Hence, the commutative property of addition is not used.
What is an expression?
A mathematical expression is in form of variables and constants separated by their arithmetic operation.
As we know that, there are three types of properties they are associative property which is [tex](a+b) + c = a + (b+c)[/tex],
Distributive property which is [tex]a(b+c) = ab + ac[/tex],
Commutative property which is [tex]a + b = b + a[/tex].
Here given that,
[tex]2 (x+5)+7x=(2x+10)+7x[/tex]
[tex](2x+10)+7x=(2x+10)+7x[/tex] ( distributive property of multiplication)
[tex](2x+7x)+10=(2x+7x)+10[/tex] ( it is associative property of addition)
[tex](8x)+10=(8x)+10[/tex] ( it is a commutative property)
Hence, the commutative property of addition is not used.
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A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12
Answer:
There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.
There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.
Step-by-step explanation:
Month No. of Mean Squared
Fatal Accidents Deviation Difference
Jan 8 -4 16
Feb 15 3 9
Mar 9 -3 9
Apr 8 -4 16
May 13 1 1
Jun 6 -6 36
Jul 17 5 25
Aug 15 3 9
Sep 10 -2 4
Oct 9 -3 9
Nov 18 6 36
Dec 12 0 0
Total 140 170
Mean = 140/12 = 12 Mean of squared deviation (Variance) = 170/12 = 14.16667
Standard deviation = square root of variance = 3.76386 = 4
The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set. It also shows how variable the data varies from the mean of approximately 12.
The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.
PLEASE HELP ! (2/4) - 50 POINTS -
Answer:
The correct answer would be 15.5 or C.
rite
8x8*8X8X8 as
power
Answer:
8×8×8×8×8
= 8^5
because there are five 8 number
I hope this helps
if u have question let me know in comments ^_^
[tex]8\cdot8\cdot8\cdot8\cdot8=8^5[/tex]
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste?
A. none of these
B. Let “1,2,3” represent preferring the toothpaste and “0,4,5,6,7,8,9” represent not recommending the toothpaste.
C. Let “1,2,3” represent preferring the toothpaste and “4,5,6,7,8,9” represent not recommending the toothpaste.
D. Let “0,1,2” represent preferring the toothpaste and “3,4,5,6,7,8” represent not recommending the toothpaste.
Reset Selection
Answer:
b
Step-by-step explanation:
only b has 10 didgets. it could be a since the didgets aren't very random, but then again, i think it's b
Let favorable event“1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste to determine.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
While going throughout the option in options C and D number so the sample is not equal to 10 so both the statement is false. Option B is the correct option because the sample space is also equal to 10 and the number of the favorable events is also 3 which is mentioned in the question.
Thus, let favorable event “1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.
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How many countries expect to have an increase in population from 1950 to 2000 and from 2000 to 2050 ?
one
two
three
four
Answer:
three
Step-by-step explanation:
The three countries expect to have an increase in population. Then the correct option is C.
What is a histogram?A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.
The bar chart of the countries is shown.
From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Australia increased.
From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Hungary first increases then decreases.
And from the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Canada increased.
From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 in South Korea first increases then decreases.
From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Egypt increased.
The three countries expect to have an increase in population.
Then the correct option is C.
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Tyler and Gabe went to the arcade and played the same two games, Tyler played five rounds of each game for 30$. Write two equations for the amounts the two boys spent. Then find the cost for one round each game.
Equations:
1. (30)(5)= 150
2. 30 + 30 + 30 + 30 + 30 = 150
I round:
30 dollars divided by 5 rounds = 6 dollars per round.
The total amount spent by the two boys is $300.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that Tyler and Gabe went to the arcade and played the same two games. Tyler played five rounds of each game for 30$.
We can write the total amount spent by the two boys as -
total amount = 2 x cost of each game x total number of games played
total amount = 2 x 30 x 5
total amount = 10 x 30
total amount = 300
Therefore, the total amount spent by the two boys is $300.
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Help me please thank you
Answer: 60°
Step-by-step explanation:
apply concept: the interior angle sum of triangle is 180°
x+x+x=180
3x=180
x=60
---------------
this is also an equilateral triangle which if you know it, you will know that each angles are all 60°
Answer: x=60°
Step-by-step explanation:
We know that the sum of the angles in a triangle is 180°. Since all of the angles are x°, we know that they are equal in degrees. Since there are 3x, we can use that to solve for x.
3x=180 [divide both sides by 3]
x=60°
Solve for X, 3^x + 3^2 = 90
3^x + 3^2 = 90
Simplify the known power:
3^x + 9 = 90
Subtract 9 from both sides:
3^x = 81
Take the cubic root of both sides:
X = 4
Suppose that 22 inches of wire costs 66 cents.
At the same rate, how much (in cents) will 17 inches of wire cost?
cents
Х
?
Answer:
51 cents for 17 inches of wire
Step-by-step explanation:
22 = 66
17 = x
22x = 66 * 17
22x = 1122
x = 51 cents
or
22 inches costs 66 cents
1 inch costs 3 cents (66 / 22 = 3 cents)
17 inches costs 51 cents (17 * 3 = 51 cents)
Chelsea played her tuba from 4:25 pm until 5:07
Answer:
42 minutes
Step-by-step explanation:
if you are asking how long it takes Chelsea to play her tuba then you do: 67 - 25 = 42
Answer:
Step-by-step explanation:
jhngjnh
Timothy invested $2,000 in an account earning 3.5% annual interest that is compounded continuously. How long will it take the investment to grow to $3,500?
Answer: 16 years
Step-by-step explanation:
The exponential function for continuous growth is given by :-
[tex]P=Ae^{rt}[/tex]
, where A = initial amount, r= rate of growth and t = time.
As per given , we have
A= $2,000, =r 3.5%=0.035 and P= $3500
put these vales in equation , we get
[tex]3500=2000e^{0.035t}\\\\\Rightarrow\ \dfrac{3500}{2000}=e^{0.035t}\\\\\Rightarrow\ 1.75=e^{0.035t}[/tex]
Taking log on both sides , we get
[tex]\ln 1.75=0.035t\\\\\Rightarrow\ t=\dfrac{\ln1.75}{0.035}=\dfrac{0.560}{0.035}=16[/tex]
Hence, it will take 16 years to grow to $3,500.
what's the standard answer for (5×1)+(7×.2)+(2×0.4)
9514 1404 393
Answer:
7.2
Step-by-step explanation:
The order of operations tells you that quantities in parentheses are evaluated first.
(5×1)+(7×.2)+(2×0.4) = 5 + 1.4 + 0.8
Then the addition is performed, left to right.
= 6.4 +0.8
= 7.2
_____
Your calculator can work this problem for you, if necessary.
In the diagram, the vertices of the square lie at the centers of the four partial circles. What is the area of the entire shape? Use the value pi = 3.1416
The area of the entire shape is 33,562 square units
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
The figure is made up of a square and four 3/4 circles. So the total area will be equal to the sum of the area of the square and the sum of the 3/4 th circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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The area of the entire shape is 33,562 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Here, we have,
The figure is made up of a square and four 3/4 circles.
So the total area will be equal to the sum of the area of the square and the sum of the 3/4 the circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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Examine the diagram. Triangle M P L. Angle P is 90 degrees and angle L is (4 x + 6) degrees. The exterior angle to angle M is 136 degrees. What is the value of x?
Answer:
x = [tex]10^{0}[/tex]
Step-by-step explanation:
From Δ MPL given that; <P = [tex]90^{0}[/tex], exterior angle to M = [tex]136^{0}[/tex] and <L = [tex](4x+6)^{0}[/tex].
In the triangle, the exterior angle is equal to the sum of the two adjacent interior angles. So that;
[tex]136^{0}[/tex] = [tex]90^{0}[/tex] + [tex](4x+6)^{0}[/tex]
= [tex]90^{0}[/tex] + 4[tex]x^{0}[/tex] + [tex]6^{0}[/tex]
[tex]136^{0}[/tex] = [tex]96^{0}[/tex] + [tex]x^{0}[/tex]
⇒ 4[tex]x^{0}[/tex] = [tex]136^{0}[/tex] - [tex]96^{0}[/tex]
4[tex]x^{0}[/tex] = [tex]40^{0}[/tex]
Divided both sides by 4 to have;
[tex]x^{0}[/tex] = [tex]10^{0}[/tex]
The value of x is [tex]10^{0}[/tex].
Answer:
The correct answer is in fact 10 degrees.
Step-by-step explanation:
I hope this helps!
Have a great day! :)
8.What side of the road will you see speed, yield, and guide signs on ?
Answer:
we see it in our left side of the road
what is the diameter of a circular swimming pool with a radius of 9 feet? enter only the number
Answer:
The answer is 18 feet
Step-by-step explanation:
To find the diameter of a circle given it's radius we use the formula
diameter = radius × 2
From the question
radius = 8
So the diameter is
diameter = 9 × 2 = 18 feetHope this helps you
Answer:
18
Step-by-step explanation:
Hey there!
Well radius is half the diameter so,
D = r*2
Plug in 9
D = 9*2
D = 18
Hope this helps :)
Answer two questions about Equations A and B: A.5x=20 \ B.x=4 1) How can we get Equation B from Equation A? Choose 1 answer: (Choice A) Multiply/divide both sides by the same non-zero constant (Choice B,) Multiply/divide both sides by the same variable expression (Choice C) Add/subtract the same quantity to/from both sides (Choice D) Add/subtract a quantity to/from only one side
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
Given the equations :
5x = 20 ___ (A)x = 4 _____ (B)To obtain the value ; x = 4 from A
We multiply (A) by the same non-zero constantHere, the constant value which can be used is 5 in other to isolate 'x'
5x/5 = 20/5
x = 4
Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
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Abel and Cedric will share a total of $180. Abel will receive half as much as Cedric. What amount. in dollars, will Cedric receive (Disregard the $ sign when gridding your answer.)
Answer:
Abel receives $60, and Cedric receives $120
Step-by-step explanation:
Let Abel's share = A
Let Cedric's share = C
we are given the following
A + C = 180 - - - - - (1) (Abel and Cedric will share a total of $180)
[tex]A = \frac{C}{2}\ - - - - - - - (2)[/tex] (Abel will receive half as much as Cedric. )
from equation 2:
[tex]A = \frac{C}{2}\\ C = 2A\ - - - - - - (3)[/tex]
putting this value of C in eqn (3) into eqn (1)
A + (2A) = 180
3A = 180
∴ A = 180 ÷ 3 = 60
to find C, let us replace the value of A in eqn (3) with 60
C = 2A - - - - (3)
C = 2 × 60
C = 120
Therefore, Abel receives $60, and Cedric receives $120
You meet with the financial aid office to discuss your costs for attending LSU next semester.Tuition is $113.67 per credit hour, and fees are a flat rate of $660. You have a grant of $350 and a scholarship of $400. If you are taking 15 credit hours what amount will you need go pay for your classes next semester?
Show you work
Answer:
$1615.05Step-by-step explanation:
Scholarship and grants are money given to the candidates to support his financial needs in school. It will serves as the means of revenue for the student.
Revenue generated = Grant + Scholarship amount
Revenue generated = $350 + $400
Revenue generated= $750
Total money needed to be spent in school = Tuition + fees
If tuition is $113.67 per credit hour and I used 15 credit hours, total amount of tuition paid = 15* $113.67 = $1705.05
Total fees = $660
Total money needed to be spent in school = $1705.05 + $660
Total money needed to be spent in school = $2365.05
Amount I will need to pay for classes next semester = Total money that will be spent - (grant+scholarship)
= $2365.05 - $750
= $1615.05
Hence, the amount I will need to pay for classes next semester is $1615.05
Add 5/20 + 1/20. Simplify your answer.
Answer:
3/10
Step-by-step explanation:
1) 5/20+1/20= 6/20
2) Both 6 and 20 lowest number on dividing: 2
6 divide by 2= 3 20 divide by 2= 10
5/20+1/20
= 5+1/20
= 6/20
= 3/10
Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x) =20x^2+40x+600 dollars.
Required:
a. At what rate was the property tax increasing with respect to time in 2008?
b. By how much did the tax change between the years 2008 and 2012?
Answer:
a) 40 dollars
b) 480 dollars
Step-by-step explanation:
Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0
T'(x) = 2(20)x¹ + 40x° + 0
T'(x) = 40x+40
At x = 0,
T'(0) = 40(0)+40
T'(0) = 40
Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).
b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)
Given T(x) =20x²+40x+600
T(4) =20(4)²+40(4)+600
T(4) = 320+160+600
T(4) = 1080 dollars
Also T(0) =20(0)²+40(0)+600
T(0) = 0+0+600
T(0)= 600 dollars
T(4) - T(0) = 1080 - 600
T(4) - T(0) = 480 dollars
Hence, the tax has changed by $480 between 2008 and 2012
Two cards are dealt at random from a standard 52 card deck (without replacement). (Ace, King, Queen, Jack are face cards.)
Required:
a. Find the probability that the first card is a face card and the second is NOT a face card.
b. Find the probability that they are both face cards.
c. Find the probability that the second is a face card given the first is NOT a face card.
Answer:
The answer is below
Step-by-step explanation:
There are 52 cards in a deck, 12 of these cards are face cards (4 kings, 4 queens and 4 jacks) and 40 are not face cards
a. Find the probability that the first card is a face card and the second is NOT a face card.
There are 12 first card, the probability that the first card is a face card is 12/52.
Since there are no replacement, after picking 1 face card the number of cards remaining is 51, the probability of the second card not being a face card = 40/51. Therefore:
The probability that the first card is a face card and the second is NOT a face card = P(first is face card) × P(second is not face card) = 12/52 × 40/51 = 40/221
b) Find the probability that they are both face cards.
The probability that the first card is a face card is 12/52.
Since there are no replacement, after picking 1 face card the number of cards remaining is 51 and the number of face card remaining is 11, the probability of the second card is a face card = 11/51. Therefore:
The probability that they are both face cards = P(first is face card) × P(second is face card) = 12/52 × 11/51 = 11/221
c) Find the probability that the second is a face card given the first is NOT a face card.
The probability that the first card is not a face card = 40/52
Since there are no replacement, after picking the first card the number of cards remaining is, the probability of the second card is a face card = 12/51. Therefore:
The probability that the second is a face card given the first is NOT a face card = P(first is not a face card) × P(second is face card) = 40/52 × 12/51 = 40/221
quick i need help so bad :(
There are 4 triangles with base of 5 and height of 8.4
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 5 x 8.4 = 21 m^2
Multiply by 4 = 21 x 4 = 84 m^2
Area of the base = length x width = 5 x 5 = 25 m^2
Total area = 84 + 25 = 109 m^2
URGENT At Garcia's Bike Rentals, it costs $ 36 to rent a bike for 9 hours. How many hours of bike use does a customer get per dollar?
Answer:
.25 hour / dollar
Step-by-step explanation:
We want hours per dollar
9 hours/ 36 dollars
1/4 hour / dollar
A segment bisector is a line, ray or segment that divides a line segment into two equal parts. in the triangle formed by points A(-1,7), B(1,2), C(7,6) what is the slope of the line that goes through point A and bisects BC?
In decimal form, this is equivalent to -0.6
=================================================
Explanation:
This segment bisector is cutting side BC in half. So we have a point D such that it is between B and C. Also, we can say BD = DC. Refer to the diagram below.
To find the location of D, we'll apply the midpoint formula to points B and C.
B(1,2) and C(7,6) have x coordinates of 1 and 7 respectively. Average those x values to get (1+7)/2 = 8/2 = 4. This is the x coordinate of point D.
Repeat this idea for the y coordinates. We'll get (2+6)/2 = 8/2 = 4 which is the y coordinate of D.
Point D is located at (4,4)
---------------------
The takeaway from that last section, if we were to summarize it in one sentence, is that D is located at (4,4).
Now focus on the points A(-1,7) and D(4,4)
We'll apply the slope formula
m = (y2-y1)/(x2-x1)
m = (4-7)/(4-(-1))
m = (4-7)/(4+1)
m = -3/5 is the slope
Notice that to go from A to D, we can drop down by 3 units and move to the right 5 units. We can say rise = -3 and run = 5; therefore, slope = rise/run = -3/5
h(x) = -x² + 3x + 10
Answer:
x = 5 or x = -2 or 3 - 2 x (derivative)
Step-by-step explanation:
Solve for x over the real numbers:
-x^2 + 3 x + 10 = 0
Multiply both sides by -1:
x^2 - 3 x - 10 = 0
x = (3 ± sqrt((-3)^2 - 4 (-10)))/2 = (3 ± sqrt(9 + 40))/2 = (3 ± sqrt(49))/2:
x = (3 + sqrt(49))/2 or x = (3 - sqrt(49))/2
sqrt(49) = sqrt(7^2) = 7:
x = (3 + 7)/2 or x = (3 - 7)/2
(3 + 7)/2 = 10/2 = 5:
x = 5 or x = (3 - 7)/2
(3 - 7)/2 = -4/2 = -2:
Answer: x = 5 or x = -2
____________________________________
Find the derivative of the following via implicit differentiation:
d/dx(H(x)) = d/dx(10 + 3 x - x^2)
Using the chain rule, d/dx(H(x)) = ( dH(u))/( du) ( du)/( dx), where u = x and d/( du)(H(u)) = H'(u):
(d/dx(x)) H'(x) = d/dx(10 + 3 x - x^2)
The derivative of x is 1:
1 H'(x) = d/dx(10 + 3 x - x^2)
Differentiate the sum term by term and factor out constants:
H'(x) = d/dx(10) + 3 (d/dx(x)) - d/dx(x^2)
The derivative of 10 is zero:
H'(x) = 3 (d/dx(x)) - d/dx(x^2) + 0
Simplify the expression:
H'(x) = 3 (d/dx(x)) - d/dx(x^2)
The derivative of x is 1:
H'(x) = -(d/dx(x^2)) + 1 3
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.
d/dx(x^2) = 2 x:
H'(x) = 3 - 2 x
Simplify the expression:
Answer: = 3 - 2 x
20.) The area of a circle is given by the equation A = nr2. If the radius of a circle is equal to 6 centimeters,
which of the following is closes to the area of the circle? (Use it = 3.14.)
113.04
18.84
36
28.26
please provide explanation
Answer:
113.04 cm^2
Step-by-step explanation:
The area of a circle is
A = pi r^2
We know the radius is 6 cm
A = 3.14 * 6^2
A = 3.14 * 36
A =113.04
The scale on a scale drawing is 1 : 30. What should you do with each measurement on the drawing to get the actual dimensions? Provide an example of a drawing that uses this scale. Include both the original and new dimensions.
Answer:
see below
Step-by-step explanation:
For the first question, you should multiply the scale dimension by 30 to get the actual dimension. This is because the scale is 1:30 where the scale dimension is the 1 and the actual dimension is 30, so therefore, the scale dimension is 1/30th of the actual dimension, so to get the actual dimension, we can multiply the scale dimension by 30. I'm not totally sure how to attach pictures from my phone on my computer (sorry) but an example of a drawing could be two rectangles, the first (this is the scale drawing) having dimensions of 1 by 2 units and the second (this is the actual drawing) having dimensions of 30 by 60 units. I hope this helps!
Find the remainder when f(x)= 8x^3+ 4x^2
13x + 3 is divided by 2x + 5.
Answer:
-129
Step-by-step explanation:
2x+5=0
x=-5/2 [By the remainder theorem]
f(-5/2)=8(-5/2)^3+4(-5/2)^2+13(-5/2)+3
=-125+25-65/2+3
=-129.
Kathy stood on the middle rung of a ladder. She climbed up 3 rungs, moved down 5 rungs, and then climbed up 9 rungs. Then she climbed up the remaining 4 rungs to the top of the ladder. How many rungs are there in the whole ladder?
Answer:
There are fourteen rungs on the ladder