3.14(a2 + ab) when a = 4 and b = 3​

Answer:

23.1 years  (nearest tenth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 1200=600\left(1+\dfrac{0.03}{12}\right)^{12t}[/tex]

[tex]\implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf 2=\left(1.0025\right)^{12t}[/tex]

Take natural logs:

[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]

[tex]\implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]

[tex]\implies t=23.13377513...[/tex]

[tex]\implies t=23.1\: \sf years \:\:(nearest\:tenth)[/tex]

The money will double in value in approximately [tex]\boxed{\sf 23.1}[/tex] years.

Used formula

[tex]\boxed{\sf A=P(1+\dfrac{r}{n})^{nt}}[/tex]

[tex]\\ \implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf 2=\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]

[tex]\\ \implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]

[tex]\\ \implies t=23.1years[/tex]

Answer:

It's most likely he was charged a late fee

The standard deviation is a better measure of spread for movies than it is for basketball games.

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

As, Movies is more centric to mean and not skewed on a particular side whereas basketball games is not centric to mean but is skewed right then left.

Now, Standard deviation just measures the deviation or spread with respect to mean of collected data.

So, In the movies the data is more collected. Thus standard deviation is best suited for movie data.

Now, interquartile range. IQR relies on if the data is skewed.

So, in the basketball data the standard deviation will not give the information.

Hence, the  standard deviation is a better measure of spread for movies than it is for basketball games.

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Answer:

1/3 and 1/4

multiplying 1/3 by 1/4 and 1/4 by 1/3 we get

1/3 * 1/4

1 *1 /3*4

1/12

1/4 * 1/3

1*1 / 4*3

1/12

now, both have same denominator.

Step-by-step explanation:

Answer:

4 pencil & 2 ruler = $8

2 pencil & 4 ruler = $10

let the no. of Pencil be X and no. of ruler be Y

4x + 2y = 8

2x + 4y= 10

solving the equation by elimination method,

multiplying eq 2 with 2

4x + 2y = 8

4x + 8y = 20

subtracting,

- 6 y = -12

y = 2

2x + 4(2)= 10

2x + 8 = 10

2x = 10 - 8

2x = 2

x = 1

Cost of 3 ruler + 3 pencil

= 3(1) + 3(2)

= 3 + 6

= 9

Answer:

$9

Step-by-step explanation:

pencil - p

ruler - r

4p + 2r = 8

2p + 4r = 10

4p + 2r = 8 {finding p in terms of r so we can substitiute it}

    - 2r    -2r

4p = 8 - 2r

÷ 2      ÷2

2p = 4 - r  {now, we can replace "2p" in our other equation}

2p + 4r = 10 becomes...

[4 - r] + 4r = 10

4 - r + 4r = 10

4 + 3r = 10

- 4        -4

    3r = 6

  ÷3    ÷3

    r = 2

when we have 4 pencils and 2 rulers, we have:

4p + 2[2] = 8

4p + 4 = 8

     -4     -4

4p = 4

÷4      ÷ 4

p = 1

{checking with our other equation:

p = 1 ; r = 2

2p + 4r = 10

2[1] + 4[2] = 10

2 + 8 = 10

10 = 10

TRUE STATEMENT;

confirms our variables}

so , we have found that the cost of a pencil is $1, and the cost of a ruler is $2,

p = 1 ; r = 2

so, let's solve our original problem:

3 rulers + 3 pencils = ?

3(2) + 3(1) = ?

6 + 3 = 9

so, the cost of this combination would be $9

hope this helps!! have a lovely day :)

Answer:

The mid-point is (9,-9/2)

Step-by-step explanation:

You would use the mid-point formula for this

[tex](\frac{x_{2} +x_{1} }{2} , \frac{y_{2}+y_{1} }{2} )[/tex]

if you plug that in it is ([tex]\frac{13-2}{2}, \frac{-7+5}{2}[/tex])

resulting in (11/2,-2/2) = (11/2,-1)

Answer:

I have no clue what I could answer that question with other than (-6,-10)

Answer:

According to the graph, g(x) is stretched by what seems to be 5, so g(x) is (x^2) / 25. (Square the stretching/compressing factor so 5^2 became 25). We also divide x^2 by this because it is being stretched. You multiply if it's being compressed.

You can check this by plugging 5 for x and trying to get 1.

g(x) = x^2 / 25

g(5) = 5^2 / 25 --> 25/25

g(5) = 1

g(x) = (x^2)/25

Answer:

1,887,436,800

Step-by-step explanation:

f(t) = a·b^t

f (t) = number of cases at year t

a = starting value = 1800 in 1983

b = growth factor = 2

t = years since 1983 = 2003 - 1983 = 20

f(t) = 1800·(2)^20 =

1,887,436,800

wyzant

philip p

Answer:

hi

Step-by-step explanation:

no

Answer:

he.....a red cap.(wants/want)

The total fencing material required to surround the playground of length l and width w and 2 flower beds of side a is 2 ( l + b ) + 8a units.

The perimeter of a two-dimensional shape is the total length of the outline.

Perimeter of rectangle = 2 ( l + b ).

Perimeter of square = 4 × side.

Given the length of the playground is l and its width is w and the length of each side of the flower beds is a.

The total fencing material required = perimeter of playground + 2 *                             Perimeter of flower bed.

                        =  2 ( l + w ) + 2 * 4a

                        = 2 ( l + w ) + 8a units.

Therefore, The total fencing material required to surround the playground and flower beds is 2 ( l + w ) + 8a units.

The question seems incomplete, its options could be:

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Answer:

  x = y = 4

Step-by-step explanation:

A 2-variable linear programming problem is nicely solved by graphing. The solution will be one of the vertices of the solution set. The attached graph shows that means it is one of (x, y) = [(0, 0), (0, 6), (4, 4), (6, 2), (7, 0)}.

__

Evaluating the objective function at each of these vertices will show you the solution that maximizes it.

(0, 0) -- P = 40·0 +50·0 = 0

(0, 6) -- P = 40·0 +50·6 = 300

(4, 4) -- P = 40·4 +50·4 = 360

(6, 2) -- P = 40·6 +50·2 = 340

(7, 0) -- P = 40·7 +50·0 = 280

_____

Additional comment

The solution set would ordinarily be the area that is covered by the shading that signifies the solution set of each of the 5 inequalities. 5 different overlapping shadings can make the graph quite messy, so we have elected to shade the areas that are NOT part of the solution set. In doing so, we have made the boundary lines dashed when they are part of the solution set

The possible solutions are the vertices of the white space on the graph.

The black line on the graph is the line corresponding to the maximum value of the objective function. To maximize the objective function, we want that line as far from the origin as possible. It is shown intersecting the vertex of the solution space that meets that condition.

Taking the change in y over the change in x. Then the correct option is A.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]

The equation of the line can be determined by the two known points.

Taking the change in y over the change in x.

Then the correct option is A.

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Answer:

[tex]m > 5[/tex]

Step-by-step explanation:

[tex] \frac{m + 4}{3} > 3 \\ \frac{m + 4}{3} \times 3 > 3 \times 3 \\ m + 4 > 9 \\ m + 4 - 4 > 9 - 4 \\ m > 5[/tex]

Answer:

c. x/7

Step-by-step explanation:

seven is dividing something, and X is the placeholder in this equation.

So, since x is being divided by seven, that rules out B., because that's backwards.

A. and D. don't involve division, so they're both incorrect as well.

Thus we are left with C. x/7

Answer:

54√2

Step-by-step explanation:

The normal distribution is also known as the Gaussian distribution. The correct option is D, while the z-score is -2.29.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Since the normal distribution is symmetrical about the mean. Therefore, 0.89 area from the left will be equal to 0.11 area from the right. Therefore, the correct option is D, while the z-score is -2.29.

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Answer:

$2,120

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

Given:

Substitute the given values into the formula and solve for A:

⇒ A = 2000(1 + 0.06(1))

⇒ A = 2000(1.06)

⇒ A = 2120

Therefore, there will be $2,120 in the account at the end of the 1 year period.

A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.

Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,

Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%

Hence, the relative change from last year to this year is 3.7%.

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Answer:

Or if you don't want any rounding it will be 115.38461538461

Because both lines have the same slope but different y-intercepts, we conclude that the lines are parallel.

Here we have the two lines:

6x - 2y = -2

y = 3x + 12

If we write both of these in the slope-intercept form, we get:

y = (-2 - 6x)/-2  = 3x + 1

y = 3x + 12

So, as you can see, both lines have the same slope but different y-intercepts. That means that the two lines are parallel, so they never do intercept.

Then we can conclude that the correct option is parallel.

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The value of a is 1 , b = 3 , c = 4 , Option B is the correct answer.

The correct question is

Which values of a, b, and c represent the answer in simplest form?

7/9 divided by 4/9 = [tex]\rm a\dfrac{b}{c}[/tex]

1: a = 1, b = 4, c = 3

2: a = 1, b = 3, c = 4

3: a = 1, b = 63, c = 36

4: a = 1, b = 36, c = 63

Reducing to simplest form means to reduce to an extent where the numerator and denominator have nothing in common to be cancelled out.

It is given in the question that

(7/9) / (4/9) =  [tex]\rm a\dfrac{b}{c}[/tex]

It can also be written as

(7*9)/(4*9) =  [tex]\rm a\dfrac{b}{c}[/tex]

7/4 = [tex]\rm a\dfrac{b}{c}[/tex]

[tex]\rm 1 \dfrac{3}{4} = a\dfrac{b}{c}[/tex]

Therefore the value of a is 1 , b = 3 , c = 4 , Option B is the correct answer.

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The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).

Let's call the point that divides the line segment point P.

Point P divides the line segment into a ratio of 2:3

The ratio of 2:3 means we are dividing the line segment into 2+3=5 equal parts.

The horizontal distance between the two coordinates is 5.

The vertical distance between the two coordinates is 10.

Dividing both vertical and horizontal distance into five equal parts, we have a horizontal distance of 1 and a vertical distance of 2.

Every time we move one unit to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.

The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).

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Answer:

9:12

Step-by-step explanation:

since the others are multiples of 2:3

but 9:12 is not a multiple

Based on the annual coupons on the bond and the current price, the current yield will be 9.27%.

This can be found as:

= Annual coupon amount / Bond price

Annual coupon:

= 10% x 100

= $10

The current yield is:

= 10 / 107.87

= 9.27%

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Regarding conditional probabilities, the keyword is always given, as a previous event is considered to have happened.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

The previous event having happened is represented by keyword given.

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Answer:

D is the correct answer.

Step-by-step explanation:

Find the portion of the graph that is above the x-axis.

Answer:

D

Step-by-step explanation:

Coming in from - inf the graph is positive and remains so until yo get to x = -1  <==== then it is zero    and continues to negative values

Answer:

f(5)=5+2(5)-2

f(5)=5+10-2

f(5)=15-2

f(5)=13