solve the problem. round your answer, if appropriate. a ladder is slipping down a vertical wall. if the ladder is 17 ft long and the top of it is slipping at the constant rate of 2 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 8 ft from the wall?

Answer: 29/48

Step-by-step explanation:

If she spent 5/12 of 1200, she's left with 7/12 of 1200 which is 700. If she spends 1/4 of that, she has 3/4 of it left. 3/4 x 700 is 525. 525 + 250 is equal to 725. To simplify 725/1200, divide both sides by 25 to get 29/48.

Answer:

26

Step-by-step explanation:

here,

the lower angle when sumed,

it is like: 154+a=180 (let angle be a) being supplementary angle sum is 180

so value of a becomes 26

then,

the above angle x is corresponding to angle a (a=x)

So value x is 26

Answer:

Hey there!

The census never asks any questions about D. Spending Habits.

Let me know if this helps :)

Answer:

Your answer will be D

6.75 is greater than 6.732

What are decimal numbers?

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

Here, we have

Given

6.75 and 6.732

We have to compare two given decimal numbers.

First, we convert to a decimal number

In 6.75 there are two digits after decimal point.

In 6.732, there are three digits after the decimal point

Therefore, we put zero in 6.75 to convert like a decimal number

Now, we get

6.750

The unit place of both decimal numbers are the same and the tenth place of both decimal number are same.

Now, the hundredth place of 6.750 is 5, and the hundredth place of 6.732 is 3

5 >3

Hence, 6.750 is greater than 6.732

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Answer:  

Step-by-step explanation:

The answer is 72 your welcome I hope that helps you

Answer:

x ≥ 89

Step-by-step explanation:

Since Jonathan needs at least an 89, his score must be greater than or equal to an 89.

Answer:

Step-by-step explanation:

(a) The possible choices are (1,3), (1,5), and (3,5), and the maximum of each pair is 3, 5, and 5, respectively.

(b) Since each pair has probability 1/3 of being chosen, the probability mass function for X is P(X=3) = 1/3 and P(X=5) = 2/3.

(c) The expectation of X is E(X) = 3(1/3) + 5(2/3) = 4.

(d) The variance of X can be calculated as Var(X) = E(X^2) - (E(X))^2 = (3^2)(1/3) + (5^2)(2/3) - 4^2 = 2/3.

(a) We can list all the possible choices of two integers from the set {1,3,5}: (1,3), (1,5), and (3,5). For each choice, we can determine the maximum of the two integers. These maximums are 3, 5, and 5, respectively.

(b) Since each pair has an equal probability of being chosen, the probability mass function for X can be calculated as the probability of getting 3 or 5. There is only one pair that results in X=3, which is (1,3). There are two pairs that result in X=5, which are (1,5) and (3,5). Thus, P(X=3) = 1/3 and P(X=5) = 2/3.

(c) To find the expectation of X, we multiply each possible value of X by its corresponding probability and sum the results. Thus, E(X) = 3(1/3) + 5(2/3) = 4.

(d) The variance of X can be calculated using the formula Var(X) = E(X^2) - (E(X))^2. We can calculate E(X^2) by multiplying each possible value of X squared by its corresponding probability and summing the results. Thus, E(X^2) = (3^2)(1/3) + (5^2)(2/3) = 16/3. Substituting E(X) = 4 and E(X^2) = 16/3 into the formula for variance gives Var(X) = 2/3.

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Step-by-step explanation:

these are projections from V and W to the same projection "screen" (SU and YX).

since the angles are equal, the ratio between projection beam length and screen length must be the same.

so,

6.

24/14 = 48/x

48/28 = 48/x

x = 28

7.

besides the projection principle, we have a basic triangle situation :

the bisector of the angle W is also bisecting the opposing side YX. that means that this is an isoceles triangle (both legs are equally long).

therefore,

y = 4×sqrt(2)

Answer:

\(\textsf{6.} \quad x = 28\)

\(\textsf{7.} \quad y = 4\sqrt{2}\)

Step-by-step explanation:

An angle bisector is a line that divides an angle into two equal parts.

An angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.

Applying the Angle Bisector Theorem:

\(\implies \dfrac{UT}{TS}=\dfrac{VU}{VS}\)

\(\implies \dfrac{x}{14}=\dfrac{48}{24}\)

Cross multiply:

\(\implies 24 \cdot x=48 \cdot 14\)

\(\implies 24x=672\)

Divide both sides by 24:

\(\implies \dfrac{24x}{24}=\dfrac{672}{24}\)

\(\implies x=28\)

Applying the Angle Bisector Theorem:

\(\implies \dfrac{XZ}{ZY}=\dfrac{WX}{WY}\)

\(\implies \dfrac{4}{4}=\dfrac{y}{4\sqrt{2}}\)

Carry out the division on the left side:

\(\implies 1=\dfrac{y}{4\sqrt{2}}\)

Multiply both sides by 4√2:

\(\implies 1\cdot 4\sqrt{2}=\dfrac{y}{4\sqrt{2}}\cdot 4\sqrt{2}\)

\(\implies 4\sqrt{2}=y\)

\(\implies y=4\sqrt{2}\)

Answer:

126

Step-by-step explanation:

There are 9 city council members.

We have to choose 4 of them.

We have to use the combination as :

\($^9C_4$\)

where, 9 is the population size

4 is the sample size.

Therefore, the total number of possible samples without replacement is given as :

\($^9C_4=\frac{9!}{4!(9-4)!}$\)

      \($=\frac{9!}{5! \ 4!}$\)

     \($=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$\)

    = 126

Step-by-step explanation:

\( - {3}^{2} m {n}^{5} m {n}^{2} {m}^{6} = \\ = - 9 {m}^{8} {n}^{7} \)

Answer:

Below in bold.

Step-by-step explanation:

- 5 - x^2 = -10

-x^2 = -10 + 5

-x^2 = -5

Divide through by -1:

x^2 = 5

x = -√5, √5.

The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.

Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)

$1,000 | 2% | 1 year | $20

$5,000 | 4% | 2 years | $400

$10,000 | 3.5% | 3 years | $1,050

$2,500 | 1.5% | 6 months | $18.75

$7,000 | 2.25% | 1.5 years | $236.25

To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.

For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.

For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.

For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.

For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.

For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.

These calculations show the interest earned for different savings principals, interest rates, and time periods.

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Answer:

x^2 + y^2 = 3^2

Step-by-step explanation:

Start with (x - h)^2 + (y - k)^2 = r^2.

If the center is at (0, 0), we then have x^2 + y^2 = r^2.

If this circle passes through (0, 9), then 0^2 + 9^2 = r^2, and r must be 3.

Then the standard equation of this circle i

x^2 + y^2 = 3^2

The equation that provides evidence of determining the best spot to build a fire station, illustrated by taking into account the towns and cities within 5 miles, would be: b. (x+3)² + (y+1)² = 25

This equation shapes a circle with a size of five units in radius with its center nestled at coordinates (-3,-1).

Postulating any city situated in or tantalizingly near this circumference would remain within the five-mile distance from the fire department. The others equations do not portray circles that have central points providing maximum coverage of settlements located within a 5-unit range.

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The  probability space and that e1 and e2 are events satisfying e1 ∪ e2 = s, p(e1) = 1/5, and p(e1 ∩ e2) = 1/30.The  p(e2) is 0.8333.

In chance principle, a probability space or a probability triple. is a mathematical construct that offers a formal model of a random manner or "test". for example, you can still outline an opportunity area that fashions the throwing of a die.

A chance area fashions random occasions and is made of three parts: pattern space: the set of all possible results. as an example, in case you toss a coin twice, the pattern space is {HH, HT, TH, TT}. The sample space is every so often denoted by way of the Greek letter omega (Ω).07-Jan-2017

A finite probability space is a fixed S and a feature p: S → R ≥zero such that p(s) > 0 (∀s ∈ S) and ∑ p(s) = 1. We re. page 1. A finite probability area is a set S and a characteristic p: S → R≥0 such that p(s) > 0. (∀s ∈ S) and ∑

Given E1 and E2 events S is the probability space

And given E1∪ E2 =S

P(E1)=1/5 and P(E1 ∩ E2 )=1/30

From given P(E1∪ E2)=P(S)

From probability axioms P(S)=1

Therefore P(E1∪E2) =1

      P(E1)+ P(E2)- P(E1 ∩E2)= 1

      (1/5) + P(E2) - (1/30) = 1

   P(E2 )= 1-(1/5) +(1/30)= 0.8333

Therefore P(E2)= 0.8333

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Since a z-score of 0.96 is within two standard deviations of the mean, it is not considered unusual. Therefore, the answer is A. unusual.

To determine if this is unusual, we need to consider the normal distribution and the concept of standard deviation. In a standard normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

To calculate the z-score, we use the formula:
z = (x - μ) / σ
Where x is the individual's score, μ is the mean, and σ is the standard deviation.

To calculate the z-score, we'll use the formula:
z-score = (individual score - class mean) / standard deviation

In this case, the individual score is 77.14, the class mean is 73, and the standard deviation is 4.6.

Step 1: Subtract the class mean from the individual score.
77.14 - 73 = 4.14

Step 2: Divide the result by the standard deviation.
4.14 / 4.6 = 0.9
Plugging in the values we get:

z = (77.14 - 73) / 4.6
z = 0.9565 (rounded to 4 decimal places)

A z-score of 0.9565 indicates that the person's score is about 0.96 standard deviations above the mean.

Now, let's determine if this is unusual or not. In general, a z-score greater than 1.96 or less than -1.96 is considered unusual, as it represents a result that is outside the 95% confidence interval. Since our calculated z-score is 0.9000, it is within the 95% confidence interval.

Answer: The z-score is 0.9000, and it is A. Not Unusual.

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The z-statistics for the given situations are 20, 12.5, 18.4766, 1.7775, and 13.6293 respectively.

To calculate the z-statistic (z), we use the formula: z = (X - μ) / (σ / √N),

where X is the observed value,

μ is the mean,

σ is the standard deviation,

and N is the sample size.

A.) X = 8.00; μ = 5; σ = 0.6; N = 16
z = (8.00 - 5) / (0.6 / √16) = 3 / (0.6 / 4) = 3 / 0.15 = 20

B.) X = 4.00; μ = 2; σ = 0.8; N = 25
z = (4.00 - 2) / (0.8 / √25) = 2 / (0.8 / 5) = 2 / 0.16 = 12.5

C.) X = 11.50; μ = 9.25; σ = 0.75; N = 38
z = (11.50 - 9.25) / (0.75 / √38) = 2.25 / (0.75 / 6.1644) = 2.25 / 0.1218 = 18.4766

D.) X = 0.95; μ = 0.82; σ = 0.31; N = 18
z = (0.95 - 0.82) / (0.31 / √18) = 0.13 / (0.31 / 4.2426) = 0.13 / 0.0731 = 1.7775

E.) X = 8.14; μ = 4.69; σ = 1.29; N = 26
z = (8.14 - 4.69) / (1.29 / √26) = 3.45 / (1.29 / 5.099) = 3.45 / 0.2531 = 13.6293

Therefore, the z-statistics for the given situations are 20, 12.5, 18.4766, 1.7775, and 13.6293 respectively.

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Derek's commission on this sales is $646.85.

Given the following data:

To find Derek's commission on this sales;

In this exercise, you're required to find the amount of money earned as commission by Derek when he sold a particular amount of a commodity or good.

Commission = \(\frac{3.4}{100}\) × \(19,025\)

Commission = \(0.034\) × \(19,025\)

Commission = $646.85

Therefore, Derek's commission on this sales is $646.85.

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The derivative g'(2) of the function g(x) = x^2 * f(x), where f(2) = 3 and f'(2) = -1, is equal to 8.

To evaluate g'(2), we need to find the derivative of the function g(x) = x^2 * f(x) and then substitute x = 2 into the derivative.

First, let's find the derivative of g(x) using the product rule. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by:

(d/dx)(u(x) * v(x)) = u'(x) * v(x) + u(x) * v'(x)

In this case, u(x) = x^2 and v(x) = f(x). Taking the derivatives, we have:

u'(x) = 2x  (derivative of x^2)

v'(x) = f'(x) (derivative of f(x))

Applying the product rule, we get:

g'(x) = (d/dx)(x^2 * f(x)) = 2x * f(x) + x^2 * f'(x)

Now, we can substitute x = 2 into g'(x) to evaluate g'(2):

g'(2) = 2(2) * f(2) + (2^2) * f'(2)

Given that f(2) = 3 and f'(2) = -1, we can substitute these values into the equation:

g'(2) = 2(2) * 3 + (2^2) * (-1)

Simplifying:

g'(2) = 4 * 3 + 4 * (-1)

g'(2) = 12 - 4

g'(2) = 8

Therefore, g'(2) = 8.

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Answer: 6.7 centimeters

a quantity of interest that can take on different values is known as a(n)

variable.

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i)The probability that a randomly selected student has a height of greater than 170 cm is 0.2389. ii) The value of h is 176.48 cm. iii) The probability that the mean sample height of 36 students is more than 163 cm is 0.8515.

For a normally distributed variable, probability can be calculated as follows, P(Z > z) = 1 - P(Z ≤ z), where Z is a standard normal variable. Standard error of sample mean, σm = σ/√n, where σ is the standard deviation of the population and n is the sample size.

i) Let X be the height of a randomly selected student. P(X > 170) = P((X - μ)/σ > (170 - 165)/7) = P(Z > 0.714) = 1 - P(Z ≤ 0.714) = 1 - 0.7611 = 0.2389.

ii) Let h be the height of a student such that 5% of the students' height is less than h cm. P(Z ≤ z) = 0.05, from standard normal table, z = -1.64P((X - μ)/σ ≤ (h - μ)/σ) = P(Z ≤ -1.64) = 0.05P((X - 165)/7 ≤ (h - 165)/7) = 0.05(h - 165)/7 = -1.64h - 165 = -11.48h = 176.48 cm.

iii) Let M be the mean sample height of 36 students. P(M > 163) = P((M - μm)/σm > (163 - 165)/[7/√36]) = P(Z > -1.029) = 1 - P(Z ≤ -1.029) = 1 - 0.1485 = 0.8515.

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Answer: Anything greater than 3

Step-by-step explanation:

The answer can be any number greater or equal to 3. This is because if you subtract 3 by 3 you get 0 and zero is still greater than -2 making the inequality true

The narrator describes the house in this way to convey a sense of decay and deterioration. It is not to show that it has a nice design, remind him of something rotting, indicate the number of people inside, or suggest that the owner had a lot of parties.

The line from "Fall of the House of Usher" describes the house using imagery of old wood-work that has rotted in a neglected vault. This description serves to create a mood of decay and deterioration. The phrase "specious totality of old wood-work" suggests that the once-grand and impressive architecture of the house has fallen into disrepair. By comparing it to something rotting in a neglected vault, the narrator conveys a sense of neglect and isolation. The description emphasizes the dilapidated state of the house, setting the tone for the eerie and decaying atmosphere that permeates the story.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

its gonna be 22.20

Step-by-step explanation:

Because you like to divide the first number and multiply it by the second

Answer:

The simplest form of (5/6)y + 1 = (1/2)y + (1/2) is -(5/6).

Step-by-step explanation:

(Given equation is (5/6)y + 1 = (1/2)y + (1/2)

⇛ (5/6)y - (1/2)y = (1/2) - 1

⇛{(5/6) - (1/2)}y = (1/2) - (1/1)

Take the LCM of the denominator 2 and 6 is 6 in LHS.

⇛{(5*1 - 1*3)/6}y = (1/2) - (1/1)

Again take the LCM of the denominator 1 and 2 is 2.

⇛{(5 - 3)/6}y = {1*1 - 1*2)/2}

⇛(2/6)y = {(1- 2)/2}

⇛(2/6)y = -(1/2)

Shift the number (2/6) from LHS to RHS, changing it's sign.

⇛y = -(1/2) - (2/6)

Take the LCM of the denominator 2 and 6 is 6 in RHS.

⇛y = {(-1*3 - 2*1)/6}

⇛y = {(-3 - 2)/6}

⇛y = -(5/6)

Therefore, y = -(5/6) →[simplest form]

Answer: Hence, the simplest form of the equation: (5/6)y + 1 = (1/2)y + (1/2) for the given problem is -(5/6).

Please let me know if you have any other questions.

Answer:

b = \(\frac{3a-8}{4}\)

Step-by-step explanation:

Given

3a - 7 = 4b + 1 ( subtract 1 from both sides )

3a - 8 = 4b ( divide both sides by 4 )

\(\frac{3a-8}{4}\) = b

Logarithms were invented by the Scottish mathematician John Napier in the early 17th century. The process of inventing logarithms involved the recognition of the need for more efficient mathematical calculations, especially in the fields of astronomy, navigation, and trigonometry.

The invention of logarithms by John Napier was driven by the growing need for faster and more accurate mathematical calculations during the Renaissance period. At that time, fields such as astronomy, navigation, and trigonometry required extensive calculations involving large numbers and complex equations. These calculations were time-consuming and prone to errors.

Napier recognized the need for a systematic approach to simplify these calculations. He developed the concept of logarithms as a means to transform multiplication and division problems into simpler addition and subtraction operations. By using logarithmic tables, which contained pre-calculated logarithms of numbers, mathematicians and scientists could quickly perform calculations by adding or subtracting logarithms instead of performing multiplications or divisions directly.

The invention of logarithms brought significant advancements to various scientific fields, allowing for more precise calculations and making complex computations more manageable. It paved the way for further developments in mathematics and contributed to the scientific and technological progress of the time.

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