Answer: (10 * 6) + (9 * 6) = 114
Step-by-step explanation:
Using the distributive property, we can write:
19 × 6 = (10 + 9) × 6
= (10 × 6) + (9 × 6) // Distributive property of multiplication over addition
= 60 + 54
= 114
Therefore, 19 × 6 = 114 when using the distributive law.
A movie theater charges 11$ for adults and 9$ for seniors. ( children pay the adult price) on a particular day when 294 people paid an admission, the total receipts were 3114. How many paid were adults? How many paid were seniors?
The number of adult that paid is 234 and the number of seniors that pad is 60.
How to find the number of seniors and adult?A movie theatre charges 11$ for adults and 9$ for seniors. On a particular day when 294 people paid an admission, the total receipts were 3114.
Therefore, let's find how many paid for adult and for seniors.
Let
x = number that paid for adult
y = number that paid for senior
Hence, the situation forms the following equation.
x + y = 294
11x + 9y = 3114
multiply equation(i) by 11
11x + 11y = 3234
11x + 9y = 3114
subtract the equation
2y = 120
y = 120 / 2
y = 60
Let's find x
x = 294 - 60
x = 234
Therefore,
number of adults that paid= 234
number of seniors that paid = 60
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Graph the feasible region and find the values of x and y that give the maximum possible value of g=8x+12y subject to the following constraints:
The solution is:
(a) A (20, 60), B = (0, 0) and C = (80, 0).
(b) The values of x and y that maximize the objective function are
(20, 60).
(c) From graph we can see that (20, 60) is the maximum value of the objective function on the feasible region.
We have,
The set of all possible points of an optimization problem that satisfy the problem's constraints—which may include inequalities, equalities, and integer constraints—is referred to in mathematics as a feasible region, feasible set, search space, or solution space.
Given,
x ≥0, y ≥ 0
x + y ≤ 80
y ≤ 3x
Objective function: z = 250x + 300y
(a) For the given constraints the feasible region is attached below.
The feasible region is ABC.
where, A (20, 60), B = (0, 0) and C = (80, 0).
(b) Now to find the values of x and y which maximize the objective function.
z = 250x + 300y
At A = (20, 60)
z = 250(20) + 300(60) = 5000 + 18000 = 23000
At B = (0, 0)
z = 250(0) + 300(0) = 0
At C(80, 0)
z = 250(80) + 300(0) = 2000 + 0 = 2000
Therefore, the values of x and y that maximize the objective function are (20, 60).
(c) From graph we can see that (20, 60) is the maximum value of the objective function on the feasible region.
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A fair spinner has eight sides. They are labelled 1, 1, 3, 3, 4, 5, 5, 5. The diagram below shows a probability scale. 0 Which arrow shows the probability of a) scoring a 4? 5 5 5 1 4 3 1 3
Find the value of x
The value of x for the intersecting chords is derived to be 14 which makes option C correct.
What is the properties of intersecting chordsThe property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
x × 32 = 16 × 28
32x = 448
32x/32 = 144/32 {divide through by 32}
x = 14
Therefore, the value of x for the intersecting chords is derived to be 14
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A direct variation includes the points (2,18) and (n,9). Find n?
The value of the n is 1
In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.
To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.
(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:
18 = k(2)
k = 18/2
k = 9
Now that we have found the value of k, we can use it to find n when y = 9:
9 = 9n
n = 1
Therefore, the value of n is 1.
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Which expression represents twice the sum of a number and six
Answer:
2(x + 6)
Step-by-step explanation:
If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:
2(x + 6)
Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)
Try These questions out and I’ll give you brainliest
The expressions are simplified to;
1. 72n² + 63n
2. 18t - 18t²
3. -18b² - 18b
4. -56r - 21r²
5. -6m + 9m²
What are algebraic expressions?Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.
These algebraic expressions are also made up of mathematical or arithmetic operations.
These operations are;
BracketParenthesesAdditionMultiplicationDivisionSubtractionFrom the information given, we have;
1. -9n (-8n -7)
expand the bracket
72n² + 63n
2. -2t(-9 + 9t)
expand the bracket
18t - 18t²
3. -3b(6b + 6)
expand the bracket
-18b² - 18b
4. -7r(8 + 3r)
expand the bracket
-56r - 21r²
5. 3m(-2 + 3m)
expand the bracket
-6m + 9m²
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Evaluate the function below it’s a given output value of 8
f(x)=40/5x-1
Graph the solution set
The graph of the inequality is on the image at the end.
How to graph the solution set of the inequality?To graph this, we need to do a solid graph of the linear equation:
y = -(7/2)x + 4
And because the symbol ≥ (and that is why we will use a solid line instead of a dashed line) is used, we need to shade all the region above that line graph.
Then the graph of the inequality will be something like the one of the graph at the end.
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A family of mice is collecting pieces of food that fall on the floor in a restaurant. If the mice collect 24 pieces of food every day for 4 days, we want to estimate the number of pieces of food they have collected. Which of the following is the closest estimate to 24?
The estimate the number of pieces of food collected by mice is 96 and closest estimate to 24 is given by option b. 20.
Number of pieces of food collected by mice every day = 24 pieces
Total number of days mice collects the food = 4 days
To estimate the total number of pieces of food collected,
Now, multiply the number of pieces collected each day by the number of days,
Total number of pieces
= 24 pieces/day × 4 days
= 96 pieces
To estimate the answer closest to 24, we can round 24 to the nearest tens.
The nearest tens to 24 is 20.
Therefore, the estimate of collection of food pieces in 4 days by mice is equal to 96 and the closest estimate to 24 is option b. 20.
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The above question is incomplete , the complete question is:
A family of mice is collecting pieces of food that fall on the floor in a restaurant. If the mice collect 24 pieces of food every day for 4 days, we want to estimate the number of pieces of food they have collected. Which of the following is the closest estimate to 24?
a. 10
b. 20
c. 30
d. 40
Determine which translations would map Figure
W onto Figure X
The sequence of steps that translates figure W to figure X are -
It is first shifted by the rule (x, y) → (x, y - 3)The image is then reflected across the y - axis.The image is then reflected across the x - axis.Refer to the image attached. It shows figure W and figure X. We can write the sequence of steps for the given translation as -
It is first shifted by the rule (x, y) → (x, y - 3)The image is then reflected across the y - axis.The image is then reflected across the x - axis.To solve more questions on translations, visit the link-
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Ted works for 160 hours in a given month, and his wage rate is $10 per hour. What amount will show as Ted's contribution to Social Security?
OA. $1,500.80
OB. $9.92
O C. $99.20.
OD. $150.08
Assuming the Social Security contribution rate is 6.2% of the wage, Ted's contribution to Social Security can be calculated as follows:
Ted's total wage for the month = 160 hours * $10/hour = $1600
Social Security contribution = 6.2% * $1600 = $99.20
Therefore, the answer is option C. $99.20.
What are the polar coordinates of the point Q shown below?
Answer:(−1,−4π/3)
Step-by-step explanation:Note that the point is on the circle whose radius is labeled 1, so r=1 or r=−1. Of the choices available, only an angle of −4π3, drawn from the negative x axis plots at the point Q. So θ=−4π3, and r must be negative, as the angle is measured from the negative x axis. Thus, the polar coordinates are (−1,−4π3).
Jenny has $1200 in her savings account. If the bank pays 3% interest per year on savings, how much interest does she earn in one year?
Jenny earns $36 in interest in one year in her savings account.
To calculate the interest that Jenny earns in one year on her savings account, we can use the formula for simple interest:
I = P x r x t
where I is the interest earned, P is the principal amount (in this case, $1200), r is the interest rate (in decimal form), and t is the time period (in years).
In this case, the interest rate is 3% per year, which can be written as 0.03 in decimal form. The time period is one year. So we have:
I = 1200 x 0.03 x 1
I = $36
Therefore, Jenny earns $36 in interest in one year in her savings account.
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Marcus jogged 1 2/5 miles on Saturday and 9/10 miles on Sunday. Rounding the
fractions to the nearest 1/2, approximately how many miles did he jog over the
weekend? Express your answer as an improper fraction.
Marcus jogged approximately 2 1/2 miles over the weekend.
How to find the how many miles did he jog over the weekendWe need to discover a common denominator to add the miles run on Saturday and Sunday. Because 10 is the least common multiple of 5 and 2,
we may convert the fractions to have a denominator of 10:
1 2/5 = 1 + 4/5 = 5/5 + 4/5 = 9/5
9/10 = 0.9 = 9/10
Now we can add the two distances:
9/5 + 9/10 = 18/10 + 9/10 = 27/10
Rounding 27/10 to the nearest 1/2 gives:
27/10 ≈ 2 1/2
Therefore, Marcus jogged approximately 2 1/2 miles over the weekend.
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The lines shown below are perpendicular. If the green line has a slope of
-1, what is the slope of the red line?
-5
5
X
O A1/
A.
114
OB. 4
O C. -1
OD. -4
Answer:
Step-by-step explanation: its c
i really need help!!!!!
there are like 5 questions.
Answer:
3
Step-by-step explanation:
The answer is three because u need to simply the fractions
PLEASE HELP
Ronald is painting wooden cylindrical columns before putting them in his yard. They are each 7 feet tall and have a diameter of 2 feet. There are 8 columns in all. How much paint will Ronald need to paint all the surfaces of the 8 Columns? Leave your answer in terms of π with proper units
Ronald will need 128π square feet to paint all the surfaces of the 8 Columns.
How calculate how much paint Ronald will need to paint all the surfaces of the 8 Columns?
The formula for the total surface area of a cylinder is given by:
A = 2πr(r + h)
Where r is the radius and h is the height
In this case, each wooden cylindrical columns is 7 feet tall and have a diameter of 2 feet. Thus:
r = 2/2 = 1 feet and h = 7 feet
Thus, the total surface area of each wooden cylindrical columns will be:
A = 2π * 1 * (1 + 7)
A = 2π * 1 * 8
A = 16π square feet
Then the total surface areas of all the 8 Columns will be:
A = 8 * 16π
A = 128π square feet
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A group of consumers were asked whether they prefermed Brand A or Brand B
Being male and preferring Brand A are independent, as:
P(male|Brand A) = P(male).
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
From the table, we are already given the relative frequencies, hence the probability of being male is given as follows:
0.5 + 0.15 = 0.65.
The conditional probability of being male, given that the person prefers brand A, is given as follows:
P(male|Brand A) = P(male and Brand A)/P(Brand A) = 0.5/0.8 = 0.625.
As the probabilities are equal, the events are independent.
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What is the sum of the rational expressions below?
2x-1
7x+x=2
X-2
OA. 9x²-5x+2
7x²-2
OB. 9x²-5x+2
7x²-14x
O C.
O D.
2x²-5x+2
7x²-14x
3x-1
8x-2
Answer:
C
Step-by-step explanation:
To find the sum of the rational expressions, we need to add the two expressions and simplify if possible:
(2x-1)/(7x+x+2) + (x-2)/(8x-2)
Simplifying the denominators, we get:
(2x-1)/(8x+2) + (x-2)/(8x-2)
Now, we need to find the LCD, which is (8x+2)(8x-2) = 64x²-4:
[(2x-1)(8x-2) + (x-2)(8x+2)] / (64x²-4)
Simplifying the numerator, we get:
[16x²-4x-16x+4+8x²-2x+16x-4] / (64x²-4)
Combining like terms, we get:
(24x²-2) / (64x²-4)
Factoring out a 2 from the numerator and denominator, we get:
2(12x²-1) / 2(32x²-2)
Simplifying further, we get:
(12x²-1) / (16x²-1)
Therefore, the sum of the rational expressions is:
12x²-1
-----------
16x²-1
So, the answer is option C.
Given:
p: Two linear functions have different coefficients of x.
q: The graphs of two functions intersect at exactly one point.
Which statement is logically equivalent to q-p?
If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one
point.
If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect
at exactly one point.
D
If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same
coefficients of x.
If the graphs of two functions intersect at exactly one point, then the two linear functions have the same
coefficients of x.
PLSSS HELP ME SOLVE THIS DUE TOMORROW!!!
Each pair of polygons is similar. Find the value of x.
Answer:
7
Step-by-step explanation:
All of the numbers are going up by 4 so what times 4 gives 28
thats 7
Question 17 of 21
A sweet potato pie with a diameter of 10 inches is cut into 8 equal slices. To
the nearest square inch, what is the area of each slice?
A. 39 in²
B. 10 in2
C. 5 in2
D. 20 in²
The coordinate grid shows points A through K. What point is a solution to the system of inequalities? (1 point) y < −2x + 10 y < 1 over 2x − 2
Answer: (B)
Step-by-step explanation:
To determine which point is a solution to the system of inequalities, we must test each point to see if it satisfies both inequalities. Starting from point A, we plug in its coordinates (2, 9) into both inequalities. However, it does not satisfy y < 1 over 2x − 2. We then move on to point B, which has coordinates (3, 0). Plugging this into both inequalities, we find that it satisfies both of them. Therefore, the point that is a solution to the system of inequalities is point B.
The work unit which you supervise is responsible for processing fifteen reports per
month.
If your unit has four clerks and the best worker completes 40% of the reports himself,
how many reports would each of the other clerks have to complete if they all do an
equal number?
Each of the other three clerks have to complete 3 reports each.
The top employee finishes 40% of the reports, or: 0.40 x 15 = 6 reports.
Therefore, the other three clerks must finish the remaining 60% of the reports.
Total reports to be completed by the other clerks = 0.60 x 15 = 9 reports
We may distribute the remaining reports evenly among the other clerks since they all have an equal number of reports to complete:
Number of reports each of the other clerks have to complete = 9 reports ÷ 3 clerks = 3 reports
Therefore, each of the other three clerks have to complete 3 reports each.
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Talia tutors and wants to save money. Talia currently has $60 and plans to save an additional $35 per month. Which graph represents the number of months it will take Talia to save at least $200? 4 number lines labeled A, B, C, and D. Line A: At 3, there is a closed circle. To the right of 3, the number line is shaded with an arrow pointing to the right. Line B: At 4, there is a closed circle. To the right of 4, the number line is shaded with an arrow pointing to the right. Line C: At 5, there is a closed circle. To the left of 5, the number line is shaded with an arrow pointing to the left. Line D: At 7, there is a closed circle. To the left of 7, the number line is shaded with an arrow pointing to the left.
The graph which represents the number of months it will take Talia to save at least $200 is Line B.
Given that,
Talia tutors and wants to save money.
Talia currently has $60 and plans to save an additional $35 per month.
Current amount = $60
Additional amount each month = $35
Let n be the number of months taken to at least save $200.
60 + 35n ≥ 200
35n ≥ 140
n ≥ 4
So the graph will be a number line which has a closed circle on 4 and pointing to the right, because number of months should be either equal to or greater than 4.
Hence the correct option is B.
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help quick thanks! math
The values that make the inequality true are given as follows:
-4, -3, -2, -1, 0.
The equivalent inequality is given as follows:
b ≥ -4.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.The inequality for this problem is given as follows:
b/2 ≥ -2.
b ≥ -4.
Which is composed by numbers that are greater than or equal to -4.
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Solve for x.
12x² -2=14
Answer:
�
=
1.154701
Step-by-step explanation:
12x sqaured - 2 = 14
so first add 2 to make it 16 in the other side.
12x sqaured =16 then divide the sqaured and get 4 on the other side
so 12x = 4 then the answer is 4/12 or 1/3
Answer:
Step-by-step explanation:
12x²-2=14 add 2 to both sides
12x²=16 divide both sides by 12
x² = 16/12 reduce by dividing top and bottom by 4
x²=4/3 take square root of both sides to cancel square
when you take sq root you also get ±
x=±[tex]\sqrt{\frac{4}{3} }[/tex] you can take square root of 4
= ± [tex]\frac{2}{\sqrt{3} }[/tex] you can never leave root on bottom so multiply by
root on top and bottom to simplify
= ± [tex]\frac{2}{\sqrt{3} } \frac{\sqrt{3} }{\sqrt{3} }[/tex]
= ± [tex]\frac{2\sqrt{3} }{3}[/tex]
Select the correct answer.
In the given diagram, line segment BD
bisects angle ABC
. Segment BD
is extended to E, where line segment EC
is parallel to line segment AB
. Write a two-column proof to show that AB/AD = BC/DC
.
The missing statement and the reason in the two-column proof:
EC = BC; property iof isosceles triangles
The corret answer is an option (A)
A two-column proof to show that AB/AD = BC/DC is:
Statement Reason
∠1 ≅ ∠2 given
∠1 ≅ ∠5 alternate interior angles theorem
∠3 ≅ ∠4 vertical angles theorem
ΔABD is similar to ΔCED AA similarity
AB/AD = EC/DC property of similar triangles
∠2 ≅ ∠5 substitution property of congruency
EC = BC property iof isosceles triangles
AB/AD = BC/DC substitution property of equality
Therefore, the correct answer is an option (A)
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Find the complete question below.
Identify the mean, median, mode, and range of the data set. 7, 6, 8, 12, 9, 13, 8
The mean is approximately 9, the median is 9, the mode is 8, and the range is 7.
To find the mean, we add up all the numbers in the data set and divide by the total number of numbers:
Mean = (7 + 6 + 8 + 12 + 9 + 13 + 8) / 7 = 63 / 7 ≈ 9
So the mean is approximately 9.
To find the median, we need to arrange the numbers in order from smallest to largest:
6, 7, 8, 8, 9, 12, 13
Since there are an odd number of values in the data set, the median is the middle value, which is 9.
To find the mode, we need to look for the value that occurs most frequently in the data set. In this case, 8 occurs twice, which is more than any other value, so the mode is 8.
To find the range, we need to subtract the smallest value from the largest value:
Range = largest value - smallest value = 13 - 6 = 7
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