Let u=ln x and v= ln y. Write ln( √x · y^2) in terms of u and v.

15 - 25% = 14.47 ounces of shampoo

The original shampoo bottle held 12 ounces before the 25% increase to 15 ounces. For the tile cleanser, the percent by mass of HCl is calculated to be 14.84%. Discussions of consumer product concentrations, like laundry detergent costs per ounce, often involve linear relationships and predictive models.

The question requires understanding percent increase and how to calculate the original amount given the increased quantity. To find the original volume of the shampoo bottle before the 25% increase, we set up the equation where the original volume (V) times 1.25 (to represent the 25% increase) equals the new volume of 15 ounces:

V x 1.25 = 15 ounces

To solve for V, we divide both sides of the equation by 1.25:

V = 15 ounces / 1.25

V = 12 ounces

Therefore, the old bottle held 12 ounces of shampoo.

To address another concept related to consumer products, the question on mass percentage, namely the percent by mass of HCl in a tile cleanser, also represents a common mathematical calculation in consumer product information. The calculation is as follows:

Percent by mass = (mass of solute / total mass of solution) x 100%

Percent by mass of HCl = (135 g / (135 g + 775 g)) x 100%

Percent by mass of HCl = (135 g / 910 g) x 100%

Percent by mass of HCl = 14.84%

Thus, the bottle of tile cleanser has 14.84% by mass of HCl.

When discussing the cost per ounce of laundry detergent in different sizes, such as a 40 oz. size or a 90 oz. size, the concept of linear relationships may be explored, as well as the possibility of identifying outliers or considering the validity of predictive models like the least-squares line.

Answer:

Step-by-step explanation:

dimes only cannot give total ending in 5 cents

so theres at least 1 nickel

n by the same reason, no.of nickels must be odd no.

most nickels is 0.65/0.05=13

combining the above, ans is D. (1,3,5,7,9,11,13)

Answer:

The Answer Is D (1,3,5,7,9,11,13)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of an area of a parallelogram:

[tex]A=bh[/tex]

b - side

h - height

We have b₁ = 18 and h₁ 10 and b₂ = 12.

[tex]b_1h_1=b_2h[/tex]

Substitute:

[tex]12h=(18)(10)[/tex]

[tex]12h=180[/tex]            divide both sides by 12

[tex]h=15[/tex]

Answer:

I believe the answer is A. 17, 17, 13, 28, 28, 26, 37, 35

The answer is C.

The stem, shows the number before the decimal point. The higher the number, the longer the stem goes down.

The leaf, shows the number after the decimal point. Each leaf is added to a row to match the stem of the original number.

1.3, 1.7, 1.7 all have a "1" before the decimal so they all go in the same row like this:

1 | 3 7 7

If we keep doing this, we see that C is the correct answer.

Best of Luck!

Answer:

23

Step-by-step explanation:

3^2+(6-2)•4-6/3

Order of operations:

= 9 + (4)•4 - 6/3

= 9 + 16 - 2

= 25 -2

= 23

32+(6−2)(4)− 6/3

your answer is =23

32+(6−2)(4)− 6/3

=9+(6−2)(4)− 6/3

=9+(4)(4)− 6/3

=9+16− 6/3

=25− 6/3

=25−2

=23

Answer:

This procedure does not result in a Binomial distribution.

Step-by-step explanation:

In a Binomial distribution there are only 2 outcomes in each trial.. In the roulette experiment there are  more than 2 possible outcomes for each trial so this condition is not met.

The spinning of an American roulette wheel 74 times doesn't result in a binomial distribution because there are more than two possible outcomes and thus the second condition - only two possible outcomes for each trial - for a binomial experiment is not met.

The procedure of spinning an American roulette wheel 74 times and recording the number the ball lands on does not result in a binomial distribution. This is because it does not meet all the conditions necessary for a statistical experiment to be classified as a binomial experiment.

For an experiment to be classified as a binomial experiment, it must meet the following conditions:

Although the procedure meets the condition of having a fixed number of trials, it fails on the second and third conditions. On a roulette wheel, there are 38 possible outcomes, not two, so it fails the condition of only having two outcomes (success or failure). Moreover, the outcome of each spin is independent but the conditions are not identical, as the chance of landing on any particular number is not the same for every spin (if we consider landing on a specific number as 'success').

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See the attached picture:

Answer:

5.1 days

Step-by-step explanation:

Given in the question,

initial amount of substance = 34 grams

k-value = 0.137

To find the half life of this substance we will use following formula

[tex]N(0)/2 = N(0)e^{-kt}[/tex]

here N(0) is initial amount of substance

        t is time in days

Plug values in the formula

[tex]34 /2 = 34e^{-0.137t}[/tex]

1/2 = e^{-0.137t}

Take logarithm on both sides

ln(1/2) = ln( e^{-0.137t})

ln(1/2) = -0.137t

t = ln(1/2) / -0.137

t = 5.059

t ≈ 5.1 days (nearest to tenths)

Answer:

11 pt  

Step-by-step explanation:

Convert all volumes to pints

Starting volume

2 gal × 4 qt/1 gal = 8 qt

 8 qt × 2 pt/1 qt  = 16 pt

Breakfast

1 qt × 2 pt/1 qt     =   2 pt

Stating volume = 16 pt

Less breakfast = -2 pt

Less lunch        = -3 pt

After lunch       = 11 pt

The Garcia family had 11 pt of milk left after lunch.

Answer:

The probability that the answer is an even number is 50%.

Step-by-step explanation:

There are 8 terms: 8, 9, 10, 11, 12, 13, 14, 15. Even numbers: 8, 10, 12, 14. So, 4 out of the 8 terms are even, which is equivalent to 50%.

The probability that the number is an even number is 1/2.

The probability is defined as the ratio of number of favourable outcomes and the the total number of possible outcome.

A number from 8 to 15 is drawn at random.

The number between 8 to 15 are 8, 9, 10, 11, 12, 13, 14, 15 = 8

Total even number = 8, 10, 12, 14 = 4

The probability that the number is an even number is;

[tex]\rm Probability =\dfrac{Total \ even \ number}{Total \ number}\\\\Probability =\dfrac{4}{8}\\\\Probability =\dfrac{1}{2}[/tex]

Hence, the probability that the number is an even number is 1/2.

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Answer:

0.0322; 0.9929

Step-by-step explanation:

Since the data is normally distributed, we use z scores for these probabilities.

The formula for a z score of a sample mean is

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

For the sample of mildly obese people, the mean, μ, is 371; the standard deviation, σ, is 65; and the sample size, n, is 6.

Using 420 for X,

z = (420-371)/(65÷√6) = 49/(65÷2.4495) = 49/26.5360 ≈ 1.85

Using a z table, we see that the area under the curve to the left of this is 0.9678.  However, we want the area to the right, so we subtract from 1:

1-0.9678 = 0.0322

For the sample of lean people, the mean, μ, is 528; the standard deviation, σ, is 108; the sample size, n, is 6.

Using 420 for X, we have

z = (420-528)/(108÷√6) = -108/(108÷2.4495) = -108/44.0906 ≈ -2.45

Using a z table, we see that the area under the curve to the left of this is 0.0071.  We want the area under the curve to the right, so we subtract from 1:

1-0.0071 = 0.9929

The probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes is about 3.2%. For the 6 lean people, this probability is approximately 0.7%.

For this type of problems, we use the concept of z-scores in statistics. The z-score is a measure of how many standard deviations a data point is from the mean. In this case, we will first calculate the standard error by dividing the standard deviation by the square root of sample size and then find the z-score by dividing the value of interest (420 minutes) minus mean by the standard error.

For mildly obese people, mean = 371 min, standard deviation = 65 min, sample size = 6. So, standard error = 65/sqrt(6) ≈26.51. The z-score for 420 min = (420-371)/ 26.51 ≈1.85. This indicates 420 minutes is 1.85 standard deviations above the mean. The probability that z-score exceeds 1.85 (assuming a one-tailed test since we are looking for the mean to be more than 420 minutes) is 0.032 (approximately). Hence, the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes is about 0.032 or 3.2%.

For lean people, mean = 528 min, standard deviation = 108 min, sample size = 6. Using the same approach, standard error = 44.11. The z-score for 420 min = (420-528)/44.11 ≈-2.45. This indicates 420 minutes is 2.45 standard deviations below the mean. The probability that z-score is less than -2.45 (assuming a one-tailed test for under 420 minutes) will be more than 99%. The probability that z-score exceeds -2.45 (420 min or more time) is about 1 - 0.993 = 0.007. Hence, the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes is about 0.007 or 0.7%.

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Answer:

A

Step-by-step explanation:

Federal law regulates a consumer's liability for fraudulent charges. Is what I got.

Answer:

A. Federal law regulates a consumer's liability for fraudulent charges.

Step-by-step explanation:

Under FCBA rules if a client reports about the lost cred card befor eit is used by someone else then the owner of the card is not responsible for any charges.  As per the rule Card holders liability for unauthorised use of their credit card ends at $50. FCBA is a federal law that was framed in 1974 and allows us to dispute charges and temporarily withhold payment without affecting credit score. It is because of FCBA that she would not be charges more than fifty dollars.

Answer:

option B [tex]D=6\ ft[/tex]

Step-by-step explanation:

we know that

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

In this problem we have

[tex]V=36\pi\ ft^{3}[/tex]

substitute and solve for r

[tex]36\pi=\frac{4}{3}\pi r^{3}[/tex]

simplify

[tex]27=r^{3}[/tex]

[tex]r=3\ ft[/tex]

Find the diameter

[tex]D=2r=2(3)=6\ ft[/tex]

Answer:

b)6

Step-by-step explanation:

Answer:45000,000,000,000

Step-by-step explanation:you just have to times it

for a cube v=a^3, so 9^3= 729

Answer:

Step-by-step explanation:

Eliminating parentheses, you get ...

  -2bx +10 = 16

Subtract 10 and divide by -2b:

  x = 6/(-2b)

  x = -3/b

__

When b=3, you have ...

  x = -3/3

  x = -1

[tex]f(x)=3x^2-4x+1[/tex] is a polynomial and thus continuous everywhere and differentiable on any open interval. (second option)

The MVT then guarantees the existence of [tex]c\in(0,2)[/tex] such that

[tex]f'(c)=\dfrac{f(2)-f(0)}{2-0}=\dfrac{5-1}2=2[/tex]

We have

[tex]f'(x)=6x-4[/tex]

so

[tex]6c-4=2\implies6c=6\implies c=1[/tex]

The true statement is: (b) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable

Mean value theorem states that:

If [tex]\mathbf{f(x)\ is\ continuous}[/tex] [a,b] and

[tex]\mathbf{f(x)\ is\ differentiable}[/tex] on (a,b),

Then there is a point c in (a,b), such that: [tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]

The function is given as:

[tex]\mathbf{f(x) = 3x^2 - 4x + 1}[/tex]

And the interval is: [tex]\mathbf{[0,2]}[/tex]

We have

[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]

This becomes

[tex]\mathbf{f'(c) = \frac{f(2) - f(0)}{2 - 0}}[/tex]

[tex]\mathbf{f'(c) = \frac{f(2) - f(0)}{2}}[/tex]

Calculate f(2) and f(0)

[tex]\mathbf{f(2) = 3\times 2^2 - 4\times 2 + 1 = 5}[/tex]

[tex]\mathbf{f(0) = 3\times 0^2 - 4\times 0 + 1 = 1}[/tex]

So, we have:

[tex]\mathbf{f'(c) = \frac{5-1}{2}}[/tex]

[tex]\mathbf{f'(c) = \frac{4}{2}}[/tex]

[tex]\mathbf{f'(c) = 2}[/tex]

Recall that:

[tex]\mathbf{f(x) = 3x^2 - 4x + 1}[/tex]

Differentiate

[tex]\mathbf{f'(x)= 6x - 4}[/tex]

Substitute c for x

[tex]\mathbf{f'(c)= 6c - 4}[/tex]

Substitute 2 for f'(c)

[tex]\mathbf{ 6c - 4 = 2}[/tex]

Collect like terms

[tex]\mathbf{ 6c = 4 + 2}[/tex]

[tex]\mathbf{ 6c = 6}[/tex]

Divide both sides by 6

[tex]\mathbf{c = 1}[/tex]

The interval is given as: [0,2]

The value of c is true for interval (0,2).

Hence, the true statement is:

(b) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable

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Answer:

its going to be d

Step-by-step explanation:

Answer:

The correct option is B.

Step-by-step explanation:

The general exponential regression model is

[tex]y=ab^x[/tex]

Using regression tool the exponential regression model for the given data is

[tex]S(x)=449.9999(1.09999)^x[/tex]

[tex]S(x)=450(1.1)^x[/tex]

The value of function at x=9 is

[tex]S(9)=450(1.1)^9=1061.07646[/tex]

The value of function at x=11 is

[tex]S(11)=450(1.1)^{11}=1283.90252[/tex]

The average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is

[tex]m=\frac{S(11)-S(9)}{11-9}[/tex]

[tex]m=\frac{1283.90252-1061.07646-}{2}=111.413\approx 11.42[/tex]

The average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is 11.42. Therefore the correct option is B.

Answer:

6387 km

Step-by-step explanation:

6378 km -9.4 km =

6386.6 km

Round to the nearest tenth: 63787 km

Hope I helped, sorry if not tho

Answer:

160 cm³

Step-by-step explanation:

1. Calculate the base area of the cone

The volume for the volume (V) of a cone is

V = ⅓Ah

Data:

V = 100 cm³

h = 15 cm

Calculation:

100 = ⅓ A× 15

100 = 5A

A = 100/5 = 20 cm²

2. Volume of Pyramid.

The volume for the volume (V) of a square pyramid is  

V = ⅓Ah

Data:

A = 20 cm²

h = 24 cm

Calculation:

V = ⅓× 20× 24 = 160 cm³

The volume of the square pyramid is 160 cm³.

Answer:

€83.60 = £62.70

Step-by-step explanation:

£3/€4 = £x/€ 83.60

¾ = x/83.60

Multiply each side by the lowest common denominator (4 × 83.60)

3 × 83.60 = 4x

Divide each side by 4

x = (3 × 83.60)/4 = £62.70

∴ €83.60 = £62.70

(The conversion factor is out of date. The current conversion factor is closer to £6 = €7.)

Using the given exchange rate, we set up a conversion equation and solve for the unknown variable. We find that €83.60 is roughly equivalent to 62.86 pounds.

Based on the given exchange rate, 1 pound (£) is equivalent to 1.33 Euros (€). Therefore, to convert €83.60 to pounds, we should do the following:

Therefore, €83.60 is approximately equivalent to 62.86 pounds.

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Answer:

Just B and C

Step-by-step explanation:

Reduce this to the lowest amount possible.

log(3abc/6a^2b) = 2

=================

log(c/2a)  = 2

c/2a = 10^2

c = 2a * 100

c = 200a

This one is also correct.

=================

The rest are just incorrect.

There is only 1 answer that works and that is B.

C is close, but it is not correct.

D is backwards. B is the right way and D is the upside down of B.

E and F are just not the way to handle logs. Subtracting logs means division, not multiplication and not 1 log.

=================

c. 25 because she gets $25 per hour

Answer:

whichever is closest to 3.032787

Answer:

36 cups

Step-by-step explanation:

If you notice, 6 times 9 is 54. So, 4 times 9 is 36. You need 36 cups of strawberries!

Answer:

The perimeter of a circle can be found by using the followinfg expression

P = 2*π*r

where

π = 3.14

r  = radius of the circle = half the diameter of the circle

In this case, if we are given the radius, we use

P = 2*π*r

If we are given the diameter, we use

P = 2*π*(D/2) = π*D

1) 27in

radius = 27in

P = 2*(3.14)*(27 in) = 169.56 in

diameter = 27 in

P = (3.14)*(27 in) = 84.78 in

2) 79 in

radius = 79 in

P = 2*(3.14)*(79 in) = 496.12 in

diameter = 79 in

P = (3.14)*(79 in) = 248.06 in

3) 1809 in

radius = 1809 in

P = 2*(3.14)*(1809 in) = 11360.52 in

diameter = 1809 in

P = (3.14)*(1809 in) = 5680.26 in

4) 152 in

radius = 152 in

P = 2*(3.14)*(152 in) = 954.56 in

diameter = 152 in

P = (3.14)*(152 in) = 477.28 in

Answer:

no

Step-by-step explanation:

ANSWER

[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]

EXPLANATION

If the polynomial has a root -2, with multiplicity 1, then (x+2) is a factor.

If the polynomial has root, 7 with multiplicity 1, then (x-7) is a factor.

If the polynomial has root 5, with multiplicity 2, then (x-5)² is a factor of the polynomial.

The fully factored form of the polynomial is

[tex]f(x) =a (x + 2)(x - 7) {(x - 5)}^{2} [/tex]

It was given that the polynomial has a leading coefficient of 1.

Hence a=1.

This implies that,

[tex]f(x) =(x + 2)(x - 7) {(x - 5)}^{2}[/tex]

Or

[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]

Answer:

f(x) = (x -7)(x - 5) {(x - 5)}(x + 2) the answer is D

Step-by-step explanation:

The value of y for the equation [tex]xy + p = 5[/tex].

An equation is a statement of equality between two mathematical expressions containing one or more variables.

According to the given question.

We have a equation

[tex]xy + p = 5[/tex]

Solve the above the equation for y

[tex]xy +p - p = 5 -p[/tex]           ( subtracting p both the sides)

[tex]\implies xy = 5-p[/tex]

[tex]\implies \frac{xy}{x} = \frac{5-p}{x}[/tex]                         (dividing both the sides by x)

[tex]\implies y = \frac{5-p}{x}[/tex]

Therefore, the value of y for the equation [tex]xy + p = 5[/tex].

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Answer:

90 square cm.

Step-by-step explanation:

For similar figures, the length of corresponding sides are proportional.

So we can write 4k = 6 where k is the proportionality constant.

Note: In terms of area, the scale factor would be k^2 and in terms of volume, it would be k^3y

Solving 4k = 6, we see that k = 6/4 or 3/2

We need area, so we multiply area of ABC by k^2 to get area of PQR.

[tex]40(\frac{3}{2})^2\\=40(\frac{9}{4})\\=90[/tex]

Area of PQR = 90 cm^2

Answer:

The area of △PQR is [tex]90\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Let

z-----> the scale factor

x---> the corresponding side triangle PQR

y---> the corresponding side triangle ABC

[tex]z=\frac{x}{y}[/tex]

substitute the values

[tex]z=\frac{6}{4}=1.5[/tex]

step 2

Find the area of triangle PQR

we know that

If two figures are similar, then the ratio of its areas  is equal to the scale factor squared

so

Let

z-----> the scale factor

x---> the area of triangle PQR

y---> the area of triangle ABC

[tex]z^{2} =\frac{x}{y}[/tex]

we have

[tex]z=1.5[/tex]

[tex]y=40\ cm^{2}[/tex]

substitute the values

[tex]1.5^{2} =\frac{x}{40}[/tex]

[tex]x=40(1.5^{2})=90\ cm^{2}[/tex]

Answer:

it would be great if you provided a question here..!

Step-by-step explanation: