An item is originally priced $25. It is on sale
for 15% off. What is the sale price?

Answer:

1/36

Step-by-step explanation:

total are 36 and it's 1

40 is 20% of what number? 200

60 is 25% of what number? 240

73 is 20% of what number?365

10 is 5% of what number? 200

12 is 24% of what number? 50

Mallorie has $5 in her wallet. If this is 10% of her monthly allowance, what is her monthly allowance? $50

Jacob has $10 in his wallet. If this is 40% of his weekly allowance, what is his weekly allowance? $25

13 is 26% of what number? 50

120 is 30% of what number? 400

In the first year, a new car can lose 20% of its value. If a car lost $4,200 of value in the first year, how much did the car originally cost? $21000

y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

The equation y= -2 -4x in the form of slope intercept form y=mx+b is y=-4x-2.

Where m represents the slope and y intercept is -2.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.

The negative reciprocal of -4 is 1/4.

Therefore, the slope of the perpendicular line is 1/4.

The perpendicular line is y=1/4x-2.

We know that the parallel lines have same slope.

y=-4x+3

Hence, y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

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The lowest score for the normally distribution with mean 72 and standard deviation 8 is equal to 82.

Mean of the normally distributed data 'μ' = 72

Standard deviation 'σ ' = 8

Lowest score with 10% ( 90percentile )

z = InvNorm(0.90)

 = 1.28

Let 'X' be the lowest score for the normal distribution

z = ( X - μ ) / σ

Substitute the values we get,

⇒ 1.28 = ( X - 72 ) / 8

⇒ X - 72 = 1.28 × 8

⇒ X = 10.24 + 72

⇒ X = 82.24

⇒ X = 82 ( round to an integer )

Therefore, the lowest score for normally distribution which will place manage on 90th percentile with given mean and standard deviation is equal to 82.

The above question is incomplete, the complete question is:

Scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8.we want to find the lowest score that will place a manager in the top 10% (90th percentile) of the distribution. Your answer is Please round to an integer number.

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The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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r = - 0.98754

Answer:

Slope = - 0.7120

SE = 1.295

Step-by-step explanation:

Given the data:

0 | 33.3

0 | 31.0

3 | 29.8

3 | 27.8

6 | 28.0

6 | 29.0

10 | 25.5

10 | 23.8

20 | 18.3

20 | 15.5

30 | 11.7

Using the relation to Obtian the slope :

Slope, b = r(Sy/Sx)

r = correlation Coefficient ; Sy = standard deviation of Y - values ; Sx = standard deviation of X-values

r = - 0.98754

Slope, b = - 0.98754(7.8471 / 10.884) = - 0.7120

SE = √SSresidual / df

df = n - 2 = 12 - 2 = 10

SSresidual = 16.7812

SE = √(16.7812/ 10)

SE = 1.295

Answer:

B

Step-by-step explanation:

Using Sine 30°

1/2 = Perpendicular/Hypoteneous

1/2 = Perpendicular/8

8=2 Perpendicular

Perpendicular= 4

Using Tangent 60°

root3= Perpendicular/Base

root3= 4/y

Yroot3=4

Y= 4/root3

Y=4/1.732

Y= 2.3094688222

We should add 25 both side by method of completing the square.

We have to given that;

A student is solving the problem

x² + 10x + _ = 16 + _

Now, We can completing the square as;

⇒ x² + 10x + 5² = 16 + 5²

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 16 + 25

Hence, We should add 25 both side by method of completing the square.

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Answer: I believe the answer you're looking for is absolute value

I hope this helps!!!

Answer:

- 3

Step-by-step explanation:

2x - 9 = 5x

- 9 = 5x - 2x

-9 = 3x

-9/3 = x

x = -3

Using sampling concepts, it is found that it is not a random sample, as it considers only the books in her bedroom, hence books from other people in the household are likely to not be considered.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which has to involve all groups in the population.

In this problem, a random sample should involve the books of all people in the household, not only Jamaya's. Hence, it is not a random sample, as it considers only the books in her bedroom, hence books from other people in the household are likely to not be considered.

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Answer:

104ft

Step-by-step explanation:

First - find the area of triangles.

h = hight

b = base
h • b / 2

5 • 8 /2 = 20ft

And

4 • 6 /2 = 12ft

And then area of the rectangle.
l • w

9 • 8 = 72 ft

Than add. Them all together

Answer:

B

Step-by-step explanation:

Class and cost per class should be multipled so must be A or B. The amount of money she has should be greater than or equal to her costs or she can't afford it! So B.

Answer:

b. 146 greater than or equal to 9c + 10

Step-by-step explanation:

hope this helped :)

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Answer:

D.

Step-by-step explanation:

2y = (2 x y) = 2 x 0 = 0

0 - 0 = 0

Answer:

0

Step-by-step explanation:

2y-0=0

y=0

2x0=0

0-0=0

\(1/2 * 2 * 1 = 1\) square unit.

Step-by-step explanation:

To find the maximum area of the triangle, we need to locate the vertex of the parabola. This occurs when x=1. The y-coordinate at x=1 is 1. We can then use this as the height of the triangle. The base of the triangle is the distance between x=0 and x=2, which is 2. Therefore, the maximum area of the triangle is 1/2 * 2 * 1 = 1 square unit.

Answer:

c=13.4

Step-by-step explanation:

Answer:

The total surface area is given by: base area + 4 * triangular face area

Substituting the values we calculated: 52441 + 4 * 10424.4 ≈ 91588.4 square meters.

Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.

1. Initial prediction for the data set with smaller Mean Absolute Deviation was Period A. Prediction was wrong.

2. The Mean Absolute Deviation for Period A is 1.8 and Period B, 1.1

This means that period B has a smaller Mean absolute deviation.

We start by finding the mean for each set;

Period A: Mean = (1×92 + 1×94 + 3×95 + 1×96 + 2×97 + 1×99 + 1×100)/10

= 960/10

= 96

Period B: Mean = (1×94 + 3×95 + 1×96 + 4×97 + 1×98)/10

= 961/10

= 96.1

Period A:

Mean Absolute Deviation = ((92-96) + (94-96) + 3(95-96) + (96-96) + 2(97-96) + (99-96) + (100-96))/10

Mean Absolute Deviation = (4 + 2 + 3 + 0 + 2 + 3 + 4)/10

Mean Absolute Deviation = 1.8

Period B:

Mean Absolute Deviation = ((94-96.1) + 3(95-96.1) + (96-96.1) + 4(97-96.1) + (98-96.1))/10

Mean Absolute Deviation = (2.1 + 3.3 + 0.1 + 3.6 + 1.9)/10

Mean Absolute Deviation = 1.1

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Answer:

19.99%

Step-by-step explanation:

hope this helps

here you go

Answer:

126.72m

Step-by-step explanation: 1.32 x 96 = 126.72, I struggled with that stuff too no shame

The the length of LJ is approximately 3.5.OptionD) is correct.

To find the length of LJ, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle.

Let's denote the length of JL as x. Then, we can set up the following proportion:

sin(23°) / LJ = sin(89°) / KL

where KL is given as 9.

We can simplify this proportion by using the fact that sin(89°) = cos(1°) (since the sine of the complement of an angle is equal to the cosine of the angle), and by using a calculator to find the values of sin(23°) and cos(1°):

0.3919 / LJ = 0.0175 / 9

Multiplying both sides by x and then dividing both sides by 0.0175, we get:

LJ = 0.3919*9/ 0.0175

x ≈ 3.5

Therefore, the length of LJ is approximately 3.5.OptionD) is correct.

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Answer:

Only one solution.

Step-by-step explanation:

y = 3x +2

y -2x =4

y - 2x = 4

=> y = 2x +4

y = 3x + 2

y = 2x + 4

Since both equations are not the same, so the answer cannot be "infinitely many solutions".

They both intersect each other 1 point, so it cannot be "no solutions".

So the answer is "Only 1 solution".

Part 1 - Circumcenter: The point where all three sides of the triangle meet and intersect, also the center of the circle that passes through all three vertices of the triangle.

Intersect is an operation used in mathematics and computing to determine the common elements of two or more sets. It is usually written as a symbol (∩) and is used to return the set of all elements that are in both sets. For example, if A is the set of all even numbers and B is the set of all prime numbers, then A ∩ B will return the set of all prime even numbers.

- Orthocenter: The point where the three altitudes of the triangle intersect.
- Centroid: The point where the three medians of the triangle intersect.

Part 3: The three centers of the triangle (circumcenter, orthocenter, and centroid) can all be constructed using a straightedge and compass. The circumcenter is located at the intersection of the three sides, the orthocenter is located at the intersection of the three altitudes, and the centroid is located at the intersection of the three medians. From this, we can make the hypothesis that these three centers of a triangle are related in that they are all located at the intersection of two or more lines that form the triangle.

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The area of ΔEFG is approximately 916 square centimeters.

Given that,

In ΔEFG

f = 88 cm ,

g = 18 cm

∠E=68°

To find the area of ΔEFG,

Use the formula:

Area = (1/2)xfxgxsin(∠E)

First, we need to convert the angle from degrees to radians.

We can do this by multiplying by π/180.

∠E = 68° * π/180 ≈ 1.19 radians

Next, we can plug in the values we have:

Area = (1/2)x88x18xsin(1.19)

        ≈ 915.56 cm²

Rounding this to the nearest square centimeter,

we get,

Area ≈ 916 cm²

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The different coordinates after respective rotation are:

1) A'(2, 0)

2) A'(0, -2)

3) A'(-2, 0)

There are different methods of transformation such as:

Translation

Rotation

Dilation

Reflection

Now, the coordinate of the given point A is: A(0, 2)

1) The rule for rotation of 90 degrees clockwise is:

(x, y) →(y,-x)

Thus, we have:

A'(2, 0)

2) The rule for rotation of 180 degrees is:

(x, y) → (-x,-y)

Thus, we have:

A'(0, -2)

3) The rule for rotation of 180 degrees is:

(x, y) → (-y,x)

Thus, we have:

A'(-2, 0)

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Answer:

The hypotenuse is 17

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

8^2 + 15^2 = c^2

64 + 225 = c^2

289 = c^2

Take the square root of each side

sqrt(289) = sqrt(c^2)

17 = c

Answer:

17 cm

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

\(a^2+b^2=c^2\)

where a and b are the legs and c is the hypotenuse.

In this triangle, 8 cm and 15 cm are the legs, because they form the right angle. The hypotenuse is unknown.

a= 8

b= 15

\(8^2 + 15^2= c^2\)

Solve the exponents on the left side of the equation.

8^2= 8*8= 64

\(64+15^2=c^2\)

15^2= 15*15= 225

\(64+225=c^2\)

Add 64 and 225

\(289=c^2\)

c is being squared. We want to get c by itself, so we must perform the inverse. The inverse would be taking the square root.

Take the square root of both sides.

\(\sqrt{289} =\sqrt{c^2}\)

\(\sqrt{289} =c\)

\(17=c\)

c= 17 cm

The length of the hypotenuse is 17 centimeters.