What is the probability of rolling a sum of 5 on at least one of two rolls of a pair of number cubes?

Answer:

y=-2x-12

Step-by-step explanation:

Make the equation into slope intercept form

-2y=-4x-12

divide by -2

y=2x+6

since the line is parallel the slope is the same

y=2x+b

plug in (4,-4)

-4=8+b

b=-12

y=-2x-12

The correct anwer is False

Explanation

According to the graph, it can be seen that a student has four hours of sleep as the minimum number of hours of sleep; two students have six hours of sleep, four students have six and a half hours of sleep, four have seven hours of sleep, three have seven and a half hours of sleep, five have eight hours of sleep, and one has eight and a half hours of sleep as maximum hours of sleep. Therefore, it can be affirmed that the statement that the difference between the maximum amount and the minimum number of hours is two and a half hours is false because between four hours and eight and a half hours there are four and a half hours of difference. So, the correct answer is False.

180º = π rad

So

(17π/18 rad) * (180/π º/rad) = (17π * 180)/(18 * π) º = 170º

Answer:

(1): -4.7 - 2.3x + 0.5 - 4x

(2):-5.3x-4.2-x

(3):-3.4-6.3x-0.8

Step-by-step explanation:

By Collecting like terms and adding the answer I get -6.3x - 4.2

(1):-4.7-2.3x+0.5-4x

Collect like terms

-2.3x-4x-4.7+0.5

-6.3x-4.2

(2):-5.3x-4.2-x

Collect like terms

-5.3x-x-4.2

-6.3x-4.2

(3): -3.4-6.3x-0.8

Collect like terms

-6.3x-3.4-0.8

-6.3x-4.2

Answer:

The first 3 are equivalent the last 3 aren't.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I’m rusty with my math, so I’m not 100% sure this is correct. My best attempt.

(1,-5) & (3,-17)

1=1x, -5=1y, 3=2x, -17=2y

Formula is y2-y1/x2-x1

-17 - -5 = -12

3 - 1 =2

So -12/2 = -6

Formula for the line is

y-y1 = m (x-x1)

In this equation m=-6

Y - -5 = -6 ( x - 1 )

Answer:C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

D. 625

Step-by-step explanation:

If the side length for each block is 2 1/2 then two blocks together make 5 so 4 blocks going up makes the height 10 and two blocks for the width make 5 and the 5 blocks on the bottom going across for length make 12 1/2 and 5*10*12 1/2= 625

Answer:

12.12%

Step-by-step explanation:

We have that the formula is given by:

A = p * e ^ (r * t)

From here, we know that A = 200000; p = 20000 and the time we can calculate 40 - 21 = 19

if we replace we have:

200000 = 20000 * e ^ (19 * r)

we must calculate r:

e ^ (19 * r) = 200000/20000

e ^ (19 * r) = 10

19 * r = ln 10

r = ln 10/19

r = 0.1212

In other words, the rate of growth is 12.12%

Answer:

12.1%

Step-by-step explanation:

Answer:

[tex]8.182X10^8 $pounds[/tex]

a=8.182 and b=8

Step-by-step explanation:

Weight of the Empire State Building =[tex]7.3X 10^8[/tex] pounds.

Weight of the One World Trade Center building= 88,200,000 pounds.

=[tex]8.82 X 10^7[/tex]

The addition of the two:

[tex]=7.3X 10^8+8.82 X 10^7\\$To make it easier to add, express both as powers of 8\\=7.3X 10^8+0.882 X 10^8\\=(7.3+0.882)X10^8\\=8.182X10^8 $ pounds[/tex]

Comparing with the form: [tex]aX10^b[/tex]

a=8.182 and b=8

Answer:

m= 0/-2

Step-by-step explanation:

The mixed number will be 13 3/4.

Answer:

48

Step-by-step explanation: 4x8=32 2x8=16 32+16=48 :)

Answer:

58.79 mL of juice

Step-by-step explanation:

To do this, let's gather the data first:

In 1 cup of orange juice we have 500 mg of potassium. A patient weights 135 lb, and he needs to take care of it's potassium intake and not exceed 2 mg of K / kg per day.

So obviously he cannot drink a whole cup of orange juice. It has to be less. In order to know this, we need to know first the weight in kg. 1 lb equals 0.4536 kg so in 135 lb:

W = 135 lb * 0.4536 kg/lb = 61.24 kg

Now, we need to know with this weight, how much potassium it can takes:

Intake = 61.24 kg * 2 mg/kg = 122.48 mg of K

So, the maximum amount of potassium per day is 122.48 mg. This means that the quantity of orange juice this person can take is:

Juice = 122.48 mg * 240 mL / 500 mg

Juice = 58.79 mL of juice or simply 59 mL

Answer:

Let's work out the intercepted points:

-4x + 8 = -3x^2 + 5x + 2

<=>

3x^2 - 9x + 6 = 0

<=>

x^2 - 3x + 2 = 0

<=>

(x - 1)(x - 2) = 0

<=>  

x = 1 => y = -4 x 1 + 8 = 4 => A(1, 4)

and

x = 2=> y = -4 x 2 + 8 = 0 =>B(2, 0)

Then, length of chord AB is calculated by:

L = sqrt [(2 - 1)^2 + (0 - 4)^2)] = ~4.123

Answer:

c

Step-by-step explanation:

You can either try each answer on the table above, or find the slope then find the function/equation.

c-y1=s(n-x1)

(x1,y1) being any pair from the table and s being the slope.

Answer:

x = -9

Step-by-step explanation:

18 ÷ x = -2

18/x = -2/1

Cross multiplying, we get

-2x = 18

x = 18/-2

x = -9

hope it helps!

Answer:

A dice of six faces has 5 numbers bigger than 1 (from 2 to 6).

Then, the number Peter is expecting is : 114 x (5/6) = 95 (times)

Hope this helps!

:)

Answer: 8 gallons of water.

Step-by-step explanation:

3 x 4 x 5 = 60.

60 divided by the number of gallons per cubic foot 7.5 = 8 gallons. :)

Answer: 2r(0)/3.

Step-by-step explanation:

So, we are given one Important data or o or parameter in the question above and that is the function of the form which is given below(that is);

S(r) = (r0 - r) ar^2 -----------------------------(1).

We will now have to differentiate S(r) with respect to r, so, check below for the differentiation:

dS/dr = 2ar (r0 - r ) + ar^2 (-1 ) ---------;(2).

dS/dr = 2ar(r0) - 2ar^2 - ar^2.

dS/dr = - 3ar^2 + 2ar(r0) ------------------(3).

Note that dS/dr = 0.

Hence, - 3ar^2 + 2ar(r0) = 0.

Making ra the subject of the formula we have;

ra[ - 3r + 2r(0) ] = 0. -------------------------(4).

Hence, r = 0 and r = 2r(0) / 3.

If we take the second derivative of S(r) too, we will have;

d^2S/dr = -6ar + 2ar(0). -------------------(5).

+ 2ar(0) > 0 for r = 0; and r = 2r(0)/3 which is the greatest.

Answer:

[tex]r =\frac{2r_{0}}{3}[/tex]

Step-by-step explanation:

We need to take the derivative of S(r) and equal to zero to maximize the function. In this conditions we will find the radius r for which the speed of the air is greatest.

Let's take the derivative:

[tex]\frac{dS}{dr}=a(2r(r_{0}-r)+r^{2}(-1))[/tex]

[tex]\frac{dS}{dr}=a(2r*r_{0}-2r^{2}-r^{2})[/tex]

[tex]\frac{dS}{dr}=a(2r*r_{0}-3r^{2})[/tex]

[tex]\frac{dS}{dr}=ar(2r_{0}-3r)[/tex]

Let's equal it to zero, to maximize S.

[tex]0=ar(2r_{0}-3r)[/tex]

We will have two solutions:

[tex]r = 0[/tex]

[tex]r =\frac{2r_{0}}{3}[/tex]

Therefore the value of r for which the speed of the air is greatest is [tex]r =\frac{2r_{0}}{3}[/tex].

I hope it helps you!

Answer:

It would take 74.5 minutes for the element to decay 17 grams.

Step-by-step explanation:

The amount of element X after t minutes is given by the follwoing equation:

[tex]X(t) = X(0)e^{rt}[/tex]

In which X(0) is the initial amount of the substance and r is the decay rate.

Half life of 14 minutes.

This means that [tex]X(14) = 0.5X(0)[/tex]

So

[tex]X(t) = X(0)e^{rt}[/tex]

[tex]0.5X(0) = X(0)e^{14r}[/tex]

[tex]e^{14r} = 0.5[/tex]

[tex]\ln{e^{14r}} = \ln{0.5}[/tex]

[tex]14r = \ln{0.5}[/tex]

[tex]r = \frac{\ln{0.5}}{14}[/tex]

[tex]r = -0.0495[/tex]

So

[tex]X(t) = X(0)e^{-0.0495t}[/tex]

There are 680 grams of element X

This means that [tex]X(0) = 680[/tex]

[tex]X(t) = X(0)e^{-0.0495t}[/tex]

[tex]X(t) = 680e^{-0.0495t}[/tex]

How long would it take the element to decay 17 grams

This is t for which X(t) = 17. So

[tex]X(t) = 680e^{-0.0495t}[/tex]

[tex]17 = 680e^{-0.0495t}[/tex]

[tex]e^{-0.0495t} = \frac{17}{680}[/tex]

[tex]e^{-0.0495t} = 0.025[/tex]

[tex]\ln{e^{-0.0495t}} = \ln{0.025}[/tex]

[tex]-0.0495t = \ln{0.025}[/tex]

[tex]0.0495t = -\ln{0.025}[/tex]

[tex]t = -\frac{\ln{0.025}}{0.0495}[/tex]

[tex]t = 74.5[/tex]

It would take 74.5 minutes for the element to decay 17 grams.

A.Equation

Step-by-step explanation:

A. Equation 30 plus 4

Answer:

40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Here are the rules;

• If the number undergoing the rounding is followed by 5, 6, 7, 8, or 9, round the number up

• If the number undergoing the rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Example: 32 and 38 rounded to the nearest ten is 30 and 40 respectively.

Answer:

Step-by-step explanation:

m is the dependent variable; it represents the value of a linear function of k:

m = f(k) = k + 3

Answer:

  $134.49

Step-by-step explanation:

Multiply the rate by the salary:

  7.65% × $1758 = $134.49

Tyler's employer should deduct $134.49.

Answer:

44 boxes

Step-by-step explanation:

778/18 = 43.222

round up cause you cant sell 2/10 of a box

Answer:

7 9/10

Step-by-step explanation:

Answer:

D. Observational Study

Explanation:

An observational  study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.  

This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study  is subject to bias because a positive or negative result might be because of other factors not related to the study.

Answer:

We conclude that the true average estimated calorie content in the population sampled exceeds the actual content.

Step-by-step explanation:

We are given that an article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories.

The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88.

Let [tex]\mu[/tex] = true average estimated calorie content in the population sampled.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 153 calories     {means that the true average estimated calorie content in the population sampled does not exceeds the actual content}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 153 calories     {means that the true average estimated calorie content in the population sampled exceeds the actual content}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                             T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean estimated calorie level = 193 calories

            s = sample standard deviation = 88

            n = sample of individuals = 58

So, the test statistics  =  [tex]\frac{193-153}{\frac{88}{\sqrt{58} } }[/tex]  ~ [tex]t_5_7[/tex]

                                       =  3.462

The value of t test statistics is 3.462.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical value of 1.6725 at 57 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 3.462 > 1.6725, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true average estimated calorie content in the population sampled exceeds the actual content.

Answer:

Step-by-step explanation:

1) The confidence interval is calculated as the following

[tex]CI = ( \bar x-1.96 \sigma ,\bar x=1.96 \sigmam)[/tex]

[tex]= (0.412-1.96 \times 0.094, 0.412 = 1.96 \times 0.094)\\\\= (0.22776, 0.59624)[/tex]

Hence, the confidence interval is [tex]0.22776 \leq \beta_G_P_A \leq 0.59624)[/tex]

11) Under two sid t-tailed test, the null hypothesis

[tex]H_0; \beta_{GPA}=0.4[/tex]

Against the alternative hypothesis

[tex]H_1 ; \beta _{GPA} \neq 0.4[/tex]

Under null hypothesis

[tex]t = \frac{\hat \beta _1 - \beta _1}{Se( \beta _1)} \\\\ =\frac{0.412-0.4}{0.094} \\\\=0.12766[/tex]

The degree of freedom is n - 1 = 140

From the t - table at 5% level of significance under two - tail is 1.96

Since , calculated value is lowe than the tabulated value, we do not reject the null hypothesis.

Answer: 220

Step-by-step explanation:

When we wanto to create a group of K elements for a set of N elements (where the order of the K elements does not matter, so we do not considerate the permutations of the K elements), the number of possible combinations is:

[tex]C = \frac{N!}{(N - K)!*K!}[/tex]

Here N = 12 and K = 3

[tex]C = \frac{12!}{9!*3!} = \frac{12*11*10}{3*2} = 220[/tex]

So there are 220 possible combinations

Answer:

220

Step-by-step explanation: