Paula knits hats. The number of hats h she can knit varies directly with the amount of yarn (y) in yards she has. The constant of proportionality is 42. Write an equation to represent the relationship between the numbers of yards of yarn Paula has and the number of hats she can knit. h=

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

Complete the table showing the yards of yarn and the number of hats Paula can knit.

Answer:

A = 7,850

Step-by-step explanation:

1. Area = 3.14(50)^2

2. A = 3.14(2500)

3. A = 7,850

Answer:120

Step-by-step explanation:

10•12=120

Answer:

120

Step-by-step explanation:

Answer:

a. Fraction of earnings that Mariano put into each piggy bank  is 1/12

b. Mariano earns $28.8

Step-by-step explanation:

Mariano divides his earning in a saving account and 3 piggy banks.  

First ,  we have to know the fraction that we divide in the 3 piggy banks.

Piggy banks =Total earning-Saving account

Saving account 3/4,  

Total earning is 1

to rest both term we have to get the same denominator , so we can say that the total earning is 4/4

Piggy banks =4/4-3/4=( 4-3)/4=1/4

Piggy banks =1/4

Each piggy bank will be 1/3 of that 1/4

1/3 x 1/4=

For fraction multiplication, multiply the numerators and then multiply the denominators to get

1×1/3×4=1/12

This fraction cannot be reduced.

b. Mariano adds $2.40

1/12 is 2.40

total earning  is ?

We use cross-multiplication

a/b=c/d  replacing   (1/12)/2.40 = 1/ ?

So,  the total earning (?) is 1 x 2.40/ (1/12)

= 2.40 x 12=$28.8

Mariano puts 3/4 of his earnings in his savings account and divides the rest equally into 3 piggy banks. The fraction of his earnings that he puts into each piggy bank is (1/12)x dollars. Mariano earns 0 dollars per week delivering papers.

To find the fraction of Mariano's earnings that he puts into each piggy bank, we need to calculate 3/4 of his earnings first. Let's assume he earns x dollars per week. Therefore, he puts 3/4 of x dollars into his savings account, which is (3/4)x dollars. The remaining (1/4)x dollars is divided equally into 3 piggy banks. So, each piggy bank gets (1/12)x dollars.

To find out how much Mariano earns per week delivering papers, we need to solve the equation (3/4)x + (1/12)x = x. Simplifying the equation, we get 9x/12 + x/12 = x. This is equivalent to (10/12)x = x. Multiplying both sides by 12, we get 10x = 12x. Subtracting 10x from both sides, we get 2x = 0. Therefore, x = 0.

2.75+3x=4.25+2.50x

3x - 2.50x = 4.25 - 2.75

0.50x = 1.50

x = 1.50 ÷ 0.50

x = 3

Understand?

Answer:

x = ± [tex]\sqrt{10}[/tex]

Step-by-step explanation:

Given

5 - 2x² = - 15 ( subtract 5 from both sides )

- 2x² = - 20 ( divide both sides by - 2 )

x² = 10 ( take the square root of both sides )

x = ± [tex]\sqrt{10}[/tex] ← exact solutions

[tex]\text{Hello there!}\\\\\text{A simple way to find the value of x is to find the scale factor}\\\\\text{When you flip the shapes to make it look exactly the same,}\\\text{you would see that the numbers are divisible to it}\\\\\text{Side 21 is congruent to side 3}\\\\\text{Divide 21 by 3 and you'll get 7 (1/7 sine we're going to a smaller shape)}\\\\\text{The x side is congruent to the 91 side}\\\\\text{Divide 91 by 7}\\\\91\div7=13\\\\\large\boxed{x=13}[/tex]

Answer: y=4

Step-by-step explanation:

7-y-y=-1

Combine like terms

7-2y=-1

Subtract seven on both sides of the equation

7-7-2y=-1-7

-2y=-8

Divide both sides by -2

-2y/-2=-8/-2

y=4

Check the answer by plugging 4 back in the equation for y.

7-4-4=3-4=-1

The final answer is y=4

Answer:

6 x 10/3= 6000

Step-by-step explanation:

take ur first digit,6,and either multiply it by 10/3 =1000 or place to its right as many zeroes as the exponent of ten (3)

The student is working with scientific notation, specifically converting 6 x [tex]10^{-3}[/tex] into standard notation, which results in the number 0.006.

The student in question appears to be dealing with scientific notation and its application in representing large or small numbers in a condensed form. In scientific notation, numbers are represented as a product of a base number and 10 raised to a certain power. For instance, 6 x 10/3 is a way to represent the number 0.006, indicating the decimal point has been moved three places to the left.

To convert 6x10/3 into standard notation, you need to recognize that the exponent -3 on the 10 denotes how many places to move the decimal. Since it is negative, we move the decimal to the left. Therefore, we rewrite 6 as 0.006, which is the standard notation.

Total 1920 cubes can fit in the given prism.

Dimensions of prism are: [tex]2\dfrac{2}{5} = \dfrac{12}{5}[/tex] ,  [tex]3\dfrac{1}{5} = \dfrac{16}{5}[/tex],  and 2 inches respectively.

Size of a side of given cube = 1/5 inch

Number of cubes that can fit in given prism.

This problem is all about spaces. Only that number of cube will fit, which the prism will allow to. The given prism has got some space in it(The volume), and the cubes have some size (their volume).

Since prism is a cuboid(which is mistakenly written as rectangular in the question), thus we have:

Volume of prism = multiplication of lengths of its sides = [tex]\dfrac{12}{5} \times \dfrac{16}{5} \times 2 = \dfrac{384}{25}[/tex] cubic inches

Volume of the cube = cube of its one side's length = [tex](\dfrac{1}{5})^3 = \dfrac{1}{125}[/tex] cubic inches

We will divide the total space with space amount each cube take so as to find number of cubes allowed by prism to be fitted in it.

Thus:

[tex]\text{Number of cubes} = \dfrac{\dfrac{384}{25}}{\dfrac{1}{125}} = 1920 \: \rm cubes[/tex]

Thus, in total, there can be 1920 cubes fitted in the prism.

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The rectangular prism can hold 1920 cubes with edge lengths of [tex]\frac{1}{5}[/tex] inch. This is calculated by finding the volume of the prism and dividing it by the volume of one small cube.

To find how many cubes with an edge length of [tex]\frac{1}{5}[/tex] inch fit into a rectangular prism with dimensions [tex]2\frac{2}{5}[/tex] inches, [tex]3\frac{1}{5}[/tex]  inches, and 2 inches, we follow these steps:

Convert the dimensions of the prism into improper fractions:

Calculate the volume of the prism:

Determine the volume of one small cube:

Find the number of small cubes by dividing the volume of the prism by the volume of one small cube:

Thus, 1920 cubes with an edge length of [tex]\frac{1}{5}[/tex] inch can fit into the given rectangular prism.

Corrected question:

A rectangular prism measures [tex]2\frac{2}{5}[/tex] inches by [tex]3\frac{1}{5}[/tex] inches by 2 inches

How many cubes with edge length [tex]\frac{1}{5}[/tex] inch fit in the prism?

Answer:

Combinations:

A committee consisting of three members with the same role

Selecting two sandwiches from a menu of 10

Step-by-step explanation:

A combination is a selection of items from a collection, such that the order of selection does not matter.

A permutation is a selection of items from a collection, such that the order of selection matters.

A. The PIN for a bank or credit card - order matters → permutation

B. A committee consisting of three members with the same role - order does not matter → combination

C. A committee consisting of a president, vice president, and secretary - order matters → permutation

D. Final standings in a professional sports league - order matters → permutation

E. Selecting two sandwiches from a menu of 10 - order does not matter → combination

Answer:  1848 feet per minute

Step-by-step explanation:

[tex]\dfrac{21\ miles}{1\ hour}\times \dfrac{1\ hour}{60\ minutes}\times \dfrac{5280\ feet}{1\ mile}\quad =\dfrac{21\times 5280\ feet}{60\ minutes}\quad =\dfrac{110,880\ feet}{60\ minutes}\\\\\\=\large\boxed{1848\ feet\ per\ minute}[/tex]

Answer:

B. −5 < x < 10

Step-by-step explanation:

−6 < x − 1 < 9

+1 + 1 + 1

_____________

−5 < x < 10

I am joyous to assist you anytime.

