Ethan's solution and reasoning for solving an equation are shown below: 4/2 x - 10 =30

Answer: 10x^2 - 4x

Step-by-step explanation:

To expand, you are not simplifying, so multiplying out is the answer here. To do this, use the distributive property. The distributive property in this case means that if you are multiplying one number by a whole expression inside parenthesis, multiply the one number by each term in the expression:

2x(5x - 2)

= 2x(5x) + 2x(-2)

= 10x^2 - 4x

The product of the expression is equivalent to -

10x² - 4x.

Given is the expression as follows -

2x(5x - 2)

The given expression is -

2x(5x - 2)

10x² - 4x

Therefore, the product of the expression is equivalent to -

10x² - 4x.

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Answer:

[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]  

The p value for this case can be calculated with this probability:

[tex]p_v =2*P(z<-1.933)=0.0532[/tex]  

For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change

Step-by-step explanation:

Information given

n=340 represent the random sample taken

[tex]\hat p=0.60[/tex] estimated proportion of readers owned a laptop

[tex]p_o=0.65[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v{/tex} represent the p value

Hypothesis to test

We want to check if the true proportion of readers owned a laptop if different from 0.65

Null hypothesis:[tex]p=0.65[/tex]  

Alternative hypothesis:[tex]p \neq 0.65[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:

[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]  

The p value for this case can be calculated with this probability:

[tex]p_v =2*P(z<-1.933)=0.0532[/tex]  

For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change

Answer:

16

Step-by-step explanation:

Please see attached photo for diagrammatic explanation.

Note: r is the radius

Using pythagoras theory, we can obtain the value of 'x' in the attached photo as shown:

|EB|= x

|FB| = 10

|EF| = 6

|EB|² = |FB|² – |EF|²

x² = 10² – 6²

x² = 100 – 36

x² = 64

Take the square root of both side.

x = √64

x = 8

Now, we can obtain line AB as follow:

|AB|= x + x

|AB|= 8 + 8

|AB|= 16

Therefore, line AB is 16

Step-by-step explanation:

positive angle =300+180=480.

negative angle = 300 -180=120

Decreased height = 10 x [tex]\frac{100 - 25}{100}[/tex]

                              = 10 x [tex]\frac{75}{100}[/tex]

                              = [tex]\frac{750}{100}[/tex]

                              = 7.5 cm

Answer:

7.5 cm

Step-by-step explanation:

Decreased height = 25% of 10

                              [tex]=\frac{25}{100}*10\\\\=0.25*10\\=2.5[/tex]

New height = 10 - 2.5 = 7.5 cm

Answer:

[tex]z=-\frac{20}{3}[/tex]

Step-by-step explanation:

[tex]\frac{3z}{10}-4=-6\\\\\frac{3z}{10}-4+4=-6+4\\\\\frac{3z}{10}=-2\\\\\frac{10\cdot \:3z}{10}=10\left(-2\right)\\\\3z=-20\\\\\frac{3z}{3}=\frac{-20}{3}\\\\z=-\frac{20}{3}[/tex]

Best Regards!

Answer:

24.5

Step-by-step explanation:

24 = 24

1/2 -->

convert to a decimal => 1 divided by 2

0.5

24+0.5 = 24.5

Hope this helps!

Answer:

P(B1) = (11/15)

P(B2) = (4/15)

P(A) = (11/15)

P(B1|A) = (5/7)

P(B2|A) = (2/7)

Step-by-step explanation:

There are 11 red chips and 4 blue chips in a box. Two chips are selected one after the other at random and without replacement from the box.

B1 is the event that the chip removed from the box at the first step of the experiment is red.

B2 is the event that the chip removed from the box at the first step of the experiment is blue. A is the event that the chip selected from the box at the second step of the experiment is red.

Note that the probability of an event is the number of elements in that event divided by the Total number of elements in the sample space.

P(E) = n(E) ÷ n(S)

P(B1) = probability that the first chip selected is a red chip = (11/15)

P(B2) = probability that the first chip selected is a blue chip = (4/15)

P(A) = probability that the second chip selected is a red chip

P(A) = P(B1 n A) + P(B2 n A) (Since events B1 and B2 are mutually exclusive)

P(B1 n A) = (11/15) × (10/14) = (11/21)

P(B2 n A) = (4/15) × (11/14) = (22/105)

P(A) = (11/21) + (22/105) = (77/105) = (11/15)

P(B1|A) = probability that the first chip selected is a red chip given that the second chip selected is a red chip

The conditional probability, P(X|Y) is given mathematically as

P(X|Y) = P(X n Y) ÷ P(Y)

So, P(B1|A) = P(B1 n A) ÷ P(A)

P(B1 n A) = (11/15) × (10/14) = (11/21)

P(A) = (11/15)

P(B1|A) = (11/21) ÷ (11/15) = (15/21) = (5/7)

P(B2|A) = probability that the first chip selected is a blue chip given that the second chip selected is a red chip

P(B2|A) = P(B2 n A) ÷ P(A)

P(B2 n A) = (4/15) × (11/14) = (22/105)

P(A) = (11/15)

P(B2|A) = (22/105) ÷ (11/15) = (2/7)

Hope this Helps!!!

Answer:

x = 8

Step-by-step explanation:

Step 1: Write out the expression

x + 2x = 24

Step 2: Combine like terms

3x = 24

Step 3: Isolate x

x = 8

And we have our final answer!

Answer:

X=8

Step-by-step explanation:

Description:

As we that that 3 of the students voted for counting .

4 Students voted for sorting

6 Students voted for shapes

7 Students voted for addition

Answer:

Counting - 3%

Sorting - 4%

Shapes-  6%

Addition-  7%

Please mark brainliest

Hope this helps.

Answer:

Counting: 15%

Sorting: 20%

Shapes: 30%

Addition: 35%

Step-by-step explanation:

Counting: [tex]\frac{3}{3+4+6+7} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%

Sorting: [tex]\frac{4}{3+4+6+7} =\frac{4}{20} =\frac{20}{100} =[/tex] 20%

Shapes: [tex]\frac{6}{3+4+6+7} =\frac{6}{20} =\frac{30}{100} =[/tex] 30%

Addition: [tex]\frac{7}{3+4+6+7} =\frac{7}{20} =\frac{35}{100} =[/tex]35%

Answer:

For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:

Null hypothesis: [tex] p \geq 0.29[/tex]

Alternative hypothesis: [tex]p< 0.29[/tex]

Step-by-step explanation:

For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:

Null hypothesis: [tex] p \geq 0.29[/tex]

Alternative hypothesis: [tex]p< 0.29[/tex]

Answer:

it should look like this

Answer:

[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]      

The degrees of freedom are given by:

[tex]df=n-1=22-1=21[/tex]  

And the p value would be given by:

[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]  

Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given

Step-by-step explanation:

Information given

[tex]\bar X=2045[/tex] represent the sample mean      

[tex]s=13[/tex] represent the standard deviation

[tex]n=22[/tex] sample size      

[tex]\mu_o =2058[/tex] represent the value to test

[tex]\alpha=0.1[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to cehck if the true mean for this case is equal to 2058 or not, the system of hypothesis would be:      

Null hypothesis:[tex]\mu = 2058[/tex]      

Alternative hypothesis:[tex]\mu \neq 2058[/tex]      

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

And replacing we got:

[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]      

The degrees of freedom are given by:

[tex]df=n-1=22-1=21[/tex]  

And the p value would be given by:

[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]  

Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given

Answer:

(A)30

(D)15

Step-by-step explanation:

Factors of 30 are 1,2,3,5,6,10,15 and 30

A composite number is any number that is not prime.

From the given options, the factors of 30 are 30, 5 and 15.

However, 5 is not a composite number.

Therefore, the number that Lacey could be thinking of will either be 30 or 15.

Answer:

The 75th percentile of this distribution is 11 .25 minutes.

Step-by-step explanation:

The random variable X is defined as the waiting time in line at an ice cream shop.

The random  variable X follows a Uniform distribution with parameters a = 3 minutes and b = 14 minutes.

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b;\ a<b[/tex]

The pth percentile is a data value such that at least p% of the data-set is less than or equal to this data value and at least (100-p)% of the data-set are more than or equal to this data value.

Then the 75th percentile of this distribution is:

[tex]P (X < x) = 0.75[/tex]

[tex]\int\limits^{x}_{3} {\frac{1}{14-3}} \, dx=0.75\\\\ \frac{1}{11}\ \cdot\ \int\limits^{x}_{3} {1} \, dx=0.75\\\\\frac{x-3}{11}=0.75\\\\x-3=8.25\\\\x=11.25[/tex]

Thus, the 75th percentile of this distribution is 11 .25 minutes.

Answer:

[tex]2x+2=-50[/tex]

Step-by-step explanation:

[tex]x+2=y\\x+y=-50\\x+x+2=-50\\2x+2=-50[/tex]

The equation that can be used to find out [tex]x[/tex] and [tex]y[/tex] is [tex]2x+2=-50[/tex]

Answer:

[tex]\mathrm{A}[/tex]

Step-by-step explanation:

Two consecutive even integers.

The first integer is even and can be as [tex]x[/tex]

The second integer is also even and can be as [tex]x+2[/tex]

Their sum is [tex]-50[/tex]

[tex]x+x+2=-50[/tex]

[tex]2x+2=-50[/tex]

Answer:

The probability that more than 2 of the sample deliveries arrive late = 0.0115

Step-by-step explanation:

This is a binomial distribution problem

A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.

It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.

The probability of each delivery arriving late = 5% = 0.05

- Each delivery is independent from the other.

- There is a fixed number of deliveries to investigate.

- Each delivery has only two possible outcomes, a success or a failure of arriving late.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of deliveries we're considering = 10

x = Number of successes required = number of deliveries that we expect to arrive late = more than 2 = > 2

p = probability of success = probability of a delivery arriving late = 0.05

q = probability of failure = probability of a delivery NOT arriving late = 0.95

P(X > 2) = 1 - P(X ≤ 2)

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.59873693924 + 0.31512470486 + 0.07463479852

= 0.98849644262

P(X > 2) = 1 - P(X ≤ 2)

= 1 - 0.98849644262

= 0.01150355738

= 0.0115

Hope this Helps!!!

Answer:

2.17609

Step-by-step explanation:

Easiest and fastest way is to just directly plug log base 10 of 150 into the calc, as it is a nasty decimal.

Answer:

The total sales in dollars to make their pay equal is: $ 3800

Step-by-step explanation:

Since we need to find the number of sales that make both function equal in value, we equal both expressions, and solve for 'x":

[tex]180+0.05 \,x=104+0.07 \,x\\180-104=0.07\,x-0.05\,x\\76=0.02x\\x=\frac{76}{0.02} \\x=3800[/tex]

Answer/Step-by-step explanation:

When solving problems like this, remember the following:

1. + × + = +

2. + × - = -

3. - × + = -

4. - × - = +

Let's solve:

a. (-4) + (+10) + (+4) + (-2)

Open the bracket

- 4 + 10 + 4 - 2

= - 4 - 2 + 10 + 4

= - 6 + 14 = 8

b. (+5) + (-8) + (+3) + (-7)

= + 5 - 8 + 3 - 7

= 5 + 3 - 8 - 7

= 8 - 15

= - 7

c. (-19) + (+14) + (+21) + (-23)

= - 19 + 14 + 21 - 23

= - 19 - 23 + 14 + 21

= - 42 + 35

= - 7

d. (+5) - (-10) - (+4)

= + 5 + 10 - 4

= 15 - 4 = 11

e. (-3) - (-3) - (-3)

= - 3 + 3 + 3

= - 3 + 9

= 6

f. (+26) - (-32) - (+15) - (-8)

= 26 + 32 - 15 + 8

= 26 + 32 + 8 - 15

= 66 - 15

= 51

Answer:

$38,645.7208

Step-by-step explanation:

Given that

Principal = $70,000

Time = 20 years

Rate = 2.2%

The calculation of the amount of saving is shown below:-

[tex]=P(1+r)^t[/tex]

A = Future amount

P = Principal amount  

[tex]r = \frac{APR}{12}[/tex]  

[tex]r = \frac{0.022}{12}[/tex]

0.001833333

t = 20 years which is equals to 240 months

[tex]A=\$70,000\times (1+0.001833333)^{240}[/tex]

[tex]A=\$70,000\times 1.552081726[/tex]

= $108,645.7208

And, the loan amount for 20 years is $70,000

So,

He would save by paying off 9 years early is

= $108,645.7208  - $70,000

= $38,645.7208

Its $3644.67  since everyone couldn't find it solved it myself ;)

Answer : The value of x is 4.1 cm.

Step-by-step explanation :

As we know that the perpendicular dropped from the center divides the chord into two equal parts.

That means,

AB = CB = [tex]\frac{15.6cm}{2}=7.8cm[/tex]

Now we have o calculate the value of x by using Pythagoras theorem.

Using Pythagoras theorem in ΔOBA :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](OA)^2=(OB)^2+(BA)^2[/tex]

Now put all the values in the above expression, we get the value of side OB.

[tex](8.8)^2=(x)^2+(7.8)^2[/tex]

[tex]x=\sqrt{(8.8)^2-(7.8)^2}[/tex]

[tex]x=\sqrt{77.44-60.84}[/tex]

[tex]x=\sqrt{16.6}[/tex]

[tex]x=4.074\approx 4.1[/tex]

Therefore, the value of x is 4.1 cm.

Answer:

[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]

Step-by-step explanation:

Given: [tex]2 cos(3x)=0.9[/tex]

To find: solutions of the given equation

Solution:

Triangle is a polygon that has three sides, three angles and three vertices.

Trigonometry explains relationship between the sides and the angles of the triangle.

Use the fact: [tex]cos x=a[/tex]⇒[tex]x=cos^{-1}(a)+2n\pi,x=2\pi-cos^{-1}(a)+2n\pi[/tex]

[tex]2 cos(3x)=0.9[/tex]

Divide both sides by 2

[tex]cos(3x)=\frac{0.9}{2}=0.45[/tex]

[tex]3x=cos^{-1}(0.45)+2n\pi,3x=2\pi- cos^{-1}(0.45)+2n\pi[/tex]

So,

[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]

Answer:

No solutions.

Step-by-step explanation:

9|x-1|=-45

Divide 9 into both sides.

|x-1| = -45/9

|x-1| = -5

Absolute value cannot be less than 0.

Answer:

No solution

Step-by-step explanation:

=> 9|x-1| = -45

Dividing both sides by 9

=> |x-1| = -5

Since, this is less than zero, hence the equation has no solutions

Answer:

-1/4 is the slope and the y intercept is -4

Step-by-step explanation:

Solve for y

x +4y = -16

Subtract x

4y = -x-16

Divide by 4

4y/4 = -x/4 -16/4

y = -1/4 x -4

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

-1/4 is the slope and the y intercept is -4

Answer:

3 wooden plank he can saw

Answer:

he can saw 3 wooden planks

Step-by-step explanation:

Answer:

Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.

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.

In this question, we have that:

[tex]\mu = 100, \sigma = 15[/tex]

If you scored 130, your score would be higher than approximately what percent of adults?

To find the proportion of scores that are lower than, we find the pvalue of Z when X = 130. So

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

[tex]Z = \frac{130 - 100}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

0.9772*100 = 97.72%.

Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.

Answer:

Is possible to make a Type I error, where we reject a true null hypothesis.

Step-by-step explanation:

We have a hypothesis test of a proportion. The claim is that the proportion of paid leave has significantly decrease from 2011 to january 2012. The P-value for this test is 0.0271 and the nunll hypothesis is rejected.

As the conclusion is to reject the null hypothesis, the only error that we may have comitted is rejecting a true null hypothesis.

The null hypothesis would have stated that there is no significant decrease in the proportion of paid leave.

This is a Type I error, where we reject a true null hypothesis.

Answer:

1

Step-by-step explanation:

The mean is the average of the sum of all integers in a data set.

Caroline has 2 pieces of cheese, Samuel has 4 pieces of cheese, Abby has 4 pieces of cheese, and Jason has 2 pieces of cheese

2 + 4 + 4 + 2 = 12

12 divides by 4, since there are 4 people, to equal the mean

12 / 4 = 3

Now since we have the mean, find the distance from the mean to each number

3 - 2 = 1

4 - 3 = 1

4 - 3 = 1

3 - 2 = 1

1 + 1 + 1 + 1 = 4

4 / 4 = 1

Answer:

4/11

Step-by-step explanation:

Total number of marbles = 2(purple) + 4(white) + 3(blue) + 2(green)

                                          = 11

Number of white marbles = 4

Probability of selecting a white marble =

         number of white marbles/total number of marbles in the jar

         = 4/11

The probability of selecting a white marble from a jar of marbles is 4/11.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Purple Marbles = 2

White Marbles = 4

Blue Marbles = 3

Green Marbles = 2

Total marbles= 2+ 4+ 3+ 2= 11

So, the probability of selecting a white marble from a jar of marbles

= 4/11

Hence, the probability is 4/11.

Learn more about probability here:

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