The time married men with children spend on child care averages 6.0 hours per week. You belong to a professional group on family practices that would like to do its own study to determine if the time married men in your area spend on child care per week differs from the reported mean of 6.0 hours per week. A sample of 40 married couples will be used with the data collected showing the hours per week the husband spends on child care. The sample data are contained in the table below. 1.4 4.9 8.5 5.2 10.2 2.6 7.2 2.6 11.1 10.6 2.3 7.8 1.8 8.7 2.1 4.5 5.3 3.5 8.8 6.7 2.9 10.8 8.4 4.9 5.7 9.8 0.9 11.9 3.5 8.7 6.5 6.5 2.0 9.7 a. What are the hypotheses if your group would like to determine if the population mean number of hours married men are spending in child care differs from the mean reported in your area? H : HA: # Ag b. What is the sample mean (to 1 decimal)? Calculate the value of the test statistic (to 2 decimals). What is the p-value? greater than .207 c. Select your own level of significance. What is your conclusion? Do not reject the null. We don't have enough evidence to disprove the reported time.

The equivalent expression for the given expression is 3(4x + 3) will be 12x+3. Option A is correct.

The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b)  in the form of (ac+bc).

It is given that the expression is,3(4x + 3)

We have to find the equivalent expression for the given expression,

Expressions that function identically but have a different appearance are called equivalent expressions. When we enter the same value for the variable, two algebraic expressions that are equivalent will have the same result.

=3(4x + 3)

=12x+3

Thus, the equivalent expression for the given expression is 3(4x + 3) will be 12x+3. Option A is correct.

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The perimeter of the quadrilateral is √2+√8+√5+√13

We can use the distance formula to find the length of the segments that make up the quadrilateral.

We must find the length of the segments between the points (0,2),(1,3)(1,3),(3,1)(3,1),(2,−1)(2,−1),(0,2)

Recall the distance formula d=√(x2−x1)2+(y2−y1)2Applying this formula to the four pairs of points gives the following.

d=√(1−0)2+(3−2)2=√1+1=√2d=√(3−1)2+(1−3)2=√4+4=√8d=√(2−3)2+(−1−1)2=√1+4=√5d=√(0−2)2+(2+1)2=√4+9=√13

So the perimeter of the quadrilateral is √2+√8+√5+√13

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The minimum grade require to get grade of B is 78.6.

In the given that;

μ = 65 (average grade)

σ = 20 (standard deviation)

X ≈ N(μ, σ^{2})

Let c be the minimum grade to required to get grade of B

Percentage of data below c = 10% + 15% + 50% =75%

If we convert the percentage to probability = 75%/100% = 0.75

Now to get the value of c we solve the equation

P(X < c) = 0.75

⇒P{(X-μ)/σ < (c-μ)/σ)=0.75

Here z = (X-μ)/σ follows normal (0,1)

z is the standard normal variable

⇒P(z<(c-μ)/σ)=0.75

⇒P(z< (c-65)/20)=0.75

From z table we get, (c-65)/20 = 0.68

⇒(c-65)/20 = 0.68

⇒c= 78.6

So, minimum grade require to get grade of B is 78.6.

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The right question is given below:

The size of each angle of triangle, starting with the largest 90°, 45° and 45°.

Polygon which has three sides and three vertices is called as triangle.

Sum of all the angles of the triangle is 180°.

Given that a right angled triangle has two equal sides.

And the largest triangle of right angled triangle is 90°.

Right angled triangle which has two equal sides can be called right angled isosceles triangle.

And if one angle of isosceles triangle have angle is 90°. Then the rest of the two angle will be 45°.

Therefore, The rest of these two angles of the right angled triangle are 45⁰.

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The equation of the line that has a slope of 5 and y-intercept of 9 will be y = 5x + 9.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is 5. Then the equation is given as,

y = 5x + c

The y-intercept of the line is 9. Then the equation of the line is given as,

y = 5x + 9

The equation of the line that has a slope of 5 and y-intercept of 9 will be y = 5x + 9.

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Answer:

10?

__________________

Hope this helps? C:

The value of x = 7 (blue)

The value of x = 6 (yellow)

The value of x = 4 (marron)

The value of x = 20 (black)

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

1,

The two angles are equal.

The sides opposite to the angles are also equal.

x = 7 (blue)

2.

The given triangle is an equilateral triangle.

All angles are equal.

The sides opposite to the angles are also equal.

x = 6 (yellow)

3.

Alternate angles are equal.

The sides opposite to the alternate angles are also equal.

x = 4 (marron)

4.

The given triangle is an isosceles triangle.

Two sides are equal.

One angle is 40.

The sum of the angles is 180.

x + x + 40 = 180

2x + 40 = 180

2x = 140

x = 20 (black)

Thus,

x = 7 (blue)

x = 6 (yellow)

x = 4 (marron)

x = 20 (black)

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Calculate how much you would have in 20 years if you saved $3,000 a year at an annual rate of 8 percent with the company contributing $750 a year. Use Exhibit 1-B. (Round time value factor to 3 decimal places and answer to the nearest whole dollar.)

69/100 you would save since it decreased in value

Step-by-step explanation:

that is a college question ?

oh my ...

to clarify :

perpendicular means intersecting or touching at a right angle (90°).

bisector means it is a line that cuts the other line in half.

1.

because of the bisector this means DF = FC = DC/2.

so, since FC = 17, so is DF (=y) = 17.

2.

for the same reason

2x - 3 = x + 8

x - 3 = 8

x = 11

the angle must be 90°.

so,

5y = 90

y = 18

3.

for the same reason

10 = 4a

a = 10/4 = 2.5

4.

for the given reasons of 1-3, this figure is a kite. that means the left side is a mirror image of the right side. so, all the lengths on one side are equation to the lengths of the other side.

x - 11 = 19

x = 30

5.

for the same reasons

3y + 5 = 26

3y = 21

y = 7

6.

the perimeter of EDP is then

EP + DP + ED = 19 + 19 + (9 + 9) = 56

because ED = EC + CD

and for the above reasons EC = CD = 9

so, ED = 9 + 9 = 18

7.

the perimeter of EDQ is then

EQ + DQ + ED = 26 + 26 + 18 = 70

8.

for the same reasons as above

x = 90°

9.

remember, the sum of all angles in a triangle is always 180°.

180 = 90 + 55 + y

y = 180 - 90 - 55 = 35°

10.

180 = y + M + z = 35 + (55+71) + z = 161 + z

z = 180 - 161 = 19°

The number of days in June is 30

The number of days in July = 31

The number of days in August = 31

The maturity date for a loan taken out on June 6 for 73 days is August 28.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The date on which the loan was taken = June 6.

The number of days for the loan to mature = 73 days.

Now,

The number of days in June is 30

The number of days in July = 31

The number of days in August = 31

Now,

There are (30 - 6) = 24 days remaining in the month of June.

So,

24 + 31(July) = 45 days.

Now,

73 - 45 = 28 days need to be taken from August.

So,

45(July) + 28(August) = 73 days.

This means,

The maturity date is August 28.

Thus,

The maturity date for a loan taken out on June 6 for 73 days is August 28.

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Answer: 8√2

Step-by-step explanation:

The perimeter of the parallelogram is 24 units

From the question, we have the following parameters that can be used in our computation:

The parallelogram is added as an attachment

When the number of units on each side of the parallelogram is counted, we have the following representation

EH = FG = 7 units

EF = GH = 5 units

The perimeter of the parallelogram is the sum of the side lengths

So, we have the following representation

Perimeter = EH + EF + FG + GH

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 7 + 7 + 5 + 5

Evaluate the sum

Perimeter = 24

Hence, the perimeter is 24 units

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Answer:

188 cents or $1.88

Step-by-step explanation:

We first want to find how many cents per one inch, and we do this by dividing 17 from 68 (68/17). This gets us 4 cents per inch. Now we need to multiply 4 by 47 (4 x 47). Now we get 188 cents. The equation for this would be y = 4x

Answer:

126 lineups

Step-by-step explanation:

This is a problem in combinatorics which asks in how many ways can a subset of 5 be formed from a larger set of 9

In general, if you were to see how many ways a subset of [tex]r[/tex] can be formed from a larger subset [tex]n[/tex] denoted by [tex]nC_r[/tex] we use the formula

[tex]nC_r = \dfrac{n!}{ r! (n - r)! }[/tex]

There are calculators that can compute this and I used a scientific calculator to do so.

[tex]9C_5 = 126[/tex]

Option-A is It comes in a variety of forms, making it possible to compare the effects of numerous groups and variables satisfy the statement.

Given that,

The most typical inferential statistical method used to evaluate trials is analysis of variance because

We have to find which of the options are suitable for the given statements.

Option-A is It comes in a variety of forms, making it possible to compare the effects of numerous groups and variables satisfy the statement.

Option-B is It comes in one form, and compared to two-sample tests, it is more accurate for comparing two groups does not satisfy the statement.

Option-C is It is the only statistical method that can test both within- and between-subjects factors does not satisfy the statement.

Option-D is The majority of academics are more focused on differences between one sample and the population as a whole does not satisfy the statement.

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Answer:

q = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• if b² - 4ac > 0 then roots are real and irrational

• if b² - 4ac = 0 then the roots are real and equal

• if b² - 4ac < 0 then the roots are not real

qx² - 6x + 18 = 0 ← is in standard form

with a = q , b = - 5 , c = 18

for one repeated (equal) real root , then

b² - 4ac = 0 ( substitute values )

(- 6)² - (4 × q × 18) = 0

36 - 72q = 0 ( subtract 36 from both sides )

- 72q = - 36 ( divide both sides by - 72 )

q = [tex]\frac{-36}{-72}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

[tex]x[/tex] is greater than 1.8

Step-by-step explanation:

Adding 1.4 to both sides of the equation yields [tex]x=3.2>1.8[/tex].

