Sachin used synthetic division to divide a polynomial, p(x), by x + 5 and found that there was no remainder. What does this tell Sachin about how p(x) and x + 5 are related?
A. x + 5 is a factor of p(x)
B. p(x) divided by x + 5 is 0
C. x + 5 is not a factor of p(x)
D. x + 5 cannot be divided evenly into p(x)

The probability of an outcome less than 5 in a discrete uniform distribution ranging from 2 to 9 inclusive is 37.5%.

In a discrete uniform distribution, each outcome has an equal probability of occurring. In this case, the range of possible outcomes is from 2 to 9 inclusive, which means there are a total of 8 possible outcomes (2, 3, 4, 5, 6, 7, 8, 9).

To calculate the probability of an outcome less than 5, we need to determine the number of outcomes that satisfy this condition. In this case, there are 4 outcomes (2, 3, 4) that are less than 5.

The probability is calculated by dividing the number of favorable outcomes (outcomes less than 5) by the total number of possible outcomes. So, the probability is 4/8, which simplifies to 1/2 or 0.5.

Therefore, the correct answer is B. 50.0%. The probability of an outcome less than 5 in this discrete uniform distribution is 50%, or equivalently, 0.5.

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Answer:

12 sides

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

since the polygon is regular then the exterior angles are congruent

number of sides = 360° ÷ 30 = 12

Answer:

12.

Step-by-step explanation:

Answer:

24d^5

Step-by-step explanation:

Answer:

10x +8y

Step-by-step explanation:

4x +5y + 3y + 6x

Combine like terms

4+6=10, 5+3=8

10x + 8y

The double integral of the function 1L 4x² dA over the region D can be found by following these steps: determine the limits of integration, set up the double integral, integrate with respect to y, integrate with respect to x, and calculate the result.

To evaluate the double integral of the function 1L 4x² dA over the region D, where D is the region in the first quadrant bounded by y = 7x and y = -x³, follow these steps:

1. Determine the limits of integration: To find the limits of integration, first find the points of intersection between y = 7x and y = -x³. Set the two functions equal to each other and solve for x:

7x = -x³
x³ + 7x = 0
x(x² + 7) = 0

The points of intersection are x = 0 and x² + 7 = 0 (which has no real solutions). So, the limits of integration for x are [0, x₁], where x₁ is the positive root of x² + 7 = 0.

2. Set up the double integral: The double integral can be set up as follows:

∬ₐᵦ 4x² dy dx

Here, a and b represent the limits of integration for x (0 and x₁), and α(y) and β(y) represent the limits of integration for y.

3. Integrate with respect to y: Since there is no y in the function 4x², the integral with respect to y becomes:

∫ₐᵦ (4x²) * (β(y) - α(y)) dx

The functions y = 7x and y = -x³ can be rewritten as x = y/7 and x = \(-y^{\frac{1}{3} }\) respectively. So, β(y) = y/7 and α(y) = \(-y^{\frac{1}{3} }\). Thus, the integral becomes:

∫₀ˣ₁ (4x²) * (y/7 - (\(-y^{\frac{1}{3} }\))

4. Integrate with respect to x: Now, we need to integrate the function with respect to x:

∫₀ˣ₁ (4x²) * (y/7 - (\(-y^{\frac{1}{3} }\)) dy = (4/3)x³(y/7 - \((-y^{\frac{1}{3} })\) evaluated from x=0 to x=x₁.

5. Calculate the result: After evaluating the expression, the result is the value of the double integral over the region D.

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Step-by-step explanation:

I guess this will help.

when

y=4/3x-1

The investment compounded periodically will be worth approximately $15,046.66, which is $(15,046.66 - 14,893.22) ≈ $153.44.

To compare the investment compounded periodically to the investment compounded annually, we need to calculate the future value of both investments after 13 years.

Investment compounded annually:

Principal (P) = $6,000

Annual interest rate (r) = 8% or 0.08

Number of years (t) = 13

Using the compound interest formula, the future value (FV) of the investment compounded annually can be calculated as:

FV_annually = P * (1 + r)^t

FV_annually = 6000 * (1 + 0.08)^13

FV_annually ≈ $14,893.22

Now let's calculate the future value of the investment compounded periodically. Since the interest is compounded 4 times a year, we need to adjust the interest rate and the number of periods.

Interest rate per period (i) = r / n, where n is the number of interest periods per year.

Number of periods (nt) = t * n

In this case, n = 4 and t = 13, so:

i = 0.08 / 4 = 0.02

nt = 13 * 4 = 52

Using the compound interest formula for periodic compounding, the future value (FV) of the investment compounded periodically can be calculated as:

FV_periodically = P * (1 + i)^nt

FV_periodically = 6000 * (1 + 0.02)^52

FV_periodically ≈ $15,046.66

Therefore, after 13 years, the investment compounded periodically will be worth approximately $15,046.66, which is $(15,046.66 - 14,893.22) ≈ $153.44 more than the investment compounded annually.

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e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

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The population for Diego's survey is people who live in the city. An example of a way Diego could collect a representative sample of this population is by randomly selecting addresses in different neighborhoods and inviting the residents to participate in the survey.

The population for Diego's survey would be the group of individuals that he wants to make inferences about. It is not specified in the question what the population is for Diego's survey. However, for example, if Diego wants to survey college students' attitudes towards online learning, the population would be all college students.

To collect a representative sample of this population, Diego could use random sampling techniques. For example, he could randomly select a certain number of colleges and then randomly select a certain number of students from each college to participate in the survey. This would help ensure that his sample is representative of the population of college students and that he can generalize his findings to the larger population.

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Step-by-step explanation:

See image below

False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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Answer:

\(y=3x-8\)

Step-by-step explanation:

There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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Answer:

Step-by-step explanation:

Angle ABE = 90°

Angle CBE = 37° (opposite angle)

90 - 37 = 53°

The required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line is called a parabola.

Given that, a parabola has the directrix x=6 and the focus (3,-5), we need to find the equation of the parabola,

The standard form of a left-right parabola is given as:

4p(x-h) = (y-k)²

Focus = (p+h, k)

Therefore,

h+p = 3....(i)

Directrix =

x = h-p

h-p = 6...(ii)

Solving the equations we get,

h = 9/2

p = -3/2

Substitute into the standard form:

4p(x-h) = (y-k)²

4(-3/2)(x-9/2) = (y+5)²

-6(x-9/2) = (y+5)²

\(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

Hence, the required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

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The question is incomplete so, i solved for the attached question

Step 1:

The formula for the area of a hexagon can also be given in terms of the apothem as,

Area of hexagon

where 'a' is the length of the apothem and 'P' is the perimeter of the hexagon.

Step 2:

Length of the sides = 15 cm

Step 3:

Find the Apothem ' a '

Find each angle

Next

The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart. The histogram for the given data is attached with the answer below.

The histogram is a diagram with rectangles whose width is similar to the specified range and whose area is equal to the regularity of variables.

The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart.

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The sampling technique used for this situation is given by:

c) Cluster.

Samples may be classified as:

In this problem, the population is divided into groups, and each element of the groups are survived, hence cluster sampling was used.

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Answer:

Final Cost= 1.09(xx - .05xx)

Step-by-step explanation:

Since its 9% tax on the new price you would take the new price which would be 1.0 and add the .09 of tax. So its ×1.09 to get the tax.

The expression for the total cost is 1.09(xx-(0.05)xx).

The total cost is the amount calculated after any discount for an item and along with the tax incurred for an item to be purchased.

For the given situation,

Ethan buys an item that costs xx dollars.

He has discount coupon of 5% = 0.05

The tax percentage is 9% = 0.09

The discounted amount will get less from the cost price. So,

⇒ \(xx-(0.05)xx\)

The tax amount for the item will get added to the final cost of an item. Thus the expression becomes,

⇒ \(1.09(xx-(0.05)xx)\)

Hence we can conclude that the expression for the total cost is    1.09(xx-(0.05)xx).

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The most suitable data type for storing annual employee salaries ranging from $25,000 to $700,000 would be option (c) decimal(10,4).

Next, we can consider float and double data types, which can store decimal values with a higher range and precision than integers. However, they can be imprecise and cause rounding errors when used to store currency values, which can be a significant issue in financial calculations.

The most appropriate data type for storing currency values is the decimal data type, which is designed to handle decimal values with high precision and accuracy. The decimal data type can store exact numeric values up to 38 digits, with a user-defined scale (the number of digits to the right of the decimal point).

Therefore, option (c) decimal(10,4) would be the best data type for storing annual employee salaries ranging from $25,000 to $700,000.

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Complete Question:

Annual salary of each employee has to be stored in dollars and cents. The salaries vary from minimum of $25,000 to maximum of $700,000. Which of the following would be the most suitable data type?

a) decimal(8.2)

b) decimal

c) decimal(10.4)

d) Small money

e) money

Answer:

x=73

Step-by-step explanation:

Nakeisha sold 8 lollipops and 5 fruit snacks yesterday to earn a total of $18.25.

Let's use a system of equations to solve this problem. Let x be the number of lollipops sold and y be the number of fruit snacks sold. From the problem, we know that:
- The price of each lollipop is $1.50, so the total amount of money earned from selling x lollipops is 1.5x.
- The price of each fruit snack is $1.25, so the total amount of money earned from selling y fruit snacks is 1.25y.
- Yesterday, Nakeisha made $18.25 from selling a total of 13 lollipops and fruit snacks, so we can write the equation:
1.5x + 1.25y = 18.25
We also know that Nakeisha sold a total of 13 lollipops and fruit snacks, so we can write the equation:
x + y = 13
Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:
- Rearrange the second equation to solve for one variable in terms of the other:
x + y = 13
y = 13 - x
- Substitute y = 13 - x into the first equation:
1.5x + 1.25y = 18.25
1.5x + 1.25(13 - x) = 18.25
- Simplify and solve for x:
1.5x + 16.25 - 1.25x = 18.25
0.25x = 2
x = 8
- Substitute x = 8 back into y = 13 - x to find y:
y = 13 - x
y = 13 - 8
y = 5
Therefore, Nakeisha sold 8 lollipops and 5 fruit snacks yesterday to earn a total of $18.25.

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Answer:

(5 + 9) + 3 = 17

Step-by-step explanation:

The Associative Property of Addition states that no matter how you group the numbers to be added, the results will still be the same. In this case:

Original:

5 + (9 + 3) = 17

5 + 12 = 17

17 = 17 (True)

Associative Property of Addition:

(5 + 9) + 3 = 17

(14) + 3 = 17

17 = 17 (True)

As you can see, the grouping does not matter as the outcome is still the same.

~

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Answer:

We rotate the point counterclockwise by an angle θ = tan⁻¹ (y/x)

Step-by-step explanation:

If we have the point (x, y), its reflection along the x-axis (x,-y). The reflection of the point (x, -y) along the y - axis is (-x, -y). So, the angle between the initial point (x, y) and the final point (-x, -y) is θ = tan⁻¹ [(-y - y)/(- x -x)] = tan⁻¹ [(-2y/(-2x)] =  tan⁻¹(y/x).

So, the point (x, y) is rotated counterclockwise by an angle of  θ = tan⁻¹ (y/x) to perform both reflections.

Answer:

0.13188 km

Step-by-step explanation:

The distance covered by the bicycle wheel can be calculated using the formula:

distance = circumference x number of revolutions

The circumference of the wheel can be calculated using the formula:

circumference = 2 x pi x radius

where pi is approximately equal to 3.14.

Substituting the given values:

circumference = 2 x 3.14 x 30 cm

circumference = 188.4 cm

Now, we can calculate the distance covered by the wheel:

distance = circumference x number of revolutions

distance = 188.4 cm x 70

distance = 13188 cm

To convert this distance from centimeters to kilometers, we need to divide by 100,000 (since there are 100,000 centimeters in a kilometer):

distance = 13188 cm ÷ 100,000

distance = 0.13188 km

Therefore, the distance covered by the bicycle wheel is approximately 0.13188 km.

Answer: \(y=-\frac{1}{2} x+3\)

Step-by-step explanation:

use the formula y=mx+b

m = slope

b = y-intercept

slope is rice over run

rise 1 run -2       m= -1/2

y- intercept is the point where the line intercepts with the y-axis

b=3

plug into equation

\(y=-\frac{1}{2} x+3\)

Answer:

what she said

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be out of 100 micrograms, 12.16 micrograms are left, so 12.16% of the original amount, or 0.1216, is still present.

A field known as mathematics studies numbers, their variations, arithmetic, as well as the area anatomy, shapes, and both their actual but also hypothetical locations. A function explains the relationship between a group of variables, each of which comes with a corresponding outcome. A function is made up of a number of components that, when united, produce a unique result for each input.

Here,

The starting value is A(0).

The numerical value for the decay rate is r.

In this issue:

Since the patient has diabetes, 100 milligrammes of insulin are administered.

A(0) = 100

According to the graph, the quantity is 90% of the minute before it, so 1-r = 0.9.

Consequently, the formula is: => A(t) = 100 (0.9)t

Item 1: Since this quantity is A'(2), the following equations follow: A'(t) = 100 ln 0.9(0.9)t => A(2) = 100ln0.9 (0.9)² = -8.53

In the second minute, 8.53 mcg of insulin were broken down.

Item 2:

This is the sum as of the twentieth minute, so:

=> A(20) = 100ln0.9 (0.9) (0.9)²⁰ = 12.16

Out of 100 micrograms, 12.16 micrograms are left, so 12.16% of the original amount, or 0.1216, is still present.

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Answer:

The 80th term is 482

Step-by-step explanation:

8,14,20,26

This is an arithmetic sequence

Find the common difference by taking the second term and subtracting the first term

14-8 = 6

We are adding 6 each time

The formula for an arithmetic sequence is

an =a1+d(n-1)  where a1 is the first term, d is the common difference and n is the term we are looking for

a80 = 8+6(80-1)

       = 8 + 6*79

     = 8+474

    = 482

The 80th term is 482

Answer: 482

Step-by-step explanation:

\(\displaystyle\ \Large \boldsymbol{Rule:} \\\\\boxed{ \huge \boxed{a_n=a_1+(n-1)d }} } \ \ \\\\\\ 8 \underbrace{}_6 14 \underbrace{}_620\underbrace{}_626 ......a_{80}=? \\\\\\a_1=8 \ \ ; \ \ d=6 \\\\\\ a_{80}=8+(80-1)\cdot 6=480+8-6=482 \\\\\\\\ Answer: \boxed{\boldsymbol{ a_{80}=482}}\)