Answers
Answer : The value of x is 4.1 cm.
Step-by-step explanation :
As we know that the perpendicular dropped from the center divides the chord into two equal parts.
That means,
AB = CB = [tex]\frac{15.6cm}{2}=7.8cm[/tex]
Now we have o calculate the value of x by using Pythagoras theorem.
Using Pythagoras theorem in ΔOBA :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](OA)^2=(OB)^2+(BA)^2[/tex]
Now put all the values in the above expression, we get the value of side OB.
[tex](8.8)^2=(x)^2+(7.8)^2[/tex]
[tex]x=\sqrt{(8.8)^2-(7.8)^2}[/tex]
[tex]x=\sqrt{77.44-60.84}[/tex]
[tex]x=\sqrt{16.6}[/tex]
[tex]x=4.074\approx 4.1[/tex]
Therefore, the value of x is 4.1 cm.
Related Questions
A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce the following results: 490 mg, 502 mg, 505 mg, 495mg, and 492 mg. The manufacturer claims that the tablet contains 500 mg of vitamin C. Do an appropriate statistical analysis to find out whether the results obtained by the student is consistent with bottle claim.
Answers
Answer:
There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.
P-value = 0.166.
Step-by-step explanation:
We start by calculating the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\[/tex]
Then, we can perform the hypothesis t-test for the mean.
The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=500\\\\H_a:\mu< 500[/tex]
The significance level is 0.05.
The sample has a size n=5.
The sample mean is M=496.8.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=5-1=4[/tex]
This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.1)=0.166[/tex]
As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.
someone pls help me! ❤️❤️❤️
Answers
Answer:
(x-1) ( x -i) (x+i)
Step-by-step explanation:
x^3 -2x^2 +x-2
Factor by grouping
x^3 -2x^2 +x-2
x^2(x-2) +1(x-2)
Factor out (x-2)
(x-2) (x^2+1)
Rewriting
(x-1) ( x^2 - (-1)^2)
(x-1) ( x -i) (x+i)
Answer:
Should be b
Step-by-step explanation:
Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.
You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.
Then, since you know the imaginary roots have to be conjugates, you get B.
Given z = 4x – 6y, solve for y.
Answers
Answer:
Step-by-step explanation:
-6y+4x=z
-6y=z-4x
y=(z-4x)/-6
Answer:
[tex]y=\frac{z-4x}{-6}[/tex]
Step-by-step explanation:
Find the equation of the line.
Use exact numbers.
Answers
Answer:
y = 2/3x + 4
Step-by-step explanation:
Step 1: Find slope
m = (4-0)/(0+6)
m = 2/3
Step 2: Write in y-int (0, 4)
y = 2/3x + 4
combine like terms to create an equivalent expression -1/2(-3y+10)
Answers
Answer:
3/2y - 5
Step-by-step explanation:
-1/2(-3y+10)
Expand the brackets.
-1/2(-3y) -1/2(10)
Multiply.
3/2y - 5
Answer:
[tex]= \frac{ 3y}{2} - 5 \\ [/tex]
Step-by-step explanation:
we know that,
[tex]( - ) \times ( - ) = ( + ) \\ ( - ) \times ( + ) = ( - )[/tex]
Let's solve now,
[tex] - \frac{1}{2} ( - 3y + 10) \\ \frac{3y}{2} - \frac{10}{2} \\ = \frac{ 3y}{2} - 5[/tex]
2x^2+8x = x^2-16
Solve for x
Answers
Answer:
x=-4
Step-by-step explanation:
[tex]2x^2+8x=x^2-16[/tex]
Move everything to one side:
[tex]x^2+8x+16=0[/tex]
Factor:
[tex](x+4)^2=0[/tex]
By the zero product rule, x=-4. Hope this helps!
Answer:
x=-4
Step-by-step explanation:
Move everything to one side and combine like-terms
x²+8x+16
Factor
(x+4)²
x=-4
Consider the set of sequences of seven letters chosen from W and L. We may think of these sequences as representing the outcomes of a match of seven games, where W means the first team wins the game and L means the second team wins the game. The match is won by the first team to win four games (thus, some games may never get played, but we need to include their hypothetical outcomes in the points in order that we have a probability space of equally likely points).A. What is the probability that a team will win the match, given that it has won the first game?B. What is the probability that a team will win the match, given that it has won the first two games? C. What is the probability that a team will win the match, given that it has won two out of the first three games?
Answers
Answer:
a) Probability that a team will win the match given that it has won the first game = 0.66
b) Probability that a team will win the match given that it has won the first two games= 0.81
c) Probability that a team will win the match, given that it has won two out of the first three games = 0.69
Step-by-step explanation:
There are a total of seven games to be played. Therefore, W and L consists of 2⁷ equi-probable sample points
a) Since one game has already been won by the team, there are 2⁶ = 64 sample points left. If the team wins three or more matches, it has won.
Number of ways of winning the three or more matches left = [tex]6C3 + 6C4 + 6C5 + 6C6[/tex]
= 20 + 15 + 6 + 1 = 42
P( a team will win the match given that it has won the first game) = 42/64 = 0.66
b) Since two games have already been won by the team, there are 2⁵ = 32 sample points left. If the team wins two or more matches, it has won.
Number of ways of winning the three or more matches left = [tex]5C2 + 5C3 + 5C4 + 5C5[/tex] = 10 + 10 + 5 +1 = 26
P( a team will win the match given that it has won the first two games) = 26/32 = 0.81
c) Probability that a team will win the match, given that it has won two out of the first three games
They have played 3 games out of 7, this means that there are 4 more games to play. The sample points remain 2⁴ = 16
They have won 2 games already, it means they have two or more games to win.
Number of ways of winning the three or more matches left = [tex]4C2 + 4C3 + 4C4[/tex] = 6 + 4 + 1 = 11
Probability that a team will win the match, given that it has won two out of the first three games = 11/16
Probability that a team will win the match, given that it has won two out of the first three games = 0.69
Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. AIB Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is
A. (76.87, 80.33)
B. (72.5, 82.9)
C. (77.1, 78.3)
D. (74.1, 81.3)
E. (74.5, 80)
Answers
Answer:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Step-by-step explanation:
Information given
[tex]\bar X=77.7[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.6 represent the sample standard deviation
n=100 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=100-1=99[/tex]
Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]
And replacing we got:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation Can the method of undetermined coefficients together with superposition be applied to find a particular solution of the given equation?
A. No, because the right side of the given equation is not the correct type of function
B, Yes °
C. No, because the differential equation is not linear.
D. No, because the differential equation does not have constant coefficients.
Answers
Answer:
D. No, because the differential equation does not have constant coefficients.
Step-by-step explanation:
The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 0.989 0.978 0.927 0.167 0.530
Answers
Answer:
0.989
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.
This means that [tex]p = 0.53[/tex]
6 randomly selected graduates
This means that [tex]n = 6[/tex]
Probability that at least one finds a job in his or her chosen field within a year of graduating:
Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]
Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)
always has an area of 2 square units.
Hint: Find the equation of the tangent line at x = a. (It will contain a’s as well as x and y.) Then find the
x-and y-intercepts for that line to find the lengths of sides of the right triangle.
Answers
Answer:
Step-by-step explanation:
given a point [tex](x_0,y_0)[/tex] the equation of a line with slope m that passes through the given point is
[tex]y-y_0 = m(x-x_0)[/tex] or equivalently
[tex] y = mx+(y_0-mx_0)[/tex].
Recall that a line of the form [tex]y=mx+b [/tex], the y intercept is b and the x intercept is [tex]\frac{-b}{m}[/tex].
So, in our case, the y intercept is [tex](y_0-mx_0)[/tex] and the x intercept is [tex]\frac{mx_0-y_0}{m}[/tex].
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph [tex](x_0,\frac{1}{x_0})[/tex]. Which means that [tex]y_0=\frac{1}{x_0}[/tex]
The slope of the tangent line is given by the derivative of the function evaluated at [tex]x_0[/tex]. Using the properties of derivatives, we get
[tex]y' = \frac{-1}{x^2}[/tex]. So evaluated at [tex]x_0[/tex] we get [tex] m = \frac{-1}{x_0^2}[/tex]
Replacing the values in our previous findings we get that the y intercept is
[tex](y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}[/tex]
The x intercept is
[tex] \frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0[/tex]
The triangle in consideration has height [tex]\frac{2}{x_0}[/tex] and base [tex]2x_0[/tex]. So the area is
[tex] \frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2[/tex]
So regardless of the point we take on the graph, the area of the triangle is always 2.
Each of the following is a confidence interval for μ = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type:(111.6, 112.4) (111.4, 112.6)(a) What is the value of the sample mean resonance frequency?
Answers
Answer:
The value of the sample mean resonance frequency is 112Hz
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this problem, we have that:
Lower bound: 111.6
Upper bound: 112.4
Sample mean: (111.6 + 112.4)/2 = 112Hz
The value of the sample mean resonance frequency is 112Hz
The value of the sample mean resonance frequency is 112 Hz.
What is the value of the sample mean resonance frequency?The value of the sample mean resonance frequency is equivalent to the average of the upper limit and the lower limit.
The sample mean resonance frequency = (lower limit + upper limit) / 2
(111.6 +112.4) / 2
= 224 / 2
= 112 Hz
To learn more about confidence interval, please check: https://brainly.com/question/15905477
5/a - 4/b as a single fraction
Answers
Answer:
I'm not completely sure what you mean by a, "single fraction," but I'm pretty sure the answer you are looking for is [tex]\frac{5-4}{a-b}[/tex]
Step-by-step explanation:
An economist at Vanderbilt University devised a study to compare different types of online auctions. In one experiment he compared a Dutch auction to a first-place sealed bid auction. In the Dutch auction the item for sale starts at a very high price and is lowered gradually until someone finds the price low enough to buy. In the first-price sealed bid auction each bidder submits a single sealed bid before a particular deadline. After the deadline, the person with the highest bid wins. The researcher auctioned off collectible trading cards from the game Magic: The Gathering. He placed pairs of identical cards up for auction; one would go into Dutch auction and the other to the first-price sealed bid auction. He then looked at the difference in the prices he received on the pair. He repeated this for a total of 88 pairs.
[a] Explained why the data should be analyzed using paired samples as opposed to two independent samples.
[b] What makes a pair?
[c] What is the explanatory variable? Is it categorical or quantitative?
[d] What is the response variable? Is it categorical or quantitative?
[e] State the relevant hypotheses in words:
Null hypothesis:
Alternative hypothesis:
[f] Define the parameter of interest and give the symbol that should be assigned to it.
[g] State the relevant hypotheses in symbols (using a parameter):
Null hypothesis:
Alternative hypothesis:
[h] Assume the p-value is 0.17 (write a conclusion).
Answers
Answer:
Step-by-step explanation:
a. The data should be analyzed using paired samples because the economist made two measurements (samples) drawn from the same pair of identical cards. Each data point in one sample is uniquely paired to a data point in the second sample.
b. A pair is made up of two identical cards where one would go into Dutch auction and the other to the first-price sealed bid auction.
c. The explanatory variables are the types of online auction which are the Dutch auction and the first price sealed bid auction. The explanation variable here is categorical: the Dutch auction and the first price sealed bid auction.
d. The response variable which is also known as the outcome variable is prices for the 2 different auction for each pair of identical cards. This variable is quantitative.
e. Null Hypothesis in words: There is no difference in the prices obtained in the two different online auction.
Alternative hypothesis: There is a difference in the prices obtained in the two different online auction.
f. The parameter of interest in this case is the mean prices of pairs of identical cards for both auction and is assigned p.
g. Null hypothesis: p(dutch) = p(first-price sealed auction)
Alternative hypothesis: p(dutch) =/ p(first-price sealed auction)
h. Assuming the p-value is 0.17 at an assed standard 0.05 significance level, our conclusion would be to fail to reject the null hypothesis as 0.17 is greater than 0.05 or even 0.01 and we can conclude that, there is no statistically significant evidence to prove that there is a difference in the prices obtained in the two different online auction.
Please answer this correctly I want genius expert or ace people to answer this correctly as soon as possible as my work is due today
Answers
Answer:
25%
Step-by-step explanation:
The last percentile always contains 25% of the observations.
Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x
3x^2
x^2 + 2x
x^2 - 10x
3x^2 + 2x
Answers
Answer:
x^2 - 10x
Step-by-step explanation:
2x^2 - 4x - x^2 +6x
You subtract x^2 from 2x^2 and you get x^2
Then you add 6x and 4x together and get 10x
So then you have x^2 - 10x
(plus I took the test and this was the correct answer.)
The figure shows a square floor plan with a smaller square area that will accommodate a combination fountain and pool.The floor with the fountain pool area removed has an area of 33 Square meters and a perimeter of 36 meters. Find the dimensions of the floor and the dimensions of the square that will accommodate the fountain and pool.
Answers
Answer:
(x, y) = (7, 4) meters
Step-by-step explanation:
The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.
The perimeter of the floor is the sum of all side lengths, so is 4x +2y.
The given dimensions tell us ...
x^2 -y^2 = 33
4x +2y = 36
From the latter equation, we can write an expression for y:
y = 18 -2x
Substituting this into the first equation gives ...
x^2 -(18 -2x)^2 = 33
x^2 -(324 -72x +4x^2) = 33
3x^2 -72x + 357 = 0 . . . . write in standard form
3(x -7)(x -17) = 0 . . . . . factor
Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.
y = 18 -2(7) = 4
The floor dimension x is 7 meters; the inset dimension y is 4 meters.
A triangular window has an area of 594 square meters. The base is 54 meters. What is the height?
Answers
Answer:
22 m
Step-by-step explanation:
Use the formula for the area of a triangle. Fill in the known values and solve for the unknown.
A = (1/2)bh
594 m^2 = (1/2)(54 m)h
h = (594 m^2)/(27 m) = 22 m
The height of the window is 22 meters.
Let x1 = 12, y1 = 15, and y2 = 3. Let y vary inversely with x. Find x2.
Answers
Answer:
x2 = 60
Step-by-step explanation:
If the variables x and y are inversely proportional, the product x * y is a constant.
So using x1 and y1 we can find the value of this constant:
[tex]x1 * y1 = k[/tex]
[tex]12 * 15 = k[/tex]
[tex]k = 180[/tex]
Now, we can use the same constant to find x2:
[tex]x2 * y2 = k[/tex]
[tex]x2 * 3 = 180[/tex]
[tex]x2 = 180 / 3 = 60[/tex]
So the value of x2 is 60.
Marie plants 12 packages of vegetable seeds in a community garden. Each package costs $1.97. What is the total cost of the seeds?
Answers
Answer:
$23.64
Step-by-step explanation:
12 * $1.97 = $23.64
Solve the system of equations. \begin{aligned} & -5y-10x = 45 \\\\ &-3y+10x=-5 \end{aligned} −5y−10x=45 −3y+10x=−5
Answers
Answer:
x = -2
y = -5
Step-by-step explanation:
We can solve this algebraically (substitution or elimination) or graphically. I will be using elimination:
Step 1: Add the 2 equations together
-8y = 40
y = -5
Step 2: Plug y into an original equation to find x
-3(-5) + 10x = -5
15 + 10x = -5
10x = -20
x = -2
And we have our final answers!
Answer:
[tex]\boxed{\sf \ \ \ x=-2 \ \ \ and \ \ \ y=-5 \ \ \ }[/tex]
Step-by-step explanation:
let s solve the following system
(1) -5y-10x=45
(2) -3y+10x=-5
let s do (1) + (2) it comes
-5y-10x-3y+10x=45-5=40
<=>
-8y=40
<=>
y = -40/8=-20/4=-5
so y = -5
let s replace y in (1)
25-10x=45
<=>
10x=25-45=-20
<=>
x = -20/10=-2
so x = -2
Find the LCM of the set of algebraic expressions.
28x2,49xy, 28y
Answer
Answers
Answer:
196x^2y
Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
Need help ASAP!! thank you sorry if u can’t see it good :(
Answers
Answer/Step-by-step explanation:
==>Given:
=>Rectangular Pyramid:
L = 5mm
W = 3mm
H = 4mm
=>Rectangular prism:
L = 5mm
W = 3mm
H = 4mm
==>Required:
a. Volume of pyramid:
Formula for calculating volume of a rectangular pyramid us given as L*W*H
V = 5*3*4
V = 60 mm³
b. Volume of prism = ⅓*L*W*H
thus,
Volume of rectangular prism given = ⅓*5*3*4
= ⅓*60
= 20mm³
c. Volume of the prism = ⅓ x volume of the pyramid
Thus, 20 = ⅓ × 60
As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.
Determine if the expressions are equivalent.
when w = 11:
2w + 3 + 4 4 + 2w + 3
2(11) + 3 + 4 4 + 2(11) + 3
22 + 3 + 4 4 + 22 + 3
25 + 4 26 + 3
29 29
Complete the statements.
Answers
Answer:
Determine if the expressions are equivalent.
when w = 11:
2w + 3 + 4 4 + 2w + 3
2(11) + 3 + 4 4 + 2(11) + 3
22 + 3 + 4 4 + 22 + 3
25 + 4 26 + 3
29 29
Complete the statements.
Now, check another value for the variable.
When w = 2, the first expression is
11
.
When w = 2, the second expression is
11
.
Therefore, the expressions are
equivalent
.
Step-by-step explanation:
i did the math hope this helps
Answer:
Hii its Nat here to help! :)
Step-by-step explanation: A is 11 and b is 11.
C is Equal
Screenshot included.
Identify the Type II error if the null hypothesis, H0, is: The capacity of Anna's car gas tank is 10 gallons. And, the alternative hypothesis, Ha, is: Anna believes the capacity of her car's gas tank is not 10 gallons.
Answers
Answer:
20gallons
Step-by-step explanation:
Kyra is using rectangular tiles of two types for a floor design. They Tyler each type is shown below:
Answers
Answer: b) the tiles are not similar because both SP:SR is 5:4 and MJ:ML is 5:2
Step-by-step explanation:
We are given that the tiles are rectangular which implies that they both have a 90° angle.
In order to prove similarity, We need to show that the lengths and widths are proportional.
P Q R S
J K L M
a) PQ : QR JK : LM
w=4 L=5 w=2 w=2
↓
We need Length (not width)
b) SP : SR MJ : ML
L=5 w=4 L=5 w=2
5 : 4 5 : 2
When comparing length to width they do not have the same ratio so the rectangles are not similar.
c) PQ : QR JK : KL
w=4 L=5 w=2 L=5
4 : 5 2 : 5
When comparing width to length they do not have the same ratio so the rectangles are not similar.
d) SR : ML PQ : JK
w=4 w=2 w=4 w=2
↓ ↓
We need Length (not width)
LA=
Round your answer to the nearest hundredth.
A
5
B
3
Answers
Answer:
You didn't state it but you need to find Angle A.
From the Pythagorean Theorem, we calculate side ac
side ac^2 = 5^2 - 3^2 =25 -9 = 16 Side AC = 4
arc tangent angle A = 3 / 4 = .75
angle A = 36.87 Degrees
Step-by-step explanation:
A basketball coach is looking over the possessions per game during last season. Assume that the possessions per game follows an unknown distribution with a mean of 56 points and a standard deviation of 12 points. The basketball coach believes it is unusual to score less than 50 points per game. To test this, she randomly selects 36 games. Use a calculator to find the probability that the sample mean is less than 50 points. Round your answer to three decimal places if necessary.
Answers
Answer:
The probability that the sample mean is less than 50 points = 0.002
Step-by-step explanation:
Step(i):-
Given mean of the normal distribution = 56 points
Given standard deviation of the normal distribution = 12 points
Random sample size 'n' = 36 games
Step(ii):-
Let x⁻ be the random variable of normal distribution
Let x⁻ = 50
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{50-56 }{\frac{12}{\sqrt{36} } }= -3[/tex]
The probability that the sample mean is less than 50 points
P( x⁻≤ 50) = P( Z≤-3)
= 0.5 - P(-3 <z<0)
= 0.5 -P(0<z<3)
= 0.5 - 0.498
= 0.002
Final answer:-
The probability that the sample mean is less than 50 points = 0.002
Answer:
56
2
.001
Step-by-step explanation:
The Central Limit Theorem for Means states that the mean of any sampling distribution of the means is equal to the mean of the population distribution. The standard deviation is equal to the standard deviation of the population divided by the square root of the sample size. So, the mean of this sampling distribution of the means with sample size 36 is 56 points and the standard deviation is 1236√=2 points. The z-score for 50 using the formula z=x¯¯¯−μσ is −3.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.0 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
-2.9 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001
-2.8 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
-2.7 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
-2.6 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
-2.5 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005
Using the Standard Normal Table, the area to the left of −3 is approximately 0.001. Therefore, the probability that the sample mean will be less than 50 points is approximately 0.001.
Can someone please help
Use the In key on your calculator to estimate
the logarithm.
In 44
Round your answer to the nearest thousandth.
Answers
Answer:
3.784
Step-by-step explanation:
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly se
Answers
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?
Answer:
P( X' ∩ Y' ) = 0.205
Step-by-step explanation:
Let X is the event that the customer insures more than one car.
Let X' is the event that the customer insures exactly one car.
Let Y is the event that customer insures a sport car.
Let Y' is the event that customer insures not a sport car.
From the given information we have
70% of customers insure more than one car.
P(X) = 0.70
20% of customers insure a sports car.
P(Y) = 0.20
Of those customers who insure more than one car, 15% insure a sports car.
P(Y | X) = 0.15
We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
P( X' ∩ Y' ) = ?
Which can be found by
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
From the rules of probability we know that,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y ) (Additive Law)
First, we have to find out P( X ∩ Y )
From the rules of probability we know that,
P( X ∩ Y ) = P(Y | X) × P(X) (Multiplicative law)
P( X ∩ Y ) = 0.15 × 0.70
P( X ∩ Y ) = 0.105
So,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )
P( X ∪ Y ) = 0.70 + 0.20 - 0.105
P( X ∪ Y ) = 0.795
Finally,
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
P( X' ∩ Y' ) = 1 - 0.795
P( X' ∩ Y' ) = 0.205
Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.