2. b = 4 in, P = 16 in, s = 12, 4 sides (base is a square) What is surface area?

The remainder when x³ + 1 is divided by x + 1 is 0

Given,

The polynomial functions; x³ + 1 and x + 1

We have to find the remainder when x³ + 1 is divided by x + 1

Polynomial function;-

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Here,

p(x) = x³ + 1

g(x) = x + 1 = 0

          x = -1

Then,

p(x) = x³ + 1

p(-1) = -1³ + 1 = -1 + 1 = 0

That is,

The remainder when x³ + 1 is divided by x + 1 is 0

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Answer:

180

Step-by-step explanation:

first we combine what Anthony and Tommy have by adding

40+50

90

And twice as many is multiplying by 2

2x90

180

Hopes this helps please mark brainliest

Answer:180

explanation:40+50=90

90x2=180

Answer:

a) BC = 8.66

b) BC = 4.33

Step-by-step explanation:

a)

solution:

cos30°=BC/AC

or, BC=0.866*10

BC=8.66

b)

solution:

BC=5*0.866

BC=4.33

The percentage increase in the time period is 6.3245%.

Given:

A pendulum of length L cm has time period T seconds.

T is directly proportional to the square root of L.

The length of the pendulum is increased by 40%.

Let L1 and T1 be the increased pecentage.

T α [tex]\sqrt{L}[/tex]

T/[tex]\sqrt{L}[/tex] = constant

T/[tex]\sqrt{L}[/tex] = T1/[tex]\sqrt{L1}[/tex]

T1 = [tex]\sqrt{L1}[/tex] * T/[tex]\sqrt{L}[/tex]

= [tex]\sqrt{L1/L}[/tex]* T

= [tex]\sqrt{40/100 *L / L}[/tex] * T

= [tex]\sqrt{0.4}[/tex] * T

= [tex]\sqrt{0.4} *100[/tex]

= 6.3245% T

Therefore The percentage increase in the time period is 6.3245%.

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Every decision we make is followed by a series of related events. The magnitude of the decision will determine how drastically it will affect the person making it and those around them. There is always a result, whether the impact is positive or negative.

Step 1: Identification of the purpose of the decision

Step 2: Information gathering

Step 3: Principles for judging the alternatives

Step 4: Brainstorm and analyze the different choices

Step 5: Evaluation of alternatives

Step 6: Select the best alternative

Step 7: Execute the decision

Step 8: Evaluate the results

When making judgments, one should always balance the potential business benefits against the drawbacks, leaning toward the former.

By doing this, potential losses to the organisation are avoided, and sustainable growth is maintained within the business. When you have to make a difficult decision, it might often seem easier to postpone doing so, especially if you encounter a lot of conflict thereafter.

However, in order to maintain control over your work and time, decisions must be made and their implications accepted.

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The speed that will martin need to drive, if he wants to take the  512 hours is 0.537 mph.

Students determine the rate of change, often referred to as the constant of proportionality (k = y/x), which is the consistent ratio between two proportional values (y/x) indicated by the symbol k, which may be a positive rational integer. The x value and the y value are directly proportional, as in the equation y = kx.

Speed and travel time vary in opposite directions.,

So v ∝ 1/t.

speed = v

time = t

So

=> v = k/t,  k=constant of proportionality.

Since it takes Kris 5 hours when driving at 55 mph,

=>   v = 55mph and t = 5 hours.

=> 55 = k/5

by doing cross multiply

=> k = 55*5

=> k = 275

Hence, to calculate for Martin to drive for 5 hours, we will take k = 275 and t = 5 into v = k/t  

=> v = 275/512

=> v = 0.537 mph

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The total number of seats are 1260 in an auditorium.

The number of seats will be calculated by the arithmetic progression -

S = n/2 [2a + (n-1)d], where s is the number of seats, n is number of rows, a is the number of seats in first row and d is the number of extra seats added in each row.

d = 29 - 25

Performing subtraction

d = 4

Keep the values in formula -

S = 20/2 [(2×25) + (20 - 1)×4]

Performing multiplication and subtraction

S = 10 [50 + (19×4)]

Performing multiplication

S = 10 [50 + 76]

Performing addition

S = 10 [126]

Performing multiplication

S = 1260

Hence, there are 1260 seats.

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The original slope's reciprocal will be the opposite of the perpendicular slope. To determine the intercept, b, enter the supplied point and the new slope into the slope-intercept form (y = mx + b). Rewrite the following equation in standard form: ax + by = c.

The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

The slope is m and the y-intercept is b in the equation y=mx+b in slope-intercept form. Some equations can also be rewritten so that they resemble slope-intercept form. For instance, y=x can be written as y=1x+0, resulting in a slope and y-intercept of 1 and 0, respectively.

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Answer:

Overall, available research suggests jurors exposed to pretrial publicity are more likely to favor the prosecution.

Height and base of a triangle with given area 48 square meters is 12meters and 8 meters respectively.

As given ,

Area of the triangle = 48 square meters

Let 'y' meters represents the height of the triangle

Then 'y - 4' meters represents the base of a triangle.

Area of a triangle = ( 1/2 ) × base × height

Substitute the values we get

48 = ( 1 / 2) × ( y - 4 ) × y

⇒ 96 = y² - 4y

⇒ y² - 4y - 96 = 0

⇒ y² - 12y + 8y - 96 = 0

⇒ ( y - 12 ) ( y + 8 ) =0

⇒ y = 12 or y = -8

Height cannot be negative.

⇒y = 12meters

Base = 12 -4

        = 8 meters

Therefore, height and base of a triangle with given area is 12 meters and 8 meters respectively.

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Answer:

No it is not irrational

Step-by-step explanation:

459.63 is a rational number.

Irrational numbers are numbers that can't be shown as simple fractions

Examples of irrational numbers are:

√2,  π(Pi), 0.45445544455544445555.. (because it doesn't end)

(a) The statement about Bayesian model "For the Bayesian linear model, the priors for intercept and slope are independent" is  False  .

(b) The statement about posterior distribution "in posterior distribution, intercept and slope may be correlated" is  False  .

In the question ,

it is given that ,

Part(a) ,

the statement is given to be "In Bayesian linear model, the priors for the intercept and slope are independent" , we have to check whether the statement is True or False .

We have the linear model as [tex]y_{i}= \alpha +\beta x_{i} +A_{i}[/tex]   , where [tex]A_{i}[/tex]≈N(0,σ²) , α is the intercept and β is the slope .

we know that priors [tex](\hat{\alpha } , \hat{\beta })[/tex]   are not independent  ,

Cov [tex](\hat{\alpha } , \hat{\beta })[/tex] = [tex]\frac{-\bar{x}}{S_{xx} }[/tex] *σ² ,

So , the priors for the intercept and for the slope are independent ,

hence the statement is False .

Part(b) ,

the statement is given to be "In posterior distribution, intercept and the slope may be correlated" ,

For Posterior distribution , as  [tex]A_{i}[/tex]≈N(0,σ²)  ,

and 2 + [tex]\beta x_{i}[/tex] is a non random part of the model ,

and Cov([tex](A_{i} , A_{i} )[/tex] = 0 for i ≠ j .

hence , we can say that the intercept and slope are not Corelated ,

the statement is False .

Therefore , both the given statement are False .

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The length of the room will be  96 ft after increasing each side by 1 foot.

Let L be the length of the room and W be the width of the room.

Given , L = 2W.

Area ,  A = LW

= 2W × W

= 2W²

On increasing each side  by 1 foot,  new area is A' = (L + 1)(W + 1)

= (2W + 1)(W + 1)

= 2W² + 3W + 1

Since,  the room would contain 145 ft more if each side were increased by 1 foot, then its new area is A' = A + 145 = 2W² + 3W + 1

2W² + 145 = 2W² + 3W + 1

145 = 3W + 1

3W = 145 - 1

3W = 144

W = 144/3

W = 48 ft.

Since its length L = 2W, substituting W = 48 into the equation, we have

L = 2(48)

L = 96 ft

Therefore the length of the room will be  96 ft.

The area of a rectangle in a two-dimensional plane is the area that it occupies. A quadrilateral, a form of two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another. It should be noted that a parallelogram also has equal and parallel opposite sides, but the angles are not exactly 90 degrees.

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Answer:

3-7n

Step-by-step explanation:

Answer:6

Step-by-step explanation:

Three less than the product of 7 is 6

Just translate the sentence into a equation:7n-3=6

A triangle's midsegment is the section created by joining any two of its sides at their midpoints.

Simply said, it equally splits the two triangle sides. A side is divided into two equal segments at its halfway. The middle segment of the triangle ABC is DE, as shown in the image below. Segment AB is divided into two equal portions at point D, and segment CB is divided into two equal parts at point E. The base of the triangle is the side on which the midsegment does not meet. The segment created by joining the midpoints of a trapezoid's two legs is known as the midsegment. Despite the fact that a trapezoid's midsegment is also helpful

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Answer:

1818.9 mi

Step-by-step explanation:

If the num of miles is directly proportional, then we can find out that she drives 348.3/9 = 38.7 mi/gal (this also works for the other two pairs)

To find the distance with 47 gallons, you multiply 38.7 by 47, to get 1818.9 mi.

The table that represents the function y = -2x + 4 is: the second table.

Considering the third table representing a function given:

x | y

0   4

1    2

2   0

Find the slope (m) using the two points (1, 2) and (2, 0):

Slope (m) = change in y / change in x = (0 - 2) / (2 - 1)

m = -2/1

m = -2.

The y-intercept (b) = 4.

Substitute m = -2 and b = 4 into y = mx + b:

y = -2x + 4

Therefore, the second table represents the function y = -2x + 4.

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The expression for the volume is V = (28 - 2x)(22 - 2x)(x), and the volume of the box is 864 cubic inches.

It is given that:

Andre wants to make an open-top box by cutting out the corners of a 22-inch by 28-inch piece of poster board and then folding up the sides.

As we know,

The volume of the box = length×width×height

V = (28 - 2x)(22 - 2x)(x)

Plug x = 2

V = (28 - 2×2)(22 - 2×2)(2)

V = (24)(18)(2) cubic inches.

V = 864 cubic inhces

Since x measures length, it is not possible for it to be smaller than zero. In addition, since the width of the box's bottom cannot be less than zero.

Thus, the expression for the volume is V = (28 - 2x)(22 - 2x)(x), and the volume of the box is 864 cubic inches.

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The equation for ftc's profit is Profit = Sales – (Variable Cost + Fixed Cost)

According to the question,

The fixed cost to produce the doll = $100,000

Variable cost = $31

Selling price during holiday season = $39

Selling price during January = $10

Demand of new toys follows normal distribution

average sales = 60,000

Standard deviation = 15,000

Demand assumed in normal distribution = 60,000

The equation for ftc's profit ;

Let demand be d , production quality be p , fixed cost be x and variable cost be y

Maximum Profit:

Profit = Sales – (Variable Cost + Fixed Cost)

During the holiday season, For 40,000 dolls

Sales = 40,000 * 39 = $1,560,000

profit = $1,560,000 – (x+ y)

Variable Cost = 31*40,000 = 1,240,000

Fixed Cost = $100,000

Total Cost = 1,240,000+100,000 = $1,340,000

Profit = 1,560,000 – 1,340,000

= $220,000

Maximum Profit = $220,000

Average Profit: Off season sale price * Demand =$10*40,000

= $400,000

average sales = ($400,000 + 1,560,000 ) / 2=$1960,000/2

= $980,000

Average profit = 980,000 – 73,000= $972,700

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A credit to cash for $318 would be included in the entry to replenish the​ fund.

The balance is the sum owing on an account in banking and accounting. The term "balance" in accounting refers to the difference between the total of debit entries and the total of credit entries made into an account over the course of a certain financial period. The account shows a negative balance when total debits exceed total credits. There is just one rule in the balancing method: Perform the identical action on both sides of the equal sign so that only the unknown variable is left on one side.

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The solution to the inequality is solved as: x ≥ -10.

To solve an inequality means to find the possible values of the variable in the inequality that will make it true.

Given the inequality:

-4x + 14 ≤ 54

Subtract 14 from both sides of the inequality:

-4x + 14 - 14 ≤ 54 - 14 [Subtraction property of equality]

-4x ≤ 40

Divide both sides by -4 then change the inequality sign:

-4x/-4 ≥ 40/-4 [division property of equality]

x ≥ -10

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The total possible number of points the team could score to earn pizzas is 700, using the inequality |x - 750| ≤ 50

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Based on the given conditions, formulate: 750 -50

Calculate the sum or difference will be 700

Hence, the inequality possible number of points the team could score to earn pizzas is 700

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The value of k in k^3=1/125 is 1/5 (optionB)

Indices is the power or exponent which is raised to a number or a variable. For example, in number 2^5, 5is the index of 2 which means 2×2×2×2×2. The plural form of index is indices.

From the law of Indices,

a^-1= 1/a

similarly, 1/125= (125)^-1

from the expression, K^3= (125)^-1

K^3= (5^3)^-1

therefore K^3=(5)^-3

multiply the power of both sides by 1/3

=K^3×1/3= (5)^-3×1/3

therefore k= 5^-1=1/5

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Using Probability,

The probability that a randomly selected student in the class likes math or English is 11/26.

We have provided the following information,

total number of students in a class = 26

number of students who likes Math = 15

number of students who likes English = 13

number of students who does not likes English or Math = 9

let x be number of students who likes both of subjects .

firstly , we have to find out the value of x i.e total number of students who likes both subjects out of 26 students class .

For this , number of students who likes any one of subjects from both = 26- 9 = 17

but we have total 28 (i.e., 15 + 13 )students who likes Math and English.

so, number of students who likes only Math = 17-15 = 2

number of students who likes only English = 4

then, number of students who likes both subjects

(x) = 26 - 4- 2-9 = 11

randomly one student is selected from the Class,

The probability that a randomly selected student in the class likes math or English = 11/26

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Complete question:

In a class of 26 students: 15 like math, 13 like English, 9 does not like both. What is the probability that a randomly selected student in the class likes math or English?

The complementary event of rolling a die and getting a number less than three is that the six-sided die is rolled and the outcome is greater than three. Where P = n < 3  is the event and its complement is P' = n > 3.

The sample space of all outcomes that are not the event in question is the complement of an event. The inverse of "a flipped coin lands on heads" is "a flipped coin lands on tails."

If the chance of drawing a red marble from a bag is 26%, the chance of the complement (picking a non-red marble ) is 74%.

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It will take approximately 11.62 years to reach a population of 7000 mice.

To solve this problem, we can use the formula for exponential growth:

[tex]\mathrm{N = N_0 \times e^{(r \times t)}}[/tex]

Where:

N = Final population size

N₀ = Initial population size

r = Growth rate

t = Time (in years)

Let's calculate the growth rate (r):

N₀ = 100

N = 4000

[tex]\mathrm{r = ln(N/N_0) / t}[/tex]

[tex]\mathrm {r = ln(4000/100) / 10}\\\\\mathrm {r = ln(40) / 10}\\\\\mathrm {r \approx 0.3688}[/tex]

Now, let's find the time required to reach 7000 mice:

[tex]\mathrm {N = 7000}\\\\\mathrm {t = ln(N/N_0) / r}[/tex]

[tex]\mathrm {t = ln(7000/100) / 0.3688}\\\\\mathrm {t \approx 11.52 \ years}[/tex]

Therefore, it will take approximately 11.62 years to reach a population of 7000 mice.

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The value of b in the equation [tex]b^{3}[/tex] = 125  will be 5. Option (b) is correct.

The question is about the system of equations. According to the question, we have the following equation:
b³ = 125.
We can find the value of b by simplifying and using the rules of equations.

First, we need to Factorize 125 on the right-Hand side, we get.

b³ = 5.5.5 = 5³

Hence we get,
b³ = 5³
We know that if there are two expressions that are equal and we add, subtract, multiply or divide into both sides of the equation, the resulting equation will also be equal. So, Multiply both sides by the cube root, and we get:

[tex]\sqrt[3]{b^{3}} = \sqrt[3]{5^{3}}[/tex]

[tex](b^{3})^{\frac{1}{3}} = (5^{3})^{\frac{1}{3}}[/tex]

[tex](b})^{\frac{3}{3}} = (5})^{\frac{3}{3}}[/tex]

[tex](b})^1 = (5})^1[/tex]

So we get the value of b = 5, hence the correction option will be (b).

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