Mark, Bridget and Sushil share £14 in a ratio 2:3:2. How much money does each person get?

Answer:

2x + 3 = -7  ---> x = -5

4.5x - 7 = 20 ---> x = 6

-3x + 7 = 28 ---> x = -7

Step-by-step explanation:

2x + 3 = -7

2x = -10

x = -5

4.5x - 7 = 20

4.5x = 27

x = 6

-3x + 7 = 28

-3x = 21

x = -7

The solution to the system of equations y = 1.5x - 4 and y = -x  is (1.6,-1.6). The correct answer is D.

The solution to the system of equations can be calculate as follows

From the question we can conclude that the equations are :

y = 1.5x - 4

y = -x

to find the value of x and y  we can substitute y = -x in the first equation so it became

-x = 1.5x - 4

-1.5x - x = -4

-2.5x = -4

x = 1.6

after we found the value of x we can find the value of y by Substitute

x = 1.6 in y = -x

y = -1.6

Therefore, the solution to the y = 1.5x - 4 and y = -x  is (1.6,-1.6).

Your question is incomplete but most probably your full question was

What is the solution to the system of equations y = 1.5x – 4 y = –x

a.(–1.6, 1.6)

b.(–1.5, 1.5)

c. (1.5, –1.5)

d. (1.6, –1.6)

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4x - 3 = 5x + 2 is -5 (D)

7b - 20 = 3b + 12 is 8.

Hope this helps.

Have a great day and God bless! :)

Answer:

1) -3 -2 = 5x - 4x

-5 = x

D is the answer

2) 7b - 3b = 12 + 20

4b = 32

b = 32/4

b = 8

none of the above

positive 8 is the answer

The given statement "The mapping x T(S(x)) is a linear transformation from Rp to Rm"  is true. Because it satisfies the properties of linearity, as shown by the computation of T(S(cu + dv)).

To show that the mapping x → T(S(x)) is a linear transformation from Rp to Rm, we need to show that it satisfies the following two properties for all vectors x, y in Rp and all scalars c, d:

Additivity: T(S(cx + dy)) = cT(S(x)) + dT(S(y))

Homogeneity: T(S(cx)) = cT(S(x))

Let's first show the additivity property:

T(S(cx + dy)) = T(S(c(x) + d(y))) [Definition of vector addition]

= T(S(c x) + S(d y)) [By linearity of S]

= T(S(c x)) + T(S(d y)) [By linearity of T]

= c T(S(x)) + d T(S(y)) [By linearity of S and T]

Therefore, T(S(x)) satisfies the additivity property.

Now let's show the homogeneity property:

T(S(cx)) = T(S(c x)) [Definition of scalar multiplication]

= c T(S(x)) [By linearity of S and T]

Therefore, T(S(x)) satisfies the homogeneity property.

Since T(S(x)) satisfies both the additivity and homogeneity properties, it is a linear transformation from Rp to Rm.

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Let's break down the expression step by step:

Let's start with the innermost function, \($\tan^{-1} 1$\) , which is the inverse tangent of 1. The inverse tangent of 1 is \($\frac{\pi}{4}$\) radians or \($45$\) degrees.

Now, let's consider the function \($\cos^{-1} \frac{1}{2}$\) , which is the inverse cosine of

\($\frac{1}{2}$\) . The inverse cosine of \($\frac{1}{2}$ is $\frac{\pi}{3}$\)  radians or \($60$\) degrees.

Now, we have  \($\sin(\cos^{-1} \frac{1}{2} - \tan^{-1} 1)$\). Substituting the values we

found earlier, we get \($\sin(\frac{\pi}{3} - \frac{\pi}{4})$\) .

We can simplify the expression within the sine function by finding a common denominator for the two angles:

\($\frac{\pi}{3} - \frac{\pi}{4} = \frac{4\pi - 3\pi}{12} = \frac{\pi}{12}$.\)

Finally, we evaluate \($\sin(\frac{\pi}{12})$\) . The exact value of  \($\sin(\frac{\pi}{12})$\)  can be found

using trigonometric identities or a reference triangle. The exact

value is \($\frac{\sqrt{6} - \sqrt{2}}{4}$.\)

Therefore, the exact value of  \($\sin(\cos^{-1} \frac{1}{2} - \tan^{-1} 1)$\)  

is   \($\frac{\sqrt{6} - \sqrt{2}}{4}$.\)

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Answer:

The coordinate point "c" is (6, 7). if start with ABCD which is rectangle

Step-by-step explanation:

Answer:

Step-by-step explanation:

Average rate of change is the slope of the two points.

Find the value using the slope formula:

Answer:

Step-by-step explanation:

The result of executing the given code is (B) an array of 6 values, ranging from 0 through 5, will be created and referenced by the variable x.

The code `int[] x = {0, 1, 2, 3, 4, 5};` is initializing an array of integers named `x`. The values inside the curly braces represent the elements of the array. In this case, the values are 0, 1, 2, 3, 4, and 5.

Option (A) is incorrect because the values in the array are not all initialized to 0. Instead, each value corresponds to its respective position in the array.

Option (C) is also incorrect because the variable `x` does not directly store the values 0 through 5. Instead, `x` is a reference to the array that contains those values.

Option (D) is not applicable as the code provided is syntactically correct and will not result in a compiler error.

Therefore, the correct answer is (B) - an array of 6 values, ranging from 0 through 5, will be created and referenced by the variable `x`.

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Answer: 39.4784

Step-by-step explanation:

The equation for area of a circle is (3.14)r^2.

Just plug in the given radius (4) into the equation and solve.

Answer:

C. x < 5

Step-by-step explanation:

12x < 60

x < 5

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

with what?

Step-by-step explanation:

The probability of choosing all five white balls correctly from a bowl of 69 white balls and the probability of choosing the correct red ball from a bowl of 29 red balls is \({}^{69}C_5/29\) .

The probability of choosing all five white balls correctly can be calculated using the formula for combinations, where the order does not matter and the balls are chosen without replacement. The probability is given by:

P(Choosing all 5 white balls correctly) = (Number of ways to choose 5 white balls correctly) / (Total number of possible combinations)

The number of ways to choose 5 white balls correctly is 1, as there is only one correct combination.

The total number of possible combinations can be calculated using the formula for combinations, where we choose 5 balls out of 69. It is given by:

Total number of combinations = \({}^{69}C_5\)

Next, we need to calculate the probability of choosing the correct red ball from a bowl of 29 red balls. Since there is only one correct red ball, the probability is 1/29.

Finally, to find the likelihood of being the winner of the Powerball lottery, we multiply the probability of choosing all five white balls correctly by the probability of choosing the correct red ball:

Likelihood = P(Choosing all 5 white balls correctly) * P(Choosing correct red ball)

=\({}^{69}C_5 \times 1/29\\\)

This gives us the probability of being the winner of the Powerball lottery.

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In a study examining the effect of ignoring text messages on distraction, the variable "trying to ignore text messages" would be the independent variable, whereas the variable "amount of distraction" would be the dependent variable.

The independent variable is the one that is manipulated or controlled by the researcher. In this case, the researchers are interested in studying the effect of attempting to ignore text messages, so they would manipulate the participants' behavior in relation to text messages (e.g., asking them to ignore the messages or not).

The dependent variable, on the other hand, is the variable that is measured or observed to determine the effect of the independent variable. Here, the researchers would measure the amount of distraction experienced by the participants as a result of trying to ignore the text messages.

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Answer:

Since the machine fills 250 bottles every 20 minutes, we can write the proportion:

250 bottles / 20 minutes = y bottles / x minutes

Simplifying this proportion, we get:

y = (x/20) * 250

This equation represents a linear relationship between the number of bottles (y) and the number of minutes (x), where the slope is 250/20 = 12.5 bottles per minute.

To create a graph, you can plot the points (0, 0) and (9, 112.5) since the y-axis only goes up to 125. This will give you a straight line that starts at the origin and goes up to about 112.5 on the y-axis at x = 9.

Step-by-step explanation:

According to the given figure, the area of tessellation is si720 in².

Hence, option C is correct.

Given that,

Width of each rectangle = 10 in

Height of each rectangle = 6 in

Since the area of the rectangle = width x length

Therefore,

Area of each rectangle =  10 x 6

Area of each rectangle =  60 in²

In the first row of tessellation, there are 4 rectangles.

In the second row of the tessellation, there are 3 rectangles and two halves of rectangles.

In the third row of tessellation, there are 4 rectangles.

So, there are a total of 12 rectangles in tessellation

Therefore,

Area of  tessellation = 12x60

Area of tessellation =  720 in², which is option C.

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The complete question is attached below:

a. The length of the hypotenuse is √5

b.  If it has one leg of length 1 and a hypotenuse of length 3,  the length of the other leg is √8

a. To find the length of the hypotenuse in a right triangle with legs of length 1 and 2, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

In this case, the legs have lengths 1 and 2, so we have:

Hypotenuse² = Leg1²+ Leg2²

Hypotenuse² = 1² + 2²

Hypotenuse² = 1 + 4

Hypotenuse² = 5

Taking the square root of both sides, we find:

Hypotenuse = √(5)

Therefore, the length of the hypotenuse in this right triangle is √(5).

For the second part of the question, if a right triangle has one leg of length 1 and a hypotenuse of length 3, we can again use the Pythagorean theorem to find the length of the other leg.

Let's assume the length of the other leg is x. We have:

Hypotenuse² = Leg1² + Leg2²

3² = 1² + x²

9 = 1 + x²

x² = 9 - 1

x² = 8

Taking the square root of both sides, we find:

x = √(8)

Therefore, the length of the other leg in this right triangle is √(8).

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Answer:

A

Step-by-step explanation:

Answer:

C)

Step-by-step explanation:

The pythagorean theorem says that a^2 + b^2 = c^2

In this case:

a^2 = x

b^2 = y

c^2 = z

That means x + y = z, which is C

Answer:

42%

Step-by-step explanation:

You add the # of students that picked the museum and factory together. You then want to remember this formula when finding percentages.

# Of students choosing choice /Total # of students/items together

if this was set up this is what it would look like

21/50 = 42%

The values of the missing angles and sides after dilation are:

m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'

m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC  (dilation)

m∠C'B'D = 180° - 34° - 51° = 95°

Thus, by way of scale factor we can say that:

BC/B'C' = BD/B'D' = 36/18 = 2

B'D' = ¹/₂BD = ¹/₂ * 22 = 11

ΔC'P'Q ∼ ΔCPQ

Thus:

C'Q'/CQ = C'D'/CD = D'Q'/DQ

CQ = 2C'Q' = 2 * 3 = 6

Therefore, m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

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The graphical representation that would be best to display the data is given as follows:

Histogram.

An histogram is a graph that shows the number of times each element of x was observed.

The four types of products are given as follows:

Each of these item would represent a bin, and the values of each bin are given as follows:

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Answer: 3/64

Step-by-step explanation:

Dividing by 8 is the same thing as multiplying by the reciprocal (just flip the fraction). Since 8/1 is the same things as 8, here, the reciprocal is 1/8. So just multiply 3/8 by 1/8. You should get 3/64. Hope this helps!

Answer: b

Step-by-step explanation: i tried it and got it correct

a. Null hypothesis (H0): The average caloric intake among female Canadian athletes is equal to or greater than the recommended amount (µ ≥ 2811.5 kcal/day).

Alternative hypothesis (H1): The average caloric intake among female Canadian athletes is less than the recommended amount (µ < 2811.5 kcal/day).

b. The value of n that should be used is 201

c. SEM = 880 / √201

d. To sketch the normal curve and label the test statistic, we need the test statistic value and the critical region corresponding to the significance level α = 0.05

e. Without the test statistic or critical region, we cannot calculate the p-value.

f. Since we don't have the test statistic, critical region, or p-value, we cannot make a decision to reject or fail to reject the null hypothesis at this point.

g. Without the test statistic, critical region, or p-value, we cannot draw a conclusion regarding the evidence for or against the deficiency in caloric intake among female Canadian athletes.

a. The appropriate null and alternative hypotheses to test whether female Canadian athletes are deficient in caloric intake can be stated as follows:

Null hypothesis (H0): The average caloric intake among female Canadian athletes is equal to or greater than the recommended amount (µ ≥ 2811.5 kcal/day).

Alternative hypothesis (H1): The average caloric intake among female Canadian athletes is less than the recommended amount (µ < 2811.5 kcal/day).

b. The value of n that should be used is 201, which represents the number of female athletes in the study. The key word in the last sentence of the paragraph ("n=201 women") indicates that the information provided specifically pertains to the female athletes, not the entire sample of 324 athletes.

c. To calculate the test statistic, we need to determine the standard error of the mean (SEM) using the formula:

SEM = σ / √n

where σ is the population standard deviation and n is the sample size. In this case, the population standard deviation is given as 880 kcal/day, and the sample size is 201.

SEM = 880 / √201

d. To sketch the normal curve and label the test statistic, we need the test statistic value and the critical region corresponding to the significance level α = 0.05. However, the critical region is not provided in the given information.

e. The p-value represents the probability of obtaining a test statistic as extreme as or more extreme than the observed value, assuming the null hypothesis is true. Without the test statistic or critical region, we cannot calculate the p-value.

f. Since we don't have the test statistic, critical region, or p-value, we cannot make a decision to reject or fail to reject the null hypothesis at this point.

g. Without the test statistic, critical region, or p-value, we cannot draw a conclusion regarding the evidence for or against the deficiency in caloric intake among female Canadian athletes. Further analysis is required to obtain the missing information and make a conclusive statement.

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Answer:

9 and 11

Step-by-step explanation:

let the consecutive odd integers be n and n + 2 , then

4n = 5(n + 2) - 19 , that is

4n = 5n + 10 - 19 ( subtract 5n from both sides )

- n = - 9 ( multiply both sides by - 1 )

n = 9 and n + 2 = 9 + 2 = 11

The 2 integers are 9 and 11

Answer:

System of equations:  \(\left \{ {{2x+y=30} \atop {5x+y=42}} \right.\)

(4, 22)

A pair of socks costs 4 dollars, and a pair of slippers cost 22 dollars.

Step-by-step explanation: