In a 36% sale, the price of a phone reduced by $135.
Find the original price of the phone.

Answer:

False

Step-by-step explanation:

I would say false.

Answer:

The circle is centered at (9, -8) and diameter 8.

Step-by-step explanation:

(x-h)^2 +(y-k)^2 =r^2

(x-9)^2+(y+8)^2=4^2

Center: (h,k) = (9,-8)

Radius: r=4

The circle is centered at (9, -8) and radius is 4 or diameter 8.

The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 8.94 feet.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In this case, the fence, building, and ladder form a right triangle, where the fence and building are the legs, and the ladder is the hypotenuse.

We know that the fence is 8 feet tall and the building is 4 feet away from the fence, so the height of the right triangle (the distance from the ground to the top of the building) is also 8 feet.

To find the length of the ladder, we need to use the Pythagorean theorem:

ladder^2 = fence^2 + height^2
ladder^2 = 8^2 + 4^2
ladder^2 = 64 + 16
ladder^2 = 80
ladder ≈ 8.94 feet

Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 8.94 feet.

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The radian measure of the angle at the center of the circle is approximately 1.6623 radians.

We are given that the radius of the circle is 77.0 cm and the length of the intercepted arc is 128 cm. We need to find the radian measure of the angle at the center of the circle.

To solve this problem, we use the formula relating the angle at the center of a circle, the radius of the circle, and the arc length intercepted by the angle.

The formula is given byθ = s/rwhereθ = angle at the center of the circle in radians s = arc length intercepted by the angle r = radius of the circle Substituting the given values, we getθ = 128/77.0 = 1.6623 radians (rounded to four decimal places)

Therefore, the radian measure of the angle at the center of the circle is approximately 1.6623 radians.

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Approximately 9.5% of the racers did not complete the marathon.

The total of those who quit and those who were disqualified represents the number of runners who did not finish the marathon

Number who did not complete = 12 + 8 = 20

To find the percentage of racers who did not complete the marathon, we need to divide this number by the total number of racers who started the marathon (210) and multiply by 100

Percentage who did not complete is

= (20 / 210) x 100

= 9.523%

Rounding this to the nearest tenth of a percent gives us a final answer of 9.5%. Therefore, approximately 9.5% of the racers did not complete the marathon.

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Answer:

Line N is a vertical line with an undefined slope

Step-by-step explanation:

To find slope we do (y2-y1)/(x2-x1)

So we do that with (-1,4) and (-1,-4)

(-4-4)/(-1-(-1))

-8/0

Since the denominator is 0, that means the slope is undefined because you cannot divide by 0

Answer:

The inequality is, -18/7 less than x less than 18/7

Step-by-step explanation:

Answer:

The second option is the correct one.

Step-by-step explanation:

The algebraic expression is as such:

\(10x^{2}y+6x^{2}-7y^{2}-6\)

Step 1: Looking at the first element

The first term/element of the final expression is \(10x^{2}y\).

Only like variables can be added or subtracted from each other (\(x\) can be added to \(x\) to give \(2x\), but \(x\) added to \(y\) doesn't yield a different result).

In the options, there are two terms which have the variables \(x^{2}y\):

\(8x^{2}y\) and \(2x^{2}y\).

In the first three options, \(8x^{2}y\) is being added to \(2x^{2}y\), which would give a result of \(10x^{2}y\):

\(8x^{2}y+2x^{2}y\\=(8+2)x^{2}y\\=10x^{2}y\)

But the fourth option subtracts \(2x^{2}y\) from  \(8x^{2}y\), which wouldn't equal to \(10x^{2}y\), and so the fourth option isn't correct.

Step 2: Looking at the second element

The second term/element of the final expression is \(6x^{2}\).

In the options, there are two terms which have the variables \(x^{2}\):

\(7x^{2}\) and \(x^{2}\).

In the rest of the three options, \(x^{2}\) is being subtracted from \(7x^{2}\), which would give a result of \(6x^{2}\):

\(7x^{2}-x^{2}\\=(7-1)x^{2}\\=6x^{2}\)

So, we can't eliminate any options based on this.

Step 3: Looking at the third element:

The same thing as the second element happens with \(-7y^{2}\), so we can't use it either.

Step 4: Looking at the 3x that are being cancelled out

We can see that the options contain the term \(3x\), even though it is nowhere to be seen in the final expression.

This means that \(3x\) is subtracted from itself to produce a result of \(0\) (\(3x-3x=0\)), thus it is not present in the final expression.

In the second and third options, we can see that \(3x\) is being subtracted from itself.

But, the first option has \(3x\) being added to itself.
This would produce a result of \(6x\):

\(3x+3x\\=(3+3)x\\=6x\)

Which isn't present in the final expression.

Thus, the first option is also incorrect.

Step 5: Looking at the fourth element

The fourth term/element of the final expression is \(-6\).

In the options, there are two terms which are also integers:

\(-2\) and \(4\).

In the second option, \(4\) is being subtracted from \(-2\), which would give a result of \(-6\):

\(-2-4\\=-6\)

But in the third option, \(4\) is being subtracted from \(2\), which would give a result of \(-2\) instead of \(-6\),
So, the third option is also wrong.

Answer:

7) B.

8) D.

Step-by-step explanation:

Answer: Unless I am missing something, there are no solutions

(guessing you need to solve for x)

(given) 2 - 2x - 4= –2x + 5 ​

(combine like terms) -2 -2x = -2x + 5

(add 2 to both sides) -2x = -2x + 5

Two ways to go from here:

(subtract 2x from both sides) 0 = 7 which I think means no solutions

Or you try to figure something out, but I am not sure what that would be currently, it's been a bit since I've done this, good luck!

The floor area of the engineer's model of the sugar factory is 10.825 square feet.

To determine the floor area of the engineer's model of a sugar factory in square feet, we need to convert the given measurements from inches to feet. Since there are 12 inches in a foot, we can divide both dimensions by 12 to convert them.

The length of the model in feet is 30 inches / 12 = 2.5 feet, and the width is 52 inches / 12 = 4.33 feet.

To find the floor area, we multiply the length by the width:

Area = Length × Width

= 2.5 feet × 4.33 feet

= 10.825 square feet

It's important to note that the given measurements are not a standard aspect ratio or scale for a sugar factory. The given dimensions may be scaled down for the model's convenience, so the calculated floor area is only applicable to the scale of the model.

In actuality, a sugar factory would have much larger dimensions.

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If a student is selected at random from this senior class,  the probability that the student is:  

(i) a male and has a driver's license is 0.3825,

(ii) a female and has a driver's license is 0.385.

We need to find the probability that a student is (i) a male and has a driver's license, and (ii) a female and has a driver's license, given that there are 400 seniors, 180 of which are males.

(i) A male and has a driver's license:
Step 1: Find the number of males with driver's licenses: 180 males * 85% = 153 males.
Step 2: Calculate the probability: (Number of males with driver's licenses) / (Total number of seniors) = 153/400.
Step 3: Simplify the probability: 153/400 = 0.3825.

(ii) A female and has a driver's license:
Step 1: Calculate the number of females: 400 seniors - 180 males = 220 females.
Step 2: Find the number of females with driver's licenses: 220 females * 70% = 154 females.
Step 3: Calculate the probability: (Number of females with driver's licenses) / (Total number of seniors) = 154/400.
Step 4: Simplify the probability: 154/400 = 0.385.

So, the probability that a student selected at random from this senior class is: (i) a male and has a driver's license is 0.3825, and (ii) a female and has a driver's license is 0.385.

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If a student is selected at random from this senior class,  the probability that the student is:  

(i) a male and has a driver's license is 0.3825,

(ii) a female and has a driver's license is 0.385.

We need to find the probability that a student is (i) a male and has a driver's license, and (ii) a female and has a driver's license, given that there are 400 seniors, 180 of which are males.

(i) A male and has a driver's license:
Step 1: Find the number of males with driver's licenses: 180 males * 85% = 153 males.
Step 2: Calculate the probability: (Number of males with driver's licenses) / (Total number of seniors) = 153/400.
Step 3: Simplify the probability: 153/400 = 0.3825.

(ii) A female and has a driver's license:
Step 1: Calculate the number of females: 400 seniors - 180 males = 220 females.
Step 2: Find the number of females with driver's licenses: 220 females * 70% = 154 females.
Step 3: Calculate the probability: (Number of females with driver's licenses) / (Total number of seniors) = 154/400.
Step 4: Simplify the probability: 154/400 = 0.385.

So, the probability that a student selected at random from this senior class is: (i) a male and has a driver's license is 0.3825, and (ii) a female and has a driver's license is 0.385.

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The lateral surface area of the rectangular prism with sides measuring 4, 5, and 2 units is 18 square units.

To find the lateral surface area of a rectangular prism, we need to calculate the sum of the areas of its four lateral faces.

In this case, the rectangular prism has sides measuring 4, 5, and 2 units. Let's label the length, width, and height of the prism accordingly:

Length = 4 units

Width = 5 units

Height = 2 units

The lateral faces of a rectangular prism are the faces that do not contribute to the top or bottom surface. For a rectangular prism, the lateral faces are pairs of equal-sized rectangles.

The lateral face area can be calculated by multiplying the length and height or the width and height. In this case, we have two pairs of lateral faces:

Pair 1: Length x Height = 4 units x 2 units = 8 square units

Pair 2: Width x Height = 5 units x 2 units = 10 square units

To find the lateral surface area, we sum the areas of the two pairs of lateral faces:

Lateral Surface Area = Pair 1 + Pair 2 = 8 square units + 10 square units = 18 square units.

Therefore, the lateral surface area of the rectangular prism with sides measuring 4, 5, and 2 units is 18 square units.

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Answer:

35/80

Step-by-step explanation:

just subtract 45 from 80 and that gives you the amount of students who do not walk to school.

Answer: 56.25 to 43.75

Step-by-step explanation: who walked/total to who didn't walk/total

Answer:

x= +5.2

Step-by-step explanation:

x=5.2

slope = y2-y1+ /x1-x2

6-4/x-4= x=5.2

a) The mean can be calculated by adding all values and then divide by the total number of values:

b) The median is the middle value in the list of numbers, then you have to order the numbers as follows: 0, 0, 1, 3, 6.

c) The mode is the value that occurs most often, as you have a 0 value twice, then

d) To calculate the sample variance you can use this formula

The sample standard deviation is the square root of sample variance, then

Answer:

Step-by-step explanation:

The solution to the system of equations is (1, 8).

From the question, we have the following parameters that can be used in our computation:

y-x=7 y=3x+5

To find the solution to the system of equations y - x = 7 and y = 3x + 5, we can substitute the second equation into the first equation to eliminate y:

y - x = 7

y = 3x + 5

Substituting y = 3x + 5 into the first equation:

3x + 5 - x = 7

2x = 2

x = 1

Now that we have found x = 1, we can substitute it back into either equation to find y:

y = 3x + 5

y = 3 * 1 + 5

y = 8

So the solution to the system is (x, y) = (1, 8).

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Answer:

It is similar by AA

Step-by-step explanation:

AA stands for angle-angle. In similar figures, angles are congruent, and the sides are proportional. the corresponding angles are the same. Hope this helps!

Answer:

10:17 (girls to total students)

7:17 (boys to total students)

10:7 (girls to boys)

7:10 (boys to girls)

Step-by-step explanation:

Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

To find the circumference of the triangle, we need to first find the lengths of its sides. Let the three sides be x, y, and z, such that x:y:z is the given ratio. Without loss of generality, we can assume that x is the shortest side.

Let k be a constant such that y = kx and z = lx, where k and l are constants. Then, we have:

x + kx + lx = 2r

Simplifying this equation, we get:

x(1 + k + l) = 2r

So, we have:

x = (2r)/(1 + k + l)

y = kx = k(2r)/(1 + k + l)

z = lx = l(2r)/(1 + k + l)

The circumference of the triangle is the sum of its three sides:

C = x + y + z

Substituting the expressions for x, y, and z, we get:

C = (2r)/(1 + k + l) + k(2r)/(1 + k + l) + l(2r)/(1 + k + l)

Simplifying this expression, we get:

C = (2r(1 + k + l))/(1 + k + l)

C = 2r

Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

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The area of the triangle is equal to A) 8.64. The Correct option is A) 8.64.

Let the lengths of the triangle be, 3x,4x,5x

Square of largest side = \(25x^{2}\)

Sum of square of other sides = \(3x^{2} + 4x^{2} = 25x^{2}\)

It is a right-angled triangle because the square of the greatest side equals the sum of the squares of the other sides.

The circumference of a right-angled triangle has a diameter equal to its hypotenuse.

hence, 5x=6 or x= \(\frac{6}{5}\)

Now, two perpendicular sides are then,  \(\frac{18 }{5} , \frac{24}{5}\)

\(Area = \frac{1}{2} \times \frac{18}{5} \times \frac{24}{5} = 8.64\)

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Question

A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to

A. 8.64

B. 12

C. 6

D. 10.5

Answer:

8) Area of triangle ABC is 60

   Area of triangle XYZ is 540

9) The ratio is 1:9

10) (use Pythagorean theorem)

     BC is 12 \(\sqrt{13^{2}-5^{2} } =12\)

     YZ=39 (the legs are the same because it is an Isosceles triangle)

11) the ratio is 1:3

Step-by-step explanation:

Answer:

|-9 - (6)|

9 + (6) = 15

Step-by-step explanation:

You just sale the exercise from the bars that makes the 2 signs positives and finally yoy just put that in the calculator.

The function (h∘j)(x) is (√(x-2) + 3) / (x^2 - 9), and the domain of the function (h∘j) is all real numbers except x = -3 and x = 3.

To find the composition of functions (h∘j)(x), we substitute j(x) into h(x) and simplify the expression.

Given h(x) = √x + 3 and j(x) = (x-2) / (x^2 - 9), we substitute j(x) into h(x):

(h∘j)(x) = h(j(x)) = h((x-2) / (x^2 - 9))

Simplifying further, we substitute j(x) = (x-2) / (x^2 - 9) into h(x):

(h∘j)(x) = √((x-2) / (x^2 - 9)) + 3

Therefore, the function (h∘j)(x) is (√(x-2) / √(x^2 - 9)) + 3.

To determine the domain of the function (h∘j)(x), we need to identify any values of x that would make the function undefined. In this case, the function (h∘j)(x) involves square roots, so we need to ensure that the expressions inside the square roots are non-negative.

First, let's consider the expression inside the square root (√(x-2)). For the square root to be defined, x-2 must be greater than or equal to 0. Therefore, we have x-2 ≥ 0, which gives us x ≥ 2.

Next, let's consider the expression inside the square root (√(x^2 - 9)). For the square root to be defined, x^2 - 9 must be greater than or equal to 0. We have (x - 3)(x + 3) ≥ 0, which gives us x ≤ -3 or x ≥ 3.

Combining both conditions, we find that the domain of (h∘j)(x) is all real numbers except x = -3 and x = 3. In interval notation, the domain can be expressed as (-∞, -3) ∪ (-3, 3) ∪ (3, ∞).

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The number of arrangements of letters of given words

(1) COMMISSION is  226800 ,

(2) HEEBIE-JEEBIES is 2162160 .

Part(a) : The word "COMMISSION" has 10 letters, with 2 each of M, I, O, and S, and 1 each of N and C.

The number of "distinguishable-arrangements" of letters is calculated as :

⇒ N = 10!/(2! × 2! × 2! × 2!)

⇒ 226800

So, there are 226800 "distinguishable-arrangements" of letters in word "COMMISSION".

Part(b) : The word "HEEBIE-JEEBIES" has 13 letters, but there are 6 "E"s and 2 "B"s, and 2 "I"s which are repeated.

So, the total number of distinguishable arrangements is :

⇒ 13!/(6! × 2! × 2!),

⇒ 12162160.

So, there are 2162160 "distinguishable-arrangements" of letters in word "HEEBIE-JEEBIES".

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The probability of getting a prime number on the spinner is 2/4 or 1/2.

There are four possible outcomes on the spinner: 6, 7, 8, and 9. To determine the probability of getting a prime number, we need to first identify which of these numbers are prime. Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves without leaving a remainder.

Out of the four possible outcomes, only two of them are prime: 7 and 9. Therefore, the probability of getting a prime number is the number of favorable outcomes (2) divided by the total number of possible outcomes (4), which simplifies to 1/2.

To see why this is true, we can think of the probability as a fraction where the numerator is the number of ways to get a prime number and the denominator is the total number of possible outcomes. In this case, there are two ways to get a prime number (7 and 9), and four possible outcomes (6, 7, 8, and 9). Therefore, the probability r is 2/4 or 1/2.

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A differential equation with some initial conditions is used to solve an initial value problem.

The required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.

Let the given equation be \($y^{1/2} dy\ dx y^{3/2} = 1\), y(0) = 9

\($(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1\) …..(1)

Divide the given equation (1)  by \($\sqrt{ y} $\)  giving

\($y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$\), which is in Bernoulli's form.

Put \($u=y^{(1+1 / 2)}=y^{(3 / 2)}$\)

Then \($(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$\).

Multiply (2) by \($\sqrt{ } y$\) and we get

\(y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1\)

(2/3) \(u^{\prime}+u=1$\) or \($u^{\prime}+(3 / 2) y=3 / 2$\),

which is a first order linear equation with an integrating factor

exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is

\(u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$\)  or

\(\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}\)

To obtain the particular solution satisfying y(0) = 4,

put x = 0, y = 4, then

8 = (9/4) + c

c = (23/4)

Hence, the required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

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