Which pairs of non-overlapping angles share a ray to make a right angle?

Answer:

a= 0

b= [tex]-\frac{\sqrt{42} }{12}[/tex]

Step-by-step explanation:

We can rewrite the expression to be:

[tex]\frac{i\sqrt{7} }{i^{2}\sqrt{24} }[/tex]

We then can cancel out the i and we get

[tex]\frac{\sqrt{7} }{\sqrt{24} i}[/tex]

Can be rewritten as

[tex]\frac{\sqrt{7} }{2\sqrt{6} i}[/tex]

We then rationalize and get

[tex]-\frac{\sqrt{42} }{12} i[/tex]

Answer:

No.

Step-by-step explanation:

A point has no length, height or depth. It only has position.

A line has one dimensional length.

Answer: 0.0965

Step-by-step explanation:

This would happen if:

First toss: Here we must have any number that is not 6.

the options are 1, 2, 3, 4, 5 so the probablity is p1 = 5/6

The same happens for the second toss, p2 = 5/6

and for the third one: p3 = 5/6

for the fourth toss, person B must roll a 6, so the probability here is p4 = 1/6

Now, the joint probability is equal to the product of the probabilities for each toss, this is:

P = p1*p2*p3*p4 = (5/6)^3*(1/6) = 0.0965

Answer:

  [tex]F^{-1}(x)=\dfrac{x-7}{4}[/tex]

Step-by-step explanation:

To find the inverse function, solve for y the relation ...

  F(y) = x

  4y +7 = x

  4y = x - 7

  y = (x -7)/4 . . . . the inverse function

  [tex]\boxed{F^{-1}(x)=\dfrac{x-7}{4}}[/tex]

Answer:

B. You shouldnt take a random sample of more than 5% of the population size.

Step-by-step explanation:

B. You shouldnt take a random sample of more than 5% of the population size. This is True, so as to avoid the research analysis to be more complex to interpret and analyzed

However, the following are not true statements:

A. Random samples only generate unbiased estimates of long-run proportions, not long-run means. This is False, as there may be sampling error, when picking the sample, which will lead to bias estimates in the long run proportions

C. There is no way that a random sample of 100 people can be representative of all adults living in the United States. This is False, as using the right factors such as gender, age, income, etc, in selecting the sample, 100 people is enough to use as sample of adults living in the United States

D. If this question is voted out, the alternate option is "larger samples are always better than smaller samples, regardless of how the sample was collected." This is False, larger samples are not always better than smaller samples. In fact, they are often difficult to analyze and interpret.

E. Nonrandom samples are always poor representations of the population: This is False, depending on the expected outcome of the research study. Some research studies required the research to use Nonrandom samples to reach verifiable conclusion.

Answer:

The range of the random variable is {0, 1, 2}.

Step-by-step explanation:

The bag contains red and blue marbles.

The experiments consists of two draws, with reposition.

The random variable assigns the number of blue  marbles to each outcome.

If we have only two draws, we can only get 0, 1 or 2 blue marbles.

The range of the random variable is {0, 1, 2}.

Answer:

28

Step-by-step explanation:

number of copies done in 5 minute 15 seconds = 147

60 seconds is equal to 1 minute

1 second is equal to 1/60 minutes

therefore 15 seconds is equal to 1/60 * 15 minutes = 1/4 minutes

thus,

number of copies done in 5 1/4 minute = 147

number of copies done in 1 minute = 147/ 5 1/4   (as 147/21 = 7)

                                                = 147/ (21/4) = 7*4 = 28

Thus, A copy machine makes 28 copies in 1 minute.

Answer:

A

Step-by-step explanation:

Volume of cone = (1/3) πr²h

Answer:

El tejado tenía un ancho de 31.4 m.

Step-by-step explanation:

Tenemos un techo rectangular, con un largo de 29.7 m y un ancho x, que debemos calcular.

Entonces, la superficie del tejado es:

[tex]S=29.7x\;\,\text{[m}^2\text{]}[/tex]

Las locetas tienen una superficie de 25x19 cm,  de las cuales 1/5 se pierde en la colocación. La superficie eficaz que ocupa cada loceta una vez colocada es:

[tex]S_L=(25\cdot19)\cdot(1-1/5)=475\cdot(0.8)=380\;\text{cm}^2[/tex]

Entonces, si se utilizaron 24552 locetas para cubrir todo el techo, podemos expresar la superfice del techo como:

[tex]S=24552\;\text{locetas}\;\cdot380\dfrac{\text{cm2}}{\text{loceta}}\cdot \left(\dfrac{1\text{m}}{100\text{cm}}\right)^2=\dfrac{24552\cdot380}{10000}\;\text{m2}=932.976\;\text{m2}[/tex]

Podemos calcular x igualando este último resultado con la primer ecuación:

[tex]S=29.7x=932.976\\\\x=932.976/29.7=31.413\approx31.4[/tex]

Answer:

line s and t would not meet even if you extend them and also they have the same slope and gradient

Answer:

idk what you mean

Step-by-step explanation:

idk

Answer:

d = 2

Step-by-step explanation:

Using the formula

A=pq/2

Dont forget to click THANKS

Answer:

So first subtract 14 from 32

That means that -6y+4y = 18

Simplify the left side 4-6=-2

-2y = 18

Divide by -2

-9 = y

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

-6y+14+4y=32

Combine like terms

-2y +14 = 32

Subtract 14 from each side

-2y +14-14 = 32-14

-2y =18

Divide each side by -2

-2y/-2 = 18/-2

y = -9

Answer:

He should pay $2,790.7.

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, in years.

After t years, the total amount of money is:

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

In this question:

Rate of 10%, so I = 0.1.

9 months, so [tex]t = \frac{9}{12} = 0.75[/tex]

How much should he pay for a note that will be worth $3,000 in 9 months?

We have to find P for which T = 3000. So

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

[tex]3000 = E + P[/tex]

[tex]E = 3000 - P[/tex]

Then

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

[tex]3000 - P = P*0.1*0.75[/tex]

[tex]1.075P = 3000[/tex]

[tex]P = \frac{3000}{1.075}[/tex]

[tex]P = 2790.7[/tex]

He should pay $2,790.7.

Answer:

y=4x

Step-by-step explanation:

an independent variable is the variable  that is changed or controlled in an experiment or observation to test the effects on the dependent variable

a dependent variable is variable being tested and measured in a scientific experiment

in this case, the number of help desk tickets  closed out is dependent on the number of hours the individual works so y is the number of tickets closed (dependent variable). The number of tickets closed of will be 4 multiplied by the number of hours worked i.e. y=4x

Answer:

Step-by-step explanation:

1) first of all, let s check for n = 1

[tex]7^1 -1=7-1=6[/tex]

that s true

2) We assume that this is true for n

[tex]7^n-1[/tex] is divisible by 6

what about [tex]7^{n+1}-1[/tex] ?

we know that there is a k natural so that [tex]7^n-1=6k[/tex]

so [tex]7^n = 1+6k[/tex]

then [tex]7^{n+1} = 7*7^n = 7(1+6k)\\[/tex]

so [tex]7^{n+1}-1 = 7(1+6k)-1 = 6+7*6k = 6(1+7k)[/tex]

so it means that [tex]7^{n+1}-1[/tex] is divisible by 6

3) finally as this is true for n=1 and if this is true for n then it is true for n+1 we can conclude that [tex]7^n-1[/tex] is divisible by 6 for n positive integer

Answer:

(a)[tex]\dfrac{2}{13}[/tex]

(b)[tex]\dfrac{3}{13}[/tex]

(c)[tex]\dfrac{4}{13}[/tex]

Step-by-step explanation:

In a standard deck, there are 52 cards which are divided into 4 suits.

