100 pts. This is an assignment because multiple people asked this question. Find the sum of the digits of the number 6+66+666+6666 + ... +666...66, where the last number contains 100 digits.

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:

-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

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:

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: x>-1

               x<-3

Step-by-step explanation:

[tex]-2x+3<5[/tex]

subtract 3 on both sides

[tex]-2x<2[/tex]

divide -2 on both sides

[tex]x>-1[/tex]

The sign changed because I divided by a negative.

[tex]-4x-3>9[/tex]

add 3 on both sides

[tex]-4x>12[/tex]

multiply -1 on both sides

[tex]4x<-12[/tex]

divide 4 on both sides

[tex]x<-3[/tex]

Brainlist please

Answer:

x > -1

x < -3

Step-by-step explanation:

-2x + 3 < 5

Subtract 3 on both sides.

-2x < 5 - 3

-2x < 2

Divide -2 into both sides.

x < 2/-2

x > -1

-4x - 3 > 9

Add 3 on both sides.

-4x > 9+3

-4x > 12

Divide -4 into both sides.

x > 12/-4

x < -3

Answer:

For a sample size of n = 609.

Step-by-step explanation:

Central limit theorem for proportions:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

We have that p = 0.58.

We have to find n for which s = 0.02. So

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

[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]

[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]

[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]

[tex]n = 609[/tex]

For a sample size of n = 609.

Answer:

root 61

Step-by-step explanation:

You can use the distance formula or draw a triangle with sides 5 and 6

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:

The home would be worth $249000 during the year of 2012.

Step-by-step explanation:

The price of the home in t years after 2004 can be modeled by the following equation:

[tex]P(t) = P(0)(1+r)^{t}[/tex]

In which P(0) is the price of the house in 2004 and r is the growth rate.

Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.

This means that [tex]r = 0.047[/tex]

$172000 in 2004

This means that [tex]P(0) = 172000[/tex]

What year would the home be worth $ 249000 ?

t years after 2004.

t is found when P(t) = 249000. So

[tex]P(t) = P(0)(1+r)^{t}[/tex]

[tex]249000 = 172000(1.047)^{t}[/tex]

[tex](1.047)^{t} = \frac{249000}{172000}[/tex]

[tex]\log{(1.047)^{t}} = \log{\frac{249000}{172000}}[/tex]

[tex]t\log(1.047) = \log{\frac{249000}{172000}}[/tex]

[tex]t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}[/tex]

[tex]t = 8.05[/tex]

2004 + 8.05 = 2012

The home would be worth $249000 during the year of 2012.

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:

it should look like this

Answer:

50%

Step-by-step explanation:

The chances of getting either heads or tails on a coin is 50/50. Convert that to probability and that is 1/2. Convert it to percentage of 100 and it is 50%.

Only time a coin isn't 50/50 is if the coin itself is a weighted coin.

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:

[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

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:

B

Step-by-step explanation:

right

have a good day, hope this helps

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

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:

Yes

Step-by-step explanation:

functions include parabolas so yes!

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:

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:

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:

$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: 6.5%

Step-by-step explanation:

Interest = Amount repaid - Amount borrowed

= 226 - 200

Interest = 26

Si = ( prt) / 100

26 = (200 x r x 2) / 100

26 = 4r

r = 6.5%

Answer:

the answer is 3

Step-by-step explanation:

i took the test

Answer:

a). 8(x + a)

b). 8(h + 2x)

Step-by-step explanation:

a). Given function is, f(x) = 8x²

    For x = a,

    f(a) = 8a²

    Now substitute these values in the expression,

    [tex]\frac{f(x)-f(a)}{x-a}[/tex] = [tex]\frac{8x^2-8a^2}{x-a}[/tex]

                  = [tex]\frac{8(x^2-a^2)}{(x-a)}[/tex]

                  = [tex]\frac{8(x-a)(x+a)}{(x-a)}[/tex]

                  = 8(x + a)

b). [tex]\frac{f(x+h)-f(x)}{h}[/tex] = [tex]\frac{8(x+h)^2-8x^2}{h}[/tex]

                      = [tex]\frac{8(x^2+h^2+2xh)-8x^2}{h}[/tex]

                      = [tex]\frac{8x^2+8h^2+16xh-8x^2}{h}[/tex]

                      = (8h + 16x)

                      = 8(h + 2x)

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

a) The probability that both adults dine out more than once per week = 0.0253

b) The probability that neither adult dines out more than once per week = 0.7069

c) The probability that at least one of the two adults dines out more than once per week = 0.2931

d) Of the three events described, the event that can be considered unusual because of its low probability of occurring, 0.0253 (2.53%), is the event that the two randomly selected adults both dine out more than once per week.

Step-by-step explanation:

In a sample of 1200 U.S. adults, 191 dine out at a restaurant more than once per week.

Assuming this sample.is a random sample and is representative of the proportion of all U.S. adults, the probability of a randomly picked U.S. adult dining out at a restaurant more than once per week = (191/1200) = 0.1591666667 = 0.1592

Now, assuming this probability per person is independent of each other.

Two adults are picked at random from the entire population of U.S. adults, with no replacement, thereby making sure these two are picked at absolute random.

a) The probability that both adults dine out more than once per week.

Probability that adult A dines out more than once per week = P(A) = 0.1592

Probability that adult B dines out more than once per week = P(B) = 0.1592

Probability that adult A and adult B dine out more than once per week = P(A n B)

= P(A) × P(B) (since the probability for each person is independent of the other person)

= 0.1592 × 0.1592

= 0.02534464 = 0.0253 to 4 d.p.

b) The probability that neither adult dines out more than once per week.

Probability that adult A dines out more than once per week = P(A) = 0.1592

Probability that adult A does NOT dine out more than once per week = P(A') = 1 - P(A) = 1 - 0.1592 = 0.8408

Probability that adult B dines out more than once per week = P(B) = 0.1592

Probability that adult B does NOT dine out more than once per week = P(B') = 1 - P(B) = 1 - 0.1592 = 0.8408

Probability that neither adult dines out more than once per week = P(A' n B')

= P(A') × P(B')

= 0.8408 × 0.8408

= 0.70694464 = 0.7069 to 4 d.p.

c) The probability that at least one of the two adults dines out more than once per week.

Probability that adult A dines out more than once per week = P(A) = 0.1592

Probability that adult A does NOT dine out more than once per week = P(A') = 1 - P(A) = 1 - 0.1592 = 0.8408

Probability that adult B dines out more than once per week = P(B) = 0.1592

Probability that adult B does NOT dine out more than once per week = P(B') = 1 - P(B) = 1 - 0.1592 = 0.8408

The probability that at least one of the two adults dines out more than once per week

= P(A n B') + P(A' n B) + P(A n B)

= [P(A) × P(B')] + [P(A') × P(B)] + [P(A) × P(B)]

= (0.1592 × 0.8408) + (0.8408 × 0.1592) + (0.1592 × 0.1592)

= 0.13385536 + 0.13385536 + 0.02534464

= 0.29305536 = 0.2931 to 4 d.p.

d) Which of the events can be considered unusual? Explain.

The event that can be considered as unusual is the event that has very low probabilities of occurring, probabilities of values less than 5% (0.05).

And of the three events described, the event that can be considered unusual because of its low probability of occurring, 0.0253 (2.53%), is the event that the two randomly selected adults both dine out more than once per week.

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:

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!!!