What’s the correct answer for this question?

Answer:

(71.28, 78.72)

Step-by-step explanation:

We have the following information from the statement:

mean (m) = 75

sample standard deviation (sd) = 5

Sample size (n) = 13

Significance level (alpha) = 1 - 0.98 = 0.02

Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12

The critical value would be:

t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)

Margin of error equals:

E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:

E = 2,681 * 5/13 ^ (1/2)

E = 3.72

Therefore, the interval of 98% confidence interval would be:

75 + 3.72 = 78.72

75 - 3.72 = 71.28

(71.28, 78.72)

Answer:

108

Step-by-step explanation:

9 times 12 is 108

Answer:

0

Step-by-step explanation:

In a suit of 52 cards

The experiment consists of drawing 1 card from the standard deck.

Since diamonds are red, there is no black jack of diamonds.

Therefore:

P(drawing a black jack of diamonds)

[tex]=\dfrac{0}{52}\\\\ =0[/tex]

Answers:

In photo below

Explanation:

I got it correct in my test :)

Answer:

The percentage would be 20% (5x20=100)

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

18. Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.

Answer:

157.6

Step-by-step explanation:

Use PEMDAS! In this rule, it is stated that we should always add/subtract before multiplying/dividing. Also, whatever you do on one side of an equation, you do to another. Therefore, in order to get rid of the -2/5, add 2/5 so we can get rid of it. We also (according to the rule), have to add it to the other side in order to balance out. So add the 2/5 to 39. Then the other side is now 39.4. Now we have to get x by itself. Divide both sides by 1/4 (or multiply by 4 on both sides) in order to get x=157.6

Answer:

The average would be 42 / 28 = $1.50 / day.

Answer:

$1.50 per day

Step-by-step explanation:

Take the dollar amount and divide by the number of days

42 dollars / 28 days

1.50 dollars per day

$1.50 per day

Answer:

slope = 3/2

Step-by-step explanation:

3x-2y=6

Get this equation in the form y = mx+b where m is the slope and b is the y intercept

Subtract 3x from each side

3x-3x-2y=-3x+6

-2y = -3x+6

Divide each side by -2

-2y/-2 = -3x/-2 +6/-2

y = 3/2x -3

The slope is 3/2 and the y intercept is -3

Answer:

3/2

Step-by-step explanation:

I got this answer by putting it in the form y=mx+b

Step 1: Subtract 3x from each side

-2y = -3x+6

Step 2: Divide each side by -2

y = 3/2x -3

The slope is 3/2 and the y intercept is -3 because m is the slope and b is the y-intercept.

Answer:

The speed of the river is 2mph.

Step-by-step explanation:

I guess that we want to find the speed of the river.

First, remember the relation: speed*time = distance

If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:

Sd = 4mph + Sr

and at this speed, in a time T, she can move 21 miles, so we have:

Sd*T = (4mph + Sr)*T = 21 mi

When moving upstream, the speed will be:

Su = (4mph - Sr)

and in the same time T as before, she moves 7 miles, so we have the equation:

Su*T = (4mph - Sr)*T = 7 mi

Then we have two equations:

(4mph + Sr)*T = 21 mi

(4mph - Sr)*T = 7 mi

Now we can take the quotient of those two equations and get:

((4mph + Sr)*T)/((4mph - Sr)*T) = 21/7

The time T vanishes, and we can solve it for Sr.

(4mph + Sr)/(4mph - Sr) = 3

4mph + Sr = 3*(4mph - Sr) = 12mph - 3*Sr

4*Sr = 12mph - 4mph = 8mph

Sr = 8mph/4 = 2mph.

Answer:

(x-2)(x-2)

Step-by-step explanation:

You should be trying to find two numbers that add to make the coefficient of x (in this case, -4), and two numbers that multiply to make the constant term (in this case, +4). The two numbers that work for both of those criteria are -2 and -2.

-2 x -2 = +4 (satisfies the constant term)

-2 + -2 = -4 (satisfies the coefficient of x)

Complete Question

A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. However, the size of the paper is unknown!

Answer:

(a)[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]

(b)[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]

(c)f(1.3)-f(0.2)

(d) f(5.6)-f(5.5)

Step-by-step explanation:

Let the Length of the paper =l  (in inches)

Let the Width of the paper =w  (in inches)

Let the length of the cutout square = x (in inches)

Volume of the box: [tex]f(x)=x(l-2x)(w-2x)[/tex]

(a)When the cutout length is 0.2 inches.

x=0.2

Volume of the box (in cubic inches) ,

[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]

(b)When the cutout length is 01.3 inches.

x=1.3

Volume of the box (in cubic inches) ,

[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]

(c)If the cutout length increases from 0.2 inches to 1.3 inches.

Change In volume (in cubic inches):

[tex]f(1.3)-f(0.2)\\=1.3(l-2.6)(w-2.6)-0.2(l-0.4)(w-0.4)[/tex]

(d)If the cutout length increases from 5.5 inches to 5.6 inches.

Change In volume (in cubic inches):

[tex]f(5.6)-f(5.5)\\=5.6(l-11.2)(w-11.2)-5.5(l-11)(w-11)[/tex]

Answer:

Option D is the correct answer.

Step-by-step explanation:

Coefficients od dividend = (4, - 17, - 15)

Dividend [tex]=4x^2 - 17x - 15[/tex]

Divisor x = 5 =>x-5= 0

Coefficients of Quotient = (4, 3)

Quotient [tex]=4x + 3[/tex]

Remainder = 0

Since,

[tex] Dividend = Divisor \times quotient + Remainder\\

\therefore 4x^2 - 17x - 15 = (x - 5)\times (4x + 3) +0 \\

\therefore 4x^2 - 17x - 15 = (x - 5)\times (4x + 3) \\

\therefore( 4x^2 - 17x - 15) \div (x - 5) = (4x + 3)

[/tex]

Answer:

Yes, it would be unusual.

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.

If [tex]Z \leq -2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered unusual.

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 = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]

Would it be unusual for this sample mean to be less than 19 days?

We have to find Z when X = 19. So

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

By the Central Limit Theorem

[tex]Z = \frac{19 - 22}{1}[/tex]

[tex]Z = -3[/tex]

[tex]Z = -3 \leq -2[/tex], so yes, the sample mean being less than 19 days would be considered an unusual outcome.

Hey there! I'm happy to help!

The only thing we have to do is solve our inequality to find the answer!

30+15x ≥ 90

We subtract 30 from both sides.

15x ≥ 60

Finally, we divide both sides by four.

x ≥ 4

Therefore, Deepak can only accept jobs that last 4 or more hours.

I hope that this helps! Have a wonderful day!

The solution for the inequality is x≥4. Therefore, option A is the correct answer.

Given that, Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The inequality for the given situation is 30+15x≥90

Subtract 30 on the both the sides of an inequality, which is

30+15x-30≥90-30

⇒ 15x≥60

Divide 15 on the both the sides of an inequality, that is

15x/15≥60/15

⇒ x≥4

The solution for the inequality is x≥4. Therefore, option A is the correct answer.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ5

Answer:

1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean

2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Step-by-step explanation:

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

Normal probability distribution

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.

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.

1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?

The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.

So

Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.

2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?

We have that:

[tex]\mu = 168000, \sigma = 40000, n = 100, s = \frac{40000}{\sqrt{100}} = 4000[/tex]

This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{164000 - 168000}{4000}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Answer:

4.700

Step-by-step explanation:

Find the number in the thousandth place  0  and look one place to the right for the rounding digit 4. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

brainliesssss plssssssssssssss

Answer and Step-by-step explanation:

The computation of annual and quarterly mortality rates per 100,000 population is shown below:-

Quarterly mortality rates are

[tex]= \frac{Deaths}{Population\ in\ the\ city}\times Population[/tex]

For the first quarter

[tex]= \frac{54}{450,000}\times 100,000[/tex]

= 12  death per 100,000 population

For the second quarter

[tex]= \frac{43}{450,000}\times 100,000[/tex]

= 9.5  death per 100,000 population

For the third quarter

[tex]= \frac{35}{450,000}\times 100,000[/tex]

= 7.7  death per 100,000 population

For the fourth quarter

[tex]= \frac{39}{450,000}\times 100,000[/tex]

= 8.6  death per 100,000 population

Now the annual mortality is

[tex]= \frac{Deaths}{Population\ in\ the\ city}\times Population[/tex]

[tex]= \frac{171}{450,000}\times 100,000[/tex]

= 38 death per 100,000 population

Answer:

15.86%

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.

Percent of area between the mean and 0.20 standard deviations from the mean:

pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2

Z = 0.2 has a pvalue of 0.5793

Z = -0.2 has a pvalue of 0.4207

0.5793 - 0.4207 = 0.1586

So this percentage is 15.86%

Answer:

(-5, 38) and

(5,18)

Step-by-step explanation:

[tex]x^2-2x+3=-2x+28\\<=> x^2-2x+3+2x=28\\<=> x^2 = 28-3=25\\<=> x^2-25=0\\<=> x^2-5^2 =0\\<=> (x-5)(x+5)=0\\<=> x = 5 \ or \ x=-5[/tex]

so the solutions are

(-5, 38) and

(5,18)

Answer:

f(1/2)=1.5

f(1/4)=0.75

Answer:

a) P(X < 30) = 0.0392.

b) P(28 < X < 32) = 0.2760

c) P(X > 35) = 0.1190

d) P(X > 31) = 0.8810

e) At least 35.7965 mpg

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, we have that:

[tex]\mu = 33, \sigma = 1.7[/tex]

a. P(X<30)

This is the pvalue of Z when X = 30. So

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

[tex]Z = \frac{30 - 33}{1.7}[/tex]

[tex]Z = -1.76[/tex]

[tex]Z = -1.76[/tex] has a pvalue of 0.0392.

Then

P(X < 30) = 0.0392.

b) P(28 < X < 32)

This is the pvalue of Z when X = 32 subtracted by the pvalue of Z when X = 28. So

X = 32

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

[tex]Z = \frac{32 - 33}{1.7}[/tex]

[tex]Z = -0.59[/tex]

[tex]Z = -0.59[/tex] has a pvalue of 0.2776.

X = 28

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

[tex]Z = \frac{28 - 33}{1.7}[/tex]

[tex]Z = -2.94[/tex]

[tex]Z = -2.94[/tex] has a pvalue of 0.0016.

0.2776 - 0.0016 = 0.2760.

So

P(28 < X < 32) = 0.2760

c) P(X>35)

This is 1 subtracted by the pvalue of Z when X = 35. So

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

[tex]Z = \frac{35 - 33}{1.7}[/tex]

[tex]Z = 1.18[/tex]

[tex]Z = 1.18[/tex] has a pvalue of 0.8810.

1 - 0.8810 = 0.1190

So

P(X > 35) = 0.1190

d. P(X>31)

This is 1 subtracted by the pvalue of Z when X = 31. So

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

[tex]Z = \frac{31 - 33}{1.7}[/tex]

[tex]Z = -1.18[/tex]

[tex]Z = -1.18[/tex] has a pvalue of 0.1190.

1 - 0.1190 = 0.8810

So

P(X > 31) = 0.8810

e. the mileage rating that the upper 5% of cars achieve.

At least the 95th percentile.

The 95th percentile is X when Z has a pvalue of 0.95. So it is X when Z = 1.645. Then

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

[tex]1.645 = \frac{X - 33}{1.7}[/tex]

[tex]X - 33 = 1.645*1.7[/tex]

[tex]X = 35.7965[/tex]

At least 35.7965 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given;  mean of 33 mpg and a standard deviation of 1.7

a) For < 30:

z = (30 - 33)/1.7 = -1.76

P(x < 30) = P(z < -1.76) = 1 - 0.8413 = 0.0392

b) For < 28:

z = (28 - 33)/1.7 = -2.94

P(x < 28) = P(z < -2.94) = 0.0016

c) For > 35:

z = (35 - 33)/1.7 = 1.18

P(x > 35) = P(z > 1.18) = 1 - P(z < 1.18) = 1 - 0.8810 = 0.119

d) For > 31:

z = (31 - 33)/1.7 = -1.18

P(x > 31) = P(z > -1.18) = 1 - P(z < -1.18) = 0.8810

e) The  upper 5% of cars achieve have a z score of 1.65, hence:

1.65 = (x - 33)/1.7

x = 35.805 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

Find out more on z score at: https://brainly.com/question/25638875

Answer:

Option D

Step-by-step explanation:

This question is based on the " Partition Postulate. " You might be familiar with it, it states that a whole is composed of several parts. In this case you could say that this " whole " is ∠ ABC, and the " parts " are ∠1 and ∠2. By this Theorem you could also state the following;

[tex]m< ABC = m< 1 + m< 2,\\\\Substitute,\\110 = 4x + ( 5x + 10 ),\\110 = 4x + 5x + 10,\\4x + 5x + 10 = 110 - Option D\\\\Solution - Option D[/tex]

Hope that helps!

Answer:

1651

Step-by-step explanation:

let s say that the price before the increase is x

to apply an increase of 9% it does x + x*0.09 = x*(1+0.09)=x*1.09

and we know that this value is 1800

so

x*1.09=1800

<=>

x = 1800/1.09=1651.376147

to the nearest penny it gives 1651

Answer:

Hello!

Answer: 1651

I hope that was correct.  Please let me know, thank you!

Step-by-step explanation:

Answer:

y= 2x+1

Step-by-step explanation:

Points:

Form of the line:

Finding the slope:

Line is now:

Using one of the given points to find out the value of b:

So the equation for the line is:

Answer:

A. Observational study

Step-by-step explanation:

In research, an observational study is a type of study in which the researcher observes a phenomenon and tries to establish some relationship between the different variables he/she is observing. In other words, the researcher only observes and doesn't give a treatment.

On the other hand, when we have a experiment, we usually have 2 different groups (one that will receive a treatment and one who won't) and the researcher compares the differences between these two groups because of the treatment. In other words, the researcher does something other than just observing.

In this example, the research is going to determine if there is a relation between hearing loss and exposure to mumps. In this example the researcher is only going to observe how people who have been exposed to mumps are regarding hearing loss (we can say this since it will be unethical for example for the researcher to create an experiment in which he/she exposes a group to mumps). Therefore, he is going to observe how the past exposure to mumps could be related with the hearing loss.

Thus, this is an observational study.

Answer:

[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]

And we can find the probability using the normal standard distribution table and with the complement rule we got:

[tex]P(z<-1.11)= 0.1335[/tex]

Step-by-step explanation:

For this problem we have the following parameters:

[tex] \mu = 520, \sigma = 90[/tex]

We select a sample size of n =100 and we want to find this probability:

[tex] P(\bar X <510) [/tex]

The distribution for the sample mean using the central limit theorem would be given by:

[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]

And we can solve this problem with the z score formula given by:

[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score formula we got:

[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]

And we can find the probability using the normal standard distribution table and with the complement rule we got:

[tex]P(z<-1.11)= 0.1335[/tex]

Answer:

The correct answer would be D) 4.8x + 1.2 = 3.6; x = 0.5 mile

Step-by-step explanation:

This is because laps would be the dependent variable, so we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant. Now we can solve to make sure this is the right equation.

4.8x + 1.2 = 3.6

4.8x = 2.4

x = 0.5

Answer:

D) 4.8x + 1.2 = 3.6; x = 0.5 miles

Answer:

Options A, B and E are correct

Step-by-step explanation:

From the information given above, we would draw a dilation that produces an image that is the same shape as the original image, but has a different size.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS

Q (-3, 3)

R (2, 4)

S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In order words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2 (x,y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes:

Q' (-6, 6)

R' (4, 8)

S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

we would graph the coordinates of the two triangles.

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

See attached the diagram for better explanation.

Let's check out each options and compare it with diagram we obtained:

a) DO, 2 (x,y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

This option is correct

b) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

= 4/(-6+2) = 4/-4

m = -1

This option is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

This option is false

d) The vertices of the image are closer to the origin than those of the pre-image

The scale factor determines how much bigger or smaller the dilation image will be compared to the preimage. In a transformation, the final figure is referred to as the image. The original figure is referred to as the preimage.

From the diagram, the vertices of the preimage (original image) are closer to the origin than those of the dilation image.

This option is false

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

This option is correct

Answer:

A,B and E is correct

Step-by-step explanation:

Answer:

  D  0.00009

Step-by-step explanation:

9 × 10^-5 = 9 × 1/10^5 = 9 × 1/100,000

  = 9 × 0.00001

  = 0.00009

_____

Comment on place value

The exponent of 10 associated with the place value in a decimal number increases from 0 to the left of the decimal point, and decreases from -1 to the right of the decimal point:

  100. = 10²

  10. = 10¹

  1. = 10⁰

  0.1 = 10⁻¹

  0.01 = 10⁻²

  0.001 = 10⁻³

  0.0001 = 10⁻⁴

  0.00001 = 10⁻⁵

This simple realization can help you immensely with scientific notation.

Answer:

3a) 30% more than original price

b) 70% of the original price

c) 17times the original price

d) 70% less than original price

e) t + 0.85t

f) t - 0.15t

g) t - 0.85t

h) t + 0.15t

4. The expression that can be used to find the amount of money in his bank = m + 0.25m

Question:

3. Match each statement with an expression that could be used to find the price.

'The expressions for a to d were not stated in the question'.

a) p+ 0.3p

b) 0.7p

c) 17p

d) p-07p

'From e to h, we were not told what to determine'.

Write the expression in terms of time

e. 85% more than the original time

f. 15% less time than the original

g. 85% time decrease

h. 15% time increase

4. Ronnie increased the amount of money in his piggy bank by 25%. Which expression can be used to find the amount of money in his bank? Let "m" represent the original​.

Step-by-step explanation:

let original price = p

a) p+ 0.3p = p + 30% of p

30% more than original price

b) 0.7p = 70% of p

= 70% of the original price

c) 17p = 17 × p

= 17times of the original price

d) p-0.7p = p - 70% of p

= 70% less than original price

Let original time = t

e) 85% more than the original time = t + 85%of t

= t + 0.85t

f) 15% less time than the original time = t - 15% of t

= t - 0.15t

g) 85% time decrease = t - 85% of t

= t - 0.85t

h) 15% time increase = t + 15% of t

= t + 0.15t

4. Since "m" represent the original amount in Hus piggy bank

An increase of 25% = original amount + 25% of original amount

= m + 25% of m

'Of' means multiplication

= m + 0.25 ×m

= m + 0.25m

= 1.25m

The expression that can be used to find the amount of money in his bank = m + 0.25m