Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises.

f(−1) =

f(1) =

f(2) =

Answer:

$17.35/h

Step-by-step explanation:

In order to get the amount per hour he made, you first need to calculate the global amount of money he made.

He was paid $2,900 then he had costs of $1,200, that leaves him a net income of $1,700 ($2,900 - $1,200)

Then he worked a total of 98 hours for that money.

A salary is an amount of money expressed by a period of time.  In this case, we'll use hours.

So, Jonah earned $1,700 after 98 hours of work:

S = $1,700 / 98 hours = $17.35/h

Answer:

3 Cans.

Step-by-step explanation:

Each cat can take one portion. so

9 ÷ 3 = 3

3  cans a day

Answer:

Step-by-step explanation:

X: (x1 + x2)/2 = (3 - 3)/2 = 0/2 = 0

y: (y1 + y1)/2 = (4 - 6)/2 = -2/2 = - 1

Midpoint (0,-1)

ANSWER

[tex](0, - 1)[/tex]

EXPLANATION

The midpoint formula is given by:

[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

To find the midpoint of the segment joining A (3,4) and B (-3,-6), we substitute the points into the formula:

[tex](\frac{3+ - 3}{2},\frac{4+ - 6}{2})[/tex]

We simplify to obtain;

[tex](\frac{0}{2},\frac{ - 2}{2})[/tex]

This gives us;

[tex](0, - 1)[/tex]

The midpoint of line segment AB is (0,-1)

Answer:  The required probability that the random student selected plays both tennis and basketball is 22%.

Step-by-step explanation:  Given that in a school, 40% of the students play tennis, 24% of the students play baseball, and 58% of the students playing neither tennis or baseball.

We are to find the probability that a random student picked plays both tennis and basketball.

Let the total number of students in the school be 100. Also, let T and B represents the set of students who play tennis and basketball respectively.

Then, according to the given information, we have

[tex]n(T)=40,~~~n(B)=24.[/tex]

The number of students who play either tennis or basketball will be represented by T ∪ B.

And so, we have

[tex]n(T\cup B)=100-58=42.[/tex]

We know that the number of students who play both tennis and basketball is denoted by T ∩ B.

From set theory, we get

[tex]n(T\cup B)=n(T)+n(B)-n(T\cap B)\\\\\Rightarrow n(T\cap B)=n(T)+n(B)-n(T\cup B)\\\\\Rightarrow n(T\cap B)=40+24-42\\\\\Rightarrow n(T\cap B)=22.[/tex]

Thus, the required probability that the random student selected plays both tennis and basketball is 22%.

Answer:

D. [tex]y=3\cos(\frac{4}{3}x-2\pi)+2[/tex]

Step-by-step explanation:

The given function is:

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

This function is of the form:

[tex]y=A\sin(Bx-C)+D[/tex], where [tex]B=\frac{2}{3}[/tex]

The period is given by:

[tex]T=\frac{2\pi}{B}[/tex]

[tex]T=\frac{2\pi}{\frac{2}{3}}=3\pi[/tex]

Half of this period is [tex]\frac{3\pi}{2}[/tex].

The function that has a period of [tex]\frac{3\pi}{2}[/tex] is

[tex]y=3\cos(\frac{4}{3}x-2\pi)+2[/tex]

Answer:

d.y = 3cos(4/3x - 2π) + 2

Step-by-step explanation:

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^{-3}\cdot x^3\cdot y^{-4}\implies \cfrac{1}{\begin{matrix} x^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot ~~\begin{matrix} x^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \cdot \cfrac{1}{y^4}\implies \cfrac{1}{y^4}[/tex]

Answer:

Step-by-step explanation:

I'm not quite sure about my answers though, sorry :(

Hope I helped :)

Answer:

6.13

Step-by-step explanation:

Using Sine Law we know that

[tex]\dfrac{a}{SinA}=\dfrac{b}{SinB}=\dfrac{c}{SinC}[/tex]

Using your figure let's assign sides and angles:

A=? B = 60° C = 70°

a = 5 b = ? c = x

If we put that into our formula:

[tex]\dfrac{5}{Sin?}=\dfrac{?}{Sin60}=\dfrac{x}{Sin70}[/tex]

Notice that we have too many unknowns. We need to complete at least one ratio to do this, so how do we do this?

