h(x)= 1/8x^3-x^2

What is the average rate of change of h over the interval −2≤x≤2?

Emily's figurine is 17 inches taller than Chen's figurine

Step-by-step explanation:

Emily and Chen built clay figurines for art class

We need to find how much taller is Emily's figurine than Chen's in inches

To solve this problem we must to change the heights of the two figurines to inch

∵ Emily's figurine is 5' 1" tall ⇒ 5 feet and 1 inch

∵ 1 foot = 12 inches

∴ The height of Emily's figurine = 5(12) + 1

∴ The height of Emily's figurine = 60 + 1

∴ The height of Emily's figurine = 61 inches

∵ Chen's figurine is 3' 8" tall ⇒ 3 feet and 8 inches

∵ 1 foot = 12 inches

∴ The height of Chen's figurine = 3(12) + 8

∴ The height of Chen's figurine = 36 + 8

∴ The height of Chen's figurine = 44 inches

To find how much taller is Emily's figurine than Chen's in inches subtract their heights

∵ The difference between the two figurine = 61 - 44

∴ The difference between the two figurine = 17 inches

∴ Emily's figurine is 17 inches taller than Chen's figurine

Emily's figurine is 17 inches taller than Chen's figurine

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Answer:

Speed of Vendelin is 60 kilometre per hour.

Step-by-step explanation:

Given:

The Distance two bus stops = [tex]\frac{3}{8}[/tex]

Speed of the bus =  60 km/h

To Find:

The Speed of  vendelin = ?

Solution:

Let the speed bof vendelin be x.  the it is stated that

" If Vendelin runs from home, he will be at the bus stop at the same time as bus."

So

Time Taken by the bus

=>[tex]\frac{ \text{ distance between the bus stop}}{\text{ speed of the bus}}[/tex]

=>[tex]\frac{\frac{3}{8}}{60}[/tex]

=>[tex]\frac{\frac{3}{8}}{\frac{1}{60}}[/tex]

=>[tex]\frac{3}{480}[/tex]------------------------------(1)

Time Taken by  Vendelin

=>[tex]\frac{ \text{ distance between the bus stop}}{\text{ speed of Vendelin }}[/tex]

=>[tex]\frac{\frac{3}{8}}{x}[/tex]

=>[tex]\frac{3}{8x}[/tex]----------------------------------(2)

Equating (1) and (2) we get

[tex]\frac{3}{480}[/tex] =  [tex]\frac{3}{8x}[/tex]

[tex]3 \times 8x = 3 \times 480[/tex]

[tex]3 \times 8x = 1440[/tex]

[tex] 8x =\frac{1440}{3}[/tex]

[tex] 8x = 480[/tex]

[tex] x =\frac{480}{8}[/tex]

x = 60

Answer:

32 ounces

Step-by-step explanation:

128oz=1gal

4quarts=1gal

128÷4=32

32oz=1 quart

Answer:

1

Step-by-step explanation:

hope this helps some one

stay safe and pease still were a mask

C. 2.3 miles

Step-by-step explanation:

The details of the image are as follows;

Ranger station to Nature Center = 90°

Nature center to petting zoo= 40°

Petting zoo to Tennis court =120°

Tennis court to Pool = 65°

Pool to Ranger station= 45°

The radius of the circular pattern = 1 mile

The formula to apply is;

Arc length = 2πr angle / 360° where r is radius and π=3.14

Finding arc length from Ranger Station to Nature Center will be;

Arc length = 2×3.14×1×90°/360°

Arc length=2×3.14×1×1/4 =1.57 miles

Finding distance from Nature Center to Petting Zoo

Arc length= 2×3.14×1×40°/360°

Arc length= 2×3.14×1×1/9 = 0.70 miles

Total =1.57+0.70 =2.27 miles

Answer to the nearest hundredth = 2.3 miles

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Answer:

The temperature at noon was 37 °F.

Step-by-step explanation:

Given:

Temperature at midnight is  34 °F.

Reduction in temperature by 6:00 a.m. is 8°. So, temperature after reduction is given as the difference in temperature at midnight and morning.

Therefore, temperature by 6:00 a.m. in the morning is given as:

Reduced temperature = Midnight temperature - Reduction in temperature.

Reduced temperature = 34 °F - 8 °F = 26 °F.

Now, by noon, the temperature is increased by 11 °F. Therefore, the final temperature by noon is addition of 11 degree to the temperature that was in the morning. Therefore,

Temperature at noon = Temperature in morning + Increase in temperature.

Temperature at noon = 26 °F + 11 °F = 37 °F.

So, the temperature at noon is a 3 °F increase to the temperature at midnight and is equal to 37 °F.

37 boiiiiiiiiiiiiiiiii

Answer:

308 cm³

Step-by-step explanation:

The volume (V) of a rectangular prism ( cuboid ) is

V = lbh ( l is the length, b the breadth and h the height )

Here l = 11, b = 7 and h = 4, thus

V = 11 × 7 × 4 = 308 cm³

Answer:

the unit rate is 1/10.

Step-by-step explanation:

4/40 divided by 4 equals 1/10

unit rate is 0.1 tickets per dollar

Answer:

Step-by-step explanation:

x = 60 + 60 = 120

Exterior angle equals the sum of opposite interior angles.

Answer:

The area of the carpet which is square in shape is  81 [tex]inches^2[/tex]

Step-by-step explanation:

Given:

side of the carpet square  = 9 inches

To Find:

area of the carpet square = ?

Solution:

The area of the carpet =  area of the square

we know that the area of the square  is

=> side X side

Substituting the side of the square, we get

=> 9 X 9

=> 81 [tex]inches^2[/tex]

1. Use the exterior angle theorem that states that an exterior angle in a triangle is equal to its two remote interior angles.

x+46=84

x=38 degrees

2. There are two parallel lines cut by transversal. We can see a same side interior relationship.

3x-5+90+2x=180

5x=95

x=19 degrees

3. Use exterior angle theorem again.

90+34=x+72

x=52 degrees

Answer:

-2/8

Step-by-step explanation:

The rule of additive inverse stays the same with fractions

Answer:

-2/8

Step-by-step explanation:

The volume of the right rectangle prism is  V = 4.252 m³.

The correct option is C.

In three-dimensional space, a prism is a polyhedron where two ends are similar.

Given:

The dimensions of a right rectangle prism are 3/4 m, 1.89 m, and 3 m.

The volume of the right rectangle prism use the formula V = l x w x h.

That means,

V = 3/4 x 1.89 x 3

V = 4.252 m³

Therefore, V = 4.252 m³.

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The markup percentage is 45.14%

Step-by-step explanation:

The given is:

We need to find the markup percentage

The markup percentage = [tex]\frac{New-Old}{old}[/tex] × 100%

∵ The selling price of a box of crackers is $1.75

∴ Old = 1.75

∵ You mark the crackers up to $2.54

∴ New = 2.54

- Substitute these values in the rule above

∵ The markup percentage = [tex]\frac{2.54-1.75}{1.75}[/tex] × 100%

∴ The markup percentage = [tex]\frac{0.79}{1.75}[/tex] × 100%

∴ The markup percentage = 0.4514 × 100%

∴ The markup percentage = 45.14%

The markup percentage is 45.14%

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Answer:

The markup percentage is 45%.

Step-by-step explanation:

Answer:

1320

Step-by-step explanation:

Write a proportion.

22 / 600 = x / 36,000

Cross multiply.

600x = 22 × 36,000

Solve for x.

x = 1320

Answer:

Step-by-step explanation:

1320

Answer:

-1

Step-by-step explanation:

add the 3 numbers together and then you get 10 so then you divide -10 by 10 and you -1

Answer:

g=5/23

Step-by-step explanation:

Answer:

x=3/2, y=10. (3/2, 10).

Step-by-step explanation:

2x-y=-7

4x-y=-4

--------------

-2(2x-y)=-2(-7)

4x-y=-4

---------------------

-4x+2y=14

4x-y=-4

-----------------

y=10

2x-10=-7

2x=-7+10

2x=3

x=3/2

To determine the students selected to go to the board, start with the fourth student and then select every ninth student thereafter. Thus, the students chosen are the 4th, 13th, 22nd, and 31st students who enter the classroom.

The question involves determining which students a professor will select to go to the board based on a specific selection process. The professor decides to randomly select the fourth student who enters the classroom and every ninth student after that. To find out who these students are, we begin by identifying the fourth student initially. After the fourth student, every ninth student subsequently means we add 9 to the initial student's number to find the next student.

The fourth student who enters

The fourth student + 9 = the 13th student

The 13th student + 9 = the 22nd student

The 22nd student + 9 = the 31st student

Therefore, the students selected to go to the board are the 4th, 13th, 22nd, and 31st students who enter the classroom.

The students who will be going to the board are students 4, 9, 18, and 27.

Let’s determine the students who will be going to the board based on the professor’s selection criteria:

1. The fourth student who enters the classroom.

2. Every ninth student after that.

Let’s find the student numbers:

1. The fourth student corresponds to the 4th position.

2. The ninth student corresponds to the 9th position.

3. The 18th student corresponds to the ninth student after that (since 9 + 9 = 18).

4. The 27th student corresponds to the ninth student after the 18th student (since 18 + 9 = 27).

Therefore, the students who will be going to the board are students 4, 9, 18, and 27.

Seth's spending on jam can be represented by two expressions: 0.80*J*(b + s) and 4*(b + s). The calculations involve finding the total cost without the discount, finding the amount of the discount, and then subtracting the discount from the total cost.

Let's denote the price of one jar of jam as J, which is $5. The number of jars of blackberry jam that Seth bought is denoted as b, and the number of jars of strawberry jam as s. Without the discount, the total cost for all the jam he bought would be J*(b + s). Given that Ms. Wells offers a 20% discount for purchasing at least two jars of jam, Seth's actual spending would be

So, Seth's spending is represented by the expression 0.80*J*(b + s) or, substituting J = $5, by 4*(b + s).

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The Question is Incomplete with the Figure,So the complete Question with Diagram is below.  

Answer:

The Proof is given Below.

Step-by-step explanation:

Given:

∠CXY ≅ ∠BXY  

∠CAX ≅ ∠BAX

AC≅ AB

To Prove:

∠XCY ≅ ∠XBY

Proof:

In  Δ AXC and Δ AXB

STATEMENT                                             REASONS

1. AC ≅ AB                                          1. Given

2. ∠CAX ≅ ∠BAX                              2. Given

3. AX ≅ AX                                        3. Reflexive Property

4. ΔAXC  ≅ ΔAXB                             4. Side-Angle-Side congruence test

5. ∴ CX ≅ BX                                     5.corresponding parts of congruent triangles........( 1 )

Now ,

In  Δ XYC and Δ XYB

STATEMENT                                             REASONS

1. CX ≅ BX                                          1. Proved above from ( 1 )

2. ∠CXY ≅ ∠BXY                              2. Given

3. XY ≅ XY                                        3. Reflexive Property

4. ΔAXC  ≅ ΔAXB                             4. Side-Angle-Side congruence test

5. ∴ ∠XCY ≅ ∠XBY                          5. Corresponding parts of congruent triangles...........Proved

Answer:

See attached image

Step-by-step explanation:

Hope this helps!

Answer:

What question? I mean all you said was 'this question' so I don't know ;-;

Step-by-step explanation:

To simplify the expression 2(x + 7) - 18x + 4/5, you distribute the 2 across (x + 7), then combine like terms to get the equivalent expression, which is -16x + 14 + 4/5.

The expression that is equivalent to 2(x + 7) - 18x + \(\frac{4}{5}\) can be simplified through the distributive property and combining like terms. First, distribute the 2 into the parentheses:

2(x) + 2(7) - 18x + \(\frac{4}{5}\)
= 2x + 14 - 18x + \(\frac{4}{5}\).

Next, combine like terms by subtracting 18x from 2x:
(2x - 18x) + 14 + \(\frac{4}{5}\)
= -16x + 14 + \(\frac{4}{5}\).

So the equivalent expression is -16x + 14 + \(\frac{4}{5}\).

Answer:

2.5 or 2 1/2 in

Step-by-step explanation:

Area = width x length

width = area / length = 11.25 / 4.5 = 2.5

Final answer:

To find the product of the given expression (7x²)(2x + 5)(x² - 4x-9), we can use the distributive property to multiply each term.

Explanation:

To find the product of the given expression (7x²)(2x + 5)(x² - 4x-9), we can use the distributive property to multiply each term.

First, multiply (2x + 5) with (x² - 4x-9) using the distributive property.
(2x + 5)(x² - 4x-9) = 2x*(x² - 4x-9) + 5*(x² - 4x-9)
= 2x³ - 8x² - 18x + 5x² - 20x-45
= 2x³ - 3x² - 38x - 45

Answer:

If X is the starting weight, total pounds lost in three months is

(0.132X + 2.37)lbs

Step-by-step explanation:

Let the starting weight be X(lb)

Let the target ending weight be Y(lb)

Since Rollie ended with 3(lbs) above goal weight, final weight is Y+3(lb)

Each month, Rollie lost 1/3 of the difference between current weight and goal weight, hence

In the first month, Rollie lost 1/3 of (X - Y)

but since Rollie ended up with 3lbs above target ending weight, the actual weight loss is 1/3(X - Y) + 3

Hence  by the end of the first month, Rollie's new weight is X - (1/3(X - Y)) + 3

which is equal to

X - 1/3X + 1/3Y - 3.

= 2/3X + 1/3Y - 3

By the second month, Rollie's starting weight is 2/3X + 1/3Y - 3(lb)

while her target ending weight still remains (Y)

but the actual ending weight is Y + 3

hence in the second month, Rollie lost 1/3(2/3X + 1/3Y - 3 - Y) + 3

= 2/9X + 1/9Y - 1 - 1/3Y + 3

=  2/9X - 2/9Y + 2

hence by the end of the second month, Rollie's new weight is

(2/3X + 1/3Y - 3) - (2/9X - 2/9Y + 2)

= 2/3X - 2/9X + 1/3Y + 2/9Y - 3 - 2

= 4/9X + 5/9Y - 5  

By the third month, Rollie's starting weight is 4/9X + 5/9Y - 5(lb)

while her target ending weight still remains (Y)

but the actual ending weight is Y + 3

hence in the third month, Rollie lost 1/3(4/9X + 5/9Y - 5 - Y) + 3

= 4/27X + 5/27Y - 5/3 - 1/3Y + 3

= 4/27X - 4/27Y + 4/3 ------------------------- eqn (*)

hence by the end of the third month, Rollie's new weight is

(4/9X + 5/9Y - 5) - (4/27X - 4/27Y + 4/3)

= 4/9X - 4/27X + 5/9Y + 4/27Y - 5 - 4/3

= 8/27X - 19/27Y - 19/3

Hence in three months, Rollie's new weight is 8/27X - 19/27Y - 19/3

To ascertain how much weight Rollie lost in three months, there is need to equate the estimated ending weight to the final weight (Y + 3)

Therefore:

8/27X - 19/27Y - 19/3 = Y + 3

this implies that

8/27X - 19/27Y - Y - 19/3 - 3 = 0

8/27X - 36/27Y -28/3 = 0

Since Y is the target ending weight

the ending weight is generated by solving the equation with respect to Y

36/27Y = 8/27X - 28/3

multiply through by 27/36

Y = 2/9X - 7

Hence weight lost in three months is generated by substituting for Y = 2/9X - 7  in eqn (*)

Since eqn * is 4/27X - 4/27Y + 4/3

the lbs lost in three months is

4/27X - 4/27(2/9X - 7 ) + 4/3

= 4/27X - 8/243X + 28/27 + 4/3

= (32/243)X + 64/27

which in decimal is

(0.132X + 2.37)lbs

The total pounds of weight that will be lost in three months will be (0.132x + 2.37)lbs.

The starting weight is illustrated by x. The target ending weight is illustrated by y.

In the first month, the weight list by Rollie will be 1/3 × (x - y) and her new weight will be:

= 2/3x + 1/3y - 3

In the second month, the starting weight will be 2/3x + 1/3y - 3. The weight lost by the end of the second month will be:

= 1/3 × (2/3x + 1/3y - 3) + 3

= 2/9x - 2/9y + 2

The new weight will be:

= (2/3x + 1/3y - 3) - (2/9x - 2/9y + 2)

= 4/9x + 5/9y - 5

In conclusion, the weight lost in three months will be:

= 4/27x - 4/27(2/9x - 7) + 4/3

= 4/27x - 8/243x + 28/27 + 4/3

= 32/343x + 64/27

= 0.132x + 2.37

In conclusion, the total pounds of weight that will be lost in three months will be (0.132x + 2.37)lbs.

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Answer:

20

Step-by-step explanation:

10 + 10 = 20

Hope this helps :)

Answer:

[tex]14 \frac{3}{8}[/tex]

Step-by-step explanation:

I assume you mean this:

[tex]8 \frac{7}{8} +(7 \frac{5}{6} -2\frac{1}{3} )[/tex]

Lets begin with the parentheses. When operating with fractions, we need them to have the same denominator. Looking at the expression in the parenthesis, we can see that the denominator of 5/6, that being 6, is twice that of 1/3, that being 3. Thus, if we multiply the numerator and denominator of 1/3 by 2, the result will be a fraction of same value, but with denominator 6, which we can work with.

[tex]\frac{1*2}{3*2}[/tex]

[tex]\frac{2}{6}[/tex]

Now we can replace this in the original parenthesis

[tex](7 \frac{5}{6} -2\frac{2}{6})[/tex]

We can now evaluate the parenthesis. 7-2=5, which leaves us with 5 5/6 - 2/6. Since the two fractions have the same denominator, we can subtract the numerator of 2/6 from 5/6. This gives us with 3/6, which we add to the 5 from before.

[tex]5\frac{3}{6}[/tex]

The numerator and denominator of 3/6 are both divisible by three, so we can simply the fraction.

[tex]5\frac{1}{2}[/tex]

Now that we have solved the parenthesis, we can plug our solution back into the original expression.

[tex]8 \frac{7}{8} +5\frac{1}{2}[/tex]

We now have a similar problem to the parenthesis, where our fractions have different denominators. However, you may notice that the denominator of 7/8 (8) is four times larger than the denominator of 1/2 (2). Thus, if we multiply the numerator and denominator of 1/2 by four, we will have a new fraction of equal value, but with denominator 8.

[tex]\frac{1*4}{2*4}[/tex]

[tex]\frac{4}{8}[/tex]

Now lets update our expression with this information.

[tex]8 \frac{7}{8} +5 \frac{4}{8}[/tex]

8+5=13[tex]13\frac{7}{8} +\frac{4}{8}[/tex], so we can further simplify the expression.

Since the denominators of the fractions are the same, we can combine the numerators. 7+4=11

[tex]13 \frac{11}{8}[/tex]

We can simplify the fraction by taking one whole out of it (8/8) and adding it as 1 instead. 11-8=3, thus the fraction that remains is 3/8.

[tex]14 \frac{3}{8}[/tex]

The operation 8 7/8+(7 5/6-2 1/3) evaluates to a final result of 14 3/8.

To evaluate this mixed number operation, we must first convert each mixed number into an improper fraction.

8 7/8 is the same as 71/8 and 7 5/6 as 47/6 and 2 1/3 as 7/3.

Now, conduct the operation inside the parenthesis, which is subtraction: 47/6 - 7/3.

To subtract fractions, they must have the same denominator. Here, the least common multiple of 3 and 6 is 6. So you have 47/6 - 14/6 equals 33/6 reduced to 5 1/2.

Then add this quantity to 8 7/8 which equals to 14 3/8 when converted to a mixed number.

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Answer:

The theorem states that if a right triangle has two sides equal to a and b, and a hypotenuse equal to c, then a squared plus b squared equals c squared. The hypotenuse of a right triangle is the side opposite the right angle.

Step-by-step explanation:

653,000 I think

since the thousands place has a 3, the first part would stay the same, 000 is added

Hope I helped :)

Answer:

653,228

Step-by-step explanation:

_________

l 700,000   l

l_________l

cause 5 is over 5 and 5 +1 to 6 +7 and all other numbers will become 0's so its 700,000

Step-by-step explanation:

Part A:

Let [tex]m[/tex] be the number of mittens and [tex]s[/tex] be the number of scarves. Then we have the inequalities:

[tex]s+m\leq 30.[/tex] This says Nivyana and Ana cannot make more than 30 scarves

[tex]50s+25m\geq 1000.[/tex] This says that Nivyana and Ana have to earn at least $1000.

Part B:

The graph is attached.

Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.

The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.

Part C:

From the graph we get two possible solutions:

15 scarves & 10 mittens

25 scarves & 5 mittens.

These two points lie on the solid lines that bound the darker shaded region (I picked those points to stress that the lines bounding the dark region are also solutions.)

Answer:

6.164414

You can figure this out because 6.164414x6.144414 is 38.