A group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June If the pattern continues, Rew many hours will they practice in November?

Answer:

Induction

Step-by-step explanation:

Induction reasoning refers to conjectures which is what you will need for this

The Inductive reasoning allows to use observation to find the next three

values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

For given example,

We have been given the number pattern 1, 4, 7, 10, . . .

Here, 4 - 1 = 3                             ..................(i)

7 - 4 = 3                                       ..................(ii)

10 - 7 = 3                                      ..................(iii)

From (i), (ii) and (iii),

the common difference between consecutive terms is 3.

The next three values would be,

10 + 3 = 13

13 + 3 = 16

16 + 3 = 19

So, the number pattern would be 1, 4, 7, 10, 13, 16, 19, . . .

Therefore, an Inductive reasoning allows to use observation to find the next three values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

Learn more about the inductive reasoning here:

https://brainly.com/question/8419798

#SPJ2

113/32

Step-by-step explanation:

7 squared is 49, 4 cubed is 64, 2 to the 5th power is 32.

49 plus 64 is 113 divided by 32

3.53125

Step-by-step explanation:

7^2+4^3/2^5

= 49+64/32

= 113/32

= 3.53125

Answer:

Step-by-step explanation:

a) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 451

x = 1.5/100 × 451 = 7

p = 7/451 = 0.02

q = 1 - 0.02 = 0.98

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.97 = 0.1

α/2 = 0.01/2 = 0.03

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.03 = 0.97

The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17

Therefore, the 97% confidence interval is

0.02 ± 2.17√(0.02)(0.98)/451

= 0.02 ± 0.014

b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.

P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.

The distribution that should be used is the normal distribution

Options:

The supplier products have a lower mean than claimed

The supplier is more accurate than they claimed

The supplier products have a higher mean than claimed

The supplier is less accurate than they have claimed

Answer:

The supplier is less accurate than they have claimed

Step-by-step explanation:

Confidence Interval for supplier claim, CI = (20.45, 21.05)

Confidence Interval for your claim, CI = (20.48, 21.02)

Calculate the mean of the Confidence Interval for the supplier's claim:

[tex]\bar{X_s} = \frac{20.45 + 21.05}{2} \\\bar{X_s} = \frac{41.50}{2}\\\bar{X_s} = 20.75[/tex]

Calculate the mean of the Confidence Interval for your claim :

[tex]\bar{X_y} = \frac{20.48 + 21.02}{2} \\\bar{X_y} = \frac{41.50}{2}\\\bar{X_y} = 20.75[/tex]

Both the supplier and you have the equal mean

Margin of Error by the supplier = 21.05 - 20.75 = 0.30

Margin of Error by you = 21.02 - 20.75 = 0.27

Since the margin of error for the supplier is more, you can conclude that the suppler is less accurate than they have claimed.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05. You take samples and find that the 95% confidence interval of what they are sending is 20.48 to 21.02. What conclusion can be made?

The supplier products have a lower mean than claimed

The supplier is more accurate than they claimed

The supplier products have a higher mean than claimed

The supplier is less accurate than they have claimed

Answer:

The margin of error reported by the supplier is greater as compared to the actual margin of error. A greater margin of error results in less accuracy.

Therefore, we can conclude that the supplier is less accurate than they have claimed.

Step-by-step explanation:

Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05.

The mean is given by

Mean = (Upper limit + Lower limit)/2

Mean = (21.05 + 20.45)/2

Mean = (41.50)/2

Mean = 20.75

The margin of error in this case is

MoE = Upper limit - Mean

MoE = 21.05 - 20.75

MoE = 0.30

You take samples and find that the 95% confidence interval of what they are sending is 20.48 to 21.02.

The mean is given by

Mean = (Upper limit + Lower limit)/2

Mean = (21.02 + 20.48)/2

Mean = (41.50)/2

Mean = 20.75

The margin of error in this case is

MoE = Upper limit - Mean

MoE = 21.02 - 20.75

MoE = 0.27

As you can notice the margin of error reported by the supplier is greater as compared to the actual margin of error. A greater margin of error results in less accuracy.

Therefore, we can conclude that the supplier is less accurate than they have claimed.

Answer:

x < 6

Step-by-step explanation:

5x < 21 +9

5x < 30

x < 30/5

x < 6

so the value of x is 5,4,3,2,1, 0, -1, ....

Answer: x<6

Step-by-step explanation:

For this problem, we approach it as if it had an equal sign instead of an inequality.

5x-9<21      [add 9 on both sides]

5x<30         [divide 5 on both sides]

x<6

Answer:

(a) The formula to calculate the amount of money (A) that Aizuddin must pay the bank after n years, with the original amount of borrowed money is 6300 RM, interest of 8%, compounded annually, is described as following:

A = principal x (1 + rate)^(time in year)

A = 6300 x (1 + 8/100)^n

(b) The amount of interest charged (AC) that Aizuddin must pay after n years:

AC = A - 6300

AC = 6300 x (1 + 8/100)^n - 6300

AC = 6300 x [(1 + 8/100)^n - 1]

Hope this helps!

