5. Use long division:
a. 483 ÷ 15
b. 907÷12​

Answer:

P(61≤ X≤94) = 49.85%

Step-by-step explanation:

From the given information:

The mean of the bell shaped fluorescent light bulb μ = 61

The standard deviation σ = 11

The objective of this question is to determine the approximate percentage of light bulb replacement requests numbering between 61 and 94 i.e P(61≤ X≤94)

Using the empirical (68-95-99.7)rule ;

At 68% , the data lies between  μ - σ and μ + σ

i.e

61 - 11 and 61 + 11

50 and 72

At  95%, the data lies between  μ - 2σ and μ + 2σ

i.e

61 - 2(11) and 61 + 2(11)

61 - 22 and 61 +22

39   and   83

At 99.7%, the data lies between  μ - 3σ and μ + 3σ

i.e

61 - 3(11) and 61 + 3(11)

61 - 33 and 61 + 33

28   and   94

the probability equivalent to 94 is when  P(28≤ X≤94) =99.7%

This implies that ,

P(28≤ X≤94) + P(61≤ X≤94) = 99.7%

P(28≤ X≤94) = P(61≤ X≤94) = 99.7 %    

This is so because the distribution is symmetric about the mean

P(61≤ X≤94) = 99.7 %/2

P(61≤ X≤94) = 49.85%

Answer:

The angles are

∠A = 90°, ∠B = 26.56°, ∠C = 63.43°

Step-by-step explanation:

We have that the angles of a vector are given as follows;

[tex]cos\left ( \theta \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}[/tex]

Whereby the vertices are represented as

A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),

AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) ,  BA = (-2, -6, 0)

BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)

AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)

θ₁ = AB·AC

a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0

Therefore, θ₁ = 90°

BA·BC = (-2)×(-5) + (-6)×(-5) = 40

[tex]{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |}[/tex] = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72

cos(θ₂) = 40/44.72 = 0.894

cos⁻¹(0.894) =θ₂= 26.56°

CA·CB = 5×3 + 5×(-1) = 10

[tex]{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |}[/tex] = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36

10/22.36 = 0.447

cos(θ₃) = 0.447

θ₃ = cos⁻¹(0.447) = 63.43°.

as the exterior angle is known

sum of that angle and f angle = 180

142 + f = 180

f = 180 - 142

f = 38

Answer:

38

Step-by-step explanation:

Hope this helps you :)

Answer:

O g(x) is shifted 4 units left and 6 units down from f(x).

Step-by-step explanation:

O g(x) is shifted 4 units left and 6 units down from f(x).

The graph of g(x) is shifted 4 units to the left and 6 units down from f(x).

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given functions are,

g(x) = 1/(x + 4) - 6

f(x) = 1/x

Here when a function f(x) changes to f(x + k) when it is translated k units left.

Here 1/x changes to 1/(x + 4).

So g(x) is shifted 4 units left.

Similarly a function f(x) changes to f(x) - k, if it is translated k units down.

So g(x) also shifted 6 units down.

Hence the correct option is D.

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Answer:

24

Step-by-step explanation:

30/100=x/80

cross multiply:

100x=2400

divide by 100:

x=24

Not quite sure how you want me to explain the other way step by step... Hope this helps!

80*.3=24

Answer:

A. They are the same.

Step-by-step explanation:

The sine of any acute angle is equal to its cosine.

Answer:

16

Step-by-step explanation:

Well first we need to plug in 10 for g and 6 for h.

2/5(10) + 3(6) - 6

4 + 18 - 6

22 - 6

16

Thus,

the answer is 16.

Hipe this helps :)

Answer:

16

Step-by-step explanation:

We are given the expression:

2/5g+ 3h - 6

We know that g=10 and h=6. Therefore, we can substitute 10 and 6 into the expression and solve according to PEMDAS( Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

2/5(10)+3(6)-6

First, multiply 2/5 and 10

4+ 3(6)-6

Next, multiply 3 and 6

4+18-6

Next, add 4 and 18

22-6

Finally, subtract 6 from 22

16

2/5g + 3h - 6 when g=10 and h= 6 is 16.

Answer:

The answer is option C.

[tex]g(x) = \frac{1}{2} |x| [/tex]

Hope this helps you

Answer: $10,000

Step-by-step explanation:

Given the following :

Profit if economy remains strong = $30,000

Profit if economy grows at moderate pace = $10, 000

Loss if economy goes into recession = $30,000

Probability that economy will remain strong = 20% = 0.2

probability the economy will grow at a moderate pace = 70% = 0.7

probability the economy will slip into recession = 10% = 0.1

Expected value = sum of (x * p(x))

Here expected value equals;

Strong economy profit = $30,000 * 0.2 = $6000

Moderate economy profit = $10,000 * 0.7 = $7000

Loss on Recession = $30,000 * 0.1 = $3000

Expected profit = $(6000 + 7000 - 3000)

Expected profit = $10,000

Answer: It represents that 2 will be divided into 3 equal parts.

Step-by-step explanation:

The given fraction : [tex]\dfrac{2}{3}[/tex]

here, Numerator = 2

Denominator = 3

It represents that 2 will be divided into 3 equal parts.

Question:

Find the value of the letter in each of the following and give reasons for the steps involved:

1 2 A

+ 6 A B =

A 0 9

Answer:

128 + 681 =  809

Step-by-step explanation:

Here, let's use the general form of numbers where any  letter must represent one value and each digit must be represented by just one letter.

Take the following:

A = 8

B = 1

Thus, A +B = 8 + 1 = 9

Also add:

8 + 2 = 10

In general form, tens digit is zero and the 1 is carried over.

I.e, A = 1 + 6 + 1 = 8

We can now see that,

A = 8

B = 1

Therefore,

1 2 A

+ 6 A B =

A 0 9

Will be written as:

128 + 681 =  809

Answer:

The formula would be

T(n) = 64 (-3/4)^n, n=0,1,2,...

or sometimes

T(n) = T(n-1)(-3/4),     T(0) =64, n=0,1,2,...

Step-by-step explanation:

The common ratio is -3/4, i.e.

(-3/4) * 64 = -48

(-3/4) * 48 = 36

(-3/4) * 36 = -27

...

The formula would be

T(n) = 64 (-3/4)^n, n=0,1,2,...

or sometimes

T(n) = T(n-1)(-3/4),     T(0) =64, n=0,1,2,...

Note: Would have been easier if the choices were supplied.

Answer:

The length of a side of the pool is 12 m²

Step-by-step explanation:

Let the area of the square plot be A. Since it is a square plot of 35 m side, its area is A = 35² = 1225 m².

Let A' be the area of the lawn. Since the area of the lawn is 1081 m², A' = 1081 m².

Now the area of the pool is the difference in area between the area of the square plot and the area of the lawn. So, let A'' be the area of the square swimming pool.

So, A'' = A - A'

A'' = 1225 m² - 1081 m²

A'' = 144 m².

Since the swimming pool is a square, the length of its side, L is thus

L = √A''

L = √144 m²

L = 12 m

So, the length of a side of the pool is 12 m.

Answer:

$ 5.65

Step-by-step explanation:

let the cost of a pencil and a ruler be $p and $r respectively.

4p +r= 1 -----(1)

6p +3r= 2.10

divide by 3 throughout:

2p +r= 0.70 -----(2)

Q: 3p +13r= ?

(1) -(2):

(4p +r) -(2p +r)= 1 -0.70

4p +r -2p -r= 0.30 (expand)

2p= 0.30 (simplify)

p= 0.30 ÷2 (÷2 on both sides)

p= 0.15

subst. into (1):

4(0.15) +r= 1

r +0.60= 1

r= 1 -0.60

r= 0.40

cost of three pencils and thirteen rulers

= 3p + 13r

= 3(0.15) + 13(0.40)

= 0.45 + 5.20

= $5.65

Answer:

Theresa is 58.82 in tall

Step-by-step explanation:

Steve: x=1.33y-6

x=72.24

Answer:

2) 30, 70, 80

Step-by-step explanation:

Well there has to be 3 angles that all add up to 180°.

1)

100+130+130

=360

2)

30+70+80

= 180

3)

25+3+35

=63

4)

45 + 105 + 120

=150

150+120

270

Answer:

Step-by-step explanation:

The length of this triangle is 10 squares

and the width is 4 squares

The diagonals divide the rectangle into four triangles

These traingles are isoceles

Each two triangles facing each others are identical

<B = 90 degree

B = alpha + Beta

Let Beta be the angle next alpha

The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:

Beta = 2x

Then B = alpha + 2x

90 = alpha +2x

90-alpha = 2x

x = (90-alpha)/2

Answer:

x = 90 - 2α

Step-by-step explanation:

Solution:-

- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".

                       < BAD > + < ADB > + < ABD > = 180°

                       < ABD > = 180 - 90° - α

                        < ABD > = 90° - α

- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".

- We name the foot of the perpendicular bisector as " F ":  " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.

                    < ABD > = < BAE >  = 90° - α   ... ( Isosceles triangle " BEA " )

Where, sides ( BE = AE ).

- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:

                     < ABF> + < BFA > + < BAF > = 180°

                     < ABF > = 180 - (90° - α) - 90°

                    < ABF > = α  

Where,       < BAF > = < BAE >

- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE >  = x.

                        < ABD > = < ABE > = < ABF > + x

                         90° - α = α + x

                        x = 90 - 2α   ... Answer

Answer:

[tex] csc (R) = \frac{13}{12} [/tex]

Step-by-step explanation:

Formula for any given angle (Ѳ) is given as csc Ѳ = length of hypotenuse side//length of opposite side. It is the inverse of sin Ѳ.

In the right triangle given above, the opposite length = 24, while the length of the hypotenuse = 26

Thus,

[tex] csc (R) = \frac{hypotenuse}{opposite} [/tex]

[tex] csc (R) = \frac{26}{24} [/tex]

[tex] csc (R) = \frac{26}{24} [/tex]

[tex] csc (R) = \frac{13}{12} [/tex]

Answer:

The answer is option D.

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

Equation of a line from given a Slope and a point is

y - y1 = m(x - x1)

Where ( x1 , y1) is the point

Equation of the line using point (-6 , -5) and slope 6 is

Hope this helps you

Answer:

1) 3x + 44

2) 2y - 8

3) x - 6

15) 5 7/8

16) 6 1/3

17) 3 7/9

Step-by-step explanation:

1) 49 + 4 - 5 - 4 + 3x = 3x + 44

2) -y - 5 + y + 2(y) - 3 = 2y - 8

3) 4x - 3 - 3(x + 1) = 4x - 3 - 3x - 3 = x - 6

15) 7 1/4 - 1 3/8 = 7 2/8 - 1 3/8 = 6 10/8 - 1 3/8 = 5 7/8

16) 9 - 2 2/3 = 8 3/3 - 2 2/3 = 6 1/3

17) 10 1/3 - 6 5/9 = 10 3/9 - 6 5/9 = 9 12/9 - 6 5/9 = 3 7/9

Answer:

3x+3y and distributive property

Step-by-step explanation:

It is given that

Gretchen buys three bags of apples = 3X

Hayley buys three bunches of bananas = 3Y

As it is also mentioned that it first it is multiplied and then it is added

So, the expression for determining the total number of fruit pieces is

3X + 3Y

And, this expression denotes the distributive property in which we multiplied the each variable and then added it

Answer:

The logarithmic parent function is the only one with negative numbers in the range

Step-by-step explanation:

Hello,

These functions have been very well known, I remind you their graphs below

The logarithmic parent function is the only one with negative numbers in the range

range for square root is [tex]\mathbb{R^{+}}[/tex]

range for logarithmic is [tex]\mathbb{R}[/tex]

range for exponential is [tex]\mathbb{R^{+}}[/tex]

THAT S TRUE

The square root and logarithmic parent functions have the same domain

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for logarithmic is [tex]\mathbb{R}[/tex]

THAT S WRONG

The square root parent function domain is the most restricted

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for exponential is [tex]\mathbb{R^{+}}[/tex]

THAT S WRONG

All three parent functions have the same domain

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for exponential is [tex]\mathbb{R^{+}}[/tex]

domain for logarithmic is [tex]\mathbb{R}[/tex]

THAT S WRONG

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

2x + 3y < 17

Step-by-step explanation:

Let x be 2-pointers and y be 3-pointers. You're trying to prove that he failed to both tie OR break the record, so he has to have under 17 points total. Knowing our x and y values, just plug it into an inequality equation, and you have your answer.

Answer:

5

Step-by-step explanation:

Due to the direction the line is facing it can be concluded that its slope is positive.

You need two definite points on the line to find the slope.

(x¹,y¹) ( x²,y²)

Points (5,20) (0, -5)

Slope = (y² - y¹) ÷ (x² - x¹)

= (-5 - 20) ÷ (0 -5)

= (-25) ÷ (-5)

= 5

Have a great day!

Answer:

Step-by-step explanation:

To find Angle X we use sine

sin∅ = opposite/ hypotenuse

From the question

WY is the opposite

WX is the hypotenuse

So we have

sin X = WY/ WX

sin X = 6/7

X = sin-¹ 6/7

X = 58.99

X = 59° to the nearest tenth

Hope this helps you

Answer:

x=arcsine (6/7) = 58.98 degrees

Step-by-step explanation:

Performing a trigonometrical function. We can find the value of the angle:

1) sin x =6/7

x=arcsine (6/7)

x= 58.98º

Answer:

The number of students that would have a test score between 61 and 71 are 154 students

Step-by-step explanation:

The given information are;

The mean test score, μ = 61

The standard deviation, σ = 10

The sample size, n = 450

The z score is given as follows;

[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]

We therefore have at x = 61,

[tex]Z=\dfrac{61-61 }{10 } = 0[/tex]

P(x > 61) = P(Z > 0) = 1 - 0.5 = 0.5

For x = 71, we  have;

[tex]Z=\dfrac{71-61 }{10 } = 1[/tex]

P(x < 71) = P(Z < 1) = 0.84134

The probability that the score will be between 61 and 71 is the difference between the two probabilities, which is 0.84134 - 0.5 = 0.34134

Given that the probability is equivalent to  the proportion of the students that would have a test score between 61 and 71, we have;

The number of students that would have a test score between 61 and 71 = 0.34134 × 450 = 153.6 ≈ 154 to the nearest whole number.

Answer: B

Step-by-step explanation:

Option A simplifies to 7/15

Option B simplifies to 11/21

If 1/2 is equal to .50, then when subtracted 7/15 would be equal to 0.46666667 and 11/21 would be equal to 0.52380952... meaning that 11/21 would be closer to 1/2 (or .50).

Hope this helps!

Answer:  

Rectangular pyramid  8 edges

Rectangular prism    12 edges

Triangular Prism   9 edges

Triangular Pyramid  6 edges

Step-by-step explanation: Faces connected at edges

Rectangular pyramid    1 Base  and 4  slanted  triangular sides

Rectangular prism    2 top and bottom bases and 4 sides

Triangular Prism   2 top and bottom triangular bases 3 rectangular sides

Triangular Pyramid    1 triangular base, 3 slanted triangular sides

The matching is as follow:

Rectangular pyramid:  8 edges

Rectangular prism:  12 edges

Triangular Prism: 9 edges

Triangular Pyramid: 6 edges

A pyramid is a triangular-sided, single-polygonal base, three-dimensional polyhedron-shaped construction. A prism is a three-dimensional polyhedron with rectangular sides that are perpendicular to the base and two polygonal bases.

Rectangular pyramid have one Base and 4 slanted triangular sides

Rectangular prism have 2 top and bottom bases and 4 sides

Triangular Prism have 2 top and bottom triangular bases 3 rectangular sides.

Triangular Pyramid have 1 triangular base, 3 slanted triangular sides.

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Answer:

Height of the kite = 86.60 meter (Approx)

Step-by-step explanation:

The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.

Given:

Length of thread = 100 meter

Angle of elevation = 60°

Find:

Height of the kite.

Computation:

Using trigonometry application:

Height of the kite / Length of thread = Sin 60°

Height of the kite / 100 = √3 / 2

Height of the kite = [√3 / 2]100

Height of the kite = 50√3

Height of the kite = 86.60 meter (Approx)