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Explanation:
Let's isolate the variable 'a' in the given inequality.
4a + 2 > 12
4a + 2-2 > 12-2
4a > 10
4a/4 > 10/4
a > 2.5
In the second step, I subtracted 2 from both sides to undo the "plus 2". In the second to last step, I divided both sides by 4 to undo the multiplication.
The solution is a > 2.5, meaning that anything larger than 2.5 will work in the original inequality.
For example, we could try a = 3 to get
4a + 2 > 12
4*3 + 2 > 12
12 + 2 > 12
14 > 12
which is true. This makes a = 3 a solution. The value a = 3.5 is a similar story, so it's also a solution.
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As an example of a non-solution, let's try a = 1
4a + 2 > 12
4*1 + 2 > 12
4 + 2 > 12
6 > 12
which is false. So we can see why a = 1 is not part of the solution set. You should find that a= 0.5 and a = 2.5 won't work as well for similar reasoning.
Write the relation between hypotenus perpendicular and base
Answer:
the area of the square on the hypotenuse is equal to the sum of the areas of squares of perpendicular and base".
A teapot,which has a capacity of one and half litters, can fill six identical mugs with tea.what is the capacity of the six mugs altogether?
Answer:250
Step-by-step explanation:
Solve for x . 7 - (2 x + 11) + 3(3 - x ) = 20
A.7/5
B.-3
C.-4
Answer:
the answer to the question is a:-3
a which matrix post multiplies to (1 3 3 4) to get (19 -3 75 13)
Answer:
[19 -1 25 3.25]
Step-by-step explanation:
just take the elements from the resultant matrix and divide it by the corresponding elements in the given matrix to find the matrix that's being asked.
How do I solve (-4.25+8)-3.5 ?
Answer:
answer must be 0.5:
Step-by-step explanation:
by simplify formula BODMAS
A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. By what age have 80% of the plan participants passed away?
Answer:
By 71 years of age 80% of the plan participants have passed away.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 68 years and a standard deviation of 4 years.
This means that [tex]\mu = 68, \sigma = 4[/tex]
By what age have 80% of the plan participants passed away?
By the 80th percentile of ages, which is X when Z has a p-value of 0.8, so X when Z = 0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 68}{4}[/tex]
[tex]X - 68 = 4*0.84[/tex]
[tex]X = 71[/tex]
By 71 years of age 80% of the plan participants have passed away.
Give the domain and range.
x –2 0 2 y –1 0 1
a. domain: {2, 0, 2}, range: {1, 0, 1} b. domain: {–2, 0, 2}, range: {–1, 0, 1} c. domain: {–1, 0, 1}, range: {–2, 0, 2} d. domain: {1, 0, 1}, range: {2, 0, 2}
Answer:
B. domain {-2, 0, 2}, range {-1, 0, 1}
Step-by-step explanation:
The x values and y values as ordered pairs would be: (-2,-1), (0,0), (2,1)
The domain is the all of the values of x and the range is all the values of y.
Simplify: - 6y^2 + 8y^3 - 4y^2 + y - 10y^3
Answer:
[tex]-6y^{2}+8y^{3}-4y^{2}+y-10y^{3}\\\\=(-6-4)y^{2}+(8-10)y^{3}+y\\\\=-2y^{3}-10y^{2}+y\\\\=y(-2y^{2}-10y+1)[/tex]
Find x. Round your answer to the nearest tenth of a degree.
Answer:
x = 55.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hypotenuse
cos x = 9/16
Taking the inverse cos of each side
cos^-1 (cos x) = cos^-1 (9/16)
x=55.77113
To the nearest tenth
x = 55.8
Answer:
Relative to x, the side of 16 is the hypotenuse, and the side of 9 is adjacent.
So we think, what trigonometric property relates hypotenuse and adjacent sides of a right triangle?
SOH CAH TOA
We can use the COSINE function to solve in this case, as we have both the ADJACENT SIDE (A) and the HYPOTENUSE (H).
Cosine = Adjacent/Hypotenuse
Cosine (x) = 9/16
Angle x = 55.8 degrees.
Let me know if this helps!
Calculate the total number of trials for an absolute frequency of five trials and a relative
frequency of 50 percent
Answer:
23456789990000000000000000000
look at the image below for the question !!!!!!
Answer:
136 cm2
Step-by-step explanation:
6*2=12 12*2=24
6*7=42 42*2=84
7*2=14 14*2=28
Add.
24+84+28=136
I hope this helps!
Divide into two triangles in a straight line
Step-by-step explanation:
I am not sure but is this question like this
if it's not i am sorry
find the probability of rolling a sum of a three first and then a sum of nine when a pair of dice is rolled twice
Answer:
Step-by-step explanation:
favorable events for a sum of 3 are 12,21
P(sum 3)=2/36=1/18
favorable events for a sum of 9 are 36,63,45,54
P(sum of 9)=9/36=1/4
Four friends go to the movies. How many different ways can they sit in a row?
Answer:
120 ways
..................
Answer:
24
Step-by-step explanation:
4 friends
1st seat: 4 different people could sit here
Now there are 3 friends left
2nd seat: 3 different people could sit here
Now there are 2 friends left
3rd seat: 2 different people could sit here
Now there are 1 friends left
4th seat: 1 different people could sit here
4*3*2*1
24 ways
Find the value of 21 - 18 \ 3•2
18
1/2
2
9
Answer:
use m a t h w a y
Step-by-step explanation:
Emily and Kate were at a cheerleading competition this fall.They cheered 12 rounds. Each round lasted 8.24 minutes. Calculate the total number of minutes, Emily cheered and the total number of minutes Kate cheered at the competition
Answer:
98.88
Step-by-step explanation:
Given: They cheered 12 rounds. Each round = 8.24
To find the total number, multiply how much one round is with the total number of rounds.
8.24
× 12
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1648
+ 8240
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98.88
Each girl cheered 98.88 minutes. If you need this estimated, the answer would be 99 minutes.
When f(x) = -3, what is x?
-29
-10
-3
-1
Answer:
The correct choice is option D. -1
Step-by-step explanation:
Find f(x) = - 3 on the table. When y = -3, what is the x value? Look on the right side, you can see it's -1, correct? So, f(x) = - 3 when x = - 1.
What is the answer to 11.24 divided by 9
Answer:
1.24
Step-by-step explanation:
oahsofhasdf0as0dfadera
Which of the following is a geometric sequence? a. 5,-25,125,-625 b.2,4,16,48 c. 13,16,19,22 d. 100,50,0,-50
Answer:
a
Step-by-step explanation:
B isn't a geometric sequence as it's last term doesn't follow the rule
C is an arithmetic sequence
D is an arithmetic sequence too
What is the image point of (4, -6) after a translation right 5 units and up 4 units?
Answer:
(9,-2)
Step-by-step explanation:
5 is the x coordinate, and 4 is the y coordinate. When you go right a certain amount of units, you add those units to your x coordinate. If you were to go left a certain amount of units, you'd subtract them. Since we're going right, 5 + 4 = 9. When you go up a certain amount of units, you add those units to you y coordinate. If you were to go down a certain amount of units, you'd subtract them. Since we're going up, -6 + 4 = -2. So, x = 9 and y = -2, or (9,-2)
Please help on my hw
Answer:
x^2 - 7x - 30 = 0
Step-by-step explanation:
since solutions are 10 and -3
a factorised quad eqn can be formed:
(x-10)(x+3)=0
expand the eqn
x^2-7x-30 = 0 is the answer
0.6 reoccurring decimal as a fraction in the simplest term
Answer:
3/5
Step-by-step explanation:
here,
0.6
in fraction = 6/10
in simplest form 6/ 10 both term can be divided by 2 so,
6/10 ÷2
= 3/5
Write the expression in exponential form.
log . N = x
Answer:
N = x2
Step-by-step explanation:
Follpwing the format
If triangle ABC has one angle measuring 90o and one angle measuring 45o, which of the following is true?
ABC is a right angle
Third angle 45°
Its a isoceles Right Triangle because base angles are equal then two sides are also equal.
Must click thanks and mark brainliest
Simplify (-2)-3⋅ (-2)4⋅
Answer: 22
Step-by-step explanation:
−2−(3)(−2)(4)
=22
Find the first six terms of the sequence.
a1=- 6, an= 4 • an-1
Answer:
I think it's 3
Step-by-step explanation:
because an=4 and the question is
an-1
=4-1
=3
If 40 men working on a U.S. government project can complete the job in 100 hours, how many men would be required to complete the job in 80 hours?
Answer:50
Step-by-step explanation:(40x100):80
Answer: 50 workers
Let the ratio be
(40×100):80
= 400/80
= 50
Therefore 50 workers will complete the same work in 80 hours.
Must click thanks and mark brainliest
The first season of the show breaking bad contain seven episodes but the second season of 13 episodes calculate the absolute and relevant change in the number of episodes from season one to season two of breaking bad
Answer:
Absolute = 13-7 = 6
if you mean relative change then it would be the multiplier of 13 / 7 = 1.85714286
as; 7 x 1.85714286 = 13
Step-by-step explanation:
The absolute change is 6 and relative change is 1.85
What is absolute and relative errors?The size of the discrepancy between the exact value and the approximation is known as the absolute error. The absolute error is multiplied by the exact value's magnitude to get the relative error.
Given
Absolute = 13-7 = 6
if you mean relative change then it would be the multiplier of 13 / 7 = 1.85714286
as; 7 x 1.85714286 = 13
To learn more about the absolute and relative errors refer to:
https://brainly.com/question/26167540
#SPJ2
Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V by slicing & find V by cylindrical shells.
Explanation:
Let [tex]f(x) = \sqrt{25x}[/tex] and [tex]g(x) = \frac{x^2}{25}[/tex]. The differential volume dV of the cylindrical shells is given by
[tex]dV = 2\pi x[f(x) - g(x)]dx[/tex]
Integrating this expression, we get
[tex]\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx[/tex]
To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:
[tex]\sqrt{25x} = \dfrac{x^2}{25}[/tex]
We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:
[tex]25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1[/tex]
or
[tex]x^3 =(25)^3 \Rightarrow x = \pm25[/tex]
Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is
[tex]\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx[/tex]
[tex]\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx[/tex]
[tex]\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}[/tex]
[tex]\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2[/tex]
A $22,000 loan was taken out. If $24,805 is due at the end of the loan after being compounded daily at 2.5%, how many
years was the loan for? (Round to the nearest tenth of a year)
Provide your answer below
9514 1404 393
Answer:
4.8 years
Step-by-step explanation:
Solving the compound interest formula for the number of years gives ...
t = log(A/P)/(n·log(1 +r/n))
where principal P invested at rate r compounded n times per year produces value A after t years.
t = log(24805/22000)/(365·log(1 +0.025/365)) ≈ 4.800
The loan was for 4.8 years.
