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In math class, the girl to boy ratio is 8 to 6. If there are 24 girls in the class, how many boys are there?
A
20
B
30
C
18
D
16

Answer:

70/17 hours or 4 2/17 hours

Step-by-step explanation:

The equation we use is 1/7 + 1/10 = 1/x, x being the time it took them together to build. x works out to 70/17 hours

Leah and her apprentice can build the wall together in 4 2/17 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Hours required by Leah to build a wall = 7 hours

So , Leah builds ( 1/7 )th of the wall per hour

Hours required by apprentice to build a wall = 10 hours

So , Apprentice builds ( 1/10 )th of the wall per hour

When they are both building the wall together , they build
( 1/7 )th + ( 1/10 )th of the wall together per hour = 1 / x

Therefore , the equation will be

1/x = 1/7 + 1/10

1/x = 17 / 70

Taking reciprocal on both sides , we get

x = 70/17

x = 4 2/17 hours  

Hence , Leah and her apprentice can build a wall together in 4 2/17 hours

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Divide everything by half

Since she doubled the recipes, divide all by half.

1 cup of sugar / 2 = 1/2 cup of sugar

3 1/2 cups of flour / 2 = 7/2/2 cups of flour = 7/4 cups of flour or 1 3/4 cups of flour.

Answer:

Sugar: 1/2  Flour: 1 3/4

Step-by-step explanation:

1 cup of sugar

3 1/2 cups of flour

Since the recipe is doubled you'll divide the ingredients by 2.

Sugar: 1÷2=1/2

Flour: 3 1/2÷2=7/4

=1 3/4

Hope this helps :)

Answer:

a. 2 1/4 cup of flour

b. 4 1/2 tsp. off sugar

Step-by-step explanation:

Since the recipe serves 2, the answer given will feed 5 (6) people.

Answer:

3e-3/2f-3/8

Step-by-step explanation:

You multiply everything in the parenthesis with 1/2. 1/2*6e=3e, 3f*1/2=3/2f, 3/4*1/2=3/8. This would be the answer.

Answer:

f(x) = 3х + 1

Step-by-step explanation:

Answer:

Swap 10 from box A and 15 from box B

Step-by-step explanation:

For calculate the ratio between the boxes we find the mean of the box A and the mean of the box B and divide this two results.

For find the mean of a set you use the next formula  [tex]\bar{x} = \frac{\text{sum numbers}}{\text{total numbers}}[/tex]

[tex]\bar{A} = \frac{4+5+9+10+12}{5} = \frac{40}{5}= 8\\\bar{B} = \frac{6+7+13+15+19}{5} = \frac{60}{5}= 12[/tex]

Then the ratio is equal to [tex]\frac{\bar{A}}{\bar{B}} = \frac{8}{12} = \frac{2}{3}[/tex]

Know the ask us for a ratio of 9:11 then we know two things about the boxes.

If you swap the numbers between them the total of numbers in the mean not change is always 5 and the sum of all the elements in both boxes is always 100. With this we can state the next equation:

The new mean of [tex]\bar{A}[/tex] is 9 then:

[tex]\frac{\text{sum of elements in box A}}{5} = 9[/tex]

[tex]\text{sum of elements in box A} = 45[/tex]

The new mean of [tex]\bar{B}[/tex] is 11 then:

[tex]\frac{\text{sum of elements in box B}}{5} = 11[/tex]

[tex]\text{sum of elements in box B} = 55[/tex]

Now we know what is the sum of the elements in both boxes, but how we find the elements for swap? Well with the next relation.

When you take out a element from the box A this elements is substracted to the total sum of the elements in the box A and get a new sum of total of elements named [tex]c[/tex] (where [tex]a[/tex] is the element taken):

[tex]40 - a = c[/tex]

And when you sum an element to the box A the current sum of total elements in the box change to (where [tex]b[/tex] is the added element):

[tex]b + c = 45[/tex]

So replace [tex]c[/tex] for the first relation and get:

[tex]b + 40 - a = 45\\b - a = 5[/tex]

From the last equation you can deduct that [tex]b[/tex] is greater than [tex]a[/tex] and the different between both values is 5. So the last step is find a number in the box B that substracted to a number from the box A give us 5. These both numbers are 15 and 10 because 15 - 10 = 5.

Step-by-step explanation:

sorry for my bad handwriting, hope it helps

Answer:

80,815,933

Step-by-step explanation:

After doing some quick calculations, we can determine that X = −35.9

I hope this helps! :)

Answer:

x = -35.9

Step-by-step explanation:

Subtract both sides by 11.2                                                                                                 11.2 - 11.2 equals zero leaving x on one side.

x = - 24.7 - 11.2

A negative minus another negative number is a larger negative number.

x= -24.7 - 11.2 = -35.9

x = -35.9

Answer:

Step-by-step explanation:

Three options for the first position

Two options for the second position

one option for the third position

3•2•1 = 6 ways

their orders could be

1) ABC

2) ACB

3) BAC

4) BCA

5) CAB

6) CBA

Answer:

Would be 6 ways

Step-by-step explanation

3x2=6

Answer:

there are 12 boys

Step-by-step explanation:

Louis is comparing the populations of several nearby cities. The population of Liberty Crossing can be written as 49 people, and the population of Harrisburg can be written as 47 people. The population of Glenview is 43 times the population of Harrisburg. Drag the cities to put them in order from least population (top) to greatest population (bottom).

The order of the cities from least population to greatest population:

Harrisburg

Glenview

Liberty Crossing

Given the information provided:

Harrisburg: This city has a population of 47 people. It's the smallest population among the three cities.

Glenview: The population of Glenview is 43 times the population of Harrisburg.

Since Harrisburg has 47 people, the population of Glenview would be 43 x 47 = 2021 people.

So, Glenview has a larger population than Harrisburg but is still smaller than Liberty Crossing.

Liberty Crossing: The population of Liberty Crossing is given as 49 people, which is the largest population among the three cities.

So, the correct order from least population to greatest population is:

Harrisburg

Glenview

Liberty Crossing

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Answer:

5+(11 x n)

Step-by-step explanation:

I hope this helps

[tex]a_2 = ar^{2-1} =ar = 6~~ ...(i)\\\\a_4 = ar^{4-1} = ar^3 = 2186 ~~....(ii)\\\\\\(ii)\div (i):\\\\\dfrac{ar^3}{ar} = \dfrac{2186}6\\\\\implies r^2 = \dfrac{2186}6 = \dfrac{1093}3\\\\\implies r = \pm \sqrt{\dfrac{1093}3}\\\\a= \pm \dfrac{6}{ \sqrt{\dfrac{1093}3}}\\\\\text{nth term} = ar^{n-1} = \pm \dfrac{6}{ \sqrt{\dfrac{1093}3}} \left( \pm{ \sqrt{\dfrac{1093}3} \right)^{n-1} = \dfrac{6}{ \sqrt{\dfrac{1093}3}} \left( { \sqrt{\dfrac{1093}3} \right)^{n-1} \\\\\\[/tex]

[tex]= 6\left(\dfrac{1093}3 \right)^{\tfrac{n-2}2}[/tex]

Answer:

Step-by-step explanation:

Given:

Equation of nth term of GP:

Substitute for 2nd and 4th terms:

Substitute the value of a₂ into a₄ and find the value of r:

Find the first term:

The equation of nth term is:

Answer:

it is 1.5

Step-by-step explanation:

if u do 4.50÷3 you will get 1.5 so the cost per jar is 1.5

Answer:

Option C is correct.

Step-by-step explanation:

In option C, the fractions are on one side and the constants are on the other. The fractions also have the same denominator. So, Option C is correct.

Answeryawa ka

Step-by-step explanation:

Answer:

Did u mean triangle? There are no angles on a line.

Or do you mean two angles of 90 degrees?

