a) The equation that models Alice's total cost of filling up her car tank using regular unleaded gas and premium gas is 4.65r + 4.95p = 874.80.
b) Based on the above equation, if Alice purchases 87 gallons of regular unleaded gas, it means that she also purchases 95 gallons of premium gas.
What is an equation?An equation is a mathematical statement equating two or more mathematical expressions using the equation sign (=).
The cost per gallon of regular unleaded gas = $4.65
The cost of premium gas per gallon = $4.95
The total cost for gas = $874.80
Let gallons of regular unleaded gas = r
Let gallons of premium gas = p
Equation:4.65r + 4.95p = 874.8
If r = 87, the value of p is:
4.65(87) + 4.95p = 874.8
404.55 + 4.95p = 874.8
4.95p = 470.25
p = 95 gallons
Thus, during Alice's first leg from the East Coast to the West Coast, she purchases 87 gallons of unleaded and 95 gallons of premium gas for her car.
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Write a situation to describe the equation below:
C=50+16x
Find the volume of the cone. Round your answer to the nearest tenth.
Answer:
261.79
Step-by-step explanation:
V= 1/3 N r2 h
Eva is going to invest in an account paying an interest rate of 6.1% compounded continuously. How much would Eva need to invest, to the nearest ten dollars, for the value of the account to reach $71,000 in 7 years?
The answer is 46320
Answer:
$46,320
Step-by-step explanation:
Given that
The rate of interest is 6.1%
The amount is $71,000
And, the time period is 7 years
We need to find out the invested amount
As we know that
In the compounded continously, the following formula should be used
Amount = Invested amount × e^(rate × time period)
$71,000 = Invested amount × e^(6.1% × 7)
$71,000 = Invested amount × e^0.427
$71,000 = Invested amount × 1.5326
So, the investment amount is
= $71,000 ÷ 1.5326
= $46324,912
= $46,320
3x + 50 = 5x - 2
Find x
Answer:
50=2x-2
52=2x
26=x
hope this helps
have a good day :)
Step-by-step explanation:
can someone solve this for me using pemdas
Answer:
24
Step-by-step explanation:
(25-10) ÷ 5 × 8
15 ÷ 5 × 8
3 × 8
24
Answer:
24
Step-by-step explanation:
Any work inside parentheses must be done first: (5^2 - 10). Also:
Exponentiation is done before addition/subtraction: 5^2 - 10 = 25 - 10 = 15
So now we have 15 / 5 * 2^3 and recognize exponentiation again:
15 / 5 * 8
Then, since multiplication and division have the same order of priority,
carry out the division in 15/5 and then multiply the result (3) by 8
to obtain 24 (final answer)
anna bought 20 christmas raffle tickets in her school. Her school sold 1500 tickets in all. What is the probability of the winning chances of anna?
The probability of Anna winning chances of buying 20 ticket out of 1500 tickets is 0.013.
What is probability?Probability simply means possibility. It deals with how likely something is to happen.
Therefore,
p(A) = number of favorable outcomes to A / total number of outcome
Hence,
Number of ticket bought by Anna = 20
Total ticket sold = 1500
Therefore,
probability of the winning chances of Anna = 20 / 1500
probability of the winning chances of Anna = 2 / 150
probability of the winning chances of Anna = 1 / 75
probability of the winning chances of Anna = 0.013
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Each root of x^2 - bx + c = 0 is decreased by 2. The resulting equation is x^2 - 2x + 1 = 0, then
(a) b= 6 , c = 9 (b) b = 3 , c = 5
(c) b=2 , c = -1 (d) b = -4 , c = 3
When the root of x²-bx+c = 0 is decreased by 2, the resulting equation is x²-2x+1, then b = 2 and c = 1
What is root of quadratic equation?The values of variables satisfying the given quadratic equation are called its roots.
if the roots of a quadratic equation ax²+bx+c = 0 are alpha and beta
alpha + beta = -b/a and
alpha × beta = c/a
when the roots are reduced by 2
alpha-2+ beta-2 = -b/a
(alpha+beta)-4 = -b/a
alpha+ Bata = -b/a + 4
the resulting equation is x²-2x+1 = 0
a = 1, b = -2 and c = 1
therefore alpha +beta = -b/a = -(-2)/1 = 2
therefore 2 = -b/a+4
a = 1
2 = -b+4
b = 4-2 = 2
alpha×beta = c/a = 1/1
(alpha -2)× ( beta -2) = (alpha)( beta) -2(alpha+beta) + 4 = 1-2(2)+4 = 1
therefore b = 2 , c = 1
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Find the explicit formula for an arithmetic sequence with a common difference of 8 and whose first term is -2.
The explicit formula of the sequence is aₙ = -10 + 8n
How to determine the explicit formula of the sequence?From the question, we have the following sequence that can be used in our computation:
The first term and the common difference
These values of the first term and the common difference are given as
First term = -2
Common difference = 8
The interpretation of the above sequence is that the 8 is added to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ = aₙ₋₁ + 8
When represented explicitly, we have
aₙ = a + (n - 1) * d
Where
a = -2 and d = 8
Substitute the known values in the above equation, so, we have the following representation
aₙ = -2 + (n - 1) * 8
Evaluate the products
aₙ = -2 + 8n - 8
Evaluate the like terms
aₙ = -10 + 8n
Hence, the explicit formula is aₙ = -10 + 8n
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To solve the equation: 14 = t +72 This is a(n)
equation (type an math operation) In order to solve it, you need to use
(type a math operation). You would
_(type a math operation and a number) on both sides of the
equation. The final answer is t =
(type a number)
Answer:
t=-58
Step-by-step explanation:
[tex]14=t+72\\14-72=t+72-72\\-58=t[/tex]
300 g of an unknown radioactive substance decays to 112 g after 180 seconds. What is the half-life of this substance?
ight now that the noobs are gone, any late nigh peeps still awake?
Find the surface area of this rectangle prism L=6 H=6 W=4
Answer:
168
Step-by-step explanation:
Surface area= 2(WL+HL+HW)
2×(4×6+6×6+6×4)
=168
I will give u brainliest if u can help me plz
Answer:
a. Volume 120km^2
Surface area 168km^2
Step-by-step explanation:
What happens if you log a log?
The guidelines apply to logarithms of any base anyway a comparable base ought to be used all through a calculation. This guideline tells us how to add two logarithms together. Adding log An and log B achieves the logarithm of the consequence of An and B, that is log Stomach muscle.
As demonstrated by the norm of logs, a log of a base with similar bases will drop and will leave simply the power. Logarithms are models, and when you increment, you will add the logarithms. The log of a thing is the number of logs.
In case you have comparable systems on the different sides of a circumstance, they offset each other! Recollect that this conceivably works when the logarithms on the different sides of the circumstance have a comparable base.
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How long is the stage?
Answer:
44 div by 4 = 11
the answer is 11
Step-by-step explanation:
In triangle JKL, tan(bº) = 3/4
and sin(bº) = 3/5. If triangle JKL is dilated by a scale factor of 3, what is cos(bº)?
bº
If triangle JKL is dilated by a scale factor of 3,cos(bº)=4/5.
Define trigonometric ratio.Trigonometric By definition, ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Why trigonometric identities are used?If you know the lengths of two of the triangle's sides, you can use trigonometric ratios to get the measurements of one (or both) of the acute angles.
tan(b)=P/B=3/4
sin(b)=P/H=3/5
cos(b)=B/H= To find
B=4, H=5
cos(b)=4/5
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Find the measure of angle A. Round your answer to the nearest whole number
Answer:
∠ A ≈ 53°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan A = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{12}{9}[/tex] , then
∠ A = [tex]tan^{-1}[/tex] ([tex]\frac{12}{9}[/tex] ) ≈ 53° ( to the nearest whole number )
1) The graph of g(x) is shown below. Which statement given below is FALSE?
Please help!
=======================================================
Explanation:
Let's go through the answer choices one by one to see which are true, and which are false.
Choice A) This is true because as we approach x = 2 from the left hand side, the y values get closer to y = 1 from the top Choice B) This is true. As we get closer to x = 4 on the left side, the blue curve is heading downward forever toward negative infinity. So this is what y is approaching when x approaches 4 from the left side.Choice C) This is true also. The function is continuous at x = -3 due to no gaps or holes at this location, so that means its limit here is equal to the function value. Choice D) This is false. The limit does exist and we find it by approaching x = -4 from either side, and we'll find that the y values are approaching y = -2. In contrast, the limit at x = 2 does not exist because we approach two different y values when we approach x = 2 from the left and right sides (approach x = 2 from the left and you get closer to y = 1; approach x = 2 from the right and you get closer to y = -2). So again, the limit does exist at x = -4; however, the function is not continuous here because its limiting value differs from its function value.Choice E) This is true because the function curve approaches the same y value from either side of x = 6. Therefore, the limit at x = 6 exists.What is the answer of 7 to the power of 2?
The answer to 7 to the power of 2 is 49.
This is because when a number is raised to a power, it means that it is multiplied by itself that number of times. 7 to the power of 2 is 7 multiplied by itself 2 times, which is 7 x 7, which equals 49.
An expression known as "power" denotes the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.
As an illustration, the power 63 demonstrates how three times the number 6 is multiplied.
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Which one of the following solids can produce this two dimensional shape when sliced vertically
The solid that can produce the given two-dimensional shape when sliced vertically is option 2.
What is vertical alignment?When we examine anything vertically, we see it from top to bottom. When something is standing, it is referred to as the alignment.
What is horizontal alignment?When we examine objects horizontally, we do it from left to right. When anything is in the sleeping posture, it is known as the alignment.
The given shape is a rectangle. When the rectangular prism is sliced in a vertical manner the solid will represent the given shape that is a rectangle.
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Two consecutive numbers with a sum of 775. What is the value of each of the two numbers?
Answer:
387 and 388
Step-by-step explanation:
775 / 2 = 387.5
387 and 388
The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
Ponies
3
Rabbits
8
Sheep
6
Write the ratio of ponies to sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, if
possible.
Answer:
1/2
Step-by-step explanation:
You are comparing ponies to sheep, so you put the ponies on top(3)
and the sheep on the bottom(6)
3/6 reduces to 1/2
What is the radius of a hemisphere with a volume of 38153 in”, to the nearest tenth
of an inch?
Answer:
26.3
Step-by-step explanation:
Delta Math
The radius of a hemisphere with a volume of [tex]38153[/tex] in", to the nearest tenth of an inch is [tex]26.3[/tex].
What is radius?A circle's or sphere's radius is any line segment that connects the object's centre to its perimeter in classical geometry; in more contemporary usage, it is also the length of those line segments.
The word "radius" is derived from the Latin word "radius," which also refers to the spoke of a chariot wheel. Use the equation [tex]r =\frac{D}{2}[/tex] to determine the radius, which is equal to half the diameter. This is the same process used to determine a circle's radius from its diameter.
A hemisphere's volume is equal to [tex]\frac{2}{3} \pi r^3[/tex] cubic units. Where is an estimated constant with a value of [tex]3.14[/tex]. The hemisphere's radius is denoted by "r."
Required calculations are:
V = r
r = radius.
Given, V = 38153 in³
[tex]38153 = \frac{2}{3} \pi r^3[/tex]
[tex]r^3 = \frac{3 \times 38153}{2 \times \pi }[/tex]
[tex]r = 3\sqrt{\frac{3 \times 38153}{2 \times \pi }}[/tex]
r =26.3 in
Therefore, the radius of a hemisphere with a volume of [tex]38153[/tex] in", to the nearest tenth of an inch is [tex]26.3[/tex].
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Find the area of the following trapezoids b1=8 cm, b2=15 cm, h=11 cm
Answer:
126.5 cm2
Step-by-step explanation:
First, the equation to find the area of a trapezoid is A= 1/2(b1 + b2)h , where b1 is the first length and b2 is the second length and h is the height. For these measurements, you would simply factor them into the equation- A= 1/2(8 + 15)11. Then using pemdas, 8+15= 23... multiplied by 1/2 equalling 11.5. Then multiply 11.5 by 11 to get your answer of 126.5 then add the units.
slove and I will give you a best anwser thing
Answer:
Below:
Step-by-step explanation:
When finding the power of a power, simplify the expression by multiplying the exponents
[tex]a^{m^n} =m^m^n[/tex]
12^4^-5 = [tex]12^{4*-5[/tex][tex]=12^-20=\frac{1}{12^{20}}[/tex]
[tex](-3)^{72}[/tex]
PLEASE HELP!! The first answer WITH STEPS gets BRAINLY!
Mr. Lehman is a piano tuner. He charges his clients a fixed amount for a house call plus his labor which is based on an hourly rate. The graph below shows how much Mr. Lehman charges as a function of the time required to tune a piano
Which of the following best represents Mr. Lehmans hourly rate for labor?
A. 10$
B. 15$
C. 20$
D. 25$
=Mr.Lehmans hourly rate for labor is 20$
=30+40=70-50=20
Answer:
The Answer is 15$
You'd need to get the slope
it tells us how he charges with respect to Time
So picking any Point on the graph. Let's say (0,10) and (2,40)
m(slope) = y2-y1/x2-x1
= 40-10/2-0
=30/2
= 15$
Picking other points would still give this value
PLEASE HELP I NEED U > I BEGG
Answer: I think 48 degrees
Step-by-step explanation: they are both diagonal
hope this helps, have a great day!! :D
Answer:
It is also 48
Step-by-step explanation:
1 and 3 are vertical to each other therefore their degree is both the same.
Jessica works 7 days a week at an internship in Paris, France. She makes 70 Euros per day. When she comes back to America she needs to know how many dollars per week she was making. What is the correct amount? ( 1 Euro = 1.17 dollars)
A. $573.30/week
B. $335.65/week
C. $479.50/week
D. $357.66/week
Answer: D
Step-by-step explanation:
i got this question before
Using the least common denominator rename 3/5 and 1/20
Answer:
12/20 and 1/20.
Step-by-step explanation:
The least common denomiator between 3/5 and 1/20 is 20.
For the first equation, we multiply the numerator and denominator by 4 to get 12/20.
The second equation's denominator is already 1/20, so we can leave it as is.
The final answer is 12/20 and 1/20.
help need answered today PLEASE
first answer thats correct will get brainly crown
Answer:
2/3
Step-by-step explanation:
Slope = rise / run = 2 / 3
Because points A, B, C, and D are collinear (meaning on the same line), the slope for line segment AB is the same as the slope for segment DC.
Answer:
2/3.
Step-by-step explanation:
The 2 triangles are similar so their corresponding sides are in same ratio.
The sides BA and CD are collinear so theire slopes are the same.
Slope of BA = rise/run = 2/3 so slope of DC is also 2/3.
I need help on finding x , please someone help!?
Answer:
30 degrees - its been a minute since I done that type of math