Suppose you throw a ball upward, with an initial velocity of 50 feet per second, from the roof of a 160-foot-high building.
Suppose that the height of the ball as a function of time is given by () = 160 + 50 − 16^2.
a) When will the ball be 10 feet above the ground?
b) When will it hit the ground?

Answer:

14 and 15

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

I this it b and d they r the only ones that pass thru the line

Step-by-step explanation:

i need points

The equation that represents the number of the bucket filled, y, after x hours is y = (2/5)Cx, where C represents the total capacity of the bucket.

To write an equation that represents the number of the bucket filled, we can use the information given. Let's break it down step by step:

1. In half an hour, the bucket was 1/5 of the way full.

  This means that after 30 minutes (0.5 hours), the bucket was 1/5 filled. We can represent this as follows:

  The amount of the bucket filled, y, after 0.5 hours is equal to 1/5 of the total capacity of the bucket.

2. Let's assume the total capacity of the bucket is C (in some unit of measurement, like liters or gallons).

  Since the bucket was 1/5 full after 0.5 hours, we can express it as:

  y = (1/5)C

3. Now, we need to find an equation that represents the number of the bucket filled, y, after x hours.

  We know that the bucket fills up at a constant rate over time, so we can set up a proportion to relate the time and the amount filled:

  (0.5 hours) / (1/5)C = x hours / y

  Solving the proportion, we can cross-multiply:

  (0.5 hours) * y = (1/5)C * x

  Simplifying further:

  0.5y = (1/5)Cx

  Dividing both sides by 0.5:

  y = (1/5)Cx / 0.5

  Simplifying once more:

  y = (2/5)Cx

Therefore, the equation that represents the number of the bucket filled, y, after x hours is y = (2/5)Cx, where C represents the total capacity of the bucket.

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Answer: A=71°

Step-by-step explanation:

A+B+C=180°

A+38°+C=180°

A+C=180°-38°

A+C=142°

142°/2=71°

∴A=71°

∴C=71°

Answer:

31 bags

Step-by-step explanation:

Divide.

975 / 32 = 30.4

Because Carrie needs at least 975 pounds of mulch, and when you divide, there is 0.4 more bags than 30, you have to round up to 31 bags, to be sure that Carrie has enough.

We conclude that there is convincing evidence to reject the null hypothesis. Therefore, the data provide convincing evidence that the distribution has changed.

Based on the given information, a chi-square goodness-of-fit test was conducted to determine whether there is convincing evidence that the distribution has changed. The test statistic is 10.13 and the p-value is 0.0175.

To interpret these results, we need to compare the p-value to a predetermined significance level (α), which is usually set at 0.05.

Step 1: Compare the p-value to the significance level
- If the p-value ≤ α, then there is convincing evidence to reject the null hypothesis (i.e., the distribution has changed).
- If the p-value > α, then there is not enough evidence to reject the null hypothesis (i.e., no convincing evidence that the distribution has changed).

In this case, the p-value (0.0175) is less than the typical significance level (0.05)

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You bought 17 pounds of rice for a group lunch at the neighborhood market the last time you went there for $12.75. This week, you'll need 38 pounds of rice to prepare another shared meal.

Step 1: Divide the percent discount by 100% to convert it to a decimal. Step 2: Construct the equation P=(1d)x P = (1 d) x where P is the sale price, d is the discount expressed as a decimal, and x is the original price of the item to get its original price.

A linear demand equation is written as Q = a - bP in standard form. The price is treated as a function of quantity required in the inverse demand equation (also known as the pricing equation): P = f(Q) (Q).

When you most recently visited the neighborhood market, you spent $12.75 on 17 pounds of rice for a communal lunch. You need 38 pounds of rice this week to create another communal supper.

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Answer:

Solving the inequality \(1<\frac{a+7}{-2}\) we get the value of a: \(\mathbf{a<-9}\)

Step-by-step explanation:

We need to solve the inequality: \(1<\frac{a+7}{-2}\)

We need to solve the inequality, to find the value of a.

Solving the inequality:

\(1<\frac{a+7}{-2}\)

First step is Switching both sides (the inequality will be reversed)

\(\frac{a+7}{-2}>1\)

The next step is to multiply both sides by -2 and reverse the inequality

\(\frac{a+7}{-2}*-2<1*-2\\a+7<-2\)

Now, subtracting 7 on both sides

\(a+7-7<-2-7\\a<-9\)

So, solving the inequality \(1<\frac{a+7}{-2}\) we get the value of a: \(\mathbf{a<-9}\)

Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.

A system of equations, involving two linear lines has solutions as follows:

In the question, we are informed that Samia created the given tables for a linear system, and concluded that no solution exists for the system.

We are asked to comment on her conclusion.

To check for her conclusion, we calculate the slopes of both the lines to check whether the relations are parallel or not, as, for parallel relations, the slopes are equal.

Slope can be calculated using the formula, m = (y₂ - y₁)/(x₂ - x₁), when (x₁, y₁), and (x₂, y₂) are the points on the line.

Thus, the slope for:-

Relation 1, is m₁ = (22 - 8)/(4 - (-3)) = 14/7 = 2.

Relation 2, is m₂ = (12 - (-2))/(4 - (-3)) = 14/7 = 2.

Since the slope of the two relations is equal, that is, m₁ = m₂, and they are not coinciding with each other, we can say that the two relations are parallel to each other.

Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.

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Answer:

5 times bigger

Step-by-step explanation:

(6-4) = 2

(6-4) x 5 = 10

Answer:

1. \( \theta = 61.9^\circ \)

2. \( x = 23.7~cm \)

Step-by-step explanation:

Problem 1.

Use the Law of Sines.

This is SSA.

\(\dfrac{a}{\sin A} = \dfrac{c}{\sin C}\)

\( \dfrac{31.2~cm}{\sin 51^\circ} = \dfrac{35.4~cm}{\sin \theta} \)

\( \sin \theta = \dfrac{35.4~cm \times \sin 51^\circ}{31.2~cm} \)

\( \sin \theta = 0.88176 \)

\( \theta = \sin^{-1} 0.88176 \)

\( \theta = 61.9^\circ \)

Problem 2.

m<A + m<B + m<C = 180°

m<A + 67° + 58° = 180°

m<A = 55°

Use the Law of Sines.

\(\dfrac{a}{\sin A} = \dfrac{c}{\sin C}\)

\(\dfrac{x}{\sin 55^\circ} = \dfrac{24.5}{\sin 58^\circ}\)

\(x = \dfrac{\sin 55^\circ \times 24.5}{\sin 58^\circ}\)

\( x = 23.7~cm \)

Answer:

50 laps

Step-by-step explanation:

20+1.25x+15+2.5x+40+1.5x+25+1.75x=450

7x+100=450

7x+200-200=450-100

7x=350

7x/7=350/7

x=50

To change to spherical coordinates, we can use the following formula:

x = ρ sin φ cos θ

y = ρ sin φ sin θ

z = ρ cos φ

We also note that the region of integration is a hemisphere with radius 3, and that the integrand contains x^2z+y^2z+z^3. Since we are integrating over a hemisphere, the bounds of ρ can be from 0 to 3, φ can be from 0 to π/2, and θ can be from 0 to 2π.

Next, we need to express the integrand in terms of ρ, φ, and θ. Substituting x, y, and z, we get:

x^2z + y^2z + z^3 = ρ^4 sin^2 φ cos^2 θ (ρ cos φ) + ρ^4 sin^2 φ sin^2 θ (ρ cos φ) + (ρ cos φ)^3

Simplifying, we get:

x^2z + y^2z + z^3 = ρ^5 cos^2 φ + ρ^3 cos^3 φ

Thus, the new integral is:

∫0^(2π) ∫0^(π/2) ∫0^3 (ρ^5 cos^2 φ + ρ^3 cos^3 φ) ρ^2 sin φ dρ dφ dθ

Integrating with respect to ρ, we get:

∫0^(2π) ∫0^(π/2) [ 1/6 ρ^6 cos^2 φ + 1/4 ρ^4 cos^3 φ ]_|ρ=0^3 sin φ dφ dθ

Simplifying and integrating with respect to φ, we get:

∫0^(2π) [ 9/5 sin^5 φ - 27/14 sin^7 φ ]_|φ=0^(π/2) dθ

Evaluating the limits, we get:

∫0^(2π) [ 9/5 - 27/14 ] dθ

Finally, evaluating the integral, we get:

∫0^(2π) [ 33/35 ] dθ = 66π/35

Therefore, the value of the integral after changing to spherical coordinates is 66π/35.

Answer:

12.056

Step-by-step explanation:

Answer:12.056

Step-by-step explanation:

Answer:

ajasjzaallxaxxzaobzab

To decide whether it is sensible for Stacy to utilize the ordinary show for the inspecting conveyance of the test extent, we got to check whether the conditions for utilizing the typical conveyance estimation are met. The conditions are:

The test estimate is expansive sufficient

The test information is autonomous

The populace is at slightest 10 times bigger than the test

The test estimate, in this case, is 50. To check whether it is expansive sufficient, ready to utilize the run the show of thumb that the test measure ought to be at the slightest 10% of the populace estimate.

Hence, based on these conditions, it is sensible for Stacy to utilize the ordinary demonstration for the inspecting conveyance of the test extent. She can accept that the testing dispersion is roughly typical with a cruel of p = 0.11 and a standard deviation of sqrt[(p(1-p))/n] = sqrt[(0.11(0.89))/50] = 0.05.

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Our final answer will be AB → Z, BC → Y, and AC → X.

In our question, points are given as (3, 2), b(4, 5), and c(7, 3) and triangle ABC was created by joining these points with the line segments.

By matching the corresponding sides, we get

A(3, 2) = reflect over x-axis A' (3, -2) = reflect over the Y axis A'' (-3, -2)

B(4, 5) = reflect over x-axis B'(4, -5) = reflect over the Y axis B''(-4, -5)

C(7, 3) =  reflect over x-axis C'(7, -3) = reflect over the Y axis C''(-7, -3)

According to the coordinate analysis of corresponding points, we get:

AB → A''B'' → Z

AC → A''C'' → X

BC → B''C'' → Y

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Answer:

both of these.will be solved by angle sum property which states that sum of all interior angles is 180 degrees

in a

one angle is 30 degrees

other is right angle means 90 degrees

total sum of these angles is 120

total sum of all angle must be 180 degrees

so the third angle is 60 degrees

in b

one angle is 45 degrees

other is a right angle means 90 degrees

total sum of these angles is 135

total sum of all angles must be 180 degrees

so the third angle is 45 degrees

hope this helps

have a good day

thanks for points

Answer:

Step-by-step explanation:

espera y termino y te ayudo vale que me falta poco vale

The width of each column is 2 inches.

Width is the measurement of something from side to side.

Let x = width of each column.

If a "gutter" is one eighth as wide as each column, then the width of the gutter can be expressed as

gutter = (1/8)x

If the document is 8.5 in. wide, then the sum of the widths of the left and right margins, the 3 columns and the 2 gutters in between columns is equal to 8.5 in.

left margin + right margin + 3 columns + 2 gutters = 8.5in

1 in + 1 in + 3x + 2(1/8)x = 8.5 in

3x + 2(1/8)x = 8.5 in - 1 in - 1 in

3 1/4 x = 6.5 in

x = 2 in

width of each column = 2 inches

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Th given number " six hundred thousand eight" can be written in the standard form as 600,008.

To write "six hundred thousand eight" in standard form, we need to write the number using digits in the appropriate place value positions.

The digit "8" is in the "ones" position, the digit "0" is in the "tens" position, the digit "0" is in the "hundreds" position, the digit "0" is in the "thousands" position, the digit "0" is in the "ten thousands" position, and the digit "6" is in the "hundred thousands" position.

Therefore, it can be concluded that we can write the given number in standard form as 600,008.

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a) The 90% confidence interval for μ when n = 144 is (34.006, 34.994).

b) The 90% confidence interval for μ when n = 576 is (34.251, 34.749).

c) The widths of the confidence intervals found in parts a is 0.494 and b is 0.249.

a) For n = 144 and a 90%  confidence interval:

The critical value for a 90% confidence level with (n - 1) degrees of freedom is approximately 1.660. Using this value:

Confidence Interval = 34.5 ± 1.660 × (3.6 / sqrt(144))

Calculating the confidence interval:

Confidence Interval = 34.5 ± 1.660 × (3.6 / 12)

Confidence Interval = 34.5 ± 0.494

Therefore, the 90% confidence interval for μ when n = 144 is (34.006, 34.994).

b) For n = 576 and a 90% confidence interval:

The critical value remains the same: 1.660.

