Country B is more efficient than Country A when it comes to producing cars and tanks.
Country A takes twice as long to produce a car (30 minutes) than Country B (12 minutes). However, Country A takes 20 minutes to produce a tank while Country B takes 10 minutes, cutting the amount of time in half.
We can measure the efficiency of each country by calculating the number of cars and tanks each country can produce in an hour. We can do this using the following formula:
Cars per hour = (60 minutes/minutes to produce car)
Tanks per hour = (60 minutes/minutes to produce tank)
For Country A, the number of cars produced in an hour is (60 minutes/30 minutes) = 2 cars per hour and the number of tanks produced in an hour is (60 minutes/20 minutes) = 3 tanks per hour.
For Country B, the number of cars produced in an hour is (60 minutes/12 minutes) = 5 cars per hour and the number of tanks produced in an hour is (60 minutes/10 minutes) = 6 tanks per hour.
Therefore, Country B is more efficient than Country A when it comes to producing cars and tanks.
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Liam left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Liam is x minutes after he left his house, until he got back home.
Note that after 15 minutes, Liam is 25 blocks away from his house. This prompt is a distance - time graph problem.
What is a distance - time graph?A distance-time graph depicts how far an object has moved in a given amount of time. It is a basic line graph that depicts distance versus time findings. The Y-axis represents distance. The X-axis represents time.
It should be noted that a distance-time graph depicts how the distance and speed of an item vary over time. The movement of three items over time is depicted in this graph. The slope, or steepness, of each line shows the speed of the item. In general, the quicker the item, the steeper the slope.
Note that by the 13th minute, Liam had already covered 25 blocks but remained stationary at that location for 3 minutes.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Consider figures 1 and 2 shown on the coordinate plane. Figure 1 has been transformed to produce figure 2.
Describe the transformation.
This transformation can be described by (x' , y') = (
Considering the attached image. This transformation can be described by (x' , y') = (x' -y')
What is transformation in geometry?Transformation refers to movements objects make especially as described on a coordinate plane
A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. the four ways include
rotationdilationreflectiontranslationPre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Examining the preimage and the image of the attached picture show that the translation involved is reflection
And the transformation rule for reflection over y axis is
(x, y) → (x, -y)
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Quadrilateral QRST is a kite. What is TU?
The value of PR when the Pythagorean formula is used would be = 33.
What is a kite?A kite is a type of quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
The value of PR can be determined with the use of the Pythagorean formula = c² = a² +b²
where c = 65
a = 56
b = PR = X
b = c² - a²
b² = 65² - 56 ²
b² = 4225 - 3136
b² = 1089
b= √ 1089
b = 33.
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Complete question:
Quadrilateral QRST is a kite. What is PR?
What is the slope of the line in the graph below?
undefined
−2
2
0
Answer:
Step-by-step explanation:
The slope of the given line in the graph is "undefined".
Define the term slope of the line?Slope, usually referred to as rise over run, is the "steepness" of the line.
By dividing the difference in y values between two points by the difference in x values, we may determine slope.
A line's slope does not summarily characterize it. As a result, even if you know a line's slope, you cannot identify the exact spots the line passes through.Any two lines with the same slope are said to be parallel. When a line is rotated 90 degrees, it becomes perpendicular and becomes parallel. A horizontal line is one that has a slope of 0. Positive lines are those that rise as they move further to the right.The y-axis is an example of a vertical line that is believed to have an "undefined" slope.Thus, as the line is passing through the y axis and parallel to the x axis, the slope of the given line is undefined.
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If 479,000 people each receive an average refund of $4,500, based on an interest rate of 1 percent, what would be the lost annual income from savings on those refunds? (Do not round intermediate calculations. )
As per the compound interest, the lost annual income from savings on those refunds is $21,555,000
In math the term called compound interest is defined as a type of interest that not only accrues on the principal but also on the accrued interest and the interest rates on loans are quoted in terms of annual percentage rate, which does not account for the compounding of interest, and therefore understates the true cost of borrowing.
Here we know that the 479,000 people each receive an average refund of $4,500, based on an interest rate of 1 percent.
Then the lost annual income from savings on those refunds is calculated as,
As we all know that the lost annual income is the amount of interest these people could have earned on their income, in which the extra tax had not been deducted.
Then With $4,500 each person,
Then the total amount of the deducted income is calculated as,
=> 479,000 x 4,500 = 2,155,500,000.
Here we have the 1% interest rate, then the net return on these fund if they were saved
=> 2,155,500,000 x 1% = 21,555,000.
Therefore the total lost annual income is 21,555,000
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a medical researcher is comparing the results of two surgical techniques to correct a skeletal deformity. there are many obvious risks of participating in this treatment trial, and participants are carefully informed about the likelihood of infection, poor treatment outcome, further damage, etc. the research design includes a questionnaire given to patients about their quality of life before and after the surgery. because this is just a simple paper and pencil questionnaire, it does not add any risks to the overall study design. is this true or false?
The questionnaire given to patients about their quality of life before and after the surgery included in the research design does add risks to the overall study design. Hence, the given statement is false.
Even though the questionnaire itself may not cause any additional physical risks, it can still have an impact on the overall study design. The questionnaire can add additional burden to the participants, who may already be dealing with physical and emotional stress from the surgery. Also, the questionnaire results may not be accurate if participants are not fully honest or unable to understand the questions being asked. Therefore, the inclusion of such a questionnaire in the research design should be carefully considered after evaluating its potential impact on the overall study.
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in 1980 the average price of a home in brainerd county was $97,000. by 1986 the average price of a home was $109,000. write a linear model for the price of a home, p, in brainerd county as a function of the year, t. let t
The linear model for the price of a home P=2,000t+97,000
if 1980 -> t=0 then, 1986 -> t=6 (six years later).
The two points are (t, price) -> (0,97000) and (6,109000)
we want an equation in the form y=mx+b,
the y-intercept(b) is the y=p value when x =tis 0: so b=
m is the slope: m={{y2-y1}/{x2-x1}}={{t2 - t1}/{P2 - P1}}
given two points
(t, P) = (0, 97k) and (6, 109k)
slope = (97 - 109)/(0 - 6)=2
P - 97 = 2(t - 0) < point-slope form
P = 2t + 97 < in thousands
P = 2,000t + 97,000
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The Stock Market Nadia is a stockbroker. She earns 14% commission each week. Last week, she sold $5,300 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answer:$742; $38,584
Step-by-step explanation: 14% of $5,300 is $742 (0.14 x 5300). There are 52 weeks in a year so $742 x 52 weeks = $38,584.
Plot a point on the coordinate plane to represent each of the ratio values in the table.
Find the measure of angles 1 and 2
Answer:
angle 1 = 118 deg
angle 2 = 62 deg
Step-by-step explanation:
To find angle one you must know that angles 1 and 118 deg are alternate angles. Therefore since these lines are parallel, angles 1 and 118 are equal.
To find angle 2 to you must know that angle 1 + angle 2 = 180.
angles on a straight line always equal 180 deg
therefore:
180
118 -
62 deg
hope this helps :)
Answer:
m<1 = 118°
m<2 = 62°
Step-by-step explanation:
The horizontal lines are parallel.
Angles 1 and 118° are alternate interior angles of parallel lines cut by a transversal, so they are congruent.
m<1 = m<2 = 118°
Angles 1 and 2 are a linear pair, so they are supplementary. That means that their measures add to 180°.
m<1 + m<2 = 180°
118° + m<2 = 180°
m<2 = 62°
Each graph represents a relation. Determine if the relation is a function. Then find the domain
and range.
For the given graphs, 3) graph represents a function.
Despite the fact that the offered collection of points does in fact depict a relation (since xs and ys are connected), the set they provided me with has two points with the same x-value: (2, 3) and (2, 3). This relation cannot be a function because x = 2 offers me two possible destinations, or two possible y-values.
The only thing I have to do to determine whether the relation they have given me is a set of points is to look at the points' x-values; if any x appears more than once, the relation is not a function.
As, there exist an image for all the elements of the given graph and there exist unique pre-image for the range.
Domain = [-6, 6]
Range = [-3, 3]
For the second graph, the image for every co-domain is 4. So, it is not a function.
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can someone help me with 11 and 12
Answer:
see below
Step-by-step explanation:
11: write 3 equiv ratio of 1:3, so it' could be 3:9, 2:6, 4:12
12. 20:15 = 4:3, 12:9, 8:6
an algebra test is worth 100 points and has 25 questions. there are multiple choice questions worth 3 points each and short answers worth 8 points each. how many short answer questions are on the test?
There are 5 short answer questions on the test.
Algebra is a common thread that runs through practically all of mathematics. It involves the study of variables and the rules for manipulating them in formulas.
let us assume,
x = the number of multiple choice questions worth 3 points each
y = the number of short answer questions worth 8 points each
since the test has total of 25 questions we have
x + y = 25
the algebra test is worth 100 points
3×x + 8×y = 100
by solving the system of equations
x + y = 25
3×x + 8×y = 100
we find
x = 20
y = 5
there are 5 short answer questions on the test.
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A total of 362 adults and children are at a theatre. There are 140 more adults than children. If x represents the number of adults and y represents the number of children, which system of equations could be used to find the number of adults and the number of children in the theatre?
A system of equations that could be used to find the number of adults and the number of children in the theatre is:
x + y = 362
y = x + 140
How to write the required system of linear equations?In order to write a system of linear equations to describe this situation, we would assign variables to the number of adults and number of cats respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of adults.Let the variable y represent the number of children.Since the total number of adults and children at this theatre is 362, a linear equation which represents this situation is given by;
x + y = 362
Additionally, there are 140 more adults than children;
y = x + 140
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Please help!!
Which of the following statements is true about the triangles below
Answer: ASA
Step-by-step explanation: Hello! You can use ASA to prove that the triangles ABC and ABD are congruent. This is because you are given two angles of each triangle. You know that your answer should be ASA or AAA, which are the only two triangle congruence postulates that involve two or more congruent angles. Lastly, you can use the reflexive property. An example of reflexive property is 3 = 3, which means anything is congruent to itself. You know that both triangles share line segment AB, meaning that they have one side and two angles that are congruent. Since you know that the two angles and the included side are congruent, ASA proves that both triangles ABC and ABD are congruent. I hope this helps you!
Consider two stars, star A and star B. Star A is 22 light-years from Earth, and star B is 34 light-years from
Earth. Viewing from Earth, the angle between them is 60 degrees. What is the distance between star A
and star B in light-years? (Round your answer to the nearest hundredth.)
The distance that exists between star A and B is given as 29.87 light years
How to solve for the distance that exists between the the starsWe can solve this by creating a triangle where Point a Is star a, point b is star b and the point c is earth
the angle is given as 60 degrees
AC = 22 light years
BC = 34 light years
ab² = ac² + bc² - 2 *ac * bc* cos60
we would have to put in the values
ab² = 22² + 34² - 2 * 34 * 22 * cos 60
ab² = 484 + 1156 - 748
ab² = 892
square both sides
ab = 29.87 light years
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I NEED HELP ASAP
A toy manufacturer is designing a new triangular-shaped toy. The company would like the toy to have a specific area. Write the equation for the area of a triangle. Solve your formula for the height. The company specified that the area of the toy must be 60 square inches and the length of the base must be 12 inches. Use your formula to determine the height of the new toy.
The height of the triangle with area of 60 square inches and the base of 12 inches is 10 in.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The area of a triangle is the amount of space it occupies. The area is the product of the base and height divided by 2. It expressed as:
Area = (1/2) * base * height
Given that the area is 60 square inches and the length of the base must be 12 inches. Let h represent the height
Therefore:
Area = (1/2) * base * height
60 = (1/2) * 12 * h
6h = 60
h = 10 in
The height of the triangle is 10 in.
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Mary, Ana, and Nata work at a coffee shop. Each day from Monday to Friday exactly two of them come to work. Mary works 3 days per week and Ana works 4 days per week. How many days per week does Nata work?
Based on the information, it can be inferred that Nata has to work 7 days a week.
How to calculate how many days Nata works?To calculate how many days Nata works we must perform the following mathematical operation.
We must find how many days in total Ana and Mary work together, that is, we must add the days that they work.
3 + 4 = 7Based on the above, we can say that Ana and Mary work 7 days a week, so Ana could work Monday, Tuesday and Wednesday and Mary could work Thursday, Friday, Saturday and Sunday.
So, Nata will have to accompany both of them every day, so she will have to work 7 days.
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Find the values of x and y in the diagram, below
(4x-7)(7x-1) (9x+4)
Applying the corresponding angles theorem, the values of x and y are:
x = 13
y = 24
What is the Corresponding Angles Theorem?The Corresponding Angles Theorem states that if two lines are cut by a transversal and the pairs of corresponding angles are congruent, then the two lines are parallel.
From the diagram given, we have:
63 + (5x - 8) + (7x - 31) = 180 [corresponding angles theorem]
63 + 5x - 8 + 7x - 31 = 180
12x + 24 = 180
12x = 180 - 24
12x = 156
x = 13
5x - 8 + 4y + 27 = 180
Plug in the value of x:
5(13) - 8 + 4y + 27 = 180
65 - 8 + 4y + 27 = 180
84 + 4y = 180
4y = 180 - 84
4y = 96
4y/4 = 96/4
y = 24
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Please help me! I need the slope
Answer:
-1.5 or 1 1/2
Step-by-step explanation:
from the graph you see on Y-axis when Y =2, x=0. so you got a point: (0,2)
then on the right lower quadrant, when x = 2, y = -1, another point (2,-1)
slope = (y2 -y1)/(x2-x1) = [2-(-1)] / (0-2) =-1.5
the way the slope's direction is, you know the slope must be negative.
An architect is designing a building. Each floor will be 12 feet tall. Write an expression for the number of floors the building can have for a given building height. Tell what the variable in your expression represents
The company claims that in the large bag of M&M's 20% of them were orange. Students bought a large bag of M&M and counted the candies they were 500. What is the probability of getting orange 21% more in that large bag.
The probability of getting orange 21% more in that large bag is 0.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
In this situation, the company claims that in the large bag of M&M's 20% of them were orange. Since the oranges are 20%, the probability of getting orange 21% more in that large bag is not possible. This will be zero.
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When Damian runs the 400 meter dash, his finishing times are normally distributed
with a mean of 60 seconds and a standard deviation of 1 second. Using the empirical
rule, determine the interval of times that represents the middle 99. 7% of his finishing
times in the 400 meter race.
The interval of times that represents the middle 99. 7% of his finishing
times in the 400 meter race = (57, 63)
We know that the empirical rule or 68-95-99.7 rule states that for a normal distribution, 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
Here, mean (μ) = 60 seconds, standard deviation (σ) = 1 second
To determine the interval of times that represents the middle 99. 7% of his finishing times in the 400 meter race.
the 99.7% are within three standard deviations would be,
μ ± 3σ
= (60 - 3(1), 60 + 3(1))
= (57, 63)
The required interval is: (57, 63)
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how many pieces of data can a variable hold at a given time? group of answer choices two infinite it depends on the data type none one
None of the options are correct. A variable can only hold one piece of data at a time.
