Tests of older baseballs showed that when dropped 24 ft onto a concrete surface, they bounced an average of 235.8 cm. In a test of 40 new baseballs, the bounce had a mean of 235.4 cm. Assume the standard deviation of baseball bounce heights is 4.5 cm. At α=0.05, are the new baseballs different?

A. There is sufficient evidence to support the claim that the new baseballs have bounce heights with a mean different from 235.8 cm

B. There is not sufficient evidence to support the claim that the new baseballs have bounce heights with a mean matching 235.8 cm



C. There is sufficient evidence to support the claim that the new baseballs have bounce heights with a mean matching 235.8 cm


D. There is not sufficient evidence to support the claim that the new baseballs have bounce heights with a mean different from 235.8 cm​

Square root functions are in the shape of a parabola, like a giant U, while cube root functions are more wide and swiggly, like a stretched out S.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, given that,

we have to say that, How is the general shape of a cube root function different from the shape of a square root function.

Now, we get,

Square root functions are in the shape of a parabola, like a giant U, while cube root functions are more wide and swiggly, like a stretched out S.

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Answers to ratios are first one is option B, second one is option A and third one is option C.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

1. Ratio of smoothie size to mangos used for Kim = 8 : 1

Ratio of smoothie size to mangos used for Bri = 24 : 3

                                                                             = 8 × 3 : 1 × 3

                                                                             = 8 : 1

Ratio of smoothie size to mangos used for Angela = 32 : 4

                                                                                    = 8 × 4 : 1 × 4

                                                                                    = 8 : 1

So the ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

So the answer is option B.

2. Ratio of width to length of larger canvas = 4 : 6 = 2 : 3

Ratio of width to length of smaller canvas = 2 : 3

So the painting's width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

So the answer is option A.

3. Ratio of students who prefer free time at the beginning of the class to students who prefer free time at the end of the class is 12/19

Total students = 12 + 19 = 31

Out of 31 students, 12 students prefer free time at the beginning of the class and 19 students prefer free time at the end of the class.

So the answer is option C.

Hence the answers on ratios are done.

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Step-by-step explanation:

please refer to the sketch

Answer:

62 degrees.

Step-by-step explanation:

I think this because it appears that ABC makes a 90 degree angle and I would think that you would just subtract 28 from 90 and get 62.

Hope it helps! =D

The missing number in the expression (5 x 7) + (n x 4) = 5 x (7+ 4) is 5.

The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.

We also know that distributive property states a(b + c) = ab + ac.

Given, An expression (5 × 7) + (n × 4) = 5 × (7 + 4).

Now, If we expand the RHS we have,

5×(7 + 4).

= (5 × 7) + (5 × 4).

Now, Writing the obtained RHS with LHS we have,

(5 × 7) + (n × 4) =  (5 × 7) + (5 × 4).

So, The missing number is 5.

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Answer:

68 words

Step-by-step explanation:

If 34 words are typed in a minute what about two minutes hence take 34×2

Answer:

68

Step-by-step explanation:

A rate can be a quantity, or frequency, measured against a different quantity or amount.

If we know that Shaikha can type at a rate of 34 words per minute, and we need to figure out how many words she can type in 2 minutes, we can use an equation that looks like this:

Let m = minutes, w = words per minute and t = total words

m × w = t

Simply just insert your numbers into the equation.

2 × 34 = 68

Therefore, the number of words, or rate, that Shaikha types in 2 minutes is 68.

Answer:

f(x)= 2x-9

f(-2)= 2(-2)-9

f(-2)= -4-9

=-13

Answer:

47 and 53

Step-by-step explanation:

list of prime numbers to 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

50 is between 47 and 53

5a) The total cost of buying the car, including the harmonized sales tax (HST) of 13%, is $36,160.

5b) Under the lease, the customer saves $14,760.

5c) The lessee after returning the car has the following lease options:

6a) The after-tax cost of the car that Jordan wants to buy is $32,199.35.

6b) The part of the Honda Civic that needs to be financed after the down payment is $26,199.35.

6c) The monthly payment will be $567.26.

6d) After four years, the total amount Jordan had paid for the vehicle is $33,228.48.

A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.

A car purchase can also be financed through loans, like home mortgages.

Value of the car = $32,000

Harmonized Sales Tax (HST) = 13%

Cost of the car with HST = $36,160 ($32,000 x 1.13)

Down payment = $1,000

Financing part = $35,160 ($36,160 - $1,000)

Installment payments = 48

Periodic payments = $425

Total lease cost = $21,400 ($1,000 + 48 x $425)

Savings from leasing = $14,760 ($36,160 - $21,400)

The value of the Honda Civic = $28,495

Harmonized Sales Tax (HST) = 13%

After-tax cost = $32,199.35 ($28,495 x 1.13)

Annual interest rate = 1.9% compounded monthly

Down payment = $6,000

Financing part = $26,199.35 ($32,199.35 -$6,000)

Financing period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 1.9%

PV (Present Value) = $26,199.35

FV (Future Value) = $0

P/Y (# of periods per year) = 12

C/Y (# of times interest compound per year) = 12

Results:

Monthly Payments (PMT) = $567.26

Sum of all periodic payments = $27,228.48

Total Interest $1,029.13

Total amount paid by Jordan after 4 years = $33,228.48 ($27,228.48 + $6,000)

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Factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)

⇒ Firstly find the factors of 32

How Do You Work Out Factors of 32?

Step 1: Let's start with the whole number 1 and work our way up to the          factors of 32.   32 ÷ 1= 32 
Step 2: Now divide 32 by two.  32 ÷ 2= 16

Step 3: Then we get.   32 ÷ 4= 8

Step 4: Similarly, we calculate all the 32 factors.

32 factors = 1, 2, 4, 8, 16, and 32.

⇒ Secondly, find factor pairs of 32

The two numbers that, when multiplied together, give 32 are the factors of 32 in pairs. The factors of 32 are listed below in pairs.

Products of 32                Factor pair of 32

1 × 32 = 32                              (1, 32)

2 × 16= 32                               (2 ,16)

4 × 8 = 32                                (4, 8)

∴Therefore, factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)

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Explanation:

Multiply out the fractions. This is because volume = length*width*height when it comes to rectangular prisms, aka blocks.

(3/8)*(5/8)*(7/8) = (3*5*7)/(8*8*8) = 105/512

This fraction cannot be reduced since 105 and 512 have no factors in common, other than 1. A clue of this is to notice how neither 3, nor 5, nor 7 share any common factors (other than 1) with 8 in the denominator.

Answer:

105/512

Step-by-step explanation:

hope this helps

By solving an expression we will see that the total cost for the tickets is $192.

We know that six families went to the food festival, each family has 2 adults and 4 children, then there are:

6*2 = 12 adults in total.

6*4 = 24 children in total.

We know that each child ticket costs $4, and an adult ticket costs $8, then the total cost of all the tickets is what we get when we solve the expression below:

12*$8 + 24*$4

That is, the number of adults times the cost of an adult ticket plus the number of children times the cost of a children ticket.

The total cost is then:

12*$8 + 24*$4 = $192

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Answer:

B, C, E

Step-by-step explanation:

Let y = length.

Then, y - 5 = width.

area = length × width

area = y(y - 5)

area = 750

y(y - 5) = 750

y² - 5y = 750

A: y(y + 5) = 750

Since y = length, width must be y - 5, not y + 5, so A does not work.

B: y² - 5y = 750

This is what we got above, so this equation works.

C: 750 - y(y - 5) = 0

750 = y(y - 5)

750 = y² - 5y

This is the same as B and works.

D: y(y - 5) + 750 = 0

y(y - 5) = -750

The area cannot be -750, so this equation does not work.

E: (y + 25)(y - 30) = 0

y = -25 or y = 30

This also works.

Answer: B, C, E

The simplified form of the expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y² is

[1/15(xy)³] and  (x, y) ≠ 0.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given, An expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y².

= 5x³3y² ÷ 243x⁴y³ ÷ 25x²y².

=  5x³3y² ÷ 25x²y² ÷ 243x⁴y³.

= (3/5)x ÷ 243x⁴y³.

= (3/5)x/(243x⁴y³).

= (3/5)/(243x³y³).

= 1/(81×5x³y³).

= [1/15(xy)³].

The restriction should be x and y can not be equal to zero as it would make the expression undefined.

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On solving the provide the question, we can say that - the value of the following function is f(x) = -5x - 1.

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

[tex]x = -2, y = 9; x = -1 , y = 4; x =0, y = -1.[/tex]

x = 0 , y = -1 so c = -1.

slope of line [tex]= (4-9) / (-1-(-2)) = -5/ 1 = -5.[/tex]

function f(x) = -5x - 1.

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Answer:

Step-by-step explanation:

1. (i) f(-1) = 3(-1) + 1 = -2 and f(3) = 3(3) + 1 = 10

(ii) To find the value of x for which f(x) = 7, we can set f(x) equal to 7 and solve for x:

3x + 1 = 7

3x = 6

x = 2

2. (i) Q = {x² - 2 | x E P} = {(-2)² - 2, (-1)² - 2, (0)² - 2, (1)² - 2, (2)² - 2} = {4, 0, -2, -1, 2}

(ii) As f(x)=x²-2, and P = {-2,-1,0,1,2} mapping into Q is {-2,-1,0,1,2} to {4,0,-2,-1,2}

3. (i) f(1 + x) = 2(1 + x) - 1 = 2x + 1

(ii) To find the range of values of x for which f(x) < -3, we can set f(x) equal to -3 and solve for x:

2x - 1 < -3

2x < -2

x < -1

so x can be any value less than -1

(iii) f(x) - g(x) = (2x - 1) - (x² + 1) = 2x - x² - 2

4. (i) f(-1) + 1 = 2(-1) - 1 + 1 = -1

(ii) To solve f(x) = g(-2), we can substitute the expressions for f(x) and g(x) into the equation:

2x - 1 = 3(-2) + 1

2x - 1 = -5

2x = -6

x = -3

5. f(x) = px + q, given that f(2)= 4 and f(4) == 10

so

4 = 2p + q

10 = 4p + q

solving for p and q we get p = 3 and q = -2

6. (i) f(--3) = 3(-3)² - 5(-3) = -27

7. (i) To solve f(x) = g(-2/-4), we can substitute the expressions for f(x) and g(x) into the equation:

x-2 = (1/4)x² - 1

x-2 = x²/4 - 1

4x-8 = x²-4

x²-4x+4 = 0

x = 2, -2

(ii) To solve f(x) + g(x) = 0

x-2 + x²-1 = 0

x²-2x+1 = 0

(x-1)² = 0

x = 1

for f(x) = -² 3 the expression does not make sense, but assuming the -² is just typo then we can solve for x by substituting f(x) = -3

into the expression of f(x) = 3x² - 5x

3x² - 5x = -3

3x² - 5

The equation has one solution.

A value of x that makes the equation true is 6 which when substituted into the equation and simplified makes the equation turn into x = 0.

A value of x that makes the equation false is 8 which when substituted into the equation and simplified makes the equation turn into x = 2.

From the information provided, we have the following equation:

x - 6 = 6 - x

Rearranging the equation by collecting like terms, we have the following solution:

x + x = 6 + 6

2x = 12

x = 12/2

x = 6

Substituting the value "6" into the equation, we have the following solution;

x - 6 = 6 - 6

x - 6 = 0

Assuming x = 8, we have the following solution;

x - 6 = 8 - 6

x - 6 = 2

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Complete Question:

Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.

x - 6 = 6 - x

The equation has _____.

A value of x that makes the equation true is ___ which when substituted into the equation and simplified makes the equation turn into ____.

A value of x that makes the equation false is ___ which when substituted into the equation and simplified makes the equation turn into ___.

The following statements are true based on the diagram below

When two or more curves, lines, or edges come together, it is called a vertex (plural: vertices or vertexes) in geometry. As a result of this definition, polygonal and polyhedral corners as well as the intersection of two lines to form an angle are referred to as vertices.

The vertex of an angle is the point at which two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location.

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On solving the provided question, we can say that we can assume that it is a rectangular backyard. Since no dimensions are provided therefore, neither volume nor area can be calculated.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

we can assume that it is a rectangular backyard.

since no dimensions are provided therefore, neither volume nor area can be calculated.

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Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.

We suppose a general triangle, for which:

The lengths and the sine of the angles are proportionally related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The segments in this problem are given as follows:

Hence it can be affirmed that:

BC > AB.

As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.

As for segment AC, we need the measure of angle B, hence nothing can be affirmed.

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The number of times each number divides is 8 divides LCM into 11 times

11 divides into LCM 8 times and 22 divides into LCM 4 times .

What is LCM ?

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.

The LCM of 8 , 11 and 22 is 88

∴ 8 divides into LCM 11 times

11 divides into LCM 8 times

22 divides into LCM 4 times

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Answer:

which one is correct about HRM?

The cost of the order can be expressed as 7x + 5, where x is the number of t-shirts ordered.

In this expression, "7x" represents the cost of the t-shirts, where each shirt is $7 and the number of shirts is represented by "x". The "$5" represents the flat shipping fee for the entire order, which does not change regardless of the number of shirts being ordered.

By adding the cost of the shirts and the shipping fee, we can find the total cost of the order. It's important to understand that the value of "x" must be specified to evaluate the expression.

For example, if 3 shirts are ordered, then x = 3 and the expression becomes:

So the total cost of the order would be $26.

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Answer:

(k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2, or p = 4k^2 - 24k + 180

Step-by-step explanation:

A rectangle has four sides, two sides both have equal width, while the other two have equal length. The perimiter is the total sum of these sides. We can use the following equation to represent the perimiter using the width and length:

p = 2w + 2l

We know that the width equals (k+3)(k+3), so 2w would equal 2(k+3)(k+3). In the form of a quadratic equation, this would equal 2k^2+12k+18.

We also know that the length equals (k-9)(k-9), so 2l would equal 2(k-9)(k-9). As a quadratic equation, this would equal 2k^2-36k+162.

Plugging these values into our equation we get:

p = (k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2.

Or in the form of a quadratic equation:

p = 2k^2 + 12k + 18 + 2k^2 - 36k + 162

=

p = 4k^2 - 24k + 180

Hope this helps!

The perimeter of the rectangle can be calculated using the formula 2(length + width). Substituting the given expressions for length and width, we get 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to the expression 4k^2-24k+180.

The perimeter of a rectangle is calculated by adding the lengths of all its sides. With the width given as (k+3)(k+3) centimeters, and the length as (k-9)(k−9) centimeters, we can substitute these into the formula for the perimeter of a rectangle, which is 2(length + width).

Therefore, the expression representing the perimeter of the rectangle is 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to 2[(k^2+6k+9)+(k^2-18k+81)], which further simplifies to 2[2k^2-12k+90], and ultimately simplifies to 4k^2-24k+180.

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We can conclude that, if --

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that the cost (y) of red grapefruit can be represented by the equation y = 2x, where {x} is the number of pounds of red grapefruit. Also the graph shows the cost of pink grapefruit.

The cost (y) of red grapefruit can be represented by the equation y = 2x. So, we can write that the cost per unit pound of red grape is $2. The graph of the pink grapefruit is not given, but its slope {m} will tell us its costs per pound.

Now, if -

Therefore, we can conclude that, if -

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The probability Richard marker is 11.The probability of anything occurring is known as probability.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

According to question:-

11/1 = 11

11/1 = 11

The probability Richard marker is 11.The probability of anything occurring is known as probability.

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