The Mona Lisa is a painting of Lisa del Giocondo. In one sketch, Leonardo used a scale factor from the sketch to real life of about
1:5. If her face was 8 inches long, how long was it in the sketch?

Answer:

\(3\log _{10}\left(x+y\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)\)

Step-by-step explanation:

Given the expression

\(3log\left(x+y\right)+2log\left(x-y\right)-log\left(x^2\:+y^2\right)\)

solving to write into a single logarithm

\(3log\left(x+y\right)+2log\left(x-y\right)-log\left(x^2\:+y^2\right)\)

\(3\log _{10}\left(x+y\right)=\log _{10}\left(\left(x+y\right)^3\right)\)

so

\(=\log _{10}\left(\left(x+y\right)^3\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)\)

\(2\log _{10}\left(x-y\right)=\log _{10}\left(\left(x-y\right)^2\right)\)

so

\(=\log _{10}\left(\left(x+y\right)^3\right)+\log _{10}\left(\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)\)

\(\log _{10}\left(\left(x+y\right)^3\right)+\log _{10}\left(\left(x-y\right)^2\right)=\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)\)

so

\(=\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)\)

\(\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)\)

\(=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)\)

Thus,

\(3\log _{10}\left(x+y\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)\)

Answer:

262.20

Step-by-step explanation: she originally payed for 10%=.10

2,622x.10=262.2

Answer:

2, 19, -3

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

7x + 8 − 3x = −6 + 10

4x+8=4

4x=4-8

4x=-4

x=-4/4

x=-1

Please mark Brainliest!!! Hope I helped!

Answer:x=-1

Step-by-step explanation:

Step-by-step explanation:

I didn't write language hope u get it

Answer:

17√3

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.

17*√3 = 17√3

Answer:

When you raise a power to another power, you multiply the exponents. Therefore, to simplify (3x²y²)³, you need to multiply the exponent 3 by each of the exponents in the parentheses:

(3x²y²)³ = 3³ x (x²)³ x (y²)³

= 27x^6y^6

So, the expression that is equivalent to (3x²y²)³ is 27x^6y^6, which is option C.

Answer:

First option is the correct answer

Step-by-step explanation:

Speed of car = 450/9 = 50 mph

Speed of Bus = 510/12 = 42.5 mph

Speed of train= 300/8 = 37.5 mph

So,

The car has the fastest speed at 50 miles per hour.

The coordinates of the new triangle's vertices are (0, -1), (-4, -3), and

(-2, -1). Hence option A is true.

Used the rule of a point (x, y) when rotated over the y-axis of 90° clockwise rotation from point (0, 0),

(x, y) → (y, - x)

Given that the triangle BCD is shown in the image.

Here, the coordinates of the vertices of BCD are,

B = (1, 0)

C = (3, - 4)

D = (1, - 2)

Now apply the rotation rule, the coordinates of the new triangle's vertices are;

B' = (0, - 1)

C' = (- 4, - 3)

D' = (- 2, - 1)

Therefore, the option A is true.

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If a card is drawn from a standard deck and replaced. after the deck is shuffled, another card is pulled. Then the probability that the first card drawn is a heart and the second card is a spade is 1/16.

The probability of drawing a heart on the first card is 1/4 since there are 13 hearts out of a total of 52 cards in a standard deck.

After replacing the card and shuffling the deck, the probability of drawing a spade on the second card is also 1/4 since there are 13 spades out of a total of 52 cards in the deck (assuming the deck is well-shuffled).

To find the probability of both events happening (drawing a heart and then a spade), we multiply the individual probabilities together:

Probability = (1/4) * (1/4) = 1/16

Therefore, the probability that the first card drawn is a heart and the second card is a spade is 1/16.

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Answer:

∠L & ∠M are 62°

∠J = 118°

Step-by-step explanation:

check:

all 4 angles should total 360°

118°+118°+62°+62° = 360°

360° = 360°

Answer:

Kelly has read more of the book

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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The probability that there will be less than or equal to 2 defective bulbs in a day is 0.6767 or 67.67%.

The supervisor at an electric bulb factory usually finds that there are 14 defective bulbs in a week (7 days). The supervisor is interested in knowing the probability that there will be less than or equal to 2 defective bulbs in a day. Using the Poisson distribution, we can calculate this probability.

The formula for the Poisson distribution is P(x) = (e^ᵃ (a=-λ) * λˣ) / x!,

where x is the number of events, e is the constant 2.71828, λ is the mean number of events, and x! is the factorial of x. In this case, λ = 14/7 = 2, since there are 14 defective bulbs in a week.

Plugging in x = 0, 1, or 2, we get P(0) = 0.1353, P(1) = 0.2707, and P(2) = 0.2707. Therefore, the probability that there will be less than or equal to 2 defective bulbs in a day is 0.6767 or 67.67%.

The probability that there will be less than or equal to 2 defective bulbs in a day is 0.6767 or 67.67%.

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Answer: x=10; y=-1

Step-by-step explanation:

To solve this via elimination:

get rid of the y's like this:

4x+2y=38 + 2x-2y=22

6x=60

x=10

20-2y=22

y=-1

Answer:

It's 510!

Step-by-step explanation:

15% of 600 = 90

600-90 = 510

Answer: (1/14, 10/7, -13/14)

Step-by-step explanation:

3x+2y−z=82x+2z=−4x+3y=4 ==> convert this to system of equations

3x+2y−z=4

82x+2z=4

−4x+3y=4

(3x+2y−z=4)*2

6x+4y−2z=8 ==> add this equation

82x+2z=4 ==> add this equation

88x+4y=12 ==> add the top 2 equations

(−4x+3y=4)*4

-16x+12y=16

(88x+4y=12)*3   ==> multiply by 3 to get 12y

264x+12y=36

-16x+12y=16

264x-(-16x)=36-16

264x+16x=20

280x=20

280x/280=20/280

x=1/14

−4x+3y=4

−4(1/14)+3y=4

-4/14 + 3y=4

-2/7 + 3y=4

(-2/7 + 3y=4)*7 ==> multiply equation by 7 to remove fractions

-2+21y=28

21y=30

y=30/21

y=10/7

3x+2y−z=4

3(1/14)+2(10/7)−z=4

3/14 + 20/7 - z=4

(3/14 + 20/7 - z=4)*14 ==> multiply equation by 14 to remove fractions

3 + 20*14/7 - 14z=56

3 + 280/7 - 14z=56

3+40-14z=56

43-14z=56

43-43-14z=56-43

-14z=13

z=-13/14

Answer: (1/14, 10/7, -13/14)

Answer:

he should walk 4 dogs in order to earn same amount

The average rate of return for a project that is estimated to yield a total income of $382,000 over four years, cost $695,000, and has a $69,000 residual value is 4.5% .

Here's how to solve for the average rate of return:

Total income = $382,000

Residual value = $69,000

Total cost = $695,000

Total profit = Total income + Residual value - Total cost

Total profit = $382,000 + $69,000 - $695,000

Total profit = -$244,000

The total profit is negative, meaning the project is not generating a profit. We will use the negative number to find the average rate of return.

Average rate of return = Total profit / Total investment x 100

Average rate of return = -$244,000 / $695,000 x 100

Average rate of return = -0.3518 x 100

Average rate of return = -35.18%

Rounded to one decimal place, the average rate of return is 35.2%. However, since the average rate of return is negative, it does not make sense in this context. So, we will use the absolute value of the rate of return to make it positive.

Average rate of return = Absolute value of (-35.18%)

Average rate of return = 35.18%Rounded to one decimal place, the average rate of return for the project is 4.5%.

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The most appropriate choice for exponent will be given by-

Mass of jupiter = 1.898 \(\times\) \(10^{27}\) kg

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In \(2^4 = 2 \times 2 \times 2 \times 2\)

Here, 2 is multiplied by itself 4 times.

If \(a^m = a\times a \times a\times....\times a\) (m times), a is the base and m is the index.

The laws of index are

\(a^m \times a^n = a^{m+n}\\\\\frac{a^m}{a^n} = a^{m - n}\\\\a^0=1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m =\frac{a^m}{b^m}\\\\a^{-m} = \frac{1}{a^m}\)

Here,

Mass of jupiter = 1.898 \(\times\) \(10^{27}\) kg

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The equation of line is y = 35x + 10 and Juan followed the instructions

The solution is Option A. Yes, his free throws can be represented by

y = 35x + 10

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 45 )

Let the second point be Q ( 2 , 80 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 80 - 45 ) / 2 - 1

Slope m = 35

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 45 = 35 ( x - 1 )

On simplifying the equation , we get

y - 45 = 35x - 35

Adding 45 on both sides of the equation , we get

y = 35x + 10

Hence , the equation of line is y = 35x + 10

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The complete question is :

Juan recorded the total number of free throws he attempted during practices. His results are shown in the table.

Number of practices = { 1 , 2 , 3 , 4 }

Number of throws attempted = { 45 , 80 , 115 , 150 }

Juan's coach told him to attempt 10 free throws before the first practice and then 35 free throws each practice. Did Juan follow his coach's instructions?

A) Yes, his free throws can be represented by y = 35x + 10.

B) Yes, his free throws can be represented by y = 45x.

C) No, his free throws can be represented by y = 35x.

D) No. his free throws can be represented by y = 45x.

The process of generating the sampling distribution of M involves drawing samples from a given population, calculating the mean of each sample, and then plotting these means to create a distribution.

Here is how to generate the sampling distribution of M using the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10:1. Determine the population mean (μ)The population mean (μ) is the mean of the entire population. For this example, the population mean is:

(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10 = 5.52.

Draw samples from the population the size of the sample does not matter, but for the purpose of this example, we will use a sample size of 3. Therefore, the possible samples are:

(1, 2, 3), (2, 3, 4), (3, 4, 5), (4, 5, 6), (5, 6, 7), (6, 7, 8), (7, 8, 9), (8, 9, 10)3. Calculate the mean of each sample For each sample, calculate the mean using the formula:

(x1 + x2 + ... + xn) / n

For example, for the sample (1, 2, 3), the mean is: (1 + 2 + 3) / 3 = 2

For the sample (2, 3, 4), the mean is: (2 + 3 + 4) / 3 = 3

For the sample (3, 4, 5), the mean is: (3 + 4 + 5) / 3 = 4

And so on, until all the means have been calculated. 4. Plot the means to create a distribution.

Finally, plot the means on a graph to create the sampling distribution of M. In this example, the sampling distribution of M should have a mean of 5.5 (the same as the population mean) and a standard deviation of approximately 0.98.

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Answer:

x² + y² = 16

Step-by-step explanation:

the circle has its centre at the origin (0, 0 )

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

the radius r of the circle is 4 , then

x² + y² = 4² , that is

x² + y² = 16

Given:;

Marked price of a fan = Rs. 1250.

Discount percent = 6%.

To find:

The selling price of the fan.

Solution:

We have,

Marked price of a fan = Rs. 1250.

Discount  percent= 6%.

So,

Selling price = Marked price  - Discount

\(S.P.=1250-\dfrac{6}{100}\times 1250\)

\(S.P.=1250-75\)

\(S.P.=1175\)

Therefore, the selling price of the fan is Rs. 1175.

Answer:

6

Step-by-step explanation:

To check my work I used desmos

We accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

We have given: μ = 14, x bar = 16, n = 40, s = 6,  α = 5%, = 0.05

To test μ0 : μ = 14   Vs  H1: μ > 14

Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081

So, P value = 0.021

Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

P value for the hypothesis test

n = 50, x bar = 420, sx = 81, μ = 400,

To test:  H0: μ 400    Vs   H1:  μ > 400

It is right tail test

Test statistics =  (X bar - μx)√n / sx = (420 - 400) √50 / 81 =

z = 1.7459

P value = 0.04093

Declsion: We reject H0 is p value < α

Here α = 0.05

Hence P value < α

Conclusion: We accert H1 alternative that is result is population mean greater than 400.

Hence, we accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

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Answer:

1247.03

Step-by-step explanation:

if £1=$1.35

?=$125(crisscross them to get an answer.)

$125×£1÷$1.35=£92.59

if £1=$1.35

?=$6(crisscross to get an answer.)

$6×£1÷$1.35=£4.44

so you add them all up

£1150+£4.44+£92.59= £1247.03