Sarah rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 2.

Answer:

a. 3 mintes = 180 seconds

Answer:

155ysec ; 23400z+ 8400 secs

Step-by-step explanation:

3y mins = 3* 60=180y sec

3y mins - 25y sec= 180y sec - 25y= 155y sec

155ysec

From B

50(3z-2)min = 50 * 60 (3z-2) sec

= 3000(3z-2)=9000z-6000

4 (z + 1) hours =4*3600(z+1) =14400z + 14400z

Adding both expression we have;

9000z+14400z-6000+14400=23400z+ 8400 secs

23400z+ 8400 secs

Hello!

[tex]\boxed{ \bf The~approximate~area~of~the~circle~is~D.~380~m^2}[/tex]

___________________________________________

We must use a certain formula to find the area of a circle.

A = πr²

Let's plug in the radius.

A = π × 11²

A = π × 121

A = 380

Answer:

Option A. The volume of the sphere is multiplied by 1/343.

Step-by-step explanation:

The volume of a sphere can be obtained by the following formula:

V = 4/3πr^3

Let the initial volume (V1) of the sphere be:

V1 = 4/3πr^3 = (4πr^3)/3

Now, if we multiply the radius by 1/7, then the new volume (V2) of the sphere will be:

V2 = 4/3 x π x (1/7r)^3

V2 = 4/3 x π x 1/343r^3

V2 = (4πr^3)/1029

Now we determine the ratio of V2 : V1 as shown below:

V2/V1 = (4πr^3)/1029 ÷ (4πr^3)/3

V2/V1 = (4πr^3)/1029 × 3/(4πr^3)

V2/V1 = 3/1029

V2/V1 = 1/343

V2 = 1/343 x V1

Therefore, the volume of the sphere is multiplied by 1/343.

Answer:

6.)66 degrees

7.)20 degrees

Step-by-step explanation:

Step-by-step explanation:

Angle 114 and angle 3 are supplementary, meaning that they can be added to get 180 degrees

If you subtract 114 from 180 you get 66 degrees

Angle D and Angle C are both complimentary, meaning that if you add them together you get 90 degrees

If you subtract 70 from 90 you get 20

Answer: B) 4/52 * 3/51

Step-by-step explanation:

the probability of drawing the first ace is 4/52 bc there are 4 aces and 52 cards. the probability of drawing the second ace is 3/51 bc there are now three aces ( bc we removed one in the first step) and there are now 51 cards (bc we removed a card in the first step and there is no replacement). combine the probabilities with multiplication because it’s a multistage event

Answer:

1) There is enough evidence to support the claim that the average hospital stay for men is longer than the average hospital stay for women. (P-value = 0.00051).

2) zc=2.33

Step-by-step explanation:

1) This is a hypothesis test for the difference between populations means.

The claim is that the average hospital stay for men is longer than the average hospital stay for women.

Then, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0

The significance level is 0.01.

The sample 1, of size n1=37 has a mean of 5.6 and a standard deviation of 1.2.

The sample 2, of size n2=35 has a mean of 4.5 and a standard deviation of 1.6.

The difference between sample means is Md=1.1.

[tex]M_d=M_1-M_2=5.6-4.5=1.1[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.2^2}{37}+\dfrac{1.6^2}{35}}\\\\\\s_{M_d}=\sqrt{0.039+0.073}=\sqrt{0.112}=0.335[/tex]

Then, as we know the population standard deviation of both, we can calculate the z-statistic as:

[tex]z=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{1.1-0}{0.335}=\dfrac{1.1}{0.335}=3.29[/tex]

This test is a right-tailed test, with z=3.29, so the P-value for this test is calculated as:

[tex]P-value=P(z>3.29)=0.00051[/tex]

As the P-value (0.00051) is smaller than the significance level (0.01), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average hospital stay for men is longer than the average hospital stay for women.

2. The critical values for this right tail test are calculated from the z-table and the significance level (α=0.01)

[tex]P(z>z_c)=0.01[/tex]

This happens for zc=2.33:

[tex]P(z>2.33)=0.01[/tex]

Step-by-step explanation:

Step 1:  Multiply them together to get the area

[tex]A = L * W[/tex]

[tex]A = (x + 4)(3x - 1)[/tex]

[tex]A = (x * 3x) + (x * -1) + (4 * 3x) + (4 * -1)[/tex]

[tex]A = 3x^2 - x + 12x - 4[/tex]

[tex]A = 3x^2 + 11x - 4[/tex]

Answer:  [tex]A = 3x^2 + 11x - 4[/tex]

Answer:

3x² + 11x - 4

Step-by-step explanation:

Area = length × width

= (x+4)(3x-1)

= 3x² + 12x - x - 4

= 3x² + 11x - 4

Answer:5

Step-by-step explanation:(1×2^2)+(0×2^1)+(1×2^0)=

1×4+0×2+1×1=

4+1=

5

Answer:

  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides in a right triangle. Here, we're given the side Adjacent and the side Opposite the angle of interest. This makes it appropriate to choose the relation ...

  Tan = Opposite/Adjacent

For our angle of elevation α, this means ...

  tan(α) = 125/72

  α = arctan(125/72) = 60.058°

  α ≈ 60°

The angle of elevation is about 60°.

Answer:

d

Step-by-step explanation:

did da math

Answer:

[tex]5cm^{3}[/tex]

Step-by-step explanation:

from the formula of cylinder and cone we can see that the volume of a cone is 3 times smaller than that of a cylinder

[tex]volume=\pi r^{2} h[/tex]....................cylinder

[tex]volume= \frac{1}{3} \pi r^{2}h[/tex].................cone

assuming all units in (cm)

Given data.

Volume of cylinder  =  [tex]15cm^{3}[/tex]

Diameter d=  [tex]2cm[/tex]

Radius r =   [tex]\frac{d}{2}[/tex][tex]= \frac{2}{2} = 1cm[/tex]

Height h=  ??

we know that the expression for the volume of a cylinder is

[tex]volume=\pi r^{2} h[/tex]

we can substitute our given data to find the height h

[tex]15= 3.142*1^{2}*h\\15= 3.142h[/tex]

divide both side by 3.142 we have

[tex]h= \frac{15}{3.142}\\ h= 4.77cm[/tex]

We can now use this height[tex]4.77cm[/tex] and radius [tex]1cm[/tex] to find the equivalent  volume of a cone.

the expression for the volume of a cone is

[tex]volume= \frac{1}{3} \pi r^{2}h[/tex]

substituting our data into the expression  we have

[tex]volume= \frac{3.142*1^{2*} 4.77}{3} \\volume= \frac{15}{3} \\voulume = 5cm^{3} \\[/tex]

Step-by-step explanation:

The answer is to your question is 192817359

Answer:

about 225-250 million years:

Answer:

The overall expected grade point average for the semester is 3.16/3.1 or 3.2 if you round it up.

Step-by-step explanation:

To get the average, you need to add up all the numbers then divide the sum by how many numbers you added.

3.5 + 3.0 + 3.0 = 9.5

9.5 / 3 = 3.16

Given Information:

expected grade in two-credit course = 3.5

expected  grade in three-credit course = 3.0

expected grade in four-credit course = 3.0

Required Information:

Expected overall grade point average = ?

Answer:

The expected overall grade point average of this college student is 3.11

Step-by-step explanation:

The overall expected grade point average is given by

E(X) = Sum of grades/Total number of credit hours

Sum of grades = ∑ weightage*expected grades

Sum of grades = 2*3.50 + 3*3.0 + 4*3.0 = 28

Total number of credit hours = 2 + 3 + 4 = 9

E(X) = Sum of grades/Total number of credit hours

E(X) = 28/9

E(X) = 3.11

Therefore, the expected overall grade point average of this college student is 3.11 .

Answer:

Isosceles

Step-by-step explanation:

An isosceles triangle is a triangle in which the length of at least two sides are same.

The triangle which Seth has two sides of same length that is 20 inches.

Third side is different.

Hence. the triangle which Seth has is  isosceles.

Answer:

x = 0

Step-by-step explanation:

[tex]\frac{1}{3} x+\frac{3}{10}x=0[/tex]

x = 0

Answer:

(4,5)

Step-by-step explanation:

To find the x coordinates of the midpoint, add the x coordinates together and divide by 2

(x1+x2)/2 = (0+8)/2 = 8/2 = 4

To find the y coordinates of the midpoint, add the y coordinates together and divide by 2

(y1+y2)/2 = (2+8)/2 = 10/2 = 5

The midpoint is (4,5)

Answer:

(4,5)

Step-by-step explanation:

Midpoint: (0+8)/2, (2+8)/2

8/2, 10/2

4,5

Answer:

Rate = (4C)cars/3(H)hrs

Step-by-step explanation:

Kelly can tune 4 cars in 3 hours.

The rate at which he dies work = 4/3

Thanks rate at which he tunes cars = 4/3 cars/hr

The expression of the above formula for C fraction of 4 cars and H fraction of 3 hours will be 4(C)/3(H)

Rate = (4C)cars/3(H)hrs

Answer:

2(x+1) or 2x+2

Answer:2

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

  $1350

Step-by-step explanation:

Apparently, we're to assume that the bill is proportional to the energy usage. Then reducing energy by 10% would reduce the bill by 10%.

10% of the bill is 0.1 × $1500 = $150.

If the bill is reduced by $150, it becomes ...

  $1500 -150 = $1350

If they are successful, their bill will be $1350.

_____

In general, utility bills have a number of fixed charges or fees that are not proportional to the quantity of utility used. Too, they can have graduated rates that make them non-proportional.

Figuring 90% of some arbitrary number might be an interesting math exercise, but it has no relation to the world of utility billing for a 10% change in usage.

Answer:

0.5361

Step-by-step explanation:

Hope this helps :)

Answer:

0.325

Step-by-step explanation:

Divide 26 by 80

Answer:

[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]

Step-by-step explanation:

For each day there are only two possible outcomes. Either it rains, or it does not. The probability of rain on a day is independent of any other day. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

In a state park where the probability of rain on any given day is 0.7.

This means that [tex]p = 0.7[/tex]

Which expression can be used to find the probability that it will rain on exactly 3 of the seven days they are there

We have to find [tex]P(X = 3)[/tex] when [tex]n = 7[/tex]

So

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

[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]

Answer:

x=7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

12 bars --- 2 boxes

42 bars --- x boxes

x = 42*2/12 = 7

Answer:

5 hours

Step-by-step explanation:

5.6 all you have to use is .6 times 5hours to make 3kmapart

Answer: The expression 2√2 + √50 is equivalent to 7√2.

Step-by-step explanation: When 2√2 + √50 is added together, the result if 7√2.

Answer:

[tex]a_{n} = 27 - 3(n-1)[/tex]

Step-by-step explanation:

Arithmetic sequences concepts:

The general rule of an arithmetic sequence is the following:[tex]a_{n+1} = a_{n} + d[/tex]

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

[tex]a_{n} = a_{1} + (n-1)*d[/tex]

And also:

[tex]a_{n} = a_{m} + (n-m)*d[/tex]

In this question:

[tex]a_{4} = 18, a_{7} = 9[/tex]

Finding the common ratio:

[tex]a_{n} = a_{m} + (n-m)*d[/tex]

[tex]a_{7} = a_{4} + (7-4)*d[/tex]

[tex]9 = 18 + 3d[/tex]

[tex]3d = -9[/tex]

[tex]d = \frac{-9}{3}[/tex]

[tex]d = -3[/tex]

Finding the first term:

[tex]a_{4} = a_{1} + (4-1)*d[/tex]

[tex]18 = a_{1} + 3*(-3)[/tex]

[tex]a_{1} = 27[/tex]

General rule:

[tex]a_{n} = a_{1} + (n-1)*d[/tex]

[tex]a_{n} = 27 - 3(n-1)[/tex]