles that are equal, then the sides of the triangles are proportional to each other. This theorem can be used to solve problems involving triangles, such as finding the lengths of missing sides.

We can use the concept of ratio to find the value of x.

12 / 5 = 16 / x

Cross multiply both sides and solve for x

12 × x = 16 × 5

12x = 80

x = 80 / 12

x = 6.67

The value of x is 6.67

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9514 1404 393

Answer:

  A.  (0, -1)

Step-by-step explanation:

The x-coordinate of the y-intercept is always zero (eliminates choices B and D. Here, we can see that extending the given line will make it cross the y-axis below the x-axis, where y-values are negative (eliminates choice C).

We can see that the slope of the line is a rise of 1 for a run of 2 units to the right. The point that is 1 above and 2 right of (-2, -2) is (0, -1), the y-intercept.

Answer:

65, given the amount of $1300 times 0.01 percent times 5 years would equal $65 over 5 years, to break it down, multiply 1300 times 0.01 times 5.

Step-by-step explanation:

The area of the square having the same length of the base of the triangle is 7245 square inches.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the given figure as the base of the triangle is an equal length of the side of a square we can obtain the area of the square by first applying Pythagoras on the right angle triangle having a height of 87 inches and a hypotenuse of 18 inches.

So,

Base = {√(87² - 18²)}.

Base = √(7245) inches.

Base = 85.11 inches.

Now, We also know that the area of a square is (side)².

Therefore it is (87.11)² which is the same as 7245 sq inches.

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Answer:

It would probably be 36t

Step-by-step explanation:

because if you think about It.

It is mainly asking you how long it is going to take, so you need a a equation to find the answer.

-John needs 36 copies

- Hp printers out 16 in 5 minutes

- Epson printer out 4 in 1 minutes

so 36 x t or 36t

Answer:

Step-by-step explanation:

-12

Answer:

c

Step-by-step explanation:

Answer:

I believe it would be 64 in 2 correct me if I am wrong.