Nicole invested $400 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment was $72. As a
percentage, what was the annual interest rate of her investment?

Step-by-step explanation:

To determine the end behavior of the functions f(x) and g(x), we need to look at the highest power terms in each function and their coefficients.

For f(x) = -2x^3, the highest power term is x^3, and the coefficient is -2. As x approaches positive or negative infinity, the value of -2x^3 becomes very large in magnitude and negative. Therefore, the end behavior of f(x) as x approaches infinity or negative infinity is that f(x) → -∞.

For g(x) = 5x^4, the highest power term is x^4, and the coefficient is 5. As x approaches positive or negative infinity, the value of 5x^4 becomes very large in magnitude and positive. Therefore, the end behavior of g(x) as x approaches infinity or negative infinity is that g(x) → ∞.

Since the end behavior of f(x) and g(x) is opposite as x approaches infinity or negative infinity, the correct answer is (D) The end behavior is opposite as x→−∞ and opposite as x→∞.

Given:

The set of data contains numerical elements between 2 and 14

Outlier = 14

Let's determine the measure of central tendency that must change if the outlier is removed from the data.

If the outlier is removed, the maximum data value will now be a value less than 14.

The formula to find the range is:

Range = Maximum data value - minimum data value

Therefore, since the maximum data value is now smaller after the outlier is removed, the range will be affected.

The mean is the average of the data set.

If the greatest data value is removed, the mean must also be affected.

The mode is the data value which appears the most, by removing the outlier we cannot tell if the mode will change since we do not have all data values.

The median is the middle data value, by removing the outlier we cannot tell if the median will change since we do not have all data values.

Therefore, the measure if central tendency that must change if the outlier of 14 is removed are:

Mean and Range.

ANSWER:

• Mean

• Range

The correct representations of the inequality are  -6x + 15 < 10 - 5x and x <-5. Options C and D

Inequalities are described as mathematical relations that makes a non-equal comparison between two elements, variables, numbers or mathematical expressions.

They are often used to compare two numbers on the number line based their sizes.

From the information given, we have the inequality;

–3(2x – 5) < 5(2 – x)

expand the bracket

-6x + 15 < 10 - 5x

collect like terms

-6x + 5x < 10 - 15

add or subtract the like terms

-x < -5

Make 'x' the subject of formula

x < 5

Hence, the value is -6x + 15 < 10 - 5x

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The complete question:

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The value of angle x in the triangle is 15°

Given: the triangle ABC with equal sides of 9 units.

Since the triangle has equal sides, it will also have equal angles (i.e. it is an equilateral triangle).

Thus, <A = <B = < C =  4x°

Since the sum of angles in a triangle is 180°. We have:

<A + <B + < C = 180°

4x + 4x + 4x = 180°

12x = 180

x = 180/12

x = 15°

Therefore, the value of x is 15°

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Answer:

Step-by-step explanation:

(x-2)(x-2)(x-4)

Answer:

Brand B is the better buy.

Step-by-step explanation:

Brand A:

$7.97 / 48 pencils = $0.166/pencil

Brand B:

$9.88 / 72 pencils = $0.137/pencil

Answer: Brand B is the better buy.

Answer: brand B is Cheaper

brand A unit price is 0.17 per pencil

Brand B unit price is 0.14 per pencil

so brand B is cheaper

Step-by-step explanation: the formula to find unit price is Price/Amount of Objects

first find the unit price of brand A: 7.97/48

second find the unit price of brand B: 9.88/72

then compare the one that has the smallest unit price is the cheapest

Answer:

To find the dimensions of a rectangle

Step-by-step explanation:

perimeter=302

let width=x

length=x+47

p=2(L+W)

302=2(x+x+47)

302=2(2x+47)

302=4x+94

subtracting 94 from the other side we have

302-94=4x

208=4x

x=52

length=99

width=52

Answer: (In order)

25/4 / 6 1/4 = 1

3 1/7 / 2/7 = 11

5/4 / 1/4 = 5

11 1/4 / 9/4 = 5

8 1/4 / 3/4 = 11

3 1/3 / 10/3 = 1

Step-by-step explanation:

Answer:

vertex: (6, -9)

y intercept: (0, 27)

X = 3, 9

Step-by-step explanation:

Finding Vertex (Part A)

Consider the formula -b/2a. This formula gives you the x-coordinate of the vertex.

y = 1x^2 - 12x + 27

a = 1

b= -12

c =27

-b/2a = - (-12)/2(1) = 12/2 = 6 (x-coordinate of vertex)

When solving for the y-coordinate of the vertex you will need to substitute your 'x" back into the equation.

y = 1(6)^2 - 12(6) + 27

y = 36 - 72 + 27 = -9 (y-coordinate of vertex)

--------------------------------------------------------------------------

Y- Intercept (Part B)

When looking for the y-intercept your "x" must always be 0.

Substitute 0 in every "x" in equation.

y = 1(0)^2 - 12(0) + 27

y = 27

y intercept: (0, 27)

------------------------------------------------------------------------------

X- Intercepts (Part C)

To find the values of "x" factor.

y = 1x^2 - 12x + 27

0 = 1x^2 - 12x + 27

0 = (x  - 3     )(x   -  9 )

(x-3) = 0             (x-9) = 0

x = 3                    x = 9

Answer:

A

Step-by-step explanation:

9514 1404 393

Answer:

  72.6 cm

Step-by-step explanation:

It is the perimeter of the overall rectangle plus twice the depth of the notch.*

  P = 2(L+W) +2d

  P = 2(16 cm + 13 cm + 7.3 cm) = 2(36.3 cm)

  P = 72.6 cm

The perimeter of the shape is 72.6 cm.

_____

* You may be able to visualize this if you imagine the bottom (top) of the notch translated out (down) to the edge of the rectangle. That translation does not affect the length of the line segment, but helps convince you that only the two legs of the notch are added to the perimeter of the rectangle.

Answer:

8

Step-by-step explanation:

ΔSTR is similar to ΔSPQ by SAS. Each side of ΔSTR is half of the corresponding side in ΔSPQ.

PQ and RT are corresponding.

So, PQ=2RT and w+58=2(w+25)

w+58=2w+50

8=w

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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Answer:

D) (0,9.5) and (10,1.5)

Step-by-step explanation:

a line of best fit is a line that is drawn through the data points on the scatter plot. Option D is the only answer that draws a linear line through the data points.

Option A makes a short line above the points. if the line is not through the points, it doesn't work

Option B is drawing a positive line (as in it's increasing) and therefore cannot work

Option C draws a line below the points and does not represent the line of best fit for this scatter plot

answer:

22 tables

explanation:

you have to divide on this one!

so,

13 divided by 289 is:

22

so,

the student council can decorate:

22 tables!

hope this helped! <3 i answered your question & hope you have a great day! if you wouldn't mind could you pls give me brainliest? (im trying to level up) thanks! :)

Answer:

15:24, 20:32 and 40:64.

Step-by-step explanation:

hope this helps

Answer:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Step-by-step explanation:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

the sum of all interior angles in a polygon is

180( n - 2)

n = number of sides

now, this polygon is a quadrilateral, so it has 4 sides, so it's total is just 180( 4 - 2) = 360.

\(360=x+4x+3x+2x\implies 360=10x\implies \cfrac{360}{10}=x\implies 36=x\)

Answer:

x = 36

Step-by-step explanation:

The angles of a trapezoid add up to 360, so add x, 4x, 3x, 2x to get 10x

10x = 360

360/10 = 36

Therefore, x = 36

(I am assuming the ()0 is a makeshift degree symbol-)

:)

Answer:

hey I gess it can help you.

THE VICE CHAIRPERSON CAN BE SELECTED BY 1 OR 29 CANDIDATES OR. 1/30*1/29=1/870 OR 870 POSSIBLE DIFFERENT SELECTIONS.

Answer:

sin A = 15/17

sec A = 17/8

Step-by-step explanation:

15 cot A = 8

First get cot A alone.

cot A = 8 / 15

Since cot is the reciprocal of tan then flip 15 and 8.

tan A = 15 / 8

Now you have the opposite and adjacent sides, just find the hypotenuse with Pythagorean's theorem

15^2 + 8^2 = 289

\(\sqrt{289}\) = 17

Now that you have all the sides use the opposite and hypotenuse to get sine and the adjacent and hypotenuse to get cosine then flip to get secant.

sin A = 15/17

cos A = 8/17

sec A = 17/8

By estimation, 3.9 turns into 4 and 5.3 turns into 5. The answer after estimation is 20 while the real answer is 20.67. Well u see by estimation we get an answer of two places right. So, real answer should also have two places.Place the decimal point after it.y43

Step-by-step explanation: i dont know if I'm right or not

Answer:5/6 x 3/4 = 0.625

Step-by-step explanation:

Answer:

the rule is scientific notation. if you are multiplying, move the decimal point over the amount of zeros to the right. if dividing, move the decimal point over to the left for the number of zeros there are.

Step-by-step explanation:

The population density of an area is the number of people living in per unit area. The most populated region is Region A.

The population density of an area is the number of people living in per unit area. It is given by the formula,

\(\text{Population Density}=\dfrac{\text{Population of the area}}{\text{Total area}}\)

The population density of the different regions is as follows,

Region A = 20,178 person /521 km² = 38.729 person/km²

Region B = 1,200 person /451 km² = 2.66 person/km²

Region C = 13,475person /395 km² = 34.114 person/km²

Region D = 6,980 person /426 km² = 16.385 person/km²

Hence, The most populated region is Region A.

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Answer:

Answer is 5

Step-by-step explanation:

You say 3 divided by 3 /5 = 5

Hope answer helps you

The equivalent equation of  r sinθ = 10 in rectangular coordinates is y²  +   y⁴/x² - 100 = 0.

The rectangular coordinates is calculated from the polar equation as follows;

r sinθ = 10

the conversion from polar to rectangular coordinates;

r² = x² + y²

r = √(x² + y²) ----- (1)

y/x = tanθ  ------ (2)

r sinθ = 10

√(x² + y²)(y/x) = 10

(x² + y²)(y²/x²) = 100

y²  +   y⁴/x² = 100

y²  +   y⁴/x² - 100 = 0

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To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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Answer:

0.5 (any number between 0 and 1)

Step-by-step explanation:

34 * 0.5 = 17

34 > 17 > 0

Answer:

Q (0,1) H (3,5) J (5,3)

Step-by-step explanation:

Anytime you rotate a shape around the origin, the numbers in the coordinates become their opposites.

(x,y) becomes (-x,-y).

So, (0, -1) becomes (0,1).

(-3,-5) becomes (3,5).

And, (-5, -3) becomes (5,3).

Answer: Here you go, hope this helps.

Step-by-step explanation: