In a recent​ year, the scores for the reading portion of a test
were normally​ distributed, with a mean of 22.5 and a standard
deviation of 5.9. Complete parts​ (a) through​ (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 21 The probability of a student scoring less than 21 is (Ro

The value are m = 2 and n = 5, and mn = 2 \cdot 5 = 10.

To simplify \sqrt[4]{400}, we can rewrite it as \sqrt[4]{16 \cdot 25}. This is because 400 can be factored into 16 \cdot 25. Taking the fourth root of each factor separately, we have \sqrt[4]{16} \cdot \sqrt[4]{25}.

\sqrt[4]{16} simplifies to 2, since2^4 = 16. \sqrt[4]{25} does not simplify further since there are no perfect fourth powers that can be multiplied together to give 25.

Therefore, the simplified form of \sqrt[4]{400} is 2\sqrt{25}. We can rewrite \sqrt{25} as 5, so the final simplified form is 2 \cdot 5.

Thus, the value of m = 2 and n = 5, and mn = 2 \cdot 5 = 10.

Learn more about simplified value https://brainly.com/question/16379469

#SPJ11

Answer:

first one u add 2 plus 5witch would be 7p

2 one u add 3 plus 10 witch would be 13p

3 one is 10x

4th one is 12x

It is also called Middle Term Splitting

Its a cool thing with which you can solve different orders of polynomials(or any algebraic expressions if you're a pro).

It is writing an expression as a product of 2 or more factors

Answer:

factorization is of writing a number or another mathematical use as a product of several factors, usually smaller of the same kind.

Step-by-step explanation

3 × 5 is a factorization of the integer 15, and is a factorization of the polynomial x² – 4.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the question:

Play 1: Quarterback was sacked for a loss of 4 yards

Play 2 : Another loss of 10 yards

Play 3: a gain of 12 yards

Write an addition expression to represent the situation. Then find the sum and explain its meaning.

A loss of 4 yards = - 4

Loss of 10 yards = - 10

Gain of 12 yards = + 12

Addition expression for the scenario :

(-4) + (-10) + 12

Result :

-4 + (-10) + 12

= - 4 - 10 + 12

= - 14 + 12

= - 2

Hence, after two consecutive losses of 4 and 10 yards, the team wins 12 yards on the third play and the aggregate yards lost is reduced to 2 yards.

Given:

Carol has 88cm of string and cuts it in the ratio 5 : 6.

To find:

How much longer is the longest piece compared to the shortest piece.

Solution:

Let the lengths of two pieces of string are 5x and 6x. Then,

\(5x+6x=88\)

\(11x=88\)

\(x=\dfrac{88}{11}\)

\(x=8\)

Now, the lengths of pieces are:

\(5x=5(8)\)

\(5x=40\)

And,

\(6x=6(8)\)

\(6x=48\)

The difference between the longer piece and shorter piece is:

\(48-40=8\)

Therefore, the longer piece is 8 m longer than the shorter piece.

Answer: Yes it is

Step-by-step explanation:

A linear relationship simply put, is a relationship between variables that when constructed, forms a straight line. This happens when y changes at a constant rate if x changes by a constant rate as well for instance, 1.

From this question, assume x is minutes and y is the total number of pieces put together. This means that every time x (minutes) increases by 1, y increases by 5 pieces.

The formula would look like this;

y = 5x + 253

This is a formula for a straight line so indeed, this relationship is linear.

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

for such more question on system of equations

https://brainly.com/question/4262258

#SPJ8

Answer:

50×100÷950=5.26

Round off 5.26

=5.3%

The two numbers are 12 and 2. The answer is (d).

Let x be the first number and y be the second number.

From the first statement, we get:

x + 3y = 18   ----(1)

From the second statement, we get:

x - 2y = 8   ----(2)

We can solve for x and y by using either substitution or elimination methods. We will use the elimination method in this case.

Multiplying equation (1) by 2, we get:

2x + 6y = 36   ----(3)

Multiplying equation (2) by 3, we get:

3x - 6y = 24   ----(4)

Adding equations (3) and (4), we get:

5x = 60

x = 12

Substituting x = 12 into equation (2), we get:

12 - 2y = 8

-2y = -4

y = 2 (option-d)

For such more questions on  numbers

https://brainly.com/question/24644930

#SPJ8

Answer:

i think one of them is

(-1,5) and (8,3)

Step-by-step explanation:

just count up how much is on both x and y axes and you'll get ur answer.

goodluck!

also, dont put my answer cuz im afraid u'll get it wrong cuz i tried my best, so jus wait untill someone else answers if u want <3

goodluck

Answer:

Step-by-step explanation:

5^2 + 10 ÷ 2

25 + 10 ÷ 2

25 + 5

30

Answer:

10

Step-by-step explanation:

Answer: So J divided by nine is five, so divided means division, is would mean equal, So I would have J divided by nine is 5. You could also write it like Jay over nine equals 5 and what you would do in order to get J by itself, you have to do the inverse of division, which is multiplication.

Answer:45

Step-by-step explanation:

write an equation to represent the following statement. So J divided by nine is five, so divided means division, is would mean equal, So I would have J divided by nine is 5. You could also write it like Jay over nine equals 5 and what you would do in order to get J by itself, you have to do the inverse of division, which is multiplication. So I'm going to multiply by nine on both sides, So nine the nines cancel out and I get J Equals nine times 5 is 45. So in these boxes I would put jay Over nine equals 5. Or you could do J divided by nine equals 5 and then J equals 45. So this is the middle school math teacher siding out.

Answer:

The answer is -80.

Step-by-step explanation:

First, you need to multiply 12x4.

-72+12x4/(-6)

-72+48/(-6)

Now, we divide 48/-6. (Using P.E.M.D.A.S)

-72+48/-6

-72+-8

Finally, we add the negatives.

This gives us... -80 as your answer.

Answer:

1.- 140 in²

2.- 2.25 in²

3.- 43.25 in²

4.- 7.5 in²

5. 349.75 in²

Step-by-step explanation:

4 congruent triangles mean 4 triangles same measurement

area 1 triangle=(B*H)/2=(10*7)/2=35in²

for area of the roof are 4 by area 1 triangle=4*35=140 in²

2.- area hole. Hole is a square so area Is side by side

area=1.5*1.5=2.25

3.- area front except the hole. As the side of front is isosceles trapezoide which it’s area is (B1+B2)H/2 where B1=8 in and B2=5 in and H=7 in

so arera with hole=(8+5)*7/2=45.5 in²

Answer:

i cant see it clearly

Step-by-step explanation:

Answer:

the slope is 1

Step-by-step explanation:

Answer:

the slope is undefined!! vertical lines don't have an exact slope!

Step-by-step explanation:

To show that β=3α, where β represents the volumetric thermal expansion coefficient and α represents the linear thermal expansion coefficient, we can calculate the infinitesimal change in volume (dv) of a cube with sides of length l when the temperature changes by dt.

The linear thermal expansion coefficient α is defined as the fractional change in length per unit change in temperature. Similarly, the volumetric thermal expansion coefficient β is defined as the fractional change in volume per unit change in temperature.

Let's consider a cube with sides of length l. The initial volume of the cube is \(V = l^3\). Now, when the temperature changes by dt, the sides of the cube will also change. Let dl be the infinitesimal change in length due to the temperature change.

The infinitesimal change in volume, dv, can be calculated using the formula for differential calculus:

\(\[dv = \frac{{\partial V}}{{\partial l}} dl = \frac{{dV}}{{dl}} dl\]\)

Since \(V = l^3,\) we can differentiate both sides of the equation with respect to l:

\(\[dV = 3l^2 dl\]\)

Substituting this back into the previous equation, we get:

\(\[dv = 3l^2 dl\]\)

Now, we can express dl in terms of dt using the linear thermal expansion coefficient α:

\(\[dl = \alpha l dt\]\)

Substituting this into the equation for dv, we have:

\(\[dv = 3l^2 \alpha l dt = 3\alpha l^3 dt\]\)

Comparing this with the definition of β (fractional change in volume per unit change in temperature), we find that:

\(\[\beta = \frac{{dv}}{{V dt}} = \frac{{3\alpha l^3 dt}}{{l^3 dt}} = 3\alpha\]\)

Therefore, we have shown that β = 3α, indicating that the volumetric thermal expansion coefficient is three times the linear thermal expansion coefficient for a cube.

To learn more about coefficient refer:

https://brainly.com/question/24068089

#SPJ11

A correct description of the transformation include the following: D. translation 10 units left and 4 units down.

In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.

On the other hand, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

By translating the pre-image of triangle ABC vertically down by 4 units and horizontally left by 10 unit, the coordinates of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 10, y - 4)

Coordinate A = (5, 2)   →    Coordinate A' (5 - 10, 2 - 4) = (-5, -2)

Coordinate B = (6, 1)   →    Coordinate B' = (6 - 10, 1 - 4) = (-4, -3)

Coordinate C = (4, 5)   →     Coordinate C' = (4 - 10, 5 - 4) = (-6, 1)

Read more on transformation here: https://brainly.com/question/18892892

#SPJ1

Complete Question:

The table below shows the coordinates of a figure that was transformed.

Pre-Image Image

A(5,2) A'(-5,-2)

B(6,1) B'(-4,-3)

C(4,5) C'(-6, 1)

Which is a correct description of the transformation?

Question 4 options: Rotation 180° clockwise B. Reflection over the x-axis. Translation 5 units left and 2 units down. Translation 10 units left and 4 units down.

The required value of y is 117°

Given AB and CD are parallel lines;

and EF is the transversal

Thus 2x + 16 = 3x - 12 { because they are corresponding angles }

On solving the above mentioned linear equation

we get,

x = 25

Thus the required angles are  2x + 16 = 50 + 16 = 66 degrees

and 3x - 12 = 75 - 12 = 63 degrees

And to find the value of y

we can use linear pair property

Thus y + 63 = 180

y = 180 - 63

y = 117 °

To know more about parallel lines ; you may visit the link which is mentioned below ;

https://brainly.com/question/13352230

#SPJ1

The confidence level used for the margin of error was 95%.

The margin of error (MOE) is calculated by dividing the critical value (z*) of the confidence level by the square root of the sample size (n). For a 95% confidence level, the critical value (z*) is 1.96. MOE = 1.96 / sqrt(350) = 4.382% Therefore, the confidence level used for the margin of error was 95%. To calculate the margin of error, we must first determine the confidence level. For a 95% confidence level, the critical value (z*) is 1.96. The margin of error (MOE) is then calculated by dividing the critical value (z*) by the square root of the sample size (n). In this case, the MOE is 1.96 / sqrt(350) = 4.382%. This means that the confidence level used for the margin of error was 95%.

Learn more about error here

https://brainly.com/question/13370015

#SPJ4

Answer: 51.54 ft

Step-by-step explanation:

The ladder should be 1 feet away from the wall by each 4-feet that the wall rises, so if we have a 50 ft wall, the distance between the bottom of the ladder and the wall must be:

50ft/4 = 12.5ft.

Now we know the cathetus of our ladder, 12.5ft and 50ft, let's find the hypotenuse, that is:

H = √(12.5^2 + 50^2) = 51.54 feet.

Which is also the lenght of our ladder, so the shortest ladder to climb safely a 50 ft wall is 51.54 ft long.

Answer:

g(x) = \((x + 8)^{2}\)

Step-by-step explanation:

Degrees of freedom for any statistic is defined as the number of independent pieces of information that go into the estimate of a parameter. It is usually denoted by df.

The term degrees of freedom is used in statistics to describe the number of values in a study that are free to vary or that have the freedom to move around in a distribution. In statistical studies, degrees of freedom can refer to a number of different things.The degrees of freedom for a statistic are typically determined by subtracting the number of parameters estimated from the sample size.

For example, in a simple linear regression, there are two parameters to be estimated: the slope and the intercept.Therefore, the degrees of freedom for the regression would be n-2, where n is the sample size. Similarly, in an independent samples t-test, the degrees of freedom are calculated as the sum of the degrees of freedom for each sample minus 2.

Therefore, if there are n1 and n2 observations in the two samples, the degrees of freedom for the t-test would be (n1-1)+(n2-1)-2=n1+n2-2. The concept of degrees of freedom is important in statistical inference because it helps to determine the distribution of test statistics and the critical values for hypothesis tests.

Know more about the Degrees of freedom

https://brainly.com/question/28527491

#SPJ11

A type II error is a statistical term used to describe the failure to reject a false null hypothesis. It occurs when the null hypothesis is actually false but is not rejected because the statistical test failed to find significant evidence against it.

In other words, it happens when an alternative hypothesis is true, but we fail to reject the null hypothesis.

Types of errors in hypothesis testing

There are two types of errors in hypothesis testing:

Type I error: Rejecting a true null hypothesis

Type II error: Failing to reject a false null hypothesis.Type I error occurs when a true null hypothesis is rejected while Type II error occurs when a false null hypothesis is not rejected. These types of errors are inversely related, meaning that a decrease in one type of error causes an increase in the other.

You can learn more about type II errors at: brainly.com/question/30403884

#SPJ11

Answer:

BC = 0.5 * AC

Step-by-step explanation:

Since B is the midpoint

B. -2.5

Step-by-step explanation:

This is asking for gradient. Pick any two points (x, y) then calculate the y change ÷ x change. example, (0, -5) and (-2, 0). with [0-(-5) ÷ -2-0] you get -2.5

Answer:

im pretty sure its 2

Step-by-step explanation:

Answer:

4

Step-by-step explanaiton:

B is 4x bigger than A