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Mum spent 3/5 of her money and put 1/8 of the remainder in the bank. If she had $750 left, how much did she start with?

Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,

sin²(x) + cos²(x) = 1

we always take the positive square root when solving for either sin(x) or cos(x).

Given that cos(α) = √11/7 and sin(β) = √11/4, we find

sin(α) = √(1 - cos²(α)) = √38/7

cos(β) = √(1 - sin²(β)) = √5/4

Now, recall the sum identity for cosine,

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

It follows that

cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28

Answers:

Problem #1: Option C, 166 yards cubed

Problem #2:  Option A, 10

Step-by-step solution:

The first problem may seem a lot more confusing that it really is and this actually happened to me when I looked at it.  Just because the cylinder is slanted that actually doesn't change any of the volume that we would have if it was straight up with the same diameter and height.

Using what we know about cylinders, let us plug all the information inside of the formula to determine the volume of the cylinder.  However, before doing that we need to determine the radius of the circle from the diameter that was given.

Divide the diameter by two to get the radius

Plug in the values

Simplify the exponent

Simplify the expression

Therefore, after simplifying the expression using the cylinder volume formula and the given information we were able to determine that the option that best fits the description of our answer is option C, 166 cube yards.

Now that we completed the first question, we can move onto the second question.  In this question we are given a figure along with 3 numbers and one unknown, x, which we need to find the value of.  We need to use the Secant-Secant Power Theorem to help determine our solution.

Make an expression to represent the scenario

We know have an expression which we can now simplify and get the value of the unknown easily.  The first step would be to distribute the 32 and 28.

Distribute both sides

Simplify the expression

We now have a simple expression where we can now subtract both sides by 1024 to help isolate x with its coefficient.

Subtract 1024 from both sides

The final step that we have to help fully isolate x by itself is to divide both sides by 32 which would remove the coefficient from x.

Divide both sides by 32

After simplifying the expression completely, we are able to see that the best option that fits our description is option A, 10.

Answer:

living beyond your means.

Step-by-step explanation:

Pay for what you need and don't go into debt.

Answer: 8.5

Step-by-step explanation:

By the intersecting chords theorem,

[tex]17(12)=24x\\204=24x\\x=\boxed{8.5}[/tex]

The number of years it will take for the money to be $2900 is 40.91 years

Using simple interest formula,

I = prt / 100

we are looking for t

where

Therefore,

I = 2900 - 1100 = 1800

1800 = 1100 × 4 × t / 100

cross multiply

180000 = 4400t

t = 180000 / 4400

t = 40.9090909091

t = 40.91 years

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Answer:

205 units

Step-by-step explanation:

The distance formula is D = √(x2-x1)^2 + (y2-y1)^2

Lets say -1 is x1 ; -4 is y1; -201 is x2 ; and -49 is y2

we just need to plug it into the formula and solve now

√ (-201 - -1)^2 + (-49 - -4)

√-200^2 + -45^2

√40000 + 2025

√42025 = 205

The distance between the two points is 205 units.

Step-by-step explanation:

According to PEMDAS parentheses are first.

2(6+1) can be simplified to 12+2.

5(3+2) can be simplified to 15+10

Add these two together.

12+2+15+10

14+15+10

29+10

y=39

Note - when you have something like this in math 2(6+1) it means you need to do 2 x 6 and 2 x 1

Answer:

1600

Step-by-step explanation:

[tex]\text{Number of terms}, ~n = 40\\\\\text{Sum of n odd integers} = n^2 = 40^2 = 1600[/tex]

This is an identity used to determine the measure of sides and angles of a triangles. The value of x from the given diagram is 7.18 units

This is an identity used to determine the measure of sides and angles of a triangles

From the given triangle

Opposite =  5.5

Hypotenuse = x

According to the theorem

sin 50 = 5.5/H

x = 5.5/sin50

x = 7.18units

Hence the value of x from the given diagram is 7.18 units

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Answer: 15120

Step-by-step explanation:

Given: The number of players at point guard = 10

The number of players at shooting guard = 12

The number of players at small forward = 7

The number of players at power forward = 2

The number of players at center = 9

Then, the number of different teams William could draft is given by :-

10∗12∗7∗2∗9=15120

Hence, William could draft 15120 different teams.

Answer:

around 904.78

Step-by-step explanation:

i got 904.78 but i cant read the answers properly so choose the closest one

The diameter [tex]d = 2r[/tex], where [tex]r[/tex] is the radius. Thus, [tex]d = 2 \times r = 2 \times 5 = 10cm[/tex]

Answer:

414

Step-by-step explanation:

312+352+480+392+368+352+416+640 divided by 8 = 414

Step-by-step explanation:

So, let the N=10a+b

N=10a+b,P(N)=ab,S(N)=a+b

10a+b=ab+a+b

9a-ab=0

a(9-b)=0

a=0 and 9-b=0, b=9. the number is 9. but 9 is not two-digit number. So there is no N which satisfied previous conditions.

Answer:

[tex]find the functions whose derivative is 0[/tex]

The conditional proposition for the given sentence is:

"For all real numbers a, b, and c, if a = b, then a−c=b−c."

A conditional statement is of the form:

If P, then Q.

Where P and Q are two propositions.

The sentence is:

"For all real numbers a, b, and c, a = b implies that a−c=b−c."

So the propositions are:

P = "a = b"

Q = " a - c = b - c"

Where we need to define that this works for all real numbers.

So the conditional proposition is:

"For all real numbers a, b, and c, if a = b, then a−c=b−c."

So the correct option is C.

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Answer:

Multiply:

[tex](x+y)by (x+y)[/tex]

[tex] : \implies(x + y)(x + y)[/tex]

[tex] : \implies \: x(x + y) + y(x + y)[/tex]

[tex] : \implies {x}^{2} + xy + xy + {y}^{2} [/tex]

[tex] : \implies{x}^{2} + 2xy + {y}^{2} [/tex]

Multiply:

[tex]a+b \: by \: a^2-b^2[/tex]

[tex]: \implies( {a}^{2} + {b}^{2} ) \times (a + b)[/tex]

[tex]: \implies \: {a}^{2} (a + b) - {b}^{2} (a + b)[/tex]

[tex]: \implies \: {a}^{3} + {a}^{2} b - {ab}^{2} - {b}^{3} [/tex]

Multiply:

[tex](a+5) by (a^2-2a-3)[/tex]

[tex]: \implies{(a + 5) \times ( {a}^{2} - 2a - 3) }[/tex]

[tex]: \implies \: a({a}^{2} - 2a - 3) + 5( {a}^{2} - 2a - 3)[/tex]

[tex]: \implies(a \times {a}^{2} - a \times 2a - a \times 3) + (5 \times {a}^{2} - 5 \times 2a - 5 \times 3)[/tex]

[tex]: \implies{a}^{3} - {2a}^{2} - 3a + 5 {a}^{2} - 10a - 15 [/tex]

[tex]: \implies{ {a}^{3} + {3a}^{2} - 13a - 15}[/tex]

Multiply:

[tex](a^2-ab+b^3) by (a+b)[/tex]

[tex]: \implies{(a + b) \times ( {a}^{2} - ab + {b}^{3} )}[/tex]

[tex]: \implies \: a( {a}^{2} - ab + {b}^{3}) + b( {a}^{2} - ab + {b}^{3} ) [/tex]

[tex]: \implies {a}^{3} - {a}^{2} b + a {b}^{3} + {a^2b} - {ab}^{2} + {b}^{4} [/tex]

[tex]: \implies{ {a}^{3}+ab^3 - ab^2+ {b}^{4} }[/tex]

Step-by-step explanation:

[tex] \blue{ \frak{Seolle_{aph.rodite}}}[/tex]

Answer:

B.  51.7699^2

Step-by-step explanation:

Last 2 wrong because it is positive.

101.... is not the definite integral for the curve

51... purrfecto

Step-by-step explanation:

I hope this will help you

Answer:

D) 9

Step-by-step explanation:

x = ½ × 13 = 6.5

y = ½ × 5 = 2.5

6.5 + 2.5 = 9

So the length of PC is 9

HOPE THIS HELPS AND HAVE A NICE DAY <3

All the samples are given as {R&R, R&G, R&B, G&R, G&G, G&B, B&R, B&G, B&B}.

A sample is a group of clearly specified components. The number of items in a finite sample is denoted by a curly bracket.

Reese, Greg, and Brad meet once a week for coffee.

They each have their favorite café and, to be fair, they use randomization to choose where they will meet.

Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad.

Each week, all three marbles are mixed well in a bag and a marble is selected.

The favorite café of the person associated with the selected marble is selected for that week's meeting.

Then the total number of the outcomes will be

Total outcomes = 3 × 3

Total outcomes = 9

All the samples are given below.

{R&R, R&G, R&B, G&R, G&G, G&B, B&R, B&G, B&B}

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Answer:

8

Step-by-step explanation:

martha conto 10 de 20 personas con ojos cafes, eso quiere decir que 50 por ciento de los contados tenien ojos cafès, 50 porciento de 16 es 8

Answer + Step-by-step explanation:

The effect of the “-“ when y = (x+3) is changed to y = -(x+3) is creating a negative slope and y-intercept,

y = -(x+3) distributed is y = -x - 3

Visual representation:

The red line: y = (x+3)

The blue line: y = -(x+3)

The volume of the slice is 40 in³. The volume of the remaining cake is 197.014 in³.

A regular hexagon is defined as a closed shape consisting of six equal sides and six equal angles.

Here we have two regular hexagons

one top small hexagon cake with side length = 3 in, height = 3 in

One big hexagon cake, side length = 4 in, Height = 4 in

A slice cut such that it removes a side segment is equivalent to an equilateral triangle with side length = length of hexagon side

Also, all angles within the equilateral triangle are 60° each

Therefore, the length of the side of the removed equilateral triangle side

Top small cake slice triangle side = 3 in.

Area of surface of small slice = 1/2 x b x h = 1/2 x 3 x 3 x sin 60

                                                 = 9√3/ 4

The volume of a small slice  

=  Area of surface small slice × Height of small cake

= 9√3/ 4  x 3

= 11. 69

Big cake slice triangle side = 4 in.

Area of the surface of big slice = 1/2 x 4 x 4 x sin 60

                                                     = 4√3

The volume of big slice =  Area of surface of big slice × Height of big slice

= 16√3

= 28

Total volume of slice = Volume of small slice + Volume of big slice

Total volume of slice = 12 in³ +28 in³ = 40 in³

For the small cake, the remaining volume = 5 x 11.69 = 58.45

For the big cake the remaining volume = 5 x 27.71 = 138.56

Total volume remaining cake = 58.45 in³ + 138.56 in³ = 197.014 in³

a = Length of side

h = Height of hexagon

The volume of each slice is, therefore,

= a^2 x h x √3/4

For the small cake, we have

a = 3 in.

h = 3 in.

Volume of small slice = a^2 x h x √3/4

                                    = 9 x 3 x √3/4 = 27√3/4

For the big cake, we have

a = 4 in.

h = 4 in.

Volume of big slice =  a^2 x h x √3/4

                                 = 16 √3

The total volume of slice = Volume of small slice + Volume of a big slice

Total volume of slice = 27√3/4 + 16 √3

The total volume of slice = 39404 in³.

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The equivalent expression for the given expression is 3i√3.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is √-27

= i√27

= i√(9×3)

= 3i√3

Therefore, the equivalent expression for the given expression is 3i√3.

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The probability of pulling a blue marble and the coin landing tails up is 360/2500

The tables of values are given as:

Color     Times

Blue        18

Green     20

Yellow    12

Heads    Tails

20          30

The probability of obtaining a blue marble is:

P(Blue) = 18/50

The probability of landing tails up is:

P(Tail) = 20/50

The required probability is:

P = P(Blue) * P(Tail)

This gives

P = 18/50 * 20/50

Evaluate the product

P = 360/2500

Hence, the probability of pulling a blue marble and the coin landing tails up is 360/2500

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Step-by-step explanation:

We know that the area of an equilateral triangle of side a cm is

Let a cm here be 9√3 then we could get our solution.

[tex] \rm\implies \rm 9 \sqrt{3} = \cfrac{ \sqrt{3} }{4} \: a {}^{2} [/tex]

[tex] \implies \rm \: \cfrac{ \sqrt{3} }{4} {a}^{2} = 9 \sqrt{3} [/tex]

[tex] \implies \rm \: a {}^{2} = 36[/tex]

[tex] \implies \rm \: a = \sqrt{36} = \sqrt{6 \times 6} [/tex]

[tex] \implies \rm \: a = 6 \: cm[/tex]

Thus, the side of the equilateral triangle is 6 cm.