Prove or disprove that when 66^66+11^n + 11^55+101^n is divided
by 165, the remainder is 22 for all
positive odd integers n and 77 for all positive even integers
n.

Answer:

The expression to find the perimeter is 12x² - 6, and the perimeter when x= 1.5 is 21

Step-by-step explanation:

The perimeter is the sum of all side lengths for a 2d shape, such as this triangle. Our perimeter is thus

4x² - 3 + 4x² - 2 + 4x² - 1

We can then separate our variables and constants to make it

4x² + 4x² + 4x² - 3 - 2 - 1

Add the constants to get

4x²+4x²+4x²  - 6

To add variables, we must first make sure that they are the same variable/letter as well as to the same degree. The coefficient only affects the result. Because all of our variables are the same letter (x) and are all to the second degree, we can add them. To do this, we simply add the coefficients together to make one big coefficient, and multiply that by the variable. Thus,

4x² + 4x² + 4x² = (4+4+4)x² = 12x²

4x²+4x²+4x²  - 6 = 12x² - 6

Another way of looking at it is that 4x² = 4(x²) = x²+x²+x²+x²

Therefore, the expression to find the perimeter is 12x² - 6, and the perimeter when x= 1.5 is 12 * 1.5² - 6 = 21

Answer:

i dont know im sorry i wish you the best bro

Step-by-step explanation:

Answer:

strictly speaking ... poly means MANY

3x+ 4 is a binomial (bi = 2 parts)

with only one part it can not be described as a "POLY-nomial"

Step-by-step explanation:

Step-by-step explanation:

given :

120, 60, 30, _, _, _

find r!

solution :

r = 60/120 = ½.

=> 120,60,30, 15, 15/2 , 15/4 , ...

Step-by-step explanation:

Calcute the ratio :

r = Un/Un-1

r = 60/120

r = ½

Calculate 4th term :

Un = ar^n-1

U4 = 120 × ½^4-1

U4 = 120 × ½³

U4 = 120 × 0.125

U4 = 15

Calculate 5th term :

Un = ar^n-1

U5 = 120 × ½^5-1

U5 = 120 × ½⁴

U5 = 120 × 0.0625

U5 = 7.5

Calculate 6th term :

Un = ar^n-1

U6 = 120 × ½^6-1

U6 = 120 × ½⁵

U6 = 120 × 0.03125

U6 = 3.75

a. We do not have convincing evidence at the 0.05 level to conclude that the fertilizer has a positive effect on the weight of the corn ears.

b. The p-value (0.095) is still greater than the level of significance (0.05), we would still fail to reject the null hypothesis and conclude that we do not have convincing evidence to support the claim that the fertilizer has a positive effect on the weight of the corn ears.

(a) Hypothesis testing:

State the hypotheses:

Null hypothesis: The fertilizer has no effect on the weight of the corn ears.

Alternative hypothesis: The fertilizer has a positive effect on the weight of the corn ears.

Set the level of significance:

α = 0.05

Compute the test statistic and p-value:

We can use a one-sample t-test to test the hypothesis.

The test statistic is:

t = (\(\bar{x}\) - μ) / (s / sqrt(n))

where \(\bar{x}\)  is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

In this case, \(\bar{x}\)  = 8.33 ounces, μ = 8 ounces, s = 1.8 ounces, and n = 38. Substituting these values, we get:

t = (8.33 - 8) / (1.8 / sqrt(38)) = 1.66

Using a t-distribution table with 37 degrees of freedom (df = n - 1), we find that the p-value for a one-tailed test with t = 1.66 is 0.054.

Make a decision:

Since the p-value (0.054) is greater than the level of significance (0.05), we fail to reject the null hypothesis.

Therefore, we do not have convincing evidence at the 0.05 level to conclude that the fertilizer has a positive effect on the weight of the corn ears.

However, it is worth noting that the p-value is very close to the significance level, so it is possible that a larger sample size might have produced a statistically significant result.

(b) If the sample mean had been 8.24 ounces instead of 8.33 ounces, the test statistic would have been:

\(t = (8.24 - 8) / (1.8 / \sqrt{(38)} ) = 1.33\)

Using the t-distribution table with 37 degrees of freedom, the p-value for a one-tailed test with t = 1.33 is 0.095.

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Answer:

Answer is a.multiplication.

Step-by-step explanation:

I hope it's helpful!

Answer:

$42?

Step-by-step explanation:

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

Explanation:

0.4 = 4/10 = 2/5

The original slope as a fraction is 2/5

Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope

The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.

Rephrased another way: -5/2 is the negative reciprocal of 2/5.

the control limits for the x-bar chart are 9.7439 minutes (LCL) and 11.0561 minutes (UCL), and the control limits for the R chart are 0 minutes (LCL) and 2.0529 minutes (UCL).

To compute the control limits for the x-bar (mean) and R (range) charts, we'll use the following formulas:

For the x-bar chart:

Upper Control Limit (UCL) for x-bar = x-double-bar + A2 * R-bar

Lower Control Limit (LCL) for x-bar = x-double-bar - A2 * R-bar

For the R chart:

Upper Control Limit (UCL) for R = D4 * R-bar

Lower Control Limit (LCL) for R = D3 * R-bar

Where:

x-double-bar = Overall mean of the sample means

R-bar = Overall mean of the sample ranges

A2 = Constant from the control chart constants table

D4 = Constant from the control chart constants table

D3 = Constant from the control chart constants table

For sample sizes of 4, the control chart constants are as follows:

A2 = 0.729

D4 = 2.281

D3 = 0

Given the information you provided:

Overall mean (x-double-bar) = 10.4 minutes

Average range (R-bar) = 0.9 minutes

Let's calculate the control limits:

For the x-bar chart:

UCL for x-bar = 10.4 + 0.729 * 0.9

             = 10.4 + 0.6561

             = 11.0561 minutes

LCL for x-bar = 10.4 - 0.729 * 0.9

             = 10.4 - 0.6561

             = 9.7439 minutes

For the R chart:

UCL for R = 2.281 * 0.9

         = 2.0529 minutes

LCL for R = 0

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Answer: 2:10 PM

Step-by-step explanati

Answer:

13,23

Step-by-step explanation:

The required number of t-shirts and hats is given as, 45 and 15 respectively

Given that,
The senior class at Northwest High School needed to raise money for the yearbook. A local sporting goods store donated hats and T-shirts. The number of T-shirts was three times the number of hats. The seniors charged $5 for each hat and $8 for each T-shirt. If the seniors sold everything and raised $435,

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

here,
let the number of hats be x and y be the number of T-shirts,
According to the question,
y = 3x  - - - - (1
And,
5x + 8y = 435
From equation 1
5x + 8{3x} = 435
5x + 24x = 435
29x = 435
x = 15
Now put x in equation -1

y = 3 × 15
y = 45

Thus, the required number of t-shirts and hats is given as, 45 and 15 respectively

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Answer:

The correct answer is 1/2×8×3.

Answer:

5/2

Step-by-step explanation:

B/5=8/16

by cross multiplying u will get,

B×16=5×8

16B=40

B=40/16

B=5/2

Answer:

b/5=1/2......b=5/2

Step-by-step explanation:

The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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Answer:

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

Step-by-step explanation:

sin(-5x)=0.1

-sin(5x)=0.1

sin(5x)=-0.1

sin(5x)=1/10

5x=arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)+2kπ

5x=π-arcsin(- 1/10)+2kπ

x=arcsin (1/10)/5 + 2kπ/5

x=arcsin (1/10)/5 + 2kπ/5

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

Answer:

-7

Step-by-step explanation:

-10÷5= -2

-2+-5= -7

So Answer is (-7)

Slove the Parenthesis ( ) and then when you get the Answer slove it with what is on the outside and then you will have your Answer.

Hope this helps

Answer:

Answer is C

Step-by-step explanation:

-Non terminating

-Non repeating

So it's irrational. You can find out which decimal are irrational by seeing if they end or if they repeat with a number. 2.9 terminates, 17 terminates, and 3/11 (0.2727...) doesn't terminate but repeats, so they're all rational

Answer: 4√5

Step-by-step explanation:

d = √ (x2 - x1)^2 + (y2 + y1)^2

Answer:

d=4\(\sqrt{5}\)

Step-by-step explanation:

d=\(\sqrt{(3-(-5)^{2} +(2-6)^{2}\)

d=\(\sqrt{(3+5)^{2} +(2-6)^{2} }\)\

d=\(\sqrt{64+16}\)

d=\(\sqrt{80}\)

d=\(4\sqrt{5}\)

Answer:

\(x^3+x^2-2x\leq140\)

Step-by-step explanation:

This is an algebra problem, and we are expected to inequality for the volume of the aquarium.

Given that the

length= 2x

width=(x – 1)

heigth=  (x + 2)

and the volume= 280 ft^3

the inequality expression for the volume is

\(2x*(x -1) * (x + 2) \leq 280\\\\\)

open the brackets

\(2x*(x -1) * (x + 2) \leq 280\\\\(2x^2-2x)*(x+2)\leq 280\\\\\2x^3+4x^2-2x^2-4x\leq 280\\\\\2x^3+2x^2-4x\leq280\)

divide through by 2 we have

\(x^3+x^2-2x\leq140\)

Answer:

(1, 5]

Step-by-step explanation:

The rate the level in the tank falling when the height of the syrup level is 3 feet is 8/π feet per minute. The result is obtained by using the rate of change concept.

A conical tank containing syrup is draining.

Find the rate of syrup level falling (dh/dt) when h = 3 ft!

See the picture in the attachment!

By the similar triangles, we get

r/h = 2/6

r/h = 1/3

r = 1/3 h

Find the volume of the syrup left at a certain height.

V = 1/3 πr²h

V = 1/3 π(1/3 h)²h

V = 1/3 π(1/9) h² h

V = 1/27 πh³

The rate of syrup level falling is

dV/dt = dV/dh . dh/dt

dV/dt = d/dt [1/27 πh³] . dh/dt

dV/dt = 1/27 π 3h² dh/dt

8 = 1/27 π 3(3)² dh/dt

8 =  π dh/dt

dh/dt = 8/π ft/min

Hence, the rate of syrup level falling is 8/π feet per minute.

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The estimated sum of  \(10\frac{17}{20}\)+\(8\frac{6}{29}\) is 19.

Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers.

The given expression is \(10\frac{17}{20}\)+\(8\frac{6}{29}\)

These are in the form of mixed fractions.

We have to convert them to improper fraction

\(10\frac{17}{20}\) =217/20

\(8\frac{6}{29}\)=238/29

So 217/20+238/29

6293+4760/580

11053/580

19.056

It is approximately 19.

Hence  the estimated sum of  \(10\frac{17}{20}\)+\(8\frac{6}{29}\) is 19.

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Answer: $12.80

Step-by-step explanation:

$1980/ 150 t shirts =$12.80 per shirt

Answer:

$12.80 for every T-shirt.

Step-by-step explanation:

Based on the sample data, we cannot support the claim that the average mean annual salary in the town is different from $30,000.

In our case, the sample size is n = 17, the sample mean is x = $22,298, the sample standard deviation is s = $14,200, and the null hypothesis mean is μ = $30,000. Plugging these values into the formula, we get:

t = (22,298 - 30,000) / (14,200 / √(17)) = -1.96

The next step is to compare the test statistic to the critical value from the t-distribution table. The critical value depends on the degrees of freedom, which is calculated as n - 1. In our case, the degrees of freedom is 16. Looking at the t-distribution table with 16 degrees of freedom and a significance level of 0.05, we find the critical value to be ±2.131.

Since our test statistic (-1.96) is not greater than the critical value (-2.131), we fail to reject the null hypothesis. This means that we do not have enough evidence to say that the mean annual salary in the town is not equal to $30,000.

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Answer:

3

Step-by-step explanation:

2 - 3

-1

-1 + 2(2)

-1 + 4

=3

This statement best illustrates money used as a medium of exchange. In this scenario, the individual goes to the store and exchanges $68 for a pair of jeans. Money serves as a medium of exchange when it is used to facilitate transactions between buyers and sellers. In this case, the buyer wants a pair of jeans, and the seller wants to sell them for $68. Without money, they would have to engage in bartering, which can be cumbersome and inefficient. Money makes the transaction smoother and allows both parties to get what they want. Overall, this example demonstrates how money is an essential tool for facilitating transactions in our modern economy.
Hi! Your question is about the function of money as illustrated by the example of paying $68 for a pair of jeans. This statement best illustrates money used as a medium of exchange.

In this scenario, money is being used as a medium of exchange because it is facilitating the transaction between you and the store. Instead of using barter or trading goods and services directly, you use money to acquire the pair of jeans. This makes transactions more efficient and convenient since it eliminates the need for a double coincidence of wants, which is when two parties each have something the other wants. As a medium of exchange, money serves as a universally accepted means to buy and sell goods and services, like your jeans purchase at the store.

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\(\sqrt[n]{3}\) is 216−−−√3 radical: Yes because of the √

A radical in mathematics can be defined as the square root of a number. It can also be said to be the opposite of exponent.

The symbol of a radical is √ also known as the square root.

Radicals are really important in mathematics as they help us find the nth term of any number.

We can conclude by saying that 216−−−√3 is a  radical, because the radical sign is carried by 3.

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The company earned 68 billion dollars from 2008 to 2018.

According to the statement

we have given that the company's particular sales in expression are represented by (t² + 10t + 68)

And we have to find the constant terms in this expression which represent the sale of the company.

So, The given expression is (t² + 10t + 68)

From above expression it is clear that the it is in the form of Quadratic Equations.

So, The Quadratic equation, is an equation containing a single variable of degree 2. Its general form is ax^2 + bx + c = 0, where x is the variable and a, b,c are the known numbers and C is the Constant.

The general representation of Quadratic equation is

ax^2 + bx + c = 0  -(1)

and the given expression are

(t² + 10t + 68)  -(2)

After comparing both equations

Here C =68 = Constant.

So, 68 is the Constant term of the expression represent in terms of the context.

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Disclaimer: The question was incomplete. Please find the full content below.

Question:

A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 10t + 68, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?

The company earned 68 billion dollars from 2008 to 2018.

The company earned 68 billion dollars in 2008.

The company earned 10 billion dollars from 2008 to 2018.

The company earned 10 billion dollars in 2008.

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