Find the missing sides.

Answer:

[tex]logb(X^5 / Y^6)[/tex]

Step-by-step explanation:

Given in the question an expression

5logbX - 6logbY

To Condense the following logs into a single log we will use logarithm rules

5logbX = logbX^5

6logbY = logbY^6

ln(x/y) = ln(x)−ln(y)

logbX^5 - logbY^6 = [tex]logb(X^5 / Y^6)[/tex]

Answer:

[tex]5\log_b(x)-6\log_b(y)=\log_b(\frac{x^5}{y^6})[/tex]

Step-by-step explanation:

The given logarithmic expression is  [tex]5\log_b(x)-6\log_b(y)[/tex]

We apply the rule: [tex]n\log_b(M)=\log_b(M^n)[/tex]

This implies that;

[tex]5\log_b(x)-6\log_b(y)=\log_b(x^5)-\log_b(y^6)[/tex]

We now apply the rule; [tex]\log_a(M)-\log_a(N)=\log_a(\frac{M}{N} )[/tex]

[tex]5\log_b(x)-6\log_b(y)=\log_b(\frac{x^5}{y^6})[/tex]

The volume of a rectangular box is calculated by multiplying its dimensions. Timmy's box has a volume of 24 cubic inches. Paul's box, with dimensions three times larger, has a volume of 5832 cubic inches which is 5808 cubic inches more than Timmy's.

The volume of a rectangular box is found by multiplying its length, width, and height. In Timmy's case, the volume is 3" * 4" * 2" which equals to 24 cubic inches. Paul's box has dimensions that are three times larger, which means the volume is (3 * 3") * (3 * 4") * (3 * 2")  = 27 * 36 *6 = 5832 cubic inches. The difference in volume is 5832 - 24 which equals to 5808 cubic inches, so Paul's box has 5808 cubic inches more volume than Timmy's.

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Answer:

Statements                       Reasons

1. 2x + 11 = 15                    1. Given

2. 2x = 4                            2. Subtraction Property of Equality

3. X = 2                              3. Division Property of Equality

Step-by-step explanation:

An equation can be solved and its solution proven using algebraic theorems and properties. To create a proof, form two columns. Label one side Statements and the other Reasons.

Begin your proof listing the any information given to you. List as the reason - Given.

Then list the next step which here would be to subtract by 11 on both side. The reason is Subtraction Property of Equality. Subtraction is the inverse of addition. Inverse axiom is another acceptable reason.

Then divide both sides by 2. The reason is Division Property of Equality or Inverse axiom once again. See the proof below.

Statements                       Reasons

1. 2x + 11 = 15                    1. Given

2. 2x = 4                            2. Subtraction Property of Equality

3. X = 2                              3. Division Property of Equality

Answer:

It would be 3 groups because 21/7 = 3

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Answer:

part 1: After one year, the cost of the refrigerator modeled by f(x) is cheaper.

part 2: 14 years

part 3: g(x)

part 4: 51

hope this helps :)

To find the cheapest refrigerator in the long run, calculate the limit of the cost per year as x approaches infinity for both given functions and compare the results. The cost of the refrigerator modeled by f(x) will be the cheapest, averaging $62 per year.

The average annual costs for owning two different refrigerators for x years can be calculated using the given functions: f(x) = 850 + (62x / x) and g(x) = 1004 + (51x / x). To determine which refrigerator will be cheaper in the long run, we need to find the limit of the cost per year as x approaches infinity for both functions. Taking the limit as x approaches infinity for f(x), we get 62. Therefore, the cost of the refrigerator modeled by f(x) will be the cheapest, averaging $62 per year.

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Answer:

128 m²

Step-by-step explanation:

The area of the rhombus can be calculated using the diagonals

area = [tex]\frac{1}{2}[/tex] diagonal × diagonal

       = [tex]\frac{1}{2}[/tex] × 16 × 16 = 8 × 16 = 128 m²

Final answer:

The area of a rhombus can be found using the formula (diagonal1 * diagonal2) / 2.

Explanation:

To find the area of a rhombus, you can use the formula:

Area = (diagonal1 * diagonal2) / 2

Where diagonal1 and diagonal2 are the lengths of the diagonals of the rhombus.

For example, if one diagonal is 8 meters and the other diagonal is 6 meters, the area would be:

Area = (8 * 6) / 2 = 24 square meters

Answer:

[tex]\large\boxed{A=240\ cm^2}[/tex]

Step-by-step explanation:

Look at the picture.

The formula of an area of a rhombus:

[tex]A+\dfrac{d_1d_2}{2}[/tex]

d₁, d₂ - diagonals

We have d₁ = 30 cm.

Use the Pythagorean theorem to calculate d₂ = 2x.

[tex]x^2+15^2=17^2[/tex]

[tex]x^2+225=289[/tex]             subtract 225 from both sides

[tex]x^2=64\to x=\sqrt{64}\\\\x=8\ cm[/tex]

d₂ = (2)(8) = 16 cm.

Substitute:

[tex]A=\dfrac{(30)(16)}{2}=(30)(8)=240[/tex]

Your answer’s 5! If not, message me, I’ll be happy to help.

The answer is 5! Hope this helps :)

Answer:

The measure of angle z is 30

Step-by-step explanation:

The angles of a triangle all add up to 180. So we can set these measures equal to 180 and solve for the unknown.

60 + 90 + z = 180

150 + z = 180

z = 30

Since this is subtraction, everything must be turned negative in the second polynomial.

(6x^2 - 5x) - (2x^2 + 3x - 2)

6x^2 - 5x - 2x^2 - 3x - (-2)

6x^2 - 5x - 2x^2 - 3x + 2

Now, reorder the terms to make it easier.

6x^2 - 2x^2 - 5x - 3x + 2

Now, just combine like terms.

4x^2 - 5x - 3x + 2

4x^2 - 8x + 2

There’s the answer!

Please consider marking this answer as Brainliest to help me advance.

Answer:

1/3.

Step-by-step explanation:

To roll a number less than 6 it must be 2 or 4 (2 numbers). There are 6 numbers on the cube.

So the probability = 2/6

= 1/3.

Answer:

The altitude to the base is [tex]5\ units[/tex]

Step-by-step explanation:

we know that

To find the length of the altitude apply the Pythagoras Theorem

Let

h-----> the altitude

[tex]h^{2}=13^{2}-(24/2)^{2}[/tex]

[tex]h^{2}=13^{2}-(12)^{2}[/tex]

[tex]h^{2}=169-144[/tex]

[tex]h^{2}=25[/tex]

[tex]h=5\ units[/tex]

Answer:

The Answer C

Step-by-step explanation:

I just did the test

No.The company ratio is yellow:red:(orange+blue+green):brown as 2:2:1:5 while the packet's ratio is 29:23:34:20

Answer: 2500 years

Step-by-step explanation:

I'm not quite sure if I'm doing this right myself but I'll give it a shot.

We use this formula to find half-life but we can just plug in the numbers we know to find t.

[tex]A(t)=A_{0}(1/2)^t^/^h[/tex]

We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For [tex]A_{0[/tex] let's just assume that there are 100 original  atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. h is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.

[tex]74=100(1/2)^t^/^5^7^3^0[/tex]

Now, solve. First, divide by 100.

[tex]0.74=(0.5)^t^/^5^7^3^0[/tex]

Take the log of everything

[tex]log(0.74)=\frac{t}{5730} log(0.5)[/tex]

Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the t and get

[tex]5730\frac{log(0.74)}{log(0.5)} =t[/tex]

Use your calculator to solve that giant mess for t and you'll get that t is roughly 2489.128182 years. Round that to the nearest hundred years, and you'll find the hopefully correct answer is 2500 years.

Really hope that all the equations that I wrote came out good and that that's right, this is definitely the longest answer I've ever written.

Answer:

40

Step-by-step explanation:

You do 480 divided by 12

To find the length of the room Alyssa wants to tile, given its area is 480 square feet and its width is 12 feet, divide the area by the width. The length is found to be 40 feet.

The question asks to find the length of a room given its area is 480 square feet and its width is 12 feet. To find the length, you use the formula for the area of a rectangle, which is Area = Length × Width. Since we're given the area and the width, we can rearrange the formula to solve for the length by dividing the area by the width.

Therefore, Length = Area / Width = 480 sq ft / 12 ft = 40 feet.

This means that the length of the room Alyssa wants to tile is 40 feet.

Answer:

24

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remarks

They want only the exponential equation, here's the point.

Equation

[tex]\text{Amount the pressure becomes} = \dfrac{101 kpa}{(1+\dfrac{ 1.8}{100} )^\frac{h}{500} }[/tex]

What this gives you is the equation for a rise every  500 feet. To figure out the %

Use

[tex]\text {\% =} \frac{\text{101 - answer from above equation}}{101}*100\%[/tex]

Example

Let h = 1000 feet

101 / (1 + 1.8/100) ^ (1000/500)

101 / (1.018)^2

101 / 1.036324

97.46

Now take this number and use the second formula

% = (101 - 97.46)/101 * 100%

% = 3.54%

The answer should be 3.6% (2 * 1.8%)

This is close enough. The question does say approximately.

1500 feet will give you 5.2% which is close to 5.4 (1.8 * 3). The higher you go, the more it is going to be out, but the results will always be close.

Answer:

[tex]7,561.12\ mm^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a cone is equal to

[tex]LA=\pi rl[/tex]

where

r is the radius of the base

l is the slant height

we have

[tex]r=80/2=40\ mm[/tex] ----> the radius is half the diameter

[tex]h=45\ mm[/tex]

To find the slant height apply the Pythagoras theorem

[tex]l^{2}=r^{2}+h^{2}[/tex]

substitute the values

[tex]l^{2}=40^{2}+45^{2}[/tex]

[tex]l^{2}=3,625[/tex]

[tex]l=60.2\ mm[/tex]

Find the lateral area

assume [tex]\pi=3.14[/tex]

[tex]LA=(3.14)(40)(60.2)=7,561.12\ mm^{2}[/tex]

b= 1/2

perpendicular slopes are those that are opposite signs and reciprocal of the original given slope

Answer:

1/2

Step-by-step explanation:

When two lines whose scopes are m₁ and m₂ are perpendicular, then the product of the scopes of both lines is -1.

Therefore,

If m₁ is the scope of line a and m₂ is the scope of line b then,

m₁m₂ = -1 and m₁ = -2

-2m₂ = -1

m₂ = -1/-2 = 1/2

The slope of line b is 1/2.

Answer:

Seven forward, seven opposite. It's like saying a footballer runs from 0 yd line to 50 yd line then turns around and runs 50 yards again, ends up right back at the 0.

Answer:

a

Step-by-step explanation:

got it right on test

Answer:

The rectangular 5 x 10 table.

Step-by-step explanation:

To find which table the office manager needs to get so he can sit more people at it is decided by one factor, the perimeter. The rectangular one, which is 5 x 10 the perimeter is (5 x 2) + (10 x 2) = 10 + 20 = 30. The circular one can be calculated by the equation[tex]\pi * d[/tex] where d = 8. Putting [tex]/pi[/tex] x 8 in my calculator and it comes out approximately at 25.132, having a less amount of perimeter space to work with, making the rectangular table the way to go.

The rectangular and circular tables offer roughly the same area, approximately 50 square feet. However, due to space utilization, traditionally, rectangular tables can seat more people as it allows seating around the sides and ends instead of wasting some space at the edges, a common issue with circular tables.

Determining which table can seat more depends on how much space each person needs. However, as a basic comparison, we can calculate the area of each table as a starting point.

The rectangular table is 5 feet wide and 10 feet long. Therefore, its area is 5 * 10 = 50 square feet.

For the circular table, we can use the formula for the area of a circle, which is pi * r^2, where r is the radius. The radius is half the diameter, so it is 4 feet here. Thus, the area is about 3.14 * 4^2 = 50.24 square feet.

Both tables have very similar areas. However, people can sit around both the sides and ends of a rectangular table, while some space might be wasted around the edges of the circular one. Therefore, the office manager might find that the rectangular table can seat more people comfortably.

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Answer:

a. 5/3

that's your answer

ANSWER

[tex]a. \: \frac{5}{3} [/tex]

EXPLANATION

The given logarithm is

[tex] log_{8}(32) [/tex]

Rewrite both the base and the number as a power to base 2.

[tex]log_{8}(32) = log_{ {2}^{3} }( {2}^{5} ) [/tex]

Use the following property:

[tex] log_{ {a}^{q} }( {a}^{p} ) = \frac{p}{q} [/tex]

This implies that,

[tex]log_{8}(32) = log_{ {2}^{3} }( {2}^{5} ) = \frac{5}{3} [/tex]

You would need to multiply the quantity of shrubs bought by the price of each one, so 4p and add that to the price of the soil to get the total cost

The equation becomes 4p + 17.50 = 53.50

Now solve for p:

4p +17.50 = 53.50

Subtract 17.50 from both sides:

4p = 36

Divide both sides by 4:

p = 36/4

p = 9

The answer would be: 4p + $17.50 = $53.50; p = $9.00

Answer:

(6.2, 8.4)

Step-by-step explanation:

Mean weight of the cats = u = 7.3 lb

Margin of Error = E = 1.1 lb

The interval estimate is calculated by subtracting and adding the margin of error to the mean value as shown below:

( u - E, u + E)

Using the given values, we get:

(7.3 - 1.1, 7.3 + 1.1)

(6.2, 8.4)

Thus, the interval estimate for the mean weight of the town’s stray cats is (6.2, 8.4)

Answer: P(A or B) = 22/26 or 11/13

Step-by-step explanation:All in all there are 26 pieces of clothing available. The probability of randomly selecting a blue piece is equal to 18/26. Also, the probability of picking up a pants is 14/26. There are 10 blue pants and the probability of picking up one of those is 10/26. The answer can be computed as follows:

               P(A or B) = (18/26) + (14/26) - (10/26) = 22/26 

                           P(A or B) = 22/26 or 11/13

Answer:

For the Critical Reading part: P = 0.6578

For the Math part: P = 0.6578

Step-by-step explanation:

See attached photo for solutions

The probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population means of 502 (Critical Reading) and 515 (Mathematics) on the SAT is approximately 68.26% for both.

To calculate the probability for each section of the SAT, we use the formula for the z score: z = (X - μ) / (σ / sqrt(n)). In this case, X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For the Critical Reading section, μ = 502, X is between 492 and 512 (502 ±10), σ = 100, and n = 90. When we input these values into the formula, we get a z value of -1 (for 492) and 1 (for 512) approximately. We then use a z-table to find the probability associated with these z-values. The probability for z = -1 is 0.1587 and for z = 1 is 0.8413. To find the probability that the sample mean lies within these z values, we subtract the lower probability from the higher one, which gives us 0.6826 or 68.26%.

The same steps are applied to the Mathematics section where μ = 515. The resulting probability also comes to around 68.26% that a sample mean test score will be within 10 points of the population mean.

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it had a 50 &#>#*(@?'ndhdjeke

Step-by-step explanation:

[tex]n!=\underbrace{1\cdot2\cdot3\cdot...\cdot n}\\\\6!=1\cdot2\cdot3\cdot4\cdot5\cdot6=720\\=======================\\_nP_r=\dfrac{n!}{(n-r)!}\\\\_8P_5=\dfrac{8!}{(8-5)!}=\dfrac{8!}{3!}=\dfrac{3!\cdot4\cdot5\cdot6\cdot7\cdot8}{3!}=4\cdot5\cdot6\cdot7\cdot8=6,720\\=======================\\_nC_r=\dfrac{n!}{r!(n-r)!}\\\\_{12}C_4=\dfrac{12!}{4!(12-4)!}=\dfrac{4!\cdot5\cdot6\cdot...\cdot12}{4!\cdot8!}=\dfrac{5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8}=495[/tex]

A) Divide total miles by total time:

21 miles /  4 hours = 5.25 miles per hour.

B) Divide miles by miles per hour:

42 miles / 5.25 miles per hour = 8 hours.

Answer:

The answer is (c) ⇒ the value is 6.6667

Step-by-step explanation:

∵ [tex]\lim_{x\to \2} _2\frac{x^{5}-32}{x^{3}-8}[/tex]

∵ 32 = 2^5 , 8 = 2³

∴ [tex]\lim_{x \to \2}_2 \frac{x^{5}-2^{5}}{x^{3}-2^{3} }[/tex]

* by using the rule:

[tex]\lim_{x\to\a}_a \frac{x^{n}-a^{n}}{x^{m}-a^{m}}=\frac{n}{m}(a)^{n-m}[/tex]

∴ [tex]\frac{5}{3}(2)^{5-3}=\frac{5}{3}(2)^{2}=\frac{20}{3}[/tex]

∴ 20/3 = 6.6667 ⇒ answer (c)

Answer:

The correct option is c.

Step-by-step explanation:

The given limit is

[tex]lim_{x\rightarrow 2}\frac{x^5-32}{x^3-8}[/tex]

It is can be written as

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}[/tex]

According to the property of limits,

[tex]lim_{x\rightarrow a}\frac{x^n-a^n}{x^m-a^m}=\frac{n}{m}(a)^{n-m}[/tex]

In the given limit, a=2, n=5 and m=3. Using the above property of limits we get

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{5-3}[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{2}[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(4)[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{20}{3}[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=6.6667[/tex]

Therefore the correct option is c.