(a^2-b^2) (c^2-d^2) +4abcd​

Answer:

4.76% probability that a randomly selected person from the population has a positive test result

Step-by-step explanation:

We have these following probabilities:

4% probability of having the disease.

If a person has a disease, 95% probability of a positive test.

100-4 = 96% probability a person does not have the disease.

If a person does not have the disease, 1% probability of a positive test.

What is the probability that a randomly selected person from the population has a positive test result

95% of 4% and 1% of 96%. So

p = 0.95*0.04 + 0.01*0.96 = 0.0476

4.76% probability that a randomly selected person from the population has a positive test result

Answer:

[tex]7x^2-2x-2[/tex]

Step-by-step explanation:

[tex]-3x^2+9+10x^2-11-2x[/tex]

Combine like terms:

[tex]10x^2-3x^2-2x+9-11[/tex]

Simplify:

[tex]7x^2-2x-2[/tex]

Hope this helps!

Answer: 7x^2 - 2x - 2

Step-by-step explanation:

in this expression, all you have to do is combine like terms. those are -3x^2 and 10x^2, 9 and -11.

-3x^2 + 9 + 10x^2 - 11 - 2x     rearrange to make easier

-3x^2 + 10x^2 - 2x + 9 - 11     combine like-terms

7x^2 - 2x - 2

Answer:

The total price of the shoes including tax is 51.45

Step-by-step explanation:

You could go about this 2 ways.

One way is if the shoes originally cost $70 and they are now 30% off, it basically means that the discounted price of the shoes is 70% of the original cost, which is $49. Then to find the total price including tax, you need to find 105% of 49, because you are adding 5% to the discounted price(100). When you do the math, you should get the answer 51.45.

The other way to do it is by first finding 30% of 70, which is 21, and then subtracting that from the original price(70) to get the discounted price, $49. Then you need to find 5% of 49 and then add that to 49 to find the total cost w/ tax, which is 51.45.

Answer:

12

Step-by-step explanation:

f(-4) = -8-5(-4) = -8+20 = 12

Answer:

f(-4) = 12

Step-by-step explanation:

f(-4) = -8 - 5(-4)

= -8 + 20

= 12

Answer:

C: Multiply the first equation by -2

Step-by-step explanation:

-2 * (x + 3y = 16) = -2x-6y=-32

The resulting equation would be -2x-6y=-32

In the next if you add the two equations, you will successfuly eliminate x and can now solve for y.

-2x-6y=-32

2x + y = -18

Answer:

c

Step-by-step explanation:

x+3y=16________________eqn 1

2x+y=-18_______________eqn 2

multiply first equation by - 2

-2(x+3y=16)

-2x-6y= -32______________eqn 3

using elimination method

-2x-6y= -32

+

2x+y= -18

0-5y= -50

-5y= -50

divide both sides by -5

-5y/5= -50/5

y=10

substitute y in eqn 2 to find the value of x

2x+y= -18

2x+(10)= -18

2x+10= -18

2x= -18-10

2x= -28

divide both sides by 2

2x/2= -28/2

x= -14

Answer:

There are approximately 171 families in the sample.

Step-by-step explanation:

Percentile meaning:

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours.

This means that 24 is 14% of the total number of families.

Approximately how many families are in the sample?

Using a rule of three.

24 - 0.14

x - 1

0.14x = 24

x = 24/0.14

x = 171.4

Rounding to the nearest integer

There are approximately 171 families in the sample.

Answer:

C. can have more than one factor, each with several treatment groups.

Step-by-step explanation:

A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.

Completely randomized design has found application in agricultural and environmental researches.

The length of the side d would be 77/18.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

[tex]\dfrac{a}{b}[/tex]

If triangles DEF and NPQ are similar, then

7/9 = d/ (11/2)

By cross multiply

9d = 7 x 11/2

d = 77/2 ÷ 9

d = 77/18

Thus, The length of the side d would be 77/18.

Learn more about ratios here:

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Answer:

Next two numbers are 15 and 32 respectively.

Step-by-step explanation:

The given pattern is  

45, 15, 44, 17, 40, 20, 31, 25, …

Here, we have two patterns.

Odd places : 45, 44, 40, 31,...

Even places : 15, 17, 20, 25,...

In series of odd places, we need to subtract square of integers.

[tex]45-(1)^2=45-1=44[/tex]

[tex]44-(2)^2=44-4=40[/tex]

[tex]40-(3)^2=40-9=31[/tex]

So, 9th term of given pattern is  

[tex]31-(4)^2=31-16=15[/tex]

In series of even places, we need to add prime numbers.

[tex]15-2=17[/tex]

[tex]17+3=20[/tex]

[tex]20+5=25[/tex]

So, 10th term of given pattern is  

[tex]25+7=32[/tex]

Therefore, the next two numbers in the pattern of numbers are 15 and 32 respectively.

Answer:its 15.7

Step-by-step explanation:

Answer:

15.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

let the height height of the tree be "h"

Hence the tree's height h=9 ft

one year later,let the height of the tree increased by x ft

hence

[tex]9 + x = 16[/tex] --------This is the equation for the growth of the tree

In order to solve for the added height(growth) of the tree we need to solve for x

[tex]9 + x = 16\\x=16-9\\x=7ft[/tex]

Answer:

Test statistic t = 5.25

P-value = 0.000002 (one-tailed test)

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=7\\\\H_a:\mu> 7[/tex]

The significance level is 0.05.

The sample has a size n=49.

The sample mean is M=8.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√s^2=√4=2.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{49}}=0.29[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{8.5-7}{0.29}=\dfrac{1.5}{0.29}=5.25[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=49-1=48[/tex]

This test is a right-tailed test, with 48 degrees of freedom and t=5.25, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>5.25)=0.000002[/tex]

As the P-value (0.000002) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.

Answer:

See Explanation

This question is answered using Microsoft Office Excel 2013

Step-by-step explanation:

Given

Browser A - 64%

Browser B - 24%

Browser C - 6%

Browser D - 3%

Browser E - 3%

Total Frequency = 50

a.

To tabulate the frequency of the choice of browser, the total frequency is multiplied by each individual percentage as follows;

Browser A - 64% * 50 = 32

Browser B - 24% * 50 = 12

Browser C - 6% * 50 = 3

Browser D - 3%* 50 = 1.5

Browser E - 3% * 50 = 1.5

See Attachment for frequency table (using software)

b. See Attachment for pie chart and bar chart.

Both charts are useful for data presentation but in this case, the pie chart is a better option to use because it shows how the distribution of each browser and how they make up as a whole.

The main circle of the pie chart shows how individual browser are distributed through segments; This is not so for the bars of the bar chart which.

c. Yes, there are changes in the choice of browser.

Aside from Browser D and E that has the same frequency, other browsers (A-C) have different frequency.

Also, the distribution shows that more users make use of browser A than other browsers and the least frequent used browser are browser D and E.

Answer:

The degrees of freedom first given by:  

[tex]df=n-1=12-1=11[/tex]  

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

[tex] t_{\alpha}= 1.796[/tex]

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Step-by-step explanation:

Information given

5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.

System of hypothesis

We want to test if the true mean is higher than 5, the system of hypothesis are :  

Null hypothesis:[tex]\mu \leq 5[/tex]  

Alternative hypothesis:[tex]\mu > 5[/tex]  

The statistic is given by:

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

The degrees of freedom first given by:  

[tex]df=n-1=12-1=11[/tex]  

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

[tex] t_{\alpha}= 1.796[/tex]

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Answer:

[tex]E_{A} =0.25*160=40[/tex]  

[tex]E_{B} =0.25*160=40[/tex]

[tex]E_{C} =0.4*160=64[/tex]

[tex]E_{D} =0.05*160=8[/tex]  

[tex]E_{F} =0.05*160=8[/tex]  

And now we can calculate the statistic:  

[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]  

The answer would be:

c. 5.25

Step-by-step explanation:

The observed values are given by:

A: 36

B: 42

C: 60

D: 14

E: 8

Total =160

We need to conduct a chi square test in order to check the following hypothesis:  

H0: There is no difference in the proportions for the final grades

H1: There is a difference in the proportions for the final grades

The level of significance assumed for this case is [tex]\alpha=0.01[/tex]  

The statistic to check the hypothesis is given by:  

[tex]\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]  

Now we just need to calculate the expected values with the following formula [tex]E_i = \% * total[/tex]  

And the calculations are given by:  

[tex]E_{A} =0.25*160=40[/tex]  

[tex]E_{B} =0.25*160=40[/tex]

[tex]E_{C} =0.4*160=64[/tex]

[tex]E_{D} =0.05*160=8[/tex]  

[tex]E_{F} =0.05*160=8[/tex]  

And now we can calculate the statistic:  

[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]  

The answer would be:

c. 5.25

Now we can calculate the degrees of freedom for the statistic given by:  

[tex]df=(categories-1)=(5-1)=4[/tex]

And we can calculate the p value given by:  

[tex]p_v = P(\chi^2_{4} >5.25)=0.263[/tex]  

The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis

the answer is 180°

Step-by-step explanation:

because it rotated 2x and 90+90 is 180

Answer:

  1.4

Step-by-step explanation:

The average rate of change is the "rise" divided by the "run".

  rise/run = (f(4) -f(-1))/(4 -(-1)) = (0 -(-7))/(4+1)

  rise/run = 7/5 = 1.4

The average rate of change on the interval [-1. 4] is 1.4.

We will see that the average rate of change in the given interval is 1.4

For a given function f(x), the average rate of change on an interval [a, b] is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this case the interval is [-1, 4], using the graph we can see that:

f(-1) = -7

f(4) = 0

replacing that in the formula we get:

[tex]r = \frac{0 - (-7)}{4 - (-1)} = \frac{7}{5} = 1.4[/tex]

If you want to learn more about rates of change, you can read:

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Answer:

Step-by-step explanation:

Answer:

B) (0,2)

Step-by-step explanation:

2 ≥ 2(0)-1

2 ≥ 0-1

2 ≥ -1

Answer:

subtract  -3

Step-by-step explanation:

–3 + 4x = 9

Add 3 to each side

This is the same as subtracting -3

-3 + 4x - (-3) = 9 - (-3)

4x = 9 +3

4x = 12

Answer:

Step-by-step explanation:

hey

(f*g)(x) = f(g(x)) = f(2) = 2

second answer is correct

thanks

Answer:

66%

Step-by-step explanation:

15% of homes have both features.

The percentage of homes that have a pool and no garage is:

Pool only = 19% - 15% = 4%

The percentage of homes that have a garage and no pool is:

Garage only = 62% - 15% = 47%

Therefore, the percentage of homes that have a pool, a garage or both is:

[tex]P = 4\%+47\%+15\%\\P=66\%[/tex]

Answer:

The simple interest rate is 5%.

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?

We have that [tex]P = 4200, E = 630, t = 3[/tex]. We have to find I.

[tex]E = P*I*t[/tex]

[tex]630 = 4200*I*3[/tex]

[tex]I = \frac{630}{4200*3}[/tex]

[tex]I = 0.05[/tex]

The simple interest rate is 5%.

Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of  return of 6%?

We have to find T when [tex]P = 4200, t = 4, I = 0.06[/tex]

So

[tex]E = P*I*t[/tex]

[tex]E = 4200*0.06*4[/tex]

[tex]E = 1008[/tex]

[tex]T = E + P = 4200 + 1008 = 5208[/tex]

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

Answer: See below

Step-by-step explanation:

The point-slope equation is y-y₁=m(x-x₁). Since we don't know our slope, we can use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to find the slope. All we have to do is use the coordinate we were given and plug it into the formula.

[tex]m=\frac{-1-(-3)}{2-(-3)} =\frac{2}{5}[/tex]

Now that we have the slope, we can fill out the point-slope equation.

y-(-3)=2/5(x-(-3))

y+6=2/5(x+3)

This is the point-slope form.

Now, we can distribute and solve to get slope-intercept form.

y+6=2/5x+6/5

y=2/5x-24/5

Answer:

The original price of the fan is $35.71

Step-by-step explanation:

Since Griffin’s General Store is having a 30% off sale on fans, it simply means that fans are paying for (100%-30%)= 70%.

Let the original price be x;

Therefore, 70% of x equal to $25;

[tex]\frac{70}{100}x=25[/tex]

70/100x = 25

0.7x = 25

[tex]x = \frac{25}{0.7}[/tex]

x = 35. 71

Hence, The original price of the fan is $35.71

Answer:

$35.71

Step-by-step explanation:

The statement indicates that Robert paid $25 for a fan and that it had a 30% discount. To be able to determine the original price, you have to divide the the price with the discount by the result of 1 minus the discount.

Original price= 25/(1-0.3)

Original price= 25/0.7

Original price= 35.71

According to this, the answer is that the original price of the fan is $35.71.

Answer:

Step-by-step explanation:

               x^2

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

2x + 1  /  2x^3     -     x^2    +      x      +    1

               2x^3    +    x^2

              -----------------------

                                    0 + x + 1

                                        x + 1

The quotient is  x^2 + ------------

                                       2x + 1

Answer:

4x -8 +4y

Step-by-step explanation:

Distribute

4(x – 2 + y)

4*x -4*2 +4*y

4x -8 +4y

Answer:

increase 40

% increase is 40 %

Step-by-step explanation:

Take the new amount and subtract the original amount

140-100 = 40

Divide by the original amount

40/100

.40

Multiply by 100 %

40%

The percent increase is 40%

Answer:

3.67 units

Step-by-step explanation:

The central angle is at the point (0,0).

Then it's at the point (1,0)

Then it moved 210 degrees.

Let's bear in mind that we start moving the degree from it's current position.

So moving 210 degrees is moving 180 degrees plus 30 degrees.

Moving 180 degrees I like transforming linearly.

Now the location is at (-1,0)

But the distance covered will be

= 2πr*210/360

r = 1

= 2*3.142*1*(210/360)

= 6.144*0.5833333

= 3.67 units

Work Shown:

v - w = ( v ) - ( w )

v - w = ( -3i ) - ( 2-4i)

v - w = ( 0-3i ) - ( 2-4i)

v - w = 0-3i   -2+4i

v - w = (0-2) + (-3i+4i)

v - w = -2 + i

Answer: 363 cm squared

Step-by-step explanation:

So we can split the shape into 1 triangle and 3 rectangles.

We can start with the top right rectangle which is a 4 by 5.

4*5 = 20 cm squared

We can now do the horizontal rectangle. We need to find the dimensions firs by subtracting 4 from 31 to find the length and add 4 and 5 to find the height.

This means the dimensions are 27 by 9.

27 * 9 = 243 cm squared

Now the final square toward the bottom left will be a 10 by 7.

10 * 7 = 70 cm squared.

Now for the final piece is the triangle in the bottom left. We need to first find the height which we can determine by taking the the right hand side values of 10 , 4 and 5 and adding those together then subtracting that number by 13 to get the missing length that will add to 6 to find the height.

10 + 4 + 5 = 19

19 - 13 = 6

6 + 6 = 12

Now that we have the height and base of the triangle we solve for the area.

0.5 * 5 * 12 = 30 cm squared

Now we add all the areas together to find the total area.

20 + 243 + 70 + 30 = 363 cm squared