Notice we have 2 angles given, so we solve for the third angle. The sum of all angles in any triangle is always 180°

∠A + ∠B + ∠C= 180°

∠A + 60° + 70° = 180°

∠A + 130° = 180°

∠A = 180° - 130°

∠A = 50°

Now we can use this to solve for x.

[tex]\dfrac{5}{Sin50}=\dfrac{x}{Sin70}\\\\\dfrac{(5)(Sin70)}{Sin50} = x\\\\\dfrac{4.6985}{0.7660}=x\\\\6.1338 =x[/tex]

So the closest answer would be 6.13

Answer:

The correct answer option is 6.13.

Step-by-step explanation:

We are given a scalene triangle which has no equal side and we are to find the unknown side length x.

Since the total measure of angles of a triangle is 180°, so we can find the measure of the unknown angle.

180° - 70° + 60° = 50°

Now we can use the sine formula to find the value of x.

[tex]\frac{x}{sin70} =\frac{5}{sin50}[/tex]

[tex]x=\frac{5}{sin50} \times sin70[/tex]

[tex]x=6.13[/tex]

Answer:

Step-by-step explanation:

A quadratic equation is an expression that has an x^2 term. Quadratic equations are most commonly expressed as ax^2+bx+c, where a, b and c are coefficients. Coefficients are numerical values. For example, in the expression 2x^2+3x-5, 2 is the coefficient of the x^2 term. Once you have identified the coefficients, you can use a formula to find the x-coordinate and the y-coordinate for the minimum or maximum value of the quadratic equation.

Determine whether the function will have a minimum or a maximum depending on the coefficient of the x^2 term. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum. For example, if you have the function 2x^2+3x-5, the function has a minimum because the x^2 coefficient, 2, is positive.

Divide the coefficient of the x term by twice the coefficient of the x^2 term. In 2x^2+3x-5, you would divide 3, the x coefficient, by 4, twice the x^2 coefficient, to get 0.75.Multiply the Step 2 result by -1 to find the x-coordinate of the minimum or maximum. In 2x^2+3x-5, you would multiply 0.75 by -1 to get -0.75 as the x-coordinate.

Plug in the x-coordinate into the expression to find the y-coordinate of the minimum or maximum. You would plug -0.75 into 2x^2+3x-5 to get 2_(-0.75)^2+3_-0.75-5, which simplifies to -6.125. This means the minimum of this equation would be x=-0.75 and y=-6.125.

If there is not a number before a variable, the coefficient is 1. For example, if your expression is x^2+5x+1, the x^2 coefficient is 1.

Answer:

hcch6z0d7gpxufufuguftrfue6oo7

Answer:

21

Step-by-step explanation:

There are 144 M&M's in the bag.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Number of red candies = 16

Also it is given that One-ninth of the candies in a bag of M&M's are red

1/9 of the candies in a bag of M&M's are red

Let x be the M&M's candies

So, we can write,

1/9 x = 16

⇒  x = 144

Thus, there are 144 M&M's in the bag.

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Answer:

[tex]a =111.1\ m/s^2[/tex]

Step-by-step explanation:

The formula to calculate the average acceleration is:

[tex]a =\frac{s_2-s_1}{t_2-t_1}[/tex]

Where s is the speed of the object and t is the time it takes the object to change its speed [tex]s_1[/tex] to the speed [tex]s_2[/tex]

In this case we have that:

[tex]t_2-t_1 = 5\ sec[/tex]

[tex]s_1 = 500\ km/h = 500*\frac{1\ h}{3600\ s}*\frac{1000\ m}{1\ km}=138.89\ m/s[/tex]

[tex]s_2= 2500\ km/h = 2500*\frac{1\ h}{3600\ s}*\frac{1000\ m}{1\ km}=694.44\ m/s[/tex]

[tex]a =\frac{694.44-138.89}{5}\ m/s^2[/tex]

[tex]a =111.1\ m/s^2[/tex]

Answer:

25

Step-by-step explanation:

A box contains 100 colored chips

Some are yellow and,

Some are green.

John has recorded 57 yellow chips and 19 green chips.

The ratio of yellow chips to green chips is 57:19 simplified becomes; 3:1

The number of green chis is [tex]\frac{1}{3 + 1}[/tex] × 100 = [tex]\frac{1}{4}[/tex] × 100 = 25

Answer:

6=n   and -2=n

Step-by-step explanation:

The distance between two points is found by

d = sqrt(( x2-x1)^2 + (y2-y1)^2)

5 = sqrt(( n-2)^2 + (4-1)^2)

5 = sqrt(( n-2)^2 + (3)^2)

Square each side

5^2 = sqrt(( n-2)^2 + (3)^2)^2

25 = ( n-2)^2 + (3)^2

25 = (n-2)^2 +9

Subtract 9 from each side

25-9 = (n-2)^2 +9-9

16 = (n-2)^2

Take the square root of each side

sqrt(16) = sqrt( (n-2)^2)

±4 = n-2

Add 2 to each side

2±4 = n-2+2

2 ±4 = n

2+4 =n   and   2-4 =n

6=n   and -2=n

Answer:

The answer is 84cm^2.

Step-by-step explanation:

To find the area, you need to find the length x width. here is an equation to help:

A=L X W

Lets plug the numbers into the equation:

A=6cm X 14cm

Now, mulitply:

A=84cm^2

hope this helps

84, you multiply 14x6 for the area

let the points of G be (a,b)

mid point of GH =(-6,-3)

point of H =(-4,4)

now,

for x coordinate,

-6=(a-4)/2

or, a-4 =-12

or, a=-8

for y coordinate,

-3=(b+4)/2

or, -6=b+4

or, b=-10

therefore, the coordinate of G is (-8,-10)

To solve the question, we use the midpoint formula, which is derived from the concept of averages. Given the midpoint and one endpoint, we can find the other endpoint by setting up and solving simple equations. The coordinates of the other endpoint are G(-4, -14).

To find the coordinates of the other endpoint of a line segment given the coordinates of the midpoint and one endpoint, we use the midpoint formula which states that the midpoint, M, of a line segment GH is given by M = [(x1 + x2)/2 , (y1 + y2)/2], where (x1,y1) and (x2,y2) are the coordinates of H and G respectively.

Given that M (-6,-3) and H (-4,4), we can write the equations: -6 = [(-4 + x2)/2] and -3 = [(4 + y2)/2]

Solving these equations gives us: x2 = -2*(-6 + 4) = -4 and y2 = -2*(-3 - 4) = -14. Therefore, the coordinates of endpoint G are G (-4, -14).

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Answer:

Hi the answer is 874.6

Step-by-step explanation:

1. Add all numbers to equal 1,045

2. Times the number by 12% so .12

to equal 125.4

3 subtract 125.4 by 1045 to equal 919.6

4. Times 9 by 5(the number of days) to equal 45

5. Finally subtract 45 by 919.6 to equal 874.6

Hope this helped. Have a great day!

The total profit of Vic for the five days of sales given the cost of ingredients and fuel is £874.60.

Total profit is the total revenue less total cost.

Total revenue = 225 + 260 + 230 + 180 + 150 = £1045

Cost of ingredients = 12% x 1045 = $125.40

Total fuel = £9 x 5 = £45

Profit = £1045 - £45 - £125,40 = £874.60

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8,076 ....................

Answer:

8076

Step-by-step explanation:

You need a 4-digit number. The leftmost digit is the thousands digit (T). The next digit to the right is the hundreds digit (H). The third digit from the left is the tens digit (E), and the rightmost digit is the ones digit (O).

Using T, H, E, and O, as shown above, the number will have the form:

THEO

Now you replace each letter with the correct digit.

"eight thousand, seventy-six" has no hundreds, so let's include hundreds:

"eight thousand (T = 8), zero hundreds (H = 0), and seventy (E= 7)-six (O = 6)"

8076

The important thing is to remember to include a 0 as the digit for the hundreds place.

ANSWER

The preimage is (-5,-3)

EXPLANATION

If the point (x,y) is rotated 90° clockwise, then the image point is (y,-x)

This implies that, the rule for 90° clockwise rotation is :

[tex](x,y)\to (y, - x)[/tex]

To find the image of the point (3,-5), we substitute it into the rule:

[tex](3, - 5)\to ( -5, -3)[/tex]

Therefore the preimage is (-5,-3)

Answer:

Step-by-step explanation:

To rotate figures, there are several rules.

Specifically, when we want to rotate a figure 90° clockwise, the transformation is

[tex](x,y) \implies (y,-x)[/tex].

If the pre-image point has coordinates (3,-5), then its 90° rotation clockwise is (-5,-3), because it must follow the rule above.

Therefore, the right answer is (-5,-3).

Answer:

At the beginning

16 men and 24 women

In the end

16 men and 20 women

Step-by-step explanation:

Call x the number of men on the bus and call y the number of women on the bus.

We know that the initial ratio between men and women is 2: 3

And the final ratio is 4: 5

So

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

After the 4 women are down, the proportion is:

[tex]\frac{x}{y-4}=\frac{4}{5}\\\\y-4 = \frac{5}{4}x\\\\y= \frac{5}{4}x +4[/tex]   (2)

Substitute the value of y in the first equation and solve for x

[tex]\frac{5}{4}x +4=\frac{3}{2}x\\\\-\frac{1}{4}x=-4\\\\x=16\ men[/tex]

Now solve for y.

[tex]y = \frac{3}{2}(16)\\\\y=24\ women[/tex]

Then at the end there were 20 women  (because 4 women got off the bus)

For this case we must simplify the following expression:

[tex](x ^ {\frac {3} {2}}) ^ 6[/tex]

We have that by definition of properties of powers that is fulfilled:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex]x ^ {\frac {3 * 6} {2}} =\\x ^ {\frac {18} {2}} =\\x ^ 9[/tex]

Answer:

[tex](x^{\frac{3}{2}})^6=x^9[/tex]

Final answer:

To simplify the expression [tex](x^{3/2)6[/tex], use the power rule of exponents to get x to the power of 9, which is the simplified form of the expression.

Explanation:

To simplify the expression [tex](x^{3/2)6[/tex], we need to apply the power of a power property, which states that when you raise a power to another power, you multiply the exponents.

So, we have:

[tex](x^{3/2)6[/tex] = [tex]x^{(3/2)\times 6[/tex]

= [tex]x^{3\times 3[/tex]

= x⁹

Therefore, [tex](x^{3/2)6[/tex] simplifies to x⁹.

This means that the expression is equivalent to x raised to the power of 9.

In summary, when you raise x to the power of 3/2 and then raise that result to the power of 6, you end up with x raised to the power of 9.

Answer:

1620

Step-by-step explanation:

180(n)-360=interior angle sum

180(11)-360=1620

n = number of sides

You also can divide it by 11 to know each interior angle.

1620/11=~147.27

Answer:

2 the answer is 2/1 but just write 2

Step-by-step explanation:

Dilation of a polygon by a factor of 8 enlarges the polygon without changing the slope of the line. Therefore, the slope of AB and A'B' are the same. Further information is needed to provide a numerical value.

Since the polygon is dilated by a scale factor of 8, the new image A′B′C′D′ is an enlargement of the original polygon ABCD by a factor of 8. The slope of a line in a dilation remains the same, even if the length of the line is changed. Essentially, the steepness of a line isn't affected by dilations. Therefore, the slope of AB and A'B' are same. Since the slope of AB is not given in the question, it's necessary to have that information to answer your question completely.

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Final Answer:

The proposed new cereal box design has dimensions of 6 inches in length, 2 inches in width, and 8 inches in height. This design maintains the original cereal volume of 96 cubic inches while reducing the surface area to 104 square inches.

Explanation:

The formula for the surface area [tex](\(A\))[/tex] of a rectangular prism is given by:

[tex]\[ A = 2lw + 2lh + 2wh \][/tex]

For the original box with dimensions 8 inches in length [tex](\(l\)),[/tex] 1 inch in width [tex](\(w\)),[/tex] and 12 inches in height [tex](\(h\))[/tex]:

[tex]\[ A_{\text{original}} = 2(8 \times 1) + 2(8 \times 12) + 2(1 \times 12) = 232 \][/tex]

For the proposed new design with dimensions 6 inches in length, 2 inches in width, and 8 inches in height:

[tex]\[ A_{\text{new}} = 2(6 \times 2) + 2(6 \times 8) + 2(2 \times 8) = 104 \][/tex]

Comparing the surface areas, the new design significantly reduces it from 232 square inches to 104 square inches. This reduction in surface area indicates that the proposed design will require less material for manufacturing.

By maintaining the original cereal volume of 96 cubic inches while decreasing the surface area, the proposed cereal box design is more cost-effective to manufacture. The optimization of dimensions ensures that the same cereal quantity can be accommodated with a reduction in manufacturing costs.

Answer:

f^-1(x) = (x - 2)/4 ⇒ 1st answer

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

∵ f(x) = 4x + 2

∴ y = 4x + 2 ⇒ switch x and y

∴ x = 4y + 2 ⇒ subtract 2 from both sides

∴ x - 2 = 4y ⇒ ÷ 4 both sides

∴ (x - 2)/4 = y

∴ f^-1(x) = (x - 2)/4

* f^-1(x) = (x - 2)/4

The best word that describes the degree of overlap between the two data sets is: low.

The degree of overlap between two sets of data can be described as the extent to which two data sets vary in terms of their centers.

In the diagram given, the two dot plots overlap between 30 and 35. The difference is minimal.

Therefore, the best word that describes the degree of overlap between the two data sets is: low.

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Answer: The word that best describes the degree is B Low

Explanation: I took the test and it was right.

Hope ya'll have a good day :)

Answer:

$0.90

Step-by-step explanation:

1 quart = 2 pints

Write a proportion:

$1.80 / 4 pint = x / 2 pint

Cross multiply:

4x = 3.60

Divide:

x = 0.90

The price per quart is $0.90.

To find the price per quart of a 4-pint carton costing $1.80, divide the total cost by the number of quarts (2), resulting in $0.90 per quart.

The question asked is: A 4-pint carton of fruit punch costs $1.80. What is the price per quart? To answer this, we first need to understand that there are 2 pints in a quart. Therefore, a 4-pint carton is equivalent to 2 quarts of fruit punch. Now, we simply divide the total cost of the carton by the number of quarts to find the price per quart.

The calculation would be $1.80 ÷ 2 quarts = $0.90 per quart.

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Answer:

x ≠ -4

Step-by-step explanation:

Division by zero is not defined, so x cannot = -4.

Answer:

383.08‬

Step-by-step explanation:

Multiply 3 times 122 which is 366

Then multiply .14 times 122 which is 17.08

Then add.

Final answer:

Brandy's mistake was not converting the diameter to the radius before applying the area formula A = πr². The correct area of a circle with a diameter of 12 cm is 113.04 cm², but it should be reported as 110 cm² to maintain two significant figures.

Explanation:

The error in Brandy's solution for finding the area of a circle with a diameter of 12 cm lies in not first converting the diameter into the radius. The formula for the area of a circle is A = πr², where r is the radius and π (pi) is approximately 3.14. Since the radius is half of the diameter, for a diameter of 12 cm, the radius is 6 cm. Thus, the correct calculation is A = 3.14 × 6².

Correct solution:

A = 3.14 × 6 cm²

A = 3.14 × 36 cm²

A = 113.04 cm²

As for the significance of figures, since the radius has two significant figures (6 cm), the calculated area should also be limited to two significant figures, rounding to 110 cm².

Answer:

x=m-a/12

the m-a should be over 12 as the numerator but it's hard to type it like that

Step-by-step explanation:

a+12x=m

12x=m-a

x=m-a/12

Answer:

[tex]x = \frac m{12a}[/tex]

Step-by-step explanation:

Hello!

Solve for x by isolating the variable.

The value of x is [tex]x = \frac m{12a}[/tex].

Answer:

Step-by-step explanation:

Mean is just another word for average.  To find the average, add up all the values then divide by the number of values.

There are 7 values in the first data set.  The average is:

(3 + 4 + 6 + 4 + 3 + 1 + 4) / 7 = 25/7 ≈ 3.57

There are 7 values in the second data set.  The average is:

(6 + 7 + 2 + 4 + 5 + 5 + 3) / 7 = 32/7 ≈ 4.57