The equation will be y = -15x + 40
Equations help us to understand a particular problem better, they give us possible insights into the situation. Equation Formation is an important aspect of Mathematics. We can form equations on the basis of the information given and then analyze it.
Given:
The biker, Dudley wants to travel 40 miles.
It is given that he travels 30 miles every 2 hours.
Obtaining Equation,
Distance traveled in 2 hours = 30 miles
Then, distance traveled in x hours = [tex]\frac{30}{2}*x = 15x[/tex]
So, the remaining distance to cover = 40 - 15x
or y = 15x - 40
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Find the sum of 1\5 And 7\10. The expression Written in equivalent form with Common denominator is.... The sum is.....
The Solution:
Given the fractions below:
[tex]\frac{1}{5}\text{ and }\frac{7}{10}[/tex]We are asked to find the sum of the above two fractions.
[tex]\frac{1}{5}+\frac{7}{10}[/tex]The Lowest Common Multiple (LCM) of 5 and 10 is 10
[tex]\frac{2+7}{10}=\frac{9}{10}[/tex]Thus, the correct answer is
[tex]\frac{9}{10}[/tex]Find the sum of two hundred even numbers from 0 to 398
The sum of two hundred even numbers in the sequence from 0 to 398 is 39800
Sum of an APTo find the sum of two hundred even numbers from 0 to 398, we can use the formula of sum of an arithmetic progression.
[tex]S_n = \frac{n}{2}[2a(n-1)]d[/tex]
n = number of termsa = first termd = common differenceThe number of terms given here is 200, the first term is 0 and the common difference is 2
Substituting the values into the equation
[tex]S_n = \frac{n}{2}[2a+(n-1)]d\\S_n = \frac{200}{2}[2*0+(200-1)*2\\S_n = 100(0+199)*2\\S_n = 39800[/tex]
The sum of two hundred even numbers from 0 to 398 is 39800
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Bessie added 1 2/3 cups of fertilizer to each bag of topsoil. She used 7 5/8 bags of topsoil. Bessie used 12 17/24 cups of fertilizer altogether. True or False?
Answer: false
Step-by-step explanation:
Use 1/4 cup per square foot
Problem 2 Charlie estimates the height of a building to be 924 feet. Charlie's father tells him that his estimate has a 20% error. Explain why this is not enough information for Charlie to find the actual height of the building. Based on this information, what are the two possible values for the actual height of this building?
The actual height of the building is 739.2 feet.
Given the height of a building estimated by Charlie is 924 feet.
His father said that there is 20% error in the estimation.
we should determine 20% of the estimated height.
⇒ height = 924 feet
⇒ error = 20%
⇒ 924 × 20/100
⇒ 924/5
= 184.8 feet
Subtract the error in height with the height given.
⇒ estimated height - error in height
⇒ 924 - 184.8
= 739.2 feet.
hence the actual height is 739.2 feet.
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if a tank holds 2000 gallons of water, andthe water can drain from the tank in 40 min-utes, then torricelli’s law gives the volumevof water remaining in the tank aftertminutesasv
V'(t) = -250(1-(1/40)t)
If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.
Given:
V =2000( 1- (1/40)t)^2 , where 0≤t≤40.
Here we have to find the derivative with respect to "t"
We have to use the chain rule to find the derivative.
V'(t) = 2 (2000)(1- (1/40)t)d/dt(1- (1/40)t)
V'(t) = 2(2000)(1-(1/40)t(-1/40)
When we simplify the above, we get
V'(t) = -250(1-(1/40)t)
If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.
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Graph the line that represents each linear equation does anyone know a 2d version I can see instead of words to explain it?
The graph of the first linear equation:
y = x + 3
Can be seen in the image at the end.
How to graph the linear equation?Let's graph the first line, which is:
y = x + 3.
To graph it, we need to find two points on the line, to find these, we can evaluate the linear equation in two values of x.
Using x = 0 we get:
y = 0 + 3
y = 3
So we have the point (0, 3).
Using x = 1, we get:
y = 1 + 3
y = 4
So we have the point (1, 4)
Now we can graph these two points on the same coordinate axis and connect them with a line. Like in the example below.
