Emma is 10 years old. She asked her father how old he was. Her father answered: "When you will be my age, I will be 70." How old is Emma's father?

We know that there are about 3.785 liters in 1 gallon. From here we could pour 3 whole liters into a one-gallon container without overflowing since 3 < 3.285 liters. But if we try to pour the next whole liter( 4 liters) it would be too much since 4 is greater then 3.785 liters. So the answer is 3 liters.  

Hope this helps. <3

Answer:

1.77 to nearest hundredth

Step-by-step explanation:

Z-score = (score - mean)  / standard deviation

98 is the highest score and its z-score is (98- 81.5) / 9.3

= 1.7742

Answer: 1.77

Step-by-step explanation:

Given : The test grades of a science class are given.

78, 75, 70, 92, 69, 83, 98, 76, 75, 82, 91, 89

The grades are normally distributed with a mean [tex]\mu= 81.5[/tex] and a standard deviation [tex]\sigma=9.3[/tex] .

let x be any random variable represents the test grades of a science class.

Formula for z-score:-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

The highest score= 98

Then , the z-score of the highest grade in the test will be :-

[tex]z=\dfrac{98-81.5}{9.3}=1.77419354839\approx1.77[/tex]

Hence, the z-score of the highest grade in the test =1.77

The values less than 6,766 are one fourth x 6,766 and one half x 6,766 (A and C options are correct)

Numbers, symbols and operators (such as and times) grouped together that show the value of something.

Given is an expression, 6,766

The values less than 6,766 are,

i) 1/4x6,766 = 1691.5

1691.5 < 6,766

ii) 1/2x6,766 = 3383

3383 < 6,766

Hence, one fourth x 6,766 and one half x 6,766 are correct answers.

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Answer:

Distance from her house to her work = 12.4 Miles

Step-by-step explanation:

Given :-

==> Automator mileage gauge read 38643.8 Miles before she left to work.

==> Automator mileage gauge read 38668.6 Miles after she came home from work.

==> She didn't drive anywhere else during the day. home to work & work to      home.

Car driven during the day = 38668.6 - 38643.8

                                           = 24.8 Miles

Let the distance from home to work be X

*It is assumed that Distance from home to work = Distance from work to home

So, Distance from work to home = X

Total distance driven during the day = Distance from home to work + Distance from work to home

Total distance driven during the day = X + X

                                                    24.8 = 2X

                                                    24.8 ÷ 2 = X

                                                    12.4 = X

Distance from her house to her work = 12.4 Miles

Answer: I think the answer is 24.8

Step-by-step explanation:

Answer: 200 yards

Step-by-step explanation:

So if 3/4 inches on the map is equal to 50 yards then you could divide the 3 inch distance from him to his home by 3/4 and then multiply that answer by 50. So 3 ÷ 3/4 = 4. 4 * 50 = 200. He is 200 yards from his home.

Answer:

Step-by-step explanation:

To solve this problem, we use the rule of three, if 50 yards represents 3/4 inches, how many yards would represent 3 inches?

[tex]x=3in\frac{50yd}{\frac{3}{4}in } =3\frac{200}{3}yd=200yd[/tex]

So, 3 inches represents 200 yards, that means Harper is 200 yards away home.

Remember that the rule of three is just about using the ratio that the problem already gave.

Therefore, the answer is 200 yards.

[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\\boxed{15^{\frac{1}{3}}=\sqrt[3]{15}}[/tex]

Radical form is the form of a equation in which the number or variable is written under some power of the root. The 15 to the 1/3 power in radical form is [tex]\sqrt[3]{15}[/tex].

15 to the 1/3 power is the 1/3 power of the number fifteen and it can be expressed as,

[tex]=(15)^{\dfrac{1}{3}[/tex]

This number has to be written in the radical form.

Radical form is the form of a equation in which the number or variable is written under some power of the root.

When a fractional exponents of the number is given the numerator becomes the power and the denominator becomes the root. Let [tex]x^{\dfrac{a}{b}[/tex] is a number with fractional exponents where a and b are the real and positive integer, then a becomes the power and the b becomes the root of the number x.

[tex]x^{\dfrac{a}{b} }=\sqrt[b]{x^a}[/tex]

For the given number,

[tex]=(15)^{\dfrac{1}{3}}=\sqrt[3]{15}[/tex]

Hence the 15  to the 1/3 power in radical form is [tex]\sqrt[3]{15}[/tex].

Learn more about the radical form here;

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Answer:

10%

Step-by-step explanation:

We have been given that the manager of a store orders model railroad sets that cost $390 and sells them for $429.  

We will use markup % formula for our given problem.

[tex]\text{Markup percentage}=\frac{\text{Selling price- Cost}}{\text{Cost}}\times 100[/tex]

[tex]\text{Markup percentage}=\frac{429-390}{390}\times 100[/tex]

[tex]\text{Markup percentage}=\frac{39}{390}\times 100[/tex]

[tex]\text{Markup percentage}=\frac{1}{10}\times 100[/tex]

[tex]\text{Markup percentage}=10[/tex]

Therefore, markup is 10% of cost.

Answer:

B four pans make 32 cookies

Given : (5b - 9) - 3(8 - 26)

⇒ (5b - 9) - 3(-18)

⇒ (5b - 9) + 54

⇒ 5b - 9 + 54

⇒ 5b + 45

Answer:

i think its 5b + 45

Step-by-step explanation:

im not 100% sure what your asking for but i just distributed the -3 to the 8 and -26 and got 5b -9 -24 + 78. then i combined the like terms to get 5b + 45.

hope this helps !!

Answer: 31.5 miles

Step-by-step explanation: know how many miles tabitha walked per hour, which is 4.5 miles. then multiply 13.5 x 2, and add 4.5 to receive your answer - 31.5.

Answer:

Step-by-step explanation: The answer is 31.5 miles. The way I got it is by multiplying 13.5 by 2 because that will be 6 hours already. That gives me 27. Then you divide 13.5 to get how much she walk for just 1 hour which is 4.5. When you add that to 27, you get 31.5. Hope this helps!!!!!  

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Answer:

in the point slop form y=2x+8

the slope is 2

the y intercept is 8

The slope-intercept form of line:

y = mx + b

m - slope

b - y-intercept

We have y = 2x + 8. Therefore:

slope m = 2

y-intercept b = 8

Answer: 25%

Step-by-step explanation:

Hi, if you buy 2 sweaters at full price (100%)

$48 x 2 = $96

"Buy one get one 1/2 off sale"´price

48 + (48/2) = 48 +24 = $72

So, the normal price for both sweaters (96) multiplied by a percentage is equal to the "buy one get one 1/2 off sale” price.

96 x =72

x =72/96 = 0.75  

Multiplying by 100 to obtain the percentage form

0.75 =75%

So, the sale price is %75 of the full price.

To obtain the percent discount.

100%-75% = 25%

Answer:

The second option is correct. The point slope form of AB is [tex]y+1=\frac{-3}{2}(x-1)[/tex].

Step-by-step explanation:

The given points are A(-3,5) and B(1,-1).

Slope of a line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope of AB is

[tex]m=\frac{-1-5}{1-(-3)}[/tex]

[tex]m=\frac{-6}{4}[/tex]

[tex]m=\frac{-3}{2}[/tex]

The point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is slope of the line.

Case 1: The slope of the line is [tex]\frac{-3}{2}[/tex] and the point is (-3,5). The point slope form of AB is

[tex]y-5=\frac{-3}{2}(x+3)[/tex]

Case 1: The slope of the line is [tex]\frac{-3}{2}[/tex] and the point is (1,-1). The point slope form of AB is

[tex]y+1=\frac{-3}{2}(x-1)[/tex]

Therefore the point slope form of AB is [tex]y+1=\frac{-3}{2}(x-1)[/tex]. Option 2 is correct.

Answer:

27 cm

Step-by-step explanation:

So the square root of 729 is 27

Answer:

y = [tex]\frac{1}{2}[/tex] x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = [tex]\frac{1}{2}[/tex], hence

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (4, 9) into the partial equation

9 = 2 + c ⇒ c = 9 - 2 = 7

y = [tex]\frac{1}{2}[/tex] x + 7 ← equation in slope-intercept form

Answer:

[tex]3x+4y=-24[/tex]

Therefore, option C is correct.

Step-by-step explanation:

We have been given the equation:

[tex]y=\frac{-3x}{4}-6[/[/tex]

We will take LCM 4 on right hand side of the above equation:

[tex]y=\frac{-3x-24}{4}[/tex]

Now, we will multiply the 4 in denominator on right hand side to the y in left hand side pof the equation we get:

[tex]4y=-3x-24[/tex]

After rearranging the terms we get:

[tex]3x+4y=-24[/tex]

Therefore, option C is correct.

Answer:

180

Step-by-step explanation:

30% of 150 = 30

because

30% of 15 = 3

30 + 150 = 180

Answer:

Step-by-step explanation:150+30=180

Answer:

(6,1)

Step-by-step explanation:

I used the Midpoint Formula.

Answer:

y-4 = 3 (x-2)

Step-by-step explanation:

To find the slope of a line

slope = (y2-y1)/(x2-x1)

slope = (1-4)/(2-3)

         = -3/-1

         =3

Now we use the point slope form for a line

y-y1 = m(x-x1)

y-4 = 3 (x-2)

Answer:

y-4 = 3 (x-2)

y=-3x+10

The percentage increase in the height of the corn stalks is 20%. This was calculated by subtracting the old height from the new height, dividing by the old height, and then multiplying by 100.

The question is asking about the percentage increase in the height of the corn stalks that Alice planted. The stalks were previously 60 inches tall and now, they are 72 inches tall.

The formula to calculate the percentage increase is:

[(New Value - Old Value) / Old Value] x 100%

Substituting the given values into the formula, we get

[ (72 - 60) / 60 ] x 100%

This simplifies to [12/60] x 100%, which equals to 20%.

Therefore, there has been a 20% increase in the height of the corn stalks.

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The simplified form of the rational expression 6x^2-54/5x^2+15x is 6(x - 3)/5x. This was achieved by factoring the original expressions, cancelling out common terms, and applying the difference of squares formula.

The subject here is the simplification of a rational expression. First, let's factor the numerator (6x^2 - 54) and the denominator (5x^2 + 15x). The common factor in the numerator is 6 and in the denominator is 5x. After factoring we get:

6x^2 - 54 = 6(x^2 - 9)

5x^2 + 15x = 5x(x + 3)

Now, we can use the property a^2 - b^2 = (a + b)(a - b) to further simplify x^2 - 9 to (x - 3)(x + 3). This gives our new numerator as 6(x - 3)(x + 3).

The denominator 5x(x + 3) remains the same. Therefore, the simplified form of the rational expression is 6(x - 3)(x + 3)/5x(x + 3). The (x + 3) terms can be cancelled out leaving us with the final simplified rational expression of:

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Answer:

x=9

Step-by-step explanation:

2x+3y =36

We know y =6, so we can substitute this into the equation

2x+ 3(6) = 36

2x+18 = 36

Subtract 18 from each side

2x+18-18 = 36-18

2x =18

Divide each side by 2

2x/2 =18/2

x=9

I really like that you put the answer out there for other people. that's pretty cool! B) 9

Answer: q²x² - p³x + 3pqx + q = 0

Step-by-step explanation:

Since a and B are the roots of x² - px + q = 0, then x = a and x = B

⇒ (x - a)(x - B) = 0

⇒ x² - ax - Bx + aB = 0

⇒ x² - (a + B)x + aB = 0

Comparing this to the given equation of x² - px + q = 0, we discover that

Next, given the roots for the new equation as [tex]x = \dfrac{a}{B^2} \quad\text{and}\quad\ x=\dfrac{B}{a^2}[/tex]

⇒ [tex]\bigg(x - \dfrac{a}{B^2}\bigg)\bigg(x-\dfrac{B}{a^2}\bigg)=0[/tex]

⇒ (B²x - a)(a²x - B) = 0

⇒ a²B²x² - a³x - B³x + aB = 0

⇒ a²B²x² - (a³ + B³)x + aB = 0

Let's look at each term individually:

1st term: a²B²x² = (aB)²x²   = q²x²  (since q = aB)

2nd term: (a³ + B³)x  cubic formula can be used

             = [(a + B)(a² - aB + B²)]x

              = [(a + B)(a² + (2aB - 3aB) + B²)]x

              = [(a + B)(a² + 2aB + B² - 3aB)]x

              = [(a + B)(a + B)² - 3aB)]x

              = [(   p   )(  p²     -  3 q      )]x      since p = a + B and q = aB

              = (p³ - 3pq)x       distributed "p" into p² - 3q

              = p³x - 3pqx       distributed "x" into p³ - 3pq

3rd term: aB = q       since q = aB  

Put it all together:

   q²x² - (p³x - 3pqx) + q = 0

⇒ q²x² - p³x + 3pqx + q = 0

Answer:

(3r-10) (r+8)

Step-by-step explanation:

3r-34r+80

The first step is to combine like terms

3r - 34r

is -31r

-31r+80

We cannot factor since 31 is a prime number and 80 is not a multiple of 31

If you mean

3r^2-34r+80

(3r-10) (r+8)

To calculate 6691 divided by 28 using long division, divide each set of numbers step by step to arrive at a quotient of 238 with a remainder of 27, resulting in a decimal of approximately 238.96 when rounded.

The question involves the process of long division which is a method used in arithmetic. The student is trying to divide 6691 by 28:

Divide 66 by 28, which goes 2 times. Write 2 above the division bar, to the right of the first quotient place.

Multiply 2 by 28, which is 56, and subtract that from 66 to get a remainder of 10. Bring down the next digit, 9, to make 109.

Divide 109 by 28, which goes 3 times. Write 3 on the division bar. Multiply 3 by 28 (equals 84) and subtract from 109 to get 25.

Bring down the next digit, 1, to make 251. Divide this by 28, which goes 8 times. Eight times 28 is 224. Subtract this from 251 to get 27.

27 is less than 28, so the division process stops here. The answer up to this point is 238, with a remainder of 27.

The long division calculation of 6691 divided by 28 is 238 with a remainder of 27 or as a decimal, 238.96.

Answer:

x² + y² = 5

Step-by-step explanation:

The circle with center (h, k) and radius r has equation ...

... (x -h)² + (y -k)² = r²

You can find r² using the Pythagorean theorem or the distance formula, or you can simply calculate what it needs to be to make one or the other of the points lie on the circle.

For (h, k) = (0, 0), the equation is ...

... (x -0)² + (y -0)² = r²

Using (-1, 2) for (x, y), we can find r² as ...

... (-1 -0)² + (2 -0)² = r² = 1 + 4 = 5

Then the circle equation is ...

... x² + y² = 5

Answer:

A

Step-by-step explanation:

Answer:

If on USA TEST PREP it is D

Step-by-step explanation:

[tex]2x^4+22x^3+60x^2=2x^2(x^2+11x+30)=2x^2(x^2+6x+5x+30)\\\\=2x^2[x(x+6)+5(x+6)]=2x^2(x+6)(x+5)\\\\Answer:\ x+5[/tex]

Answer:

(x+5) is the final answer.

Step-by-step explanation:

We have to find the factors of [tex]2x^4+22x^3+60x^2[/tex]

Then select correct choice or choices from the given options.

[tex]2x^4+22x^3+60x^2[/tex]

[tex]=2x^2(x^2+11x+30)[/tex]

[tex]=2x^2(x^2+6x+5x+30)[/tex]

[tex]=2x^2(x(x+6)+5(x+6))[/tex]

[tex]=2x^2((x+5)(x+6))[/tex]

[tex]=2x^2(x+5)(x+6)[/tex]

From above factors, we see that only (x+5) is correct.

Hence (x+5) is the final answer.