Answer:
64√2 or 64 StartRoot 2 EndRoot
Step-by-step explanation:
A 45-45-90 traingle is a special traingle. Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem. Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2. 2(x)^2=c^2. You then square root both sides and get c= x√2.
Therefore, the two legs are x and the hypotenuse is x√2. x√2=128 because the question says that the hypotenuse is 128. Solve for x by dividing both sides by √2. X=128/√2. You rationalize it by multiplying the numberator and denominator of the fraction by √2. √2*√2= 2.
X=(128√2)/2= 64√2 cm.
Since X is the leg, the answer would be 64√2
Answer:
B.
Step-by-step explanation:
- Find the length of the side a of the triangle ABC given that <A= 70°,
<B = 50° and b = 4cm.
Answer:
4.91 cm
Step-by-step explanation:
The Law of Sines tells you ...
a/sin(A) = b/sin(B)
a = b(sin(A)/sin(B)) = (4 cm)(sin(70°)/sin(50°))
a ≈ 4.91 cm
We have two fractions,
and
and we want to rewrite them so that they have a common denominator
12 4.
(and whole number numerators).
imi
What numbers could we use for the denominator?
ent
Choose 2 answers:
A
12
ond
8
Band
nom
24
18
Answer:
Options (A) and (C).
Step-by-step explanation:
There are two fractions given as
[tex]\frac{5}{12},\frac{3}{4}[/tex]
If we rewrite the fractions by making denominators common we can convert the fraction as,
[tex]\frac{5}{12}, \frac{3\times 3}{3\times 4}[/tex]
Or [tex]\frac{5}{12}, \frac{9}{12}[/tex]
Similarly, both the fractions with common denominators may be[tex]\frac{5\times 2}{12\times 2},\frac{3\times 6}{4\times 6}[/tex]
Or [tex]\frac{10}{24},\frac{18}{24}[/tex]
Therefore, denominators of both the fractions will be 12 and 24.
Options (A) and (C) will be the answer.
Four different positive integers have a product of 110.
What is the sum of the four integers?
Given:
Four different positive intergers as a product of 110
To find:
The sumnof the four numbers whose product is 110
Solution:
1) To find the number we have to find the prime factorization of the given number 110
2) Prime factorization of 110 is
110 = 1×2 × 5 = 11
3) So the four numbers whose product is 110 are 1,2,5 and 11
4) The sum of number's are
1+2+5+11=19
SO THE FINAL ANSWER IS 19Use the function rule f(x)=x^2
Find f(2.5)__
Answer:
6.25
Step-by-step explanation:
f(x)=x^2
f(2.5) = (2.5)^2
=6.25
Answer: 6.25
Step-by-step explanation: Notice that f is a function of x.
So we want to find f(2.5).
We find f(2.5) by plugging 2.5 in for x
everywhere that x appears in the function.
So we have f(2.5) = (2.5)².
(2.5)² is 6.25.
So our answer is 6.25.
Please answer this correctly
Answer:
9 5/7
Step-by-step explanation:
You add all the 13/14 then divided it by 14
Then add all the while numbers then add then add them all together
There are 500 people in a building. 20% of half of them went out. 15% of those who went out came back in. How many people are in the building now?
Answer:
415people
Step-by-step explanation:
20%of250=100people
15%of the 100people=15people
So 100 went out remaining(500-100)400
Then 15 returned=400+15
415
Answer:
458 people in the building now.
Step-by-step explanation:
20%x500/2 = 20% x 250=50
15% x 50 = 7.5
7.5 + (500 - 50) =457.5 =458people.
Tell me if it's correct plz.
Hope this helps..
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. The point estimate of the mean content of the bottles is:__________.
Select one:
a. 0.02
b. 0.22
c. 121
d. 4
Answer:
option D is correct, 4 ounces.
Step-by-step explanation:
In this case we have a random sample of 121 cologne bottles that showed an average content of 4 ounces.
The point estimate of the mean content of the bottles is average value.
What 4 ounces means is the correct answer since this is the mean, therefore the option D is correct
A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 7.45 minutes with a standard deviation of 1.52 minutes.
Answer:
4.65% probability that a randomly selected customer takes more than 10 minutes
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 7.45, \sigma = 1.52[/tex]
Probability that a customer takes more than 10 minutes:
This is 1 subtracted by the pvalue of Z when X = 10. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 7.45}{1.52}[/tex]
[tex]Z = 1.68[/tex]
[tex]Z = 1.68[/tex] has a pvalue of 0.9535
1 - 0.9535 = 0.0465
4.65% probability that a randomly selected customer takes more than 10 minutes
Determine whether the following relation represents a function. Give the domain and range for the relation. StartSet (7 comma 2 )comma (5 comma negative 4 )comma (3 comma 3 )comma (negative 4 comma negative 4 )EndSet
Answer:
is a functiondomain: {-4. 3. 5. 7}range: {-4, 2, 3}Step-by-step explanation:
Given:
{(7, 2), (5, -4), (3, 3), (-4, -4)}
__
The domain is the set of first numbers:
{7, 5, 3, -4} . . . domain
The range is the set of second numbers:
{2, -4, 3} . . . range
No domain values are repeated, so this relation is a function.
What’s the correct answer for this?
Answer:
YT AND RQ
Step-by-step explanation:
NEED HELP ASAP!!!!
The steps below show the work of a student used to calculate the number of yards in 6,436 meters.
(1 mile = 1,609 meters)
(1 mile = 1,760 yards)
Step 1: 6,436 meters multiplied by conversion factor 1 mile over 1,609 meters equals 4 miles
Step 2: conversion factor of 1,760 yards over 1 mile divided by 4 miles equals 440 yards
Step 3: 440 yards
(1 mile = 1,609 meters)
(1 mile = 1,760 yards)
How can the error in the student's work be corrected? (1 point)
a
The 6,436 meters and the 1,609 meters in Step 1 should be switched.
b
The 1 mile and the 1,609 meters in Step 1 should be switched.
c
The conversion factor should be multiplied in Step 2 instead of being divided.
d
The conversion factor should be added in Step 2 instead of being divided.
Answer:
You usually wouldn't divide lengths
Step-by-step explanation:
A collection of 36 coins consists of nickels, dimes and quarters. There are three fewer quarters than nickels and six more dimes than quarters. How many of each kind of coin are there?
Answer:
9 quarters, 12 nickels, and 15 dimes.
Step-by-step explanation:
Let's start by naming the number of quarters x.
That means that the number of nickels is x+3.
(There are three fewer quarters than nickels)
The number of dimes would be x+6.
(There are six more dimes than quarters)
We know the total number of coins is 36.
We can set up an equation.
quarters+nickels+dimes=36
x+x+3+x+6=36
Combine like terms.
3x+9=36
Subtract 9 from both sides.
3x=27
Divide both sides by 3.
x=9
There are 9 quarters.
Use given info to find the number of other coins.
9+3=12
There are 12 nickels.
9+6=15
There are 15 dimes.
Find the circumference
Answer:
C = pi or approximately 3.14
Step-by-step explanation:
The circumference is equal to
C = 2 * pi *r
C = 2 * pi *.5
C = pi
We can approximate pi by 3.14
C = pi or approximately 3.14
A national college researcher reported that 65% of students who graduated from high school in 2012 enrolled in college. Twenty nine high school graduates are sampled. Round the answers to four decimal places.
(a) What is the probability that exactly 17 of them enroll in college? The probability that exactly 17 of them enroll in college is_______
(b) What is the probability that more than 14 enroll in college? The probability that more than 14 enroll in college is_______ .
(c) What is the probability that fewer than 11 enroll in college? The probability that fewer than 11 enroll in college is_______ .
(d) Would it be unusual if more than 24 of them enroll in college? It (Choose one) be unusual if more than 24 of them enroll in college since the probability is ________.
Answer:
a) The probability that exactly 17 of them enroll in college is 0.116.
b) The probability that more than 14 enroll in college is 0.995.
c) The probability that fewer than 11 enroll in college is 0.001.
d) It would be be unusual if more than 24 of them enroll in college since the probability is 0.009.
Step-by-step explanation:
We can model this with a binomial distribution, with n=29 and p=0.65.
The probability that k students from the sample who graduated from high school in 2012 enrolled in college is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{29}{k} 0.65^{k} 0.35^{29-k}\\\\\\[/tex]
a) The probability that exactly 17 of them enroll in college is:
[tex]P(x=17) = \dbinom{29}{17} p^{17}(1-p)^{12}=51895935*0.0007*0=0.116\\\\\\[/tex]
b) The probability that more than 14 of them enroll in college is:
[tex]P(X>14)=\sum_{15}^{29} P(X=k_i)=1-\sum_{0}^{14} P(X=k_i)\\\\\\P(x=0)=0\\\\P(x=1)=0\\\\P(x=2)=0\\\\P(x=3)=0\\\\P(x=4)=0\\\\P(x=5)=0\\\\P(x=6)=0\\\\P(x=7)=0\\\\P(x=8)=0\\\\P(x=9)=0\\\\P(x=10)=0.001\\\\P(x=11)=0.002\\\\P(x=12)=0.005\\\\P(x=13)=0.013\\\\P(x=14)=0.027\\\\\\P(X>14)=1-0.005=0.995[/tex]
c) Using the probabilities calculated in the point b, we have:
[tex]P(X<11)=\sum_0^{10}P(X=k_i)\approx0.001[/tex]
d) The probabilities that more than 24 enroll in college is:
[tex]P(X>24)=\sum_{25}^{29}P(X=k_i)\\\\\\ P(x=25) = \dbinom{29}{25} p^{25}(1-p)^{4}=23751*0*0.015=0.007\\\\\\P(x=26) = \dbinom{29}{26} p^{26}(1-p)^{3}=3654*0*0.043=0.002\\\\\\P(x=27) = \dbinom{29}{27} p^{27}(1-p)^{2}=406*0*0.123=0\\\\\\P(x=28) = \dbinom{29}{28} p^{28}(1-p)^{1}=29*0*0.35=0\\\\\\P(x=29) = \dbinom{29}{29} p^{29}(1-p)^{0}=1*0*1=0\\\\\\\\P(X>24)=0.007+0.002+0+0+0=0.009[/tex]
what is a unit rate?
Answer:
5
Step-by-step explanation:
Answer:
the answer is-
Step-by-step explanation:
When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.
HOPE IT HELPS!!!
Solve the system of equations. 3x + 4y = 8 x + 2y = 4
Answer:
x=0, y=2
Step-by-step explanation:
3x+4y=8
x+2y=4
Multiply the second equation by 2:
2x+4y=8
Subract it from the first equation:
x=0
y=2
Hope this helps!
what is the solution of this equation 4(x-8)+10=-10
Start by subtracting 10 from both sides.
This gives us 4x - 32 = -20.
Now add 32 to both sides to get 4x = 12.
Now divide both sides by 3 to get x = 3.
Lataycia has 188 but she is spending 14 per week.
Answer:
90
Step-by-step explanation:
14×7=98
188-98=90 so she had 90 left
Answer:
90
Step-by-step explanation:
14×7=98
188-98=90 so she had 90 left
If a circle was cut into 8 equal pieces, what fraction of the circle would be each piece?
Answer:
1/8
Step-by-step explanation:
there are 8 pieces therefore the numerator would be 1 and the denominator 8.
The mathematics department at a community college collected data for the number of students enrolled in 40 math classes over the course of one year. The following stem-and-leaf display shows the total number of students enrolled in each class. Choose the statement below that describes the enrollment data. Key: 10|5 denotes 105 students; 7|2 denotes 72 students3 6 6 7 8 9 4 2 3 3 6 6 5 3 3 8 9 6 2 2 3 5 9 7 2 5 7 8 0 0 3 7 7 9 1 3 5 7 10 0 2 5 7 1 1 3 4 12 1 2 2 A. The distribution of the number of students enrolled in each of 40 math courses is skewed to the right, with a typical class size of 69 students. The smallest class size was 36 and the largest was 122. B. The distribution of the number of students enrolled in each of 40 math courses is unimodal and symmetric. The smallest class size was 36 and the largest was 122. The center (as measured by the median) of the distribution was around 73 students. C. The distribution of the number of students enrolled in each of 40 math courses is skewed to the left, with a typical class size of 88 students. The smallest class size was 36 and the largest was 122. D. The distribution of the number of students enrolled in each of 40 math courses is nearly uniform. The smallest class size was 36 and the largest was 122. The center (as measured by the median) of the distribution was around 73 students. E. The distribution of the number of students enrolled in each of 40 math courses is nearly uniform. The smallest class size was 36 and the largest was 122. The center (as measured by the median) of the distribution was around 88 students.
Answer:
D.
Step-by-step explanation:
What’s the correct answer for this?
Answer:
x = 4
Step-by-step explanation:
Given 2 intersecting chords, then
The product of the parts of one chord is equal to the product of the parts of the other chord, that is
4x = 2 × 8 = 16 ( divide both sides by 4 )
x = 4
find a in a=6b if b=2
Answer:
a=12
Step-by-step explanation:
if a=6b
and b=2
a=2×6
a=12
The driving distance from Chicago to San Francisco is 2,142 miles. The Hathaway family left Chicago on Monday morning, December 6. They averaged 50 miles an hour and drove 6 hours each day. On what day and date did they reach San Francisco?
Answer:
They arrive on Monday, December 13th
Step-by-step explanation:
First, we know that this family must drive a total of 2,142 miles.
They average 50 miles per hour and drive 6 hours each day, thus we can see that they drive (50)(6)=300 miles per day.
Now, to know how many days it will take them to drive the total of 2,142 miles we are going to divide the total amount of miles between the number of miles driven per day:
2,142÷300= 7.14
Thus, it takes them 7.14 days to drive 2,142 miles.
If we round this (since the number is greater than 7 this would mean it takes them more than 7 days and they would stop at 7 for the day) to the next digit, we would have that it will take them 8 days to get to San Francisco.
Thus, since they start on December 6th (day 1), December 7th would be day 2 and following this pattern we would have that the eighth day would be December 13th.
Now, since the days repeat every 7 days and we now that December 6th was monday, we would have that the day they arrive to San Francisco (December 13th) is monday too.
7. 12, 24, 4, 18, 12, 9
Using the data, create a histogram.
Answer:
import pandas as pd
vec = pd.Series([7.12,24,4,18,12,9])
vec.plot(kind = 'hist')
Step-by-step explanation:
You can use python for that.
By doing
import pandas as pd
vec = pd.Series([7.12,24,4,18,12,9])
vec.plot(kind = 'hist')
And this is the result you get
Angie and Irene had the same amount of money at first.At a shopping mall, Angie spent $2595 while Irene spent $297.Irene then had thrice as much money as Angie. How much money did Irene have at first?
Answer:
Irene had $3744 at first.
Step-by-step explanation:
Let Angie and Irene had the money initially = $a
At a shopping mall Angie spent money = $2595
Money left with Angie = $(a - 2595)
Similarly, Irene spent the money = $297
Money left with Irene = $(a - 297)
Money left with Irene was thrice as much as Angie,
(a - 297) = 3(a - 2595)
a - 297 = 3a - 7785
3a - a = 7785 - 297
2a = 7488
a = [tex]\frac{7488}{2}[/tex]
a = $3744
Therefore, Irene had $3744 at first.
Answer:
$3746
Step-by-step explanation:
A=2595. I=2595
(x-293)=(x-2595)
X-293=3x-7785
-293+7785=2x
7492/2=x
So. x=3746
Solve the equation for the indicated variable.
660w
C=
for w
h2
W=
(Simplify your answer.)
The first step is to multiply both sides by h^2. Afterwards, divide both sides by 660 to fully isolate w.
c = 660w/(h^2)
ch^2 = 660w
660w = ch^2
w = (ch^2)/660 is the answer
Over several years, students of Professor Robin Lock have flipped a large number of coins and recorded whether the flip landed on heads or tails. As reported in a 2002 issue of Chance News, these students has observed 14,709 heads in a total of 29,015 flips.
Required:
a. What are the observational units for this study?
b. Determine the theory-based p-value for testing whether the long-run proportion of heads differs from 0.50.
c. What conclusion would you draw at the 0.05 significance level?
d. Are your results practically important? Why/why not?
Answer:
a) The observational units for this study are coins
b) The test is a two-tailed test.
c) Since the p-value is < α, we can therefore conclude that long-run proportion of heads significantly differ from 0.50
d) The findings are known as statistically important, due to the very large sample size. But the difference between the 0.50 ratio hypothesized and the 0.51 ratio observed isn't very large. Consequently , the findings are not relevant
Step-by-step explanation:
a) The observational units for this study are coins
b) Number of heads = x = 14709
Number of flips = n = 29015
Sample proportion = [tex]\bar{p}[/tex] = x ÷ n = 14709 ÷ 29015=0.51
H[tex]_{o}[/tex] : p =0.50
H[tex]_{a}:[/tex] p [tex]\ne[/tex] 0.50
z = [tex](\bar{p}-p)/\sqrt{p(1-p)/n} = (0.51-0.50)/\sqrt{0.50 \times (1-0.50)/29015}[/tex]
z = 2.366
Using the normal distribution table, area under the normal curve to the right of z;
z = 2.366 = 0.009
The test is a two-tailed test.
Hence, p-value = [tex]0.009 \times 2[/tex] = 0.018
c) α = 0.05
p-value < α = 0.05, we reject the null hypothesis.
We can therefore conclude that long-run proportion of heads significantly differ from 0.50
d) The findings are known as statistically important, due to the very large sample size. But the difference between the 0.50 ratio hypothesized and the 0.51 ratio observed isn't very large. Consequently , the findings are not relevant
What is fo)?
O O only
0 -6 only
0-2, 1, 1, and 3 only
0 -6, -2, 1, 1, and 3 only
Answer:
-6 only
Step-by-step explanation:
f(0) is the value of y when x=0. This is the graph of a 4th-degree polynomial, so is a function. There is only one y-value for x=0. That is where the graph crosses the y-axis, at y = -6.
f(0) = -6 . . . . only
Please answer this correctly without making mistakes
Answer:
i think its da second image!!!
Step-by-step explanation:
happy to help ya!
What is the missing value from the set of data if the mean is 4?
{5,2,_,2,4,8}
Answer: The missing value from the data set is 4.
Step-by-step explanation: Let's put it from least to greatest to figure it out...
2, 2, (4, 4,) 5, 8,
It would have to be 4, because 8 divided by 2 will equal 4. And because there's an even amount of numbers we have to add two numbers then divide it by 2.
4 + 4 = 8
8 ÷ 2 = 4
The mean is 4, and the missing value from the data set is 4.
I hope this helps!