The required reasoning for the given expression is that x is greater than 1.8. Option B is correct.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.

here,
Given expression,
x  - 1.4 = 1.8

The above expression refers that, when we subtract 1.4 from x it gives 1.8, which implies that x is a number greater than 1.8.
So the reasoning can be complied as x is greater than 1.8.

Thus, the required reasoning for the given expression is that x is greater than 1.8. Option B is correct.

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The probability that a row in the test set belongs to a Stanford student is 0.4167.

Given that,

Thomas has come up with a plan for dividing the training and test set. From the coordinates, for each row:

Students from Stanford have a 50% chance of being assigned to the test set and a 50% chance of being assigned to the train set for their rows.

20% of Berkeley students' rows are assigned to the test set, while 80% are assigned to the train set.

We have to find what is the probability that a row in the test set belongs to a Stanford student.

We know that,

Let us define events are as

B: Student in the coordinate is Berkeley student

S: Student in the coordinate is Stanford student

Tr: Rows is in the  train set

Ts: Rows is in the  test set  

Since there are 77 Berkeley student  and 23  Stanford student  in coordinate

Hence,

P(B) = Probability that Student in the coordinate is Berkeley student

= 77/(77+23) = 77/100 = 0.77

P(S) = Probability that Student in the coordinate is Stanford student  =23/(77+23) = 23/100 = 0.23

Conditional probability,

P(Ts|B) = Probability that Student placed in  the  test set   when the student is Berkeley student   = P(Ts|B) = 0.20

P(Ts|S) = Probability that Student placed in  the  test set   when the student is Stanford student   = P(Ts|S) = 0.5

Required probability,

Given that  a row is in the test se, Probability that it corresponds to a Stanford student  =

Probability of Stanford students = P(S|Ts) =

By Bayes theorem,

P(S|Ts) = P(Ts|S)×P(S)/P(Ts|S)×P(S)+P(Ts|B)×P(B)

P(S|Ts) = 0.22×0.5/0.22×0.5+0.20×0.77

P(S|Ts) = 0.4167

Therefore, The probability that a row in the test set belongs to a Stanford student is 0.4167.

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The total number of feet that the plumber's helper should order for drain pipes is 19 feet.

The plumber's helper has been given the list of places in the house that will need a drain pipe. The total number of feet of pipes that he should buy should therefore be the total number of pipes that each of these places in the house need.

The number of feet of pipes is therefore:

= Kitchen sink + Bath tub + Lavatory + Laundry tub + Second lavatory

= 5  + 4 + 3 + 5 + 2

= 19 feet

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The name starts with letter g as the variable has highest value.

What is variable?

A variable is associate degree alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables square measure specially utilized in the case of algebraical expression or pure mathematics.

Main body:

according to question:

7j = 105

simplifying the value , we get

j = 105/7

j = 15

similarly

g - 16 = 2

simplifying the value , we get

g = 18

value of g is greater than j .

Hence the name starts with letter g.

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Answer:

4x  +  1   -  2/x  +  6/(20x³ - 15x² -15x+16)

Step-by-step explanation:

                4x  +  1   -  2/x  +  6/(20x³ - 15x² -15x+16)

             ________________

5x ²-5x | 20x³ - 15x² -15x+16

1            -(20x³ - 20x²)                      ==> -15x²-(-20x²)= -15x²+20x² = 5x²

                         5x² - 15x

2                       -(5x² - 5x)                 ==> -15x-(-5x)= -15x+5x = -10x

                                 -10x+16

3                                -(10x+10)

                                           6           ==> 16-10 = 6           

1: At step 1, (4x) * (5x²-5x) = (20x³ - 20x²)

2: At step 2, 1 * (5x² - 5x) = 5x² - 5x

3: At step 3, (2/x) * (5x² - 5x) = 10x+10

To view the circle graph (pie chart) of the chungs' budget check the attached file.

What is pie chart?

A pie chart is a graphical representation technique that displays data in a circular-shaped graph.

Pie charts are often used to represent sample data with data points belonging to a combination of different categories.

Chung's budget in percentage:

Charity = 30/2145 x 100%

            = 1.39%

            = 1.4%

Clothes = 185/2145 x 100%  

             = 8.62%

Entertainment = 178/2145 x 100%

                        = 8.29%

Food = 424/2145 x 100%

         = 19.76%

Rent = 1050/2145 x 100%

        = 48.95%

Transportation = 213/2145 x 100%        

                 = 9.93%

Others = 65/2145 x 100%

           = 3.03%

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The number of half gallons that that store bought with the amount of profit they made would be = 41 half gallons.

A refrigerated milk is the milk that is preserved in a refrigerator to prevent spoilage and prolong the shelf life of the milk.

A refrigerator is an electrical electronic device that is used for the preservation and storage of food and food products such as milk.

The amount that half gallon of milk was bought = $2.30 per half gallon.

The amount of half gallons of milk that was ruined= 14

The remaining milk was sold at = $3.90 per half gallon.

The profit made by the store = $105.40

The amount of half gallons that was bought,

= 105.40/3.90

= 27 + 14 ruined half gallon= 41 half gallons.

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Answer:1285.7 meters per second.

Step-by-step explanation: divide 900,000 meters by 700 seconds

Answer:

A plane travels 360,000 meters in 900 seconds

Step-by-step explanation:

The side lengths of the triangle are 11.1, 21.4, and 18.5 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

The given sides of the right triangle are 3m, 2m+14, and 5m.

As per the Pythagorean theorem, it follows:

(2m + 14)² = (3m)² + (5m)²

4m² + 196 + 56m = 9m² + 25m²

30m² -56m - 196 = 0

15m² - 28m - 98 = 0

[tex]m=\frac{-(-28)\pm\sqrt{(-28)^2-4(15)(-98)}}{2(15)}\\\\m=\frac{28\pm\sqrt{6664}}{2(15)}\\\\m =\frac{28\pm81.6}{2(15)}\\\\m=3.7\text{ or } m=-1.8[/tex]

Since the lengths cannot be negative, the value of m is m = 3.7.

Therefore, the side lengths of the triangle are:

3m = 3(3.7)

= 11.1

2m + 14

= 2(3.7) + 14

= 21.4

and,

5m

=5(3.7)

= 18.5

Hence, the side lengths of the triangle are 11.1, 21.4, and 18.5 units.

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Using the Green's Theorem, the one along which the work done by the force is 11π/16.

In the given question we have to find the one along which the work done by the force is the greatest.

The given closed curves in the plane is

[tex]F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}[/tex]

Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.

Let S be the interior of C.

Let P = [tex]\frac{x^{2}y}{4} + \frac{y^3}{3}[/tex] and Q = x

So the partial differentiation is

[tex]\frac{\partial P}{\partial y}=\frac{x^2}{4}+y^2[/tex] and  [tex]\frac{\partial Q}{\partial x}[/tex] = 1

By the Green's Theorem, work done by F is given as

W= [tex]\oint \vec{F}d\vec{r}[/tex]

W= [tex]\iint_{S}\left ( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right )dxdy[/tex]

W= [tex]\iint_{S}\left ( 1-\frac{x^2}{y}-y^2 \right )dxdy[/tex]

Let C = x^2+y^2 = 1 and

x = rcosθ, y = rsinθ

0≤r≤1; 0≤θ≤2π

There;

W = [tex]\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )\left|\frac{\partial(x,y)}{\partial{r,\theta}}\right|d\theta dr[/tex]

and [tex]\frac{\partial (x,y)}{\partial(r, \theta)}=\left|\begin{matrix}\cos\theta &-r\sin\theta \\ \sin\theta & r\cos\theta\end{matrix} \right |[/tex] = r

Thus;

W = [tex]\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )rd\theta dr[/tex]

After solving

W = 11π/16

Hence, the one along which the work done by the force is 11π/16.

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The right question is:

Among all simple smooth closed curves in the plane, oriented counterclockwise, find the one along which the work done by the force:

[tex]F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}[/tex]

is the greatest. (Hint: First, use Green’s theorem to obtain an area integral—you will get partial credit if you only manage to complete this step.)

The value(s) of a where the tangent line to the graph of the function f(x) = -11x + is parallel to the line y = -19x - 18 is x=1,-1.

What is Slope of function?

Finding the rate at which the value of y (the dependent variable) changes in relation to x is what this method entails (independent variable). The slope itself identifies the line's slope and direction. Write the equation of the line in slope-intercept form to determine the slope from the equation. Utilize inverse procedures to find y, then write it as y=mx+b. Since the slope is the x variable's coefficient, or the number before x, you can thus readily observe the slope.

[tex]f(x)=-11 x+\frac{8}{x}$$[/tex]

Slope of function [tex]$\rightarrow f^{\prime}(x)=\frac{-21-8}{x^2}$[/tex]

Given line: y=-19 x-18

Slope [tex]$\rightarrow y^{\prime} \rightarrow-19$[/tex]

Since function and line both are parallel, hence slope of both will be equal.

[tex]$$\begin{aligned}-19 & =-11-\frac{8}{x^2} \\-8 & =\frac{-8}{x^2} \\x & =1,-1\end{aligned}$$[/tex]

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