Answers
Answer:
x = 2\(\sqrt{5} \)
Step-by-step explanation:
Okay first you need to find the side of the other triangle (the side that also is a hypotenuse for the other triangle).
So we can use pythagorean's theorum
\(a^{2} +b^{2} =c^{2} \) with c being the hypotenuse
\(a^{2} +2^{2} =7^{2} \)
a^2 + 4 = 49 subtract 4 from both sides
a^2 = 45 then do the sqaure root
a = \(\sqrt{45} \) which can be simplified to 3\(\sqrt{5} \)
so... 3\(\sqrt{5} \) or \(\sqrt{45} \) is our hypotenuse for the other triangle
\(5^{2} +b^{2} = \sqrt{45} ^{2} \)
25 + b^2 = 45 subtract 25 from both sides
b^2 = 20 then do the square root
b (or x in this problem) = \(\sqrt{20} \)
or when simplified, 2\(\sqrt{5} \)
Related Questions
Julianne is using a biking app that compares his position to a simulated bike or traveling Julianne’s target speed. When Julianne is behind the simulated biker he has a negative position. I took a screenshot of the problem I am having difficulty with.
Answers
Given
\(\begin{gathered} Speed=20\frac{km}{h} \\ Time\text{ }taken=15\text{ }minutes \\ Initial\text{ }distance=2\frac{1}{4}km \end{gathered}\)To find:
The average speed of Julian.
Explanation:
It is given that,
\(\begin{gathered} Speed=20\frac{km}{h} \\ Time\text{ }taken=15\text{ }minutes \\ Initial\text{ }distance=2\frac{1}{4}km \end{gathered}\)That implies,
\(\begin{gathered} Distance\text{ }traveled=Speed\times Time \\ =20\frac{km}{h}\times15minutes \\ =20\frac{km}{h}\times15(\frac{1}{60})h \\ =20\frac{km}{h}\times\frac{1}{4}h \\ =5km \end{gathered}\)Therefore,
\(\begin{gathered} Average\text{ }speed=\frac{Final\text{ }distance-Initial\text{ }distance}{Time\text{ }taken} \\ =\frac{(5-2\frac{1}{4})km}{\frac{1}{4}h} \\ =\frac{5-\frac{9}{4}}{\frac{1}{4}}\frac{km}{h} \\ =\frac{\frac{20-9}{4}}{\frac{1}{4}}\frac{km}{h} \\ =11\frac{km}{h} \end{gathered}\)Hence, the average speed of Jean is 11 km/h.
Philip is having a party and wants to spend less than $572. He has already spent $500. The only item left on his list is sodas, which cost $8 per case. How many cases of soda, x, can Philip purchase and stay under his budget? Select the number line that includes the largest number of cases of soda that Philip can purchase and still stay under his budget.
Answers
Answer:
x = 8
Step-by-step explanation:
572 - 500 = 72
72 / 8 = 9.
But in order to spend less than 572, he has to buy 8 cases. If he buys 9 cases he will be exactly 572.
Answer:
9 or fewer cases
Step-by-step explanation:
Solving a two step equation:
First, determine how much he has left to spend
572 - 500 = 72
He has 72 dollars left to spend on soda
Each case is 8 dollars.
Divide how much he has to spend by the cost of each case
72/8 = 9
He can buy up to 9 cases and stay under budget.
What is the mathematical expression for modified Reynolds Analogy, also known as Chilton-Colburn analogy?
Answers
The modified Reynolds analogy, also known as the Chilton-Colburn analogy, is expressed mathematically as Nu = f * Re^m * Pr^n. It relates the convective heat transfer coefficient (h) to the skin friction coefficient (Cf) in fluid flow. This equation is widely used in heat transfer analysis and design applications involving forced convection.
The modified Reynolds analogy is a useful tool in heat transfer analysis, especially for situations involving forced convection. It provides a correlation between the heat transfer and fluid flow characteristics. The Nusselt number (Nu) represents the ratio of convective heat transfer to conductive heat transfer, while the Reynolds number (Re) characterizes the flow regime. The Prandtl number (Pr) relates the momentum diffusivity to the thermal diffusivity of the fluid.
The equation incorporates the friction factor (f) to account for the energy dissipation due to fluid flow. The values of the constants m and n depend on the flow conditions and geometry, and they are determined experimentally or by empirical correlations. The modified Reynolds analogy is widely used in engineering calculations and design of heat exchangers, cooling systems, and other applications involving heat transfer in fluid flow.
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Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Jose's account has gone into overdraft. His balance is $-27.14. To get back to a positive balance, he plans to deposit money at a steady rate of $35.03 per week. How much will be in his account after 7 weeks?
Answers
Answer:
yo your dûmb asl
Step-by-step explanation:
Was the caste system a fair system based on religious beliefs or was it a social
structure that promoted inequality?
I really need help!!!
Answers
Imagine the speed limit on the highway is 65 miles per hour. What are some speeds at which you could drive without going over the speed limit?
Answers
As long as Speed < 65mph, you’re safe
0 < Speed > 65 miles per hour
Math:
-x + 6 is greater than or equal to 10
Answers
Answer:
It is actually less than 10.
Step-by-step explanation:
2. Find the solution set to this inequality: 2x - 3>
2x - 5/2
A. \(x
B.x >1/2
C. x <_ 1 / 2
D.x>_2
Answers
think of an event that might occur at three different speeds and describe it.
Answers
Answer:
tornado!
Step-by-step explanation:
sometimes tornados can start off slow and sometimes they can go really fast.
there are 2 senators from each of tahe 50 states. we wish to make a 3 senator committe in which no two how many ways can ewe choose a senator from a chosen state
Answers
There are 3 ways to select a senator from a state if you wish to make a 3-senator committee in which no two senators are from the same state.
There are two senators from each of the 50 states, we wish to create a committee of three senators so that no two senators are from the same state.
Therefore, there are three different ways to choose a senator from a particular state, because we have to pick one out of two senators to ensure that no two senators are from the same state.For example, if we choose a senator from the state of New York, we can pick 1 senator from New York and then select 2 senators from the remaining 98 senators, giving us 298 ways to pick 2 senators.Therefore, the total number of ways to choose a 3-senator committee is: 2 C 98 + 3 = 2,941 ways.
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To calculate the _____ line of a control chart you compute the average of the mean for every period.
Answers
To calculate the center line of a control chart, you compute the average of the mean for every period.
A control chart is a graphical representation of a process's performance over time. It is utilized to determine whether a process is in control (i.e., consistent and predictable) or out of control (i.e., unstable and unpredictable).
The center line is used to represent the procedure average on a control chart. When the procedure is in control, the center line is the process's average. When the process is out of control, it can be utilized to assist in identifying where the out-of-control signal began.
The control chart is a valuable quality control tool because it helps detect process variability, identify the source of variability, and determine if process modifications have improved process quality. Additionally, the chart can serve as a visual guide, alerting employees to process variations and assisting them in responding appropriately.
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Write the mathematical model and use Solver to answer the following question:
A farm co-op has 6,000 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1hour of labor to harvest. The co-op has available at most 40,501 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the maximum profit if the profits per acre are $75 for corn and $40 for soybeans. Round your answer to the nearest cent if necessary.
a. $210,000.00
b. $393,750.00
c. $371,255.83
d. $180,004.44
e. $318,744.17
Answers
The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.
To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.
Let x be the number of acres of corn and y be the number of acres of soybeans.
1. Total acre constraint: x + y ≤ 6,000
2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501
3. Labor constraint: 0.75x + y ≤ 5,250
The objective function to maximize is the profit function: P(x,y) = 75x + 40y
Now, we will use the Solver to find the maximum profit:
Step 1: Set up a spreadsheet with the constraints and the objective function.
Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.
Step 3: Set the objective function by selecting the cell with the profit function.
Step 4: Choose "Max" for the objective.
Step 5: Add the constraints by selecting the corresponding cells.
Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.
After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83
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10. What should be the order of the polynomial coefficients if
(3x - 4x3 + 6x4 + 1) / (x + 3)
a) 3 0 4 6 1
b) 6 4 3 1 0
C) 6 4 0 3 1
d) -6 4 0 -3 -1
Answers
Answer:
6 -4 0 3 1
Step-by-step explanation:
Decide which of the following are true statements. Provide a short justification for those that are valid and a counterexample for those that are not:
(a) Two real numbers satisfy a0 . (b) Two real numbers satisfy a0 . (c) Two real numbers satisfy a≤b if and only if a0 .
Answers
All the three statements given in the question are valid.
(a) Two real numbers satisfy a^2 < b^2 if and only if |a| < |b|. This is a valid statement, and the justification follows from the fact that the square of any real number is non-negative, i.e., a^2 ≥ 0 and b^2 ≥ 0, and if a^2 < b^2, then taking square roots of both sides yields |a| < |b|.
(b) Two real numbers satisfy a^2 > b^2 if and only if |a| > |b|. This is also a valid statement, and the justification follows from the fact that the square of any non-zero real number is positive, i.e., a^2 > 0 and b^2 > 0, and if a^2 > b^2, then taking square roots of both sides yields |a| > |b|.
(c) Two real numbers satisfy if and only if |a| ≤ |b|. This statement is also valid, and the justification follows from the fact that the square of any real number is non-negative, i.e., a^2 ≥ 0 and b^2 ≥ 0, and if a^2 ≤ b^2, then taking square roots of both sides yields |a| ≤ |b|.
Therefore, all three statements are valid.
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find the perimeter of the shaded figure.
Answers
Answer:
38
Step-by-step explanation:
Count the unit squares for each side, starting from the left it's 7, 10, 7, 2, 2, 6, 2, and 2
Now add them together:
7 + 10 + 7 + 2 + 2 + 6 + 2 + 2 = 17 + 9 + 8 + 4 = 26 + 12 = 38
Answer: 38 units
Step-by-step explanation: Perimeter is asking for the total length of all the sides that make up a figure. The top border is 10 units, the two outer sides are 7 each (14 in total), if you add all the downward facing edges you get another 10 units, and the two inside sides are 2 units each (4 in total).
10+14+10+4 = 38
help will give brainliest asap
Answers
Answer: m<CGE = 74˚
Step-by-step explanation:
<CGE is congruent to <AGF by the Vertical Angles Theorem. therefore, m<CGE equals 74˚
Answer:
m<CGE=74º
Step-by-step explanation:
since it bisects then FGD is 74º
and angles across form each other are congrunent
5) A warehouse outside of a factory currently has an inventory of 1245 boxes. After an 8-
hour work day, the warehouse has 2000 boxes. Assume the warehouse was being filled at a
constant (linear) rate.
a) How many boxes per hour is the factory able to provide to the warehouse?
b) What would be the inventory at the end of a 40-hour work week?
c) How long will it take to fill the warehouse to its 50,000 box capacity?
6) In the year 2007, a FOREVER stamp cost cost $0.41. In 2023, the cost of a FOREVER
stamp was $0.63. Assume that the cost of stamps increased at a constant (linear) rate.
a) If price increases continue at the current rate, how much will a FOREVER stamp
cost in 2035?
b) In what year would you expect a FOREVER stamp to cost one dollar?
7) In January of 2021, there were 980,000 games available on the Apple App Store. By July
of 2021, there were 984,200 games available. If we assume that the number of available
games is steadily increasing at a constant (linear) rate,
a) How many games does this pattern predict will be available in January 2022?
b) At this rate, when will there be 1,000,000 games available for purchase in the Apple
App Store?
Answers
Thee factory is able to provide 94.38 boxes per hour to the warehouse.
How to calculate the valueRate = (2000 - 1245) / 8 = 94.38 boxes per hour
Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.
Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2
Therefore, the inventory at the end of a 40-hour work week would be:
1245 + 3775.2 = 5020.2 boxes
rate = (50000 - 1245) / time
Simplifying this equation, we get:
time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).
Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,
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uppose , i.e. has a t-distribution with 10 degrees of freedom. What proportion of this t-distribution falls within and
Answers
95% of the t-distribution with 10 degrees of freedom falls within the interval from -2.228 to 2.228.
To answer this question, we need to use the t-distribution table or a statistical software that can calculate t-distribution probabilities.
Assuming you meant to specify the interval between -2.228 and 2.228, which is the 95% confidence interval for a two-tailed test with 10 degrees of freedom, we can use the t-distribution table to find the proportion of the t-distribution that falls within this interval. Alternatively, we can use a statistical software to calculate this proportion directly.
Using the t-distribution table, we can find the cumulative probability for t = -2.228 and t = 2.228 with 10 degrees of freedom. The cumulative probability for t = -2.228 is 0.025, and the cumulative probability for t = 2.228 is 0.975. Therefore, the proportion of the t-distribution that falls within the interval from -2.228 to 2.228 is:
0.975 - 0.025 = 0.95
This means that 95% of the t-distribution with 10 degrees of freedom falls within the interval from -2.228 to 2.228.
Alternatively, we can use a statistical software, such as R or Python, to calculate the same probability. For example, in R, we can use the pt() function to calculate the cumulative probability for a given t-value and degrees of freedom. The code would look like:
pt(2.228, df = 10) - pt(-2.228, df = 10)
This would give us the same result of 0.95.
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howard collected data from a random sample of 600 people in his town asking whether or not they attend church. based on the results, he reports that 48% of the people in his state attend church. why is this statistic misleading?
Answers
This statistic is misleading because Howard surveys only his department and not members of all the departments that the company has.
When studying anything from a population, it is usual practice in statistics to identify a sample of that group.
However, the sample has to be representative.
For example: I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, let's say, 1000 randomly selected Buffalo residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. This is not representative of all New York State residents, just Buffalo residents.
Howard wants to know the proportion of employees of a company who use the company's healthcare. He asks only his department. However, a company as multiple departments, which leads to the statistics found in Howard's survey being misleading.
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Michelle has made 18 note cards for her friends. She plans to send out a total of sixty cards. What percentage of the cards has she finished?
Answers
Answer:
30%
Step-by-step explanation:
Since she has made 18 of the total 60 cards, you divide 18 by 60.
18/60 = 0.30
To convert a decimal to a percentage, you multiply it by 100.
0.30 x 100 = 30%
4x - 9y = 1
2x + y = -5
Answers
Answer:
y=1
x=5/2
Step-by-step explanation:
4x-9y=1
(2x+y=-5)-2
4x-9y=1
-4x-2y=10
_________
-11y=11
y=-1
4x-9y=1
4x-9(1)=1
4x=10
x=10/4
x=5/2
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box
Quick please!!!! 50 points!!
Answers
Answer:
2,1
Step-by-step explanation:
30 POINTS FOR AN EXPLANATION TOO (DETAILED PLS)
Answers
The value of x based on the equation given as 3(4x + 6) = 9x + 12 is -2.
How to illustrate the equation?It should be noted that an equation shows that relationship between the variables that are given or illustrated in the data.
The value for x based on the equation will be:
3(4x + 6) = 9x + 12
Open bracket
12x + 18 = 9x + 12
Collect like terms
12x - 9x = 12 - 18
3x = -6
Divide
x = -6/3
x = -2
Therefore, x is -2.
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15 , 21 , 24 , 28 , 30
What is the next number?
Answers
Answer:
36
Step-by-step explanation:
Explanation:
15 (+ 6), 21 (+3), 24 (+4), 28( +2), 30 then so on and so on. 30(+6), 36. If they were to ask you what’s the next 2 numbers, 36(+3), 39 would be after 36. Hope this helped.
now find all real solutions for the real cubic x 3 − 3x 2 − 36x 56 = 0 by first depressing and then solving the resulting equation via cardano. how many real solutions did you get?
Answers
Depressing the equation x^3 - 3x^2 - 36x + 56 = 0 by substituting x = y + 1 yields the depressed cubic y^3 - 39y + 13 = 0.
Solving this using Cardano's formula gives one real solution.
To depress the given equation, we substitute x = y + 1. This gives y^3 - 3y^2 - 42y + 24 = 0. We can then add and subtract (1/3)(-3)^2 to obtain y^3 - 3y^2 - 42y + 27 - 3 = 0. This can be rewritten as (y-3)^3 = 54, which has one real solution y = 3 + (2sqrt(3)). We can then solve for x by substituting y back into x = y + 1, giving x = 4 + (2*sqrt(3)).
Therefore, the real cubic equation x^3 - 3x^2 - 36x + 56 = 0 has one real solution.
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rcentage of people who completed or more years of college listed by state are the percentages of the population who have completed or more years of a college education. construct a frequency distribution with classes.
Answers
The frequency distribution table of the data is illustrated below.
The data we have been given represents the percentage of people who have completed 4 or more years of college education in different states. To create a frequency distribution, we need to first decide on the number of classes we want to use. In this case, we will use 7 classes.
Next, we need to determine the range of values for each class. To do this, we first find the minimum and maximum values in the data set, which are 18.9 and 37.9, respectively.
The range of values for each class will be (max value - min value) / number of classes, which in this case is (37.9 - 18.9) / 7 = 2.86.
We will start with the first class, which will include all values from 18.9 to 21.76 (the lower limit of the first class plus the range of values for each class). The next class will include values from 21.76 to 24.62, and so on, until we reach the final class which will include all values from 33.18 to 36.04 (the upper limit of the final class plus the range of values for each class).
To create the frequency distribution, we count the number of values in the data set that fall into each class. For example, the first class includes values between 18.9 and 21.76, and there are 2 values in the data set that fall into this range (21.4 and 20.0). We continue this process for each class until we have a table that shows the frequency of values in each class.
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Complete Question:
Percentage of People Who Completed 4 or More Years of College Listed by state are the percentages of the population who have completed 4 or more years of a college education. Construct a frequency distribution with 7 classes.
21.4,26.0,25.3,19.3,29.5,35.0,34.7,26.1,25.8,23.4,27.1,29.2,24.5,29.5,22.1,24,3,28.8,20,0,20.4,26.7,35.2,37.9,24.7,31.0,18.9,24.5,27.0
A blueberry muffin recipe calls for 3/4 cup of
sugar. How many cups of sugar would be
needed to make the muffin recipe 3 times?
Answers
Answer:
9/4 or 2 1/4 cups of sugar.
Step-by-step explanation:
To find the answer we multiply 3/4 by 3. Because the bottom stays the same, we wont multiply it. Since 3 x 3 = 9, it will be 9/4. Therefore, 9/4 or 2 1/4 is your answer.
There will be 45 adults going to a museum. There will be twice as many students as adults. Adult tickets cost $25 each. Student tickets cost $12 each.
Part A: What is the total cost for students and adults?
Question 2
Part B: 10 more adults and 15 more students decide to attend the trip at the last minute. How much will cost increase?
Question 3
Part C: What is the total cost of the trip with the additional adults and students?
Answers
Answer:
=P
Step-by-step explanation:
suppose that 0.4% of a given population has a particular disease. a diagnostic test returns positive with probability .99 for someone who has the disease and returns negative with probability 0.97 for someone who does not have the disease. (a) (10 points) if a person is chosen at random, the test is administered, and the person tests positive, what is the probability that this person has the disease? simplify your answe
Answers
The probability that a person has a disease given that they test positive, when 0.4% of the population has the disease and the test is positive with probability 0.99 if they have the disease and 0.03 if they don't have it, is 0.116 or about 11.6%.
Let D be the event that the person has the disease and T be the event that the person tests positive. We need to calculate P(D|T), the probability that the person has the disease given that they test positive.
Using Bayes' theorem, we have
P(D|T) = P(T|D) * P(D) / P(T)
where P(T|D) is the probability of testing positive given that the person has the disease, P(D) is the prior probability of having the disease, and P(T) is the total probability of testing positive, which can be calculated as
P(T) = P(T|D) * P(D) + P(T|D') * P(D')
where P(T|D') is the probability of testing positive given that the person does not have the disease, and P(D') is the complement of P(D), which is the probability of not having the disease.
Substituting the given values, we get
P(D|T) = (0.99 * 0.004) / [(0.99 * 0.004) + (0.03 * 0.996)]
= 0.116
Therefore, the probability that the person has the disease given that they test positive is 0.116 or about 11.6%.
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every then or else block of an if-then statement is reachable by some value, regardless of the test conditions specified by the if statement.
Answers
The statement given "every then or else block of an if-then statement is reachable by some value, regardless of the test conditions specified by the if statement." is false because the "then" block of an if-then statement is only executed when the specified test condition is true, and not all values will satisfy the test condition.
The "then" block of an if-then statement is executed only when the specified test condition in the if statement evaluates to true. If the test condition is false, the "then" block is skipped, and the program proceeds to the next statement following the if-then statement. The "else" block, if present, is executed when the test condition is false. Therefore, not every "then" or "else" block is reachable by any value, but rather by the evaluation of the test condition.
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