Ken’s seventh grade class plans to collect empty aluminum pop cans as a fund raiser to buy two new books for the school library. The books will cost a total of $50.

a. If $0. 25 per pound is the current price for aluminum at the recycling center, how many pounds of empty cans will the class have to collect? (3 points) Work: Answer __________________

b. Six empty cans weigh about 3. 5 ounces. How many empty cans will the class have to collect to meet their quota of pounds? Round your answer to the nearest whole number. (3 points) Work: Answer __________________

Answer: 12/48 = 25%

Step-by-step explanation: If the unit rate that characterizes my juice reflects its concentration, then there are 36 + 12 = 48 ounces of matter in total. The orange juice mix that we add is 12 ounces of mix, therefore the concentration is 12/48 = 25%.

The only option that is true for the function g is; Option D: g(3) = 18

The function, g, has;

Domain; -1 ≤ x ≤ 4

Range: 0 ≤ g(x) ≤ 18

g(-1) = 2 and g(2) = 8

Then the following properties must hold to be true;

The value(s) of x must be between -1 and 4

The values of g(x) must be between 0 and 18.

We consider the options and state why they are true or otherwise.

Option A: g(5) = 12

When x = 5, g(5) = 12. This contradicts property 1 stated above and as such it is not true.

Option B: g(1) = -2

When x = 1,  g(x) = -2. This contradicts property 2 stated above and as such, it is not true.

Option C: g(2) = 4

When x = 2, g(2) = 4. However by property 4 stated above, g(2)=9. Therefore, we can say that it is not true.

Option D: g(3) = 18

When x =3 means that its domain lies between -1 and 4 and its range  lies between 0 and 18.

Therefore, Option D is true.

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The missing options are;

A) g(5)=12

B) g(1) = -2

C) g(2) = 4

D) g(3) = 18

Answer:

Step-by-step explanation:

X =90

There are 720 ways that personnel director for a corporation fills the positions

It is the ordered arrangement of members belonging to a set with no repeats.

To solve this problem the formula and the permutation procedure we must use is:

nPr = n! / (n-r)!

Where:

Information about the problem:

Applying the permutation formula we have:

nPr = n! / (n-r)!

10P3 = 10! / (10-3)!

10P3 = 10! / 7!

10P3 = 10*9*8*7! / 7!

10P3 = 10*9*8

10P3= 720

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The transformation represented by the figure is (c) translation

From the question, we have the following parameters that can be used in our computation:

The figure

On the figure, we have the following

A figure and its translated image

When a shape is translated to form another, then the transformation is a translation

Hence, the transformation is translation

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The equation for the linear function is  y=3x -5.

A linear function can be represented by a linear equation. The standard form for the linear equation is: y= mx+b , for example, y=10x+6.

The standard for the linear equation( y= mx+b), also it is known as the Slope-Intercept Form.

Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=10 and b=6.

The question gives some points of the linear function, see below.

x    y

1    -2

2   1

3   4

4  7

From the given data you can find the slope by solving the system linear equation.

For example, you can write a system linear equation from the points: (1,-2) and (4,7).

-2=m+b  (1)

7=4m+b    (2)

Multiplying equation 1 by -1, you have

2= -m -b     (1)

7= 4m+b    (2)

Summing the previous equation, you can find the slope (m):

9=3m

m= 9/3

m= 3

If m=3, from equation 2, you can find the coefficient b.

7 = 4m + b

7 = 4*3 +b

7=12 + b

b= 7-12

b= -5

Thus, the standard form for the linear equation represented by the given table is y=3x -5.

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The frequency table has been created in the attachment

Given that 56 respondents did not belong to any clubs, we know that the number of 7th graders who belong to zero clubs is 56.

Given that twice as many 7th graders belonged to one club as no clubs, we can set up the equation:

x = 2 * 56

Given that 10 fewer 7th graders belonged to more than one club than no clubs, we can set up the equation:

y = 56 - 10

Given that twice as many 8th graders belonged to one club as more than one club, we can set up the equation:

z = 2*w

Now we have the following system of equations:

x = 2 * 56

y = 56 - 10

z = 2*w

x+z = 150

y+w = 150

By solving the above system of equations we get:

x = 112

y = 46

z = 112

w = 56

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The linear equation parallel to y=(2/3)x+1 that passes through (3, 0) is:

y = (2/3)*x - 2

A general linear equation can be written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Particularly, two linear equations are parallel only if both equations have the same slope and different y-intercepts.

Then a line parallel to:

y = (2/3)*x + 1

Is of the form:

y = (2/3)*x + b

And we want this line to pass through the point (3, 0), replacing these values we will get:

0 = (2/3)*3 + b

0 = 2 + b

-2 = b

Then the linear equation is:

y = (2/3)*x - 2

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After inspecting the graph, when x=0  y is 6 so the constant is +6 which is Positive

What is polynomial function ?

A polynomial characteristic is a function that includes handiest non-bad integer powers or simplest tremendous integer exponents of a variable in an equation like the quadratic equation, cubic equation, and so forth. for example, 2x+5 is a polynomial that has exponent same to one.

Given ,

The graph is a polynomial function.

This is an odd degree polynomial since end behavior is +infinitely when x is positive and -infinity when x is negative

For an even degree polynomial en behavior will be positive regardless of the sign as a negative number raised to an even power is always positive

The leading coefficient is positive other wise the function would be flipped around the x axis

Inspect the graph. when x=0  y is 6 so the constant is +6 which is Positive

Hence , After inspecting the graph, when x=0  y is 6 so the constant is +6 which is Positive

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The statement that best describes Annie’s attitude toward her upcoming assignment in this excerpt is "she is studious and eager to share her knowledge"

Annie is all about maintaining optimism and hope throughout life's journey, no matter the circumstances.

The young orphan Annie has led a difficult life in the cruel matriarch Miss Agatha Hannigan's anything-but-cheerful orphanage. With a shattered necklace, she stealthily leaves her orphanage and goes in search of her parents, who she hopes would adopt her.

She may be the offspring of a Marleyan and an Eldian liaison, and her parents abandoned her when she was a baby. But after being transported to the Internment Zone, a guy took her up and started to train her as a warrior so that he could live better in Marley.

Therefore, Annie is studious and eager to share her knowledge.

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The probability that a death will result from an accident is 0.105, or 10.5%.

Given:

In foggy conditions, 25% of accidents result in fatalities.

Rain-related accidents result in fatalities in 12.5% of cases.

In sunny weather, 5% of accidents result in fatalities.

To find : The probability that a death will result from an accidents

The likelihood that a death will ensue from an accident

5% of 60%(sunny) (sunny)

25% of 20%(foggy) (foggy)

12.5% of 20%(rainy) (rainy)

Probability = 0.05 x 0.6 x 0.25 x 0.125 x 0.22

Chance is 0.105

Chance is 10.5%.

There is a 10.5% chance that a fatal accident may occur.

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The standard deviation of the household income will be increased by $5,000.

The standard deviation is a measure of variation from the mean that takes spread, dispersion, and spread into account. The standard deviation reveals a "typical" divergence from the mean. It is a popular measure of variability since it retains the original units of measurement from the data set.

standard deviation is increased by 5x/100 = 0.05x

Change in standard deviation = $5000

There is little variety when data points are near to the mean, and there is a lot of variation when they are far from the mean. How much the data differ from the mean is determined by the standard deviation. Standard deviation, which is based on all data, is the most often used metric for measuring dispersion. As a result, the standard deviation's value can be affected by even a slight change in one number.

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A list that shows the possible outcomes of one day one method of travel:

Monday, bus,

Monday, subway,

Monday, taxi,

Tuesday, bus,

Tuesday, subway,

Tuesday, taxi

The correct answer is an option (B)

Let A represents the set of days.

A = {Monday, Tuesday}

And set B represents the method of transportaion/travel.

B = {bus, subway,  taxi }

To find the list of possible outcomes of one day one method of travel we find the product of set A and set B.

We know that for non-empty sets A and B the Cartesian Product is given by AxB = {(a,b) | a ∈ A and b ∈ B}.

It is a set of all ordered pairs (a, b)

For above sets A and B,

A × B = {(Monday, bus), (Monday, subway), (Monday, taxi), (Tuesday, bus), (Tuesday, subway), (Tuesday, taxi)}

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Find the complete question below.

The resultant answer of the given equation 7 – 5p + 3q is 23.

A math formula is a formula that uses the equal sign to represent the equivalence of two expressions.

The meanings of the word equation and its cognates in various languages can vary slightly.

For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.

by inserting the provided values, we must determine the value of the given equation.

The result is obtained by changing the values of p and q in the above equation.

Thus, if p = 1 and q = 7.

So, we get the equation: 7 – 5p + 3q

Calculate as follows:

7 – 5(1) + 3(7)

7 – 5 + 21

28 – 5

23

Therefore, the resultant answer of the given equation 7 – 5p + 3q is 23.

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Correct question:

Evaluate 7-5{p}+3q7−5p+3q7, minus, 5, p, plus, 3, q when p=1p=1p, equals, 1 and q=7q=7q, equal, 7.

The correct answer is Non-existent. If the Earth's spin axis were perpendicular to the Earth's orbital plane, the seasons and seasonal variation would be greatly reduced or eliminated.

This is because the tilt of the Earth's axis (currently at 23.5 degrees) causes the change in the amount of sunlight received at different latitudes during the year, leading to the seasons we experience.

After all, it causes our seasons in the first place. If the Earth's axis were vertical to its orbital airplane, there would be no seasons. Still, there would be minor variations in temperatures and rush throughout each time as Earth moves slightly closer and further down from the sun If the earth and ringed in an upright position around the sun.

If the Earth's spin axis were perpendicular to the ecliptic plane, the Northern and Southern hemispheres would receive roughly the same amount of sunlight throughout the year, and there would be little temperature variation, thus leading to little or no seasonal changes.

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The right response is Nonexistent. Seasons and seasonal fluctuation would be significantly diminished or completely gone if the Earth's spin axis were parallel to its orbital plane.

This is so that the seasons we experience may be attributed to the tilt of the Earth's axis, which is now 23.5 degrees, which affects the quantity of sunlight received at various latitudes throughout the year.

After all, it is the primary cause of our seasons. Seasons wouldn't exist if the Earth's axis were vertical to its orbital plane. If the earth were circled in an upright position around the sun, there would still be modest fluctuations in temperature and rush throughout each period as Earth travels a little closer to and further away from the sun.

The Northern and Southern hemispheres would get nearly the same amount of sunshine throughout the year, and there would be no temperature difference, which would result in little to no seasonal variations if the Earth's spin axis were perpendicular to the ecliptic plane.

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keeping in mind that since a year is 12 months, then 4 months is really 4/12 of a year, so

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 20\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ 20 = (1000)(\frac{r}{100})(\frac{1}{3})\implies 20=\cfrac{1000r}{300} \implies 6000=1000r \\\\\\ \cfrac{6000}{1000}=r\implies \stackrel{\%}{6}=r[/tex]

The system of equations are:

15 + x = y

13 + 2x = y

The weight of the package is 2 pounds.

The delivery cost for both services is 17$.

Here is a system of equations you can use to represent the cost of the two courier services:

First courier: 15 + x = y

Second courier: 13 + 2x = y

Where x is the weight of the package in pounds and y is the total cost of delivery.

We know that the two courier services are equivalent in terms of cost, so we can set the two equations equal to each other:

15 + x = 13 + 2x

then we can subtract 15 from both sides

x = 13 + 2x -15

x = -2 + 2x

then we can subtract x from both sides

-x = -2

then we can divide both sides by -1

x = 2

The package weighs 2 pounds, and the delivery cost for both services is 15 + 2 = 17$.

