Answer:
Haha proofs are an interesting thing. Usually, nothing is to scale, which is why you can't measure anything. They are pretty annoying, but it helps to know why certain things are the way that they are and develop justification skills for higher level math.
Sorry to discourage you, but you're going to see "Justify" quite a lot in calculus and beyond which is basically a more informal version of a proof
you can never escape it tbh lol
We can't just measure the two figures to see if they are congruent as congruence is about shape and size.
What is congruence?It should be noted that congruence simply means that the shapes have identical length, angles, and size.
Therefore, we can't just measure the two figures to see if they are congruent as congruence is about shape and size.
Learn more about geometry on:
brainly.com/question/24375372
#SPJ9
LA=
Round your answer to the nearest hundredth.
A
5
B
3
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 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.
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.
If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion?
When a number is divisible by 9, the number is divisible by 3.
then the number is divisible by 3
then the number is divisible by 9
O if a number is divisible by 3
O if a number is divisible by 9
Answer:
Correct statement: "the number is divisible by 3".
Step-by-step explanation:
The statement provided is:
When a number is divisible by 9, the number is divisible by 3.
The general form of a conditional statement in if-then form is:
[tex]p\rightarrow q[/tex]
This implies that if p, then q.
The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.
The if-then form of the provided statement is:
If a number is divisible by 9, then the number is divisible by 3.
So, the conclusion is:
"the number is divisible by 3"
Answer:
a
Step-by-step explanation:
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.
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.
Please answer this correctly
Answer:
54
Step-by-step explanation:
The pink parts are 9 out of total 11 parts.
9/11
Multiply with 66.
9/11 × 66
= 54
Hey there! :)
Answer:
P(Pink) = 54.
Step-by-step explanation:
Begin by calculating the possibility of the spinner landing on pink:
[tex]P(pink) = \frac{pink}{total}[/tex]
Therefore:
[tex]P(Pink) = \frac{9}{11}[/tex]
In this question, the spinner was spun 66 times. Since we have solved for the probability, we can set up ratios to find the probability of the spinner landing on pink out of 66.
[tex]\frac{9}{11}= \frac{x}{66}[/tex]
Cross multiply:
594 = 11x
Divide both sides by 11:
x = 54.
P(Pink) = 54.
Find the equation of the line.
Use exact numbers.
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
from what area of the world is the earliest dated inscription with a symbol for zero?
Answer:
india
Step-by-step explanation:
Can someone please help me??
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.
Kyra is using rectangular tiles of two types for a floor design. They Tyler each type is shown below:
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)
PLEASE answer pic provided
Answer:
50 to 60 seconds is the answer
Pls Help!
Given the polynomial function below, find F(3).
F(x) = 2x3 - 7x + 1
A. 34
B. -8
C. 26
D. -2
Answer:
34
Step-by-step explanation:
F(x) = 2x^3 - 7x + 1
Let x= 3
F(3) = 2* 3^3 - 7*3 + 1
= 2 * 27 -21+1
= 54 -21 + 1
= 34
Answer: 34
Step-by-step explanation:
It is known that 4% of children carry a certain virus, but a leading health researcher suspects that the percentage is actually higher. Which of the following provides the most convincing evidence to support the researcher's suspicion?
A. Out of 5,000 randomly chosen children, 210 children carry the virus.
B. Out of 60 randomly chosen children, 3 children carry the virus.
C. Out of 5,000 randomly chosen children, 250 children carry the virus.
D. Out of 20 randomly chosen children, 1 child carries the virus.
Answer:
(C)Out of 5,000 randomly chosen children, 250 children carry the virus.
Step-by-step explanation:
[tex]\text{Option A}: \dfrac{210}{5000}=0.042=4.2\% \\\text{Option B}: \dfrac{3}{60}=0.05=5\% \\\text{Option C}: \dfrac{250}{5000}=0.05=5\% \\\text{Option D}: \dfrac{1}{20}=0.05=5\%[/tex]
The higher the research sample, the more credible the results. In options A and C, the research sample was 5000. However, since the relative frequency of children carrying the virus is 5% in both, we take the result with a higher number of positives.
Option C is the correct option.
20 points answer thisssss
area =πr²
6.5²xπ=132.73
2.3²xπ=16.62
132.73-16.62= 116.11
116cm^2
i think its this anyway
Answer:
116 cm^2 to 3 s f's.
Step-by-step explanation:
The area of the shaded part = area of the outer circle - area of the inner circle
= π * 6.5^2 - π * 2.3^2
= 132.732 - 16.619
= 116.113 cm^2.
segment AB is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by?
1/2
2
3
4
Answer:
the answer is 3
Step-by-step explanation:
i took the test
What is the product? (3x-b)(2x^2-7x+1) A. -12x^2+42x-6 B. -12x^2+21x+6 C. 6x^3-33x^2+45x-6 D. 6x^3-27x^2-39x+6
Answer:
C.6x³-33x² + 45x-6
Step-by-step explanation:
(3x-6)(2x^2-7x+1)
= 3x(2x² - 21x +1) -6(2x² - 7x+1)
= (6x³ - 21x² + 3x) - (12x² - 42x+6)
= 6x³ - 21x² + 3x -12x² + 42x -6
= 6x³-33x² + 45x-6
5/a - 4/b as a single fraction
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:
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?
