Answer:
0.6946 = 69.46% probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Republican
Event B: From a household that makes at least $50,000.
Probability of Republican:
43% of 36%(makes less than $50,000).
55% of 64%(makes more than $50,000).
So
[tex]P(A) = 0.43*0.36 + 0.55*0.64 = 0.5068[/tex]
Republican and from a household that makes at least $50,000.
55% of 64%. So
[tex]P(A \cap B) = 0.55*0.64 = 0.352[/tex]
What is the probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.352}{0.5068} = 0.6946[/tex]
0.6946 = 69.46% probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000.
a candy distributor needs to mix a 10% fat content chocolate with a 30% fat content chocolate to create 100 kg of at 18% fat content chocolate. how many kilograms of each kind of chocolate must they use?
Solving a system of equations we will see that they need to use:
40 kg of the 30% fat content chocolate.60 kg of the 10% fat content chocolate.How many kilograms of each kind of chocolate must they use?Let's define the variables:
x = kilograms of the 10% fat-content chocolate.
y = kilograms of the 30% fat-content chocolate.
We know that they want to create 100kg, then:
x + y =100
And the fat content must be 18%, then we can write the concentration equation:
0.1*x + 0.3*y = 0.18*100 = 18
The coefficients are the percentages in decimal form.
Now we have a little system of equations:
x + y =100
0.1*x + 0.3*y = 18
Isolating x on the first one we get:
x = 100 - y
Replacing that in the other equation we get:
0.1*(100 - y) + 0.3*y = 18
10 + 0.2*y = 18
0.2*y = 18 - 10 = 8
y = 8/0.2 = 40
They need to use 40kg of the 30% chocolate and 60kg of the 10% chocolate.
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The value of car decreases at the rate of 10% per year. If the current price of the car is 245000 calculate it’s price after 3 years
Answer:
year 1: 90% × 245000 = 220500
year 2: 90% × 220500 = 198450
year 3: 90% × 198450 = 178605
∴ the car price after 3 years is 178605
explanation:
the value of car decreases 10%. that means the car price is 90%
The price of the car after 3 years will be 178605
We can calculate the value in the following way
Rate of decrease in car's price: 10%
Current price of the car: 245000
Value after 1 year, say value1= current value-10% of current value
[tex]value1=245000-\frac{10*245000}{100}[/tex]
=245000-24500
=220500
After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.
Value of car after 2 years, say value2= value1- 10% of value1
[tex]value2=220500- (\frac{10*220500}{100})[/tex]
=220500-22050
=198450
Similarly,
Value of car after 3 years, say value3= value2- 10% of value2
[tex]value3=198450- (\frac{10*198450}{100})[/tex]
=198450-19845
=178605
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Consider two securities, a and b. security a and b have a correlation coefficient of 0.65. security a has standard deviation of 12, and security b has standard deviation of 25. calculate the covariance between these two securities.
a. 300
b. 461.54
c. 261.54
d. 195
e. 200
The correct answer is option D. The covariance between securities a and b is 195.
To calculate the covariance between securities a and b, we can use the formula:
covariance = correlation coefficient * standard deviation of security a * standard deviation of security b
Plugging in the given values, we get:
covariance = 0.65 * 12 * 25 = 195
Therefore, the answer is (d) 195.
The covariance between two securities measures the extent to which the two securities tend to move together. A positive covariance indicates that the securities tend to move in the same direction, while a negative covariance indicates that the securities tend to move in opposite directions.
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2
Write the correct answer in the box. Substitute numerical values into the expression for all known variables.
Jeff wants to purchase a television for his first apartment. The television costs $750. He can get a zero-interest loan for the television if he pays $100
per month. At the same time, he puts away $200 per month in savings. To figure out when his savings will equal the remaining amount he owes on
the television, he starts writing a system of equations:
Equation 1: y=200x
Equation 2:
Write the second equation in the system.
y=??????
Answer:
Equation 2: y=750-100x
Step-by-step explanation:
The ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1,60),(2,240),(3,960),(4,3840)}
What is the function equation in sequence notation?
wt=
Answer:
The answer is in my screen shot:
Explanation:
It's a geometric sequence with common ratio 3. You can calculate the common ratio by dividing the 240 by 80 or likewise 720 by 240.
Solve the quadratic equation numerically (using tables of x- and y- values).
x squared minus 3 = 2 x
a.
x = -1 or x = 3
c.
x = -3 or x = -3
b.
x = 2 or x = -3
d.
x =1 or x = -1
The quadratic equation numerically (using tables of x- and y- values).
Correct option: (a). The value of x are x = -1 and x = 3.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x with the formula; ax² + bx + c = 0, where a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.
The given quadratic equation is:
x² - 3 = 2x
or, x² - 2x - 3 = 0
or, x² - 3x + x - 3 = 0
or, x (x - 3) +1 (x - 3) = 0
or, (x - 3) ( x +1 ) = 0
or, x = +3 , -1
The value of x are x = -1 and x = 3.
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is this a function (1, 8.5)(2, 8)(3, 7.5)(4, 7)(5, 6.5)(6, 6)
Yes, because no x values repeat.
How many 1/2 cup servings are in a package of cheese that contains 5 1/4 cups altogether?
There are 10.5 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether.
How to calculate the number of cups?A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other.Because the numerator is a decimal value, the ratio 10.2/34 isn't one. This number can be expressed as a ratio by multiplying the numerator and denominator by the appropriate power of ten to get rid of the decimal point.To find the number of 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether, we first need to convert the total amount of cheese in cups to a number of 1/2 cup servings.
We can do this by dividing the total amount of cheese by the size of a 1/2 cup serving.
First, we need to convert the amount of cheese in cups to a decimal number. Since there are two 1/2 cups in a cup, the decimal equivalent of 1/2 cup is 0.5. Therefore, the decimal equivalent of 5 1/4 cups is 5.25 cups.
Next, we need to divide the total amount of cheese in cups by the size of a 1/2 cup serving. Since the size of a 1/2 cup serving is 0.5 cups,
we can divide 5.25 cups by 0.5 cups to find the number of 1/2 cup servings as follows:
5.25 cups / 0.5 cups = 10.5
Therefore, there are 10.5 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether.
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In each of the following scenarios, determine whether the data is paired or not paired.
Part A: Compare pre- (beginning of semester) and post-test (end of semester) scores of students.
Part B: Assess gender-related salary gap by comparing salaries of randomly sampled men and women.
Part C: Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Part D: Assess effectiveness of a diet regimen by comparing the before and after weights of subjects.
Part (A) = Paired, Part (B) = Not Paired, Part (C) = Paired, Part (D) = Paired
Part A:
Compare pre- (beginning of the semester) and post-test (end of the semester) scores of students
Paired, as a subject are the same in both.
Score
A score is a group of 20 (often used in combination with a cardinal number, i.e. fourscore to mean 80), but also often used as an indefinite number.
Part B:
Assess the gender-related salary gap by comparing the salaries of randomly sampled men and women.
Not paired.
Sample
A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample. The possible values and the likelihood of each are determined by the random variable's probability distribution.
Part C:
Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Paired, as a subject are the same in both.
Vitamin E
Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.
Part D:
Assess the effectiveness of a diet regimen by comparing the before and after weights of subjects.
Paired, as a subject are the same in both.
Weight
The weight of an object refers to the force of gravity that is acting on the object. Furthermore, its calculation is mass times the acceleration of gravity, w = mg. The SI unit of weight is the newton because weight is a force.
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Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Paired, as a subject are the same in both.
Vitamin E
Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.
Part A USE A MODEL Express the statement using an inequality involving absolute value. Let x represent the number of students attending the dance. The dance committee expects attendance to number within 25 of last year's 87 students.
Step-by-step explanation:
The dance committee expects attendance to number within 25 of last year's 87 students can be expressed using an inequality involving absolute value as:
|x - 87| <= 25
This inequality states that the absolute difference between the number of students attending the dance (x) and 87, which was the number of students attending last year, must be less than or equal to 25. This means that the number of students attending the dance this year must be within 25 of the number of students attending last year.
Mason used a 30% coupon to buy a new computer. After the discount, the cost of the computer was $728. Determine the original price of the computer. Show your work.Calculate how much money Mason saved by using the coupon. Show your work.
The original price is $1049 and the amount saved is $321
How to determine the original price?From the question, we have the following parameters that can be used in our computation:
Cost after discount = $728
Discount = 30% off
The original price is calculated as
Cost after discount = Original price * (1 - Discount)
So, we have
Original price = Cost after discount/(1 - Discount)
This gives
Original price = 728/(1 - 30%)
Evaluate
Original price = 1049
The amount savedHere, we have
Amount saved = Original price - Cost after discount
So, we have
Amount saved = 1049 - 728
Evaluate
Amount saved = 321
Hence, the amount saved is $321
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8 identically sized pieces of timber are x cm long when put together .how long is each individual piece
The length of each individual piece is x/8
How to determine the length of each piece?From the question, we have the following parameters that can be used in our computation:
Number of pieces = 8
Length of timber put together = x
The length of each piece of timber is calculated as
The length of each piece = Length of timber put together/Number of pieces
Substitute the known values in the above equation, so, we have the following representation
The length of each piece = x/8
Hence, the length of each piece is x/8
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Function f is a linear function and function g is defined by g(x)=f(x)+k t . If the value of k is 7 , how does the graph of g compare with the graph of P?
The graph of g is the graph of f
Choose...
translated up 7 units translated left 7 units translated right 7 units translated down 7 units stretched vertically by a scale factor of 7 stretched horizontally by a scale factor of 7
The graph of g is the graph of f translated up 7 units
How to determine the equation of the graph of the function g(x)?From the question, we have the following parameters that can be used in our computation:
g(x) = f(x) + k
Also, we have the value of k to be
k = 7
From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units
This means that
g(x) = f(x) + k
So, we have
g(x) = f(x) + 7
Hence, the transformation is (a) translated up 7 units
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Jolie is buying a shirt and a hat at the mall. The shirt costs $34.67, and the hat costs $19.48. If she gave the sales clerk $100.00, how much change should she receive?
Answer:
Jolie will get 45.85 change
Step-by-step explanation:
34.67+19.48=54.48
100.00-54.15=45.85
6. Calculate the number that you need to add to each side of the equation w 2– 3w = 350 to create a perfect square trinomial. Add this number to each side of the equation. Show your work. (3 points)
7. Factor the trinomial. (3 points)
The number that we need to add is 1.5^2 = 2.25, we will get the perfect square trinomial:
(w - 1.5)^2 = 352.25
How to complete squares here?Remember that a perfect square trinomial is:
(a - b)^2 = a^2 - 2ab + b^2
Here we have the quadratic equation:
w^2 - 3w = 350
We can rewrite this as:
w^2 - 2*1.5*w = 350
Then what we need to add and subtract is 1.5^2, then we will get:
w^2 - 2*1.5*w = 350
w^2 - 2*1.5*w + 1.5^2 - 1,5^2 = 350
Grouping the first 3 terms we will get:
(w - 1.5)^2 - 1.5^2 = 350
(w - 1.5)^2 = 350 + 1.5^2
(w - 1.5)^2 = 352.25
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The farm's owner wants to increase the income from the sale of strawberries to at least $70,000 per year. What change would you suggest that would allow the farm's owner to meet this goal?
Answer:
Possible changes —
(i) Increase farmland
(ii) Sow healthy strawberry seeds
(iii) Choose a nutrient-rich, suitable plot of land
7. Sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants
she packed. The total number of pairs of pants and shirts was 16.
A. Let x = the number of pants she packed and let y = the number of shirts she packed. Write a system of
equations to represent the problem.
B. Solve the system of equations using substitution to find the number of shirts and pairs of pants Sylvia
brought.
The system of equations is x + y = 16 and y = 2x - 2
The number of shirts and pairs of pants Sylvia brought are 10 and 6, respectively
How to determine the system of equations?From the question, we have the following parameters that can be used in our computation:
x = the number of pants she packed y = the number of shirts she packedWhen the statements are interpreted, we have the system of equations to be
x + y = 16
y = 2x - 2
The solution of the equationIn (a), we have
x + y = 16
y = 2x - 2
This gives
x + 2x - 2 = 16
Evaluate the like terms
3x = 18
Divide
x = 6
Recall that
y = 2x - 2
So, we have
y = 2 x 6 - 2
y = 10
Hence, the number of shirts she packed is 10
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Which solids have more than five planes of symmetry? Check all that apply. cylinders cubes rectangular prisms square pyramids cones regular triangular prisms
Sphere, right cylinder and cube have more than five planes of symmetry.
Define symmetry.Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. A symmetrical likeness between two halves of an object, when one half is the mirror image of the other, is defined as being proportionate and balanced. As an illustration, many shapes such as square, rectangle, and circle are symmetric along their respective lines of symmetry.
Given,
Sphere and right cylinder have more than five planes of symmetry.
The number of symmetry planes depends on each solid by definition (a figure of three dimensions). The solid is split into two congruent, mirror-imaged parts by the plane of symmetry.
A cube has nine planes of symmetry, a square pyramid has four, hexagonal prims have thirteen, and spheres and cylinders have an infinite number of planes of symmetry, according to the information presented above.
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Answer nah the correct answer is cylinders cubes and cones
Step-by-step explanation:
seen it irl on edgennuitiy
Convert loo percent to a decimal
Natalie takes a car to a title loan business to borrow some money. Natalie is given $3,200.00. She must pay back the $3,200.00 in addition to a $1,000.00 fee in 4 months.
What simple interest rate is she being
charged?
Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.
Natalie is being charged a simply interest rate of ______.
Answer:
7.8125%
Step-by-step explanation:
(4200/3200-1)/4 the difference for every month
so this would result to 7.8125% every month
Answer:
Rate = (Percentage/Base)/Time
Rate =(1 000/3 200)/4
Rate = 0.3125/4
Rate = 0.078125 (convert to percent)
Rate = 7.9% (nearest tenth)
Therefore, Natalie will pay 7.9% interest per month
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Clare would like to buy a video game that costs at least $130. She has saved $48 so far and plans on saving $5 of her allowance each week. Write an inequality to find out the number of weeks it will take until she has enough money to buy the game.
Answer:
To determine how many weeks it will take Clare to save enough money to buy the video game, we need to find the number of weeks it will take for her to save at least $130. Let w be the number of weeks it will take for Clare to save enough money. We can set up the following inequality to represent this situation:
$48 + $5w >= $130
To solve this inequality, we can first add $48 to both sides to get rid of the constant on the left side:
$48 + $48 + $5w >= $130
This simplifies to $96 + $5w >= $130. Subtracting $96 from both sides gives us $5w >= $34. Dividing both sides by $5 gives us w >= 6.8. Since w represents the number of weeks, the solution must be a whole number. Therefore, Clare will need to save for at least 7 weeks in order to have enough money to buy the video game.
What is the missing number, what property did you use? –––=0×5
Answer:
0 is the answer
Step-by-step explanation:
0*5=0
0=0*5 ==> use Zero property of multiplication
This property states that any number multiplied by 0 equals 0.
A 2010 study of 240 randomly-selected residents of a subtropical resort city with 82,000 residents found that 5.4% of them had been exposed to the mosquito-borne virus that causes Dengue fever. Suppose the actual percentage of people in the city who have been exposed to the virus is 3%. Let p^= the proportion of residents who have been exposed in a random sample of 240.
The standard deviation of p^ is approximately...
The standard deviation of p^ is approximately 0.00012.
What do you mean by standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.
How to calculate standard deviation?The formula for standard deviation S.D is given below:
By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.
Calculation:
The formula for standard deviation S.D is given below:
Here,P = 3% = 0.03 and N = 240
∴ S.D = √0.03(1 - 0.03)/240
∴ S.D = 0.00012.
The standard deviation of p^ is approximately 0.00012.
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May I require assisstant?
Answer: the answer to a is 50% chance the answer to b is also 50% chance
Step-by-step explanation:
You are given the figure below as well as following. Explain how a and b are parallel. Explain giving measurements and angels. Angels should be part of your answer.
Answer:
Since angle 9 is 110 degrees, that means that angle 10 must be 70 degrees, because the angle is on a straight line, so the angles must add to be 180 degrees, because they are supplementary angles. Since p ll q (p is parallel to q), that means that angle 1 is 110 degrees and angle 2 is 70 degrees. Because angles 1, 2, 5, and 6 have to add to be 360 degrees and angles 1+2 equals 180 degrees, that means that 5+6 equals 180 degrees as well. Angle 6 equals 110 degrees so that means angle 5 is 70 degrees. On the other side, angle 8 is 70 degrees, and since the two angles are the same, p and q are the same.
part 1: 2 airplanes left the same airport at the same time. One is traveling at 422 mph straight east, the other is traveling 384 mph straight west.
How long will it take before they are 6045 miles apart?
part 2: 2 airplanes left the same airport at the same time. One is traveling at 422 mph straight NORTH, the other is traveling 384 mph straight WEST.
How long will it take before they are 1997 miles apart?
The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
2 planes left a similar air terminal simultaneously. One is going at 422 mph straight east, the other is voyaging 384 mph straight west.
If the distance between them is 6045 miles. Then the time is calculated as,
T = 6045 / (384 + 422)
T = 6045 / 806
T = 7.5 hours
2 planes left a similar air terminal simultaneously. One is going at 422 mph straight NORTH, the other is voyaging 384 mph straight WEST.
If the distance between them is 1997 miles. Then the time is calculated as,
T = 1997 / (384 + 422)
T = 1997 / 806
T = 2.48 hours
The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.
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a histogram showing u.s. household income is highly skewed right. which of following statistics would best describe the center of the distribution? question 10 options: 1) median 2) variance 3) mean 4) mode
......,,........,.....-.......
The median would best describe the centre of the distribution for a highly skewed right histogram of US household income. The correct option is A.
What is the median?The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.
Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.
The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.
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it is expected that 35% of students in a math course offered at northern university will earn an a. using excel to approximate the binomial distribution with a normal distribution, find the probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn an a.
The probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn is 0.9998..
We have given that,
A data of students in a math course offered at northern university will earn .
Total number of randomly selected students enrolled in the course = 300
i.e total number of trials, n = 300
probability of success, p = 35% = 0.35
probability of failure, q = 1-0.35 = 0.65
np = 300× 0.35 =
n(1-p) = 300×0.65 =
both np and n(1-p) are greater than 10 , so we can use normal approximation here.
We have to calculate probability that more than 75 of them will earn an , P(X>75). Using Binomial Probability distribution, X~ Bin(300, 0.35)
P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾
Now, P(X>75) = 1 - P(X=<75)
but here data is large, that is n= 300, x = 75 so tough to calculate it by hands , thus we use Excel function to find out the required probability. Excel Command: =BINOM.DIST(number_s,trials,probability_s,cumulative)
where, Number_s (required argument) -->the number of successes in trials,i.e "x" Trials (required argument) --> the number of independent trials i.e , "n" must 0≤ n. Probability_s (required argument) --> the probability of success in each trial.
Cumulative (required argument)-->A logical value that determines the form of the function. It can either be: TRUE--> Uses the cumulative distribution function and FALSE--> Uses the probability mass function. Now, for P(X ≤ 75) , the function is look like as
=BINOM.DIST(75,300, 0.35, TRUE) =0.000126081
=BINOM.DIST(75,300, 0.35, FALSE)
= 5.0305E-05
Now, the required probability, P(X> 75)
= 1 - P(X ≤75)
= 1 - 5.03095E-05 = 0.999949691
or using cumulative distribution function,
P(X>75) = 0.999873919
both are give approx. same results
.So, required probability is 0.9998.
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Belinda is thinking about buying a house for $286,000. The table below shows the projected value of two different houses for three years:
Number of years 1 2 3
House 1 (value in dollars) 294,580 303,417.40 312,519.92
House 2 (value in dollars) 295,000 304,000 313,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer.
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years.
Part C: Belinda wants to purchase a house that would have the greatest value in 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years.
a) The type of function for each case is given as follows:
House 1: Exponential.House 2: Linear.b) The functions for each house are given as follows:
House 1: 294580(1.03)^x.House 2: 295000 + 9000x.c) The value of each house after 25 years is given as follows:
House 1: $616,785.10.House 2: $520,000.There is a significant difference in these valuations, as an exponential function increases faster than a linear function.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
Hence House 1 is an exponential function, as:
312519.92/303417.40 = 303417.40/294580 = 1.03.
And the definition is given as follows:
294580(1.03)^x.
The value of the house after 25 years is given as follows:
294580(1.03)^25 = $616,785.10.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
Hence House 2 is a linear function, as each year, the value of the house is increased by 9000.
Then the definition is given as follows;
295000 + 9000x.
The value of the house after 25 years is given as follows:
295000 + 9000(25) = $520,000.
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A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 5 child bikes and 15 adult bikes in a week? (1 point)
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
The company can build 5 child bikes and 15 adult bikes in a week.
The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".
Linear Equations:Linear Equations are mathematical statements, which can be used to find an unknown quantity or any value in a given problem. Here we use variables like x, y .. etc. to represent unknown values.
Here we will use Linear Equations to solve the equations.
Here we have
One child bike requires 4 hours to build and 4 hours to test
Number of hours to build 'c' number of child bikes = 4c
Number of hours to test 'c' number of child bikes = 4c
One adult bike requires 6 hours to build and 4 hours to test.
Number of hours to build 'a' number of adult bikes = 6a
Number of hours to test 'a' number of adult bikes = 4a
Number of hours taken to build bikes in one week = 120
=> 4c + 6a ≤ 120 --- (1)
Number of hours taken to test the bikes in one week = 100
=> 4c + 4a ≤ 100 --- (2)
Assume that
The company can build 5 child bikes and 15 adult bikes in a week
Substitute c = 5 and a = 15 in (1) and (2)
(1) => 4(5) + 6(15) ≤ 120
=> 110 ≤ 120 [ which can be true ]
(2) => 4(5) + 4(15) ≤ 100
=> 80 ≤ 100 [ which can be true ]
From the above calculations,
Both (1) and (2) are satisfied
Therefore,
The company can build 5 child bikes and 15 adult bikes in a week.
The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".
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