Answer: x = 0
Step-by-step explanation:
The first step would be to convert everything to one form. I'll do the fractions, since 1/3 is hard to represent in decimal.
3 1/4 + 1/2x + 1 1/3 + 5/6x = 5 11/12
Now, the fractions will be converted via GCF. 12 is easily divisible by 4, 2, 3 and 6, so that I'll be the denominator used.
3 1/4 -> 3 3/12
1/2x -> 6/12x
1 1/3 -> 1 4/12
5/6x -> 10/12x
5 11/12 will stay the same.
The new equation is:
3 3/12 + 6/12x + 1 4/12 + 10/12x = 5 11/12
Combine like terms:
4 7/12 + 1 4/12x = 5 11/12
Subtract 4 7/12 from both sides
1 4/12x = 1 4/12
Divide both sides by 1 4/12x
x= 0
Answer:
x= 1
Step-by-step explanation:
Convert 5\frac{11}{12}5
12
11
to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a
c
b
=
c
ac+b
3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1
3
1
+
6
5
x=
12
5×12+11
2 Simplify 5\times 125×12 to 6060
3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1
3
1
+
6
5
x=
12
60+11
3 Simplify 60+1160+11 to 7171
3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1
3
1
+
6
5
x=
12
71
4 Simplify \frac{5}{6}x
6
5
x to \frac{5x}{6}
6
5x
3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1
3
1
+
6
5x
=
12
71
5 Convert 1\frac{1}{3}1
3
1
to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a
c
b
=
c
ac+b
3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+
3
1×3+1
+
6
5x
=
12
71
6 Simplify 1\times 31×3 to 33
3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+
3
3+1
+
6
5x
=
12
71
7 Simplify 3+13+1 to 44
3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+
3
4
+
6
5x
=
12
71
8 Simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+
3
4
+
6
5x
to \frac{13.75}{3}+\frac{4x}{3}
3
13.75
+
3
4x
\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}
3
13.75
+
3
4x
=
12
71
9 Simplify \frac{13.75}{3}
3
13.75
to 4.5833334.583333
4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+
3
4x
=
12
71
10 Subtract 4.5833334.583333 from both sides
\frac{4x}{3}=\frac{71}{12}-4.583333
3
4x
=
12
71
−4.583333
11 Simplify \frac{71}{12}-4.583333
12
71
−4.583333 to \frac{4}{3}
3
4
\frac{4x}{3}=\frac{4}{3}
3
4x
=
3
4
12 Multiply both sides by 33
4x=\frac{4}{3}\times 34x=
3
4
×3
13 Simplify \frac{4}{3}\times 3
3
4
×3 to \frac{12}{3}
3
12
4x=\frac{12}{3}4x=
3
12
14 Simplify \frac{12}{3}
3
12
to 44
4x=44x=4
15 Divide both sides by 44
x=1
For what value of p will the pair of linear equations have infinitely many solutions (p-3)x + 3y = p , px+ py = 12
Answer: p = 6
Step-by-step explanation:
HI !
px + 3y - ( p-3)=0
a₁ = p , b₁ = 3 , c₁ = - (p-3)
=====================
12x + py - p=0
a₂ = 12 , b₂ = p , c₂ = -p
since , the equations have infinite solutions ,
a₁/a₂ = b₁/b₂ = c₁/c₂
p/12 = 3/p = p-3/p
--------------------------------------
p/12 = 3/p
cross multiply ,
p² = 36
p = √36
p = 6
for the value of p = 6 , the equations will have infinitely many solutions
Evaluate the expression: –(31 + 2) + 72 – (–5)2.
A. –40
B. 41
C. –5
D. –9
Answer:
The correct answer is 49.
Step-by-step explanation:
We are given the following expression and we are supposed to evaluate it:
– (31 + 2) + 72 – (–5) 2
Solving the terms inside the brackets first, following the order of operations to solve a mathematical expression to get:
= - (33) + 72 - (-5) 2
Then we will do the multiplications to get:
= - (33) + 72 - (-10)
Further adding and subtracting the terms:
= 39 - (-10)
= 39 + 10
= 49
Answer:
D. -9
Step-by-step explanation:
-33 +49 -25 = -9
Jim needs to rent a car. A rental company charges $21.00 per day to rent a car and $0.10 for every mile driven.
• He will travel 250 miles.
• He has $115.00 to spend.
Write an inequality that can be used to determine , the maximum number of days that Jim can rent a car.
_______________________________
Jim believes the maximum whole number of days he can rent the car is 5. Is he correct? Why or why not?
.
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Final answer:
Jim can rent the car for a maximum of 4 whole days with his budget of $115, as the inequality 21d + 0.10(250) <= 115 reveals that he doesn't have enough funds to cover the fifth day.
Explanation:
To determine the maximum number of days Jim can rent a car, we can set up an inequality. The cost per day to rent the car is $21.00, and he will be charged $0.10 for every mile he drives. Jim will travel 250 miles in total. Jim has a budget of $115.00 to spend.
Let d represent the number of days Jim can rent the car for. The inequality would be:
21d + 0.10(250) ≤ 115
To solve for d, you would perform the following steps:
Multiply 0.10 by 250 to get the total cost for miles driven, which is $25.00.Subtract this cost from Jim's total budget to see how much is left for renting the car, which gives us 115 - 25 = $90.00.Divide the remaining budget by the cost per day to find the maximum number of days Jim can rent the car, which is 90 / 21.Solving the inequality:
21d ≤ 90
d ≤ 90 / 21
d ≤ 4.2857
Since Jim can only rent the car for a whole number of days, the maximum number of days he can rent the car is 4 days.
Therefore, Jim's belief that he can rent the car for a maximum of 5 whole days is incorrect because he does not have sufficient funds for the fifth day.
one pan pizza and two beef burritos provide 3570 calories. Two pan pizzas and one beef burrito provide 3450 calories. Find the caloric content of each item.
The caloric content of the pan pizza is 1110 calories and the caloric content of the beef burrito is 1230 calories.
Let's assign variables to the caloric content of the items. Let x represent the caloric content of the pan pizza and y represent the caloric content of the beef burrito. We can form two equations based on the given information:
One pan pizza + two beef burritos = 3570 calories:x + 2y = 3570
Two pan pizzas + one beef burrito = 3450 calories:2x + y = 3450
To solve this system of equations, we can use either substitution or elimination method. Let's use substitution method:
Solve equation 2 for y:y = 3450 - 2x
Substitute the value of y in equation 1:x + 2(3450 - 2x) = 3570
Simplify and solve for x:x + 6900 - 4x = 3570
-3x = -3330
x = 1110
Substitute the value of x in equation 2:2(1110) + y = 3450
Simplify and solve for y:2220 + y = 3450
y = 1230
Therefore, the caloric content of the pan pizza is 1110 calories and the caloric content of the beef burrito is 1230 calories.
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Maya is camping at the top of Mount Armstrong at an elevation of 7832 meters. Juan is scuba diving 160 meters below sea level. The two decide to meet at the midpoint. At what elevation will Maya & Juan meet?
Answer:
They will meet at 3836 meters
Step-by-step explanation:
Maya is at 7832 meters
Juan is at -160 meters ( below sea level)
If they are meeting at the midpoint, we add them together and divide by 2
Midpoint = (7832 + -160)/2
= (7672)/2
=3836 m
Answer:
The midpoint elevation will be 3,836 meters.
Step-by-step explanation:
Maya's elevation of 7832 can be represented by the positive integer +7832 since she is above sea level. Sea level would represent 0 on our number line. However, Juan is below sea level, so we can represent his distance at -160. When we add these two integers together +7832 + (-160) = 7672 meters above sea level. Since Maya and Juan are going to meet at the midpoint, we would divide our overall distance (7672) by two to get 3836 meters.
please help!!!!!!! it would be very appreciated
Answer:
x = 17.5 and y = 35
Step-by-step explanation:
2x + 10 = y + 10 ( alternate angles )
subtract 10 from both sides
2x = y ⇒ 6x = 3y → (1)
the sum of the 3 angles in the triangle = 180°
6x + y + 10 + 30 = 180 ( replace 6x by 3y )
3y + y + 40 = 180
4y + 40 = 180 ( subtract 40 from both sides )
4y = 140 ( divide both sides by 4 )
y = 35
substitute y = 35 into (1)
2x = 35 ( divide both sides by 2 )
x = 17.5
Free points for anyone if they can say what x-3=53+17
Answer:
X = 73
Step-by-step explanation:
X - 3 = 53 + 17
Add 53 and 17
It gives you 70
Add 3 to boths sides
you get 73 on right side
Cancels out the negative 3 on left side and gives you 73 for final answer
X = 73
"The area of a triangle is given by the formula A = 1/2bh. Solve this equation for the height, h, in terms of the base, b, and area, A." Help!!!!
Answer:
2A/b =h
Step-by-step explanation:
A = 1/2bh
Multiply each side by 2
2*A = 2*1/2bh
2A = bh
Divide each side by b
2A/b = bh/b
2A/b =h
Put in number in order 439.216 439.126 439.261 439.261
Step by step problem solving for 3.99 + 39.9 decimal problem
Answer:
You are going to line up the decimal points to each other and add a zero to the end of the shortest decimal.
3.99+39.9=43.89
Step-by-step explanation:
You are going to take the 3.99 and add that to the 39.9 like normal but you are first going to line up the decimals.
Jada and Tonya ran 400-meter race. Jada ran the race in 75.2 seconds. Tonga ran the race 69.07 seconds. How much faster did Tonya run the race
Final answer:
Tonya ran the race approximately 6.13 seconds faster than Jada.
Explanation:
To find out how much faster Tonya ran the race, we need to calculate the difference between their race times.
Tonya's race time is 69.07 seconds, while Jada's race time is 75.2 seconds.
To calculate the difference, we subtract Jada's race time from Tonya's race time: 69.07 - 75.2 = -6.13 seconds.
Therefore, Tonya ran the race approximately 6.13 seconds faster than Jada.
Which set of ordered pairs represents a function?
Answer:
The second one that starts with 3
Step-by-step explanation:
To know if it's a function , check all the domains and make sure there are no repeating ones, if there is a repeating domain , it's not a function
Use the table below to evaluate i^52
Answer:
i squared + 5
Step-by-step explanation:
The diagram represents the relationship of number sets. The four choices given will complete the diagram. Which BEST describes the set of numbers in block B?
A) Integers
B) Whole Numbers
C) Natural Numbers
D) Rational Numbers
Answer:
A.Integers
Step-by-step explanation:
We are given that a diagram that represents the relationship of a number sets.
We have to find that which describes the best set of numbers in block B
In block B
{....,-2,-1,0,1,2,....}
{0,1,2,3,...}
{1,2,3,...}
Integers:{...,-3,-2,-1,0,1,2,...}
Whole numbers:{0,1,2,...}
Natural numbers :{1,2,3,...}
Rational number: That number which can be written in the form of [tex]\frac{p}{q}[/tex] where q is not equal to zero , p and q are integers.
Hence, block B represent the set of integers.
Answer:A.Integers
x + 2y = 5
x - 3y = 7
What is the value of the y-determinant?
-2
-1
2
Answer:
y-determinant = 2
Step-by-step explanation:
Given the following system of equation:
x + 2y = 5 x - 3y = 7Let's represent it using a matrix:
[tex]\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] = \left[\begin{array}{ccc}5\\7\end{array}\right][/tex]
The y‐numerator determinant is formed by taking the constant terms from the system and placing them in the y‐coefficient positions and retaining the x‐coefficients. Then:
[tex]\left[\begin{array}{ccc}1&5\\1&7\end{array}\right] [/tex]
y-determinant = (1)(7) - (5)(1) = 2.
Therefore, the y-determinant = 2
In 1990 sales at ABC electronics totaled 4.9 million dollars 1996 total sales amounted to 12.1 million. Assuming the growth in sales is a linear relation, what total sales can the company expect in 2001
Answer:
18.1 million
Step-by-step explanation:
12.1 - 4.9 = 7.2 million increase in 6 years
7.2 / 6 = increase of 1.2 million a year
1.2 x 5 years = 6 million
12.1 million + 6 million = sales of 18.1 million in 2001
Based on linear growth from 1990 to 1996, ABC Electronics can expect total sales of approximately $18.1 million in 2001.
To predict sales for ABC Electronics in 2001 based on a linear growth pattern from 1990 to 1996, we first calculate the annual increase in sales over that period. In 1990, sales were $4.9 million and in 1996, sales were $12.1 million. This is an increase of $12.1 million - $4.9 million = $7.2 million over 6 years, which gives us an annual increase of $7.2 million / 6 years = $1.2 million per year.
Since we're assuming linear growth, we can extend this annual increase to predict sales for subsequent years. From 1996 to 2001 is 5 years, so we calculate the expected sales for 2001 by adding 5 times the annual increase to the 1996 sales figures: $12.1 million + (5 × $1.2 million) = $12.1 million + $6.0 million = $18.1 million.
Therefore, we can expect ABC Electronics to have total sales of approximately $18.1 million in the year 2001 if the linear growth trend continues.
The coordinates of a triangle are given as A(3, 2), B(-4, 1), C(-3, -2). What are the coordinates of the image after the triangle is reflected in the line y = x? A'( a0, a1) B'( a2, a3) C'( a4, a5)
Look at the picture.
[tex]A(3,\ 2)\to A'(2,\ 3)\\\\B(-4,\ 1)\to B(1,\ -4)\\\\C(-3,\ -2)\to C'(-2,\ -3)[/tex]
if you have a net spendable income of $1,450 per month, what is the maximum amount of money you should spend on food each month
Answer:
The maximum amount of money that should be spent on housing each month is $522.
The maximum amount of money that should be spent on transportation each month is $290.
The maximum amount of money that should be spent on food each month is $246.50.
The maximum amount of money that should be spent on entertainment each month is $116.
Answer:
$522
Step-by-step explanation:
The maximum amount of money that should be spent on housing each month is $522.
The maximum amount of money that should be spent on transportation each month is $290.
The maximum amount of money that should be spent on food each month is $246.50.
The maximum amount of money that should be spent on entertainment each month is $116.
Russell has a collection of 1,200 pennies. Of these pennies, 25% are dated before 1980, 35% are dated from 1980 to 2000, and the rest are dated after 2000. How many pennies in Russell’s collection are dated after 2000
Answer:
The total pennies in Russell's collection dated after 2000 is 800
Step-by-step explanation:
Given
Total Pennies: 1,200
Pennies before 1980: 25%
Pennies between 1980 and 2000: 35%
Required
Number of pennies in Russell’s collection are dated after 2000
Let P1 represent pennies dated before 1980
Let P2 represent pennies dated between 1980 and 2000
Let P3 represent pennies dated after 2000
To calculate the number of pennies dated after 2,000. you have to understand that his total collection of pennies is 100%
This means that
P1 + P2 + P3 = 100%
Where P1 = 25% and P2 = 35%.
So, we're solving for P3
By substituting, P1 = 25% and P2 = 35%, we have
25% + 35% + P3 = 100%
60% + P3 = 100%
Make P3 the subject of formula
P3 = 100% - 60%
P3 = 40%
The quantity of pennies dated after 2,000 is then calculated by P3 * Total.
i.e. 40% * 2000
= 0.4 * 2000
= 800
Hence, the total pennies in Russell's collection dated after 2000 is 800
$3-n=24¢
what does n=?
Answer:
N=3.24
Step-by-step explanation:
$3.00-n=0.24 Subtract $3
-n= -3.24 Divide by -1 to make the variable positive
n=3.24
Mario has a fish tank with 70 goldfish in it. One of the goldfish has unique pelvic fins, which are located on the bottom of the fish. He wants to show his friend the pelvic fins. What is the probability that Mario will randomly catch the right goldfish on the first 5 attempts?
0.034
0.049
0.069
0.091
Answer:
The probability that Mario will randomly catch the right goldfish on the first 5 attempts = 0.069
Step-by-step explanation:
From geometric distribution.
If the probability of success on each trial = P,
then the probability that the Nth trial is the first success
Pr (X = N) = [tex](1 - P)^{N - 1}[/tex] P
Now,
P = [tex]\frac{1}{70}[/tex]
Maximum attempt = 5
Probability that Mario will randomly catch the right goldfish on the first 5 attempts
= [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{1}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{2}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{3}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{4}[/tex] [tex]\frac{1}{70}[/tex]
= [tex]\frac{1}{70}[/tex] + [tex]\frac{69}{70}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{2}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{3}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{4}[/tex] [tex]\frac{1}{70}[/tex]
= 0.069
Answer: 1. A) 0.14
2. C) 46%
3. D) 86%
4. B) 0.513
5. A) 0.003
6. C) 0.069
7. C) 0.25%
8. D) 0.03
9. C) 71%
10. A) 10%
Step-by-step explanation: 100% :)
what is 7x+14 = to 7(1+x), 7x-7 or 7(x+2)
Answer:
7(x + 2)
Step-by-step explanation:
7x + 14 =
7 can be factored out of each term.
= 7 * x + 7 * 2
= 7(x + 2)
A scientist repeated an experiment three times, making 1.42, 3.81, and 4.08 gallons of a new product. How many gallons were made in all?
Answer:
So, total gallons were made in all =9.31 gallons
Step-by-step explanation:
We are given
A scientist repeated an experiment three times, making 1.42, 3.81, and 4.08 gallons of a new product
so,
first experiment =1.42 gallons
Second experiment =3.81 gallons
Third experiment =4.08 gallons
now, we can find total gallons
total gallons = first experiment + second experiment + third experiment
total gallons =1.42 gallons + 3.81 gallons +4.08 gallons
total gallons =9.31 gallons
what expressions are equivalent to 2(4x+2y)
Answer:4 • (2x + y)
Step by step solution :
Step 1 :
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
4x + 2y = 2 • (2x + y)
Final result :
4 • (2x + y)
Step-by-step explanation:
The expression 2(4x+2y) is equivalent to 8x + 4y.
The expression 2(4x + 2y) can be simplified using the distributive property, also known as the distributive law or the distributive property of multiplication over addition.
This property allows you to distribute the factor outside the parentheses to each term inside the parentheses. Here are some equivalent expressions:
Distributing the 2:
2(4x + 2y) = 2 * 4x + 2 * 2y = 8x + 4y
Using the distributive property in reverse:
2(4x + 2y) = 4x(2) + 2y(2) = 8x + 4y
Factoring out a common factor:
2(4x + 2y) = 2 * (2 * 2x + 2 * y) = 2 * 2(2x + y) = 4(2x + y)
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SOME ONE FILL IN THE BLANK PLZZZ
The diameter of a sphere is 24 cm. The volume of the sphere is____?
Volume: πr^2h (where h = height and r = radius)
Radius: 12
Height: 24
12^2 * pi * 24 = 10,857.34 cubic centimeters
what is a reasonable estimate for the problem 3 3/4 x (- 2/5) a.-2 b.-1/2 c.1/2 d.2
Answer:
a. -2
Step-by-step explanation:
3¾ ≈ 4
-⅖≈ -½
4 × (-½) = -2
A reasonable estimate is -2.
Answer:
Step-by-step explanation: -2
there are 657 lights on your set. on any given day 6 of them burn out and need to be replaced. if each cost $45 how. much do you spend replacing them each week ?
Answer:
1890, thats the cost per week to replace them.
Step-by-step explanation:
Find the distance using the modulus of the difference between z1 = -8 + 3i and z2 = 7 - 4i. Show all work for full credit.
Answer:
[tex]\sqrt{274}[/tex]
Step-by-step explanation:
Given [tex]z_1=-8+3i,\ z_2=7-4i.[/tex]
1. Find the difference [tex]z_1-z_2:[/tex]
[tex]z=z_1-z_2=-8+3i-(7-4i)=-8+3i-7+4i=(-8-7)+(3i+4i)=-15+7i.[/tex]
This complex number has real part [tex]Rez=-15[/tex] and imaginary part [tex]Imz=7.[/tex]
2. The modulus of complex number z is
[tex]|z|=\sqrt{Re^2z+Im^2z}=\sqrt{(-15)^2+7^2}=\sqrt{225+49}=\sqrt{274}.[/tex]
The distance between [tex]z_1\ \text{and}\ z_2[/tex] is:
16.5529 units
Step-by-step explanation:We know that the difference between two complex numbers:
[tex]z_1=a_1+ib_1\ \text{and}\ z_2=a_2+ib_2[/tex] is given by:
[tex]|z_1-z_2|=|(a_1+ib_1)-(a_2+ib_2)|\\\\i.e.\\\\|z_1-z_2|=|(a_1-a_2)+i(b_1-b_2)|\\\\|z_1-z_2|=\sqrt{(a_1-a_2)^2+(b_1-b_2)^2}[/tex]
Here we have:
[tex]z_1=-8+3i\ \text{and}\ z_2=7-4i[/tex]
i.e.
[tex]a_1=-8\ ,\ b_1=3,\ a_2=7\ \text{and}\ b_2=-4[/tex]
i.e. we have:
[tex]|z_1-z_2|=\sqrt{(-8-7)^2+(3-(-4))^2}\\\\|z_1-z_2|=\sqrt{15^2+7^2}\\\\|z_1-z_2|=\sqrt{225+49}\\\\|z_1-z_2|=\sqrt{274}\\\\|z_1-z_2|=16.5529[/tex]
In three rolls of 630 m of paper. In the first and second rolls - 345 m, and in the second and third rolls 450. How many meters of paper in the second roll.
You have the number 1-25 written on slips of paper. If you choose one slip at random, what is the probability that you will not select a number which is divisible by 3?
Answer:
8/25
Step-by-step explanation:
Steps:
1. First you count how many number are divisible by three. The numbers are 3, 6, 9, 12, 15, 18, 21, and 24, which is a total count of 8 numbers.
2. Then you count the numbers of slips of paper, which you know is 25.
3. Finally, put the number of numbers that are divisible by three or the total slips of paper to find your answer.