The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
What is multiplication ?
Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.
To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.
The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:
10 years x 12 months/year x 1,000 units/month = 120,000 units
The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:
$50,000 ÷ 120,000 units = $0.4167 per unit
Rounding this to the nearest penny gives us the final answer of:
$0.42 per unit (option a)
Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
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What is the ratio of the smaller circle's area to the larger circle's area?
The ratio between the areas is 4, which means that the area of the large circle is 4 times the area of the other one.
What is the ratio between the areas of the circles?Remember that for a circle of radius R, the area is given by:
A = 3.14*R²
Here we can see that the diameter of the smaller circle is equal to the radius of the larger circle, then if R is the radius of the larger circle, the radius of the smaller one is R/2.
Then the area of the smaller circle is:
a = 3.14*(R/2)² = (1/4)*3.14*R²
The ratio between these two is:
A/a = 3.14*R²/( (1/4)*3.14*R²) = 4
That means that the area of the large circle is 4 times the area of the smaller one.
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Technetium-99m is used as a radioactive tracer for certain medical tests. It has a half-life of 1 day. Consider the function T where T (d) = 100(2)^-2 is the percent of Technetium-99m remaining d days after the tests. Write an expression that represents the number of days until only 5% remains.
The expression that represents the number of days until only 5% of Technetium-99m remains is approximately 3.79 days.
The given function [tex]T(d) =[/tex] [tex]100 \cdot 2^{-2d}$[/tex]represents the percent of Technetium-99m remaining d days after the test.
To find the number of days until only 5% remains, we need to solve the following equation:
[tex]$100 \cdot 2^{-2d} = 5$[/tex]
Dividing both sides by 100, we get:
[tex]$2^{-2d}$[/tex] [tex]= 0.05[/tex]
Taking the natural logarithm of both sides, we get:
[tex]$\ln{(2^{-2d})}$[/tex] = [tex]ln(0.05)[/tex]
Using the logarithmic identity log(base a)(bⁿ) = nlog(base a)(b), we can simplify the left side as:
[tex]-2d \cdot ln(2) = ln(0.05)[/tex]
Dividing both sides by -2 ln(2), we get:
[tex]d = ln(0.05) / (-2 \cdot ln(2))[/tex]
Using a calculator, we get:
[tex]d = 3.79[/tex]
Therefore, the expression that represents the number of days until only 5% of Technetium-99m remains is approximately 3.79 days.
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The sample space for tossing a coin 3 times is {hhh, hht, hth, htt, thh, tht, tth, ttt}. determine p(2 tails). a. 12.5% b. 37.5% c. 50% d. 75%
The probability of getting 2 tails is option (b) 37.5%
The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.
Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:
P(htt) = 1/2 × 1/2 × 1/2 = 1/8
P(tht) = 1/2 × 1/2 × 1/2 = 1/8
P(tth) = 1/2 × 1/2 × 1/2 = 1/8
So, the probability of getting 2 tails is:
P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8
= 0.375
0.375 multiplied by 100% gives:
P(2 tails) = 37.5%
Therefore, the correct option is (b) 37.5%
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What linear equation represents the graph of the line that coincides with the x axis?
Is it y = (x)0 PLEASE HELP
Answer:
Step-by-step explanation:
5
Answer:Option b. y = 0.
Step-by-step explanation:
Which three of these number add up to 180, 128 90 34 80 56
The three numbers which add up to 180 are 90, 34 and 56.
To find the sum of three numbers as 180, we simply add the three numbers together.
In this case, the numbers are given as 128, 90, 34, 80 and 56;
We see that the three numbers whose sum is 180 are 90, 34 and 56,
Let 90 represents one quantity, 34 represents another quantity, and 56 represents yet another quantity.
When we add these three quantities together, we get the total sum of all three quantities, which is 180.
Therefore, the numbers 90, 34 and 56 adds up to 180.
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The given question is incomplete, the complete question is
Which three of these number add up to 180? 128, 90, 34, 80, 56.
hi need help i eill give you many points like a lot help due soon
Answer:
E
Step-by-step explanation:
To solve this question we have to count which one of the options have five red square and which of the options have 7 blue squares.
By looking at the options we can see that E is the only one that matches the requirements!
We have to be careful that we are looking for 5 red squares and not 5 blue squares as our answer would be wrong.
We can find this out in the question, we see that in the question it says red and blue defining that red goes first. This is why we consider red to be 5 and blue to be 7
Hope this helps, have a lovely day! :)
A store buys paper at $15 per bundle. It then sells the bundles at a price that includes a 40% markup. The store offers a discount of To off the price of each
bundle if two or more bundles are purchased. What is the price to purchase 3 bundles of paper?
A store buys paper at $15 per bundle. It then sells the bundles at a price that includes a 40% markup. The store offers a discount of To off the price of each bundle if two or more bundles are purchased. The price to purchase 3 bundles of paper is $51
$15 x 3 bundles = $45 + 40% markup = $63 - 20% discount = $51.
In short, a purchase price is the economic value, usually defined in fiat currency at a given point in time, for which a buyer purchases a product, service, or asset. The compensation paid for this value can be fiat currency or other, such as services as payment or benefits in kind.the amount of money someone pays for something .The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.
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Jack interpreted the mean of the given data set, 7.96, as meaning half the cats weighed less than 7.96 pounds and half weighed more What was Jack's error? Explain
Click the icon to view the dot plot
Select the correct choice below, and fill in the answer box to complete your choice
(Type an integer or a decimal)
OA. Jack interpreted the mean as the range. Half the cats weighed less than
OB. Jack incorrectly calculated the mean. Half the cats weighed less than
OC. Jack interpreted the mean as the median. Half the cats weighed less than
OD. Jack interpreted the mean as the mode. Half the cats weighed less than
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pounds and half weighed more.
pounds and half weghed more
pounds and half weighed more
pounds and half weighed more
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I NEED AN ANSWER FAST
Based on the given options, the correct answer is: OC. Jack interpreted the mean as the median. Half the cats weighed less than 7.96 pounds and half weighed more.
The mean is a measure of central tendency that represents the average of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.
In this case, Jack interpreted the mean of 7.96 as meaning that half the cats weighed less than 7.96 pounds and half weighed more. However, this is incorrect because the mean does not necessarily divide the data set into two equal halves.
The median, on the other hand, is the middle value in a sorted list of numbers. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.
If Jack had interpreted the median as meaning half the cats weighed less than its value and half weighed more, he would have been correct. However, he incorrectly interpreted the mean as the median.
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The sum of 2 numbers is
99. The difference of the two numbers is
51. What are the two numbers
Answer:
75, 24
Step-by-step explanation:
Answer: 75, 24
Step-by-step explanation:
Let the two numbers be x and y. Then,
1. x+y=99
2. x-y=51
If you add these two equations together, you get:
2x=150
x=75
Plug in x.
75+y=99
y=24
K Write the inequality represented by each graph, using the variable x. b. 50 51 52 53 54 ← 10 11 H 55 56 57 58 59 ++ 12 13 14 15 16 17 18 19
The inequality represented by the graph is 10 ≤ x ≤ 20.
What is inequality?Inequality is the unequal distribution of resources or opportunities among individuals or groups in a society. It can be measured in multiple ways, including income, wealth, access to education, health care, and political power. It is a major social problem, as it can lead to poverty, lack of opportunity, and even violence. The root causes of inequality are complex, but can include discrimination, unequal access to resources, and social and cultural norms. In order to address inequality, governments must create policies that provide access to resources for all individuals, regardless of their social, economic, or other backgrounds. Additionally, it is important to recognize that the effects of inequality are not limited to one group of people – everyone is affected by it in some way.
The graph shows that x must be a number between 10 and 20 (inclusive). This means that the value of x must be at least 10, but it cannot be greater than 20. This is because the graph shows that the values of x between 50 and 59 are not included in the range.
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Which is the solution set of the compound inequality 3.5x-10>-3 and 8x-9 <39?
-2
-2
2
2
Answer:
OPTION C: 2 < x < 6
Step-by-step explanation:
3.5x - 10 > -3
Adding 10 to both sides:
3.5x > 7
Dividing by 3.5:
x > 2
8x - 9 < 39
Adding 9 to both sides:
8x < 48
Dividing by 8:
x < 6
Therefore, the solution set of the compound inequality is:
2 < x < 6
XY=8 and YZ=4 find XZ
If XY = 8 and YZ = 4, the length οf XZ is 4√5 cm.
What is the Pythagοrean theοrem?The Pythagοrean theοrem states that in a right-angled triangle, the square οf the length οf the hypοtenuse (c) is equal tο the sum οf the squares οf the lengths οf the οther twο sides (a and b) c² = a² + b².
We can use the Pythagοrean theοrem tο find the length οf the hypοtenuse XZ οf the right-angled triangle XYZ.
In this case, X is the right angle, sο XY is the adjacent side and XZ is the hypοtenuse. YZ is οn the οppοsite side. We are given that XY = 8cm and YZ = 4cm.
So, we have:
XZ² = XY² + YZ²
XZ² = 8² + 4²
XZ² = 64 + 16
XZ² = 80
Taking the square root of both sides, we get:
XZ = √80 = √(16 × 5) = √16 × √5 = 4√5
Therefore, the length of XZ is 4√5 cm.
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Complete question:
If XY=8 and YZ=4 find the length XZ
How many sides does a regular polygon have if each interior angle measures 156°?
The answer is 15 sides
Two pipes can fill a tank in 12 minutes & 15 minutes respectively. If first pipe is changed with a pipe having twice of its radius while second with a pipe having half of second’s radius. Now the tank will be filled in:
The tank will be filled in 6 minutes with the new pipes.
How to calculate how long it will take the tank to be filledLet the capacity of the tank be C.
Then the rate at which the first pipe can fill the tank is C/12 per minute, and the rate at which the second pipe can fill the tank is C/15 per minute.
If the first pipe is changed with a pipe having twice of its radius, then the rate at which the new pipe can fill the tank is (2C)/12 = C/6 per minute.
If the second pipe is changed with a pipe having half of second’s radius, then the rate at which the new pipe can fill the tank is (1/2)C/15 = C/30 per minute.
Let t be the number of minutes it takes to fill the tank with the new pipes. Then we have:
(C/6 + C/30)t = C
Simplifying this equation, we get:
5Ct/30 = C
Multiplying both sides by 30/5C, we get:
t = 6 minutes
Therefore, the tank will be filled in 6 minutes with the new pipes.
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A physics class has 40 students. Of these,15 students are physics majors and 18students are female. Of the physics majors, are female. Find the probability that a randomly selected student is female or a physics major
The probability that a randomly selected student is either female or a physics major is 27/40 or approximately 0.675.
To find the probability that a randomly selected student is either female or a physics major, we need to add the probability of selecting a female student to the probability of selecting a physics major, but subtract the probability of selecting a student who is both female and a physics major to avoid double-counting.
Let F be the event of selecting a female student, and M be the event of selecting a physics major. We are given that:
P(M) = 15/40 (15 students out of 40 are physics majors)
P(F) = 18/40 (18 students out of 40 are female)
P(F ∩ M) = 6/40 (6 students out of 40 are both female and physics majors)
To find the probability of selecting a student who is either female or a physics major, we use the formula:
P(F ∪ M) = P(F) + P(M) - P(F ∩ M)
Substituting the given probabilities, we get:
P(F ∪ M) = 18/40 + 15/40 - 6/40
Simplifying, we get:
P(F ∪ M) = 27/40
Therefore, the probability that a randomly selected student is either female or a physics major is 27/40 or approximately 0.675.
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Ali takes a full-time position as a makeup artist in Atlanta. Her starting salary is $29,000. Her taxes are 28%. What is her net monthly income?
b. $3,840
c. $2,088
d. $1,740
The correct answer is (c) Ali has a monthly net income of $2,088 after paying 28% in taxes.
.
To calculate Ali's net monthly income, we first need to find out the amount of tax she pays, and then we can subtract it from her annual income to get her net annual income. We'll then divide it by 12 to get her monthly net income.
Calculations: Ali's tax rate is 28%. 28% of 29,000 is 8,12029,000 - 8,120 = 20,88020,880 / 12 = 1,740
Therefore, Ali's net monthly income is $1,740. The correct answer is option D, $1,740. ($29,000 salary x 28% taxes = $8,120 in taxes annually; $8,120 / 12 months = $677 in taxes per month; $29,000 - $677 = $2,088 net monthly income).
Net income refers to the amount of money that a company or an individual has earned after deducting all the expenses and taxes from their gross income. In the context of a company, net income is also called profit, and it is an important measure of a company's financial performance.
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A survey is given to students about the servings of friuts and vegetables that each student typically eats in a day. The students in the survey represent a popultion of 200
In this scenario, a survey is being conducted to gather information about the fruit and vegetable consumption habits of a population of 200 students. The survey will help to determine the typical servings of fruits and vegetables that students consume in a day.
To ensure that the survey results are accurate and representative of the population, a random sample of students should be selected for the survey. This means that each student in the population has an equal chance of being selected for the survey. The sample size should also be large enough to ensure that the survey results are statistically significant and reliable.
Once the survey has been conducted and the data has been collected, it can be analyzed to determine the average servings of fruits and vegetables that students in the population typically consume in a day. This information can then be used to develop strategies for promoting healthy eating habits among students.
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Daniel earns $18. 50 an hour, with time-and-a-half for hours worked over 37 a week. His clock hours for a week are 9. 5, 8. 5, 10, 10, and 10. 75. How much is his weekly
To calculate Daniel's weekly pay, add his regular pay and overtime pay: Weekly pay = $1038.31.
To calculate Daniel's weekly pay, we need to determine his regular hours and his overtime hours.
Regular hours = 37 hours
Overtime hours = Total hours worked - Regular hours
Total hours worked = 9.5 + 8.5 + 10 + 10 + 10.75 = 49.75 hours
Overtime hours = 49.75 - 37 = 12.75 hours
Daniel's regular pay for 37 hours is:
$18.50/hour x 37 hours = $684.50
Daniel's overtime pay for 12.75 hours is:
$18.50/hour x 1.5 = $27.75/hour (time-and-a-half rate)
$27.75/hour x 12.75 hours = $353.81
Therefore, Daniel's weekly pay is the sum of his regular pay and overtime pay:
Weekly pay = $684.50 + $353.81 = $1038.31
Therefore, Daniel's weekly pay is $1038.31.
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Complete question:
Daniel earns $18.50 an hour, with time-and-a-half for hours worked over 37 a week. His clock hours for a week are 9. 5, 8. 5, 10, 10, and 10.75. How much is his weekly pay?
A circle has a circumference of 452.16What is the radius of the circle?
Answer:this is the answer
Step-by-step explanation:
Please solve this Question!!
I'll give u Brainliest:)
The angle AOB will be a right angle if x = 27.5
What value of x will make AOB a right angle?
AOB will be a right angle if the angle AOB is 90°, then we can write the linear equation:
2x + 30 + 2x - 50 = 90
These are the two measures that conform AOB.
Solving that linear equation we will get:
2x + 30 + 2x -50 = 90
4x - 20 = 90
4x = 90 + 20 = 110
x = 110/4 = 27.5
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suppose that all conditions are met. compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer. group of answer choices (0.341, 0.559) (0.45, 0.5) (0.394, 0.506) (0.4, 0.45)
None of above options are correct.
To compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer:
Follow these steps:
STEP 1: Determine the sample proportion (p) and sample size (n).
STEP 2:Calculate the standard error (SE) using the formula
SE = √(p(1-p)/n).
STEP 3: Determine the critical value (z) for a 95% confidence level
(1.96 for a two-tailed test).
STEP 4: Calculate the margin of error (ME) using the formula
ME = z * SE.
STEP 5: Find the confidence interval by adding and subtracting the margin of error from the sample proportion:
CI = (p - ME, p + ME).
Unfortunately, without the sample proportion (p) and sample size (n), it's not possible to compute the confidence interval.
However, once you have these values, you can follow the steps above to find the 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer.
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Eric had only red pens and Kai had only blue pens. There were thrice as many red pens as blue pens. Then Eric gave 2/5 of his red pens to Kai, while Ka gave 1/2 of his blue pens to Eric.
(a) What fraction of Kai's pens were blue after that?
(b) For them to have equal nurber of pens in the end, Eric had to give Kai 7 blue pens and 8 red pens in another round of transfer.
How many pens did Eric have in the beginning?
(a) Let in the beginning Eric had 3x red pens and Kai had x blue pens
2/5 * 3x = 6x/5
Eric gave 6x/5 red pens to Kai.
Now Eric has 3x - 6x/5 = 9x/5 red pens.
Kai gave x/2 blue pens to Eric
Now Eric has a 9x/5 + x/2 = (18x + 5x)/10 = 23x/10
Now Kai has x - x/2 = x/2 blue pens.
Now Kai has total x/2 + 6x/5 = 17x/10 pens.
required fraction = (x/2)/(17x/10) = x/2 * 10/17x = 5/17
5/17 is the answer.
(b) After another round of transfer Eric has total 23x/10 - 15 pens and Kai has total 17x/10 + 15 pens.
23x/10 - 15 = 17x/10 + 15
(23x - 150)/10 = (17x + 150)/10
23x - 150 = 17x + 150
6x = 300
3x = 150
Eric had 150 pens in the beginning.
Helpppppppp!!!!! Pleaseeeeeeeee!!!! I need an answer help
Answer:
39
Step-by-step explanation:
[tex]sin(x)=\frac{10}{16}\\ x=sin^{-1} (\frac{10}{16})\\ x=38.682....\\x=39[/tex]
Rewrite cos 4x I'm terms of cos x.
Answer: Using the multiple angle formula for cosine, we have:
cos 4x = 2cos^2 2x - 1
Now we need to rewrite cos 2x in terms of cos x. Again, using the multiple angle formula for cosine, we have:
cos 2x = 2cos^2 x - 1
Substituting this expression into the previous equation, we get:
cos 4x = 2(cos^2 x)^2 - 1
Simplifying the expression further, we have:
cos 4x = 2(cos^4 x) - 1
Therefore, cos 4x can be written in terms of cos x as 2(cos^4 x) - 1.
Step-by-step explanation:
A. Jace collected data on the distances electric vehicles can travel on one charge. He wants to show the average distance and the range an electric vehicle can travel on one charge.
Choose and make an appropriate display of the data
b. Jace wants to compare the range and shape of his electric-vehicle data to related data he collected on gas-powered vehicles. Choose and make appropriate data displays
A box-and-whisker plot is the appropriate data display for Jace's electric-vehicle data and gas-powered vehicle data, and it will give him a visual representation of the difference between the two datasets.
The appropriate data displays for Jace's electric-vehicle data and gas-powered vehicle data would be a box-and-whisker plot. This type of plot is a graphical representation of the five-number summary of a dataset. The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. It can be calculated using the following formulas:
Minimum = smallest value
Q1 = 25th percentile (the value below which 25% of the data lies)
Median = 50th percentile (the value below which 50% of the data lies)
Q3 = 75th percentile (the value below which 75% of the data lies)
Maximum = largest value
Using these formulas, Jace can calculate the five-number summary for his electric-vehicle data and his gas-powered vehicle data. He can then use these values to create a box-and-whisker plot that compares the range and shape of each dataset. The box-and-whisker plot will give him a clear visual representation of the difference between the two datasets. By comparing the range and shape of the two datasets, Jace can get a better understanding of the difference between the electric-vehicle data and the gas-powered vehicle data. From there, he can draw conclusions about the differences between the two vehicle types.
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A store sells packages of comic books with a poster write a linear function in the form Y equals MX plus B that represents the cost Y of a package containing any number of comic books X suppose another store sells a similar package modeled by a linear function with one with initial value $7. 99 which store has a better deal explain one poster +6 comics $12. 75 or one poster and 13 comics $19. 75
The cost of a package containing x comic books and a poster is given by the equation y = 0.91x + 7.08.
Let's start by using the information given to form two equations. Let x be the number of comic books and let y be the cost of package.
From the first sentence, we can form the equation:
y = 7.99 + 2x
From the second sentence, we can form the equation:
y = 16.99 + 11x
Now we can use these equations to find the linear function rule that models the cost of a package containing any number of comic books.
First, we can set the two equations equal to each other since they both represent the cost of a package:
7.99 + 2x = 16.99 + 11x
Solving for x, we get:
9x = 9
x = 1
Now that we know that 1 comic book costs $4, we can substitute that value into either of the original equations to find the cost of a package with a poster and 1 comic book:
y = 7.99 + 2(1) = 9.99
So a package with a poster and 1 comic book costs $9.99.
Finally, we can use the slope of the line to find the linear function rule that models the cost of a package containing any number of comic books. We know that the slope is the change in y over the change in x, or:
m = (16.99 - 7.99)/(11 - 2) = 0.91
So the linear function rule is:
y = 0.91x + 7.08
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The given question is incomplete, the complete question is:
A store sells packages of comic books with a poster. A poster and 2 comics cost $7.99. A poster and 11 comics cost $16.99. Write a linear function rule that models the cost y of a package containing any number x of comic books.
A circle has a radius of 14 feet. Find the exact area in feet squared (meaning
leave your answer as pi)
Answer:
196pie
Step-by-step explanation:
Hi please help 100 points+brainliest ( it is supposed to be answered like an expenecial function )
1. The table shows the Total Expenses y (in dollars) of the College or University for year 2020-2021 and 2021-2022. Mine it's 21,211
a) Write a function that represents the Total Expenses y (in dollars) of that College or University you would like to attend after t years.
b) Use the function to estimate the Total Expenses your first year of school. *This year (t) is not the same for everyone since there are 8th graders to 11th graders in the class.
c) Sketch a graph (by hand) to model your function.
d) Identify the y-intercept and asymptotes of the graph. Find the domain and range of your function. Then describe the end behavior of the function.
Answer:
a) The Total Expenses y (in dollars) of the College or University for t years can be modeled by an exponential function of the form:
y = ab^t
Where "a" is the initial amount and "b" is the growth rate.
b) Using the given data, we can find the value of "a" by plugging in the first year's data into the equation:
y = ab^t
21211 = a * b^0
a = 21211
Thus, the function representing the Total Expenses y (in dollars) of the College or University after t years is:
y = 21211b^t
c) The graph of the exponential function will be an upward-sloping curve that starts at the point (0, 21211) and grows at a rate determined by the value of "b".
d) The y-intercept of the graph is (0, 21211), which represents the initial expense at the start of the first year. The function has no asymptotes. The domain of the function is all real numbers, while the range of the function is y > 21211. As t approaches infinity, the function grows without bound, which means the end behavior is that the expenses continue to increase exponentially over time.
I really need help with this equation can someone help??
Answer:
x = 11[tex]\sqrt{3}[/tex] , y = 33
Step-by-step explanation:
using the cosine and sine ratios in the right triangle and the exact values
cos60° = [tex]\frac{1}{2}[/tex] , sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{22\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 22[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 11[tex]\sqrt{3}[/tex]
and
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{22\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2y = 22[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 22 × 3 = 66 ( divide both sides by 2 )
y = 33
Jasper and corey have saved up a total of $78. 0. Jasper has saved 6 dollars more then twice as much as corey. How much has cory saved?
Corey has saved $24 and Jasper has saved $54.
Let x be the amount of money Corey has saved.
Then, we know that Jasper has saved $6 more than twice as much as Corey, which can be expressed as:
J = 2x + 6
We also know that the total amount saved by both Jasper and Corey is $78, so we can set up another equation:
J + x = 78
Now we can use these equations to solve for x, which will give us the amount of money Corey has saved:
J + x = 78 (substitute J = 2x + 6)
(2x + 6) + x = 78
3x + 6 = 78
3x = 72
x = 24
Therefore, Corey has saved $24.
To check this answer, we can substitute x = 24 into the equation we found for J:
J = 2x + 6
J = 2(24) + 6
J = 54
So Jasper has saved $54.
We can verify that $24 + $54 = $78, which matches the total amount saved by both Jasper and Corey.
In summary, Corey has saved $24 and Jasper has saved $54. It's important to remember to set up equations to represent the given information in a problem and to check our answers to make sure they are reasonable and match the given information.
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