Simplify the following expression. −3√84x3

Answer:

[tex]2\dfrac{11}{12}[/tex]

Step-by-step explanation:

The first step is to ensure that all of the fractions have a common denominator.

[tex]3\dfrac{1}{3}+\left( -2\dfrac{1}{4} \right) + 1\dfrac{5}{6}= \\\\3\dfrac{4}{12} - 2\dfrac{3}{12} +1 \dfrac{10}{12}= \\\\1\dfrac{1}{12}+1\dfrac{10}{12}= \\\\\boxed{2\dfrac{11}{12}}[/tex]

Hope this helps!

Answer:

t = 6.3

Step-by-step explanation:

N=Noe^(-kt)

No = 14 grams

k = .1092

We want to find t when N = 7 or 1/2 of 14

N=Noe^(-kt)

7 = 14 e ^ (-.1092t)

Divide each side by 14

1/2 = e ^ (-.1092t)

take the natural log of each side

ln (1/2) = ln e ^ (-.1092t)

ln (1/2) = -.1092t

Divide each side by -.1092

ln (1/2)/ -.1092 = t

t≈6.3475

Rounding to the nearest tenth

t = 6.3

Answer: 6.3

Step-by-step explanation:

Answer:

24 g

Step-by-step explanation:

We first find the mass of 24 % alcohol in 400 g of hand sanitizer. Let x be the mass of alcohol. So, x/400 × 100 % = 24 %

x/400 = 0.24

x = 0.24 × 400

  = 96 g

The mass of the other chemicals is thus 400 g - 96 g = 304 g

We now find the mass of 30 % alcohol in 400 g of hand sanitizer. Let y be the mass of alcohol. So, y/400 × 100 % = 30 %

y/400 = 0.30

y = 0.30 × 400

  = 120 g

The mass of the other chemicals is thus 400 g - 120 g = 280 g

The mass of other chemicals that needs to be evaporated is thus 304 g - 280 g = 24 g

Answer:

The probability that next year Greenville will receive the following amount of rainfall A) At most 55 inches of rain is 0.7734, B) at least 62 inches of rain is 0.0516, C) Between 46 and 55 inches of rain is 0.0387

D Having rainfall of above 65 inches would be considered as an extremely wet year

Step-by-step explanation:

A. To find the probability that next year Greenville will receive at most 55 inches of rain we would have to make the following calculation:

P(X<55)

=P((X-mean)/s<(55-49)/8)

=P(Z<0.75)

=0.7734

The probability that next year Greenville will receive at most 55 inches of rain is 0.7734

B. To find the probability that next year Greenville will receive at most 62 inches of rain we would have to make the following calculation:

P(X>62)

=P(Z>(62-49)/8)

=P(Z>1.63)

=0.0516

The probability that next year Greenville will receive at most 62 inches of rain is 0.0516

C. To find the probability that next year Greenville will receive at Between 46 and 55 inches of rain we would have to make the following calculation:

P(46<X<54)

=P((46-49)/8 <Z<(54-49)/8)

=P(-0.38 <Z< 0.63)

=0.3837

The probability that next year Greenville will receive Between 46 and 55 inches of rain is 0.3837

D. Here consider a value that is more two standard deviations above the mean as an unusual vale. That is:

X=2σ+μ

=2(8)+49

=65

Therefore, having rainfall of above 65 inches would be considered as an extremely wet year.

Answer:

3 x^2 y^2

Step-by-step explanation:

Simplify the following:

3 x y x y

3 x y x y = 3 x^2 y^2:

Answer: 3 x^2 y^2

Answer:

46

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

8 + 15 + 17 = 40

**Hope this helped!!**

**If I was right then please mark brainliest!!**

Answer:

Step-by-step explanation:

We are given the equation [tex](x+1)^2-4(x+1)+2=0[/tex]. Consider the substitution u = (x+1). Then the equation turns out to be [tex]u^2-4u+2=0[/tex]

Recall that given a second degree polynomial of the form [tex]ax^2+bx+c =0[/tex] then its solutions are given by the expression

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

In our case, a = 1, b = -4 and c =2. Then the solutions are

[tex]u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}[/tex]

[tex]u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}[/tex]

We have that x = u-1. So the original solutions are

[tex]x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}[/tex]

[tex]x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}[/tex]

Answer: x+4

Step-by-step explanation: part one- x+4

Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4

5

Step-by-step explanation:

5 goes into 10 but 2 does not go into 5

Answer:

y=3

Step-by-step explanation:

If we use LCM and take 3 plus y it equals x so if x equals x it is then y

Answer:

D

Step-by-step explanation:

I took the Plato Course

Answer:

1.625 when convert it to 1.6 pounds

Step-by-step explanation:

The given bag of mill shrugged 1. 625 pounds.

1.625 ≈ 1.6 poundest to the nearest tenth.

Frank can build a fence in twice the time it would take Sandy. Working together, they can build it in 7 hours. How long will it take each of them to do it alone?

Answer

If Frank and Sandy can build the fence in 7 hours, they must be building

1

7

of the fence every hour.

Now, let the amount of time it takes Sandy be

x

hours so that Frank takes

2

x

hours. Sandy can build

1

x

of the fence every hour and Frank can build

1

2

x

of the fence every hour.

We now have the following equation to solve.

1

x

+

1

2

x

=

1

7

2

+

1

2

x

=

1

7

21

=

2

x

x

=

21

2

=

10.50

Thus, Sandy takes

10.50

hours and Frank takes

21

hours.

Answer:

47.85

Step-by-step explanation:

33% of 145

of means multiply

Changing to decimal form

.33* 145

47.85

Step-by-step explanation:

cross multiply, set up ur equation like so

33. x

100 = 145

100x=4785

100

x=47.85

Answer:

B) 0.0069

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]

Find the probability that their mean rebuild time exceeds 9.1 hours.

This is 1 subtracted by the pvalue of Z when X = 9.1. So

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

By the Central Limit Theorem

[tex]Z = \frac{9.1 - 8.4}{0.2846}[/tex]

[tex]Z = 2.46[/tex]

[tex]Z = 2.46[/tex] has a pvalue of 0.9931

1 - 0.9931 = 0.0069

So the answer is B.

Answer: student tickets = 208

Adult tickets = 97

Step-by-step explanation:

x + y = 305

x = 305 - y

5x + y = 693

Substituting

5 (305 - y) + y = 693

1525 - 5y + y = 693

-4y = -832

y = 832 / 4 = 208

Answer:

It would be 131.95 if they want the answer in pi it would be 42 pi

Step-by-step explanation:

Answer:

a) 11.03% probability that exactly two are red.

b) 98.64% probability that at most 2 are red.

Step-by-step explanation:

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

In this question, the order in which the skittles are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

[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]

In this question:

12 + 10 + 8 + 9 + 22 = 61 skittles.

A). exactly 2 are red

Desired outcomes:

2 red, from a set of 8.

3 non-red, from a set of 61 - 8 = 53.

So

[tex]D = C_{8,2}*C_{53,3} = \frac{8!}{2!(8-2)!}*\frac{53!}{3!(53-3)!} = 655928[/tex]

Total outcomes:

Five skittles from a set of 61. So

[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{655928}{5949147} = 0.1103[/tex]

11.03% probability that exactly two are red.

B). At most 2 are red

Desired outcomes:

None red(5 from a set of 53)...

One red(from a set of 8), and four non-read(4 from a set of 53).

Two red(655928), as found in a.

So

[tex]D = C_{53,5} + C_{8,1}*C_{53,4} + 655928 = \frac{53!}{5!48!} + \frac{8!}{1!7!}*\frac{53!}{4!49!} + 655928 = 5868213[/tex]

Total outcomes:

Five skittles from a set of 61. So

[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{5868213}{5949147} = 0.9864[/tex]

98.64% probability that at most 2 are red.

Answer:

Step-by-step explanation:

To check which option is correct we will first make transition matrix.

Let the state 1 and state 2 represent the automobile and light rail

So, the transition is given by

[tex]P=\left[\begin{array}{ccc}0.80+0.05&0.15\\0.5+0.15&0.80\end{array}\right][/tex]

[tex]P=\left[\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right][/tex]

Since P as no any entry zero so, P as not absorbing stochastic matrix

Also,

[tex]|P| = \left|\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right| \\\\=0.85\times0.8-0.15\times0.2\\\\=0.65\neq0[/tex]

since |P| ≠ 0

Answer:

Step-by-step explanation:

The data is incorrect. The correct data is:

Deluxe standard

39 27

39 28

45 35

38 30

40 30

39 34

35 29

Solution:

Deluxe standard difference

39 27 12

39 28 11

45 35 10

38 30 8

40 30 10

39 34 5

35 29 6

a) The mean difference between the selling prices of both models is

xd = (12 + 11 + 10 + 8 + 10 + 5 + 6)/7 = 8.86

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

n = 7

Summation(x - mean)² = (12 - 8.86)^2 + (11 - 8.86)^2 + (10 - 8.86)^2 + (8 - 8.86)^2 + (10 - 8.86)^2 + (5 - 8.86)^2 + (6 - 8.86)^2 = 40.8572

Standard deviation = √(40.8572/7

sd = 2.42

For the null hypothesis

H0: μd = 10

For the alternative hypothesis

H1: μd ≠ 10

This is a two tailed test.

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 7 - 1 = 6

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (8.86 - 10)/(2.42/√7)

t = - 1.25

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

p = 0.26

Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis.

b) Confidence interval is expressed as

Mean difference ± margin of error

Mean difference = 8.86

Margin of error = z × s/√n

z is the test score for the 95% confidence level and it is determined from the t distribution table.

df = 7 - 1 = 6

From the table, test score = 2.447

Margin of error = 2.447 × 2.42/√7 = 2.24

Confidence interval is 8.86 ± 2.24

Answer:

  81

Step-by-step explanation:

2-digit squares are 16, 25, 36, 49, 64, 81.

Their sums of digits, are ...

  7, 7, 9, 13, 10, 9

The square 81 has a sum of digits equal to its square root.

Answer:

[tex]4a^3(5a^3-11)[/tex]

Step-by-step explanation:

→Take out the GCF (Greatest Common Factor). The GCF is [tex]4a^3[/tex] because both [tex]-44a^3[/tex] and [tex]20a^6[/tex] can be divided by it, like so:

[tex]-44a^3+20a^6[/tex]

[tex]4a^3(5a^3-11)[/tex]

Answer:

14.69% of men are SHORTER than 67 inches

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches.

This means that [tex]\mu = 69.8, \sigma = 2.67[/tex]

What percentage of men are SHORTER than 67 inches

This is the pvalue of Z when X = 67. So

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

[tex]Z = \frac{67 - 69.8}{2.67}[/tex]

[tex]Z = -1.05[/tex]

[tex]Z = -1.05[/tex] has a pvalue of 0.1469

14.69% of men are SHORTER than 67 inches

Answer:

0.1069 = 10.69%

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 45, \sigma = 10[/tex]

Between 57 and 69

This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So

X = 69

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

[tex]Z = \frac{69 - 45}{10}[/tex]

[tex]Z = 2.4[/tex]

[tex]Z = 2.4[/tex] has a pvalue of 0.9918

X = 57

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

[tex]Z = \frac{57 - 45}{10}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a pvalue of 0.8849

0.9918 - 0.8849 = 0.1069 = 10.69%

Answer:

7 3/10

Step-by-step explanation:

7.3=7+0.3= 7+ 3/10= 7 3/10

Answer:

165 different teams of 3 students can be formed for competitions

Step-by-step explanation:

Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:

That is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.

To calculate the number of combinations, the following expression is applied:

[tex]C=\frac{m!}{n!*(m-n)!}[/tex]

It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.

In this case:

Replacing:

[tex]C=\frac{11!}{3!*(11-3)!}[/tex]

Solving:

[tex]C=\frac{11!}{3!*8!}[/tex]

being:

So:

[tex]C=\frac{39,916,800}{6*40,320}[/tex]

C= 165

165 different teams of 3 students can be formed for competitions

Answer:

There will be 3 teams of 3 students, and one team of 2 students, so there will be 4 teams with one team one student short, but only 3 teams that can hold 3 students

Answer:

h=7.65

Step-by-step explanation:

H is directly proportional to the square root of p;

Let k be the constant of proportionality;

Means h=k√p

This means for corresponding points of h and p such that (h1,p1) and (h2,p2) we have;

h1/√p1=h2/√p2

Let h= 5.4 when p = 1.44 and h when p =2.89 be respectively (h1,p1) and (h2,p2)

So that

5.4/√1.44=h/√2.89

5.4/√1.44 ×√2.89 = h

7.65= h

h=7.65

Answer:

21.6m

Step-by-step explanation:

Brian throws a ball from point 'a'

The ball travels a distance of:

The ball travels a total distance of 0.6m + 1.2m + 1.8m + 2.4m + 3.0m + 3.6m + 4.2m + 4.8m = 21.6m from point 'a' to point 'b'.

Answer:

100

Step-by-step explanation:

40 / 100= .4

.4 x 45 = 18

18/18= 1

1x 100= 100

Answer:

100

Step-by-step explanation:

:D

Answer:

a) 0.505,0.995

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 12, \pi = \frac{9}{12} = 0.75[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.505[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.995[/tex]

So the correct answer is:

a) 0.505,0.995

Answer:

I). X= 1,0. II) 1.72

Step-by-step explanation:

Using quadratic formula

Answer:

Step-by-step explanation:

Hello!

There was a special program funded, designed to reduce crime in 8 areas of Miami.

The number of crimes per area was recorded before and after the program was established in each area. This is an example of a paired data situation. For each are in Miami you have recorded a pair of values:

X₁: Number of crimes recorded in one of the eight areas of Miami before applying the special program.

X₂: Number of crimes recorded in one of the eight areas of Miami after applying the special program.

Area: (Before; After)

A: (14; 2)

B: (7; 7)

C; (4; 3)

D: (5; 6)

E: (17; 8)

F: (12; 13)

G: (8; 3)

H; (9; 5)

To apply a paired sample test you have to define the variable "difference":

Xd= X₁ - X₂

I'll define it as the difference between the crime rate before the program and after the program.

If the original populations have a normal distribution, we can assume that the  variable defined from them will also have a normal distribution.

Xd~N(μd; σd²)

If the crime rate decreased after the special program started, you'd expect the population mean of the difference between the crime rates before and after the program started to be less than zero, symbolically μd<0

The hypotheses are:

H₀: μd≥0

H₁: μd<0

α: 0.01

[tex]t= \frac{X[bar]_d-Mu_d}{\frac{S_d}{\sqrt{n} } } ~~t_{n-1}[/tex]

To calculate the sample mean and standard deviation of the variable difference, you have to calculate the difference between each value of each pair:

A= 14 - 2= 12

B= 7 - 7= 0

C= 4 - 3= 1

D= 5 - 6= -1

E= 17 - 8= 9

F= 12 - 13= -1

G= 8 - 3= 5

H= 9 - 5= 4

∑Xdi= 12 + 0 + 1 + (-1) + 9 + (-1) + 5 + 4= 29

∑Xdi²= 12²+0²+1²+1²+9²+1²+5²4²= 269

X[bar]d= 29/8= 3.625= 3.63

[tex]S_d=\sqrt{\frac{1}{n-1}[sumX_d^2-\frac{(sumX_d)^2}{n} ] } = \sqrt{\frac{1}{7}[269-\frac{29^2}{8} ] } = 4.84[/tex]

[tex]t_{H_0}= \frac{3.63-0}{\frac{4.86}{\sqrt{8} } } = 2.11[/tex]

This test is one-tailed to the left and so is the p-value, under a t with n-1= 8-1=7 degrees of freedom, the probability of obtaining a value as extreme as the calculated value is:

P(t₇≤-2.11)= 0.0364

The p-value is greater than the significance level, so the decision is to not reject the null hypothesis. Then at a 1% significance level, you can conclude that the special program didn't reduce the crime rate in the 8 designated areas of Miami.

I hope it helps!

Using the t-distribution, it is found that since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.

At the null hypothesis, it is tested if there has been no reduction, that is, the subtraction of the mean after by the mean before is at least 0, hence:

[tex]H_0: \mu_A - \mu_B \geq 0[/tex]

At the alternative hypothesis, it is tested if there has been a reduction, that is, the subtraction of the mean after by the mean before is negative, hence:

[tex]H_1: \mu_A - \mu_B < 0[/tex]

For both before and after, the mean, standard deviation of the sample(this is why the t-distribution is used) and sample sizes are given by:

[tex]\mu_B = 9.5, s_B = 4.504, n_B = 8[/tex]

[tex]\mu_A = 5.875, s_A = 3.5632, n_A = 8[/tex]

The standard errors are given by:

[tex]s_A = \frac{3.5632}{\sqrt{8}} = 1.2596[/tex]

[tex]s_B = \frac{4.504}{\sqrt{8}} = 1.5924[/tex]

For the distribution of differences, the mean and standard error are given by:

[tex]\overline{x} = \mu_A - \mu_B = 5.875 - 9.5 = -3.625[/tex]

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{1.2596^2 + 1.5924^2} = 2.0304[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

Hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{-3.625 - 0}{2.0304}[/tex]

[tex]t = -1.7854[/tex]

The p-value is found using a t-distribution calculator, with t = -1.7854, 8 + 8 - 2 = 14 df and a left-tailed test with a significance level of 0.01, as we are tested if the mean is less than a value.

Since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.

You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/13873630