Which pair shows equivalent expressions?
2(x+2) = 2x+1
02(x+2) = x+4
02(x+4)=x+2
02(x+4)= 2/x+8

Answer:

range

Step-by-step explanation:

The difference between the lowest and the highest number is called the range. The middle value is the median (it's in the "mid"dle, median) The mean is the average. And the mode is the most frequent value.

The largest area the rectangle can have is -1024 square units.

To solve the given problem, follow the steps given below:

Step 1: Sketch the given graph on a coordinate plane as shown below:

Step 2: Let's assume that the base of the rectangle is x units and its height is y units.

Step 3: As the base of the rectangle is on x-axis, we have the length of the base as the x-coordinate of the upper two vertices of the rectangle.

Now, the x-coordinate of the upper two vertices of the rectangle lie on the given semicircle whose equation is y = V1 - 32.

So, we can write:

y = V1 - 32x^2 = (y + 32)^2 ⇒ x^2 = y^2 + 64y + 1024

Step 4: Now, we can write the area of the rectangle as: A = base × height= x × y

Using the value of x from equation (1), we get: A = (y^2 + 64y + 1024)1/2 y

So, we have an equation for area in terms of y. Let's differentiate it with respect to y to find the maximum value of A. dA/dy = (y^2 + 64y + 1024)-1/2 (2y + 64)

By equating dA/dy = 0, we get: 2y + 64 = 0y = -32

Substituting the value of y in equation (2), we get:x^2 = 1024 ⇒ x = ±32

The given rectangle lies in the first quadrant.

Hence, the length of the base of the rectangle is x = 32 units.

So, we have the dimensions of the rectangle as length = 32 units and breadth = height = y = -32 units.

However, as the length and breadth of the rectangle cannot be negative, we cannot consider the negative value of y.

Therefore, the maximum area of the rectangle is: A = base × height= 32 × (-32)= -1024 sq. units

Hence, the largest area the rectangle can have is -1024 square units.

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The data set represent a population.

The range for this data set is 9.

The variance for this data set is 14.05.

The standard deviation for this data set is 3.748.

In Statistics, a population simply refers to a set of similar items or events that comprises every member of a group i.e the total number of elements.

Based on the given data set, we would calculate the range by using the following formula:

Range = Highest number - Lowest number

Range = 24 - 15

Range = 9.

Next, we would determine the mean as follows;

Mean = ∑fx/n

Mean = (24 + 16 +23+22+17+15+24+24+24+16)/10

Mean = 205/10 = 20.5

Now, we can calculate the standard deviation and variance by using this formula:

Standard deviation, δ = √(1/n × ∑(xi - μ)²)

Standard deviation, δ = √[1/10 × (24 - 20.5)² + (16 - 20.5)² + (23 - 20.5)² + (22 - 20.5)² + (17 - 20.5)² + (15 - 20.5)² + (24 - 20.5)² + (24 - 20.5)² + (24 - 20.5)² + (16 - 20.5)²]

Standard deviation, δ = √140.5/10

Standard deviation, δ = 3.748.

For the variance, we have:

Variance = δ²

Variance = 3.75²

Variance = 14.05

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Answer:

5/6 probability

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

This is actually pretty easy. Keep this in mind.

There are 34 total students. 16 of them like bananas and the rest like apples. All you really need to do is count up from 16 to 34 to find the answer.

The simple equation for this is: 34-16

Thus, the answer is 18.

Population: The set of all possible customers in the store.

Sample: The 82 customers randomly surveyed.

Variable: Age of the customers Type of variable: Quantitative parameter

Parameter: The mean age of all the customers in the store.

Statistic: The sample mean age of the 82 customers surveyed.

Analysis: The mean age of all customers is a parameter since the store owner is interested in knowing the mean age of all the customers that come to her store.

The store owner will be interested in collecting data on all the customers who come to her store. Since this will be difficult, she will sample some customers instead. The store owner randomly surveyed 82 customers, which is the sample size. The variable of interest is the age of the customers. This is a quantitative variable since it is measured using numerical values. The sample mean age of the 82 customers surveyed is a statistic.

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Answer:

464

Step-by-step explanation:

the number has one, zero at the end. same for the ten.

just take zero for zero and you end up with 464

The temperature that separates the top 7% from the bottom 93% is 98.78°F.

To solve this problem, we need to use the concept of the normal distribution. In a normal distribution, data is symmetrically distributed around the mean, with the majority of values falling within a certain range determined by the standard deviation. In this case, we are given a normal distribution of human body temperatures with a mean of 98.20°F and a standard deviation of 0.62°F.

To find the temperature that separates the top 7% from the bottom 93%, we need to locate the value on the distribution that corresponds to the 93rd percentile. The 93rd percentile represents the point below which 93% of the data falls. Conversely, the top 7% of the data lies above this point.

Using statistical tables or a calculator, we can determine the z-score corresponding to the 93rd percentile. The z-score measures the number of standard deviations a given value is away from the mean. Once we find the z-score, we can use it to calculate the temperature value.

In this case, the z-score corresponding to the 93rd percentile is approximately 1.475. We can then use the z-score formula: z = (x - mean) / standard deviation. Rearranging the formula to solve for x (the temperature value), we get x = (z * standard deviation) + mean. Plugging in the values, we find x = (1.475 * 0.62) + 98.20 = 98.78°F.

Therefore, the temperature that separates the top 7% from the bottom 93% is approximately 98.78°F. This means that 93% of human body temperatures are below 98.78°F, while the top 7% are above this value.

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For every divisor d of the order n of a cyclic group G=⟨a⟩, there exists a subgroup of G whose order is d.

To approach this, we can consider the properties of cyclic groups. A cyclic group G generated by a single element "a" has elements that are powers of "a" in the form of [tex]a^k[/tex], where k takes values from 0 to n-1. The order of an element "a" in G is the smallest positive integer k such that [tex]a^k[/tex] equals the identity element.

Now, let's focus on the divisors of n. Each divisor d divides n evenly, meaning n/d is an integer. We can consider the element "[tex]a^(^n^/^d^)[/tex]" in G. The order of "[tex]a^(^n^/^d^)[/tex]" is d because [tex](a^(^n^/^d^))^d = a^n = e[/tex], where e is the identity element of G.

Hence, the subgroup generated by "[tex]a^(^n^/^d^)[/tex]" has an order of d, since it consists of elements of the form [tex](a^(^n^/^d^))^k[/tex], where k takes values from 0 to d-1. Therefore, for every divisor d of n, there exists a subgroup of G whose order is d.

This demonstrates the relationship between the divisors of n and the order of the subgroups in the cyclic group G.

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Answer:

Step-by-step explanation:

it's kinda confusing b/c of the minus signs.. huh...  but -5 is less than -2 sooo

start with

-2 1/2  - (-5 3/4 )

=5 3/4 - 2 1/2

=5 3/4 - 2 2/4

=23/4 - 10/4

=13/4

there you go...  :)

if you want it back in proper fractions

3 1/4

Answer:

h = 403.92in or 1026cm

Step-by-step explanation:

Given

Let x represent the density of mercury, and y the density of water.

[tex]y = 13.5x[/tex]

[tex]Mercury\ barometer =76cm[/tex] or [tex]Mercury\ barometer =29.92in[/tex]

Required

Determine the height of the barometer

At standard atmospheric pressure, the relationship between the mercury barometer and the height (h) of the barometer is:

[tex]h = 13.5 * Mercury\ barometer[/tex]

In centimeters, we have:

[tex]h = 13.5 * 76cm[/tex]

[tex]h = 1026cm[/tex]

In inches, we have:

[tex]h = 13.5 * 29.92in[/tex]

[tex]h = 403.92in[/tex]

Answer:

x^3

Step-by-step explanation:

quotient property of exponents

I think the answer is c. x^3

Answer:

Step-by-step explanation:

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm.

Answer:

Step-by-step explanation:

Volume of prism = length * width * height  

                            = 8 1/2 *  7 * 4

                            [tex]= \frac{17}{2}*7*4\\\\=17 * 7 * 2\\\\= 238 cubic m[/tex]

Answer:8.5 is x but there is an extra 1

Step-by-step explanation:18x8.5=153+8=162 with an extra one is 162

Answer:

perimeter of rectangle = 2 (length + breadth)

= 2(9x + 6y + 13x + 2y)

= 2(22x +8y)

= 44x + 16y

Step-by-step explanation:

9x+6y

9-9x+6-9y both side subtract 9

x+(-3)y

x-3y the answer

13x+2y

13-13x+2-13y

x+(-11)y

x-11y .

follow me

Answer:

the answer is 675.70 or 4,504.33

Step-by-step explanation:

the right answer is that

Answer:

at first , you need the sum of both equations . It will be like :

2y= 0 + 2

Y=1

_____

now that you know the value of Y , place it in the one of the equation that you like , forexample i place it in the second equation and find out that the value of x is ( -3/2)

1= 2X+5

-4=2X

X= -2

Hope it helps , good luck ^.^

Answer:

12.5 minutes

Step-by-step explanation:

Multiply 1/8 by 100. Convert 25/2 to a decimal by dividing 25 by 2. The answer is 12.5 minutes.

Answer:

16.0(?)

Step-by-step explanation:

I’m not really sure if it’s correct. But I’m assume it’s correct.

The minimum percentage of data values that lie within the range of $48 to $60 an hour for the mechanic's labor is 86.64%.

To find the minimum percentage of data values that lie within the range of $48 to $60 an hour for the mechanic's labor.

We need to calculate the z-scores for both values and use a z-table to find area under the normal curve between those two scores.

First, we calculate the z-score for $48 an hour:

z = (48 - 54) / 4 = -1.5

Next, we calculate the z-score for $60 an hour:

z = (60 - 54) / 4 = 1.5

Using a standard normal distribution table, we can find that the area under the curve between -1.5 and 1.5 is approximately 0.8664 or 86.64%.

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To determine the value of k in the function f(x) = [tex]x^4[/tex] + k[tex]x^3[/tex] - 3x - 5, we can consider the remainders when f(x) is divided by (x-3) and (x+3).

a) When f(x) is divided by (x-3), the remainder is -10. To find the remainder, we can use the Remainder Theorem, which states that if a polynomial f(x) is divided by (x - a), the remainder is equal to f(a). Plugging in x = 3 into f(x), we get:

f(3) = [tex]3^4[/tex] + k([tex]3^3[/tex]) - 3(3) - 5

     = 81 + 27k - 9 - 5

     = 27k + 67

Since the remainder is -10, we can set up the equation:

27k + 67 = -10

Solving this equation, we find:

27k = -77

k = -77/27

b) To determine the remainder when f(x) is divided by (x+3), we can follow a similar process. Plugging in x = -3 into f(x), we get:

f(-3) =[tex](-3)^4[/tex] + k[tex](-3)^3[/tex] - 3(-3) - 5

       = 81 - 27k + 9 - 5

       = -27k + 85

The remainder is given by f(-3), so we can set up the equation:

-27k + 85 = remainder

Hence, the remainder when f(x) is divided by (x+3) is -27k + 85.

In summary, the value of k such that the remainder when f(x) is divided by (x-3) is -10 is k = -77/27. Additionally, the remainder when f(x) is divided by (x+3) is -27k + 85.

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Answer:

Reconciled balance $3,142.11

Step-by-step explanation:

The computation of the reconciled balance is shown below:

Debit balance as per check book $1,955.81

Add: interest earned $31.55

Collection of note $3,100

Outstanding checks $2,919.43

Less: service charges -$22.80

Less: deposit in transit -$3,991.88

Less: forgot a check -$850

Reconciled balance $3,142.11

The same would be relevant and considered too

Step-by-step explanation:

[tex]5x - 2[/tex]

...........

Answer:

2-5x

Step-by-step explanation:

let the number be x, 5 *x = 5x.

2 less means ,2 minus,

>> 2-5x.

Answer:

Z max  = 1500

x₁  = 15

x₂ = 0

Step-by-step explanation:

From problem statement:

                                                      Plant A              Plant B     Profit $/each

Product 1 (Doors )          x₁                  2                          4            100

Product  2 (windows )   x₂                  3                           4              80

Product  2 (windows )   x₂   above 10 is scrap

Objective function to maximize

z = 100*x₁   +  80*x₂

Subject to:

Plant A capacity

2*x₁ + 3*x₂   ≤  40

Plant B capacity

4*x₁  + 4*x₂  ≤ 60

Windows condition:

0*x₁  + x₂  ≤  10

Model:

Max      z  =  100*x₁   +  80*x₂

Subject to:

2*x₁ + 3*x₂   ≤  40

4*x₁  + 4*x₂  ≤ 60

              x₂ ≤ 10

x₁ , x₂ ≥  0    and integers

Afther 6 iterations using Simplex Solver AtomZmath

Z max  = 1500

x₁  = 15

x₂ = 0

Answer:

20pi

Step-by-step explanation:

150/360 = 5/12

5/12 * 2*24*pi = 20pi

==============

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[tex]\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}[/tex]

[tex]\Huge \textsf{Step-by-step explanation}[/tex]

[tex]\LARGE \bold{\textsf{Step 1: Assign Variables}}[/tex]

[tex]\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}[/tex]

[tex]\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}[/tex]

[tex]\large \bold{ \textsf{From the problem, we know that:}}[/tex]

[tex]\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}[/tex]

[tex]\large \bold{ \textsf{We can use this information to write two equations:}}[/tex]

[tex]\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}[/tex]

[tex]\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}[/tex]

[tex]\LARGE \bold{\textsf{Step 3: Solve the system of equations}}[/tex]

[tex]\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}[/tex]

[tex]\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}[/tex]

[tex]\large \textsf{Simplifying this expression gives us:}[/tex]

[tex]\textsf{10\textit{p} + 10 = 260}[/tex]

[tex]\large \textsf{Subtracting 10 from both sides:}[/tex]

[tex]\textsf{10\textit{p} = 250}[/tex]

[tex]\large \textsf{Dividing both sides by 10}[/tex]

[tex]\textsf{\textit{p} = 25}[/tex]

[tex]\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}[/tex]

[tex]\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}[/tex]

[tex]\large \textsf{So, 25 pizzas and 80 sodas were sold.}[/tex]

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The domain of the function f(x) = x² - 2x + 1 is all real numbers, which is denoted as (-∞, +∞).

To find the domain of the function f(x) = x² - 2x + 1, we determine the set of all possible values for x that make the function well-defined.

The given function is a polynomial-function, and polynomial functions are defined for all real numbers. So, the domain of f(x) = x² - 2x + 1 is the set of all real numbers, which can be represented as (-∞, +∞).

It means that any real-number can be substituted into the function, and it will give a valid output. There are no limitations on the possible values of x in this case.

Therefore, the domain is all real numbers.

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The given question is incomplete, the complete question is

Find the domain of the function f(x) = x² - 2x + 1.

An increase in the real interest rate will most likely lower the reward to savings. The correct answer is D.

When the real interest rate increases, it means that the return on savings and investments is higher in real terms, adjusted for inflation. As a result, individuals are incentivized to save more as they can earn a higher return on their savings.

When the reward to savings is lower, it becomes less attractive for individuals to save. Higher interest rates can discourage borrowing and encourage saving, which reduces consumer spending on durable goods and other discretionary purchases.

Option A is incorrect because an increase in the real interest rate would likely lead to a decrease in consumer's purchases of durable goods, as higher interest rates increase the cost of borrowing, making it more expensive to finance large purchases.

Option B is incorrect because an increase in the real interest rate generally makes borrowing more expensive, as it increases the cost of borrowing for individuals and businesses.

Option C is incorrect because an increase in the real interest rate usually encourages individuals to save more and spend less, as the potential return on savings is higher.

The correct answer is D.

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Answer: 12 claps per second

Step-by-step explanation: divide both by 60 and yield 12 times -1 second