4. Gilbert needs his work double-checked. Choose the best answer for Gilbert's total estimate. Estimate to the nearest dollar amount. Show each step.​

[tex]\bold{n\equiv 91a+40b\ mod \ 130}[/tex]

Given that a is the remainder when n is divided by 10. Then, [tex]n\equiv a\ mod 10[/tex]

Also b is the remainder when n is divided by 13 i.e., [tex]n\equiv b\ mod 13[/tex]

Then by Division algorithm, there are integers k and m such that n = a + 10k and n = b + 13m

These two equations are equivalent to

13n = 13a +130k and 10n = 10b + 130m

Adding these two equations, 23n = 13a + 10b + 130(k + m)

⇒ [tex]23n\equiv 13a+10b\ mod\ 130[/tex]

gcd (23,130) = 1

So 23 has an inverse modulo 130.

Therefore, [tex]n\equiv 23^{-1} (13a+10b) \ mod\ 130[/tex]

Applying Euclidean algorithm for 130 and 23,

130 = 23 x 5 + 15

23 = 1 x 15 +8

15 = 1 x 8 +7

8 = 1 x 7 + 1

Therefore, 1 = 8 - 7 = 8 - (15 -8 ) = 2 x 8 - 15 = 2( 23 - 15 ) - 15

                    = 2 x 23 -3 x 15 = 2(23) -3(130-5x23) =17(23) -3(130)

So inverse of 23 = 17

So, [tex]n\equiv 17 (13a+10b) \ mod\ 130\equiv 221a +170b \ mod \ 130 \equiv \bold{91a+40b \ mod\ 130}[/tex]

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There are 152 boys who are present in the class with ratio 19:6.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given:

ratio = 19:6

let the common ratio be x

number of boys = 19 x

number of girls = 6x

Also,

number of boys = number of girls + 104

19x = 6x +104

13 x = 104

x= 8

Hence, the number of boys are 19x= 19*8 = 152 boys.

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Answer:

-2x + y = -6

To isolate a single variable when rearranging equations, move all other variables to the other side of the equation.

According to the statement

We have to find that the rearrangement of the variables.

So, For this purpose, we know that the

A variable is a symbol and placeholder for any mathematical object.

From the given information:

To isolate a single variable when rearranging equations.

Then for this:

To isolate a single variable when rearranging equations,

Then move all other variables to the other side of the equation by using the opposite function on them and remembering to perform that operation on both sides of the equation. Make sure the rearrangement has the target variable in the numerator, not the denominator.

So, To isolate a single variable when rearranging equations, move all other variables to the other side of the equation.

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At time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.

To find the position:

The derivative of x with respect to t is zero when the velocity is zero. That is to say,

Use the quadratic formula to solve.

When t =0.5858 s, the position is:

When t=3.4142 s, the position is:

Reject the negative answer.

So, when t = 0.586 s, the velocity is zero and the distance is 2.83 m.

The second derivative of x with respect to t is zero when the acceleration is zero.

That is to say,

The distance traveled is:

So, when the acceleration is zero, t = 2 s, and the distance traveled is zero.

Therefore, at time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.

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The correct question is given below:

A girl operates a radio-controlled model car in a vacant parking lot. the girl’s position is at the origin of the XY coordinate axes, and the surface of the parking lot lies in the XY plane. she drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t + 2 where x and t are expressed in meters and seconds, respectively. determine when the velocity is 0 m/s, and the position and the total distance traveled when the acceleration is zero.

After solving the expressions we get the value for each of it as:

a. 1/108

b. 7/18

Given:

a. 12x⁰(x⁻⁴)

Apply the multiplication property of exponents.

when variables multiply, the powers are added.

12x⁰⁻⁴

12x⁻⁴

substitute the value of x = 6 in the above term.

12(6)⁻⁴

12 × 1/6⁴

12 × 1/1296

1/108

b. 14(x⁻²)

The algebraic technique for resolving simultaneous linear equations is called the substitution method. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.

directly substitute the value of the x in the expression.

14(6)⁻²

14 × 1/6²

14 × 1/36

7/18

hence after evaluating expressions we get the values as 1/108 and 7/18.

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Answer:

x> -2

Step-by-step explanation:

The combined cost of one pound of pork and one pound of beef is $ 15.5.

The total cost is equal to the sum of the products of unit price and quantity of an article. In this problem we find the sum of the quantities of two products (pork roast, beef roast), whose expression can be described below:

67.50 = (3.25) · (x - 0.50) + (5.5) · x

Where x is the unit cost of the beef roast.

Now we proceed to solve the equation for x:

67.50 = 3.25 · x - 1.625 + 5.5 · x

69.125 = 8.75 · x

x = 7.9

A pound of beef roast costs $ 7.9 and a pound of pork roast costs $ 7.4. Then, the combined cost of one pound of prok and one pound of beef is:

C = 1 · 7.9 + 1 · 7.4

C = 15.5

The combined cost of one pound of pork and one pound of beef is $ 15.5.

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Answer: Delila is correct about this determination.

Step-by-step explanation: The rule for multiplying two negatives is that a negative and a negative always equal a positive. Therefore, multiplying two negatives will give a positive. However, we still have to multiply that positive by another negative to get our answer. Another multiplication rule states a negative and a positive always equals a negative. Let's set up an example with the numbers -7, -8, and -4:

Using the first multiplication rule mentioned above, let's multiply:

-8 x -7 = 56

Using the second multiplication rule mentioned above, we can finish the equation and get our answer:

56 x (-4) = -224

-7 x -8 x -4 = -224.

Final answer: Delila is correct. Multiplying three negatives will result in a negative solution.

The pedestrian route that runs diagonally across the park is 5√10 miles.

It states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

We have,

A rectangle:

Length = 15 miles

Wide = 5 miles

Diagonal length can be considered as the hypotenuse.

Applying the Pythagorean theorem.

Diagonal side² = length² + wide²

Diagonal side² = 15² + 5²

Diagonal side² = 225 + 25 = 250

Diagonal side = √250 = 5√10 miles.

Thus the pedestrian route that runs diagonally across the park is 5√10 miles.

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1. The meters of fencing that he installed on each day will be 6.54 meters.

2. The amount of money that Jenny will make will be $127.05.

1. Number to be installed = 42.6m

It should be noted that the person already installed on Monday and Tuesday. Therefore, the amount to install from Wednesday to Friday will be illustrated as:

= (42.6) - (13.45 + 9.5) / 3

= 42.6 - 22.95 / 3

= 6.54 meters per day.

2. The amount of money that Jenny will make will be:

= (9.15 × 9) + (7.45 × 6)

= 82.35 + 44.7

= $127.05

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Answer:

Step-by-step explanation: its 32

Answer:

Step-by-step explanation:

A + B + C = 180

A = 47

B = 62

C = ???

We don't know what "C" is??

So..

A + B + C = 180

C = 180 - A - B

C = 180 - 47 - 62

Subtract those numbers and you should get 71

Soo..

C = 71

we can also add up

47 + 62 + 71 = 180

so if you get 180 when you add them up then that's your correct answer!!

YOUR WELCOME FOR THE HELP!!!!!1

[tex]2xy \sqrt[3]{3y {}^{ \: 2} } [/tex]

The angle, its complement, and its supplement are 36, 54 and 144 degrees respectively

The sum of complementary angles s 90 degrees while that of supplementary angles is 180 degrees.

Let the complement of an angle be 90 -x and its supplement be 180 -x

If three times the measure of a supplement of an angle is eight times the measure of a complement of the angle, then;

3(180-x) = 8(90-x)

Expand

540-3x = 730 - 8x

540-720 = -8x + 3x

180 = 5x

x = 180/5

x = 36 degrees

Complement  = 90 - 36 = 54degrees

Supplement = 180 - 36 = 144 degrees

Hence the angle, its complement, and its supplement are 36, 54 and 144 degrees respectively

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Step-by-step explanation:

Therefore, the distance between E ( 3 , 7 ) E(3,7) E(3,7) and F ( 6 , 5 ) F(6,5) F(6,5) is approximately 3.61 \textbf{3.61} 3.61 units.

Solving a quadratic equation, the youngest age for which the average income of the lawyer is of $250,000 is of 26 years.

A quadratic function is given according to the following rule:

y = ax² + bx + c

[tex]\Delta = b^2 - 4ac[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

For this problem, the equation that models the income as function of age is given by:

I(x) = -425x² + 45500x - 650000.

The income is of 250,000 when I(x) = 250000, hence:

250000 = -425x² + 45500x - 650000.

425x² - 45500x + 900000 = 0.

Hence the coefficients are a = 425, b = -45500 and c = 900000, then:

The youngest age for which the average income of the lawyer is of $250,000 is of 26 years. (the oldest is of 81 years).

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Answer: c = 12

Step-by-step explanation: r is 2 since in the circle it shows the length from the center to the arc. now multiply 2(3)(2) and you will end up with 12.

Answer:

Circumference = 12

Step-by-step explanation:

C=2πr

where,

➟ C = 2πr

Insert values

➟ C = (2)(3)(2)

➟ C = (6)(2)

➟ C = 12

Answer:

Step-by-step explanation:

The statement is flipped, and saying different sayings.

Answer:

If n + 4 is odd,  then n is odd.

Step-by-step explanation:

Contrapositive statements negate the original statement and interchanges(flips) it.

So the negated statement would be ' If n is odd, then n + 4 is  odd'.

Then we interchange that statement so  ' If n is odd, then n + 4 is odd' becomes, ' if n + 4 is odd,  then n is odd.'

The simple interest rate will be 19.2% per year.

We need to find the simple interest which is I = P * R * T

where,

I is the interest,

P is the principal,

R is the interest rate and

T is the time period.

Here, I = the amount you payed - the amount that you owed

= $1800 - $1300 = $500

Now, I = 500

T = 2 years

P = 1300

According to the formula,

500 = 1300 * R * 2

⇒ 500 = 2600* R

∴R = 500/2600 = 0.1923

Multiplying it by 100, we get 19.23%.

Rounding off 1 decimal place, we get 19.2%.

Therefore, you will pay simple interest rate of 19.2% per year.

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Answer:

14. 41

15. 4

Step-by-step explanation:

I used Substitution.

2(14)+13 = 41

3(2) - 2 = 4

Answer: EF = 29 units and KM = 22 units

Step-by-step explanation: For the first one, we just add EF and FG, x+14 and 14, and make it equal to EG, 2x+13. We then get x+28 = 2x+13, x = 15. EF = x + 14 and then sub in 15 for x to get 29.

For KM, same deal as the first one. KL and LM, 6 and 2x, equals to KM, 3x-2. 2x+6 = 3x - 2. x = 8. KM = 3x - 2. sub in 8 for x and then we get 22.

Answer: 180 tickets for $40

Step-by-step explanation:

    To answer this question, we need to find a pattern;

15 / 3 = 5

60 / 15 = 4

-> If you divide, we find a pattern of the quotient with 5... 4... so we can assume the next is 3

    Using this pattern;

60 * 3 = 180 tickets for $40

When the numbers 1-7 is put in the seven circles so that the numbers in each group of three circles connected with a straight line add up to 12 then the number 4 is kept at the center

Let say A , B , C , D , E  , F  & G are 7 numbers  from 1 to 7

& D is in center

So, A & G , B & F , C & E are opposite

A + D + G  = B + D + F  = C + D  + E

=> A + G = B + F = C + E

Adding all numbers

A + B + C + D + E + F + G  + 2D

( A + B + C + D + E + F + G = 28  ( 1 to 7 sum)

= 28 + 2D

28 + 2D  is Divisible by  3 numbers

Hence

D = 1   ,  4   ,   7  

Case 1  

D = 1

28 + 2D = 30    Sum of Each   = 10   ,  D = 1

=> A + G = B + F = C + E  = 9

2 + 7 = 3 + 6  = 4 + 5

Sum is not equal to 12. So this case is invalid

Case 2  

D = 4

28 + 2D = 36    Sum of Each   = 12   ,  D = 4

=> A + G = B + F = C + E  = 98

only possible solution

1+ 7 = 2 + 6  = 3 + 5

Case 3

D = 7

28 + 2D = 42    Sum of Each   = 14   ,  D = 7

=> A + G = B + F = C + E  = 97

1 + 6 = 2 + 5  = 3 + 4

Sum is not equal to 12, so case is invalid

Hence the solution will have 4 in the center.

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10 mph more unusual.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a larger range, a low standard deviation suggests that the values tend to be near to the mean (also known as the anticipated value) of the collection.

The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical literature and equations to indicate standard deviation. Standard deviation may be written as SD.

EXPLANATION : The speed recordings follow an approximately normal distribution the mean of

100 readings was 2384 mph. with a standard deviation of 3.56mph

The speed limit read 20 mph

We have to find the number of standard deviations from the mean that the car going

under the speed hmit would be

Let the car going under the speed 20mph bey standard deviations away from mean

That is.

20 — 23.84 +y(3.56)

20—2384 —1.078651685

So the car going under the speed limit would be less than or equal to 107865 standard

A car traveling 34 mph

The number of standard deviations from the mean that the car is going at 34mph is given by

That is the car going at 34mph is 2.8539 standard deviations above the mean

A car traveling at 10mph

The number of standard deviations from the mean that the car going at 10mph is given by.

y= 2.8539

That is. the car going at 10mph is 3.8876 standard deviations

We know from the empirical nile that 99.7% of the observations he with in ±3 standard

deviations from the mean for a normally distributed data

But the speed of 10mph is not within these limits, where as 34 mph is within these limits

So the car is  travelling t 10mph is more unusual

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The combination of hours that Keitaro can walk and run in a month to reach his goal will be A. 2 hours walking; 12 hours running

From the information, Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles.

The equation is

3w + 6r ≥ 36

3w + 6r ≤ 90

The combination of hours that Keitaro can walk and run in a month to reach his goal will be 2 hours walking, and 12 hours running.

This will be:

3w + 6r ≤ 90

3(2) + 6(12)

6 + 72 = 78

Therefore, 78 is less than 90.

The correct option is A.

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By taking a quotient between the total area and the number of children, we conclude that each one will get 9 ⁴/₅ acres.

Here we know that a farmer has a total of 49 acres, and he wants to divide it evenly among his 5 children.

So we just need to take the quotient between 49 and 5, this is:

49/5

First, we can rewrite:

49 = 45 + 4

Replacing that in the quotient we get:

49/5 = (45 + 4)/5 = 45/5 + 4/5

The first term is equal to 9, then we can rewrite:

49/5 = (45 + 4)/5 = 45/5 + 4/5 = 9 + 4/5

From this quotient, we conclude that each one of the 5 children gets an area of 9 + 4/5 acres. Written as a mixed number this would be:

A = 9 ⁴/₅ acres.

So the correct option is the first one.

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Answer:

7. I attached my answer ... have a nice day

The circle is shaded and on number 5 with the arrow is pointing in the left direction. This shows that the required solution is x ≤5

Inequality are expressions that are not separated by an equal sign. Number lines on the other hand is a picture of a graduated straight line that serves as visual representation of the real numbers.

Every point of a number line is assumed to correspond to a real number, and every real number to a point.

From the given number line, you can see that  the circle is shaded and on number 5 with the arrow is pointing in the left direction. This shows that the required solution is x ≤5

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Answer:

≈649 kg/m[tex]^{3}[/tex]

Step-by-step explanation:

Density is equal to mass/volume

25 / 0.385 ≈ 649 kg/m[tex]^{3}[/tex]