Which is the graph of the system of inequalities y > 4/5x – 1/5 and y < 2x + 6

To determine how well Feng must score on exam B, we can use z-scores and the concept of standard deviations.

First, let's calculate the z-score for Feng's score on exam A:

z-score = (x - mean) / standard deviation

z-score for exam A = (81 - 76) / 10 = 0.5

This means that Feng's score on exam A is 0.5 standard deviations above the mean of exam A.

To find out how well Feng must score on exam B, we need to calculate the equivalent score in terms of z-scores for exam B.

x = mean + (z-score * standard deviation)

x = 300 + (0.5 * 50) = 325

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Answer:

11.6m

Step-by-step explanation:

A 13.5​-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall​ (above the fire​ truck) if the ladder makes an angle of 59 22' with the horizontal.

We solve the above question using the Trigonometric function of Sine.

sin θ = Opposite/ Hypotenuse

Hypotenuse = Length of the ladder = 13.5m

Opposite = d

θ = 59° 22'

= 59° + 22/60

= 59° + 0.367

= 59.367°

Hence,

sin 59.367 = d/13.5m

d = sin 59.367 × 13.5m

d = 11.616057416m

Approximately = 11.6m

Therefore, the distance d the ladder goes up the wall is 11.6m

Answer:

D

Step-by-step explanation:

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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The frequency of G when C (520 Hz) is raised by a fifth is 780 Hz.

The frequency of D when G is lowered by a fourth is 1040 Hz.

A. To find the frequency when C (520 Hz) is raised by a fifth to G, we can use the ratio of frequencies between the notes.

A fifth interval corresponds to a frequency ratio of 3:2.

So, we can calculate the frequency of G using the following equation:

Frequency of G = Frequency of C x (3/2)

Frequency of G = 520 Hz x (3/2) = 780 Hz

Therefore, the frequency of G when C (520 Hz) is raised by a fifth is 780 Hz.

B. To find the frequency when G is lowered by a fourth to D, we can use the ratio of frequencies between the notes.

A fourth interval corresponds to a frequency ratio of 4:3. So, we can calculate the frequency of D using the following equation:

Frequency of D = Frequency of G x (4/3)

Frequency of D = 780 Hz x (4/3) = 1040 Hz

Therefore, the frequency of D when G is lowered by a fourth is 1040 Hz.

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Answer:

B.$0.15

Step-by-step explanation:

is the correct answer

Answer:

-2.1 i guess

Step-by-step explanation:3.1 minus 5 =-2.1

The required expression will be x = 3.1 n - 5

It is given that a number is 5 less than 3.1 times a number "n" .

We have to find the expression for the given statement.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as multiplication , division , etc.

Let's assume the number be x.

So ,

3.1 times of number n = 3.1 × n = 3.1 n

Let's subtract 5 from the above number, i.e.,

3.1 n  - 5

and , the required expression will be ;

x = 3.1 n - 5

Thus , the required expression will be x = 3.1 n - 5

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we have 5^4 . (5^-2)^3 = 5^4 . 5^-6 = 5^ (4-6) = 5^-2

ok done. Thank to me :>

The expression representing a rational number is :

because it's value = 6

Numerele rationale din multime vor fi cele care sub radical au un patrat perfect: 1; 4; 9; 16; 25; 36; 49; 64; 81\(\sqrt{36} \\are, multimea, 6\)

Step-by-step explanation:

The significance level, also denoted as alpha or α, is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference

The length of time that the certain type of watch will run follows an exponential distribution with an average of 31 months.

In probability theory, the exponential distribution is often used to model the time until an event occurs. In this case, the length of time that the watch will run is an exponential random variable. The average of the exponential distribution is represented by the parameter λ, which is the reciprocal of the average.

Given that the average time the watch runs is 31 months, we can determine the value of λ by taking the reciprocal: λ = 1/31. This means that, on average, the watch will experience 1 failure in 31 months.

The exponential distribution has the property that the probability density function (PDF) is given by f(x) = λ * exp(-λx), where x is the time variable. In this case, the PDF represents the likelihood of the watch running for a certain amount of time.

By knowing the average of the exponential distribution, we can make predictions about the watch's reliability. For example, we can calculate the probability that the watch will run for a specific duration, such as more than 40 months or less than 20 months, by integrating the PDF over the desired range.

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Answer:

5

Step-by-step explanation:

The change in x from (0,5) to (3,9) is 3 - 0 which is 3. The change in y is 9 - 5 which is 4. Using the Pythagorean theorem (using the two points as the endpoints of the hypotenuse in a right triangle) we get:

\(3^2+4^2=c^2\) where c is the distance between the two points (the hypotenuse of the right triangle). The equation simplifies to:

\(9+16=c^2\)

Which simplifies to:

\(\sqrt{25} =c\)

Thus, c (the distance between (0,5) and (3,9) is 5.

Hope this helps :)

Answer:

78.5 ft3

Step-by-step explanation:

First we need to find the volume of both containers.

The volume of a cylinder is given by the equation:

Volume = pi * diameter^2 * height / 4

If cylinder A has a diameter of 6 feet and height of 15 feet, we have:

Volume_A = pi * 6^2 * 15 / 4 = 424.115 ft3

If cylinder B has a diameter of 8 feet and height of 10 feet, we have:

Volume_A = pi * 8^2 * 10 / 4 = 502.6548 ft3

After pumping the water from A to B, the volume of the empty portion of B will be the difference of their volumes:

Volume_B - Volume_A = 502.6548 - 424.115 = 78.5398 ft3

Rounding to the nearest 10th of a cubic foot, we have a difference of 78.5 ft3

The values of b and a for the logarithmic function in this problem are given as follows:

The logarithmic function in the context of this problem has the format given as follows:

\(y = b\log_3{x + a}\)

The vertical asymptote is at x = -4, hence:

\(y = b\log_3{x - 4}\)

When x = 5, y = -1, hence the parameter b is obtained as follows:

\(-1 = b\log_3{5 - 4}\)

0.477b = -1

b = -1/0.477

b = -2.1.

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Answer:

It stands for "Nothing But Trouble"

Step-by-step explanation:

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

length × width × height.

Step-by-step explanation:

Answer:

length × width × height

Step-by-step explanation:

That is the standard formula for a rectangular shape

Answer:

When 2 lines are parallel, the sum of interior corresponding angles = 180

120 + b = 180

b = 180 - 120 = 60

a + 30 = 180

a = 180 - 30 = 150

Answer:

Fx=Px

Plants=3

(Fish)x=(Plants)3

Step-by-step explanation:
I hope this helps

The proportional relationship for the number of fish when there are P plants is given by:

F = .4P;

Hence, when there are 3 plants, there are 1.2 fish, and option 3 is correct.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

\(y = kx\)

In which k is the constant of proportionality.

In this problem, when there are 15 plants there are 6 fish and when there are 20 plants there are 8 fish, hence the constant is:

\(k = \frac{6}{15} = \frac{8}{20} = 0.4\)

Then, the equation is:

\(F = 0.4P\)

When there are 3 plants:

\(F = 0.4(3) = 1.2\)

There are 1.2 fish.

Hence option 3 is correct.

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Answer:

-6n or -6*n

Step-by-step explanation:

product is multiplication

a number is n

-6*n can also be shown as -6n

Step-by-step explanation:

hope it helps you

here is ur answer

Answer:

The answer is C. 8 mm

Step-by-step explanation:

For me, i was able to divide the 80 by 12 and get 6.667 thus i was able to round up and conclude the answer in the answer choices

Answer:

c

Step-by-step explanation:

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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Step-by-step explanation:

In a parallelogram, opposite sides are equal and parallel. Therefore,

QT = PS = 3y ...(1)

PT + TR = PS

y + 2x + 1 = 3x + 9

2x - y = 4 .....(2)

PR = QT = 3y

PR = SQ = 3x + 9 ....(3)

From equations (1) and (3), we can see that:

3y = 3x + 9

y = x + 3

Substitute this value of y in equation (2):

2x - (x + 3) = 4

x = 7

To find the value of y, we can substitute x = 7 in equation (2):

2(7) - y = 4

y = 10

Therefore, x = 7 and y = 10.

Answer:

Volume of the cylinder is 588π cm³ Or 1846.32 cm³

Step-by-step explanation:

Area of a cylinder is given by the formula,

Volume = πr²h

Here, r = Radius of the circular base

h = Height of the cylinder

From the picture attached,

Radius of the given cylinder = 7 cm

Height of the cylinder = 12 cm

By substituting these values in the formula,

Volume of the cylinder = π(7)²(12)

                                      = 588π cm³

                                      ≈ 1846.32 cm³

Therefore, volume of the cylinder is 588π cm³ Or 1846.32 cm³.

Answer:

c

Step-by-step explanation:

i think