Answer:

It's the option D

6 root 2 units

Answer:

(-3,18) and (-1,6)

Step-by-step explanation:

[tex]x^2-2x+3=-6x\\<=> x^2+4x+3 = 0\\<=> (x+2)^2 -4+3=0\\<=> (x+2)^2-1^2 = 0\\<=> (x+2+1)(x+2-1) = 0\\<=> (x+1)(x+3) = 0\\<=> x+1 = 0 \ or \ x+3 = 0\\<=> x = -1 \ or \ x=-3[/tex]

so the solutions are

(-3,-6*-3=18) that we can write (-3,18)

and

(-1,-6*-1=6) that we can write (-1,6)

Answer:  b) Each sold the same number of vehicles

Step-by-step explanation:

This question is only asking for the quantity of vehicles (not the total amount earned) so we can disregard the second matrix and find the sum of each row in the first matrix.

Kelly: 8 + 2 + 6 = 16

Scott: 7 + 8 + 1 = 16

Mark: 10 + 4 + 2 = 16

The total number of vehicles sold by each person is the same

Answer:

Yes

Step-by-step explanation:

1 book = $4

2 books = 2*$4

3 books = 3*$4

4 books = 4*$4

5 books = 5*$4

This can be shown as:  y=4x

y=ax+b is linear function, Irena is right

Answer:

$5073.37

Step-by-step explanation:

We can use the simple interest rate (appreciation) formula: A = P(1 + r)^t

Because it gives us 3 months, we need to put it in terms of years. That will give us 1/4 of a year:

A = 5000(1 + 0.06)^0.25

When you plug that into the calc, you should get 5073.37 as your final answer!

Answer:

So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.

70+N/4 = 120

480 = 70+N

So then we subtract 70 from both sides.  Then we get 410 = N.

The answer is

The complete question is;

The height of water in a bathtub,h, is a function of time,t. Let P represent this function. Height is measured in inches and time in minutes.

Match each statement in function notation with a description.

A: P(0) = 0

B: P(4) = 10

C: P(10) = 4

D: P(20) = 0

1:After 20 minutes, the bathtub is empty.

2:The bathtub starts out with no water.

3:After 10 minutes, the height of the water is 4 inches.

4:The height of the water is 10 inches after 4 minutes.

Answer:

-option D is the correct answer for sentence 1.

-option A is the correct answer for sentence 2.

-option C is the correct answer for sentence 3.

-option B is the correct answer for sentence 4

Step-by-step explanation:

The height of water in a bathtub h is a function of time t.

-If t = 20 minutes, then height of water represented by P is empty so, P(20) = 0. Thus, option D is the correct option for sentence 1.

-The bath tub starts out with no water. Thus, P(0) = 0. So option A is the correct option for sentence 2.

-After 10 minutes, the height of the water is 4 inches. Thus, P(10) = 4. So, option C is the correct option for sentence 3.

- The height of the water is 10 inches after 4 minutes. Thus, P(4) = 10. So option B is the correct answer for sentence 4

Answer

A. 18(3/4)π

Explanation

In the attached file

Corrected Question

A cylinder with a base diameter of x units has a volume of  [tex]\pi x^3[/tex] cubic units

Which statements about the cylinder are true? Check all that apply.

Answer:

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]

Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]

Volume =Base Area X Height

[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]

Therefore:

Answer:

8,15 and 17 are Pythagorean triplets,the Pythagorean triplets of 15 are: (15,112 and113),(15,8 and 17),(15,20 and 25),(15,9and 12),(15,36 and 39)

Answer:

Step-by-step explanation:

If

[tex]a=m^2-n^2;\ b=2mn;\ c=m^2+n^2[/tex]

for m > n, then a, b, c make a Pythagorean triplet.

[tex]m^2-n^2=15\to(m-n)(m+n)=15\\\\(m-n)(m+n)=(3)(5)\to m-n=3\ \wedge\ m+n=5[/tex]

We have the system of equations:

[tex]\underline{+\left\{\begin{array}{ccc}m-n=3\\m+n=5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2m=8\qquad\text{divide both sides by 2}\\.\qquad\boxed{m=4}[/tex]

Substitute to the second equation:

[tex]4+n=5\qquad\text{subtract 4 from both sides}\\\boxed{n=1[/tex]

Therefore we have:

[tex]a=4^2-1^2=16-1=15\\b=2(4)(1)=8\\c=4^2+1^2=16+1=17[/tex]

[tex]2mn=15[/tex]  it's impossible, because 15 is not an even number.

[tex]m^2+n^2=15[/tex]

Let's consider all possible sums of two numbers resulting in 15.

We will check which of the numbers are perfect squares.

1 + 14

2 + 13

3 + 12

4 + 11

5 + 10

6 + 9

7 + 8

(Bold not perfect squares)

There are no two perfect squares among the listed pairs of numbers.

Other:

15, 112, 113

We know the Egyptian triangle with sides of length 3, 4, 5.

By modifying this Pythagorean triplet by multiplying by 3 we get:

(3)(3) = 9; (3)(4) = 12; (3)(5) = 15

By modifying this Pythagorean triplet by multiplying by 5 we get:

(5)(3) = 15; (5)(4) = 20; (5)(5) = 25

Answer:

-10

Step-by-step explanation:

[tex]-\dfrac{3}{5}x=6 \\\\\\x=\dfrac{6}{-\dfrac{3}{5}} \\\\\\x=6\times -\dfrac{5}{3} \\\\\\x=-10[/tex]

Hope this helps!

Answer:

x = -10

Step-by-step explanation:

So first and easily we have to multiply to --> -3/5x = 6

After that you just do the regular formula -->

Factor divided by the x

6 / (-3/5) = -10

-10

Hope this helps

Answer:

9cm

Step-by-step explanation:

Area of a Triangle [tex]=\dfrac12$ X Base X Height[/tex]

[tex]Given:\\$Area of \triangle GHK =117cm^2\\$Base = 26cm\\Therefore:\\117=\dfrac12$ X 26 X h\\117=13h\\Divide both sides by 13 to obtain h\\h=117 \div 13\\$Height of Triangle GHK, h=9cm[/tex]

Answer:

9

Step-by-step explanation:

Answer:

Option C is correct.

The 437 county residents were a random sample of all county residents.

a) If p is the proportion of Hispanics in the county,

The null hypothesis is represented as

H₀: p = 0.16

The alternative hypothesis is represented as

Hₐ: p ≠ 0.35

b) The model of the test is two-tailled, one-proportion test. And it satisfies all of the required conditions for an hypothesis test.

c) The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).

Test statistic = -4.09

p-value = 0.000043

d) We can conclude that the proportion of the county that are Hispanics is different from the proportion of the country that are Hispanics.

Step-by-step explanation:

According to the question, it was clearly stated that the 437 county residents are a random sample of the residents in the county, hence, it is evident that option C is the right statement.

a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the county supervisor wants to check if proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. (0.16).

Hence, the null hypothesis is that there isn't enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. That is, there is no significant difference between the proportion of the county that are Hispanics and the proportion of the whole nation that are Hispanics. (0.16).

The alternative hypothesis will now be that enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics (0.16).

Mathematically,

The null hypothesis is represented as

H₀: p = 0.16

The alternative hypothesis is represented as

Hₐ: p ≠ 0.16

b) To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough.

Hence, the model of this test is two-tailled, one-proportion test.

And the major conditions for an hypothesis test is that

- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another. This is already clearly given in the question.

- The sample must be a normal distribution sample or approximate a normal distribution.

The conditions to check this is that

np ≥ 10

and

np(1-p) ≥ 10

p = sample proportion = (44/437) = 0.101

np = 437×0.101 = 44 ≥ 10

np(1-p) = 437×0.101×(1-0.101) = 39.7 ≥ 10

The two conditions are satisfied, hence, we can conclude that this distribution at least approximates a normal distribution.

c) So, we compute the t-test statistic

z = (x - μ)/σₓ

x = sample proportion = 0.101

μ = p₀ = The proportion we are comparing against = 0.16

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 437

σₓ = √[0.101×0.899/437] = 0.0144145066 = 0.0144

z = (0.101 - 0.16) ÷ 0.0144

z = -4.093 = -4.09

checking the tables for the p-value of this z-statistic

Degree of freedom = df = n - 1 = 437 - 1 = 436

Significance level = 0.05 (when the significance level isn't stated, 0.05 is used)

The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).

p-value (for z = -4.09, at 0.05 significance level, df = 436, with a two tailed condition) = 0.000043

The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).

d) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.000043

0.000043 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics.

Hope this Helps!!!

Answer:

Step-by-step explanation:

if N=2.0

4.9 N=4.9×2=9.8

9.8/1.4=7

which is an integer.

so N=2.0

Answer:

r = 4.2805cm

Step-by-step explanation:

ok first the shape its made of two slant height and and an arc of degree 70°

The total perimeter = 28cm

The formula for the total perimeter= 2l + 2πl(70/360)

Where l is the radius of the shape.

But l = 2r

So

= 2l + 1.2217l

= 3.2217l

28 = 3.2217l

l = 28/3.2217

l = 8.691

Recall that l = 2r

8.691= 2r

r = 8.691/2

r = 4.2805cm

Step-by-step explanation:

I don't know if the first set of numbers is all in one set, but I'll do my best to give you an answer.

Really all you need to do is use PEMDAS for the first question.

(Parentheses, exponents, multiply, divide, add, subtract. In that order)

[tex]1 2 + 8 \div (9 - 5) \\ 12 + 8 \div 4 \\ 12 + 2 \\ 14[/tex]

Then to simplify that fraction next to it, notice that 0.018 is 3x 0.06.

that's a 3:1 ratio, so it ends up simplifying to this:

[tex] \frac{3}{1} [/tex]

Lastly, to solve the division of that fraction. If you divide by a fraction, you multiply whatever it's dividing by its inverse.

So...

[tex] \frac{5}{7} \div \frac{2}{5} \\ \frac{5}{7} \times \frac{5}{2} \\ \frac{25}{14} [/tex]

Answer:

a) C. The population must be normally distributed.

b) P(x < 65.8) = 0.8159

c) P(x > 64.2) = 0.3015

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

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 = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me

n < 30, so the distribution of the population must be normal.

The correct answer is:

C. The population must be normally distributed.

(b) Assuming the normal model can be used, determine P(x < 65.8).

This is the pvalue of Z when X = 65.8. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{65.8 - 62}{4.22}[/tex]

[tex]Z = 0.9[/tex]

[tex]Z = 0.9[/tex] has a pvalue of 0.8159.

So

P(x < 65.8) = 0.8159

(c) Assuming the normal model can be used, determine P(x > 64.2).

This is 1 subtracted by the pvalue of Z when X = 64.2. So

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

[tex]Z = \frac{64.2 - 62}{4.22}[/tex]

[tex]Z = 0.52[/tex]

[tex]Z = 0.52[/tex] has a pvalue of 0.6985.

1 - 0.6985 = 0.3015

So

P(x > 64.2) = 0.3015

Answer:

(1,0)

Step-by-step explanation:

(-1+3)/2 = 1

(-1+1)/2 = 0

Answer:

12

Step-by-step explanation:

1:4 = 3:12

Answer:

12 cups of water

Step-by-step explanation:

The ratio of fertilizer is 1. To get to 3 you times it by 3. Therefore to find how much water you need you'd have to do the same to the other side of the ratio, times it by three. So it would be 3:12

Answer:

12x8+5=101/8

101/8-74/5

40/8=5

5x101=505

40/5=8

8x74=592

therefore 505/40-592/40=

-87/40=-2.175

Answer:

The correct answer would be 2.175

Step-by-step explanation:

i got it right :))

Answer:

b

Step-by-step explanation:

she walked for the first place in a while to be crying for a sec

If one of the vertices on the x-axis is (x, 0), then the other vertex on the same axis is (-x, 0), so that the rectangle has base 2x. The other two vertices on the parabola are the points (x, 6 - x²) and (-x, 6 - x²), so the height of the rectangle is 6 - x².

Then the area of the rectangle is given by the function

[tex]A(x)=2x(6-x^2)=12x-2x^3[/tex]

Compute the critical points of A:

[tex]A'(x)=12-6x^2=0\implies x=\pm\sqrt2[/tex]

So the maximum area is obtained when the vertices are the points (-√2, 0), (√2, 0), (√2, 4), and (-√2, 4). This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.

The maximum area is obtained when the vertices are the points

(-√2, 0), (√2, 0), (√2, 4), and (-√2, 4).

This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.

The area of a rectangle is expressed as shown:

A = xy

x is the length of the rectangle

y is the width

Given that y = 6 - x²

If its other two vertices above the x-axis and lying on the parabola, hence

the length of the rectangle will be 2x

The area of the rectangle will be A = 2x(6-x²)

If the dimension of the rectangle is at the maximum, hence dA/dx=0

A = 12x - 2x³

dA/dx = 12 - 6x²

0 = 12 - 6x²

6x² = 12

x² = 12/6

x² = 2

x = ±√2

Hence the maximum area is obtained when the vertices are the points

(-√2, 0), (√2, 0), (√2, 4), and (-√2, 4).

This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.

Learn more here: https://brainly.com/question/16925800

The correct answer is B. 24

Explanation:

If you consider the shaded part of the rectangle is a triangle the best way to calculate the area of this is by calculating the total area or space occupied by this triangle. This can be done if you multiply the base by the height and divide the result in 2 or b x h / 2.

6 squares (base) x 8 squares (height) = 48 / 2 = 24 squares

Also, the shaded area is approximately the half area of all the rectangle, in this case, you can calculate the area of the rectangle by multiplying side x side or length by width. This means 6 squares x 8 squares = 48 squares (total area), which divided by 2 (shaded area) is also equal to 24.

Answer:

B, 24.

Step-by-step explanation:

I solved it with my teacher

Answer:

-4 · [tex]4^{7}[/tex]

Step-by-step explanation: