scores on an english test are normally distributed with a mean of 30.6 and a standard deviation of 6. a) what percentage of students score below 33? b) find the score that is at the 80th percentile.

You can infer that the exponential model is a better fit for the data in the experiment, as it has smaller residuals than the quadratic model.

Residuals are the difference between the actual data points and the predicted values generated by the model. They are a measure of how well a model fits the data, and a lower residual indicates a better fit. Therefore, if the student's exponential model has smaller residuals than their quadratic model, it can be concluded that the exponential model is a better fit for the experiment data.

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Answer:

7000

Step-by-step explanation:

70×100=7000

there is 100g in 1kg

Answer:

70,000 grams

Step-by-step explanation:

1. convert kilograms to grams

1000 grams = 1 kilogram

2. use dimensional analysis

[tex]\frac{70 kilograms }{1 gram}[/tex] * [tex]\frac{1000 grams}{1 kilogram}[/tex]

3. multiple straight across

70 * 1000 = 70,000 grams

There is no such a number whose absolute value is -2. This is because the absolute value of any number is its distance from 0 irrespective of the direction.

An absolute value of a number is the distance of the number from 0 on a number line irrespective of the direction.

Consider the number "x".

Then its absolute value is written as

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

For example x = -9; then its absolute value is

|(-9)| = -(-9) = 9; (Since x = -9 < 0; we applied |x| = -x)

So, we can conclude that irrespective of the direction (positive or negative), the absolute value of any number remains positive.

We know that the absolute value of any number is calculated by

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

And the absolute value of any number irrespective of its direction on the number line remains positive.

So, no such number has a negative absolute value.

Hence, the answer is none for the given question.

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Answer: 7

Step-by-step explanation:

We substitute n for 14 to get the equation 14-7, which equals 7.

The number of years it will take such that amount spent on each vehicle is the same will be 2.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose after x years the amount will be the same.

5000 + 2500x = 8000 + 800x

2500x - 800x = 8000 - 5000

1700x = 3000

x = 1.76

Since x must be a whole number so it will round up so x = 2.

Hence "The number of years it will take such that amount spent on each vehicle is the same will be 2".

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Addition is used to find the sum of the number of miles lauren ran

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

Given,

Lanren ran 2.76. Miles in a track event.

Then she ran 0.4 Mile home after the event

We need to find the sum of the number of miles lauren ran.

By addition we find the sum of the number of miles lauren ran.

Two point seven six plus zero point four

2.76+0.4

Three point one six

3.16

Hence, addition is used to find the sum of the number of miles lauren ran

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Answer:

1/2 & 0.5

Step-by-step explanation:

The required lines are parallel to x-axis and they are horizontal lines.So option (B) is correct.

Given two points  on a line, we can compose a condition for that line by finding the slant between those places, then, at that point, settling for the y-intercept in the slope-intercept equation y=mx+b.

a) y =9

It is equation of line parallel to x-axis.

b) A line passing through the points (0, 1) and (1, 1).

Using two point formula,

(y - 1) = [tex]\frac{1-1}{1-0}[/tex](x - 0)

y = 1

So, it is also a line parallel to x-axis.

Thus, both the lines are parallel to x- axis or can say horizontal lines.

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To solve this problem, we can use the standard normal distribution and the Z-score formula to find the probability that a pregnancy will last at least 300 days.

The Z-score is a measure of how many standard deviations a value is from the mean. We can use the Z-score to standardize a value, which means we can express it in terms of how many standard deviations it is from the mean of the distribution.

The Z-score formula is:

Z = (x - μ) / σ

Where x is the value we are standardizing, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

To find the probability that a pregnancy will last at least 300 days, we can use the Z-score formula to standardize 300 days:

Z = (300 - 268) / 15 = 4

This means that 300 days is 4 standard deviations above the mean of 268 days.

To find the probability that a pregnancy will last at least 300 days, we can use a Z-table or a calculator to find the area under the standard normal curve that is greater than or equal to 4 standard deviations.

Using a calculator or a Z-table, we find that the probability that a pregnancy will last at least 300 days is approximately 0.0165, which corresponds to answer choice D: 0.0165.

Answer:

The day before, Mike had 34 apples. Today, he had 24 times as much as the apples that he had the day before. How many apples did he have today?

Step-by-step explanation:

1st, gather information: The day before, Mike had 34 apples, Today, he had 24 times as much as the apples that he had the day before

2nd, plan to solve: I will do 34 x 24.

3rd, Solve: 34 x 24= 816.

4th, is it resonable? : Yes. 816/34=24.

We can show that these data can be modeled using a linear function in the following manner:

a) We must compute the differences in the number of high school graduates in each year in order to model the data using a linear function. For instance, the difference between the 1993 and 1994 graduation rates is 5,479 - 5,410, or 69. This pattern of differences suggests that a linear function can be used to model the data.

The annual change in the number of graduates serves as the slope for the linear function. The slope, for instance, is 69 between 1993 and 1994 and 76 between 1994 and 1995. The slope for the linear function is, in general, the difference between the number of graduates in successive years, therefore it is the slope between graduates in consecutive years.

b) Y = mx + b, where y is the number of graduates, x is the year, m is the slope, and b is the y-intercept, is the formula for a linear function that represents the data. We need to know the values of m and b in order to calculate the formula for the linear function that describes the data.

We can use the slope between any two consecutive years to get the value of m. For instance, m = 69 since the slope from 1993 to 1994 is 69. The number of graduates in the first year of the data, which is the y-intercept, can be used to determine the value of b.

For instance, if the first year of the data is 1993 and that year had 5,479 graduates, then b = 5,479. Consequently, y = 69x + 5,479 is the equation for the linear function that models the data.

c) Functional notation can be used to indicate the number of high school graduates in 1994. The formula is y = 69x + 5,479, where x is the year and y is the total number of graduates. Therefore, y = 69(1994) + 5,479 = 137,123 is the total number of graduates in 1994. We may enter the numbers of x and b into the formula from section c to obtain y = 69 (1994) + 5,479 = 137,123.

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Answer:

q = -4

Step-by-step explanation:

0.0009 = 9 × 10^(-4)

q = -4

The null hypothesis is R = 0

In this question we have been given a hypothesis that the fraction of people with severe depression is higher in country a than in country b.

We need to test the hypothesis.

Suppose that we have chosen the statistic of interest to be PAPB.

Let the ratio R be the fraction of depressed people in country a divided by fraction in country b

We need to find the null hypothesis.

We know that the null hypothesis as statement says that  there is no relationship between two measured variables/phenommena.

In this case, for null hypothesis the ratio must be zero.

Therefore, for given situation the null hypothesis is R = 0

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The complete question is:

We want to test the hypothesis: the fraction of people with severe depression is higher in country A than in country B.

We have chosen the statistic of interest to be PAPB (fraction of depressed people in country A divided by fraction in country B). We call this ratio R.

What is the null hypothesis?

Group of answer choices

1 R=0

2 R=1

The statistical test in which the mean difference between two groups are compared to a distribution of differences between means is (b) paired-samples t-test.

The t-test, one of the most used statistical tests, is used to ascertain whether the means of two groups are equal. The test's underlying presumption is that samples from normal distributions with similar variances were used for both groups.

The two means are equal, which is the null hypothesis; otherwise, they are not. We can calculate a t-statistic that will follow a t-distribution with n1 + n2 - 2 degrees of freedom under the null hypothesis.

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Answer: 75 minutes to 25 minutes

Step-by-step explanation:

To find the ratio between 1 1/4 hours and 25 minutes, we first need to convert both quantities to the same unit of time. Since 1 hour is equal to 60 minutes, 1 1/4 hours is equal to 1.25 * 60 = 75 minutes. Therefore, the ratio between 1 1/4 hours and 25 minutes is 75 minutes to 25 minutes, or 3 to 1.

The amount of commission the agent receives if the bonus amount is Rs. 1,500, is Rs. 24,000.

To find the commission received by the agent, we first determine the excess sales using the bonus rate and bonus amount.

The excess sales are added to Rs. 900,000 to determine the total sales for the year.

The commission rate is applied to the total sales to ascertain the amount of the commission the agent received.

Commission on the total annual sales = 2%

Bonus on the excess of sales over Rs. 900,000 = 0.5%

Bonus amount = Rs. 1,500

Excess sales over Rs. 900,000 = Rs. 300,000 (Rs. 1,500/0.5%)

Total sales = Rs. 1,200,000 (Rs. 900,000 + Rs. 300,000)

Commission amount = Rs. 24,000 (Rs 1,200,000 x 2%)

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Answer:

A

Step-by-step explanation:

The probability that there are no more than 3 cars in the system is 0.50

Probability:

In math, the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is referred as probability.

Given,

Because of limited space availability and a desire to provide an acceptable level of service, the bank manager would like to have no more than three cars in the system at any time.

Here we need to find the probability that there are no more than 3 cars in the system.

Here we know that the present level of service for three or fewer cars is the probability that there are 0, 1, 2, or 3 cars in the system.

As per the Model 1, Exhibit 8A.8, the probability of having more than three cars in the system is 1.0 minus the probability of three or fewer cars => 1.0 − 0.685 = 31.5 percent

And the 95 percent service level of three or fewer cars, this states that

=> P0 + P1 + P2 + P3 = 95 percent.

When we can solve this by trial and error for values of λ/μ.

Therefore, the value of λ/μ = 0.50

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On solving the provided question we can say that the answer is - nnual rate of return will he need to get in order to accomplish his goal if interest is compounded continuously is [tex]A(t) = 2800^e(20)t.[/tex]

Simple interest and compound interest are the two methods for calculating interest. Simple interest is computed on a loan's principle, or initial loan amount. Compound interest is sometimes referred to as "interest on interest" since it is computed using both the principal and the accrued interest from prior periods.

Formula for Monthly Compound Interest. 12 times a year are used to compute interest that is compounded monthly., Formula for Quarterly Compounding. Four times a year are used to compute interest that is compounded quarterly., Formula for Daily Compound Interest., Formula for Annual Compound Interest.

[tex]3300 = 2800e^20t\\ (33/28) = e^20t\\ ln(33/28) = 20t\\ 0.05ln(33/28 = t.[/tex]

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the correct answer is A cause × +5 is linear polynomial

Hello,

I hope you and your family are doing well!

To find the point and slope given by the equation y + 2 = -7(x-1), we can start by rearranging the equation to solve for y:

y + 2 = -7(x-1)

y = -7(x-1) - 2

y = -7x + 7 + (-2)

y = -7x - 9

This is the slope-intercept form of the equation, where y = -7x - 9 is the slope and (-9, 0) is the y-intercept.

The slope of the line is -7, and the point on the line is (-9, 0).

Therefore, the point and slope given by the equation y + 2 = -7(x-1) are (-9, 0) and -7, respectively.

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-25x+800=0

-25x =-800

25x=800

x=32

Answer:

x = 32

Step-by-step explanation:

0=-25x+800

To solve for x, add 25x to each side

0+25x=-25x+800+25x

25x = 800

Divide each side by 25

25x/25 = 800/25

x = 32

Answer: 100 Hours

Step-by-step explanation:

We know the ratio is 1:1:1

So now the ratio is 100 times so that it will take 100 hours

The quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.

ax2 + bx + c = 0 is a quadratic equation or a second-order polynomial equation with a single variable.

The algebraic's theorem guarantees that it is a second-order polynomial equation, hence it must have at least one solution.

The answer might be straightforward or challenging.

x2 - 5x - 3x + 15 = 0 are the roots of the quadratic equation x2 - 8x + 15 = 0.

x(x-5)-3(x-5)

(x-3)(x-5)=0

x = 3, 5

So, the correct answer is  x² - 8x + 15 = 0.

Therefore, the quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.

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the vector fields F with the plots labeled I-IV, Then give a one sentence description of the vector field would look like if you plotted it. F(x, y) = (x, xy): rot(F) = 0; The vector field would look like a series of straight lines that move away from the origin

I: F(x, y) = (y, x) - This vector field corresponds with plot I, as it forms a series of counter-clockwise circular paths.

II: F(x, y) = (1, sin y) - This vector field corresponds with plot II, as it forms a series of parallel lines.

III: F(x, y) = (x - 2, x + 1) - This vector field corresponds with plot III, as it forms a series of diagonal lines that move outward from the origin.

IV: F(x, y) = (y, 1/x) - This vector field corresponds with plot IV, as it forms a series of concentric circles with the origin as their center.

F(x, y) = (x, y): rot(F) = 0; The vector field would look like a grid of straight lines.

F(x, y) = y i = x j: rot(F) = 1; The vector field would look like a series of counter-clockwise circular paths.

F(x, y) = (y, -x): rot(F) = -1; The vector field would look like a series of clockwise circular paths.

F(x, y) = (1 + xy)i + x^2 sin y j: rot(F) = x^2; The vector field would look like a series of curves that rotate counter-clockwise around the origin.

F(x, y) = (x, xy): rot(F) = 0; The vector field would look like a series of straight lines that move away from the origin

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Answer:

x ≤ -3 or x ≥ 3

Step-by-step explanation:

Answer:

To solve this inequality, you can start by isolating the absolute value term on one side of the inequality. To do this, you can subtract 9x from both sides, which gives you:

|9x| - 9x ≥ 27 - 9x

|9x| - 9x ≥ -9x

Next, you can apply the properties of absolute values to simplify the expression. The absolute value of a number is always positive, so the absolute value of any expression will be equal to the expression itself if it is positive, and equal to the negative of the expression if it is negative.

Since the inequality is "greater than or equal to," you need to consider both cases.

If 9x is positive:

9x - 9x ≥ -9x

0 ≥ -9x

x ≤ 0

If 9x is negative:

-9x - 9x ≥ -9x

-18x ≥ -9x

-9x ≥ 0

x ≤ 0

In both cases, the solution is x ≤ 0. This means that any value of x that is less than or equal to 0 will satisfy the inequality.

To write this solution in interval notation, you can use the notation [0,∞) to represent all values of x that are greater than or equal to 0. Alternatively, you can use the notation (-∞,0] to represent all values of x that are less than or equal to 0.

Step-by-step explanation:

1) The percentage of the products last between 9 and 15 days is 68.26%.

2)The percent of the products last between 12 and 15 days is 34.13%.

3) The percentage of the people in line waited for more than 28 minutes 2.28%.

4) The percentage of the people wait for less than 16 minutes 15.87%

Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

What is the number whose 20% is 150?

20% of 150 is 30.

1) µ = 12

sd = 3

a) P(9<X<15)=P

(\frac{9-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})

9-12\sP(\s15\s12

= P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

= 68.26%

b) P(12<X<15)=P

(\frac{12-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})

12 - 12\sP(\s15\s12

= P(0 < Z < 1)

= P(Z < 1) - P(Z < 0)

= 0.8413 - 0.5

= 0.3413

= 34.13%

c) P(X6) = P(frac X-mu sigma frac 6 mu sigma)

=P(Z<\frac{6-12}{3})

= P(Z < -2)

= 0.0228

= 2.28%

d) P(X>15)=P(frac X–mu–sigma>frac X–mu–sigma)

=P(Z>\frac{15-12}{3})

= P(Z > 1)

= 1 - P(Z < 1)

= 1 - 0.8413

= 0.1587

= 15.87%

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Answer:(29.85km/h)

Step-by-step explanation:

1000m=1km

200m=x  [x=(200m/1000m)x1km]

x=0.2km

3600second= 1 hour  

24 seconds =b   [b=(24s/3600s)x1 hour ]

b=0.0067(in 2 decimal place)

velocity in km/h will be

0.2km/0,0067secs

=29.85(in 2 decimal place)

Answer:

speed = 30 km/h

Step-by-step explanation:

We are told that a 200 metres race is run by an athlete in 24 seconds. The question then asks us to calculate the athlete's speed in km/h.

To do this, let's first convert the given data into the required units:

• Converting from metres to kilometres:
To convert from 200 metres to kilometres, we have to divide it by 1000:

200 m = 200 m ÷ 1000 m/km

           = 0.2 km

• Converting from seconds to hours:
To convert 24 seconds to hours, we have to divide it by 3600:

24 s = 24 s ÷ 3600 s/h

        = [tex]\frac{24}{3600}[/tex] h

Now that we have the data in the appropriate units, we can use the following formula to calculate speed:

[tex]\boxed{\mathrm{speed = \frac{distance}{time}}}[/tex]

⇒ speed = [tex]\mathrm{\frac{0.2 \ km}{24/3600 \ h}}[/tex]

⇒ speed = 30 km/h

Therefore, the speed of the athlete is 30 km/h.

Therefore, the probability that the lifetime X of the first component exceeds 5 is 0.006737, based on process.

Probability theory examines numerical illustrations of the probability that an event will happen or that a statement is true. An event's probability is expressed as a number between 0 and 1, with 1 generally denoting certainty and 0 generally denoting impossibility.

Here,

f(x,y) =[tex]xe^{-x(1+y)}[/tex]

Took the double integral of the equation above, first the integral with respect to y (from 0 to infinity) and then with respect to x (from 5 to infinity).

therefore the integration,

[tex]\int\limits^ {infinity}_0{xe^{-x(1+y)} } \, dx[/tex]

[tex]\left \{ {{y=infinity} \atop {x=0}} \right. \frac{-x}{y+1} e^{-x(y+1)} + \frac{1}{y+1} \int\limits^{infinity} _0{ e^{-x(y+1)} \, dx[/tex]

[tex]=\frac{1}{(y+1)^2}[/tex]

[tex]fX(x)[/tex] is easier with:fX(x) =[tex]\int\limits^{infinity}_0 {x}e^{-(x(y+1))} \, dy[/tex]=[tex]xe^{-x} \int\limits^{infinity}_0 x {e^{-xy} } \, dy=e^{-x}[/tex]

We get

We used u substitution to end up with    [tex]e^{-x(1+y)}[/tex] which is needed to evaluate from 0 to infinity, which left me with [tex]e^{-x}[/tex]

Then the integral with respect to x from 5 to infinity which left with an answer of [tex]e^{-5}[/tex]

So the probability that the lifetime X of the first component exceeds 5 is 0.006737, based on my process.

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