The solution to the inequality will be −5 < x < 10. Then the correct option is C.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

−6 < x − 1 < 9

Solve the inequality for x, then the value of x will be

Add 1 on each side of the inequality, then we have

−6 + 1 < x − 1 + 1 < 9 + 1

−5 < x < 10

The solution to the inequality will be −5 < x < 10. Then the correct option is C.

More about the inequality link is given below.

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Answer:

3/12

Step-by-step explanation:

it was right on, you know, where its from

The product Square root of 3/16 • Square root of 3/9  = 3/12 = 1/4.

The root is figuring out what number accelerated by way of itself is the same as the variety under the square root image. So: √9= 3, due to the fact 3² $ -3² = 9

square root, in mathematics, a component of a variety of that, while accelerated by way of itself, gives the authentic quantity. for example, each 3 and –3 are square roots of 9.

The square root of 3/16 • Square root of 3/9

⇒[tex]\sqrt{\frac{3}{16} }[/tex]×[tex]\sqrt{\frac{3}{9} }[/tex]

⇒3/4*3

⇒1/4.

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Answer: x = 1.5

Step-by-step explanation:

First, we need to isolate the absolute value.

+ 3 to each side.

|2x + 3| - 4 = 4

Then, add 4 more to each side.

|2x + 3| = 8

Subtract 3 from each side.

|2x| = 5

Divide each side by 2

|x| = 1.5

Answer:

no solutions

Step-by-step explanation:

[tex]-3|2x+3|-4=1[/tex]

[tex]-3|2x+3|=1+4[/tex]

[tex]-3|2x+3|=5[/tex]

[tex]{\left|2x+3\right|}=\frac{5}{-3}[/tex]

The absolute value of a number is always positive or zero.

Answer:

6

Step-by-step explanation:

[tex] - \frac{8}{3} \div - \frac{4}{9} = - \frac{8}{3} \times -\frac{9}{4} = \frac{72}{12} = 6[/tex]

I am joyous to assist you anytime.

Answer:

-3.3, -3.5, -3.7

9514 1404 393

Answer:

  (a)  A and B are similar but not congruent

Step-by-step explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.

  A and B are similar, but not congruent.

Answer:

5⁷

Step-by-step explanation:

5*5*5*5*5*5*5

here,

count how many 5 are there - 7

so,

exponential notation form:

5*5*5*5*5*5*5 = 5⁷

Answer:

5*5*5*5*5*5*5 in exponential notation form is 5⁷

Step-by-step explanation:

-4r+5=5-4r

-4r+4r=5-5

r=0

Answer:

the answer should be 2, -2, 7, -7

Answer:

7/96 m

Step-by-step explanation:

7/12 ÷ 8 = 7/96

Answer:

your adding 6 each time so just find the 15th term

Step-by-step explanation:

-3 + 6= 3 and 3+6 = 9

it equals b 37 58 it welcome

Answer:

b≥−  37/76

​  

Step-by-step explanation:

\begin{aligned}-67b+6 & \leq 9b + 43 \\\\ -67b&\leq 9b+37 &(\text{Subtract } 6 \text{ from both sides}) \\\\ -76b &\leq 37 &(\text{Subtract } 9b \text{ from both sides})\\\\ 76b&\geq -37&(\text{Multiply both sides by }-1)\\\\ b&\geq-\dfrac{37}{76}&(\text{Divide both sides by }76) \end{aligned}  

−67b+6

−67b

−76b

76b

b

​  

≤9b+43

≤9b+37

≤37

≥−37

≥−  

76

37

​  

​  

(Subtract 6 from both sides)

(Subtract 9b from both sides)

(Multiply both sides by −1)

(Divide both sides by 76)

​

Answer:

A and D

Step-by-step explanation:

Edg 2022

Check the picture below.

Answer:

The perimeter of the equilateral triangle is 90 units.

Step-by-step explanation:

Let the side of the triangle be = s

So, perimeter of equilateral triangle = [tex]s+s+s=3s[/tex]

One side measures 9+3x and the measure of another side is 5x-5.

Both are equal, so we get the sides as:

[tex]9+3x=5x-5[/tex]

[tex]3x-5x=-5-9[/tex]

[tex]-2x=-14[/tex]

x = 7

We get the sides as :

First side [tex]9+3(7)[/tex]

= 30

OR

Second side [tex]5(7)-5[/tex]

= 30

And the third side will also be 30 as it is equilateral triangle.

Hence, the perimeter is = [tex]30+30+30=90[/tex] units

Therefore, the perimeter of the equilateral triangle is 90 units.

Answer:

A. The sum is a rational expression.

Step-by-step explanation:

The complete questions is:

Let P be the set of polynomials. Let a, b, c, and d be elements of P such that b and d are non-zero elements of P. Which of the following is  true regarding the sum below?

a/b+c/d

A) The sum is a rational expression

B) The sum is an integer

C) The sum is a rational number

D) The sum is a polynomial

Solution:

We are given:

a/b + c/d

b and d are non-zero elements:

Therefore:

a/b is a rational number.

c/d is a rational number.

We see that there is an addition sign between the two terms:

So, sum of rational expression is also a rational expression  

Thus, The correct option is:

A. The sum is a rational expression.

The sum of the given fractions a/b + c/d, where a, b, c, and d are polynomials, can be calculated by finding a common denominator, which is typically the product of polynomials b and d, and combining the adjusted numerators.

The question deals with the operation of addition of fractions where the denominators are polynomials. Given the expression a/b + c/d, where a, b, c, and d are polynomials, and b and d are non-zero polynomials, we want to find their sum. It is important to note that adding or subtracting fractions requires a common denominator.

To combine a/b with c/d, we must first find a common denominator, which will be the product of b and d if they have no common factors. After that, we adjust the numerators accordingly and perform the addition. The resulting fraction will have a numerator that is the polynomial sum of ad and bc, and a denominator that is the polynomial product bd.

To create the formula, identify the relationship between cost and number of journeys from the graph. Assume a simple linear function y = mx + b. Calculate the slope (rate of cost per journey) and y-intercept (initial or fixed cost) to find final equation: c = mn + b.

In order to work out a formula for c (cost) in terms of n (number of journeys), we need to understand the relationship between these two variables. From the graph, we can make the assumption that this relationship is linear, suggesting a simple algebraic formula of the form y = mx + b, where y is the dependent variable (cost), x is the independent variable (number of journeys), m is the slope of the line and b is the y-intercept.

To establish our formula, we need to calculate the slope and y-intercept. The slope is found by taking the change in y over the change in x (the 'rise' over 'run'). The y-intercept is the cost (c) when the number of journeys (n) is zero.

Once these quantities are determined from the graph, your formula could look like: c = mn + b, where m is the slope (change in cost per journey) and b is the cost for zero journeys (fixed cost).

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For this case we must factor the following expression:

[tex]x ^ 2-3x-4[/tex]

We must find two numbers that, when multiplied, result in -4, and when added, result in -3.

These numbers are: -4 and +1

[tex]-4 + 1 = -3\\-4 * (+ 1) = - 4[/tex]

So:

[tex]x ^ 2-3x-4 = (x-4) (x + 1)[/tex]

Answer:

[tex](x-4) (x + 1)[/tex]

Option A

Answer:

(x+1) and (x-4)

Step-by-step explanation:

Since, factors of an expression is the values which after multiplying together give the same expression.

Given quadratic equation,

[tex]x^2 - 3x - 4[/tex]

By the middle term splitting,

[tex]x^2 - (4 - 1)x - 4[/tex]

By distributive property,

[tex]x^2 - 4x + x - 4[/tex]

[tex]x(x-4)+1(x-4)[/tex]

[tex](x+1)(x-4)[/tex]

Since,

[tex]x^2 - 3x - 4=(x+1)(x-4)[/tex]

i.e. the factors of [tex]x^2 - 3x - 4[/tex] are (x+1) and (x-4).

Answer:

Her daughters age: 1/2x

Step-by-step explanation:

Let's say Rani's present age is x. Her age is twice the age of her daughter.

So if Rani's age is 20, her daughters age would be 10, because Rani is twice the age of 10; so 10 times 2 would be 20.

1/2(20)=daughter's age

so if you substitute x into 20 because we don't actually know Rani's age, it would be 1/2(x)=daughter's age.

hope this helped :-) <3