which of the following is the probability that a blue marble will be selected from a bag containing 9 red marbles,6 blue marbles,7green marbles, and 11 yellow marbles if one is selected randomly?​

Answer:

Option D

Step-by-step explanation:

x is given to be 4 in this case, so all we would have to is plug it into the following function -

[tex]f ( x ) = \left \{ {{x - 2, x < 4 } \atop {x + 2, x \geq 4 }} \right[/tex]

Through substitution, you would receive the following function -

[tex]f ( x ) = \left \{ {{2, 4 < 4 } \atop 6, 4 \geq 4 }} \right[/tex]

Now the graph proves that this function is closer to 4, and thus proves that the y - coordinate is about 2 at the same time. However, the graph is cut off, so the limit doesn't exists.

Answer:

- Was the car speeding?

Yes, the car was speeding as its current speed of 57.65 mph was more than the speed limit of that freeway.

- Do you agree with Nico or with Katya?

I agree somewhat with both Nico and Katya, but, I agree more with Nico.

- Explain your reasoning.

Like I said, I agree more with Nico's method of rounding the speed to the nearest whole number. This is because in this question, the standard speed we want to compare the calculated speed with is given as a whole number. Hence, it is more proper to estimate the calculated speed to its nearest whole number too.

Step-by-step explanation:

Speed during a travel is given as distance travelled divided by time taken

Speed = (Distance/time)

Distance = 98 miles

Time = 1.7 hours

Speed = (98/1.7) = 57.6470588235 = 57.65 mph = 58 mph

- Was the car speeding?

The speed limit for the road is 55 mph and the current speed of the car = 57.65 mph

Since 57.65 > 55

The car was overspeeding.

- Nico says it's okay to round what his calculator says to the nearest whole number. Katya says that because the calculator displays eight numbers after the decimal point, they shouldn't round. She says they should write down exactly what the calculator shows. Do you agree with Nico or with Katya?

I agree somewhat with both Nico and Katya as the both methods of recording the speed ate right, depending on what the speed is required for.

Although, I agree more with Nico's method as it seems like a better fit for the situation described in the question.

- explain who you agree with and provide the reasons why.

Like I said earlier, I agree more with Nico's method of rounding the speed to the nearest whole number. This is because in this question, the standard speed we want to compare the calculated speed with is given as a whole number. Hence, it is more proper to estimate the calculated speed to its nearest whole number too.

Katya's method of writing the calculated speed as is will be correct in cases where extreme accuracy is required, not an estimate. For this question, the estimate will do.

Hope this Helps!!!

Answer:

Yes, the car was speeding as its current speed of 57.65 mph was more than the speed limit of that freeway.

Step-by-step explanation:

Nico and Katya i agree with.

Answer:

5000

Step-by-step explanation:

500×2=1000

1000=1.00

1000×5=5.00

Answer:

The writer worries about being left out.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B. 1788

Step-by-step explanation:

The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by

length * height * width

The volume for current object is :

12 * 28 * 5

= 1788 cubic yards.

Answer: 1778

Step-by-step explanation:

because Ik I had the question

Answer:

3n>15

Step-by-step explanation:

So basically, this three times a number, 3n, is greater than 15. So, this is 3n>15.

Answer:

(a) matched pair design

(b) n = 30

(c) Reject the null hypothesis.

Step-by-step explanation:

The complete question is:

A researcher records the amount of time (in minutes) that parent child pairs spend on social networking sites to test whether they show any generational differences. From the following findings in APA format, interpret these results by stating the research design used (repeated measures or matched pairs), the sample size, the decision, and the effect size. Parents spend significantly less time on social networking sites compared their children (MD = -42 minutes),t(29)=4.021,p<.05,d=0.49.(a) What research design was used? (Repeated measures or matched pairs?)(b) What is the sample size? (n = ?)(c) What is the decision? (Retain or reject the null?)

Solution:

(a)

It s provided that the researcher records the amount of time (in minutes) that parent-child pairs spend on social networking sites.

This implies that the data collected is in the form of paired data.

Thus, the research design that was used was matched pair design.

(b)

Consider the t-statistics provided:

t (29) = 4.021

The number 29 in the bracket is the degrees of freedom.

The degrees of freedom for a matched pair design is,

df = n - 1

Compute the value of n as follows:

df = n - 1

29 = n - 1

n = 29 + 1

n = 30

Thus, the sample size is n = 30.

(c)

The p-value of the test is:

p < 0.05

The p-value of the test is less than the 5% significance level.

This implies that the null hypothesis will be rejected at 5% significance level.

Answer:

28 miles

Step-by-step explanation:

to fin the actual distance you must multiply the didtance on the map by the map scale

3.5*8=28

Answer:

4/5 gallon per wall

Step-by-step explanation:

We can find the unit rate

1/5 gallon

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

1/4 wall

1/5 ÷ 1/4

Copy dot flip

1/5 * 4/1

4/5 gallon per wall

Answer:

4/5 gallon of paint

Step-by-step explanation:

1/5 gallon of paint is needed to cover 1/4 of the wall.

To cover the whole wall:

1/4 × 4 = 1 (whole)

1/5 × 4 = 4/5

Answer: b) 180° rotation & reflection over x-axis

Step-by-step explanation:

Rotation of 180° changes the signs of both x and y.

(x, y) → (-x, -y)

Reflection over the x-axis changes the sign of y.

(-x, -y) → (-x, y)

 (x, y)        (-x, y)  

 (0, 1)   →    (0, 1)

 (1, -1)   →   (-1, -1)

 (5, 3)   →   (-5, 3)

Answer:

4/7

Step-by-step explanation:

5+2=7

7 children

4 boys Out of 7 children

Answer:1/7

Step-by-step explanation:

Khan academy

Answer: -6.4

Step-by-step explanation:

(0.4)(8)(-2)

3.2*-2

-6.4

Answer:

  1

Step-by-step explanation:

The lateral area of a cylinder is ...

  LA = 2πrh

The total area is that added to the areas of the two circular bases:

  A = 2πr² +2πrh

We want the ratio of these to be 1/2:

  LA/A = (2πrh)/(2πr² +2πrh) = h/(r+h) = 1/2 . . . . cancel factors of 2πr

Multiplying by 2(r+h) gives ...

  2h = r+h

  h = r . . . . . subtract h

So, the desired ratio is ...

  h/r = h/h = 1

The ratio between height and radius is 1.

Answer:

152.3

Step-by-step explanation:

area of a parralellogram is L×B

since a degree is given

it will make it

sin 65×14×12

sin 65=0.9063

so 0.9063×14×12

=152.3

Answer:

  0 +256i

Step-by-step explanation:

According to Euler's formula, ...

  (4 cis π/8)^4 = (4^4) cis (4×π/8) = 256 cis π/2 = 0 +256i

_____

"cis" is an abbreviation sometimes used for "cosine + i×sine". It simplifies writing the expression. Engineers sometimes simplify it further, writing 4∠(π/8) for the expression in this problem statement.

Answer:  [tex]\bold{\dfrac{b_1}{b_2}=\dfrac{3}{2}}[/tex]

Step-by-step explanation:

Inversely proportional means a x b = k   --> b = k/a

Given that a₁ = 2   --> b₁ = k/2

Given that a₂ = 3   -->  b₂ = k/3

[tex]\dfrac{b_1}{b_2}=\dfrac{\frac{k}{2}}{\frac{k}{3}}=\large\boxed{\dfrac{3}{2}}[/tex]

Answer:

[tex] P(14.8< X<16.5)= \frac{16.5-11.1}{19.2-11.1} -\frac{14.8-11.1}{19.2-11.1}= 0.667-0.457= 0.210[/tex]

The probability that it will require between 14.8 and 16.5 minutes to perform the task is 0.210

Step-by-step explanation:

Let X the random variable "completion times for a job task" , and we know that the distribution for X is given by:

[tex] X \sim Unif (a= 11.1, b= 19.2)[/tex]

And for this case we wantto find the following probability:

[tex] P(14.8< X<16.5)[/tex]

And for this case we can use the cumulative distribution given by:

[tex] F(x) =\frac{x-a}{b-a} , a\leq X \leq b[/tex]

And using this formula we got:

[tex] P(14.8< X<16.5)= \frac{16.5-11.1}{19.2-11.1} -\frac{14.8-11.1}{19.2-11.1}= 0.667-0.457= 0.210[/tex]

The probability that it will require between 14.8 and 16.5 minutes to perform the task is 0.210

Answer:

[tex] P(X=7)[/tex]

And using the probability mass function we got:

[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]  

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=15, p=0.23)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

And we want to find the following probability:

[tex] P(X=7)[/tex]

And using the probability mass function we got:

[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]  

Answer:

a) [tex]\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}[/tex]

b) [tex]\mathbf{x = 2000 - 2000e^{-0.015t}}[/tex]

c)  the  steady state mass of the drug is 2000 mg

d) t ≅ 153.51  minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

[tex]Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min[/tex]

[tex]Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min[/tex]

Therefore;

[tex]\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}[/tex]

with respect to  x(0) = 0

[tex]\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}[/tex]

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

[tex]\dfrac{dx}{dt} = -0.015(x - 2000)[/tex]

[tex]\dfrac{dx}{(x - 2000)} = -0.015 \times dt[/tex]

By Using Integration Method:

[tex]ln(x - 2000) = -0.015t + C[/tex]

[tex]x -2000 = Ce^{(-0.015t)[/tex]

[tex]x = 2000 + Ce^{(-0.015t)}[/tex]

However; if x(0) = 0 ;

Then

C = -2000

Therefore

[tex]\mathbf{x = 2000 - 2000e^{-0.015t}}[/tex]

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

[tex]\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}[/tex]

x = 2000 - 0

x = 2000

Thus; the  steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

[tex]\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}[/tex]

[tex]0.1 = e^{(-0.015t)[/tex]

[tex]ln(0.1) = -0.015t[/tex]

[tex]t = -\dfrac{In(0.1)}{0.015}[/tex]

t = 153.5056729

t ≅ 153.51  minutes

The answer is option A

Step-by-step explanation:

Thirteen less than a number is written as

n - 13

Equate it to 42

We have

n - 13 = 42

Hope this helps you

Answer:

Probability (N more than 2) = 0.3773

Step-by-step explanation:

Given:

Average number of crashes (N) = 2.2

Find:

Probability (N more than 2)

Computation:

Probability (N more than 2) = [1-P(N=0)-P(N=1)-P(N=2)]

Probability (N more than 2) = [1 - e⁻²°² - 2.2e⁻²°² - (2.2²e⁻²°²)/2]

Probability (N more than 2) = 0.3773

Answer:

[tex]\huge\boxed{A=3\sqrt{255}\ in^2\approx47.91\ in^2}[/tex]

Step-by-step explanation:

We have two sides

[tex]a=12in;\ b=14in[/tex]

and the preimeter

[tex]P=34in[/tex]

We can calculate the length of the third side:

[tex]c=P-a-b[/tex]

substitute

[tex]c=34-12-14=8\ (in)[/tex]

Use the Heron's formula:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)[/tex]

where

[tex]p=\dfrac{P}{2}[/tex]

substitute:

[tex]p=\dfrac{34}{2}=17\ (in)\\\\A=\sqrt{17(17-12)(17-14)(17-8)}=\sqrt{(17)(5)(3)(9)}\\\\=\sqrt{9}\cdot\sqrt{(17)(5)(3)}=3\sqrt{255}\ (in^2)\approx47.91\ (in^2)[/tex]

Answer:

C. 5 is solution of the inequality: B>2.1

Answer:

Selling price = $190003.206 and total interest paid is $135640.794

Step-by-step explanation:

The down payment of house = $25404

Monthly payment = $834 per month.

Total number of years = 30 years = 30*12 = 360 months.

Interest rate compounded monthly = 4.5 % * 1/12 = 0.375% per month or 0.00375.

Now we have to calculate the selling price of house and total interest paid.

Loan amount = Present value of monthly payments.

[tex]\text{Loan amount} = \frac{ Monthly \ payment \times [1- (1+r)^{-n}]}{r} \\= \frac{ 834 \times [1- (1+ 0.00375)^{-360}]}{0.00375} \\= 164599.206[/tex]

Selling price of house = 25404 + 164599.206 = 190003.206

Interest amount = total amount of installment – loan amount

Interest amount = 834*360 – 164599.206 = 135640.794 dollars.

Answer:

0.14% probability of a person guessing the right​ combination

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the numbers are selected is important. For example, 1,3,2 is a different combination than 3,1,2. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Desired outcomes:

One right combination, so [tex]P = 1[/tex]

Total outcomes:

10 numbers from a set of 3. So

[tex]P_{(10,3)} = \frac{10!}{(10-3)!} = 720[/tex]

What is the probability of a person guessing the right​ combination?

[tex]p = \frac{D}{T} = \frac{1}{720} = 0.0014[/tex]

0.14% probability of a person guessing the right​ combination

Answer:

247

49

Step-by-step explanation:

a) f•g (4) =

f•g (x) =  f(g(x)) = (x + 9)^2 + 6(x + 9)

f•g (4) =  (4 + 9)^2 + 6(4 + 9)

= 13^2 + 6(13)

= 247

B) g•f (4) =

g•f (x) = g(f(x)) = x^2 + 6x + 9

g•f (4) = 4^2 + 6(4) + 9

= 16 + 24 + 9

= 49

Answer:

$833

Step-by-step explanation:

Since there are 9 people, we need to determine the cost of accommodation and flights for all 9 people:

9(273) + 9(184) = 2457 + 1656 = 4167 for 9 people

We then subtract that amount from the amount of money she won:

5000 - 4167 = 833

Answer:

24 oz costs $3.75

The rice cost per oz is $0.16

Step-by-step explanation:

Step 1: Set up proportion

16/2.5 = 24/x

Step 2: Cross multiply

16x = 24(2.5)

Step 3: Solve

16x = 60

x = 15/4 or 3.75

Complete Question

Jessica is organizing a guided tour of the rain forest. The average profit per person that the touring company makes is given by the rational expression 18x+35/x, where x is the number of people going on the tour. What does the denominator of this rational expression represents?

Answer:

Number of people going on the tour

Step-by-step explanation:

Given that the average profit per person  [tex]=\dfrac{18x+35}{x}[/tex]

[tex]\text{Average}=\dfrac{\text{Sum of Total Items}}{\text{Number of Items}}[/tex]

Therefore:

[tex]\text{Average Profit}=\dfrac{(18x+35)\text{ profit}}{x\text{ persons}}[/tex]

The denominator, x represents the number of people going on the tour.

Answer:

btw 35/x represents epresents a fixed cost, like a cover charge for the tour, that is not affected by the number of people attending the tour. So, the quotient 35/x represents the profit that the tour company makes from the cover charge per person.

Step-by-step explanation:

PLATO