Money McGuire invests $50.00 in an account that she expects to double each year. How long will it take her investment to reach $3,200.00?

The segments' lengths and the angles' measurements are FE = 11,  CF = 10,  d = 54, and e = 126

As this is a parallelogram c = e

so 9y = 7y + 28

9y - 7y = 28

2y = 28

y = 14

So e would be 7(14) + 28

= 98 + 28

= 126.

And as d + e = 180, d = 180 - 126

d = 54

And as CF = DE

2x = x + 5

2x - x = 5

x = 5

CF = 2x

= 2(5)

= 10

And lastly CD = FE

CD = 3x - 4

CD = 3(5) - 4

= 15 - 4

= 11

FE = 11

So the answers are:

FE = 11,  CF = 10,  d = 54, and e = 126

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Answer:

The height of an equilateral triangle can be found using the Pythagorean theorem by treating it as a 30-60-90 triangle. In a 30-60-90 triangle, the ratio of the side lengths is 1:√3:2. In this case, the side length of 3 cm is the shorter leg, so the height (the longer leg) is 3√3 cm. Rounding to 1 decimal place, the height is approximately 5.1 cm.

The average change in weight calculated by the researcher for the sample of 25 freshmen is an example of a statistic.

A statistic is a numerical summary of a sample that is used to make inferences about a population. In this case, the sample is the 25 freshmen, and the population could be all freshmen entering college.

The average change in weight is a statistic because it summarizes the data collected from the sample, and is used to make conclusions about the population.

It represents the typical or average amount of weight gained or lost by the freshmen in the sample during their first semester in college.

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Answer:

Step-by-step explanation:

your picture is blur. can you repost it?

The surface area of the triangular prism is 62 square units.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.

The side length of each of the three squares is 4 units.

The area of each would be:

4² = 16 sq. units.  

For the three squares we have:

16(3) = 48 sq. units.

The area of each triangle is 7 sq. units.

This means together the area of the two triangles is 2(7) = 14 sq. units.

The surface area of the prism is:

14 + 48 = 62 sq. units.

Hence, the surface area of the triangular prism is 62 square units.

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There are 71,536,320 ways to arrange a standard deck of 52 cards so that all cards in a given suit appear contiguously.

There are 4 suits in a standard deck of 52 cards, and we need to arrange all the cards in a given suit contiguously. Once we choose a suit to be arranged in this way, we can treat it as a block of 13 cards that need to be arranged. Therefore, we have reduced the problem to arranging 4 blocks of 13 cards each, where each block represents a suit.

Within each suit, there are 13! ways to arrange the cards. However, once we arrange the cards in one suit, we fix the relative positions of the cards in the other suits. Therefore, we only need to consider the number of ways to arrange the suits themselves.

There are 4! = 24 ways to arrange the 4 suits. For each of these arrangements, there is only one way to arrange the cards within each suit contiguously. Therefore, the total number of ways to arrange the deck of cards so that all cards in a given suit appear contiguously is:

13! x 24 = 71,536,320

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Answer:

=3y - x =0

Step-by-step explanation:

[tex] \frac{y - y1}{x - x1} = m[/tex]

Therefore the gradient ( m ) is not given

from the question point =(-9,-3) and (-12,-4).

Gradient (m) =

[tex] \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 4 - ( - 3)}{ - 12 - ( - 9)} \\ = \frac{ - 4 + 3}{ - 12 + 9} \\ = \frac{ - 1}{ - 3} \\ = \frac{1}{3} [/tex]

therefore m = 1/3.

The equation

[tex] = \frac{y - y1}{x - x1} = m \\ \frac{y - ( - 3)}{x - ( - 9)} = \frac{1}{3} \\ \frac{y + 3}{x + 9} = \frac{1}{3} \\ 3(y + 3) = 1(x + 9) \\ 3y + 9 = x + 9 \\ 3y = x + 9 - 9 \\ 3y = x + 0 \\ 3y - x = 0[/tex]

therefore the equation of the line = 3y-x=0

The surface area is changing at a rate of approximately 2.94 square meters per second when the volume is 36 cubic meters and the balloon is being inflated at 3 cubic meters per second.

Volume of a sphere in terms of its radius = V = (4/3)π[tex]r^3\\[/tex]     .......(1)

Differentiating on both sides,                       [tex]\frac{dV}{dt}[/tex] = 4π[tex]r^{2}[/tex][tex]\frac{dr}{dt}[/tex]      .......(2)      

r = radius of the sphere.

Spherical balloon is being inflated at a rate of 3 cubic meters per second.

[tex]\frac{dV}{dt}[/tex] = 3 [tex]m^3/sec[/tex]

Volume is 36 cubic meters.

V = 36 [tex]m^3[/tex]

From equation (1), [tex]r^3[/tex] = [tex]\frac{3V}{4\pi }[/tex]

                              [tex]r^3[/tex] = [tex]\frac{3*36}{4*\pi }[/tex]

                              [tex]r^3\\[/tex] = [tex]8.59^1^/^3[/tex]

                               r = 2.04 meters

Substituting this in equation (2),  [tex]\frac{dr}{dt}[/tex]  =   [tex]\frac{dV}{dt}[/tex] / 4π[tex]r^{2}[/tex]

                                                     [tex]\frac{dr}{dt}[/tex]  =   3/(4π[tex]2.04^{2}[/tex])

                                                     [tex]\frac{dr}{dt}[/tex]  =   0.05737 m/sec

Now, surface area of sphere = A = 4π[tex]r^{2}[/tex]

Differentiating on both sides,

Rate of change of surface area  [tex]\frac{dA}{dt}[/tex] = [tex]8\pi r\frac{dr}{dt}[/tex]

                                                       = 8* 3.14* 2.04* 0.05737

                                                       = 2.94 [tex]m^2/sec\\[/tex]

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Answer:

Step-by-step explanation:

y=kx+b

b=3

(1,5)

1*k+3=5

k=2

so, 2x+3=y

Mary  age  is ( x -1 ) years old now.  4 years ago=  ( x -1 )-4 =0,  x=4+1=5,

now he is x -1 =5-1=4,  4 years ago=5-4=1 year,  iii) (3*8/3+8)=16 year old

Will he be 8 years from now  .now she is 4  year old now.

if he is x year old . he will be 8 years from now=(3x+8)=0

x=- 8/3. now his age is (3x+8) =(3*8/3+8)=16

A time of human existence, defined in years starting at birth, that is typically characterized by a certain stage or degree of mental or physical development and involves the potential for legal responsibility. the discretionary age. the legal drinking age. The legal drinking age was increased by the state from 18 to 21. Age is a notion that describes a person's age at a specific period. It is described as the measurement of the amount of time that has passed between the date of the live birth to a particular point in time, typically the date the data was collected. Age range, according to the Longman Dictionary of Contemporary English, is the term for a group of people who fall between two certain ages.

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Step-by-step explanation:

So working from the bottom

The last line for x > 20 shows 13 because of the top graph, the last line is 13 and there is nothing below it.

Now for x > 16, we go up a line and see 14

That's where you would add 14 + any number below it

14 + 13 = 27. So for x > 16, you'd write 27

Going up, we have X > 12. Same thing, we go up a line and see 19. So now we just add 29 and any number below that

19 + 14 + 13 = 46. So for x > 12, you'd write 46.

You'll do that for the rest of the table. hope that helps

Answer:

AAS

Step-by-step explanation:

[tex]\overline{PR} \cong \overline{PR}[/tex] by the reflexive property.

Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.

Therefore,

Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.. In this instance, the likelihood of Q and R is equal to P(Q) × P(R), which is 0.1804. The solution to this issue is this.

The complete question is:

Suppose Q and R are independent events. Find the probability of Q and R when P(Q)=0.41 Ans P(R)=0.44.

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Calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations.

When the equations are solved simultaneously, they are known as simultaneous equations.

Jogging be considered as x

Cycling be considered as y

Shelly spent 40 minutes jogging and 22 minutes cycling, and burned 620 calories to write this in equation we get,

40x + 22y = 620

Shelly swapped times,

22 minutes of jogging and 40 minutes of cycling and burned the same number of calories,

22x + 40y = 620

By multiplying two equation we get,

multiply equation 1 by 22 and equation 2 by 40 we get,

880x + 484y = 13640

880x + 1600y = 24800

Now subtracting equation 1 from 2 we get,

1116y = 11160

y = 11160/1116

y = 10

Therefore, putting value of y in equation 1 we get,

880x + 484(10) = 13640

880x = 13640 - 4840

x = 8800/880

x = 10

Therefore, calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

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Answer:

7n - 4

Step-by-step explanation:

The sequence 3, 18, 108, 648, ..... is a geometric sequence.

The sequence 3.9, 19.5, 97.5, -487.5, ..... is a geometric sequence.

The sequence 1.1, -2.2, 4.4, -8.8, ..... is a geometric sequence.

The sequence 4, 20, 4, 20, ..... is not a geometric sequence.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁ = a₃/a₂

Common ratio, r = 18/3 = 108/18

Common ratio, r = 6 = 6 (geometric sequence).

Common ratio, r = -19.5/3.9 = 97.5/-19.5

Common ratio, r = -5 = -5 (geometric sequence).

Common ratio, r = -2.2/1.1 = 4.4/-2.2

Common ratio, r = -2 = -2 (geometric sequence).

Common ratio, r = 20/4 = 4/20

Common ratio, r = 5 = 0.2 (not a geometric sequence).

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Answer:

Step-by-step explanation: A congruence statement expresses that two figures have the same size and shape. Here's how you can write a congruence statement step by step:

Write the two figures you want to compare. For example, you could write "Triangle ABC" and "Triangle DEF".

Use the symbol "≅" to indicate congruence. Place the symbol between the two figures, like this: "Triangle ABC ≅ Triangle DEF".

Label the corresponding parts of the two figures to show that they are congruent. For example, you could write "AB = DE", "BC = EF", and "AC = DF".

The final congruence statement would look like this: "Triangle ABC ≅ Triangle DEF, with AB = DE, BC = EF, and AC = DF". This statement says that Triangle ABC is congruent to Triangle DEF, and that the lengths of their corresponding sides are equal.

Answer:

Step-by-step explanation:

2.75 x 8 = 22

Step-by-step explanation:

an inscribed angle has its vertex on the circle, and the sides of the angle are two chords of the circle.

the inscribed angle is half the size of the arc angle (the angle at the center of the circle) of the arc that the two sides cut out of the circle.

110° is the arc angle (at the center of the circle) of the arc GJ.

for the inscribed angle GFJ the vertex is F, and the angle there is half of the arc angle :

angle GFJ = 110/2 = 55°

the second problem is the opposite "direction".

we have the inscribed angle FJH = 36°.

and we want the arc angle FH.

now, since the inscribed angle is half of the arc angle, the arc angle is twice the inscribed angle :

arc angle FH = 36×2 = 72°

In given lines, y = -1/4 x + 7 represents a transversal line.

A transversal is a line that, at two different locations, cuts through two lines in the same plane. Various types of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.      

Here we have

y = 1/6x - 3  ---- (1)    

y = -1/4 x + 7 ---- (2)  

y = 1/6x - 9 ---- (3)        

Here given lines are in y = mx + c form

The slope of the line (1) is 1/6

The slope of the line (2) is -1/4

The slope of the line (3) is 1/6

As we can see that line (1) and line (3) have the same slope,

Hence, Lines (1) and (3) are two parallel lines

where Line (2) is transversal which cuts the given two parallel lines  

Therefore,

In given lines, y = -1/4 x + 7 represents a transversal line.

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The coordinates  ( 6,-8 ) are plotted by moving 6 units right and 8 units down.

The intersection of the x- and y-axes creates the two-dimensional coordinate plane known as the cartesian plane. The origin is the point at which the x- and y-axes cross perpendicularly.

here, we have,

Given coordinates (6,-8)

for  the cartesian plane, we know that the origin has points (0, 0)

and divided into four Quadrants,

the left side of the origin is a negative x-axis and the right side is a positive x-axis.

and the upside of the origin is a positive y-axis and the downside is a negative y-axis.

here coordinates of x =6 and y = -8

6 is 6 units right from the origin

and -8 is 8 units down from the origin.

Hence for the coordinates , 6 units to the right and 8 units down , is correct.

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The given statement about the disjunction is true.

A compound statement with two distinct statements (disjuncts) connected by the wedge symbol (v) is called Disjunction.

Given is the statement -

(S~T) v (~U.W)

The given statement about the disjunction is true.

Therefore, the given statement about the disjunction is true.

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There will be enough water for all the guests.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

Total number of bottles = 24

Capacity of each bottle = 12 oz

Total capacity of the 24 water bottles = 12 × 24 = 288 oz

Now we have,

8 ounces = 1 cup

288 ounces = 288 / 8 = 36 cups

So there are 36 cups of water in total.

Number of guests = 30

If each guest drinks one cup of water, there will be 36 - 30 = 6 cups of water remaining.

Hence there will be enough water for the guests with 6 cups of water remaining.

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Your question is incomplete. Probably the correct question is as follows.

Before a party, Ashley bought a tray of 24 water bottles, each bottle has a capacity of 12 oz. There are 30 guests. If each guest drinks I cup of water, is there enough water for all the guests?

Check the picture below.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x) \qquad \begin{cases} x_1=-4\\ x_2=-3 \end{cases}\implies \cfrac{f(-3)-f(-4)}{-3 - (-4)}\implies \cfrac{[-6]~~ - ~~[-4]}{-3+4} \\\\\\ \cfrac{-6~~ + ~~4}{1}\implies \text{\LARGE -2}[/tex]

Answer:

-2

[tex]\hrulefill[/tex]

Step-by-step explanation:

The average rate of change of a function f(x) on the interval a ≤ x ≤ b can be calculated using the formula:

[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]

The given interval is -4 ≤ x ≤ -3, so:

From observation of the given graph, the values of f(a) and f(b) are:

[tex]f(a)=f(-4)=-4[/tex]

[tex]f(b)=f(-3)=-6[/tex]

Substitute the values of a, b, f(a) and f(b) into the formula to calculate the average rate of change of the function f(x) on the interval -4 ≤ x ≤ -3:

[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(-3)-f(-4)}{-3-(-4)}\\\\&=\dfrac{-6-(-4)}{-3-(-4)}\\\\&=\dfrac{-6+4}{-3+4}\\\\&=\dfrac{-2}{1}\\\\&=-2\end{aligned}[/tex]

Therefore, the average rate of change of the function f(x) on the given interval is -2.

The probability of a gym member attending yoga is 0.625 or 62.5%.

Probability is the likelihood or chance of an event happening. In this scenario, we have information about the number of gym members attending yoga and dance, which can be used to calculate the probability of a gym member attending yoga.

Out of the 400 gym members, 300 regularly attend yoga, and 50 attend both yoga and dance. This means that the number of gym members attending only yoga is 300-50=250. The probability of a gym member attending yoga can be calculated by dividing the number of gym members attending yoga by the total number of gym members.

Probability of a gym member attending yoga= Number of gym members attending yoga/Total number of gym members

Probability of a gym member attending yoga= 250/400

Probability of a gym member attending yoga= 0.625 or 62.5%

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Complete Question:

400 gym members, 300 regularly attend yoga, 80 regularly attend dance, and 50 regularly attend yoga and dance. Using this information, answer each of the following questions.

What is the probability that a gym member attends yoga?

The equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m. The first option from the given options is

Algebraic expressions that produce the same final expression are said to be equivalent expressions. If the values of two algebraic expressions can be obtained by replacing the variables, then the expressions are equivalent. Using the equal symbol (=), equivalent phrases are represented or illustrated to one another.

From the information given;

= 7m - (2 + 4m)

= 7m - 2 - 4m

Therefore, we can conclude that the equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m.

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Answer: 3/17 or 17.64%

Step-by-step explanation:

Just add everything (adds up to 17), then you put the color frequency number as the numerator of the fraction, then have the added up number as the denominator.

The crane's shadow is 45 meters long when the crane is 24 meters tall.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"

Let the shadow cast by the crane be x.

The triangle formed by the tower and by the crane are similar.

Using the rule of similar triangles we have:

16/24 = 30/x

16x = (30)(24)

x = 45

Hence, the crane's shadow is 45 meters long.

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Answer:104

Step-by-step explanation:

If 1/2 d=52,

d/2=52

Multiply both sides by 2.

Thus, d=52×2= 104.

Hope this helps! :)