the scores in an exam were normally distributed with unknown mean and a standard deviation of 5 . if 30.85 % of students scored more than 72.5 . what is the value of the mean? ( round to a whole number

Answer:

The slope is -2 and the y-intercept is (0,1)

The probability that both children are boys is 1/2.

What is probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty).

Given in the question,

Mr. Smith has two children, one of them is boy.

So, the possible combinations are,

(Boy, Boy) and (Boy, Girl)

It means number of total outcomes is 2,

we have to find probability of (Boy, Boy)

It means number of favorable outcomes is 1,

The formula for the calculation of probability is:

Probability = number of favorable outcomes/ number of total outcomes,

So,

Probability = 1/2

Therefore, The probability that both children are boys is 1/2.

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solve for y

y = 1.5x + 2

notice this is in form y = mx + b

m is slope, b is y intercept

m = 1.5

slope is 1.5

hope this helps :)

jeron

the equation of the line that passes through the points − 1/3 and 1 11 is

y = 3x + 8 with slope 12 1/3.

1. Find the slope of the line.

m = (11 - -1/3) / (1 - -1/3)

m = 12 1/3

2. Using the point-slope equation, substitute the slope and one point from the line

y - y1 = m(x - x1)

y - -1/3 = 12 1/3 (x - (-1/3))

3. Solve for y

y = 12 1/3x + 8

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The perimeter of the triangle is 50.96 inches.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

An isosceles triangle.

This means,
Two sides are equal.

Now,

The length of the altitude = 15 inches.

The length of the base = 11 inches.

Now,

The right triangle:

Base = 11/2 = 5.5 inches.

Height = 15 inches.

The other side = x

Applying the Pythagorean theorem.

x² = 5.5² + 15²

x² = 30.25 + 225

x² = 255.25

x = √255.25

x = 19.98 inches.

Now,

The perimeter of the triangle.

= 2x + 11

= 2 x 19.98 + 11

= 50.96 inches.

Thus,

The triangle's perimeter is 50.96 inches.

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Answer: the area of a rectangle is l x w length x width

Step-by-step explanation:

Answer: Formula of an area of a rectangle: Length x Width

Step-by-step explanation:

Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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option 3

The mean is the same as the average.

The area of the surface is  5/3 [tex]\sqrt{14}[/tex][tex]\pi[/tex]

Consider that the part of the plane x+2y +3z=1 that lies inside the cylinder [tex]x^{2}[/tex] + [tex]y^{2}[/tex] =5

The surface area of an equation z= g(x,y) is given by the following formula:

[tex]\int\limits^d_d \sqrt {\alpha z/\alpha x]^{2} . [\alpha z/\alpha y]^{2} +1da[/tex]

where the D is the domain of integration.

Since the plane lies inside the cylinder[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = 5, we have the domain of

D= ( (r,0) |0 [tex]\leq[/tex]r [tex]\leq[/tex][tex]\sqrt{5}[/tex],0[tex]\leq[/tex]θ[tex]\leq[/tex]2[tex]\pi[/tex])

The partial derivatives of z = 1/3 ( 1 - x - 2y) are

[tex]\alpha z/ \alpha x[/tex] = 1/3, [tex]\alpha z / \alpha y[/tex] = - 2/3

[tex]\int\limits^d_d \sqrt {[-1/3]^{2} . [-2/3]^{2} +1da[/tex]

= [tex]\int\limits^d_d \sqrt{14} / 9 da[/tex]

= [tex]\sqrt{14}/3 \int\limits^0_ {2^{\pi }[/tex] [tex]\int\limits^\sqrt{5[/tex]r dr dθ

Evaluating the integral we have

[tex]\sqrt{14}/3 \int\limits^0_ {2^{\pi }[/tex][tex]\int\limits^\sqrt{5[/tex]rdrdθ = [tex]\sqrt{14} /3[/tex] 2 [tex]\pi[/tex] [ 5/2]

                           = 5/3 [tex]\sqrt{14}[/tex][tex]\pi[/tex]

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By algebra properties, the quadratic function x² - x - 20 = 0 is equivalent to the quadratic function (x + 1 / 2)² - 81 / 4 = 0.

In this problem we have a quadratic function whose form does not correspond with a perfect square trinomial, that is, a polynomial of the form (x + a)² = x² + 2 · a · x + a². Herein we can modify part of the function by means of completing the square, an application of algebra properties.

First, write the quadratic function described in the statement:

x² - x - 20 = 0

Second, use algebra properties until the square is complete:

x² - x - 20 = 0

x² - x = 20

x² - x + 1 / 4 = 20 + 1 / 4

(x + 1 / 2)² = 81 / 4

(x + 1 / 2)² - 81 / 4 = 0

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The coefficient of determination resulting from a particular regression analysis was 0.85. Then, the correlation coefficient, assuming a positive linear relationship is 0.922.

The coefficient of determination, denoted R2 or r2 and pronounced "R-squared," is the proportion of predictable variation in the dependent variable from the independent variables.

R2 has several definitions, sometimes the same. One class of such cases involves simple linear regression where r2 is used instead of R2. If only one bin is included, r2 is simply the square of the sample correlation coefficient (that is, r) between the observed outcome and the observed prediction. If additional regressors are included, R2 is the square of the multiple correlation coefficient. In both cases, the coefficient of determination is usually between 0 and 1.

Regression analysis consists of a dependent variable (often called the "outcome" or "response" variable, or "label" in machine learning parlance) and one or more independent variables (often called "predictors"). ). ', 'covariate', 'explanatory variable' or 'feature'). The most common form of regression analysis is linear regression, which finds the best fit line (or more complex linear combination) to the data according to mathematical criteria. For example, the ordinary least-squares method computes a unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For certain mathematical reasons (see linear regression), researchers can estimate the conditional expected value (or population mean) of the dependent variable given that the independent variable takes on a particular set of values . Less common forms of regression use slightly different techniques to estimate alternative site parameters (such as quantile regression and requirement analysis, or conditional expectations on a broader collection of nonlinear models. estimating values ​​(such as nonparametric regression). Regression analysis is primarily used for two conceptually distinct purposes.

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The number of inches of a segment is 1.06 inches if a segment is 2.7 centimeters long.

In geometry, a line segment is a portion of a straight line that is bounded by two distinct end points and includes all of the points on the line that fall inside those endpoints. A line segment's length is determined by the Euclidean distance between its endpoints.

In geometry, a line segment is a portion of a straight line that is bounded by two distinct end points and includes all of the points on the line that fall inside those endpoints. A line segment's length is determined by the Euclidean distance between its endpoints.

Given,

In 1 inch there are about 2.54centimeters

And the segment is 2.7 centimeters long

The number of inches=?

2.7/2.54=1.0629

When it is rounded to the nearest 100, we get

1.06 inches.

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The required demand function for the marginal revenue function is P = 0.02x² - 0.025x.

Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold; there is a marginal cost attached to it, which must be accounted for.

The marginal revenue function, find the demand capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

Considering that,

We need to find for the peripheral income capability, find the interest capability.

Recollect that the pay is zero assuming no things are sold:

R'(x) = 0.06x² - 0.05x + 138

p(x) is what.

That's what we know,

MR = dTR/dx = 0.06x² - 0.05x + 138

Incorporating the marginal revenue function , we get complete income capability,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x

= (0.06x³)/3 - (0.05x²)/2 + 138 x

TR = 0.02 x³ - 0.025 x² + 138 x

TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 138 x

P = ( 0.02 x³ - 0.025 x² + 138 x)/x

P = 0.02x² - 0.025x + 138

In this manner, The marginal revenue function, find the interest capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

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The mode in this situation is not defined because there is only one value for each of the mean and median.

Mean (15) and median (10) are two different measures of central tendency. The mean is the average of all values, while the median is the middle value when all the values are arranged in order. The mode is the most frequent value in a set of data, and there can be more than one mode. Since there is only one value for both the mean and median, there is no mode in this situation.

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Answer:9 : 20

Step-by-step explanation:

1) The value of the expression x + y is; 30

2) The value of the expression m + n is; 16

1) We are told that segments LJ and A F are perpendicular. This means that; 4x + 50 = 90 and 7y - 50 = 90

Let us solve for x and y;

4x + 50 = 90

4x = 90 - 50

4x = 40

x = 10

Similarly;

7y - 50 = 90

7y = 90 + 50

7y = 140

y = 140/7

y = 20

Thus;

x + y = 10 + 20

x + y = 30

2) We are told that LJ is a perpendicular-bisector of A F. Thus;

AJ = FJ and AL = FL

Thus;

FL = AL gives;

3m = 42

m = 42/3

m = 14

Similarly;

2m + 3n = 34

2(14) + 3n = 34

28 + 3n = 34

3n = 6

n = 2

m + n = 14 + 2 = 16

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The length L of an edge of each small cube if adjacent cubes touch but don't overlap is 3.45 nm.

The formula to be used for calculation is -

PV = Nkt, where P is pressure, V is volume, N is number of molecules, k is Boltzmann constant and T is temperature in Kelvin.

T = 273 + 27

Performing addition on Right Hand Side of the equation

T = 300 K

P = 101325 Pa

k = 1.38 × [tex] {10}^{-23} [/tex] J/K

Now finding the volume

V = (1 × 1.38 × [tex] {10}^{-23} [/tex] × 300)/101325

Performing multiplication and division on Right Hand Side of the equation

V = 4.09 × [tex] {10}^{-3} [/tex] m³

As we know, V = L³

So, L = [tex] {V}^{1/3} [/tex]

Keep the value of volume

L = [tex] { (4.09/1000) }^{1/3} [/tex]

Performing calculations

L = 3.45 × [tex] {10}^{-9} [/tex] m

Hence, length is 3.45 nm.

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The shorted distance from Asheboro to Fort Jennings is, 20.4 miles.

What is Pythagorean theorem?

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

In this problem we have to find the shortest  route from Asheboro to Fort Jennings using the roads shown.

From the given route the shorted distance from Asheboro to Fort Jennings is,

= 3 mi + 8 mi + (distance from North lean to Fort Jennings)

Let distance from North lean to Fort Jennings is x.

To find the value of x using Pythagorean theorem.

x^2 = 8^2 + 5^2

x^2 = 64 + 25

x^2 = 89

x = 9.433

x = 9.4

So, the total distance is, 3 mi + 8 mi + 9.4 mi =20.4 miles.

Hence, the shorted distance from Asheboro to Fort Jennings is, 20.4 miles.

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Complete question:

Complete question is attached below.

The slope is the measure of the steepness and direction of a line. You can predict whether lines in a coordinate plane are parallel, perpendicular, or none by finding the slope of the lines.

There are two distinct points on any line that can be used to calculate its slope. Between two distinct points on a line, the slope formula calculates the ratio of vertical and horizontal changes. In mathematics, the slope is calculated as the ratio of the rise to the run, or as the rise divided by the run. The slope is a measure of how steep a line is in a coordinate plane.

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Answer:

Step-by-step explanation:

I will try to get the answer for you just give me a minute.!

There is enough evidence to conclude that the new components have reduced the rate of defective chips produced.

At the null hypothesis, it is tested if there is not enough evidence that the amount has decreased, that it still is of 12, hence:

[tex]H_0: \mu = 12[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the amount has decreased, that is, it is less than 12, hence:

[tex]H_1: \mu < 12[/tex]

We have a left-tailed test, with a significance level of 0.05, hence the test statistic needed for there to be enough evidence is less than -1.645, which is the critical value.

The equation that determines the test statistic is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters in this problem are of:

[tex]\overline{x} = 8, \mu = 12, \sigma = 3.3586, n = 12[/tex]

Hence the test statistic is of:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{8 - 12}{\frac{3.3586}{\sqrt{12}}}[/tex]

z = -4.13.

Less than the critical value, hence there is enough evidence that the amount has decreased.

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The radius of the circle having the equation x² + y² - 10x + 6y + 18 = 0 is 4  units , the correct option is (b) .

In the question ,

it is given that ,

the circle is having equation ⇒ x² + y² - 10x + 6y + 18 = 0 ,

we know that ,

general equation of circle is ⇒ x² + y² + 2fx + 2gy + c = 0 ;

So , radius of circle is calculated using the below formula ,

radius [tex]=[/tex] √(f² + g² - c)

On comparing,  given equation of circle with general equation of circle ,

we get , the values of f = -5 and g = 3 .

So after substituting values of f , g and c in radius formula ,

we get ,

radius = √(25 + 9 - 18)

= √(34 - 18)

= √16 = 4 .

Therefore , the given circle has radius = 4 units .

The given question is incomplete , the complete question is

What is the radius of a circle whose equation is x² + y² - 10x + 6y + 18 = 0 ?

(a) 2 units

(b) 4 units

(c) 8 units

(d) 16 units

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The correct statement regarding whether the graph represents a function is given as follows:

B. No, because it fails the vertical line test.

A graph is a relation, and it represents a function if each value of the input is mapped to only one output, that is, if the graph does not contain vertically aligned points.

From the graph given by the image at the end of the answer, the inputs for x > 2 are mapped to multiple outputs, meaning that a vertical line at any of these points would cross the function twice, meaning that the graph has vertically aligned points.

Since the graph has vertically aligned points, it fails the vertical line test, and hence the graph does not represent a function, and option B is correct.

The problem is given by the image shown at the end of the answer.

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Answer:

Step-by-step explanation:

It's asking you to find the measures for all the angles.

For example, angle 1 would be 59° because it is equal to the angle across from it.

Angle 2 would equal 31° because it's a supplement angle to 59° and so on

Answer:

Below

Step-by-step explanation:

35 choices for first number

34 choices for second number (because it cannot be same as first)

34 choices for third number  ( because it cannot be same a second)

35 x 34 x 34 = 40 460 combos

The statements that are true concerning the study that was carried out by the pharmaceutical company include the following: This study uses random sampling, This study uses blinding and This study uses a control group. That is option A, B and E.

A pharmaceutical company is defined as the company that has been certified to manufacture and distribute drugs such as the children's vitamin.

While selecting sample for the study, it was stated that 500 children grouped by age was randomly selected.

Out of the total samples, 250 was given the vitamin while the remaining half was given a placebo ( a blind) which would serve as concealment of the group allocation from them as they are serving as the control.

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Answer:

A,B,C,

Step-by-step explanation:

PLATO

To dilate an image with a scale factor, multiply the scale factor with the dimensions of the image

The dilation is the process of changing the size of the given shape or figure ,the shape of the figure will be always same. Therefore dilation is one form transformation of shapes

The scale factor is the ratio of the measurement of the new shape to the measurement of the original shape.

We can use the scale factor for the dilation

To get the dilate and image with scale factor, we have to multiply the scale factor with the measurement of the original shape

The equation will be

The dimension after dilation = scale factor × original dimensions

Therefore, to dilate an image, multiply the scale factor and the original dimensions

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Answer: 12.5 meters!

Step-by-step explanation:

1km = 1000 meters

So 5km = 5000 meters

So take 5000 divided by 400 = 12.5 meters

Answer:

12.5 is the answer for this question