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Answer:

x=1, y=4

Step-by-step explanation:

5x+y=9

10x-7y=-18

(Multiply top equation by -2)

-10x-2y=-18

10x-7y=-18

(Add)

-9y=-36

(Divide -36 by -9)

y=4

(Substitute y(4) into the top equation)

5x+4=9

(Subtract 4)

5x=5

(Divide 5)

x=1

Answer: x=1 , y=4

Step-by-step explanation:

5x+y =9          y=9-5x

10x - 7y = -18

10x-7(9-5x)=-18                   y=9-5x

10x-63+35x=-18                  y=9-5(1)

45x-63=-18                          y=4

45x=-18+63

45x=45

x=1

The value of 0.6 is greater than the value of 0.39 because; C 0.6 is greater than 0.39 because 6 tenths is greater than 9 hundredths.

When we are talking about decimals, the left hand side before the decimal are referred to as whole numbers while the first digit after the decimal represents the tenths place, the next digit after the tenths place  represents the hundredths place, the next digit after the hundredths place represents the thousandths place and so on.

Now, we are given two decimals 0.6 and 0.39.

We see clearly that 0.6 has a greater tenths digit than the hundredths digit in 0.39. This is seen as;

0.6 = 6/10 while 0.39 = 39/100

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From the triangle KLM inside the circle, the value of KM is calculated. And, the value is 1.2079.

A triangle is a polygon made up of three vertices, three angles, and three sides. First, draw a circle with a midpoint represented by O. Then, draw a triangle KLM inside a circle. Now, construct the line segments KO, MO, and LO because they form the circle's radius.

Given that KL = LM. Since two sides of the triangle KLM is equal, it is an isosceles triangle. Also, ∠K=∠M=17°. The total angle of this triangle is 180°. Then, ∠L=180°-17°-17°=146°.

Half the angle L is 73°. Then, ∠KLO=∠MLO=73°.

Consider triangle KLO, this triangle is also isosceles because KO = LO. Then, ∠KLO=∠OKL=73°.

Now, ∠KOL is calculated as follows from the triangle KLO,

[tex]\begin{aligned}\angle KOL&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]

Similarly, consider triangle MLO, this triangle is also isosceles because LO=MO. Then, ∠MLO=∠OML=73°.

Now, ∠LOM is calculated as follows from the triangle MLO,

[tex]\begin{aligned}\angle LOM&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]

Then,

[tex]\begin{aligned}\angle KOM&=\angle KOL+\angle LOM\\&=34^{\circ}+34^{\circ}\\&=68^{\circ}\end{aligned}[/tex]

Using, the cosine law of the triangle KOM, we get,

[tex]\begin{aligned}(KM)^2&=1.08^2+1.08^2-2(1.08)(1.08)\cos 68^{\circ}\\&=2.3328-2.3328(\cos 68^{\circ})\\&=2.3328(1-\cos 68^{\circ})\\&=2.3328(0.6254)\\&=1.4589\\KM&=\sqrt{1.4589}\\&=1.2079\end{aligned}[/tex]

Therefore, the required answer is 1.2079.

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Answer:

See below

Step-by-step explanation:

1/2 + 1/3 w = 1/6     subtract 1/2 from both sides of the equation

1/3 w = - 2/6           multiply both sides by 3

w = -1

Broderick needs $610.00 in his account to cover his checks.

We know that the balance Boderick has is $420.

First, we will calculate the total amount of the 6 deposits made by Broderick each of $35.50 deposit as follows -

$35.50 x 6 = $213.00

Hence, the total amount of the 6 deposits made by Broderick is $213.00

Next, we will calculate the total amount of the 4 checks he needs to write-

$310.75 x 4 = $1243.00

Hence, the total amount of the 4 checks that Broderick needs to write is $1243.00

Now we will find the final balance of Broderick's account after all the deposits and check withdrawals. We can do this by adding the total amount of the deposits to his initial balance and subtracting the total amount of the checks as follows-

$420.00 + $213.00 - $1243.00 = -$610.00

Thus, Broderick needs $610.00 in his account to cover his checks.

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The complete question is -

Broderick had $420 in his checking account. He made 6 deposits of $35.50 each. He needs to write 4 checks for $310.75 each. How much money does Boderick need to add to his account to cover his checks? Show your work.

We would need to add 8 more sets of 3 candies to 23 candies in order to have the same amount as Casey.

To find this, we can divide the total amount of candy Johnny has (23) by the amount of candy Casey has (3) and round up to the nearest whole number:

(23) / (3) = 7.666...

Since we can't have a fraction of a set of candies, we must round up to the nearest whole number, which is 8.

So, to have the same amount of candy as Casey, we would need to add 8 more sets of 3 candies to Johnny's 23 candies.

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Answer: x=10

Step-by-step explanation:

x is an unknown number trying to figure out what number equals 20? You subtract 10 from 20 to figure out x.

Samuel pay 5.81 for the 3 bottles of juice.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Samuel buys 3 bottles of juice that each have an original price of 2.80.

And, He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%.

Here, The original cost of 3 bottles of juice = 3 × 2.80

                                                                   = 8.40

Now, He uses a coupon for 35% off.

Hence, The off price = 35% of 8.40

                                = 35/100 × 8.40

                                = 2.94

So, The amount of 3 bottles of juice = 8.40 - 2.94

                                                        = 5.46

And, He is changed sales tax at a rate of 6.5%.

Thus, The sales tax on bottles = 6.5% of 5.46

                                               = 6.5/100 × 5.46

                                               = 0.35

Thus, The actual amount of 3 bottles of juice = 5.46 + 0.35

                                                                     = 5.81

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Answer for the conveyer belt moves at 100ft/min from bales of hay to barn loft is given by :

1. Seconds taken by conveyer belt is 60 seconds.

2. Hypotenuse represents the conveyer belt in right triangle.

3. Distance is other information to calculate time.

4. 1 minute = 60 seconds.

Rate at which conveyer belts moves = 100ft/min

⇒1 minute = 100ft

⇒60seconds = 100 ft

1. Seconds taken by bale of hay to move from ground to barn loft is 60 seconds.

2. Conveyer felt represent the hypotenuse of the right triangle.

Feet represents the height , and minutes (time) represents the base.

3. Speed is given to us , to calculate time we should have distance.

4. Relation between minutes and seconds is given by:

1 minute = 60 seconds.

Therefore, for the given conveyer belt moves with 100ft/min answer of the following question are:

1. Seconds taken by moving bale of hay to barn loft is 60 seconds.

2. Conveyer belt represent hypotenuse.

3. To calculate time we need distance apart from speed.

4. One minute is equal to sixty seconds.

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A geometric sequence begins with 72, 36, 18, 9, is Of(n) is 72(2)+1.

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Answer:

f(n) = 72(0.5)n−1

Step-by-step explanation:

Got right.

You can "find algebraically" if a function is even, odd, or neither by taking it, substituting -x for x, simplifying it, and then comparing the results to what you had initially.

The function is even if it is exactly the same as what you started with (that is, if f(-x) = f (x), with all the signs remaining the same. The function is odd if it is exactly the opposite of what you started with (that is, if f(-x) = -f(x), with all the signs switched.

The function is neither even nor odd if the outcome is neither exactly the same nor exactly the opposite (that is, neither having all the same words but with all the signs reversed).

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The equation of the line in slope intercept form is y = -2.65x + 25.

The x-intercept means when the gift card has a balance of zero dollars.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore. let's find the slope of the line using (2, 19.7) and (4, 14.4).

Hence,

m = slope = 14.4 - 19.7 / 4 - 2

m = - 5.3 / 2

m = - 2.65

Therefore, let's find the y-intercept using (2, 19.7).

y = -2.65x + b

19.7 = -2.65(2) + b

b = 19.7 + 5.3

b = 25

Therefore, the equation of the line is y = -2.65x + 25.

The x-intercept is the value of x when y = 0.

Hence,

0 = -2.65x + 25

-25 = -2.65x

x = -25 / -2.65

x = 9.4

The x-intercept means the gift card has zero balance. At this point the medium cup of coffee is 9.4 .

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The probability that tails will turn up and that he will choose a red card is 1/6.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The probability of choosing a tail is 0.5.

The probability of choosing ref card is 1/3.

Therefore, the probability will be:

= 1/2 × 1/3

= 1/6

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