If you rolled two dice, what is the probability
that you would roll a sum of 4?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
3
second
first
1 2
4 5 6
11,1 1,2 1,3 1,4 1,5 1,6
22,1 2,2 2,3 2,4 2,5 2,6
33,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
55,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Enter

Answer:

Hello! answer: 42

Step-by-step explanation:

These are vertical angles meaning it will have the same measure so p = 42 hope that helps!

Answer:

AB = 9

Step-by-step explanation:

Here is a simple case of a proportion.

We see that:

3:4

x:12

what can we do to make 4 into 12?

we multiply it by 3

so we do the same to 3

3*3=9

Answer: The probability that a value is less than 36.8 is 0.9993.

Step-by-step explanation:

Let X be the random variable that normally distributed.

Given: [tex]\mu=32,\sigma=1.5[/tex]

The probability that a value is less than 36.8 = [tex]P(X<36.8)[/tex]

[tex]=P(\frac{X-\mu}{\sigma}<\frac{36.8-32}{1.5})\\\\=P(Z<3.2)\ \ \ [Z=\frac{X-\mu}{\sigma}]\\\\=0.9993[/tex][Using P-value calculator]

Therefore, The probability that a value is less than 36.8 is 0.9993.

Answer:

P(x > 10) = 0.6981.

Step-by-step explanation:

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 this question:

[tex]n = 14, p = 0.8[/tex]

P(x>10)

[tex]P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)[/tex]

In which

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

[tex]P(X = 11) = C_{14,11}.(0.8)^{11}.(0.2)^{3} = 0.2501[/tex]

[tex]P(X = 12) = C_{14,12}.(0.8)^{12}.(0.2)^{2} = 0.2501[/tex]

[tex]P(X = 13) = C_{14,13}.(0.8)^{13}.(0.2)^{1} = 0.1539[/tex]

[tex]P(X = 14) = C_{14,14}.(0.8)^{14}.(0.2)^{0} = 0.0440[/tex]

[tex]P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.2501 + 0.2501 + 0.1539 + 0.0440 = 0.6981[/tex]

So P(x > 10) = 0.6981.

Answer:

I think C. is it

Step-by-step explanation:

Answer:

too much salt will not bring taste to the cup cakes

Step-by-step explanation:

Answer:

what is the question?

Step-by-step explanation:

Answer:

i answered

Step-by-step explanation:

Answer:

7 yards

Step-by-step explanation:

Answer:

y intercept: [tex]y = 1[/tex]

x intercept: [tex]x = -1[/tex] and [tex]x = -3[/tex]

Step-by-step explanation:

Given

The attached graph

Solving (a): The y intercepts

This is the point where [tex]x = 0[/tex]

From the attached graph, [tex]x = 0[/tex] when

[tex]y = 1[/tex]

Hence, the y intercept is 1

Solving (b): The x intercepts

This is the point where [tex]y = 0[/tex]

From the attached graph, [tex]y = 0[/tex] when

[tex]x = -1[/tex] and [tex]x = -3[/tex]

Hence, the x intercept are -1 and -3

Answer:

SA = 484 cm²

Step-by-step explanation:

Surface area of the composite figure = surface area of the larger rectangular prism + (surface area of the smaller rectangular prism - base area of the smaller rectangular prism)

✔️Surface are of the larger rectangular prism = 2(LW + LH + WH)

L = 7 cm

W = 7 cm

H = 12 cm

S.A = 2(7*7 + 7*12 + 7*12) = 434 cm²

✔️Surface are of the smaller rectangular prism = 2(LW + LH + WH)

L = 7 cm

W = 2 cm

H = 2 cm

S.A = 2(7*2 + 7*2 + 2*2) = 64 cm²

✔️Base area of the smaller rectangular prism = L*W

L = 7 cm

W = 2 cm

Area = 7*2 = 14 cm²

✅Surface area of the composite figure = 434 + (64 - 14)

= 434 + 50

= 484 cm²

Answer:

It's C, 4/3! Just did the question and got it right

Step-by-step explanation:

The limit of f(x) as x approaches negative 1 is four thirds.

Limits are defined as the value of a function as the input approaches a certain number. Limits are the concepts used essentially in calculus to define continuity, integrals and derivatives.

Given function is,

[tex]f(x) =\left \{ {{x^{2} -\frac{1}{3}x, x\neq -1 } \atop {-1, x=-1}} \right.[/tex]

We have to find the value of the limit as x approaches to negative 1.

This is not the same value as the value of the function at negative 1. Limit of the function as x approaches some value is the value of the function which is closest to the exact value of the function at the input.

We have,

f(x) = x² - [tex]\frac{1}{3}[/tex] x when x ≠ -1

Substitute x = -1 in the above equation

x² - [tex]\frac{1}{3}[/tex] x  = (-1)² - (1 / 3) (-1)

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

            =  [tex]\frac{4}{3}[/tex]

[tex]\lim_{x \to -1} x^{2} -\frac{x}{3}[/tex] = [tex]\frac{4}{3}[/tex]

Hence the limit of f(x) = x² - [tex]\frac{1}{3}[/tex] x when x tends to -1 is 4/3.

To learn more about Limits, click on the link given below :

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Answer:

A. A triangle can be equilateral and obtuse at the same time

Step-by-step explanation:

All angles in an equilateral triangle are 60° therefore they cannot be above 90° and less than 180°

Answer:

Adam scored 60, Brandon scored 66, Chen scored 74, Damion scored 75, and Erica scored 75.

Step-by-step explanation:

Since five friends took the maths test, and Adam, Brandon, and Chen together together scored 200 marks; Brandon, Chen and Damion together scored 215; Chen, Damion and Erica together scored 224; and Damion and Erica scored more than Chen; While the five of them together scored 350 marks, to determine what are their individual scores the following calculations must be done:

Adam + Brandon + Chen = 200

Damion + Erica = 150

Brandon + Chen + Damion = 215

Adam + Erica = 135

Chen + Damion + Erica = 224

Adam + Brandon = 126

Adam + Brandon = 126 + Chen = 200

Chen = 200 - 126

Chen = 74

Damion and Erica scored more than Chen

Chen + Damion + Erica = 224

74 + Damion + Erica = 224

Damion + Erica = 150

Damion = 75

Erica = 75

Brandon + Chen + Damion = 215

Brandon + 74 + 75 = 215

Brandon = 215 - 74 - 75

Brandon = 66

Adam = 350 - 75 - 75 - 74 - 66

Adam = 60

Therefore, Adam scored 60, Brandon scored 66, Chen scored 74, Damion scored 75, and Erica scored 75.

Answer:

65 degrees

Step-by-step explanation:

Angles in a triangle add to 180°.

Answer:

By the Central Limit Theorem, the mean is 78, the standard deviation is [tex]s = \frac{6}{\sqrt{n}}[/tex] and the shape is approximately normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 78 and a standard deviation of 6

This means that [tex]\mu = 78, \sigma = 6[/tex]

Samples of n:

This means that the standard deviation is:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{n}}[/tex]

What are the mean, standard deviation, and shape of the distribution of x-bar for n?

By the Central Limit Theorem, the mean is 78, the standard deviation is [tex]s = \frac{6}{\sqrt{n}}[/tex] and the shape is approximately normal.

Answer:

The distance between the two towns is of 1000 km.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

We have that:

3 cm represents a distance of 400 km.

What is the distance represented by 7.5 cm?

3 cm - 400 km

7.5 cm - x km

Applying cross multiplication:

[tex]3x = 400*7.5[/tex]

[tex]x = \frac{400*7.5}{3}[/tex]

[tex]x = 1000[/tex]

The distance between the two towns is of 1000 km.

Answer:

57.5

Step-by-step explanation:

The expected frequency of West Campus and Failed :

Let :

Failed = F

East Campus = C

West Campus = W

Passed = P

Frequency of FnW :

[(FnE) + (FnW) * (PnW) + (FnW)] / total samples

[(52 + 63) * (63 + 37)] / 200

[(115 * 100)] / 200

11500 / 200

= 57.5

n(Failed n East campus)

Answer:

57.5

Step-by-step explanation:

Got it right on the test.

Answer:

1/18

Step-by-step explanation:

[tex]\frac{1}{9}[/tex]÷2

make 2 a fraction

[tex]\frac{1}{9}[/tex]÷[tex]\frac{2}{1}[/tex]

cross multiply

1*1

9*2

[tex]\frac{1*1}{9*2}[/tex]

[tex]\frac{1}{18}[/tex]

Answer:

Step-by-step explanation:

You always invert the second number in a division question and then multiply. This one is a little different. It has three levels. What do you do about that?

[tex]\frac{\frac{1}{9} }{\frac{2}{1} }[/tex]

Now you have a four level question which is handled the same way as all four level question.

Invert the bottom and multiply. Invert means turn upside down. So you turn the 2/1 upside down and you get 1/2

[tex]\frac{1}{9}*\frac{1}{2}[/tex]

What you get is 1/18 The green box with the question mark is a 1.

9514 1404 393

Answer:

  7x^3 +11x^2 -5x -8

Step-by-step explanation:

Combine like terms.

  (4x^3+6x^2+2x^2-3) + (3x^3+3x^2-5x-5)

  = (4 +3)x^3 +(6 +2 +3)x^2 +(-5)x + (-3 -5)

  = 7x^3 +11x^2 -5x -8

_____

Noting that the first expression contains two x^2 terms, we wonder if you actually want the sum ...

  (4x^3+6x^2+2x-3) + (3x^3+3x^2-5x-5)

  = (4 +3)x^3 +(6 +3)x^2 +(2 -5)x +(-3 -5)

  = 7x^3 +9x^2 -3x -8

Answer:

[tex]0.4138[/tex]

Step-by-step explanation:

Given

[tex]x \to storm[/tex]

[tex]\mu_x = 1.0[/tex]

[tex]y \to fire[/tex]

[tex]\mu_y = 1.5[/tex]

[tex]z \to theft[/tex]

[tex]\mu_z = 2.4[/tex]

Let the event that the above three factors is greater than 3 be represented as:

[tex]P(A > 3)[/tex]

Using complement rule, we have:

[tex]P(A > 3) = 1 - P(A \le 3)[/tex]

This gives:

[tex]P(A > 3) = 1 - P(\{x \le 3\}\ n\ \{y \le 3\}\ n \{z \le 3\}\)[/tex]

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

The exponential distribution formula of each is:

[tex]P(x \le k) = 1 - e^{-\frac{k}{\mu}}[/tex]

So, we have:

[tex]k = 3; \mu_x = 1[/tex]

[tex]P(x \le 3) = 1 - e^{-\frac{3}{1}} = 1 - e^{-3} = 0.9502[/tex]

[tex]k=3; \mu_y = 1.5[/tex]

[tex]P(y \le 3) = 1 - e^{-\frac{3}{1.5}} = 1 - e^{-2} = 0.8647[/tex]

[tex]k = 3; \mu_z = 2.4[/tex]

[tex]P(z \le 3) = 1 - e^{-\frac{3}{2.4}} = 1 - e^{-1.25} = 0.7135[/tex]

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

[tex]P(A > 3) = 1 - P(\{x \le 3\}\ n\ \{y \le 3\}\ n \{z \le 3\}\)[/tex]

[tex]P(A > 3) = 1 - (0.9502 * 0.8647 *0.7135)[/tex]

[tex]P(A > 3) = 1 - 0.5862[/tex]

[tex]P(A > 3) = 0.4138[/tex]

Answer:

A= πr^2

45=πr^2

45/1 =22/7×r^2

45/1=22r^2/7 cross multiply

22r^2 ×1=45×7

22r^2=315 divide both sides by 22

22r^2/22=315/22

r^2=14.318

Answer:

1 = 100% probability that a person will wait for more than 33 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean waiting time is 55 minutes and the variance of the waiting time is 11.

This means that [tex]\mu = 55, \sigma = \sqrt{11}[/tex]

Find the probability that a person will wait for more than 33 minutes.

This is 1 subtracted by the p-value of Z when X = 33. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33 - 55}{\sqrt{11}}[/tex]

[tex]Z = -6.63[/tex]

[tex]Z = -6.63[/tex] has a p-value of 0.

1 - 0 = 1

1 = 100% probability that a person will wait for more than 33 minutes.

Answer:

34

Step-by-step explanation:

Hypotenuse is the longest side

I hope this helped have a great day

Answer:

take 28 degree as reference angle

using sine angle

sin28=p/h

0.46=10/h

0.46h=10

h=10/0.46

h=21.73

therefore hypotenuse =21.73

again using sine rule

take 25 degree as reference angle

sin 25=p/h

0.42=SR/21.73

0.42*21.73=SR

9.12=SR

9.1=SR

Step-by-step explanation:

Answer:

mu = the population true mean time spent by teenagers playing computer game this year

Step-by-step explanation:

Dear student, there is no much information given to answer this question but we will try as much as possible to explain  (what is the parameter) of the true mean.

In 1990s;

μ = 10.2 hours/week

From the information given,we understand that the parameter is linked to the population, and we're looking for the population average time spent playing computer games by teens in the current situation.

In this situation, the population parameter is the population true mean mu = the population true mean.

Answer:

w = 6ft 8in

Step-by-step explanation:

the proportions will be the same

w/7.5 = 12/13.5

multiply both sides by 7.5

w = 12/13.5 * 7.5

w = 6.6666666667ft

w = 6ft 8in

The original truck was 6.67 feet wide.

"It is a comparison of two or more numbers that indicates their sizes in relation to each other."

"It is an equation in which two ratios are set equal to each other."

For given example,

A model truck is 13.5 inches long 7.5 inches wide.

The ratio of length to width of a model truck would be,

13.5 : 7.5                       ...........................(1)

The original truck was 12 feet long.

This means the original truck was 144 inches long.

Let 'x' be the width (in inches) of the original truck.

So, the ratio of the length to the width of the original truck would be,

144 : x                           .................................(2)

Also, the ratios given by (1) and (2) must be in proportion.

[tex]\Rightarrow \frac{13.5}{7.5} = \frac{144}{x} \\\\\Rightarrow 13.5 \times x = 144 \times 7.5\\\\\Rightarrow \bold{x=80~inches}\\\\\Rightarrow \bold{x=6.67~feet}[/tex]

Therefore, the original truck was 6.67 feet wide.

Learn more about ratio and proportion here:

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Answer:

9

Step-by-step explanation:

0.001 · 9 = 0.009

Answer:

C. y = 8x

Step-by-step explanation:

Using the slope formula, we can calculate the rate of Marisol's and Timothy's Machines.

[tex]m = \frac{y_1-y_2}{x_1-x_2}[/tex]

Marisol:

[tex]m = \frac{18-12}{3-2} \\m=6[/tex]

Timothy:

[tex]m=\frac{54-36}{6-4} \\m=\frac{18}{2} \\m=9[/tex]

Now that we know the rate of their machines, we need to choose a rate that is between 6 and 9. Therefore, the rate of Zorian's machine needs to be y = 8x.

Answer:

geometry

Step-by-step explanation:

left side of paper