=====================================================
Explanation:
The rule is that if [tex]|a| \le k[/tex] for some positive number k, then it can be written as the compound inequality [tex]-k \le a \le k[/tex]. This is a shorthand way of writing the two inequalities [tex]a \ge -k \ \text{ and } \ a \le k[/tex] combined together.
note: [tex]-k \le a[/tex] is the same as [tex]a \ge -k[/tex]
From here, we replace k with 3
Therefore, [tex]|a| \le 3[/tex] turns into [tex]-3 \le a \le 3[/tex] which breaks down further to [tex]a \ge -3 \ \text{ and } \ a \le 3[/tex]
The keyword "and" is important as we can't pick one or the other. We must pick both [tex]a \ge -3[/tex] and also [tex]a \le 3[/tex]
Answer:
Choice 2.
Step-by-step explanation:
A polar bear migrates north during winter to hunt for its food on sea ice. The daily
average temperature decreases 3°C for every 100 km traveled. At the start of the bear's
journey, the temperature is 2°C. What is the temperature after 200 km of its journey?
Answer:
-4 degrees
Step-by-step explanation:
Starting at 2 degrees, you need to subract 6 since 200 km= 6 degrees and it decreases.
The temperature after 200 km of the polar bear's journey is -4° C.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The daily average temperature decreases 3°C for every 100 km traveled
At the start of the bear's journey, the temperature is 2°C
The total distance traveled by the polar bear = 200 km
For 200 km, [tex](3+3)[/tex] totally 6° C should get decreased.
⇒ [tex](2-6)[/tex]
⇒ [tex]-4[/tex]
Hence we can conclude that the temperature after 200 km of the polar bear's journey is -4° C.
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Plz plz help me plz plz plzplzplzplz
Answer: C
Step-by-step explanation: its C
What is the slope for the line PERPENDICULAR to the line shown in the graph?
A) -3
B) -1/3
C) 3
D) 1/3
Which statement must be true according to the box plot? The data is symmetric, and the lowest number of crackers in a package was 7. The data is symmetric, and the lowest number of crackers in a package was 8. The data is skewed, and the lowest number of crackers in a package was 7. The data is skewed, and the lowest number of crackers in a package was 8.
Answer:
C
Step-by-step explanation:
The data is skewed, and the lowest number of crackers in a package was 7
Answer:
they are correct the answer is C
Step-by-step explanation:
help!! answer needed fast plz!
Answer:
umm whats the question?
Step-by-step explanation:
g(x) = 4x+1
What is g(3)?
Answer
13
Step-by-step explanation:
4(3)+1
12+1=13
Please help me with these coordinates! ;) ❤️
Answer:
(7,3)
Step-by-step explanation:
Given,7 units away from x axis and 3 units away from y axis,
Coordinates are written in (x,y) form
(x,y)=(7,3)(Given)
Answer:
A
Step-by-step explanation:
7 units away from the origin in the direction of the x-axis
So it can be (7, ?) or (-7, ?)
3 units away in the direction of the y-axis
So it can be (7, 3) or (-7, -3) or other things
Remember: (X, Y)
A is (7,3) which is a possible based on this
B would not work based on this
C would not work either
D wouldn't too
Damian likes to shoot baskets. He took 50 shots a day to keep track of how many he made for 10 days. Here are the number of shots made:
22, 25, 27, 37, 32, 19, 25, 45, 32, 33.
What is the RANGE of made shots?
Oa 26
Ob 45
Oc 32
Od 19
Answer:
a because that seems the most accurate
Step-by-step explanation:
of
6. Which set of three numbers can be used
to make a right triangle?
A 39, 41, 45
B 39, 49, 59
C 39, 69, 99
D 39, 80, 89
Answer:
The set (39, 80, 89) can be used to make a right triangle. Thus, option D is correct.
Explanation:
We know that right-angle triangles obey the Pythagoras theorem, i.e.,
a² + b² = c²
Let's check for each set:
(39, 41, 45): 39² + 41² ≠ 45²
(39, 49, 59): 39² + 49² ≠ 59²
(39, 69, 99): 39² + 69² ≠ 99²
(39, 80, 89): 39² + 80² = 89²
help wanted pls math
Answer:
39 ft²
Step-by-step explanation:
Area of a triangle = 1/2bh
Let:
base = b = 4 ft
height = h = 3 ft
Solve for the area of the triangle:
A = 1/2(4)(3)
A = 2 * 3
A = 6 ft²
Area of a rectangle = bh
Let:
base = b = 9 ft
height = h = 5 ft
Solve for the area of the rectangle:
A = (9)(5)
A = 9 * 5
A = 45 ft²
Subtract the area of the triangle from the area of the rectangle:
45 - 6 = 39 ft²
39 ft² is your answer.
~
Answer:
39 ft²
Step-by-step explanation:
Shaded area = rectangle - triangle
(5 × 9) - (½ × 3 × 4)
45 - 6
39 ft²
A crew is made up of 8 men; the rest are women. If 32 % of the crew are men, how many people are in the crew?
Answer:
12
Step-by-step explanation:
(66 2/3)
---------- (x) = 8
100
Solve for x
(66 2/3)x = 800
x = 800/(66 2/3)
x = 800/(200/3)
x = 800(3/200)
x = 4(3)
x = 12
Write the general solution to y = arcsin 0
Answer:
y=+/- π k
Step-by-step explanation:
The general solution of the given function is [tex]y=0[/tex]
Inverse trigonometric function:Inverse trigonometric functions are simply defined as the inverse functions of the basic trigonometric functions which are sine, cosine, tangent, cotangent, secant, and cosecant functions.
Given function is,
[tex]y=sin^{-1}(0) \\\\y=0[/tex]
The general solution of the given function is [tex]y=0[/tex]
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Type A is 10 feet tall and grows at a rate of 9 inches per year. Type B is 7 feet tall and grows at a rate of 21 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
3 years
Step-by-step explanation:
Solve each of the quadratic equations.
0 = 5.
3x = 0.522
o x = -6 or x = 0
0 x= -4 or x = 3
o x= -2 or x = 1.5
O x = 0 or x = 6
DONEC
DON
Answer:
1.
3x = 0.5x2
x = -6 or x = 0
x = -4 or x = 3
x = -2 or x = 1.5
x = 0 or x = 6
2.
0 = 5x2 - 2x + 6
D. & C.
What is the product? 12x/2y • 3y^2/24x^3
Answer: [tex]\frac{3}{4} x^4y^3[/tex]
Answer the question simplify no work needed
1st page : 16 , 32 , 7
2nd page : (Going down) 8 , 4 , 2 , 15 , 3 , 35 , 12 , 1 , 105 , 25 , 21 , 90
Plz correct me if I'm wrong
Which of the following is the measure of XBA if ray BA bisects XBY which measures 70 degrees
Answer: The correct answer is C.35.
Step-by-step explanation:
70÷2=35
The value of the measure of XBA is,
⇒ 35 degree
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
We have to given that;
Here, ray BA bisects XBY which measures 70 degrees
Hence, The value of the measure of XBA is half of the measure of XBY.
So, We get;
the measure of XBA is,
⇒ 70 / 2
⇒ 35 degree
Thus, The value of the measure of XBA is,
⇒ 35 degree
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Helps the first 2 questions
Answer:
The first one is 5m - 4y.
The second one is 3x - 4y.
Step-by-step explanation:
GIVING AWAY BRAINLIEST
In a rectangle ABCD the diagonals intersect each other at point O, E is a midpoint of the side AB , and m∠BAC = 50°. Find the measure of angle EOD.
Answer:
130°
Step-by-step explanation:
In the picture attached, the rectangle can be seen.
We know that m∠BAC = 50°, then m∠ADB is also 50°. m∠AOE must be 180° - 90° - 50° = 40°, and m∠OAD = 90° - 50° = 40°, then m∠DOA = 180° - 40° - 50° = 90°. Finally m∠EOD = m∠DOA + m∠AOE = 90° + 40° = 130°
Answer:
140 degrees
Step-by-step explanation:
Gabriella asked 555 of her hundreds of coworkers how much storage space they were currently using on their computer. Here are their responses (in gigabytes): 4, 8, 8, 9, 114,8,8,9,114, comma, 8, comma, 8, comma, 9, comma, 11 The mean of these amounts is \bar x=8 x ˉ =8x, with, \bar, on top, equals, 8 gigabytes. What is the standard deviation? Round your answer to two decimal places. s_x\approxs x ≈s, start subscript, x, end subscript, approximately equals gigabytes
Answer:
The standard deviation of the sample is 2.55 gigabytes
Step-by-step explanation:
Here we have the responses as follows;
Storage space usage on their computer [tex]x_i[/tex]
The number of respondents or sample size, n = 5
[tex]x_i[/tex] [tex](x_i - \bar x)[/tex] [tex](x_i - \bar x)^{2}[/tex]
4 -4 16
8 0 0
8 0 0
9 1 1
11 3 9
∑ 40 26
The sum = ∑X = 4 + 8 + 8 + 9 + 11 = 40
The mean = (The sum)/(The count) = 40/5 = 8
Formula for population standard deviation is;
[tex]\sigma = \sqrt{\frac{\Sigma (x_i - \mu)^2}{n } }[/tex]
Where:
σ = Population standard deviation
μ = Population mean
Since we are dealing with only 5 out of her hundreds of coworkers we are dealing with a sample therefore;
The formula for sample standard deviation is;
[tex]s = \sqrt{\frac{\Sigma (x_i - \bar x)^2}{n - 1} }[/tex]
Where:
s = Sample standard deviation
n = Sample size
[tex]x_i[/tex] = Each value of the sample
[tex]\bar x[/tex] = Sample mean
We find each value of [tex](x_i - \bar x)[/tex] by subtracting the x values from the mean, 8, as in the table above, next we find [tex](x_i - \bar x)^{2}[/tex] by squaring the [tex](x_i - \bar x)[/tex].
Next, we find the sum of the differences from the mean square values from the table after which we divide by n - 1, to get [tex]{\frac{\Sigma (x_i - \bar x)^2}{n - 1} } = \frac{26}{5 - 1} = \frac{26}{4} = 6.5[/tex]
We find the root of the result which gives us the standard deviation hence
√6.5 = 2.5495.
Standard deviation, s = 2.5495 ≈ 2.55 to two significant places of decimal.
After making a table for summation the standard deviation of the sample is 2.55 gigabytes.
Use the formula for population standard deviation is:
[tex]\sqrt{\dfrac{\sum{(x_i - \mu)^2}}{n}[/tex]
Where:
σ = Population standard deviation
μ = Population mean
The formula for sample standard deviation is;
[tex]\sqrt{\dfrac{\sum{(x_i - X)^2}}{n-1}[/tex]
Where:
s = Sample standard deviation
n = Sample size
[tex]x_i[/tex] = Each value of the sample
X = Sample mean
Since we are dealing with only 5 out of her hundreds of coworkers we are dealing with a sample, therefore;
The storage used is represented by [tex]x_i[/tex]
The number of respondents or sample size represented by n
Then n = 5
The table for summation is attached below.
Find the sum of the differences from the mean square values from the table after which we divide by n - 1,
[tex]\dfrac{\sum{(x_i - X)^2}}{n-1} = \dfrac{26}{5-1}\\\\\dfrac{\sum{(x_i - X)^2}}{n-1} =6.5[/tex]
Find the root of the result which gives us the standard deviation hence
√6.5 = 2.5495.
Hence,
Standard deviation,
s ≈ 2.55 about two significant places of decimal.
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Tim had $150 to spend on 3 pairs of pants. After buying
them, he had $30 left over. What equation expresses how
much each pair of pants cost?
A.30x/3 = 150
B.3x - 30 = 150
C.3x = 180
D.3x + 30 = 150
Which graph shows a non-proportional linear relationship between x and y?
Answer: It is B
Step-by-step explanation: this is it because a linear line has a point 0,0 and B is the only one who does have that point.
Translate the sentence and solve: "4 is 2 less than double a number".
x = -2
x= 2
х=-3
x= 3
Answer: x = 3
Step-by-step explanation:
you would double each number meamong multiply by 2 until you get the opposite of 4 being 2 less of a number so 6.
3 x 2 = 6
and 2 less than 6 is 4 so theres your answer :)
Twenty eight slips of paper are numbered 1 through 28 and are distributed among a group of people. A random number generator is used to select a single number between 1 and 28, inclusively
A fair decision is made using this process
How many people could be in this group?
A. 3
B. 6
C. 7
D. 12
Answer:
Option D, 7, is the right answer.
Step-by-step explanation:
It is given that 28 slips of papers are numbered through 1 to 28.
Accordingly, there are 28 numbers.
For a fair decision, the number of slips with each one must be the same.
Therefore, the decision will only be fair if the number of people in the group is a factor of 28.
The factors of 28 are - 1, 2, 4, 7, 14 and 28.
In this way, 7 is the only factor of 28 among the given options.
Hence, the answer will be 7.
Super easy geometry please help
Here Is a trick my dad taught me for this geometry, every time I did geometry I would've gotten mad about it so we made a trick
M-ultiply
A-nd
D-ivide
Hope this trick helps you!
The current year’s depreciation expense using the straight-line method and assuming only one depreciable property, is P20,000. What is the machine’s useful life when it was purchased for P200,000 with a salvage value of P20,000?
Answer:
Machine's useful number of years = 9 years
Step-by-step explanation:
Using the straight line method, depreciation is calculated as the difference between the cost of the equipment minus the salvage value, all divided by the number of useful years.
Yearly Depreciation
= (Cost - Salvage value) ÷ (Number of useful years)
Yearly depreciation = P20,000
Cost = P200,000
Salvage Value = P20,000
Number of useful years = n
20000 = (200000 - 20000) ÷ n
20000 = (180000/n)
n = (180000/20000) = 9 years
Hope this Helps!!!
Simplify the expression: 3x2(x2 - 4x - 2) + (5x3 + 7x2 + 2x + 11)
Show and explain your steps. PLEASE!!!
Answer:
[tex]3x^4-7x^3+x^2+2x+11[/tex]
Step-by-step explanation:
[tex]3x^2(x^2 - 4x - 2) + (5x^3 + 7x^2 + 2x + 11)[/tex]
First, I will expand the expression [tex]3x^2(x^2 - 4x - 2)[/tex]
[tex]3x^2(x^2 - 4x - 2) \\3x^4-12x^3-6x^2[/tex]
So, we got
[tex]3x^4-12x^3-6x^2+ 5x^3 + 7x^2 + 2x + 11[/tex]
Adding similar elements, we get:
[tex]3x^4-7x^3+x^2+2x+11[/tex]
Please help! Will mark Brainliets (when it will let me, but answer has to be right!) (I have 3-4 other questions that need to be answered, if possible please answer them) Stay Safe!
Answer:
It is A
Step-by-step explanation: It's the same as finding the area of a cube but you have to divide by 2
Answer:
300
Step-by-step explanation:
To find the volume of a prism (it doesn't matter if it is rectangular or triangular) we multiply the area of the base, called the base area B, by the height h. 6x10=60 which is the base times the height 5 and you get 300.
Hope this helps!
An investing group has $50,000 to invest. They put the money in an account that has an annual interest rate of 6%, compounded monthly. How much money will the group have at the end of 10 years?
The investing group will have $90970 at the end of 10 years.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We can use the formula for compound interest to solve this problem:
[tex]A = P(1 + r/n)^(^n^t^)[/tex]
where A is the total amount,
P is the principal
r is the annual interest rate,
n is the number of times the interest is compounded per year, and
t is the number of years.
P = $50,000, r = 0.06, n = 12 and t = 10.
Substituting these values into the formula, we get:
A = 50000(1 + 0.06/12)¹²⁰
A = 50000(1.005)¹²⁰
A=$90970
Therefore, the investing group will have $90970 at the end of 10 years.
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Which of the following is(are) the solution(s) to 4 |x+3|>8
Answer:
x>-1 or x<-5
Step-by-step explanation:
4 |x+3|>8
Divide each side by 4
4/4 |x+3|>8/4
|x+3|>2
Absolute value inequalities have 2 solutions, one positive and one negative
Remember to flip the inequality when finding the negative solution
x+3 >2 or x+3 <-2
Subtract 3 from each side
x+3-3>2-3 or x+3-3 <-2-3
x>-1 or x<-5