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
The mean annual tuition and fees for a sample of 15 private colleges was with a standard deviation of . A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from 32,500 a) state the null and alternate hypotheses b) calculate the standard error c) calculate the test statistic d) find the p - value .
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500
Solution
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 32500
For the alternative hypothesis,
Ha: µ ≠ 32500
This is a two tailed test.
Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.
Since n = 15,
Degrees of freedom, df = n - 1 = 15 - 1 = 14
t = (x - µ)/(s/√n)
Where
x = sample mean = 35500
µ = population mean = 32500
s = samples standard deviation = 6500
t = (35500 - 32500)/(6500/√15) = 1.79
We would determine the p value using the t test calculator. It becomes
p = 0.095
Assuming alpha = 0.05
Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.
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
Answer:
25%
Step-by-step explanation:
The last percentile always contains 25% of the observations.
Tamar is measuring the sides and angles of Triangle T U V to determine whether it is congruent to the triangle below. For triangle K L M, side K M is 27 millimeters, side L M is 20 millimeters, and side K L is 12 millimeters. Angle K is 45 degrees, angle M is 25 degrees, angle L is 110 degrees. Which pair of measurements would eliminate the possibility that the triangles are congruent? Measure of angle T = 25 degrees and Measure of angle U = 45 degrees Measure of angle T = 110 degrees and Measure of angle V = 25 degrees Measure of angle T = 25 degrees and TU = 12 Measure of angle T = 110 degrees and UV = 27
Answer: Measure of angle T = 25 degrees and Measure of angle U = 45 degrees
Step-by-step explanation:
Measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.
What are congruent triangles?
" Triangles are said to be congruent if the corresponding sides and angles of the one triangle are equals to the other triangles."
According to the question,
In triangle KLM,
KM =27millimeters
LM = 20millimeters
KL = 12 millimeters
∠K= 45degrees
∠M= 25 degrees
∠L = 110degrees
From the given measurements of the triangle we have,
side with measure 27millimeters is opposite to angle 110° .
side with measure 12millimeters is opposite to angle 25° .
side with measure 20millimeters is opposite to angle 45°.
From the conditions in triangle TUV to be congruent to triangle KLM ,
Measure of angle T = 25 degrees and TU = 12 is against the given condition of congruent triangle.
As angle T and side TU are adjacent to each other, which is against the correspondence of the given triangle.
Hence, measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.
Learn more about congruent triangle here
https://brainly.com/question/12413243
#SPJ2
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?
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
Two fair dice are tossed and the number on each die is recorded, e.g. (3,2) indicates the first die had 3 and the second die had a 2. In total, there are 36 (equally likely) outcomes in the sample space. What is the probability the sum of the two dice is 7 or 11? Group of answer choices
Answer:
P(7 or 11) = 0.2222
Step-by-step explanation:
First let's find the cases where we get a sum of 7 and a sum of 11:
The cases where we get a sum of 7 are:
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
And the cases where we get a sum of 11 are:
(5,6), (6,5)
So we have a total of 8 cases among the 36 total possible outcomes.
So the probability of the sum of the two dice being 7 or 11 is:
P(7 or 11) = 8 / 36 = 0.2222
Please answer this correctly
Answer:
3/10
Step-by-step explanation:
what is the solution to the equation y=2/3x+3 X=-2
Answer: The solution is [tex](-2,\frac{5}{3} )[/tex]
Step-by-step explanation:
it already gives you the solution for x so just plot it into the equation to solve for y.
y= [tex]\frac{2}{3} *\frac{-2}{1}+3[/tex]
y= [tex]\frac{-4}{3}+\frac{3}{1}[/tex]
y= [tex]\frac{5}{3}[/tex]
Answer: -2 5/3
Step-by-step explanation:
y= 2/3*-2/1+3
y= -4+3/1
-2 5/3
The sum of a number and twice the number is 24 what is the number?
Answer:
x = 8
Step-by-step explanation:
Step 1: Write out the expression
x + 2x = 24
Step 2: Combine like terms
3x = 24
Step 3: Isolate x
x = 8
And we have our final answer!
Answer:
X=8
Step-by-step explanation:
The percentage of households that include at least one frequent gamer is 58%. A gaming magazine is interested in studying this further to see how it impacts their magazine advertisements. For what sample size, n, will the sampling distribution of sample proportions have a standard deviation of 0.02
Answer:
For a sample size of n = 609.
Step-by-step explanation:
Central limit theorem for proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have that p = 0.58.
We have to find n for which s = 0.02. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]
[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]
[tex]n = 609[/tex]
For a sample size of n = 609.
Solve the system of equations. \begin{aligned} & -5y-10x = 45 \\\\ &-3y+10x=-5 \end{aligned} −5y−10x=45 −3y+10x=−5
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
Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the number of times that she will roll a number that is greater than 4? P (number greater than 4) = StartFraction 1 over 6 EndFraction (50) P (number greater than 4) = StartFraction 2 over 6 EndFraction (50) P (number greater than 4) = StartFraction 3 over 6 EndFraction (50) P (number greater than 4) = StartFraction 4 over 6 EndFraction (50)
Answer:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
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.
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.
what is the length of the line?
Answer:
root 61
Step-by-step explanation:
You can use the distance formula or draw a triangle with sides 5 and 6