3) The height of a ball above the ground t seconds after it is thrown is h(t) = 20 + 32t - 16t².
a) How long will it take for the ball to hit the ground?
b) How long does it take to reach its maximum height?
c) What is the ball's maximum height?
d) If the ball was thrown from a height of 30 feet what would the equation be?

The two integers are 5 and 6.

To solve this problem, we need to set up an algebraic equation based on the information given.

Let's call the first integer x and the second integer y. According to the problem, an integer (x) is 14 less than 4 times another (y).

This can be written as: x = 4y - 14

We are also told that the product of the two integers is 30. This can be written as:

xy = 30

Now we can substitute the first equation into the second equation to solve for one of the variables.

Let's solve for y:

(4y - 14)y = 30

4y^2 - 14y = 30

4y^2 - 14y - 30 = 0

Using the quadratic formula, we can solve for y:

y = (-(-14) ± √((-14)^2 - 4(4)(-30)))/(2(4))

y = (14 ± √(196 + 480))/8

y = (14 ± √676)/8

y = (14 ± 26)/8

y = 5 or y = -1.5

Now we can plug these values of y back into the first equation to find the corresponding values of x:

x = 4(5) - 14 = 6

x = 4(-1.5) - 14 = -20

So the two integers are either 5 and 6, or -1.5 and -20. However, since the problem asks for integers, we can eliminate the second solution.

Therefore, the two integers are 5 and 6.

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The value of x is

x=-5

Generally, An angle is a figure formed by two rays (or line segments) that share a common endpoint. Angles are usually measured in degrees, with a full angle measuring 360 degrees.

Considering that the angle on a point is 630 , we have that the missing angle is

y=360-(148+92)

y=120

Therefore

y=x+125

Hence

x=y-125

x=120-125

x=-5

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Answer:

-3 < y < -1

Step-by-step explanation:

|4y+8| < 4                                   |4y+8| > -4

4y + 8 < 4                                   4y + 8 > -4

4y < -4                                         4y > -12

y < -1                                             y > -3

So, the answer is -3 < y < -1

The values of w and v in the given right triangle are 1.68 and 4.7

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

Given is a right triangle, with hypotenuse 5, and an acute angle of 71°, we need to find the value of v and w, using trigonometric ratios,

The other acute angle will be = 90°-71° = 19°

Taking 19° as reference angle,

Sin 19° = w/5

w = 1.68

Cos 19° = v/5

v = 4.7

Hence, the values of w and v in the given right triangle are 1.68 and 4.7

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The value of x on the straight line is 43 degrees

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

The straight line

The sum of angles on a straight line is 180 degrees

Using the above as a guide, we have the following equation

3x + 51 = 180

Evaluate

3x = 129

Divide by 3

x = 43

Hence, the value of x is 43 degrees

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The angle of elevation of the sun is 19. 75 degrees

It is crucial to know there are six trigonometric identities.

These identities are;

From the information given,  we have that;

The angle of elevation = θ

The opposite side = The height of the building

The adjacent side = shadow of the building

Using cosine identity, we have;

cos θ = 48/51

divide the values

cos θ = 0. 9412

Take the cosine inverse

θ = 19. 75 degrees

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Heather runs 3 miles in 28 minutes, so at the same rate, she would run 4.494 miles in 42 minutes.

To find out how many miles Heather would run in 42 minutes at the same rate, we use the concept of unit rate. Unit rate is a comparison of two different quantities when they are combined together. In this case, we need to find the unit rate of Heather's running speed in miles per minute.

Step 1: Find the unit rate of Heather's running speed in miles per minute.

To do this, we divide the distance she ran by the time she took to run it:

3 miles ÷ 28 minutes = 0.107 miles per minute

Step 2: Use the unit rate to find out how many miles Heather would run in 42 minutes.

To do this, we multiply the unit rate by the time she runs:

0.107 miles per minute × 42 minutes = 4.494 miles

Therefore, Heather would run 4.494 miles in 42 minutes at the same rate.

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.

The distribution is binomial.

a) The probability that exactly 3 in the sample are unemployed is 0.0311, b) The probability that there are fewer than 3 in the sample are unemployed is 0.5354, c) The probability that there are more than 2 in the sample are unemployed is 0.4646, d) The probability that there are at most 3 in the sample are unemployed is 0.5665.

The binomial distribution formula is P(x) = (nCx)(p^x)(q^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.

a) To find the probability that exactly 3 in the sample are unemployed, we plug in the values: n = 20, x = 3, p = 0.065, and q = 0.935.
P(3) = (20C3)(0.065^3)(0.935^17) = 1140(0.000274625)(0.099961375) = 0.0311

b) To find the probability that there are fewer than 3 in the sample are unemployed, we need to find the probability that 0, 1, or 2 are unemployed and add them together.
P(0) = (20C0)(0.065^0)(0.935^20) = 1(1)(0.1645) = 0.1645
P(1) = (20C1)(0.065^1)(0.935^19) = 20(0.065)(0.1725) = 0.2249
P(2) = (20C2)(0.065^2)(0.935^18) = 190(0.004225)(0.1812) = 0.1460
P(<3) = P(0) + P(1) + P(2) = 0.1645 + 0.2249 + 0.1460 = 0.5354

c) To find the probability that there are more than 2 in the sample are unemployed, we can subtract the probability that there are fewer than 3 from 1.
P(>2) = 1 - P(<3) = 1 - 0.5354 = 0.4646

d) To find the probability that there are at most 3 in the sample are unemployed, we can add the probabilities that there are 0, 1, 2, or 3 unemployed.
P(≤3) = P(0) + P(1) + P(2) + P(3) = 0.1645 + 0.2249 + 0.1460 + 0.0311 = 0.5665

Therefore, the answers are:
a) 0.0311
b) 0.5354
c) 0.4646
d) 0.5665

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The measure of the angles e, d, a, and f will be 26°, 122°, 102°, and 58°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

By the supplementary property, the equation is given as,

f + 78° + 44° = 180°

f = 58°

By the complementary property, the equation is given as,

e + 64° = 90°

e = 26°

By the corresponding angles property, the equation is given as,

c = f

c = 58°

By the supplementary property, the equation is given as,

c + d = 180°

58° + d = 180°

d = 122°

By the corresponding angles property, the equation is given as,

b = 78°

By the supplementary property, the equation is given as,

a + b = 180°

a + 78° = 180°

a = 102°

The diagram is given below.

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The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C

The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.

This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.

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Answer:

6

Step-by-step explanation:

Step 1: How many males are there?

40% of 60 = 0.4 × 60 = 24

There are 24 males.

Step 2: Of the 24 males, how many wear a hat?

25% of 24 = 0.25 × 24 = 6

Answer: 6

Kai drives 470 miles in 10 hours at a constant speed of 47 miles per hour. To find out how far Kai drives in 10 hours, we can use the distance formula d=rt, where d is the distance, r is the rate (or speed), and t is the time.

First, we need to find Kai's rate (or speed). We can do this by rearranging the formula to solve for r:

r = d/t

Plug in the values we know:

r = 376 miles / 8 hours

Simplify:

r = 47 miles per hour

Now that we know Kai's rate, we can plug it back into the distance formula to find out how far he drives in 10 hours:

d = rt

d = (47 miles per hour) (10 hours)

Simplify:

d = 470 miles

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As our calculated t-value of 3.032 is greater than the critical value of ±1.645, we can reject the null hypothesis at the 0.1 significance level and conclude that the coefficient for the variable is statistically significant and different from zero.

The hypotheses that we want to test are:

H0: The coefficient for the variable is equal to zero.

H1: The coefficient for the variable is not equal to zero.

Using the given output, we can see that the coefficient for the variable is 15.509, and the standard error of the coefficient is 5.123. The t-value for the coefficient is calculated by dividing the coefficient estimate by its standard error, so:

t = 15.509 / 5.123 = 3.032

To test the hypothesis, we can compare the calculated t-value with the critical value of the t-distribution with n-k-1 degrees of freedom (where n is the sample size and k is the number of independent variables), at a significance level of 0.1 and using a two-tailed test.

Since the sample size and number of independent variables are not provided, we cannot determine the degrees of freedom or the critical value directly. However, we can use a t-distribution calculator or look up the critical value from a t-distribution table. For example, with n=50 and k=2 (based on the given output), the critical value for a two-tailed test at a significance level of 0.1 is approximately ±1.645.

Since our calculated t-value of 3.032 is greater than the critical value of ±1.645, we can reject the null hypothesis at the 0.1 significance level and conclude that the coefficient for the variable is statistically significant and different from zero. In other words, there is evidence to suggest that the variable has a significant effect on the outcome being predicted by the regression model.

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The lateral surface area of the cylinders {W} and {Y} are same.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given are the dimensions of the cylinder as shown in the image.

The lateral surface area of the cylinder is -

L.S.A = 2πrh

{ 1 } -

L.S.A {W} = 2π x 3 x 9 = 54π

{ 2 } -

L.S.A {X} = 2π x 4 x 2 = 16π

{ 3 } -

L.S.A {Y} = 2π x 4.5 x 6 = 54π

Therefore, the lateral surface area of the cylinders {W} and {Y} are same.

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Answer:

-12?

Step-by-step explanation:

Answer:

y = 3x + 3

Step-by-step explanation:

The equation of the line is in standard form, which means we need to convert it into slope intercept form [tex]y=mx+b[/tex], where m is the slope and b is the y intercept.

[tex]3x-y=3[/tex]

Add 3x to both sides

[tex]y=3x+3[/tex]

Now we need to graph it:

The y intercept is 3, so we start at 3. Our slope is [tex]\frac{3}{1}[/tex] or 3, so we go down 3 and 1 to the left.

Your monthly house payment given that the bank charges 6.25% APR for a loan of 15 years will be $51.95.

To find the monthly house payment for a loan of $65,000 with a 6.25% APR for 15 years, we can use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

Where:
M = monthly payment
P = principal amount
i = monthly interest rate
n = number of monthly payments

First, we need to find the monthly interest rate and the number of monthly payments:
i = 6.25% / 12 = 0.00625
n = 15 years(12 months/year) = 180 months

Now we can plug these values into the formula:
M = 65,000 [ 0.00625(1 + 0.00625)^180 ] / [ (1 + 0.00625)^180 - 1]

M = 65,000 [ 0.00625(1.00625)^180 ] / [ (1.00625)^180 - 1]

M = 65,000 [ 0.024636 ] / [ 0.171184 ]

M = 65,000 [ 0.143875 ]

M = 9,351.88

So, the monthly house payment will be $9,351.88 / 180 = $51.95.

Therefore, the monthly house payment for a loan of $65,000 with a 6.25% APR for 15 years will be $51.95.

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The correct statements according to the model are: if the delivery location is 0 miles away, the order will take 5 minutes to be delivered, and if the delivery location is 10 miles away, the order will take 30 minutes to be delivered.

What is statements ?

A statement is a sentence that expresses a complete thought and can be either true or false. In mathematics, statements are often used to make claims or propositions that can be proven or disproven using logical reasoning and evidence.

The equation y = 2.5x + 5 models the average amount of time from when an order is placed until when it is delivered for a sandwich shop that makes home deliveries, where x is the number of miles between the shop and the delivery location, and y is the time in minutes.

To answer the question, we need to look at the statements and see which ones are correct according to the model:

If the delivery location is 0 miles away, the order will take 5 minutes to be delivered.

This statement is true because if x=0, then y=2.5(0)+5=5, which means the order will take 5 minutes to be delivered.

If the delivery location is 10 miles away, the order will take 30 minutes to be delivered.

This statement is true because if x=10, then y=2.5(10)+5=30, which means the order will take 30 minutes to be delivered.

If the delivery location is 1 mile away, the order will take 2.5 minutes to be delivered.

This statement is false because if x=1, then y=2.5(1)+5=7.5, which means the order will take 7.5 minutes to be delivered, not 2.5 minutes.

If the delivery location is 5 miles away, the order will take 20 minutes to be delivered.

This statement is false because if x=5, then y=2.5(5)+5=17.5, which means the order will take 17.5 minutes to be delivered, not 20 minutes.

Therefore, the correct statements according to the model are: if the delivery location is 0 miles away, the order will take 5 minutes to be delivered, and if the delivery location is 10 miles away, the order will take 30 minutes to be delivered.

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Answer: 13,024

Step-by-step explanation:

used a converter

Answer:

Step-by-step explanation:

16 ounces is equal to 1 pound so to convert ounces to pounds just multiply by 16. 814 times 16 is equal to 13,024 or thirteen thousand and twenty-four.

Because 6 cannot equal 2, this statement is false. As a result, this equation cannot be solved.

By fusing two expressions, the equation generates a mathematical expression, similar to an expression. A common equation would have been 3x - 5 = 16. The solution to this equation reveals that the variable x has a value of 7.

First, we employ the distributive property to simplify the left side of the equation:

3(x + 2) = 3x + 6

The right side of the calculation is then made simpler by grouping related terms together:

x+2x+2 = 3x+2

The initial equation is now:

3x + 6 = 3x + 2

3x both from sides are subtracted, giving us:

6 = 2

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The key to finding the value of x in a right triangle is to choose the appropriate trigonometric ratio based on the sides given and to use a calculator to find the value of x to the nearest tenth of a degree.

To find the value of x in a right triangle, we can use the trigonometric ratios of sine, cosine, and tangent. The ratio we choose depends on the information given in the question and the sides and angles we are trying to find.

To find x to the nearest tenth of a degree, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Choose the appropriate trigonometric ratio based on the sides given. For example, if we are given the opposite side and the hypotenuse, we would use the sine ratio.
c. Set up the equation and solve for x. For example, if we are using the sine ratio, the equation would be sin(x) = opposite/hypotenuse.
d. Use a calculator to find the value of x to the nearest tenth of a degree.

To find x using the aulend method, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Use the Pythagorean theorem, a^2 + b^2 = c^2, to find the missing side.
c. Use the appropriate trigonometric ratio to find the value of x.

To approximate x to the nearest tenth of a degree, we can use a calculator to find the value of x and then round to the nearest tenth.

To find x in the given right triangle, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Choose the appropriate trigonometric ratio based on the sides given.
c. Set up the equation and solve for x.
d. Use a calculator to find the value of x.

Overall, the key to finding the value of x in a right triangle is to choose the appropriate trigonometric ratio based on the sides given and to use a calculator to find the value of x to the nearest tenth of a degree.

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The two triangles cannot be similar, because they have one pair of corresponding angles that are not equal.

What is triangle ?

A triangle is a geometric shape consisting of three straight sides and three angles. The sum of the angles in a triangle is always 180 degrees. The point where two sides of a triangle meet is called a vertex. The side opposite to a vertex is called the opposite side, and the angle opposite to a side is called the opposite angle.

To determine if two triangles are similar, we need to check if their corresponding angles are equal and their corresponding sides are proportional.

Let's start with the angles:

In triangle CBA, we can use the Law of Cosines to find the measure of angle C:

[tex]cos(C) = (a^2 + b^2 - c^2) / (2ab)[/tex]

where a, b, and c are the side lengths opposite to angles A, B, and C, respectively.

[tex]cos(C) = (72^2 + 48^2 - 84^2) / (2 x 72 x 48)[/tex]

cos(C) = -0.25

Since cos(C) is negative, we know that angle C is obtuse.

Now, let's consider triangle FGH. By the Law of Cosines, we can find the measure of angle H:

[tex]cos(H) = (f^2 + g^2 - h^2) / (2fg)[/tex]

[tex]cos(H) = (8^2 + 12^2 - 14^2) / (2 x 8 x 12)[/tex]

cos(H) = 0.25

Since cos(H) is positive, we know that angle H is acute.

Therefore, the two triangles cannot be similar, because they have one pair of corresponding angles that are not equal.

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The blanks are filled by the following

8-3x   3x-6  4x-5  -2x+5

2x-3    3       2-x      x

1-2x    4x-1  3x-2  -3x+4

5x-4   6-5x -4x+7  6x-7

The blanks are filled by adding the complete row, this will be used for comparison and solve for other missing spaces.

let the missing value in each case be y

Adding the complete row gives

2x - 3 + 3 + 2 - x + x = 2x + 2

Column 1

8 - 3x + 2x - 3 + 1 - 2x + y = 2x + 2

6 - 3x + y = 2x + 2

y = 5x - 4

Column 2

y + 3 + 4x - 1 + 6 - 5x = 2x + 2

y + 8 - x = 2x + 2

y = 3x - 6

Row 4

5x - 4 + 6 - 5x + y + 6x - 7 = 2x + 2

6x - 5 + y  = 2x + 2

y = -4x + 7

Column 3

y + 2 - x + 3x - 2 - 4x + 7 = 2x + 2

y + 7 - 2x = 2x + 2

y = 4x - 5

Row 1

8 - 3x + 3x - 6 + 4x - 5 + y = 2x + 2

-3 + 4x + y = 2x + 2

y = -2x + 5

Row 3

1 - 2x + 4x - 1 + 3x - 2 + y = 2x + 2

5x - 2 + y = 2x + 2

y = -3x + 4

check

This should be equal to Row 1 which is y = -2x + 5

Column 4

y + x - 3x + 4 + 6x - 7 = 2x + 2

y + 4x - 3 = 2x + 2

y = -2x + 5

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The trinomial 4x²-20x+25 is factorable. The correct factorization of the trinomial 4x²-20x+25 is H (2x+5)².

To factor a trinomial, we need to find two numbers that multiply to give the constant term (25) and add to give the coefficient of the middle term (-20). In this case, the two numbers are -5 and -5. We can then write the trinomial as (4x²-10x-10x+25), and factor by grouping:

4x²-10x-10x+25 = (4x^(2)-10x) + (-10x+25) = 2x(2x-5) - 5(2x-5) = (2x-5)(2x-5) = (2x+5)²

Therefore, the correct factorization of the trinomial is H (2x+5)²

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The answer is \( f(3) = 5 \) with no spaces.

Given the function \( f(x) = \left\{ \begin{array}{llr} -x^2 & \text{for} & x < 0 \\ x+2 & \text{for} & x \ge 0 \end{array} \right. \), we need to evaluate \( f(3) \).

Since \( 3 \ge 0 \), we will use the second part of the function, which is \( f(x) = x + 2 \).

So, we plug in \( x = 3 \) into the function and get:

\( f(3) = 3 + 2 = 5 \)

Therefore, the answer is \( f(3) = 5 \) with no spaces.

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The result of the division is a monomial, and it is in standard form: [tex]-0.195b^4[/tex]

The result of the division of the monomials is a monomial. To find the result, we need to divide the coefficients and subtract the exponents of the same variables.

The steps are as follows:

Divide the coefficients: -0.26 ÷ (4(1)/(3)) = -0.26 ÷ (4/3) = -0.26 × (3/4) = -0.195

Subtract the exponents of the same variables: a^(3-3) = a^0 = 1, b^(6-2) = b^4

Multiply the result of step 1 and step 2: -0.195 × 1 × b^4 = -0.195b^4

Therefore, the result of the division is a monomial, and it is in standard form: -0.195b^4.

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The measure of ∠A is 77 degrees.

A round-shaped figure that has no corners or edges is called as Circle.

ABCD is the quadrilateral which is inscribed in the circle.

We have to find angle A measure.

The opposite angles of a cyclic quadrilateral are supplementary so we apply to find the measure.

Therefore, angle A + angle C = 180 degrees

2x+9+3x+1=180

5x+10=180

Subtract 10 from both sides

5x=170

Divide both sides by 5

x=34

Now plug in x value in angle A, 2x+9.

∠A=2x+9

=2(34)+9

=68+9

=77 degrees.

Hence, the measure of ∠A is 77 degrees.

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The final answer of inverse function for f(x)=2/5 (x-5)^2 is y = √(5/2 * x) + 5

The inverse function for f(x)=2/5 (x-5)^2 would become x= 2/5 (y-5)^2, and

We need to solve for y. Here is a step-by-step explanation of how to solve for y:

Now, multiply both sides of the equation by 5/2 to get rid of the fraction on the right side of the equation:

5/2 * x = (y-5)^2

Then, Take the square root of both sides of the equation to get rid of the exponent on the right side of the equation:

√(5/2 * x) = y-5

Add 5 to both sides of the equation to isolate y on one side of the equation:

√(5/2 * x) + 5 = y

Simplify the equation to get the final answer:

y = √(5/2 * x) + 5

Therefore, the inverse function for f(x)=2/5 (x-5)^2 is y = √(5/2 * x) + 5.

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Answer:

Below in bold.

Step-by-step explanation:

The right triangle of which ∅ is a part has

Hypotenuse = sqrt(8^2 + 15^2)

=  sqrt289

= 17,

So, sin ∅ = 8/17 and cos ∅ = 15/17

and

sin∅ + cos∅(1- cos∅)

= 8/17 + 15/17(1 - 15/17)

= 8/17 + 15/17 - 225/289

= 166/289.

(b)  tan 30 = h/96      where h is height of the mast

h = 96 tan 30.

= 55.4256

tan 60 = 55.4256/d        where d is the required distance

d = 55.4256/ tAN60

  = 32 M

Answer:

-1

Step-by-step explanation:

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