THE AP CALCULUS EXAM SCORES WERE RELEASED IN JULY. THE SECONDARY MATH SPECIALIST PREPARED THE BOX PLOT SHOWN TO PRESENT THE SCORES TO THE SUPERINTENDENT. WHAT'S THE RANGE OF SCORES THAT REPRESENTS THE MIDDLE 50 PERCENT OF THE STUDENTS WHO TOOK THE TEST?
    
  A. 65%–89%
  B. 65%–94%
  C. 81%–89%
  D. 65%–81%

Answer:

3050

Step-by-step explanation:

We are given side length of a cube = (3x+2y).

Volume is given by formula [tex]V=s^3[/tex], where s is the side of cube.

We have s = (3x+2y).

Plugging s = (3x+2y) in formula now.

We get,

[tex]V=(3x+2y)^3[/tex]

Expanding by applying formula [tex](a+b)^3=(a)^3 + 3a^2b+3b^2a+(b)^3.[/tex]

[tex](3x+2y)^3 =(3x)^3+3(3x)^2(2y)+3(2y)^2(3x)+(2y)^3[/tex]

[tex](3x+2y)^3 = 27x^3+54x^2y+36xy^2+8y^3[/tex]

Answer:

D

The side length, s, of a cube is 3x + 2y. If V = s3, what is the volume of the cube?

3x3 + 18x2y + 36xy2 + 8y3

27x3 + 54x2y + 18xy2 + 2y3

27x3 + 18x2y + 12xy2 + 2y3

27x3 + 54x2y + 36xy2 + 8y3

Answer:

 Total weight of the nuts bought by Dan =  5.4 kg

Explanation:

Number of packets of nuts bought by Dan = 24

Weight of each packet of nuts = 225g

 Total weight of the nuts bought by Dan = Number of packets of nuts bought by Dan * Weight of each packet of nuts

    Total weight of the nuts bought by Dan = 24 * 225 = 5400 g = 5400/1000 kg = 5.4 kg

    Total weight of the nuts bought by Dan =  5.4 kg

The answer is the first option: Even.

The explanation for this exercise is shown below:

1. By definition, if [tex]f(x)=f(-x)[/tex] the fucntion is even.

2. When the graph is symmetric with respect to the y-axis, it is an even function.

3. As you you can see in the graph attached in the problem, the graph is symmetric about the y-axis. Therefore, you can conclude it is an even function.

91/7= 13

13 portraits in 1 week

13x4=52

52 portraits in 4 weeks

Answer:

The first and third one

Step-by-step explanation:

Answer:

[tex]\frac{7y^{2} +9x}{4}[/tex] and 6y²+5x

Step-by-step explanation:

Polynomials are algebraic expressions involving one, or even more than one variables raised to any power summing each other. Generally speaking, in other words an one variable Polynomial is

[tex]a_{0}+a_{1} x+a_{2} x^{2}...a_{n} x^{n}[/tex]

So a multivariate polynomial expression are [tex]\frac{7y^{2} +9x}{4}[/tex] and 6y²+ 5x.

Because in the other options:

We have a Radical of an Irrational number[tex]\sqrt{3} =3^{\frac{1}{3}}[/tex] times x (2nd option) what does not configure a polynomial.

And a Polynomial Quotient with a variable on the denominator, described by:

[tex]P(x)=\frac{Q(x)}{R(x)} \\ P(x)=q(x)*Q(x)+R(x)[/tex]

Like the last option:

[tex]\frac{7x^{2}+8}{4x}[/tex]

(A) j || k by the converse of the same-side interior angle Theorem is your answer

Note that " j || k" means that line j & k are parallel (True)

Note that both ∠1 & ∠2 are on the same side, and that they are located inside the parallelogram produced by the transversal lines (Same Side - Interior Angle Theorem)

Therefore, (A) is your answer

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~Rise Above the Ordinary

Lines are parallel if they have the same slope, not necessarily if the sum of their angles equals to 180.

The statement 'm1 + m2 = 180' typically holds true for two lines that are straight, where m1 and m2 are the angles measured from each line to a common line. If the sum of m1 and m2 adds up to 180º, the lines are supplementary, meaning they add up to form a straight line. However, they are not parallel.

In the context of lines that are parallel, they would have the same slope, but not necessarily the same angle. For instance, in a coordinate plane, the lines y = 4x + 1 and y = 4x - 3 are parallel because they have the same slope (4), but their y-intercepts are different.

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The value of f(12) which represents the amount of interest he will receive after 12 months is; $120.

Evidently, the sequence is an arithmetic progression;

As such, we must evaluate the common difference, d as follows;

The first term, a = $10

Therefore; From the nth term formula for an arithmetic progression;

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Add 15 to both sides.

8a>88

divide by 8

a>11

so b

8a-15>73

8a-15+15>73+15

Add 15 to both sides

8÷8a>88÷8

Divide both sides by 8

a>11

So you answer is B because the sign is only greater than and not and greater than equal to sign. Also remember if the sign is going > than the line goes to your right and if the sign is < than the line goes to the left of it.

The vertex of  f ( x )  is at  x  =  − 8/ 2   =  − 4

Answer:

Correct answer is D (-1,9)

A.

(-4,2)

B.

(4,-2)

C.

(1,-9)

D.

(-1,9)

Step-by-step explanation:

The 8 is in the hundredths place.

Hope this helps & good luck. :)

If the velocity of the rower is V1=3mph and velocity of the river is V2=7mph and

V1 ⊥V2 then

tanα=7/3 => tanα ≈ 2.33 => α≈ 66.8° ≈ 67°

The correct answer is 67°

Good luck!!!

Final answer:

To find the angle at which the man drifts downstream, we use the arctangent function on the ratio of the river's speed to the man's rowing speed. The calculation is θ ≈ arctan(7/3), which results in an angle of approximately 67 degrees.

Explanation:

The student's question involves finding the angle of drift for a man rowing across a river with a current. The man rows at 3 mph in still water, while the river flows at 7 mph. To find the angle of drift, we must use the concept of vectors and solve a vector addition problem, where one vector represents the man's rowing speed and the other represents the current of the river.

We can visualize this with a right triangle where the horizontal side represents the river flow and the vertical side represents the man's rowing speed. The angle of drift (\( \theta \)) between the resulting vector (the hypotenuse) and the direction the man is heading (across the river) can be found using the arctangent function:

[tex]\( \theta = \arctan(\frac{river\ speed}{man's\ rowing\ speed}) \)[/tex]

[tex]\( \theta = \arctan(\frac{7\ mph}{3\ mph}) \)Solving this, we find:[/tex]

[tex]\( \theta \approx \arctan(2.333) \)\( \theta \approx 66.8^\circ \)[/tex]

Therefore, rounding to the nearest degree, the angle to the line on which he is heading that the man drifts downstream is approximately 67 degrees.

Where is the question?

If you're referring to factorials, then,

6! = 6*5*4*3*2*1 = 720

You start with 6 and count your way down to 1, multiplying along the way.

Since there's a negative in front of the parenthesis, it switches the values inside. So that it's -2h+18=7h. h = 2

1. 5(5 + w) = 25 + 5w

2. 1.5(3 - 8c) = 4.5 - 12c

You simply use the distributive property to distribute the number outside of the parentheses to each term within the parentheses.

Answer : $1,174.70

A circular pool has  diameter of 18 ft will have a uniform 4 ft concrete walkway   around it.

Diameter = 18ft . So radius = [tex]\frac{18}{2} = 9ft[/tex]

Area of circular pool = [tex]\pi r^2= 3.14 *9*9= 254.34 ft^2[/tex]

Radius of the pool with concrete = 9 + 4= 13

Area of circular pool with concrete=  [tex]\pi r^2= 3.14 *13*13= 530.66 ft^2[/tex]

Now surface area of concrete = area of pool with concrete - area of pool

Surface area = 530.66 - 254.34 = 276.32 square feet

the concrete cost $4.25 a square foot of surface area

So the cost for the concrete =  276.32 * 4.25 = $ 1174.36

We used the approximate value of pi that is 3.14 . so we got approximate answer

The option close to our answer is $1,174.70

$1,174.70 is the cost for the concrete

Charity donated by Tillman = $3540

Number of employees who donated = 118

Contribution of Tillman = 40%

Let the average contribution of employees be = x

Then the amount contributed by employees = 118x

Then contribution of Tillman = [tex]\frac{40}{100}\times118x[/tex]

As Tillman donated 3540 , then

[tex]3540=\frac{40}{100}\times118x[/tex]

[tex]3540=47.20x[/tex]

[tex]x=75[/tex]

Hence, average contribution by each employee is $75.

Option C is correct.

Answer:

$75

Tillman's donation = .40(total employees' donations)

$3540 = .40x

x = 8850

8850

118

= $75 for each employeeep explanation:

$75

Tillman's donation = .40(total employees' donations)

$3540 = .40x

x = 8850

8850

118

= $75 for each employee

Answer:

A) (3, 12)

Step-by-step explanation:

For such a problem, I like to use a graphing calculator. It shows the answer quickly without a lot of fuss.

_____

If you want to solve this analytically, set the difference in y-values equal to zero and solve the resulting quadratic in the usual way. This will give the x-value at which the y-values are equal. (After we find x, we still need to find y.)

... y - y = 0

... x² -2x +9 -4x = 0

... x² -6x +9 = 0 . . . . . . collect terms. Recognize this as a perfect square.

... (x -3)² = 0

... x = 3 is the solution to this

... y = 4x = 4·3 = 12

The point on each of the given curves is (x, y) = (3, 12). The line is tangent to the parabola there, so there is only one point of intersection.

The line y = 4x and the parabola y = x^2 - 2x + 9 intersect at the point (3, 12).

To find the intersection points of the line y = 4x and the parabola y = x^2 - 2x + 9, we set the two equations equal to each other and solve for x. Hence the equation to solve is 4x = x^2 - 2x + 9. Rearranging this gives the quadratic equation x^2 - 6x + 9 = 0. This factors to (x - 3)^2 = 0, so x = 3 is the only solution, meaning the line and the parabola intersect at x = 3. Substituting x = 3 back into either the line or parabola equation gives y = 12, so the point of intersection is (3, 12).

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Answer:

 729 is a perfect cube. The number whose cube is 729 is 9.

Explanation:

 Let us find the cubes of natural numbers from starting

     1 x 1 x 1 = 1

     2 x 2 x 2 = 8

     3 x 3 x 3 = 27

     4 x 4 x 4 = 64

     5 x 5 x 5 = 125

     6 x 6 x 6 = 216

     7 x 7 x 7 = 343

     8 x 8 x 8 = 512

     9 x 9 x 9 = 729

    10 x 10 x 10 = 1000

So we got that 729 is the cube of 9, so 729 is a perfect cube.

The number whose cube is 729 is 9.

Final answer:

Yes, 729 is a perfect cube and the number whose cube is 729 is 9.

Explanation:

Yes, 729 is a perfect cube.

To find the number whose cube is 729, we can take the cube root of 729, which is denoted as ∛729.

∛729 = 9

Therefore, the number whose cube is 729 is 9.

No! Nadia is not correct, the maximum is actually 4 hours. I know this because

4(9.75h+3)=150          distribute

39h-12=150              get the value h alone by adding 12

39h = 162                 divide both sides by 39

h=4.15

No, Nadia is incorrect, the maximum is actually 4 hours.

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that the equation below can be used to determine the number of hours, h , the 4 friends can rent bikes with $150.

4 (9.75h - 3) = 150

Solving;

4(9.75h+3)=150          

Now distribute

39h-12=150              

To get the value h alone by adding 12;

39h = 162                

Then divide both sides by 39

h=4.15

She have enough money to rent bikes for a maximum of 4 hours.

Learn more about equations here;

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You did everything right all the way up to one small thing at the end.  When you moved the decimal to the left and made 10.35 into 1.035, you would need to make the exponent an 11.  Raising the exponent will show that you have moved the decimal more than the original problem started with.  

Hope this helps?

In the second to the last step (10.35 x 10¹⁰), you moved the decimal of 10.35 one place to the left but you did not balance it by moving 10¹⁰ one place to the right. FYI: Moving the exponent one place to the right means to add one to the exponent.

The correct answer: 1.035 x 10¹¹

To estimate the value of y when x = 14 using exponential regression, we first find the equation that best fits the data, and then substitute x = 14 into it. The estimated value of y when x = 14 is approximately 223.7.

To find the value of y when x = 14 using exponential regression, we need to first find the equation that best fits the data. We can do this by using a graphing calculator or software that can perform exponential regression. Once we have the equation, we can substitute x = 14 into it to find the estimated value of y.

The exponential regression equation that best fits the data is [tex]y = 4 \times 2.0487^x.[/tex] Plugging in x = 14 into this equation gives us  [tex]y = 4 \times 2.0487^{14} = 223.7.[/tex]

Therefore, the estimated value of y when x = 14 is approximately 223.7.

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To estimate the value of y when x = 14 using exponential regression, we first need to find the exponential equation that best fits the given data points. The estimated value of y when x = 14 is approximately D. 223.7.

To estimate the value of y when x = 14 using exponential regression, we first need to find the exponential equation that best fits the given data points.

We can do this by using a graphing calculator or a statistical software. Once we have the equation, we can substitute x = 14 into the equation to find the estimated value of y.

Using the given data points, the exponential regression equation that best fits the data is y = 3.6841 * (1.5693)^x. Substituting x = 14 into the equation, we get: y = 3.6841 * (1.5693)^14 ≈ 223.7.

Therefore, the estimated value of y when x = 14 is approximately 223.7. Therefore, the correct answer is D. 223.7.

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Answer:

The statement is false because the conclusion is false.

Step-by-step explanation:

"then it is 0" is the conclusion. This is false because not all integers are 0.

Answer:

D

Step-by-step explanation:

Start by subtracting 64 from both sides:

[tex]25x^2=225[/tex]

Factor this by taking roots.  Divide both sides by 25 first:

[tex]x^2=9[/tex]

We "undo" a square by taking the square roots of both sides.  Taking the square root leaves the possibilities of both the positive and negative roots of 9.  Therefore, the solutions to this are

[tex]x=\sqrt{3},-\sqrt{3}[/tex]

Hello!

The function f/g means that that f(x) is written in the numerator and g(x) is written in the denominator because we are dividing the functions f(x) and g(x). (f/g = f(x)/g(x))

f(x)/g(x) is shown as: (3x - 6)/(x - 2).

The function shown above can be factored before we find the domain, since the greatest common factor of the numerator is 3.

f(x)/g(x) = 3(x - 2)/(x - 2)

f(x)/g(x) = 3

The function y = 3 is a horizontal line, so it has a domain of all real numbers.

Therefore, f/g is 3, and its domain is all real numbers, which is choice D.

Final answer:

The quotient of the functions f(x) = 3x - 6 and g(x) = x - 2 is 3. The domain of this quotient function is all real numbers except x = 2.

Explanation:

To find the quotient of the functions f(x) = 3x - 6 and g(x) = x - 2, we divide f(x) by g(x):

f/g = (3x - 6) / (x - 2).

Simplifying the expression:

f/g = 3(x - 2) / (x - 2).

Since (x - 2) is a common factor in both the numerator and the denominator, we can cancel it out as long as x is not equal to 2 (since division by zero is undefined):

f/g = 3; for all x ≠ 2.

Therefore, the quotient of f and g is 3, and the domain of this quotient function is all real numbers except x = 2.

Final answer:

If we want to plot the graph of the equation y = -56x - 4, we can select two points on the line by choosing arbitrary values for x and then calculating the corresponding y-values.

Step-by-step explanation:

Let's choose x = 0 and x = 1 for simplicity:

1. When x = 0:

- Substitute x = 0 into the equation: y = -56(0) - 4

- Simplify the expression: y = 0 - 4 = -4

- So, the first point is (0, -4).

2. When x = 1:

- Substitute x = 1 into the equation: y = -56(1) - 4

- Simplify the expression: y = -56 - 4 = -60

- So, the second point is (1, -60).

Now we have two points on the line: (0, -4) and (1, -60). We can plot these points on a coordinate plane and draw a straight line passing through them to graph the equation y = -56x - 4.

Answer: The total amount of bacteria present after [tex]10^3[/tex] hours is [tex]10^{14}[/tex].

Explanation:

It is given that the Strep throat is caused by Streptococcus bacteria. The amount of bacteria multiplies at a rate of 10^13 per 10^2 hrs.

[tex]10^2[/tex] hours = [tex]10^3[/tex] bacteria

The amount of bacteria in one hours is,

[tex]\text{Bacteria}=\frac{10^{13}}{10^2}[/tex]

The amount of bacteria after [tex]10^3[/tex] hours is,

[tex]\text{Bacteria}=\frac{10^{13}}{10^2}\times (10^3)[/tex]

[tex]\text{Bacteria}=10^{13}\times 10[/tex]

[tex]\text{Bacteria}=10^{14}[/tex]

Therefore, the total amount of bacteria present after [tex]10^3[/tex] hours is [tex]10^{14}[/tex].