Answers
Step-by-step explanation:
The Pythagorean theorem is:
\( {c}^{2} = {a}^{2} + {b}^{2} \)
where c is the hypotenuse.
The two wires in the sketch are the hypotenuse so we just use the formula
let the wires=x
So:
\( {x}^{2} = {12}^{2} + {6}^{2} \)
\( {x}^{2} = 144 + 36\)
\( {x}^{2} = 180\)
\(x = \sqrt{180} \)
\(x = 13.42\) feet
Related Questions
You toss a pair of dice (a) Determine the number of possible pairs of outcomes. (Recall that there are six possible outcomes for each die.) (b) There are three even numbers on each die. How many outcomes are possible with even numbers appearing on each die? (c) Probability extension: What is the probability that both dice will show an even number?
Answers
The answers are a- 36
b- 9
c-0.1111
What do you mean by Probability?In mathematics or the field of statistics, probability is defined as the extent or the likelihood of something happening.
(a)- We have two dice in this question,
A die is known to be make up of 6 faces.
Therefore, the number of faces for two dice = 6 x 6
= 36
(b)- Out of these two dice, one die has 3 odd numbers and three even numbers,
Therefore,
the number of even number outcomes for both dice = 3 x 3
= 9
(c)- The probability of having an even number,
This is 1/9, remember 9 is the total number of even numbers = 0.1111
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you have 51 coins in your pocket, all dimes and quarters. You have $10.20. How many dimes and quarters do you have?
Answers
To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.
To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.
We know that there are 51 coins in total, so we can write the equation: d + q = 51.
We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.
To solve this system of equations, we can use substitution or elimination. Let's use substitution:
Rearrange the first equation to solve for d: d = 51 - q.
Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.
Simplify and solve for q: 510 - 10q + 25q = 1020.
Combine like terms: 15q = 510.
Divide both sides by 15: q = 34.
Now substitute this value back into the first equation to solve for d: d + 34 = 51.
Subtract 34 from both sides: d = 17.
Therefore, you have 17 dimes and 34 quarters.
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Adam can paint 38 feet of fence per hour. How many yards of fence can he paint per hour?
Answers
Answer:
12
Step-by-step explanation:
Answer:
12 yards per hour
Step-by-step explanation:
Alan is growing carrots, parsnips and turnips. He has grown h carrots, 2h parsnips and 5 turnips. In total he has grown 11 vegetables. What is the value of H?
Answers
Hello !
Answer:
\( \boxed{h = 6}\)
Step-by-step explanation:
He has grown :
h carrots2h parsnips5 turnipsWe also know that in total, he has grown 11 vegetables.
We will have to solve an equation !
\(h + 2h + 5 = 11\)
\( \iff3h + 5 = 11\)
We want to isolate h.
\(3h + 5 - 5= 11 - 5 \\ \iff3h = 6 \\ \iff \frac{3h}{3} = \frac{6}{3} = 2\)
The value of h is 2.
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What is the answer to all three boxes. Please help
Answers
Answer:
Box A: 6 feet
Box B: 16 feet
Box C: 12 feet
Step-by-step explanation:
B-16
C-12
A : 1.5x4=6
B : 4x4=16
C : 3x4=12
If a number ends in zero, then it is divisible by five
Answers
Answer:
Yes
Step-by-step explanation:
10,20,30,40,50 are all divisible by 5.
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 312 seconds. Group of answer choices
Answers
Answer:
0.0107 = 1.07% the probability that a randomly selected boy in secondary school can run the mile in less than 312 seconds.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
\(\mu = 450, \sigma = 60\)
Find the probability that a randomly selected boy in secondary school can run the mile in less than 312 seconds.
This is the pvalue of Z when X = 312. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{312 - 450}{60}\)
\(Z = -2.3\)
\(Z = -2.3\) has a pvalue of 0.0107
0.0107 = 1.07% the probability that a randomly selected boy in secondary school can run the mile in less than 312 seconds.
The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,941 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 115 of their customers and calculates that these customers used an average of 11,425kWh of electricity last year. Assuming that the population standard deviation is 3217kWh, is there sufficient evidence to support the power company's claim at the 0.02 level of significance
Answers
Answer:
The pvalue of the test is 0.0537 > 0.02, which means that there is not sufficient evidence to support the power company's claim at the 0.02 level of significance.
Step-by-step explanation:
The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,941 kilowatt hours (kWh) of electricity this year.
This means that the null hypothesis is:
\(H_0: \mu = 10941\)
A local power company believes that residents in their area use more electricity on average than EIA's reported average.
This means that the alternate hypothesis is:
\(H_a: \mu > 10941\)
The test statistic is:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.
10941 is tested at the null hypothesis:
This means that \(\mu = 10941\)
To test their claim, the company chooses a random sample of 115 of their customers and calculates that these customers used an average of 11,425kWh of electricity last year. The population standard deviation is of 3217kWh:
This means that \(n = 115, X = 11425, \sigma = 3217\)
Value of the z-statistic:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z = \frac{11425 - 10941}{\frac{3217}{\sqrt{115}}}\)
\(z = 1.61\)
Pvalue of the test:
Probability of finding a mean above 11425, which is 1 subtracted by the pvalue of z = 1.61.
Looking at the z-table, z = 1.61 has a pvalue of 0.9463.
1 - 0.9463 = 0.0537
The pvalue of the test is 0.0537 > 0.02, which means that there is not sufficient evidence to support the power company's claim at the 0.02 level of significance.
What happens to a consistent slope when the y value starts to decrease and the x value remains the same over time?
A. Y decreases and X decreases
B. Y decreases and X increases
C. Y increases and X increases
D. Y increases and X decreases
Answers
When the y-value starts to decrease and the x-value remains constant over time, Y decreases and X increases to a consistent slope.
A consistent slope represents a constant rate of change between two variables, typically represented by the ratio of the change in y to the change in x.
When the y-value starts to decrease and the x-value remains the same over time, the consistent slope represents a negative correlation between y and x.
This means that as the value of y decreases, the value of x remains the same or may increase, depending on the context of the problem.
Therefore, the answer is option B: Y decreases and X increases.
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I need help on question 27
Answers
A = \(\frac{1}{2}h(b_{1} +b_{2} )\)
If A = 136 when \(b_{1}\) = 7 and h = 16, find \(b_{2}\)
Givens:We are given the equation that we are working with:
A = \(\frac{1}{2}h(b_{1} +b_{2} )\)
We are given certain values that the variables, in this case, are equal to:
A = 136
\(b_{1}\) = 7
h = 16
Steps:Substitute the given variables in the given equation for the corresponding numbers:
A = \(\frac{1}{2}h(b_{1} +b_{2} )\)
136 = \(\frac{1}{2}\) * 16 (7 + \(b_{2}\))
We know all the values in the equation except \(b_{2}\). In order to find \(b_{2}\) we must isolate it on one side of the equation
136 = 8 (7 + \(b_{2}\))
\(\frac{136}{8}\) = \(\frac{8 (7 + b_{2}) }{8}\)
17 = 7 + \(b_{2}\)
17 - 7 = 7 - 7 + \(b_{2}\)
10 = \(b_{2}\)
Check:If \(b_{2}\) is equal to 10 then if we plug it back into the given equation both sides of the equation should equal each other. Remember to use PEMDAS
136 = \(\frac{1}{2}\) * 16 (7 + \(b_{2}\))
136 = \(\frac{1}{2}\) * 16 (7 + 10)
136 = \(\frac{1}{2}\) * 16 (17)
136 = 8 (17)
136 = 136
\(b_{2}\) = 10
HELP! A runner jogs 250 yards down the street and then turns down a pathway into the park and jogs another 110 yards. The angle between the two sidewalks is equal to 100 degrees. How far would the runner have gone if they ran in a straight path through the grass from the starting position directly to the park?
A. 142.953 yards
B. 340.680 yards
C. 290.087 yards
D. 13,541.107 yards
Answers
The resultant of the movement of the runner is 290.087 yards
What is cosine rule?The cosine rule states that if a , b ,c are sides of a triangle and A,B ,C are the opposite angles of the sides, then, c² = a² + b² − 2ab cos(C).
The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.
c² = 250² + 110² -2( 110) (250) cos 100
c² = 62500 + 12100 - 55000(-0.1738)
c² = 74600 + 9570
c² = 84170
c = √ 84170
c = 290.87 yards
Therefore the resultant of the runner pathway is 290.87 yards
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Write an inequality to describe each situation. a. The minimum age for voting in the United States is 18 years old. Let a represent a voter's age. b. A theater seats up to 275 people. Let p represent the number of people attending a performance in the theater.
Answers
According to this inequality, the number of persons attending a theatrical inequality play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.
What is inequality?In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. We resuming our current status quo. Yet a variety of things lead to inequality: Negative values on both sides are split or added.
a. The disparity in representing the voting age in the United States is as follows:
a ≥ 18
In order to be eligible to vote, a voter's age, denoted by a, must be more than or equal to 18 years old.
b. The inequality used to depict a theater's seating capacity is:
p ≤ 275
According to this inequality, the number of persons attending a theatrical play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.
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0.18 divided by 0.04
Answers
what is the sum 3/x+9+5/x-9
Answers
Answer:
\(\frac{8}{x}\)
Step-by-step explanation:
what is the sum 3/x+9+5/x-9
\(\frac{3}{x} + 9 + \frac{5}{x} - 9 =\) (add \(\frac{3}{x}\) and \(\frac{5}{x}\))
\(\frac{8}{x} + 9 - 9 =\) (solve 9 - 9 = 0)
\(\frac{8}{x}\) ( your answer)
Compare the values of the following numbers, using the symbols > (greater than), < (less than), and = (equal to).
0.5 _____0.500
Answers
Answer:
0.5 = 0.500
Step-by-step explanation:
Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.
0.5 = 0.500
PLS HELP ASAP
Erin recycles milk bottles, soda cans, and newspapers. If the following items are in the trash bin, what percent of the items can be recycled?
3 milk bottles, 1 banana peel, 6 newspapers, 3 soda cans, 7 apple cores
A. 60%
B. 12%
C. 45%
D. 100%
Answers
The percentage of items that can be recycled is 12%
3 4/5 • 3 1/2 divide reduce to the lowest term
Answers
Answer:
133/10
Step-by-step explanation:
first turn into proper fraction
19/5 * 7/2 = 133/10
Solve for the two variables in the following system of equations. 7x-8y=-12
--4x+2y=3
Answers
Answer:
x=0, y=3/2. (0, 3/2).
Step-by-step explanation:
7x-8y=-12
-4x+2y=3
----------------
7x-8y=-12
4(-4x+2y)=4(3)
-----------------------
7x-8y=-12
-16x+8y=12
----------------
-9x=0
x=0/-9
x=0
7(0)-8y=-12
0-8y=-12
8y=0-(-12)
8y=0+12
8y=12
y=12/8
simplify
y=3/2
What angle corresponds to 1/6 of a circle
Answers
Carlos has eight tickets. Carlos has 8 fewer tickets then Etta. How many tickets does Etta have?
Answers
Answer:
16
Step-by-step explanation:
This morning, Kendall drank a cup of coffee that had 95 milligrams of caffeine in it. She didn't have any more caffeine for the rest of the day. Kendall read online that the amount of caffeine in her body will decrease by approximately 13% each hour. Write an exponential equation in the form y=a(b)x that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = ____. To the nearest milligram, how much caffeine will be in Kendall's body after 12 hours?
Answers
An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is
The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.
What is an exponential function?In Mathematics, an exponential function can be modeled by using the following mathematical equation:
f(x) = a(b)^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:
Rate of change (decay rate) = 100 - 13 = 87% = 0.87.
By substituting the parameters into the exponential equation, we have the following;
\(f(x) = 95(0.87)^x\)
When x = 12, we have;
\(f(12) = 95(0.87)^{12}\)
f(12) = 17.86 ≈ 18 milligrams.
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a book is marked down by 28% from the original price of 19.50 what is the new price
Answers
Answer:
$14.04
Step-by-step explanation:
to find the answer we can multiply 19.5 by 28% and use that answer to subtract to 19.5 or we can just directly multiply 19.5 by 72%
19.5 * 72% = 14.04
it costs $14.04 after a markdown of 28%
What is 11:7 equivalent too
Answers
The ratio 11:7 is equivalent to 61% and 39%.
What is a ratio?A ratio shows the mathematical relationship between two variables.
For example, one can say that for every 11 green balls, there are 7 white balls.
In this example, the relationship of green and white balls can be expressed mathematically as 11:7. In other words, it means that there are 61% green balls where there are 39% white balls.
Data and Calculations:Ratio = 11:7
Sum of ratio = 18 (11 + 7)
In percent terms, 11/18 = 61% (11/18 x 100)
Whereas 7/18 = 39% (7/18 x 100)
Thus, the ratio 11:7 is equivalent to 61% and 39%.
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PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answers
Answer:
<KLN and <MLI
Step-by-step explanation:
vertical angles are made by opposite angles that are made by two intersecting lines
hope this helps :), brainliest??
I need help with this plzzzzzzz
Answers
Answer: -4
Step-by-step explanation: If you add all the numbers marked, -7 + -4 + -3 + 2 + 7 you will get -4.
What is 12 divided by 2/5?
Show your work
Answers
Reduce numbers with GCF (2)
6 • 5
Multiply numbers
30
12 x 5/2
60/2
=30
Fill in the table using this function rule y = 4 + 5x
Answers
The missing values of y are 19, 29, 34, and 49.
What are the values of y in the table?
The values of y missing in the table is determined by substituting the value of x into the given linear equation.
y = 4 + 5x
when x = 3, the value of y is calculated as;
y = 4 + 5 (3) = 19
when x = 5, the value of y is calculated as;
y = 4 + 5 (5) = 29
when x = 6, the value of y is calculated as;
y = 4 + 5 (6) = 34
when x = 9, the value of y is calculated as;
y = 4 + 5 (9) = 49
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y=7x+7 standard form
Answers
Answer:
7x - y = -7
Step-by-step explanation:
Hope this helps!
When you graph y ≥ 2x - 5, what part of the half-plane you will shade?
Correct answer= all my points and brainlist wrong= report and take back my points
Answers
The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.
What is graph of inequality?The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.
In the given problem, the inequality presented is;
y ≥ 2x - 5
To graph this, we would use a graphing calculator to find the boundary lines and plane.
In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.
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10. Given that xy = a², show that + a+x a+y
Answers
Employing the identity (a+b)² = a² + 2ab + b², where a and b are any real numbers.
Substituting a and b with a and x/y, respectively:
(a + x/y)² = a² + 2a(x/y) + (x/y)²
(a + x/y)² = (a + x/y)(a + x/y)
= a² + ax/y + ax/y + x²/y²
= a² + 2ax/y + x²/y²
add a² to both sides of the equation:
a² + (a + x/y)² = a² + 2ax/y + x²/y² + a²
a² + (a + x/y)² = (a² + x²/y²) + 2ax/y + a²
xy = a² substitute a² for xy in the last term:
a² + (a + x/y)² = (a² + x²/y²) + 2axy/xy + a²
a² + (a + x/y)² = (a² + x²/y²) + 2a + a²
We have that x²/y² = (xy)/(y²) = a/y, and substituting this back into the equation:
a² + (a + x/y)² = (a² + a/y + a/y) + 2a + a²
= 2a² + (2a/x) + (2a/y)
What are real numbers?A real number is described as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
Therefore from the mathematical expression shown above, we have shown that:
a² + (a + x/y)² = 2a² + (2a/x) + (2a/y)
This is the mathematical expression we wanted to prove.
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