A fish tank is 3/4 full. 2/3 of the water leak out. After the water leaks out, 10 gallons are left in the tank. How many gallons of water does the tank hold when full?

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: 169

Step-by-step explanation:

You just multiply 13 by 13

When simplifying 13 to the power of 2, you multiply 13 by itself, resulting in 13 x 13, which equals 169. This is known as squaring a number.

The question you've asked involves exponents, which is a way to express repeated multiplication of the same number. When you write 13 with a tiny 2 next to it, you're indicating that 13 should be multiplied by itself once, which is what squaring a number means. In other words, 13 to the power of 2 is 132, which is 13 × 13.

Let's simplify 132:

So, 132 equals 169. This process is using an integer power, which involves multiplying the base (in this case, 13) by itself as many times as indicated by the exponent (in this case, 2). This can apply to any number, where for example 53 (5 cubed) equals 5 × 5 × 5, which is 125.

The sum of two numbers is 60

The answer is

40 and 20

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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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

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:

(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:

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]

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

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❣❣... ℏ✺℘ḙ !т ℏḙℓ℘ṧ ʏ✺ṳ...❣❣

Answer:

The possible solution that is obtained from the system of equation are:

(1,3) and (6,13)

Step-by-step explanation:

We are asked to find the solution set of the given system of equation as:

[tex]y=x^2-5x+7-----------(1)[/tex]

and [tex]y=2x+1--------(2)[/tex]

We know that the solution of the system of equations is the possible set of x and y-values that satisfy both the equations.

Or we may say the point of intersection of the graph that is obtained from both the equations.

We solve the system by substitution method as:

We put the value of y from equation (1) in equation (2) to obtain:

[tex]x^2-5x+7=2x+1[/tex]

which is further written by combining the like terms as:

[tex]x^2-5x-2x+7-1=0\\\\x^2-7x+6=0\\\\x^2-6x-x+6=0\\\\x(x-6)-1(x-6)\\\\(x-1)(x-6)=0[/tex]

Hence, we get the possible values of x as:

x=1   and x=6

   y=2×1+1=2+1  ( Putting the value of x in equation (2))

         y=3

          y=2×6+1

             y=13

Hence, the possible solutions are:

(1,3) and (6,13)

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:

Step-by-step explanation:

B

The normal distribution describes how the values of a variable are distributed. Given a mean of 15 and standard deviation of 5.95, the area within which values lie could be found using the properties of a normal distribution, which state that ~68% of data falls within one standard deviation of the mean, ~95% within two standard deviations, and ~99.7% within three standard deviations.

This question is related to the normal distribution in statistics. The normal distribution is a probability function that describes how the values of a variable are distributed. It is a symmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. Extreme values in both tails of the distribution are similarly unlikely.

Given a normal distribution with a mean of 15 and a standard deviation of 5.95, we are asked to find the area within which the values lie. Using the properties of a normal distribution, we know that:

So, if we wanted to find the area within one standard deviation of the mean, for instance, we would calculate the values of (mean - standard deviation) and (mean + standard deviation), which would represent the range within which approximately 68% of the data lies.

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Answer:

Step-by-step explanation:

Draw a generic normal curve.  Subdivide the x-axis on each side of the center (mean) into four approx. = parts.

Label the mean with '50.'

1 std. dev. below the mean would be 50-2 = 48;

2 std. dev.                             would be 48-2= 46, and

3 std dev.                               would be 46 - 2 = 44

Do the same on the other side of the mean.  

The 3 corresponding values will be 52, 54 and 56.

Answer:

It would be 3 groups because 21/7 = 3

MARK AS BRAINIEST PLEASE

Answer: 26.24

32% of 82

0.32 • 82 = 26.24

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

[tex] \tan(60°) = \frac{x}{OR} \\ \Leftrightarrow x = OR \tan(60°) = OP \sqrt{3} = 12 \sqrt{3} [/tex]

Answer:

The answer is C. 9^-2

Step-by-step explanation:

Don’t know but not the first one

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:

It is B. hyperbola, 45 degrees.

SteIt is p-by-step explanation:

If we rotate the standard form  x^2 - y^2 = 1 through 45 degrees we get xy = 1/2.

xy = -2.5 comes from x^2 - y^2 = -5  being rotated 45 degrees.

Answer:

The correct option is b

Step-by-step explanation:

The given equation is

[tex]xy=-2.5[/tex]

It can be written as

[tex]xy+2.5=0[/tex]              .... (1)

The general forms of conic is

[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]             .... (2)

From (1) and (2), we get

[tex]A=0,B=1,C=0,D=0,E=0,E=2.5[/tex]

[tex]B^2-4AC=1-4(0)(0)=1>0[/tex]

Since the value of B²- 4AC > 0, then it is hyperbola.

The formula form angle of rotation is

[tex]\tan 2\theta=\frac{B}{A-C}[/tex]

[tex]\tan 2\theta=\frac{1}{0-0}[/tex]

[tex]\tan 2\theta=\infty[/tex]

[tex]\tan 2\theta=\tan (90^{\circ})[/tex]

[tex]2\theta=90^{\circ}[/tex]

[tex]\theta=45^{\circ}[/tex]

The angle of rotation is 45°. Therefore the correct option is b.

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:

  5

Step-by-step explanation:

The integers 5 and 5 sum to 10 and have the largest possible product.

___

The two numbers will be x and (10-x). Their product is x(10-x), which describes a downward-opening parabola with zeros at x=0 and x=10. The maximum (vertex) of that parabola is halfway between the zeros, at x=5. Both integers have the same value: 5. Their product is 25.

If there is a requirement the integers be distinct, then 6 and 4 are the integers of choice. Their product is 24.

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:

[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]

Diameter is the distance all the way across a circle (going through the center), and radius is the distance from the center to the edge. This means that the radius is always half of the diameter. If the diameter is 24, the radius is 24/2 = 12 inches.

Answer:

12

Step-by-step explanation:

it would be half of 24 which is half of the wheel

Answer:

the answer is A, 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Stem Leaf Plot : A special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

So, In the Given Stem leaf plot the numbers are :

100,101,90,93,94,94,95,81,86,87,89,70,72,76,69,56,58,49

Arrange in ascending order

49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101

Now we are supposed to find how many data points would be contained in the bar from 95-105

49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101

So, we can see there are 3 data points are contained in bar from 95 -105.

Hence 3 data points are contained in bar from 95 -105.

Answer:

[tex]y=\frac{1}{3}x+2[/tex]

Step-by-step explanation:

The given system of equation is;

[tex]x-3y=-6...(1)[/tex]

and

[tex]2x-7y=10...(2)[/tex]

To solve for y in the first equation; we add [tex]-x[/tex] to both sides.

[tex]-3y=-6-x[/tex]

We now divide through by -3;

This implies that;

[tex]y=\frac{1}{3}x+2[/tex]

Wendy can ride 17.5 miles in 2.5 hours

Answer:

17.5 miles

Step-by-step explanation:

[tex]\frac{miles}{min} = \frac{miles}{min} \\\\\\[/tex]

Convert hours to minutes

60 minutes = 1 hour

[tex]2.5*60=150[/tex]

2.5 hours = 150 minutes

[tex]\frac{0.7}{6} = \frac{x}{150} \\\\\\[/tex]

Cross multiply

[tex]0.7*150=6*x\\105=6x\\\frac{105}{6} =x\\17.5=x[/tex]

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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