Find the length of the third side. If necessary, write in simplest radical form.
Answers
Answer:
[tex]\boxed {\boxed {\sf 8}}[/tex]
Step-by-step explanation:
This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs of the triangle and c is the hypotenuse.
In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:
[tex]a= 7 \\b= \sqrt{15}[/tex]
Substitute these values into the formula.
[tex](7)^2+(\sqrt{15})^2=c^2[/tex]
Solve the exponents.
(7)²= 7*7=49[tex]49+ (\sqrt{15})^2=c^2[/tex]
(√15)²=√15*√15=15[tex]49+15=c^2[/tex]
Add.
[tex]64=c^2[/tex]
Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.
[tex]\sqrt{64}=\sqrt{c^2} \\\sqrt{64}= c\\8=c[/tex]
The third side length is 8.
Answer:
8
Step-by-step explanation:
Related Questions
The charitable foundation for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498. To perform this study, we should form a null hypothesis stating that the average is
Answers
Answer:
The null hypothesis will be that the average annual donor income is less or equal to $ 100,000
Step-by-step explanation:
The claim is mostly treated as alternate hypothesis .
In this question the claim is given as the average annual donor income has increased therefore it is written as
Ha: u > 100,000
The null hypothesis is reverse of the alternate hypothesis
H0: u ≤ 100,000
The null hypothesis will be that the average annual donor income is less or equal to $ 100,000
An experiment examined the impact of THC (the active ingredient in marijuana) on various physiological and psychological variables. The study recruited a sample of 18 young adults who were habitual marijuana smokers. Subjects came to the lab 3 times, each time smoking a different marijuana cigarette: one with 3.9% THC, one with 1.8% THC, and one with no THC (a placebo). The order of the conditions was randomized in a double-blind design. At the start of each session, no subject reported being "high." After smoking the cigarette, participants rated how "high" they felt, using a positive continuous scale (0 representing not at all "high"). For the placebo condition, participants reported a mean "high" feeling of 11.3, with a standard deviation of 15.5. A 95% confidence interval for the population mean feeling of "high" after smoking a placebo marijuana cigarette is
Answers
Answer:
OOO
Step-by-step explanation:
In a recent survey by the National Association of Colleges and Employers, the average starting salary for college graduate with a computer and information sciences degree was reported to be $62,194.40 You are planning to do a survey of starting salaries for recent computer science majors from your university. Using an estimated standard deviation of $11,605, what sample size do you need to have a margin of error equal to $5000 with 95% confidence
Answers
Answer:
A sample size of 21 is needed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Using an estimated standard deviation of $11,605
This means that [tex]\sigma = 11605[/tex]
What sample size do you need to have a margin of error equal to $5000 with 95% confidence
A sample size of n is needed. n is found when M = 5000. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5000 = 1.96\frac{11605}{\sqrt{n}}[/tex]
[tex]5000\sqrt{n} = 1.96*11605[/tex]
[tex]\sqrt{n} = \frac{1.96*11605}{5000}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*11605}{5000})^2[/tex]
[tex]n = 20.69[/tex]
Rounding up,
A sample size of 21 is needed.
Translate the English expression into an equivalent mathematical expression, then simplify.
If a person earns $326 for working 40 hours, what is that person’s hourly wage?
Answers
Sorry I am on mobile so I don’t have the sign.
This will show you how much hourly pay is though because the given salary is for 40 hours.
Krysta knit a total of 16 centimeters of scarf over 8 nights. How many nights will Krysta have
to spend knitting in order to knit a total of 46 centimeters of scarf? Assume the relationship is
directly proportional.
nights
Answers
Answer:
23 nights
Step-by-step explanation:
What does "Proportional" Mean? Proportional means that the ratio is the same throughout.
Step One: First, to set this up, we will put the 16 centimeters for the numerator and then the 8 nights on the bottom. The bottom is the independent variable because we can't physically change the number of nights. 16/8.
Step Two: Now, we have to scale this up to 46. Because the 46 is the centimeters, we have to do 46/16 to see how much we need to scale it by: 46/16= 2.875.
Step Three: Lastly, we can multiply 8 by 2.875 to see how many nights it took: 8 times 2.875 is 23 nights.
Use the model to find the expected number of automobile registrations (in millions) for year 1,988.
Express you answer as a decimal rounded to the nearest hundredth. Do not include units with your answer.
Answers
Answer:
6.26 automobile registrations
Step-by-step explanation:
Given
[tex]y=0.3949x-778.7[/tex] --- [function, missing from the question]
Required
The expected number in 1988
To do this, we substitute 1988 for x in: [tex]y=0.3949x-778.7[/tex]
[tex]y = 0.3949 * 1988 - 778.8[/tex]
[tex]y = 785.0612 - 778.8[/tex]
[tex]y = 6.2612[/tex]
[tex]y \approx 6.26[/tex] --- approximated to the nearest hundredth
A jar contains black and white jelly beans. What is the probability of reaching into the jar and
selecting a black jelly bean?
Answers
Answer:
50% because there are only 2 colors
Step-by-step explanation:
Answer:50%
Step-by-step explanation:
The probability is 50% or 1/2 because there's only 2 types of jelly bean in the jar unless either one has more amount than the other's
Can someone watch number 10 ?
Answers
Answer:
-9
Step-by-step explanation:
Hello! So, we need to find log_6 1/6. The definition of log is the power that you need to multiply that number by to get the next number. 1/6=6^-1, so our equation would be:
-1=x/9, so x is clearly -9.
Have a nice day.
~cloud
Answer:
You are correct
Step-by-step explanation:
[tex]log_{6} \frac{1}{6} =\frac{x}{9}[/tex]
[tex]log_{6} 6^{-1} =\frac{x}{9}[/tex]
[tex](-1)log_{6}6=\frac{x}{9}[/tex]
[tex]-1=x/9[/tex]
[tex]-9=x[/tex]
Hope that helps :)
Question 8 of 10 This circle is centered at the origin, and the length of its radius is 3. What is the circle's equation?
Answers
Answer: is x^2 + y^2 = 100
Marcelo can select from 2 types of oranges and 3 types of peaches. If he randomly selects 1 orange and 1 peach, how many possible choices does he have? ___________ possible choices
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2x3=6
oranges-
peaches-
possible combination:
1-
2-
3-
4-
5-
6-
Someone please help me answer this!!!
Answers
eAnswer:
B, C, E, F
Step-by-step explanation:
what is the answer for 1/3x+y=4 and if you use big ideas math program and you got the right answer lemme know
Answers
Answer:
x=-3y+12
Step-by-step explanation:
Yes.
You invest $17,804 in a CD that has a 6.275% annual interest rate, compounded continuously. How much will you have in 25 years?Round to the nearest cent.
Answers
Answer:
R = 3.813% per year.
Step-by-step explanation:
A = Accrued amount (principal + interest) P = Principal amount r = Annual nominal interest rate as a decimal R = Annual nominal interest rate as a percent r = R/100 n = number of compounding periods per unit of time t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years. I = Interest amount ln = natural logarithm.A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Let x represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket.
Answers
x would be multiplied by 19 then after it’s getting multiplied by 4.
Using the following data, calculate the mean absolute deviation: 7 2 8 5 9 9 5 6 8 1 What is the mean absolute deviation for these data? (4 points)
Answers
Answer:
The mean absolute deviation is 2. Hope this helps
Step-by-step explanation:
7+2+8+9+9+5+6+8+1=5.5
7-5.5=1.5
5.5-2=3.5
8-5.5=2.5
9-5.5=3.5
9-5.5=3.5
5.5-5=0.5
6-5.5=1.5
8-5.5 2.5
5.5-1=4.5
1.5+3.5+2.5+3.5+3.5+0.5+1.5+2.5+4.5=2
Answer is 2.
I hope this can help!
Have a nice day :)
~Amy
D. If the scale factor for the dilation of the figure is 0.9, then the dilation is an enlargement
Answers
Answer:
Option C.
Step-by-step explanation:
Suppose that we have a point (x, y)
If we do a dilation with a center in the origin of scale factor K, then the new coordinates of our point will be:
(k*x, k*y)
If k > 1, we have an elargement.
if 0 < k < 1, we have the opposite case.
Now, suppose that one random vertex of the preimage is A (a, b)
Then after we do the dilation, the new coordinate of this vertex will be:
A' = (k*a, k*b) (this is, the original coordinates multiplied by the scale factor)
And this will happen for all points actually, so particularly the corresponding coordinates of the vertices of the image are the vertices of the preimage multiplied by the scale factor.
Then the correct option is C
Reflect across the x-axis. Then rotate the shape around point B' 120 degrees clockwise.
Answers
9514 1404 393
Answer:
see below
Step-by-step explanation:
Reflection across the x-axis just changes the signs of the y-coordinates. Rotation -120° about B' is difficult to do by hand. The transformation rule for that is ...
(x, y) ⇒ (x·cos(-120°) +y·sin(-120°), -x·sin(-120°) +y·cos(-120°))
(x, y) ⇒ ((-(x-3) +(y+2)√3)/2 +3, (-(x-3)√3 -(y+2))/2 -2)
__
It looks like your problem is presented in GeoGebra, which makes reflection and rotation easy.
Max used a base ten blocks to solve the division problem 9.15 divided by 3.
Which set of blocks shows the quotient for 9.15 divided by3?
A. 3 Ones,5 Tenths,0 Hundredths
B. 5 ones, 0 tenths, 3 hundredths
C. 0 ones, 3 tenths, hundredths
D 3 ones, 0 tenths, 5 hundredths
Answers
Answer:
D 3 ones, 0 tenths, 5 hundredths
Step-by-step explanation:
9.15 divided by 3.
915/3 = 305
Then, moving the decimal point two units to the left, we have 3.05.
The last number before the decimal point is called ones, which means that we have 3 ones.
The first number after the decimal point is called tenths, which means that we have 0 tenths.
The second number after the decimal point is called hundredths, which means that we have 5 hundredths.
The correct answer is given by option D.
Terry buys an orange for 22p.
He pays with a £1 coin.
How much change does he get?
Give your answer in pence.
Answers
100-22=78p
He gets 78p
Two sides of a right triangle have lengths of 78 inches and 30 inches. The third side is not the hypotenuse. How long is the third side ?
Answers
Answer:
the answer is 72 inches
Step-by-step explanation:
a²+b²=c²
a²+900=6084
a²=5184
a=72
Pleaseee help is he right or wrong and why!!!
Answers
Answer:
No, Andre is not correct.
Step-by-step explanation:
I believe Andre is not correct because each 1 on the left balances with a 1 on the right. So taking away the two 1s on the left only leaves the hanger balanced if two 1s are removed on the right. This leaves on the left and three 1s on the right, so x=3. This is like x+2=5 if you subtract 2 from the x side then you get x=3. Hope this helps!
HELP!!! Quick and easy!
Answers
Answer:
2r + 6 = 16
r = 5
f(x) = 3x^2 - 7 4x^2 – 3 Find f(2)
Answers
Answer:
f=5/8x^2+-3/2Divide both sides by two
Step-by-step explanation:
Hope that helped
When Tyee runs the 400 meter dash, his finishing times are normally distributed with a mean of 61 seconds and a standard deviation of 1.5 seconds. If Tyee were to run 39 practice trials of the 400 meter dash, how many of those trials would be faster than 62 seconds, to the nearest whole number?
Answers
To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.
We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.
The z-score formula is:
z = (x - μ) / σ
Where:
x = value (62 seconds)
μ = mean (61 seconds)
σ = standard deviation (1.5 seconds)
Calculating the z-score:
z = (62 - 61) / 1.5
z ≈ 0.6667
Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.
Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.
To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:
Number of trials = Proportion * Total number of trials
Number of trials = 0.7461 * 39
Number of trials ≈ 29.08
Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.
#SPJ1
Which of the following is the radical expression of2 times d to the seven tenths power? (2 points)
a
seventh root of 2 d to the tenth power
b
tenth root of 2 d to the seventh power
c
2 times the tenth root of d to the seventh power
d
2 times the seventh root of d to the tenth power
Answers
can you guys help me on this please
Answers
[tex]9^{2}+a^{2}=15^{2} \\144=a^{2}\\a=12[/tex]
a home mortgage for a home that costs $672096 with a 4% interest rate for 24 years. How much is the monthly payment for the mortgage with the interest?
Answers
9514 1404 393
Answer:
$3633.96
Step-by-step explanation:
The monthly payment is given by the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
monthly payment for principal P at annual rate r for t years.
A = $672096(0.04/12)/(1 -(1 +0.04/12)^(-12·24)) = $3633.96
The monthly payment for the mortgage is $3633.96.
Which of the following statements about opposites is true? Choose all correct answers.
A. The opposite of 5 is −5.
B. −(−8)=−8
C. The opposite of 0 is 0.
D. −(−2)=2
Answers
Answer:
A
Step-by-step explanation:
The sum of two numbers is 50. One number is 23 more than the other one. Find the numbers.
Answers
It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately Normally distributed with mean 376 minutes and standard deviation 67 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 520 minutes and standard deviation 110 minutes. A researcher records the minutes of activity for an SRS of 7 mildly obese people and an SRS of 7 lean people.
A) What is the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes?
B) What is the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?
Answers
Answer:
a) 0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes
b) 0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mildly obese:
Mean 376 minutes and standard deviation 67 minutes, which means that [tex]\mu = 376, \sigma = 67[/tex]
Sample of 6
This means that [tex]n = 6, s = \frac{67}{\sqrt{6}} = 27.35[/tex]
Lean
Mean 520 minutes and standard deviation 110 minutes, which means that [tex]\mu = 520, \sigma = 110[/tex]
Sample of 6
[tex]n = 6, s = \frac{110}{\sqrt{6}} = 44.91[/tex]
A) What is the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes?
This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for mildly obese people. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{420 - 376}{27.35}[/tex]
[tex]Z = 1.61[/tex]
[tex]Z = 1.61[/tex] has a pvalue of 0.9463
1 - 0.9463 = 0.0537
0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes.
B) What is the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?
This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for lean people. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{420 - 520}{44.91}[/tex]
[tex]Z = -2.23[/tex]
[tex]Z = -2.23[/tex] has a pvalue of 0.0129
1 - 0.0129 = 0.9871
0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes