Laura opened a deposit account. In the first month, she made an initial deposit of $2500. She plans to contribute $225 a month after her initial deposit. The account does not pay any interest.

After how many months will she have a total of $6,775?

A. 18
B. 15
C. 20
D. 21

The potential roots of the function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex] are -10,-5,3,15.

Given function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex]

We have to find the potential roots of the function according to rational root theorem.

Root is the solution of an equation usually expressed as a number or an algebraic formula.

The rational root theorem is used to find the potential roots of function.

For a polynomial function:

p(x)=p[tex]x^{n}[/tex]+..............................+q

The potential roots are:

Roots =±factors of q/factors of p

Th factors of 60 are =±1,±2,±3,±4,±5,±6,±10,±12.

The factors of 1 is ±1.

So we have factors are:±1,±2,±3,±4,±5,±6,±10,±12,±15,±20/±1

The  roots are =±1,±2,±3,±4,±5,±6,±0.

Factors:-10,-5,3,15.

Hence the potential roots are -10,-5,3,15.

Question is incomplete as it should includes options :-10,-7,-5,3,15,24

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The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).

Since the expression is √7x² ÷ √3x

So, one need to  rationalize the denominator and thus:

√7x² ÷ √3x  x √3x  ÷ √3x  

or write as √7x² x√3x ÷ √3x

or write as√(21x³)/3x

or write as √3*7*x³/3x

or write as √3*7*x/3

= √7x/√3

Therefore, The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).

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The option that's true regarding the sum and difference of the polynomial p(x) and b is B. The sum and difference of p(x) and b are polynomials.

From the information given, it was stated that p(x) is a polynomial and is given as p(=) = a₁ + a₁ + a₂=² + ... + an.

In this case, it should be noted that the sum and difference of p(x) and b are polynomials.

They can't be integers as the function given is represented as a polynomial.

In conclusion, the correct option is B.

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C is the right answer.

Trust me char!!

Na bakla na yswa!

Using the normal distribution, it is found that 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 20.66, \sigma = 2.4[/tex]

The proportion of students that are 21 or older is one subtracted by the p-value of Z when X = 21, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21 - 20.66}{2.4}[/tex]

Z = 0.14

Z = 0.14 has a p-value of 0.5557.

1 - 0.5557 = 0.4443 = 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.

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Answer:

Recognize the equation as that of a vertical line passing through the x-axis at 8

Answer:

the first option : vertical line passing through the x-axis at 8.

Step-by-step explanation:

x = 8

is a special case of a line equation.

it means that it contains all points for which x = 8.

so, e.g.

(8, -26), (8, - 7), (8, 0), (8, 3), (8, 57), ...

in other words, any y value is possible, but x is constant 8.

therefore, it is one vertical line going through 8 on the x-axis.

the is therefore no y-intercept.

this line equation maps all y values from -infinty to +infinity to the x value of 8. and FYI - it is therefore not a function (where each x value has exactly one assigned y value).

the slope of such a line is infinite or even more accurate undefined.

as the slope is y difference / x difference, x difference is always 0. something divided by 0 is officially undefined and often considered as infinite.

the opposite extreme is something like

y = 8

this is now the line that contains all points with y = 8.

any x-value is possible, but y is always 8.

that is a horizontal line that goes through the y-axis at 8.

and in fact, this is a function, as every x value has exactly one assigned y value (they are all 8, but that does not matter).

there is no x-intercept, of course.

and the slope is 0, as the slope is y difference / x difference, and the y difference is always 0. 0 divided by something is 0.

The formula that calculates the compound rate from the given values is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

The compound interest formula is:

[tex]I = P(1 + \frac rn)^{nt} - P[/tex]

Where:

We start by adding P to both sides

[tex]P + I = P(1 + \frac rn)^{nt}[/tex]

Divide through by P

[tex]\frac{P + I}{P} = (1 + \frac rn)^{nt}[/tex]

Take the nt-th root of both sides

[tex]\sqrt[nt]{\frac{P + I}{P}} = 1 + \frac rn[/tex]

Subtract 1 from both sides

[tex]-1 + \sqrt[nt]{\frac{P + I}{P}} = \frac rn[/tex]

Multiply through by n

[tex]r = n(-1 + \sqrt[nt]{\frac{P + I}{P}})[/tex]

In this case, t = 10

So, we have:

[tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

Hence, the formula that calculates the compound rate is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

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Thus, the required equation is given by Y = 5/2X.

Given data can tabulate is
Days overdue(x)  = 0  2  4  6  8  10

Amount of fine(y) = 0  5  10  15  20  25

equation is the relationship between variable and represented as     is example of polynomial equation.

Since, the as for every value of x, y grows linerely.

Equation can be given as for every 2 step of x, y increase 5 steps
therefore, y = 5/2x

Thus, The required equation is given by  y = 5/2x

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The function r =f(t) is f(t) = 1 - 8t/3

The function is given as:

3r + 8t = 3

Make r the subject

3r = 3 - 8t

Divide by 3

r = 1 - 8t/3

This means that:

f(t) = 1 - 8t/3

To calculate f(-3), we have:

f(3) = 1 - 8 * 3/3

Evaluate

f(3) = -7

Also, we have:

1 - 8t/3 = 2

Add 2 to both sides

-8t/3 = 3

Solve for t

t = -9/8

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Complete question

Consider the relationship 3r+8t=3

Write the relationship as a function  r = f(t)

Evalute f(-3)

Solve for f(t) = 2

The mean of the distribution sample is 0.62 and the standard error of the distribution sample is 0.069

Mean is the study of central tendency of a data set. The average value of the data points is the mean.

It is given that

The probability that the students have the student loan is  = 62% = 0.62

The probability that the students do not have student loan is

   1 - p

= 1 - 0.62

= 0.38

Total number of students is

n = 50

1) [tex]\rm \mu \;\hat p[/tex] = p = 0.62

2) [tex]\rm \sigma\hat p[/tex]  = [tex]\rm \sqrt {p ( 1 - p ) / n}[/tex]

=  [tex]\rm \sqrt {(0.62 * 0.38) / 50}[/tex]

= 0.069

Therefore the mean of the distribution sample is 0.62 and the standard error of the distribution sample is 0.069.

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No, John is incorrect.

[tex]\sf x^2 - 6x - 7 = 0[/tex]

[tex]\sf x^2 - 6x = 7[/tex]

[tex]\sf x^2 - 6x + 9= 7 + 9[/tex]

[tex]\sf (x-3)^2= 16[/tex]

[tex]\sf x-3=\pm \sqrt{16}[/tex]

[tex]\sf x-3= \pm 4[/tex]

[tex]\sf x= + 4 + 3 \quad or \quad x = -4 + 3[/tex]

[tex]\sf x= 7 \quad or \quad x = -1[/tex]

The correct answer should be x = 7 or x = -1

Step-by-step explanation:

assuming you are looking for angles and not angels:

Zero Angle (0° in Measure)

Acute Angle (0 to 90° in Measure)

Right Angle (90° in Measure)

Obtuse Angle (90 to 180° in Measure)

Straight Angle (180° in Measure)

Reflex Angle (180 to 360° in Measure)

Complete Angle (360° in Measure)

The difference between m and r from the given expressions is 8

Given the following exponents

x^m/x^5=x^7

x^m = x^5 * x^7

x^m = x^12

Equate the powers

m = 12

For the expression

(x^r)³ = x^12

x^3r = x^12

3r = 12

r = 4

Take the difference

m - r = 12 - 4

m - r = 8

Hence the difference between m and r is 8

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Answer:

Square Root of 7 = 7^1/2    = 2.646

Cubed Root of 7 = 7^1/3    = 1.913

Square Root of 7^3 = 7^3/2     = 3.659

The mortgage that will give the lowest monthly payment is EMI1 which translates to $ 1,708.16; and method one will require payment of the highest interest.

A mortgage is an arrangement between you and a lender that provides the lender the right to repossess your property if you fail to repay the loan plus interest.

Mortgage loans are used to purchase a property or to borrow money against the value of an existing home.

Given that:

Total amount = $525,000

Down payment = 20% = 0.2

Method 1: Time is 30 years and rate is 2.72%

Method 2: Time is 15 years  and the rate is 2.25%

Loan amount  = total amount less down-payment

= 525,000  - (0.2 * 525,000)

= $420, 000

Given that t = 30 year or 360 months

r = 2.72% or 0.0272

EMI1 =  [ 420, 000 * (0.0272/12) * ( 1 + (0.0272/12)³⁶⁰]/ [( 1 + (0.0272/12)³⁶⁰ -1]

= [952  * 2.259]/1.259

EMI1 = $ 1,708.16

t = 15 years or 180 months

Rate = 2.25% or 0.0225

EMI2 =  [420,000 * (0.0225/12) * ( 1 + (0.0225/12)¹⁸⁰]/ [( 1 + (0.0225/12)¹⁸⁰ --1]

= [787.5 * 1.401]/0.401

EMI2 = $2,751.34

Method 1

Interest = EMI1 x total months - loan amount

=  1,708.16 x 360 - 420,000

= $194, 937.6

Method 2

Interest = EMI2 x total months - loan amount

2,751.34 x 180 - 420,000

= $75,241.2

From the above method 1 requires the highest interest.

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Answer:

Step-by-step explanation:

let the numbers be x& y

y=4x+17

xy=-18

x(4x+17)=-18

4x²+17x+18=0

4x²+8x+9x+18=0

4x(x+2)+9(x+2)=0

(x+2)(4x+9)=0

x=-2

x=-9/4 (rejected as it is not an integer.)

y=4×(-2)+17=-8+17=9

so numbers are -2,9

Answer:

5

Step-by-step explanation:

Each trip adds up to 8/4 = 2 km

According to this, to travel 10 km is required:

10/2 = 5 trips

Hope this helps

If the price of a barrel of crude oil went up to $75, the amount that would be paid per barrel is $75.

The U.S. dollar is the main currency for trade around the world which includes the trade of crude oil.

This means barrels of crude oil are denominated in dollars. An increase of crude oil to $75 per barrel means that Americans would be $75 because they already use the currency that the oil is denominated in.

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Using the normal distribution, the probabilities are given as follows:

a) 0.6517 = 65.17%

b) 0.0823 = 8.23%.

c) 0.6109 = 61.09%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 8.9, \sigma = 2.8[/tex]

Item a:

The probability is the p-value of Z when X = 10, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 8.9}{2.8}[/tex]

Z = 0.39

Z = 0.39 has a p-value of 0.6517.

0.6517 = 65.17% probability that the time is less than 10 minutes.

Item b:

The probability is the one subtracted by the p-value of Z when X = 5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 8.9}{2.8}[/tex]

Z = -1.39

Z = -1.39 has a p-value of 0.0823.

0.0823 = 8.23% probability that the time is more than 5 minutes.

Item c:

The probability is the p-value of Z when X = 15 subtracted by the p-value of Z when X = 8, hence:

X = 15:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{15 - 8.9}{2.8}[/tex]

Z = 2.18

Z = 2.18 has a p-value of 0.9854.

X = 8:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8 - 8.9}{2.8}[/tex]

Z = -0.32

Z = -0.32 has a p-value of 0.3745.

0.9854 - 0.3745 = 0.6109 = 61.09%.

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f td d,ts#=#=sr#=rs$/,% gu gu hijkojibgu yf ,tdts$_, %_g g hu

the inequality in the number-line is:

x ≤ -1.5

We know that we have a closed circle at -1.5, this means that the value is a solution of the inequality.

Then we have a line that goes to the left of that circle, so the inequality will have solutions that are less than or equal to -1.5

Then the inequality is:

x ≤ -1.5

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Answer:c

Step-by-step explanation:

trust me

It's not an accurate value for the data based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means practically no correlation, while the points on the graph are moderately correlated

1. Part A:

Since the points in the scatter plot show a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.

The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to  1.

Here, r = - 1 is a perfect negative correlation as the points will adjust perfectly to a line with negative slope.

r =  + 1 is a perfect positive correlation: the points will ajdust perfectly to a line with positive slope.

r = 0 means that the variables are not correlated at all.

Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows other thing.

Therefore, the calculated value of r = 0.01 is not accurate for this scatter plot.

2. Part B.

A causal relationship means that the explanatory variable (the independent variable) is the cause of the dependent variable.

Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.

Thus, the scenario could be:

Amout of rainfall in mm (x)         Number of strawberries picked (y)

      100                                                     20

        50                                                     40

        25                                                     80

        12.5                                                  160

        6.25                                                 320

The amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.

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Answer:

[tex]\huge\boxed{\sf 900}[/tex]

Step-by-step explanation:

Sides of the figure = n = 7

(n - 2)×180

Where n is the number of sides in the polygon

So,

= (n - 2) × 180

= (7 - 2) × 180

= 5 × 180

= 900

[tex]\rule[225]{225}{2}[/tex]

Answer: 720°

Step-by-step explanation:

- Assuming this is a regular hexagon, all the sides are equal and all the angles are equal

- One of the properties of a regular hexagon is that the sum of all the interior angles is 720°

- Since the sum of all the interior angles is 720°, this means each interior angle is 120°

hope this helps :)

Answer: Recognize the equation as that of a vertical line passing through the x-axis at −3

The number of homes sold in the Southwest region in 2017was B. 102.

Regional sales refer to the sales recorded by marketing and sales regions through which an organization distributes its products and services.

Recording sales by region helps management to determine regional managers' performances and contributions to the sales efforts.

Sales in Washington county:

Southeast = 48%

Southwest = 12%

Northwest = 25%

Northeast = 15%

Sales of homes in the Southwest region = 102 (850 x 12%)

A. 1,020

B. 102

C. 588

D. 1,231

Thus, the homes sold in the Southwest region in 2017 were B. 102.

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Answer:

3x+13 units

Step-by-step explanation:

square perimeter of 12x +52 units

perimeter= 12x +52

12x + 52= 4(sides)

divide both sides by 4 = 12x/4 + 52/4= 3x+13

which give you 3x +13 units

Answer:

5.71428571429

Step-by-step explanation:

If the bet is done 762 times then expected value is that we may have a loss of $1562.1if the bet is that is heart comes we will get $16 and lose $3 if not comes.

Given We will get $16 if hearts come and lose $3 when not comes and bet is made 762 times. We have to calculate the expected win after 762 times.

We know that there are 13 hearts in the standard deck of cards.

Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:

Probability= number of items/ total number of items.

When two cards are chosen at random without replacement then the probability of getting two hearts is 13/52*12/51

=156/2652

=0.05

When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-0.05

=0.95

When  bet is made only 1 time expected value will be 0.05*16-0.95*3

=0.8-2.85

=-2.05 means we are expecting to lose $2.05.

When bet is made 762 times then the expected value will be -2.05*762=-1562.1.

Hence the expected value when bet is made 762 times is that we will lose $1562.1 .

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Answer:

$72

Step-by-step explanation:

100%-$60

1%-$0.60

100%-30%=70%

70%-$0.60x70=$42