A line has a slope of -3 and passes through the point (-3, 8). What is the equation of the line?
o y=-3x+6
o y--3x+8
o y=bx-
o y=8x-3

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

Question 2  is $500 and Question 3 is 5

Step-by-step explanation:

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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This means that she made a 20% return on the money she invested in the property. For every dollar she invested, she earned 20 cents in profit.

To calculate Jennifer Aniston's return on investment (ROI), we can use the formula:

ROI = (Net Profit / Initial Investment) * 100

First, let's calculate the net profit. The net profit is the selling price minus the initial investment:

Net Profit = Selling Price - Initial Investment

Net Profit = $2,200,000 - $2,000,000

Net Profit = $200,000

Next, we calculate the ROI:

ROI = (Net Profit / Initial Investment) * 100

ROI = ($200,000 / $1,000,000) * 100

ROI = 0.2 * 100

ROI = 20%

Jennifer Aniston's return on investment for this property is 20%.

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The required solution of the number to the nearest 10 , 100 and 1000 is 1260, 1300, 1000.

A number that is easily multiplied, divided, etc., and especially a number that ends in zero.

Given:

A school has 1256 pupils write this number to the nearest 10 , 100 and 1000

According to given question we have

⇒ Round off to 10 for 1256 is 1250 or 1260 but nearest to 1256 is 1260.

⇒  So, round off to the nearest 10 is 1260.

⇒ Round off to 100 for 1256 is 1200 or 1300 but nearest to 1260 is 1300.

⇒  So, round off to the nearest 100 is 1300.

⇒  Round off to 1000 for 1256 is 1000 or 2000 but nearest to 1256 is 1000.

⇒  So, round off to the nearest 1000 is 1000.

∴  The answer is 1260,1300,1000.

Therefore, the required solution of the number to the nearest 10 , 100 and 1000 is 1260, 1300, 1000.

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Answer:

8

Step-by-step explanation:

The user above is correct. The square root of 61 is equal to 7.810249676 which can be rounded up to 8.

Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

Answer:

A) measures the space inside in cubic units

Step-by-step explanation:

Answer:

46.8 cm²

Step-by-step explanation:

The diagonal of the square has length \(\sqrt{6^2+10^2}=2\sqrt{34}\). Therefore, the radius of the circle is \(\sqrt{34}\), meaning the area is \(\pi(\sqrt{34})^2 \approx 34(3.14)=106.76\).

The area of the rectangle is \((6)(10)=60\) cm².

Subtracting the areas, the answer is 46.76 cm², which is 46.8 cm² to the nearest tenth.

Answer:

Decay rate K = -2.44%

Step-by-step explanation:

From the question, we want to know the decay rate of strontium 90

Mathematically, this is accessible from its decay equation

From the decay equation, we can see that that ;

At = Ao e^-0.0244t

Generally, the decay equation of a radioactive sample can be written as

At = Ao e^-kt

where K represents the decay constant

From the equation, we can see that;

k = 0.0244 which when represented as a percentage is 2.44%

Since it’s a decay we can say that the decay rate is -2.44%

The answer is : -2.44%

Answer:

Dependent Variable = tips left by male customers

Independent Variable = T-Shirt color worn by waitresses

Step-by-step explanation:

Dependent variable is the variable that changes when the independent variable changes.

In other words, when the independent variable is varied, the dependent variable changes. The dependent variable is the effect or outcome of the manipulation of the independent variable.

In the study referred to in the question above, the amount of tips given to waitresses is dependent on the color of the T-shirt the waitresses wear.

Therefore, the dependent variable is T-Shirt color, while the independent variable is the amount of tips given.

a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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Answer:

\(6 - 18x \geqslant 4 - 17x \\ \\6 - 4 \geqslant 17x + 18x \\ 2 \geqslant x\)

The distance of the straight line is √17 miles and the angle formed is

75.96°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A bus drives 1 mile west and 4 miles north.

Let, The distance the bus travels along the west be adjacent and the distance traveled in the north be the height.

So, By Pythagoras' theorem,

The straight line distance = √(1² + 4²).

= √(1 + 16) miles.

= √17 miles.

Now, We know tan = opposite/adjacent.

tan = 4/1.

tan⁻¹(4/1) = Ф.

Ф = 75.96°.

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Answer:

∠ ABC = 49°

Step-by-step explanation:

the chord- tangent angle ABC is half the measure of the intercepted arc AB

∠ ABC = \(\frac{1}{2}\) AB = \(\frac{1}{2}\) × 98° = 49°

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

Answer:

C

Step-by-step explanation:

Answer:

29 degrees

Step-by-step explanation:

Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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We have the following equation:

since we need P, we must move k and V to the left hand side as

By substituting the given values, we get

that is, P is equal to 2.

Answer:

\(\frac{7}{10}\)

Step-by-step explanation:

100\(m^{2}\) -5 = 44  Add 5 to both sides

100\(m^{2}\) = 49  Divide both sides by 100

\(m^{2}\) = \(\frac{49}{100}\)

\(\sqrt{m^{2} }\) = \(\frac{\sqrt{49} }{\sqrt{100} }\)

m = \(\frac{7}{10}\)

The mean is  2,071,798.33

The Median is 1,485,552

The range is 7,425,310

The standard deviation is given as 1961105.68

Mean = (Sum of all populations) / (Number of cities)

= (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12

= 24,861,580 / 12

= 2,071,798.33

To find the median, we need to arrange the populations in increasing order and find the middle value. If we arrange these values, we get:

911,507, 978,908, 979,576, 1,021,795, 1,343,573, 1,423,851, 1,547,253, 1,584,064, 1,680,992, 2,320,268, 2,693,976, 8,336,817

Since there are 12 cities (an even number), the median would be the average of the 6th and 7th values:

Median = (1,423,851 + 1,547,253) / 2

= 1,485,552

The mode isn't applicable here as no city population repeats.

The range is the highest population minus the lowest population:

Range = 8,336,817 - 911,507

= 7,425,310

Standard deviation  =  (911507- 2068548.3333333)² +  (978908 - 2068548.3333333)² + (979576  - 2068548.3333333)²  + ( 1021795 -  2068548.3333333)² +  (1343573- 2068548.3333333)²  +( 1423851- 2068548.3333333)² + (1547253- 2068548.3333333)² +( 1584064- 2068548.3333333)² + (1680992- 2068548.3333333)² + ( 2320268- 2068548.3333333)²  +(2693976- 2068548.3333333)² +( 8336817 - 2068548.3333333)² / 12

= 46151226311869 / 12

=  3845935525989.1

\(standard deviation = \sqrt{ 3845935525989.1}\)

=  1961105.6896529

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The volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells is \($4\pi$\) cubic units.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

To find the volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells, we need to follow these steps:

Sketch the region and the axis of rotation. The region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) is a quarter-circle with radius 2 centered at the origin. The axis of rotation is the x-axis.

Choose a vertical strip with width $\Delta x$ that runs parallel to the y-axis and intersects the region. The height of this strip is given by the equation $y = 4 - x^2$.

Imagine rotating this strip around the x-axis to form a cylindrical shell with thickness \($\Delta x$\), height \($4 - x^2$\), and radius \($x$\).

The volume of this cylindrical shell is given by the formula \($V = 2\pi x(4-x^2)\Delta x$\).

To find the total volume of the solid, we need to add up the volumes of all the cylindrical shells. This can be done by taking the limit as the width of the strips $\Delta x$ approaches zero and summing up the volumes of the resulting shells. This gives us the integral:

\($V = \int_{0}^{2} 2\pi x(4-x^2) dx$\)

We can simplify this integral by expanding the expression inside the parentheses, which gives us:

\($V = \int_{0}^{2} 8\pi x - 2\pi x^3 dx$\)

We can then integrate each term separately to get:

\($V = [4\pi x^2 - \frac{1}{2}\pi x^4]_{0}^{2}$\)

\($V = (4\pi \cdot 2^2 - \frac{1}{2}\pi \cdot 2^4) - (4\pi \cdot 0^2 - \frac{1}{2}\pi \cdot 0^4)$\)

\($V = 8\pi - 4\pi = 4\pi$\)

Therefore, the volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells is \($4\pi$\) cubic units.

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Answer:

6  1 / 24

Step-by-step explanation:

in 1 hour - 5 / 6 tons of dust

Total dust = 7  1 / 4 = 29 / 4

1 ----- 5 / 6

x ----- 29 / 4

x = (29 / 4 ) * (5 / 6)

x = 145 / 24

x = 6  1 / 24

There are no two Real numbers that add up to -2 and multiply to 10.

The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:

Equation 1: x + y = -2

Equation 2: x * y = 10

To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:

1. Solve Equation 1 for x:

  x = -2 - y

2. Substitute the value of x in Equation 2:

  (-2 - y) * y = 10

3. Simplify the equation:

  -2y - y^2 = 10

4. Rearrange the equation to standard form:

  y^2 + 2y + 10 = 0

5. Since the equation is a quadratic equation, we can apply the quadratic formula:

  y = (-b ± √(b^2 - 4ac)) / (2a)

  In this case, a = 1, b = 2, and c = 10.

6. Calculate the discriminant: b^2 - 4ac:

  2^2 - 4(1)(10) = 4 - 40 = -36

7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.

In conclusion, there are no two real numbers that add up to -2 and multiply to 10.

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Answer:

m∠C = 122°

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary. This means

m∠A + m∠C = 180°

m∠B + m∠D = 180°

To find angle C we need to find x, then subtract m∠A from 180°

x+20=3x

20=2x

x=10

Now we substitute 10 in for x

m∠A=2(10)+38

m∠A=20+38

m∠A=58°

Now we subtract this value from 180.

m∠C=180-58

m∠C=122°

Answer:

62°

i took the test and this is the right answer

Answer: answer 2

Step-by-step explanation:

We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.

a) The problem asks for the volume of ice cream in one scoop.

b) The given fact is that the radius of the scoop is 2 inches.

c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.

d) Number Sentence:

  - Given: Radius (r) = 2 inches

  - Formula: V = (4/3)πr³

  - Substituting the value: V = (4/3)π(2)³

  - Simplifying: V = (4/3)π(8)

  - Evaluating: V = (4/3)(3.14)(8)

  - Multiplying: V = 33.49333333 (approx.)

e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.

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Answer:

m=25/28

Step-by-step explanation: