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.
Answers
Answer: D $30
Step-by-step explanation:
$12.79 rounds to $13
$2.33 round to $2
$14.65 rounds to $15
Add the estimates: 13+2+15= $30
Related Questions
when $n$ is divided by 10, the remainder is $a$. when $n$ is divided by 13, the remainder is $b$. what is $n$ modulo 130, in terms of $a$ and $b$? (your answer should be in the form $ra sb$, where $r$ and $s$ are replaced by nonnegative integers less than 130.)
Answers
[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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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
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
To isolate a single variable when rearranging equations, move all other variables to the.
Answers
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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A rectangular park is 15 miles long and 5 miles wide. How long is a pedestrian route that runs diagonally across the park?
Answers
The pedestrian route that runs diagonally across the park is 5√10 miles.
What is the Pythagorean theorem?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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Find the distance between the points E(3, 7) and F(6, 5).
Answers
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.
Delila is multiplying three negative numbers and determines that the solution will be negative . Is she correct or incorrect? Justify your thinking.
Answers
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.
note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. 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 x-y plane. she drives the car in a straight line so that the x coordinate is defined by the relation x(t)
Answers
At time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.
What are coordinates?Coordinates are two numbers (Cartesian coordinates) or a letter and a number that point to a specific point on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical).To find the position:
The derivative of x with respect to t is zero when the velocity is zero. That is to say,
x' = 1.5t² - 6t + 3 = 0 or t² - 4t + 2 = 0Use the quadratic formula to solve.
t = (1/2) [ 4 +/- √(16 - 8)] = 3.4142 or 0.5858 sWhen t =0.5858 s, the position is:
x = 0.5(0.5858³) - 3(0.5858²) + 3(0.5858) + 2 = 2.828 mWhen t=3.4142 s, the position is:
x = 0.5(3.4142³) - 3(3.4142²) + 3(3.4142) + 2 = -2.828 mReject 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,
3t - 6 = 0t = 2The distance traveled is:
x = 0.5(2³) - 3(2²) + 3(2) + 2 = 0So, 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.
Christy buys 3 1/4 pounds of pork roast and 5 1/2 pounds of beef roast. She pays a total of $67.50. The pork costs $0.50 per pound less than the beef. What is the combined cost of one pound of pork and one pound of beef?
Answers
The combined cost of one pound of pork and one pound of beef is $ 15.5.
How to estimate the combine cost of two articles bought in a butchery
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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Find the measures of the angle, its complement, and its suplement if three times the measure of a suplement of an angle is eight times the measure of a complement of the angle.
Answers
The angle, its complement, and its supplement are 36, 54 and 144 degrees respectively
Supplementary and complementary anglesThe 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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Which answer shows the equation
written in standard form? y+4=2(x-1)
y=2x-6
-2x+y=-5
-2x+y-6
y=2x-5
Answers
Answer:
-2x + y = -6
Important Please Help!!!!
Answers
Answer:
C.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.'
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 system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
Answers
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
How to illustrate the information?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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1. Put the numbers 1-7 in the seven
circles so that the numbers in each
group of three circles connected
with a straight line add up to 12.
Use each number only once?
Answers
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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The average income,I, in dollars, of a lawyer with an age of x years is modeled with the following function:
Answers
Solving a quadratic equation, the youngest age for which the average income of the lawyer is of $250,000 is of 26 years.
What is a quadratic function?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:
[tex]\Delta = (-45500)^2 - 4(425)(900000) = 540250000[/tex][tex]x_1 = \frac{45500 + \sqrt{540250000}}{2(425)} = 80.87[/tex][tex]x_2 = \frac{45500 - \sqrt{540250000}}{2(425)} = 26.18[/tex]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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Simplify each expression for x=6 a. 12x^0(x^-4) b. 14(x-2)
Answers
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 the 2 questions in photo [ Brainliest + easy points ]
Answers
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.
what value of c is in the solution set of
2(3x-1)>4x-6
Answers
Answer:
x> -2
Step-by-step explanation:
What is the density of a piece of wood with a mass of 25 kg and a volume of 0.0385 m 3
Answers
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]
Which one? I need help
Answers
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 expressionInequality 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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please simplify! i do not understand, work shown please!
Answers
[tex]2xy \sqrt[3]{3y {}^{ \: 2} } [/tex]
17 Select the correct answer.
What are the solutions of this quadratic equation?
4x² + 3 = 4x + 2
OA. x = 1/ 2
OB. x = -2 ± √3
OC. x = 2
OD. x = 1+√3
Answers
help me with 1 and 2 pls
Answers
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.
How to illustrate the information?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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There are boys and girls in a class in the ratio 19:6 There are 104 more boys than girls. How many boys are there?
Answers
There are 152 boys who are present in the class with ratio 19:6.
What is ratio?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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what Is the value of 343 ⅓ ?
Answers
Answer:
7. I attached my answer ... have a nice day
You borrow $1,300 from a friend and promise to pay back $1,800 in 2 years. What simple interest rate in percent will you pay?
Answers
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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Exact and Approximate Pi
Answers
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,
π = 3r = 2➟ C = 2πr
Insert values
➟ C = (2)(3)(2)
➟ C = (6)(2)
➟ C = 12
The picture has the question.
Answers
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
john beale of stanford, ca, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. the mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (he actually recorded every car for a two-month period. these are 100 representative readings.) to see how many cars are speeding, john subtracts 20 mph from all speeds. a) what is the mean speed now? what is the new standard deviation? b) his friend in berlin wants to study the speeds, so john converts all the original miles-per-hour readings to kilometers per hour by multiplying all speeds by 1.609 (km per mile). what is the mean now? what is the new standard deviation?
Answers
10 mph more unusual.
What is Standard deviation?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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pls help can you help ne choose all of the aswer that are right this is my last attempt
Answers
By taking a quotient between the total area and the number of children, we conclude that each one will get 9 ⁴/₅ acres.
How much should each of the children get?
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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simplify -(6x + 22) - 8(3 - x)
Answers
-6x + x - 22 - 24
-5x - 46