The absolute value equation is |x - 70| = 0.02, while the minimum and maximum torque are 69.98 and 70.02 foot pounds
How to determine the absolute value equation?From the question, the given parameters are:
Specification = 70 foot pounds
Margin of error = 0.02 foot pounds
The absolute value equation of the scenario is then calculated as
|x - Specification| = Margin of error
Substitute the known values in the above equation
So, we have
|x - 70| = 0.02
Solving the equation, we have
x - 70 = 0.02 and x - 70 = -0.02
Add 70 to all sides
x = 70.02 and x = 69.98
Hence, the range is 69.98 to 70.02
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A roofer tosses a hammer off the roof of a house that is 12 feet above the surface of the ground. the graph shows the height above the surface of the ground, y, in feet the hammer is x seconds after being thrown from the roof
Given
A roofer tosses a hammer off the roof of a house that is 12 feet above the surface of the ground. the graph shows the height above the surface of the ground, y, in feet the hammer is x seconds after being thrown from the roof
Solution
The final answer
Option C
State the law of logic that is illustrated.
4
Statement: If x > 12, then x +9>20. The value of x is 14. Therefore, x +9>20.
The given statement " If x > 12, then x +9>20. The value of x is 14. Therefore, x +9>20" is Hypotesis of a true conditional statement is true, so the conclusion is also true. This is Law of Detachment.
What is the hypothesis and conclusion of a conditional statement?The Hypothesis is the first or “If” portion of the conditional statement or p. The Conclusion is the second or “then” part of the conditional statement or q.
What is the truth of the conditional statement when the hypothesis true and the conclusion in true?If the hypothesis is true and the conclusion is true, the conditional statement if p, then q is true. If the hypothesis is true but the conclusion is false, the statement is false.
The following assertion "X + 9 > 20 if x > 12. X has a value of 14. Thus, x + 9 > 20 "The conclusion follows logically from the hypothesized truth of the conditional statement. This is the Detachment Law.
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a rectangular plot of ground is 30 meters longer than it is wide. Its area is 20,000 square meters. which equation will help you find the detentions?
The equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0
How to find the dimensions of the plot of land?Let
L = length of rectangular plot of land, W = width of plot of rectangular plot landSince the rectangular plot of ground is 30 meters longer than it is wide, we have that
L = W + 30
Since the area of the rectangular plot is A = LW where
L = length of rectangular plot of land, W = width of plot of landSince A = 20,000 m², we have that
LW = 20,000
(W + 30)W = 20,000
W² + 30W = 20,000
W² + 30W - 20,000 = 0
Using the quadratic formula, we have that
[tex]W = \frac{-30 +/- \sqrt{30^{2} - 4 X (-20000)} }{2 X 1} \\W = \frac{-30 +/- \sqrt{900 + 80000} }{2} \\W = \frac{-30 +/- \sqrt{80900} }{2} \\W = \frac{-30 +/- 284.43}{2} \\W = \frac{-30 +/- 284.43}{2}\\W = \frac{-30 - 284.43}{2} or \frac{-30 + 284.43}{2}\\W = \frac{-314.43}{2} or \frac{254.43}{2}\\W = -157.22 or 127.23\\[/tex]
Since W cannot be negative, we have W = 127.23
Since L = W + 30
L = 127.23 + 30
L = 157.23
So, the dimensions are
Length = 157.23 mWidth = 127.23 mSo, the equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0
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Toby’s Tiny Toys have fixed expenses of $53,900 for the production of their tiny toys.
Toby’s has a variable expense of $12.50 a piece for each toy they produce, and they
sell their toys for $16.50 a piece. How many tiny toys do they have to sell to reach
their breakeven point?
The number of tiny toys that Toby's Tiny Toys need to sell to reach its break-even point is 13,475.
What is the break-even point?The break-even point is the production and sales units that will ensure that Toby's Tiny Toys does not incur a loss or generate a profit.
At the break-even point, the total revenues are equal to the total costs (fixed and variable).
Selling price per unit = $16.50
Variable expenses per unit = $12.50
Contribution margin per unit = $4 ($16.50 - $12.50)
Fixed expenses = $53,900
Break-even point in units = Fixed costs/Contribution margin per unit
= 13,475 ($53,900/$4)
Thus, we can conclude that Toby’s Tiny Toys needs to sell 13,475 to break even.
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The number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.
The overall revenues and entire costs are equal at the break-even point (fixed and variable).
The production and sales units that will verify that Toby's Tiny Toys does not suffer a loss or make a profit are the break-even point.
$16.50 is the selling price per unit.
Variable costs amount to $12.50 per unit.
The contribution margin = $16.50 - $12.50 = $4 per unit equals
Fixed costs is $53,900.
Break-even point = Fixed costs / Contribution margin
Break-even point = $53,900/$4
Apply division operation to get
Break-even point = 13,475
Thus, the number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.
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Simplify to a single power of 3:
3^{6}\cdot 3^{5}
3
6
⋅3
5 this isnt an abc choice you have to find the small number????
The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.
Given,
The exponents; 3^6 and 3^5.
We have to simplify this into a single power of 3.
In multiplication;
For exponents with same base, simply add the exponents.That is,
aᵇ . aⁿ = a^(b + n)
For exponents with different base, multiply the base and add the exponents.a^b . c^d = a x c ^ (b + d) = ac^bd
So,
3⁶ . 3⁵ = 3^(6 + 5) = 3¹¹
That is,
The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.
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A car’s velocity increases from 4.2m/s to 14.8 m/s, E, in 2.5 sec. What is its acceleration?
Answer:
4.24ms-²
Step-by-step explanation:
S: x. write suvat and sub in values
u:4.2
v:14.8
a:?
t:2.5
use correct equation
v=u+at
sub values in
14.8=4.2+2.5a
rearrange to get a
10.6/2.5= a
a=4.24
Which ratios have the unit rate less than 1?choose all the apply
2 feet : 12/5 minutes
1/8 foot: 1 2/3 minutes
3 feet : 4 2/3 minutes
1 5/8 feet :2 minutes
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, whereas the ratio of lemons to oranges is 6:8. Ratios contrast two figures by typically dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
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URGENT!!! PLEASE HELP ME!!!
Mr Tan had 2 kg of sugar
He usedkg of sugar to make dessert and kg of sugar to ooke
some cakes.
(a) What was the total mass of sugar used?
(b) How much sugar did he have left?
a) The total mass of sugar used is 1.7 kg.
b)The mass of sugar he has left is 0.3 kg.
What are fractions?A fraction is a numerical value that represents a piece of a total in mathematics. The total can be any number, a specific value, or a single item. Fractions are denoted by the symbol p/q.
Given:
Total mass of sugar Mr tan has = 2 kg
Fraction of sugar used to make dessert = 1/4 kg
Fraction of sugar used to bake some cakes = 3/5 kg
The total mass of sugar used is determined as,
= Mass of sugar used to make dessert + Mass of sugar used to bake some cakes
Mass of sugar used to make dessert = (1/4 of 2) kg = 1/2 kg
Mass of sugar used to bake some cakes = (3/5 of 2) kg = 6/5 kg
Total mass of sugar used = (1/2 + 6/5) kg = 17/10 = 1.7 kg
Mass of sugar left with him = Total mass of sugar - Total mass of sugar used
= 2 kg - 1.7 kg = 0.3 kg
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The complete question is: "Mr tan had 2 kg of sugar. He used 1/4 kg of sugar to make dessert and 3/5 kg of sugar to bake some cakes.
(a) What was the total mass of sugar used?
(b) How much sugar did he have left?"
ms. Torres has a box of scraps of wood. She measures the length of each scrap of wood to the nearest half inch results are represented on the line plot below.
The length of the scraps of wood when placed side by side is 53 inches.
What is the length of the scraps of wood?A line plot is a graph that is made up of a number line and check marks above the numbers on the number line. The check marks above the number line represents the frequency of the data. For example, there are two checkmarks above 7. This means that there are two scraps of woods that measure 7 inches.
In order to determine the approximate length of the scraps of wood if they are placed side by side, add the length of each scrap of wood together.
Addition is a mathematical operation that is used to determine the sum of two or more numbers. The sign that is used to denote addition is +.
[tex]5\frac{1}{2} + 6 + (6\frac{1}{2}. 3) + (7. 2) + 8[/tex] =
[tex]5\frac{1}{2} + 6 + 19\frac{1}{2} + 14 + 8[/tex] = 53 inches
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As the x-value increases by 20, the y-value increases by 10. Which of the following equations represents the relationship between the x and y-values
An equation which represents the proportional relationship between the x and y-values is: C. y = 2x.
What is direct variation?A direct variation represents two variables that are directly proportional to each other, which simply means as one variable increases, the other variable also increases and vice-versa.
How to determine the equation?Mathematically, a proportional relationship can be represented by the following equation:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Next, we would determine the constant of proportionality (k) based on the data points given:
k = y/x
k = 20/10
k = 2
Therefore, the required equation is as follows:
y = 2x
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Complete Question:
As the x-value increases by 20, the y-value increases by 10. Which of the following equations represents the relationship between the x and y-values?
A. y = 2 + x
B. y = 2 - x
C. y = 2x
Danny measured a house and its lot and made a scale drawing. The scale of the drawing was 1 inch : 5 feet. The houses driveway is 20 feet widein real life. How wide is the driveway in the drawing?
The width of the house driveway in the scale drawing is 4 inches.
What is scale drawing?Scale drawing is drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale).
Therefore, he measured a house and its lot and made a scale drawing.
The scale of the drawing was 1 inch : 5 feet.
The houses driveway is 20 feet wide in real life.
Therefore,
5 feet = 1 inch
20 feet = ?
cross multiply
Therefore,
width of the driveway on the scale drawing = 20 × 1 / 5
width of the driveway on the scale drawing = 20 / 5
width of the driveway on the scale drawing = 4 inches.
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PLS HELP!!!!!
31 POINTS
Three students have summer jobs. The proportional relationship between their pay and the hours they work is shown.
Student A:
Time (hours) 5 13
Pay (dollars) 67.50 175.50
Student B: $189.00 for 14 hours
Student C: The equation p = 13.5h, where p represents total pay and h represents hours worked
Which student is paid the most for 20 hours of work?
All the students are paid equal amount of $270. Therefore, no oneis paid more.
How to illustrate the information?For student A, the amount paid for 20 hours will be:
= (67.50 / 5) × 20
= 13.50 × 20
= $270
For student B, the amount paid for 20 hours will be:
= (189/14) × 20.
= $270
For Student C, the amount paid for 20 hours will be:
p = 13.5h
where h = number of hours
p = 13.5 × 20 = $270
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Answer:
D yeyeyeye! <3
after cynthia microwaves her bowl of morning porridge, it is either too cold, just right, or too hot. she estimates that there is a 35\55, percent chance that it will be too cold and a 50\pp, percent chance that it will be too hot. what is the probability that cynthia's morning porridge will be just right?
The probability that Cynthia's morning porridge will be just right is 15%.
Probability is defined as the likeliness of an event to happen. It can be determined by dividing the total number of the desired outcome by the total number of samples.
The sum of the probabilities in a probability distribution is always 1.
If there are three outcomes: too cold, just right, and too hot, then the sum of their probabilities is equal to 1 or 100%.
P(too cold) + P(just right) + P(too hot) = 100%
35% + P(just right) + 50% = 100%
P(just right) = 100 - (35 + 50)
P(just right) = 100 - 85
P(just right) = 15%
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A coin box contains $26.50 in dimes and quarters. There are 157 coins altogether. How many of each
type of coin are in the box?
======================================================
Work Shown:
x = number of dimes
y = number of quarters
x+y = 157 coins total
-------------------------------
$26.50 = 2650 cents
1 dime = 10 cents
x dimes = 10x cents
1 quarter = 25 cents
y quarters = 25y cents
total value = 10x+25y = 2650 cents
-------------------------------
We have this system of equations
x+y = 157
10x+25y = 2650
Let's solve for y in the first equation
x+y = 157
y = 157-x
Then plug this into the second equation and solve for x.
10x+25y = 2650
10x+25(157-x) = 2650
10x+25(157)+25(-x) = 2650
10x+3925-25x = 2650
-15x+3925 = 2650
-15x = 2650-3925
-15x = -1275
x = -1275/(-15)
x = 85 is the number of dimes
Then use this to find the value of y
y = 157-x
y = 157-85
y = 72 is the number of quarters
-------------------------------
Check:
85 dimes + 72 quarters = 157 coins total
85 dimes = 85*10 = 850 cents
72 quarters = 72*25 = 1800 cents
850 cents + 1800 cents = 2650 cents = $26.50
This confirms the answers.
Answer:
so 85 dimes and 72 quarter coins are in the box
Step-by-step explanation:
Given; Total number of coin =1557 Total amount money =26.50 To find Number of dimes and quarters in the box. In order to find the solution, make equation of number of coin and amount money. solve for unknown.Let, Number of dimes = x Number of quarters = y As, it is given that total number of coin is 157. x + y = 157 ......(a) Also, the total money is $ 26.50. .. 0.10x+0.25y = 26.50 ..(b)To, solve equation (a) & (b), put value of y from (a) to (b); From (b); From (a); y= 157 0.10x+0.25(157 - x) = 26.50 0.10x+39.25 - 0.25x = 26.50 0.15x+39.25 = 26.50 39.25 26.50 = 0.15x 12.75 = 0.15x 12.75 0.15 = x 85 = x Now, put value of x in equation (a); x + y 85+ y = y= 72
AThe formula for the circumference of a circle is C = 2tr. Find the circumference of acircle with a diameter of 4 ft.
Given the formula for the circumference of a circle:
C = 2πr
Let's find the circumference of a circle with a diameter of 4 ft.
Where r is the radius.
To find the radius, we have:
[tex]\text{radius}=\frac{\text{diameter}}{2}=\frac{4}{2}=2ft[/tex]The radius of the circle is 2 ft.
Take π = 3.14
Hence, to find the circumference of the circle, C, substitute 2 for r, 3.14 for π, and evaluate.
Thus, we have:
[tex]\begin{gathered} C=2\pi r \\ \\ C=2\ast3.14\ast2 \\ \\ C=12.56\text{ ft} \end{gathered}[/tex]Therefore, the circumference of the circle is 12.56 ft
ANSWER:
C. 12.56 ft
A right cylinder has a radius of 5 and a height of 9. What is its surface area? O A. 72 units O B. 90 units O c. 45rt units O D. 108r units
The formula to find the surface area of a cylinder is:
[tex]\begin{gathered} SA=2\pi r^2+2\pi rh\text{ } \\ \text{ Where} \\ SA\text{ is the surface area} \\ r\text{ is the radius} \\ h\text{ is the height} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} r=5 \\ h=9 \end{gathered}[/tex][tex]\begin{gathered} SA=2\pi r^2+2\pi rh \\ SA=2\pi(5^2)+2\pi(5)(9) \\ SA=2\pi(25)+90\pi \\ SA=50\pi+90\pi \\ SA=140\pi \end{gathered}[/tex]AnswerB. 140π units²
RUNNING Stella ran her first half marathon in 2.7 hours. By how many hours must Stella reduce her time to run her next half marathon in fewer than 2.3 hours? Enter an inequality to represent the situation.
Answer:
2.7 - h < 2.3
Step-by-step explanation:
You want an inequality to represent the relationship described by "Stella wants to know the number of hours (h) by which she must reduce her 2.7 hour half-marathon time to run in under 2.3 hours."
InequalityIf h is the number of hours by which the time is reduced, Stella wants ...
2.7 -h < 2.3 . . . . . . . . . representative inequality
__
Additional comment
The solution would be h > 0.4. Stella must reduce her time by more than 0.4 hours.
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Lilly has a bag only containing blue beads and purple beads.
3/8 of the beads are blue.
If there are 9 blue beads in the bag, how many beads are purple?
Answer:
15 purple beads
Step-by-step explanation:
Calculate total beads
[tex]\frac{9}{\frac{3}{8} } =\frac{72}{3} =24[/tex]
Calculate how many beads are purple
[tex]24-9=15[/tex]
Hope this helps
There are total 15 purple beads.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
given:
Fraction of blue beads = 3/8
Total blue beads = 9
let the total number of beads be x.
So, 3/8x = 9
x= 9. 8/3
x= 72/3
x= 24
So, number of purple beads = 24 -9= 15 beads
Hence, there total 15 purple beads.
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A committee of 3 members is selected from a club made up of junior members and senior members. What is the expected number of juniors in the committee?.
The expected number of juniors in the committee is 1.3
The question is incomplete, the complete question is given below:
A committee of 3 members is selected from a club made up of 13 juniors members and 17 senior members. What is the expected number of juniors in the committee?
The expected number of juniors in the committee is computed here as:
Juniors in the committee=13
Seniors in the committee=17
Total number of members=(13+17)=30
Fraction of juniors in total members=13/30
So expected number of juniors in the committee:
=Fraction of juniors in total members*Total number of members to be selected
=(13/30)*3
=1.3
Therefore 1.30 is the expected number of juniors in the committee
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Find x so that q || r.
X =
Answer:
x = 12
Step-by-step explanation:
To justify q || r :
11x - 28 + 7x - 8 = 180 because they would be supplementary angles and their sum would be equal to 180°
add like terms
18x - 36 = 180 add 36 to both sides
18x = 216 divide both sides by 18
x = 12
Help me with this please
Answer:
first plot the positive 2 on the y axis
plot (0,2)
Then from (0,2) go up 2 and right 2.
Answer in attached image
John and Nelly are cleaning their house, Nelly takes 3 hours longer than John if she cleans alone, If they can do the cleaning together in 2 hours, how long can John clean all b yh himself
Answer: 3 hours
Let john take x hours to finish the work
Let nelly take y hours to finish the work
given, y =x+3
Portion of work done by john alone in one hour = 1/x
Portion of work done by Nelly alone in one hour = 1/y
∴Portion of work done by both john and nelly in one hour = 1/x + 1/y
[tex]= \frac{1}{x} + \frac{1}{x+3}\\=\frac{x+3+x}{x*(x+3)}\\=\frac{2x+3}{x^2+3x}[/tex]
Total time taken by John and nelly to finish the work = 2 hours
[tex]\therefore [2(2x+3)]/[x^2 + 3x] = 1\\= > 4x + 6 = x^2 + 3x\\= > x^2 -x -6 =0\\= > x^2 - 3x + 2x -6 =0\\= > x(x-3) + 2(x-3)=0\\= > (x+2)(x-3)=0[/tex]
Hence either x = -2 or x = 3
Since x is time taken, it cannot be negative, hence x = 3
∴Time taken by john to finish the work = 3 hours
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please help quickly.
Answer:
Step-by-step explanation:
5) Domain: -3<=x<=2
Range: 4<=y<=-3
6) Domain: {-3,-2,-1,0,1,2}
Range: {4,3,2,1,0,-1,-2,-3}
Do you need number 7 too?
:]
What is the slope of the line that passes through the points (-4, 2)(−4,2) and (-5, 0)(−5,0)? Write your answer in simplest form.
Answer: 2
Step-by-step explanation:
We will use the slope formula to find the slope of the line going through these two points.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{0-2}{-5--4} =\frac{-2}{-5+4} =\frac{-2}{-1} =2[/tex]
The slope of this line is 2.
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Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
After four years, the investment is worth £8934.34.
How does compound interest work?The interest you earn on interest is known as compound interest. For instance, if you start with $100 and it generates 5% interest annually, you will conclude the first year with $105 in your account. You'll have $110.25 after the second year is over.
We employ the formula approach to determine the entire amount,
A = P(1+r)^n
The amount invested, or principal(P), is £8,000.
Interest rate r is 2.8%, or 0.028.
n = 4 years have passed.
Now, immediately enter these values into the formula, A = P(1+r)n.
A = 8000 * (1 + 0.028) ^ 4
= 8000 * 1.028 ^ 4
= 8934.34
Consequently, the investment's value after four years is £8934.34.
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The first of two numbers is twice the second. Seven more than the second number is equalto 6 less than the first number. Find the numbers.
Let's call x to the first number ans y to the second number.
The first of two numbers is twice the second:
x = 2y
Seven more than the second number is equal to 6 less than the first number:
7 + y = x - 6
Isolating x:
7 + y + 6 = x
13 + y = x
Combining last equation with first equation:
2y = 13 + y
2y - y = 13
y = 13
Then:
x = 2*13
x = 26
difference between a number and its positive square root is 12.find the number
Answer:16
Step-by-step explanation:
x-[tex]\sqrt{x}[/tex]=12
x=16
There are 8 batteries in a package of AA batteries, and 12 batteries in
a package of AAA batteries. If you buy 10 packages of AA batteries and
6 packages of AAA batteries, how many batteries would you have?
A- 156 batteries
B- 36 batteries
C- 152 batteries
Answer:
C. 152
Step-by-step explanation:
8 × 10 + 6 × 12 = 80 + 72 = 152