A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?
In similar triangles, both the two triangles must satisfy the two properties. One is the side proportional, and the other is equal in angles. There are three criteria in similarity. They are AA similarity, SSS similarity, and SAS similarity. The below one satisfies the AA similarity.

The answers are 285 and 7392.

Answer:4

Step-by-step explanation:

distribute 1/2 into x-8 and distribute 2 into 1/8x-1 on other side

1/2x-4+1=1/4x-2

combine like terms

1/4x=1

multiply both sides by 4 to solve x

x=4

The assumptions of the two-sample t-test for comparing two population means:

1. The two samples are independent of one another.

2. The two populations have equal variance or spread.

3. The two populations are normally distributed.

The Wilcoxon test is based upon ranking the nA +nB observations of the combined sample. Each observation has a rank: the smallest has rank 1, the 2nd smallest rank 2, and so on. The wilcoxon rank-sum test statistic is the sum of the ranks for observations from one of the samples.

The Wilcoxon signed rank test is a non-paracontinuouse-level test, in contrast to the dependent samples t-test.

Wilcoxon tests have about 95% of the power of a t-test if the data really are normal, and are often far more powerful if the data is not, so just use a Wilcoxon.

The Wilcoxon test may produce misleading results if many measurements are the same value. When many values are the same, their relative ranks are the same, and this has the effect of diluting the test.

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The box portion of a boxplot display the middle half of the data.

We know that  a box and whisker plot which is also known as a box plot.

It represents the five-number summary of dataset.

This five-number summary is nothing but the minimum, first quartile, median, third quartile, and maximum.

In box and whisker plot, we draw a box from the first quartile to the third quartile.

In bosplot, the left and right sides of the box are the lower and upper quartiles.

The box covers the 50% of the data is found. It covers the interquartile range.

Therefore, the box portion displays the middle half of the data.

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The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.

What is the unit price?

The average price of a product is calculated by dividing the total sales revenue by the total units sold. Managers must define "comparable" units when a single product is sold in variants, such as bottle sizes.

To find the unit price of an object, You divide the price by the Object. We need to find how much an object cost per unit.

Let, us consider an Example we have 50lbs of Kulfi (Object) that cost 8.00 dollars(price).

To find the Unit cost, We take the 8.00 and divide it by 50, which results in 0.16 cents per pound. We can check this by multiplying 0.16 by 50=8.00

So, Object= Number of units in cell = C2

Price of Object = B2

Unit Price Formula = D2

Therefore, by considering the above example.,

Object = C2 = 50

Price = B2 = 8.00

D2 Formula= Price of Object/ Number of Units

Therefore, The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.

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the error bound for the mean U.S. household income is +/- $234, while the point estimate is $63179.

A yearly census identical to the one performed every ten years is conducted by the American Community Survey (ACS), a division of the United States Census Bureau, but with a lower participation rate. Since the most recent poll has high confidence that the mean household income in the United States is between, the point estimate for that income is $63179, and the error bound is +/- $234.

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The measure of angle A in this triangle is 50°.

It is important to note that a triangle has three sides and the total angle is 180°.

Therefore A = 2x - 10

B = 70

C = x + 30

The angles will be illustrated thus:

2x - 10 + 70 + x + 30 = 180

3x + 90 = 180

3x = 180 - 90

3x = 90

Divide

x = 90/3

x = 30

Therefore A will be:

= 2x - 10

= 2(30) - 10

= 60 - 10

= 50°

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The trigonometric function, Y = -4·cos 5·x - 10 is undefined at Y = 0, but the function arranged as Y = -4·cos(5·x - 10) has an x-intercept at x = π/10 + 2

A trigonometric function indicates the relationship between angles and the lengths of sides of angles.

The specified function can be presented as follows;

Y = -4·co(5·x) - 10

There are two unknown variables

The number of equations is one

The function, at Y = 0, can be evaluated as follows;

Y = 0 = -4·co(5·x) - 10

cos(5·x) = 10/(-4) = -2.5

5·x = arccos(-2.5) = Undefined

However, when the function is; Y = -4·cos((5·x) - 10), we get;

At Y = 0

0 = -4·cos((5·x) - 10)

cos((5·x) - 10) = 0/(-4) = 0

5·x - 10 = arccos(0) = π/2

Therefore;

x = (π/2 + 10)/5 = π/10 + 2

(-π/2 + 10)/5

An x-intercept is at x = π/10 + 2

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The correct statement regarding the scatter plot is given as follows:

The data shows a negative linear association between the number of magazines checked out and the number of books checked out.

The scatter plot, as shown by the image given at the end of the answer, is a series of points of the data-set in the following format:

(Number of books checked out, Number of magazines checked out).

From the graph, the points are given as follows:

(2,4), (3,6), (4,0), (4,2), (5,7), (6,5), (7,2), (9,1).

Inserting these points into a linear regression calculator, the line of best fit is given as follows:

y = -0.36x + 5.18

Which has a negative slope, meaning that it is a negative linear relationship and the first option is correct.

The scatter plot is given by the image shown at the end of the answer.

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From the given properties of the functions,

Functions given in the picture are 'f', 'g' and 'h'.

From the graph given for function 'f',

y - intercept = 1

Increasing in the interval → (-∞, -0.8] and (0.6, ∞)

Decreasing in the interval → [-0.8, 0.6]

From the table given for the function 'g',

Decreasing in the interval → [-2, 2]

y-intercept = -1

For function 'h',

h(x) = 4x³ + 3

Table of the input-output values for function will be,

x           h(x)

-2         -29

-1            -1

0            3

1             7

2           35

Therefore, function 'h' will increase in the interval → (-∞, ∞)

y-intercept → y = 3

Therefore, from these properties of the functions we conclude,

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The 90% confidence interval for the population mean estimate is  (1362.9167,1637.0833).

Given that,

n=36 residents

Standard deviation = 500 dollars

Mean u = 1500 dollars

X = 1500 dollars

(1-α)% = 90%

(1-α)= 0.9

α = 0.10

α/2 = 0.05

Z α/2 = Z 0.05

Z α/2 = 1.645

90%-confidence interval for the population mean estimate is

=X ± Z α/2 (σ/√n)

= 1500 ± (1.645)(500/√36)

=(1362.9167,1637.0833)

Therefore, the 90%-confidence interval for the population mean estimate is  (1362.9167,1637.0833).

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Answer:

sin(x) = 12/13

Step-by-step explanation:

cos^(-1)(5/13) = 0.176

tan^(-1)(12/5) = 0.176

sin(0.176 radians) = 12/13

-3(x-4)=-9(x-1)

-3x+12=-9x+9

-3x+9x=9-12

6x=-3

x= -3/6

x=-1/2

Step-by-step explanation:

2000-1360=640

%change=640/2000×100

=32%

The amount of money borrowed by the man from the bank on on 2 May 2000 is  $6346.15.

The formula for calculating simple interest;

SI = P R T/100,

where

In the case of simple interest, the principal is the amount of money that does not change over the course of a year.

Time = 4/12 year

For the given values-

137.50 = P × 6.5 × 4 /1200

P = 137.50 × 1200 / 6.5 × 4

P = $6346.15

Thus, the amount of money borrowed by the man from the bank on on 2 May 2000 is  $6346.15.

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The value of the function f(1)-f(-7) = -11

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

Given are a function,

For x = 1, take -x²-3x

f(1) = -1²-3 = -4

For x = -7, take |x+5|-9

f(-7) = |-7+5|-9 = -7

f(1)-f(-7) = -7-4 = -11

Hence, The value of the function f(1)-f(-7) = -11

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The number of positive integers with exactly four decimal digits that is positive integers between 1000 and 9999 is 4536.

The positive integers between 1000 and 9999 inclusive have 4 digits.

The first digit cannot be zero because otherwise, it will become a  digit integer.

So, the first digit can be filled in 9 ways.

The second digit can be filled by 9 different ways.

Because the second digit cannot be the same as that of the first digit but zero can be the second digit.

The third digit can be filled by 8 different ways.

The fourth digit can be filled in 7 different ways.

Number of four decimals digits = 9 * 9 * 8 * 7

= 81 * 8 * 7

= 81 * 56

= 4536 digits.

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The polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3 thanks to the factor theorem.

A factor theorem is a tool used in mathematics to thoroughly factor polynomials.

It is a theorem that connects the polynomial's zeros and factors.

The factor theorem states that (x-a) is a factor of f(x) if f(a)=0 and f(x) is a polynomial of degree n 1 and 'a' is any real number.

So, the Factor Theorem states that P(k) must equal zero if (x - k) is a factor of polynomial P(x).

A polynomial function with the zeros 2, 3, and -3 is provided to us. As a result, we can set k = 2, 3, -3.

The Factor Theorem states that P(2), P(3,) and P(-3) must all equal 0.

Tests of each option reveal that only option A is accurate:

f(x) = x³ – 2x² – 3x + 6

Testing each of the three results in:

[tex]\begin{aligned}f(2) & =(2)^3-2(2)^2-3(2)+6 \\& =(8)-(8)-(6)+(6) \\& =0 \stackrel{\checkmark}{=} 0 \\f(\sqrt{3}) & =(\sqrt{3})^3-2(\sqrt{3})^2-3(\sqrt{3})+6 \\& =(3 \sqrt{3})-(6)-(3 \sqrt{3})+6 \\& =0=0 \\f(-\sqrt{3}) & =(-\sqrt{3})^3-2(-\sqrt{3})^2-3(-\sqrt{3})+6 \\& =(-3 \sqrt{3})-(6)+(3 \sqrt{3})+6 \\& =0=0\end{aligned}[/tex]

Therefore, with the help of the factor theorem, polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3.

