A rectangle is 4 meters longer than it is wide. Find the dimensions of the rectangle if its area is 165 sq-meters.

The amount earned by $3000 deposited in the account after 6 months is $60.30

What does quarterly compounding mean?

Quarterly compounding means that the interest is computed and credited to the account every quarter, that is every 3 months, in other words, our future value formula would indicate quarterly interest rate rather than an annual interest rate

FV=PV*(1+r)^N

FV=the amount in the account after 6 months=unknown\

PV=initial amount deposited in the account=$3,000

r=quarterly interest rate=4%/4=0.01

N=number of quarters in 6 months=2

FV=$3000*(1+0.01)^2

FV=$3000*(1.01)^2

FV=$3000*1.0201

FV=$ 3,060.30

amount earned=FV-PV

amount earned=$3060.30-$3000

amount earned=$60.30

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Surface area of a sphere: 4 π r^2

Where:

r = radius = d/2 = 14/2 = 7

Replacing

SA = 4 π 7^2 = 4 π 49 = 196π cm2

A.) [tex]x = 2[/tex]

B.) [tex]x=1[/tex] (Nothing further can be done with this.)

C.)  [tex]x=2[/tex]

_____________________________________

Hope this helps! If not, feel free to comment below on the matter and I'll see what else I can do to assist you further. If it did help though, feel free to lmk! Thanks and good luck!

Answer:

AAAAAAAAAA

Step-by-step explanation: AAAAAAAAAAAAAAAA

The slope of line passing through the pair of points (4,3) and (2,2) is 1/2.

Slope is simply expressed as change in y-values over the change in x-values.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1( 4,3 )

Point 2( 2,2 )

Slope m = ?

Plug the given coordinates into the slope formula and solve for m.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 2 - 3 )/( 2 - 4 )

Slope m = ( -1 )/(-2 )

Slope m = ( 1 )/( 2 )

Slope m = 1/2

Therefore, the slope of the line segment with the given coordinates is 1/2.

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⇒In this case what is in the brackets is being treated as being the term . so this means that if we are to expand then we expand the whole term in full detail.

⇒In this case we have x+7 as the term of the expression which means when we expand we are going to expand the whole term x+7

[tex]=(x+7)^{2} \\=(x+7)(x+7)[/tex]

The third option is the answer.

GOODLUCK!!

the height in the first case will be 191 cm and the weight in the second case will be 106 kg.

We are given the function as:

BSA = √( w h / 3600)

where:

h = height

w = weight

BSA = body surface area

1) Now, for w = 68 kg and BSA = 1.9, we get the height as:

1.9 = √( (68) h / 3600)

3.61 = 68 h / 3600

12,996 = 68 h

h = 12996 / 68

h = 191.12 cm

h ≈ 191 cm

2) for h = 165 cm and BSA = 2.2, we get the weight as:

2.2 = √( w (165) / 3600)

4.48 = 165 w / 3600

17424 = 165 w

w = 17424/ 165

w = 105.6 kg.

w ≈ 106 kg

Therefore, we get that, the height in the first case will be 191 cm and the weight in the second case will be 106 kg.

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Let x represent the number of math problems that you completed.

Let y represent the number of biology problems that you completed

From the information given,

You completed a total of 15 problems. This means that

x + y = 15

If each math problem takes 5 minutes to complete, it means that the time to complete x math problems is 5 * x = 5x

If each biology problem takes 3 minutes to complete, it means that the time to complete y biology problems is 3 * y = 3y

If you spent 51 minutes working on your homework problems for math and

biology, it means that

5x + 3y = 51

Thus, the system of equations is

x + y = 15

5x + 3y = 51

The probability she will need to attend more than 3 try-outs is 0.7049.

The probability of an actress getting a job after a tryout is 0.11.

The actress wants to keep trying out for new jobs until she gets offered one.

The number of trials necessary for success in a series of independent trials follows a geometric distribution with parameter p, where p is the probability of success in a single trial.

The probability mass function is given as:

[tex]P(X=k)=q^{k-1}p[/tex] where k = 1, 2, 3

We have p = 0.11

q = 1 - 0.11 = 0.89

If X is the number of tryouts,

[tex]P(X=k)=q^{k-1}p\\P(X=k)=(0.89)^{k-1}(0.11)[/tex]

[tex]P(X\leq r)=1-q^r\\P(X\leq r)=1-(0.89)^r[/tex]

Therefore, the probability that she will need to attend more than 3 try outs will be:

P = P( X > 3 )

P = 1 - P( X ≤ 3 )

P = 1 - [ 1 - 0.89³ ]

P = 1 - 1 + 0.89³

P = 0.704969

P = 0.7049

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The game's expected value is -$0.83.

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The given table shows that does not show a proportional relationship, as the ratio between the output and the input is not the same for all terms of the table.

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as defined below.

y = kx

In this problem, we have that:

To verify if it shows a proportional relationship, we have to divide the output by the input in each case, hence:

Due to the different constant for 4 pounds, the table does not show a proportional relationship,

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Based on the number of states and their electoral votes in the 2020 presidential election, the intervals with 11 states are:

The graph on electoral votes by state in 202, gives the number of electoral votes as a range from 0 to 21 but in intervals of 3.

In 0 - 3 electoral votes, the number of states is 16.

In 3 - 6 electoral vote interval, number of states is 11.

In 6 - 9 electoral vote interval, number of states is 11.

In 9 - 12 electoral vote interval, number of states is 3.

In 12 - 15 electoral vote interval, number of states is 3.

In 15 - 18 electoral vote interval, number of states is 3.

In 18 - 21 electoral vote interval, number of states is 4.

The two intervals with 11 states are therefore 3 - 6 and 6 - 9.

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Consider the given radical,

Factorize the number,

Consider the following properties,

Then the radical can be simplified as,

Thus, the radical is simplified as,

Answer:

2.5×10^-11

Step-by-step explanation:

Put the point in the middle of 2 and 5 and count how many times you need to get there ...

like 0.05 to put point after 5 you have to jump 2 steps so it is 5×10^-2.

Dividing (2x³ - 9x² + 14x - 2) by (x - 1) with synthetic division method given the remainder 5 and the quotient 2x² - 7x + 7 + (5/x-1).

So, 2x³ - 9x² + 14x - 2 ÷ x - 1 by synthetic division as follows:

2x³ - 9x² + 14x - 2 ÷ x - 1:

Therefore, dividing (2x³ - 9x² + 14x - 2) by (x - 1) with synthetic division method given the remainder 5 and the quotient 2x² - 7x + 7 + (5/x-1).

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Step-by-step explanation:

you would take half of 15 and then square it to get to number, which is 56.25

Answer:

[tex](\frac{15}{2} )^2=\frac{225}{4}[/tex]

Step-by-step explanation:

[tex]x^2+15x-23=0\\x^2+15x+(\frac{15}{2} )^2-(\frac{15}{2})^2-23=0\\(x^2+15x+(\frac{15}{2})^2)=23+(\frac{15}{2})^2\\(x+\frac{15}{2})^2=(23*4+15^2)/4=317/4\\x+\frac{15}{2}=+\frac{\sqrt{317}}{4}\\, -\frac{\sqrt{317}}{4}\\\\x=-\frac{15}{2}-\frac{\sqrt{317}}{4}\\\\, -\frac{15}{2}+\frac{\sqrt{317}}{4}\\\\[/tex]

Answer:

-4/7, 18/7

Step-by-step explanation:

[tex]4x+7y=18 \\ \\ 7y=-4x+18 \\ \\ y=-\frac{4}{7}x+\frac{18}{7}[/tex]

There are two possibilities for answers none of which require subtraction based on the expression given:

With the question none of which involves subtraction. First is that this is a simple multiplication in which case the answer is 1,400;

Second that the above expression actually means 14x * 25x * 4 in which case the answer is 1400x²

Explanation 1

14 x 25 x 4

= 350 x 4

= 1,400

Explanation 2

14x * 25x * 4
= 1400 * x * x

= 1400x²

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The terminating category consists of 2%, 3/4, and 105/15.

The non-terminating category consists of  1/3, 15/7, and 81/11.

Given: 2%, 3/4, 105/15, 1/3, 15/7, 81/11

To determine whether these fractions are terminating or non-terminating decimals,

2% = 2/100 = 0.02

It is a terminating decimal.

3/4 = 0.75

It is a terminating decimal.

105/15 = 7

It is an integer, hence terminating.

1/3 = 0.3333333...

It is a non-terminating decimal.

15/7 = 2.14285714

It is a non-terminating decimal.

81/11 = 7.36363636

It is a non-terminating decimal.

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Notice that the parent function of y is:

Now, recall that a function h(x) translated n units to the left is represented by:

translated m units up :is represented by

reflected across the x-axis :is represented by

vertically compressed by a factor of 1/k :is represented by

Therefore, y is f(x) translated 3 units to the left, reflected over the x-axis, vertically compressed, and translated 2 units up.

y is its parent function translated 3 units to the left, reflected over the x-axis, vertically compressed, and translated 2 units up.

iven:

he fucnction is,

xplanation:

he graph fo the function cnan be obtained by graph of cube root of x.

If we shift the graph of cube root by x by one unit left then then function changed to,

If the obtained graph shrink vertically by a factor of 3/4 then graph changed to function,

This is the requied function for which we need the graph.

So graph can be obtained by horizontal shift of 1 unit to left, shrink by a factor of 3/4 and there is no vertical shift and graph will not flip over any axis.

Thus answer is, All statements are true.

a. Absolute value function the reference beam is g(x) = |8x/5|.

b. g(x) = +8x/5 ; x < 5 and g(x) = -8x/5 > 5.

For the given function;

Part a: The reference beam is passing from the points;

(x₁, y₁) = (5, 8)

(x₂, y₂) = (0, 0)

Then the slope of the line is -

m = (y₂ - y₁)/(x₂ - x₁)

Put the values ;

m = (0 - 8)/(0 - 5)

m = 8/5

The equation of the line is;

y - y₁ = m(x - x₁)

Put the values;

y - 0 = 8/5(x - 0)

y = 8x/5

Or in absolute modulus function for the path of reference beam; y = |8x/5|.

Part b: absolute function in terms of piecewise function;

g(x) = +8x/5 ; x < 5 as the slope is increasing.

and g(x) = -8x/5 > 5.;  as the slope is decreasing.

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Explanation

In the question, we are given that

First, we will get the standard deviation of the sample mean as

Then, we can find the probability that the sample mean will be less than $21,635 for a sample of 193 persons

Therefore, using the z score calculator

Answer: 0.7232

Answer:

260+325 = 585

260 where instructors that were full time and 325 were already full time. this is correct if I am reading your question correctly if not the answer is likely 260

The formula for the area(A) of the sector is,

Given:

Therefore,

Simplify

Hence,

Answer:

Slope: 2

Y-intercept: -3

Step-by-step explanation:

y=2x-3

The slope is always the number(s) before the x and the y-intercept is what is added or subtracted

Step-by-step explanation:

Let use the following rules to construct a polynomial,

Rule 1:

If r is a zero of some polynomial, f(x), then

[tex](x - r)[/tex]

is a factor of the polynomial

We first know that one of our zeroes are real, which is 0.

So since r=0

[tex](x - 0) = x[/tex]

is a factor

However, since the root ,0, has a multiplicty of 4, that basically means we have 0 as a root 4 times or basically we multiply the factor 4 times.

[tex]x \times x \times x \times x = x {}^{4} [/tex]

This leads to an another rule:

If a polynomial has a zero, r that has a multiplicty of k,

we represent the factor as

[tex](x - r) {}^{k} [/tex]

where k is all integers greater than 0.

So to reinforce myself, since 0 has a multiplicty of 4, we have

[tex](x - 0) {}^{4} = {x}^{4} [/tex]

So our first factor is

[tex] {x}^{4} [/tex]

Part 2: Complex Zeroes.

When dealing with complex zeroes, we must note this rule.

if (a+bi) is a zero of some polynomial, p then its conjugate (a-bi) is a factor as well.

So if 3-2i is a factor, then

3+2i is a factor as well.

Using Rule 1, our factors now become

[tex](x - (3 + 2i))[/tex]

and

[tex](x - (3 - 2i))[/tex]

So our factors are

[tex] {x}^{4} (x - (3 - 2i)(x - (3 + 2i))[/tex]

To simplify use FOIL Method,

[tex] {x}^{4} ( {x}^{2} - x(3 + 2i) - x(3 - 2i) + 9 - 4 {i}^{2} )[/tex]

[tex] {x}^{4} ( {x}^{2} - 6x + 13)[/tex]

[tex] {x}^{6} - 6 {x}^{5} + 13 {x}^{4} [/tex]

So our polynomial is

[tex] {x}^{6} - 6 {x}^{5} + 13 {x}^{4} [/tex]

Answer:

Write down one equation or inequality that has more than two solutions, but not infinitely many solutions

Step-by-step explanation:

Based on the annuity payment that Marie will make and the number of years, the nt value that she will use in her formula is 360 months.

The nt value is the number of periods that Marie will need to pay her annuity payment. This value can be yearly, monthly, weekly and even daily.

As the mortgage compounds monthly in this instance, the nt value will need to be monthly as well.

To find the nt value, the formula is:
= Number of years x number of compounding periods per year

= 30 x 12 times a year

= 360 months

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Answer:

360

Step-by-step explanation:

i did that and i got it right

EXPLANATION

To solve the given equation:

Step 1:

Multiply both-side of the equation by 2 in other to eliminate the denominator.

At the right-hand side of the equation, 2 add the numerator will cancel-out 2 at the denominator.

- 8 = v+ 6

step 2:

Subtract 6 from both-side of the equation.

That is;

-8 - 6 = v + 6 - 6

-14 = v

Hence, the value of v = -14