A variable is a named storage location in a computer's memory that is used to store a single value. The value can be of any data type, such as a number, a string, or a boolean. A variable can only hold one piece of data at a time, meaning that it cannot store multiple pieces of data simultaneously. This is why it is important to use multiple variables if you need to store multiple pieces of data. Each variable should be given a unique name so that it can be easily referenced and identified when needed.
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The figure shows the measurements, in inches, of a rectangular prism. 8 in 12 in 7 in What is the volume of the prism
A:92 in B: 236 in C: 472 D: 672
Answer:
672 in.³
Step-by-step explanation:
V = LWH
V = 8 in. × 12 in. × 7 in.
V = 672 in.³
Answer: D 672
Step-by-step explanation: The formula for volume is L x W x H = V so if you plug all those numbers in and multiply u get 672
20/3 / 1/6 what is the miles per gallon
Answer: 20/3 / 1/6 is a division problem that can be simplified as follows:
20/3 divided by 1/6 = (20/3) * (6/1) = (206) / (31) = 120/3 = 40
The value of the division is 40. However, without knowing the context, it is impossible to know what the meaning of this value is. In particular, without knowing the units of 20/3 and 1/6, it is not possible to interpret the division as miles per gallon or any other unit.
It is important to note that 20/3 and 1/6 should be represented as mixed numbers (6 2/3 and 1/6) or as decimal numbers (6.66 and 0.16666) in order to be able to proceed with the division.
Step-by-step explanation:
what is (8/9)^2 pls i need it
Answer: about 0.79
Step-by-step explanation:
First divide 8 by 9 --> (8/9) = about 0.8889
then square that value --> (0.8889)^2 = about 0.79.
PEMDAS is your friend!
The heights of a species of plant are approximately Normally distributed, have a mean of 9. 31 cm, and have a standard deviation of 0. 55 cm. If 20 of the plants are randomly selected, what is the probability that the mean plant height is less than 9. 5 cm?
If heights of a species of plant are approximately Normally distributed, have a mean of 9.31 cm, and standard deviation of 0.55 cm , If 20 of the plants are randomly selected , then the probability that the mean plant height is less than 9.5 cm is 0.9388 .
We can use the Z-score formula to find the probability that a randomly selected plant has a height less than 9.5 cm:
Z = (x - mean)/(standard deviation/sqrt(sample size)) ;
Where x is the value we want to find the probability for, in this case x = 9.5
So , Z = (9.5 - 9.31)/(0.55/√20) = (0.19)/(0.123) = 1.54
Now we can use the standard normal table to find the probability that a Z-score is less than 1.54 .
From the z table ; we get , the p value is 0.9388 .
Therefore , The probability that a randomly selected plant from this species has a height less than 9.5 cm is about 0.9388 .
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adams awesome pawnshop will lend up to 42% of the value of a borrowers collateral. andy want wants to use his 10000 signed michael jordan rookie card. his 3000 signed joe monntana cleats & his 2000 signed tiger woods golf ball as collateral for a loan. with the loan andy wants to buy a signed michael jackson white glove that costs 6500. will the loan be enough for andy to get the glove?
No, Andy do not have enough loan, he need $200 more dollars to purchase Michael Jackson white glove.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Adams awesome pawnshop will lend up to 42% of the value of a borrowers collateral.
Andy want wants to use his $10000 signed Michael Jordan Rookie card. his $3000 signed Joe Montana cleats and his $2000 signed Tiger Woods golf ball as collateral for a loan.
Now, 42% of (10000+3000+2000)
= 42/100 ×15000
= 0.42×15000
= $6300
Cost of Michael Jackson white glove costs $6500
No, Andy do not have enough loan, he need $200 more dollars to purchase Michael Jackson white glove.
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Multiple Choice 1. Which proportion can be used to determine what number is 15% of 30? (1 point) 15/30=x/100 15/100=x/30 15/100=x/30 30/100=x/15
Answer:4.5
Step-by-step explanation: