1. The measure of angle A is [tex]\(22^\circ\).[/tex]
2. The measure of angle B is[tex]\(68^\circ\).[/tex]
Explanation:To find the measures of angles A and B, we can use the fact that they are complementary, meaning their measures add up to[tex]\(90^\circ\).[/tex]Let's set up an equation using the given information:
[m_A + m_B = 90]
Given that[tex]\(m_A = 3x - 8\)[/tex]and (m_B = 5x + 10), substitute these expressions into the equation:
3x - 8 + 5x + 10 = 9
Combine like terms:
8x + 2 = 90
Subtract 2 from both sides:
8x = 88
Divide by 8:
x = 11
Now that we know the value of (x), we can find the measures of angles A and B:
[tex]\[m_A = 3x - 8 = 3(11) - 8 = 33 - 8 = 25\][/tex]
[tex]\[m_B = 5x + 10 = 5(11) + 10 = 55 + 10 = 65\][/tex]
Therefore, the measure of angle A is \(25^\circ\) and the measure of angle B is [tex]\(65^\circ\).[/tex] To check, we can verify that these angles are indeed complementary:
25 + 65 = 90
So, angles A and B satisfy the condition of being complementary.
The circumference of a circle is 25.12 yards. What is the radius of the circle?
Andrew bought 3 baseball cards for $240. After a few months, he got an offer from his friend Jack to buy the first card for double its original value, along with either the second or third card. Andrew decided to sell the first card (at double its original value) along with the second card (at its original price) and got $320 for it. Or, selling the first card (at double its original value) card along with the third card (at its original price) would have only got him $280. What were the original prices for each of the 3 baseball cards?
The original prices for the baseball cards are $120, $80, and $40.
Explanation:Let's say the original prices of the first, second, and third baseball cards are x, y, and z respectively.
From the given information, we can form the following equations:
2x + y = 320 2x + z = 280 x + y + z = 240
Solving these equations simultaneously, we can find the original prices:
x = $120 y = $80 z = $40
Therefore, the original prices for the first, second, and third baseball cards are $120, $80, and $40 respectively.
Final answer:
The original prices of the 3 baseball cards were $88 for the first card, $56 for the second card, and $96 for the third card, worked out via a system of equations derived from the given information.
Explanation:
We're given that Andrew bought 3 baseball cards for a total of $240. When he sells the first card at double its original value along with the second card at its original price, the total is $320. Conversely, if he sells the first card at double its original value along with the third card, the total is $280.
Let's denote the original prices of the first, second, and third cards as F, S, and T respectively. We have two equations based on the information provided:
2F + S = $320
2F + T = $280
We also know the sum of the original prices:
F + S + T = $240
Subtracting each equation from the combined original price, we get:
S = $240 - T
T = $240 - S
Plugging these into our original equations:
2F + ($240 - T) = $320
2F + ($240 - S) = $280
Solving these equations, we find:
2F = $320 - ($240 - T) => 2F = $80 + T
2F = $280 - ($240 - S) => 2F = $40 + S
Therefore, T - S = $40. Now, using equation 3, F = $240 - S - T, we substitute T = S + $40 to get:
F = $240 - S - (S + $40) => F = $200 - 2S
And if we substitute this into 2F = $80 + T:
2($200 - 2S) = $80 + T
$400 - 4S = $80 + T
T = $320 - 4S
Combining this with T = S + $40, we get:
S + $40 = $320 - 4S => 5S = $280 => S = $56
Now we can find T and F:
T = $56 + $40 => T = $96
F = $200 - 2($56) => F = $88
Thus, the original prices of the baseball cards were $88 for the first card, $56 for the second card, and $96 for the third card.
A tortilla chip workstation produces 1,000 chips in 20 seconds. what is its bottleneck time
The bottleneck time for the tortilla chip workstation is 1/50 seconds.
Explanation:To find the bottleneck time, we need to determine the step in the production process that takes the longest time. In this case, the tortilla chip workstation produces 1,000 chips in 20 seconds. So, each chip takes 20/1000 = 1/50 seconds to produce. Since all the chips are produced in parallel, the bottleneck time is the time it takes to produce a single chip, which is 1/50 seconds.
2/5 of the fish in a tank are guppies. 1/4 of the guppies are red. what fraction of the fish in the tank are red guppies.
multiply 2/5 by 1/4
2/5 * 1/4 = 2/20 = 1/10 of the fish are red guppies
Which of these is a step in constructing an inscribed equilateral triangle using technology?
A. Construct segment DB, segment BC, segment CE, segment EG, segment GI, and segment ID.
B.Create circle A with point B on the original circle.
C.Create circle E, which passes through points A and C.
D.Draw point E anywhere on segment DB.
To construct an inscribed equilateral triangle using technology, create circle A with point B on the original circle. This step is essential in forming the triangle.
Step by Step Solution:
To construct an inscribed equilateral triangle using technology, follow these steps:
Identify a point A on the circumference of the original circle.Create circle A with point B on the original circle.Ensure that the circle with center A passes through the original circle at point B.Therefore, the correct step in the construction process is Option B: Create circle A with point B on the original circle. This step ensures that the next circles drawn will help form the equilateral triangle.
factor the polynomial 5x^2(x-1)-7(x-1)
(02.01) Solve for x: −2(x + 3) = −2(x + 1) − 4.
Which lines or segments are parallel? Justify your answer.
Parallel lines or segments are equidistant from each other and do not intersect. This principle also applies to vectors with identical directions and magnitudes, and to other instances like horizontal lines on a grid or parallel patterns in sentence construction.
Parallel lines or segments are those that are equidistant from each other and never intersect, regardless of how far they extend. In the context of vectors, two vectors are said to be parallel if they have identical directions, denoted by A = B if and only if they have equal magnitudes.
As illustrated in geometry, the horizontal lines on a grid can be parallel. Even visually, parallelism denotes a close resemblance and continuity, as seen in electric field lines drawn parallel to the wire placed on the x-axis.
The horizontal lines in this figure are parallel loops. This is because they remain an equal distance apart at all points. A similar concept of parallel patterns can be seen in grammatical structures and construction of a sentence.
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Which shape best describes the object generated when square is rotated about the axis?
hollow rectangular prism
solid rectangular prism
hollow cylinder
solid cylinder
Which three-dimensional object is formed when the shape is rotated about the axis as shown?
sphere
cylinder
cone
hemisphere
Which description best describes the three-dimensional object that is formed when the shape is rotated about the axis as shown?
a hollow cylinder
a flat disk with a hole in the center
a square pyramid
a rectangular prism that is open on the ends
Answer:
Ques 1) Hollow cylinder.
Ques 2) sphere.
Ques 3) Hollow cylinder.
Step-by-step explanation:
Ques 1)
on rotating the first figure about the axis:
If you rotate the square around the axis as shown in the first diagram, then the square will form a 3D ring around the vertical axis. This ring is essentially a hollow cylinder as the region in between is left empty.
Ques 2)
Rotating that semi-circle around the axis shown will generate a full sphere.
Ques 3)
As we have done in ques 1) now this time in place of square we are given a rectangle so on rotating this rectangle a hollow cylinder will be formed.
It should be noted that the shape that describes the object generated when square is rotated about the axis is C. Hollow cylinder.
ShapesThe three-dimensional object that is formed when the shape is rotated about the axis as shown is a sphere.
In the third diagram, the three-dimensional object that is formed when the shape is rotated about the axis as shown is a hollow cylinder.
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How do I find the value of x?
opposite angle equal each other so:
(12x-10) = (5x+53)
add 10 to both sides
12x = 5x+63
subtract 5x from each side
7x=63
divide both sides by 7
x = 63/7
x = 9
The college of arts and science at delta university has nine departments. the number of faculty in each department is shown below. what is the median number of faculty in the college of arts and science? 8, 12, 9, 15, 17, 11, 13, 14, 7
The median of the number of faculty in the college of arts and science is 12.
What is median?When a group of values is sorted from smallest to greatest, the median is the number in the middle of the range.
Given that,
Number of faculties in 9 departments of arts and science in the college
= 8, 12,9, 15, 17, 11, 13, 14, and 7
To find median number of the faculty in the college of arts and science,
Arrange number in increasing order,
= 7, 8, 9, 11, 12, 13, 14, 15, 17
The middle number of the sequence is 12.
So, the median of the sequence will be 12.
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If 3 pumpkins make 9 pumpkin pies, how many are needed to make 204 pies?
In a certain city, 30 percent of the people are conservatives, 50 percent are liberals, and 20 percent are independents. records show that in a particular election, 65 percent of the conservatives voted, 82 percent of the liberals voted, and 50 percent of the independents voted. if a person in the city is selected at random and it is learned that she did not vote in the last election, what is the probability that she is a liberal?
The probability that a randomly selected person from the city who did not vote in the last election is a liberal is about 16.7 percent.
We are trying to find the probability that a person selected at random from the city is a liberal given that they did not vote in the last election. We can use Bayes' theorem and the law of total probability to solve this problem. First, we need to calculate the probability of a person not voting, P(NV), and then find the probability of being a liberal who did not vote, P(L and NV).
The total probability of not voting is P(NV) = P(C) \'97 P(V|C) + P(L) \'97 P(V|L) + P(I) \'97 P(V|I), where P(C) is the probability of being conservative, P(L) is the being liberal, P(I) is the probability of being independent, and P(V|C), P(V|L), P(V|I) are the probabilities of a conservative, liberal, and independent voting, respectively.
So, P(NV) = 0.30 \'97 0.65 + 0.50 \'97 0.82 + 0.20 \'97 0.50 = 0.35 + 0.09 + 0.10 = 0.54. This is the probability that a random person did not vote. Now, we need to find the probability that a person is a liberal and did not vote, P(L and NV) = P(L) \'97 P(NV|L), where P(NV|L) is the probability of a liberal not voting.
P(L and NV) = 0.50 \'97 (1 - 0.82) = 0.50 \'97 0.18 = 0.09. This is the probability that a person is a liberal who did not vote. Finally, to find the probability that a person is a liberal given they did not vote, P(L|NV), we use Bayes' theorem: P(L|NV) = P(L and NV) / P(NV) = 0.09 / 0.54 = 1/6 or approximately 0.167.
In conclusion, the probability that a person selected at random from the city is a liberal given that they did not vote in the last election is about 16.7 percent.
how do you find the equation of x^2 = 7 by square rooting
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box
Answer:
[tex]y=-\frac{1}{3}x-5[/tex]
Step-by-step explanation:
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(-6,-3)\ B(6,-7)[/tex]
Substitute the values
[tex]m=\frac{-7+3}{6+6}[/tex]
[tex]m=\frac{-4}{12}=-\frac{1}{3}[/tex]
step 2
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{1}{3}[/tex]
[tex]B(6,-7)[/tex]
substitute and solve for b
[tex]y=mx+b[/tex] ------> [tex]-7=-\frac{1}{3}*6+b[/tex]
[tex]-7=-2+b[/tex]
[tex]b=-5[/tex]
The equation of the line is equal to
[tex]y=-\frac{1}{3}x-5[/tex]
The bells at Kings School ring every 6 minutes. At Queens School the bells ring every 5 minutes. At Princess School the bells ring every 9 minutes. All three bells ring together at 8.30 am. When is the next time the bells of the three schools will ring together?
The table lists the number of pitches seen by a player in 6 games. What is the mean of the data set? 11 14.5 18.5 20 Done Game Pitches Seen 1 25 2 20 3 20 4 17 5 15 6 14
The mean of the data set is:
18.5
Step-by-step explanation:The data values are given as:
Done Game Pitches Seen
1 25
2 20
3 20
4 17
5 15
6 14
We know the mean of the data set is calculated as the average of the data values.
Hence, here the mean of the data set is ratio of the total number of pitches to the total number of games.
Total number of pitches=25+20+20+17+15+14=111
Number of games=6
[tex]Mean=\dfrac{111}{6}=18.5[/tex]
Hence, Mean of the data set= 18.5
What is the solution to the following system of equations?
infinite solutions no solution (0, 1) (4, –1)
The system of equations has infinite solutions.
Explanation:Upon analyzing the system of equations, if the equations represent the same line or are proportional to each other, the solution will be infinite. Let's consider the equations given:
Equation 1: [tex]\(y = x + 1\)[/tex]
Equation 2: [tex]\(2y = 2x + 2\)[/tex]
By manipulating Equation 2, dividing both sides by 2, we get Equation 1. This indicates that the equations represent the same line. When graphed, both equations will yield the same line. Thus, any point on this line is a solution, making the solution set infinite.
Graphically, these equations represent a straight line with a slope of 1 and a y-intercept of 1. Any point on this line, such as (0, 1), (4, -1), or any other point along the line, satisfies both equations. Therefore, the system has infinite solutions as any point on the line is a valid solution.
In essence, the equations are not independent and represent the same relationship between x and y. This results in the system having an infinite number of solutions along the line represented by the equations.
A 6 pound watermelon cost $2.40 before 30% discount. Which equation would allow you to find the discount price of the watermelon
Given: The watermelon costs $2.40 before a 30% discount.
To Find: An equation to find out the discounted price of the watermelon
Calculation/Explanation:
As the discount is 30%, this means a value of [tex](\frac{30}{100}).(2.40) = 0.72 $[/tex] should be deducted from the original price to find the new price after discount.
Thus, new price of the watermelon after the discount is [tex]2.40-0.72=1.68[/tex] dollars.
Thus, the expresion that denotes the new price after the discount is [tex]2.40 - ((\frac{30}{100}).(2.40)) \\=2.40-0.72\\=1.68 $[/tex]
Solve for x.
Enter your answer in the box.
x =
°
A bin contains three components from supplier a, four from supplier b, and five from supplier
c. if four of the components are randomly selected for testing, what is the probability that each supplier would have at least one component tested?
Convert 0.005090 Mega-liters to Liters. Record your answer in whole liters. Please show ALL of your work! Thanks! :)
Answer: 5,090 L
Step-by-step explanation:
Mega, in mathematical terms means million. The "M" represents million in the word mega.
Now, how many zeros does 1 million have? If you said 6, you are correct! Since 1 million has six zeros, we will move the decimal point 6 times. You'll have to multiply 0.005090 by 1,000,000. Let's do that!
So, we see that decimal point is by 2 zeros. If we move it 6 times by multiplying 0.005090 by 1,000,000, we'll get our answer. (Skip this if you want the answer)
0.005090 Original.
0.0509 One...
0.509 Two...
5.09 Three...
50.9 Four...
509 Five...
5090 Six!
Or, you could do it like this:
0.005090 × 1,000,000 = 5,090
Hence, your answer is 5,090 L.
Jim’s fundraiser BBQ needs to make at least $1000 in sales on Saturday. He sells hot dogs for $2 each and hamburgers for $3 each, and he wants to sell at least twice as many hamburgers as hot dogs. He brought 300 hot dogs and 800 hamburgers to sell. The graph shows the feasible region, where x represents the number of hot dogs sold and y represents the number of hamburgers sold. Which ordered pairs meet all the constraints for a successful fundraiser and make sense in context of the situation? Select each correct answer.
Answer:
Both (0,350) and (250,700) are correct i think
Step-by-step explanation:
To find the ordered pairs for a successful fundraiser, multiple constraints need to be considered. These include the goal of making $1000 from sales, selling at least twice as many hamburgers as hot dogs, and the physical limit of burgers and hot dogs available.
Explanation:The problem presents a set of inequalities to be solved. Firstly, to meet the $1000 objective, Jim needs to sell a combination of hamburgers (denoted by y) and hot dogs (x) such that 2x + 3y ≥ 1000. Secondly, he wants to sell at least twice as many hamburgers as hot dogs, which gives: y ≥ 2x. Lastly, Jim has a physical limit on the number of burgers and hot dogs he can sell, which gives: x ≤ 300 and y ≤ 800. The ordered pairs that satisfy all these constraints form the feasible region for Jim’s sales. We are looking for integer values in this region as it is not possible to sell a fractional number of hamburgers or hot dogs. Thus, we need to attentively examine the feasible region on the graph provided. Calculations can also help in confirming the graphical representation.
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You and your friend are selling magazine subscriptions for a fundraiser. after ww weeks, you have sold (3w+4)(3w+4) subscriptions and your friend has sold (5w+1)(5w+1) subscriptions.
a. write an expression in simplest form that represents the difference between the number of subscriptions your friend has sold and the number you have sold. an expression is .
Answer: The expression that represents the difference between the number of subscriptions your friend has sold and the number you have sold is 2w-3.
Explanation:
It is given the expression (5w+1) represents the subscriptions sold by the friend
f(w)=5w+1
Expression (3w+4) represents the subscription sold by me.
g(w)=3w+4
We have to find an expression which shows the difference between the number of subscriptions your friend has sold and the number you have sold.
[tex]h(w)=f(w)-g(w)[/tex]
[tex]h(w)=(5w+1)-(3w+4)[/tex]
[tex]h(w)=5w+1-3w-4[/tex]
Combine like terms.
[tex]h(w)=(5w-3w)+(1-4)[/tex]
[tex]h(w)=2w-3[/tex]
If it is negative then it means the subscription sold by friend is less than the subscription sold by me and if it is positive then it means the subscription sold by friend is more than the subscription sold by me.
Every social security number consists of nine digits, 0 through 9. if repetition of digits is permitted, how many possible social security numbers are there?
One positive integer is 3 less than twice another. the sum of their squares is 170
The larger of two numbers is 10 less than 5 times the smaller.their sum is 146 .find the smaller number
If i add to my number a number that is 17 more than twice my number, the sum will be 65. what is my number?
n +2n+17 = 65
3n+17 = 65
3n = 48
n = 48/3 = 16
Number is 16
PLEASE HELP!
Solve the equation for x.
4x + 2 = 2(x + 3) + 2x – 4
Infinitely many solutions
No Solution
x = 2
x = 4
Their total bill for lunch was $56. Toni paid the check with three twenty dollar bills. Write an algebraic expression that represents the difference between how much Toni paid and actual amount of bill. Do not simplify.
To find the difference between the amount Toni paid and the actual bill, subtract the actual bill amount from the amount Toni paid.
Explanation:To find the difference between how much Toni paid and the actual amount of the bill, we can subtract the actual amount of the bill from the amount Toni paid. Let's represent the actual amount of the bill as 'b'. Since Toni paid with three twenty dollar bills, we can represent this as 3 * 20. Now, the algebraic expression that represents the difference between how much Toni paid and the actual amount of the bill is:
3 * 20 - b
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