Solve a Mixture Word Problem
Question
Orlando is mixing nuts and cereal squares to make a party mix. Nuts sell for $7 a pound and cereal squares sell for $4 a
pound. If Orlando wants to make 30 pounds of party mix at a cost of $6.50 a pound, how many pounds of nuts and how
many pounds of cereal squares should he use?
Provide your answer below:
lb cereal squares,
Ib nuts
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Final answer:

The value of 3x for a rectangle with a length of x+7, a width of 2x-3, and a perimeter of 32 is 12, which corresponds to option B.

Explanation:

The question asks to find the value of 3x for a rectangle with given dimensions and perimeter. The dimensions of the rectangle are length x + 7 and width 2x - 3, with a perimeter of 32.

The perimeter (P) of a rectangle is calculated using the formula P = 2l + 2w, where l is the length and w is the width.

By substituting the given dimensions into the perimeter formula, we get:
32 = 2(x + 7) + 2(2x - 3). Simplifying this, we get:
32 = 2x + 14 + 4x - 6.
Combining like terms, we get:
32 = 6x + 8. Subtracting 8 from both sides gives us:
24 = 6x. Dividing both sides by 6 gives us the value of x, which is 4.

Finally, to find the value of 3x, we simply multiply 3 by 4, giving us an answer of 12, which corresponds with option B in the provided choices.

Answer:

x > -13

Step-by-step explanation:

-[tex]\frac{1}{4}[/tex] x (12x + 8) < -2x + 11

Factor out 4 from expression

-[tex]\frac{1}{4}[/tex] x 4 (3x + 2) < -2x + 11

reduce numbers wit greatest common divisor 4

- (3x + 2) < =2x + 11

When a - is in front of parenthesis change the sign

-3x -2 < -2x + 11

Move variable to left side and change the sign

-3x + 2x -2 < 11

Move constant to the right and change the sign

-3x + 2x < 11 + 2

Collect like terms

-x < 11 + 2

add

-x < 13

Change the signs on both sides of the inequality and flip the inequality sign

x > -13

Answer:

x > -13

Step-by-step explanation:

-13 with the red dot and go to the right where it passes -5

            ➡️ ➡️➡️

-17 -15 -13 -11 -9 -7 -5

Answer:

7

Step-by-step explanation:

12+9=21

21 divided by 3 is 7

Answer:

[tex]Find[/tex]  [tex]the[/tex]  [tex]number[/tex]  [tex]that[/tex]  [tex]multiplies[/tex]  [tex]itself[/tex]  [tex]twice[/tex]

Step-by-step explanation:

When you have a square root number, it should look like this:

[tex]\sqrt{4}[/tex]

[tex]\sqrt{9}[/tex]

Then you're asking how to solve it, simple.

All you have to do is find a number that times itself twice to get that specific number.

Let's look back at the examples I gave you:

[tex]\sqrt{4}[/tex]

This means that you need to find a number that multiples itself twice to get 4.

In this case, it would be two, so:

2 x 2 = 4

[tex]\sqrt{4}[/tex]  =  2

So remember, when you have a square root, you have to find a number that multiples itself twice to get the number in the square root

Answer:MAFS.912.A-CED.1.1

The measures of three sides of a triangle can be represented by 2x, 3x - 5, and 4x + 2.

The perimeter of the triangle is 65 inches.

a) Give an equation to represent this situation.

b) Solve for x.

c) What are the three lengths of the triangle?

Answer:

8 hours

Step-by-step explanation:

81 - 17 = 64

64/8 = 8

A: 8 hours

A function assigns the value of each element of one set to the other specific element of another set. The number of hours for which Emily rents the bike is 8.

A function assigns the value of each element of one set to the other specific element of another set.

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given that Molly's Bikes rents bikes for $17 plus $8 per hour. Therefore, for x number of hours the function to calculate the total rent can be written as,

Total rent, f(x) = $17 + $8(x)

Now, if Emily paid $81 to rent a bike. The number of hours can be calculated as,

f(x) = $17 + $8(x)

$81 = $17 + $8(x)

$81 - $17 = $8(x)

$64 = $8(x)

x = $64 / 8x

x = 8

Hence, the number of hours for which Emily rents the bike is 8.

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Answer:

1. 0.4

2. 0.8888888889

3. 3.75

4. 0.7

5. 2.375

6. 0.3 the three is ongoing

Step-by-step explanation:

All you have to do is divide the numerator(top) by the denominator(bottom) and if there is a whole number than put that before the decimal

Answer:

[tex]-3x^4+3x^3+8x^2-2x-5[/tex]

Step-by-step explanation:

Here we need to move the negative sign to the rest of the variables, and then only add the ones with the same power:

[tex](-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)\\-2x^4-2x^3+8x^2+2 - x^4+5x^3-2x-7[/tex]

And then move the variables with the same power closer together

[tex]-2x^4-x^4-2x^3+5x^3+8x^2-2x+2-7[/tex]

See how -x^4 and -2x^4 are together?

All we have to do now is combine.

[tex]-2x^4-x^4-2x^3+5x^3+8x^2-2x+2-7\\-3x^4+3x^3+8x^2-2x-5[/tex]

So our answer is [tex]-3x^4+3x^3+8x^2-2x-5[/tex]

Answer:

-x^4-10x^3-16^x2-14

-7x+5y=10

4x-5y=-10

Find x first by eliminating the y.

Add the two equations together.

-7x+4y=-3y

+5y-+5y= 5y-5y=0

10-+10=0

-3x=0

divide both sides by -3

-3x/-3=0/-3

x=0

Find y by using x=0 into -7x+5y=10 ( using substitution  method)

-7(0)+5y=10

0+5y=10

5y=10

divide both sides by 5

5y/5=10/5

y=2

Answer:

(0,2)

Answer:

c + 9.

Step-by-step explanation:

That is simply c + 9. More means 'plus'.

Answer:

Step-by-step explanation:

x = c + 9

Answer:

hey user!

your answer is here...

laws ( rules ) of reflection are :-

• angle of incidence is equal to angle of reflection.

• the incident ray, Normal ray and reflected ray all lie in same plane.

cheers!!

Step-by-step explanation:

Bi weekly is a check every 2 weeks, so she would get 26 checks per year.

Monthly would be 12 checks per year.

When she gets paid monthly her pay increased by $2,800 each check.

Let x be one bi-weekly paycheck.

12(x+2800) = 26x

12x +33600 = 26x

Subtract 12x from both sides

33600 = 14x

Divide both sides by 14:

x = 33600/14

x = 2400

Her pay increased by 2800 each period:

2400 + 2800 = 5200 per check.

5200 x 12 months = 62400

Her annual salary is $62,400

Final answer:

Michelle's annual salary is $179,200, calculated by first understanding the pay period change from bi-weekly to monthly and then multiplying the additional $2,800 monthly increase by 12 to add to her bi-weekly annual salary.

Explanation:

Michelle Hong's gross pay per period increased by $2,800 when her employer switched from a bi-weekly pay plan to a monthly pay plan. To find Michelle's annual salary, we need to understand the terms of her payment cycle changes. On a bi-weekly plan, there are 26 pay periods per year since there are 52 weeks in a year. Under a monthly plan, there are 12 pay periods per year.

First, we calculate the pay for two bi-weekly periods: $2,800 x 2 = $5,600. This is because a bi-weekly pay period should be roughly half of the monthly pay since there are two bi-weekly periods in a standard month. Next, we will calculate the annual salary: $5,600 x 26 = $145,600. This is Michelle's annual salary on a bi-weekly pay plan.

For the monthly pay plan, we would simply take the increased pay of $2,800 and multiply by 12 months to find the annual salary: $2,800 x 12 = $33,600. This is the additional amount she earns by switching to the monthly plan. To find her total annual salary, we add this to her original annual bi-weekly salary: $145,600 + $33,600 = $179,200.

Therefore, Michelle's annual salary on the monthly pay plan is $179,200.

Answer:

The answer is 23/y

Step-by-step explanation:

This is because the question is asking 23 divided into y. So, your answer is 23/y. I hope tis helps, I am sorry if it is wrong.

The expression for 23 divided into y is written as y / 23, which signifies dividing y by 23 into equal parts.

The expression for 23 divided into y is y / 23. This represents a division operation where y is being divided by 23. To explain this concept further, imagine you have y amount of something, and you want to divide it into 23 equal parts; the amount in each part is represented by the expression y / 23. This operation is fundamental in algebra and helps understand how to express the division of variables and constants.

An example to illustrate this could be if y is equal to 46, then 46 divided by 23 would give us 2. This means each of the 23 parts has a value of 2.

Answer:

the last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

the last one

Answer:

See below in bold.

Step-by-step explanation:

(1) cosec ( x + 10) = 3

Now cosec x = 1/sin x so

1 / sin (x + 10) = 3

3 sin (x + 10) = 1

sin (x + 10) = 1/3

x + 10 = 19.47 , 160.53 degrees

x = 9.47, 150.53 degrees.

(ii) cot (x - 30) =0.45

cot (x - 30)= 1 /tan (x- 30) so we have

tan (x - 30) = 1 / 0.45 = 2.2222

x - 30 = 65.77 degrees

x = 95.77 degrees.

To solve the given equations, we need to find the values of x between 0° and 180°. For the equation cosec(x+10°) = 3, we solve for sin(x+10°) = 1/3. For the equation cot(x-30°) = 0.45, we solve for tan(x-30°) = 1/0.45.

(i) To solve the equation cosec(x+10°) = 3, we need to find the value of x between 0° and 180°. To do this, we can use the reciprocal identity for cosecant: csc(x) = 1/sin(x). Therefore, csc(x+10°) = 1/sin(x+10°). Solving for sin(x+10°), we have sin(x+10°) = 1/3. From the unit circle, we know that the sine function is positive in the first and second quadrants. So, we need to find the values of x+10° between 0° and 180° where sin(x+10°) = 1/3.

(ii)To solve the equation cot(x-30°) = 0.45, we need to find the value of x between 0° and 180°. The cotangent function is defined as cot(x) = 1/tan(x), so cot(x-30°) = 1/tan(x-30°). Solving for tan(x-30°), we have tan(x-30°) = 1/0.45. From the unit circle, we know that the tangent function is positive in the first and third quadrants. So, we need to find the values of x-30° between 0° and 180° where tan(x-30°) = 1/0.45.

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To find out the total cost after using a coupon, you first add the prices of the items - $1.29 for chips and $0.89 for a drink, totalling $2.18. Then subtract the value of the coupon, $0.75, from this amount. The final cost would be $1.43.

The first step in solving this problem is to add the prices of the bag of chips and the drink. According to the prices given, the chips cost $1.29 and the drink costs $0.89.

By adding these together, you will get the total cost before using the coupon. The sum of $1.29 and $0.89 equals $2.18. This is the total cost without any discounts.

Next, you need to take into account the coupon for $0.75 off the total price. Subtracting this from the initial cost, we get: $2.18 - $0.75 = $1.43.

So, the final cost of the bag of chips and the drink after using the 75 cents coupon would be $1.43.

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Answer:

470

Step-by-step explanation:

1000 x 0.53 = 530

1000 - 530 = 470

Answer:

Part 1) The equation is [tex]h=42y[/tex]

Part 2) The number of hats Paula can knit is 42 per yard of yarn

Part 3) see the procedure

Part 4) For 378 yards of yarn Paula can knit 9 hats

Step-by-step explanation:

Let

h -----> the number of hats

y ----> the amount of yarn in yards  

k ---> constant of proportionality

Part 1) Write an equation to represent the relationship between the numbers of yards of yarn Paula has and the number of hats she can knit

we know that

A relationship between two variables, h, and y, represent a proportional variation if it can be expressed in the form [tex]h/y=k[/tex] or [tex]h=ky[/tex]

we have

[tex]k=42[/tex]

substitute

[tex]h=42y[/tex]

Part 2) What does the constant if proportionality 42, represent in this problem?

The constant of proportionality represent the slope of the linear equation

The value of the slope is [tex]42\ \frac{hats}{yd}[/tex]

That means that the number of hats Paula can knit is 42 per yard of yarn

Part 3) Complete the table showing the yards of yarn and the number of hats Paula can knit

we have

[tex]h=42y[/tex]

Part a) For y=0 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(0)=0\ hats[/tex]

Part b) For h=3 hats Find the value of y

substitute in the linear equation the value of h and solve for y

[tex]3=42y[/tex]

[tex]y=3/42\ yd[/tex]  ----> [tex]y=1/14\ yd[/tex]

Part c) For y=210 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(210)=8,820\ hats[/tex]

Part d) For y=378 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(378)=15,876\ hats[/tex]

Part 3) For h=11 hats Find the value of y

substitute in the linear equation the value of h and solve for y

[tex]11=42y[/tex]

[tex]y=11/42\ yd[/tex]  

Part 4) Interpret the meaning of the point (378,9)

we have that

y=378 yd

h=9 hats

That means -----> For 378 yards of yarn Paula can knit 9 hats

Answer:

yes

Step-by-step explanation:

yes thank you this is helping me a lot

Answer:

all work is shown and pictured

Answer:

x = -11

Step-by-step explanation:

5x + 2 = 4x - 9

-2            -2

5x = 4x - 11

-4x   -4x

x = -11

Answer:

width = 7 cm

Step-by-step explanation:

length = 35 cm

Perimeter = 84 cm

2 * ( l + b) = 84

2 * ( 35 +b ) = 84

       35 +b  = 84 / 2

        35 + b = 42

                 b = 42 -35

                   b = 7

width = 7 cm

Adam is carrying a total of 15.4 pounds of books to the classroom, calculated by multiplying the weight of one book (3.85 pounds) by the number of books (4).

The subject of this question is Mathematics, and it is appropriate for a middle school grade level. The student has asked about the total weight Adam is carrying when he transports four books to the classroom, with each book weighing 3.85 pounds.

To find the total weight of the books Adam is carrying, we multiply the weight of one book by the number of books:

Therefore, Adam is carrying approximately 15.4 pounds of books to the classroom.

Answer: 0.667feet

Step-by-step explanation:

You divide 8in by 12

Answer:

The cost of the lessons taken

Step-by-step explanation:

Let

y -----> the total paid for the baseball bat and the lessons

c ----> the number of lessons

we have

y=25c+75

This is a linear equation in slope intercept form

y=mx+b

where

b=$75 -----> the price of he baseball bat (y-intercept)

m=25 $/lesson ----> the slope of the linear equation

therefore

25c represent the cost of the lessons taken

Answer:

g(3)=9-7=2

f(2)=5×2-4=10-4=6

Answer:

Step-by-step explanation:

f(x)=5x-4 g(x)=3x-7

g(3) = 3(3)-7=2

f(g(3))=f(2) =5(2)-4 = 6

Good evening ,

______

Answer:

The second table.

___________________

Step-by-step explanation:

Look at the photos below for the answer.

:)

Answer:

[tex] \sqrt{72} = \sqrt{36 \times 2} = 6 \sqrt{2} [/tex]

the simplified form

Answer: 6√2

Step-by-step explanation: The easiest way to do this problem is to factor 72 as 2 · 36 then recognize 36 as a perfect square, 6 · 6.

There is no need to factor further because the 6's pair up.

So a 6 comes out of the radical leaving a 2 inside.

Since the 2 doesn't pair up, it becomes the radicand.

When simplifying radicals using the factor tree,

always be on the lookout for perfect squares.

Answer:

-1 3/8

Step-by-step explanation:

Answer:-3/4 = -6/8

-6/8 + 5/8= -1/8

Step-by-step explanation:

Answer:Prime factorization of 46 is 2 * 23

Step-by-step explanation:

Answer:

14.14

Step-by-step explanation:

10[tex]10^{2} +10^{2} =x^{2}[/tex]

Simplifying gives you:

10\sqrt{2} ≈ 14.14213562...

The length of the path through Chi's flower garden is approximately 14.14 feet, rounded to two decimal places.

We have,

To find the length of the path through the flower garden, you can use the Pythagorean theorem since the path forms a right-angled triangle inside the square garden.

The garden is a square with a side length of 10 feet.

The path goes from one corner of the square to the opposite corner, forming the hypotenuse of a right-angled triangle.

The other two sides of the triangle are the sides of the square, which are also 10 feet each.

Using the Pythagorean theorem, you can find the length of the hypotenuse (the path):

[tex]c^2 = a^2 + b^2[/tex]

where c is the length of the hypotenuse (the path), and a and b are the lengths of the other two sides (which are both 10 feet in this case).

[tex]c^2 = 10^2 + 10^2[/tex]

c² = 100 + 100

c² = 200

Now, take the square root of both sides to find the length of the path (c):

c = √200 ≈ 14.14 feet

Thus,

The length of the path through Chi's flower garden is approximately 14.14 feet, rounded to two decimal places.

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