What is the value of 't' in the equation: + ( − ) = 26

xAnswer:

-10   -8   -6   -4

Step-by-step explanation:

The numbers are  

first =x

second= x+2

third=x+4

4th= x+6

2(x + (x+4)) = 3(x+6)-20

4x+8 = 3x+18–20

4x-3x=18–20–8

x=-10

So the numbers are       -10,           -8,              -6,            -4

                                       first           2nd          3rd             4th

           Check:

         2( -10-6)  = 3(-4) -20

            2(-16) =  -12-20

-32 = -32

Based on the information given regarding the equation, it can be noted that Tania doesn't have enough money.

Your information is incomplete. Therefore, an overview will be given. Let's assume that the price of a jawbreaker is 0.45.

Therefore, the cost of 21 jawbreakers will be:

= 21 × 0.45

= 9.45

In this case, the person has 8.32. Therefore, it can be noted that she doesn't have enough money.

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The instantaneous rate of change of f equals the average rate of change of f at 2 points in the closed interval [0, √π]: x = 0.673 and x = 1.325.

To find the points in the closed interval where the instantaneous rate of change of f equals the average rate of change of f, we need to set up the equation for the derivative of f and the formula for the average rate of change of f on the interval.

First, we can evaluate the integral to get:

f(x) = ∫x^2 0 (sin t) dt = 1 - cos x^2

Next, we can find the derivative of f:

f'(x) = sin x^2 * 2x

To find the average rate of change of f on the interval [0, √π], we can use the formula:

Average rate of change of f = [f(√π) - f(0)] / (√π - 0)

= [1 - cos π] / √π

= 2 / √π

Now, we can set up the equation:

f'(x) = 2 / √π

sin x^2 * 2x = 2 / √π

sin x^2 = 1 / (√π x)

We can solve for x numerically using a graphing calculator or computer software. The solutions are approximately x = 0.673 and x = 1.325. Since these solutions are within the interval [0, √π], they are valid solutions.

Therefore, the instantaneous rate of change of f equals the average rate of change of f at 2 points in the closed interval [0, √π]: x = 0.673 and x = 1.325.

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Step-by-step explanation:

b^2-4b+3=0

b²-3x-b+3=0

b(b-3)-1(b-3)=0

(b-3)(b-1)=0

either

b=3 or b=1

.

2n^2 + 7 = -4n + 5

2n²+4n+7-5=0

2n²+4n+2=0

2(n²+2n+1)=0

(n+1)²=0/2

:.n=-1

.

x - 3x^2 = 5+ 2x - x^2

0=5+ 2x - x^2-x +3x^2

0=5+x+2x²

2x²+x+5=0

comparing above equation with ax²+bx +c we get

a=2

b=1

c=5

x={-b±√(b²-4ac)}/2a ={-1±√(1²-4×2×5)}/2×1

={-1±√-39}/2

Yes, the given sequence is geometric. The common ratio between any two consecutive terms can be found by dividing the second term by the first term or the third term by the second term, and so on.

In this case, the common ratio is calculated as follows:

Divide -3 by 0.3: -3/0.3 = -10

Divide 30 by -3: 30/-3 = -10

Divide -300 by 30: -300/30 = -10

Divide 3000 by -300: 3000/-300 = -10

Since the common ratio is the same for all consecutive terms, we can conclude that the given sequence is a geometric sequence with a common ratio of -10.

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Answer:

-----------------------

The total cost of repair is expressed by the function:

As we see,

Therefore the answer is option A.

Answer: 25x + 75

Step-by-step explanation:

The 25 is the monthly fee, x stands for the number of months and the 75 is the set fee

To implement the LP problem in a spreadsheet, we first need to set up the objective function and constraints in separate cells. Then, we can use Solver to solve the problem and create a Sensitivity Report.

The objective function is 4X2 + 2X2, which we enter in cell C1 as "=4B1+2B2". This means that the value of the objective function is determined by the values of X1 and X2, which are entered in cells A1 and B1, respectively.

The first constraint is 2X1 + 4X2 ≤ 20, which we enter in cell C2 as "=2A2+4B2<=20". This means that the sum of 2 times X1 and 4 times X2 cannot exceed 20.

The second constraint is 3X1 + 5X2 ≤ 15, which we enter in cell C3 as "=3A3+5B3<=15". This means that the sum of 3 times X1 and 5 times X2 cannot exceed 15.

We also need to add the non-negativity constraints X1, X2 ≥ 0 by setting the lower bounds of cells A1 and B1 to 0 in Solver.

To solve the LP problem using Solver, we select the "Max" objective and add the constraints as described above. We then run Solver and obtain the optimal solution X1 = 0, X2 = 2.5, and the optimal objective function value of 15.00.

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(a) For f(x) = 2x^2 for 0 ≤ x ≤ C, integrating and solving for C gives us the value of C. (b) For f(x) = Cx for 0 ≤ x ≤ 3, integrating and solving for C gives us the value of C. (c) For f(x) = ex for 0 ≤ x ≤ C, integrating and solving for C gives us the value of C. (d) Similarly, for the remaining functions (e), (f), (g), and (h), integrating and solving for C will give us the values of C in each case.

In order to find the value of C for each probability density function, we need to ensure that the integral of the function over its given range equals 1, since the total area under the probability density function represents the probability of the random variable occurring.

(a) To find C for f(x) = 2x^2 for 0 ≤ x ≤ C, we need to integrate the function over its given range and set it equal to 1:

∫[0,C] 2x^2 dx = 1

After integrating and solving for C, we can determine the value.

(b) For f(x) = Cx for 0 ≤ x ≤ 3, we integrate the function and set it equal to 1:

∫[0,3] Cx dx = 1

After integrating and solving for C, we can find its value.

(c) For f(x) = ex for 0 ≤ x ≤ C, we integrate the function and set it equal to 1:

∫[0,C] ex dx = 1

After integrating and solving for C, we can determine the value.

(d), (e), (f), (g), and (h) follow a similar process. By integrating each function over its given range and equating the result to 1, we can solve for C and find its value in each case.

By finding the appropriate antiderivatives and solving the resulting equations, we can determine the values of C for each probability density function.

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We should use a sample size of at least 154 to estimate the mean fuel efficiency for the new type of motorcycle within 0.5 mpg. The confidence interval in Part A is between 60.725 and 65.555 mpg.

To construct a 95% confidence interval for the mean fuel efficiency for this vehicle, we can use the formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, let's calculate the sample mean and standard deviation for the given data:

Sample mean = (57.5 + 62.3 + 67.2 + 58.1 + 59.6 + 71.9 + 55.2 + 57.6 + 71.9 + 68.8 + 69.1 + 65.3 + 62.3 + 64.7 + 59.9 + 62.1 + 63.5 + 62.9 + 66.7 + 61.3) / 20

= 63.14

Sample standard deviation = √(((57.5 - 63.14)² + (62.3 - 63.14)² + (67.2 - 63.14)² + ... + (61.3 - 63.14)²) / 19)

= 4.97

Next, we need to find the critical value for a 95% confidence level. Since the sample size is small (20), we will use a t-distribution. The degrees of freedom for this calculation is 20 - 1 = 19. Consulting a t-table or using statistical software, we find the critical value to be approximately 2.093.

Plugging the values into the formula, we get:

Confidence interval = 63.14 ± (2.093) * (4.97 / √(20)) ≈ 63.14 ± 2.415

Interpreting the confidence interval, we can say with 95% confidence that the true mean fuel efficiency for this vehicle falls between 60.725 and 65.555 mpg.

To determine if the new motorcycle has greater fuel efficiency than the previous model, we can perform a hypothesis test. The null hypothesis (H0) is that there is no difference in fuel efficiency between the two models, and the alternative hypothesis (Ha) is that the new model has greater fuel efficiency.

We can use a t-test to compare the means of two independent samples. The test statistic is calculated as:
t = (sample mean 1 - sample mean 2) / sqrt((sample variance 1 / sample size 1) + (sample variance 2 / sample size 2))

For this case, the sample mean for the new model is 65.9 mpg, and the sample standard deviation is 3.2 mpg. The sample mean and standard deviation for the previous model were calculated in Part A. We can use the same sample size of 20 for both models.

Calculating the test statistic:

t = (65.9 - 63.14) / √((4.97² / 20) + (3.2² / 20))

t ≈ 1.376

Looking up the critical value for a t-distribution with 20 - 1 = 19 degrees of freedom at a 95% confidence level, we find it to be approximately 2.093.

Since the test statistic (1.376) is less than the critical value (2.093), we do not have enough evidence to convincingly claim that the new model has greater fuel efficiency than the previous model.

To construct a 98% confidence interval for the mean fuel efficiency of the older model, we can use the same formula as in Part A. The only difference is the critical value. For a 98% confidence level, the critical value for a t-distribution with 20 - 1 = 19 degrees of freedom is approximately 2.861.

Plugging the values into the formula:

Confidence interval = 63.14 ± (2.861) * (4.97 / √(20))

≈ 63.14 ± 3.303

Interpreting the confidence interval, we can say with 98% confidence that the true mean fuel efficiency for the older model falls between 59.837 and 66.443 mpg.

The change in confidence level from 95% to 98% does not change the conclusion in Part B. The hypothesis test is based on comparing the test statistic to the critical value, and the confidence interval is based on the sample mean and standard deviation. The change in confidence level does not alter these values or the comparison between them.

To estimate the mean fuel efficiency for the new type of motorcycle within 0.5 mpg, we need to calculate the sample size required. The formula for the sample size is:

Sample size = (Z-score * standard deviation / margin of error)²

Plugging in the values:

Z-score = critical value for the desired confidence level (let's assume 95%)

Standard deviation = 3.2 mpg (from the given data)

Margin of error = 0.5 mpg

Using a Z-score of approximately 1.96 for a 95% confidence level:

Sample size = (1.96 * 3.2 / 0.5)² ≈ 153.86

We should use a sample size of at least 154 to estimate the mean fuel efficiency for the new type of motorcycle within 0.5 mpg.

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The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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The given function is

f(x) = - 2|x+5| + 2

The x intercept is the value of x when f(x) = 0

Substituting f(x) = 0 into the function, we have

0 = - 2|x+5| + 2

Subtract 2 from both sides

0 - 2 = - 2|x+5| + 2 - 2

- 2 = - 2|x+5|

Divide both sides by - 2. It becomes

- 2/- 2 = - 2|x+5|/- 2

1 = |x+5|

x + 5 = 1 or x + 5 = - 1

x = 1 - 5 or x = - 1 - 5

x = - 4 or x = - 6

x intercepts are x = - 6, x = - 4

Writing the x intercepts as points, they are

(- 6, 0) and (- 4, 0)

The y intercept is the value of f(x) when x = 0

substituting x = 0 into the function, we have

f(0) = - 2|0+5| + 2

f(0) = - 2|5| + 2 = - 2(5) + 2 = - 10 + 2

f(0) = - 8

y intercept = (0, - 8)

Answer:

B

Step-by-step explanation:

Total ounces of nuts is cashews (12.3 ounces) plus almonds (15.2 ounces) is 27.5 ounces. If you divide 27.5 ounces by 5 people, 27.5 / 5 = 5.5 ounces each.

Answer:

120

Step-by-step explanation:

took quiz it was correct!

Answer:

120

Step-by-step explanation:

Answer:

.6

Step-by-step explanation:

7/11 would be around .63, rounded to the nearest tenth is .6,

Answer:

The answer would be .6

Step-by-step explanation:

Hope this helps

The amount of concrete required to make 80 pots is 0.24192 cubic meters after adding 5% of the required concrete.

Given that:External dimensions of the prism, a = 18 cmHeight of the prism, h = 16 cm Thickness of the walls, t = 3 cmNumber of pots, n = 80Wastage is 5% of the required concreteLet the side of the inner square be 'a1'. Then,a = a1 + 2t⇒ a1 = a - 2t = 18 - 2×3 = 12 cmVolume of the pot = volume of the outer prism - volume of the inner prismVolume of the outer prismVolume of the outer prism = a²hVolume of the outer prism = 18²×16 = 5184 cm³Volume of the inner prismVolume of the inner prism = a1²hVolume of the inner prism = 12²×16 = 2304 cm³Volume of the potVolume of the pot = 5184 - 2304 = 2880 cm³In m³, Volume of the pot = 2880/1000000 m³Volume of 80 such potsVolume of 80 pots = 80 × 2880/1000000 m³= 0.2304 m³Concrete required for the potsConcrete required = volume of 80 pots × (100 + 5)/100Concrete required = 0.2304 × 105/100 m³Concrete required = 0.24192 m³

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Is the relation a function: C. No, because for each input there is not exactly one output.

In Mathematics, a function is typically used for uniquely mapping an independent value (input variable or domain) to a dependent value (range or output variable).

This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.

Since the independent value (12) is mapped to multiple dependent values (-4 and -2), we can logically deduce that the relation does not represent a function.

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Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

Answer:

D is the correct answer.

ZY + YX = ZX

Answer:

Step-by-step expla

The statistical technique that combines results of a large number of studies is called meta-analysis.

It means that you will take data from various sources, such as studies, combine them together, and then create this mixture of various results that you can use in your own research. If something occurs often in those studies, it means that it is good and reliable information.

Answer

d

Step-by-step explanation:

I already know and i did the test

2 miles per day? Maybe that’s the answer

Answer: 4/3 miles or 1 1/3 miles per day

Answer:  A rectangular prism with a height of two inches, length of seven inches, and a width of three inches.

Step-by-step explanation:

Multiply the dimensions given, then select the one that matches Jorge's required 42 in³

5×5×5 = 125

5×4×4 = 80

2×7×3 = 42

6×3×2 = 36

Answer:

A

Step-by-step explanation:

The experimental probability of rolling a number smaller than 5 is: 6 successful outcomes / 10 total outcomes = 0.6 or 60%

The theoretical probability of rolling a number smaller than 5 is 2/3 because this is what the cube shows (1, 2, 3, 4).

The experimental probability of rolling a number smaller than 5 is 0.6 or 60% because this is what is obtained from rolling the cube 10 times.

Given that the number cube has six sides, numbered 1 to 6 and Luka rolled it 10 times, we can find the theoretical probability of rolling a number smaller than 5 by dividing the possible number of outcomes by the total number of outcomes.

The possible outcomes that are smaller than 5 are 1, 2, 3, and 4, which is a total of four outcomes. The total number of outcomes is six since the cube has six sides. The theoretical probability of rolling a number smaller than 5 is:

4 possible outcomes / 6 total outcomes = 2/3

The experimental probability of rolling a number smaller than 5 is obtained by calculating the ratio of the number of times Luka obtained a number smaller than 5 and the total number of times he rolled the cube.

In this case, the number of times Luka obtained a number smaller than 5 is 6 since there are 6 numbers less than 5, and the total number of times he rolled the cube is 10.

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Answer:

orientation is preserved (stays the same)

Step-by-step explanation:

Answer:

2. 36

3. 8

4. 64 - 32

5. 7

I hope that this helps you, I'm not sure if number 4 is correct, but I am 100% sure that the rest are correct. I did the math for all of the questions and they should all be correct. I hope you have a wonderful evening!

Answer:

Step-by-step explanation:

1.  0.40

2. 0.5