57⁰
Diagram not
drawn accurately
(i) Work out the size of the angle marked p.

Answer:

75

Step-by-step explanation:

Answer:

75. ..... ............................

Solution

A

Using pythagorean theorem

The final answer

The height of window A is

We divide both sides by 5 so we can eliminate the parenthesis:

We rearrange the terms so the terms with the unkown variable y are on the left side and the other ones on the right side:

y - 10 = -1

↓ adding 10 both sides

y - 10 + 10 = -1 + 10

y + 0 = 9

y = 9

Remember that the domain is the numbers that x can take

x=5 has a domain of only 5

y = 1/x cannot have a value of x=0 because 1/0 is undefined

t = sqrt(x) cannot have negative values because sqrt( negative numbers) is not defined in the real number system

y = |x| is defined for all values of x so it has a domain of all real numbers

Answer:

We need to determine 50% of 100 now and the procedure explaining it as such

Step 1: In the given case Output Value is 100.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 100 = 100%.

Step 4: In the Same way, x = 50%.

Step 5: On dividing the pair of simple equations we got the equation as under

100 = 100% (1).

x = 50% (2).

(100%)/(x%) = 100/50

Step 6: Reciprocal of both the sides results in the following equation

x%/100% = 50/100

Step 7: Simplifying the above obtained equation further will tell what is 50% of 100

x = 50%

Therefore, 50% of 100 is 50

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-3x - 4y = -5

12x - 3y = -18

Multiply the first equation by 4, and add both

-12x - 16y = -20

+

12x - 3y = -18

___________

-19y = -38

Solve for y:

y = -38/-19

y= 2

Replace y on any equation and solve for x

-3x - 4(2)=-5

-3x -8 = -5

-3x = -5+8

-3x = 3

x=3/-3

x=-1

Solution = (-1,2)

The result of the function f(3) is 3.

Given:

f(x) = -x² + 8x - 12

x = 3

Putting the value of x in the given function to obtain the outcome of the function,

f(3) = -(3)² + 8 × 3 - 12

     = -9 + 24 - 12

     = 24 - 21

     = 3

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We want to find the value of the expression;

When x = 4 and y = 2.

All we have to do is substitute these values; when we do that, we have;

Therefore, the answer is 30.

The amount of times that 14 goes into 78 is; 5 times

We want to find how many 14 goes into 78.

Now, it is pertinent to note that this expression is used in our common daily lives for basic things of life. For example, if i want to know how many 10 dollars can go into 100 dollars, i will just divide 100 by 10.

Similarly another example is if i want to know how many 5 liters container of fuel would go into a 60 liters tank, i will just divide 60 by 5 to get the number.

In a similar vein, we can solve this question by dividing 78 by 14 to get;

78/14 = 5 ⁸/₁₄

This means 14 can only go in 5 full times as we will not count the fraction.

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The total number of strawberries needed for making all the smoothies can be represented by the expression -

y = 15x

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Amy who is making all three smoothies for each of her x number friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6.

Number of friends [n] = x

Each of the three friends will get smoothies made from recipe 1, recipe 2 and recipe 3.

Then -

Number of strawberries needed for smoothie made from recipe 1 for x friends = n[1] = 4x

Similarly, for smoothies made from recipe 2 and 3 will need -

n[2] = 5x and n[3] = 6x number of strawberries.

Assume that total number of strawberries needed for making all the smoothies are y. Then, we can write -

y = 4x + 5x + 6x

y = 15x

Therefore, the total number of strawberries needed for making all the smoothies can be represented by the expression -

y = 15x

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In total, he spend $510 after discount.

A deduction taken from the gross amount or worth of anything, such as  a price decrease made from the standard or list price, giving clients a 10% discount to purchase tickets. A proportionate withdrawal from a loan account, typically done in exchange for cash or quick payment.

Given Data

Coats are discounted 30%

Suits are discounted 25%

Joe purchased a coat of $300

= 300 - [tex]\frac{30}{100}[/tex] × 300

= 300 - 90

= 210

He purchased coat for $210.

He purchased a suit $400.

Suits are discounted 25%

= 400 - [tex]\frac{25}{100}[/tex] × 400

= 400 - 100

= 300

He purchased suit for $300.

In total, he spend $510 after discount.

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Answer:

the first answer option : all lengths and angles stay the same.

Step-by-step explanation:

imagine you have a piece of plastic or glass of a triangular shape on your table.

now, lower your hand on the table, so that your thumb touches the table and one of your other fingers touches the triangle on the top.

and now twist your hand that your thumb stays at the same point, and your finger holding the triangle starts making a circular motion.

that finger is dragging the triangle along.

what happens to the triangle ? it keeps its original shape, and changes only its location and orientation.

that is what a rotation is.

The table of values of the relationship between time and earnings is a linear relation

From the question, we have the following parameters:

Number of hours = 2 hours

Total earnings in this time = $35

Also from the question, we understand that:

She makes a constant hourly wage

A constant hourly wage implies that the table of values has a linear relationship

In this case, the linear relationship is represented as

A(t) = constant hourly wage * t

Where

A(t) represents the earnings

t represents the number of hours

So, we have

constant hourly wage * 2 = 35

Divide both sides of the equation by 2

So, we have

constant hourly wage = 17.5

Substitute constant hourly wage = 17.5 in A(t) = constant hourly wage * t

A(t) = 17.5 * t

Evaluate

A(t) = 17.5t

Using the values of t as:

t = 0, 2, 4, 6

We have the following table of values

Number of hours (t) || Amount earned

0                                              0

2                                              35

4                                              70

6                                              105

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Answer: Well, 10 x 3, 10 x 3

Step-by-step explanation: I think thats what you are asking?

The probability that the student will be prepared for exactly 4​ questions is; 0.3427

Hypergeometric distribution is defined as a discrete probability distribution that expresses the probability of k successes in n draws, done without replacement, from a finite population of size N that contains exactly K objects with that feature. In this disdtribution, each draw is either a success or a failure.

The probability mass function of Hypergeometric distribution is given by the formula;

P(K = k) = KCk * N-KCn-k ]/NCn

Now, the probability that the student will be prepared for exactly 4​ questions will be;

P(K = 4) where;

N = 16

K = 9

n = 8

Solving P(K = 4) = 9C4* 16-9C8-4 ]/16C8 = 0.3427

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15) Magnitude of projection is 6.325

17) Projection is <-3.6, 10.8>

19) The acute angle between and vector is 34.509°.

The magnitude of the projection of A vector onto B vector could be deduced as,

Proj V(a) ÷ V(b) = (V(a) · V(b)) ÷ |V(b)|

15)  Given, coordinates <8,-4> and <1,-3>

|V(b)| = √((1)² + (-3)²)

|V(b)| = √(1+9)

|V(b)| = √10

Proj V(a) ÷ V(b) = (V(a) · V(b)) ÷ |V(b)|

Proj V(a) ÷ V(b) = (8, -4) · (1, -3) ÷ √10

Proj V(a) ÷ V(b) = (8 + 12) ÷ √10

Proj V(a) ÷ V(b) = 20 ÷ √10

Proj V(a) ÷ V(b) = 2√10 = 6.325

17) Given, coordinates <-6,10> and <1,-3>

Projection = Proj V(a) ÷ V(b) = ((V(a) · V(b)) ÷ |V(b)|) × <1, -3>

|V(b)| = √((1)² + (-3)²)

|V(b)| = √(1+9)

|V(b)| = √10

Proj V(a) ÷ V(b) = (V(a) · V(b)) ÷ |V(b)| × <1, -3>

Proj V(a) ÷ V(b) = ((-6, 10) + (1, (-3)) ÷ √10) × <1, -3>

Proj V(a) ÷ V(b) = ((-6 × 1) + (10 × (-3)²) ÷ √10) × <1, -3>

Proj V(a) ÷ V(b) = ((-6 + 90) ÷ √10) × <1, -3>

Proj V(a) ÷ V(b) = ((84) ÷ √5) × <1, -3>

Proj V(a) ÷ V(b) = <-3.6, 10.8>

19) The vector are <2,3> and <-5,-2>. The acute angle between and vector is 34.509°.

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Answer: $4.20

Step-by-step explanation:

The sale price is $12 * .35 = 4.2

Answer:
domain: [-1,4]
range: [-2,4]
the graph is not a function, this is proven by using the vertical line test.

hope this helps :)

Solution

Number 6

for this case we can see that we have two common angles and one equal side. By the way we have also a common side and then since we have right triangles the correct postulate would be:

SSS

Number 9

Answer:

D

Step-by-step explanation:

A and B don't prove anything because we have the slopes of sides LM and ON to worry about. C could mean that yes, the figure is a quadrilateral, but with those parameters it could be a square, a rectangle, or trapezoid. Therefore D is the correct answer

Diagonal Mo bisects diagonal LN.

Midpoint of line MO =  Midpoint of line LN

Option C is the correct answer.

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

In a rhombus,

- All sides are equal

- Opposite sides are parallel

- Diagonals bisect each other

- opposite angles are equal

Now,

Midpoint of line MO =  Midpoint of line LN

Since diagonals bisect each other

Thus,

Diagonal Mo bisects diagonal LN.

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All adults in the country and considered as population. 1003 men in the country are adults that are selected.

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

Given Data

In a​ poll, 1,004 men in a country were asked whether they favor or oppose the use of​ "federal tax dollars to fund medical research using stem cells obtained from human​ embryos." Among the​ respondents, 48​% said that they were in favor.

1)Population

All adults in the country and considered as population.

2) Sample is

1003 men in the country are adults that are selected.

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The pairs of angles that are linear pairs involving point F are:

A. ∠DFC and ∠CFG

D. ∠HFD and ∠CFD

E. ∠GFH and ∠GFC

F. ∠HFG and ∠DFH

When two angles that are adjacent to each other, (that is, they share the same vertex and the same side), are located on a straight line, these angles are linear pairs and are also supplementary angles.

Making reference to the image given, angles DFC and CFG share a common vertex F and a common side CF. Also, they lie on a straight line. Therefore, angle DFC and angle CFG are a linear pair.

Angles HFD and CFD share a common vertex F and a common side FD. They lie on a straight line. Thus, angle HFD and angle CFD are also a linear pair.

The same thing applies to angle GFH and angle GFC, as well as angle HFG and angle DFH.

The linear pairs are:

A. angle DFC and angle CFG

D. angle HFD and angle CFD

E. angle GFH and angle GFC

F. angle HFG and angle DFH

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The new speed of Ms.Torres is 119/4 miles/ hour for the driving.

For the given question;

The distance covered by Ms.Torres; 178 1/2 miles

Convert mixed fraction to fraction; 357/2 miles.

The time taken by Ms.Torres; 4 1/2 hours

Convert mixed fraction to fraction; 9/2 hours.

Speed = distance/ time

Speed = 357/2 miles/9/2 hours

Original Speed = 119/3 miles/ hour.

Now, the speed covered by her is 3/4 of the original speed.

Thus,

= (3/4)×(119/3)

= 119/4

Therefore, the new speed of Ms.Torres is 119/4 miles/ hour.

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Answer:

A) 40

B) $ 15

Step-by-step explanation:

A)An equation for the number of​ 30-day periods until the value of the gift cards will be equal

Let x be the number of time periods for which the gift card is not used, then

For the gift card $ 155 if it is not used for x periods, then the amount that will be lost is

155 - 3.50 x---------------------(1)

For the gift card $ 135 if it is not used for x periods, then the amount that will be lost is

135 - 3x---------------------- (2)

Now when both the amount lost is equal

solving the equation, we get

20 =  0.5x

x = 40Thus the value of gift cards will be equal for 40 ,30 day periods. B)The value of each card be when they have equal​ value The two cards  will have equal value after 40 30 day periods, this denotes that at this time, the value of each card will be equal.Then substituting  x = 40, we get when they have equal​ value, the value of each card will be $15

Step-by-step explanation:

1 m = 4 cm

therefore,

A = 2.5 m = 2.5×1 m = 2.5×4 cm = 10 cm

B = 2.75 m = 2.75×1 m = 2.75×4 cm = 11 cm

D = 3.75 m = 3.75×1 m = 3.75×4 cm = 15 cm

Solution

Now, the circle equation

Rewrite in standard form

Therefore the circle properties

The final answer

Answer: 31.25%

Step-by-step explanation:

Draw a Ven diagram in a rectangle with 2 circles one for F and the other for C. The intersection overlap will have the 10 who play both outside the circles but within the rectangle the 7 who do neither so then fill the rest of F with 4 to give a total of 14 and 11 for the C to total 21. When you add all the numbers you’ll get a class total of 32. Then the % who play both F and C is = (10/32)*100 = 31.25%

An estimate for the number of pet dogs and cats in the United States based on a recent survey, written as a single digit times an integer power of 10 is 2 x 10⁸.

An estimate is a rough calculation or judgment arrived at when the details are not required or available.

We can apply number approximation, rounding, and scientific notations in estimation, as above.

First, the number, 183,900,000, can be approximated to 200 million pet dogs as an estimate.

Then, 200,000,000 can be written in a standard form or scientific notation by using an integer that indicates the place value in the power of 10.

Thus, 183,900,000 pet dogs can be estimated as 2 x 10⁸.

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Translation: add or subtract to the coordinates x ,y

A = (3,2)

A'= (6,-2)

(3+3, 2-4 ) = (6,2)

Solution:

(x,y) (x+3,y-4)→