Susan is buying supplies for a party. If spoons only come in bags of 8 and
forks only come in bags of 6, what is the least number of spoons and the
least number of forks she can buy so that she has the same number of
each?

Using proportions, it is found that:

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(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

In the first row of the table, we are given the scale factors of 1 and 1.25. From the second row, we have that the width for a scale of 1 is of 8 inches, and for a scale of 1.25 is of A, hence:

A = 1.25 x 8 = 10.

For the third row, we have that the scale of 1 is of 28 inches, while the scale of 1.25 is of B, hence:

B = 1.25 x 28 = 35.

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The cups of vinegar needed will be 1 1/3 cups.

From the information, the salad dressing recipe calls for 3/4 cup of olive oil for every 1/2 cup of vinegar.

Let the.cuos needed for the.olive.oio be represented by x.

Therefore, this will be:

1/2 / 3/4 = x/2

Cross multiply

0.75 × x = 2 × 1/2

0.75x = 1

x = 1/0.75

x = 1 1/3

Therefore the cups of vinegar needed will be 1 1/3 cups.

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Answer: The height of the water was 2 inches before any water was added.

Answer:

x+40

Step-by-step explanation:

I'm assuming you need to write a mathematical equation from a sentence. You need to take each word and make it into a mathematical symbol. The forty stays as 40, the more becomes a +, and the number is x because it is unknown

The Area of  the circle is 36π mm²

Radius of a circle = 6 mm

A circle's area is expressed as as A = πr²,

Where,

Radius (r) = 6 mm

Area = π(6)²

= 36π mm²

Hence the Area of the circle is 36π mm².

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Mike is the best shooter than Jason mike Jim or dave  .

Mike and Jim are faster and more accurate shooters than Jason and Dave. Mike is the quickest because Jim is the second fastest. Because no one individual is the greatest (for example, tallest, fastest, or best shooter) in more than one category, Dave is the tallest.

Mike and Jim are faster and more accurate shooters than Jason and Dave. Mike is the quickest because Jim is the second fastest. Because no one individual is the greatest (for example, tallest, fastest, or best shooter) in more than one category, Dave is the tallest.

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Answer:

1

Step-by-step explanation:

R=red Y=yellow B=black

2(R)+4(B)

=6

2(Y)/6(R+B)

2/6 to get 50=50 or 3/6=1/2

you need 1 more yellow

Yes the the equation is following direct variation. Correct option is A, Yes, k = 4/9

The change in one quantity as a result of the change in another is known as direct variation. This implies that if one quantity increases or decreases, the other must do the same.

Direct variation describes how one quantity directly affects the other when it varies. The precise reverse of this is called inverse variation. You will discover what direct and inverse variants are in this article, along with various cases that have been solved.

4y = 9x

standard equation for direct variation is y = kx

y = 9/4 x

On comparing the equation with standard equation,

k = 9/4

Hence, the equation is following direct variation

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Answer: 174

Step-by-step explanation:

For this problem, let's divide the number by two since we know it's a combination of two numbers in a series as they are two consecutive book pages.

349 / 2 = 174.5

Note, that the number we have is a decimal, and page numbers cannot be partial numbers, they must be integers.  With this, we can take the lower and the upper of our decimal numbers to retrieve the two-page numbers.

174.5 (Upper) ==> 175

174.5 (Lower) ==> 174

With this, we can verify these numbers have a sum of 349.

175 + 174 =? 349

349 == 349

So indeed, these numbers are a sum of 349.  Now that we know these are our page numbers, we know 174 will come before 175 since page numbers are sequential.

Cheers.

Answer:

Gallons of gas

Step-by-step explanation:

Answer:

11.3

Step-by-step explanation:

1.1 + 4.1 = 5.2

5.2 + 6.1 = 11.3

The number of students in the third grade at Roaring Brook School is 400

The number of students in the third grade at Roaring Brook School is given as

Students = three hundred fifty-six third

Express as digits

Students = 356

When the above number is approximated to the nearest hundred, we have

Students = 400

Hence, the number of students in the third grade at Roaring Brook School is 400

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The original price of the Sofa is $620

The original price is reduced by 60%

After this reduction the price reduced to $280

Therefore the original price can be calculated as follows

The first step is to subtract 60% from 100%

= 100-60

= 40%

The original price can be calculated as follows

280 × 100/40

= 28,000/40

= 700

Hence the original price of the sofa is $700

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By further simplifying the quadratic equation the answer is  13x²+5x+9.

=(9x² - 2x + 7) + (4x²+7x+2)

= 9x²+4x²+7x-2x+7+2

= 13x²+5x+9

Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

When a problem is factorable, factoring is often the quickest and simplest solution. Factoring won't help us because many times the quadratic we're working with can't be factored. Therefore, it is quick and simple when it is useable but not always factorable.

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Answer:

3.

Step-by-step explanation:

1) in the given sequence position no. 13 can be calculated easy:

16-(6+7)=3 (see the attachment), then

2) it is possible to calculate the position no. 11 (=7), then no.10(=3), then no.9 (=6), then it is visible repeating of subsequence '637', it means

3) the number of the given credit card is

37637637637637;

4) finally, the value of A is 3.

Answer:

-3

Step-by-step explanation:

Answer:

x-intercepts: (6,0)

y-intercepts: (0,3)

Answer:

49

Step-by-step explanation:

Answer:

the diagonal of a square is seven root feet

√2a=√7 a=√7/2 perimeter =

Step-b

y-step explanation:

In proportion , [tex]1\frac{3}{4}[/tex] pound of ground beef requires [tex]1\frac{1}{20}[/tex] cup of breadcrumbs.

What in mathematics is a proportion?

It is given that Dominic uses 3/4 cups of breadcrumbs for every [tex]1\frac{1}{4}[/tex]  pounds of ground beef. Therefore for 1 pound of ground beef he will required .

[tex]1\frac{1}{4}[/tex]   → 3/4

5/4  →  3/4

1 →  12/20

1 →  3/5  cups of breadcrumbs

Therefore, Dominic need 3/5 cups of breadcrumbs when he uses 1 pound of ground beef.

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By factor decomposition, area of a square and power and root properties, the length of the side is between 72 yards and 76 yards. (Correct choice: B)

The area of a triangle is equal to the square of its side length and the area of land is a composite number, that is, a product of prime numbers. By factor decomposition, the equivalent form of 5,280 square yards is:

5,280 = 2⁵ × 3 × 5 × 11

Then, the equivalent side is equal to the square product of the product:

x = √(2⁵ × 3 × 5 × 11)

x = √(2⁴) × √(2 × 3 × 5 × 11)

x = 2² × √(2 × 3 × 5 × 11)

x = 4√330

As for √330 is between √324 = 18 and √361 = 19, then the length of the side is between 72 yards and 76 yards.

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Answer: A: 9

please mark me brainlyest i hope i helped you

The third quartile of the date is Q₃=75

The numbers known as quartiles are used to divide the provided data set into four equal portions, or three points. Thus, the values that split the provided data into three quarters are known as quartiles. The center point of distribution is shown by the middle portion of the quartiles. The interquartile range is determined by the difference between the higher and lower quartiles so established.

Data 26, 34, 38, 49, 65, 75, 81  

First arrange the data from smallest to greatest

26, 34, 38, 49, 65, 75, 81  

Then find the median of the data,

Since, the data is in odd numbers median is mid term i.e. 49.

To find the third quartile we take the upper half of data

Upper half of data set, 65, 75, 81  

Third quartile is the median of the upper half of the data.

