How do you solve simple interest
$600 at 5% for 2 years
and
%1500 at 4% for 4 years

Answer:

an inequality

Step-by-step explanation:

An inequality is the relation between two expressions that are not equal.  The symbols generally used are less than (<) or greater than (>), as in:

4 > 3 or 4 < 9

That means that each side of the symbol represents a value that  is different from the other side.  The relationship is described with the sign to indicate which side has a greater value.

If both sides have an equal value, then it's an equation.

There are 126 slices of sausage pizza sold

Answer:

  D.  (x + 7, y - 2)

Step-by-step explanation:

To get back the original after translating left 7 and up 2, you must translate right 7 and down 2. The transformation of choice D does that.

Answer:

a

Step-by-step explanation:

Answer:

correct options are A, C and D

Step-by-step explanation:

While formulating an equation the first step is to read the problem carefully and then draw a picture if needed and the third step is write each fact as a variable.

so the steps which are used when formulating are as follows

Read the problem

Draw a picture if needed

Write each fact as a variable expression

27 dimes for my answer

hope it works

Answer:

weak negative

Step-by-step explanation:

we know that

The correlation coefficient r measures the direction and strength of a linear relationship. It can take a range of values from +1 to -1.

Values between -0.5 and -1.0 or 0.5 and 1.0 indicate a strong negative/positive linear relationship

Values between -0.3 to -0.1 or 0.1 to 0.3 indicate a weak negative/positive linear relationship

In this problem

The correlation coefficient for the data is −0.31

therefore

Is a weak negative correlation

[tex]\bf \textit{Product to Sum Identities} \\\\sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5\theta )cos(2\theta )\implies \cfrac{1}{2}[sin(5\theta +2\theta )+sin(5\theta -2\theta )]\implies \cfrac{sin(7\theta )+sin(3\theta )}{2}[/tex]

The required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.

The product-to-sum formulae are used to represent the sum of the sine and cosine functions. These are generated from trigonometry's sum and difference formulae.

sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]

The trigonometry expression is given in the question

sin (5θ) cos (2θ)

According to  the product to sum Identities

sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]

Here A = 5θ and B = 2θ

sin (5θ) cos (2θ) = (1/2) [sin(5θ + 2θ) + sin(5θ - 2θ)]

sin (5θ) cos (2θ) = (1/2) [sin(7θ) + sin(3θ)]

sin (5θ) cos (2θ) =  [sin(7θ) + sin(3θ)] / 2

Thus, the required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.

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f(x)=3x^2-18x+10

a = 3, b = -18 and c = 10

The vertex of a parabola is in form a(x+d)^2 + e

d = b/2a = -18/2(3) = -18/6 = -3

e = c-b^2/4a = 10 - -18^2/4(3) = 10-27 = -17

Now the vertex form of the parabola becomes 3(x-3)^2 -17

Use the vertex form of the parabola in the vertex form of y = a(x-h)^2 +k

Where a = 3, h = -3 and k = -17

Now you have y = 3(x-(-3))^2 +(-17)

Simplify: y = 3(x+3)^2 -17

The vertex becomes the h and k values of (3,-17)

Answer:

N/A

Step-by-step explanation:

Not enough context is given for the problem.

Just remember, though:

And = Multiplication

Or = Addition

1/8 chance for each section

Answer:

(A) P(gray), P(green)

Step-by-step explanation:

Notice that there are 2 tiles in each, so it should be A as the answer.

Please mark me brainiest!

Hope you have a good day!

The answer is 80%

Correct me if I’m wrong

I think the answer is six

(1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6)

Answer:

Either x = 2 or y = 6, depending on the original line

Step-by-step explanation:

So, if the original line is horizontal, our new line is vertical, and all vertical lines in a graph is x = some number. To pass through the point (2, 6), x has to equal 2, since the point's x-coordinate is 2.

On the other hand, if the original line is vertical, our new line is horizontal, which is y = some number. Our point's y-coordinate is 6, so our line should be that y = 6.

It's A, x=2. I hope i helped!!

Answer:

Option C. [tex]y = (x-8) ^ 2[/tex]

Step-by-step explanation:

If we have a parent function f(x) and we want to make a transformation that translates the graph of f(x) horizontally then we do

[tex]y = f (x + h)[/tex]

Where h is a constant such that:

If [tex]h> 0[/tex] then the graph of f(x) moves h units to the left

If [tex]h <0[/tex] then the graph of f(x) moves h units to the right.

In this case we have the function [tex]y = x ^ 2[/tex] and we know that 8 units are moved to the right. If you move 8 units to the right This means that

[tex]h <0[/tex] and [tex]h = -8[/tex]

So if [tex]f(x) = x ^ 2[/tex] the transformed function will be:

[tex]y = f(x -8)[/tex]

[tex]y = (x-8) ^ 2[/tex]

Answer:

25 possible outcomes

19 non-red outcomes

Step-by-step explanation:

there are 25 cards. if you remove the 6 red card outcomes you have 19.

Step-by-step explanation:

Having proven that the triangles are similar, we can write the proportion:

AP / CP = CP / MP

9 / CP = CP / 16

CP² = 144

CP = 12

Now, we can simply use Pythagorean theorem to find the other sides.

AC² = AP² + CP²

AC² = 9² + 12²

AC = 15

CM² = CP² + PM²

CM² = 12² + 16²

CM = 20

Answer: Option C

the approximate height of the souvenir of the Eiffel Tower to the nearest tenth is __13 in___.

Step-by-step explanation:

We know that each foot of height of the Eiffel Tower is equivalent to 1/80 inch of height of the souvenir.

The Eiffel Tower is 1,069 feet high.

Then the height of the souvenir the 1,069 times 1/80 in

[tex]h = 1,069 *\frac{1}{80}\\\\h=13.3\ in[/tex]

The answer is the option C

Answer:

The measures of angles of triangle EFQ are

1) [tex]m\angle EFQ=100\°[/tex]

2) [tex]m\angle FEQ=66\°[/tex]

3) [tex]m\angle EQF=14\°[/tex]

Step-by-step explanation:

step 1

Find the measure of arc QD

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle DFQ=\frac{1}{2}(arc\ QD)[/tex]

substitute the given value

[tex]10\°=\frac{1}{2}(arc\ QD)[/tex]

[tex]20\°=(arc\ QD)[/tex]

[tex]arc\ QD=20\°[/tex]

step 2

Find the measure of arc FQ

we know that

[tex]arc\ QD+arc\ FQ+arc\ EF=180\°[/tex] ---> because ED is a diameter (the diameter divide the circle into two equal parts)

substitute the given values

[tex]20\°+arc\ FQ+28\°=180\°[/tex]

[tex]arc\ FQ=180\°-48\°=132\°[/tex]

step 3

Find the measure of angle EFQ

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle EFQ=\frac{1}{2}(arc\ QD+arc\ ED)[/tex]

substitute the given value

[tex]m\angle EFQ=\frac{1}{2}(20\°+180\°)=100\°[/tex]

step 4

Find the measure of angle FEQ

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle FEQ=\frac{1}{2}(arc\ FQ)[/tex]

substitute the given value

[tex]m\angle FEQ=\frac{1}{2}(132\°)=66\°[/tex]

step 5

Find the measure of angle EQF

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle EQF=\frac{1}{2}(arc\ EF)[/tex]

substitute the given value

[tex]m\angle EQF=\frac{1}{2}(28\°)=14\°[/tex]

Answer:

The first choice is the correct one

Step-by-step explanation:

That funny symbol is the Greek symbol for "the sum of".  Sum means to add, so whatever numbers we have we are definitely adding them.  The index goes from a starting point of 1 up to 4.  That's those 2 numbers, one below and one above the sum symbol.  The "n" in 7/n is what we are replacing with each number starting at 1 and ending at 4.  7/1, 7/2, 7/3, 7/4.  Those are the numbers, now just put them together with plus signs between them and you're done.

Answer:

A) The equation in factored form is (4t + 1)(t - 2) = 0

B) The solutions of the equation are t = -1/4 and t = 2

C) It will take 2 seconds for the rocket to hit the ground

Step-by-step explanation:

* Lets study the information in the problem

- A child launches a toy rocket from the top of a slide

- The equation of the motion is -16² + 28t + 8 = 0, where t is the time

 of rocket to hit the ground

* Now lets solve the problem

- At first simplify the equation

∵ -16t² + 28t + 8 = 0

∵ Al the terms have a factor 4

- Divide all terms by 4

∴ -4t² + 7t + 2 = 0 ⇒ multiply all terms by -1

∴ 4t² - 7t - 2 = 0

- Lets factorize

∵ 4t² = 4t × 1t ⇒ 1st term in the 1st bracket × 1st term in the 2nd bracket

∵ -2 = 1 × -2 ⇒ 2nd term in the 1st bracket × 2nd term in the 2nd bracket

∵ 4t + -2 = -8t ⇒ product of the extremes

∵ 1t × 1 = 1t ⇒ product of means

∵ -8t + 1t = -7t ⇒ middle term

∴ The factorization of 4t² - 7t - 2 is (4t + 1)(t - 2)

∴ (4t + 1)(t - 2) = 0

A) The equation in factored form is (4t + 1)(t - 2) = 0

- Lets use the zero product property to solve the equation

∵ (4t + 1)(t - 2) = 0

- Equate each factor by 0

∵ 4t + 1 = 0 ⇒ subtract 1 from both sides

∴ 4t = -1 ⇒ divide both sides by 4

∴ t = -1/4

OR

∵ t - 2 = 0 ⇒ add 2 for both sides

∴ t = 2

B) The solutions of the equation are t = -1/4 and t = 2

C) We can not accept the answer t = -1/4 because there is no negative

    value for the time

∴ The answer is t = 2 only

* It will take 2 seconds for the rocket to hit the ground

Answer:

Step-by-step explanation:

Set up a table for a distance = rate × time problem.  We are considering the trips taken on Monday and Tuesday.

                         d     =     r     ×     t

Monday

Tuesday

Now let's start filling in what we know.  First off, Fran went to her Mother's both days.  Unless her Mother moved overnight from Monday to Tuesday, the distance from Fran to her mom is the same both days, even though we don't know how far it is.  So we will just call that "d".

                           d     =     r     ×     t

Monday               d     =

Tuesday              d     =

Now we are told about the times it took to get there on both days.  Monday took 2.7 hours and Tuesday took 3 hours.  Filling in that:

                            d     =     r     ×     t

Monday                d     =           ×     2.7

Tuesday               d     =           ×     3

We're getting there.  Now let's look at rates.  Again, we don't know her rate (that's what we are solving for!) but we do know that she drove faster on Monday than Tuesday.  Tuesday she was 6 miles per hour slower than Monday.  Since we don't know Monday's rate, we will call it r.  Since we don't know Tuesday's rate, but only that it is 6 mph slower than Monday, we will call it r - 6

                            d     =     r     ×     t

Monday               d     =     r      ×     2.7

Tuesday               d     =    r-6   ×     3

Now we have our equations.  We know that d = rt.  Since the distances are the same, d = d, by the transitive property of equality, we can set the 2 expressions equal to each other:

2.7r = 3(r - 6) and solve for r:

2.7r = 3r - 18

-.3r = -18

r = 60

If r = 60, then that r value goes in for Monday.  That means that Tuesday is 60 - 6 which is 54

What was her average speed on Tuesday is 54 mph

Monday

Time = 2.7 hours

Date = r mph

Distance = 4.5r miles

Tuesday

Time = 3 hours

rate = r-6 mph

Distance = 3(r-6) miles

Hence:

Distance = distance

2.7r=3(r-6)

2.7r = 3r - 18

0.3r = 18

r =18/0.3

r 60 mph ( Monday rate)

r-6=60-3  (Tuesday rate)

r-6 = 54 mph (Tuesday rate)

Inconclusion  What was her average speed on Tuesday is 54 mph.

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The correct option will be No, she made an error in step 2, she should have found y=0.5

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have been Given the system of linear equations:

-3x + 2y = 8 --- eqn. 1

3x + 2y = -6 ---eqn. 1

First add both equations together

4y = 2

Now, divide both sides by 4:

y = 2/4

y = 0.5

Thus Kaitlyn got y = 2 instead of 0.5 in this second step. The solution she would get will be incorrect due to an error has occurred here.

Therefore, the error made by Kaitlyn while solving the equations is in step 2. Her solution will be incorrect.

The correct option will be: No

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Answer:

The correct answer is letter C

Answer:

Part 2) Option D. yes; k = 1/4 and y = 1/4x

Part 6) Option D. y = 1/5x-1

Part 8) Option C. line b

Part 11) Option D. -1/5

Part 15) Option A. line a

Step-by-step explanation:

Part 2) we know that

A relationship between two variables, x, and y, represent a directly variation if it can be expressed in the form  [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the line passes through the origin

therefore

Yes. y varies directly with x

Let

A(4,1)

The constant k is equal to

[tex]k=y/x[/tex]

substitute

[tex]k=1/4[/tex]

the equation is equal to

[tex]y=(1/4)x[/tex]

Part 6) we know that

The y-intercept of the trend line is -1 (For x=0)

The slope of the trend line is positive

The x-intercept of the trend line is 5 (For y=0)

therefore

the equation is equal to

[tex]y=(1/5)x-1[/tex]

Part 8) we have

[tex]y+4=-\frac{2}{3}x[/tex]

This is the equation of a line into point slope form

The slope is negative [tex]m=-2/3[/tex]

Pass through the point (0,-4) ----> y-intercept

The x-intercept is equal to

[tex]0+4=-\frac{2}{3}x[/tex]

[tex]x=-4*3/2=-6[/tex]

therefore

Is the line b

Part 11)

What is the slope of the line through the points (–2, –1) and (8, –3)?

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-3+1}{8+2}[/tex]

[tex]m=\frac{-2}{10}[/tex]

simplify

[tex]m=-\frac{1}{5}[/tex]

Part 15) we have

[tex]y=3x-2[/tex]

The slope is positive [tex]m=3[/tex]

The y-intercept is -2 (For x=0)

The x-intercept is  (For y=0)

[tex]0=3x-2[/tex]

[tex]3x=2[/tex]

[tex]x=2/3[/tex]

therefore the line is a

Answer:

No.

Step-by-step explanation:

The square root of an integer is rational only if that integer is a square number. The closest squares to 8 are 2^2 = 4 and 3^2 = 9. 8 is not a square number, so has an irrational square root.

The square root of 8 is an irrational number.

A square root is a mathematical operation that, when applied to a number, finds a value that, when multiplied by itself, equals the original number. For example, the square root of 25 is 5 because 5 x 5 = 25. It is denoted by the √ symbol. Whether the square root of 8 is a rational number or not can be determined by finding the square root and checking if it can be expressed as a fraction.

The square root of 8 is approximately 2.828, which is an irrational number because it cannot be expressed as a fraction. To further prove that it is irrational, we can use the prime factorization method and show that 8 does not have a perfect square factor.

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Answer: 42,504

There Are 42,504 Different Combinations For The Swimmers

Answer:i dont

Step-by-step explanation:

Answer

the rectangle

Step-by-step explanation:

the cylinder folds like a circle but it is not a circle.

A rectangular shape can be rotated about an axis to form a cylinder.

A cylindrical shape is a three-dimensional geometrical shape consisting of two parallel circular bases which are connected by some height h.

We know that cylinder has some height h and two base circles.

If we compare the curved part of the cylinder then we can see that its shape is similar to a rectangle.

The length of the rectangle is similar to the circumference of the circular base of a cylinder and the height of the cylinder with the breadth of the rectangle.

Thus, a rectangular shape can be rotated about an axis to form a cylinder.

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Answer:

4750

Step-by-step explanation:

475000/100 = 4750

4750 * 6 = 28500

4750 * 5 = 23750

28500 - 23750 = 4750

Answer:

4750

explanation:

Answer:

[tex]3,744.45\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of a sector is equal to

[tex]A=\frac{\theta}{360\°}\pi r^{2}[/tex]

where

[tex]\theta[/tex] ------> is the angle in degrees

r is the radius of the circle

In this problem we have

[tex]r=45\ m[/tex]

[tex]\theta=212\°[/tex]

assume

[tex]\pi =3.14[/tex]

substitute the values

[tex]A=\frac{212\°}{360\°}(3.14)(45)^{2}[/tex]

[tex]A=3,744.45\ m^{2}[/tex]

Answer:

  (x +8)² +(y +1)² = 9

Step-by-step explanation:

The formula for a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Filling in your given numbers gives ...

  (x -(-8))² +(y -(-1))² = 3²

Simplifying that results in ...

  (x +8)² +(y +1)² = 9

Answer:

5/16

Step-by-step explanation:

If Vanessa pulls out a 2 from the first bag, then the possibilities based on the second bag are:

X = 2*3 = 6

X = 2*4 = 8

X = 2*5 = 10

X = 2*6 = 12

Repeat this for the other values from the first bag.  If she pulls a 3, the possibilities are:

X = 3*3 = 9

X = 3*4 = 12

X = 3*5 = 15

X = 3*6 = 18

If she pulls a 4:

X = 4*3 = 12

X = 4*4 = 16

X = 4*5 = 20

X = 4*6 = 24

And finally, if she pulls a 5:

X = 5*3 = 15

X = 5*4 = 20

X = 5*5 = 25

X = 5*6 = 30

Of the 16 total combinations, 5 are greater than or equal to 12 and less than or equal to 15.

Therefore, P(12 ≤ X ≤ 15) = 5/16.

Answer:

Step-by-step explanation:

A regular polygon is defined to be a convex polygon with congruent sides and congruent angles.

Convex means that all interior angles are less than 180 degrees.  However, if all interior angles are equal, the polygon has to be convex.

Final answer:

A regular polygon is a convex shape with sides and angles that are all congruent, exemplified by the faces of an icosahedron or an equilateral triangle.

Explanation:

A regular polygon is defined to be a convex polygon with congruent sides and congruent angles. This means that all sides are the same length and all interior angles are equal in measure, which contributes to the polygon's symmetry. As an example from three-dimensional geometry, an icosahedron is a symmetrical, solid shape with 20 faces, each of which is an equilateral triangle.