(a)

Number of Seven Cards =4

Number of King cards =4

Probability of randomly selecting a seven or king

=P(Seven)+P(King)

[tex]=\dfrac{4}{52} +\dfrac{4}{52} \\=\dfrac{8}{52}\\=\dfrac{2}{13}[/tex]

(b)

Number of Seven Cards =4

Number of King cards =4

Number of Jack(J) cards =4

Probability of randomly selecting a seven or king

=P(Seven)+P(King)+P(Jack)

[tex]=\dfrac{4}{52} +\dfrac{4}{52}+\dfrac{4}{52} \\=\dfrac{12}{52}\\=\dfrac{3}{13}[/tex]

(c)

Number of Queen Cards =4

Number of Spade cards =13

Number of Queen and Spade cards =1

Probability of randomly selecting a seven or king

[tex]=P$(Queen)+P(Spade)-P(Queen and Spade Card)\\=\dfrac{4}{52} +\dfrac{13}{52} -\dfrac{1}{52} \\=\dfrac{16}{52} \\=\dfrac{4}{13}[/tex]

[tex]g(x)=4(x+1)-2[/tex]

[tex]g(x)=4x+4-2[/tex]

[tex]g(x)=4x+2[/tex]

Image attached below for graph.

Answer:

a. How much will she have to pay back at the end of the 1 year?

Answer: $540

b. How much interest does she have to pay?

Answer: $40

Step-by-step explanation:

Simple interest for any amount p is given by

SI = p*r*t/100

where r is the annual rate rate of interest

t is the time

____________________________________________

Given

p= $500 (loan taken)

r = 8%

t = 1 year

SI = 500*8*1/100 = 40

Thus, $40 is the interest charged in a year.

Total money paid at the end of one year = loan taken  + interest charged

                                                                    = $500 + $40

                                                                    = $540

a. How much will she have to pay back at the end of the 1 year?

Answer: $540

b. How much interest does she have to pay?

Answer: $40

Answer:

Step-by-step explanation:

Corresponding means for population 1 and population 2 form matched pairs.

The data for the test are the differences between the mean for population 1 and mean for population 2.

μd =​ the mean for population 1 minus the mean for population 2.

Population 1 population 2 diff

19 24 - 5

25 27 - 2

31 36 - 5

52 53 - 1

49 55 - 6

34 34 0

59 66 - 7

47 51 - 4

17 20 - 3

51 55 - 4

Sample mean, xd

= (- 5 - 2 - 5 - 1 - 6 + 0 - 7 - 4 - 3 - 4)/10 = - 3.7

xd = - 3.7

Standard deviation = √(summation(x - mean)²/n

n = 10

Summation(x - mean)² = (- 5 + 3.7)^2 + (- - 2 + 3.7)^2 + (- 5 + 3.7)^2+ (- 1 + 3.7)^2 + (- 6 + 3.7)^2 + (0 + 3.7)^2 + (- 7 + 3.7)^2 + (- 4 + 3.7)^2 + (- 3 + 3.7)^2 + (- 4 + 3.7)^2 = 73.7

Standard - eviation = √(73.7/10

sd = 2.71

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (- 3.7 - 0)/(2.71/√10)

t = - 4.32

We would determine the probability value by using the t test calculator.

p = 0.00097

Since alpha, 0.1 > than the p value, 0.00097, then we would reject the null hypothesis. Therefore, at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.

3) for population 1,

Mean = (19 + 25 + 31 + 52 + 55 + 34 + 59 + 47 + 17 + 51)/10 = 38.4

Summation(x - mean)² = (19 - 38.4)^2 + (25 - 38.4)^2 + (31 - 38.4)^2+ (52 - 38.4)^2 + (49 - 38.4)^2 + (34 - 38.4)^2 + (59 - 38.4)^2 + (47 - 38.4)^2 + (17 - 38.4)^2 + (51 - 38.4)^2 = 2042.4

Standard deviation, s1 = √2042.4/10 = 14.3

for population 2,

Mean = (24 + 27 + 36 + 53 + 55 + 34 + 66 + 51 + 20 + 55)/10 = 42.1

Summation(x - mean)² = (24 - 42.1)^2 + (27 - 42.1)^2 + (36 - 42.1)^2 + (53 - 42.1)^2 + (55 - 42.1)^2 + (34 - 42.1)^2 + (66 - 42.1)^2 + (51 - 42.1)^2 + (20 - 42.1)^2 + (55 - 42.1)^2 = 2248.9

Standard deviation, s2 = √2248.9/10 = 15

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (10 - 1) + (10 - 1) = 18

z = 1.734

x1 - x2 = 38.4 - 42.1 = - 3.7

√(s1²/n1 + s2²/n2) = √(14.3²/10 + 15²/10)

= 6.55

Margin of error = 1.734 × 6.55 = 11.4

The 90% confidence interval is

- 3.7 ± 11.4

Answer:

X=22/5

Step-by-step explanation:

By cross multiplication

5/2 =11/x

5x = 2(11)

5x =22

X=22/5

Hope this helps..

Answer:

isosceles

Step-by-step explanation:

Answer:

The experimental group in this case are the group of bees that are put in the small cage.

Step-by-step explanation:

The experimental group is the group of subjects that participate in the test. They are usually assigned to the treatments in study. In some cases there is a control group, with no assigned treatment.

In this case, the bees that she put in the cage, and they are not assigned to a particular treatment. It can be considered a control group.

Answer:

# of broken crayons    # of boces

           1-5                            1

          6-10                          4

          11-15                          5

          16-20                        3

          21-25                         1

Step-by-step explanation:

1-5: 4 (1 number)

6-10: 6, 6, 8, 9 (4 numbers)

11-15: 12, 13, 14, 14, 15 (5 numbers)

16-20: 17, 17, 19 (3 numbers)

21-25: 24 (1 number)

Answer:

Number of broken crayons Number of boxes

1-5 = 4

6-10 = 9

11-15 = 14

16-20 =19

21-25 =24

Step-by-step explanation:

To find the number of boxes compared to the number of broken crayons you have to find 5 consecutive (hence there being five boxes to fill in) numbers with a constant rate of change. Start with the largest number possible that you can pick and then find the second largest so 24 and 19 the rate of change is 5. Compared to 17 and 19 the rate of change is 2 so it doesn’t have the same rate of change but if you try 19-5 you get 14 which is an option if you subtract 14-5 you get 9 which is another option 9-5 is 4 the lowest number you could possibly pick and they all have a constant rate of change of 5 so the answer is correct.

Answer:

[tex]\fbox{\begin{minipage}{5em}A = 18.3\end{minipage}}[/tex]

Step-by-step explanation:

Given:

Dan was thinking of a number.

Dan adds 10 to it, then doubles it and gets an answer of 56.6.

Solve for:

Dan's original number

Step 1: Clarify the problem:

Denote Dan's original number as A

Dan adds 10 to A => 10 + A, then

Dan doubles this sum => 2 x (10 + A), then

Dan gets an answer of 56.6 => 2 x (10 + A) = 56.6

Step 2: Solve for the defined equation:

2 x (10 + A) = 56.6

Let's divide both sides of equation by 2:

2 x (10 + A)/2 = 56.6/2

We simplify both sides after division:

10 + A = 28.3

Let's transfer all numbers to the right side, except A (the sign of 10 is changed from + to -)

A = 28.3 - 10

Let's perform the subtraction to get A:

A = 18.3

Hope this helps!

:)

Answer:

The inverse function is [tex]f^{-1}(x) = \frac{x-1}{2}[/tex]

Step-by-step explanation:

We have the following function:

y = 2x + 1

Finding the inverse:

Exchange y and x, and then isolate y again. So

y = 2x + 1

Exchange y and x

x = 2y + 1

2y = x - 1

[tex]y = \frac{x-1}{2}[/tex]

So

The inverse function is [tex]f^{-1}(x) = \frac{x-1}{2}[/tex]

Answer:

a. $840

b. $1,260

Step-by-step explanation:

a. 2/5 x 2100 = 840

b. 2100 - 840 = 1,260

Answer:both sides will be equal

Step-by-step explanation:

Answer:

113.09 hope this helps

Step-by-step explanation: