What is the difference written in scientific notation?

Answer:

[tex]x=\frac{5}{7}[/tex]

Step-by-step explanation:

[tex]3x - 2 = 3 - 4x[/tex]

Add [tex]2[/tex] and [tex]4x[/tex] on both sides of the equation.

[tex]3x - 2 +2+4x= 3 - 4x+2+4x[/tex]

[tex]3x+4x=-4x+5+4x[/tex]

[tex]7x=5[/tex]

Divide [tex]7[/tex] on both sides of the equation.

[tex]\frac{7x}{7}=\frac{5}{7}[/tex]

[tex]x=\frac{5}{7}[/tex]

Answer:

LIFE: Your life purpose consists of the central motivating aims of your life—the reasons you get up in the morning. Purpose can guide life decisions, influence behavior, shape goals, offer a sense of direction, and create meaning. For some people, purpose is connected to vocation—meaningful, satisfying work. Also always be your self (:

Corona: I think corona depending on were you live will stop next year when they find a treatment for it.

Hope this helped!

Answer:

Your life is the most important thing. It shouldn't be worth 1 million dollars, or even 1 billion dollars, because it's worth everything.  

Corona can't really stop. It's a matter of the government to try to contain the virus, so it won't spread even further. I think the right time to reopen the economy is when we find a vaccine. But of course, places all over the U.S. are already reopening which will cause a spike in cases, therefore making our "self-isolation" even longer.

Answer:

260 stickers

Step-by-step explanation:

Let Gareth's stickers be x.

Hence Cheryl sticker is 160+x;

If Cheryl gave 185 stickers

to Gareth, it means:

Cheryl has at the moment;

160 + x - 185 = x - 25

At this time when Gareth receives 185 he now has:

x+ 185

Also when he receives x +185, he has 3 times Cherry's meaning:

x+185 =3(x-25)

x + 185 = 3x -75

185 + 75 = 3x-2x

260= x

x = 260.

Hence Gareth has 260 stickers

Answer:

113 feet

Step-by-step explanation:

Use the ratio 1:50 to calculate the height of the tower.

The scale model height is 2.25 feet, so multiply that by 50

2.25 x 50 = 112.5

Round to 113 feet

Answer:

D. 113 feet

Step-by-step explanation:

We know that Josephine made a smaller model that is one-fiftieth the size of the real model. That means the height of the real model is fifty times as big as this model. All we need to do to find the height of the real thing is to multiply 50 and 2.25. (50) 2.25 = 112.5. That will round to 113 feet, which is the height of the new water tower.

Hope this helps ^-^

Answer:

1/4

Step-by-step explanation:

Flip a fair two sided coin 4 times, the probability the first or last flip is a tail is

P = (1/2) x 1 x 1 x (1/2) = 1/4

(The probability of getting tail in first flip = 1/2, in the 2nd and 3rd flip, tail and head are both accepted, the probability of getting tail in last flip = 1/2)

Hope this helps!

Answer:

Step-by-step explanation:

A=πr^2

But A=88/63

88/63=πr^2

88/63π=r^2

√88/63π=r

Answer:

1

Step-by-step explanation:

x^2−2x=3

Take the coefficient of x

-2

Divide by 2

-2/2 =-1

Square it

(-1)^2 = 1

Add this to each side

Answer:

$8.5

Step-by-step explanation:

We need to propose a system of equations with the information provided to us.

two large pizzas and one small pizza cost $36:

[tex]2L+S=36[/tex]

where

[tex]L[/tex]: Large pizza

[tex]S:[/tex] Small pizza

and the difference in cost between a large and small pizza is $5.25:

[tex]L-S=5.25[/tex]

our system of equations is:

[tex]2L+S=36[/tex]

[tex]L-S=5.25[/tex]

We are asked for the price of small pizza, so we must manipulate the equations in such a way that adding or subtracting them removes the variable L and we are left with an equation for S.

Multiply the second equation of the system by -2

[tex](-2)(L-S=5.25)\\\\-2L+2S=-10.5[/tex]

and now we sum this with the first equation of the system:

[tex]-2L+2S=-10.5\\+(2L+S=36)\\-------------\\-2L+2L+2S+S=-10.5+36[/tex]

simplifying the result:

[tex]3S=25.5[/tex]

and solving for S (the price of a small pizza)

[tex]S=25.5/3\\S=8.5[/tex]

Answer:

Step-by-step explanation:

2(f^4)^2/8(f^12)

2/8= 1/4

f^16/f^12

f^(16-12)= f^4

f^4/4 is the solution

Answer:

The more extreme height was the case for the shortest living man at that time (12.1017 standard deviation units below the population's mean) compare with the tallest living man (at that time) that was 9.3374 standard deviation units above the population's mean.

Step-by-step explanation:

To answer this question, we need to use standardized values, and we can obtain them using the formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]  

Where

A z-score "tells us" the distance from [tex] \\ \mu[/tex] in standard deviation units, and a positive value indicates that the raw score is above the mean and a negative that the raw score is below the mean.

In a normal distribution, the more extreme values are those with bigger z-scores, above and below the mean. We also need to remember that the normal distribution is symmetrical.

Heights of men at that time had:

Let us see the z-score for each case:

Case 1: The tallest living man at that time

The tallest man had a height of 252 cm.

Using [1], we have (without using units):

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ z = \frac{252 - 176.74}{8.06}[/tex]

[tex] \\ z = \frac{75.26}{8.06}[/tex]

[tex] \\ z = 9.3374[/tex]  

That is, the tallest living man was 9.3374 standard deviation units above the population's mean.

Case 2: The shortest living man at that time

The shortest man had a height of 79.2 cm.

Following the same procedure as before, we have:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ z = \frac{79.2 - 176.74}{8.06}[/tex]

[tex] \\ z = \frac{-97.54}{8.06}[/tex]

[tex] \\ z = -12.1017[/tex]

That is, the shortest living man was 12.1017 standard deviation units below the population's mean (because of the negative value for the standardized value.)

The normal distribution is symmetrical (as we previously told). The height for the shortest man was at the other extreme of the normal distribution in [tex] \\ 12.1017 - 9.3374 = 2.7643[/tex] standard deviation units more than the tallest man.

Then, the more extreme height was the case for the shortest living man (12.1017 standard deviation units below the population's mean) compare with the tallest man that was 9.3374 standard deviation units above the population's mean.

Answer:

Distance between 2 boats= 5.86m (3 s.f.)

Actual distance from farther boat from top of cliff= 16m

Step-by-step explanation:

Please see the attached pictures for full solution.

Answer:

c.(x+1)^2=10

Step-by-step explanation:

Completing the square:

We use the following relation:

[tex](x + a)^{2} = x^{2} + 2ax + a^{2}[/tex]

In this question:

[tex](x + a)^{2} = x^{2} + 2ax + a^{2} = x^{2} + 2x + a^{2}[/tex]

We have to find a.

[tex]2a = 2[/tex]

[tex]a = \frac{2}{2}[/tex]

[tex]a = 1[/tex]

[tex]x^{2} + 2x + 1 = (x+1)^{2}[/tex]

Thus, we have to add 1 on the right side of the equality.

We end up with:

[tex](x+1)^{2} = 9 + 1[/tex]

[tex](x+1)^{2} = 10[/tex]

So the correct answer is:

c.(x+1)^2=10

Answer:

= ( $72.756, $110.804)

Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)

Critical value at 90% confidence = 1.645

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $91.78

Standard deviation r = $23.13

Number of samples n = 4

Confidence interval = 90%

Using the z table;

z(α=0.05) = 1.645

Critical value at 90% confidence = 1.645

Substituting the values we have;

$91.78+/-1.645($23.13/√4)

$91.78+/-1.645($11.565)

$91.78+/-$19.024425

$91.78+/-$19.024

= ( $72.756, $110.804)

Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)

Answer:

Dear User,

Answer to your query is provided below

(i) Total Loss = Rs.15

(ii) Loss percent = 5%

Step-by-step explanation:

Eggs purchased = 5x12 = 60

Total Cost = 60x5 = Rs 300

Eggs Broken = 10

Eggs Broken cost = 10x5= Rs. 50

Eggs sold = 60-10 = 50

Egg Sale cost = 50x5.70 = Rs 285

(i) Total Loss = C.p. - S.p. = 300 - 285 = 15

(ii) Loss Percent = (Loss/CP)x100 = (15/300)x100 = 5%

Answer:

The number of weeks it will take for the  beetle population to reach 236 is 28.75.

Step-by-step explanation:

If a quantity starts at size P₀ and grows by d every time period, then the

quantity after n time periods can be determined using explicit form:

[tex]P_{n} = P_{0} + d \cdot n[/tex]

Here,

d = the common difference, i.e. the amount  that the population changes each time n is increased by 1.

In this case it is provided that the original population of beetle was:

P₀ = 6; (week 0)

And the population after 8 weeks was,

P₈ = 86

Compute the value of d as follows:

[tex]P_{8} = P_{0} + d \cdot 8\\86=6+8d\\86-6=8d\\80=8d\\d=10[/tex]

Thus, the explicit formula for the beetle population after n weeks is:

[tex]P_{n}=P_{0}+8n[/tex]

Compute the number of weeks it will take for the  beetle population to reach 236 as follows:

[tex]P_{n}=P_{0}+8n\\\\236=6+8n\\\\8n=236-6\\\\8n=230\\\\n=28.75[/tex]

Thus, the number of weeks it will take for the  beetle population to reach 236 is 28.75.

Answer:

x <= 48

Step-by-step explanation:

Subtract 3 from both sides

x/12 <= 4

Multiply by 12

x <= 48

Answer:

C. Parameter since the data set of all 14 teams is a population.

Explanation:

Find the attachment

Answer:

16:0

Step-by-step explanation:

Answer:

[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]

And we can find this probability with this difference

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]

And we can find the difference with the normal standard distirbution or excel:

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]

Step-by-step explanation:

Let X the random variable that represent the hotel room cost of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(202,70)[/tex]  

Where [tex]\mu=202[/tex] and [tex]\sigma=70[/tex]

We are interested on this probability

[tex]P(210<X<290)[/tex]

The z score formula is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the formula we got:

[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]

And we can find this probability with this difference

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]

And we can find the difference with the normal standard distirbution or excel:

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]

Answer:

[tex] m_{fresh}= 1000 \frac{Kg}{m^3} * 2.5x10^{-4} m^3 = 0.25 Kg[/tex]

And we can do a similar procedure for the sea water:

[tex] m_{sea}= \rho_{sea} V_{sea} [/tex]

And after convert the volume to m^3 we got:

[tex] m_{sea}= 1030 \frac{Kg}{m^3} * 1x10^{-4} m^3 = 0.103 Kg[/tex]

And then the density for the mixture would be given by:

[tex] \rho_{mixture}= \frac{m_{fresh} +m_{sea}}{v_{fresh} +v_{sea}}[/tex]

And replacing we got:

[tex] \rho_{mixt}= \frac{0.25 +0.103 Kg}{2.5x10^{-4} m^3 +1x10^{-4} m^3} = 1008.571 \frac{Kg}{m^3}[/tex]

Step-by-step explanation:

For this case we can begin calculating the mass for each type of water:

[tex] m_{fresh}= \rho_{fresh} V_{fresh} [/tex]

And after convert the volume to m^3 we got:

[tex] m_{fresh}= 1000 \frac{Kg}{m^3} * 2.5x10^{-4} m^3 = 0.25 Kg[/tex]

And we can do a similar procedure for the sea water:

[tex] m_{sea}= \rho_{sea} V_{sea} [/tex]

And after convert the volume to m^3 we got:

[tex] m_{sea}= 1030 \frac{Kg}{m^3} * 1x10^{-4} m^3 = 0.103 Kg[/tex]

And then the density for the mixture would be given by:

[tex] \rho_{mixture}= \frac{m_{fresh} +m_{sea}}{v_{fresh} +v_{sea}}[/tex]

And replacing we got:

[tex] \rho_{mixt}= \frac{0.25 +0.103 Kg}{2.5x10^{-4} m^3 +1x10^{-4} m^3} = 1008.571 \frac{Kg}{m^3}[/tex]

Step-by-step explanation:

multiple 6 by 9 then 2 by 5 then subtract them

Answer:

44

Step-by-step explanation:

(6*9) - (2*5)

54 - 10

44

Answer:

  C.  y ≤ 1

Step-by-step explanation:

The maximum value of the function is 1. So, the range is all values of y less than or equal to that.

  y ≤ 1

Answer:

3/5

Step-by-step explanation:

because there are more red than blue and the fraction is 3/5 and the probability to pick a red worm is a lot higher than the blue. well there are 4 red worms and 1 blue so it would be 3 red worms out of 5 in total. this is more than 1 blue over 5. 3/5 is more than 1/5

hope this helped

Answer: 3/5

Step-by-step explanation:

Since 4 red gummies you have four out of 5 chance of getting red gummies. Without replacement there are now 4 gummies left and 3 red gummies. There for 3 out of 4 chance of getting another red gummy. Since at same time multiply. 4/5*3/4 = 12/20

Which can be simplified to 3/5

Answer:

π

Step-by-step explanation:

For a circle, arc length is equal to the radius times the angle.

s = rθ

s = (1) (π − 0)

s = π

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion," (lower ​ "hic" values correspond to safer​ cars). The listed values correspond to cars​ A, B,​ C, D,​ E, F, and​ G, respectively.

514 541 302 400 507 406 369

Find the

a.​ mean,

b.​ median,

c.​ midrange,

d. mode for the data.

Also complete parts e. and f.

e. Which car appears to be the safest?

f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

Answer:

a) Mean = 434.14

b) Median = 406

c) Midrange = 421.5

d) Mode = 0

e) Car C appears to be the safest

f) The small cars does not appear to have about the same risk of head injury in a crash.

Step-by-step explanation:

We are given the head injury measurements from small cars that were tested in crashes.

The measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion.

The listed values are;

A = 514

B = 541

​C = 302

D = 400

​E = 507

F = 406

G = 369

a)​ Mean

The mean of the measurements is given by

Mean = Sum of measurements/ Number of measurements

Mean = (514 + 541 + 302 + 400 + 507 + 406 + 369)/7

Mean = 3039/7

Mean = 434.14

b)​ Median

Arrange the measurements in ascending order (low to high)

302, 369, 400, 406, 507, 514, 541

The median is given by

Median = (n + 1)/2

Median = (7 + 1)/2

Median = 8/2

Median = 4th

Therefore, the 4th measurement is the median that is 406

Median = 406

c)​ Mid-range

The midrange is given by

Midrange = (Max + Min)/2

The maximum measurement in the data set is 541

The minimum measurement in the data set is 302

Midrange = (541 + 302)/2

Midrange = 843/2

Midrange = 421.5

d)​ Mode for the data

The mode of the data set is the most repeated measurement.

302, 369, 400, 406, 507, 514, 541

In the given data set we don't have any repeated measurement therefore, there is no mode or we can say the mode of this data set is 0.

Mode = 0

e) Which car appears to be the safest?

Since we are given that the measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion," (lower ​ "hic" values correspond to safer​ cars)

The lowest hic value corresponds to car C that is 302

Therefore, car C appears to be the safest among other cars.

f) Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

302, 369, 400, 406, 507, 514, 541

As you can notice, the hic values differ a lot from each other therefore, we can conclude that the small cars does not appear to have about the same risk of head injury in a crash.

Answer:

Omar can put together 6 outfits.

66.67% probability of Omar’s outfits including a red T-shirt or red shorts

Step-by-step explanation:

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

-How many different outfits can Omar put together?

For each t-shirt, that are two options of shorts.

There are 3 t-shirts.

3*2 = 6

Omar can put together 6 outfits.

What is the probability of Omar’s outfits including a red T-shirt or red shorts?

Red t-shirt and red shorts

Red t-shirt and black shorts

Green shirt and red shorts

Yellow shirt and red shorts

4 desired outcomes.

4/6 = 0.6667

66.67% probability of Omar’s outfits including a red T-shirt or red shorts

Answer:

The percentage of the students who completed the poll preferred rock and roll music.

P(RR) = 0.1423 = 14.23 %

Step-by-step explanation:

Explanation:-

Given total number of students n(S) = 1960

Given the Students at a high school were polled to determine the type of music they preferred.

Rap 916

Alternative 46

Rock and Roll 279

Country 183

Jazz 32

Other 89

Let ' RR' be the event of Rock and Roll preferred music

given Rock and Roll = 279

n( RR) =  279

The percentage of the students who completed the poll preferred rock and roll music.

[tex]P(RR) = \frac{n(RR)}{n(s)} = \frac{279}{1960}[/tex]

P(RR) = 0.1423 = 14.23 %

Answer:

0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.

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 = 160, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]

Find the probability that the researcher observes an average weight of the 100 people to be between 150 and 170.

This is the pvalue of Z when X = 170 subtracted by the pvalue of Z when X = 150. So

X = 170

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

By the Central Limit Theorem

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

[tex]Z = \frac{170 - 160}{5}[/tex]

[tex]Z = 2[/tex]

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

X = 150

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

[tex]Z = \frac{150 - 160}{5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.

Answer:

(0,2)

Step-by-step explanation:

2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB

Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0

Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2

The point is (0,2)