Subtract -1/2n - (-1/2n)

Answer:

[tex]6\frac{1}{3}[/tex]

Step-by-step explanation:

You can divide 19 by 3 a total of 6 times with a remainder of 1.  

Answer:

13 is D. 32

14 is x=41

15 is 72

Answer:

The answer is "1.555"

Step-by-step explanation:

In the given question choices were not defined som the correct answer to this question can be defined as follows:

Given:

The value of  z* for 88% confidence interval are:

[tex]\to \frac{Z_{\alpha}}{2} \\\\\to Z_{0.06}\\\\\to \boxed{1.555}[/tex]

Answer:

See steps

Step-by-step explanation:

Volume of cubes is proportional to the cube of the side length.

Using proportions,

Volume of smaller cube / 1728 = (3/4)^3

Cross multiply,

Volume of smaller cube

= 1728 * (3/4)^3

= 1728 * (27/64)

= 729 cubic metres.

Note: all cubes are similar and each has 6 congruent faces.

Answer:

The margin of error is of 0.038 = 3.8%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 320, \pi = \frac{70}{320} = 0.21875[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.645\sqrt{\frac{0.21875(1-0.21875)}{320}}[/tex]

[tex]M = 0.038[/tex]

The margin of error is of 0.038 = 3.8%.

Answer:

It would take 1 more mile if he took route Street A and then Street B rather than just Street C.

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

We use the Pythagorean Theorem to find the length of Street C:

2² + 1.5² = c²

c = √6.25

c = 2.5

Now we find how much longer route A and B is compared to C:

3.5 - (2 + 1.5) = 3.5 - 2.5 = 1

Answer:

mean score of class B = 1778/25 = 71.12

Step-by-step explanation:

This was your question : Class A has 12 pupils and class B has 25 pupils. Both classes sit the same maths test. The mean score for class A is 80. The mean score for both classes is 74. What is the mean score (rounded to 2 DP) in the maths test for class B?

mean of class A = Σfx/Σf

mean of class A =  80

Σfx = 80 × 12 = 960

Mean score for both classes = 74

where

b = Σfx  of class B

960 + b/37 = 74

cross multiply

960 + b = 2738

b = 2738 - 960

b = 1778

mean score of class B = Σfx/Σf

Σfx = 1778

Σf = 25

Therefore,

1778/25 = 71.12

Answer:

lower 95% Cl is 0.292

Step-by-step explanation:

p^ = 0.4783

n = 23

for 95% Cl,

z = 1.9600

Inputting all the available data into P as attached below

LCL = 0.292

UCL = 0.670

therefore, lower 95% Cl = 0.292

Answer:

56 ft

Step-by-step explanation:

Because the bedroom is similar to the bed we can write that

7 : 15 = 6 : x

x = 15*6/7 ≈ 12.86 ft

Perimeter of the bedroom is

15*2 + 12.86 *2 ≈ 56 ft

Answer:

S = 2π/9 [³/₂√10 − ½ ln(-3 + √10)]

S ≈ 3.946

Step-by-step explanation:

For a curve rotated about the x-axis, the surface area is:

S = ∫ₐᵇ 2πy ds,

where ds = √(1 + (dy/dx)²) dx.

y = e⁻³ˣ

dy/dx = -3e⁻³ˣ

ds = √(1 + (-3e⁻³ˣ)²) dx

S = ∫₀°° 2πe⁻³ˣ √(1 + (-3e⁻³ˣ)²) dx

If u = -3e⁻³ˣ, then du = 9e⁻³ˣ dx, or du/9 = e⁻³ˣ dx.

When x = 0, u = -3.  When x = ∞, u = 0.

S = ∫₋₃⁰ 2π √(1 + u²) (du/9)

S = 2π/9 ∫₋₃⁰ √(1 + u²) du

S = 2π/9 [ ½ u √(1 + u²) + ½ ln|u + √(1 + u²)| ] |₋₃⁰

S = 2π/9 {[0] − [ -³/₂√10 + ½ ln(-3 + √10) ]}

S = 2π/9 [³/₂√10 − ½ ln(-3 + √10)]

S ≈ 3.946

The area of a surface is the amount of space it occupies.

The area of the resulting surface is [tex]3.947[/tex] square units

The infinite curve is given as:

[tex]y =e^{-3x},\ \ x \ge 0[/tex]

Integrate y, with respect to x

[tex]\frac{dy}{dx} = -3e^{-3x}[/tex]

The area of the curve about the x-axis is:

[tex]S = \int\limits^a_b {2\pi y} \, ds[/tex]

[tex]ds = \sqrt{(1 + (\frac{dy}{dx})^2)}\ dx[/tex]

Substitute [tex]\frac{dy}{dx} = -3e^{-3x}[/tex] in [tex]ds = \sqrt{(1 + (\frac{dy}{dx})^2)}\ dx[/tex]

[tex]ds = \sqrt{(1 + (-3e^{-3x})^2)}\ dx[/tex]

Let

[tex]u = -3e^{-3x}[/tex]

So:

[tex]\frac{du}{dx} = 9e^{-3x}[/tex]

Make [tex]e^{-3x}\ dx[/tex] the subject

[tex]e^{-3x}\ dx = \frac{du}9[/tex]

[tex]x \ge 0[/tex] means that, the value of x is: [tex][0,\infty][/tex]

When [tex]x = 0[/tex]

[tex]u = -3e^{-3x}[/tex]

[tex]u = -3 \times e^{-3 \times 0} = -3[/tex]

When [tex]x = \infty[/tex]

[tex]u = -3 \times e^{-3 \times \infty} = 0[/tex]

Recall that:

[tex]S = \int\limits^a_b {2\pi y} \, ds[/tex]

Substitute [tex]ds = \sqrt{(1 + (-3e^{-3x})^2)}\ dx[/tex] and [tex]y =e^{-3x}[/tex]

This gives

[tex]S = \int\limits^0_{-3} {2\pi (e^{-3x}) \sqrt{(1 + (-3e^{-3x})^2)}\ dx}[/tex]

Rewrite as:

[tex]S = \int\limits^0_{-3} {2\pi \sqrt{(1 + (-3e^{-3x})^2)}\ (e^{-3x})\ dx}[/tex]

Substitute [tex]u = -3e^{-3x}[/tex] and [tex]e^{-3x}\ dx = \frac{du}9[/tex]

[tex]S = \int\limits^0_{-3} {2\pi \sqrt{(1 + u^2)}\ \frac{du}9}[/tex]

This gives

[tex]S = \frac{2\pi}{9} \int\limits^0_{-3} {\sqrt{(1 + u^2)}\ du}[/tex]

Integrate with respect to u

[tex]S = \frac{2\pi}{9}[\frac 12 u\sqrt{(1 + u^2)} + \frac 12\ln|u + \sqrt{1 + u^2}|\ ]|\limits^0_{-3}[/tex]

Substitute 0 and -3 for u

[tex]S = \frac{2\pi}{9}([\frac 12\times 0 \times \sqrt{(1 + 0^2)} + \frac 12\ln|0 + \sqrt{1 + 0^2} ] - [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}([0] - [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}(- [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}(- [\frac{-3}2 \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}( [\frac{3}2 \times \sqrt{10} - \frac 12\ln(-3 + \sqrt{10}\ )] )[/tex]

[tex]S = \frac{2\pi}{9}( [4.743 + 0.909] )[/tex]

[tex]S = \frac{2\pi}{9}( 5.652 )[/tex]

[tex]S = 3.947[/tex]

Hence, the area of the resulting surface is [tex]3.947[/tex] square units

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Answer:

[tex]\boxed{CD = 7.1}[/tex]

Step-by-step explanation:

The coordinates are (6,-5) and (-1,-4)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

CD = [tex]\sqrt{(-1-6)^2+(-4+5)^2}[/tex]

CD = [tex]\sqrt{(-7)^2+(1)^2}[/tex]

CD = [tex]\sqrt{49+1}[/tex]

CD = [tex]\sqrt{50}[/tex]

CD = 7.1 units (nearest tenth)

Answer: CD = 7.1

Step-by-step explanation:

Plug in each x coordinate and y coordinate into the distance formula.

d = √(-1 - 6)² + (-4 + 5)²

d = √(-7)² + (1)²

d = √49 + 1

d = √50

√50 = 7.1

d = 7.1

Answer:

a. Test statistic t = -0.14

b. P-value = 0.443

c. D. Fail to reject H0. There is insufficient evidence to support the claim that those given a sham treatment have pain reductions that vary more than those treated with magnets.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0[/tex]

The significance level is α=0.05.

The sample 1 (sham), of size n1=20 has a mean of 0.44 and a standard deviation of 1.24.

The sample 2 (magnet), of size n2=20 has a mean of 0.49 and a standard deviation of 0.95.

The difference between sample means is Md=-0.05.

[tex]M_d=M_1-M_2=0.44-0.49=-0.05[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1.24^2+0.95^2}{20}}\\\\\\s_{M_d}=\sqrt{\dfrac{2.4401}{20}}=\sqrt{0.122}=0.3493[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-0.05-0}{0.3493}=\dfrac{-0.05}{0.3493}=-0.14[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=20+20-2=38[/tex]

This test is a left-tailed test, with 38 degrees of freedom and t=-0.14, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t<-0.14)=0.443[/tex]

As the P-value (0.443) is greater 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 those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.

The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

We have,

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = X ± (Z * (σ/√n))

where:

CI is the confidence interval

X is the sample mean

Z is the critical value corresponding to the desired confidence level (90% confidence level corresponds to Z = 1.645 for a large sample size)

σ is the population standard deviation

n is the sample size

Given that the sample mean X of the net change in LDL cholesterol is 2.7, the standard deviation (σ) is 17.8, and the sample size (n) is 47, we can calculate the confidence interval as follows:

CI = 2.7 ± (1.645 * (17.8/√47))

Calculating the standard error (SE):

SE = σ/√n = 17.8/√47 ≈ 2.587

Substituting the values into the confidence interval formula:

CI = 2.7 ± (1.645 * 2.587)

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 2.7 + (1.645 * 2.587) ≈ 7.199

Lower bound = 2.7 - (1.645 * 2.587) ≈ -1.799

Therefore, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199.

Interpreting the confidence interval:

Since the confidence interval contains both positive and negative values, it suggests that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

The interval includes zero, indicating that there is a possibility that the mean net change in LDL cholesterol after the garlic treatment could be zero (no change).

However, it is important to note that further studies or a larger sample size may be needed to draw more definitive conclusions.

Thus,

The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

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The 90% confidence interval suggests that the true mean net change in LDL cholesterol after the garlic treatment lies between -1.57 and 6.97 mg/dL. Since the interval contains both positive and negative values, it indicates that the garlic treatment may or may not be effective in reducing LDL cholesterol.

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = mean ± (Z * (standard deviation / √n))

Here, n represents the sample size (47), Z is the critical value corresponding to a 90% confidence level (Z = 1.645 for a 90% confidence level), and the mean is 2.7 with a standard deviation of 17.8.

Plugging in the values:

CI = 2.7 ± (1.645 * (17.8 / √47))

CI = 2.7 ± (1.645 * (17.8 / 6.856))

CI = 2.7 ± (1.645 * (2.596))

CI = 2.7 ± 4.270

CI = 2.7 + 4.270  ;  CI = 2.7 - 4.270

CI = 6.97             ;  CI = -1.57

Thus, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately (-1.57, 6.97).

The confidence interval suggests that the effectiveness of garlic in reducing LDL cholesterol is inconclusive. The interval spans both positive and negative values, indicating that the true mean change in LDL cholesterol could be anywhere within this range. Further research or a larger sample size might be needed to draw a more definitive conclusion about the effectiveness of garlic in lowering LDL cholesterol.

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Step-by-step explanation:

just just solve the equation and then substitute the value of the first equation in the second one.

Answer:

x=-18 or x=67

Step-by-step explanation:

you can either make it so 48 remains the largest number and so take 66 from 48 (=-18) or you can leave one as the smallest number and add 66 to one(=67)

Answer:

0

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

    = (4-4)/(3-4)

     = 0/-1

   = 0

Answer:

100

Step-by-step explanation:

So this equation would look something like this -->

8(9.75 - 3.25) + 12 x 4 => Since we have decimals then we should subtract in the parenthasees.

9.75 - 3.25 = 6.5

--> 8(6.5) + 12 x 4 --> 8(6.5) + 48 =>

8(6.5) = 52 --> 52 + 48 = 50 + 50 = 100

Thus, we have our answer of 100

Hope this helps!

Answer:

The answer is 100

Step-by-step explanation:

The equation that we are solving is 8(9.75 - 3.25) + 12 x 4

The order of operations are:

These are my steps that I did to solve the problem:

The final answer is 100.

Answer:

5

Step-by-step explanation:

=> 2x+3

For x = 1

=> 2(1) + 3

=> 2+3

=> 5

Answer:

5

Step-by-step explanation:

2x + 3

Put x as 1 and evaluate.

2(1) + 3

2 + 3

= 5

Answer:

Richard will have $60,000 in his account in 20 years.

Step-by-step explanation:

(1) Multiply $250 x 12

(2) Multiply the answer of $250 x 12 which is 3000 by 20

(3) Final answer would be $60,000

Answer:

One ounce of almonds is $0.78

One ounce of cashews is $0.63

Step-by-step explanation:

Set up a system of equations where a is the price of one ounce of almonds and c is the price of one ounce of cashews:

20a + 12c = 23.16

18a + 14c = 22.86

Solve by elimination by multiplying the top equation by 7 and the bottom equation by -6:

140a + 84c = 162.12

-108a - 84c = -137.16

Add them together and solve:

32a = 24.96

a = 0.78

Now, plug in 0.78 for a and solve for c:

20a + 12c = 23.16

20(0.78) + 12c = 23.16

15.6 + 12c = 23.16

12c = 7.56

c = 0.63

Answer:

the second one

Step-by-step explanation:

We can see that the fence is made by a rectangle and a trapezoid

A1 is the area of the rectangle and A2 is the area of the trapezoid

Answer:

B / px= k

Step-by-step explanation:

B = kpx

Divide each side by px

B / px= kpx/px

B / px= k

Answer:

First option

Step-by-step explanation:

B=kpx

B=k*(px)

Then,

[tex]k = \frac{b}{px} [/tex]

Answer:

y=3

Step-by-step explanation:

y + 3 = –y + 9

Add y to each side

y+y + 3 = –y+y + 9

2y+3 = 9

Subtract 3 from each side

2y+3-3 = 9-3

2y = 6

Divide by 2

2y/2 = 6/3

y =3

Answer:

Hello!

_______________________

Your answer would be (B) y = 3

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you!

Answer:

The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.

Step-by-step explanation:

First we need to find the z-value for a confidence of 99%

The value of alpha for a 99% confidence is:

[tex]1-\alpha/2 = 0.99[/tex]

[tex]\alpha/2 = 0.01[/tex]

[tex]\alpha = 0.005[/tex]

Looking in the z-table, we have z = 2.575.

Now we can find the standard error of the mean:

[tex]\sigma_{\bar{x} }= s_x/\sqrt{n}[/tex]

[tex]\sigma_{\bar{x} }= 14.4/\sqrt{100}[/tex]

[tex]\sigma_{\bar{x} }=1.44[/tex]

Finding the 99% confidence interval, we have:

[tex]99\%\ interval = (\bar{x} - z\sigma_{\bar{x}}, \bar{x} + z\sigma_{\bar{x}})[/tex]

[tex]99\%\ interval = (32.2 - 2.575*1.44, 32.2 + 2.575*1.44)[/tex]

[tex]99\%\ interval = (28.492, 35.908)[/tex]

The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.

Answer:

Step-by-step explanation:

(4+1)/(-3-4)= -5/7

y + 1 = -5/7(x - 4)

or

y - 4= -5/7(x + 3)

Answer:

D

Step-by-step explanation:

We can plug in the numbers (15, 23, 25, 38, 53) into the equation for x, and see if we get the values given for the number of hits (4, 12, 14, 27, 47)

Answer:

The formula is 10 - 3n

Step-by-step explanation:

For an nth term in an arithmetic sequence

U( n ) = a + ( n - 1)d

Where n is the number of terms

a is the first term

d is the common difference

From the sequence above

a = 7

d = 4 - 7 = - 3

The formula for an nth term is

U(n) = 7 + (n - 1)-3

= 7 - 3n + 3

The final answer is

= 10 - 3n

Hope this helps you.

Answer:

the 3rd and last option

Step-by-step explanation:

Answers are: choice C, choice D

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

Explanation:

Let

a = adult admission fee

c = child admission fee

Focus on row 1 for now

45a = cost of having 45 adults total

30c = cost of having 30 children total

45a+30c = total cost of 45 adults and 30 children = 315

So, 45a+30c = 315 is the first equation

-----------

Now move to row 2

For similar reasoning, 50a+40c = 370 is the other equation

50a = cost of having 50 adults buy a ticket

40c = cost of having 40 children buy a ticket

50a+40c = total cost of having 50 adults and 40 children = 370

Answer:

A

Step-by-step explanation:

Answer:

A True, law of detachment.

Answer:

no solution

Step-by-step explanation:

hello

[tex]6(x+5)=6x+11\\<=> 6x+30=6x+11\\<=> 30=11[/tex]

this is always false so there is no solution

Let's to expand this equation:

[tex]6(x+5) = 6x+11\\6x + 6\times 5 = 6x + 11\\6x + 30 = 6x + 11[/tex]

Perceive that in two members of equations, we have "6x", so we can to eliminate it. But, when we make it, we have this situation:

[tex]6x + 30 = 6x + 11\\30 = 11[/tex]

How [tex]30 \neq 11[/tex] this is a absurd. Therefore, this equation don't have solutions.