Harriet has a square piece of paper. She folds it in half again to form a second rectangle (the high is not a square). The perimeter of the second rectangle is 30cm. What is the area of the original piece of paper?

Answer:

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

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:

Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then

[tex]n = 1537, \pi = \frac{353}{1537} = 0.2297[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507[/tex]

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

Answer:

20

Step-by-step explanation:

If the two triangles are similar, then corresponding sides must share a constant ratio. This means that:

[tex]\dfrac{10}{6}=\dfrac{25}{15}=\dfrac{x}{12}[/tex]

Let's use the second ratio:

[tex]\dfrac{25}{15}=\dfrac{x}{12}[/tex]

Multiply both sides by 12:

[tex]\dfrac{25\cdot 12}{15}=x \\\\x=20[/tex]

Hope this helps!

Answer:

A. Shift down 2 units.

B. Vertically stretch by a factor of 4.

Step-by-step explanation:

Given the function

f(x)=x

If we stretch y vertically by a factor of m, we have: y=m·f (x)

Therefore:

Vertically stretching f(x) by a factor of 4, we have: 4x.

Next, if we take down f(x) by k units we have: y= f(x)-k

Therefore: Taking down 4x by 2 units, we obtain:

g(x)=4x-2

Therefore, Options A and B applies.

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36[/tex]  

And rounded up we have that n=656

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by [tex]\alpha=1-0.80=0.20[/tex] and [tex]\alpha/2 =0.10[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=\pm 1.28 [/tex]

Solution to the problem

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

Since we don't have prior info for the proportion of interest we can use [tex]\hat p=0.5[/tex] as estimator. And on this case we have that [tex]ME =\pm 0.025[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36[/tex]  

And rounded up we have that n=656

Answer:

5/3 is an improper fraction because 5 is higher then 3. So the correct way of writing it would be 1 2/3.

Step-by-step explanation:

Answer: x=3 y=1

Step-by-step explanation:

Answer:

(3a+2b-4c)[4z+1]

Step-by-step explanation:

4z(3a+2b-4c)+(3a+2b-4c)

Factor out (3a+2b-4c)

(3a+2b-4c)[4z+1]

Answer:

3a+2b-4c)[4z+1]

Step-by-step explanation:

4z(3a+2b-4c)+(3a+2b-4c)

Factor out (3a+2b-4c)

(3a+2b-4c)[4z+1]

Answer:

AB = 37 units.

Step-by-step explanation:

Solve for AB using the Pythagorean theorem:

c² = a² + b² (c being AB in this instance)

Plug in the values of the legs of the triangle:

c² = 12² + 35²

c² = 144 + 1225

c² = 1369

c = √1369

c = 37

Therefore, AB = 37.

Answer:

Second option is the correct choice.

Step-by-step explanation:

"The discriminant is −4, so the equation has no real solutions."

[tex]x^2-4x+5=0\\\\a=1,\:b=-4,\:c=5:\\\\b^2-4ac=\left(-4\right)^2-4\cdot \:1\cdot \:5=-4[/tex]

Best Regards!

Answer: B

The discriminant is −4, so the equation has no real solutions.

Step-by-step explanation:

Just took quiz EDG2021

Mark Brainliest

Answer:

0.75 ML of insulin contains 75 units of insulin

Step-by-step explanation:

U - 100 insulin hold 100 units of insulin per ml

This means that:

1 ML = 100 units

∴ 0.75 ML = 100 × 0.75 = 75  units

Therefore 0.75 ML of insulin contains 75 units of insulin

Answer:

Brianliest!

Step-by-step explanation:

4

1 in 500

500 x 4 = 2000

4 in 2000

Answer:

C (the third graph)

Step-by-step explanation:

This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.

Answer:

see below

Step-by-step explanation:

This graph has an asymptote at y = 0 and x=0

This excludes these values

The domain excludes x =0

The range excludes y=0

Answer:

The length of a 95% confidence interval for mean Age is 3.72.

Step-by-step explanation:

The data is provided for the age of 100 adults.

The mean and standard deviation are:

[tex]\bar x=47.8\\\\s=9.3744[/tex]

As the sample size is too large the z-interval will be used for the 95% confidence interval for mean.

The critical value of z for 95% confidence level is, z = 1.96.

The length of a confidence interval is given by:

[tex]\text{Length}=2\cdot z_{\alpha/2}\cdot\frac{s}{\sqrt{n}}[/tex]

           [tex]=2\times 1.96\times\frac{9.3744}{\sqrt{100}}\\\\=3.6747648\\\\\approx 3.67\\\\\approx 3.72[/tex]

Thus, the length of a 95% confidence interval for mean Age is 3.72.

Answer:

The relative change from 6546 and 4392 is 49.04

Step-by-step explanation:

Answer:

Step-by-step explanation:

Baltimore orioles : 1,000,000 + 1,000,000 + 500,000

Click 2 full bag and 1 half bag

Kansas city royals : 1,000,000 +500,000

Click 1 full bag and 1 half bag

Newyork Yankees  : 1,000,000 + 1,000,000 + 1,000,000 +1,000,000 +1,000,000 + 500,000

Click 5 full bag + 1 half bag

Answer:

Step-by-step explanation:

a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S

Write the probability of energy supplied by these energy sources in the next 10 years  

P(energy supplied) = P(S ∪ F) -----(1)

Rewrite eqn (1)

P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)

substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources

P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)

= 0.85 + 0.7 - (0.595)

= 1.55 - 0.595

= 0.955

Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955

B) write the probability of only one source of energy available

P(only one source of energy available) = [tex]P(\bar F S)[/tex] ∪ [tex]P( \bar S F)[/tex] ---(3)

Rewrite the equation (3)

P(only one source of energy available) =

[tex]=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)[/tex]

[tex]=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36[/tex]

Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36

Answer:

A) 0.028

Step-by-step explanation:

Given:

Sample size, n = 115

Population parameter, p = 0.1

The X-Bin(n=155, p=0.1)

Required:

Find the standard deviation of the normal curve that can be used to approximate the binomial probability histogram.

To find the standard deviation, use the formula below:

[tex]\sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]

Substitute figures in the equation:

[tex]\sigma = \sqrt{\frac{0.1(1 - 0.1)}{115}}[/tex]

[tex]\sigma = \sqrt{\frac{0.1 * 0.9}{115}}[/tex]

[tex]\sigma = \sqrt{\frac{0.09}{115}}[/tex]

[tex] \sigma = \sqrt{7.826*10^-^4}[/tex]

[tex] \sigma = 0.028 [/tex]

The Standard deviation of the normal curve that can be used to approximate the binomial probability histogram is 0.028

Answer:

  about 50.8 cubic meters

Step-by-step explanation:

The formula for the volume of a cone is ...

  V = (1/3)πr²h

Put the given values into the formula and do the arithmetic.

  V = (1/3)π(3.4 m)²(4.2 m) = 16.194π m³

__

For π to calculator precision, this is ...

  V ≈ 50.84 m³

For π = 3.14, this is ...

  V ≈ 50.82 m³

Answer:

2x - y - 3 = 0

Step-by-step explanation:

Find slope-intercept form first: y = mx + b

Step 1: Pick out 2 points

In this case, I picked out (2, 1) and (0, -3) from the graph

Step 2: Using slope formula y2 - y1/x2 - x1 to find slope

-3 - 1/0 - 2

m = 2

Step 3: Place slope formula results into point-slope form

y = 2x + b

Step 4: Plug in a point to find b

-3 = 2(0) + b

b = -3

Step 5: Write slope-intercept form

y = 2x - 3

Step 6: Move all variables and constants to one side

0 = 2x - 3 - y

Step 7: Rearrange

2x - y - 3 = 0 is your answer

Answer:

(x-1)/13

Step-by-step explanation:

y = 13x+1

To find the inverse, exchange x and y

x = 13y+1

Solve for y

Subtract 1 from each side

x-1 =13y+1-1

x-1 = 13y

Divide each side by 13

(x-1)/13 = y

The inverse is (x-1)/13

Answer:

f(x) = 13x + 1

To find the inverse let f(x) = y

y = 13x + 1

x = 13y + 1

13y = x - 1

y = (x-1)/13

The inverse is x-1/13.

Answer:

r₁ = 3.583cm

V₁= 192.55cm³

r₂= 5.176cm

V₂ = 580.283cm³

r₃ = 5.255cm

V₃ = 607.479cm³

Step-by-step explanation:

assuming circumferences of each balloons are given as follows C₁ = 22.5cm, C₂ = 32.5cm and C₃ = 33cm

Recall C = 2πr

volume of a sphere is 4/3πr³

Answer:

24

Step-by-step explanation:

hello

let's note x the number we are looking for

[tex]\dfrac{x}{12}=6\\<=> x = 6*12=72[/tex]

so 1/3 of it equals

[tex]\dfrac{72}{3}=24[/tex]

another way to see it is that 12=4*3

so 1/3 of it equals 6*4=24

hope this helps

Answer:

$2.70+/-$0.33

= ( $2.37, $3.03)

Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $2.70

Standard deviation r = $0.93

Number of samples n = 22

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

$2.70+/-1.645($0.93/√22)

$2.70+/-1.645($0.198276666210)

$2.70+/-$0.326165115916

$2.70+/-$0.33

= ( $2.37, $3.03)

Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)

Answer:

So in this problem, we're told that a polynomial is fact herbal and it's not a perfect square. Try no meal or a difference of two squares. Can you factor the pie? Nomi bite or polynomial without finding the G C F. So no Jacey after is allowed. So if it's not a perfect squared, try no meal. So not a perfect square. We know it's not this, and we also know it's not a difference of two squirt if it's not any of these or if it's not either of these, but we can't find the G. C F. There are three different ways we could find the factored form. You could do it by grouping where you separating the polynomial into two parts and factor them individually before combining. You could also use the sum or a difference of cubes. This is for a cubic or a um, polynomial of third degree, and you could also use fractional or negative exponents. So even if you can't find the G c f or use these methods, there are still three ways you can factor the

Step-by-step explanation:

Glad i could help!

Answer:

a) x = 94 units/month

b) s = 51.50 units/month

Step-by-step explanation:

The adequate point estimation of the population mean and standard deviation are the sample mean and sample standard deviation.

a) Point estimation of the population (sample mean)

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(94+105+85+94+92)\\\\\\M=\dfrac{470}{5}\\\\\\M=94\\\\\\[/tex]

b) Point estimation of the population standard deviation (sample standard deviation)

[tex]s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{4}((94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2)\\\\\\s=\dfrac{206}{4}\\\\\\s=51.50\\\\\\[/tex]

Using statistical concepts, it is found that:

a) The point estimate for the population mean is of: [tex]\overline{x} = 94[/tex]

b) The point estimate for the population standard deviation is of: [tex]s = 7.18[/tex]

Item a:

In this problem, the sample is: 94, 105, 85, 94, 92.

Thus, the mean is:

[tex]\overline{x} = \frac{94 + 105 + 85 + 94 + 92}{5} = 94[/tex]

Item b:

Then:

[tex]s = \sqrt{\frac{(94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2}{4}} = 7.18[/tex]

A similar problem is given at https://brainly.com/question/13451786

Answer:

0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The components operate independently. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Eight components:

This means that [tex]n = 8[/tex]

Probability of 0.45 of failing in less than 1,000 hours.

So 1 - 0.45 = 0.55 probability of working for longer than 1000 hours, which means that [tex]p = 0.55[/tex]

Find the probability that the subsystem operates longer than 1000 hours.

We need at least four of the components operating. So

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{8,4}.(0.55)^{4}.(0.45)^{4} = 0.2627[/tex]

[tex]P(X = 5) = C_{8,5}.(0.55)^{5}.(0.45)^{3} = 0.2568[/tex]

[tex]P(X = 6) = C_{8,6}.(0.55)^{6}.(0.45)^{2} = 0.1569[/tex]

[tex]P(X = 7) = C_{8,7}.(0.55)^{7}.(0.45)^{1} = 0.0548[/tex]

[tex]P(X = 8) = C_{8,8}.(0.55)^{8}.(0.45)^{0} = 0.0084[/tex]

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2627 + 0.2568 + 0.1569 + 0.0548 + 0.0084 = 0.7396[/tex]

0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.

Answer:

To solve for x we can write:

x² - y² = 55

x² = y² + 55

x = ±√(y² + 55)

To solve for y:

x² - y² = 55

y² = x² - 55

y = ±√(x² - 55)

Answer:

[tex]\mathrm{12\sqrt{5} \: \: inches}[/tex]

Step-by-step explanation:

Use Pythagorean theorem, where:

[tex]a^2+b^2=c^2[/tex]

Substitute in the values.

[tex]24^2+12^2=c^2[/tex]

[tex]c^2=576+144[/tex]

[tex]c^2=720[/tex]

[tex]c=\sqrt{720}[/tex]

[tex]c=12\sqrt{5}[/tex]

[tex]c=26.83281[/tex]

Answer:

Volume of a cone = 1/3πr²h

h = height

r = radius

r = 3cm h = 4cm

Volume = 1/3π(3)²(4)

= 36 × 1/3π

= 12π

= 36.69cm³

= 37cm³ to the nearest tenth

Hope this helps

Answer:

37.7

_______

NOT 37

Step-by-step explanation:

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]3^{2}[/tex] · [tex]4 = 12\pi = 37.69911 =[/tex] 37.7