6
3
3
C
C
6
6
C
C
3
3
6
Solve for c.
= √ [?]
C =
Enter the number
that goes beneath
the radical symbol.

Answer:

12x^2 + 12

Step-by-step explanation:

1. Remove the parentheses:

x^4 + 8x^2 + 16 - x^4 + 4x^2 - 4

2. Cancel out terms:

8x^2 + 16 + 4x^2 - 4

3. Combine like terms:

12x^2 + 12

Step-by-step explanation:

Find Object Volume Rotation

Suppose That \( R \) Is The Finite Region Bounded By \( Y=X, Y=X+1, X=0 \), And \( X=3 \). find the exact value of the volume of the object we obtain when rotating about the -axis.

The region R is a triangular region defined by the lines y = x, y = x + 1, x = 0, and x = 3. To find the volume of the object obtained by rotating this region about the x-axis, we can use the method of cylindrical shells.

The height of the cylindrical shell is given by the difference between y = x and y = x + 1, or 1 unit. The radius of the cylindrical shell is given by x. Therefore, the volume of the object is given by:

\begin{align*}

V &= \int_{x=0}^{x=3} \pi x^2 \cdot 1, dx \

&= \pi \int_{x=0}^{x=3} x^2, dx \

&= \pi \left[ \frac{x^3}{3} \right]_{x=0}^{x=3} \

&= \pi \left( \frac{27}{3} - \frac{0}{3} \right) \

&= 9\pi

\end{align*}

So the volume of the object is equal to 9π cubic units.

Answer:

50

Step-by-step explanation:

To find the number of students, we can use the formula: average = (sum of marks) / (number of students).

Substituting the given values: 40 = 2000 / number of students

Solving for the number of students: number of students = 2000 / 40 = 50

So, there are 50 students in the series.

The total tax that the business paid on its purchases only was 769720.25.

In order to pay for general public institutions, goods, and activities, local, state, and federal governments must collect mandated payments or charges from citizens and corporations.

We must first figure out the complete cost of the goods in order to determine the total taxable income the corporation paid

The cost of the 16,000 network routers is:

16,000 units x $79.25/unit = $1,268,000

The cost of the 12,000 wireless LAN adapters is:

12,000 units x $129.95/unit = $1,559,400

The cost of the 13,500 computer boards is:

13,500 units x $229.15/unit = $3,092,025

The total cost of all purchases is:

$1,268,000 + $1,559,400 + $3,092,025 = $5,919,425

To calculate the total tax amount, we need to multiply the total cost by the tax rate. Assuming a tax rate of 13%, the total tax amount is:

$5,919,425 x 0.13 = $768,527.25

Therefore, the total tax amount that the company paid on their purchases only is $768,527.25, rounded off to 2 decimal places.

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Answer:

  x = 22

  y = 59

Step-by-step explanation:

You want the values of x and y as shown in the figure where angles (2x)° and (y-15)° are vertical angles, and (2x)° and (2x+2)° are complementary.

Two angles are complementary when their sum is 90°.

  (2x)° +(2x+2)° = 90°

  4x = 88 . . . . . . . . . . . divide by °, subtract 2

  x = 22

Vertical angles have the same measure:

  (2x)° = (y -15)°

  2·22 = y -15 . . . . . . divide by °, substitute for x

  59 = y . . . . . . . . .  add 15

The value of x is 22.

The value of y is 59.

On a dot plot, the statement saying that Four people said they rode a Ferris wheel five times would be represented with four dots above the input five.

A dot plot shows the number of times that each observation was accrued in a data-set, which the number of dots representing the number of observations of each input.

The parameters for this problem are given as follows:

Hence the statement would be represented with four dots above the input five.

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Two equivalent fractions is 16/4, 100/25

Equivalent fractions are two or more fractions that are all equal even though they have different numerators and denominators. For example, the fraction 1/2 is equivalent to (or the same as) 25/50 or 500/1000. Each time the fraction in its simplest form is 'one half'.

Given here : The two fractions 40/

Now the quotient is 40/10=4

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½

Thus two equivalent fractions here are 16/4,100/25 both will equal to 4

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The surface area of figure is 784 ft² and the volume of the figure is 576 ft³.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The shape created by Jeff is a cube + square pyramid.

The height of square pyramid is = 3 ft

The sides of cube = 8 ft

The formula for volume of cube = (side)³

Volume of cube = (8)³

Volume of cube = 512 ft³

The formula for volume of square pyramid = (base)² × height / 3

Volume of square pyramid = (8)² × 3/3

Volume of square pyramid = 64 × 1

Volume of square pyramid = 64 ft³

Total volume of the figure -

Volume of cube + Volume of square pyramid

Total volume = 512 + 64

Total volume = 576 ft³

The formula for surface area of cube = 6(side)²

Surface Area of cube = 6 × (8)²

Surface Area of cube = 6 × 64

Surface Area of cube = 384 ft²

The formula for surface area of square pyramid = 6(side)²

Surface Area of square pyramid = (side)² + 2(side) √[{(side)²/4} + (height)²]

Surface Area of square pyramid = (8)² + 2(8) √[{(8)²/4} + (3)²]

Surface Area of square pyramid = 64 + 16 √[{64/4} + 9]

Surface Area of square pyramid = 80 √[16 + 9]

Surface Area of square pyramid = 80 √25

Surface Area of square pyramid = 80 × 5

Surface Area of square pyramid = 400 ft²

Total surface area of the figure -

Surface Area of cube + Surface Area of square pyramid

Total Surface Area = 384 + 400

Total Surface Area = 784 ft²

Therefore, the volume and surface area of the figure is 576 ft³ and 784 ft² respectively.

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The rate for a ratio of the two different quantities would be 13 over 2 puppies per litter. That is option D.

The total number of puppies that Mallory's Border Collie has = 13 puppies.

The number of litters that the puppies are being placed = 2 litters.

Therefore, the rate of puppies per litter is calculated as follows:

13 puppies = 2 litters

X puppies = 1 litter

Make X the subject of formula;

X = 13×1/2

X= 13/2 puppies per litter

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Answer:Alex has a collection of vehicle models. He built 8 model airplanes, 4 model trains, and 12 model cars. Write a ratio to represent the ratio of cars to trains.

Step-by-step explanation:3/1 ur welcome

the expected value for the given data set will be 0.423

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, a data set gives prizes and probabilities of winning (on a single $1 ticket) for the Multi-State Powerball lottery.

We have to determine the expected value of winnings when buying one ticket. This can be computed using the expected value formula.

Recall the formula for the expected value E for events A and B whose probabilities of occurring are P(A) and P(B), respectively:

E  = (P(A)×value for A)+(P(B)×value for B)

​Using the formula above and extending it to 99 events yields:

E(x) = (1/ 292, 201,338 * 30,000,000) + (1 / 11,688,053 * 1,000,000) + (1/913,129 * 50,000) + (1/ 36,525 * 100) + (1/14,494 * 100) + (1/ 580 *7) + (1 /701 * 7) + (1/92 * 4) + (1/ 38 * 4)

E = 0.423

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Answer:

9

Step-by-step explanation:

9 makes it so that each set becomes a whole number.

Answer:

15 and 8

Step-by-step explanation:

Let the legs be a, b

a+b=23

ab=120

Then, 23b-b^2=120. so b^2-23b+120=0. Thus (b-8)(b-15)=0. Thus b=8,15, and if b=8, then the other length a is 15.

The regression equation is linear in the explained and explanatory variables.

In order for Ordinary Least Squares (OLS) estimates to be unbiased, the regression equation must be linear in both the explained and explanatory variables. This means that the relationship between the dependent variable (what is being explained) and the independent variables (what is being used to explain the dependent variable) must be linear. This is important because it ensures that the estimated coefficients of the regression equation accurately reflect the true relationship between the variables. Additionally, the error term must have an expected value of 0, given any value of the explanatory variable, and have the same variance given any value of the explanatory variable. This ensures that the estimated coefficients do not suffer from bias and that the OLS estimates are unbiased.

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Answer:

see below

Step-by-step explanation:

a. amount of time = t

Value = 32000*(1-16.3%)^t

b. in 35 years Value = 32000*(1-16.3%)^35 = 63.17

Answer:

4 1/5

Step-by-step explanation:

6/10 = 3/5

2+1=3

3+6/5 = 4 1/5

Answer:2 one

Step-by-step explanation:

Answer:

$500.000 × 0.08 = $40,000

$40,000/12 = $3.333.33

Step-by-step explanation:

El interés simple mensual se puede calcular como una fracción del interés anual. Para calcular el interés simple mensual, primero debemos calcular el interés anual y luego dividirlo entre 12 para obtener el interés mensual.

El interés anual se puede calcular multiplicando el capital por la tasa de interés:

$500,000 × 0.08 = $40,000

Luego, para obtener el interés simple mensual, dividimos el interés anual por 12:

$40,000 / 12 = $3,333.33

Por lo tanto, un capital de $500,000 al 8% de interés simple generará $3,333.33 de interés simple mensual.

The value of a and c in the right triangle are 38.28 and 66.89 respectively.

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.

From the diagram:

sin(55.0892) = 54.855/c

c = 66.89

Also:

tan(55.0892) = 54.855/a

a = 38.28

The value of a and c are 38.28 and 66.89 respectively.

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The marginal revenue when q = 29 is 510 dollars.

To find the marginal revenue we need to differentiate the revenue equation, here we know that:

R(q) = -5q² + 800q

Differentiating that, we will get:

R'(q) = MR(q) = 2*(-5)*q + 800

                     = -10q + 800

The marginal revenue when q = 29 is

MR(29) = -10*29 + 800 = 510

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The required, given expression is completely factored as  (4y -5)(3x - 5).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

To factor the expression 12xy - 15x - 20y + 25, we can use the distributive property to factor out a common factor from each of the first two terms and the last two terms:

12xy - 15x - 20y + 25

= (12x)(y) - (15x)(1) - (20)(y) + (5)(5)

= (3x)(4y) - (5)(3x) - (4)(5y) + (5)(5)

= 3x(4y - 5) - 5(4y - 5)

= (4y -5)(3x - 5)

So, the expression is completely factored as, (4y -5)(3x - 5).

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A polygon with seven congruent sides and angles is called HEPTAGON. In this case

A polygon is a two-dimensional closed figure with three vertices, three angles, and at least three straight sides. The words "Poly" and "gon" both mean many and angle, respectively. A triangle, for instance, has three vertices, three sides, and three angles. Therefore, it qualifies as a polygon.

Chantal "draws a polygon with seven congruent sides and angles," according to the statement. Heptagon is the name for a polygon with seven identical sides and angles. This polygon is a regular one because all of its sides and angles are equal. A regular polygon must have equal side lengths and angles by definition.

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Answer:

If m∠1=95°, then m∠8 can be found by using the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this case, m∠8 = 180 - (m∠1 + m∠3) = 180 - (95° + 55°) = 30.

The tape diagram is attached in the solution.

A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication.

Given is an equation x+4 = 17,

We need to draw a tape diagram for the same,

So, for that, since we have x + 4 which is equal to 17, so, we will draw a box, divide into two parts one will show the x part and ine will show the 4 part, and collectively it will show 17.

The value of the x+4 and 17 is the same, because, according to the diagram, the quantity x+4 collectively showing 17, therefore, they have same values.

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The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

a) P(Z < -1.35) =0.8708

b) P(Z > 1.48) =0.5714

c) P(-0.4 < Z < 1.5) =0.000

d) P(| Z | >2)=0.3830

Z-Score Table. A z-table, also known as the standard normal table, provides the area under the curve to the left of a z-score. This area represents the probability that z-values will fall within a region of the standard normal distribution.

Given:

The given condition is Z~N(μ = 0,σ = 1).

(a)

Find the value for .P(Z < -1.35)

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .P(Z < -1.35) =0.8708

(b)

Find the value for .P(Z > 1.48)

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of  .P(Z > 1.48) =0.5714

(c)

Find the value for .) P(-0.4 < Z < 1.5)

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .) P(-0.4 < Z < 1.5) =0.000

(d)

Find the value for .P(| Z | >2)

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .P(| Z | >2)=0.3830

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The probability distribution is calculated z-table.

Z-table is also known as standard normal table which is used to find the area under the curve to the left of a z-score.

(a)P(Z<-1.35)

Here Z value negative so it is lies left of the curve, using standard normal table , P(Z<-1.35) = 0.0885

(b)P(Z>1.48)

z value is positive it lies right of the curve, using standard normal table, area under the curve P(Z>1.48)= 0.9306

(c)P(-0.4 < Z < 1.5) = P(Z<1.5) - P(-0.4<Z)

                             = 0.9332 - 0.3446

                             = 0.5886

(d)P(| Z | >2), |Z| is both positive and negative we have,

  P(| Z | >2) = P(-2 < Z <2)

                  = P(Z<2) - P(-2<Z)

                  = 0.9772 - 0.0228

                 = 0.9544.

Hence, (a)P(Z<-1.35) = 0.0885

(b)P(Z>1.48) = 0.9306

(c)P(-0.4<Z<1.5) = 0.5886

(d)P(|Z|>2)  = 1.9544

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Answer:

[tex]\textsf{LCM}=(x+3)^3(x-3)^2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6cm}\underline{Difference of Two Squares Formula}\\\\$a^2-b^2=\left(a+b\right)\left(a-b\right)$\\ \end{minipage}}[/tex]

Factor x² - 9 by applying the Difference of Two Squares formula:

[tex]\begin{aligned}\implies x^2-9&=x^2-3^2\\&=(x+3)(x-3)\end{aligned}[/tex]

Rewrite each of the given expressions as an expansion of their factors:

[tex]\bullet \quad (x-3)^2=(x-3)(x-3)[/tex]

[tex]\bullet \quad x^2-9=(x+3)(x-3)[/tex]

[tex]\bullet \quad (x+3)^3=(x+3)(x+3)(x+3)[/tex]

Therefore, we can see that each expression has a factor of (x - 3), (x + 3) or both (x - 3) and (x + 3).

The least common multiple (LCM) of a, b, and c is the smallest multiplier that is divisible by a, b and c.

Therefore, to find the LCM of the given expressions, multiply each factor with the highest power:

Answer:

the answer is A

Step-by-step explanation:

use the formula y=mx+b

25.95 is the slope because its a constant arte of change and 50 is the y-intercept because you gain $50 in addition to the slope

Answer:

y=25.95x+50

Step-by-step explanation:

25.95 is the dependent variable, so it is the coefficient. The starting amount, or the y-intercept, is 50. This makes the equation y=25.95x+50.

The project average is 100% of the student's grade, and if the student has the given averages, their course grade would be 89%.

The project average is the only component of the student's grade that is not weighted. The homework average accounts for 20% of the grade, while the quiz average accounts for 80%. Therefore, the project average is 100% of the student's grade. If the student has the given averages, then their course grade can be calculated by multiplying the homework and quiz averages by their respective percentages and adding the two products. In this case, the student's course grade would be (95 * 0.2) + (80 * 0.8) + 88 = 89%. The student's course grade would then be rounded to the nearest whole number, which is 89%.

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Answer:

24

Step-by-step explanation:

You multiply the number of positions (2), by the number of people (12).

Therefore, standard deviation problem solution is at least 90% of the​ trucks can be expected to travel 55,36 miles or less per year.

Statistics uses variance as a gauge of difference. The following equation of that number is used to determine the average variance in between data and the mean. It includes all data points in with its computations, in contrast to other numeric measures of variability, by comparing the value of each data point to the mean.

Here,

a.

z1 = (23 - 40) / 12 = -1.42

z2 = (40 - 40) / 12 = 0

P(-1.42 < z < 0) = 0.4199

So, approximately 0.4199 or 41.99% of trucks can be expected to travel between 23 and 40 thousand miles in a​ year.

b.

z1 = (30 - 40) / 12 = -0.83

z2 = (60 - 40) / 12 = 1.67

P(z < -0.83) + P(z > 1.67) = 0.2023 + 0.0475 = 0.2498

So, approximately 24.98% of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a​ year.

c.  Thus:

x = 40 + 1.28(12) = 55.36

So, standard deviation problem solution is at least 90% of the​ trucks can be expected to travel 55,36 miles or less per year.

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The value of the functions are (f o g) (2) = 0 and  (g o f) (2) = 4.

What are functions?

In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.

y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x). In other words, for the same x value, there cannot be more than one value for f(x).

We are given two functions, f(x) and g(x).

Their graphs are also given.

We are asked to solve the following questions using the given graphs.

1) (f o g) (2) = f( g(2) )

To solve this we have to first start with inner functions.

g(2) = value of y when x = 2  

    From the g(x) graph it is given that g(2) = 2 when x = 2

Now we substitute this in f( g(2) )

i.e f(2) = value of y when x = 2 = 0

From the f(x) graph it is given that f(2) = 0 when x = 2.

So (f o g) (2) = 0

2) (g o f) (2) = g( f(2) )

  f(2) = 0 ( as mentioned above)

Substituting,

 g( f(2) = g (0) = 4

So (g o f) (2) = 4

Therefore the value of the functions are (f o g) (2) = 0 and

(g o f) (2) = 4.

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