Exponential properties

Answer:

The probability that at least one of the 5 donors has Group O blood type is 0.9497.

Step-by-step explanation:

We can model this as a binomial random variable, with n=5 (the sample size) and p=0.45.

The probability that exactly k donors have Group O blood type in the sample can be written as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{5}{k} 0.45^{k} 0.55^{5-k}\\\\\\[/tex]

We have to calculate the probability P(x≥1). In this case it easy to substract from 1 the probabitity that x is exactly 0:

[tex]P(X\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=0.55^5=0.0503\\\\\\P(x\geq1)=1-0.0503=0.9497[/tex]

Answer: shifted by  3*pi/2 units to the right.

Step-by-step explanation:

Here we have:

y = sin(x - 3*pi/2)

now, you need to remember this:

if we have y = f(x)

then y' = f(x - A) is the graph of y, shifted A units to the right (where A is a positive number).

If A is negative, the shift is to the left.

Then in this case, we have:

sin(x) -----> sin( x - 3*pi/2)

A = 3*pi/2

Then we have the graph shifted by  3*pi/2 units to the right.

Answer:

C. 3pi/2 units to the right

Step-by-step explanation:

(I got it right on edge)

Answer:

x=1/2, y=5

Step-by-step explanation:

This can be solved using substitution!

Hope this helped!

Answer:

{x,y}={ 1/2, 5)

Step-by-step explanation:

[1]    8x + 7y = 39

[2]    4x - 14y = -68

Solve equation [2] for the variable  x

 [2]    4x = 14y - 68

 [2]    x = 7y/2 - 17

// Plug this in for variable  x  in equation [1]

  [1]    8•(7y/2-17) + 7y = 39

  [1]    35y = 175

// Solve equation [1] for the variable  y

  [1]    35y = 175

  [1]    y = 5

// By now we know this much :

   x = 7y/2-17

   y = 5

// Use the  y  value to solve for  x

   x = (7/2)(5)-17 = 1/2

Answer:

125

Step-by-step explanation:

5³ is equal to 5(5)(5):

5(5) = 25(5) = 125

Answer:

Step-by-step explanation:

5^3=5x5x5

5x5x5=125

Answer:

There are 0.01 meters in a centimeter.

Step-by-step explanation:

cent means 100th

Hope this helps :)

Answer:

19 weeks and 3 days.

Step-by-step explanation:

8+10=18

4+6=10

18 weeks and 10 days is equal to 19 weeks and 3 days.

Answer:

D. Find the x- and y-intercepts and then graph

Step-by-step explanation:

Answer:

Independent measures, or repeated measures,

Step-by-step explanation:

I would use those experimental designs because it is used to compare different participants over a length of time.  

Answer:

→VU

→TU

Step-by-step explanation:

→ stands for "ray" these sides are rays that form ∠VUT

Answer:

k = 79

Step-by-step explanation:

3(k-99) = -60

(k-99) = -20

k= -20+99

k=79

Answer:

7i + 11j

Step-by-step explanation:

DE = 8i + 6j - i + 5j

     = 7i + 11j

Complete Question

A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 210 students who averaged 28 texts per day. The standard deviation was 21 texts.

Round your answers to two decimal places.

A. The sampling distribution follows a                        [ Select ] ["F", "normal", "T", "Chi-square"] distribution.

B. With 95% confidence the population mean number of texts per day of is between                        [ Select ] ["24.92", "25.79", "27.37", "25.14"] and    [ Select ] ["31.19", "31.20", "29.28", "30.86"] texts.

C. If many groups of 210 randomly selected students are studied, then a different confidence interval would be produced from each group. About [ Select ] ["5", "95", "1", "99"] percent of these confidence intervals will contain the true population mean number of texts per day and about    [ Select ] ["95", "99", "5", "1"] percent will not contain the true population mean number of texts per day.

Answer:

a. With 95% confidence the population mean number of texts per day is between  [tex]I = 21.06[/tex]    and    [tex]I = 30.33[/tex]  texts.

b

If many groups of 132 randomly selected members are studied, then a different confidence interval would be produced from each group. About 95%   percent of these confidence intervals will contain the true population number of texts per day and about   5%    percent will not contain the true population mean number of texts per day.

Step-by-step explanation:

From the question we are told that

    The  sample size is  [tex]n = 102[/tex]

     The population mean is  [tex]\mu = 25.7[/tex]

     The  standard deviation is  [tex]\sigma = 23.9[/tex]

Generally the standard error of mean is mathematically evaluated as  

       [tex]\sigma_e = \frac{\sigma}{\sqrt{n } }[/tex]

substituting values

     [tex]\sigma_e = \frac{23.9}{\sqrt{102 } }[/tex]

     [tex]\sigma_e = 2.3665[/tex]

Given that the level of confidence is  95% then the level of significance will be  

   [tex]\alpha = 100 -95[/tex]

   [tex]\alpha =[/tex]5%

=>   [tex]\alpha = 0.05[/tex]

Now the critical values of this level of significance is obtained from the critical value table as

     [tex]t_{n,\alpha } = t_{102,0.05} = 1.96[/tex]

Generally the 95% confidence interval is mathematically represented as

     [tex]I = \mu \pm t_{102, 0.05} * \sigma_e[/tex]

substituting values  

    [tex]I = 25.7 \pm 1.96 *2.3665[/tex]

   [tex]I = 25.7 \pm 4.638[/tex]

   [tex]I = 30.33[/tex]   and  [tex]I = 21.06[/tex]

So the interval  is  

Answer:

0.875

Step-by-step explanation:

Here we are tasked with calculating E[F]

The probability of success here is given by;

P = 5/40 = 1/8 or 0.125

Now according to the question, our sample size is 7 i.e n = 7

Mathematically, expected value E(x) is given as np

= 7 * 0.125 = 0.875

Thus E[F] = 0.875

Answer:

The probability of "heads" is ½ and the probability of "tails" is ½.

This means that if we flip this coin several times, we expect it to land on "heads" for half of the time.

If we flip the coin 4000 times, we would expect it to land on "heads" 2000 times, because ½ × 4000 = 2000

Answer:

The answer is option A

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

y = - 2x + 5

Comparing with the above equation

Slope = - 2

The y intercept is ( 0 , 5)

Hope this helps you

Answer = c, slope = 5

steps = Substitute x = 0

y = -2 x 0 + 5

answer y = 5 / slope = 5

Complete Question

Which of the following statements are true?

I. The sampling distribution of [tex]\= x[/tex] has standard deviation [tex]\frac{\sigma}{\sqrt{n} }[/tex] even if the population is not normally distributed.

II. The sampling distribution of [tex]\= x[/tex]   is normal if the population has a normal distribution.

III. When  n is large, the sampling distribution of [tex]\= x[/tex]  is approximately normal even if the the population is not normally distributed.

A  I and II

B  I and III

C II and III

D I, II, and III

None of the above gives the complete set of true responses.

Answer:

The correct option is  D

Step-by-step explanation:

Generally the mathematically equation for evaluating the standard deviation of the mean([tex]\= x[/tex]) of samples is  [tex]\frac{\sigma}{\sqrt{n} }[/tex]  hence the the first statement is correct

   Generally the second statement is true, that is the sampling distribution of the mean ([tex]\= x[/tex]) is  normal given that the population distribution is  normal

 Now  according to central limiting theorem given that the sample size is  large the distribution of the mean ([tex]\= x[/tex]) is approximately  normal notwithstanding the distribution of the population

Answer:

Step-by-step explanation:

Answer:

3.47

Step-by-step explanation:

p varies inversely with q, so:

p = k/q, where k is a constant.

When q = 17, p = 10.

10 = k/17

k = 170

p = 170/q

When q = 49:

p = 170 / 49

p ≈ 3.47

Answer:

20

Step-by-step explanation:

It seems like the rule of this sequence is to add 5 (since 2 + 5 = 7 and 7 + 5 = 12). We already are given that we have 2 2-digit numbers (12 and 17) so let's see if there are any more. The sequence continues to 22, 27, 32, 37, 42, 47, ..., 92, 97. We need to count how many numbers are in the list 12, 17 ... 92, 97. To do this, let's add 3 to every term in the list to get 15, 20, ... 95, 100. Since the list is now full of multiples of 5 we can divide the list by 5 to get 3, 4, ... 19, 20 and then subtract 2 to get 1, 2, ... 17, 18 which means that there are 18 2-digit numbers.

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

a

 [tex]z = 6.25 \ cm/yr[/tex]

b

   [tex]k = -0.25 \ cm /yr[/tex]

Step-by-step explanation:

From the first image  the rate of  rate of change of the height from age 8 to 16  

  is  mathematically evaluated from the graph as  

             [tex]z = \frac{175 - 125}{16-8}[/tex]

            [tex]z = 6.25 \ cm/yr[/tex]

From the first image  the rate of  rate of change of the height from age 60 to 80.

  is  mathematically evaluated from the graph as

             [tex]k = \frac{175 - 170}{60-80}[/tex]

            [tex]k = -0.25 \ cm /yr[/tex]

Answer:

488p - 244

Step-by-step explanation:

Step 1: Add

61(8p - 4)

Step 2: Distribute

488p - 244

Answer:

d no because one value corresponds to two different y values

Answer:

The height of triangle is 12cm.

The base of triangle is 25 cm.

The area of triangle is 150cm².

Step-by-step explanation:

Given that the area of triangle is Area = 1/2×base×height. So you have to substitute the values into the formula :

[tex]area = \frac{1}{2} \times base \times height[/tex]

[tex]let \: base = 25 \\ let \: height = 12[/tex]

[tex]area = \frac{1}{2} \times 25 \times 12[/tex]

[tex]area = \frac{1}{2} \times 300[/tex]

[tex]area = 150 \: {cm}^{2} [/tex]

Answer:

1. a. Weak

2. r^2=0.0169

The variation in the price of the wine explained by the variation in the weight of the bottle is 1.69%.

Step-by-step explanation:

The correlation between the weight of the wine bottles and the price of the wine is r=0.13.

The values for r goes from r=-1, where a perfect negative correlation to r=1 for a perfect positive correlation. The value r=0 indicates no correlation at all.

Then, a value of r close to 0 indicates very weak correlation between the two variables.

The value for r^2 in this case is:

[tex]r^2=0.13^2=0.0169[/tex]

The value of r2 can be interpreted as the proportion of the variation in the dependant variable explained by the independent vairable. In this case, the variation in the price of the wine explained by the variation in the weight of the bottle is 1.69%, which is very close to 0.

Answer:

the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166

Step-by-step explanation:

The summary of the given statistical data set are:

Sample Mean = 186

Standard deviation = 29

Maximum capacity 3,417 pounds or 17 persons.

sample size = 17

population mean =3417

The objective is to determine the probability  that a random sample of 17 persons will exceed the weight limit of 3,417 pounds

In order to do that;

Let assume X to be the random variable that follows the normal distribution;

where;

Mean [tex]\mu[/tex] = 186 × 17 = 3162

Standard deviation = [tex]29* \sqrt{17}[/tex]

Standard deviation = 119.57

[tex]P(X>3417) = P(\dfrac{X - \mu}{\sigma}>\dfrac{X - \mu}{\sigma})[/tex]

[tex]P(X>3417) = P(\dfrac{3417 - \mu}{\sigma}>\dfrac{3417 - 3162}{119.57})[/tex]

[tex]P(X>3417) = P(Z>\dfrac{255}{119.57})[/tex]

[tex]P(X>3417) = P(Z>2.133)[/tex]

[tex]P(X>3417) =1- 0.9834[/tex]

[tex]P(X>3417) =0.0166[/tex]

Therefore; the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166

Answer:

∠2 = 75° because of alternate interior angles. Since ∠1 and ∠2 form a linear pair, they are also supplementary which means that ∠1 = 180 - ∠2 = 180 - 75 = 105°.

The value of angles are,

⇒ ∠1 = 105°

⇒ ∠2 = 75°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Now, We get;

∠2 = 75°

Because of alternate interior angles.

And, Since ∠1 and ∠2 form a linear pair,

Hence,  they are also supplementary which means that;

⇒ ∠1 = 180 - ∠2

⇒ ∠1 = 180 - 75

⇒ ∠1 = 105°

Thus, The value of angles are,

⇒ ∠1 = 105°

⇒ ∠2 = 75°

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ7

Answer:

124

Step-by-step explanation:

2x+100=6x+52

solve for variable x = 12

plug it in

2(12)+100

sj= 124

Answer:

x^2-2x+1

Step-by-step explanation:

We can solve this by using FOIL

First, Outside, Inside, Last

Multiply the x with the x to get x^2

Then x times -1 for the outside numbers to get -x

Then -1 times x for the inside numbers to get -x

And finally -1 and -1 for the last numbers to get 1

Add the two -x to get -2x.

Put it all together

x^2-2x+1

Answer:

[tex]x^2-2x+1[/tex]

Step-by-step explanation:

=> (x-1)(x-1)

USING FOIL

=> [tex]x^2-x-x+1[/tex]

=> [tex]x^2-2x+1[/tex]

Answer:

184

Step-by-step explanation:

The prime numbers between 40 and 56​ are 41, 43, 47, and 53.

Add the prime numbers.

41 + 43 + 47 + 53

= 184

Answer:

184

Step-by-step explanation:

Prime numbers between 40 and 56: 41, 43, 47, 53.

41+43+47+53=

84+47+53=

131+53=

184

Answer:

( -2,1)

Step-by-step explanation:

y = x+3

X = -2

Substitute x = -2 into the first equation

y = -2 +3

y = 1

( -2,1)