There are 18 male students and 24 female students in a grade 10 math class. The math teacher
wants to divide the class into groups that will have equal amounts of girls in each
equal amounts of boys in each group. What is the greatest number of groups that the teacher can
make?

Answer:

…………………………………………/,,/,,..,,.,…….

Step-by-step explanation:

Answer:.

Step-by-step explanation: .

Answer:

3rd choice

No, it is NOT a linear function because the variable x is in the denominator. x will be multiplied by y.

when you are interrogating the external validity of a sample, option(b). how was the sample collected? is the most important question to ask.

What is External validity?

The concept of external validity is related to the concept of generalization. It's imperative to keep that in mind. It is important to remember that validity refers to the approximate truth of a proposition, an inference, or a conclusion. In other words, external validity refers to the relative truth of generalizations based on generalizations. The external validity of your study is the degree to which the conclusions are applicable to other people, places, and times.

An external validity threat is an explanation of how a generalization could be flawed. A study you conducted in a particular place, with certain types of people, at a particular time, can be generalized to another context (for instance, another place, with slightly different people, at a slightly different time). External validity can be compromised in three ways: people, places, and times.

Question

When you are interrogating the external validity of a sample, which is the most important question to ask?

a. how many people are in the sample?

b. how was the sample collected?

c. how were the participants measured?

d. how many people are in the population?

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The coordinates to the intercepts of the functions are given as follows:

c - i) Point P: P(-4,0).

c - ii) Point Q: Q(0,2).

d - i) Point P: P(-3,0).

d - ii) Point Q: Q(0,9).

The x-intercept of a function is the value of x at which the function crosses the x-axis, that is, the value of x when y = 0.

For item c, the function is:

2y = x + 4.

Hence the x-intercept is obtained as follows:

x + 4 = 0

x = -4.

Then the coordinates of point P are:

P(-4,0).

For item d, the function is:

y = 3x + 9

Hence the x-intercept is obtained as follows:

3x + 9 = 0

3x = -9

x = -3.

Then the coordinates of point P are:

P(-3,0).

The x-intercept of a function is the value of y at which the function crosses the y-axis, that is, the value of y when x = 0.

For item c, the function is:

2y = x + 4.

Hence the y-intercept is:

2y = 4

y = 2.

The coordinates of Q are:

Q(0,2).

For item d, the function is:

y = 3x + 9.

Hence the y-intercept is:

y = 3(0) + 9 = 9.

The coordinates of Q are:

Q(0,9).

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The probability of a type I error is 0.022.

Given,

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.

The null hypothesis is given as "the individual does not have the disease".

We have to find the probability of type l error if the new blood test is used;

Here,

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

Then, probability;

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)  = 0.022

That is,

The probability of a type I error is 0.022.

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Yes, the triangle with the given side lengths exists because the triangle inequality holds true.

At first, students might think that the lengths of the sides of a triangle can be any three lengths, but that is not so. The triangle inequality says that the length of any side must be less than the sum of the lengths of the other two sides.

We are given a set of three side lengths. The side lengths are 3, 4, and 5. We need to check whether a triangle can be formed using the given three side lengths. We will use the triangle inequality.

The first inequality is 3 + 4 > 5. This inequality holds true because 7 is greater than 5. The second inequality is 4 + 5 > 3. This inequality holds true because 9 is greater than 3. The first inequality is 5 + 3 > 4. This inequality holds true because 8 is greater than 4. The triangle inequality holds true, so a triangle with the given side lengths exists.

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The example demonstrating the commutative property is 12*8 = 8*12, the examples demonstrating associative property are (2+3)+6 = 2+(3+6) and 6*(7*3) = (6*7)*3 and the examples for the distributive property are 5*(2+5) = 10+25 and 4*(3+6) = 12+24.

According to the question,

We have the following information:

1) 5*(2+5) = 10+25

2) (2+3)+6 = 2+(3+6)

3) 4*(3+6) = 12+24

4) 6*(7*3) = (6*7)*3

5) 12*8 = 8*12

We know that commutative property of multiplication states:

a*b = b*a

So, this applies to 5th one.

Associative property of addition:

(a+b)+c = a+(b+c)

Associative property of multiplication:

(a*b)*c = a*(b*c)

Now, this applies to 2nd and 4th one.

Distributive property:

a*(b+c) = a*b+a*c

This applies to 1st and 3rd one.

Hence, the example demonstrating the commutative property is 12*8 = 8*12, the examples demonstrating associative property are (2+3)+6 = 2+(3+6) and 6*(7*3) = (6*7)*3 and the examples for the distributive property are 5*(2+5) = 10+25 and 4*(3+6) = 12+24.

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The equation for the line that runs between the points (8, 4) and (0, 2) has the following slope-intercept form is : y = 1/4 x + 2

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

Here,

A line's equation can be written as y = mx + b in slope-intercept form.

slope = m and y-intercept = b.

You can rewrite the equation in point-slope form as y = mx + b.

Given,

y - 4 = 1/4 (x - 8)

Change the formula to y = mx + b.

So,

y - 4 = 1/4 x - 2

We have to add 4 on both sides,

y - 4 + 4 = 1/4 x - 2 + 4

y = 1/4 x + 2

As a result, the equation of the line passing through the points (8, 4) and (0, 2) has the slope-intercept form is y = 1/4 x + 2 .

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The speed of the output shaft is 182 rpm.

Given:

Gear index i = 0.33

Input speed = 60 rpm.

Let output shaft speed is x.

we know that:

gear index = [tex]\frac{n_{in} }{n_{out} }[/tex]

i = 60/x

0.33 = 60/x

x = 60/0.33

= 60/033/100

= 60*100/33

= 6000/33

= 181.818 ≈ 182 rpm.

Therefore The speed of the output shaft is 182 rpm.

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Answer:

Answer:The total change in the number of bushels she has for sale after 5 days is 83.125 bushelsStep-by-step explanation:The given parameters are;The initial number pf bushels the farmer has = 120 bushelsThe amount of bushels of wheat the farmer sells each day = 16⁵/₈ = 16.625 The number of bushels sold after 5 days = 16.625 × 5 = 83.125 bushelsThe total change in the number of bushels she has for sale after 5 days = The number of bushels sold after 5 daysThe total change in the number of bushels she has for sale after 5 days = 83.125 bushels.

Step-by-step explanation:

Answer:127.5

Step-by-step explanation:

15% of 150 = 22.5

150-22.5=127.5

Answer:

Step-by-step explanation:

The logarithm of 5.238 with solution is  0.71916549409.

= log(5.238)

= log(5238/1000)

= log(5238) - log(1000)

= 3.71916549409 - log([tex]10^{3}[/tex])

= 3.71916549409 - 3log10

= 3.71916549409 - 3

=  0.71916549409.

Therefore the logarithm of 5.238 with solution is 0.71916549409.

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Answer:

see explanation

Step-by-step explanation:

4x + 9 = 16

the error being made is that on dividing both sides by 4 all terms must be divided by 4.

to obtain x + 9 = 4 from 4x + 9 = 16

the term 9 has not been divided by 4

correct solution is

4x + 9 = 16 ( divide through by 4 )

x + [tex]\frac{9}{4}[/tex] = 4 ( each term being divided by 4 )

x + [tex]\frac{9}{4}[/tex] = 4 ( subtract [tex]\frac{9}{4}[/tex] from both sides )

x = 4 - [tex]\frac{9}{4}[/tex] = [tex]\frac{16}{4}[/tex] - [tex]\frac{9}{4}[/tex] = [tex]\frac{7}{4}[/tex] = 1.75

or

4x + 9 = 16 ( subtract 9 from both sides )

4x = 7 ( divide both sides by 4 )

x = [tex]\frac{7}{4}[/tex] = 1.75

A farmer has 180 bushels of wheat to sell at her roadside stand. She sells an average of 14 5/8 bushels each day.

The total change in the number of bushels she has for sale after 5 days can be represented as [tex]\frac{117}{8} X 5[/tex].

Define average.

The average is defined as the mean value, which is equal to the ratio of the sum of the number of values in a given set to the total number of values present in the set.

In plain English, an average is a single number taken as representative of a list of numbers, typically the sum of the numbers divided by how many numbers are in the list. For instance, the average of the digits 2, 3, 4, 7, and 9 is 5.

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The value for expression 1 that is 3z+8 is 29 and for expression 2 that is 8y-x is 12 by substituting the values.

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation.

Here,

For expression 1,

3z+8 where z=7

3*7+8=29

For expression 2,

8y-x where x=20 and y=4

8*4-20=12

By substituting the values, the value for expression 1 ,(3z+8) is 29, and the value for expression 2, (8y-x) is 12.

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Answer:

To make straight commission the better offer, you would have to sell more than $16666.67  per week.

Step-by-step explanation:

Set inequality, assuming the sales amount is x:

Answer:

More than $16,666.67.

Step-by-step explanation:

Define the variables:

Create an equation for each job offer using the defined variables and given information.

Job Offer 1

Straight commission of 5% of sales:

[tex]\implies y=0.05x[/tex]

Job Offer 2

A salary of $500 per week plus 2% of sales:

[tex]\implies y=500+0.02x[/tex]

For Job Offer 1 to be better, set the expression for this offer to be greater than the expression for Job Offer 2 and solve the inequality:

[tex]\implies 0.05x > 500+0.02x[/tex]

[tex]\implies 0.05x-0.02x > 500+0.02x-0.02x[/tex]

[tex]\implies 0.03x > 500[/tex]

[tex]\implies \dfrac{0.03x}{0.03} > \dfrac{500}{0.03}[/tex]

[tex]\implies x > 16666.66666...[/tex]

Therefore, to make straight commission (Job Offer 1) the better offer, you would have to sell more than $16,666.67 (nearest cent) per week.

Answer:

10.6m

Step-by-step explanation:

height of cylinder:

h= V/pie r^2

h= 48/3.14x1.2^2

h=48/3.14x1.44

h=48/4.5216

h=10.61meter

round to the nearest tenth

= 10.6m

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The equation of the situation is t = 400 - 25w. The y-intercept and slope of the equation are 400 and - 25 respectively.

You have 400 turkeys on your farm and you decide to shoot 25 each week. The slope and y-intercept for the situation can be represented as follows;

Using slope intercept form equation,

y = mx + b

where

t = 400 - 25w

where

Therefore, the y-intercept is 400 and the slope is - 25.

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Answer: It does not appear to show a function because the numbers are not multiples of each other

Step-by-step explanation: Hope this helps :-)

Answer: 0.865 to (1dp)

Step-by-step explanation:

Answer:

x=54.5

Step-by-step explanation:

x+62+x+9=180

2x+71=180

2x+71-71=180-71(subtract 71 from both sides)

2x=109

2x/2=109/2(divide both sides by 2)

x=54.5

Answer:

x=54.5

Step-by-step explanation:

1. Combine like terms

x+62+x+9=180

2x+71=180

You can only combine the x and 62 and 9 in this equation.

2. Subtraction property of equality

2x+71=180

    -71 = -71

2x=109

Subtract 71 from both sides to isolate the variable, x.

3. Division property of equality

2x=109

/2     /2

x=54.5

Hope this helps!

The minimum value of the expression is -9

From the question, we have

the expression is 4cosx–3sinx−4.

minimum value of the expression =[tex]c- \sqrt{a^{2} +b^{2} }[/tex]

[tex]=-4- \sqrt{4^{2} +(-3)^{2} }\\=-4-5\\=-9[/tex]

Subtraction:

The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign. For instance, supposing there are nine oranges stacked together (as indicated in the above image), four oranges are taken out and put in a basket, leaving nine – four oranges, or five oranges, in the stack. Therefore, 9 minus 4 equals 5, or the difference between 9 and 4.

Different kinds of numbers can also use subtraction, which is not just applicable to natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.

The minuend, from which we subtract another number, is the first number in a subtraction process.

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We must find p′, q′ in order to calculate the confidence interval; the sample proportion is p′ = 0.842; This is the population proportion's point estimate. Since CL = 0.95 is the requested confidence level, = 1 – CL = 1 – 0.95 = 0.05 (2) (2) = 0.025.

For P, what is the confidence interval at 95 percent?

Since 95% of the area under the curve falls within this interval, the interval (-1.96, 1.96) serves as a 95% confidence interval for the standard normal distribution.

What is the 95 percent confidence interval for the population's proportion of smokers?

Standard Error for Proportion Calculating a 95% Confidence Interval for each group separately is another way to consider whether smokers and nonsmokers have significantly different proportions with wrinkles. For the smokers, we have a certainty time period ± 2(0.0394) or 0.63 ± 0.0788.

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Rewrite [tex]x^4y^2-3x^3y^3[/tex] using a common factor.

A) [tex]3xy(x^3y-x^2y)[/tex]

B) [tex]3xy^2(x2-x^2y)[/tex]

C) [tex]x^2y(xy-3xy^2)[/tex]

D) [tex]x^2y^2(x^2-3xy)[/tex]

option d

Answer:

B 1/4

Step-by-step explanation:

f(x) = y = x⁴ + 5

the inverse function is

y - 5 = x⁴

x = 4th root(y - 5)

now we rename y and x to make it a regular function definition :

g(x) = y = ±4th root(x - 5) = ±(x - 5)^(1/4)

because g(6) = 1 (positive), we have

g(x) = (x - 5)^(1/4)

and since we are using the positive branch, it means also that all the tangent slopes (= g'(x)) are positive.

g'(x) = 1/4 × (x - 5)^(-3/4) × 1 = 1/4 × (x - 5)^(-3/4)

because (x - 5)' = 1

g'(6) = 1/4 × (6 - 5)^(-3/4) = 1/4 × (1/1³)^(1/4) =

= 1/4 × 1^(1/4) = 1/4 × 1 = 1/4

please note, we are using only the positive root result in this case to get a positive result as tangent slope for g(x) as enforced by g(6) = 1.

Answer:

1. 3  donuts

2.$76.90

Step-by-step explanation: