Assume a significance level of alpha = 0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm. The hypothesis test results in a​P-value of 0.2761.a. State a conclusion about the null hypothesis.​(Reject H0 or fail to reject H0​.) Choose the correct answer below.A. Fail to reject H0​ because the​ P-value is less than or equal to alphaα.B. Reject H0​ because the​ P-value is less than or equal to alphaα.C.Fail to reject H0​ because the​ P-value is greater than alphaα.D. Reject H0​ because the​ P-value is greater than alphaα.b. Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion?A. The standard deviation of pulse rates of the group of adult males is more than 11 bpm.B. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 11 bpm.C. The standard deviation of pulse rates of the group of adult males is less than or equal to 11 bpm.D. There is sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 11 bpm.

Answers

Answer 1

Answer:

a

   The  correct option is  B

b

   The  correct option is  D

Step-by-step explanation:

From the  question we are told that

     The level of significance is  [tex]\alpha = 0.05[/tex]

      The p-value is  [tex]p = 0.2761[/tex]

Considering question b

      Given that the  [tex]p< \alpha[/tex] then the null hypothesis is  rejected

Considering question b

Given that the original claim is The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm

Then the null hypothesis is   [tex]H_o : \sigma = 11[/tex]

The  reason why the null hypothesis is write like this above is because a null hypothesis expression can not contain only a > or a < but only allows = [tex]\le , \ and \ \ge[/tex]

  and  the alternative hypothesis is  [tex]H_a : \sigma > 11[/tex]

Now given that the null hypothesis is rejected, it mean that there is sufficient evidence to support original claim


Related Questions

Write an equation for a line perpendicular to y = − 5 x + 5 and passing through the point (5,5)

Answers

Answer:

The answer is

[tex]y = \frac{1}{5} x + 4[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the line perpendicular to

y = -5x + 5 we must first find the slope of

Comparing with the general equation above

Slope = - 5

The slope of the perpendicular line is the negative inverse of the slope of the original line

Slope of perpendicular line = 1/5

Equation of the line using point (5,5) and slope 1/5 is

[tex]y - 5 = \frac{1}{5} (x - 5)[/tex][tex]y - 5 = \frac{1}{5} x - 1[/tex][tex]y = \frac{1}{5} x - 1 + 5[/tex]

We have the final answer as

[tex]y = \frac{1}{5} x + 4[/tex]

Hope this helps you

Answer:

y=0.2x+4 or y=1/5 x+4.

Step-by-step explanation:

When one line is perpendicular to another, you have to find the opposite reciprocal for the slope of the given equation.

For instance, if you have the number 5, the reciprocal of 5 is 1/5 or 0.2. The opposite of positive is negative. Therefore, it is -0.2.

Therefore, if the slope of the first equation is -5, the slope for the next equation is 1/5. Reciprocal of -5 is -1/5. The opposite of -1/5 is positive 1/5. Or, the opposite of negative is positive. Therefore, it would be 1/5x.

However, we are not done.

Since we are given that the line passes through the point (5,5), we need to find the y-intercept of this equation.

The formula for slope-intercept is y=mx+b.

M is your slope

B is your y-intercept.

We can find the y-intercept by actually plugging in the point (5,5) into the new equation.

5=0.2(5)+b.

5 is x and 5 is also y.

(x,y).

Simplify the equation by multiplying 0.2 times 5. That is equal to 1.

We now have 5=1+b.

Isolate for the letter "b" by subtracting 1 from both sides.

1-1 is 0.

5-1 is 4.

Therefore, b=4.

Finally, we can plug in the y-intercept into the new equation.

y=0.2 or 1/5x+4.

I hope this helps! I also hope you have a great rest of your day!

Which statements about the sum of the interior angle measures of a triangle in Euclidean and non-Euclidean geometries are true? A. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees. B. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees. C. In Euclidian geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees. D. In Euclidian geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees. E. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

Answers

Answer:

its b and e

Step-by-step explanation:

The statements given in options B and E are   true so options B and E are right options.  

Given some statements we have to determine that which of the following statements are true

The given statements are as follows

A. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.

B. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.

C. In Euclidean geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.

D. In Euclidean geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

E. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

We know some facts about each type of geometry

In Euclidean geometry  plane is used to plot the points and line.

In spherical geometry uses the sphere to plot the points and circles

Elliptical geometry is such a geometry where no parallel lines exists.

The sum of interior angles of a triangle is dependent on the type of geometry we are dealing with   and they can be written down in the following points

In Euclidean geometry the sum of interior angles of  a triangle is 180° In spherical or elliptical geometry the sum of interior angles of a triangle is more than 180°  In hyperbolic geometry  the sum of interior angles  of a triangle is less than 180°  

So from the above observations we can conclude that statements given in options B and E are   true so options B and E are right options.  

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rational number between 2 and 3 ?

Answers

Answer:

2:3

Step-by-step explanation:

It’s easy

Answer:

2.5

Step-by-step explanation:

i think

What is numbers 1-30 added all together

Answers

Answer:

465

Step-by-step explanation:

The sum of consecutive numbers has a formula, and it's

[tex]\frac{n(n+1)}{2}[/tex].

Where n is the amount of numbers.

From 1-30, it's 30 numbers, so:

[tex]\frac{30(30+1)}{2} \\\\\frac{30(31)}{2} \\\\\frac{930)}{2} \\\\\\465[/tex]

Hope this helped!

The numbers 1-30 added together is 465

According to the U.S. Energy Information Administration the average number of televisions per household in the United States was 2.3. A college student claims the average number of TV’s per household in the United States is different. He obtains a random sample of 73 households and finds the mean number of TV’s to be 2.1 with a standard deviation of 0.84. Test the student’s claim at the 0.01 significance level.

Answers

Answer with explanation:

Let [tex]\mu[/tex] be the average number of televisions per household in the United States .

As per given ,

[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]

Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.

For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.

[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]

[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]

T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]

Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]

This means we cannot reject null hypothesis.

We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.

PLEASE HELP !! (4/5) -50 POINTS-

Answers

First equation:

2 -7 6 | 7

Second: x + 3y - 4z = 5
1 3 -4 | 5

Third: x + 6y - 15z = -6
1 6 -15 | -6

Arranged augmented matrix:

2 -7 6 | 7
1 3 -4 | 5
1 6 -15 | -6

Answer:

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Step-by-step explanation:

An augmented matrix is the coefficients of the variables and then the solution in rows

Rewriting the equations

2x -7y +6x = 7

x +3y -4z = 5

x +6y -15z = -6

The matrix is

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.

Answers

Answer:

The resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].

Step-by-step explanation:

The distributive property of multiplication is:

[tex]a\times (b+c)=(a\times b)+(a\times c)[/tex]

The two polynomials provided are:

[tex](2x+3)\\(x^{2}+x-2)[/tex]

Determine the final expression by multiplying the two polynomials as follows:

[tex](2x+3)\times (x^{2}+x-2)=[2x\times(x^{2}+x-2)]+[3\times(x^{2}+x-2)][/tex]

[tex]=[(2x\times x^{2})+(2x\times x)-(2x\times 2)]+[(3\times x^{2})+(3\times x)-(3\times 2)]\\\\=[2x^{3}+2x^{2}-4x]+[3x^{2}+3x-6]\\\\=2x^{3}+2x^{2}+3x^{2}-4x+3x-6\\\\=2x^{3}+5x^{2}-x-6[/tex]

Thus, the resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].

Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have? Assume that the planes cutting the prism do not intersect anywhere in or on the prism. EXPLAIN PLS

Answers

Answer:

  36

Step-by-step explanation:

Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.

The new figure has 12+24 = 36 edges.

Alonso brings $21 to the market to buy eggs and avocados. He gets eggs that cost $2.50. Then, he notices
that the store only sells avocados in bags of 3 for $5. He wants to buy as many avocados as he can with his
remaining money.
Let B represent the number of bags of avocados that Alonso buys.
1) Which inequality describes this scenario?

Answers

Answer:

Step-by-step explanation:

The money Alonso has is $21 which he wants to use to buy eggs and Avocados. The eggs he bought costs $2.50. Therefore the money remaining after the egg is bought is $18.50 (21 - 2.50)

Each bag of avocado cost $5, therefore the number of bags that can be bought with $18.50 is:

Bags of Avocado = $18.50 / $5 = 3.7 = 3 (to the previous whole number).

This means that the maximum number of bags of Avocado that can be bought is 3 bags. It can be represented by the inequality:

Bags ≤ 3  

Answer:

2.50 + 5B ≤ 21;

Step-by-step explanation:

Cost of eggs = $2.50

Cost of avocado = $5 (bag of 3)

Total budgeted amount = $21

Bags of avocado = B

Therefore :

(Cost of eggs + cost of avocado) ≤ total budgeted amount

($2.50 + $5(B)) ≤ 21

2.50 + 5B ≤ 21

5B ≤ 21 - 2.50

5B ≤ 18.50

B ≤ 18.50 / 5

B ≤ 3.7

Therefore the maximum number of bags can purchase is 3(whole number without exceeding $21)

Which parent functions have an intercept at (0,0)Choose all that are correct.
Linear
Quadratic
Radical
Absolute Value
Rational
Exponential
Logarithmic (Log)
Cubic
Cube Root

Answers

Answer:

Linear, Quadratic, Radical, Absolute Value, Cubic, Cube Root

Step-by-step explanation:

To find:

Which functions have an intercept at (0, 0).

That means, when we put a value [tex]x=0[/tex] in the [tex]y =f(x)[/tex], value of [tex]y=0[/tex].

Let us discuss each parent function one by one:

1. Linear:

[tex]y = x[/tex]

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

2. Quadratic:

[tex]y = x^2[/tex]

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

3. Radical:

[tex]y = \sqrt x[/tex]

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

4. Absolute Value:

[tex]y = |x|[/tex]

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

5. Rational:

[tex]y = \dfrac{1}{x}[/tex]

When we put [tex]x = 0\Rightarrow y \rightarrow \infty[/tex]

Therefore, it does not have intercept at (0, 0).

6. Exponential:

[tex]y = b^x[/tex]

b is any base

When we put [tex]x = 0\Rightarrow y =1[/tex]

Therefore, it does not have intercept at (0, 0).

7. Logarithmic:

[tex]y = logx[/tex]

When we put [tex]x = 0 \Rightarrow y\rightarrow[/tex] Not defined

Therefore, it does not have intercept at (0, 0).

8. Cubic:

[tex]y = x^3[/tex]

When we put [tex]x = 0\Rightarrow y =0[/tex]

Therefore, it has intercept at (0, 0).

9. Cube Root:

[tex]y = \sqrt[3]x[/tex]

When we put [tex]x = 0\Rightarrow y =0[/tex]

Therefore, it has intercept at (0, 0).

A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆ y = 3 − 5 x y^=3-5x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way:
1.) When amount of schooling increases by one year, the number of pregnancies decreases by 4.
2.) When amount of schooling increases by one year, the number of pregnancies increases by 4.
3.) When amount of schooling increases by one year, the number of pregnancies increases by 5.
4.) When amount of schooling increases by one year, the number of pregnancies decreases by 5.

Answers

Answer:

1. When amount of schooling increases by one year, the number of pregnancies will decrease by 4.

Step-by-step explanation:

Regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, there is regression equation given. X and Y are considered as dependent variables. When number of schooling increases by 1 year then number of pregnancies will decrease by 4

Write an equation showing the relationship between the lengths of the three sides of a right triangle.​

Answers

Answer:

Below

Step-by-step explanation:

First triangle)

This triangle is a right one so we will apply the pythagorian theorem.

● 25 is the hypotenus

● 25^2 = b^2 + 24^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Seconde triangle)

Again it's a right triangle

x is the hypotenus.

● x^2 = 12^2 +5^2

● 12^2 = x^2-5^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

This is a right triangle

AC is the hypotenus.

● AC^2 = BC^2 + BA^2

Notice that: BC = BE+EC and BA=BD+DA

● AC^2 = (BE+EC)^2 + (BD+DA)^2

Answer:  2) b = 7       3) x = [tex]\sqrt{119}[/tex]

Step-by-step explanation:

Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²

2) b² + 24² = 25²

   b² + 576 = 625

            b² = 49

         [tex]\sqrt{b^2}=\sqrt{49}[/tex]

            b = 7

3) 5² + x² = 12²

   25 + x² = 144

            x² = 119

        [tex]\sqrt{x^2}=\sqrt{119}[/tex]

           [tex]x=\sqrt{119}[/tex]

3.24 (4 being repeated) to a fraction

Answers

Answer:

  146/45

Step-by-step explanation:

Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.

  [tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]

__

Comment on procedure

The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.

What is the approximate diameter of a sphere whose surface area is 83.96 square inches? Use π = 3.14.

Answers

Answer:

5.17

Step-by-step explanation:

The surface area of a sphere is 4[tex]\pi[/tex]r².

83.96=4[tex]\pi[/tex]r²

Divide by 4

20.99=3.14r²

divide by 3.14

6.6847=r²

take the square root

2.585=r

mulitply by 2 (diameter is twice the radius)

5.17

The diameter of the sphere is 5.17 inches.

What is surface area?

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called as the surface area.

The surface area of a sphere is 4πr².

83.96=4πr²

Divide by 4

20.99=3.14r²

Divide by 3.14

6.6847=r²

Take the square root.

2.585=r

Multiply by 2 (diameter is twice the radius).

r= 2 x 2.585

r = 5.17 inches

Therefore, the diameter of the sphere is 5.17 inches.

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A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 27t

Answers

The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.

Answer:

s = 17 units

Step-by-step explanation:

Given f(t) = t³ - 8t² + 27t

Differentiating f(t), we have

f'(t) = 3t² - 16 t + 27

At t = 0

f'(t) = 27

This is the required obtainaible distance, s.

Find the sum to infinity of the series 2+5/4+11/16+23/64+..........up to the infinity.
infinity​

Answers

We have

[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]

(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)

Recall for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

So we have

[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]

Simplify to create an equivalent expression.
\qquad{7n-(4n-3)}7n−(4n−3)

Answers

Answer:

[tex]3n + 3[/tex]

[tex]3(n+1)[/tex]

Step-by-step explanation:

Given

[tex]7n - (4n - 3)[/tex]

Required

Simplify

To simplify the given expression, you start by opening  the bracket

[tex]7n - (4n - 3)[/tex]

[tex]7n - 4n + 3[/tex]

Next, you perform arithmetic operations on like terms

[tex]3n + 3[/tex]

The answer can be further simplified;

Factorize [tex]3n + 3[/tex]

[tex]3(n+1)[/tex]

Hence;

[tex]7n - (4n - 3)[/tex] when simplified is equivalent to [tex]3n + 3[/tex] or [tex]3(n+1)[/tex]

Answer:

3n+n

Step-by-step explanation:

Two trains are moving towards each other on the same railroad track. From this track there's an offshoot piece of railroad − the length of which is shorter than the length of the train but longer than the length of one train car. How can the trains pass each other?

Answers

Answer:

  one car at a time

Step-by-step explanation:

For each car in the shorter train* (A) ...

train A leaves one of its cars on the offshootboth trains move until train B can move the car from the offshoot to the portion of track away from train Atrain B moves to allow the cycle to repeat

When there are no more train A cars in front of train B, both trains can continue on their journey.

We assume cars can be decoupled at any point in the train, so that any required order of cars can be preserved. We further assume that train B can move any one of train A's cars in addition to all of its own.

_____

* The total number of car lengths that must pass the offshoot is (at least) the product of the number of cars in both trains, so it doesn't seem to matter which train makes use of the offshoot. We choose to decouple the cars of train A so that the minimum number of cycles is required--even though each cycle is longer.

Someone help me understand

Answers

Answer:

f¯¹(x) = 23/ (6x + 3)

Step-by-step explanation:

f(x) = (23 – 3x)/6x

The inverse, f¯¹, for the above function can be obtained as follow:

f(x) = (23 – 3x)/6x

Let y be equal to f(x)

Therefore, f(x) = (23 – 3x)/6x will be written as:

y = (23 – 3x)/6x

Next, interchange x and y.

This is illustrated below:

y = (23 – 3x)/6x

x = (23 – 3y)/6y

Next, make y the subject of the above expression. This is illustrated below:

x = (23 – 3y)/6y

Cross multiply

6xy = 23 – 3y

Collect like terms

6xy + 3y = 23

Factorise

y(6x + 3) = 23

Divide both side by (6x + 3)

y = 23/ (6x + 3)

Finally, replace y with f¯¹(x)

y = 23/ (6x + 3)

f¯¹(x) = 23/ (6x + 3)

Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is

f¯¹(x) = 23/ (6x + 3)

Claire has to go to the movie theater the movie starts at 4:15 pm it is a 25min walk to the theater from her home what time dose the have to leave the house to get there on time

Answers

Answer:

3:50 pm

Step-by-step explanation:

Count backwards with the 25 min.

4:15 - 15 min >

25 - 15 = 10 >

4:00 - 10 = 3:50

Answer:

3:50 pm

Step-by-step explanation:

Starting Time + Time Interval = Ending Time

=> Ending Time - Time Interval = Starting Time

Ending Time = 4:15 pm

Time Interval = 25 minutes

Starting Time = x

=> 4:15 - 25 = x

=> 4:15 - 15 - 10 = x

=> (4:15 - 15) - 10 = x

=> 4:00 - 10 = x

=> 3:50 pm = x

So, she needs to leave the house at 3:50 pm to get to the movie theater on time.

graph the linear equation using the slope and y-intercept y=1/9x+5

Answers

Answer:

Slope= 1/9

Y-Intercept= 5

round 1,965 to the nearest tenth

Answers

Step-by-step explanation:

1965 round to the nearest tenth is 1970

Answer:

1965.0

Step-by-step explanation:

Write as an equation: The sum of a number and 12 is 78.

Answers

Answer:

x+12=78

Step-by-step explanation:

like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.

Answer:

n + 12 = 78

Step-by-step explanation:

Let n = number.

n + 12 = 78

Suppose that you are standing 150 feet from a building and the angle of elevation to the top of the building is 42°. What is the building's height?

Answers

Answer:

135.06 feet

Step-by-step explanation:

Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.

opposite side = x

adjacent side = 150 feet

angle = 42°

tan(42°) = x/150 feet

150 feet * tan(42°) = x

x = 135.06 feet

Simplify -12w + 7w - 3 - 6

Answers

Answer: Hi!

We can simplify this by combining like terms:

-12w + 7w - 3 - 6

-12w + 7w = -5w

-3 - 6 = -9

Out equation now looks like this:

-5w - 9

There's nothing left to simplify, so we're done!

Hope this helps!

Please tell me the answer ASAP Lynette's average score on five tests is 18. If she scores 24 points on her sixth test, what is her average score on all six tests? Show Your Work

Answers

Answer:

The average score of 6 tests is 19.

Step-by-step explanation:

Given that the average score of 5 tests is 18. So first, we have to find the total number of scores for 5 tests :

[tex]let \: x = total \: no. \: of \: scores[/tex]

[tex] \frac{x}{5} = 18[/tex]

[tex]x = 18 \times 5[/tex]

[tex]x = 90[/tex]

We have found out that the total scores for 5 tests is 90. So we have to find the average of 6 scores :

[tex] \frac{x + 24}{5 + 1} = \frac{90 + 24}{6} = \frac{114}{6} = 19[/tex]

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution : )}}}}[/tex]

Given:Average score in 5 tests = 18He scored 24 points in 6th point

To FinD:Find the average score in all six tests?

How to find?

We need to know how to find the average

☄ For this case, We are gonna find average score...!

[tex] \large{ \boxed{ \sf{Avg. \: score = \frac{Total \: score}{No. \: of \: tests} }}}[/tex]

So, Let's proceed further towards solution....

Solution:

We have,

Avg. score = 18No. of tests = 5

Finding total score in 5 tests,

⇛ Total score = Avg. score × No. of tests

⇛ Total score = 18 × 5

⇛ Total score = 90

According to question,

He scored 24 marks in 6th test

⇛ Total score now = 90 + 24 = 114

No. of tests = 6

Finding the average score of 6 tests,

⇛ Avg. score = 114 / 6

⇛ Avg. score = 19 points

☄ Avg. score of lynette in 6 tests = 19

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What is the answer, what are the steps to solve this, and what do the parts of the equation represent?

Answers

Answer:

[tex]\sum_{a=1}^{7}(500-a)=3472[/tex]

Step-by-step explanation:

[tex]\sum_{a=1}^{7}(500-a)[/tex] will form a sequence as,

499, 498, 497.......7 terms

Since there is a common difference between successive and previous term,

d = 498 - 499 = -1

This sequence is an arithmetic sequence.

Sum of n terms of an arithmetic sequence is,

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

where a = first term of the sequence

n = number of term

d = common difference

For the given given sequence,

[tex]S_{7}=\frac{7}{2}[2(499)+(7-1)(-1)][/tex]

    = [tex]\frac{7}{2}[998-6][/tex]

    = [tex]\frac{7}{2}(992)[/tex]

    = 3472

Therefore, sum of seven terms of the given sequence will be 3472.

Solve the following equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week: x = 0.7x + 24 How many total items were stocked for that week? 14 56 80 10

Answers

Answer:

80

Step-by-step explanation:

The total of 80 items were stocked for that week.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Solve equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week:

x = 0.7x + 24

We need to find How many total items were stocked for that week

Solving;

x = 0.7x + 24

x - 0.7x = 24

0.3x = 24

x = 80

Therefore, the total of 80 items were stocked for that week.

Learn more about equations here;

https://brainly.com/question/10413253

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Describe all numbers x that are at a distance of 2 from the number 8. Express this using absolute value notation.

Answers

Answer:

The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:

|x - 8| = 2

Step-by-step explanation:

The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:

|x - 8| = 2

The equation is written in the notation of absolute value as required.


Help please!!! Thank you

Answers

Answer:

Option (G)

Step-by-step explanation:

Let the length of the race = a miles

Since, Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

Time taken to cover 'a' miles with the speed = 12 mph,

Time taken '[tex]t_1[/tex]' = [tex]\frac{a}{12}[/tex]

Time taken to cover 'a' miles with the speed = 11 mph,

Time taken '[tex]t_2[/tex]' = [tex]\frac{a}{11}[/tex]

Since the time taken by David to cover 'a' miles was 10 minutes Or [tex]\frac{1}{6}[/tex] hours more than the time he expected.

So, [tex]t_2=t_1+\frac{1}{6}[/tex]

[tex]\frac{a}{11}=\frac{a}{12}+\frac{1}{6}[/tex]

[tex]\frac{a}{11}-\frac{a}{12}=\frac{1}{6}[/tex]

[tex]\frac{12a-11a}{132}=\frac{1}{6}[/tex]

a = 22 mi

Therefore, distance of the race = 22 mi

Option (G) is the correct option.

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