Median of upper half is

Q3 = (n+1)th

Q3 =(3+1)th

Q3 = 2th term

Q3 = 75term

Therefore, The third quartile is Q3 = 75term

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Answer:

4th choice [tex]\bold{f^{-1}(x) = \sqrt{x} + 4}[/tex]

Step-by-step explanation:

Definition of the inverse of a function

A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing. We can write this in terms of the composition of f and g as g(f(x))=x. The domain of f becomes the range of g and the range of f becomes the domain of g

To solve for the inverse of the function [tex]f(x) =\left(x-4\right)^2[/tex]

Let [tex]y=\left(x-4\right)^2[/tex]

[tex]\mathrm{Replace}\:x\:\mathrm{with}\:y[/tex] [tex]\text{ and replace }\:y\:\mathrm{with}\:x[/tex]

[tex]x=\left(y-4\right)^2[/tex]

Switch sides
[tex]\left(y-4\right)^2=x[/tex]

Take square roots on both sides
[tex]y-4=\pm\sqrt{x}[/tex]

Add 4 on both sides to solve for y

[tex]y = \pm\sqrt{x} + 4[/tex]

We have two solutions

[tex]y=\sqrt{x}+4,\:y=-\sqrt{x}+4[/tex]

To determine which one of these to be chosen not that in the given choices we can eliminate the first two since x cannot be negative

The third choice can also be eliminated since
[tex]-\sqrt{x} + 4[/tex] is a decreasing function for [tex]x \ge 0[/tex]

So the last answer choice is correct and the inverse of[tex]f(x) = (x-4)^2[/tex]

is given by  [tex]f^{-1}(x) = \sqrt{x} + 4[/tex]

Answer:4th choice [tex]\bold{f^{-1}(x) = \sqrt{x} + 4}[/tex]

Note

Domain of  (x-4)² is [4, ∞) since x ≥ 4 and (x-4)²  cannot be negative

Range of (x-4)²  is [0,  ∞)

Domain of [tex]\sqrt{x}\:+\:4[/tex] is [0, ∞)

Range of [tex]\sqrt{x}\:+\:4[/tex] is [4, ∞)

so indeed the domain of (x-4)² has become the range of [tex]\sqrt{x}\:+\:4[/tex] and the range of (x-4)² has become the domain of [tex]\sqrt{x}\:+\:4[/tex]

The expression [ (2.7) [tex]4]^{6}[/tex] is not equivalent to [ (2.7) 8 ] ³.

An exponent refers to the number of times a number is multiplied by itself.

Example:

a², a³

2 and 3 are exponents.

We have,

[ (2.7) [tex]4]^{6}[/tex]

Here 6 is the exponent.

We can write 6 as 2 x 3

Now,

= [ (2.7) [tex]4]^{2\times3}[/tex]

We can take 2 inside [ (2.7) 4 ]

= [ (2.7)² 4² ] ³

= [ (2.7)² 16 ] ³

We can see that it is not equivalent to [ (2.7) 8 ] ³.

Thus the expression [ (2.7) [tex]4]^{6}[/tex] is not equivalent to [ (2.7) 8 ] ³.

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Answer:

x = 21

Step-by-step explanation:

As the quadrilaterals are similar, their corresponding sides will be in the same proportion.

     PS ~ TW   and SR ~ WV

 [tex]\sf \dfrac{PS}{SR} = \dfrac{TW}{WV}\\\\\dfrac{x}{35}=\dfrac{15}{25}\\\\ x = \dfrac{15}{25}*35\\\\ x = 3*7\\\\x = 21[/tex]

The greatest possible sum for the two integers ( c and d) is 1.

The question gives:

The possible values for c and d for a product equals -6 are:

Now you should sum the possible values of c and d for each option.

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the range of the function g(x) = x^6 is: R: [0, ∞)

Here we have the function:

g(x) = x^6

First, notice that we have an even exponent. This means that the outcome of the function will always be a positive number, then the minimum of the range is:

g(0) = 0^6 = 6

And we don't have a maximum, the function tends to positive infinity in both ends (as x → -∞ and as x → ∞).

So the range is: R: [0, ∞)

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The answer choice which represents the rewritten form of; 2,290,000 in scientific notation is; 2.29 × 10⁶.

The scientific notation of a number is the form of the number such that only one digit appears before the decimal and the rest of the place value is represented by exponents of 10.

Hence, since the highest place value in the number is million; it follows that the science notation representation is; 2.29 × 10⁶.

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Answer: x = 138

Step-by-step explanation:

[tex]108+117+x=3 * 121\\3 * 121 = 363\\Rearrange unknown terms to the left side of the equation\\x=(363-108)-117\\\\255-117=138\\x=138[/tex]