FACTORIZE AND Split the middle term: 72 + b - b^2​

Answer:

15 more jobs

Step-by-step explanation:

So you do 15 x 15 and that equals 225. Then you take 225 + 75 and that equals 300 so in total you just need 15 more jobs to get 300 dollars.

Answer:

y = \(\frac{3}{8}\)x - 2

Step-by-step explanation:

The answer to this problem is a simple plug-in of the given values into the slope-intercept formula.

Slope intercept formula: y = mx + b

(m = slope)

(b = y intercept)

If the equation has a slope of m = \(\frac{3}{8}\), then the slope-intercept form would be:

y = \(\frac{3}{8}\)x

If the y-intercept of an equation is (0 , -2), then the slope intercept form would be:

y = mx - 2

Putting both of these values into an equation would give option A:

y = \(\frac{3}{8}\)x - 2

The present value of Mark's prize, considering the $10,000 annual payments for 10 years and the subsequent $20,000 annual payments for 30 years, with an 8% discount rate, amounts to $171,391.44.

To calculate the present value of Mark's prize, we need to determine the current worth of the future cash flows he will receive. The $10,000 annual payments for 10 years can be considered an annuity, while the subsequent $20,000 annual payments for 30 years can be viewed as a perpetuity starting from the 11th year.

First, we calculate the present value of the annuity using the formula for the present value of an ordinary annuity:

PV_annuity = \(C * [1 - (1 + r)^(-n)] / r\),

where PV_annuity is the present value of the annuity, C is the annual cash flow, r is the discount rate, and n is the number of years. Plugging in the values, we have:

PV_annuity = $10,000\(* [1 - (1 + 0.08)^(-10)] / 0.08\) = $85,394.45.

Next, we calculate the present value of the perpetuity using the formula for the present value of a perpetuity:

PV_perpetuity = C / r,

where PV_perpetuity is the present value of the perpetuity. Plugging in the values, we have:

PV_perpetuity = $20,000 / 0.08 = $250,000.

Finally, we sum up the present values of the annuity and the perpetuity to obtain the total present value:

Total present value = PV_annuity + PV_perpetuity = $85,394.45 + $250,000 = $335,394.45.

Therefore, with an 8% discount rate, the present value of Mark's prize is $171,391.44.

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Answer:

The test is left - tailed

We cannot reject the organization's claim ( its cheapest screens will truly last less than 2.8 years)

Step-by-step explanation:

Sample size, n = 61

Sample mean, \(\bar{X} = 2.4\)

Standard deviation, \(\sigma = 0.88\)

Significance level,  α=0.02

Null hypothesis, \(H_{o} : \mu = 2.8\)

Alternative hypothesis, \(H_{a} : \mu < 2.8\)

It is clearly seen from the alternative hypothesis, that it is a left tailed test. It is not tailed towards the two directions.

Calculate the test statistic:

\(Z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n} } \\Z = \frac{2.4 - 2.8}{0.88/\sqrt{61} }\\Z = - 3.55\)

Calculate the P-value:

P(Z < -3.35) = 0.0002

Since (p-value = 0.0002) < (α=0.02), the null hypothesis is rejected.

It can therefore be concluded that the mean of the cheapest screen is less than 2.8 years. i.e. the cheapest screen will last less than 2.8 years

Answer:

The null and alternative hypotheses:

H0: u = 2.8

H1: u < 2.8

This is a left - tailed test.

For test statistics, use the formula:

\( Z = \frac{x' - u}{\sigma/ \sqrt{n}} \)

Where,

Mean, u = 2.8

Sample mean,x' = 2.4

Sample size, n = 61

Standard deviation \( \sigma \) = 0.88

Significance level = 0.02

\( Z = \frac{2.4 - 0.02}{0.88/ \sqrt{61}} =-3.55\)

Test statistics, Z = -3.55

Pvalue:

Pvalue of Z = -3.55 using standard normal table,

NORMSTID(-3.55) = 0.00019

Pvalue = 0.0002

Critical value:

Since this is a left tailed test, the critical value at 0.02 level of significance is:

\( Z_\alpha = Z_0_._0_2 = -2.05 \)

Decision: If pvalue is less than level of significance reject null hypothesis H0.

Conclusion:

Since pvalue, 0.00019 is less than level of significance, 0.02, reject null hypothesis, H0.

We conclude that the mean life of the cheapest screen is less than 2.8 years

Answer:

119cm

Step-by-step explanation:

add 37 and 24 you get 61 and the size of a triangle no matter what is going to be 180 so then subtract 180 from 61 and get 119.

The number of permutations of n letters whose mth power is the identity permutation can be calculated using generating functions.

A generating function is a formal power series that represents a sequence of numbers. In this case, we can use the generating function to represent the number of permutations of n letters whose mth power is the identity permutation.

To find the generating function for this problem, we can consider the cycle notation of a permutation. The cycle notation represents a permutation as a product of disjoint cycles.

For example, the permutation (1 2)(3 4) has two cycles: (1 2) and (3 4).

The mth power of a permutation can be obtained by raising each cycle to the power of m.

Now, let's consider the generating function for a single cycle. Let's say we have a cycle of length k. The generating function for this cycle is \(\left(\frac{x^k}{1-x^k}\right)\).

To find the generating function for the mth power of a cycle, we raise the generating function of the cycle to the power of m.

So, the generating function for a cycle of length k raised to the power of m is \(\left(\frac{x^k}{1-x^k}\right)^m\).

To find the generating function for the number of permutations of n letters whose mth power is the identity permutation, we need to consider all possible combinations of cycles.

The generating function for the number of permutations of n letters whose mth power is the identity permutation is the product of the generating functions for each cycle raised to the power of m.

Therefore, the generating function is the product of \(\left(\frac{x^k}{1-x^k}\right)^m\) for all possible cycle lengths k.

In conclusion, the generating function for the number of permutations of n letters whose mth power is the identity permutation can be calculated by finding the product of\(\left(\frac{x^k}{1-x^k}\right)^m\) for all possible cycle lengths k.

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named width in java with a value of 1.55.

double length = 3.5; double width = 1.55;

Double is a data type in Java that supports storing decimal numbers. It is used to represent values that include a fractional component and is a 64-bit floating-point data type. When exact decimal numbers are required, as in financial or scientific computations, the double data type is frequently utilized. A double's range is roughly  ±\(5.0 \times 10^{-324}\) to ±\(1.7 \times 10^{308\) having a 15–17 decimal digit degree of accuracy.

For example:

double myDouble = 3.14; Alternatively, you may define a double variable without first giving it a value and then give it one later on in your code.

3.5 double length, 1.55 double width;

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Using the conversion factors, we find that 3 cubic miles is approximately equal to 1.2504543 × 10^10 cubic meters. 5 cubic feet per second is equal to 2244.156 gallons per minute. 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.

1.1. One mile is equal to 1609.34 meters. Since we're dealing with cubic units, we cube the conversion factor.

1 mile = 1609.34 meters

1 mile³ = (1609.34 meters)³ = 4.168181 × 10^9 cubic meters

Therefore, 3 cubic miles is equal to 3 * 4.168181 × 10^9 cubic meters, which is approximately 1.2504543 × 10^10 cubic meters.

1.2. To convert from cubic feet per second (ft³/s) to gallons per minute (gal/min), we use the appropriate conversion factors.

Here are the conversion factors:

1 cubic foot = 7.48052 gallons

1 minute = 60 seconds

So, we set up the conversion as follows:

5 ft³/s * 7.48052 gal/ft³ * 60 s/min = 2244.156 gal/min

Therefore, 5 cubic feet per second is equal to 2244.156 gallons per minute.

1.3. To convert centimeters (cm) to nanometers per second squared (nm/sec²), we use the appropriate conversion factors. Here are the conversion factors:

1 centimeter = 10^7 nanometers

1 second = 1 second

So, we set up the conversion as follows:

9.50 cm * (10^7 nm/cm) / (1 sec)² = 9.50 * 10^7 nm/sec²

Therefore, 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.

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\(6x + y = 10 \\ y = 10 - 6x \\ y = 10 - 6x,x∈ℝ\)

Answer:

y = 10 - 6x

Step-by-step explanation:

6x + y = 10

=> y = 10 - 6x

Given:

The compound inequality is

\(85\leq 17m\leq 136\)

To find:

The solution of given compound inequality.

Solution:

We have,

\(85\leq 17m\leq 136\)

On dividing all sides by 17, we get

\(\dfrac{85}{17}\leq \dfrac{17m}{17}\leq \dfrac{136}{17}\)

\(5\leq m\leq 8\)

Therefore, the solution of given compound inequality is \(5\leq m\leq 8\). It can be written as [5,8].

Answer:

45 meters

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

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The sum of the parts 11/7 and 12/5 of pizza is 139/35.

It is given that the parts of pizza are:

\(1. 11/7\\2. 12/5\\\)

It is required to find sum of the parts of pizza.

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called denominator.

Calculating the sum of the parts of pizza:

\(=\frac{11}{7}+\frac{12}{5}\)

\(=\frac{139}{35}\)    

Thus, the sum of the parts 11/7 and 12/5 of pizza is 139/35.

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Iku is correct, because the function has no real zeros because there are no x-intercepts.

We have to given that;

Iku and Zachary are finding the number of real zeros of the function graphed at the right.

Here, By graph we see that;

The graph is not cut at x - axis.

Hence, There is no real solution.

So, Iku is correct, because the function has no real zeros because there are no x-intercepts.

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Plotting the points into the rectangular coordinate system :

The next point should be in the same level as the point (9, 2)

The measurement of top and bottom side must be the same.

By counting, the measurement of top is 3, so the bottom must be 3 also.

Counting 3 units to the left of (9, 2), we will get the point (6, 2)

The answer is (6, 2)

Answer:

y=-3/2x-8

Step-by-step explanation:

Answer:

it means y intercept

Step-by-step explanation:

The number of pet owners who owned a cat but not a dog is 57.

Here, we are given that a survey was conducted of 126 pet owners.

Let A = people who own a dog

A = 27

B = people who own a cat

B = 78

Thus, the people who own both a cat and a dog will be depicted as-

A ∩ B which is given to be 21

Now, here-

B = people who own only a cat + people who own both a cat and a dog

Thus, we get the following equation-

78 = people who own only a cat + 21

people who own only a cat + 21 = 78

people who own only a cat = 78 - 21

= 57

Thus, the number of pet owners who owned a cat but not a dog is 57.

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By writing a check for 1000.00 dollars involves filling out the date, recipient, amount in both numeric and written form, memo (if needed), and signing the check with the correct currency.

First, start by filling out the date in the top right corner of the check. Be sure to write out the month, day, and year in the correct format.

Next, write the name of the recipient on the "Pay to the Order of" line. This should be the full legal name of the person or business that you are giving the check to.

After that, fill out the amount of the check in both numeric and written form. For 1000.00 dollars, you would write "1000.00" in the box provided and "One Thousand and 00/100" on the line below. Be sure to include the decimal point and double-check that the amounts match.

Then, write a memo in the bottom left corner of the check if needed. This is optional but can help you remember what the check was for in case you need to reference it later.

Finally, sign the check in the bottom right corner. Make sure your signature matches the name printed on the account and that the currency you are using is correct.

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Answer:

(1) Hundred

(2) Numerator

(3) Percent

Step-by-step explanation:

The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.

As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.

In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.

It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.

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Answer

:Identity Property of Addition

Step-by-step explanation:

The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6

What is perimeter of the rectangle?

The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x+ 6

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2( l + w)

Given the following parameters

length l = 8x - 1

width w = 2x + 4

Substitute the expressions for the length and width into the formula;

P = 2(8x - 1 + 2x + 4)

P = 2(10x + 3)

Distribute 2 over each term in the parenthesis

P = 2(10x) + 2(3)

P = 20x + 6

Hence the perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6.

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The complete question is -

The perimeter formula for a rectangle is 2l + 2w, where l is the length and w is the width. Complete the steps to find an expression that represents the perimeter of the rectangle. Substitute the expressions for length and width into the formula 2l + 2w. Distribute 2 to each term in the parentheses. Combine like terms. inches

Answer: x+42x-2

Step-by-step explanation:

Answer: Part A: 4x    Part B: 4x

Step-by-step explanation: you have to add them

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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The relationship between the standard deviation and variance is that the standard deviation is the square root of the variance.

The correct option is -C

Hence, the correct option is (c) Standard deviation is the square root of the variance. Variance is the arithmetic mean of the squared differences from the mean of a set of data. It is a statistical measure that measures the spread of a dataset. The squared difference from the mean value is used to determine the variance of the given data set.

It is represented by the symbol 'σ²'. Standard deviation is the square root of the variance. It is used to calculate how far the data points are from the mean value. It is used to measure the dispersion of a dataset. The symbol 'σ' represents the standard deviation. The formula for standard deviation is:σ = √(Σ(X-M)²/N) Where X is the data point, M is the mean value, and N is the number of data points.

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Problem 10

Work Shown: 80-0 = 80

You subtract the values on the protractor where the two angle arms line up.

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

Problem 11

Work Shown: 45-0 = 45

Same idea as problem 10

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

Problem 12

Work Shown: 128-45 = 83

Same idea as the others. The arm TS isn't fully on 130 degrees, and it's a bit short of it. It looks to be about 128 degrees or so.

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

Problem 13

Explanation: Luis forgot to subtract the value of each arm of the angle. So he should have done 80-45 = 35. The answer would be 80 degrees if arm TQ was at 0 degrees (so 80-0 = 80), but instead TQ is at 45 degrees.

Answer:

Step-by-step explanation:

Taking $50 each month causes  - $50 change to bank balance

Repeating same for 7 month:

Correct option is B

Answer:

A

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

The second one y=11-4

Step-by-step explanation:

The band boosters had custom t-shirts made for homecoming and need to sell a certain number of shirts to cover their expenses. An equation, 10x = 25.90 + 8.15x, can be used to determine the number of shirts they need to sell to break even.

Let's break down the given information and formulate an equation to represent the situation.

The band boosters paid a setup fee of $25.90 and an additional cost of $8.15 per shirt to have the custom t-shirts made. They plan to sell each shirt for $10.

Let's represent the number of shirts they need to sell as 'x'. The cost to produce 'x' shirts would be the sum of the setup fee and the cost per shirt multiplied by the number of shirts:

Cost to produce 'x' shirts = Setup fee + (Cost per shirt × Number of shirts)

Using the given values, the equation becomes:

Cost to produce 'x' shirts = $25.90 + ($8.15 × x)

To break even, the revenue from selling the shirts should equal the cost to produce them. The revenue can be calculated by multiplying the selling price per shirt ($10) by the number of shirts sold:

Revenue from selling 'x' shirts = Selling price per shirt × Number of shirts sold

The equation representing the situation can be written as:

$10x = $25.90 + ($8.15 × x)

Simplifying the equation, we have:

10x = 25.90 + 8.15x

Now we have the equation that represents the situation.

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It is proven that area of the logo is 460 cm² approximately.

Divide the logo into three parts as one sector and two similar triangles and find the area of each part using the appropriate formula

Formulas used:

Area of a sector = (θ / 360) x π x r²    

Where 'r' is the radius of the sector

Area of triangle = √s(s - a)(s - b)(s - c)

Where a, b, and c are sides of the triangle

Here we have

The diagram shows a logo  

Where BEC represents a sector

ABE and CDE are two similar triangles

ED = 14 cm and DC = 27 cm

We can find the side EC by using cosine

As we know c² = a²  + b² – 2ab cos C  

=> Length of EC = √[ (14)² + (27)² - (14)(27) (cos 32°) ]  

= √[ (14)² + (27)² - 2 (14)(27) (cos 32°) ]  

= √[ 196 + 729 - 378 (0.84) ]    

= 16.85  cm

Hence, the Radius of the sector = 16.85 cm  

Using the formula, Area of a sector = (θ / 360) x π x r².  

Area of the sector = (105 / 360) x π x (16.85)².  

= 260.16 cm²    

Now find the area of triangle CDE

Semi perimeter of the triangle, s = [ 14 + 27 + 16.85 ]/2 = 28.93  

So Area of triangle CDE

= √ [ 28.93(28.93 - 14)(28.93 - 27)(28.93 - 16.85) ]

=√ [ 28.93(28.93 - 14)(28.93 - 27)(28.93 - 16.85) ]  

= √ [ 28.93(14.93)(1.9)(12.08) ]

= √ [ (9913.54) ]

= 99.57  

Since the two triangles are similar

Area of two triangles = 2 (99.57) = 199.14 cm²  

Area of the logo = Area of sector + Area of triangles  

= 260.16 cm²  + 199.14

= 459.3 ≅ 460 cm²  

Therefore,

It is proven that area of the logo is 460 cm² approximately.

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Complete Question and logo diagram given in picture