Answer:
[tex]|x - 98.6| > 1.5[/tex]
Step-by-step explanation:
Given
Temperature = 98.6F
Range = 1.5F
Required
Write the absolute value inequality
Let the temperature be represented by x
We start by writing an expression for the difference between x and 98.6.
This can be written as x - 98.6
From the question, we understand that this difference is more than 1.5F
Representing this using absolute value inequality; we have
[tex]|x - 98.6| > 1.5[/tex]
Solving further; this gives
[tex]x - 98.6 > 1.5[/tex] or [tex]x - 98.6 < -1.5[/tex]
Make x the subject of formula in both cases
[tex]x >98.6 +1.5[/tex] or [tex]x < 98.6-1.5[/tex]
[tex]x >100.1[/tex] or [tex]x < 97.1[/tex]
This can be rewritten as
[tex]x >100.1[/tex] or [tex]97.1>x[/tex]
Combining these two inequalities;
[tex]97.1 > x > 100.1[/tex]
Hence;
The absolute inequality is [tex]|x - 98.6| > 1.5[/tex]
And the range of value is [tex]97.1 > x > 100.1[/tex]
Jessica purchased a 600-minute pre-paid phone card and called her sister at college. After talking to her sister "t" minutes, she had less than 600 minutes on her calling card. (a) Write an equation to determine the number of minutes remaining on the card. (b) Now, suppose she talked to her sister for 65 minutes, determine how many minutes she has left on her card.
Answer:
1) 600-t
2) 600-t=65
=>t=535
NY Newsstand has an annual payroll of $288,000. What is the FICA for NY
Newsstand?
A. $22,032
B. $76,500
C. $25,684
O D. $28,800
Answer:
It is A $288,000
Step-by-step explanation:
Answer:
A. $22,032
Step-by-step explanation:
FICA includes both social security tax (6.2%) and Medicare tax (1.45%), for a total tax rate of 7.65%.
0.0765 × $288,000 = $22,032 . . . FICA tax
Help! I'm trying to solve this for A and B, and it keeps telling me I'm wrong. The equation is:
√x(7x-4√x)=Ax^(3/2) + Bx
Where A =
and B =
Answer:
A must be 7 and B must be -4
Step-by-step explanation:
Perform the indicated multiplication, obtaining:
7x^(3/2) - 4x = Ax^(3/2) + Bx
Then A must be 7 and B must be -4
PLZ HELP!! HURRY!!!30POINTS!!
Answer:
c. We use tan∅ to solve
d. x ≈ 45.64 ft
Step-by-step explanation:
Step 1: Draw out the picture
When we do so, we should be able to see that we are solving for the horizontal leg.
Step 2: Find the trig
tan78° = 214.7/x
xtan78° = 214.7
x = 214.7/tan78°
x = 45.6359
Write each ratio in its simplest form.
A) 9 feet: 4 yards
B) 5 gallons : 8 quarts
C) 800 centimeters: 2 meters
Answer:
A. 4 yards = 12 ft
9 ft : 12 ft = 3:4
B. 5 gallons = 20 quarts
20 quarts : 8 quarts = 5:2
C. 2 meters = 200 cm
800 cm : 200 cm = 4:1
Answers:
A) 3:4
B) 5:2
C) 4:1
Step-by-step explanation:
Convert 4 yards to feet.
1 yard = 3 feet
4 yards = 12 feet
9 feet : 12 feet
Simplify the ratio.
9/3 : 12/3
3 feet : 4 feet
3 : 4
Convert 8 quarts to gallons.
1 quart = 0.25 gallons
8 quarts = 2 gallons
5 gallons : 2 gallons
5 : 2
Convert 2 meters into centimeters.
1 meter = 100 centimeters
2 meters = 200 centimeters
800 centimeters : 200 centimeters
Simplify the ratio.
4 : 1
A factory can work its employees no more than 6 days a week, and no less than 2 days per
week. Create an inequality to represent the range of days an employee can work. Solve
the inequality to determine the range in hours if the work day is 6.5 hours. Show all of your
work.
Answer:
Step-by-step explanation:
Answer: A.) 2 <= X <= 6
B.) 13 < = X < = 39
Step-by-step explanation:
Given that a factory can work its employees no more than 6 days a week, that is, less than or equal to 6 days a week
And also, no less than 2 days per week. That is, greater than or equal to 2 day a week.
Let X represent the number of days an employee can work per week.
According to the first statement,
X < = 6
According to the second statement,
X >= 2
An inequality to represent the range of days an employee can work will be
2 < = X <= 6
To represent the range in hours, first convert the number of days to hour. Given that an employee can work
1 day = 6.5 hours
2 days = 2 × 6.5 = 13 hours
5 days = 6 × 6.5 = 39 hours
Therefore, the range will be
13 < = X < = 39
Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form
Answer:
f(x) = (x - (-5))^2 + (-18)
Step-by-step explanation:
Given:
f(x) = x^2 + 10x + 7
Rewrite f(x) in vertex form
Solution:
f(x) = ax^2 + bx + c is a quadratic function.
The vertex form of f(x) is a(x - h)^2 + k, where (h, k) is the vertex.
=> f(x) = x^2 + 10x + 7
= x^2 + 10x + 25 - 18
= (x + 5)^ - 18
= (x - (-5))^2 + (-18)
=> f(x) can be rewritten in form of a(x - h)^2 + k, where (h, k) is the vertex, with a = 1, h = -5, k = -18
For each beton, state whether it represents a function
Answer:
so
no two points on a random vertical line in the graph
1 no
2 no
3 yes
4 no
5 yes
6 yes
Which of these sets of points lie within plane w?
A.
Cand G
B.
Hand E
C.
C and E
D
A and D
Answer:
option c boo if it's for plata
Does this table represent a function? Why or why not?
Hours of
Training
10
20
30
40
50
60
70
Monthly
Pay
1100
1200
1300
1400
1500
1600
1700
O A. Yes, because every x-value corresponds to exactly one y-value.
O B. Yes, because the y-values are positive numbers.
O C. No, because none of the yvalues are the same.
O D. No, because each x-value is different,
The answer is A; every x-value must correspond to ONE y-value only. y-values can correspond with as many x-values as they want, but if you see an x-value corresponding with more than one y-value, that's not a function.
The table represent the function because every x-value corresponds to exactly one y-value.
What is function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
Hours of Training Monthly Pay
10 1100
20 1200
30 1300
40 1400
50 1500
60 1600
70 1700
As, We can see the input values are distinct and have corresponding output.
Hence, the table represent the function because every x-value corresponds to exactly one y-value.
Learn more about Function here:
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A photo is 8 cm long and 6 cm wide. It is enlarged to make a print that is 18 cm wide.
What is the length of the enlargement?
Answer:
24 cm
Step-by-step explanation:
The photo was 6 cm wide, and was made into 18 cm wide. Divide 18 with 6:
18/6 = 3
To solve for the length enlargement, multiply 3 with the length, or 8 cm:
8 x 3 = 24
24 cm is the length of the enlargement.
~
Shelby has already knit 8 centimeters of scarf, and can knit 1 centimeter reach night. How many nights will Shelby have to spend knitting in order to knit a total of 47 centimeters of scarf?
Answer:
39 nights.
Step-by-step explanation:
If Shelby can knit 1 centimeter per night, the amount of centimeters = the amount of nights.
Equation:
47-8=39
39 nights.
Hope this helps! :) :)
Suppose f(x) = x2 and g(x)= (1/4x)2Which statement best compares the
graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted į units right.
B. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 4
C. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 4.
D. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 4.
Answer:
B.
Step-by-step explanation:
Since the variable b is manipulated in f(x) = a(bx - h)² + k, we are dealing with horizontal compression and stretching. Since b < 1, that means the graph is being horizontally compressed.
Solve -8x+4 ≤ 36
A. x ≥ -4
B. x ≤ 4
C. x ≥ 4
D. x ≤ -4
Answer:
x≥-4
Step-by-step explanation:
-8x≤36-4
-8x≤32
x≥32/-8 when divide by minus you flip from≤ to ≥
x≥-4
Answer:
x ≥-4
Step-by-step explanation:
-8x+4 ≤ 36
Subtract 4 from each side
-8x+4-4 ≤ 36-4
-8x ≤ 32
Divide by -8 remembering to flip the inequality
-8x/-8 ≥ 32/-8
x ≥-4
In a class full of men and women, [tex]\frac{2}{9}[/tex] of the class are women. What is the ratio of men to women in its simplest form?
Answer:
Hey there!
Let's pretend that there are only 9 people in that class. Thus, if 2/9 were women, then 2 people would be women.
Thus, 7 people would be men.
The ratio of men to women would be 7:2.
Hope this helps :)
Please help me with this question
Answer:
E.
Step-by-step explanation:
so first you would add 8 to both sides to get
3w = t + 8
then divide both sides by 3
w = (t + 8) / 3
So the answer is E.
Answer: E) w = (t+8)/3
Step-by-step explanation:
Solve for w in terms of t means you have to isolate w. Thus, simply do the following:
[tex]3w-8=t\\3w=t+8\\w=\frac{t+8}{3}[/tex]
Hope it helps <3
find the sum of these polynomials (x^2-x+8) + (10x^2+7)
[tex](x {}^{2} - x + 8) + (10x {}^{2} + 7)[/tex]
[tex]10x {}^{4} - 10x {}^{3} + 87x {}^{2 } - 7x + 56[/tex]
Evaluate the following expression when x = 6 and y = 2: Fraction with x squared plus y cubed in the numerator and 2 plus x in the denominator. 2.25 5.5 17.25 27.5
Answer:
Option B.
Step-by-step explanation:
The given expression is
[tex]\dfrac{x^2+y^3}{2+x}[/tex]
We need to find the value of given expression when x=6 and y=2.
Substitute x=6 and y=2 in the given expression.
[tex]\dfrac{x^2+y^3}{2+x}=\dfrac{(6)^2+(2)^3}{2+(6)}[/tex]
[tex]=\dfrac{36+8}{8}[/tex]
[tex]=\dfrac{44}{8}[/tex]
[tex]=5.5[/tex]
The value of given expression is 5.5 when x=6 and y=2.
Therefore, the correct option is B.
Answer:
he given expression is
We need to find the value of given expression when x=6 and y=2.
Substitute x=6 and y=2 in the given expression.
The value of given expression is 5.5 when x=6 and y=2.
Therefore, the correct option is B.
Step-by-step explanation:
Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual's score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers 1 through 10. Each throw hits the target in a region with a different value. The scores are: Alice—16 points, Ben—4 points, Cindy—7 points, Dave—11 points, and Ellen 17—points. Who hit the region worth 6 points?
Answer:
Alice
Step-by-step explanation
Ben=1+3
Cindy=2+5
Dave=4+7
Alice=10+6
Ellen is 9+8
The answer is gonna be Alice because you can only use each number once.
POSSIBLE SCORES
Alice 16
6,10
7,9
(8+8 won't work because that would be a repeating number)
Ben 4
1,3
(2+2 won't work because that would be a repeating number)
Cindy 7
1,6
2,5
3,4
Dave 11
1,10
2,9
3,8
4,7
5,6
Ellen 17
7,10
8,9
Since the only possibilities for Ben is hitting 1 and 3, all other people can't hit 1 or 3.
Alice 16
6,10
7,9
Cindy 7
2,5
Dave 11
2,9
4,7
5,6
Ellen 17
7,10
8,9
Since the only possibilities for Cindy is hitting 2 and 5, all other people can't hit 2 or 5.
Alice 16
6,10
7,9
Dave 11
4,7
Ellen 17
7,10
8,9
Since the only possibilities for Dave is hitting 4 and 7, all other people can't hit 4 or 7.
Alice 16
6,10
Ellen 17
8,9
Ellen must have hit 8 and 9. Alice must have hit 6 and 10.
Alice hit 6 points.
Find the y-intercept for the parabola defined by
this equation:
y=-2x^2 – 9x + 5
Answer:
(0,5) is the Y intercept.
Step-by-step explanation:
At Y intercept, x=0.
Answer: y intercept is (0,5)
Step-by-step explanation:
4x-9x=-5x
y=-5x+5
add 5x on both sides
5x+y=5
a number cube numbered 1-6 is rolled 30 times and lands on an even number 18 times. How does this frequency compare to the expected frequency based on the probability of the number cube landing on an even number?
Answer:
The frequency is 3 more than expected
Step-by-step explanation:
There are 3 favourable outcomes: {2, 4, 6}
There are 6 possible outcomes: {1, 2, 3, 4, 5, 6}
probability of the number cube landing on an even number = favourable outcomes / possible outcomes = 3/6 = 1/2
If the cube is rolled 30 times, it is expected that in 1/2*30 = 15 times landed on an even number. The frequency: 18 is 3 more than expected
I honestly don't know how to explain this further
Answer:
24
Step-by-step explanation:
divide 65/8 and then multiply that by 3 and round to the nearest whole number
Parents sold 275 tickets for a fundraiser at the community center. Student tickets cost $3, and adult tickets cost $5. The total value of tickets sold is $1,025. Which system of equations represents the problem? 3x + y = 275 x + 5y = 1025 y = 275 3x + y = 1025 x + y = 275 3x + 5y = 1025 y = x + 275 x + y = 1025
Answer:
3x+5y=1025
x+y=275
Step-by-step explanation:
We can use system of equations to solve this problem. Let's use x for student tickets and y for adult tickets.
Equation 1
3x+5y=1025
This equation comes from the cost of tickets. Each child ticket costs $3 and each adult ticket costs $5. The total value of tickets sold is $1025.
Equation 2
x+y=275
The total amount of tickets sold was 275.
you worked 6 and three fourths hours on Monday Seven and one fourth on Tuesday eight and one fourth on wendsey seven and one fourth on Thursday seven and three fourths on Friday how many hours did you work for the week
Answer:
37.25
Step-by-step explanation:
6.75+7.25+8.25+7.25+7.75=37.25
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the number 4,928 will be rounded to the nearest hundred. what is the rounding digit
Answer:
4928 rounded to the nearest hundred is:
4900
Step-by-step explanation:
Hope this hepls you!!
The number 4,928 will be rounded to the nearest hundred is 4900.
What is rounding off numbers?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The crucial figures are preserved when numbers are rounded off.
Given to round off 4928 to the nearest 100
steps to round off,
Determine the two consecutive multiples of 100 that bracket 4928
4928 is between 4900 and 5000
4950 is the midpoint between 4900 and 5000
from the number line, 4928 is less than the midpoint 4950,
Therefore, 4928 rounded to the nearest 100 is 4900.
Hence the digit is 4900.
Learn more about rounding off numbers;
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to make it easier to explain you can say. Number 1 box is 57 number 2 box is77 something like that
Answer:
Box 1=5 Box2=6 Box3=8 Box4=200
Step-by-step explanation:
Answer:
Step-by-step explanation:
No.of balloons each will get = 5
no.of greeting cards = 6
no.of apples in each basket = 8
no. of words = 200words
hope it helps
A-29
B-81
C-87
D-93
Please someone help I don’t get this
Answer:
B-29...b-29...b-29...B-29... B-29
Find the equation of the exponential function represented by the table below:
HELLPPP
Answer:
y = 4 [tex](\frac{1}{2}) ^{x}[/tex]
Step-by-step explanation:
For an exponential function in the form
y = a [tex]b^{x}[/tex]
Use ordered pairs from the table to find values of a and b
Using (0, 4 ), then
4 = a [tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ), thus
a = 4, so
y = 4 [tex]b^{x}[/tex]
Using (1, 2 ) , then
2 = 4 [tex]b^{1}[/tex] = 4b ( divide both sides by 4 )
b = [tex]\frac{1}{2}[/tex]
Thus exponential function is
y = 4 [tex](\frac{1}{2}) ^{x}[/tex]
Answer:
y = 4 (\frac{1}{2}) ^{x}
13/4-1=
2 1/4
1 1/2
2 1/2
1 1/4
Answer:
2 1/4
Step-by-step explanation:
13/4 is 3 1/4 because 13 divided by 4 is 3 with a remainder of 1. So from there you subtract 1 from the whole number 3 and are left with 2 1/4. I hope that makes sense! :)
Answer:
2 1/4
Step-by-step explanation:
13/4 = 3 1/4
1 = 1
3 - 1 = 2 1/4
what is a point-slope equation of the line with slope -13 that goes through the point (5,7)
Answer:
y - 7 = -13( x-5)
Step-by-step explanation:
The point slope form of a line is
y-y1 = m(x-x1)
The slope is -13 and the point is (5,7)
y - 7 = -13( x-5)
Answer:
PoInTsSsSsSsSs
Step-by-step explanation: