You ask your best friend to lend you 200 to buy your favourite toy. She says she can lend you the money
only if you give her an extra 2 for every month that passes before you return it.
What is the annual rate of interest she is charging you?

Answer: x=26

Step-by-step explanation:

a^2+b^2=c^2

28.2^2-16^2=539.24

square root 539.24=23.2

23.2^2+11^2=659.24

square root 659.24=25.7

x=25.7 or 26

Answer:

25

Step-by-step explanation:

9/x = 36/100

9 x 4 = 36

? x 4 = 100

100 ÷ 4 = 25

Answer:

90% is the answer

Step-by-step explanation:

hope this helps.

Answer:

b = 72

Step-by-step explanation:

Since AB and AC are congruent then Δ ABC is isosceles with base angles also congruent, that is

∠ ACB = ∠ ABC = b

the sum of the 3 angles in the triangle is 180° , then

b + b + 36 = 180

2b + 36 = 180 ( subtract 36 from both sides )

2b = 144 ( divide both sides by 2 )

b = 72

118°

The overall shape is a quadrilateral. meaning total angles on the inside = 360°

each side is equal and therefore both CDE and CFE are the same. 90 + 34 = 124

360 - 124 = 236

236/2 = 118 therefore you answer is 118°

Answer:

152°

Step-by-step explanation:

Circle Theorem vocabulary

Secant: a straight line that intersects a circle at two points.

Arc: the curve between two points on the circumference of a circle

Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

Angles of Intersecting Secants Theorem

If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.

[tex]\implies m \angle PRD=\dfrac{1}{2}\left(m\overset{\frown}{PD}-m\overset{\frown}{QS} \right)[/tex]

From inspection of the given diagram:

Substitute these into the formula and solve for x:

[tex]\implies 50^{\circ}=\dfrac{1}{2}\left((12x+8)-(4x+4)\right)^{\circ}[/tex]

[tex]\implies 50^{\circ}=\dfrac{1}{2}\left(8x+4\right)^{\circ}[/tex]

[tex]\implies 100^{\circ}=(8x+4)^{\circ}[/tex]

[tex]\implies 96^{\circ}=8x^{\circ}[/tex]

[tex]\implies x=12[/tex]

Substitute the found value of x into the expression for arc PD:

[tex]\implies m\overset{\frown}{PD}=(12x+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=(12 \cdot 12+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=(144+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=152^{\circ}[/tex]

Therefore, the measure of arc PD is 152°.

Answer:

[tex]2x^2+7x+6[/tex]

Step-by-step explanation:

Use the FOIL method to multiply these two expressions:

[tex](x+2)(2x+3)\\x(2x)+2(2x)+3(x)+2(3)\\2x^2+4x+3x+6\\2x^2+7x+6[/tex]

Answer: $4

Step-by-step explanation: To find how much each family paid, we must do this:

80-44

That gets us to 36. Now, we do 36 / 9, and get 4!

TIP: Don't worry about the negative signs, It won't be used in this. I hope this helped!

The GPA of the girls is 3.12

In this question, we have been given a class has 12 boys and 18 girls.

The class as a whole has a GPA (grade point average) of 2.88, and the boys have a GPA of 2.52

We need to find the GPA of girls.

Let m be the GPA of girls.

The weighted average GPA would be,

(12(2.52) + 18m)/ (12+18) = 2.88

We solve above equation to find the value of m

30.24 + 18m = 30 * 2.88

18m = 86.4 - 30.24

18m = 56.16

m = 3.12

Therefore, the GPA of the girls in the class is 3.12

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The interpretations of the equations are

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

The function `P` gives the number of people, in millions,

Years = t

The function P(17) = 2320

Recall that, we have

P(t) = the number of people, in millions,

This means that the year is

Year = 2000 + 17

Year = 2017

So, the interpretation is there are 2320 million people in 2017

The function P(-10) = 0

So, we have

Year = t + 2000

Substitute the known values in the above equation, so, we have the following representation

Year = -10 + 2000

Evaluate

Year = 1990

So, the interpretation is there are 0 million people in 1990

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Complete question

The function gives the number of people , in millions. who own smarphone t years alter the year 2000

What does each equaton tell us about smartphone ownership?

(a) P(17) = 2320

(b) P(-10) = 0

The equation of the line is y = -2x + c

What is an equation ?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another.

To find the slope, use the two points (4.5,0) and (0,9) and substitute these in the slope formula:

m = [tex]\frac{(y_{2} - y_{1})}{(x_{2} - x_{1} )}[/tex]

   = (9 - 0) / (0 - 4.5)

   = -2

The equation of the line is

y = mx + c

y = -2x + c

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Answer:

B

Step-by-step explanation:

[tex]6(2x+4) - x^2+15-x\\=12x + 24-x^2+15-x\\=-x^2+24+15+12x-x\\=-x^2+11x+39[/tex]

The closest answer you have provided is B.

Answer:

54 is the answer

Step-by-step explanation:

hope this helps

Answer:

54 is your answer

Step-by-step explanation:

the person above is right

567 feet does the car travel before coming to a complete stop .

What is the definition of a velocity simple?

The direction of the movement of the body or the object is defined by its velocity. In its basic form, speed is a scalar quantity.

                        In essence, velocity is a vector quantity. It measures how quickly a distance changes. It is the displacement change rate.

vo = 48     v(t) = integral of a(t) plus vo, the initial velocity

a(t) = -2

v(t) = -2t + 48 = 0 when t= 21 seconds, the time to stop

s(t) = -t^2 +48t  

s(21) = -(21)^2 + 48(21) = 1008-441 = 567 feet

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(a) The fraction for the given percentage is 3% = 3/100 and its decimal number is 0.03.

(b) The fraction for the given percentage is 15% = 15/100 = 3/20 and its decimal number is 0.15.

Here the fractions 15/100 and 3/20 are equivalents.

Two fractions whose numerators and denominators are different but whose value is the same are said to be equivalent fractions.

For example, a/b = k and c/d = k. Then a/b = c/d.

The fractions a/b and c/d are equivalent fractions.

Given percentages are 3% and 15%.

A percentage is a ratio of the parts in the whole of 100 parts.

So, 3% = 3/100

This is nothing but a fraction.

To convert it into decimals, divide the numerator by the denominator. So, we get 3/100 = 0.03.

Similarly, for 15%, the fraction is 15/100

This fraction when divided by 5 in both numerator and denomiantor, we get (15/5)/(100/5) = 3/20

So, the fraction 3/20 is the equivalent fraction for the fraction 15/100 Since their values are the same i.e., 0.15. Thus, the decimal number for those fractions is 0.15.

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Answer: A. No, because two points with the same x-value have different y values.

Step-by-step explanation: A function is a relation in which each element in the domain (the set of x-values) is paired with exactly one element in the range (the set of y-values). If there are two points with the same x-value but different y-values, then there is more than one y-value for a given x-value, which violates the definition of a function. Therefore, the given relation is not a function.

If the correlation between variables a and b is +0.52, then it shows that as value on A increases, the value on B increases

The correlation between variable a and variable b = +0.52

The correlation is defined as the statistical variable that show the relationship between the variables. So when one variable increases another variable increase or if one variable decreases another variable decreases. So correlation show the the variable changes at constant rate.

In the given details

The correlation between variable a and variable b is +0.52. The sign of the correlation is positive so variable a is increasing and the variable b will also increases at constant rate

Therefore, the best interpretation of correlation is as value on A increases, the value on B increases

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Answer:

YES

Step-by-step explanation

it is just vocab words you probably have to study

The probability that their average score is between 200 and 250 is 42.49%.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree

Given:

Mean = 240

and standard deviation = 27

So, P( 200 < x < 250) =  P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] < x <  x- [tex]\mu[/tex])/ [tex]\sigma[/tex])

                                    = P (200- 240 / 27  < x < 250- 240 /27)

                                    = P( -1.481 < x < 0.370)

                                    = 0.42499

Hence, the probability that their average score is between 200 and 250 is 42.49%.

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The equations of the line that passes though points (2,-1) and (8,4) are

The linear function written in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as (2,-1) and (8,4)

m = (y₂ - y₁) / (x₂ - x₁)

substituting the values

= (-1 - 4 ) / (2 - 8 )

= -4 / -6

= 2/3

using the point slope formula which is

(2, -1)

(y - y') = m(x - x')

(y - (-1)) = 2/3(x - 2)

y + 1 = 2x/3 - 4/3

y = 2x/3 - 4/3 - 1

y = 2x/3 - 7/3

(8,4)

(y - 4) = 2/3(x - 8)

y - 4 = 2x/3 - 16/3

y = 2x/3 - 16/3 + 4

y = 2x/3 - 28/3

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Answer: 2.666666etc..

Step-by-step explanation:

Answer:

2.64

Step by step explanation

4/9=0.44

0.44×6=2.64

An elevator stop for 23 floor.

it went up so +18

it came down so -11

again it went upward +16

so... 18-11+16

=18+16-11

=34-11

=23

An elevator or lift is a cable-assisted, hydraulic cylinder-assisted, or roller-track assisted machine that vertically transports people or freight between floors, levels, or decks of a building, vessel, or other structure. They are typically powered by electric motors that drive traction cables and counterweight systems such as a hoist, although some pump hydraulic fluid to raise a cylindrical piston like a jack.

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Answer:

  24th floor

Step-by-step explanation:

You want to know where an elevator stopped if it started at the first floor, went up 18, down 11, and back up 16.

If it started at the first floor and went up 1, it would be at the 2nd floor. Starting from the first floor and going up 18, it would be at the 19th floor.

Down 11 floors from there is the 8th floor. Back up 16 floors from the 8th floor puts the elevator at the 24th floor.

The elevator stopped at the 24th floor.

__

Additional comment

If there is no 13th floor, then it may have stopped at the 25th floor.

The rate of change of base is 5 cm/min.

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another. The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity.

Let us assume that

h = height of the triangle

[tex]\frac{dh}{dt}[/tex] = rate of increase of height = 1 cm/min

A = Area of triangle

[tex]\frac{dA}{dt}[/tex] = rate of increase of area = 13 cm²/min

Area of traingle, A = 1/2*(b*h)

When A = 12 cm² and h = 4 cm,

Put in above formula,

12 = 1/2 * (b)(4)

∴ b = 6 cm

A = 1/2 * b*h

[tex]\frac{dA}{dT} = \frac{1}{2}h\frac{db}{dt} + \frac{1}{2}b\frac{dh}{dt} \\\\13 = \frac{1}{2}*4* \frac{db}{dt} + \frac{1}{2}*6*1\\\frac{db}{dt} = 5 cm/min[/tex]

Thus, rate of change of base is 5 cm/min.

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Answer:

x (in simple terms)< -11/7 or -1 4/7

Step-by-step explanation:

1) Place x on one side: The point of this is to islolate x (and to keep things simple make x a positive variable if you can). One way of doing this is adding 8x on both sides what we now get is 14 < 14x + 36

2) Subtract 36 on both sides: We doing this for the same reason as the 1st step which is to islolate x so after this the new equation is -22 < 14x

3) Divide 14 on both sides: Since we aren't dividing by a negative number the sign remains the same the answer is -22/14 < x or x> -22/14 but to simply find the greatest common factor for both the numberator and demonationr which is 2 and divide from there the answer is x> -11/7 or x> -1 4/7

After the linear equation method the answer is 6 Zoomas and 5 Popsies.

What is an linear equation?

Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.

There is a linear equation in one variable and a linear equation in two variables.

It is given that there are two types of alien live on the planet Starlight Zoomas and Popsies.

Zoomas have 3 eyes and 2 legs

Popsies have 4 eyes and 5 legs

There are total 38 eyes and 37 legs

Let there are x number of Zoomas and y number of Popsies.

According to question:

3x + 4y = 38 ..........(1)

2x + 5y = 37 ...............(2)

Solve the above system of equation.

Find the value of x from the equation(1)

3x + 4y = 38

3x = 38 - 4y

x = [tex]\frac{38-4y}{3}[/tex]

Substitute this value of x in equation(2)

2( [tex]\frac{38-4y}{3}[/tex]) + 5y = 37

⇒ [tex]\frac{76-8y}{3}+5y = 37[/tex]

⇒ [tex]\frac{76-8y+15y}{3}=37[/tex]

⇒ 76 + 7y = 111

⇒ 7y = 111 - 76

⇒ 7y = 35

⇒ y = 35/7 = 5

Substitute this value of y in the value of x

x = [tex]\frac{38-4y}{3}[/tex]

x = [tex]\frac{38-4(5)}{3}=\frac{38-20}{3}=\frac{18}{3}=6[/tex]

Therefore, there are 6 Zoomas and 5 Popsies.

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The area of the circle-shaped rug is 379.94 square inches

The formula for calculating the area of a circle is expressed as;

Area = πr^2

Where;

From the information given, we have the value of the circumference as 69.08 inches

We need to find the value of the radius.

The formula for calculating the circumference of a circle is mathematically expressed as;

Circumference = 2πr

Where: r is the radius of the circle and π takes the value 3. 14

Now, substitute the value into the formula for circumference of a circle, we have;

69.08= 2(3.14)r

Divide both sides by the coefficient of r

r = 69.08/6. 28

r = 11 inches

Then, area = 3.14 × (11)^2

Area = 3.14 × 121

Area = 379.94 square inches

Hence, the value is 379.94 square inches

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Complete question:

Marcy is making a hooked circle-shaped rug for her mother. The circumference of the circle-shaped rug is 69.08 inches. Find the area

The probability that  is more likely between selecting a tube of blue or yellow paint, OR selecting a tube of green or red paint id; Both are equally lilkely.

We are given;

Number of blue tubes = 7

Number of red tubes = 4

Number of yellow tubes = 3

Number of green tubes = 6

Thus;

Total number of painted tubes = 7 + 4 + 3 + 6 = 20

Probability of selecting a blue tube = 7/20

Probability of selecting a red tube = 4/20

Probability of selecting a yellow tube = 3/20

Probability of selecting a green tube = 6/20

Thus;

P(selecting a tube of blue or yellow paint) = (7/20) + (3/20) = 10/20

P(selecting a tube of green or red paint) = (6/20) + (4/20) = 10/20

Thus, they are equally likely.

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Answer:

Step-by-step explanation:

2x - 3y = 6

-3y = -2x + 6

y = 2/3x - 2

correct answer is A

In the online auction for an autograph, losing bid is 10 less than the winning bid.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Losing bid in online auction of Autograph = $40,

Also, Losing bid is 80% of the winning bid,

Let winning bid is 100%.

Therefore, winning bid is 20% more than losing bid.

Since,

80% = 40

20 % = 10

Hence, losing bid is 10 less than the winning bid.

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