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2 years ago

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Kari bought 3 boxes of cookies to share with a book club. Each box contains 12 cookies. The expression represents the number of

cookies that each person, p, can have if the cookies are divided equally. Which evaluations of the expression are correct? Select three options.

2 answers:

ivanzaharov [21]2 years ago

7 0

<u>ANSWER:</u>

Kari bought 3 boxes of cookies to share. The algebraic expression is $\frac{36}{x}$

<u>Solution:</u>

Given, Kari bought 3 boxes of cookies to share with a book club.

Each box contains 12 cookies.

So, in total we have 3 x 12 cookies = 36 cookies.

Now, we have to find how many cookies can each person p will get.

Let, the total number of persons be x.

Then, after equally sharing the cookies,

$\text { Number of cookies with each person }=\frac{\text {number } of \text { cookies available.}}{\text {total number of persons}}$

$=\frac{36}{x} \text { cookies. }$

Hence, the algebraic expression is $\frac{36}{x}$

mrs_skeptik [129]2 years ago

6 0

Answer:

If p = 7, then each person would get 5 cookies, with 1 cookie left over.

If p = 10, then each person would get 3 cookies, with 6 cookies left over.

If p = 11, then each person would get 3 cookies, with 3 cookies left over.

B

D

E

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in a random sample of 200 people, 154 said that they watched educational television. fine the 90% confidence interval of the tru

melisa1 [442]

Answer:

[0.7210,0.8189] = [72.10%, 81.89%]

Step-by-step explanation:

The sample size is

n = 200

the proportion is

p = 154/200 = 0.77

<em>Since both np ≥ 10 and n(1-p) ≥ 10 </em>

<em>We can approximate this discrete binomial distribution with the continuous Normal distribution. As the sample size is large enough, not applying the continuity correction factor makes no significant difference. </em>

The approximation would be to a Normal curve with this parameters:

<em>Mean </em>

p = 0.77

<em>Standard deviation </em>

$\bf s=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.77*0.23}{200}}=0.0298$

The 90% confidence interval for the proportion would be then

$\bf [0.77-z^*0.0298, 0.77+z^*0.0298]$

where $\bf z^*$ is the 10% critical value for the Normal N(0,1) distribution , this is a value such that the area under the N(0,1) curve outside the interval $\bf [-z^*,z^*]$ is 10%=0.1

We can either use a table, a calculator or a spreadsheet to get this value.

In Excel or OpenOffice Calc we use the function

<em>NORMSINV(0.95) and we get a value of 1.645 </em>

The 90% confidence interval for the proportion is then

$\bf [0.77-1.645^*0.0298, 0.77+1.645^*0.0298]=[0.7210,0.8189]$

This means there is a 90% probability that the proportion of people who watch educational television is between 72.10% and 81.89%

If the television company wanted to publicize the proportion of viewers, do you think it should use the 90% confidence interval?

Yes, I do.

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2 years ago

Regular pentagonal tiles and triangular tiles are arranged in the pattern shown. The pentagonal tiles are all the same size and

professor190 [17]

First of all you have to find the missing measurements. The actual measurements for the angles in the hexagon are not given, but they give you an expression. You have to solve for x first so that you can plug it in and find the angle measurement. You have to equal the two sides that are given to you like this: 20x+48=33x+9. You solve for x and then plug it into each angle measurement. This should give you 108. Since it is a regular hexagon all of the sides are equal. If you look at the angle at the top of the hexagon you'll see two triangles and the angle. Since it lies on a straight line, it is all equal to 180. You already have the angle measurement of the hexagon and are missing the triangles. So 180-108=72. 72 is the missing part of the angle. You divide this by 2 in order to find each triangle angle measurements. the answer is 36 degrees.

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2 years ago

Which expression has the same GCF as 15x2 - 21x?

Mice21 [21]

Answer:

$15x^2 +21 x$

Step-by-step explanation:

We have the following expression:

$15x^2 -21 x$

We can find the GCF with the following steps.

1. Find the GCF for the numerical part 15 and -21

The factors for 15 are : 1,3,5,15

The factors for -21 are -21,-7,-3,-1,1,3,7,21

And the common factors are 1,3

The GCF for the numerical part is 3*1 = 3

2. Find the GCF for the variable

The factors of x^2 are : x*x

The factors of x are: x

The common factors are x for this case, so then the GCF for the variable part is x

3. Multiply the two results from steps 1 and 2

GCf= 3*x = 3x

If we consider the new expression:

$15x^2 +21x$

We can find the GCF with the following steps.

1. Find the GCF for the numerical part 15 and -21

The factors for 15 are : 1,3,5,15

The factors for -21 are 1,3,7,21

And the common factors are 1,3

The GCF for the numerical part is 3*1 = 3

2. Find the GCF for the variable

The factors of x^2 are : x*x

The factors of x are: x

The common factors are x for this case, so then the GCF for the variable part is x

3. Multiply the two results from steps 1 and 2

GCf= 3*x = 3x

And as we can see both GCF are equal. So then we satisfy the condition required.

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2 years ago

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During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Fi

Afina-wow [57]

The second question:

Consider the division expression $7\frac{1}{2} / 2$ . Select all multiplication equations that correspond to this division expression.

$2 * ? = 7\frac{1}{2}$ $7\frac{1}{2} * ?= 2$ $? * 2 = 7\frac{1}{2}$

$2* 7\frac{1}{2} = ?$ $? * 7\frac{1}{2} = 2$

Answer:

1. See Explanation

2. $2 * ? = 7\frac{1}{2}$ and $? * 2 = 7\frac{1}{2}$

Step-by-step explanation:

Solving (a):

Given

$Students = 60$

$Group = Equal\ Sized$

Required

Interpret $\frac{60}{5}$ in 2 ways

<u>Interpretation 1:</u> Number of groups if there are 5 students in each

<u>Interpretation 2:</u> Number of students in each group if there are 5 groups

<u>Solving the quotient</u>

$Quotient = \frac{60}{5}$

$Quotient = 12$

<u>For Interpretation 1:</u>

The quotient means: 12 groups

<u>For Interpretation 2:</u>

The quotient means: 12 students

Solving (b):

Given

$7\frac{1}{2} / 2$

Required

Select all equivalent multiplication equations

Let ? be the quotient of t $7\frac{1}{2} / 2$

So, we have:

$7\frac{1}{2}/2 = ?$

Multiply through by 2

$2 * 7\frac{1}{2}/2 = ? * 2$

$7\frac{1}{2} = ? * 2$

Rewrite as:

$? * 2 = 7\frac{1}{2}$ --- This is 1 equivalent expression

Apply commutative law of addition:

$2 * ? = 7\frac{1}{2}$ --- This is another equivalent expression

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blsea [12.9K]

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1 year ago

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