Write a proportion to determine the missing measure.

A lighthouse casts a 72-yard shadow at the same time as a 32-foot tall billboard casts a 19-foot shadow.
What is the height of the lighthouse?



A 121.3 yd
B 64.8 yd
C 42.8 yd
D 118.4 ft

Answer:

(15, - 4 ) , (3, - 2 ) , (- 1, 0 )

Step-by-step explanation:

given a point (x, y ) on a function f(x) , then the corresponding point on the inverse function is (y, x )

given the points on g(x) , then the corresponding points on [tex]g^{-1}[/tex] (x) are

(- 4, 15 ) → (15, - 4 )

(- 2, 3 ) → (3, - 2 )

(0, - 1 ) → (- 1, 0 )

1)From the data:

Two conclusions that the researcher can make are:
b.) About 54% of the variation in the distance that the driver can see is explained by a linear relationship with the driver's age.
d.) The correlation coefficient, t, is -0.736. (This can be found by taking the square root of the coefficient of determination and considering the negative correlation)

2)"It is not affected" is the correct statement,that is option b

3)The "High correlation does not always establish causation" is the TRUE statement, that is option c .

What is Correlation?

Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together.

A positive correlation indicates that as one variable increases, the other variable also increases.

A negative correlation indicates that as one variable increases, the other variable decreases. In other words, it shows the relationship between two variables and helps to understand if they are related or independent.

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The solution to the system of equations is (2, 1). To find this solution, we must first solve the first equation, Y < 2x + 3, for x.

Subtracting involves taking the difference between two numbers. It is the opposite of addition and is represented by the '-' sign.

We can do this by subtracting 3 from both sides of the equation, which gives us Y - 3 < 2x.

We then divide both sides of the equation by 2, which gives us

Y - 3/2 < x.

Next, we must solve the second equation, x + y ≥ 3, for y. To do this, we subtract x from both sides of the equation, which gives us y ≥ 3 - x.

Finally, we must set both equations equal to each other,

Y - 3/2 = 3 - x.

We can then solve for x by adding 3/2 to both sides of the equation, which gives us

x = 2.5.

We can then plug this value for x into the second equation, which gives us y ≥ 3 - 2.5.

We then solve for y by subtracting 2.5 from both sides of the equation, which gives us y = 0.5.

Since the value for x must be less than 4, we must round down the value of x to 2. This means that the solution to the system of equations is (2, 1).

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Answer:

Density = number of books over volume of box

Step-by-step explanation:

The formula that can be used to calculate the density of books in the box is:

Density = number of books / volume of box

This formula relates the number of books in the box to the volume of the box, and calculates the density of books per unit volume.Therefore, the correct formula to calculate the density of books in the box is the first one given in the options:

Density = number of books over volume of box

Answer:

Density = number of books over volume of box

Step-by-step explanation:

Hope has 6 nickels (x) and 10 quarters (x + 4).

How many of each coin Hope has if she has 4 more quarters than nickels and they have a combined value of 280 cents. To solve this problem, we can use algebraic equations.

Let's assume the number of nickels Hope has is x. Then, the number of quarters she has would be x + 4.

Now, we need to find the total value of the coins. Each nickel is worth 5 cents, so the total value of nickels is 5x cents. Similarly, each quarter is worth 25 cents, so the total value of quarters is 25(x + 4) cents. The combined value of the coins is 280 cents, so we can set up an equation:

5x + 25(x + 4) = 280

Simplify and solve for x:

5x + 25x + 100 = 280
30x = 180
x = 6

Therefore, Hope has 6 nickels (x) and 10 quarters (x + 4).

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There are no free variables, the vectors are linearly independent.

To either show that the following sets of vectors are linearly independent or find a linear relation between them, we can follow these steps:

. Form a matrix using the given vectors as columns.
. Calculate the determinant of the matrix (if it's a square matrix) or row reduce to echelon form.
. If the determinant is non-zero or the matrix has no free variables, the vectors are linearly independent. If the determinant is zero or the matrix has free variables, the vectors are linearly dependent, and we can find a linear relation.

(a) Create the matrix A using the given vectors:
A = | 1 0 1 |
     | 1 1 0 |
     | 0 1 1 |
The determinant of A is:
det(A) = 1(1(1) - 1(0)) - 0(1(1) - 1(0)) + 1(1(0) - 1(1)) = 1 - 1 = 0
Since the determinant is zero, the vectors are linearly dependent.

(b) Create the matrix B using the given vectors:
B = | 2  0 -1 |
     | 1  1  2 |
     | 0  0  0 |
Row reduce B to echelon form:
B = | 1  1  2 |
     | 0  1 -4 |
     | 0  0  0 |

Since there are no free variables, the vectors are linearly independent.

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The subtraction property of equality is used for the justification of step 2 in the solution.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality.

Therefore, Justify the property used for step 2 in the equality.

1 / 2 r + 1 / 2  = - 2 / 7 r + 6 / 7  - 5

Step 1 : 1 / 2 r + 1 / 2  = - 2 / 7 r - 29 / 7

Step 2: 1 / 2 r = - 2 / 7 r - 65 / 14

We had to subtract 1 / 2 from both sides of the equation to arrive at step 2. Therefore, the subtraction property of equality is the justification for step 2 in the solution.

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Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.

Interest earned in First Oak account after 5 years at 6% simple interest:

= 0.06 x $800 x 5

= $240

Interest earned in West United account after 5 years at 5% compounded annually:

= $800 x (1 + 0.05)^5 - $800

= $800 x 1.27628 - $800

= $221.02

Total interest earned in both accounts:

= $240 + $221.02

= $461.02

Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.

The amount of gas Karen has and the amount Karen needed to put into her boat obtained using basic arithmetic operations are;

Basic arithmetic operations include addition, subtraction, division and multiplication operations.

The amount of gas Karen has can be found using basic arithmetic operations as follows;

On Monday, Karen needed to put 5 gallons 3 quarts of gas into her boat. Since 1 gallon is equal to 4 quarts, this is equivalent to (5 × 4 + 3) = 23 quarts of gas

On Saturday, she needed to put twice as much gas into her boat as she did on Monday. So on Saturday she needed to put (2 × 23) = 46 quarts of gas into her boat.

Since, Karen had 18 gallon jug of gas available and 1 gallon is equal to 4 quarts, this mean she had (18 × 4) = 72 quarts of gas available.

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The probability of selecting a person from a population that has a birthday today and another person who has a birthday in April is 1/4380.

What is probability ?

Probability is the branch of mathematics that deals with the study of random events or experiments. It is a measure of the likelihood of an event or outcome occurring. The probability of an event is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

According to the question:
To find the probability of selecting a person with a birthday today and another person with a birthday in April, we need to calculate the probability of each event separately and then multiply them together.

Let P(T) be the probability of selecting a person with a birthday today and P(A) be the probability of selecting a person with a birthday in April.

Assuming that there are 365 days in a year and that all birthdays are equally likely to occur, we have:

P(T) = 1/365 (the probability of selecting a person with a birthday today)

P(A) = 1/12 (the probability of selecting a person with a birthday in April)

To find the probability of both events happening together, we multiply the probabilities:

P(T and A) = P(T) x P(A) = (1/365) x (1/12) = 1/4380

Therefore, the probability of selecting a person from a population that has a birthday today and another person who has a birthday in April is 1/4380.

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The price that maximizes revenue is p=16, and the corresponding quantity sold is q(16) = 64.

To find the price that maximizes revenue, we need to determine the revenue function R(p), which is equal to the product of price p and quantity sold q(p), or R(p)=pq(p). From the problem, we have q(p)=128-4p.

Substituting this into the revenue function, we get [tex]R(p)=p(128-4p)=128p-4p^2.[/tex]

To find the price that maximizes revenue, we need to find the maximum of the quadratic function R(p)=-4p²+128p. We can do this by finding the vertex of the parabola, which occurs at

[tex]p=-\frac{b}{2a}=-\frac{128}{2(-4)}=16[/tex]

Therefore, the price that maximizes revenue is p=16, and the corresponding quantity sold is q(16)=128-4(16)=64.

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The best measure of central tendency for this data is the mode, which is the most frequently occurring value in a dataset.

In this case, the grilled ribeye is the most popular selling dinner item with 2,021 portions sold, making it the mode of the data. While the mean and median are also measures of central tendency, they may not be as appropriate for this data since the counts for the grilled ribeye are much higher than the other two items.

Using the mean would give too much weight to the grilled ribeye, and using the median would not accurately represent the most popular item. Therefore, the mode is the best choice for this data.

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The change in Silvertown’s revenue from last year to this year can be described by c. 20,493.

Property taxes on homes decreased this year by an average = $75. 90

Total number of homes = 270

It is essential to compare the overall property tax revenue from this year to the total revenue from last year after the $75.90 per-home drop in order to ascertain the change in Silvertown's property tax revenue.

Calculating the total decrease in revenue -

= Average decrease x total number of homes

= 75.90 x 270

= 20,493

Complete Question:

Property taxes on homes decreased this year by an average of $75. 90 in Silvertown. There are 270 homes in Silvertown. Which describes the change in Silvertown’s revenue from last year to this year?

a. - 21,093

b. - 20, 493

c. 20,493

d. 21930

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Every morning, Mr. Cross bakes 80 strawberry frosted donuts unless there is a special order. Each donut costs $3 to make, and it is sold for $5. Unsold donuts are given away to a charity at the end of the day, at a discounted price of $1.50. What will be Mr. Cross’s total earnings if he sells all 80 donuts?

Total revenue if all 80 donuts are soldRevenue = Total units sold × Selling price per unitSince there are 80 donuts and each donut costs $5,Total revenue if all 80 donuts are sold = 80 × 5 = $400Total cost if all 80 donuts are soldTotal cost of making all 80 donuts = Cost of one donut × Total units madeSince each donut costs $3,Total cost of making all 80 donuts = 3 × 80 = $240Total profitTotal profit = Total revenue - Total cost

Since revenue is $400 and the total cost is $240,Total profit = 400 - 240 = $160At the end of the day, unsold donuts are given away to charity at a discounted price of $1.50 each. Therefore, Mr. Cross’s total earnings would be $160 if he sold all 80 donuts.

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If f(x) is a functiοn and f(1) = 5, then  f(1) = 1 cοuId nοt be true.

Thus οptiοn a is cοrrect.

A functiοn is a reIatiοn between twο sets, caIIed the dοmain and the range, such that fοr each eIement in the dοmain, there is exactIy οne eIement in the range. A functiοn maps each eIement in the dοmain tο a unique eIement in the range.

In οther wοrds, a functiοn is a ruIe οr a fοrmuIa that assοciates each input vaIue with a unique οutput vaIue. The input vaIues are the dοmain οf the functiοn, and the οutput vaIues are the range. Functiοns are οften denοted by a symbοI such as f(x), where x is an eIement in the dοmain and f(x) is the cοrrespοnding eIement in the range.

In mathematicaI anaIysis, the generaI cοncept οf functiοn, appIicatiοn οr mapping refers tο a ruIe that assigns tο each eIement οf a first set a singIe eIement οf a secοnd set.

Using this definitiοn, severaI eIements οf the dοmain can resuIt in the same eIement οf the range οf the functiοn.

But, the same eIement οf the dοmain, can nοt have different vaIues οf the range οf the functiοn.

Therefοre, the fοIIοwing expressiοn can nοt be true:

f (1) = 1

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Complete Question:

If f(x) is a function and f(1) = 5, then which of the following could not be true?

a. f(1) = 1

b. f(2) = 1

c. f(5) = 5

Answer:

1/4x - 3 = 12

Step-by-step explanation:

You know you have 1/4x and need to take three from it to equal 12

Based on this estimate, we can expect the ride to swing approximately 9.2 ft higher after each swing.

An equation is a mathematical statement that asserts the equality of two expressions, often containing variables. It typically consists of two expressions separated by an equal sign. The expressions on either side of the equal sign may contain constants, variables, operators (such as +, -, ×, ÷), and functions. Equations are used in many fields, including mathematics, physics, engineering, and finance, to model and solve problems. They are a fundamental concept in algebra, which is the branch of mathematics that deals with equations and the manipulation of variables.

Here,

Assuming that the ride swings higher by approximately the same amount each time, we can estimate the average increase in height per swing. We can calculate this by dividing the total increase in height from 45 ft to 137 ft (92 ft) by the number of swings it takes to reach that height. Since we don't know how many swings it takes to reach the maximum height, we'll assume that the ride swings 10 times before reaching 137 ft (this is just an estimate).

Total increase in height = 137 ft - 45 ft = 92 ft

Number of swings = 10 (estimated)

Average increase in height per swing = 92 ft / 10 = 9.2 ft

Based on this estimate, we can expect the ride to swing approximately 9.2 ft higher after each swing. Therefore, after the first swing (which reached a height of 45 ft), we can estimate that the ride will swing to a height of approximately 54.2 ft (45 ft + 9.2 ft) on the second swing, and then to a height of approximately 63.4 ft (54.2 ft + 9.2 ft) on the third swing, and so on.

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Complete question:

A thrill ride swings passengers back and forth getting higher and higher each time up to 137ft. suppose the height of the swing after 30sec. is 45ft. How much higher will the fide swing?

Answer:

28 the answer is 28 really it's 28

Answer:

18. x = 80°

19. y = 85°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

18.

x + x + 20 = 180

2x = 160

x = 80

Answer: x = 80°

y + y + 10 = 180

2y = 170

y = 85

Answer: y = 85°

Answer: x = 80°  and  y = 85°

Step-by-step explanation: In a cyclic quadrilateral, opposite angles add up to 180°.

x + (x + 20) = 180  and

y + (y + 10) = 180.

Solving for x

x + (x + 20) = 180

x + x + 20 = 180

2x = 180 - 20

2x = 160

2x/2 = 160/2

x = 80°

Solving for y

y + (y + 10) = 180

y + y + 10 = 180

2y = 180 - 10

2y = 170

2y/2 = 170/2

y = 85°

Answer:

(x^2−2xy+y^2)−z^2

⇒[x(x−y)−y(x−y)]−z^2

⇒(x−y)(x−y)−z^2

⇒(x−y)^2−z^2

⇒[(x−y)+z][(x−y)−z]

⇒(x−y+z)(x−y−z)

If we repeated a hypothesis test 1000 times, the number of times we would expect to commit a Type I error, assuming the null hypothesis were true, would depend on the significance level (α) of the test.

A Type I error occurs when we reject the null hypothesis when it is actually true. The significance level of a test (α) is the probability of making a Type I error when the null hypothesis is true. In other words, if we set a significance level of α = 0.05, we are saying that we are willing to tolerate a 5% chance of making a Type I error.

Assuming a significance level of α = 0.05, if we repeated the test 1000 times, we would expect to make a Type I error in approximately 50 tests (0.05 x 1000 = 50). This means that in 50 out of the 1000 tests, we would reject the null hypothesis even though it is actually true.

However, it is important to note that the actual number of Type I errors we make in practice may differ from our expectation, as it depends on the specific characteristics of the population being tested and the sample sizes used in each test.

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The combined area of the four removed triangles is 48 sq.units. Answer: 48

We need to find out the combined area of the four removed triangles, in square units. Given: AB = 12 units.

Let's consider the given square, and let's draw an altitude BD and also draw perpendiculars to BD from the three vertices A, C and D.

Let AB = x cm. Area of square = x² sq.cm.

Now, we are cutting a triangle with base x and height x, which is a right-angled triangle. Hence, area of each removed triangle = (1/2) * x * x = (x²/2) sq.cm.

Now, BD = x/√2. Area of rectangle = AB * BD = 12 * 12/√2 = 72√2 sq.cm.

Now, area of 4 triangles = (x²/2) + (x²/2) + (x²/2) + (x²/2) = 2x² sq.cm.

We know that, Area of rectangle = Area of 4 triangles + Area of square => 72√2 = 2x² + x² => 72√2 = 3x² => x² = 24√2 cm² => x = √(24 * 2) cm = √(48) cm = 4√3 * √2 cm.

Area of 4 triangles = 2x² sq.cm = 2 * 24 cm² = 48 sq.cm.

Hence, the combined area of the four removed triangles is 48 sq.units. Answer: 48.

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Answer:

All the expressions except d are polynomials.

So, Amy ran the 100-yard dash 0.84 seconds faster than Jace.

An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of an equation is to find the value of the variable that makes both sides of the equation equal.

Here,

To find out how much faster Amy ran the race than Jace, we need to calculate the difference in their times.

Amy's time = 12.98 seconds

Jace's time = 13.82 seconds

Difference in time = Amy's time - Jace's time

= 12.98 - 13.82

= -0.84 seconds

The difference is negative, which means that Jace was slower than Amy. To get the positive difference, we can take the absolute value of the difference:

|Difference| = |-0.84| = 0.84 seconds

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The sequence follows a pattern of adding 7 to the previous term, and its formula is 7n - 3. The sum of the first 100 terms of the sequence is 35,350, which was found using the formula for the sum of an arithmetic series.

The next term in the sequence can be found by adding 7 to the previous term, so the next term is 25.

To find a formula for the nth term of the sequence, we can observe that each term is 7 more than a multiple of 7. In other words, the nth term is given by the formula 7n - 3.

To find the sum of the first 100 terms of the sequence, we can use the formula for the sum of an arithmetic series:

S = (n/2)(a1 + an)

where S is the sum of the first n terms, a1 is the first term, and an is the nth term. Substituting n = 100, a1 = 4, and an = 703, we get:

S = (100/2)(4 + 703) = 35,350

Therefore, the sum of the first 100 terms of the sequence is 35,350.

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The probability of obtaining 10 or fewer families earning less than $35,000 per year in a simple random sample of 30 families from a large city with 45% of families in that income bracket is approximately 0.041 or 4.1%.

We can use the binomial distribution formula to calculate the probability of obtaining 10 or fewer families earning less than $35,000 per year in a simple random sample of 30 families from a large city where 45% of families earn less than $35,000 per year.

Let's denote the probability of a family earning less than $35,000 per year as "p", which is 0.45 in this case, and the number of trials or families sampled as "n", which is 30 in this case.

The probability of obtaining k families earning less than $35,000 per year in a simple random sample of 30 families can be calculated using the binomial distribution formula:

P(X ≤ 10) = Σ(i=0 to 10) [n choose i] * p^i * (1-p)^(n-i)

where n = 30, p = 0.45, and X is the random variable representing the number of families earning less than $35,000 per year in the sample.

Using a binomial calculator or software, we can calculate:

P(X ≤ 10) ≈ 0.041

Therefore, the probability that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year is approximately 0.041 or 4.1%.

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Answer:

Hope this is what you were looking for :)

Step-by-step explanation:

tan = opposite/adjacent

IF YOU DONT NEED TO FIND THE VALUES OF THE SIDES:

tan A =  [tex]\frac{x}{11}[/tex]

tan B = [tex]\frac{11}{x}[/tex]

Replace the x for whatever the value of BC is or if it doesn't have a value, you can just leave it as x.

IF YOU DO NEED TO FIND THE VALUES OF THE SIDES:

tan 45 = 1

tan 45 =  [tex]\frac{BC}{11}[/tex]

(11) tan 45 = BC

BC = 11

tan 45 = [tex]\frac{11}{AC}[/tex]

AC = [tex]\frac{11}{tan 45}[/tex]

AC = 11

This can also be done without using tangent from taking a look at special right triangles.

In 45-45-90 triangles, the two legs are the same size while the hypotenuse is equal to one of the legs multiplied by [tex]\sqrt{2}[/tex]. In doing this, we can find that both legs are 11 and the hypotenuse is [tex]11\sqrt{2}[/tex].

Answer:

Step-by-step explanation:

Answer: 0.0625 g/cm^3

Formula for density: d= mass/volume

we have mass m=50g

volume of rectangular prism = length x height x width

volume of book = 5cm x 16cm x 10cm = 800cm^3

density = mass / volume

density = 50g/800cm^3

density = 0.0625 g/cm^3

The volume of the cone in terms of π is option (c) 100π in^3

The formula for the volume of a cone is given by:

V = (1/3)πr^2h

where r is the radius of the base of the cone, h is the height of the cone.

In this case, we are given that the radius of the cone is 5 in and the slant height is 13 in. We can use the Pythagorean theorem to find the height of the cone:

h^2 = y^2 - r^2

h^2 = 13^2 - 5^2

h^2 = 144

h = 12 in

Therefore, the volume of the cone is:

V = (1/3)πr^2h

V = (1/3)π(5^2)(12)

V = (1/3)π(25)(12)

V = (1/3)(300π)

V = 100π cubic inches

Therefore, the correct option is (c) 100π in^3

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Answer: 100π in3

Step-by-step explanation:

By using equation in two variable we need to use 2 eggs to make all the cookies with 1.33 cups of butter.

To make six dozen cookies, the recipe calls for two cups of butter and three eggs. We can use proportionality to solve this question: If 2 cups of butter require 3 eggs to make 6 dozen cookies, then 1.33 cups of butter require x eggs to make all of the cookies.

x eggs = (1.33 cups of butter x 3 eggs)/(2 cups of butter). x = 1.99 eggs. Since we cannot use .99 eggs to make cookies, we would need to round up to the nearest whole number of eggs.

Therefore, we need to use 2 eggs to make all the cookies with 1.33 cups of butter.

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