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Complete question:

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3, and negative radical 3?

a. f(x) = x3 – 2x2 – 3x + 6

b. f(x)= x3 – 2x2 + 3x + 6

c. f(x) = x3 + 2x2 – 3x + 6

d. f(x) = x3 + 2x2 – 3x – 6

By using Binomial Distribution, it can be calculated that -

P(X = 1) = 0.0005

What is Binomial Distribution?

Binomial distribution is a discrete type probability distribution whose probability density function is given by

P(X = x) = [tex]{n \choose x} p^xq^{n - x}[/tex]

Where p is the probability of success and q is the probability of failure

Here, Binomial Distribution of probability is used

k = 1

p = 0.9

q = 1 - 0.9 = 0.1

n = 5

P(X = 1) = [tex]{5 \choose 1} (0.9)^1(0.1)^{5 - 1}[/tex]

            = 0.00045

            = 0.0005

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Th number of possible ways for

a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)

b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)

In this question, we have been given that there are four players. the select cards from the standard deck of 52 cards.

We need to find the number of possible ways for given situations.

(a) each player gets exactly 13 cards.

Using combination, we get an expression,

^{52}C_13 * ^{39}C_13 * ^{26}C_13 * ^{13}C_13

= 52! / (13! 13! 13! 13!)

= 53644737765488792839237440000

(b) each player gets seven cards and the rest of the cards remain in the deck

Using combination, we get an expression,

^{52}C_7 * ^{45}C_7 * ^{38}C_7 * ^{31}C_7 * ^{24}C_24

= 52! / (7! 7! 7! 7! 24!)

Therefore, a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)

b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)

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The expression in terms of x that represents the total amount that Zoe paid is 1.2075x

Expression are simply used to illustrate the datathat are given. It should be noted that it's usually represented by the variables given.

From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.

The expression will be:

= x + (5% × x) + (15% × 1.05x)

= x + 0.05x + 0.1575x

= 1.2075x

Therefore, the expression based on the above will be 1.2075x.

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Answer:

Step-by-step explanation:

0

Answer:

x = 3

Step-by-step explanation:

1/4 (6x - 2) = x - 2

1.5x - 0.5 = x - 2

1.5x = x - 1.5

0.5x = 1.5

x = 3

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The average waist size of the population is 85 cm, and the standard deviation is 15 cm. then A sample mean waist size of at least 86.3 cm has a 0.931 probability of occurring.

We can use the Z-score formula to find the probability.

Z = (86.3 - 85) / (15 / sqrt(277))

Z = 0.2 / 0.106

Z = 1.89

The probability of a sample mean waist size of at least 86.3 cm is 0.931.

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The answer of the given question is A rectangular block of mass m has an inertia moment of Bh3/3.

When a body resists having the direction of its rotation along an axis changed by the application of a torque, this resistance is referred to as having moment of inertia. There are four types of axes: internal, external, fixed, and moving. It is possible to calculate the moment of inertia (I), which is always expressed in terms of that axis, by adding the results of multiplying each particle's mass by the square of its distance from the axis within the particular body. Moment of inertia is the same as mass in linear momentum when calculating the angular momentum of a rigid body.

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Answer: What is the last part of the question?

Step-by-step explanation:

I can't answer the question because it is incomplete. Sorry :(

The student will be out of class for 2n days if the coin comes up tails, where n is the result of the die roll, which the probability will be 25.

An unfortunate student must recover from illness before washing laundry. The following formula is used to calculate the student's illness duration. We roll a fair 6-sided die and toss a fair coin. The student is absent from class for n days if the coin comes up heads, where n is the result of the die roll.

Ex(u) = (1/2)(1/6)*5+(1/2)(1/6)10+(1/2)(1/6)15+(1/2)(1/6)20 + (1/2)(1/6)25+(1/2)(1/6)*30

Probability = 25

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Answer:

x = 126

Step-by-step explanation:

1. 120 + 120(.50) = 180

2. 180 - 180(.30) = 126

Answer:

Step-by-step explanation:

try 6

Answer: 6

Step-by-step explanation: 6 x 8 = 48

The balance sheet that correctly represents the daycare's income, expenses, and balance is given as follows:

C; Income

Amount

Weekly Income $15,000.00

Total Monthly Income $60,000.00

Expenses

Percent Amount

Employee Wages 40% $24,000.00

Building Rent 5% $3,000.00

Supplies 15% $9,000.00

Equipment 5% $3,000.00

Educational Licensing 2% $1,200.00

Food 13% $7,800.00

Utilities 10% $3,000.00

Maintenance 5% $3,000.00

Emergency/Repair 5% $1,500.00

$60,000.00

Balance

Income $60,000.00

Expenses $60,000.00

Balance $0

The first step in obtaining the balance sheet is obtaining the total monthly income.

The weekly income is of $15,000, while a month is composed by four weeks, hence the monthly income is of:

4 x $15,000 = $60,000.

Then the percentages of each expenses are applied to find the values, for example, 40% of that is for employee wages, hence:

0.4 x 60,000 = $24,000.

From the percentages stated in the problem, 100% of the income is turned into expenses, hence the balance will be of zero and option C is correct.

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