We could use the standard form of subtraction.
We put 71.120 on top and we put 2.359 at the bottom.
Then, we subtract the thousandths place. It involves a carry-over.
Then, we subtract and the answer is:
68.761
The subtraction of 71.120 and 2.359 equals 68.761.
Explanation:This question is asking for the subtraction of two decimal numbers, the first being 71.120 and the second being 2.359. To do this, you would stack the numbers on top of each other, aligning the decimal points, and subtract as you would with whole numbers.
So, your subtraction would look like this:
71.120
So, 71.120-2.359 equals 68.761.
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What is the value of m inthe figure below? In this diagram, ABD~BCD
Answer:
C. sqrt(95)
Step-by-step explanation:
The three triangles are similar, so you can use the right triangle altitude theorem.
(14 + 5)/m = m/5
19/m = m/5
m^2 = 19 * 5
m^2 = 95
m = sqrt(95)
Answer: C. sqrt(95)
What are the x- and y-intercepts of the graph of y = x2 + 3x − 10? x-intercepts: (−2, 0) and (5, 0) y-intercept: (0, 10) x-intercepts: (−2, 0) and (−5, 0) y-intercept: (0, 10) x-intercepts: (−2, 0) and (5, 0) y-intercept: (0, −10) x-intercepts: (2, 0) and (−5, 0) y-intercept: (0, −10)
We have the following function:
[tex]f(x)=x^2+3x-10[/tex]
So, we need to find the x- and y-intercepts of the graph of that function, therefore:
1. x-intercepts
x-intercepts can be found when [tex]y=0[/tex], so:
[tex]0=x^2+3x-10 \\ \\ Using \ Quadratic \ Formula \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ Where: \\ \\ a=1, b=3, c=-10 \\ \\ x=\frac{-3 \pm \sqrt{3^2-4(1)(-10)}}{2(1)} \\ \\ Two \ values: \\ \\ x=2 \ and \ x=-5[/tex]
So, the x-intercepts are:
[tex]\boxed{(2,0) \ and \ (-5, 0)}[/tex]
2. y-intercepts
x-intercepts can be found when [tex]x=0[/tex], so:
[tex]y=(0)^2+3(0)-10 \\ \\ \therefore y=-10[/tex]
So, the y-intercept is:
[tex]\boxed{(0,-10)}[/tex]
_______________________________________
Therefore the right answer is:
x-intercepts: (2, 0) and (−5, 0) y-intercept: (0, −10)
This is indicated in the Figure bellow.
Answer:
2, 0) and (−5, 0)
Step-by-step explanation:
PLEASE HELP THIS IS URGENT!
The engine torque y (in foot-pounds) of one model of car is given by y=−3.75x^2+23.2x+38.8, where x is the speed (in thousands of revolutions per minute) of the engine.
a. To the nearest ten, what is the engine speed that maximizes torque? ------____ revolutions per minute
To the nearest hundredth, what is the maximum torque?
____ ft-lbs
Question 2
b. Explain what happens to the engine torque as the speed of the engine increases.
As the engine speed increases, the torque _____ until the engine speed reaches
_____ thousand revolutions per minute and then the torque ______
Answer-
a. The engine speed that maximizes torque is 3.1 thousand revolutions per minute and the maximum torque is 74.68 ft-lbs
b. As the engine speed increases, the torque increases until the engine speed reaches 3.1 thousand revolutions per minute and then the torque decreases.
Solution-
The given equation is,
[tex]y=-3.75x^2+23.2x+38.8[/tex]
Where x = the speed of the engine (in thousands of revolutions per minute)
y = the engine torque y (in foot-pounds)
a.
In order to calculate the max torque and when it is max, we have to take the help of maxima and minima concepts from application of derivatives.
[tex]\Rightarrow y=-3.75x^2+23.2x+38.8[/tex]
[tex]\Rightarrow {y}'=-7.5x+23.2[/tex]
[tex]\Rightarrow {y}''=-7.5[/tex]
Equating the first derivative to 0, in order to find critical points,
[tex]\Rightarrow {y}'=0[/tex]
[tex]\Rightarrow -7.5x+23.2=0[/tex]
[tex]\Rightarrow x=\frac{-23.2}{-7.5} = 3.093 \approx 3.1[/tex]
As the value of second derivative is negative, hence the value of the function at x=3.1 will be maximum.
The value of max torque is,
[tex]y(3.1)=-3.75(3.1)^2+23.2(3.1)+38.8=74.682 \approx 74.68[/tex]
b.
Calculating the roots of the function,
[tex]\Rightarrow y=0[/tex]
[tex]\Rightarrow -3.75x^2+23.2x+38.8=0[/tex]
[tex]x=-1.369,7.556[/tex]
As these are the roots or x-intercept, the value of the function at these points is zero.
As shown in the graph, the function increases from x=0 to x=3.1 (as the speed can not be negative, so neglecting negative values) and after x=3.1 it decreases.
At about 3093 revolutions per minute, the engine torque reaches its maximum of 44.97 ft-lbs. Prior to this, the torque increases with engine speed, but starts to decrease once the speed surpasses this point.
Explanation:The equation given is that of a downward opening parabola, which means it has a maximum point. The vertex (h, k) of a parabola given by the equation y = a(x-h)^2 + k is at x = -b/2a. For the given equation, a = -3.75 and b = 23.2.
Substituting these values, we get x = -23.2/(2*-3.75) = 3.093 to the nearest thousand, which translates to 3093 revolutions per minute. Substituting this value of x in the equation gives the maximum torque y = -3.75*(3.093)^2 + 23.2*3.093 + 38.8 = 44.97 ft-lbs to the nearest hundredth.
As the engine speed increases, the torque increases until the engine speed reaches about 3093 revolutions per minute. After this, "the torque then starts to decrease".
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Suzanne can read 1 page in 4 minutes. How many pages can she read in 5 hours?
Answer:
75 pages
Step-by-step explanation:
please help asap 23 pts
Solve for r by simplifying both sides of the equation, then isolating the variable.
Your answer is A.
please help asap 25 pts
2y - 3 > -1 |add 3 to both sides
2y > 2 |divide both sides by 2
y > 1
-----------------------------
5 - y > 4 |subtract 5 from both sides
-y > -1 |change the signs
y < 1
y > 1 or y < 1
Therefore your answer is d.Which of the following angles is an angle of depression?
we know that
The Angle of Depression. is the angle below the horizontal that an observer must look to see an object that is lower than the observer
in this problem
the angle below the horizontal is the angle C
therefore
the answer is
The angle of depression is the angle C
At the end of the summer, Caitlin had saved $120 from her summer job. This was her initial deposit into a new savings account at the bank. As the school year starts, Caitlin is going to deposit another $5 each week from her allowance. Is her account balance proportional to the number of weeks of deposits? Explain your reasoning.
Let X be the number of weeks she deposits money.
The equation to solve for the account balance would be 120 + 5x ( She started with 120 dollars and is adding 5 dollars per week)
week 1: balance = 120 +5(1) = $125
week 2: balance = 120 +5(2) = $130
week 3: balance = 120 + 5(3) = $135
week 4: balance = 120 +5(4) = $140
Now to see if it proportional divide each total by the number of weeks:
week 1: 125 / 1 = 125
week 2: 130 / 2 = 65
week 3: 135 / 3 = 45
week 4: 140 / 4 = 35
Find the difference between the weeks:
Week 1 & 2 : 125 - 65 = 60
Week 2 & 3: 65 -45 - 20
Week 3 & 4: 45 -35 = 10
Since the 3 differences are not the same, the balance is not proportional to the number of weeks.
2 different pairs of decimals whose sum are 8.69 one pair should involve regrouping
Random cell phone calls sent out to a sample size of 850 people is what type of sampling method? (I.e. simple random, etc.)?
Answer: Simple Random Sampling (SRS)
The people chosen are basically picked out of a hat at random, though likely they are chosen by a computer.
Answer:
Random cell phone calls sent out to a sample size of 850 people would typically be considered a form of random sampling. However, the specific type of random sampling can vary. It could be simple random sampling if each person in the population has an equal chance of being called, and the selection is done entirely by chance, such as using a random number generator to select phone numbers.
Alternatively, it could be stratified random sampling if the population is divided into different groups or strata (e.g., age groups, geographic regions), and then random samples are taken from each stratum in proportion to its size.
The exact method used depends on the sampling strategy and goals of the study, but as long as the selection of individuals is based on randomness and each person has an equal chance of being included, it falls under the broad category of random sampling.
Step-by-step explanation:
What is the product of the polynomials below? (6x3 + 3x)(x2 + 4)
The number of seconds in a 40-hour work week can be calculated as follows:
First we can calculate how many seconds there are in an hour:
Since 1 hour has 60 minutes and each minute has 60 seconds.
Then 1 hour = 60 minutes * 60 seconds/1minute = 3,600 seconds.
Now we have to multiply x 40 to calculate how many seconds there are in 40 hours.
In a 40-hour work week = 40 hours * 3,600 seconds/1hour = 144,000 seconds
Answer : 144,000 seconds there are in a 40-hour work week
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
The correct formula to calculate the number of seconds in a 40-hour work week is 40 hours * 60 minutes/hour * 60 seconds/minute (option a). This method accurately converts hours to minutes and then minutes to seconds.
The correct formula for calculating the number of seconds in a 40-hour work week is as follows:
a. 40 hours * 60 minutes/hour * 60 seconds/minute
Here's the breakdown:
1. Start with the number of hours, which is 40 hours.
2. Convert hours to minutes using the conversion factor of 60 minutes per hour.
3. Convert minutes to seconds using the conversion factor of 60 seconds per minute.
By multiplying these three factors together, you obtain the total number of seconds in a 40-hour work week.
The other options (b, c, d) do not correctly set up the conversion factors and units, leading to incorrect results.
So, the correct answer is (a), as it correctly converts 40 hours into seconds using the appropriate conversion factors.
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Juan Ramirez sells suits in a major department store on weekends. He earns a commission of 5 percent on the first 10 suits, and if he sells more than 10, he earns an additional 3 percent on the additional suits. Last weekend Juan sold 13 suits at a price of $250 each. What was his commission? A. $147.50 B. $210.40 C. $185.00 D. $260.00
Given
He earns a commission of 5 percent on the first 10 suits.
he sells more than 10, he earns an additional 3 percent on the additional suits
Last weekend Juan sold 13 suits at a price of $250 each.
Find out Juan Ramirez commission
To proof
As given in the question
Juan sold 13 suits at a price of $250 each
13 suit selling price = 13 × 250
= $ 3250
As given
He earns a commission of 5 percent on the first 10 suits.
and for more than 10, he earns an additional 3 percent on the additional suits
Juan Ramirez sells 13 suit which are more than the 10 suits
Hence
commission percent for the 13 suits = 8 %
First write 8% in the decimal form
[tex]= \frac{8}{100}[/tex]
=0.08
Than commission on the 13 suits = 0.08 × 3250
= $260.
Therefore option ( D) is correct.
Hence proved
Use the place value chart to write 9,000+800+50
The answer is 9,850 if you are adding the numbers together.
Answer:
9,000 + 800 + 50 = 9,850
Step-by-step explanation:
Hope it helped!
Rewrite using a single positive exponent (8^3)/8
The expression 8³ / 8 in the simplified form will be 8².
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Exponentiation is a numerical activity, composed as bⁿ, including two numbers, the base b, and the type of power n, and articulated as "b to the n".
The expression is given below.
⇒ 8³ / 8
We know that 1/aⁿ will be written as a⁻ⁿ. Then the expression is written as,
⇒ 8³ / 8
⇒ 8³ × 8⁻¹
⇒ 8⁽³ ⁻ ¹⁾
⇒ 8²
The expression 8³ / 8 in the simplified form will be 8².
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In a parallel circuit, ET = 277 V, R = 56 kΩ, and XL = 68 kΩ. What is the phase angle (angle theta)?
Answer:
Phase angle is 50.527°
Step-by-step explanation:
Given that in a parallel circuit [tex]E_{T}=277V[/tex], R=56kΩ and [tex]X_{L} =[/tex]68kΩ.
And we are asked to find phase angle.
In any circuit, phase angle[tex]\theta=tan^{-1}(\frac{X_L-X_C} {R})[/tex]
Since we don't have any capacitor,[tex]X_{C}=0[/tex]
Hence phase angle,[tex]\theta=tan^{-1}(\frac{68000}{56000})[/tex]
[tex]=tan^{-1}(1.2143)[/tex]=50.527°≈50.53°
A child has 48 quarters and 80 dimes. The child wishes to stack the coins so that each stack has the same number of coins, and each stack contains only one kind of coin. What is the
largest number of coins that the child can place in each stack?
Since the greatest common factor for 48 and 80 is 16 then we conclude the largest number of stack is 16
The largest number of coins that the child can place in each stack is 16, which is the greatest common divisor of the number of quarters (48) and dimes (80) they have.
Explanation:In this problem, we're looking for the greatest number of coins that can evenly divide both the total number of quarters and the total number of dimes the child has. This can be solved by finding the greatest common divisor (GCD) of the numbers, 48 and 80.
The GCD of 48 and 80 is 16. Therefore, the child can create stacks of 16 coins each (either quarters or dimes), ensuring that each stack has the same number of coins and that all coins are used.
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HELP PLZSS :)
Is 2H2 + O2 →2H2O a balanced chemical equation? Is it obeying the law of conservation of matter?
No, the equation is not balanced. The Hydrogen (H) in the equation has less atoms represented on the products.
No, the equation is not balanced. The Oxygen (O) in the equation has less atoms represented on the products.
Yes, the equation is balanced. There are the same number of Hydrogen (H) and Oxygen (O) atoms on both sides of the equation.
Answer:
It IS balanced. There are 4 Hydrogen atoms on the left and the right and 2 Oxygen atoms on the left and the right.
Step-by-step explanation:
The given reaction follows the law of conservation of mass and is balanced. Thus, the correct option is C.
The balanced chemical equation for the reaction has been:
[tex]\rm 2\;H_2\;+\;O_2\;\rightarrow\;2\;H_2O[/tex]
The law of conservation of mass states that the mass of each element on the product and the reactant side has been equal. The mass has been proportional to the number of atoms, thus the atoms have been equal on both sides of the reaction.
In the given reaction:
The number of atoms of Hydrogen:Reactant = 4
Product = 4
The number of atoms of Oxygen:Reactant = 2
Product = 2
Since there has been the same number of atoms of each element on both sides of the reaction, the reaction has been termed a balanced reaction. The law of conservation of mass has been followed in the equation.
Thus, option C is correct.
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Last week you worked the following hours: Monday, 5½ Wednesday, 6¾ Friday, 4½ How many hours did you work in all last week? A. 16¾ B. 17½ C. 17¾ D. 18½
Answer:
A. 16¾
Step-by-step explanation:
We will convert all the mixed fractions to improper fractions.
Monday, 5½ = [tex]\frac{11}{2}[/tex]
Wednesday, 6¾ = [tex]\frac{27}{4}[/tex]
Friday, 4½ = [tex]\frac{9}{2}[/tex]
Now, we will add all these fractions by taking the LCM of denominator.
The LCM of 2,4 and 2 is 4.
We get the following result after addition.
[tex]\frac{11}{2} +\frac{27}{4} +\frac{9}{2}[/tex]
= [tex]\frac{22+27+18}{4}[/tex]
= [tex]\frac{67}{4}[/tex] hours
In mixed fraction it becomes 16¾ hours.
A triangular window has a base of 8 feet and a height of 6 feet. What is its area?
Answer:
24 feet^2
Step-by-step explanation:
Area = 1/2 × base × height
Base = 8 feet
Height = 6 feet
Area = 1/2 × 8 feet × 6 feet = 24 feet²
Answer:
Area = 24 square feet.
Step-by-step explanation:
Given : A triangular window has a base of 8 feet and a height of 6 feet.
To find :What is its area?
Solution : We have given
Base of triangular window = 8 feet.
Height of triangular window = 6 feet.
Area = [tex]\frac{1}{2} * base*height[/tex].
Plugging the values.
Area = [tex]\frac{1}{2} *8* 6[/tex].
Area = 24 square feet.
Therefore, Area = 24 square feet.
- What is the y-intercept of 6x + 12y = 60? A. 5 B. 10 C .60 - What is the slope of the line that contains the points (1, −1) and (−2, 8)? A. −3 B. 7 over 3 negative C. 1 over 3 negative
The y-intercept of the equation 6x + 12y = 60 is 5, and the slope of the line through points (1, -1) and (-2, 8) is -3. Therefore the correct option is A.
Finding the Y-Intercept of a Linear Equation
To find the y-intercept of the linear equation 6x + 12y = 60, we need to set x to 0. If x=0, the equation simplifies to 12y = 60. Dividing both sides by 12 gives us the y-intercept: y = 5. Therefore, the correct answer is A: 5.
Calculating the Slope between Two Points
The slope of a line containing the points (1, -1) and (-2, 8) can be found by using the formula (y2 - y1) / (x2 - x1). Substituting the given points into the formula results in: (8 - (-1)) / (-2 - 1) = 9 / -3 = -3.
How many degrees is one sixth of a circle or 1/6 of a full turn
On a number line, the distance from zero to -7 is 7 units.
Which equation demonstrates this concept?
A.
|-7| = 7
B.
|-7| = -7
C.
72 = 49
D.
0 + 7 = 7
Answer: Option A. |-7| = 7
Solution:
The distance is a positive value, then we must not take in account the sign, and using:
|a| =-a if a<0
with a=-7
|-7| = -(-7)
|-7| = 7
Yellow to red 50 yellow and 45 red what it the ratio
50 : 45
10 : 9 (10 yellow : 9 red)
50 yellow and 45 red
The ratio of yellow to red = 50/45 = 10/9
Answer
The ratio of yellow to red is 10/9 or 10:9
Look at the following sequence. 128, 320, 800, 2000, . . . If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose “not geometric.” 4 not geometric 2.5 1200
Answer:
It is a geometric sequence en the common ratio is: [tex]r=\frac{5}{2}[/tex].
Step-by-step explanation:
1. By definition, a geometric sequence is a sequence in which you obtain a term by multiplying the previous one by a common ratio.
2. The common ratio is obtained by dividing a term by its preceding term.
3. Keeping this on mind, you have:
[tex]\frac{320}{128}=\frac{5}{2}\\[/tex]
[tex]\frac{800}{320}=\frac{5}{2}[/tex]
[tex]\frac{2000}{800}=\frac{5}{2}[/tex]
4. As you can see, the common ratio is [tex]\frac{5}{2}[/tex]
Answer:
2.5!!
Step-by-step explanation:
100% correct
What is an equivalent expression to q(2a+1)
You can distribute the q to both terms to get
[tex] q(2a+1) = q\cdot 2a + q\cdot 1 = 2aq+q [/tex]
Answer:
2aq +q is an equivalent expression for q(2a+1)
Step-by-step explanation:
an equivalent expression to q(2a+1)
To get equivalent expression we need to multiply q inside the parenthesis
q times 2a = 2aq
q times 1 is q
Now we combine both term
q(2a+1)= 2aq + q
So 2aq +q is an equivalent expression for q(2a+1)
$2500 was invested for 3 years and earned $450 in intrest. Fine the rate of intrest
Answer:
Step-by-step explanation:
130
Mark bought 12 cookies for $2.70 at this rate how much would it cost him to buy 20 cookies
For Mark to buy 20 cookies, it'll cost him about $4.40
The cost of 20 cookies if 12 cookies cost $2.70 is $4.50.
How much would it cost him to buy 20 cookies?12 cookies cost $2.70
Then,
20 cookies cost $x
Set up the ratio
12 : 2.70 = 20 : x
12/2.70 = 20/x
cross product
12 × x = 2.70 × 20
12x = 54
Divide both sides by 12
x = 54/12
x = $4.50
Therefore, 20 cookies cost $4.50
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In which measurement situations would the most appropriate unit of measurement be meters?
Choose exactly two answers that are correct.
A.
width of a finger
B.
height of a tree
C.
depth of a well
D.
distance from the earth to the sun
Which ordered pair is a solution to this equation?
2x - 9y = 38
(7, 5)
(4, -1)
(3, -3)
(1, -4)
Let's test each alternative :
2 x - 9 y = 38 ( 7,5 ) :
( 2 * 7 ) - ( 9 * 5 ) = 38
14 - 45 = 38
-31 ≠ 38 ( wrong )
( 4 , - 1 ) :
( 2 * 4 ) - ( 9 * ( - 1 ) = 38
8 + 9 = 38
17 ≠ 38 ( wrong )
( 3 , - 3 ) :
2 * ( 3 ) - ( 9 * ( - 3 ) = 38
6 + 27 = 38
33 ≠ 38 ( wrong )
( 1 , - 4 ) :
2* ( 1 ) - 9 * ( - 4 ) = 38
2 + 36 = 38
38 = 38 ( Correct alternative )
( 1 , - 4 ) is correct alternative