Confidence Interval = 34.5 ± 1.660 × (3.6 / sqrt(576))

Calculating the confidence interval:

Confidence Interval = 34.5 ± 1.660 × (3.6 / 24)

Confidence Interval = 34.5 ± 0.249

Therefore, the 90% confidence interval for μ when n = 576 is (34.251, 34.749).

c) The width of a confidence interval is given by:

Width of confidence interval = 2 × (critical value) × (standard deviation / sqrt(n))

For part a:

Width of confidence interval = 2 × 1.660 × (3.6 / sqrt(144))

Width of confidence interval = 0.494

For part b:

Width of confidence interval = 2 × 1.660 × (3.6 / sqrt(576))

Width of confidence interval = 0.249

Therefore, the widths of the confidence intervals in parts a and b are 0.494 and 0.249, respectively.

To compare the effect of quadrupling the sample size while holding the confidence coefficient fixed, we can calculate the ratio of the widths:

Ratio of widths = W2 / W1 = 0.249 / 0.494 = 0.504

So, quadrupling the sample size while holding the confidence coefficient fixed reduces the width of the confidence interval by approximately 50.4%.

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Answer:

y=5x

Step-by-step explanation:

Because it has the same slope, both equations must have 5x as their slope. The 2 equations are not going to have the same y intercept, so the +3 can be ignored and replaced with b. You want to plug in (1,5) into you new equation of y=5x+b, to get 5=5(1)+b. Multiply 5 by 1 to get 5, and then subtract 5 from both sides, which gives you 0=b. This means that the y intercept is the origin, so your new equation is y=5x

The Spearman rank-order correlation coefficient is a measure of the direction and strength of the linear relationship between two ordinal variables.

Spearman's rank-order correlation is used when two variables are measured on an ordinal scale.

What is the Spearman Rank-Order Correlation Coefficient?

The Spearman Rank-Order Correlation Coefficient is a non-parametric statistical measure that estimates the relationship between two variables using ordinal data.

It evaluates the strength and direction of a relationship between two variables by rank-ordering the data.

The Spearman correlation coefficient, named after Charles Spearman, calculates the association between two variables' rankings.

The correlation coefficient ranges from -1 to +1. A value of +1 indicates that there is a perfect positive relationship between the variables, whereas a value of -1 indicates that there is a perfect negative relationship between the variables.

In contrast, a value of 0 indicates that there is no correlation between the variables.

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Answer:

If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.

Step-by-step explanation:

Answer:

3y=10-2xor y=(1/3) (10-2x)

The floor function of a number is taken out to get the greatest integer that is less than or equal to the number.

To get the floor of any number assume the y-axis of the graph and on that axis plot the number, when you plot the number, the integer just below that point is known as the floor for that number.

function,  \(f(x)=\lfloor{x}\rfloor\)

a.)  for f(2),

\(f(x)=\lfloor{x}\rfloor\\f(2)=\lfloor{2}\rfloor\)

for a whole number, the number itself is the floor of the number. thus, the function will return the value as 2.

b.)  for f(6.8),

\(f(x)=\lfloor{x}\rfloor\\f(6.8)=\lfloor{6.8}\rfloor\\f(6.8)=6\)

for the number 6.8, the ceiling will be 6 as 6 is the greatest integer that is less than 6.8.

c.)  for f(-3.3),

\(f(x)=\lfloor{x}\rfloor\\f(-3.3)=\lfloor{-3.3}\rfloor\\f(-3.3)=-4\)

for the number -3.3, the ceiling will be -4 as -4 is the integer that will be on the floor when seen on the negative number line.

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Answer:

The correct answer is - Two-paragraph proof.

A paragraph proof is only a two-column proof that is written in sentences. However, since it is easier to leave steps out when writing a paragraph proof.

The solution to the given problem does not need any columns and can be proved in just sentences. Therefore, it is a two-paragraph proof.

Step-by-step explanation:

The volume of the figure is the sum of the volume of the square prism and the volume of the square pyramid which is 67.2cm³

To calculate the volume of the figure, we need to find the volume of the square prism and the volume of the square pyramid.

The volume of a square prism is given as;

V = L³

V = 4³

V = 64cm³

The volume of the square pyramid is given as;

V = 1/3lh

V = 1/3 * 4 * 2.4

V = 3.2cm³

The volume of the figure is 64cm³ + 3.2cm³ = 67.2cm³

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