Write the fraction in simplest form. (3/6) x (7/10)

Answer:

Step-by-step explanation:

When the net is folded into the rectangular prism

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. Another name for it is a cuboid.

Applying science of vision to see technical details in the prism, seeing letter B on the top means that D will be on the bottom.

the side we face will be C while the bac will be A

on the other side, the left end not showing is E and this make up all the part of the prism

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Answer:

BC = 16 units

Step-by-step explanation:

Since DE is the midsegment of the triangle, based on the midsegment theorem, thus:

DE = ½(BC)

DE = 8 units

Plug in the value

8 = ½(BC)

Multiply both sides by 2

2*8 = BC

BC = 16 units

∠LMN is an obtuse angle.

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

Explanation

Let's go through the answer choices to see which are true, and which are false.

Answer:

p = 3 dollars    d = 4 dollars

Step-by-step explanation:

2 p + 1 d  = 10     given

4 p + 1 d  = 16     given       Subtract second equation from first to get:

-2p = - 6

p = 3 dollars        then use this value in either of the equations to find  'd'

2(3)   + d = 10

d = 4

Answer:

Step-by-step explanation:

Answer:

.266666... or \(\frac{4}{15}\)

Step-by-step explanation:

Multiply the numerator by the other numerator, in this case it would be 2 * 2, to get 4. This is your numerator for the answer.

Then do the same for the denominators. 5 * 3 is 15.

Therefore, your answer is \(\frac{4}{15}\)

Hope that this helps!

To evaluate (g - f)(2), we first need to find f(2) and g(2).

We start by finding f(2):

f(x) = (x + 3) / (x^2 + 2x - 3)

f(2) = (2 + 3) / (2^2 + 2(2) - 3) = 5 / 7

Next, we find g(2):

g(x) = log4x

g(2) = log4(2)

Now we can evaluate (g - f)(2):

(g - f)(2) = g(2) - f(2) = log4(2) - 5/7

Using a calculator, we can approximate log4(2) to be approximately -0.415.

So, (g - f)(2) is approximately:

(g - f)(2) ≈ -0.415 - 5/7 ≈ -1.125

Therefore, (g - f)(2) is approximately -1.125.

Answer:

- \(\frac{1}{2}\)

Step-by-step explanation:

(g - f)(2)

= g(2) - f(2)

to find g(2) use the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

then

\(log_{4}\) 2 = n

2 = \(4^{n}\)

2 = \((2^2)^{n}\)

2 = \(2^{2n}\), so equating exponents gives

2n = 1 ( divide both sides by 2 )

n = \(\frac{1}{2}\)

so g(2) = \(\frac{1}{2}\)

and

f(2) = \(\frac{2+3}{2^2+2(2)-3}\) = \(\frac{5}{4+4-3}\) = \(\frac{5}{5}\) = 1

Then

(g - f)(2)

= g(2) - f(2)

= \(\frac{1}{2}\) - 1

= - \(\frac{1}{2}\)

The relationship between logarithms and exponential functions is fundamental and provides a powerful tool for finding solutions in various mathematical and scientific contexts.

Logarithms are the inverse functions of exponential functions. They allow us to solve equations and manipulate exponential expressions in a more manageable way. By taking the logarithm of both sides of an exponential equation, we can convert it into a linear equation, which is often easier to solve.

One of the key properties of logarithms is the ability to condense multiplication and division operations into addition and subtraction operations. For example, the logarithm of a product is equal to the sum of the logarithms, and the logarithm of a quotient is equal to the difference of the logarithms.

Logarithms also help us solve equations involving exponential growth or decay. By taking the logarithm of both sides of an exponential growth or decay equation, we can isolate the exponent and solve for the unknown variable.

This is particularly useful in fields such as finance, population modeling, and radioactive decay, where exponential functions are commonly used.

Furthermore, logarithms provide a way to express very large or very small numbers in a more manageable form. The logarithmic scale allows us to compress a wide range of values into a smaller range, making it easier to analyze and compare data.

In summary, the relationship between logarithms and exponential functions enables us to simplify and solve equations involving exponential expressions, model exponential growth or decay, and manipulate large or small numbers more effectively.

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Answer:D

Step-by-step explanation:

This is D because your dividing by 5 or each one and thats how you get Your output number

Proportional relationship between x and y is x/y = 5. Only table D shows a proportional relationship between x and y.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in other expression as well. Generally it is represented as x/y = k, where x and y are two expressions and k is constant.

In order to solve this problem, first we’ll have to figure out the proportionality ratio between the x and y.

that is x/y = k (let), it should be constant.

In the table A;

first term, 3/4 = 0.75

second term, 10/6 = 1.667

Since the value of constant is not the same. Therefore the table A does not show the proportional relationship between x and y.

In the table B;

first term, 4/2 = 2

second term, 8/4 = 2

third term, 12/8 = 1.5

Since the value of constant is not the same. Therefore the table B does not show the proportional relationship between x and y.

In the table C;

first term, 12/6 = 2

second term, 14/12 = 1.667

Since the value of constant is not the same. Therefore the table B does not show the proportional relationship between x and y.

In the table D;

first term, 5/1 = 5

second term, 10/2 = 5

third term, 15/3 = 5

Since the value of constant is the same in every term. Therefore the table B shows the proportional relationship between x and y.

Therefore, proportional relationship between x and y is x/y = 5. Only table D shows a proportional relationship between x and y.

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Given

You need to calculate the value of x for g(x)=3, replace it in the equation as follows:

And calculate for x, to do so, you can pass the "+1" to the other side of the equal sign by performin the oposite operation "-1" to both sides:

For x=2 g(x)=3

Answer:

x =35

Step-by-step explanation:

The sum of the angles of a triangle add to 180

x+10 +x + 3x-5 = 180

Combine like terms

5x+5 = 180

Subtract 5 from each side

5x+5-5 =180-5

5x = 175

Divide by 5

5x/5 =175/5

x =35

Brian's gross income last month will be $3319.

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, Brian is a salesman for a wholesome computer parts company. He earn straight commission at a rate of 4% last month is total sales were 82,968.

Brian's gross income last month will be:

= 4% × 82968

= $3319

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Therefore, the explicit formula for f(n) is: f(n) = 10 * \(3^{(n - 1)}\)

f(1)=10

An explicit formula for f(n), the number of members the creators have a goal of getting n weeks after the website is made available, can be determined by using the information provided that the number of members is tripled every week.

So, we can start with the initial number of members (10) and multiply it by 3 for each week.

Therefore, the explicit formula for f(n) is:

f(n) = 10 * \(3^{(n - 1)}\)

A recursive formula for f(n) can be determined by using the information that the number of members is tripled every week, and the initial number of members is 10.

So, we can start with the initial number of members (f(1)=10) and use the previous value of f(n-1) to calculate the current value of f(n).

Therefore, the recursive formula for f(n) is:

f(n) = 3f(n-1) + 10

for n>1

f(1)=10

In this way, we can calculate the number of members for any week using the explicit formula or the recursive formula.

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Step-by-step explanation:

slope = rise/run = (y2-y1)/(x2-x1)

= (3-2)/(0-3)

=(1)/(-3)=-1/3

The intercept is given in one of the points, (0.3).

y=mx+b

y=(-1/3)x+3

I can't tell if this is one of your options bc I think the copy paste didn't quite come through correctly.

Answer: C

Step-by-step explanation: I just know the answer

The equation of the perpendicular line is y = (-3/2)x + 2.

Option A is the correct answer.

We have,

From the graph,

The line has coordinates: (0, -1), and (-3, -3).

Now,

The equation of the line can be written as:

y = mx + c

m = (-3 +1) / (-3 - 0) = -2/-3 = 2/3

(0, -1) = (x, y)

-1 = 2/3 x 0 + c

c = -2

So,

y = (2/3)x - 2

Now,

Any line y = m(2)x + c perpendicular to y = (2/3)x -2 will have slope as:

m(2) x m = - 1

m(2) = - 1 / (2/3) = -3/2

Thus,

The equation of the perpendicular line is y = (-3/2)x + 2.

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The adjusted balance of Blossom's inventory account is $214,680.

The rate of interest, also known as the interest rate, is the percentage amount charged by a lender or financial institution for the use of borrowed money or for the extension of credit. It is the cost of borrowing money, typically expressed as an annual percentage of the amount borrowed or owed.

Therefore, the adjusted balance of Blossom's inventory account is $214,680.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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The digits from 0-9 should Jimmy use to represent him winning is 4-9.

We are given that;

Hockey games won= 609

Now,

To use a random number table to determine the probability of him winning the next two games, Jimmy needs to assign digits from 0 to 9 to represent him winning or losing.

Since he wins 60% of his games, he should assign 6 digits to represent him winning and 4 digits to represent him losing.

One possible way to do this is to use 0-5 to represent him winning and 6-9 to represent him losing.

Another possible way is to use 4-9 to represent him winning and 0-3 to represent him losing.

Therefore, by probability the answer will be 4-9.

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Answer:

2

Step-by-step explanation:

Answer:

I think its the second answer

Answer:

The y intercept is (0,-22)

Step-by-step explanation:

The y intercept is the value when x =0

Y=5x-22

y = 5*0 -22

y = -22

The y intercept is (0,-22)

The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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Answer:

Average: 4

Standard Deviation: 0

Step-by-step explanation:

Because we don't know how each student did we are going to assume that they all got 20% of the questions right

20% of 20 is 4

Which means that we can assume each student got 4 questions correct

Because all entries are the same the standard deviation is 0

Answer:

  (d)  5/8 in

Step-by-step explanation:

You want the measure indicated by the compass points in the figure.

The largest mark between the end of the ruler and the mark labeled 1 is at the 1/2 inch point. The compass is to the right of that.

The mark halfway between the 1/2 inch mark and the 1 inch mark is 3/4 inches. The compass is to the left of that.

The mark halfway between 1/2 inch and 3/4 inch is 5/8 inch. The compass seems to be nearer this mark than it is to the 1/2 inch mark.

The measure of the distance between compass points is about 5/8 inch.

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The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.

The increase of population can be found by using the logistic equation. It is

\(P(t) = \frac{K}{1 + Ae^{-kt} }\)

Where

Sunset Lake is stocked with the rainbow trout. We have

Find the growth constant k and time t when P(t) = 14600!

A = (K - P₀)/P₀

A = (28000 - 2800)/2800

A = 25200/2800

A = 9

After 1 year, we have 7000 rainbow trout. The growth constant is

\(7000 = \frac{28000}{1 + 9e^{-k(1)} }\)

\(1 + 9e^{-k} = 4\)

\(9e^{-k} = 3\)

\(e^{-k} = \frac{1}{3}\)

k = - ln (1/3)

k = 1.0986

Use k value to find the time when the population will increase to 14600!

\(14600 = \frac{28000}{1 + 9e^{-1.0986t} }\)

\(1.9178 = 1 + 9e^{-1.0986t}\)

\(0.9178 = 9e^{-1.0986t}\)

\(\frac{0.9178 }{9} = e^{-1.0986t}\)

\(t = \frac{ln \: 0.10198}{-1.0986}\)

t = 2.078

t ≈ 2.1 years

It is in another 1.1 years after t = 1.

Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.

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The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.

An acute triangle with sides measuring 7, 4, and 2

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .

According to the Pythagorean Theorem.

Here, 7² is greater than (4² + 2²).

So this is not possible.

An isosceles triangle with angles measuring 20° and 80°

In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,

Then the third angle measures is

180° - 20° - 80°= 80°

Two angles are congruent implies two sides are congruent.

It is possible to form isosceles triangle.

An obtuse triangle with sides measuring 5, 10, and 15

In an obtuse triangle, the longest side is opposite the largest angle.

Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.

However, 15²is greater than (5²+ 10²),

so this is not possible.

A scalene triangle with angles measuring 110° and 35°

The sum of the angles of any triangle is 180°,

so the third angle must measure

180° - 110° - 35° = 35°.

Two angles are congruent so it is isosceles triangle.

It is not possible to form scalene triangle.

Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.

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The time taken for the money to grow to $8670 at compound interest is approximately 9.24 years.

Given the amount of money that is the principal = $6000

Rate = 4% compounded quarterly.

Time = t

Amount = $8670

Now we know that the amount is calculated by the formula:

A = P(1+r/4)ⁿ

8670 = 6000(1+0.01)ⁿ

Hence

log 1.445 = n log 1.01

or, n = 36.99

Number of years = 36.99 / 4 = 9.24 years.

The interest that is added to a loan or deposit is referred to as compound interest. Compound interest is computed for a sum utilizing both the principal and interest already paid. The main distinction between compound interest and simple interest is this.

If we look at our bank statements, interest is usually credited to our account once a year. While the principle remains constant, the interest changes annually.

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The equation for total cost of buying and shipping the records is

76.4x + 80

We have,

She buys 3 in good condition

So, the cost for 3 good condition

= 3 (10.5x)

= 31.5 x

and, She buys 1 in Fair condition

So, the for 1 fair condition

= 5x

and, She buy 2 new condition then the price is

= 39.9 x

So, the equation for total cost of buying and shipping the records is

= 31.5x + 5x + 39.9x + 8

= 76.4x + 8

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The instantaneous rate of change of y = √x at x = 2 is √2 / 2.

To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.

Taking the derivative of y = √x using the power rule for differentiation, we have:

dy/dx = (1/2) × x^(-1/2)

Now, substituting x = 2 into the derivative expression:

dy/dx = (1/2) × 2^(-1/2)

= (1/2) × √2

= √2 / 2

Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.

None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.

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