log 5 + log y =log40

Answer:

In one gallon of paint there are about 3.8 liters so 8 gallons is about 30.3 liters.

answer

for the median its 7

for the mean its 6.

the mode is 9

Step-by-step explanation:

The mode is the value that appears most frequently in a data set.

Median:The number in the MIDDLE when they are IN ORDER!

Mean- The AVERAGE OF ALL NUMBERS: You add up all the numbers then you divide it by the TOTAL NUMBER of NUMBERS!

Answer:

see explanation

Step-by-step explanation:

calculate slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

consider the middle dotted line

with

(x₁, y₁ ) = (- 5, - 3) and (x₂, y₂ ) = (6, 8) ← 2 points on the line

m = \(\frac{8-(-3)}{6-(-5)}\) = \(\frac{8+3}{6+5}\) = \(\frac{11}{11}\) = 1

consider the line of reflection ( the solid line )

with

(x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (- 1, 4) ← 2 points on the line

m = \(\frac{4-3}{-1-0}\) = \(\frac{1}{-1}\) = - 1

Answer:

The answer is 17 packets

Answer:

17 or 17.25

Step-by-step explanation:

20 oz is 69 grams divided by 4 and its 17

Answer:

\(\sec^2(\theta)=\frac{25}{16}\)

Step-by-step explanation:

Recall what the relationship between cosine and secant:

\(\sec(\theta)=\frac{1}{\cos(\theta)}\)

In other words, secant is the reciprocal of cosine.

So, if we know cosine, we only need to find its reciprocal to find secant.

We are given that cosine is:

\(\cos(\theta)=\frac{4}{5}\)

Then secant must be:

\(\sec(\theta)=\frac{5}{4}\)

So:

\(\sec^2(\theta)=(\frac{5}{4})^2\)

Square:

\(\sec^2(\theta)=\frac{25}{16}\)

And we're done!

The shaded area under the normal curve is determined using the 68 - 95 - 99.7 rule to be 68.27%

The 68 95 99 rule, also known as the empirical rule in statistics, states that given normal distributions,

considering the figure and using the 68 - 95 - 99 rule, the shaded part is the reads 68% of the population and falls under the mean's 1 standard deviation.

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Answer: a. 1.981 < μ < 2.18

              b. Yes.

Step-by-step explanation:

A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.

First, we calculate mean of the sample:

\(\overline{x}=\frac{\Sigma x}{n}\)

\(\overline{x}=\frac{2.31=2.09+...+1.97+2.02}{12}\)

\(\overline{x}=\) 2.08

Now, we estimate standard deviation:

\(s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }\)

\(s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }\)

s = 0.1564

For t-score, we need to determine degree of freedom and \(\frac{\alpha}{2}\):

df = 12 - 1

df = 11

\(\alpha\) = 1 - 0.95

α = 0.05

\(\frac{\alpha}{2}=\) 0.025

Then, t-score is

\(t_{11,0.025}\) = 2.201

The interval will be

\(\overline{x}\) ± \(t.\frac{s}{\sqrt{n} }\)

2.08 ± \(2.201\frac{0.1564}{\sqrt{12} }\)

2.08 ± 0.099

The 95% two-sided CI on the mean is 1.981 < μ < 2.18.

B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.

Answer:

\(v=wr\)

Step-by-step explanation:

The formula relating linear velocity v and angular velocity ω for a circle of radius r is

\(v=wr------1\)

where v = linear velocity in m/s

           w= angular velocity in rad/s

            r= radius of curve

Both linear and angular velocity relates to speeds of objects, while linear velocity is to objects that moves, angular velocity is to objects that turns

The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.

The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:

A(t) = A₀ * (1/2)^(t/30)

We are asked to find the initial amount A₀ and the amount remaining after 50 years.

1. Initial amount:

The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:

A(0) = A₀ * (1/2)^(0/30)

A(0) = A₀ * 1

Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.

Therefore, the initial amount of the sample is A₀.

2. Amount after 50 years:

To find the amount remaining after 50 years, we substitute t = 50 into the equation:

A(50) = A₀ * (1/2)^(50/30)

Now we can calculate the amount using the given formula:

A(50) = A₀ * (1/2)^(5/3)

To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:

A(50) = A₀ * 0.455

A(50) ≈ A₀ * 0.455

Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.

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The slope of the given lines are representing that these lines are perpendicular.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36

Slope intercept form of both equations of a line

1)  y = -7/8x - 1

it is already in a slope intercept form

2) 32x - 28y = -36

-28y = -32x -36

y = 8/7x + 9/7

Since their slope is inverse and had a negative constant.

The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.

Therefore, The slope of the given lines are representing that these lines are perpendicular.

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Answer:

x=75

Step-by-step explanation:

\(\dfrac{x}{5}=15\)

\(x=5 \cdot15\)

\(x=75\)

Answer:

\(x=75\)

Step-by-step explanation:

\(\frac{x}{5} =15\)    

\((5)\frac{x}{5} =15(5)\)  multiply 5 on both sides so we can just have the variable x on one side

\(x =15(5)\\x= 75\)

Answer:

2 gallons

Step-by-step explanation:

(1.5 gallons)/(3/4 Room) = 2 gallons/Room

Answer:

Hey there!

I belive the answer is 17952 ft

which if you multiply 3.4 miles x 5280 is equal to 17952 ft.

Hope this can help! Please correct me if im wrong!

Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

Answer:

14

Step-by-step explanation:

cuz that's the answer and I'm the smartest person on urt

Answer:

Gretta's Contribution = $52,500

Interest = $125,588.79

Step-by-step explanation:

Gretta contributes $125 each month, for 35 years. Therefore, to find the amount she contributed, we multiply those pieces together (12 months in each year).

125 x 12 x 35 = $52,500

Therefore, over the 35 years, Gretta contributed $52,500.

If there was $178,088.79 in her account, and she contributed $52,500, then the rest is interest.

$178,088.79 − $52,500 = $125,588.79

There was $125,588.79 in interest earned on Gretta's account.

The completion of the table on simple interest would be :

The simple interest will be the same every year which is why it would keep increasing by $ 30 for each year up to the 4 years. It will go from $ 30 to $ 60 to $ 90, and then $120 so that the total in the account after 4 years is:

= 600 + 120

= $ 720

The simple interest formula to help find out after 4 years is:

= Principal + ( Principal x Rate x Time)

= 600 + ( 600 x 5 % x 4 )

= 600 + 120

= $ 720

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Answer:

JLKACQSCVWMNDV

Step-by-step explanation:

QSQW VMBW DVNWD VMW V

Answer:y = -3x +9

Step-by-step explanation:

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

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Answer:

good the idea work

the common multiple are you find the for work

Answer:

8/15

Step-by-step explanation:

Assuming that a is in the 1st quadrant, based on sin a = 8/17 you can build a right triangle as in the picture. Third side you compute with Pythagoras \(x^2 + 8^2 = 17^2 \implies x = 15\).

At this point the tangent is the ratio of the two segments, or 8/15.

Else, you can calculate cos a  based on the fact that \(cos\ a = \sqrt{1-sin^2\ a}\) (under the same assumption as the beginning. Then it's just a matter of plugging numbers.

Answer:

volume = 33.5 in³

Step-by-step explanation:

Formula:

\(\sf volume \ of \ a \ cone=\dfrac13\pi r^2h\)

Given:

Substituting the given values into the formula:

\(\sf \implies volume=\dfrac13 \times 3.14 \times 2^2 \times 8\)

                  \(=\dfrac13 \times 3.14 \times 4 \times 8\)

                  \(\sf =33.49333333...\)

                  \(\sf =33.5 \ in^3 \ (nearest \ tenth)\)

Region I's value is 15. Region II is valued at 16. 18 is the value of Region III. 33 pupils are enrolled in math or English classes. There are 18 students that do not speak English. There are 15 pupils in English classes who do not take math.

The Venn diagram uses circles to represent the relationships between sets and the region that they overlap. Set operations such as set intersection, set union, and set difference are shown in a Venn diagram, also called a set diagram. It may also be used to symbolize parts of a set. The diagrammatic depiction of two or more sets is called a Venn diagram.

Here,

Region I,

=31-16

=15

Region II,

=16

Region III,

=34-16

=18

Students in English or Math,

=15+18

=33

Students not in English,

=18

Students in English and not in Math,

=15

The value of Region I is 15. The value of Region II is 16. The value of Region III is 18. Number of students in English or Math is 33. Number of student not in English is 18. Number of students in English and not in Math is 15.

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Answer:

A=3.1

B=4.2

C=2.7

Step-by-step explanation:

The profit made by Mustafa's soccer team from the school dance as a fundraiser is 5(n - 60) dollars.

Profit is the financial gain obtained by a business or an individual after deducting all the expenses associated with producing and selling goods or services.

It is difference between the total revenue earned and total costs incurred.

The total cost of the dance is $200 + $100 = $300.

If each student is charged $5.00 to attend, the total revenue from n students attending is 5n dollars.

The profit is equal to the revenue minus the cost, so it is given by:

Profit = 5n - 300

To express this profit in simplest form, we can factor out a common factor of 5:

Profit = 5(n - 60)

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The soccer squad of Mustafa earned 5(n - 60)dollars from the school dance as a profit.

Profit is the financial gain realised by a company or a person after all costs related to creating and disbursing goods and services have been subtracted.

The amount in issue is the difference among total revenue received and total expenses paid.

The total cost of the dance is $200 + $100 = $300.

If each student pays $5 to join, then $5 will be the total revenue when n students show up.

The profit is determined by: Since the profit is equivalent to the revenue minus the cost:

Profit = 5n - 300

The simplest way to describe this profit is to factor out a common factor of five:

Profit = 5(n - 60)

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The complete question is,

Mustafa’s soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit?

Answer:

1384.5

Step-by-step explanation

Diviseion is just the oppisite of multiplication so you can think to yourself that what times two equals 2769. If you multiply 1384.5 on a calculater you get 2769.

x+11.95≤30

Then x≤30−11.95x≤30−11.95

x≤18.05x≤18.05Answer:

Step-by-step explanation: