6. Which process was used to obtain the equation shown in Step 2?
Step 1: 1-5-5
Step 2:
4y— 3 = 60
A added to both sides of the equation
B. added 5 to both sides of the equation
C. multiplied both sides of the equation by 12
D. divided both sides of the equation by 12

Answer:

The cylinder with a height of 7.0 cm and a diameter of 10.0 cm

Step-by-step explanation:

v = πr²h

---------------------

cylinder with a height of 10.0 cm and a diameter of 7.0 cm

v = π(3.5²)10

v = 384.65 cm³

cylinder with a height of 7.0 cm and a diameter of 10.0 cm

v = π(5²)7

v = 549.5 cm²

549.5 > 384.65

The second cylinder holds more

Answer:

C

Step-by-step explanation:

We have 16% (8 out of 50) students from a random sample of 50 students from a population report having no student debt, we conclude from the sampling distribution suggests that it is highly likely to obtain a sample in which the proportion of students reporting no debt falls within the range of 4% to 28%.

Sampling Distribution- In statistics, the sampling distribution is the probability distribution of a particular statistic (such as the mean) for a particular sample size. To put it another way, it is the distribution of the statistic for all possible samples of a given sample size from the population.

The sampling distribution is defined as the probability distribution of a statistic for a random sample taken from a population. The sampling distribution is an essential concept in statistics because it enables researchers to analyze and make inferences about a population without examining every member of the population.

A sample is a subset of the population, and when we analyze a sample, we use sampling distributions to help us make inferences about the population. In the above scenario, the sampling distribution concludes that there is a high probability of selecting a sample where the percentage of students with no debt is between 4% and 28%.

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Fitted value is a prediction of the mean response value.

According to the statement

we have to explain the fitted value for the regression model and the data which uses to collect the value.

So, For this purpose, we know that the  

A Fitted value is a statistical model's prediction of the mean response value when you input the values of the predictors, factor levels, or components into the model.

An the fitted value used in this model is called the predicted values of response variable in the case of multiple regression model.

And data which is used to create the fitted value is the simple data by which we create the fitted value by the predict the value of given data.

So, Fitted value is a prediction of the mean response value.

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Answer:

x= -1/7 y=1/4

The probability that their score is at least  P(X> 555.3) = 0.8275

What is a normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

Here, we have

Let x denotes the score of a man.

standard deviation (σ) = 104

mean (μ) = 507

If 1 of the men is randomly selected, find the probability that his score is at least 553.5 will be :-

P(X > 553.5) = 1 - P(X ≤ x)

= 1 - P{((x - μ)/σ) ≤ (553.5 - 507/104)}

= 1 - P(z ≤ 0.447)

= 1 - 0.1725

= 0.8275

Hence, the probability that their score is at least  P(X> 555.3) = 0.8275

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Answer:

(0, 1)

(3, 0)

(6, -1)

(9, -2)

The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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The composite function g(h(8)) when evaluated is 94.

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

g(a) = 4a - 2

h(a) = 3a

To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.

h(a) is defined as 3a, so h(8) = 3(8) = 24.

Now we can plug in 24 for a in g(a) and simplify:

g(a) = 4a - 2

g(h(8)) = g(24) = 4(24) - 2 = 94

Therefore, g(h(8)) = 94.

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Answer:

C 0.0361

Step-by-step explanation:

The probability that the color of the first car is silver and the color of the second car is also siver is 0.0361.

Given that,

Based on the above information, the calculation is as follows:

\(= 0.19\times 0.19\)

= 0.0361

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The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .

We need to Know about Hypothesis testing and independent t test to answer this-

Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.

An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.

We can find the difference caffeine content following these steps -

1)H0=Null hypothesis=tea and coffee has same caffeine level

HA=tea and coffee has different caffeine level

2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.

The t value obtained should be then performed under hypothesis testing.

3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.

Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.

Hence null hypothesis will be rejected.

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Yes, the equation y = 5x represents a proportional relationship

Two or more expressions with an Equal sign is called as Equation.

The given equation is y=5x.

In a proportional relationship, the ratio of y to x is constant.

In the given equation the variable x and y has a proportional relationship.

The equation is in the form of y=mx+b

the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.

Hence,  Yes, the equation y = 5x represents a proportional relationship

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Answer:

We can use the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Plugging in the given values, we get:

6,430.72 = π(16)^2h

Simplifying:

6,430.72 = 256πh

Dividing both sides by 256π:

h = 6,430.72 / (256π)

h ≈ 8.05

Therefore, the height of the cylinder is approximately 8.05 yards.

The solution of the equation log(t - 3) = log(17 - 4t), is 4.

option A.

To find the solution for the equation log(t - 3) = log(17 - 4t), we can use the properties of logarithms.

Step 1: Remove the logarithms on both sides.

Applying the property of logarithms that states log(a) = log(b) if and only if a = b, we can remove the logarithms from both sides of the equation:

t - 3 = 17 - 4t

Step 2: Add 4t to both sides.

Adding 4t to both sides of the equation to isolate the t term on one side:

t + 4t - 3 = 17

Step 3: Combine like terms.

Combining like terms on the left-hand side:

5t - 3 = 17

Step 4: Add 3 to both sides.

Adding 3 to both sides of the equation to isolate the t term:

5t - 3 + 3 = 17 + 3

5t = 20

Step 5: Divide by 5.

Dividing both sides of the equation by 5 to solve for t:

5t/5 = 20/5

t = 4

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The proportionality used in the given diagram is 4/3=12/x if ΔABC and ΔDEF are similar. So, option 4 is correct.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.

We have to assume that ΔABC and ΔDEF are similar.

If the triangles are similar,

Then the proportionality is:

AB/BC=DE/EF

4/3=12/x

Therefore, the proportionality used in the given diagram is 4/3=12/x.

So, option 4 is correct.

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When the length is 14 cm and the width is 4 cm, the area of the rectangle is increasing at a rate of 140 cm²/s.

To find how fast the area of the rectangle is increasing, we will follow these steps:

1. Write the formula for the area of a rectangle: Area = length × width
2. Differentiate both sides of the formula with respect to time (t): d(Area)/dt = (d(length)/dt) × width + length × (d(width)/dt)
3. Plug in the given values: length = 14 cm, width = 4 cm, d(length)/dt = 7 cm/s, and d(width)/dt = 8 cm/s.
4. Calculate d(Area)/dt.


1. Area = length × width
2. d(Area)/dt = (d(length)/dt) × width + length × (d(width)/dt)
3. d(Area)/dt = (7 cm/s) × 4 cm + 14 cm × (8 cm/s)
4. d(Area)/dt = 28 cm²/s + 112 cm²/s = 140 cm²/s

So, when the length is 14 cm and the width is 4 cm, the area of the rectangle is increasing at a rate of 140 cm²/s.

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When the length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s, and the length is 14 cm and the width is 4 cm, the rate of change of the area of the rectangle is 92 cm²/s.

The formula for the area of the rectangle is A=l*w

where A is the area of the rectangle,

l is the length of the rectangle, and

w is the width of the rectangle.

According to the problem, the length of the rectangle is increasing at a rate of 7 cm/s:

dl/dt = 7 cm/s.

The width of the rectangle is increasing at a rate of 8 cm/s:

dw/dt = 8 cm/s.The length of the rectangle is 14 cm: l = 14 cm.

The width of the rectangle is 4 cm:

w = 4 cm.

We have to find how fast the area of the rectangle is increasing, i.e., dA/dt.

We know that A=l*w

Taking the derivative of both sides with respect to time, we get

dA/dt = dl/dt*w + l*dw/dt

dA/dt = 7*4 + 14*8

dA/dt = 28 + 112

dA/dt = 140 cm²/s

Therefore, the rate of change of the area of the rectangle is 140 cm²/s.

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Answer:

b = 4 - 2a

Step-by-step explanation:

2b = 8 - 4a

b = (8 - 4a) / 2

b = 4 - 2a

Answer:

b=4-2a

Step-by-step explanation:

4a+2b=8

2a+b=4

b=4-2a

Answer:

\(\frac{m^{6}}{5}\) / \(\frac{5}{m^2}\) = \(\frac{m^8}{25}\)

Step-by-step explanation:

  \(\frac{m^{6}}{5}\) / \(\frac{5}{m^2}\)

= \(\frac{m^{6}}{5}\) * \(\frac{m^2}{5}\)

= \(\frac{m^8}{25}\)

Answer:

x^2 + 8x + 12

Step-by-step explanation:

(x + 6)(x + 2)

x^2 + 6x + 2x + 12

x^2 + 8x + 12

Answer:

Initial Question: How to find percent of a number?

What I know: Percents can be written as decimals.

Points of confusions: What do I do next after turning the percent into a decimal?

Steps: *Example* What is 60% of 30:

60% = .60

.60 x 30 = 18

Step-by-step explanation:

Hope this helps.

Answer:

0

Step-by-step explanation:

V-5V = -4V

-4V-5V = -9V

-9V+9V = 0

We have that, if we have nine-digit numbers, the number of codes that are greater than 700 is 999,999,299

If we are viewing the codes as nine-digit numbers, then there are a total of 999,999,999 possible codes. However, we are only interested in those that are greater than 700.

To find the number of codes greater than 700, we can subtract the number of codes less than or equal to 700 from the total number of codes.

There are 700 codes that are less than or equal to 700 (from 001 to 700), so the number of codes greater than 700 is:

999,999,999 - 700 = 999,999,299

Therefore, there are 999,999,299 codes that are greater than 700 when viewed as nine-digit numbers.

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Answer:

Step-by-step explanation:

2x + 50 = 5x - 80

50 + 80 = 5x - 2x

130 = 3x

/3 to both sides

x = 43.3333333

The population of the world be in 2030 is 8.6 billion.

Given that,

a. = 6.9 billion

V= 1.1 % = 0. 011

a ) Let An represents The population on year after

2010 .

Population grow rate= 1.1%.

So ,

an = an-1 + an-1 ( 1.1 % )

an = an-1 + an-1 (0. 011 )

an = an- 1 ( 1.011 )

(B)

Given ,

ao = 6.9 billion

an = ( 1 .011 ) an- 1

an = (1 .011 ) an- 1 = (1 .011 ) (1 .011) an - 2 = ( 1 .011) (1 .011 ) an- 3

= ( 1.031 ) 3 ( 1 1018 ) an-4 .. . .

an = ( 1 1 012 ) " - ( 1 012 ) am-n

an = ( 1 .01 1 ) " ap

(ao = 6.9 )

an = 6 .9 ( 1 . 01 1 ) h

Now ,

an = 6 . 9 ( 1 . 0 1 1 ) 2

( means 20 year Later from 2010. )

at 2030

So , n = 20

2 20 = 6.9 ( 1 . 0 11 ) 20

a20 = 609 ( 1. 24 4 580 8428 )

a20 = 8.58 7607815 billion

or

azo = 8.6 billion

( rounded to + decimal place)

Thus, 8.6 billion people will live on Earth in 2030.

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Answer:

multiply both the x value and y value by -1

Answer:

Answer 1; Angles forming a linear sum to 180°

Answer 2; Substitution

Answer 3; Definition of perpendicular lines

Step-by-step explanation:

The two column proof is presented as follows;

Statement  \({}\)                               Reason

1. ∠SWT ≅ ∠TWU \({}\)                    Given

2. m∠SWT + m∠TWU = 180°  \({}\)  Angles forming a linear sum to 180°

3. m∠SWT + m∠SWT = 180° \({}\)    Substitution

4. m∠SWT = 90°  \({}\)                      Algebra

5. \(\underset{TV}{\leftrightarrow }\)⊥ \(\underset{SU}{\leftrightarrow }\) \({}\)                                  Definition of perpendicular lines

Perpendicular lines are defined as lines that are at right angles (90°) to each other, therefore given that the angle formed by the lines \(\underset{TV}{\leftrightarrow }\) and \(\underset{SU}{\leftrightarrow }\) m∠SWT = 90°, therefore, the lines \(\underset{TV}{\leftrightarrow }\) and \(\underset{SU}{\leftrightarrow }\) are perpendicular to each other.

Answer:

C

Step-by-step explanation:

A linear relationship looks like a line.  Which scatter plot comes closest to looking like a line (not a curve of some kind)?

Answer:

what numbers

Step-by-step explanation:

please explain