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Answer:

Three numbers are : 6 , 21 and 3

Step-by-step explanation:

Given,

Ratio of 3 numbers is 2:7:1 .

We can assume 3 numbers as : 2x ,7x and x respectively.

According to the problem :

2x + 7x + x = 30    {The sum of the 3 numbers is 30}

10x = 30

x = 3

Hence 3 numbers are,   x = 3

                                     2x = 2*3 = 6

                                     7x = 7*3 = 21

Therefore we get three numbers as : 6 , 21 and 3

Remember , you can check their ratios to cross check the correct answer.

Answer:

6, 21, and 3

Step-by-step explanation:

Answer:

B and E

Step-by-step explanation:

The rules of indicies states:

[tex]x^{a}[/tex] ÷[tex]x^{b}[/tex] = [tex]x^{a-b}[/tex]

So [tex]3^{-8}[/tex] ÷  [tex]3^{-4}[/tex] =  [tex]3^{-8 - - 4}[/tex] =  [tex]3^{-4}[/tex]

So that means B is one of the correct answers.

To find the other correct value, you can divide the two fractions as stated in the question:

[tex]3^{-8}[/tex] by [tex]3^{-4}[/tex] = [tex]\frac{1}{81}[/tex]

81 is equivalent to 3⁴

So that means E is also correct.

[tex]\text{Use}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\a^{-n}=\dfrac{1}{a^n}\\-----------------------\\\\\dfrac{3^{-8}}{3^{-4}}=3^{-8-(-4)}=3^{-8+4}=\underbrace{\boxed{3^{-4}}}_{\boxed{B.}}=\underbrace{\boxed{\dfrac{1}{3^4}}}_{\boxed{E.}}\\\\Answer:\ \boxed{B.\ and\ E.}[/tex]

the TV screen would have an area of 122.88 inches

to find this all you would have to do is multiply the 38.4 by 3.2

Answer:

The size of the tv is 122.88", or 122.88 in²

Step-by-step explanation:

a = w * h

w = 38.4

h = 3.2

a = (38.4) * (3.2)

a = 122.88

The probability that the red die shows a number larger than three or the green die shows a number less than three is 0.83 or 83%.

The question relates to the topic of probability in mathematics, which is the measure of the likelihood that an event will occur. In this case, we are looking at the probability of combined events with two standard six-sided dice, one red, and one green.

Firstly, the probability that the red die rolls a number larger than three is 3/6 or 0.5 since, out of 6 possible outcomes (1, 2, 3, 4, 5, 6), 3 (4, 5, 6) are favorable outcomes.

Secondly, the probability that the green die shows a number less than 3 is also 2/6 or approximately 0.33, as there are two favorable outcomes (1 and 2).

To find the probability of the red die showing a number larger than three OR the green die showing a number less than three, we add the two individual probabilities because these are independent events. Hence Probability = 0.5+0.33 = 0.83 or 83%

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The probability of the red die showing a number larger than three or the green die showing a number less than three is 1/9.

To calculate the probability of the red die showing a number larger than three or the green die showing a number less than three, we need to determine the number of favorable outcomes and the total number of possible outcomes.

The favorable outcomes are when the red die shows a number larger than three (i.e., 4, 5, or 6) or when the green die shows a number less than three (i.e., 1 or 2).

Since each die has 6 sides, the total number of possible outcomes for each die is 6. Therefore, the total number of possible outcomes for both dice is 6 * 6 = 36.

The number of favorable outcomes is 3 (for the red die) + 2 (for the green die) - 1 (for the outcome where both dice show a number larger than three and a number less than three) = 4.

Therefore, the probability is 4/36 = 1/9.

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Final answer:

The quadratic equation 2x² + 18 = 0 is solved by isolating the x² term and taking the square root of both sides, yielding solutions x = 3i and x = -3i.

Explanation:

To solve the quadratic equation 2x² + 18 = 0, you need to first move all terms to one side of the equation to set it equal to zero, which is already done in this case. Next, you would typically factor the quadratic or use the quadratic formula.

However, this equation can be simply factored since it is missing the x term. So, subtract 18 from both sides to isolate the x² term.

2x² = -18

Now, divide both sides by 2 to solve for x².

x² = -9

To solve for x, take the square root of both sides. Remember, when taking the square root of a number, you will have both a positive and negative solution.

x = √{-9} = ±3i

The solutions to the equation are x = 3i and x = -3i, where i is the imaginary unit.

Answer:

Step-by-step explanation:

4x=2z+5/y

X= 1/4(2z+5/y)

Answer:

The answer would be 20.05 hours per day.

Answer: There are 20.05 kwh that Luke use per day during the month of April.

Step-by-step explanation:

Since we have given that

Amount of electric bill = $84.21

Charges of electric company = $ 0.14 per kWh

We need to find the number of kilowatt hours.

Number of days in the month of April = 30 days

According to question,

[tex]84.21=0.14\times 30\times x\\\\84.21=4.2\times x\\\\\dfrac{84.21}{4.2}=x\\\\x=20.05\ kwh[/tex]

Hence, there are 20.05 kwh that Luke use per day during the month of April.

Answer:

27 children.

Step-by-step explanation:

For every 9 children there are 4 adults .

x + y = 39  where x = number of children and y = number of adults.

and x/y = 9/4

so  4x = 9y

then x =  9y/4 , so substituting for x in the first equation:-

y + 9y/4 = 39        Multiplying through by 4:-

4y + 9y =  156

y = 156/13 = 12  so there are 12 adults

and 39 - 12 = 27 children

The problem is solved by using the ratio of children to adults and setting up a proportion. After cross-multiplying and solving the equation, it is determined that there are 27 children at the movie.

This is a problem of ratio and proportion. In this case, the ratio of children to adults at the movie is 9 to 4. This means that for every 13 people at the movie (9 children plus 4 adults), 9 are children. We can set up a proportion to determine how many out of the total 39 people at the movie are children.

The proportion is:
9 children / 13 total people = x children / 39 total people

We can solve this problem by cross multiplying: 9 * 39 = 13 * x, which gives us: 351 = 13x. Dividing both sides of the equation by 13, we get: x = 27.

Therefore, 27 children are at the movie.

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Answer:

3 3/5 lbs

Step-by-step explanation:

We will multiply the pounds of berries by the faction she used to see how much she used for the pie

4 4/5 * 3/4 = amount used in pie

We need to convert the mixed number to an improper fraction

4 4/5 = (5*4+4)/5 = 24/5

24/5 * 3/4 =

I will change the order to make the math easier

24/4 * 3/5

6 * 3/5 =

18/5

Now we need to change it back to a mixed number

5 goes into 18   3 times with 3 left over

3 3/5 lbs

She used 3 3/5 lbs

Answer:

n-20

--------

3a

Step-by-step explanation:

(3ax - n)/5 = -4

The first step is to multiply each side by 5 to get rid of the fraction

(3ax - n)/5  * 5= -4* 5

3ax - n = -20

Then we need to add n to each side.

3ax -n+n = -20+n

3ax = n-20

Divide each side by 3a to isolate x

3ax/3a = (n-20)/3a

x = (n-20)/(3a)

Let the number of toys Teddy has on Monday = x

On Monday Harry has = 75% of x or 0.75x

As given, On Tuesday, after Harry acquired 32 more toys and Teddy acquired 15% more than he had on Monday, Harry had as many toys as Teddy did.

Toys Teddy has = [tex]x+\frac{15x}{100}[/tex]

=[tex]\frac{100x+15x}{100} =\frac{115x}{100}[/tex] = 1.15x   .... (i)

Toys Harry has = 0.75x+32   ...... (ii)

As both have equal toys now, so equation (i) equals equation (ii)

[tex]1.15x=0.75x+32[/tex]

[tex]1.15x-0.75x=32[/tex]

[tex]0.4x=32[/tex]

x=80

Hence, Teddy had 80 toys on Monday.

And Harry had 75% of 80 toys = 60 toys on Monday.

Answer:

m

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values 45m and 6m. Each has numbers which multiply together to give the number. We need to find the highest value or most in common they share. Each has the factors:

45m: 1, 5, 9, 45, m

6m: 1, 2, 3, 6, m

Both have 1 and m as factors. Our GCF is these two factors multiplied which is 1m=m.

Answer:

Positive association and nonlinear

Step-by-step explanation:

Answer:

Positive association & Linear Association  

Step-by-step explanation:

Positive charts go up from left to right (which this plot does)

Liner plots are any plots that can form a straight line (which this one does)

Answer:

He could use 104 pages in the photo books .

Step-by-step explanation:

Given :

A photographer has 591 photos of animals and 234 photos of plants.

Each page of the photo books holds 8 photos.

To Find : Fewest number of pages he could use in the photo books.

Solution :

A photographer has 591 photos of animals and 234 photos of plants.

Thus total no. of photos he have = 591+234 = 825 photos

Since he wants to put all the photos into photo book  

No. of pages required for 8 photos = 1

No. of pages required for 1 photo = 1/8

No. of pages required for 825 photos:

= [tex]\frac{1}{8} *825[/tex]  

⇒103.125 pages ≈ 104 pages

Hence he could use 104 pages in the photo books .

Answer:

4.8

Step-by-step explanation:

b to c is 3.6

b to d is 8.4

if c is in the middle , you would subtract 8.4 and 3.6

Answer:

The equation of the line is y = 6x - 2 .

Step-by-step explanation:

Formula for the equation of line is.

[tex](y - y_{1}) = m (x - x_{1})[/tex]

Where m is the slope.

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

As given

If (-6,-38) and (5,28) are two anchor points on the trend line.

Than

[tex]m = \frac{28 - (-38)}{5 - (-6)}[/tex]

[tex]m = \frac{28 + 38}{5 + 6}[/tex]

[tex]m = \frac{66}{11}[/tex]

m = 6

Put the value in the equation of a line.

[tex](y - (-38)) = 6 (x - (-6))[/tex]

[tex](y + 38) = 6 (x + 6)[/tex]

[tex](y + 38) = 6x + 6\times 6[/tex]

[tex](y + 38) = 6x + 36[/tex]

y = 6x +36 - 38

y = 6x - 2

Therefore the equation of the line is y = 6x - 2 .

I used Google and got 90%...if you simplify it you will get 9/10 which is a 90%

If 18 out of 20 is given. Then the percentage will be 90%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.

The given number statement is 18 out of 20.

Then the percentage will be

P = 18/20 x 100

P = 90%

More about the percentage link is given below.

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The value in cents of n nickels: 5n

The value in cents of d dimes and p pennies: 10d + p

The value in cents of w dollars: 100w

The next whole number following a whole number w: w + 1

The value in cents of n nickels can be written as a numerical or variable expression as 5n, with n representing the number of nickels. This is because each nickel is worth 5 cents.

The quantity in cents of n nickels can be written as a numerical or variable expression. Because each nickel is worth 5 cents, you multiply the number of nickels, represented by n, by 5. This can be written as 5n. For example, if you have 4 nickels, you could calculate the total value in cents by multiplying 5 by 4, giving you 20 cents.

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Answer: 53

52.85 is closer to 53, than it is to 52

The digit after the ones digit is 8, which is 5 or larger, so that tells us to round up from 52 to 53. We drop everything after the ones digit.

the correct answer to this question would be: y=8

−(−y+18)+11  =1

y−18+11        =1

y−7              =1

y                  =8

Answer:

2 feet per year

Step-by-step explanation:

First, we need to find the amount it grew:

13 - 3 = 10

So between 2005 and 2010 it grew 10 feet.

Now to find the yearly growth we need to divide the distance by time:

10 ÷ 5 = 2

So it grew 2 feet per year.

Answer: Salesperson A made $7,428.30 in commission which is $569.10 more than Salesperson A.

Step-by-step explanation:

A: $67,530 * 0.11  = $7,428.30

B: $85,740 * 0.08 = $6,859.20

                                   $ 569.10

Answer:

12 hours

Step-by-step explanation:

Answer:

-79/20 < x< -17/20

Step-by-step explanation:

-4| 5x+12| -13> -44

The first step is to add 13 to each side

-4| 5x+12| -13+13> -44+13

-4| 5x+12| > -31

Divide each side by -4.  Remember when dividing by a negative to flip the inequality

-4/-4| 5x+12| < -31/-4

| 5x+12| < 31/4

Now we will have 2 equations, one positive and one negative.  Remember to flip the inequality for the negative

5x+12 < 31/4   and 5x+12 >-31/4

Subtract 12 from each side

5x+12-12 < 31/4-12   and 5x+12-12 >-31/4-12

5x < 31/4-12   and 5x >-31/4-12

Get a common denominator of 4

5x < 31/4-48/4   and 5x >-31/4-48/4

5x < -17/4       and   5x > -79/4

Divide each side by 5

x < -17/20    and x >-79/20

-79/20 < x< -17/20

Answer:

60 degrees.

Step-by-step explanation:

The total measure of the exterior angles of all polygons is 360 degrees,

A regular hexagon has 6 equal exterior angles so the measure of each angle is 360 / 6 = 60 degrees.

Answer:

Measure of each exterior angle for regular hexagon = 60°

Step-by-step explanation:

We have sum of interior angles of a polygon with n sides = (n-2) x 180

Sum of exterior angles =  n x 180 - (n-2) x 180 = 2 x 180 = 360 degree.

So whatever be the number of sides the sum of exterior angles of a polygon is 360°.

Here we are asked to find the measure of each exterior angle for regular hexagon.

We know sum of exterior angles = 360°

Number of exterior angles = 6

Measure of each exterior angle for regular hexagon = 360/6 = 60°

Measure of each exterior angle for regular hexagon = 60°

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

The rectangle is a quadrilateral that has four sides and the opposites are always parallel.

The statement "Some rectangles are not parallelograms" is false.

Option B is the correct answer.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

Some rectangles are not parallelograms.

The rectangle is a quadrilateral that has four sides and the opposites are always parallel.

So,

All rectangles are parallelograms.

Thus,

The rectangle is a quadrilateral that has four sides and the opposites are always parallel.

The statement "Some rectangles are not parallelograms" is false.

Option B is the correct answer.

Learn more about parallelograms here:

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