Step-by-step explanation:

Answer:

equal 11

Step-by-step explanation:

:>

hmmm wonder what else it would be

Answer:

104 bracelets

Step-by-step explanation:

182 ÷ 1.75 = 104

Answer:

A'(-2,3) B'(-1,1) C'(-4,0)

Step-by-step explanation:

Translating just means adding whatever numbers to each coordinate. Point A translated from (3,0) to (-2,3) because 3-5 is -2 and 0+3 is 3.

Answer:

19

Step-by-step explanation:

Note that

[tex]\dfrac{10a}{b+c} + \dfrac{10b}{a+c} + \dfrac{10c}{a+b} = 10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right)[/tex]

and

[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b}=\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]

from [tex]a+b+c=7 \implies a=7-bc; b = 7-a-c; c = 7-a-b[/tex]

and

[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b} = 7\left(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{a+c}\right)-3[/tex]

because it is not difficult to note that

[tex]$\sum \dfrac a{b+c}=\dfrac a{b+c}+\dfrac b{c+a}+\dfrac c{a+b}$[/tex]

Therefore,

[tex]7\left(\dfrac{7}{10}\right)-3 = \dfrac{49}{10}-3 =\boxed{ \dfrac{19}{10}} = \dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]

Finally,

[tex]10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right) = 10 \cdot \dfrac{19}{10} = 19[/tex]

Answer:

1/20

Step-by-step explanation:

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 8 by 4, and get 32.

Then we multiply 3 by 10, and get 30.

Next we give both terms new denominators -- 10 × 4 = 40.

So now our fractions look like this:

32/40−30/40

Step 2

Since our denominators match, we can subtract the numerators.

32 − 30 = 2

So the answer is:2/40

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

2/40÷ 2 =1/20

Let's try dividing by 2 again...

No good. 2 is larger than 1. So we're done reducing.

There you have it! The final answer is:

1/20

Answer:

It is congruent to M

Step-by-step explanation:

Answer:

It's C.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

just put the x and y values into the equations and see which equation stays true.

for example, point (4, 68) rules out A and C even without detailed calculation, because these 2 expressions can produce for positive x only negative y (and 68 is clearly a positive y).

so, when using this point in B :

68 = 4×4² + 2×4 - 4 = 4×16 + 8 - 4 = 64 + 8 - 4 = 68

correct.

and it is correct also for the other points.

so, B is the right answer.

[tex]\boxed{\sf E=Pt}[/tex]

E is energy

P is power

t is time in hours

Cost

Answer:

$0.12

Step-by-step explanation:

Conversions

  1000 watts = 1 kilowatt-hour
  ⇒ 1200 watts = 1.2 kilowatt-hour

  60 minutes = 1 hour
  ⇒ 30 minutes = 0.5 hour

A microwave requiring 1200 watts will use 1.2 kilowatts per hour.

If the microwave is used for a total of 30 minutes, it will use:

⇒ 1.2 × 0.5 =  0.6 kWh

If the cost is $0.20 per kWh, the cost of running the 1200 watt microwave for 30 minutes is:

⇒ 0.6 × $0.20 = $0.12

~equality

x + 12 = x√+2

= x + 12 = √2 x

= x = √2 x - 12

= x - √2 x = -12

= (1 - √2)x = -12

= x = -12/1- √2

= x = -(-12(1 + √2))

= x = -(-12 - 12√12)

= x = 12 + 12√2 ✔️

~ nice to help you ^^

Answer:

Both

Step-by-step explanation:

An arithmetic sequence is given by the next form:

[tex]a_{n} = a_{1} + (n-1)d[/tex]

Where [tex]a[/tex] is the [tex]n^{th}[/tex] term of the sequence, [tex]a_{1}[/tex] the first term of the sequence and [tex]d[/tex] the common difference between terms.  

So the given sequence is of the form, because the common difference between terms is 0.

[tex]a_{n} = 31 + (n - 1) 0 = 31[/tex]

A geometric sequence is given by the next form

[tex]ar^0, ar^1, ar^2, ar^3, ar^4, \cdot \cdot \cdot[/tex]

When [tex]r\neq 0[/tex]

In this occasion our [tex]a=31[/tex] and the [tex]r = 1[/tex]

So both sequence represent the given one.