Answer:
The contrapositive of the statement is true.
Step-by-step explanation:
For a general statement:
p ⇒ q
The contrapositive statement is:
¬q ⇒ ¬p
where:
¬q is the negation of the proposition q.
Here we have the statement:
If two angles are not complements, then their measures do not add up to 180°
So we have:
p = two angles are not complements
q = their measures do not add up to 180°
Then the negations are:
¬p = two angles are complements
¬q = their measures do add up to 180°
The contrapositive statement is:
"if for two angles their measures do add up to 180°, then the two angles are complements"
This is true, if for two angles the sum of their measures is equal to 180°, then these angles are complementary.
Then: The contrapositive of the statement is true.
Which of the following pairs consists of equivalent fractions? .4/6 and 3/5 or 9/16 and 3/32 or 18/48 and 15/40 or 7/10 and 10/7
Answer:
18/48 and 15/40
Step-by-step explanation:
18/48 = 3/8
15/40 = 3/8
•°• 18/48 is equivalent to 15/40
Use the distributive property to write the next step in simplifying th
numerical expression
7(2 + 7)
A. 7• 2+7•7
B. 7• 2+7
C. (7+2) • (7 + 7)
D. 7+2 • 7+ 7
Answer:
A)
Step-by-step explanation:
Which statement proves the given triangles are similar?
Answer:
it's the second one
Step-by-step explanation:
How do you find the amplitude, period, and shift for f(x)=−4cos(3x−π)+1?
Answer:
(a) Amplitude = 4
(b) [tex]T = \frac{2\pi}{3}[/tex] --- Period
(c)
[tex]C = \frac{\pi}{3}[/tex] --- phase shift
[tex]D =1[/tex] --- vertical shift
Step-by-step explanation:
Given
[tex]f(x) = -4\cos(3x - \pi) + 1[/tex]
Rewrite the function as:
[tex]f(x) = -4\cos(3(x - \frac{\pi}{3}) + 1[/tex]
Solving (a): The amplitude
A cosine function is represented as:
[tex]f(x) = A\cos[B(x - C)] + D[/tex]
Where:
[tex]|A| \to Amplitude[/tex]
So, in this equation (by comparison):
[tex]|A| = |-4|[/tex]
[tex]|A| = 4[/tex]
The amplitude is 4
Solving (b): The period (T)
This is calculated as:
[tex]T = \frac{2\pi}{B}[/tex]
By comparison:
[tex]B =3[/tex]
So:
[tex]T = \frac{2\pi}{3}[/tex]
Solving (c): The shift
The phase shift is C
The vertical shift is D
By comparison:
[tex]C = \frac{\pi}{3}[/tex] --- phase shift
[tex]D =1[/tex] --- vertical shift
Consider random samples of size 86 drawn from population A with proportion 0.43 and random samples of size 60 drawn from population B with proportion 0.15
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
(b) Are the sample sizes large enough for the Central Limit Theorem toa
Yes or No?
Answer:
a) The standard error is s = 0.071.
b) Yes, as both sample sizes are above 30.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
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]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Samples of size 86 drawn from population A with proportion 0.43
This means that [tex]n = 86, p = 0.43[/tex]. So:
[tex]s_A = \sqrt{\frac{0.43*0.57}{86}} = 0.0534[/tex]
Samples of size 60 drawn from population B with proportion 0.15:
This means that [tex]n = 60, p = 0.15[/tex]. So:
[tex]s_B = \sqrt{\frac{0.15*0.85}{60}} = 0.0461[/tex]
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
This is:
[tex]s = \sqrt{s_A^2 + s_B^2}[/tex]
[tex]s = \sqrt{(0.0534)^2 + (0.0461)^2}[/tex]
[tex]s = 0.071[/tex]
The standard error is s = 0.071.
(b) Are the sample sizes large enough for the Central Limit Theorem. Yes or No?
Yes, as both sample sizes are above 30.
PLEASE ANSWER ASAP FOR BRANLIEST!!!!!!!!!!!!
Answer:
1. zero
2. seven over eight
3. one over three
4. one
5. one over two
PLEASE GIVE BRAINLYIST!!
How many numbers lie between the squares of 39 and 40
Answer:
i guess its 1...
Step-by-step explanation:
Answer:
79 numbers
Step-by-step explanation:
39 x 39 = 1521 ( Find the square of 39)
40 x 40 = 1600 (Find the square of 40)
1600 - 1521 = 79 ( Finding the difference of the two squares)
Find all derivatives of y^n of the function y=√x+5
Hello,
As somebody has distroyed my question, (may be he have not understood ?)
i will reply to y=(√x)+5
[tex]\displaystyle \boxed{\dfrac{d^n y}{dx^n} =(-1)^n*n!! *\dfrac{1}{2^n} *x^{-\frac{2n+1}{2} }\\}\\y'=\dfrac{1}{2} *x^{-\frac{1}{2}} \\\\y''=-\dfrac{1}{4} *x^{-\frac{3}{2}} \\...\\[/tex]
Susan uses the function p(x) = 4x to determine the perimeter of a square when she knows the side length, x. Which statements are true about the function?
The perimeter is the dependent variable.
The length of the side of the square is the dependent variable.
The value of p(x) depends on the value of x.
The length of the side of the square is the independent variable.
The value p(x) can be found by multiplying p by x.
The perimeter is the independent variable.
Answer:
Step-by-step explanation:
The perimeter is the dependent variable. TRUE
The length of the side of the square is the dependent variable. FALSE
The value of p(x) depends on the value of x. TRUE
The length of the side of the square is the independent variable. TRUE
The value p(x) can be found by multiplying p by x. FALSE
The perimeter is the independent variable. FALSE
Find Trig Ratios (with Radicals)
Answer:
the answer is 45 + 5-75 is equals to 30 +5
plzzzzzzzzzzzzzzzzz help meeeeeeeeeeeeeeeeeee
i do anything just help
1.) Create a table of x and y values that represents a proportional relationship.
a) Explain how you know the relationship is proportional.
b) What equation models the values in the table?
2) Create a table of x and y values that represents a linear, non-proportional relationship.
a) Explain how you know the relationship is non-proportional.
b) What equation models the values in the table?
Answer:
Table could be first x = 2, y = 4, then x = 4, y = 8. It is proportional because both (x,y) values equal 1/2. The equation is x = 1/2y. Last, the table could be the same, or you could do first, x = 6, y = 12, then x = 12, y = 24, because they still equal 1/2.
Step-by-step explanation:
Question attached below
Answer:
s(8) = 1162
Step-by-step explanation:
We are told that the acceleration is;
a(t) = 18t + 16
Now, acceleration is the first derivative of velocity. Thus, we will integrate the acceleration function to get the velocity function.
v(t) = ∫a(t) = ∫(18t + 16)
v(t) = 9t² + 16t + c
We are told that at t = 0, v(0) = 16
Thus;
9(0)² + 16(0) + c = 16
c = 16
Thus;
v(t) = 9t² + 16t + 16
Also, the velocity is the first derivative of distance. Thus;
S = ∫v(t) = ∫9t² + 16t + 16
S = 3t³ + 8t² + 16t + c
At t = 0, s(t) = 10. Thus;
10 = 3(0³) + 8(0²) + 16(0) + c
c = 10
Thus;
s(t) = 3t³ + 8t² + 16t + 10
At t = 8;
s(8) = 3(8³) + 8(8²) + 16(8) + 10
s(8) = 1162
approximate 10.54 to the nearest ten
Answer:
11 because <.5 is rounded to the next ten
Plz help 1+1 PLZ SEND ANSWER
Answer:
2
Step-by-step explanation:
Find f(5) for f(x)-1/9(3)*
O A. 27
O B. 81
O C. 9
O D. 3
Describe the process for taking a set of data and creating a circle graph from it.
Answer:
Step-by-step explanation:
A circle chart can be referred to as a pie chart. This is a chart that expresses each fraction of total data in degrees.
The set of data given is summed so as to determine the total value. Then each data in the set is expressed as a ration of the total value, which is multiplied by [tex]360^{o}[/tex]. This is to determine the degree of angles that represent each data in the data set. These angles in degrees can now be used to divide the sum of angles in a circle into wedges.
With each wedge in the circle showing the fractional relationship between each data and the total value in degrees.
which elements in the following set are integers -8,3/4,-0.18,0,0.16,5,-2/7,6
Answer:
345
Step-by-step explanation:
eople
Find the perimeter and area of the figure pictured below.
odules
fice 365
3.7 m
om
11.4 m
ades
2.3 m
9.2 m
Q
Perimeter
m
Area -
m2
Answer:
Perimeter: 41.2 m
Area: 54.83 m^2
Step-by-step explanation:
REFER TO THE IMAGE ATTACHED AS A
GUIDE.
PERIMETER:
(ADD UP ALL THE LENGTHS OF EACH SIDE)
Must be all 6 sides (see image, I solved for the two missing lengths)
3.7 + 9.1 + 11.4 + 9.2 + 2.3 + 5.5 = 41.2
perimeter is 41.2 m
AREA:
(See image again)
Shape is divided into two rectangles:
Top rectangle area: 11.4 x 3.7 = 42.18 m^2
Bottom triangle area: 5.5 x 2.3 = 12.65 m^2
ADD:
42.18 m^2 + 12.65 m^2 = 54.83 m^2
The area of the whole figure is 54.83 m^2
HOPE THIS HELPS
PLEASE HELPPPPP ASAP
A function is shown in the table.
x g(x)
−3 17
−1 −3
0 −4
2 13
Which of the following is a true statement for this function?
The function is increasing from x = −3 to x = −1.
The function is increasing from x = −1 to x = 0.
The function is decreasing from x = 0 to x = 2.
The function is decreasing from x = −3 to x = −1.
Answer:
it's the last one, the function is decreasing from x=-3 to x=-1
Which of the following phrases would represent this expression?
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3
Answer:
the quotient of x and 3
Step-by-step explanation:
x divided by 3
division answers are called quotients
Answer:
Step-by-step explanation:
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3 is correct. We are dividing x into 3, not 3 into x.
You want to test the claim that the average age of students at Gorka College is greater than the average age of students at Yapoah College. You take a simple random sample of 53 people from Gorka and compute an average age of 21.2 (years) and a standard deviation of 1.1. Then you take a simple random sample of 46 students from Yapoah College and compute an average age of 20.7 and a standard deviation of 1.2.
Compute the t-statistic for testing the alternative hypothesis that the average age of Gorka students is greater than the average age of Yapoah students (set things up so that t is positive).
What are the degrees of freedom (using the conservative method)?
What is the P-value?
Is there significant evidence at the 0.05 level to support the hypothesis that the average age of Gorka students is higher than for Yapoah?
Answer:
Kindly check explanation
Step-by-step explanation:
The hypothesis :
H0 : μ1 = μ2
H1 : μ1 > μ2
Given :
x1 = 21.1 ; n1 = 53 ; s1 = 1.1
x2 = 20.7 ; n2 = 46 ; s2 = 1.2
The test statistic :
(x1 - x2) / √[(s1²/n1 + s2²/n2)]
(21.1 - 20.7) / √[(1.1²/53 + 1.2²/46)]
0.4 / 0.2326682
Test statistic = 1.719
The degree of freedom using the conservative method :
Comparing :
Degree of freedom = n - 1
Degree of freedom 1 = 53 - 1 = 52
Degree of freedom 2 = 46 - 1 = 45
Smaller degree of freedom is chosen ;
The Pvalue from Test statistic, using df = 45
Pvalue = 0.0462
Pvalue < α ; Hence, there is significant evidence to conclude that average age of Gorka student is higher than Yaphoa.
a binomial distribution
has 30% rate of SUCCESS.
there are 6 triats. what
is probability that there
will be exactly 2 Successes
Answer:
0.324
Step-by-step explanation:
Given that :
Success rate = 30%
p = 30% = 0.3
q = 1 - p = 1 - 0.3 = 0.7
Number of trials, n = 6
Probability of having exactly 2 successes ; x = 2
P(x = 2)
Usibgbtge binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 2) = 6C2 * 0.3^2 * 0.7^4
P(x = 2) = 15 * 0.3^2 * 0.7^4
P(x = 2). = 0.324135
P(x = 2) = 0.324
What is f(-2) for f(x)=(1/2)x^2
Answer:
[tex]{ \bf{f(x) = \frac{1}{2} {x}^{2} }} \\ \\ { \tt{f( - 2) = \frac{1}{2} {( - 2)}^{2} }} \\ = 2[/tex]
Given m n, find the value of X.
Answer:
x = 62
Step-by-step explanation:
62 and x are alternate exterior angles and alternate exterior angles are equal when the lines are parallel
Quick !
The perimeter of the rectangle below is 118 units. Find the length of side AD.
Answer:
24
Step-by-step explanation:
the perimeter is all sides added up
therefore to solve for "z"
3z + 3z + 4z + 3 + 4z + 3 = 118
simplify
14z + 6 = 118
isolate z by first subtracting 6 from both sides and then dividing by 14 for both sides
z=8
plug z into side CB as AD and CB are congruent
3(8)
=24
This question difficult and i need some help would anyone please help me
Answer:
x = 30
F = 130
G = 50
Step-by-step explanation:
f and g are supplementary which means they add to 180
5x-20 + 3x - 40 = 180
Combine like terms
8x - 60 = 180
Add 60 to each side
8x-60+60 = 180+60
8x = 240
Divide by 8
8x/8 = 240/8
x = 30
F = 5x -20 = 5*30 -20 = 150 -20 = 130
G = 3x-40 = 3*30 -40 = 90-40 = 50
Answer:
Because a straight line = 180, we can find x like this :
(5x - 20) + (3x - 40) = 180
Step 1 - collect like terms
8x - 60 = 180
Step 2 - Move terms around to isolate x
8x = 180 + 60
Step 3 - Divide both sides by 8
x = 30
Now you can find the value of the angles by plugging in x
∠f = (5 x 30) - 20
= 130 degrees
∠g = (3 x 30) - 40
= 50 degrees
We can check to see if this works by adding them up
130 + 50 = 180, so this is correct
Hope this helps! I would really appreciate a brainliest if possible :)
Find the value of each shape so that they will add up to give you the specified sums in each row and each column.
How does this solving problem relate to system of equations?
Answer:
Step-by-step explanation:
What is the output of the following function for x=2
F(x)= 2x^4-x^3+5x-9
Answer:25
Step-by-step explanation:
emma can read 4 pages of a book in 8 minutes how many pages can she read per minute if she still had it 24 pages how many pages are there in the book
Answer:
Emma can read 30 pages per minute
Number of book pages 28
Step-by-step explanation:
ASAP PLEASE!!The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed. Find the probability P(T=1). write your answer as a fraction.
Answer:
[tex]P(T = 1) = \frac{3}{8}[/tex]
Step-by-step explanation:
The table, along with the relative frequency chart, state that the probabilities are:
[tex]P(T = 0) = \frac{1}{8}[/tex]
[tex]P(T = 1) = \frac{3}{8}[/tex]
[tex]P(T = 2) = \frac{3}{8}[/tex]
[tex]P(T = 3) = \frac{1}{8}[/tex]
Find the probability P(T=1)
As given by the table, and by the relative frequency chart, [tex]P(T = 1) = \frac{3}{8}[/tex]