You have one type of candy that sells for $2.00/lb and another type of candy that sells for $8.90/lb. You would like to have 55.2 lbs of a candy mixture that sells for $2.50/lb. How much of each candy will you need to obtain the desired mixture?

You will need ___ lbs of the cheaper candy
and ____ lbs of the expensive candy.

Answer:

y = [tex]\frac{1}{8}[/tex]x

Step-by-step explanation:

You need to find the unit rate.  In a proportional relationship,  you can find this by taking any point on the line and putting it the form y/x

Look at point (16,2)  y/x = 2/16 = 1/8

Answer:

Lucas 71 inches

Tamika 66 inches

Answer:

1/8 or 0.125

Step-by-step explanation:

1/2×1/8

multiply the numerators 1×1=1 and multiply the denominators 2×4=8

Final answer =1/8 or 0.125

The image of the polygon after a reflection in the line y=x is having vertices at A'(-3, 6), B'(-2, 1) and C'(1, 4) as shown in the diagram attached.

A reflection is a sort of transformation that creates a new shape by flipping a shape, called the preimage, across a line, called the line of reflection (called the image). You may imagine what would occur if the form were turned over the line to graph a reflection.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image).

You can picture what would happen if you flipped the form over the line in order to graph a reflection.

If a point A(x, y) is reflected about the line y = x,

the new point would be at A'(y, x)

Given the polygon with vertices at A(6, -3), B(1, -2) and C(4, 1).

The image of the polygon after a reflection in the line y=x has vertices at:

A'(-3, 6), B'(-2, 1) and C'(1, 4)

The image of the polygon is attached.

Therefore, according to the attached graphic, the vertices of the polygon's image after a reflection in the line y=x are located at A'(-3, 6), B'(-2, 1), and C'(1, 4).

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Answer:

No solution

Step-by-step explanation:

The absolute value function outputs non-negative values.

Answer:  No solutions

This is because absolute value is never negative. It represents distance, and negative distance does not make sense.

The smallest possible output of |x+5| is zero.

Answer:

25

Step-by-step explanation:

This raffle's expected value per ticket is $ 0.25.

Given that 5,000 tickets are sold at $1 apiece for a charity raffle, and tickets are to be picked at random, the following monetary prizes will be awarded.

To estimate the expected value of this raffle if you buy 1 ticket, apply the following calculation: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5.

⇒ (500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X

⇒ (500 + 600 + 50 + 100) / 5000 = X

⇒ 1250/5000 = X

Apply the division operation, and we get

⇒ 0.25 = X

Therefore, this raffle's expected value per ticket is $ 0.25.

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When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.

From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.

It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.

Therefore, the number of flags is 40.

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Answer: 17 packs

Step-by-step explanation: 16 packs of 10 equals 160 beads, and one pack of 5 will give you 164 beads with 1 left over.

Answer: -48

Step-by-step explanation:

-18-30 = -48

let's take it from the basic of one dolla!, how long will it take for $1 to become $2, namely double, at 10.5%?

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ t=years \end{cases} \\\\\\ 2=1e^{0.105\cdot t} \implies \log_e(2)=\log_e(e^{0.105t})\implies \log_e(2)=0.105t \\\\\\ \ln(2)=0.105t\implies \cfrac{\ln(2)}{0.105}=t\implies 6.6\approx t\qquad \textit{about 6 years and 219 days}[/tex]

Answer:

A. 147

Step-by-step explanation:

Divide the polygon into rectangles.

You will have 2 rectangles:

1) 3 x 10

2) 9 x 13

Now you just need to find the area of this 2 rectangles and add them up.

The option that can be the model when Dwayne has collected data on the number of occupants of cars travelling on the road is Table B.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true

Given the information, the probability for a will be illustrated as:

a. = 0.6 + 0.2 + 0.2 + 0.1 + 0.05 = 1.15 > 1

b. = 0.5 + 0.25 + 0.05 + 0.06 + 0.04 = 1

c. 2 + 1 + 0.1 + 0.1 + 0.4 = 3.6 > 1

d. 0.5 + 0.25 + 0.25 + 0.125 + 0.125 = 1.25 > 1

e. 0.5 + 0.2 + 0.1 + 0.05 + 0.05 = 0.9 < 1

The correct option that illustrates this is Table B.

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The positive numbers are 36 and 47.

What is a positive number?

Any positive number is one that is higher than zero.

A number can be zero, negative, or positive. Zero has no positive or bad aspects. The most frequent positive numbers in daily life include 34, 9.22, and other examples such as these. They are typically depicted on a number line to the right of zero, increasing bigger as you move to the right.

Assume that the positive numbers be x and y.

Given that the difference x and y is 11.

Therefore x - y = 11

x = y + 11 ....(i)

The product of the numbers is 1692.

xy = 1692 .....(ii)

Putting x = y - 11 in equation (ii):

(y + 11)y = 1692

y² +11y = 1692

y² +11y - 1692 = 0

y² +47y - 36y - 1692 = 0

y(y + 47) - 36(y+47) = 0

(y + 47) (y-36)=0

y = -47 and 36

Since the numbers are positive, thus y = 36.

The value of x is 36 + 11 = 47

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Coffee A is 12.241 pounds, Coffee B is 18.269 pounds and Coffee C is 24.482 pounds.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let a pounds of coffee A needed

Let b pounds of coffee B needed

Let c pounds of coffee C needed

c= 2a.................(1)

a+ b+c= 55..........(2)

and, 14.99 a+ 13.99 b + 10.39 c /55 = 12.61

1499a + 1399 b + 1039 c = 69,355...............(3)

Subtract (2) from (3), we get

  1499 a+ 1399 b + 1039 c= 69355

-  1039 a - 1039 b - 1039 c = 57145

_____________________________

  460 a + 360 b = 12210

 46a+ 36 b = 1221

b= 1221/ 36 - 46 a/ 36

b= 407 / 12 - 23 a / 18

Put b in Equation (2)

a + 407 / 12 - 23 a / 18 + 2a= 55

-5a / 18 + 2a + 407/ 12 = 55

31a/ 18 = 253/ 12

a= 4554 / 372

a = 2277/ 186

a= 759/ 62

a= 12.241

and, c=2a = 24.482

b= 33.91 - 15.641

b= 18.269

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The equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.

What is the equivalent measure?

In mathematics, and more specifically in measure theory, equivalence refers to the idea that two measures are qualitatively similar. The two measures specifically agree on which events have measure zero.

The unit "qt" stands for quart, which is a unit of volume.

It is equal to 32 fluid ounces or 0.946 liters.

Therefore, 19 quarts is equal to 19 * 32 = 1932= 608  fluid ounces,

or 19 * 0.946 = 190.946 =18.094 liters.

Hence, the equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.

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Using synthetic division we get, the remainder is 24
and the quotient is [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex]

What is synthetic division?

Particularly when we need to divide the polynomial by a linear factor, the Synthetic division provides a faster method of doing so. Instead of dividing factors, it is typically employed to determine the polynomial's zeroes or roots.

Here, in the question we have [tex]\frac{-x^{4} +2x^{3}+12x^{2} -16 }{x+2}[/tex]

First we find x from the divisor,

x+2=0

x=-2

Next, we arrange it in the division form with only the coefficients of the dividend terms.

[tex]-2 | -1 \space\ \space\ 2 \space\ \space\ 12 \space\ \space\ 0 \space\ \space\ -16\\[/tex]

             [tex]2 \space\ -2 \space\ -20 \space\ 40[/tex]

 ----------------------------------

     [tex]-1 \space\ \space\ 0 \space\ \space\ 10 \space\ \space\ -20 \space\ \space\ 24[/tex]

Therefore, we get the remainder as 24

And the quotient as [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex].

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Using the speed formula, we know that Liam finished in 1 hour as opposed to Sam's 1/ 19 hours, earning him the victory.

Speed is calculated as follows: speed = distance * time.

Knowing the units for distance and time is necessary to calculate the units for speed.

The units will be in meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).

So, the speed formula is:

Speed = Distance/Time

Taking time for the subject:

Time = distance/Speed

Now, Sam:
Time spent ascending the hill = 1/1 = 1 hour

Time spent descending the hill = 1/9 hours

Sam spent 1 1/the9 total minutes climbing and descending the hill.

Now, Lian:

Time spent ascending the hill = 1/2 hours

Time spent descending the hill = 1/2 hour

Total time spent ascending and descending the hill = 1/2 + 1/2 = 1 hour

Sam, therefore, took 1/9 hour longer than Liam.

Therefore, using the speed formula, we know that Liam finished in 1 hour as opposed to Sam's 1/ 19 hours, earning him victory.

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The of interest earned by Cedric's account  after 1 year and 9 months is $34.83.

The simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for interest.

I = P × r × t

I = $796 × 2.5% × 21/12

I = $796 × 0.025 × 1.75

I = $796 × 0.025 × 1.75

I = $34.83

Therefore, the interest earned in the account is $34.83.

Option B is the correct answer.

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If in a recent poll, 280 people were asked if they liked dogs, and 42% said they did. the margin of error of this poll, at the 90% confidence level is 0.05.

Sample proportion =42%(phat)

Sample size =280

Standard error = √(0.42×( 1- 0.42)/280)

Standard error = √(0.42×(.58)/280)

Standard error =0.029

Hence,

Margin of error = z-critical for 90% confidence level× Standard error

Zα/2 = 1.645 for 90% confidence

Margin of error =  1.645 × 0.029

Margin of error  = 0.047

Margin of error =0.05 (Approximately)

Therefore the margin of error is 0.05.

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As per the given least square regression line, the correlation between the height and the arm span is (a) greater than zero.

Regression line:

In statistics, regression line refers the an estimate of the line that describes the true, but unknown, linear relationship between the two variables.

Given,

Here we need to find the correlation between the height and the arm span by using the given least square regression line.

Let us consider the following situation,

"Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm)."

While we looking into this one we have identified that the predicted function y = 6.4 + 0.93x, is defines the value of height.

So, here y is the dependent variable and the x is the independent value.

This means that the value x is smaller comparatively y value.

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The value of x is 4.

What are vertical angles?

The opposing angles formed when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.

Here, we have

Given the following parameters

m∠A= (6x +29)° and

m∠B = (7x+25)°

Now, we equate both angles to find the value of x and we get

6x+29 = 7x + 25

6x-7x = 25 - 29

-x = -4

x = 4

Hence,  the value of x is 4.

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Answer:

log(2)√xy

________

y

there good luck

The number of catnip toys that Jose can buy will be 3 catnip toys. All the steps are described below.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The table is given below.

       Product                 Cost

Bag of Dog Food          $35

Bag of Cat Food            $18

Chew Toy                      $12

Catnip Toy                      $9

In the event that, your numbers are unique, you should simply supplant the qualities you have with the methodology here, and you ought to find an exact solution.

Presently, Emma has $100 to spend at the store. Along these lines, we really want to ascertain the amount she spends on shopping:

$35 + 2 x $12 = $59

In this way, she burned through $59 in the store, so she has left:

$100 - $59 = $41

She has $41 left to spend on something different. How about we check whether she has sufficient means to purchase multiple times catnip toys as bite toys:

Chew toys: 3 x 12 = $36

Catnip toy: 3 x 9 = $27

Furthermore, Emma has $41 left, so she can either purchase multiple times bite toys or multiple times catnip toys, however not the two of them at that point, on the grounds that the all-out would be 63% dollars, and she will be missing $22.

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The quantities we need circumference for are: A and C.

The quantities we need area for are: B and D.

The circumference of a circular shape is described as the distance around the circular shape. It is calculated using the formula, 2πr.

On the other hand, the area of a circular shape is the amount of space a circular shape has. It is calculated as πr².

Therefore:

For quantity A, to know the distance around a Ferris wheel, we would need to calculate is the circumference, so also for quantity C.

For quantity B, to know the amount of paint needed, we would calculate the area, so also is it for quantity D.

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The surface area of the composite figure is calculated as: 640 square inches.

The surface area of a rectangular prism = 2(w*l + h*l + h*w), where:

The composite figure can be decomposed into two rectangular prisms, 1 and 2.

Rectangular prism 1:

l = 10 in.

w = 0.5 ft. = 6 in.

h = 4 + 7 = 11 in.

Surface area = 2*(6*10 + 11*10 + 11*6) = 472 in.²

Rectangular prism 2:

l = 10 in.

w = 0.5 ft. = 6 in.

h = 4 in.

Surface area = 2·(6·10+4·10+4·6) = 248 in.²

The area of the surface where both meet = (l)(w) = (10)(4) = 40 in.²

Therefore:

Surface area of the composite figure = 472 + 248 - 2(40) = 640 in.².

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Answer:

O y = mx + b

Step-by-step explanation:

y = y coordinate

m = slope

x = x coordinate

b = y intercept

The probability of having fewer than three television sets in the apartment is 0.7

Probability is solved by finding the ratio of required outcome to the total sample

In the given problem the total sample space is the sum of the frequencies which

sum of the frequencies

= 1 + 6 + 14 + 7 + 2

= 30

The required outcome is the number of people that have less than three tv sets in their apartment, In this case 3 is not inclusive from 2 to o is added

= 1 + 6 + 14

= 21

The probability P(X < 3) = 0.7

= 21 / 30

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The inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) quadratic function is

The problem seeks the inequality that will be less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).

Therefore the quadratic function should have zeros at -7 and 1

Substituting the point (2, 27/2) to the quadratic function to check the one that gives the points shows that

3/2 x² + 9 x - 21/2 at x = 2

3/2 * 2² + 9 * 2 - 21/2

= 27/2

Solving for the zeros in the quadratic function 3/2 x² + 9 x - 21/2

shows that the zero are at

x = -7 and

Therefore the inequality that meets the condition is y < 3/2 x² + 9 x - 21/2

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