Answer: You will need 18 containers of 1-quart to fill the gearbox with 16.3 liters of oil.
Step-by-step explanation:
Knowing that you have 1-quart containers, you need to make the conversion from quarts to liters. This is:
[tex]1\ quart=0.946\ liters[/tex]
Now, since the gearbox holds 16.3 liters of oil, you can divide the volume of oil the gearbox holds by the volume of a container (which is 0.946 liters or 1-quart) to calculate how many containers of 1-quart you will need to fill the gearbox with 16.3 liters of oil.
[tex]number\ of\ containers=\frac{16.3\ liters}{0.946\ liters}=17.2[/tex]
Based on the result, you will need 18 containers of 1-quart to fill the gearbox with 16.3 liters of oil.
You will need 17 one-quart containers of oil to fill the 16.3-liter gearbox.
Explanation:To determine how many 1-quart containers of oil you will need to fill the 16.3-liter gearbox, we can convert the 16.3 liters to quarts by using the conversion factor of 1 liter = 1.05668821 quarts. So, 16.3 liters would be approximately 17.229 quarts. Since each 1-quart container holds exactly 1 quart of oil, you will need 17 of the 1-quart containers to fill the gearbox with 16.3 liters of oil.
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According to the synthetic division below which of the following statements are true? Check all that apply.
Answer:
A and D
Step-by-step explanation:
The remainder after division is 8, that is the 8 at the end of 2 - 4 8
Given f(x) divided by (x + h)
Then if (x + h) is a factor the remainder = 0
Hence (x + 7) is not a factor since remainder is 8
and f(- h) = remainder
that is f(- 7) = 8 → D
A and D are the correct statements.
How to know which are the following statements are true?We know that when f(x) is divided by (x - h) then f(h) is the remainder.In option A f(-7) is the remainder which gives the value 8.
So, option A is correct.
Here the value x = 7 does not satisfy the function.When we put x = 7 in the function it is coming 99
So, option B and C are wrong.
On putting x = -7 in the function we are getting 8So options D is correct
Again, the value of f(7) is 99.So, (x - 7) when divides the given function, 8 is not the remainder.So, option E is wrong.
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At which root does the graph of f (x) = (x - 5)3 (x + 2)2 touch the xaxis
ANSWER
x=-2
EXPLANATION
The given polynomial function is:
[tex]f(x) = {(x - 5)}^{3} {(x + 2)}^{2} [/tex]
The polynomial has two factors, one with an odd multiplicity which is
[tex] {(x - 5)}^{3} [/tex]
and the other with an even multiplicity which is
[tex] {(x + 2)}^{2} [/tex]
The graph does not cross the x-axis at where the multiplicity is even.
Therefore the graph touches the x-axis at
[tex]x = - 2[/tex]
We got this by solving
[tex]{(x + 2)}^{2} = 0[/tex]
(05.05)On the coordinate plane below, what is the length of AB.
7 units
8 units
15 units
16 units
Each line on the graph is one unit.
AB = 15 units long
Answer:
15 units
Step-by-step explanation:
Since A and B are along the same horizontal line, we count count the number of units to determine the distance
The horizontal distance from A to B is 15 units
What is 25% more than 80?
Answer:
100
Step-by-step explanation:
When being asked what is x% more than y (y is something), you can use the formula 25% * y + y. However, you must convert the percent into a decimal for it to be used mathematically.
25% = 0.25
Now we can plug all of the numbers in.
0.25 * 80 + 80
20 + 80
100
f(x) = x + 2 g(x) = x – 4
(f g)(x) =
Answer:
x^2 -2x-8
Step-by-step explanation:
f(x) = x + 2
g(x) = x – 4
(f*g) (x) = (x+2) (x-4)
FOIL
first x*x = x^2
outer -4*x = -4x
inner 2*x = 2x
last = -4*2 = -8
Add them together
x^2 -4x+2x -8
x^2 -2x-8
Answer:
C on ed
Step-by-step explanation:
What’s the total power in a circuit with a current of 4A and a resistance of 12 ohm?
Power = Current *Voltage
You already have the current, but not the voltage.
But you are given resistance, and you know that
Voltage=Current*Resistance
Therefore
V=I*R=4*12=48V
So you have 48V
Now you can figure out the Power
P=I*V=4*48=192W
Therefore you have 192W.
hope this helps
The total power in a circuit is 192W.
PowerPower exists at the time rate of excess or absorbing energy. The power delivered or absorbed by an element exists as the product of the current flowing through the component and the voltage across the element. Power exists estimated in watts. If the power exists positive then it exists absorbed by the component and if it exists negative then it is supplied by the element.
Power = Current [tex]*[/tex] Voltage
We have the current, but not the voltage.
But you are given resistance, and you know that
Voltage = Current [tex]*[/tex] Resistance
Therefore,
[tex]V=I*R=4*12=48V[/tex]
So you have 48V
Thus, we get the Power
[tex]P=I*V=4*48=192W[/tex]
Therefore, the total power in a circuit is 192W.
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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?
Answer:
[tex]\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}[/tex]
Step-by-step explanation:
The explicit formula for a geometric sequence:
[tex]a_n=a_1r^{n-1}[/tex]
[tex]a_n[/tex] - n-th term
[tex]a_1[/tex] - first term
[tex]r[/tex] - common ratio
[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}[/tex]
We have
[tex]a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...[/tex]
The common ratio:
[tex]r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}[/tex]
It's not a geometric sequence.If [tex]a_3=-\dfrac{1}{16}[/tex] then the common ratio is [tex]r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}[/tex]
Put to the explicit formula:
[tex]a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}[/tex]
Put [tex]a_n=\dfrac{1}{1024}[/tex] and solve for n :
[tex]-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1[/tex]
[tex]\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6[/tex]
Evaluate the expression below for
x= -4
6(x + 15)
Answer:
66
Step-by-step explanation:
We know x = -4. To solve, we just need to plug in -4 for x.
6 (-4 + 15) =
6 (11) =
66
Answer:
66
Step-by-step explanation:
x= -4
6(x + 15)
Substitute x =-4 into the second equation
6(-4+15)
6(11)
66
If two dice are rolled one time find the probability
A 3 on one die or both dice
[tex]|\Omega|=6^2=36\\|A|=1\cdot5\cdot2+1=11\\\\P(A)=\dfrac{11}{36}\approx30.6\%[/tex]
Answer:
[tex]P=\frac{13}{36}=0.361[/tex]
Step-by-step explanation:
There are six possible outcomes when rolling a die. Therefore the probability of obtaining a 3 is a given is
[tex]P = \frac{1}{6}[/tex].
When throwing the two dice together, the probability of obtaining a 3 is the same:
[tex]P_1 = \frac{1}{6} * \frac{5}{6} + \frac{5}{6} * \frac{1}{6}=\frac{5}{18}[/tex]
Since the events are independent then the probability of obtaining a three in both dice is:
[tex]P_2 = \frac{1}{6} * \frac{1}{6} = \frac{1}{12}[/tex].
Finally the probability of obtaining a 3 on a given or both is equal to the sum of the probabilities [tex]P_1[/tex] and [tex]P_2[/tex]
[tex]P=\frac{1}{12}+\frac{5}{18}=\frac{13}{36}=0.361[/tex]
Write parametric equations of the line -4x+y=-2.
Answer:
x(t)=-t/4
y(t)=-t-2
(answer can vary)
Step-by-step explanation:
Many different ways to do... you are just introducing a different variable, t, to rewrite x and y. We are rewriting x and y as functions of t.
So if we let -4x=t then x=t/-4 or x=-t/4
So if -4x=t then t+y=-2 so y=-t-2
So you could write the following:
x(t)=-t/4
y(t)=-t-2
Answer: the answer is a)x=t,y=4t-2
Step-by-step explanation: I guessed and got it right so sorry i do not know how to explain anything but hopefully it helps someone in the future at least
Compare and contrast interpolations and extrapolations based on a scatterplot
Answer:
An interpolation has a result which lies within the scatterplot’s cluster of data points. An extrapolation lies outside the cluster. An interpolation is more reliable than an extrapolation.
Step-by-step explanation:
Interpolations and extrapolations are both methods used to estimate values based on a scatterplot, but they differ in their approach.
Explanation:Interpolations and extrapolations are both methods used to estimate values based on a scatterplot, but they differ in their approach.
Interpolations involve estimating values within the range of the given data points, while extrapolations involve estimating values beyond the range of the given data points.
For example, if we have a scatterplot of temperature measurements at different times throughout a day, interpolation would involve estimating the temperature at a specific time between the given measurements, while extrapolation would involve estimating the temperature at a time outside of the given measurements, such as predicting the temperature at midnight.
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Which is the graph of the function f(x)=x3+x2+4?
this is what the graph look like
ANSWER
See attachment.
EXPLANATION
The given function is
[tex]f(x) = {x}^{3} + {x}^{2} + 4[/tex]
The degree of this function is odd and the leading coefficient is positive.
The graph of this function rises on the left and keeps rising on the right.
The y-intercept of this graph is 4.
The graph intersects the y-axis at 4.
The graph of this function is the one shown in the attachment.
Solve -2(4y + 6) = 52. 5 -5 8 -8
please help and hurry!!!!!!!!!!!
Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table.

Which equation models the motion of the ball?
y = –17(x)(x – 4)
y = –16(x)(x – 4)
y = –16(x – 2)2 + 68
y = –17(x – 2)2 + 68
y = –16(x – 2)² + 68 is the equation which models the motion of the ball.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Ryan throws a tennis ball straight up into the air.
The ball reaches its maximum height at 2 seconds.
The approximate height of the ball x seconds after being thrown is shown in the table.
We need to find the equation of the motion of the ball.
Let us take a point (0, 4) from the table.
The right equation is the point in which the equation satisfies.
y=-17(0)(0-4)
4=0
So y = –17(x)(x – 4) is false.
y = –16(x – 2)² + 68
4=-16(4)+68
The point (0, 4 ) satisfies the equation y = –16(x – 2)² + 68
Hence, y = –16(x – 2)² + 68 is the equation which models the motion of the ball.
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What is 3^2/3 equal to?
Answer:
A
Step-by-step explanation:
ABC to CAB, use that method to help you. You can research more on it.
What percent is equivalent to 1/25?
4%
5%
20%
25%
plss help me also this how to answer this a quadratic equation there is 4 categories to put some answer standard forms and a set of a b and c help me guys i need an answer before june 30 2019♀️♀️
Answer:
see explanation
Step-by-step explanation:
The standard form of a quadratic equation is
ax² + bx + c = 0 : a ≠ 0
Express the equations in this form and extract the coefficients
1
4 - 2x + 3x² = 0 , that is
3x² - 2x + 4 = 0 ← in standard form
with a = 3, b = - 2 and c = 4
2
x(x + 5) - 2x = 0 ← distribute parenthesis
x² + 5x - 2x = 0
x² + 3x = 0 ← in standard form
with a = 1, b = 3 and c = 0
3
x² - 2x(x - 2) + 5 = 0 ← distribute parenthesis and simplify
x² - 2x² + 4x + 5 = 0
- x² + 4x + 5 = 0 ← in standard form
with a = - 1, b = 4 and c = 5
Emma gets paid $5,000 per month.
1,250 a month for rent. What percent of her monthly pay goes to rent?
Answer:
25 percent.
Step-by-step explanation:
1,000 would be 20% of 5,000
250 is 5% of 5,000
20+5=25
25% of Emma's monthly income goes towards rent.
To calculate the percentage of Emma's monthly pay that goes towards rent, we need to divide the amount spent on rent by the total monthly income, and then multiply that result by 100 to convert it to a percentage.
Emma spends $1,250 a month on rent and earns $5,000 per month. The calculation is as follows:
Divide the monthly rent by the monthly income: $1,250 / $5,000 = 0.25.
Convert the decimal to a percentage: 0.25 * 100 = 25%.
Therefore, 25% of Emma's monthly income goes towards rent.
If y = 12x-2 were changed to y = 12x, how would the graph of the new
function compare with the original?
O
A. It would be shifted up.
B. It would be steeper.
C. It would be shifted down.
D. It would be less steep.
Answer: A. It would be shifted up.
Step-by-step explanation: the only thing that is changing in the two equations is the last number. The last number is not there in the second equation because the y-intercept is 0. The y-intercept in the first equation is -2 and shifts up 2 to y-intercept if 0. Therefore, your answer would be A. It would shift up.
The graph of the new equation compared with the original graph is the new graph would be shifted up.
Option A is the correct answer.
We have,
If the equation y = 12x - 2 were changed to y = 12x, the graph of the new function would be different from the original.
The original equation y = 12x - 2 represents a linear function with a slope of 12 and a y-intercept of -2.
The graph of this equation would be a straight line that is steep (with a slope of 12) and shifted downward by 2 units (due to the y-intercept of -2).
However, if we change the equation to y = 12x, the new equation represents a linear function with the same slope of 12 but with no y-intercept (it passes through the origin).
The graph of this equation would still be a straight line, but it would be shifted up compared to the original equation since the y-intercept has been removed.
Therefore,
It would be shifted up.
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50.441−6.203=? help asap
Answer:
44.238
Step-by-step explanation:
50.441-6.203=44.238
Can someone help me plz
Answer:
- (- 10)
Step-by-step explanation:
Point A is positioned at - 10 on the number line.
The opposite is the negative of the value
That is the opposite of - 10 is - (- 10)
Please help with ratios of the area of triangles.....thank you
Answer:
Part 1) The ratio of the areas of triangle TOS to triangle TQR is [tex]\frac{4}{25}[/tex]
Part 2) The ratio of the areas of triangle TOS to triangle QOP is [tex]\frac{4}{9}[/tex]
Step-by-step explanation:
Part 1) Find the ratio of the areas of triangle TOS to triangle TQR
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
The scale factor is equal to
TS/TR
substitute the values
6/(6+9)
6/15=2/5
step 2
Find the ratio of the areas of triangle TOS to triangle TQR
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
[tex](\frac{2}{5})^{2}=\frac{4}{25}[/tex]
Part 2) Find the ratio of the areas of triangle TOS to triangle QOP
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
The scale factor is equal to
TS/QP
substitute the values
6/9
6/9=2/3
step 2
Find the ratio of the areas of triangle TOS to triangle QOP
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
[tex](\frac{2}{3})^{2}=\frac{4}{9}[/tex]
in 2015 han was paid £1350 per month what was his average pay per hour in 2016
His average pay was:
Answer:
£1350
----------- = £8.44/hr based upon 160 work hours per week
160 hr
Step-by-step explanation:
We must assume that Han works a standard 40-hour week, and that there are 4 weeks in each month. That comes to 160 hours.
Then his average hourly pay rate was
£1350
--------- = £8.44
160 hr
i know it’s not a ser choice a but im still not sure
Step-by-step explanation:
[tex]f(x)=\dfrac{2}{x}\ and\ g(x)=\dfrac{2}{x}\\\\(f\circ g)(x)=f(g(x))\to\text{substitute}\ 2-3x\ \text{instead}\ x\ \text{in}\ f(x):\\\\(f\circ g)(x)=\dfrac{2}{\frac{2}{x}}=2\cdot\dfrac{x}{2}=x[/tex]
Complete the missing parts of the table for the following function
Answer:
At x=-2, y=16
At x=0, y=1
At x=3, y=1/64
Step-by-step explanation:
As we know that the function is given by:
[tex]y=(\frac{1}{4})^{x}[/tex]
The table represents the output values on given inputs.
So, when the input is -2:
[tex]y=(\frac{1}{4} )^{-2}\\y= \frac{(1)^{-2}}{(4)^{-2}}[/tex]
To convert the power in positive:
[tex]y=\frac{(4)^{2}}{(1)^{2} }\\y=16[/tex]
So the output for x=-2 is 16.
For x=0
[tex]y=(\frac{1}{4})^{0}[/tex]
Anything whose exponent is zero equals to 1, so y=1
For x=3, output is incomplete.
To complete,
[tex]y=(\frac{1}{4})^{3}\\y=\frac{(1)^{2} }{(4)^{2} }\\y=\frac{1}{64}[/tex] ..
An 'A' is considered 4.0, a 'B' is 3.0, a 'C' is 2.0, a 'D' is 1.0, and an 'F' is 0. If you received the following grades in your first semester, what would your grade point average be?
To calculate the GPA, convert each grade to its numerical equivalent, add these up, and then divide by the total number of grades given. For example, the GPA for grades 'A', 'A', 'B', 'C', and 'D' would be 2.8.
Explanation:To find the grade point average (GPA), you add up all the grade points and then divide by the total number of grades. Let's imagine you received the following grades: 'A', 'A', 'B', 'C', and 'D'.
First convert each grade to its grade point: A=4.0, B=3.0, C=2.0, D=1.0Next, add these up: 4.0 + 4.0 + 3.0 + 2.0 + 1.0 = 14.0Then, count the number of grades which is 5 in this case.Finally, divide the total grade points by the number of grades: 14.0 / 5 = 2.8
So your GPA would be 2.8.
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Final answer:
To calculate your grade point average (GPA), assign numerical values to each letter grade and average them. In this case, the GPA would be 2.5 for the given grades.
Explanation:
To calculate your grade point average (GPA), you need to assign the respective numerical value to each letter grade and then average them. In the given scenario, an 'A' is equal to 4.0, a 'B' is 3.0, a 'C' is 2.0, a 'D' is 1.0, and an 'F' is 0.0. Let's assume the grades for your first semester are A, B, C, and D. To calculate your GPA, add up the numerical values of the grades and divide by the number of grades you have.
So, the calculation would be: (4.0 + 3.0 + 2.0 + 1.0) / 4 = 2.5.
Therefore, your grade point average for the first semester would be 2.5.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
Answer: 84
Step-by-step explanation:
Set up a proportion as follows: [tex]\dfrac{\text{students that practice everyday}}{\text{total students}}[/tex]
[tex]\dfrac{7}{12}=\dfrac{x}{144}[/tex]
Cross multiply: 12x = 7 × 144
Divide by 12: x = 7 × 12
Simplify: x = 84
What is the answer to this question
Answer:
Number of Black grapes = 32
Step-by-step explanation:
This is a problem related to ratio and proportion. We are given the number of Green Grapes and the ration of Green Grapes to the Black Grapes
The ratio is 3:4
This means
[tex]\frac{G_g}{G_b} = \frac{3}{4}[/tex]
Now assume that the number of Black Grapes = x
Given that [tex]G_g[/tex]=24
Substituting these values in [tex]\frac{G_g}{G_b} = \frac{3}{4}[/tex]
[tex]\frac{24}{x} = \frac{3}{4}[/tex]
[tex]24*4 = 3*x\\x=\frac{24*4}{3}\\x=\frac{8*4}{1}\\x=32[/tex]
Hence the number of Black Grapes are 32
Answer:
32
Step-by-step explanation:
If 3:4 then 24:x (x represent the unknown)
So you have to divide 24 by 3 and the answer you get, which is 8, you multiply with four to get 32.
So we can say that both types of grapes are 8 times the amount that they originally were.
A radius of the base cone is 3cm and altitude is 9cm calculate the volume.
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=\stackrel{altitude}{height}\\ \cline{1-1} r=3\\ h=9 \end{cases}\implies V=\cfrac{\pi (3)^2(9)}{3}\implies V=27\pi \implies V\approx 84.8[/tex]
What is the common ratio of the sequence?
-2,6,-18,54
ANSWER
The common ratio is -3.
EXPLANATION
In general, the common ratio of a Geometric Sequence is given by:
[tex] r = \frac{a_{n+1}}{a_{n}} [/tex]
We can find the common ratio using any two consecutive terms of the geometric sequence by dividing the subsequent term by the previous term.
The given sequence is -2,6,-18,54
Using the first two terms the common ratio is
[tex]r = \frac{6}{ - 2} = - 3[/tex]
We could also used the second and third terms to get
[tex]r = \frac{ - 18}{6} = - 3[/tex]
and so on and so forth.
Therefore the common ratio is -3.