Answer:
160
Step-by-step explanation:
22+18=40, and this was 25% of the cars.
So, 40(4)=160 cars were sold that week.
The number of cars Captain's Autos sold in total that week is 160.
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Number of used car on monday= 22
Number of cars on tuesday= 18
Now,
Let's call the total number of cars sold during the week "x".
We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:
22 + 18 = 0.25x
Simplifying, we get:
40 = 0.25x
Dividing both sides by 0.25, we get:
x = 160
Therefore, by the unitary method the answer will be 160.
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In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 27% with a margin of error of 1.9% . Describe the conclusion about p using an absolute value inequality.
The conclusion for p, from the confidence interval, using an absolute value inequality is:
[tex]|p - 0.27| \leq 0.019[/tex]
What is a confidence interval?A confidence interval is given by the estimate plus minus the margin of error. As an inequality, we have that the absolute value of the difference between the proportion and the estimate is of at most the margin of error, that is:
[tex]|p - E| \leq M[/tex]
For this problem, the estimate and the margin of error are:
E = 0.27, M = 0.019.
Hence the inequality is:
[tex]|p - 0.27| \leq 0.019[/tex]
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A chemist has three different acid solutions. The first acid solution contains
20
%
acid, the second contains
30
%
and the third contains
60
%
. They want to use all three solutions to obtain a mixture of
72
liters containing
35
%
acid, using
2
times as much of the
60
%
solution as the
30
%
solution. How many liters of each solution should be used?
Let [tex]x,y,z[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% solutions used in the mixture, respectively.
The chemist wants to end up with 72 L of solution, so
[tex]x+y+z=72[/tex]
while using twice as much of the 60% solution as the 30% solution, so
[tex]z = 2y[/tex]
The mixture needs to have a concentration of 35%, so that it contains 0.35•75 = 26.25 L of pure acid. For each liter of acid solution with concentration [tex]c\%[/tex], there is a contribution of [tex]\frac c{100}[/tex] liters of pure acid. This means
[tex]0.20x + 0.30y + 0.60z = 26.25[/tex]
Substitute [tex]z=2y[/tex] into the total volume and acid volume equations.
[tex]\begin{cases}x+3y = 72 \\ 0.20x + 1.50y = 26.25\end{cases}[/tex]
Solve for [tex]x[/tex] and [tex]y[/tex]. Multiply both sides of the second equation by 5 to get
[tex]\begin{cases}x+3y = 72 \\ x + 7.50y = 131.25\end{cases}[/tex]
By elimination,
[tex](x+3y) - (x+7.50y) = 72 - 131.25 \implies -4.50y = -59.25 \implies \boxed{y=\dfrac{79}6} \approx 13.17[/tex]
so that
[tex]x+3\cdot\dfrac{79}6 = 72 \implies x = \boxed{\dfrac{65}2} = 32.5[/tex]
and
[tex]z=2\cdot\dfrac{79}6 = \boxed{\dfrac{79}3} \approx 26.33[/tex]
Please select the best answer from the choices provided:
A. Unbounded
B. Infeasible
C. One optimal solution.
D. Alternate optimal solutions
The system of inequalities has Infeasible solutions option (B) Infeasible is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The inequality:
2x + y ≤ 5
3x + y ≤ 12
First plot the above two inequality on a coordinate plane.
As we can see the intersection region on a coordinate plane for both the inequality:
f(x, y) = 2x + 2y
As we can see there is so many points in the intersection region for the above function so there will no single solution.
Thus, the system of inequalities has Infeasible solutions option (B) Infeasible is correct.
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Solve.
|7x -5| = |8x -4
Answer:
9/25 or -1/11
Step-by-step explanation:
2 outcome
1; 7x-5=18x-4
2;-(7x-5)=18-4
4. Raquel is presented with two loan options for a $60,000 student loan. Option A is a 10-year fixed rate loan at 4% interest compounded monthly, while Option B is a 20-year fixed-rate loan at 3% interest compounded monthly. What is the monthly payment under each option? What is the total interest for each option? Round your answers to the nearest cent.
5. Write a paragraph discussing what factors might influence Raquel’s decision when choosing between Option A and Option B for her student loan. Please discuss at least two different factors. Your paragraph should be at least 4 sentences.
Step-by-step explanation:
chicken nuggets are so bussing that the answer is c
Describe at least two differences between constructing parallel lines and constructing perpendicular lines
Answer:
Step-by-step explanation:
parallel lines are the same so they dont touch u-u
perpendicular lines do touch eachother and intersect
The required two differences between constructing parallel lines and constructing perpendicular lines are,
1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.
Parallel lines are defined as the pair of lines in which points on both the lines are equidistant from each other, and the line never intersects each other.
The differences between constructing parallel lines and constructing perpendicular lines are as follows.
1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.
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Find the area and perimeter
for each polygon.
Answer:
5. P = 23 m
A = 15 [tex]m^{2}[/tex]
6. P = 24.4 in
A = 15.3 [tex]in^{2}[/tex]
Step-by-step explanation:
Area formula of a triangle is A = 1/2 bh
Area formula of a parallelogram is A = bh
5. The height of a triangle is perpendicular to the base.
A = 1/2 * 10 * 3
A = 15 [tex]m^{2}[/tex]
6. The height of the parallelogram is also perpendicular to the base.
A = 9 * 1.7
A = 15.3 [tex]in^{2}[/tex]
Perimeter means you add all the side lengths.
5. The side lengths are 5m, 8m, and 10m. Adding those together, you get 23m.
6. A parallelogram has congruent opposite sides. That means your side lengths are 9 in, 3.2 in, 9 in and 3.2 in. Adding those together, you get 24.4 in.
PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
Given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.
What is the height of the building?
Given the data in the question;
Angle of elevation θ = 35°Distance between the person and the building | Adjacent = 80ftHeight of the person h = 4ft.Height of the building from the eye level | opposite = xSince the scenario depicts a right angle triangle, we use trigonometric ratio.
tanθ = Opposite / Adjacent
We height of the building from the eye level x
Substitute given into the equation,
tan( 35 ) = x / 80ft
x = tan( 35 ) × 80ft
x = 0.7002075 × 80ft
x = 56ft
Now, to get the height of the building, we add the height of the person and the height of the building from the eye level of the person.
Height of building = x + 4ft
Height of building = 56ft + 4ft
Height of building = 60ft
Therefore, given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.
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Find the intercepts of y=−7x+3
Answer:
X-intercepts:
[tex] (\frac{3}{7} ,0)[/tex]
Y-intercepts:(0,3)
Step-by-step explanation:
Hello!
given expression
[tex]y = - 7x + 3[/tex]
x-intercept is the point on the graph where y=0
solve
[tex] - 7x + 3 = 0 \\ - 7x = - 3 \\ x = \frac{3}{7} [/tex]
Thus, x-intercept
[tex]( \frac{3}{7} ,0)[/tex]
y-intercept is the point on the graph where x=0
solve
[tex]y = - 7(0) + 3 \\ y = 0 + 3 \\ y = 3[/tex]
Thus, y-intercept (0,3)
Hope it helps!
17 + x =31
i need help
Answer:
x= 14
Step-by-step explanation:
First (and only) we subtract 17 from both sides :
17 + x - 17 = 31 - 17
x = 31 - 17
x = 14
Hope this helped and have a good day
The answer is 14.
To solve this, only one step is required, which is : Subtract 17 from each side.
17 + x - 17 = 31 - 17x = 14which of the following best describes the graph below?
The correct answer is the option A because in one-to-one functions, each y value corresponds to only one x value.
Find the arc length, x, when
r = 1 and 0 = 5 radians.
п
9
5л
9
1
X
X =
?TT
The arc length of the circle is 5π/9 units
How to determine the arc length?From the question, we have the following parameters
Angle, ∅ = 5π/9
Radius, r = 1 unit
The arc length (x) is calculated as
x = r∅
Substitute the known values in the above equation
x = 5π/9 * 1
Evaluate the product
x = 5π/9
Hence, the arc length of the circle is 5π/9 units
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Merger_Model_Evaluation_-_Question.xlsx 19 The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is: $92,165 $30,498 $92,661
$91,669
The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is $91,669
How to calculate the value?Share Price, P = 44.29
Premium on the acquisition, p = 20%
Therefore, effective share price for acquisition, P* = P x (1 + p) = 44.29 x (1 + 20%) = $ 53.15
Number of shares outstanding, N = 1,734 MM
Equity value, E = P* x N = 53 x 1,734
= $92,158.63 MM
Net Debt, D = - 496
Hence, the implied enterprise value:
= Equity value + net debt
= 92,158.63 + (- 496)
= $$91,669
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Which expression could represent the length of a rectangle that has an area equal to 4x2+12x?
there are two expressions that can represent the length of the rectangle, these two expressions are:
L = x
or
L = (4x + 12)
Which expression could represent the length of the rectangle?
Remember that for a rectangle of length L and width W, the area is given by:
A = L*W
In this case, we know that the area is:
[tex]A = 4x^2 + 12x[/tex]
We can factorize that expression into:
[tex]A = x*(4x + 12)[/tex]
So there are two expressions that can represent the length of the rectangle, these two expressions are:
L = x
or
L = (4x + 12)
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Find the critical value. Assume that the test is two -tailed and that n denotes the number of pairs of data. n =
20, α = 0.01
A) -0.570
B) 0.570
C) +0.447
D) +0.570
Using a calculator, the critical value for the t-distribution, with a confidence level of 99%, a sample size n = 20 and a two-tailed test is of Tc = 2.8609.
How to find the critical value of the t-distribution?It is found using a calculator, with three inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.The tail.In this problem, the inputs are given as follows:
Confidence level of 99%, as 1 - 0.01 = 0.99 = 99%.19 df, as 20 - 1 = 19.Two-tailed test, as stated in this problem.Hence, using a calculator, the critical value is of is of Tc = 2.8609.
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What is the least common multiple of 6x^2+39x and 6x^2+54x+84?
Answer: 6x[tex]6x{2}+93x-126andx{2}+84[/tex]
Step-by-step explanation: The only thing you do is just to keep multiplying until you get your answer.
I just need to know what the answer is
Answer:
C
Step-by-step explanation:
Compare your response to the sample response. Which of these did your response include? Check all of the boxes that apply.
The real number is on the number line, but the complex number is in the complex plane.
Both are distances.
Both are positive values.
The distance formula or the Pythagorean theorem is used to calculate the absolute value of a complex number.
The responses include:
The real number is on the number line, but the complex number is in the complex plane.Both are distances.Both are positive values.How to illustrate the information?In mathematics, a real number simply means a value of a continuous quantity which can represent a distance along a line.
In this case, real numbers are the numbers that include both rational and irrational numbers. Here, Rmrational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and the irrational numbers such as √3, π(22/7), etc., are all real numbers.
In conclusion, the correct options are A, B, and C.
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give the answers to the remaining boxes left blank, you can give the answers all in one sentence starting from the first blank box all the way to the last
The domain of the functions are:
The domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2The domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10The domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5The domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10What are the domains of a function?The domain of a function is the set of input values the function can take i.e. the set of values the independent variable can assume?
How to determine the domain of the functions?Function 1
The function is given as:
f(x) = √4x + 6
Set the radicand greater than 0
4x + 6 > 0
Subtract 6 from both sides
4x > -6
Divide by 4
x > -3/2
Express as interval notation
[-3/2, ∞)
Hence, the domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2
Function 2
The function is given as:
g(x) = -4√-20x - 6
Set the radicand greater than 0
-20x - 6 > 0
Add 6 to both sides
-20x > 6
Divide by -20
x < -6/20
Simplify
x < -3/10
Express as interval notation
(-∞, -3/10]
Hence, the domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10
Function 3
The function is given as:
f(x) = 15 + √5x - 16
Set the radicand greater than 0
5x - 16 > 0
Add 16 to both sides
5x > 16
Divide by 5
x > 16/5
Express as interval notation
[16/5, ∞)
Hence, the domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5
Function 4
The function is given as:
p(x) = √20x + 6
Set the radicand greater than 0
20x + 6 > 0
Subtract 6 from both sides
20x > -6
Divide by 20
x > -6/20
Simplify
x > -3/10
Express as interval notation
(-3/10, ∞]
Hence, the domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10
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What is The solution to -122 < -3(-2 - 8x) - 8x
A. x<8
B. x<-2
C. x>5
D. x>-8
Answer:
D.
Step-by-step explanation:
We can solve by simply isolating x:
[tex]-122 < -3(-2-8x)-8x\\-122 < 6+24x-8x\\-122 < 6+16x\\-128 < 16x\\-8 < x\\OR\\x > -8[/tex]
You can check by plugging in any value greater than -8
-122<-3(-2-8(-7))-8*-7
-122<-3(-2+56)+56
-122<-3(54)+56
-122<-162+56
-122<-106
A man gave out $24000 to his three brothers A,B and C to be shared among themselves . If A takes twice as much as B and B is given one third of what C takes , how much did each of them receive?
Answer:
A = 8000
B = 4000
C = 12000
Step-by-step explanation:
$24000 = A,B and C
A = 2B
B = 1/3C
solve for the letter that gets described the most
that letter is B
A =2B
B = 1/3C -> C = 3B
24000 = A + B + C
24000 = 2B + B + 3B
24000 = 6B
B = 4000
A =2B = 8000
C = 3B = 12000
HELP PLS
Name the intersection of plane K and plane L.
Answer:
line MN
Step-by-step explanation:
If two planes intersect, then the intersection is a line.
Answer: line MN
A ship left a port and sailed east at the rate of 30 miles per hour. One hour later, a second ship left the same port at the rate of 40 miles per hour, also traveling east. In how many hours did the second ship overtake the first ship?
Answer:
3 hours
Step-by-step explanation:
When the ships meet each other, that means the the distance travelled for both ships are the same, that is where the 2nd ship will overtake the ship.
Distance = Speed * Time
So, given information from the question, and letting x be the time in hours (from when the 1st ship departs), we can deduce:
Distance travelled of 1st ship = Distance travelled of 2nd ship
30x = 40(x-1)
30x = 40x - 40
-10x = - 40
x = [tex]\frac{-40}{-10}[/tex]
= 4
Since we are calculating based on the 2nd ship,
Time taken for 2nd ship to overtake first ship = x - 1 = 4 - 1 = 3 hours.
All pies at the baked goods booth were cut into eighths. When Justina Hartley’s sift in the boot began, there were eight and one forth pies waiting to be sold. At the end of her shift there were only five pieces of apple pie left. How many pieces of apple pie were sold during Justina’s shift?
Answer: 3 1/4
Step-by-step explanation: you started with 8 1/4 subtract the 1/4 now ur left with 8-3 which equals 5
HELP!!! (05.06 HC) During a laboratory experiment, a 2.36g sample of NaHCO3 was thermally decomposed to generate 1.57g of carbonic acid (H2CO3). Calculate the percent yield of carbonic acid for the reaction. Show all your work (10 points). NaHCO3 → Na2CO3 + H2CO3
The percentage yield of carbonic acid is 66 percent.
How to find percentage yield?The percentage yield of the carbonic acid can be found as follows:
NaHCO₃ → Na₂CO₃ + H₂CO₃
Hence, 2.36g sample of NaHCO₃ was thermally decomposed to generate 1.57g of carbonic acid (H₂CO₃)
Using law on conservation, the mass of the reactant is equals to the product.
Therefore,
percentage yield of carbonic acid = 1.57 / 2.36 × 100
percentage yield of carbonic acid = 157 / 2.36
percentage yield of carbonic acid = 66.2447257384
percentage yield of carbonic acid = 66 %
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Find the midsegment of the triangle which is parallel to CA.
Answer:
[tex] \pmb{ \pink{QUESTION�}}[/tex]
Find the midsegment of the triangle which is parallel to CA.
[tex] \pmb{ \pink{ANSWER:-}}[/tex]
Tip
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle.This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.If two segments are congruent, then they have the same length or measure.In other words, congruent sides of a triangle have the same length.[tex] \frak{Explanation:-} [/tex]
We have to find the segment which is parallel to CA.
From the given data,
The segment EG is the midsegment of the triangle[tex]\triangle[/tex] ABC.
So we have,
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side.
[tex]\implies\rm{midsegment \: EG \: parallel \: to \: CA}[/tex]
[tex]\frak{RainbowSalt}[/tex]~
Answer:
[tex]\fbox {EG}[/tex]
Step-by-step explanation:
Based on the given diagram, we can clearly see the midsegment (lies in the middle of the figure) that is parallel to AC is EG
I hope it helped you solve the problem.
Good luck on your studies!
Part 2 - Find the error(s) and solve the problem correctly.
Convert the polar equation to rectangular form and identify the graph. Support your answer by sketching the graph. Show and explain your work.
r = − 4 cos θ
Answer:
Cosine graph reflected over x-axis with amplitude 4
Comparing A and B we find the value of the variables as
x = radius
Centre (-2,0)
Radius 2
The sketch of the image is attached below
What is sketching the graph?Generally, the equation for is mathematically given as
x = -4 cos -(i)
Multiply -(i) both sides by & we
x^2= -4xcos\theta
We know that and
x= x cos\theta
y = rsino
x² + y² = x² (cos²∅ + sin²∅).
x² + y² = x² ....sin² ∅ + cos 2∅=1
so, putting rates in (ii) we get
x²+y² = -4x
x²+4² +4 + y²=4
(2 + 2)² + y² =4
The rectangular form of
x = -4cos∅ is (x + 2)² + y² = 4 ---- A
We can see that A is a graph of circles. The general equation of a circle is
= (x-h)² + (y)² = x² ----B
where (h, k) = centre
Comparing A and B we find
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Z+1 3. Given that Z & W are complex numbers. Prove that |Z + W|² - |z − w|² = 4Re(Z)Re(W)
Let z=a+bi, w=c+di
[tex]|z+w|^2 -|z-w|^2 \\ \\ = |(a+c)+i(b+d)|^2 -|(a-c)^2 +i(b-d)|^2\\\\=(a+c)^2 +(b+d)^2-(a-c)^2 -(b-d)^2\\\\=a^2 +2ac+c^2 +b^2 +2bd+d^2 -a^2 +2ac-c^2 -b^2+2bd-d^2\\\\=4ac+4bd\\\\=4Re(z)Re(w)+4Im(z)Im(w)[/tex]
What is an equation of the line that passes through the points (-6,0) and (8,7) ?
Answer:
y = 1/2 x + 3
Step-by-step explanation:
Find slope, m = (y1-y2)/(x1-x2) = (7-0) / (8- - 6) = 7/14 = 1/2
( does not matter which one you assign as point 1 or point 2)
Point (-6,0) slope form ( you can use either point)
(y-0) = 1/2 (x- -6)
y = 1/2 x +3
NO LINKS!! Please help me with this problem
Answer:
[tex]\frac{x^2}{784}+\frac{y^2}{400}=1[/tex]
Step-by-step explanation:
Horizontal Major Axis:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]
Vertical Major Axis:
[tex]\frac{(y-k)^2}{a^2}+\frac{(x-h)^2}{b^2}+[/tex]
So these two expressions are essentially the same with the only difference being the location of "a" and "b". The length of the major axis will be "2a" and the length of the minor axis will be "2b". The way I remember this is because when you have the horizontal major axis the "a" value is in the denominator of the (x-h) and I think of "x" as a horizontal value, since it moves a point horizontally. When you have a vertical major axis the "a" value is in the denominator of (y-k) and I think of "x" as a vertical value, since it moves a point vertically.
So just by looking at the graph, you can easily determine that the eclipse has a horizontal major axis. This can be further proven, since the distance from the origin on the right side is 28, and the distance from the the top to the origin is only 20.
So you could set up an equation to solve for a, since 2a = length of major axis, but since we're given the two points, the "a" value is really just the length from the origin to the right/left side, and combining these together you get the value of 2a/major axis, but you don't have to do that. So by looking at the graph you'll see the distance from the origin to the right side is 28. This means "a=28"
You can do the same thing here for the "b" value, and since the top is 20 units away from the origin, "b = 20"
So now let's set up the equation:
[tex]\frac{x^2}{28^2} + \frac{y^2}{20^2}=1[/tex]
Square the values in the denominator
[tex]\frac{x^2}{784}+\frac{y^2}{400}=1[/tex]