After applying the distributive property, Ezra's expression was 8y + 16.
After he used the commutative property, his expression was 16 + 8y.
How to use the distributive and commutative properties?When using the distributive property, we are able to expand an expression with a bracket by multiplying the things in the bracket with the things outside:
8( y + 2) becomes:
= (8 x y) + (8 x 2)
= 8y + 16
The commutative property on the other hand, means that when adding, the position of the number does not matter. For instance, a + b = b + a
When the commutative property is applied therefore, we get:
8y + 16 = 16 + 8y
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What is the image of the point (-7,5)(−7,5) after a rotation of 180^{\circ}180
∘
counterclockwise about the origin?
The coordinates of the image of the point (-7, 5) are (7, -5).
We are given point P. The coordinates of the point P are (-7, 5). We perform a transformation on the given point. We rotate the given point about the origin counter-clockwise. The angle of rotation is 180°. We need to find the coordinates of the image of the point after rotation.
Let the new coordinates of the image of the point after rotation be denoted by (X, Y). If the coordinates of the original point are (x, y), then the relations between the coordinates of the point and the image are given below.
X = x*cosθ - y*sinθ
X = (-7)*cos(180°) - (5)*sin(180°)
X = (-7)*(-1) - (5)*(0)
X = 7
Y = x*sinθ + y*cosθ
Y = (-7)*sin(180°) + (5)*cos(180°)
Y = (-7)*(0) + (5)*(-1)
Y = -5
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Caleb solved this equation and recorded his work.
7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6
1. 7.4x + 8.2x − 16.4 = −2.3x + 13.8 − 21.6
2. 15.6x − 16.4 = −2.3x + 35.4
3. 17.9x − 16.4 = 35.4
4. 17.9x = 51.8
5. x ≈ 2.89
When Caleb verified his solution, it didn’t work. What mistake did he make?
In step 1, the distributive property was not used properly on the right side of the equation.
In step 2, the like terms were not combined properly on the right side of the equation.
In step 3, the addition property of equality was not used properly to isolate the variable term.
In step 5, the division property of equality was not used properly to solve for x.
hurry pls :,)
Answer:
the mistake was in subtracting 21.6 from 13.8
Step-by-step explanation:
the answer was suppose to be -7.8 and not 35.4
Answer:
the mistake was in subtracting 21.6 from 13.8
Step-by-step explanation
the answer was suppose to be -7.8 and not 35.4
As the sample size increases, the standard deviation of the sampling distribution.
False, As the sample size is increased, the standard deviation of a sampling distribution of the sample's mean drops.
The term "standard error" also refers to the sample mean's standard deviation. The high dimensionality theorem establishes that as sample size increases, the sample mean's sampling distribution becomes more or less normal.
Using the formula below, the sample mean's standard deviation is determined.
σ ÷ √n
where n is the sample size and would be the population standard deviation.
As the denominator, or n, increases, the standard variance of the sample average would also decrease, as shown by the aforementioned calculation.
It follows that the standard deviation of a sample's average decreases as the sample size grows.
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Which inequality is equivalent to 2/3x -5 < 11
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] x - 5 < 11 ( multiply through by 3 to clear the fraction )
2x - 15 < 33 ← equivalent inequality
to solve add 15 to both sides
2x < 48 ( divide both sides by 2 )
x < 24
Determine the value of the expression −2(42−7)+(−5) .
The value of the expression −2(42−7)+(−5) is -75.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, we want to calculate the value of the expression:
−2(42−7)+(−5)
= -2(35) + (-5)
= -70 - 5
= -75
The value is -75.
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Please help me I don’t get it
Step-by-step explanation:
3.
we need to find the map size based on actual miles.
so, we find how many map ft are 1 actual mile :
5 ft / 20.5 corresponds to 1 actual mile.
5 / 20.5 = 10/41 ft
now, we have 15.5 actual miles, that is 15.5 times the 1 standard actual mile.
and so, this is
10/41 × 15.5 = 155/41 = 3.7804878048780... map ft
4.
30.5 model cm = 70.6 actual m
1 model cm = 70.6/30.5 = 2.314754098... actual m.
8 model cm = 8×2.314754098... =
= 18.51803279... actual m
5.
7 map m = 14 actual miles
1 map m = 14/7 = 2 actual miles.
14 map m = 14×2 = 28 actual miles.
6.
8 map km = 6 actual miles
we need to calculate the map km, so we need the standard actual mile
1 actual mile = 8/6 = 4/3 = 1.3333333... map km.
50.2 actual miles = 50.2×1.333333... =
= 66.93333333... map km.
7.
80.2 model cm = 40.2 actual m
1 model cm = 40.2/80.2 = 0.501246883... actual m
10 model cm = 10×0.501246883... =
= 5.01246883... actual m
8.
6 map m = 15 actual miles
1 map m = 15/6 = 5/2 = 2.5 actual miles
8.8 map m = 8.8×2.5 = 22 actual miles
9.
5 map ft = 16.5 actual miles
1 actual mile = 5/16.5 = 0.303030303... map ft
45.6 actual miles = 45.6×0.303030303... =
= 13.81818181... map ft
10.
65.8 model cm = 95.6 actual m
1 model cm = 95.6/65.8 = 1.452887538... actual m
12 model cm = 12×1.452887538... =
= 17.43465046... actual m
A group of 4 people go to a restaurant and the bill without tax comes to $105.73. Tax is 6%. Remember to round to the nearest hundredth because this is money. After tax is added, you want to leave a 20% tip on the new total. The group of 4 people decides to split the total cost equally. How much will each person pay?
i need the answer fasttttt
Each person need to pay $ 80.88345.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Bill without tax = 105.73
Tax = 6%
So, bill amount after tax = 105. 73 + 105. 73 x 6/100
= 105.73 + 6.3438
= $112.0738
Addition of 20% tip = 112.0738 + 211.46 = $323.5338.
If the amount is divided among 4 people, each will pay
= 323.5338/4
= $ 80.88345
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along a river is to be fenced. suppose that no fence is needed along the river, the fence on the side opposite the river costs $40 per foot, and the fence on the other sides costs $10 per foot. if the field must contain 64,800 square feet, what dimensions will minimize costs?
The dimensions required to minimize the cost of fencing is 180ft and 360 ft.
According to question
The cost of fence on opposite side of river is $40.
The cost of fence on other sides of river is $10.
Total yield = 64800 sq. feet
Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.
Area of fence = xy = 64800 sq feet
⇒ [tex]y = \frac{64800}{x}[/tex]
Let C be the cost of making fence.
For cost to be minimum, dC/dx should be equal to zero.
C = 40x + 10y * 2
⇒ C = [tex]40x + 10(\frac{64800}{x})*2[/tex]
⇒ [tex]\frac{dC}{dx} = 40 + 20 * 64800 * \frac{-1}{x^{2} } = 0[/tex]
⇒ [tex]40x^{2} = 20 * 64800[/tex]
⇒ [tex]x^{2} = 32400[/tex]
⇒ [tex]x = 180[/tex]
⇒ [tex]y = \frac{64800}{180} = 360[/tex]
So, the dimensions needed will be 180 ft and 360 ft.
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a person has a 5% chance of winning a free ticket in a state lottery. she plays the game 12 times. what is the probability she will win two or more tickets? round your answers to three decimal places.
The probability to win two or more tickets in the lottery is 0.118
It is given that there is a 5% chance to win a lottery ticket.
Therefore, the probability to win a lottery ticket is
0.05
The girl here plays the game 12 times. The above distribution is clearly a Binomial Distribution
ⁿCₓ X pˣ X (1 - p)ⁿ⁻ˣ
We need to calculate the probability to win 2 or more tickets
= 1 - the probability to win at least one ticket
= 1 - P(X = 0) + P(X = 1)
here,
p = 0.05
1 - p = 0.95
n = 12
P(X = 0)
= ¹²C₀ X 0.05⁰ X 0.95¹²
= 0.54036
P(X = 1)
= ¹²C₁ X 0.05¹ X 0.95¹¹
= 0.34128
Hence we get
P(X ≥ 2) = 1 - 0.54036 - 0.34128
= 0.118
Therefore, we get the probability that the person will win 2 or more tickets to be 0.118
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Lines t and u are parallel and intersected by transversal s.
Which statement is true?
Answer:
1) ∠5 and ∠6 are supplementary angles not vertical angles this statement is false.
2) ∠2 and ∠7 are alternally interior angles yeah that statement is true.
3) ∠2 and ∠4 are supplementary angles no they are not complementary, because sum of those two angles i.e. ∠2+∠4 =180.
so this statement is false
Step-by-step explanation:
Step-by-step explanation:
here ∠2+∠5=180°; ∠1+∠6=180; ∠4+∠7=180°; and for ∠3+∠7=180°;
here ∠6+∠8=180°; ∠1+∠3=180°; ∠2+∠4=180°; ∠5+∠7=180; here the
∠1=∠4; ∠2=∠3; ∠5=∠8; ∠6=∠7 (opposite angles are equal)
A rectangle plot of land has a width of 3x+5 feet, and a length of 2x-1 feet.
A- express the area of the plot as a function of x.
B- express the perimeter of the plot as a function of x
A- the area of the plot as a function of x. is 6 x^2 +10x-5
B- the perimeter of the plot as a function of x is 10x+8
A rectangle plot of land has a width of 3x+5 feet,
and a length of 2x-1 feet.
A) the area of the plot as a function of x is given by
A= length * width
= ( 2x-1) * ( 3x+5)
=6 x^2 +10x-5
B) the perimeter of the plot as a function of x
P = 2( l+ W)
= 2 (( 2x-1) +( 3x+5))
= 2( 5x +4)
= 10x +8
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Factorise the following:
a) x + 3x - 4
b) x-2x-3
c) x +2x-8
Ester sarai and kurry chose a number esters number is 1/10 of saris kurrys number is 10 times as much as sarais sarais number is 0.09. what number did each person choose?
Ester, Sarai, and Kurry each selected a number: 0.009, 0.09, and 0.9, respectively.
One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes. For instance, 3+3+3+3+3 can be expressed as 3 5.
the ester's number is equal to one-tenth of the Sarai number.
= 1 / 10 × 0.09 = 0.009
to determine Kurry's number, multiply Sarai's number by 10
= 10 × 0.09 = 0.9
Therefore, it can be inferred that Kurry chose 0.9, Ester chose 0.009, and Sarai chose 0.09.
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Please help i need this today.
Answer:
option c this is no solution for the equations
Answer:
x=5 y=-8 the calc are in the photo
given f(x) =2x^2+5, evaluate f(4)
Answer:
f(4) = - 27
Step-by-step explanation:
substitute x = 4 into f(x) , that is
f(4) = - 2(4)² + 5 = - 2(16) + 5 = - 32 + 5 = - 27
Answer:
69
Step-by-step explanation:
Replace x with 4
-2(4)^2 +5
-8^2+5
64+5
69
ABCD is a square. If LABC = (6x - 12)° and CD= (x + 15). Find the length of AD.
Answer:
AD = 32
Step-by-step explanation:
You want the length of side AD of square ABCD, when CD = (x+15) and angle ABC is (6x-12)°.
Value of xThe value of x can be found by recognizing that the measure of any angle in a square is 90°.
(6x -12)° = 90°
6x = 102 . . . . . . . . divide by °, add 12
x = 17
Measure of ADThe sides of a square are congruent, so ...
AD = CD = (x +15) = 17 +15 = 32
The length of AD is 32 units.
70% of the light aircraft that disappear while in flight in a certain country are subsequently found. of the aircraft that are found, 60\`% have an emergency locator, whereas only 10\% of the aircraft not found have such a locator. suppose a light aircraft has disappeared. if the aircraft has an emergency locator, what is the probability that it will not be found? round your answer to three decimal places.
P(The aircraft is discoverd and has no locator) = P(discovered) x P(no locator/discoved =0.28)
Acc to our question-The information is based on the disappearance of the of the light aircraft in the flight in the in a certain country . 70% of the aircraft that disapear while in the flight were discovered . The probability that there is an emergency locator
in the aircraft given that it is discovered is 60% and the probability that the aircraft that has not discovered have an emergenncy locator is 90%.
a) To determine probiblity it wount be discoverd
Calculation
P(the aircraft is discovered and has a locator) = P(discovered) X P(locator/discovered)
= 0.7 x 0.6 = 0.42The probability of the flight discovered and has locator is obatained as given below:
P(The aircraft is discoverd and has no locator) = P(discovered) x P(no locator/discovered)
= 0.7 x 0.4 =0.28The probability of the flight not discovered and has a locator is obatained below.
P(The aircraft is not discovered and has a locator) = P(not discovered) x P (locator | not discorverd) = 1-0
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HELP!
I will name you the BRAINLIEST!
The thing is in the photo.
I do not understand it because it looks like it has "!" Please help.
The expression 11! / 9!(11-9)! evaluates to 55
How to evaluate numbers with the factorial sign?The symbol ! is called factorial in mathematics.
Factorial can be defined as the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point.
Thus, factorial five is written as 5! meaning 5×4×3×2×1
It can also be written in shortened form as 5×4! or 5×4×3!
Let's evaluate 11! / 9!(11-9)! now:
11! / 9!(11-9)! = 11! / 9!(2)!
= 11×10×9! / 9!2!
= 11×10/ 2 (Note: 2! = 2×1 =2 )
= 110/2
= 55
Note: We shortened 11! to 11×10×9! because we want the 9! to cancel out each other. This is usually done to ease the evaluation. Also, note that 0! = 1
Therefore, the result of the evaluation of the expression 11! / 9!(11-9)! is 55
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Solve the inequality -y +3 ≤ 8 and y + 2> 9.
Answer:
y ≥ -5 and y > 7
Step-by-step explanation:
Collect like terms
-y ≤ 8 - 3
-y ≤ 5
Divide both sides by -1
-1y/-1 ≤ 5/-1
y ≥ -5
And
y > 9 - 2
y > 7
Please help quick this is due tomorrow and I forgot how to find x
Answer:
you have to add x outside of the parentheses
Step-by-step explanation: hope this helps
Is (4, 1) a solution to this system of inequalities?
3x + y ≤ 14
3x + 5y < 19
(4, 1) is the solution for the given inequalities
Given,
The system of inequalities;
3x + y ≤ 14
3x + 5y < 19
We have to find that (4, 1) is a solution to the given system of inequalities;
So,
(x, y) = (4, 1)
Then,
Substitute the values of x and y in the equation;
3x + y ≤ 14
3 x 4 + 1 ≤ 14
12 + 1 ≤ 14
13 ≤ 14
Next,
3x + 5y < 19
3 x 4 + 5 x 1 < 19
12 + 5 < 19
17 < 19
Here,
(4, 1) is the solution for the given inequalities
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9x – 17 = -17 + 9x help me pls
Answer:
Step-by-step explanation:
um ok so
Answer:
x=0
Step-by-step explanation:
the rest of this is so i can reach twenty characters.
Phil lives in a state where his tax rate does not change when his income changes. This is an example of a(n) ____ ?
Phil lives in a state where his tax rate does not change when his income changes. This is an example of a proportional or flat tax.
What is tax?Tax is defined as the official way individuals contribute to their state revenue through the compulsory deduction of some amount of money from their monthly income.
There are two types of tax which include the following:
Regressive tax,Progressive tax, andProportional or flat tax.Proportional or flat tax: This is defined as the type of tax that is being paid by individuals from different class in the society whereby all are expected to pay tax with the same rate irrespective of the income.
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A tank in the shape of a hemisphere has a radius of 14 feet. If the liquid that fills the tank has a density of 83.1 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
477,577 lb
Step-by-step explanation:
Volume of sphere:
V = (4/3)πr³
V = (1/2)(4/3)(3.14159)(14 ft)³ = 5,747.015 ft³
d = 83.1 lb/ft³
W = Vd
W = 5,747.105 ft³ × 83.1 lb/ft³
W = 477,577 lb
1. Solve the system by substitution.
y=x²-2x+1
y = 2x+1
On solving the system of equations by substitution method , the solution is x = 0 , y = 1 and x = 4 , y = 9 .
In the question ,
it is given that
the system of equation is
y = x² - 2x + 1
y = 2x + 1
by using substitution method ,
Substituting y = 2x + 1 in y = x² - 2x + 1
we get
2x [tex]+[/tex] 1 [tex]=[/tex] x² - 2x [tex]+[/tex] 1
x² - 2x [tex]+[/tex] 1 - 2x - 1 [tex]=[/tex] 0
x² - 4x = 0
x(x-4) = 0
So , x=0 or x = 4
for x=0 , y = 2x+1 = 1
for x = 4, y = 2(4) + 1 = 9
Therefore, the solution for the system of equations is x=0 , y=1 and x=4 , y=9 .
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help pls pls pls pls pled
The sum of all angles in a triangle sum up to 180.
∠1 = x+37
∠2=x+67
∠3=90° (right triangle)
∠1+∠2+∠3 = 180°
(x+37)+(x+67)+90=180
2x+104+90=180
2x+194=180
2x=-14
x=-7
An angle can't be negative, but when plugged in it works!!
∠1 = -7+37=30
∠2=-7+67=60
30+60+90=180
Hope it helps!
In the first week of July, a record 1,040 people went to the local swimming pool. In the second week, 110 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 139 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
62%
Step-by-step explanation:
1040-110-145-139=646
646/1040=62%
Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.
T=
U=
V=
W=
The coordinates of the vertices after a rotation 270° counterclockwise around the origin is
T' = (-8, -4)
U' = (-8, -6)
V' = (-3, -9)
W' = (-3, -7)
The coordinates of T = (4, -8)
The coordinates of U = (6, -8)
The coordinates of V = (9, -3)
The coordinates of W = (7, -3)
The rule of rotating 270 degree clockwise around the origin is
P(x, y) = P'(y, -x)
The coordinates of T' = (-8, -4)
The coordinates of U' = (-8, -6)
The coordinates of V' = (-3, -9)
The coordinates of W' = (-3, -7)
Hence, The coordinates of the vertices after a rotation 270° counterclockwise around the origin is
T' = (-8, -4)
U' = (-8, -6)
V' = (-3, -9)
W' = (-3, -7)
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Bridgette has 9 dogs. Every day, she feeds them a total of 9/10 of a can of food, where each dog is fed the same amount of food. How many cans of food does Bridgette give to each dog?
Bridgette gives 1/10 cans of food to each dog.
According to the question,
We have the following information:
Bridgette has 9 dogs. Every day, she feeds them a total of 9/10 of a can of food, where each dog is fed the same amount of food.
Now, we have the following expression:
9 dogs = 9/10 can
Now, we can easily find the cans given to each dog using division. We will divide the total number of cans of food by the number of dogs.
1 dog = 9/(10*9) cans
1 dog = 1/10 cans of food
Hence, Bridgette gives 1/10 cans of food to each dog.
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please help. what is the equation??
Answer:
y = -x + 4
Step-by-step explanation:
The equation of a line follows the form y=mx+c, where x and y are the coordinates, c is the y-intercept (the value of x where the line crosses the y-axis), and m is the slope.
We are given two points/coordinates - (-3,7) and (1,3) - so we know the following is true for our equation:
7=-3m+c
3=m+c
Rearranging the second equation above, we get c=3-m. Sub this into the first one, and we get
7=-3m+3-m
4=-4m
m=-1
Knowing c=3-m, we can say c=3-(-1)=3+1=4
Having found values for m and c, we can now write our equation:
y = -x + 4
Hope this helps :)