Diastolic blood pressures are assumed to follow a normal distribution with a mean of 85 and a standard deviation of 12. What proportion of people has diastolic blood pressures less than 80?

36 - k = 4 + k

36 - 4 = k + k

32 = 2k

32/2 = k

16 = k

Steps:

Step 1: Simplify both sides of the equation

36−k=4+k

36+−k=4+k

−k+36=k+4

Step 2: Subtract k from both sides

−k+36−k=k+4−k

−2k+36=4

Step 3: Subtract 36 from both sides

−2k+36−36=4−36

−2k=−32

Step 4: Divide both sides by -2

−2k/−2 = −32/−2

Description:

Since we are trying to find the value of K, we need to simplify both sides of the equation. After that your answer will come as −k+36=k+4.  Now the second step is to  subtract k from both sides, your equation will come as −2k+36=4.  Thirdly we need to subtract 36 from both sides, your equation will come as −2k=−32.  Now you need to divide both sides by -2. After you do that, you will get your answer which is k=16.

Answer: k=16

Please mark brainliest

Hope this helps.

Answer:

displacement x = - 0.046sin4t +0.006cos4t

Step-by-step explanation:

The model of the equation of motion is a forced motion equation and to determine the displacement of the weight as a function of time; we have:

the weight balances of the  elastic force in the spring  to be expressed by the relation:

mg = kx

where;

x=4 in (i.e  1/3 ft )

mass m = 6lb

let make k the subject; then:

k = mg/x = 6×32/(1/3) = 576

assuming  x to be the displacement form equilibrium;

Then;

[tex]F = 27sin 4t-3cos4t +k(x+1/3) - mg -3v[/tex]

(since F(t)=27sin 4t-3cos4t somehow faces downwards, mg=downwards and k(x+1/3)= upwards and medium resistance 3v =  upwards)

SO;

[tex]d2x/dt2 = 27sin 4t-3cos4t +kx - 3dx/dt[/tex]

[tex]d2x/dt2 +3dx/dt - 576x = 27sin 4t-3cos4t[/tex]

Assuming : [tex]x = asin4t + bcos4t[/tex]

[tex]dx/dt = 4acos4t - 4bsin4t[/tex]

[tex]d2x/dt2 = -16asin4t - 14bcos4t[/tex]

replacing  these values in the above equation

[tex]= -16asin4t - 14bcos4t + 12acos4t - 12bsin4t -576asin4t-576bcos4t = 27sin 4t-3cos4t[/tex]

[tex]= sin4t (-592a-12b) + cos4t(12a -590b) = 27sin 4t-3cos4t[/tex]

equating sin and cos terms

a = - 0.046 ;  b = 0.006

displacement x = - 0.046sin4t +0.006cos4t

Answer:

Average speed v = 24.29 mph

Total time taken ∆t = 7 hours

Step-by-step explanation:

Given;

the first 2 hours, they travel at a rate of 25 miles per hour

t1 = 2 hours

v1 = 25 mph

then take a break for 2 hours and do not travel during that time

t2 = 2 hours

v2 = 0

They finally travel again for another 3 hours at a rate of 40 miles per hour before stopping for the day.

t3 = 3 hours

v3 = 40 mph

Total time taken ∆t = sum of time taken for the day travel

∆t = t1 + t2 + t3

Substituting the values;

∆t = 2 + 2 + 3 = 7 hours

The average speed v = total distance travelled/total time taken

v = d/∆t .......1

Total distance travelled d = Σ(velocity × time)

d = v1t1 + v2t2 + v3t3

d = 25 × 2 + 0×2 + 40 × 3

d = 50 + 0 + 120

d = 170 miles

Substituting into equation 1.

v = 170 miles ÷ 7 hours

Average speed v = 24.29 mph

Answer:

1/5x = h(x)

Step-by-step explanation:

6x+y = 4x+ 11y

Subtract y from each side

6x+y -y = 4x+ 11y-y

6x = 4x+10y

Subtract 4x from each side

6x-4x = 4x+10y-4x

2x = 10y

Divide each side by 10

2x/10 = 10y/10

1/5x = y

1/5x = h(x)

Answer:

40+5x=y

60+3x=y

Step-by-step explanation:

The first park is 40+5x

The second park is 60+3x

Now set them both equal to y

Answer:

S, Z, F

Step-by-step explanation:

i know its not the question but its for anyone who found this and needs it for edge lol

Answer: 26

Step-by-step explanation:

32-6 = 26

Answer:

fifth angle = 102°

Step-by-step explanation:

A pentagon is a polygon that have 5 sides. A pentagon can be divided into 3 triangles .And the sum of angle in a triangle is 180°. Therefore the sum of interior angle in a pentagon will  be 180 × 3 = 540°. The sum of interior angles of a pentagon = 540°.

The general rule for calculating sum of the interior angles of a polygon is

sum of interior angle = (n−2) × 180°

where

n = number of sides

n = 5 since we are dealing with a  pentagon.

sum of interior  angle of a pentagon = 540°

The fifth angle can be computed when you subtract the sum of the 4 angles from 540°.

fifth angle = 540 - (88 + 118 + 132 + 100)

fifth angle = 540 - 438

fifth angle = 102°

Answer:

its C on edg

Step-by-step explanation:

Answer:

no.

Step-by-step explanation:

Answer: -2x-18

Step-by-step explanation:

Answer:

The answer will be 1.25

Step-by-step explanation:

In order to make 512 into a decimal, you take the top number or numerator, which is 5 , and take your bottom number or your denominator, which is 12 , and divide 5 by 12 which will give you0.416666667

Hey there! :)

Answer:

1.25

Step-by-step explanation:

Begin by multiplying the fractions:

[tex]\frac{3}{1}* \frac{5}{12}= \frac{3*5}{1*12} = \frac{15}{12}= \frac{5}{4}[/tex]

Convert [tex]\frac{5}{4}[/tex] into a decimal:

5/4 = 1.25.

Answer:

$ 44

Step-by-step explanation:

If we analyze the statement well, we can observe something very crucial to solve it, the jumbo biscuits require 2 oz of flour and give a profit of $ 0.08, the Regular one that only requires 1 oz of flour leaves a profit of $ 0.11, which means that requiring a smaller quantity of flour leaves a greater profit, so in terms of profit it is not profitable to make Jumbo, only Regular.

Therefore, since you can make 400 biscuits, they would all be regular since there are 600 oz of flour available, it is enough to make 400, therefore the maximum profit would be:

$ 0.11 * 400 = 44

The maximum possible profit is $ 44

Answer:

A

Step-by-step explanation:

2/3x=1-5

2/3x=-4

x=-4/2/3

x=-6

Step-by-step explanation:

The way i like to remember it is that the exponent inside of the radical will be the numerator of the fraction and the index of the radical will be the denominator so the answer is 2^(-5/3).

Answer:

P=48 millimeters

Step-by-step explanation:

p=4l

p=4 x 12

p=48 mm

Answer:

what is this it is not understand able

Answer:

11

Step-by-step explanation:

<TKF = 90° ( BECAUSE OF THE BISECTOR)

BUT

<TKF = 5(x+7)

So

5(x+7) = 90

5x+35 = 90

5x = 90-35

5x = 55

Dividing by 5(both sides)

x = 11

Answer:

f(x) = 15

Step-by-step explanation:

"If f(x)= 5x + 40, what is f(x) when x = -5?"

Substitute x for -5:

f(x) = 5x + 40

f(x) = 5(-5) + 40

f(x) = -25 + 40

f(x) = 15

Answer:

Yes! Extrapolation is fine. Don't worry about it.

Step-by-step explanation:

Because the data we have ranges from 8 to 22 inches, an extrapolation should be made, which is the process of estimating beyond the original observation interval, the value of the variable based on its relationship to another variable. It is similar to interpolation, which produces estimates between known observations, unlike this, extrapolation is subject to greater uncertainty and a higher risk of producing insignificant results, but because the value is 24 inches, it is not too far away. of the upper limit which is 22, the error should not be very big, therefore the answer is: Yes! Extrapolation is fine. Don't worry about it.

Answer:

[tex]r=\frac{-a+p}{a+p}[/tex]

Step-by-step explanation:

[tex]-pr+p=ar+a[/tex]

[tex]-ar-pr+p=a[/tex]

[tex]-ar-pr=a-p[/tex]

[tex]r(-a-p)=a-p[/tex]

[tex]r=\frac{-a+p}{a+p}[/tex]

Answer:

[tex]r = \frac{p - a}{(p + a)} [/tex]

Step-by-step explanation:

[tex]p = \frac{a(1 + r)}{(1 - r)} \\ p(1 - r) = a(1 + r) \\ p - pr = a + ar \\ p - a = pr + ar \\ p - a = r(p + a) \\ \frac{p - a}{(p + a)} = \frac{r(p + a)}{(p + a)} \\ \frac{p - a}{(p + a)} = r[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

14.25°

Step-by-step explanation:

distance from middle of the net = 8 m

width of the net = 2 m

this is a case of a triangle with height 8 m, and base 2 m. We are required to find the angle facing the base.

We can get this angle by splitting the triangle into two right angle triangles with base of 1 m, and then solve for the angle facing the base.

We use the trigonometric function;   tan∅ = opp/adj

opp is the side facing the angle = 1 m

adj is the height of the triangle (usually, it is the side besides the opposite side and the longest side; the hypothenus)

adj = 8 m

tan∅ = [tex]\frac{1}{8}[/tex] = 0.125

∅ = [tex]tan^{-1}[/tex] 0.125 = 7.125°

Angle within which Lars must fire his shot = 2 x ∅

= 2 x 7.125° = 14.25°

Step-by-step explanation:

[tex]sin(1 \div 4a + 20) = \sqrt{3} \div 2 \\ sin(1 \div 4a + 20) =sin 60[/tex]

1÷4a+20=60

1÷4a=4

a=1/160

Answer:

a) For this case and using the empirical rule we can find the limits in order to have 9% of the values:

[tex] \mu -2\sigma = 55 -2*6 =43[/tex]

[tex] \mu +2\sigma = 55 +2*6 =67[/tex]

95% of the widget weights lie between 43 and 67

b) For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:

[tex] 100 -0.15-2.5 = 97.85[/tex]

c) We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%

Step-by-step explanation:

For this case our random variable of interest for the weights is bell shaped and we know the following parameters.

[tex]\mu = 55, \sigma =6[/tex]

We can see the illustration of the curve in the figure attached. We need to remember that from the empirical rule we have 68% of the values within one deviation from the mean, 95% of the data within 2 deviations and 99.7% of the values within 3 deviations from the mean.

Part a

For this case and using the empirical rule we can find the limits in order to have 9% of the values:

[tex] \mu -2\sigma = 55 -2*6 =43[/tex]

[tex] \mu +2\sigma = 55 +2*6 =67[/tex]

95% of the widget weights lie between 43 and 67

Part b

For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:

[tex] 100 -0.15-2.5 = 97.85[/tex]

Part c

We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%

Answer:

150(10s + h)

Step-by-step explanation:

We need to write an expression for the total items they shipped.

Let each skateboard be s.

Let each helmets be h.

The factory ships 100 boxes with 15 skateboards in each box. That is:

100 * (15 * s) = 1500s

The factory ships 10 boxes with 15 helmets in each box. That is:

10 * (15 * h) = 150h

The total number of items shipped is therefore:

1500s + 150h = 150(10s + h)

This expression represents the total number of items shipped.

Answer:

T15 = 31

Step-by-step explanation:

Its in the picture

I hope it helps :)

Answer:

[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value would be:

[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.

Step-by-step explanation:

Information given

22, 17, 27, 20, 23, 19, 24, 18, 19, and 24

The sample mean and deviation for these data are:

[tex]\bar X=21.3[/tex] represent the ample mean

[tex]s=3.199[/tex] represent the sample standard deviation for the sample  

[tex]n=10[/tex] sample size  

[tex]\mu_o =20[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if the true mean is equal to 20 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 20[/tex]  

Alternative hypothesis:[tex]\mu \neq 20[/tex]  

The statistic would be:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing the info given we got:

[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value would be:

[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.

Answer:

48.30

Step-by-step explanation:

First determine the tip

42 *15%

42 *.15 =6.30

Add this to the amount of the tip

42 + 6.30 =48.30

The total amount is 48.30

Answer:

Step-by-step explanation:

$48.30

Answer:

a. It is not likely that a winning ticket will be selected

b. The probability of winning enough to pay for the ticket expressed as a simplified fraction is 13/71

Step-by-step explanation:

To answer this question, there are some important notes to know.

1. The selection is only once

2. To win, you have to select a note which has a greater value than $8

Now, the total number of notes that we have = 38 + 20 + 7 + 5 + 1 = 71

The number of bills present that are greater than $8 are; 7 $10 bills , 5 $20 bills and 1 $100 bill

This makes a total of 7 + 5 + 1 = 13

Thus, the probability of selecting a bill which would pay for the charges is 13/71

Now, the probability of not selecting is 1- probability of selecting = 1-13/71 = 58/71

Since the probability of not selecting is greater than the probability of selecting, it means that it is not likely that a winning ticket will be selected

Answer:

(a)  0.2650

(b)  0.0111

(c)  0.0105

(d)  0.0006

Step-by-step explanation:

Given that:

In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample.

Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with mean μ = 15.       &;

If the area of the agar plate is 75cm²;

what is the probability  of observing fewer than 4 CFUs in a 25 cm² area of the plate.

We can determine the mean number of CFUs that appear on a 25cm² area of the plate as follows;

75cm²/25cm² = 3

Since;

mean  μ = 15  

mean number of CFUs that appear on a 25cm² = 15/3 = 5 CFUs

Thus ; the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate is estimated as:

= P(X < 4)

Using the EXCEL FUNCTION ( = poisson.dist(3, 5, TRUE) )

we have ;

P(X < 4) = 0.2650

b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs?

Given that the total number of CFUs = 5 plates; then the mean number of CFUs in 5 plates =  15×5 = 75 CFUs

The probability is therefore = P( X > 95 )

= 1 - P(X ≤ 95)

= 1 - poisson.dist(95,75,TRUE) ( by using the excel function)

= 0.0111

c) Repeat the probability calculation in part (b) but now use the normal approximation.

Let assume that the mean and the variance of the poisson distribution are equal

Then;

[tex]X \sim N (\mu = 75 , \sigma^2 = 75)[/tex]

We are to repeated the probability calculation in part (b) from above;

So:

P( X > 95 )

use the normal approximation

From standard normal variable table:

P(Z > 2.3094)

Using normal table

P(Z > 2.3094) = 0.0105

(d)  Find the difference between this value and your answer in part (b).

So;

the difference between the value in part c and part b is;

=  0.0111 - 0.0105

[tex]= 6*10^{-4}[/tex]

= 0.0006 to four decimal places

Answer:

1) a^4 + 16b^4

2) x^4 + 5x^2 + 9

3) p^2 − 10px − q^2 + 6qx + 16x^2

Step-by-step explanation:

1) a^4 + (2b)^4

= a^4 + 16b^4

2) x^4 + 5x^2 + 9

There are no like terms.

Answer:

= x^4 + 5x^2 + 9

3) p2 − 10xp + 16x2 − q2 + 6xq

= p^2 − 10px − q^2 + 6qx + 16x^2