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Carlita had -$15 in her checking account. She earned $87.99 from her job and decided to pay her phone bill for $47.82. After paying her phone bill, how much money is left in her account? Responses
Carlita has $25.17 in her checking account.
A deposit account held at a bank or other financial institution is known as a transaction account.
It is also referred to at credit unions as a share draught account, checking account, chequing account, current account, and demand deposit account. It is accessible frequently and instantly to both the account holder and any other users they may name. The account owner can access it "on demand." It is possible to gain access using a variety of techniques, including cash withdrawals, debit card use, cheques, and electronic transfers. Economically speaking, the funds in a transaction account are regarded as liquid funds. They are treated as currency in the context of accounting.The amount of money in her checking account = -$ 15
She earned $87.99
Now money in her checking account = -15+87.99 = $ 72.99
She paid her phone bill worth $47.82
money in her checking account = $ ( 72.99 - 47.82 ) = $25.17
Therefore she has $25.17 in her checking account.
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find w, given that the line joining a(3,4) to b(w,-5) is perpendicular to a line with slope -2/3
Answer:
w is -3
Step-by-step explanation:
A line with a perpendicular slope with have a slope that is the negative inverse of the reference line. If the reference line is -(2/3), the perpendicular line will have a slope of (3/2).
The line formed by ab: y = (3/2)x + b
We have one given point on line ab with one coordinate known, (3,4), so let's use it to find b:
y = (3/2)x + b
4 = (3/2)*3 + b for (3,4)
4 = (9/2) + b
b = 4 - (9/2)
b = - 0.5
The equation is y = (3/2)x - 0.5
The slope of (3/2) is equal to the Rise/Run of two points on the line: (3,4) and (w,-5):
Rise = (4 - (-5)) = 9
Run = (3 - w)
Slope = 9/(3-w)
(3/2) = 9/(3-w)
(3/2)(3-w) = 9
(9/2) - (3/2)w = 9
9 - 3w = 18
-3w = 9
w = -3
Point b is (-3, -5)
See attached graph.
Supposed Justins graph had an empty circle at 12. Write the inequality represented by this graph.
the inequality is
x> 12
all real numbers greater than 12
interval (12, infinite)
Which of the given number sequences represents an arithmetic sequence?
A) 32, 16, 8, 4, 2,...
B 5, 10, 20, 40, 80,...
C)-4, -1/2, 3, 13/2, 10,…
D) 4, 8/3, 16/9, 32/27, 64/81,…
-4, -1/2, 3, 13/2, 10,… represents an arithmetic sequence.
An arithmetic sequence progresses with a common difference which is the difference of consecutive terms.
So for each of the number sequences, we will try to check if the consecutive terms has a common difference.
A) 32, 16, 8, 4, 2,...
16-32 = -16
8-16 = -8
4-8 = -4
2-4 = -2
As the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
B)5, 10, 20, 40, 80,...
10-5 = 5
20-10 = 10
40-20 = 20
80-40 = 40
Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
C) -4, -1/2, 3, 13/2, 10,…
-1/2- -4 = 7/2
3- -1/2 = 7/2
13/2-3 = 7/2
10-13/2 = 7/2
This sequence has a common difference and hence is an arithmetic sequence.
D) 4, 8/3, 16/9, 32/27, 64/81,…
8/3-4 = -4/3
16/9-8/3 = -8/9
32/27-16/9 = -16/27
64/81-32/27 = -32/81
Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
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write an equation of the line in slope intercept format (-3,3) (0,-1)
write an equation of the line in slope intercept format (-3,3) (0,-1)
the equation of the line is
y=mx+b
so
step 1
Find the slope
m=(-1-3)/(0+3)
m=-4/3
step 2
Find the equation
we have
m=-4/3
b=-1 ----> is given
substitute
y=-(4/3)x-1Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $225. Now the cost is $310. What is the percent increase? Responses 38% 38% 27% 27% 73% 73%
The percentage increase in the cost of the airline tickets is 38%.
What is the percentage increase?Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency. In order to convert a value to a percentage, multiply the value by 100.
in order to determine the percentage increase, multiply the fraction of the change in price and the initial price by 100.
Percentage increase = (change in price / initial price) 100
Change in price = new price - initial price = $310 - $225 = $85
Initial price = $225
($85 / $225) x 100 = 38%
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if test scores for an exam were normally distributed with a mean of 75 and a standard deviation of 5, find the probability that a randomly selected student scored less than 82
The probability that a randomly selected student in the class test scored marks which is less than 82 is 0.9192
It is given that in a test, the scores for an exam normally distributed has a mean of 75 and a standard deviation of 5. We have been asked to find the probability that a randomly selected student scored less than 82.
From the question we have,
Mean = 75
Standard deviation (SD) = 5
Therefore, the probability that a randomly chosen student has a score of less than 82 is represented as:
(P) Probability ( X < 82) = P { Z < [tex]\frac{82-75}{5}[/tex] }
= P {Z < 7/5}
= P {Z <1.4}
= Area from - ∞ to 1.4
= 0.9192
From the z table the area under the normal curve that corresponds to 1.4 is 0.9192
Hence the required probability of that a randomly selected student scored less than 82 is 0.9192
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Solve for f(-2).
f(x) = 2x - 4
f(-2) = [?]
Answer:
f(-2) = -8
Step-by-step explanation:
GivensWe are given a function:
[tex]f(x)=2x-4[/tex]
We are told to find f(-2).
SolveFirst, substitute -2 as x in f(x):
[tex]f(x) = 2x-4\\\\f(-2) = 2x-4[/tex]
Then, substitute -2 as x in the equation itself:
[tex]f(-2) = 2(-2) - 4[/tex]
Then, simplify by multiplying 2(-2):
[tex]f(-2) = 2(-2) - 4\\\\f(-2) = -4 - 4[/tex]
Finally, simplify by performing the final arithmetic:
[tex]f(-2) = -4 - 4\\\\f(-2) = -8[/tex]
Final AnswerTherefore, f(-2) = -8.
7(u + 2) = 42 solve for u simplify your answer as much as possible
Answer:
7(u+2)=42
7u+14=42
-14 -14
7u=28
u=4
− is 55 units to the right of 0
use the drop down menus to complete the statement about x
x is ------- units to the -------- 0
The value illustrated shows that x is -55 units to the left of 0.
How to illustrate the information?From the given statement we have the value of x is negative. Therefore, we need the complete statement about x being positive.
Therefore we have to put an alternate sign to the given statement we get -x is 55 units to the right of 0.
Negation to the given statement about x is -(-x) is -(55) units to the left of 0. The statement will be that x is -55 units to the left of 0.
By using the drop-down menus to complete the given statement about x is -55 units to the left of 0.
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For #26-30, use the diagram at the right. Name the lines
that are parallel for the two given angles. Then classify the
angles.
Mr musa since the servant to the market to buy orange is 15 naira the servants have eaten three oranges on the way ,mr musa a 25 cover orange more than the market price. taking x to be number of oranges mr musa received ,form an equation in x and find x .
Mr musa since the servant to the market to buy orange is 15 naira the servants have eaten three oranges on the way ,mr musa a 25 cover orange more than the market price. Hence 12 be number of oranges mr musa received.
What is Equation?Two or more expressions with an equal sign is called as equation.
Let market price be M
(M+0.25)x=15
Oranges brought=15M
Servent ate 15M-3=x
15M=x+3
Divide both sides by 15.
M=(x+3)/15
((x+3)/15+1/4)x=15
Calculate the LCM and solve
(4x+12+15)x/60=15
Apply cross multiplication
4x²+27x=900
4x²+27x-900=0
By solving it we get x=12
Hence 12 be number of oranges mr musa received.
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2u - 17 = 11 solve for u simplify your answer as much as possible
Answer:
u = 14
Step-by-step explanation:
2u - 17 = 11
add 17 to both sides:
2u - 17 + 17 = 11 + 17
2u = 28
divide both sides by 2:
2u/2 = 28/2
u = 14
3 to the power of -3 =1/3
Answer: -27
Step-by-step explanation: -3 raised to the power of 3 is written (-3) 3 = -27. Note that in this case the answer is the same for both -3 3 and (-3) 3 however they are still calculated differently. -3 3 = -1 * 3 * 3 * 3 = (-3) 3 = -3 * -3 * -3 = -27. For 0 raised to the 0 power the answer is 1 however this is considered a definition and not an actual calculation.
6,095 divided by
Two answers
Answer: Last Digit Method: If the last digit in 6095 is 0, 2, 4, 6, or 8, then 6095 is divisible by 2. The last digit in 6095 is 5, thus 6095 is not divisible by 2.
Step-by-step explanation:
Please help I beg of y’all
Answer:
I think its 180
Step-by-step explanation:
find the perimeter of the regular hexagon
9 ft. 2 in.
please help asap thank u so much
Answer:660 in
Step-by-step explanation: Just add 6 sides, 9 ft= 108 in, + 2 in = 110, 110x6 = 660
Write an equation of a line that is parallel to 6x-2y=4 and goes through (-5,2)
Answer:
y = -1/3 x + 1/3
Step-by-step explanation:
In the picture.
according to a study by the centers for disease control and prevention, about 33% of u.s. births are caesarean deliveries. suppose seven expectant mothers are randomly selected. what is the probability that at least one of the expectant mothers will have a caesarean delivery?
The probability that at least one of the expectant mothers will have a cesarean delivery is 0.9394.
What is probability?Probability is the likelihood that something will happen. Based on the information, about 33% of u.s. births are cesarean deliveries.
The number (n) is also given as 7.
p = 33% = 0.33
n! / (n – r)!
N is the number of things you are choosing from,
r is the number of items.
P(x:n,p) = ⁿCˣ x pˣ(1-p)ⁿ⁻ˣ
n is the number of trials (occurrences)
X is the number of successful trials
p is probability of success in a single trial
ⁿCₓ is the combination of n and x
Therefore, the probability will be:
= 1 - P(no mother will have a Caesarean section)
= 1 - P(X = 0)
= 1 - ⁷C₀ (0.33)^0(0.67)^7
= 1 - 0.0606
= 0.9394
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8 circles and 20 squares what is the simplest ratio of total shapes
Answer
8:28 Hope this helps.
shirt sold at buyer for $7.00 each.
buyer sells shirt for $10.50, what is
his gain?
Answer:
His gain is 3.50$ which is also 50% of 7
Step-by-step explanation:
for next time so you dont gotta waste points all you have to do is go 10.50 -7.00 =3.50 and then just ask go ogle if you are able what percentage is 3.50 of 7.00 because 7.00$ is what he had to pay for so he is making a 50% gain
What is the slope of 7x + 2y = -10
What is the area of the square aboye?
156 square units
52 square units
65 square units
169 square units
OA.
OB.
OC.
OD.
13 units
Will mark brainiest
The area of the square with a side length of 13 units is 169 square units.
What is the area of the given square?A square is simply a regular quadrilateral having all four sides and angles equal.
The area of a square is expressed as;
A = a²
Where a is the side length.
Given the data in the question;
Side length of the square a = 13 unitsArea A = ?To determine the area of the square, plug the given value into the area of square formula and solve for A.
A = a²
A = ( 13 )²
Area A = 169 square units.
Therefore, the area of the square is 169 square units.
Option D) is the correct answer.
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What is 6 2/3 divided 1/5
Hello!
Let's solve:
[tex]\text{Write down the equation}\\\dfrac{6\dfrac{2}{3} }{\dfrac{1}{5} } \\\\\\\text{Convert the nominator, a mixed partial fraction to an improper fraction}\\\dfrac{\dfrac{20}{3} }{\dfrac{1}{5} } \\\\\\\text{When dividing by a fraction, flip the fraction over and multiply its reciprocal}\\\dfrac{20}{3} *\dfrac{5}{1} = \dfrac{100}{3} \\\\\\\text{Convert the improper fraction back mixed partial fraction}\\\dfrac{100}{3} =33\dfrac{1}{3}[/tex]
Answer: [tex]\dfrac{100}{3} \text{ or }33\dfrac{1}{3}[/tex]
Hope that helps!