4. (a) Two years ago a woman was 7 times as old as her daughter, but in 3 years time
she would be only 4
times as old as the girl. How old are they now?

Answer:

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]

  = [tex]-\frac{36}{7}[/tex]

y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]

  = [tex]\frac{40}{7}[/tex]

Therefore, coordinates of pint B will be,

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Answer:

the guarantee period should be less than 136010 miles

Step-by-step explanation:

From the given information;

Let consider Y to be the life of a car engine

with a mean μ = 170000

and a standard deviation σ = 16500

The objective is to determine what should be the guarantee period T if the company wants less than 2% of the engines to fail.

i.e

P(Y < T ) < 0.02

For the variable of z ; we have:

[tex]z = \dfrac{x - \mu }{\sigma}[/tex]

[tex]z = \dfrac{x - 170000 }{16500}[/tex]

Now;

[tex]P(Y < T ) = P( Z < \dfrac{T- 170000}{16500})[/tex]

[tex]P( Z < \dfrac{T- 170000}{16500})< 0.02[/tex]

From Z table ;

At P(Z < -2.06) ≅ 0.0197  which is close to 0.02

[tex]\dfrac{T- 170000}{16500}<- 2.06[/tex]

[tex]{T- 170000}<- 2.06({16500})[/tex]

[tex]{T- 170000}< - 33990[/tex]

[tex]{T}< - 33990+ 170000[/tex]

[tex]{T}<136010[/tex]

Thus; the guarantee period should be less than 136010 miles

Answer:

(0, 3), (4, -1)

(1, 2)

Step-by-step explanation:

If the answers that have been provided to you are only in pairs then it'd just be the first answer I wrote. The points (1, 2) also are on the graph of y=x+3 but if the answers aren't individual than I'd just stick with the (0, 3), (4, -1). Does that make sense? I used a graphing calculator online called Desmos, it's very good. I highly recommend it for problems like these.

I hope this helps:) Select as brainliest because I actually put work into this and tried.

Answer:

they divied the turkey into 14 pices

Step-by-step explanation:

Step-by-step explanation:

Tell the whole question please

Answer:

Step-by-step explanation:

even function are symmetrical about the y axis or f(-x)=f(x)

odd function are symmetrical about the origin -f(-x)=f(x)

f(x)=x^6 + 10x^4-11x^2+19

f(-x)=(-x)^6+10(-x)^4+11(-x)^2+19=x^6 + 10x^4-11x^2+19

the function is even

Answer:

5

Step-by-step explanation:

25/5

=5✖️5=25

=5/1

Answer:

25÷5 = 5 and 25/5 = 125

Step-by-step explanation:

hope this helps!

Answer:

9x9= 81

3x3x3x3=81

81 to the first power.

Step-by-step explanation:

I hope this helps in any way:)

Answer:

[tex]\huge\boxed{a_3=9,216}[/tex]

Step-by-step explanation:

[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]

Answer: -4/3

Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.

So the negative reciprocal of 3/4 is -4/3.

Answer:

option (c) 4

Step-by-step explanation:

sides opposite to equal angles are equal

so ML = MN

that is 4x = x+3

4x - x = 3

3x = 3

x= 1

ML= 4x = 4*1 = 4 units

MN = x+3= 1+3= 4 units

so answer is option (c) 4

hope this answer help you

Answer:

3/8x - 9 4/5

Step-by-step explanation:

Well we need to simplify the following expression,

[tex]\frac{3}{4} (\frac{1}{2}x - 12) + \frac{4}{5}[/tex]

So we need to distribute 3/4 to (1/2x - 12)

3/8x - 9 + 4/5

3/8x - 9 4/5

Thus,

the answer is 3/8x - 9 4/5.

Hope this helps :)

Answer:

3 or -3

Step-by-step explanation:

sqrt(9)

What number multiplied by itself will give you 9

3*3 =9

-3 * -3 =9

The square root of 9 is 3 or -3

=========================================

Work Shown:

1.5/3 = 31.5/x

1.5x = 3*31.5  cross multiply

1.5x = 94.5

x = 94.5/1.5  dividing both sides by 1.5

x = 63

-----------

An alternative equation to solve is

1.5/31.5 = 3/x

1.5x = 31.5*3

1.5x = 94.5

The remainder of the steps are the same as in the previous section above.

Answer:

4d/k or [tex]\frac{4d}{k}[/tex]

Step-by-step explanation:

first multiply both sides by four

you will have 4d=fk

then divide by k

4d/k=f

Answer:

d = 115.4 mi

Step-by-step explanation:

Since it gives us the distance in between the locations, we simply label the distances:

From the Garbage to the Hotel is 58.3 miles.

From the Hotel to the Hardware Store is 57.1 miles.

We are trying to find the distance from the Garbage to the Hardware Store, we simply add the distances between:

58.3 mi + 57.1 mi = 115.4 mi

Answer:

[tex]y=\frac{4}{3}x-1.75[/tex]

Step-by-step explanation:

If the slope of a line is 4/3,

and we wanna find the equation of a line that is parallel to it and crosses through (5,5).

So we already have the slope because the slope of 2 parallel lines are the same.

y = 4/3x

Look at the image below↓

So now we just need to find the y-intercept.

After some numbers we got,

[tex]y=\frac{4}{3}x-1.75[/tex]

Look at the other image below↓

Thus,

the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].

Hope this helps :)

Complete Question

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 ​respondents, 12 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 5 percentage points.What values do ​ [tex]\r p , \ \r q[/tex], ​n, E, and p​ represent? If the confidence level is 90​%, what is the value of [tex]\alpha[/tex] ​?

Answer:

a

   [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

   [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

   [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e                        [tex]\r q = 1- \r p[/tex]

b

   [tex]\alpha = 10\%[/tex]

Step-by-step explanation:

Here

    [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

    [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e  

      [tex]\r q = 1- \r p[/tex]

      [tex]\r q = 1- 0.12[/tex]

      [tex]\r q = 0.88[/tex]

     [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as

     [tex]\alpha = ( 100 - C )\%[/tex]

Where  [tex]C[/tex] is the confidence level which is given in this question as  [tex]C = 90 \%[/tex]

So  

    [tex]\alpha = ( 100 - 90 )\%[/tex]

    [tex]\alpha = 10\%[/tex]

Answer:

-4,4,16

Step-by-step explanation:

They are all even integers.

-4^2=16

4^2=16

16^2=256

the square of the third,16 is 256 which is more than the square of the second,4=16

The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

Let the three even consecutive integers are 2n-2, 2n and 2n + 2.

According to the question,

So,

(2n + 2)² = (2n)² - 60

4n² + 4 + 8n = 4n² -60

8n = -64

n = -8

That means, the integers are -18, -16 and -14.

Therefore, the required even integers are -18, -16 and -14.

To learn more about the integers;

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Answer:

Taylor sold 42 pizzas

Step-by-step explanation:

Make a system of equations where t represents the number of pizzas Taylor sold and j represents the number that Jeff sold:

t + j = 126

j = 2t

We can solve this system by substitution, since we can substitute 2t as j.

t + j = 126

t + 2t = 126

3t = 126

t = 42

Taylor sold 42 pizzas.

Answer:

Step-by-step explanation:

Let x represent the number of pizzas that Tailor sold.

Let y represent the number of pizzas that Jeff sold.

Together they have sold a total of 126 pizzas. This means that

x + y = 126- - - - - - - - -1

Taylor has sold half as many

pizzas as Jeff. This means that

x = 1/2 × y = y/2

Substituting x = y/2 into equation 1, it becomes

y/2 + y = 126

Multiplying both sides of the equation by 2, it becomes

y + 2y = 252

3y = 252

y = 252/3

y = 84

x = y/2 = 84/2

x = 42

Taylor sold 42 pizzas

Answer:

A. The mean represents the center.

A. The median represents the center.

B. The mode does not represent the center because it is the smallest data value.

Step-by-step explanation:

Mean

(9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11)/13 = 120/13 = 9.2

The mean 9.2 and it represents the center of data.

Median

By arranging the set of data, the median, the median is the center number

8,8,8,8,8,8,(9),9,9,10,11,12,12

The median is 9 and it represents the center of data.

Mode

The mode is the number that appears most in the set of data.

The number that appears most in the set of data is 8 and does not represent the set of data.

Given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:

A. The mean does represents the center of the data set

Given the following data set:

9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11

Let's find the mean, median, and mode.

Mean of the data set:

Mean = sum of all values / number of values

Mean = [tex]\frac{9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11}{13}[/tex]

Mean = [tex]\frac{120}{13} = 9.2[/tex]

Median of the data set:

Order the data from the least to the greatest then find the middle value.

8, 8, 8, 8, 8, 8, (9,) 9, 9, 10, 11, 12, 12

The middle value is 9.

Mode of the data set:

The mode = the data value that appears most

8 appeared the most, therefore, the mode = 8

If you observe, you will note that the mean and median of the data set are similar. We can as well conclude that the mean represents the center of the data set.

In summary, given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:

A. The mean does represents the center of the data set

Learn more here:

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Answer:

monomial

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

≈3318 miles per day....

Step-by-step explanation:

Answer:

156.7 miles

Step-by-step explanation:

Since [tex]x[/tex] is tangent to the circle, then it is also a right angle with the radius, from here, just do Pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to solve for [tex]x[/tex].

Since 1 leg and the hypotenuse is given to you, you want to solve for the other leg, which is [tex]x[/tex] (either [tex]a[/tex] or [tex]b[/tex]). Lets use [tex]b[/tex] for [tex]x[/tex] and set up the equation.

[tex]b^{2}=c^2-a^2[/tex]

[tex]b^2=(3959+3.1)^2-3959^2[/tex]

[tex]b^2 = 3962.1^2 - 3959^2[/tex]

[tex]b^2 = 15,698,236.41 - 15,673,681[/tex]

[tex]b^2 = 24,555.41[/tex]

[tex]\sqrt{b^2}=\sqrt{24,555.41}[/tex]

[tex]b=156.7016592[/tex]

[tex]b=156.7[/tex] (round to nearest tenth)

The distance to the earth’s horizon from point P is 281.6 miles

The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

here, we have,

to determine the distance to the earth’s horizon from point P:

The tangent line from P meets the radius of the earth at a right angle.

This means that the triangle is a right triangle.

The length of x is then calculated as:

(3959 + 10)^2= 3959^2 + x^2

Rewrite as:

x^2 = (3959 + 10)^2- 3959^2

Evaluate

x^2 = 79280

Take the square root of both sides

x = 281.6

Hence, the distance to the earth’s horizon from point P is 281.6 miles

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Answer:

what

Step-by-step explanation:

Answer:

1. Debit Petty cash for $400; and Credit Cash for $400.

2. Total petty cash payment = $270.57

3(a) Cash reimbursement is $279.58; and Cash over and short is $9.01.

3(b) Debit Petty cash for $100; and Credit Cash for $100.

Step-by-step explanation:

Note: This question is not complete. The full complete question is therefore provided before answering the question. See the attached pdf file for the full question.

The explanations to the answers are now given as follows:

1. Prepare the journal entry to establish the petty cash fund.

Note: See the journal entry in the attached excel file

2. Prepare a petty cash payments report for February with these categories: delivery expense, mileage expense, postage expense, merchandise inventory (for transportation-in), and office supplies expense. Sort the payments into the appropriate categories and total the expenditures in each category.

Note: See the petty cash payments report in the attached excel file.

3. Prepare the journal entries for required 2 to both (a) reimburse and (b) increase the fund amount.

Note: See the journal entries (a) and (b) in the attached excel file

3(a) Reimburse Workings:

w.1: Calculation of Cash reimbursement

Cash reimbursement = Petty cash fund - Petty cash fund balance = $400 - $120.42 = $279.58

w.2: Calculation of the Cash over and short

Cash over and short = Cash reimbursement – Total expenses = $279.58 - $270.57 - $120.42 = $9.01

Answer:

A: (–0.3, 2.1)

Answer:a

Step-by-step explanation:

Answer:

ln(60)

Step-by-step explanation:

We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].

Answer:

x = 1.5

Step-by-step explanation:

5(4x-10)+10x=4(2x-3)+2(x-4)

Distribute(5)

20x-50+10x=4(2x-3)+2(x-4)

Distribute(4)

20x-50+10x=8x-12+2(x-4)

Distribute(2)

20x-50+10x=8x-12+2x-8

Combine like terms

30x-50=10x-20

Subtract(10x)

20x-50=-20

Add(50)

20x=30

Divide(20)

x = 1.5

Hope it helps <3

Answer:

Step-by-step explanation:

5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)

Expand the terms

That's

20x - 50 + 10x = 8x - 12 + 2x - 8

Simplify

30x - 50 = 10x - 20

Group the constants at the right side of the equation

That's

30x - 10x = - 20 + 50

20x = 30

Divide both sides by 20

x = 3/2

Hope this helps you