Jennifer has 25 coins with a total value of $4.25. The coins are quarters and nickels. How many of each does she have?

Answer:

1/4 cups of milk and 1 1/3 Tbsp of butter.

Step-by-step explanation:

Milk : 3/4 multiplied by 1/3 = 3/12 = 1/4
Butter : 4 multiplied by 1/3 = 4/3 = 1 1/3

The expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰

From the question, we are to determine the expression that represents the number of reams of paper the company produced during the second year

From the given information,

During the first year of operation,

The company produced 8.4 × 10⁹ reams of paper

And

During the second year,

the company produced 5.6 times the number of reams of paper that it produced during the first year.

Thus,

The number of reams of paper the company produced during the second year = 5.6 × 8.4 × 10⁹ reams of paper

The number of reams of paper the company produced during the second year = 47.04 × 10⁹ reams of paper

= 4.704 × 10¹ × 10⁹ reams of paper

= 4.704 × 10¹⁰ reams of paper

Hence, the expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰

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Answer: Rational, Irrational, Rational, Natural, Natural, Integer

Step-by-step explanation:

-4.2 is a rational number as it can be converted into a fraction

3√5 is an irrational number as it can't be converted into a fraction

5/3 is a rational number as it is a fraction

9 is a natural number as it is a positive whole number

√16 is a natural number as despite the square root, √16 is 4 which is a natural number

-8/2 is an integer as -8/2 is -4 which is a negative whole number

Answer:

(3+3) x (3+1)

Step-by-step explanation:

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

Answer:

d 1-12-3-5 is the answer

Due to length restrictions, we kindly invite to read the explanation of this question and the image of parabola on Cartesian plane attached below to see the results.

To graph a parabola, we shall follow the following procedure:

By following all the steps, we generate the curve with the help of a graphing tool.

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the minimum amortization is given as 20300 dollars

We have the value of A to be $3235000

while we have the value of B to be $3474000

Of these two values the greatest or the highest is that of the option B.

Next we have to find the corridor value using 10 percent

0.10 * 3474000

= 347400

$505740 -  347400

= 158340

The number of years = 7.8

minimum amortization = 158340/7.8

= 20300 dollars

Hence the minimum amortization is given as 20300 dollars

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Answer:

A)  See attached for graph.

B)  (-3, 0)  (0, 0)  (18, 0)

C)   (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}[/tex]

Therefore, the function has two definitions:

When graphing piecewise functions:

First piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies g(3)=(3)^3-9(3)=0 \implies (3,0)[/tex]

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)[/tex]

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the first piece of the function to zero and solve for x:

[tex]\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}[/tex]

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the second piece to zero and solve for x:

[tex]\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}[/tex]

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation:  (-3, 0) ∪ [3, 18)

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Answer:

4900

Step-by-step explanation:

When rounding a number such as 4928 to the nearest hundred, we use the following rules:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

In this case, Rule B applies and 4928 rounded to the nearest hundred is:

4900

Answer:

Step-by-step explanation:

4,928, look at the last two numbers 28 if they are above 50 you round up, if below 50 round down,

The answer is 4,900

The equivalent expression of -14 - 6 is -14 - (+6)

Equivalent expressions are expressions that have the same value when evaluated

The expression is given as:

-14 - 6

Put the terms of the expression in brackets

-14 - (6)

Rewrite 6 as +6

-14 - (+6)

Hence, the equivalent expression of -14 - 6 is -14 - (+6)

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Answer:

34.51ft³

Step-by-step explanation:

The formula to find the volume of a cylinder is :

V = π r² h

Here,

r ⇒ radius ⇒ 1.3ft

h ⇒ height ⇒ 6.5ft

Let us find now.

V = π r² h

V = π × ( 1.3 )² × 6.5

V = π × 1.69 × 6.5

V = 34.51ft³

According to the direct inspection, we conclude that the best approximation of the two solutions to the system of quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)

Herein we have two parabolae, that is, polynomials of the form a · x² + b · x + c, that pass through each other twice according to the image attached to this question. We need to estimate the location of the points by visual inspection on the Cartesian plane.

According to the direct inspection, we conclude that the best approximation of the two solutions, that is, the point where the two parabolae intercepts each other, to the system of two quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)

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Answer:

123 soda and 87 hot dogs

Step-by-step explanation:

Let s = # soda and h = # hot dogs

s +  h = 210         s = h + 36  Substitute the h + 36 for s into the first equation

s + h = 210

(h + 36) + h = 210  

h + 36 + h = 210  Combine the h's

2h + 36 = 210  Subtract 36 from both sides

2h = 174  Divide both sides by 2

h = 87  This is the number of hot dogs.  Substitute this into either equation above to find the sodas.        

s + h = 210

s + 87 = 210

s = 123  

OR

s = h + 36

s = 87 + 36

s = 123

The value of f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].

Given a function f(x)=4-2x+6[tex]x^{2}[/tex].

We are told to find out the value of f(a), f(a+h) and [f(a+h)-f(a)]/hwhere h≠0.

Function is like a relationship between two or more variables expressed in equal to form.The value which we entered in the function is known as domain and the value which we get after entering the values is known as codomain or range.

f(a)=4-2a+6[tex]a^{2}[/tex] (By just putting x=a).

f(a+h)==[tex]4-2(a+h)+6(a+h)^{2}[/tex]

=4-2a-2h+6([tex]a^{2} +h^{2} +2ah[/tex])

=4-2a-2h+6[tex]a^{2} +6h^{2} +12ah[/tex]

=[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]

[f(a+h)-f(a)]/h=[[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]-(4-2a+6[tex]a^{2}[/tex] )]/h

=[tex](6a^{2} +6h^{2} -2a-2h+12ah)/h[/tex]

=[tex](6h^{2} -2h+12ah)/h[/tex]

=6h+12a-2.

Hence the value of function f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].

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Using proportions, it is found that the correct option for when the machine will stop running the algorithm is:

B) 9 P.M. on Saturday.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The algorithm runs for 972 hours. Each day has 24 hours, hence we apply the proportion to find the number of days as follows:

972/24 = 40.5 days.

The remainder of the division of 40.5 by 7, as a week has 7 days, is of 5.5, which means that the code will finish running 5.5 days after the 9 A. M. Monday, that is at 9 P. M. on a Saturday, which means that option B is correct.

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Using the z-distribution, it is found that since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.

At the null hypothesis, it is tested if the proportion is still of 44%, that is:

[tex]H_0: p = 0.44[/tex]

At the alternative hypothesis, it is tested if the proportion is now different of 44%, that is:

[tex]H_1: p \neq 0.44[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]p = 0.44, n = 1360, \overline{p} = \frac{626}{1360} = 0.4603[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.4603 - 0.44}{\sqrt{\frac{0.44(0.56)}{1360}}}[/tex]

z = 1.51

Using a z-distribution calculator, for a two-tailed test, as we are testing if the proportion is different of a value, with z = 1.51, the p-value is of 0.1310.

Since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.

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Step-by-step explanation:

1.

the expected sample mean is always the general mean : 168.5 pounds.

2.

the SD of a sample is the general SD / sqrt(sample size).

in our case

the sample SD = 68/sqrt(150) = 5.55217675...

3.

if we are looking for only the probability that any single woman is below 160 pounds, we would use the normal z calculation :

z = (x - mean)/SD = (160 - 168.5)/68 = -8.5/68

but we have here the question about the probability of the mean value of a whole sample of 150 women.

so, we need to adapt the z-calculation by the principle of 2) for the SD of a sample :

z = (x - mean)/(SD × sqrt(sample size)) =

= (160 - 168.5)/(68 × sqrt(150)) = -8.5/(68×sqrt(150)) =

= -0.010206207 ≈ -0.01

that gives us in the z-table the p-value 0.49601

this 0.49601 is the probability that a sample of 150 women has a mean value of below 160 pounds.

4.

similar to 3.

the z value we are looking for

z = (175 - 168.5)/(68 × sqrt(150)) = 6.5/(68 × sqrt(150)) =

= 0.007804747... ≈ 0.01

that gives us the p-value 0.50399.

that would be the probability of a sample mean of 175 or below.

to get above 175 we need to get the other side of the bell-curve :

1 - 0.50399 = 0.49601

so, this case has about the same probability as 3.

5.

as 3), just with the sqrt(200) instead of the sqrt(150).

z = -8.5/(68 × sqrt(200)) = -0.008838835... ≈ 0.01

so, the probability is still about the same as in 3) :

0.49601

6.

as 4) just with sqrt(200).

z = 6.5/(68 × sqrt(200)) = 0.006759109... ≈ 0.01

so, the probability is still about the same as for 4) :

0.49601

The answers are :

1) The expected mean for a sample of 150 women is 168.5 pounds.

2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.

3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.

4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.

5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.

6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.

What is probability ?

Probability is a measure of the likelihood of event to occur. The probability of all the events in a sample space adds up to 1.

1)

We know that the expected mean of a sample is always equal to general mean.

As per the question, mean weight is 168.5 pounds.

This implies :

The expected mean for a sample of 150 women is :

= 168.5 pounds

2)

The standard deviation (SD) of the mean for a sample of 150 women is :

= 68 / (√150)

= 5.55

3)

The probability of 150 women having a sample mean below 160 pounds will be represented by z and will be :

z = ( x - mean) / ( SD × (√sample size))

= (160 - 168.5) / (68 × √150)

= 0.01

If we use the z table then the probability will be :

= 0.49601

4)

Similarly as part 3 :

z = (175 - 168.5) / (68 × √150)

z  = 0.01 (approximately)

The probability of 150 women having a sample mean below 175 pounds will be :

= 0.50399

And the probability of 150 women having a sample mean above 175 pounds will be :

= 1 - 0.50399

= 0.49601

5)

Here , we have to find probability of 200 women , so 150 in formula of z in 3rd part will be replaced by 200.

i.e.,

z = (160 - 168.5) / (68 × √200)

z = 0.01 ( approximately)

and probability will be :

= 0.49601

6)

Here , we have to find probability of 200 women , so 150 in formula of z in 4th part will be replaced by 200.

z = (175 - 168.5) / (68 × √200)

z = 0.01

And probability equal to :

= 0.49601

Therefore , the answers are :

1) The expected mean for a sample of 150 women is 168.5 pounds.

2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.

3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.

4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.

5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.

6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.

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If the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.

Given sample size of 1488, percentage of those polled own a home be 69% and confidence level be 99%.

We are required to find the approximate margin of error.

Margin of error is the difference between calculated values and real values.

n=1488

p=0.69

Margin of error=z*[tex]\sqrt{p(1-p)/n}[/tex]

Z score when confidence level is 99%=2.576.

Margin of error=2.576*[tex]\sqrt{0.69(1-0.69)/1488}[/tex]

=2.576*[tex]\sqrt{(0.69*0.31)/1488}[/tex]

=2.576*[tex]\sqrt{0.2139/1488}[/tex]

=2.576*[tex]\sqrt{0.0001437}[/tex]

=2.576*0.01198

=0.03088

Hence if the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.

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Answer:

0.031

Step-by-step explanation:

Plato/Edmentum

Answer:

x-1 gave ggs is it correct

The solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)

From the question, we are to determine the solution to the given system of equations

The given system of equation is

y = 2/3 x + 3     ----------- (1)

x= -2                 ----------- (2)

The value of x has been given in the second equation of the system of equations.

Now, we will determine the value of y

From the second equation, we have that

x = -2

Substitute the value of x into the first equation,

y = 2/3 x + 3

y = 2/3 (-2) + 3

y = -4/3  + 3

y = 5/3

Hence, the solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)

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Answer:

160

Step-by-step explanation:

22 + 18 = 25 percent

40 = 25 percent

100 / 25 = 4

40 x 4 = 160.

Answer:

x = 1.086

Step-by-step explanation:

Formula

6^x = 7                     Take the log of both sides.

Solution

log 6^x = log 7         Bring the power down You are now dealing with log 6

x * log 6 = log 7        Divide by log 6

x = log 7/log 6

x = .8451 / .7782       Divide

Answer

x = 1.086

Using the sample space and probability concepts, we have that:

A) All the possibilities for the sample space are: {{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.

B) The probability is: 7/8.

C) The probability is: 1/2.

D) The probability is: 1/4.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The sample space is the set that contains all possible outcomes, hence in this problem, considering G for girl and B for boy, it is given by:

{{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.

For item B, 7 outcomes have at most two boys, hence the probability is 7/8.

For item C, 4 outcomes have at least two girls, hence the probability is 4/8 = 1/2.

For item D, 2 outcomes have all the babies with the same sex, hence the probability is 2/8 = 1/4.

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Combining the terms into one fraction, we have

[tex]kx + b - \dfrac{x^3+1}{x^2+1} = \dfrac{(k-1)x^3 + bx^2 + kx + b - 1}{x^2+1}[/tex]

If this converges to 0 as [tex]x\to\infty[/tex], then the degree of the numerator must be smaller than the degree of the denominator.

To ensure this, take [tex]k=1[/tex] and [tex]b=0[/tex]. This eliminates the cubic and quadratic terms in the numerator, and we do have

[tex]\displaystyle \lim_{x\to\infty} \frac{x - 1}{x^2 + 1} = \lim_{x\to\infty} \frac{\frac1x - \frac1{x^2}}{1 + \frac1{x^2}} = 0[/tex]

Alternatively, we can compute the quotient and remainder of the rational expression.

[tex]\dfrac{x^3+1}{x^2+1} = x - \dfrac{x-1}{x^2+1}[/tex]

Then in the limit, we have

[tex]\displaystyle \lim_{x\to\infty} \left(kx + b - x + \frac{x-1}{x^2+1}\right) = (k-1) \lim_{x\to\infty} x + b = 0[/tex]

Both terms on the left vanish if [tex]k=1[/tex] and [tex]b=0[/tex].

Answer: C. 5.4 Blocks

Step-by-step explanation:

Given information

5 bags = 3 blocks

Set variable

Let x be the number of blocks

Constructure proportional equation

[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]

Cross multiply the fraction

[tex](3)~*~(9)~=~(5)~*~(x)[/tex]

[tex]27~=~5x[/tex]

Divide 5 on both sides

[tex]27~/~5~=~5x~/~5[/tex]

[tex]\Large\boxed{x=5.4~blocks}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

oc

Step-by-step explanation:

5 times .6 equals 3

9 times .6 equals 5.4

Carey's weekly salary before tax is  $1300.

The mathematical operation that would be used to determine the required value is division. Division is a mathematical operation that entails grouping a number into equal parts using another number.

In order to determine Carey's weekly salary before tax, divide the yearly salary by the number of weeks in a year.

Carey's weekly salary before tax = yearly salary / number of weeks in a year

$67,600 / 52 = $1300

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Answer:

10 mph

Step-by-step explanation:

speed of boat in still water = x

speed of current = 5

speed of boat with current (downstream) = x + 5

speed of boat against current (upstream) = x - 5

distance downstream = 9

distance upstream = 3

time = t

speed = distance/time

distance = speed × time

downstream:

9 = (x + 5)t

upstream:

3 = (x - 5)t

9 = xt + 5t

3 = xt - 5t

9 = xt + 5t

-3 = -xt + 5t

-----------------

6 = 10t

t = 0.6

9 = (x + 5)0.6

15 = x + 5

x = 10

The five-number summary is:

Minimum: 4

Quartile Q1: 11.25

Median: 12.5

Quartile Q3: 16.5

Maximum: 20

The box plot is attached below.

The five-number summary of a data that is displayed on a box plot include: minimum and maximum values, lower and upper quartiles, and the median.

Given the data, 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19, the five-number summary is:

Minimum: 4

Quartile Q1: 11.25

Median: 12.5

Quartile Q3: 16.5

Maximum: 20

There are no outliers. Thus, the box plot that represents the five-number summary is shown in the image attached below.

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Answer: it is correct i got it from edmentum

Step-by-step explanation: