Evaluate the following question given below
The solution is, simplification of the expression is; 71.19.
Here, we have,
the given expression is:
(5/2)^4/2 * (3/2)^6
=(5/2)^2 * (3/2)^6
as we know that, 4/2 = 2.
now, we have,
(5/2)^2 * (3/2)^6
=5²/2² ^ 3⁶/2⁶
= 5² * 3⁶ / 2² * 2⁶
=5² * 3⁶ / 2 ^ (2+6)
=5² * 3⁶ / 2 ^8
=25 * 729/ 256
=18225/ 256
=71.19
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y intercepts of f((x)=x^{2}+2x-3
Answer:
The y-intercept is -3
Written as a point it is (0, -3)
Step-by-step explanation:
To find the y-intercept, let x = 0
(and to find x-intercepts, let y = 0)
So let's let x = 0
f(x) = x^2 + 2x - 3
y = x^2 + 2x - 3
y = 0^2 + 2(0) - 3
y = -3
This means the y-intercept is -3. The graph crosses the y-axis at -3. This is the point (0, -3).
In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer. There are 9 students who play neither. Create a table to find probabilities.
5. What is the probability that a student chosen randomly from the class plays golf or
soccer?
6. What is the probability that a student chosen randomly from the class plays golf and soccer?
I rlly need the help!
The solution is:
20/29 is the probability that a student chosen randomly from the class plays golf or soccer.
0 is the probability that a student chosen randomly from the class plays golf and soccer.
Here, we have,
given that,
In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer.
There are 9 students who play neither.
Number of students that play = 20
let, students play golf = A
students play soccer = B
so, given that,
n ( A) = 6 and, n ( B) = 14
so, total sample space = 29
now, P(A) = 6/29
P(B) = 14/29
and, P(students who play neither) = 9/29
we get, 6/29 + 14/ 29 + 9/29 = 29/29 = 1
i.e. there are no students who play both golf and soccer = 0
all the events are independent.
so, we have,
the probability that a student chosen randomly from the class plays golf or soccer = P(A) + P(B)
= 6/29 + 14/ 29
= 20/29
and, the probability that a student chosen randomly from the class plays golf and soccer = 0.
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Which of the following statements are true regarding the reflection of A(1 1/2,-2)? Select all that apply..
The correct statements are:
A) When this point is reflected across the x-axis, the x-coordinate stays the same and the y-coordinates are opposites.C) When this point is reflected across the y-axis, the x-coordinates are opposites and the y-coordinate stays the same.D) When this point is reflected across the x-axis, the x-coordinates are opposites and the y-coordinate stays the same.How to explain the statementsWhen a point is reflected across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. Therefore, statement A) is true.
When a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate changes sign. Therefore, statement C) is true.
It should be noted that to represent the reflection of point A (1,-2) across the y-axis, we flip the sign of the x-coordinate to obtain the image point A' (-1,-2). Therefore, statement D) is true.
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PLEASE HELP ME
Which of these triangles are definitely right triangles?
(Note that not all triangles are drawn to scale.)
(Select all that apply.)
A
B
C
D
E
Answer:
I'd like to explain more but I have limited comment
chat me up
A
Which expression is a function that has zeros at 4 and –3?
Answer:
[tex]f(x) = (x - 4)(x + 3) [/tex]
[tex]f(x) = {x}^{2} - x - 12[/tex]
If the Coach chooses the Three-Year Plan, what is the total amount he will spend after 12 months? ANSWER QUICK ILL GIVE BRAINLIST!
Answer:
$17,320 after 12 months.
Step-by-step explanation:
f the Coach chooses the Three-Year Plan, the total amount he will spend after 12 months can be calculated as follows:
First, we need to calculate the total amount of monthly payments made in 12 months:
12 months x $610 per month = $7,320
Then, we need to add the down payment made at the time of purchase:
$7,320 + $10,000 = $17,320
Therefore, if the Coach chooses the Three-Year Plan, he will spend a total of $17,320 after 12 months.
The equation a(s) = 37.5s - 1.5s2 models the function
represented in the table. Fill in the blank to complete the
restricted domain of the function. D = {0 ≤s ≤
The restricted domain of the function is 0≤s≤25
The equation is a(s) = 37.5s - 1.5s² models the function represented in the table
a(s) = s(37.5 - 1.5s)
The critical points are s=0 or
37.5 - 1.5s
37.5 = 1.5s
s=25
As area can not be negative, the area should be positive
s< 0 and s>25
Therefore, restricted domain is 0≤s≤25
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Question
Evaluate |—15u| + |3v| + 3 when u
=
3 and v = 3.
The value of given expression is 57.
We are given that;
|—15u| + |3v| + 3
u=3, v = 3
Now,
To evaluate the expression, you need to substitute the values of u and v and simplify. The absolute value of a number is the distance from zero on the number line, so it is always positive or zero. You can write your solution as:
|—15u| + |3v| + 3 = |—15(3)| + |3(3)| + 3 = |—45| + |9| + 3 = 45 + 9 + 3 = 57
Therefore, by the given expression the answer will be 57.
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Find the sum of -17x,-15x,-2x
If p(x)=0.5(x-5)^2+14, what is the value of p(3)
Answer:
p(3) = 16
Step-by-step explanation:
to evaluate p(3) substitute x = 3 into p(x)
p(3) = 0.5(3 - 5)² + 14
= 0.5(- 2)² + 14
= 0.5(4) + 14
= 2 + 14
= 16
The equilateral triangle shown has a perimeter of 30 inches and a height of a inches.
What is the value of a?
O 5 in
O 5√3 in
O10 in
•10√3 in
The height of the equilateral triangle is a = 5√3 inches
Given data ,
Since the triangle is equilateral, all sides are of equal length.
Let's call the length of one side x.
Therefore, the perimeter of the triangle is 3x, which is given to be 30 inches.
On simplifying , we get
3x = 30
x = 10
Now, we know that the height of an equilateral triangle is given by the formula:
height = √3/2 x
Substituting the value of x, we get:
height = √3/2 x 10
height = 5√3 inches
Hence , the height of triangle is 5√3 inches
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If a town's population doubles every 4 years, how
many people will be in the down 12 years later if the
current population is 28,100? y = ab*
The population of the town 12 years later will be 224,800 if the current population is 28,100 and the population doubles every 4 years.
Since the population doubles every 4 years, we can use the formula:
P = P0 x [tex]2^{t/4}[/tex]
where P0 is the initial population, t is the time elapsed in years, and P is the population after time t.
In this case, the initial population P0 is 28,100, and we want to know the population after 12 years, so t = 12. Substituting these values into the formula, we get:
P = 28,100 2^(12/4)
= 28,100 x 2³
= 28,100 * 8 = 224,800
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Enter the number that belongs in the green box
Answer:
Set your calculator to Degree mode.
10² = 6.78² + 4² - 2(6.78)(4)(cos x)
100 = 61.9684 - 54.24(cos x)
38.0316 = -54.24(cos x)
cos x = -.701173
[tex]x = {cos}^{ - 1} ( - .701173)[/tex]
x = 134.52°
Please help really urgent
Answer:
0.0909
Step-by-step explanation:
4 blue + 5 red + 3 black = 12 chips in total.
p=probability
1st draw:
p (blue) = 4/12
there are now 11 chips in the bag, 4-1 =3 are blue.
2nd draw?
p (blue) = 3/11
probability of pulling one blue chip followed by another blue chip is:
(4/12) X (3/11) = (4X3)/12X11)
= (12)/(132)
= 1/11
0.0909
QUESTION 8 1 POINT
.
Find the GCF of the following three monomials:
21x³y5
63x5y²
45x¹y³
The greatest common factor (GCF) of the three monomial, 21x³y⁵, 63x⁵y² and 45x¹y³ is 3xy²
How do i determine the greatest common factor (GCF)?The greatest common factor (GCF) of the three monomials, 21x³y5, 63x5y² and 45x¹y³ can be obtained as follow:
First, we shall determine the factors of each monomials. This is illustrated below:
21x³y⁵ = 3 × 7 × x × x × x × y × y × y × y × y
63x⁵y² = 3 × 3 × 7 × x × x × x × x × x × y × y
45x¹y³ = 3 × 3 × 5 × x × y × y × y
Finally, we shall determine the greatest common factor (GCF) from the factors listed above. This is shown below:
3 × x × y × y = 3xy²
Thus, we can conlude that the greatest common factor (GCF) of the three monomials is 3xy²
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In Exercises
frequencies.
9.
Gender
9 and 10, find and interpret the marginal
(See Example 1.)
Male
Female
Set Academic Goals
No
168
142
Yes
64
54
suport
no sas8
09. The total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals.
10. The total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.
In order to find the marginal frequencies, we need to calculate the totals for each category separately.
For question 9:
The marginal frequency for "Set Academic Goals - yes" is 64 + 54 = 118. This represents the total number of individuals who answered "yes" to setting academic goals.
The marginal frequency for "Set Academic Goals - no" is 168 + 142 = 310. This represents the total number of individuals who answered "no" to setting academic goals.
The marginal frequency for "Male" is 64 + 168 = 232. This represents the total number of males.
The marginal frequency for "Female" is 54 + 142 = 196. This represents the total number of females.
Interpretation:
The marginal frequencies provide us with the total counts for each category in a contingency table. In this case, we can see that out of the total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals. Additionally, there were 232 males and 196 females in the sample.
For question 10:
The marginal frequency for "Cat - yes" is 104 + 186 = 290. This represents the total number of individuals who have cats.
The marginal frequency for "Cat - no" is 208 + 98 = 306. This represents the total number of individuals who do not have cats.
The marginal frequency for "Dog - yes" is 104 + 208 = 312. This represents the total number of individuals who have dogs.
The marginal frequency for "Dog - no" is 186 + 98 = 284. This represents the total number of individuals who do not have dogs.
Interpretation:
The marginal frequencies reveal the total counts for each category in the contingency table. In this case, we can observe that out of the total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.
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100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer:
Refer to the step-by-step.
Step-by-step explanation:
Verify the given identity.
[tex]E_0\cos^4(\theta)=E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2[/tex]
Pick the more complex side to manipulate, in this case it is the R.H.S.
(1) - Apply the following double-angle identity
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Double-Angle Identity:}}\\\\\cos(2A)=1-2\sin^2(A)\end{array}\right}[/tex]
[tex]E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2\\\\\Longrightarrow \boxed{ E_0\Big(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2}\Big )^2}[/tex]
(2) - Split of the right fraction
[tex]E_0(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2} )^2\\\\\Longrightarrow E_0(\frac{1}{2} +\frac{1}{2} -\frac{2\sin^2(\theta)}{2})^2\\\\\Longrightarrow \boxed{E_0(1 -sin^2(\theta))^2}[/tex]
Apply the following Pythagorean identity
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\sin^2(A)=\cos^2(A)\end{array}\right}[/tex]
[tex]E_0(1 -sin^2(\theta))^2\\ \\\Longrightarrow E_0(\cos^2(\theta))^2\\\\\therefore \boxed{E_0\cos^4(\theta)=E_0\cos^4(\theta)}[/tex]
Thus, the identity is verified.
It has been proven and verified that [tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex] below.
How to verify the equality of the cosine function?In Mathematics and Geometry, the standard equation of a cosine function is represented or modeled by the following mathematical equation (formula):
y = Acos(Bx - C) + D
Where:
A represents the amplitude.B = 2π/P.P represents the period.C represents the phase shift.D represents the center line (midline).In this exercise, you are required to prove that the right-hand side of the cosine function is equal to left-hand side of the cosine function;
[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex]
From the double-angle formulas, we have:
2sin²θ = 1 - cos2θ
cos2θ = 1 - 2sin²θ
Next, we would evaluate the right-hand side of the cosine function by substituting "1 - 2sin²θ" for cos2θ as follows;
[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1-2sin^2 \theta}{2} )^2\\\\E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1}{2} -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -sin^2 \theta)^2\\\\[/tex]
E₀cos⁴θ = E₀(1² - (sin²θ)²)
E₀cos⁴θ = E₀(1 - sin⁴θ) ⇒ (Verified).
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1,3,5,7,9…. What is the next number
Answer: 11
Step-by-step explanation:
this is a sequence of odd numbers.
it goes;
1,3,5,7,9,11,13,15,17,19,21,23....
(22-26)²+(34-26)²+(30-26)²+(14-26)²+(30-26)[tex]\frac{x}{y}[/tex]5
Answer:
[tex]20x+240y/y[/tex]
Step-by-step explanation:
1. Subtract the numbers
2. Evaluate the exponents
3. Subtract the numbers, again
4. Have a great day and thx for your inquiry :)
i really need the answer to this, can anyone help me please?
The value of total area of the shape is,
⇒ 82 cm²
We have to given that;
Figure of shape is shown.
Since, Figure is made by three rectangles.
And, Area of rectangle is,
A = length x width
Hence, The area of upper rectangle is,
A = 3 x 8
A = 24 cm²
Area of middle rectangle is,
A = (11 - (3 + 5)) x (8 - 2)
A = 3 × 6
A = 18 cm²
Area of lower rectangle is,
A = 5 x 8
A = 40 cm²
Thus, The value of total area of the shape is,
⇒ 24 + 18 + 40 cm²
⇒ 82 cm²
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Five runners need to be arranged in 5 lanes for a race so that there is a runner in each lane
How many unique ways are there to arrange the numbers in the 5 lanes
Step-by-step explanation:
5 P 5 = 120 ways = 5!
Bir saat 4:15 saat ve dört yarım saat kaç şey kaç saat eder
Answer:
dört yarım saat 2 saattir
Step-by-step explanation:
Help please im not that good in math
Answer: the awnser is b
Step-by-step explanation:
The equation y=195(1.10)x can be used to represent growth in the number of Salad Supreme restaurants since 2005. Which is the most reasonable conclusion based on this information? A. Salad Supreme had 110 restaurants in 2005. B. Salad Supreme is increasing the number of restaurants by 10% each year. C. Salad Supreme is increasing the number of restaurants by 195 each year. D. Salad Supreme is increasing the number of restaurants by 110% each year.
The most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year. Option B
How to determine the most reasonable conclusionBased on the given equation y = 195(1.10)^x, where x represents the number of years since 2005 and y represents the number of Salad Supreme restaurants, we can draw the following conclusions:
A. Salad Supreme had 110 restaurants in 2005: This conclusion is not supported by the given equation.
B. Salad Supreme is increasing the number of restaurants by 10% each year: This conclusion is supported by the equation.
C. Salad Supreme is increasing the number of restaurants by 195 each year: This conclusion is not supported by the equation.
D. Salad Supreme is increasing the number of restaurants by 110% each year: This conclusion is not supported by the equation. The growth factor of 1.10 (or 10%) indicates a 10% increase each year, not 110%.
Therefore, the most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year.
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John collected data to determine how many minutes his teammates spend practicing basketball each night. Identify the outlier in his data.
Question 1 options:
10 minutes
40 minutes
30 minutes
5 minutes
Answer:
Step-by-step explanation:
5 minutes is the outlier. It sticks out from the rest.
convert 500 cm to m?
Hello!
m dm cm mm
5 , 0 0
500cm = 5m
A random sample of 16 ATM transactions shows the mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. Can you show the width of the 90 percent confidence interval for the true mean transaction time?
The width of the confidence interval is 1.2786.
From the question we are told that
The sample size is n = 16
The mean time is x = 2.8 minutes
The standard deviation is = 1.2 minutes
Generally, the degree of freedom is mathematically represented as
df = n-1
df = 15
From the question we are told the confidence level is 95%, hence the level of significance is =
α = 100-95
α = 0.05
Generally, the margin of error is mathematically represented as =
[tex]E = t_{\alpha/2}, 15 \times \sigma/\sqrt{n}[/tex]
E = 2.131 × 1.6 / √16
E = 0.6393
Generally, the width the confidence 95% confidence interval
W = 2E
W = 1.2786
Hence the width of the confidence interval is 1.2786.
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Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer: 29.9986-----30.0 degrees
Step-by-step explanation:
x = [tex]tan^-^1(5.6/9.7)\\\\toa[/tex]
[tex]\tan(x )=\cfrac{\stackrel{opposite}{5.6}}{\underset{adjacent}{9.7}} \implies \tan^{-1}(~~\tan( x )~~) \approx \tan^{-1}\left( 0.58 \right) \\\\\\ x \approx\tan^{-1}\left( 0.58 \right)\implies x \approx 30.0^o[/tex]
What is the range of the function y=−7x−5?
Step-by-step explanation:
"Range'' is the values of 'y' that a graph can have....there are no limits on this one
(-∞,+∞)
