A group of 66 randomly selected students have a mean score of 22.4 with a standard deviation of 2.8 on a placement test. What is the 90% confidence interval for the mean score, μ, of all students taking the test? 21.5 < μ < 23.3 21.8 < μ < 23.0 21.6 < μ < 23.2 21.7 < μ < 23.1

The time taken depends upon velocity and distance so the time taken by both balls to reach the same height will be 30 seconds.

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

Units of velocity are given by ⇒ meter/second

For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.

Difference between their initial height = 40 - 25 = 15 feet

It means if baseball cover x feet distance then football will cover x + 15 feet.

Now,

Time = distance covered / velocity

Since the time will be the same for both balls to meet them.

So,

Distance covered by baseball/velocity of baseball = Distance covered by football/ velocity of football

x/2.5 = (x + 15)/3

3x = 2.5x + 37.5

0.5x = 37.5

x = 75

So,

Time taken = 75/2.5 = 30 seconds.

Hence "After 30 seconds both balls will go to reach the same height".

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The given statement fraction numerator 6 y plus 2 x over denominator 5 end fraction in numerical form 18 is 6y + 2x = 90.

A linear equation in two variables has the highest degree of 1 and contains two variables generally in x and y.

Given in numerator we have 6y + 2 and in the denominator, we have 5 and this fraction equals to 18, This can be numerically represented as

(6y + 2x)/5 = 18.

6y + 2x = 90.

This is a linear equation in two variables x and y and for every value of x we get a corresponding value of y or vice-versa and all (x,y) ∈ R.

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Answer:Average Speed = 126.6 mph

Step-by-step explanation:

Answer:

In order to round 25.691 to the greatest place or the nearest whole number, first start at the last digit behind the decimal, in the case, being the 1. When it comes to things like this, if the digit is 4&under meaning its the number 4,3,2,1 or 0. If it is 5&up, that means it could be 5-9, making the digit go up (but if its 2, then the digit just goes away, you wont have to worry about that one specific number).

Next step is to round the 9 which makes the 6 go up one digit (meaning it turns into a 7). Now, when you round the seven, it will make the whole number go up one digit, but if you want to round that as well, to start, it's first rounding equaled up to 26. If you're rounding it to a whole tens number, it would be 30. I hope that this helps you understand this subject or topic much better! :3

Step-by-step explanation:

5x + 13y is prime ,  it cannot be factored.

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial .

Some trinomials cannot be factored. If none of the pairs total b, then the trinomial cannot be factored.

Given equation is 5x + 13y

If a polynomial is prime, then it cannot be factored. 5x + 13y is prime.

In this regard,

The law of detachment states that

1) If p happens, then q happens;

2) p is true;

Then, a there is a third statement that is

3) q is also true.

In this question,

If a polynomial is prime, then it cannot be factored.

The statements in the question can be represented as:

(1) If 5x + 3y is a polynomial and is prime then it cannot be factored

(2) It cannot be factored

Using the above representations of p and q, as an illustration; the third statement would be:

(3) 5x + 3y is a polynomial and is prime then we can conclude that

5x + 13y cannot be factored.

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Answer:

-1020

Step-by-step explanation:

-17 x - 5 x - 12 =

- 17 x 60 =

- 1020

The rate of change of the linear function for the given table is determined as: C. 120.

A linear relationship function is represented as a straight line graph which can be expressed as a linear equation in slope-intercept form as, y = mx + b.

The rate of change of the function is represented as m, which is also the slope of the graph, and the y-intercept is b.

A linear function has a rate of change/slope which can be found using the formula:

m = y2 - y1/x2 - x1.

Given the set of table values that represents a linear function below, we can use two pairs of values to find the rate of change as follows:

(0.5, 60) = (x1, y1)

(1.5, 180) = (x2, y2)

Plug in the values

Rate of change (m) = (180 - 60)/(1.5 - 0.5)

Rate of change (m) = (120)/(1)

Rate of change (m) = 120

Therefore, the rate of change of the linear function for the given table is determined as: C. 120.

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A coefficient in the algebraic expression is: 5

The constant is: 12

A variable is: x

A term in the algebraic expression can be: 5x or 12.

An algebraic expression consist of terms, which can be:

Thus, given the algebraic expression, 5x + 12, the following parts of the algebraic expression can be identified as shown below:

A coefficient in the algebraic expression is: 5 (tis is the number multiplied by the variable x)

The constant is: 12 (this is the number standing alone)

A variable is: x (this is the alphabet in the algebraic expression)

A term in the algebraic expression can be: 5x or 12.

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Find the altitude of the top of the hill by adding the difference to the altitude of the check point 3:

Find the difference between the two altitudes:

You got it correct.

Answer: c=√29

Step-by-step explanation:

We use Pythagoras' theorem:

[tex]c^2=5^2+2^2\\c^2=5*5+2*2\\c^2=25+4\\c^2=29\\[/tex]

Extract the square root of both parts of the equation:

[tex]\sqrt{c^2}=\sqrt{29} \\ c=\sqrt{29}[/tex]

Check the picture below.

Answer: I'm pretty sure its 14.

Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14

25 percent of the original price was saved during the purchase of the futon bed

The percent of the original price that is saved can be calculated as follows

The original price is $700

The new price is $525

The first step is to calculate the percentage change

= 700-525

= 175

Therefore the percent saved can be calculated as follows

= 175/700 × 100

= 0.25 × 100

= 25

Hence 25 percent of the original price was saved

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Answer:

4736 because count add them together or do it your way

The five number summary are as follows:

The range of the data sets is 25.

The interquartile range of the sets is 12.

The five number summary describes where data values occur, their central tendency, variability, and the general shape of their distribution.

The five number summary includes minimum number, maximum number, median(Q₂), first quartile(Q₁) and third quartile(Q₃).

Therefore, the five number summary are as follows:

27, 30, 41, 27, 20, 22, 36, 37, 44, 45, 29, 29

Arrange the data in ascending order.

20, 22, 27, 27, 29, 29, 30, 36, 37, 41, 44, 45

There are as follows;

Therefore,

Range of the data sets = 45 - 20 = 25

Interquartile range (IQR) = Q₃ - Q₁ = 39 - 27 = 12

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Answer:

3

Step-by-step explanation:

See the attached image.

Answer:5.05y

Step-by-step explanation:

Therefore, the expanded form of the expression y (0.5 + 8) is 0.5y + 8y

Using this example we can find out that 0.5y+5 y=5.05 y thats the answer

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If by eating 2 eggs and 1​ cupcake, a child consumes 571 mg of cholesterol. The amount of cholesterol that is in each​ item are; 19 mg, 276mg, 8 mg.

E + C + P = 303

Where:

Egg=E

Cupcake=C

Pizza=P

Hence,

3C + 4P =89

4P = 89-3C

P = (89-3C)/4

2E + C = 571

2E = 571-C

E = (571-C)/2

(571-C)/2 + C + (89-3C)/4 = 303

(571-C)2 + 4C + 89-3C = 303×4

(571-C)2 + 4C + 89-3C = 1212

1142 -2C + 4C + 89-3C = 1212

-C = 1212-89-1142

C =19mg (1 cupcake)

E = (571-C)/2

E= (571-19)/2

E=552/2

E= 276mg  (1 egg)

P = (89-3C)/4

P = (89-3(19))/4

P = (89-57)/4

P=32/4

P=8 mg (1 pizza)

So,

Egg=E=19 mg

Cupcake=C=276 mg

Pizza=P=8 mg

Check:

19+276 + 8 = 303 mg

Therefore If by eating 2 eggs and 1​ cupcake, a child consumes 571 mg of cholesterol. The amount of cholesterol that is in each​ item are; 19 mg, 276mg, 8 mg.

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From the temperatures given, we have that:

a) The regression equation is: y = 2.91x + 64.61.

b) The predicted temperature at 2 pm is of 88 ºF.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the input and the output are given as follows:

We have that an hour is 60 minutes, hence:

Thus the points are given as follows:

(0, 65), (0.75, 67), (1.5, 68), (2.5, 72), (3, 74), (3.75, 75), (4.5, 77), (5,80).

Inserting these points into the calculator, the equation is:

y = 2.91x + 64.61.

2 pm is 8 hours after 6 am, hence x = 8 and the predicted temperature, in ºF, is given by:

y = 2.91(8) + 64.61 = 88 ºF.

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(2,3) is a solution to the system of equations.

A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).

Consider the system of equations,

2x - 3y = - 5                                                                                 --------(1)

4x - 4y = - 4                                                                                 --------(2)

Multiplying equation (1) with 2.

4x - 6y = - 10

4x - 4y = - 4

Now, subtracting the above equations:

4x - 6y - ( 4x - 4y) = - 10 + 4

4x - 6y - 4x + 4y = - 6

- 2y = - 6

2y = 6

y = 3

Then,

4x - 4y = - 4

4x - 4 × 3 = - 4

4x - 12 = - 4

Adding 12 on both sides of the equation,

4x - 12 + 12 = - 4 + 12

4x = 8

x = ( 8/4 )

x = 2

Therefore, (x, y) = ( 2, 3) is a solution to the system of equations.

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Answer:

Yes

Step-by-step explanation:

Answer:

8.391

1. Compare the first digit. If they are the same, move on to the next digit. In this case, we have to look at the hundredths place.

2. Check to see which number is bigger. We are looking at 9 and 7. 9 is the bigger number. this means that 8.391 is bigger.

The solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).

Herein we find a system formed by one linear equation and one nonlinear equation (quadratic equation). First, we equalize the two equations to eliminate the variable y:

2 · x² - 5 · x - 7 = 2 · x + 2

2 · x² - 7 · x - 9 = 0

2 · [x² - (7 / 2) · x - 9 / 2] = 0

2 · (x - 9 / 2) · (x + 1)

There are two solutions to x: x₁ = 9 / 2, x₂ = - 1. And the solutions for y are:

y₁ = 2 · (9 / 2) + 2

y₁ = 11

y₂ = 2 · (- 1) + 2

y₂ = 0

Then, the solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).

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Answer:

1.) 85+ (-10) = 95 is false.

2.)  5x+7 = 17 is false.

3.) -8(-2) - 7 = 14 – 5 is false.

Step-by-step explanation:

1. is false because since 85 ≠ 95, then 85 + ( - 10) = 95 is false.

2. is false because since 12 ≠ 17, then 5x + 7 = 17 is false.

3. is false because since -15 ≠ 14, then -8( - 2) - 7 = 14–5 is false.

Answer:

If they all had to equal 360 when put together then the answer would be 22. If they All had to equal 180 when put together, then the answer would be 2.

Step-by-step explanation:

The directions are not quite clear but I have two answers just in case.

Answer:b B

Step-by-step explanation:or a

Answer:

Triangle B is a dilation of A with approximately what scale factor

Triangle B is a dilation of A with approximately a scale factor of 8.

Triangle A is a dilation of B with approximately a scale factor of 1/8.

Triangle B is a dilation of C with approximately a scale factor of 3/4.

We have,

In mathematics, dilation refers to the transformation of a shape, object, or figure by uniformly scaling it up or down.

When the constant factor is greater than 1, the dilation results in an enlargement of the shape, making it larger.

Conversely, when the constant factor is between 0 and 1, the dilation leads to a reduction of the shape, making it smaller.

Now,

Triangle B is a dilation of A with approximately by a scale factor of:

Since triangle B is greater than A.

The scale factor is greater than 1.

Triangle B looks 8 times of triangle A.

So,

The scale factor is 8.

And,

Triangle A is a dilation of B with approximately by a scale factor of:

Since triangle B is smaller than A.

The scale factor is less than 1.

Triangle A looks like 12.5 % of triangle C.

12.5% = 1/8

So,

The scale factor is 1/8.

Triangle B is a dilation of C with approximately by a scale factor of:

Since triangle B is smaller than A.

The scale factor is less than 1.

Let's say,

Triangle B looks 75% of triangle C.

So,

The scale factor is 3/4.

Thus,

Triangle B is a dilation of A with approximately a scale factor of 8.

Triangle A is a dilation of B with approximately a scale factor of 1/8.

Triangle B is a dilation of C with approximately a scale factor of 3/4.

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