Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 1.99 and draw a sketch of the region.

Step-by-step explanation:

Consider the following rules.

even + odd = odd

even - odd = odd

even × odd = even

even ÷ odd = even (if divisible)

Now for the two consectives terms...

One will surely be even and the other, odd.

So using the rule

Their product will always be odd

Hope it helps....

BRAINLIEST PRETTY PLEASE!!

Step-by-step explanation:

When you have a ratio, you put one number as the numerator and than one number as the denominator.

so it would be (12/34)=(x/68)

In this example I made the ratio you are comparing it to have 68 dollars, so when you solve for the amount of quarters you need it should be 24, since all of the numbers in this example are just being doubled.

To solve for x, you multiply 68 on both sides of the equation, 68×(12/34)=x

24=x

So this proves that this is how ratios, are used. It also does not matter what number you place on the numerator or denominator.

Take

[tex]u=\ln x\implies\mathrm du=\dfrac{\mathrm dx}x[/tex]

[tex]\mathrm dv=4x^2\,\mathrm dx\implies v=\dfrac43x^3[/tex]

Then

[tex]\displaystyle\int4x^2\ln x\,\mathrm dx=\frac43x^3\ln x-\frac43\int x^2\,\mathrm dx=\frac43x^3\ln x-\frac49x^3+C[/tex]

[tex]=\boxed{\dfrac49x^3(3\ln x-1)+C}[/tex]

The required integration is,

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C

The given integral is,

∫4x² lnx dx

Using integration by parts, choose u and dv.

In this case, we choose u = lnx and dv = 4x²dx.

Using the formula for integration by parts, we have:

∫ u dv = uv - ∫ v du

Substituting the values of u and dv, we get:

∫4x² lnx dx = (lnx) (∫ 4x² dx) - ∫ [(d/dx)lnx] (∫4x² dx) dx

Simplifying the first term using the power rule of integration, we get:

∫ 4x² dx = (4/3)x³ + C₁

For the second term, we need to evaluate (d/dx)lnx,

Which is simply 1/x. Substituting this value, we get:

∫ [(d/dx)lnx] (∫4x² dx) dx = ∫ [(1/x) ((4/3)x³ + C₁)] dx

Simplifying this expression, we get:

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - ∫ [(4/3)x³/x] dx

Using the power rule of integration again, we get:

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C

Where C is the constant of integration.

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[tex]13ab^3+39a^2b^5\\\\\boxed{\boxed{\boxed{13ab^3(1+3ab^2)}}}\\\\[/tex]

Brazil number one.

Answer:

there's no answer for that equation

Answer:

Step-by-step explanation:

time = 49 hours

speed =  7 miles/hour

speed = distance / time

∴ distance = speed × time

= 7 × 49

= 343 miles

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of a line given two points first find the slope of the line and use the formula

y - y1 = m( x - x1) to find the Equation of the line using any of the points given

Slope of the line using points

(3,2) and (4,6) is

[tex]m = \frac{6 - 2}{4 - 3} = \frac{4}{1} = 4[/tex]

So the equation of the line using point

( 3 , 2 ) and slope 4 is

Hope this helps you

Answer:

Put 25 in the box.

Step-by-step explanation:

Apply the exponent rule: (ax)^n = a^n × x^n

So we have:

(5x)^2 = 5^2 × x^2

= 25x^2

Best Regards!

Step-by-step explanation:

Find the z-score.

z = (x − μ) / σ

z = (109.8 − 106.9) / 14.5

z = 0.2

Use a chart or calculator to find the probability.

P(Z < 0.2) = 0.5793

Find the mean and standard deviation of the sampling distribution.

μ = 106.9

σ = 14.5 / √20 = 3.242

Find the z-score.

z = (x − μ) / σ

z = (109.8 − 106.9) / 3.242

z = 0.894

Use a calculator to find the probability.

P(Z < 0.894) = 0.8145

This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).

Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.

Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.

Answer:

A

Step-by-step explanation:

because it has a + sign

Answer:

Step-by-step explanation:

The coefficient of determination which is also known as the R² value is expressed as shown;

[tex]R^{2} = \frac{sum\ of \ squares \ of \ regression}{sum\ of \ squares \ of total}[/tex]

Sum of square of total (SST)= sum of square of error (SSE )+ sum of square of regression (SSR)

Given SSE = 60 and SSR = 140

SST = 60 + 140

SST = 200

Since R² = SSR/SST

R² = 140/200

R² = 0.7

Hence, the coefficient of determination is 0.7. Note that the coefficient of determination always lies between 0 and 1.

The coefficient of determination of the dataset is 0.7

The given parameters are:

[tex]SSE = 60[/tex] --- sum of squared error

[tex]SSR = 140[/tex] --- sum of squared regression

Start by calculating the sum of squared total (SST)

This is calculated using

[tex]SST =SSE + SSR[/tex]

So, we have:

[tex]SST =60 +140[/tex]

[tex]SST =200[/tex]

The coefficient of determination (R^2) is then calculated using

[tex]R^2 = \frac{SSR}{SST}[/tex]

So, we have:

[tex]R^2 = \frac{140}{200}[/tex]

Divide

[tex]R^2 = 0.7[/tex]

Hence, the coefficient of determination is 0.7

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Answer:

The distribution is positively skewed.

Step-by-step explanation:

A measure of skewness is defined in such a way that the measure should always be zero when the distribution is symmetric and measure should be a pure number i.e independent of origin and units of measurement.

The shape of the distribution can be found by finding the coefficient of skewness.

The coefficient of skewness can be found by  

Sk= 3(Mean-Median)/ Standard Deviation

Sk= 3( 50-40)5= 30/5=6

The shape will be positively skewed.

In a positively skewed distribution the mean > median > mode. It has a long right tail.

Using the skewness formula, it is found that the distribution is right-skewed.

------------------

[tex]S = \frac{3(M - M_e)}{s}[/tex]

------------------

The coefficient is:

[tex]S = \frac{3(M - M_e)}{s} = \frac{3(50 - 40)}{5} = \frac{30}{5} = 6[/tex]

Thus, the distribution is right-skewed.

A similar problem is given at https://brainly.com/question/24415645

Answer:

4/5

Step-by-step explanation:

237/1185 = .2 = 1/5

meaning there's 4/5 left

Answer:

6720 in ^3

Step-by-step explanation:

Volume = length * width * height

            = 30*16*14

                =6720 in ^3

Answer:

Yes it is reasonable to conclude the mean rate charged is greater than 14%

Step-by-step explanation:

From the question we are told that

    The  population mean is  [tex]\mu = 0.14[/tex]

    The sample size is  [tex]n = 10[/tex]

    The  sample mean is  [tex]\= x = 0.1564[/tex]

     The  standard deviation is  [tex]\sigma = 0.01561[/tex]

     The level of significance is  [tex]\alpha = 0.01[/tex]

The null hypothesis is    [tex]H_o: \mu = 0.14[/tex]

The  alternative hypothesis is  [tex]H_a : \mu > 0.14[/tex]

 Generally the test statistic is mathematically represented as

              [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

              [tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]

              [tex]t = 3.322[/tex]

Now the p-value obtained from the z-table is

        [tex]p-value = P(t > 3.322) = 0.00044687[/tex]

Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that  the mean rate charged is greater than 14%

Answer:

a. 3.35

Step-by-step explanation:

Given that :

an experiment with 3 groups  consist of 10 participant in each group.

This implies that:

number of group k = 3

number of participants n = 10

N = nk

N =  10 × 3 = 30

The degree of freedom within can be calculate as:

dfw = N - k

dfw = 30 - 3

dfw = 27

The degree of freedom for the critical value

dfc = n- 1

dfc = 3 - 1

dfc = 2

At the level of significance ∝ = 0.05

The F critical value from the standard normal F table

i.e

[tex]F_{critical { (2, 27)}=[/tex] 3.35

Answer:

10 9/20

Step-by-step explanation:

Hey there!

If Hillsboro to Campbell is 16 2/20 and Hillsboro to Oxford is 5 13/20,

we’ll do

16 2/20 - 5 13/20

Imrpoper form

322/20 - 113/20

322 - 113

209/20

10 9/20 miles from Oxford to Campbell.

Hope this helps :)

Answer:

A. 385.56 square meters.

B. 142.56 square meters.

Step-by-step explanation:

A house 27m by 9m is surrounded by a walkway 1.8m wide.

a) Find the area of the region covered by the house and the walkway.

​b) Find the area of the walkway.

Let

Length of the house=l=27m

Width of the house=w=9m

Wideness of the walkway=x=1.8m

Area of the region covered by the house and the walkway

=( L + 2*x) * (w + 2*x)

= (27+2*1.8)*(9+2*1.8)

=(27+3.6)*(9+3.6)

=(30.6)*(12.6)

=385.56 square meters.

​b) Area of the walkway

= (L + 2*x)*(w + 2*x) - l*w

= (27+2*1.8)*(9+2*1.8) - 27*9

=(27+3.6)*(9+3.6) - 243

=(30.6)*(12.6) - 243

=385.56 - 243

=142.56 square meters.

[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]

Answer:

see below

Step-by-step explanation:

4x + 10 = 2(2x + 5)

Distribute

4x+10 = 4x+10

Since the left side is identical to the right side, there are infinite solutions

4x - 5 = 4x + 10

Subtract 4x from each side

-5 = 10

This is never true, so there are no solutions

4x-5 = -5

Add 5 to each side

4x = 0

x=0

There is one solutions

Answer:

Z > ± 1.645

z= 3.968

Step-by-step explanation:

We formulate the null and alternate hypotheses as

H0 =μ2 ≥ μ1   Ha: μ2  <μ1  one sided

Let α= 0.05

Since the sample sizes are large therefore the test statistic used under H0 is

The critical region for α= 0.05 for a one tailed test Z > ± 1.645

Z = (x`2- x`1) /s/ √n

Z= 154.8-128.746.5/√50

z= 26.1/6.577

z= 3.968

Since the calculated value of z lies in the critical region we reject H0 that internet users spend more time  or equal time.

Answer:

96

Step-by-step explanation:

From the given information:

At 95% Confidence interval level,Level of significance [tex]\alpha[/tex] 0.05, the value of Z from the standard normal tables = 1.96

Margin of Error = 0.10

Let assume that the estimated proportion = 0.5

therefore; the sample size n can be determined by using the formula: [tex]n =(\dfrac{Z}{E})^2 \times p\times (1-p)[/tex]

[tex]n =(\dfrac{1.96}{0.1})^2 \times 0.5\times (1-0.5)[/tex]

[tex]n =(19.6)^2 \times 0.5\times (0.5)[/tex]

n = 96.04

n [tex]\approx[/tex] 96

Answer:

ii. 75 steps

iii. 75 steps

iv. 106 steps, and [tex]315^{0}[/tex]

Step-by-step explanation:

Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.

ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;

bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]

To determine distance AB,

[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex]   +  [tex]/25/^{2}[/tex]

          = 25000 + 625

          = 3125

AB = [tex]\sqrt{3125}[/tex]

     = 55.90

AB ≅ 56 steps

Thus, AC = 50 steps + 56 steps

               = 106 steps

From ΔACD,

Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]

⇒ x = 106 × Sin [tex]45^{0}[/tex]

      = 74.9533

     ≅ 75 steps

Musah's distance west from centre to final point is 75 steps

iii. From the secon attachment, Musah's distance north, y, can be determined by;

Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]

⇒ y = 106 × Cos [tex]45^{0}[/tex]

      = 74.9533

      ≅ 75 steps

Musah's distance north from centre to final point is 75 steps.

iv. Musah's distance from centre to final point is AC = AB + BC

                                     = 50 steps + 56 steps

                                     = 106 steps

From ΔACD,

Tan θ = [tex]\frac{75}{75}[/tex]

          = 1.0

θ = [tex]Tan^{-1}[/tex]  1.0

 = [tex]45^{0}[/tex]

Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]

                                                           =  [tex]315^{0}[/tex]

Answer:

6h + 12 = 30

Step-by-step explanation:

Hence, the equation obtained for number of hours worked is given as  12 + 6h = 30.

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

The total money required is given as $30.

Suppose the number of hours for babysitting be h.

Then, the money earned by doing it is $6h.

And, the total money with Karl is 12 + 6h.

As per the question, the following equations can be written as,

12 + 6h = 30

Hence, the equation for finding the number of hours is given as 12 + 6h = 30.

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Answer:

Tetragonal unit cell.

Step-by-step explanation:

A unit cell is the smallest part of a material which is formed by a well arranged lattice points. Some common types are; face centered, body center, tetragonal, cubic etc

Tetragonal unit cell has a square top and base, with rectangular sides. The internal angles are [tex]90^{0}[/tex] each, and consists of molecules, atoms, or ions (lattice points) arranged at each corners of the unit cell.

The crystal as described in the given question is a tetragonal unit cell.

Answer:

2.8

Step-by-step explanation:

Hey there!

Well to find the amount of minutes needed to fill a 46.2 gallon bathtub we’ll divide.

46.2 / 16.5

= 2.8

2.58 minutes

Hope this helps :)

Answer:

Top left: no

Top middle: one

Top right: no

Bottom left: infinite

Bottom middle: one

Bottom right: one

Step-by-step explanation:

Top left: no

Top middle: one

Top right: no

Bottom left: infinite

Bottom middle: one

Bottom right: one

Answer:

7.88 or 7.9

Step-by-step explanation:

To find the mean, we need to do:

=> (12 + 10 + 11 + 8 + 6 + 5 + 3 + 7 + 9) / 9

=> 71/9

=> 7.88 or 7.9

I divided the sum of all numbers by 9 because we added 9 numbers.

Answer:

10

Step-by-step explanation:

2x + 5 = 8x

Subtract 2x from each side

2x-2x + 5 = 8x-2x

5 = 6x

We want 12x so multiply each side by 2

2*5 = 6x*2

10 = 12x

Answer:

B. 10

Step-by-step explanation:

To find 12x, you first need to find the value of x using the first equation:

[tex]2x+5=8x[/tex]

You need to get the variables (x) on the same side of the equation in order to simplify them. To do this, use reverse operations. Subtract 2x from both sides to keep the equation balanced:

[tex]2x-2x+5=8x-2x\\\\5=6x[/tex]

Now isolate the variable (x) by dividing both sides of the equation by 6 (using reverse operations):

[tex]\frac{5}{6}=\frac{6x}{6} \\\\\frac{5}{6}=x[/tex]

Now insert the given value of x into 12x:

[tex]12(\frac{5}{6})[/tex]

Simplify:

[tex]12*\frac{5}{6} \\\\\frac{12}{1}*\frac{5}{6}\\\\\frac{60}{6}=10[/tex]

12x equals 10.

:Done

Answer:

[tex]\boxed{(3,-1)}[/tex]

Step-by-step explanation:

Hey there!

Well to find the solution the the given system,

3y - 2x = -9

y = -2x + 5

So to find x lets plug in -2x + 5 for y in 3y - 2x = -9.

3(-2x + 5) - 2x = -9

Distribute

-6x + 15 - 2x = -9

-8x + 15 = -9

-15 to both sides

-8x = -24

Divide -8 to both sides

x = 3

Now that we have x which is 3, we can plug in 3 for x in y = -2x + 5.

y = -2(3) + 5

y = -6 + 5

y = -1

So the solution is (3,-1).

Hope this helps :)