2 + 4x - 4 = 0 which gives x =

Answer:

(n- 2/3)²

Step-by-step explanation:

We have:

It can be put as:

Here we consider n = a and -2/3 = b, then

Now we add 4/9 to a given binomial to make it perfect square:

So, added 4/9 and got a perfect square (n- 2/3)²

Answer:

4.167(10²)

Step-by-step explanation:

Step 1: Put number into proper decimal form

416.7 = 4.167

Step 2: Figure out exponent

Since we are moving the decimal places 2 places to the right, our exponent is 2

Answer:

4.167 × 10^2

Step-by-step explanation:

= 4.167 × 10^2

(scientific notation)

= 4.167e2

(scientific e notation)

= 416.7 × 10^0

(engineering notation)

(one)

= 416.7

(real number)

Answer:

yes, because they intercept the same arc

Step-by-step explanation:

Answer:

yes, because they intercept the same arc

Step-by-step explanation:

Answer:

There is not enough evidence to support the claim that the population mean is significantly less than 5.4.

This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.

If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean is significantly less than 5.4.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=5.4\\\\H_a:\mu< 5.4[/tex]

The significance level is 0.05.

The sample has a size n=44.

The sample mean is M=5.31.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.51.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.51}{\sqrt{44}}=0.077[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{5.31-5.4}{0.077}=\dfrac{-0.09}{0.077}=-1.171[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=44-1=43[/tex]

This test is a left-tailed test, with 43 degrees of freedom and t=-1.171, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.171)=0.124[/tex]

As the P-value (0.124) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the population mean is significantly less than 5.4.

This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.

If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.

Answer:

220 grams.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question:

[tex]\mu = 212, \sigma = 20, n = 22, s = \frac{20}{\sqrt{22}} = 4.264[/tex]

If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?

We have to find the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.

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

By the Central Limit Theorem

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

[tex]1.88 = \frac{X - 212}{4.264}[/tex]

[tex]X - 212 = 1.88*4.264[/tex]

[tex]X = 220[/tex]

The answer is 220 grams.

Answer:

  1.23

Step-by-step explanation:

"Appropriate technology" makes short work of this.

Answer:

50%

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

Heads coming up at most 600 times when a fair coin is flipped 1000 times.

600/1000

= 0.6

0.6 × 100

= 60

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▹ Answer

20 - 12 or 8 (depending on what you need to find)

▹ Step-by-Step Explanation

4(5 - 3)

Distribute 4 * 5 and 4 * -3

This will give 20 - 12

If you are looking for the final answer, it would be 8.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

273 Touchdowns

Step-by-step explanation:

You divide the amount of confetti cannons set off by the amount of confetti cannons set off every time there is a touchdown scored. So in this case 181818 ÷ 666

Answer:

tan∅ = 3√29/10

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

cos∅ = adjacent/hypotenuse

Since we are given cos∅ = 10/19, we know that one leg is 10 and the hypotenuse is 19. We need to find the missing leg length:

10² + b² = 19²

b² = 19² - 10²

b = √261

b = 3√29

We know that tan∅ equals opposite over adjacent. Our adjacent is given to us by cos∅, so we simply plug in our values:

tan∅ = opposite/adjacent

tan∅ = 3√29/10

Answer:

There are 8568 ways to combine the shoes.

Step-by-step explanation:

In this case Connie wants to create smaller subsets from a larger group of things, therefore we must do a combination, which can be applied by using the following formula:

[tex]C_{(n,r)} = \frac{n!}{r!*(n - r)!}[/tex]

In our case n = 18, which is the total number of shoes and r = 5, which is the subset she wants to create.

[tex]C_{(18,5)} = \frac{18!}{5!*(18 - 5)!} = \frac{18!}{5!*13!} = \frac{18*17*16*15*14*13!}{5!*13!}\\C_{(18,5)} = \frac{18*17*16*15*14}{5*4*3*2} = 8568[/tex]

There are 8568 ways to combine the shoes.

The number of ways can she choose which shoes to take is 8,568.

Given that,

Based on the above information, the calculation is as follows:

[tex]= \frac{n!}{k!(n-k)!} \\\\= \frac{18!}{5!13!} \\\\= \frac{18\times 17\times 16\times\15\times \times 14}{5\times 4\times 3\times2\times 1}[/tex]

= 8,568

Therefore we can conclude that The number of ways can she choose which shoes to take is 8,568.

Learn more: brainly.com/question/17429689

Answer:

more info is needed

Step-by-step explanation:

Answer:

Probability of answering 5out of 10 correctly= 0.246

Step-by-step explanation:

Total question answered= 2

Question answered correctly= 1

Probability of answered correctly= 1/2

Probability of answered correctly= 0.5

Probability of answered incorrectly = 0.5

Probability of answering 5out of 10 correctly= 10C5(0.5)^5(0.5)^5

Probability of answering 5out of 10 correctly = 10!/5!5!(0.5)^5(0.5)^5

Probability of answering 5out of 10 correctly = 252(0.03125)(0.03125)

Probability of answering 5out of 10 correctly= 0.246

Answer:

2800

Step-by-step explanation:

2826 to the nearest hundred is 2800

Hey there! :)

Answer:

[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]

Step-by-step explanation:

Given:

f(x) = 5x² + 2

Switch the x and y variables in the equation:

x = 5y² + 2

Subtract 2 from both sides:

x - 2 = 5y²

Divide 5 from both sides:

[tex]\frac{1}{5}(x-2) = y^{2}[/tex]

Square root both sides:

y = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]

**Make sure to add a ±  sign when finding the inverse of a parabolic function.

Therefore, the inverse of this function is:

[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]

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▹ Answer

(3x + 4) * (4x - 5)

▹ Step-by-Step Explanation

12x² + x - 20

Rewrite

12x² + 16x - 15x - 20

Factor out

4x(3x + 4) - 15x - 20

4x(3x + 4) - 5(3x + 4)

Factor

(3x + 4) * (4x - 5)

Hope this helps!

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Answer:

A. 7√3 in

Step-by-step explanation:

We first have to draw out the altitude on the triangle. When we do so, we should see that we will get 2 congruent 30-60-90 triangles. From there, our h height is x and we use tan∅ to solve:

tan60° = x/7

x = 7tan60°

x = 7√3

Answer:

It's A

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

The range of a data set is

Largest data value - Smallest data value

62 - 5

= 57

The range of the data set is 57 pounds.

Answer:

[tex]\boxed{\red{57}}[/tex]

Step-by-step explanation:

[tex]\blue {range \: \: of \: \: a \: \: data \: \: set \: \: means}[/tex]

you have to subtract the smallest value from the largest value in the data set.

[tex]\boxed{\green{largest \: \: value - smallest \: \: value}} \\ \boxed{\green{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 62 - 5}} \\ \: \: \: \: \: \: \: \: \boxed{\pink{ =57}}[/tex]

Answer:

The reciprocal is cosecant that is option B

The reciprocal function of sine is cosecant.

It is the opposite of a function meaning by if a function is f(x) then the reciprocal function will be 1/f(x).

They are real function which relates with the angle of a right angle triangle to ratios of two sides.

We have to find the reciprocal function of sine.

f=sine

Reciprocal of f=1/sine

=cosecant

Hence the reciprocal of sine is cosecant.

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Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                          P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = 94.3

            n = sample of car drivers = 16

            [tex]\mu[/tex] = population mean number of chips in a bag

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95

P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                   = [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]

                                   = [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Answer:

Number of ways = 3612 ways

Step-by-step explanation:

I have attached a diagram representing two scenarios on the chess board. The scenarios are; when the first king takes away 4 squares (label A) while the second scenario is when it takes 6 squares (label B).

Now, If the white king is in a corner, it has 4 possibilities while the black king can be at any of (64 − 4 =) 60 positions.

If the white king is at the boundary, but not in a corner which is 24 possibilities, the black king can be at any of (64 − 6 =) 58 positions

Finally, in all other cases, for the white king which has 36 possibilities, the black king can be at any of (64 − 9 =) 55 positions.

So, in total, the number of ways would be;

(60 × 4) + (58 × 24) + (55 × 36) = 3612 ways

Answer:

tan theta = 2 sqrt(5) /15

Step-by-step explanation:

sin theta = opp / hypotenuse

sin theta = 2/7

We can use the Pythagorean theorem to find the length of the adjacent side

a^2 + b^2 = c^2

2^2 +adj^2 = 7^2

4 + adj^2 = 49

adj ^2 = 49-4

adj^2 = 45

Taking the square root of each side

adj = sqrt(45) = sqrt(9*5) =sqrt(9) sqrt(5) = 3 sqrt(5)

The tan theta = opp/ adj

tan theta = 2 / 3 sqrt(5)

Multiply by sqrt(5) / sqrt(5)

                = 2 sqrt(5) / 3 *5

                 = 2 sqrt(5) /15

Answer:

Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.

Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.

Step-by-step explanation:

Question:

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

30

∑  (−3i+5)

i=1

Answer:

The first three terms are : 2, -1 and -4

The last term is: -85

The sum of the sequence is: -1245

Step-by-step explanation:

Given;

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

30

∑  (−3i+5)                    -------------------(i)

i=1

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

Where the ith term aₙ is given by;

[tex]a_{i}[/tex] = [tex]-3i + 5[/tex]         -------------------(ii)

(a) Therefore, to get the first three terms ([tex]a_1, a_2, a_3[/tex]), we substitute i=1,2 and 3 into equation (ii) as follows;

[tex]a_{1}[/tex] = [tex]-3(1) + 5[/tex] = 2

[tex]a_2 = -3(2) + 5 = -1[/tex]

[tex]a_3 = -3(3) + 5[/tex][tex]= -4[/tex]

Since the sum expression in equation (i) goes from i=1 to 30, then the last term of the sequence is when i = 30. This is given by;

[tex]a_{30} = -3(30) + 5 = -85[/tex]

(b) The sum [tex]s_n[/tex] of an arithmetic sequence is given by;

[tex]s_n = \frac{n}{2}[a_1 + a_n][/tex]   -----------------(iii)

Where;

n = number of terms in the sequence = 30

[tex]a_1[/tex] = first term = 2

[tex]a_n[/tex] = last term = -85

Substitute the corresponding values of n, [tex]a_1[/tex] and [tex]a_n[/tex] into equation (iii) as follows;

[tex]s_n = \frac{30}{2}[2 + (-85)][/tex]

[tex]s_n[/tex] = 15[-83]

[tex]s_n[/tex] = -1245

Answer:

Step-by-step explanation:

H0: mu is equal to $108.50

Ha: mu is not equal to $108.50

This test is a two tailed test and using the z tat formula, we can ascertain if there is a difference.

z = x-u / sd/√n

Where x is $112, u is $108.50 sd is $16 and n is 64

z = 112-108.50 / 16/√64

z = 3.5/(16/8)

z = 3.5/2

z = 1.75

To help us arrive at a conclusion, we need to find the p value using alpha id = 0.05. The p value is 0.08. Since the p value is great than 0.05, we fail to reject the null and conclude that there is not enough statistical evidence to prove that the average room price is significantly different from $108.50

Answer:

63.00

Step-by-step explanation:

25.1 × 2.51

Multiply.

= 63.001

Round to two decimal places.

63.00

Answer:

63.00

Step-by-step explanation:

when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00

The correct answer is $216

Explanation:

The chart shows the price users need to pay for visiting the museum or riding on the train. This includes a difference in price between adults and students. However, as the club includes only students (27 students) the price that should be considered are $3 for visiting the museum and $5 for the train ride. Additionally, you can know the total the student spend if you multiply the prices by the total number of students.

27 (number of students) x $3 (price for visiting the museum) =  $81 (total for visiting the museum)

27 (number of students) x $5 (price for the train ride) =  $135 (total for the train ride)

Additionally, you will need to add both results to know the total: $81 + $135 = $216

You can also get the same result if you consider each student will spend $8 (price for visiting the museum and for the train ride) and then multiply this by the number of students ($8 x 27 = $216)

Answer:

angle of bc= 180-168= 12°

length of bc= 12/360 × π × diameter

= 12/360 × 22/7 × 21

= 12/360 × 66

= 2,20 cm (b)

WY = a = 4

ZY = b = 3

As WYZ is forming a right angle triangle, therefore, we can use pythagorean theorem to find the value of c

a2+b2=c2 (4)2+(3)2=C2 16+9=C2 C2=25

Taking square root on both sides

√c2= √25 c=5

The value of c is 5 units.

The value of c is 5 units

The complete question is an illustration of a right-triangle, where the equation to calculate the value of c is:

c^2 = a^2 + b^2

The equation becomes

c^2 = 3^2 + 4^2

Evaluate the exponents

c^2 = 9 + 16

Evaluate the sum

c^2 = 25

Take the square root of both sides

c =5

Hence, the value of c is 5 units

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