What is the m GE bisects Find m

Answer: [tex]n=13[/tex]

Step-by-step explanation:

Given

Sum of the first 10 terms is equal to sum of 20, 21, and 22 term

[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]

No of terms to give a sum of 960

[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]

Value of first term is less than 20

[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]

Answer:

15

Step-by-step explanation:

In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))

Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.

When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.

To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.

Then in the expression: (n÷2)×(2a+(n-1)×d)

substitute:

n = 14 (must be an even number for the equation to work)

a = 15

d = 7

This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)

substituting:

n = 15

a = 15

d = 7

This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.

I hope this has helped you.

P.S. Everything in the previous solution was right apart from the start of the last section and the answer

Given: ????=????−2????+5????

and ????=2????+????+3????

To find: We need to find the value of ????×????

Solution: Here given,

????=????−2????+5????

and ????=2????+????+3????

Therefore, solving these two we have, ????=0

So,????×????=0

Answer:

D is the correct answer.

Step-by-step explanation:

You can get every y value by multiplying the x value by 3/2. This value never changes and there are no extra limitations.

Answer:

28% She didn't make a profit over 30%

Step-by-step explanation:

She buys the clocks for 50 pounds

She sells them for 22 + 22 + 20 = 64 pounds.

The profit is 14 pounds

What's the % profit.

Profit % = 14/50*100 = 28%

She's not quite right.

Answer:

1) x = 2

Step-by-step explanation:

Hope it helps. I'll try to solve the second one too

9514 1404 393

Answer:

Step-by-step explanation:

1. Substitution can work for this.

  2x +3(4x -5) = 13

  14x = 28 . . . . . add 15

  x = 2 . . . . . . . divide by 14

__

2. The equation z=6 eliminates all but the 1st and 3rd choices. Using that value in the first equation gives ...

  x + y + 6 = 5

  x + y = -1

Only the 3rd choice satisfies this equation.

  (x, y, z) = (-5, 4, 6)

Answer:

d. The sample mean used to build this interval was 170 pounds.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

In this question:

Bounds 160 and 180, so the sample mean used was (160+180)/2 = 170, and thus the correct answer is given by option d.

Answer:

157.8

Step-by-step explanation:

Add them all up to get 789 and divide them by 5 as there are five numbers to get the answer:)

Answer:

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

Step-by-step explanation:

The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. Test if the mean cost has increased.

At the null hypothesis, we test if the mean cost is still the same, that is:

[tex]H_0: \mu = 13252[/tex]

At the alternative hypothesis, we test if the mean cost has increased, that is:

[tex]H_1: \mu > 13252[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

13252 is tested at the null hypothesis:

This means that [tex]\mu = 13252[/tex]

The following year, a random sample of 20 two-year institutions had a mean of $15,560 and a standard deviation of $3500.

This means that [tex]n = 20, X = 15560, s = 3500[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{15560 - 13252}{\frac{3500}{\sqrt{20}}}[/tex]

[tex]t = 2.95[/tex]

P-value of the test and decision:

The p-value of the test is found using a t-score calculator, with a right-tailed test, with 20-1 = 19 degrees of freedom and t = 2.95. Thus, the p-value of the test is 0.0041.

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

Answer:

900 at 12%

2100 at 10%

Step-by-step explanation:

Let x= amount invested at 12%

let y= amount invested at 10%

with that being said we can write the two equation

Equation 1: x+y=3000

Equation 2: 3000*.106=.12x+.1y

isolte x from equation 1

x= 3000-y

plug this into equation 2

318=.12(3000-y)+.1y

318=360-.12y+.1y

-42= -.02y

y= 2100

Plug this into equation 1

x+2100=3000

x=900

she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.

Let's denote the amount of money Hattie invests at 12% as \(x\) dollars, and the amount she invests at 10% as \(\$3000 - x\) dollars.

The formula for calculating interest is: \(\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}\).

For the 12% account:

Interest_12% = \(x \times 0.12 \times 1\) (1 year)

For the 10% account:

Interest_10% = \((3000 - x) \times 0.10 \times 1\) (1 year)

Hattie wants to earn 10.6% interest on the total investment, so we can set up the equation:

\(\text{Total Interest} = \text{Interest}_12% + \text{Interest}_10%\)

\(3000 \times 0.106 = x \times 0.12 + (3000 - x) \times 0.10\)

Now, solve for \(x\):

\(318 = 0.12x + 300 - 0.10x\)

\(318 = 0.02x + 300\)

\(18 = 0.02x\)

\(x = 900\)

Hattie should invest $900 at 12% and \(3000 - 900 = 2100\) at 10%.

Therefore, she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.

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Answer:

y = 5/4 x - 23/4

Step-by-step explanation:

4x + 5y = 31

5y = - 4x +31

y = -4/5 x + 31/5

⊥ slope = 5/4

-7 = 5/4 (-1) + B

-28 = -5 + 4b

-23 = 4B

b = -23/4

Answer:

B

Step-by-step explanation:

B is the correct equation

Answer:

A) [ 7/3,  (-7/9)(x/2),  7/27(x-2)^2,  (-7/81)(x-2)^3 ]

B) attached below

Step-by-step explanation:

A)  Using the definition of a Taylor series

The first four nonzero terms of the series for f(x) = 7/ (1 +x), a = 2

= [ 7/3,  (-7/9)(x/2),  7/27(x-2)^2,  (-7/81)(x-2)^3 ]

attached below is the detailed solution

B) Finding Maclaurin series for f(x)

f(x) = e^-5x

attached below

Associated radius of convergence = ∞  ( infinity )

Answer : barry

12<15

Barry's unit rate is 15 minutes per mile and Robin's unit rate is 12 minutes per mile

We have:

Barry

Distance = 2 miles

Time = 30 minutes

Unit rate = Time/Distance

Unit rate = 30 minutes/2 miles

Unit rate = 15 minutes per mile

Robin

Distance = 3 miles

Time = 36 minutes

Unit rate = Time/Distance

Unit rate = 36 minutes/3 miles

Unit rate = 12 minutes per mile

Hence, Barry's unit rate is 15 minutes per mile and Robin's unit rate is 12 minutes per mile

The unit rates mean that:

Hence, Robin walks faster

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Answer:

0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A hotel manager believes that 23% of the hotel rooms are booked.

This means that [tex]p = 0.23[/tex]

Sample of 610 rooms

This means that [tex]n = 610[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.23[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{610}} = 0.017[/tex]

What is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%?

p-value of Z when X = 0.23 + 0.03 = 0.26 subtracted by the p-value of Z when X = 0.23 - 0.03 = 0.2. So

X = 0.26

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.26 - 0.23}{0.017}[/tex]

[tex]Z = 1.76[/tex]

[tex]Z = 1.76[/tex] has a p-value of 0.9608

X = 0.2

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.2 - 0.23}{0.017}[/tex]

[tex]Z = -1.76[/tex]

[tex]Z = -1.76[/tex] has a p-value of 0.0392

0.9608 - 0.0392 = 0.9216

0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%

Answer:

No solution

Step-by-step explanation:

5x+10y=3 equation 1

10x+20y=8 equation 2

-2(5x+10y)=-2(3) multiply equation 1 by -2 to eliminate x

-10x-20y=-6 equation 1 multiplied by -2

10x+20y=8 equation 2

0  +  0  =2. Add above equations

    0      =2  

no solution

Step-by-step explanation:

Recall that

[tex]1 + \tan^2 x = \sec^2 x[/tex]

and

[tex]\dfrac{d}{dx}(\tan x) = \sec^2 x[/tex]

so that

[tex]\displaystyle \int \tan^2 x = \int (\sec^2 x - 1)dx[/tex]

[tex]\:\:\:\:\:\:\:\:\:=\int \sec^2 xdx - \int dx[/tex]

[tex]\:\:\:\:\:\:\:\:\:=\tan x - x + C[/tex]

where C is the constant of integration.

Step-by-step explanation:

1/6

1/6- 1/2 = 1/4

1/4*1/2= 1/8

Answer:

Problem 1 has a greater answer.

Step-by-step explanation:

Solve problem 1 using the order of operatiobs PEMDAS (Parentheses, Exponents, multiplication/division, and addition/subtraction):

Multiplication/division depends from left to right of the expression, the same goes to addition/subtraction.

(2 + 3) (5 + 5)

= (5)(10)

= 50

SOLVE problem 2 using PEMDAS:

2 + 3 x 5 + 5

= 2 + 15 + 5

= 17 + 5

= 22

Answer 1 (50) compared to Answer 2 (22):

50 > 22

HOPE THIS HELPS!

9514 1404 393

Answer:

  P(x) = x³ -5x² +12x -8

Step-by-step explanation:

If the coefficients are real, then the complex roots must be conjugates. The third root is 2+2i. For root r, (x -r) is a factor, so the factorization is ...

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

Expanding further, we find ...

  P(x) = x³ -5x² +12x -8

Answer:

66

Step-by-step explanation:

Add both of the angles given together

43 + 23

Answer:

3( [tex]\frac{s}{q}[/tex] + r)  

Answer:

[tex](a)\ t =\frac{d}{v}[/tex]

[tex](b)\ d = vt[/tex]

Step-by-step explanation:

The question is mixed up with details of another question. See comment for original question

Given

[tex]v = \frac{d}{t}[/tex]

[tex]v \to velocity[/tex]

[tex]d \to distance[/tex]

[tex]t \to time[/tex]

Solving (a): Solve for time

We have:

[tex]v = \frac{d}{t}[/tex]

Cross multiply

[tex]t * v = d[/tex]

Make t the subject

[tex]t =\frac{d}{v}[/tex]

Solving (b): Solve for distance

We have:

[tex]v = \frac{d}{t}[/tex]

Cross multiply

[tex]d = v * t[/tex]

[tex]d = vt[/tex]

Answer:

Probability of defective televisions : Now, If two televisions are randomly​ selected, then the probability that both televisions work. Hence, the probability that both televisions work is 0.5289 . Hence, the probability at least one of the two televisions does not​ work is 0.4711.

It is false

Step-by-step explanation:

Hope it will help you

Answer:

6m + 8 is the answer.

Step-by-step explanation:

( m x 6 ) + 8

= 6m + 8

Answer:

Mrs. Cabrini has a total of 2 1/8 quarts of tomato sauce.

Step-by-step explanation:

Since Mrs. Cabrini needs 2 quarts of tomato sauce to make a large batch of her spaghetti sauce. she has 1 1/4 quarts of her own, and she borrows 1/2 quart from the neighbor across the hall and 3/8 quart from the neighbor next door, to determine how many quarts does she have in all of her own must perform the following calculation:

1/4 = 0.25

1/2 = 0.5

3/8 = 0.375

0.25 + 0.5 + 0.375 = X

1.125 = X

1 + 1,125 = 2,125

Therefore, Mrs. Cabrini has a total of 2 1/8 quarts of tomato sauce.

Cross sections of the volume are washers or annuli with outer radii x(y) + 1, where

y = x(y) ² - 1   ==>   x(y) = √(y + 1)

and inner radii 1. The distance between the outermost edge of each shell to the axis of revolution is then 1 + √(y + 1), and the distance between the innermost edge of R on the y-axis to the axis of revolution is 1.

For each value of y in the interval [-1, 3], the corresponding cross section has an area of

π (1 + √(y + 1))² - π (1)² = π (2√(y + 1) + y + 1)

Then the volume of the solid is the integral of this area over [-1, 3]:

[tex]\displaystyle\int_{-1}^3\pi y\,\mathrm dy = \frac{\pi y^2}2\bigg|_{-1}^3 = \boxed{4\pi}[/tex]

[tex]\displaystyle\int_{-1}^3 \pi\left(2\sqrt{y+1}+y+1\right)\,\mathrm dy = \pi\left(\frac43(y+1)^{3/2}+\frac{y^2}2+y\right)\bigg|_{-1}^3 = \boxed{\frac{56\pi}3}[/tex]