Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72
inches and standard deviation 3.17 inches. Compute the probability that a simple random sample of size n=
10 results in a sample mean greater than 40 inches. That is, compute P(mean >40).
Gestation period The length of human pregnancies is approximately normally distributed with mean u = 266
days and standard deviation o = 16 days.
Tagged
Math
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days
or less?
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days
or less?
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of
the mean?
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Answer:

5 Minutes

take 10 and add 12 for each minute until you pass 60

Answer:

A.

B.

C.

Step-by-step explanation:

all three are used in 3 dimensional objects hence the name 3 dimensions.

Answer:

53.06°F

Step-by-step explanation:

Given the equation of best fit :

y=-3.32x +97.05.

The average temperature for a month with 13.25 inches of Rainfall

Amount of Rainfall = x

Average temperature = y

To make our prediction ; put x = 13.25 in the equation and solve for y ;

y = -3.32x +97.05

Put x = 13.25

y = -3.32(13.25) +97.05

y = - 43.99 + 97.05

y = 53.06°F

Answer:

It's the last one

Step-by-step explanation:

(3x-1)-(x²+4)

3x-1-x²-4

-x²+3x-5

Answer:

8.35714285714

Step-by-step explanation:

Hope it help you

Answer:

3 hrs

Step-by-step explanation:

5 * 24 = 120 miles

64x = 120 + 24x

40x = 120

x = 3 hrs

Answer:

[tex]f(h(xc)) = 2xc-4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x - 7[/tex]

[tex]h(x) = 2x + 3[/tex]

Required

[tex]f(h(xc))[/tex]

First, calculate h(xc)

If [tex]h(x) = 2x + 3[/tex]

Then

[tex]h(xc) = 2xc + 3[/tex]

Solving further:

[tex]f(x) = x - 7[/tex]

Substitute h(xc) for x

[tex]f(h(xc)) = h(xc) - 7[/tex]

Substitute [tex]h(xc) = 2xc + 3[/tex]

[tex]f(h(xc)) = 2xc + 3 - 7[/tex]

[tex]f(h(xc)) = 2xc-4[/tex]

Answer:

absolute value of the determinant, adjacent to, equal to

Step-by-step explanation:

The absolute value of a determinant  of the [tex]\text{matrix whose}[/tex] columns are the vectors and they define the [tex]\text{sides}[/tex] of a [tex]\text{parallelogram}[/tex] which is adjacent to  one another and is equal to the [tex]\text{area}[/tex] of the [tex]\text{parallelogram}[/tex].

The determinant is a real number. They are like matrices, but we use absolute value bars to show determinants whereas to represent a matric, we use square brackets.

Answer:

first option : sqrt(26) + 6 units

Step-by-step explanation:

distance office to supermarket OS

OS² = (-7 - -2)² + (-5 - -6)² = (-7+2)² + (-5+6)² = (-5)² + 1² =

= 25 + 1 = 26

OS = sqrt(26)

distance supermarket to home SH

SH² = (-2 - 4)² + (-6 - -6)² = (-6)² + 0² = 36

SH = 6

so in total she travels sqrt(26) + 6 units

Answer:

24,48,72

Step-by-step explanation:

multiples of 6- 6,12,18,24,30,36,42,48,54,60,66,72

multiples of 8- 8,16,24,32,40,48,56,64,74,80

Answer:

[tex]ac - bd[/tex]

Step-by-step explanation:

[tex]ac - bd [/tex]

Looking at Point A to A', the rectangle moves 5 places to the left which is the x value + 5 and it shifts 1 place down which would be the y value - 1

This gets written as:

(x+5, y-1)

Step-by-step explanation:

6t-12+15t | 25+15t

21t-12 | 25+15t

21t-12 < 25+15t

hence proved..

Answer:

21t - 12 < 25 + 15t

Step-by-step explanation:

6( t - 2 ) + 15t < 5 ( 5 + 3t )

6t - 12 + 15t < 25 + 15t

21t - 12 < 25 + 15t.

Hence , Proved.

Answer:

option (B) is the answer

40

Step-by-step explanation:

Each number is followed by a number that is half its value, so the sequence goes like

320, 160, 80, 40, 20, 10.

Answer:

1) 0.6838

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]

35.45% of small businesses experience cash flow problems in their first 5 years.

This means that [tex]p = 0.3545[/tex]

Sample of 530 businesses

This means that [tex]n = 530[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.3545[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.3545(1-0.3545)}{530}} = 0.0208[/tex]

What is the probability that between 34.2% and 39.03% of the businesses have experienced cash flow problems?

This is the p-value of Z when X = 0.3903 subtracted by the p-value of Z when X = 0.342.

X = 0.3903

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.3903 - 0.3545}{0.0208}[/tex]

[tex]Z = 1.72[/tex]

[tex]Z = 1.72[/tex] has a p-value of 0.9573

X = 0.342

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

[tex]Z = \frac{0.342 - 0.3545}{0.0208}[/tex]

[tex]Z = -0.6[/tex]

[tex]Z = -0.6[/tex] has a p-value of 0.27425

0.9573 - 0.2743 = 0.683

With a little bit of rounding, 0.6838, so option 1) is the answer.

Answer: There are 16 Capulets and 6 Montaques.

Step-by-step explanation:Other choices were either less than or greater than 200 multiplied by each other. If we do 16x8 which is 128 for the Capulets. Also, if we do 12x6 which is 72 for the Montaques. 128+72=200 essays in total

Answer:

sensory measurement are lower after hypnotism

Step-by-step explanation:

Given the data :

Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6

After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0

The difference ;

After - Before, d = 0.2, - 4.1, - 1.6, - 1.8, - 3.2, - 2, - 2.9, - 9.6

Hypothesis :

H0 : μd = 0

H0 : μ < 0

The test statistic ;

T = μd / sd/√n

Where, xd = mean of difference

sd = standard deviation of difference

n = sample size

Mean of difference, μd = Σx/n = - 3.13

Standard deviation of difference, sd = 2.91

T = - 3.13 / 2.91/√8

T = - 3.13 / 1.0288403

T = - 3.042

α = 0.01

The Pvalue using a Pvalue calculator ;

Degree of freedom, df = n - 1 ; 8-1 = 7

Pvalue(-3.042, 7) = 0.00939

Pvalue < α ; we reject the null and conclude that sensory measurement are lower after hypnotism

Answer:

925



Step-by-step explanation:

Formula =592 x 100/64 = 925

Answer:

The maximum value of the objective function is 112 when x = 0 and y = 7.

Step-by-step explanation:

Given the constraints:

5x+3y≤37, 3x+5y≤35, x≥0, y≥0

Plotting the above constraints using geogebra online graphing tool, we get the solution to the constraints as:

A(0, 7), B(7.4, 0), C(5, 4) and D(0, 0)

The objective function is given as E =2x+16y, therefore:

At point A(0, 7):  E = 2(0) + 16(7) = 112

At point B(7.4, 0): E = 2(7.4) + 16(0) = 14.8

At point C(5, 4): E = 2(5) + 16(4) = 74

At point D(0, 0): E = 2(0) + 16(0) = 0

Therefore the maximum value of the objective function is at A(0, 7).

The maximum value of the objective function is 112 when x = 0 and y = 7.

Answer:

£2120.27

Step-by-step explanation:

A = P (1 + r100)

A = 2000 (1+ 0.03/365)^365(2)

A = 2000 ( 1.00008)^730

A = 2000 (1.060)

A = £2120.27

Answer:

C. YES

Step-by-step explanation:

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Answer:

|a|

Step-by-step explanation:

For any positive or negative a, when you square it, the answer is positive.

The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.

Answer: |a|

a hour,.....................

Answer:

Problem 17)

[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]

Problem 18)

[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]

Step-by-step explanation:

Problem 17)

We have the curve represented by the equation:

[tex]\displaystyle 4x^2+2xy+y^2=7[/tex]

And we want to find the equation of the tangent line to the point (1, 1).

First, let's find the derivative dy/dx. Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}\left[4x^2+2xy+y^2\right]=\frac{d}{dx}[7][/tex]

Simplify. Recall that the derivative of a constant is zero.

[tex]\displaystyle \frac{d}{dx}[4x^2]+\frac{d}{dx}[2xy]+\frac{d}{dx}[y^2]=0[/tex]

Differentiate. We can differentiate the first term normally. The second term will require the product rule. Hence:

[tex]\displaystyle 8x+\left(2y+2x\frac{dy}{dx}\right)+2y\frac{dy}{dx}=0[/tex]

Rewrite:

[tex]\displaystyle \frac{dy}{dx}\left(2x+2y\right)=-8x-2y[/tex]

Therefore:

[tex]\displaystyle \frac{dy}{dx}=\frac{-8x-2y}{2x+2y}=-\frac{4x+y}{x+y}[/tex]

So, the slope of the tangent line at the point (1, 1) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=-\frac{4(1)+(1)}{(1)+(1)}=-\frac{5}{2}[/tex]

And since we know that it passes through the point (1, 1), by the point-slope form:

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

If desired, we can simplify this into slope-intercept form. Therefore, our equation is:

[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]

Problem 18)

We have the equation:

[tex]\displaystyle y=\tan^{-1}\left(x^3\right)[/tex]

And we want to find the equation of the tangent line to the graph at the point (1, π/4).

Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\tan^{-1}(x^3)][/tex]

We can use the chain rule:

[tex]\displaystyle \frac{d}{dx}[u(v(x))]=u'(v(x))\cdot v(x)[/tex]

Let u(x) = tan⁻¹(x) and let v(x) = x³. Thus:

(Recall that d/dx [arctan(x)] = 1 / (1 + x²).)

[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2[/tex]

Substitute and simplify. Hence:

[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2=\frac{3x^2}{1+x^6}[/tex]

Then the slope of the tangent line at the point (1, π/4) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{x=1}=\frac{3(1)^2}{1+(1)^6}=\frac{3}{2}[/tex]

Then by the point-slope form:

[tex]\displaystyle y-\frac{\pi}{4}=\frac{3}{2}(x-1)[/tex]

Or in slope-intercept form:

[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]

The equation "a - 3x = 0" is correctly written because it follows the standard format of an algebraic equation.

Given that,

All the equations are,

1. a + 0.2x

2. 5b - 5x + 2

3. a - 3x = 0

Now, from equation ''a - 3x = 0'',

In this equation, the variable "a" subtracted from 3 times the variable "x" equals zero.

The equal sign (=) indicates that the expression on both sides of the equation is equivalent.

The equation is properly balanced and expresses equality between the two sides.

It accurately represents a relationship between the variables "a" and "x" where the value of "a" is dependent on the value of "x" in order to satisfy the equation.

So, The correctly written algebraic equation is:

a - 3x = 0

To learn more about the equation visit:

brainly.com/question/28871326

#SPJ4

Answer:

the answer is false

Step-by-step explanation:

comment if you want explanation

Answer:

True

Step-by-step explanation:

When using the formulas to find the surface area, both have equal surface area