Rebecca Pearson is a widow and needs to take care of the expenses in her household. Her budget is below.

Find her net monthly cash flow. (Assume 1 month = 4 weeks)

Income Expenses
Salary: $2300/month



Rent: $1090/month
Groceries: $200/week
Utilities: $125/month
Car Insurance: $525 semiannually
Gasoline: $25/week
Miscellaneous: $200/month
Phone: $50/month

Answer: Choice C

Step-by-step explanation:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.

3/10≠3/5*1/4

so event A and B are not independent.

Answer:

0

Step-by-step explanation:

1x=x

-x/1=-x

x-x=0

Answer:

Brainleist !

Step-by-step explanation:

x - x /1

x - x = nothing or 0

Answer:

$900

Step-by-step explanation:

If she holds $500 and she is charged 15%; it means

The interest she pays per month is ;

$500 × 15/100 = $75

Then annually meaning for 12 months, she pays;

$75 × 12 = $900

Her annual interest on her current card is $900.

Therefore,

She will be taxed 15% if she holds $500, which means

The monthly interest she pays is;

$500 × 15/100 = $75

She then pays annually, which is for a full year;

$75 × 12 = $900

Hence, Her annual interest on her current card is $900.

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Answer:

Height of this missing bar would be 1

Step-by-step explanation:

Since there is 1 and only 1 quantity between 80-99.

Answer:

1

There is 1 number that is between 80 and 99 which is 99 so there should be 1 bar.

Step-by-step explanation:

Answer:

[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]

Step-by-step explanation:

For a hyperbolic mirror the two foci are 42 cm apart.

The distance between the foci = 2c.

Therefore:

The distance of the vertex from one focus = 6 cm

The distance of the vertex from the other focus = 36 cm

2a=36-6=30

Now:

[tex]c^2=a^2+b^2\\21^2=15^2+b^2\\b^2=21^2-15^2\\b^2=216\\b=6\sqrt{6}[/tex]

If the transverse axis lies on the y-axis, and the hyperbola is centered at the origin. Then the hyperbola has an equation of the form:

[tex]\dfrac{y^2}{a^2} -\dfrac{x^2}{b^2}=1[/tex]

Therefore, the equation of the hyperbola is:

[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]

Answer:   b) 1510 vehicles

Step-by-step explanation:

Total: 5 miles x 5280 ft per mile = 26,400

Cars: 80% of vehicles are cars with a length of 13.5 =  0.8(13.5)v = 10.8v

Trucks: 20% of vehicles are trucks with length of 20 = 0.2(20)v = 4v

Between: Distance between two vehicles is 3: (3/2)v = 1.5v

Total  = Cars + Trucks + Between

26,400 = 10.8v + 4v + 1.5v

26,400 = 16.3v

1619.6 = v

the closest number of all of the options is (b) 1510

Answer:

A. d= 45t

Step-by-step explanation:

(assuming that you meant 67.5 in the last 1.5 hours)

67.5 miles = distance

1.5 hours = time

therefore:

[tex]\frac{d}{t\\}[/tex] = 67.5/1.5

making your answer 45

leaving a as your correct answer:

d= 45t

The proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

Given that, A train travels at a constant speed and has travelled 67.5 miles in the last 1.5 hours. (assuming that you meant 67.5 in the last 1.5 hours)

67.5 miles = distance

1.5 hours = time

We know that, speed = distance / time

s = 67.5/1.5

s = 45 mph

Now, distance = speed × time

d = 45t

Hence, the proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).

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Answer:

19.51% probability that none of them voted in the last election

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

42% of Americans voted in the previous national election.

This means that [tex]p = 0.42[/tex]

Three Americans are randomly selected

This means that [tex]n = 3[/tex]

What is the probability that none of them voted in the last election

This is P(X = 0).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951[/tex]

19.51% probability that none of them voted in the last election

Answer:

10

-5

Step-by-step explanation:

5 - -5

Subtracting a negative is like adding

5+5 = 10

-9 - -4

-9+4

-5

Answer:

Step-by-step explanation:

5+5 = 10

-9+4 = -5

Answer:

Step-by-step explanation:

it is -12 because -6 plus -6 is also like 6 plus 6

and then you have to add the negative Sign.

pls brainliest me

-6 - 6 = - 12

Happy to help! Please mark as the brainliest!

Answer:

We know that:

The original price was $515

and

It was $125 off

so we need to find the price of the sofa after the discount.

$515 - $125 = $390

The sale price of the sofa after the discount was $390

hope This helps and pls mark me brainliest if it did :)

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The point of diminishing returns (x , y ) is  (11, 21462)

Step-by-step explanation:

From the question we are told that

     The function is  [tex]R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20[/tex]

Here R(x)  represents revenue (in thousands of​ dollars) and  x  represents the amount spent on advertising​ (in thousands of​ dollars).

           Now  differentiating  R(x) we have  

               [tex]R'(x) = -3x^2 +66x + 800[/tex]

Finding the second derivative of R(x)

              [tex]R''(x) = -6x +66[/tex]

at  inflection point    [tex]R''(x) = 0[/tex]

    So      [tex]-6x +66 = 0[/tex]

=>           [tex]x= 11[/tex]

    substituting value of x into R(x)

     [tex]R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,[/tex]

      [tex]R(x) = 21462[/tex]

Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is

     (11, 21462)

Answer:

[tex]x^2-4x+4[/tex]

Step-by-step explanation:

[tex](x - 2)^2[/tex]

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

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

[tex]x^2-2x-2x+4[/tex]

[tex]x^2-4x+4[/tex]

Answer:

[tex]{x}^{2} - 4x + 4 \\ [/tex]

Step-by-step explanation:

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

hope this helps you

Answer:

i dont really know what it is

Answer:

[tex]cos150 = -\frac{\sqrt{3} }{2}[/tex]

Step-by-step explanation:

Recall the unit circle. At 150 deg, the point value is (-sqrt3/2, 1/2)

Remember the cosine is always the x-value, and sine is always the y-value.

This means that cosine will be -sqrt3/2.

Answer:

11 1/4

Step-by-step explanation:

first make the fractions equal. So 9 1/6 would be 9 2/12 so that we canadd them together.

9 2/12 + 2 1/12 = 11 3/12

but u can simplify the answer so itll be 11 1/4

[tex]answer = 11 \ \frac{3}{12} \\ solution \\ 9 \ \frac{1}{6} + 2 \ \frac{1}{12} \\ = \frac{55}{6} + \frac{25}{12} \\ = \frac{55 \times 2 + 25}{12} \\ = \frac{110 + 25}{12} \\ = \frac{135}{12} \\ = 11 \ \ \frac{3}{12} \\ hope \: it \: helps[/tex]

Answer:

5.625 = 45/8 = 5 5/8

Step-by-step explanation:

Answer:

[tex]y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]

Step-by-step explanation:

Solution:-

- Given is the 2nd order linear ODE as follows:

                      [tex]ty'' + ( 2t - 1 )*y' - 2y = 6t^2 . e^(^-^2^t^)[/tex]

- The complementary two independent solution to the homogeneous 2nd order linear ODE are given as follows:

                     [tex]y_1(t) = 2t - 1\\\\y_2 (t ) = e^-^2^t[/tex]

- The particular solution ( yp ) to the non-homogeneous 2nd order linear ODE is expressed as:

                    [tex]y_p(t) = u_1(t)*y_1(t) + u_2(t)*y_2(t)[/tex]

Where,

              [tex]u_1(t) , u_2(t)[/tex] are linearly independent functions of parameter ( t )

- To determine [  [tex]u_1(t) , u_2(t)[/tex] ], we will employ the use of wronskian ( W ).

- The functions [[tex]u_1(t) , u_2(t)[/tex] ] are defined as:

                       [tex]u_1(t) = - \int {\frac{F(t). y_2(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\\\u_2(t) = \int {\frac{F(t). y_1(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\[/tex]

Where,

      F(t): Non-homogeneous part of the ODE

      W [ y1(t) , y2(t) ]: the wronskian of independent complementary solutions

- To compute the wronskian W [ y1(t) , y2(t) ] we will follow the procedure to find the determinant of the matrix below:

                      [tex]W [ y_1 ( t ) , y_2(t) ] = | \left[\begin{array}{cc}y_1(t)&y_2(t)\\y'_1(t)&y'_2(t)\end{array}\right] |[/tex]

                      [tex]W [ (2t-1) , (e^-^2^t) ] = | \left[\begin{array}{cc}2t - 1&e^-^2^t\\2&-2e^-^2^t\end{array}\right] |\\\\W [ (2t-1) , (e^-^2^t) ]= [ (2t - 1 ) * (-2e^-^2^t) - ( e^-^2^t ) * (2 ) ]\\\\W [ (2t-1) , (e^-^2^t) ] = [ -4t*e^-^2^t ]\\[/tex]

- Now we will evaluate function. Using the relation given for u1(t) we have:

                     [tex]u_1 (t ) = - \int {\frac{6t^2*e^(^-^2^t^) . ( e^-^2^t)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_1 (t ) = \frac{3}{2} \int [ t*e^(^-^2^t^) ] \, dt\\\\u_1 (t ) = \frac{3}{2}* [ ( -\frac{1}{2} t*e^(^-^2^t^) - \int {( -\frac{1}{2}*e^(^-^2^t^) )} \, dt] \\\\u_1 (t ) = -e^(^-^2^t^)* [ ( \frac{3}{4} t + \frac{3}{8} )] \\\\[/tex]

- Similarly for the function u2(t):

                     [tex]u_2 (t ) = \int {\frac{6t^2*e^(^-^2^t^) . ( 2t-1)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_2 (t ) = -\frac{3}{2} \int [2t^2 -t ] \, dt\\\\u_2 (t ) = -\frac{3}{2}* [\frac{2}{3}t^3 - \frac{1}{2}t^2 ] \\\\u_2 (t ) = t^2 [\frac{3}{4} - t ][/tex]

- We can now express the particular solution ( yp ) in the form expressed initially:

                    [tex]y_p(t) = -e^(^-^2^t^)* [\frac{3}{2}t^2 + \frac{3}{4}t - \frac{3}{8} ] + e^(^-^2^t^)*[\frac{3}{4}t^2 - t^3 ]\\\\y_p(t) = -e^(^-^2^t^)* [t^3 + \frac{3}{4}t^2 + \frac{3}{4}t - \frac{3}{8} ] \\[/tex]

Where the term: 3/8 e^(-2t) is common to both complementary and particular solution; hence, dependent term is excluded from general solution.

- The general solution is the superposition of complementary and particular solution as follows:

                    [tex]y_g(t) = y_c(t) + y_p(t)\\\\y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]

Answer:

a.vertical translation

Answer:

67

Step-by-step explanation:

Using triangle property

127+x=180

x=53

53+60+y=180

113+y=108

y=67

Answer:

14, 32

Step-by-step explanation:

45,15,44,17,40,20,31,25

this is combination of 2 series:

In the first series we can see the pattern as:

In the second series we can see the pattern as:

The series will continue as:

Answer:

14, 32

Step-by-step explanation:

lol :D

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y: family spending

X₁: income of a family

X₂: family size

X₃: additions to savings of a family

And the regression output (see attachment)

The population model is Y= α + β₁X₁ + β₂X₂ + β₃X₃

a)

To write the estimated regression equation of the relationship between the variables you have to use the information given in the regression output. Under the column "coefficients", the value that corresponds to "intercept" is the estimation of the y-intercept (a), the value under X₁ corresponds to the estimation for the slop for the variable "income of the family" (b₁), under X₂ is the estimation of the slope for the variable "family size" (b₂) and under X₃ is the estimation for the slope corresponding to the variable "additions to savings" (b₃)

The estimated regression equation is:

^Y= a + b₁X₁ + b₂X₂ + b₃X₃

^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃

b)

Using the SS information you can calculate the coefficient of determination as:

SStotal= SSReg+SSError= 45.9634+2.6218= 48.5852

[tex]R^2= \frac{SS_{Reg}}{SS_{Total}} = \frac{45.9634}{(48.5852)} = 0.946[/tex]

R²= 94.6%

This means that 94.6% of the variability of the average family spending is explained jointly by the family income, the family size and the addition to saving under the estimated model ^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃

c)

The hypotheses are:

H₀: β₁= β₂= β₃= 0

H₁: At least one βi≠0 ∀ i=1, 2, 3

α: 0.05

The statistic for the multiple regression is

[tex]F=\frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg};Df_{Error}}[/tex]

[tex]MS_{Reg}= \frac{SS_{reg}}{Df_{Reg}}= \frac{45.9634}{3} = 15.32[/tex]

[tex]MS_{Error}= \frac{SS_{Error}}{Df_{Error}} = \frac{2.6218}{11} = 0.238[/tex]

[tex]F_{H_0}= \frac{MS_{Reg}}{MS_{Error}}= \frac{15.32}{0.238}= 64.37[/tex]

p-value  < .00001

At a 5% significance level, there is enough evidence to reject the null hypothesis. This means that the family income, family size and the addition to savings modify jointly the average spending of families.

d.

Individual tests:

There are two possible statistics to test the significance of each independent variable: [tex]t= \frac{b_i-\beta_i }{S_{b_i}} ~~t_{n-3}[/tex] ∀ i= 1, 2, 3, or [tex]F=\frac{MS_{X_i}}{MS_{Error}} ~F_{Df_{X_i}; Df_{Error\\}}[/tex]

Since the output doesn't give us the information of the individual ANOVA, you have to use the t-test (Df: n-3= 12-3= 9) for these hypotheses. Using the p-value approach. the decision rule for the three hypothesis will be:

If p-value ≤ α ⇒ Reject null hypothesis.

If p-value > α ⇒ Do not reject the null hypothesis.

1)

H₀: β₁ = 0

H₁: β₁ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}= \frac{0.7992-0}{0.074}= 10.8[/tex]

p-value < .00001 ⇒ Decision is to reject the null hypothesis.

2)

H₀: β₂ = 0

H₁: β₂ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}= \frac{0.2280-0}{0.190}= 1.2[/tex]

p-value: 0.260773 ⇒ The decision is to not reject the null hypothesis.

3)

H₀: β₃ = 0

H₁: β₃ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}= \frac{-0.5796-0}{0.920}= -0.63[/tex]

p-value: 0.544355 ⇒ The decision is to not reject the null hypothesis.

So, at a 5% significance level, it seems that the three independent variables influence jointly the variation on the average spending of the families, but looking at them separately, only the income of the families seems to affect their spending habits significantly while the family size or their addition to savings don't seem to have major effect over their spending habits.

I hope this helps!

Answer:

See attachment

Step-by-step explanation:

The solution is given in the image.

The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.

An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.

Learn more about graphs here: brainly.com/question/4025726

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Answer:

a) The CDF of X/Y is calculated as:

[tex]F_{z} (\zeta) = \frac{\zeta}{\zeta + 2}[/tex] for [tex]0 < \zeta < \infty[/tex]  

[tex]F_{z} (\zeta) = 0[/tex] for [tex]\zeta \leq 0[/tex]

Note: Z = X/Y

b) Probability that A finishes before B = 1/3

Step-by-step explanation:

For clarity and easiness of expression, this solution is handwritten and attached as a file. Check the complete solution in the attached file.

Answer:

A

Step-by-step explanation:

(2,1) - only one in the table. Remember (x,y)

Answer:

  3.84 units

Step-by-step explanation:

By the properties of angle bisectors, ...

  WZ/ZX = WY/YX

Solving for WY, we have ...

  WY = (YX)(WZ)/(ZX) = (6.5/6)(WZ)

The length YZ is ...

  YZ = 8 = WY +WZ

  8 = (6.5/6)(WZ) +WZ = 12.5/6(WZ) . . . . substitute for WY

  WZ = 8(6/12.5) . . . . multiply by 6/12.5

  WZ = 3.84

Answer:

The correct answer is indeed 3.84 units

Step-by-step explanation:

I just took the test and got it correct hope this helps ☺

Answer:

Step-by-step explanation:

Corresponding net sales before 1 month and after 1 month form matched pairs.

The data for the test are the differences between the net sales before and after 1 month.

μd = the​ net sales before 1 month minus the​ net sales after 1 month.

Before after diff

57.1 63.5 - 6.4

94.6 101.8 - 7.2

49.2 57.8 - 8.6

77.4 81.2 - 3.8

43.2 41.9 1.3

Sample mean, xd

= (- 6.4 - 7.2 - 8.6 - 3.8 + 1.3)/5 = - 4.94

xd = - 4.94

Standard deviation = √(summation(x - mean)²/n

n = 5

Summation(x - mean)² = (- 6.4 + 4.94)^2 + (- 7.2 + 4.94)^2 + (- 8.6 + 4.94)^2+ (- 3.8 + 4.94)^2 + (1.3 + 4.94)^2 = 60.872

Standard deviation = √(60.872/5

sd = 3.49

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 5 - 1 = 4

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (- 4.94 - 0)/(3.49/√5)

t = - 3.17

We would determine the probability value by using the t test calculator.

p = 0.017

Since alpha, 0.05 > than the p value, 0.017, then we would reject the null hypothesis. Therefore, at 5% significance level, the data indicate that the average net sales improved.

d-Denis

e-Earl

d+e=42

e+8=d

e+8+e=42

2e+8=42

2e=34

e=17

d=17+8=25

Denis is 25 and Earl is 17

Answer

Earl is 17 years old.

Denis is 25 years old.

See? Easy!

Step-by-step explanation:

Answer:

I think it is 288.6 ft. Lol hope this helps

Step-by-step explanation: