Answer:
184 square cm
Step-by-step explanation:
The ratio of areas is the square of the ratio of the scale factor. The larger triangle has an area of ...
(15 cm²)(3.5²) = 183.75 cm²
The area of the similar triangle is about 184 cm².
Need Help!...anyone!
(a)
[tex] \sqrt[5]{ {x}^{3} } [/tex]
(b)
[tex] \sqrt[8]{x} [/tex]
(c)
[tex] \sqrt[3]{ {x}^{5} } [/tex]
(d)
[tex] \sqrt{ {x}^{3} } [/tex]
An insurance policy pays a total medical benefit consisting of two parts for each claim. Let X represent the part of the benefit that is paid to the surgeon, and let Y represent the part that is paid to the hospital. The variance of X is 5000, the variance of Y is 10,000, and the variance of the total benefit, X + Y, is 17,000. Due to increasing medical costs, the company that issues the policy decides to increase X by a flat amount of 100 per claim and to increase Y by 10% per claim. Calculate the variance of the total benefit after these revisions have been made
Answer:
= 19300
Step-by-step explanation:
Each claim consists of two parts = X + Y
where
X = the benefit that is paid to the surgeon and
Y = benefit that is paid to the hospital
V(X) = 5000, V(Y) = 10000 and V(X+Y) = 17000
So V(X+Y) = V(X) + V(Y) + 2cov(X,Y)
17000 = 5000 + 10000 +2 cov(X,Y)
17000 -15000 = 2cov(X,Y)
2000 = 2cov(X,Y)
cov(X,Y) = 1000
Now X is increased by flat Rs. 100 per claim and Y by 10% per claim
total benefit = X+100+Y+0.1Y = X+100 + 1.1Y
V(total benefit) = V(X) + 1.1²V(Y) +2(1.1)cov(X,Y) [ V(aX+bY)
= a²V(X) +b²V(Y) +2abcov(X,Y) and V(X+c) = V(X)]
= 5000 + (1.21*10000) + (2.2*1000)
= 5000 + 12100 + 2200
= 19300
Parker marks sixths on number line. He writes 5/6 just before 1. What fraction does he write on the first mark to the right of 1?
Answer:
The first fraction at the right of 1 is [tex]\frac{7}{6}[/tex] or [tex]1\frac{1}{6}[/tex]
Step-by-step explanation:
Given
Marks of 6ths on a number line
Fraction 5/6 just before 1
Required
What fraction is at the right 1
To get the first fraction at the right of 1, we need to get the difference between each fraction;
This is calculated as follows;
[tex]Difference = 1 - \frac{5}{6}[/tex]
Take LCM
[tex]Difference = \frac{6 - 5}{6}[/tex]
[tex]Difference = \frac{1}{6}[/tex]
This implies that the difference between each mark is [tex]\frac{1}{6}[/tex].
To get the first mark at the right of 1;
We simply add the difference to 1;
This implies that;
[tex]Mark = 1 + \frac{1}{6}[/tex]
Take LCM
[tex]Mark = \frac{6 + 1}{6}[/tex]
[tex]Mark = \frac{7}{6}[/tex]
Convert to mixed fraction
[tex]Mark = 1\frac{1}{6}[/tex]
Hence, the first fraction at the right of 1 is [tex]\frac{7}{6}[/tex] or [tex]1\frac{1}{6}[/tex]
A laptop producing company also produces laptop batteries, and claims that the batteries
it produces power a laptop for about 4:00 hours. But, you doubted the claim and collected
data from 500 laptop users of the same brand and battery, and you found out the battery
powers the laptop for about 3:00 hours and 30 minutes. Considering an alpha of 0.05,
prove the claim of the company is true or false or show whether you accept the
company’s claim or reject it? Please also write H0 and Ha statements for testing your
hypothesis
Answer:
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).
The null and alternative hypothesis are:
[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]
Step-by-step explanation:
The question is incomplete: To test this claim a sample or population standard deviation is needed.
We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.
NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.
This is a hypothesis test for the population mean.
The claim is that the batteries power the laptops for significantly less than 4 hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]
The significance level is 0.05.
The sample has a size n=500.
The sample mean is M=3.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=500-1=499[/tex]
This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-5.5902)=0[/tex]
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.
Two machines used to fill soft drink containers are being compared. The number of containers filled each minute is counted for 60 minutes for each machine. During the 60 minutes, machine 1 filled an average of 73.8 cans per minute with a standard deviation of 5.2 cans per minute, and machine 2 filled an avaerage of 76.1 cans per minute with a standard deviation of 4.1 cans per minute.
Required:
a. If the counts are made each minute for 60 consecutiveminutes, what assumption necessary to the validity of a hypothesistest may be violated?
b. Assuming that all necessary assumptions are met, perform a hypothesis test. Can you conclude that machine 2 is faster than machine 1?
Answer:
The calculated value |t| = | - 2.6932 | = 2.6932 > 1.9803 at 0.05 level of significance
Alternative hypothesis is accepted
The average of machine two is faster than machine one
Step-by-step explanation:
Step(i):-
Given sample size n₁ = n₂ = 60 minutes
The average of first sample 'x⁻₁ = 73.8
The standard deviation of the first sample 'S₁ ' = 5.2 cans per minute
The average of second sample 'x⁻₂ = 76.1
The standard deviation of the second sample 'S₂ ' = 4.1 cans per minute
step(ii):-
Null Hypothesis : H₀: 'x⁻₁ = 'x⁻₂
Alternative Hypothesis : H₁ : 'x⁻₁ > 'x⁻₂
Test statistic
[tex]t = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S^{2} _{1} }{n_{1} } +\frac{S^{2} _{2} }{n_{2} } } }[/tex]
[tex]t = \frac{73.8 - 76.1 }{\sqrt{\frac{(5.2)^{2} }{60 } +\frac{(4.1)^{2} }{60 } } }[/tex]
t = - 2.6932
|t| = | - 2.6932 | = 2.6932
Step(iii):-
Degrees of freedom
ν = n₁ + n₂ -2 = 60 +60 -2 = 118
t₀.₀₅ = 1.9803
The calculated value |t| = | - 2.6932 | = 2.6932 > 1.9803 at 0.05 level of significance
Final answer:-
Null hypothesis is rejected at 0.05 level of significance
Alternative hypothesis is accepted
The average of machine two is faster than the average of machine one
Which rule describes the translation?
5
B
С
(x, y) - (x - 8, y-3)
O (x, y) — (x - 3, y + 8)
O (x, y) = (x + 8, Y-3)
O(x, y) = (x + 3, y + 8)
B'
A
5
D
A
D
5
Answer:
look to rule number five
Step-by-step explanation:
Rule Number 5 best explains the answer
Several surveys in the United States and Europe have asked people to rate their happiness on a scale of 3 = "very happy," 2 = "fairly happy," and 1 = "not too happy," and then tried to correlate the answer with the person's income. For those in one income group (making $25,000 to $55,000) it was found that their "happiness" was approximately given by y = 0.065x − 0.613, where x is in thousands of dollars.† Find the reported "happiness" of a person with the following incomes (rounding your answers to one decimal place).
Answer:
Step-by-step explanation:
We have to find the reported happiness of person of family income of $25,000, $35,000 and $45,000
Given that the formula for finding relation between a people happiness and his income is
y = 0.065x - 0.613
a) find the happiness of person of family income os $25,000
we put x = 25 as in the equation above
[tex]y=0.065(25)-0.613\\\\=1.625-0.613\\\\=1.02 \approx 1[/tex]
Hence, person happiness with with family income of $25,000 on a scale of 3 is y = 1
That means they come under catergory "not to happy"
b) Find the happiness of person of family income os $35,000
we put x = 35 as in the equation above
[tex]y=0.065(35)-0.613\\\\=1.667-0.613\\\\=1.667 \approx 1.7[/tex]
Hence, person happiness with with family income of $35,000 on a scale of 3 is y = 1.7
That means they come under catergory "not to happy" and "fairly happy"
c) Find the happiness of person of family income os $45,000
we put x = 45 as in the equation above
[tex]y=0.065(45)-0.613\\\\=2.925-0.613\\\\=2.312 \approx 2.3[/tex]
Hence, person happiness with with family income of $45,000 on a scale of 3 is y = 2.3
That means they come under catergory "fairly happy"
The scale would show the data as follows:
Happiness Scale at Income 25, 35, 45 & 55 thousand :
1.012 (Not too happy), 1.662 (Fairly Happy), 2.315 (Fairly Happy) , 2.965 (Very Happy)
Determine the scaleImportant Information :
Relationship between happiness scale 'y' and income in 1000s 'x' :y = 0.065x − 0.613, for people in income group between [tex]25000 & 55000[/tex]
Happiness scale : At level of income, between 25 and 55 thousands.
Putting value of income 'x' to find scale of happiness i.e. 'y'
For income 'x' = 25 thousand : [tex]y = 0.065 (25) - 0.613 = 1.625 - 0.613 = 1.012[/tex] For income 'x' = 35 thousand : [tex]y = 0.065 (35) - 0.613 = 2.275 - 0.613 = 1.662[/tex]For income 'x' = 45 thousand : [tex]y = 0.065 (45) - 0.613 = 2.925 - 0.61 = 2.315[/tex] For income 'x' = 55 thousand :[tex]y = 0.065 (55) - 0.613 = 3.575 - 0.61 = 2.965[/tex]
Learn more about "Happiness Scale" here:
brainly.com/question/25609130
(07.01 MC)Of the following sets, which numbers in {0, 1, 2, 3, 4} make the inequality 7x + 3 < 17 true? {0} {0, 1} {0, 1, 2} {2, 3, 4}
Answer:
{0, 1}
Step-by-step explanation:
Solving for 'x' in the inequality:
[tex]7x+3<17\\7x+3-3<17-3 \leftarrow \text{Subtraction Property of Equality}\\7x<14\\7x/7<14/7 \leftarrow \text{Division Property of Equality}\\\boxed{x<2}[/tex]
X's value has to be less than two to make the inequality true. So, {0, 1} should be the correct answer.
Answer:
I took the quiz and the answer is B
Step-by-step explanation:
What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation.
Answer:
4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-(-2))/(3-1)
m=8/2
m=4
Help asap giving branlist!!!
Answer:
Option A.
The heartbeat has a pattern of 60 + (5 x minutes) and linear graphs are straight. The only way the linear graph is straight if there is a pattern.
Step-by-step explanation:
Write an equation of the line containing the point (2,1) and perpendicular to the line 5x – 2y = 3.
So first, you want to isolate your Y. To do this, you must get it alone on ONE SIDE of the equation.
5x - 2y = 3
-5x -5x
[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{3-5x}{-2}[/tex]
ANSWER: y = \frac{3-5x}{-2}
The function g is defined by g(x) = 1/2x - 1. What is
the value of g(6) ?
Answer:
2
Step-by-step explanation:
g(x) = 1/2x - 1
g(6= 1/2*6-1= 3-1= 2
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money fro
the account. Which equation below gives the amount of money you will have in the account after tyears?
Al = 2,000 20.05
Al = 2,000(1.5)
A10 = 2,000(105)
A1 = 2.000 e5
Answer:
[tex]A(t) = 2,000(1.05)^{t}[/tex]
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
You invest $2,000
This means that [tex]P = 2,000[/tex]
Compounded anually
Once a year, so [tex]n = 1[/tex]
Interest rate of 5%.
This means that [tex]r = 0.05[/tex]
Amount after t years:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 2,000(1 + \frac{0.05}{1})^{t}[/tex]
[tex]A(t) = 2,000(1.05)^{t}[/tex]
f(x)=x^2-2x+3; f(x)=-2x+28
Answer:
(-5, 38) and
(5,18)
Step-by-step explanation:
[tex]x^2-2x+3=-2x+28\\<=> x^2-2x+3+2x=28\\<=> x^2 = 28-3=25\\<=> x^2-25=0\\<=> x^2-5^2 =0\\<=> (x-5)(x+5)=0\\<=> x = 5 \ or \ x=-5[/tex]
so the solutions are
(-5, 38) and
(5,18)
Find sin 2x, cos 2x, and tan 2x if sinx =
5
13
and x terminates in quadrant I.
ala
sin 2x
U
х
cos 2x
=
tan 2x
10
Answer:
12/13 ; 5/13; 12/5
Step-by-step explanation:
sinx =5/13 =opposite/ hypothenus
By Pythagoras rule the hypothenus side can be obtained as
√ 13^2 -5^2 = √169 -25 = √144 = 12
cos x= adjacent/ hypothenus = 12/13
Now Cos2x= Sinx
And Sin2x = Cosx
Hence ;
Sin2x=12/13
Cos2x =5/13
Tan2x= Sin 2x/ Cos 2x
= 12/13 ÷ 5/13
= 12/13 × 13/5 = 12/5
In a car dealership there are 5 models that get displayed in a line in the front of the parking lot for prime viewing. The dealership sells 15 different models. In how many ways can the 5 models be displayed
Answer:
360360
Step-by-step explanation:
We have the following information:
Number of ways of choosing 5 car models from 15 different models = 15C5
Number of arranging above 5 models = 5!
Therefore, the total number of displayong 5 models would be:
15C5 * 5!
nCr = n! / (r! * (n-r)!)
we replace:
15! / (5! * (15-5)!) * 5! = 15! / 10! = 360360
So there are a total of 360 360 ways to display the 5 car models.
Answer: 360,360
Step-by-step explanation:
Find the inverse of f(x)=1/(x^3)
Answer:
Step-by-step explanation:
y[tex]f(x)^{-1} = inverse\\f(x)=y \\y = 1/(x^{3} \\Inverse: y=x ------------> x = 1/y^{3}\\y^{3} - \frac{1}{x} = 0\\y^{3} = \frac{1}{x}\\y = \sqrt[3]{\frac{1}{x}} \\y = \frac{\sqrt[3]{1} }{\sqrt[3]{x}} \\y = \frac{1}{\sqrt[3]{x}}[/tex]
9. In 2002 the Georgia department of education reported a mean reading test score of 850 from Tattnall County Career Academy with a standard deviation of 50. The sample was taken from 100 11th grade students. Assuming the test scores are normally distributed, what is the standard error
Answer:
The standard error = 5
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 100
Given mean reading test score μ = 850
Given standard deviation of the population 'σ' = 50
The standard error is determined by
Standard error = [tex]\frac{S.D}{\sqrt{n} }[/tex]
S.E = σ/√n
[tex]S.E = \frac{S.D}{\sqrt{n} } = \frac{50}{\sqrt{100} } = 5[/tex]
Final answer:-
The standard error ( S.E) = 5
Can someone solve this?
Answer:
32°CDAStep-by-step explanation:
1. The angle facing the given arcs is half their sum, so is (180 +116)/2 = 148°. Angle 1 is the supplement of this, ...
angle 1 = 180° -148° = 32°
__
2. Short arc WY is the supplement of 70°, Long arc WVY is the difference of that and 360°:
arc WVY = 360° -(180° -70°) = 180°+70°
arc WVY = 250° . . . . . matches choice C
__
3. Call the point of intersection of the secants X. The rule for secants is ...
(XA)(XC) = (XB)(XD)
So, the length XC is ...
XC = (XB)(XD)/(XA) = 2.4
and ...
AC = XA +XC = 3.2 +2.4 = 5.6 . . . . . matches choice D
__
4. As in problem 3, the product of lengths from the point of secant intersection to the points of circle intersection is the same for both secants.
(NQ)(NR) = (NP)(NS)
Substituting segment sums where necessary, we have ...
NQ(NQ +QR) = NP(NP +PS)
Solving for PS, we have ...
PS = NQ(NQ +QR)/NP - NP . . . . . matches choice A
a consumer affairs company is interested in testing at the 5% level of significance that the average weight of a package of butter is less than 16 oz if the p value is 0.003 the conclusion is
Jack buys a bag of 5 apples, each
equal in size. He eats of 1/2 of one apple.
What fraction of the bag of
apples did he eat?
Answer:
4 1/2
Step-by-step explanation:
5 apples - 1/2 apple =
4 1/2 apple
or
9/2
SL Part 1: Function Families > 01: Graphs and Functions
22. Find the constant of variation k for the direct variation.
х
f(x)
2
-1
7
-3.5
Ok= -2
Ok=0
Ok=0.5
Ok= -0.5
NEED HELP ASAP!!! a hexagon-based pyramid has a height of 54cm. The volume of the pyramid is 1080cm3. What is the area of the base?
Answer:
32
Step-by-step explanation:
Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. What will Arun’s total bill be? $10.44 $47.56 $68.44 $76.00
Answer:
The Answer is 68.44. I wish it helpsAnswer:
68.44$
Step-by-step explanation:
x=18*58/100=10.44 $(the tip)
58+10.44=68.44 ( the bill )
4(x – 2 + y)
What the answer
Answer:
4x -8 +4y
Step-by-step explanation:
Distribute
4(x – 2 + y)
4*x -4*2 +4*y
4x -8 +4y
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positive positive that is the probability that the bureau finds a match given that the lead at the crime scene and the lead in the possession of the suspect are actually from two differant melts or sources. To estimate the false positive rate the bureau collected 1851 bullets that the agency was confident all came from differant melts. The using its established ctireria the bureau examined every possible pair of bullets and found 658 matches. Use this info to to compute the chance of a false positive.
Answer:
Step-by-step explanation:
Given that, we have 1851 bullets that we KNOW are NOT MATCHES of one another. One by one they examine two bullets at a time.
So, there are 1851 bullets but each time we choose 2.
We have, N choose K = N! / K! (N-k)!
Here, N = 1851 and K = 2
Therefore, 1851 choose 2 = 1851! / 2! (1851-2)!
= 1851! / 2! * 1849!
= 1712175 Possible Combinations
Out of these 653 are false positive.
The chance of getting false positive is = 658 / 1712175
= 0.000384
= 0.0384 %
Therefore, The correct option is
The chance of false positive is 0.0384% Because this probability is sufficiently small (< or = 1%) There is high confidence in the agency's forensic evidence.
WILL GIVE BRAINLIEST HURRY
Answer: C
Step-by-step explanation:
To get all the constant terms on one side and variable terms on another, all we have to do is to add or subtract them on both sides.
3x+2x=10+5
Now that the like terms are on one side, we can combine them.
5x=15
To get x alone, we divide both sides by 5.
x=3
Now, we notice that x=3 is not an answer choice, but the next option that is equivalent to x=3 is C.
For C, if you divide both sides by -5, you still get x=3.
-15=-5x
x=3
g You run a regression analysis on a bivariate set of data ( n = 14 ). With ¯ x = 27.7 and ¯ y = 26.5 , you obtain the regression equation y = 0.495 x − 14.914 with a correlation coefficient of r = 0.39 . You want to predict what value (on average) for the response variable will be obtained from a value of 110 as the explanatory variable. What is the predicted response value?
Answer:
Predicted response value = 39.536
Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.
Step-by-step explanation:
The response variable is the dependent variable (y) whose value is obtained from the expression involving the independent variable (x).
For this question, although the correlation coefficient, r = 0.39, is far from 1, the regression equation is
y = 0.495x - 14.914
The predicted response value will be obtained from the explanatory variable and the regression equation
x = 110
y = 0.495x - 14.914
y = (0.495×110) - 14.914 = 39.536
Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.
Hope this Helps!!!
The probability that an event will happen is P(E)=34. Find the probability that the event will not happen.
Answer:
.66
Step-by-step explanation:
1minus .34
Correct me if I am wrong
The sum of three numbers is 10. Two times the second number minus the first number is equal to 12. The first number minus the second number plus twice the third number equals 7. Find the numbers. Listed in order from smallest to largest, the numbers are , , and .
Answer:
[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]
The numbers are [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]
Step-by-step explanation:
Step(i):-
Given sum of the three numbers is 10
Let x , y , z be the three numbers is 10
x +y + z = 10 ...(i)
Given two times the second number minus the first number is equal to 12
2 × y - x = 12 ...(ii)
Given the first number minus the second number plus twice the third number equals 7
x + y + 2 z = 7 ...(iii)
Step(ii):-
Solving (i) and (iii) equations
x + y + z = 10 ...(i)
x + y + 2 z = 7 .. (iii)
- - - -
0 0 -z = 3
Now we know that z = -3 ...(a)
from (ii) equation
2 × y - x = 12 ...(ii)
x = 2 y -12 ...(b)
Step(iii):-
substitute equations (a) and (b) in equation (i)
x+y+z =10
2 y - 12 + y -3 =10
3 y -15 =10
3 y = 10 +15
3 y =25
[tex]y = \frac{25}{3}[/tex]
Substitute [tex]y = \frac{25}{3}[/tex] and z = -3 in equation(i) we will get
x+y+z =10
[tex]x + \frac{25}{3} -3 = 10[/tex]
[tex]x +\frac{25-9}{3} = 10[/tex]
[tex]x +\frac{16}{3} = 10[/tex]
[tex]x = 10 - \frac{16}{3}[/tex]
[tex]x = \frac{30 -16}{3} = \frac{14}{3}[/tex]
Final answer :-
[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]
The numbers are [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]
Answer:
-2, 5, 7 on Edge.
Step-by-step explanation:
I got the Answer right.