what is the slope on the line ?
please help me.

x + y = 71.5

x = 47.8

y = 71.5 - 47.8

71.5 - 47.8 = 23.7

y = 23.7 pounds

Answer:

9 - 3 x = -3 x - 20

Step-by-step explanation:

the equation has one solution

mark me as brainiest if im correct:)

Teen awareness refers to the level of knowledge, understanding, and consciousness that teenagers have about various issues, including but not limited to social, environmental, health-related, and global concerns.

1) In Colorado, teens' awareness of seat belt messages increased by __ percentage points.
The answer choices provided are a.) 6 b.) 14 c.) 17 d.) 23.

2) In Nevada, teens' awareness of seat belt messages increased by __ percentage points.
The answer choices provided are a.) 6 b.) 14 c.) 17 d.) 23.

3) The result of changes in teen seat belt use is unclear as you did not provide any specific information or data to analyze.

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The 3 significant figures of 87,569 is 87,600

They are non-zero numbers which are digits 1 - 9

Zero’s between integers are always significant

Zero’s before the first integers are insignificant

All zero’s after the decimal point are always significant.

All zeroes used for spacing the decimal point are not significant

Hence,

87,569 correct to 3 significant figures is 87,600

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The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Answer:

D

Step-by-step explanation:

It is D because the scuba diver was 35 m below the surface of the water at the start of the ascent. Meaning that the Y value is showing how deep the diver was in the water

Answer:  resultant

Step-by-step explanation:

The number which is absent in the first 31 digits of pi = 0

We know that a number pi is nothing but the ratio of the circumference of a circle to its diameter.

It is represented by a symbol 'π'

pi is an irrational number. This means that it is not equal to the ratio of any two whole numbers.

Its digits do not repeat.

An approximation 3.14 or 22/7 is often used for everyday calculations.

To 31 decimal places, the value of pi is 3.1415926535897932384626433832795

The numbers present in the first 31 digits of pi are:

1, 2, 3, 4, 5, 6, 7, 8, 9

Only '0' is not present.

Therefore, the number which is absent in the first 31 digits of pi = 0

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Answer: 6

Step-by-step explanation:

Given: A team of 3 employees is preparing 20 reports. Mary takes 30 minutes to complete a report. Matt takes 45 minutes to complete a report.

All reports are completed in 4 1/2 hours. To Find: How long does it take the third team member to complete a report?Solution: Let the third employee takes x minutes to complete a report work done by Mary in 1 minute = 1/30Work done by Matt in 1 minute = 1/45Work done by the third employee in 1 minute = 1/x Total work done by all three in 1 minute = 1/30 + 1/45 + 1/x (As all are working together) a Total number of reports to be prepared = 20Therefore, total work = 20Now,

we know that all reports are completed in 4 1/2 hours = 9/2 hours∴ Total time = 9/2 x 60 = 270 minutes according to the problem statement, Total work = Total time x Total work done by all three in 1 minute20 = 270 (1/30 + 1/45 + 1/x)Solving the above equation for x, we get :x = 90 minutes therefore, it takes the third team member 90 minutes to complete a report.

Answer: 90 minutes.

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Let's represent the third team member as t. Mary takes 30 minutes to complete a report, while Matt takes 45 minutes to complete a report.

Thus, it takes the third team member 3 hours to complete a report.

Therefore, we can use the information given to form an equation. We are given that the team is preparing 20 reports, so:

30 minutes/report × M reports + 45 minutes/report × N reports + T minutes/report × O reports = 4.5 hours

To make the equation simpler, let the unit conversion 4.5 hours to minutes:

4.5 hours × 60 minutes/hour = 270 minutes

Thus:

30M + 45N + TO = 270

O= 20 - M - N

From the third team member: TO = T × 20

Therefore:

30M + 45N + T × 20 = 270

Solving for T:

30M + 45N + 20T = 270

T = (270 - 30M - 45N)/20

We know that there are only three members in the team, and that M and N have already been defined, so we can substitute these values:

T = (270 - 30(20) - 45(0))/20

T = 3

Thus, the time taken by the third team member is 3 hours to complete a report.

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Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

On solving the question, A bubble with a volume of 1,000 cm3 of air has a 12.4 cm diameter.

Any linear segment that traverses a circle's center and has its ends on the circle is referred to as a circle's diameter in geometry. It is also known as the circle's longest chord.

A sphere is a three-dimensional object that resembles a ball in form.

A sphere's volume is determined by:

Volume is = \((\frac{4}{3} ) r^{3}\) where r is the sphere's radius.

The volume of the sphere is 1000 cm3, hence

=>  1000 = \((\frac{4}{3} ) r^{3}\)

 =>  238.73 = \(r^{3} ,,\)

=> r = 6.2 cm

Diameter: 2  X  r => 2  X  6.2 = 12.4 cm.

A bubble with a volume of 1,000 cm3 of air has a 12.4 cm diameter.

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The value of the probability {(D) is 0.74

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

The tree diagram

Using the above as a guide, we have the following:

P(D and A) = 0.6 * 0.7 = 0.42

P(D and B) = 0.4 * 0.8 = 0.32

Add the probability values

so, we have the following representation

P(D) = 0.42 + 0.32

Evaluate

P(D) = 0.74

Hence, the probability is 0.74

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Answer:

C

Step-by-step explanation:

Answer:

C.- x = 80

Step-by-step explanation:

A) La probabilidad de que la cantidad total de la solución contenida en 50 tambores sea mayor a 1 500 L es del 50%.

B) La probabilidad de que puedan llenarse 80 tambores sin que se acabe la solución es del 75%.

C) La tina debe contener 2160 litros para que la probabilidad sea 0,9 de que puedan llenarse 80 tambores sin que se acabe la solución.

Dado que unos tambores, con una etiqueta de 30 L, son llenados con una solución proveniente de una tina grande, y se agrega una cantidad aleatoriamente de la solución en cada tambor con media de 30.01 L y desviación estándar de 0.1 L, para determinar A) ¿Cuál es la probabilidad de que la cantidad total de la solución contenida en 50 tambores sea mayor a 1 500 L?; B) Si la cantidad total de la solución en la tina es de 2 401 L, ¿cuál es la probabilidad de que puedan llenarse 80 tambores sin que se acabe la solución?; y C) ¿Cuánta solución debe contener la tina para que la probabilidad sea 0,9 de que puedan llenarse 80 tambores sin que se acabe la solución?, se deben realizar los siguientes cálculos:

A)

B)

C)

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Answer:

C.

Step-by-step explanation:

got it right on edge :)

The given trig function consist of trig values of common angles;

The values that represent the solution to \(\mathbf{cos \left(\dfrac{\pi}{4} - x\right)} = \dfrac{\sqrt{2} }{2} \cdot sin \, x\), x ∈ [0, 2·π) are;

\(x = \left\{\dfrac{\pi}{2} , \, or \ \dfrac{3 \cdot \pi}{2} \right \}\)

Reason:

The given function is presented as follows;

\(cos \left(\dfrac{\pi}{4} - x\right) = \dfrac{\sqrt{2} }{2} \cdot sin \, x\)

Where;

x ∈ [0, 2·π)

We have;

cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B)

\(cos \left(\dfrac{\pi}{4} \right) = \dfrac{\sqrt{2} }{2}, \ sin\left(\dfrac{\pi}{4} \right) = \dfrac{\sqrt{2} }{2}\)

Which gives

\(cos \left(\dfrac{\pi}{4} - x\right) =\dfrac{\sqrt{2} }{2} \cdot cos \, x + \dfrac{\sqrt{2} }{2} \cdot sin \, x\)

Therefore, we get;

\(\dfrac{\sqrt{2} }{2} \cdot cos \, x = \dfrac{\sqrt{2} }{2} \cdot sin \, x - \dfrac{\sqrt{2} }{2} \cdot sin \, x = 0\)

cos x = 0

Therefore;

Where;

n = 1, 3, 5, ...

x ∈ [0, 2·π)

We get;

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Answer:N

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

a. The distribution of XPX is approximately normal (Gaussian).

b. The probability that an indoor cat dies between 10.2 and 13.4 years old needs to be calculated.

c. The middle 30% of indoor cats' age of death lies between two numbers, which need to be determined.

a. In this scenario, we are given that the age at death of indoor cats follows a normal distribution with a mean of 13 years and a standard deviation of 2.7 years. The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetric and bell-shaped.

b. To find the probability that an indoor cat dies between 10.2 and 13.4 years old, we can calculate the area under the normal curve within that range.

Using the properties of the normal distribution, we can standardize the values by subtracting the mean from each value and dividing by the standard deviation.

Then, we can use a standard normal distribution table or statistical software to find the corresponding probabilities. By finding the probability for 10.2 and subtracting the probability for 13.4, we get the desired probability.

c. The middle 30% of indoor cats' age of death lies between two numbers. We need to find the values that correspond to the lower and upper percentiles that enclose the middle 30% of the distribution.

Using the properties of the normal distribution, we can find the z-scores associated with the lower and upper percentiles. The lower percentile corresponds to the area under the curve that includes 15% below it, and the upper percentile corresponds to the area under the curve that includes 85% below it.

By converting these z-scores back to the original scale, we can find the corresponding ages that enclose the middle 30% of indoor cats' age of death.

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Mr. Schwartz will need to order more wheels after building 12 cars.

The number of cars x Mr. Schwartz builds before he places an order for more wheels can use the following steps:

Determine how many wheels are used per car:

4 wheels/car

Determine the number of wheels available at the start of the week:

85 wheels

Determine the minimum number of wheels needed to be available before placing an order:

40 wheels

Set up an inequality to represent the situation using x to represent the number of cars built before an order is placed:

Number of wheels used = 4x

Number of wheels remaining = 85 - 4x

Order is placed when number of wheels remaining is less than 40:

85 - 4x < 40

Solve for x by isolating the variable:

85 - 4x < 40

-4x < -45

x > 11.25

Since x represents the number of cars built can't have a fractional value for x.

The nearest integer to get the minimum number of cars that need to be built before an order is placed:

x > 12

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The probability best prediction for the number of times that Ellen will draw a blue marble is 200.

Number of blue marbles: 222

Number of red marbles: 333

Total number of marbles: 555

Probability of drawing a blue marble:

222/555

= 0.4

Number of times drawing a blue marble:

300300300 x 0.4

= 120,120,120

Rounded to nearest whole number:

120,120

Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is

222/555

= 0.4.

Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.

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Answer:

Step-by-step explanation:

Step 1: Move the decimal point to the left until you have a number greater than or equal to 1 and less than 10. Step 2: Count the number of decimal places you moved the decimal point to the left and use that number as the positive power of 10. Step 3: Multiply the decimal (in Step 1) by the power of 10 (in Step 2).

Answer:

Step 1: Move the decimal point to the left until you have a number greater than or equal to 1 and less than 10.

Step 2: Count the number of decimal places you moved the decimal point to the left and use that number as the positive power of 10.

Step 3: Multiply the decimal (in Step 1) by the power of 10

The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

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Answer:

r = - 189

first:

-13 -8 = -21

add the two negative number together and get -21

second:

r/9 >> 9 * -21

multiply 9 and -21 together and get -189

r = -189

Distance and recession velocity the Hubble relation links two characteristics of distant objects in the universe:

their redshift and their distance from Earth. This relationship is crucial for understanding the expansion of the universe, as it helps us measure the distances to faraway celestial objects and study their motion relative to us.

What are Distance Sensors?

Distance sensors, as the name implies, are used to determine the distance of an object from another object or barrier without the use of physical touch (unlike a measuring tape, for example).

What is the sensor equation?

The sensor size may be estimated by multiplying the pixel size by the resolution along each of the two dimensions. The focal length may be computed using the formula: Focal Length x FOV = Sensor Size x Working Distance.

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A minimum sample size of 121 individuals needs to be surveyed, ensuring a rounded-up value to estimate the proportion of non-graduates within the 25 to 30 age group with a 10% margin of error and 90% confidence.

To determine the sample size required to estimate the proportion of non-graduates within the 25 to 30 age group with a certain level of confidence and margin of error, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n is the required sample size

Z is the Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of approximately 1.645)

p is the estimated proportion of non-graduates (0.21 based on the information provided)

E is the desired margin of error (10% or 0.10)

Substituting the values into the formula:

n = (1.645^2 * 0.21 * (1 - 0.21)) / 0.10^2

n ≈ 120.41

Rounding up to the nearest integer, the required sample size is 121.

Therefore, you would need to survey at least 121 individuals in the 25 to 30 age group to estimate the proportion of non-graduates within 10% margin of error with 90% confidence.

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Answer:

Step-by-step explanation:

There are two ways to write the relationship, hence two constants of proportionality.

  d = kt

  k = d/t = (2 mi)/(30 min) = 1/15 mi/min

  t = kd

  k = t/d = (30 min)/(2 mi) = 15 min/mi

__

As you can tell from the way the constants are computed, they are reciprocals of each other.

The solution to the radical equation √√x+28 - √√x-20 = 4 is x = 1296.

To solve the given radical equation √√x+28 - √√x-20 = 4, we can follow these steps:

Step 1: Let's simplify the equation by introducing a new variable. Let's set u = √√x. This substitution will help us simplify the equation.

Substituting u back into the equation, we get:

√(u + 28) - √(u - 20) = 4

Step 2: To eliminate the radicals, we'll isolate one of them on one side of the equation. Let's isolate the first radical term √(u + 28).

√(u + 28) = 4 + √(u - 20)

Step 3: Square both sides of the equation to eliminate the remaining radicals:

(√(u + 28))^2 = (4 + √(u - 20))^2

Simplifying the equation:

u + 28 = 16 + 8√(u - 20) + (u - 20)

Step 4: Combine like terms:

u + 28 = 16 + u - 20 + 8√(u - 20)

Simplifying further:

u + 28 = u - 4 + 8√(u - 20)

Step 5: Simplify the equation further by canceling out the 'u' terms:

28 = -4 + 8√(u - 20)

Step 6: Move the constant term to the other side:

32 = 8√(u - 20)

Step 7: Divide both sides by 8:

4 = √(u - 20)

Step 8: Square both sides to eliminate the remaining radical:

16 = u - 20

Step 9: Add 20 to both sides:

36 = u

Step 10: Substitute back u = √√x:

36 = √√x

Step 11: Square both sides again to remove the radical:

36^2 = (√√x)^2

1296 = (√x)^2

Taking the square root of both sides:

√1296 = √(√x)^2

36 = √x

Step 12: Square both sides one more time:

36^2 = (√x)^2

1296 = x

Therefore, the solution to the radical equation √√x+28 - √√x-20 = 4 is x = 1296.

So, the correct choice is:

A. The solution set is (1296).

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