The price of a cd was decreased by 20% to £7.68. What was the price before the decrease?

By applying dilatation and congruency theorem, it can be concluded that the distance between points R and R' is 3 units (option A).

Dilation is a transformation of a geometric shape, either becoming larger or smaller, without changing the original shape using a certain scale factor.

Two shapes are said to be congruent if a pair of corresponding sides have the same ratio and the corresponding angles have the same measure.

From the problem we obtained the following information:

QR is dilated to create Q'R' ⇒ QR // Q'R'

The dilatation factor is 1.5 ⇒ Q'R'/QR = 1.5

Now we look at the ΔTRQ and ΔTR'Q':

QR // Q'R'

∠TRQ = ∠TR'Q'

So ΔTRQ is congruent to ΔTR'Q' and TR'/TR = Q'R'/QR

Now we can calculate y using this equation:

   TR'/TR = Q'R'/QR

(6 + y) / 6 = 1.5

      6 + y = 9

            y = 3

Thus, the distance between points R and R' is 3 units.

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Check the picture below.

so the surface area is really just the area of four triangles with a base of 6 and a height of 8, and a 6x6 square.

\(\stackrel{ \textit{\LARGE Areas} }{\stackrel{ square }{(6)(6)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(6)(8) \right]}}\implies 36+96\implies \text{\LARGE 132}~yd^2\)

Answer:

108

Step-by-step explanation:

Add the sides of the triangle

5+3+4 = 12 then look for the height

which is 9

12*9 is 108

The inverse equation of the equation is: A =T2/3

The equation is given as:

T = A3/2

To calculate the inverse equation, we start by multiplying both sides of the equation by 2

T2 = A3

Next, we divide both sides of the equation by 3

A =T2/3

The equation cannot be further simplified

Hence, the inverse of the equation is: A =T2/3

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The  value of A in terms of T is \(A=\frac{2}{3}T\)

The given equation is,

                       \(T=\frac{3}{2}A\)

We have to find value of A in terms of T.

                      \(T=\frac{3}{2}A\\\\A=T\div \frac{3}{2}\\ \\A=T*\frac{2}{3}\\ \\A=\frac{2}{3}T\)

Thus, the  value of A in terms of T is \(A=\frac{2}{3}T\)

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Answer:

$28

Step-by-step explanation:

80% means 80/100

Of means multiplication

So, 80% of $35

= 80/100 X 35

= 0.8 X 35

= 28

Answer:

0.93

Step-by-step explanation:

Answer:

17C5+11C5

Step-by-step explanation:

Well there are 17 and chooses 5 that's 17C5

there are 11 men abd chooses 5 that's 11C5

so add them up

17C5+11C5

The combination helps us to know the number of ways an object can be selected without a particular manner. The number of ways in which 5 men and 5 women can be selected is 2,858,856.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be selected without a particular manner. A combination is denoted by 'C'.

\(^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}\)

where,

n is the number of choices available,

r is the choices to be made.

Given that from a group of 17 women and 11 men, a researcher wants to randomly select 5 women and 5 men for a study.

Now, the number of ways for selection can be written as,

Number of ways in which men can be selected = ¹¹C₅ = 462

Number of ways in which women can be selected = ¹⁷C₅ = 6188

Further, the number of ways for selection can be written as,

Number of ways = Number of ways in which men can be selected × Number of ways in which women can be selected

Number of ways = 462 × 6188

Number of ways = 2,858,856

Hence, the number of ways in which 5 men and 5 women can be selected is 2,858,856.

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Answer:

Each book cost $37 dollars.

Step-by-step explanation:

351 - 18 = 333

333 ÷ 9 = 37

Answer:

11x + 4y - y^2

Step-by-step explanation:

You plus the same variables, in this time you got 9x and 2x so it's 11x!

Answer:

11x + 4y - y²

Step-by-step explanation:

9x + 4y + 2x - y²

combine like terms

11x + 4y - y²

a.2.5 The probability of 3 cabs passing by 6:30 p.m. can be calculated using the Poisson distribution. b. The expected number of cabs passing by 6:10 p.m. is found by multiplying the mean rate by the duration. c. The probability of waiting more than 10 minutes for a cab can be obtained using the CDF of the exponential distribution.

a. The probability of 3 cabs passing by 6:30 p.m. can be calculated using the Poisson distribution. b. The expected number of cabs passing by 6:10 p.m. is found by multiplying the mean rate by the duration. c. The probability of waiting more than 10 minutes for a cab can be obtained using the CDF of the exponential distribution.a. The probability that 3 cabs pass by 6:30 p.m. can be calculated using the Poisson distribution. The mean number of cabs per hour is given as 5. From 6:00 p.m. to 6:30 p.m., the duration is 30 minutes, which is half an hour. The expected number of cabs passing by during this time period can be calculated as the product of the mean rate and the duration, i.e., 5 * 0.5 = 2.5. Using the Poisson distribution formula, we can find the probability of observing exactly 3 cabs during this time period.

b. The expected number of cabs that pass by 6:10 p.m. can be calculated using the same approach. The duration from 6:00 p.m. to 6:10 p.m. is 10 minutes, which is 1/6th of an hour. Multiplying the mean rate of 5 cabs per hour by the duration, we get the expected number of cabs passing by during this time period as 5 * (1/6) = 5/6.

c. To calculate the probability of waiting more than 10 minutes for a cab, we need to consider the inter-arrival time of the cabs. The inter-arrival time follows an exponential distribution, which is the reciprocal of the Poisson distribution. In this case, the mean inter-arrival time is 1/5 of an hour (since the mean rate is 5 cabs per hour). We can use the cumulative distribution function (CDF) of the exponential distribution to find the probability of waiting more than 10 minutes, which is equivalent to waiting more than 1/6th of an hour. The CDF of the exponential distribution can be evaluated to obtain the desired probability.

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Answer:

450 sq.feet

Step-by-step explanation:

Given,

Length ( l ) = 25 feet

Width ( b ) = 18 feet

To find :

Area ( rectangle ) = ?

Formula : -

Area ( rectangle ) = l x b

Area ( rectangle )

= 25 x 18

= 450 sq.feet

Answer:

y^2 + 8y + 15

Step-by-step explanation:

y * y = y^2

y * 5 = 5y

3 * y = 3y

3 * 5 = 15

y^2 + 5y + 3y + 15

Answer:

3.5

7 divided by 50=3.5

3.5x2=7

Step-by-step explanation:

The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1

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

Parent function: y = 2^x

The graph of the transformed exponential function g(x) passes through the points  (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)

So, we have the following transformation steps:

1st Transformation:

Reflect y = 2^x across the y-axis

So, we have

y = 2^-x

2nd Transformation:

Translate y = 2^-x down by 1 unit

So, we have

y = 2^-x - 1

This means that

g(x) = 2^-x - 1

Hence, the equation of the function g(x) is g(x) = 2^-x - 1

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Answer:

D 6,520

Step-by-step explanation:

according to my English this means :

100 times greater than the 5 in 65.2 ...

the 5 in 65.2 is a 5 - it is on the 10⁰ position, and therefore 5×10⁰ = 5.

100 times greater than that 5 is 500.

so, which answer option has a number that contains a 500 (a 5 at the 10² position)?

only D has that : 6 thousand 5 hundred twenty.

this 5 here is at 10² position so it is 5×10² = 5×100 = 500.

and therefore this fulfills the request.

The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%

The Z-Score of the 80th percentile is 0.8416

The formula for Z-Score is presented as follows;

\(z = \frac{x - \mu}{ \sigma} \)

Where;

\( \sigma = The \: standard \: deviation\)

\( \mu = The \: mean = 90\%\)

x = The given score

Taking the mean as a proportion, we have;

\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)

Which gives;

\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)

Therefore, when z = 0.8416, gives;

\(0.8416 = \frac{x - 0.9}{ 0.03} \)

x = 0.8416 × 0.03 + 0.9 ≈ 0.925

Therefore;

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Answer:

Hey so I graphed it for you in the picture, It should be between 2 and 3

Answer:

slope m=--3/-2=-3/2 is required slope

Answer:

m = -3, b = -2

Step-by-step explanation:

The equation is written in the form of slope-intercept, where m = slope and b = y-intercept.

The slope is the number before x. For the equation y = -3x - 2, it's -3.

The y-intercept is the constant. For the equation y = -3x - 2, it's -2.

Hence, m = -3, and b = -2.

\(\rule{350}{4}\)

\(\frak{-Dream-}\)

Answer with Step-by-step explanation:

\(a) {n}^{2} + 3 \\ \\ n = 1 \\ {1}^{2} + 3 \\ 1 + 3 \\ = 4 \\ \\ n = 2 \\ {2}^{2} + 3 \\ 4 + 3 \\ = 7 \\ \\ n = 3 \\ {3}^{2} + 3 \\ 9 + 3 \\ = 12 \\ \\ n = 4 \\ {4}^{2} + 3 \\ 16 + 3 \\ = 19 \\ \\ n = 10 \\ {10}^{2} + 3 \\ 100 + 3 \\ = 103\)

In this sequence,

1st term = 4

2nd term = 7

3rd term = 12

4th term = 19

10th term = 103

\(b)2 {n}^{2} \\ \\ n = 1 \\ 2 \times {1}^{2} \\ 2 \times 1 \\ = 2 \\ \\ n = 2 \\ 2 \times {2}^{2} \\ 2 \times 4 \\ = 8 \\ \\ n = 3 \\ 2 \times {3}^{2} \\ 2 \times 9 \\ = 18 \\ \\ n = 4 \\ 2 \times {4}^{2} \\ 2 \times 16 \\ = 32 \\ \\ n = 10 \\ 2 \times {10}^{2} \\ 2 \times 100 \\ = 200\)

in this sequence,

1st term = 2

2nd term =8

3rd term = 18

4th term =32

10th term = 200

Answer:

52 years

Step-by-step explanation:

Since the mean age of 5 people in that room is 28 years,

∴ Sum₍₅₎= (28×5) years

             = 140 years

Then, one person enters the room which makes the mean age 32 years.

∴Sum₍₆₎= (32×6)years

             = 192 years

∴The age of the person who enters the room= (192 - 140) years

                                                                             = 52 years

Answer:

5916.08( rounded of to nearest tenth.)

Answer:

x/3 ≤ 5

I'm not sure if this is what you were looking for. If not, please be more specific in your questions!

The trigonometric function for the given graph is given as follows:

f(t) = 3sin(4t).

The sine function is defined by the rule presented as follows:

g(x) = asin(bx+c)+d.

The coefficients of the sine function have the roles listed as follows:

From the graph shown by the image at the end of the answer, the function oscillates between -3 and 3, hence the amplitude is of:

a = 3.

The period is of π/2, hence the parameter B is obtained as follows:

2π/B = π/2

B = 4 (applying cross multiplication).

Hence the definition of the function is:

f(t) = 3sin(4t).

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

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Answer:

The constant of proportionality is 1/2

Step-by-step explanation:

The plants grow 1/2 in per week

The constant of proportionality is 1/2 inches/week.

Option D is the correct answer.

We have,

To find the constant of proportionality, we need to determine the rate at which the plant grows, which is the change in height per unit of time (inches per week in this case).

We can do this by calculating the rate of change between any two given data points.

Let's consider the data points for weeks 4 and 6:

Change in height = 3 inches - 2 inches = 1 inch

Change in time = 6 weeks - 4 weeks = 2 weeks

To find the rate, we divide the change in height by the change in time:

Rate = Change in height / Change in time

= 1 inch / 2 weeks

= 0.5 inches/week

or

= 1/2 inches/week

Similarly, we can calculate the rate between weeks 6 and 8:

Change in height = 4 inches - 3 inches = 1 inch

Change in time = 8 weeks - 6 weeks = 2 weeks

Rate = Change in height / Change in time = 1 inch / 2 weeks = 0.5 inches/week

Since the rate of change is the same for both intervals, we can conclude that the constant of proportionality, which represents the rate at which the plant grows, is 0.5 inches per week.

Thus,

The constant of proportionality is 1/2 inches/week.

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Given data:Width of flume (B) = 3 mDepth of flume (D) = 1.5 mChezy’s constant (C) = 0.013Slope of the bed (S) = 0.0025We know that,Q = (1/C) * A * R^(2/3) * S^(1/2)

Where,Q = Discharge of rectangular flumeA = Area of cross-sectionR = Hydraulic radiusS = Slope of the bedCalculation:Area of cross-section, A = B * D = 3 * 1.5 = 4.5 m²Wetted perimeter, P = B + 2 * D = 3 + 2 * 1.5 = 6 mHydraulic radius,

R = A / P = 4.5 / 6 = 0.75 mSubstituting the given values,Q = (1 / 0.013) * 4.5 * 0.75^(2/3) * 0.0025^(1/2)Q = 0.796 m³/sBoundary shear stress, τo = ρ * g * R * Sρ = Density of water = 1000 kg/m³g = Acceleration due to gravity = 9.81 m/s²Substituting the given values,τo = 1000 * 9.81 * 0.75 * 0.0025τo = 18.23 N/m²

The discharge of a rectangular flume 3 m wide and 1.5 m deep on a slope of 0.0025 is 0.796 m³/s and the boundary shear stress is 18.23 N/m².

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First, we convert 1/2% to a decimal.

Similarly:

A function assigns the values. The value of a, b, and c will be 9, 160, and 5, respectively.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function of C= 5(F-32)/9, this can be written for F as,

C= 5(F-32)/9

9C = 5(F-32)

9C/5 = F - 32

(9C/5) + 32 = F

(9C+160)/5 = F

If we compare it with (aC+b)/c, then the value of a, b, and c will be 9, 160, and 5, respectively.

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A) H0: μ = 8mg, Ha: μ ≠ 8mg.

B) \(t = (x̄ - μ) / (s / sqrt(n)) = (10.3 - 8) / (2 / sqrt(25)) = 5.5\).

C) Degrees of freedom = n - 1 = 24, two-tailed t-test, α = 0.01, critical values are  ±2.492. p-value < 0.01.

D) We reject the null hypothesis and conclude that there is strong evidence that the mean amount of active ingredient in all dosages produced is different from 8 mg. The sample mean is significantly higher than 8 mg, indicating that the production process needs improvement.

(A) The null hypothesis is that the population mean of the active ingredient is equal to 8 mg, while the alternative hypothesis is that it is different from 8 mg. In symbols, H0: μ = 8 vs. Ha: μ ≠ 8.

(B) We apply the t-test formula to determine the value for the test statistic:

\(t = (xbar - μ) / (s / sqrt(n))\)

where Î14 is the estimated population mean, n is the number of samples size, x bar represents the sample mean, and s is the standard deviation of the sample. Plugging in the values from the problem, we get:

\(t = (10.3 - 8) / (2 / sqrt(25)) = 3.25\)

(C) To determine the critical value or the p-value, we look up the t-distribution with 24 degrees of freedom ( df = n - 1) and a two-tailed significance level of 0.01. The critical values are  ±2.492, while the p-value is less than 0.01.

(D) Based on the results, we reject the null hypothesis and conclude that the mean amount of active ingredient in all dosages produced is different from 8 mg at the 1% significance level. In practical terms, this means that the drug production process needs to be investigated and improved to ensure that the correct amount of active ingredient is consistently delivered in each dosage.

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The height of the office building casting a shadow of 107ft is approximately 124.83 ft.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

Given the data in the question;

Ratio of height of office building and its height = x / 107

Ratio of height of post and its height = 7 / 6

Equate the two to get the height of the office building.

x / 107 = 7 / 6

Solve for x

x × 6 = 7 × 107

6x = 749

x = 746 / 6

x = 124.83 ft

Therefore, the height of the building is 124.83 ft.

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