The station earned $1485 in revenue from selling the gas.
In this problem, we are given two vectors, v and w, representing the number of gallons of gas sold at a station and the corresponding prices per gallon, respectively. We are asked to find the dot product of these two vectors, which is a scalar quantity known as the "Vw". We will then interpret the meaning of this dot product in practical terms.
To find the dot product of v and w, we will use the formula:
Vw = v . w = (210)(2.8) + (300)(2.99)
Vw = 588 + 897 = 1485
Therefore, the value of Vw is 1485.
Practical terms: The dot product of two vectors is a scalar quantity that represents the "projection" of one vector onto the other. In this case, the dot product Vw represents the total revenue earned by selling regular and premium gasoline at the given station.
The components of v represent the number of gallons of regular and premium gas sold, while the components of w represent the respective prices per gallon for each kind of gas. Multiplying the number of gallons sold by the price per gallon gives the total revenue earned for each type of gas. Adding these two values together gives the total revenue earned for both types of gas.
Therefore, the dot product Vw represents the total revenue earned by selling all the gas at the given station. In practical terms, this means that the station earned $1485 in revenue from selling the gas.
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A company produces two products, A and B. At
least 30 units of product A and at least 10 units of
product B must be produced. The maximum
number of units that can be produced per day is
80. Product A yields a profit of $15 and product B
yields a profit of $8. Let a = the number of units of
product A and b = the number of units of product
B.
What objective function can be used to maximize
the profit?
P=
DONE✔
a+
b
The objective function that can be used to maximize the profit is Profit = 15a + 8b
Let a is the number of units of product A and b is the number of units of product B.
Profit = 15a + 8b
This function represents the total profit earned by producing a units of product A and b units of product B
Given that the profit per unit of product A is $15 and the profit per unit of product B is $8.
To maximize the profit, we would need to find the values of a and b that satisfy the constraints given in the problem and maximize the value of the objective function
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Find the value of x.
The value of x in the chord is 3 units.
How to find line segment when chord intersect?The chord intersection theorem states that the products of the lengths of the line segments on each chord are equal.
Therefore,
6(x + 5) = 4(2x + 6)
Open the brackets
6x + 30 = 8x + 24
subtract 8x from both sides of the equation
6x - 8x + 30 = 24
-2x + 30 = 24
subtract 30 from both sides of the equation'
-2x + 30 - 30 = 24 - 30
-2x = -6
divide both sides by -2
x = -6 / 2
x = 3
Therefore,
x = 3
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If x=3t+t^2 and y=7−2t, find an equation y=mx+b of the tangent to the curve at t=2.
m=
b=
The values of m and b after evaluation is -2 and 23 under the condition that If x=3t+t² and y=7−2t, and tangent to the curve at t=2.
In orde to evaluate the equation of the tangent to the curve at t=2, we have to calculate the slope of the curve at t=2.
The slope of the curve at t=2 is presented by the derivative of y with respect to x at t=2.
y = 7 - 2t
x = 3t + t²
dy/dx = -2
Then, the slope of the tangent to the curve at t=2 is -2.
Now we have to evaluate the point on the curve at t=2.
x = 3(2) + (2)² = 10
y = 7 - 2(2) = 3
So, the point on the curve at t=2 is (10,3).
Applying point-slope form of equation of line:
y - y₁ = m(x -x₁)
Here,
m = slope and (x₁,y1) is a point on the line.
Staging m=-2 and (x₁,y₁)=(10,3),
y - 3 = -2(x - 10)
Applying simplification
y = -2x + 23
Then, the equation of the tangent to the curve at t=2 is y=-2x+23.
So, m=-2 and b=23.
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Prove the following this : Let H be a subgroup of a group G . The left cosets of H constitute a partition of G ; the right cosets of H constitute a partition of G ?
To prove that the left cosets of H constitute a partition of G, we need to show that they satisfy two conditions:
1) Each element of G belongs to some left coset of H.
2) Any two distinct left cosets of H are disjoint.
Let g be any element of G. Then, by definition of a left coset, there exists an element h of H such that g = h·x for some x in G. Therefore, g belongs to the left coset H·x. Since this holds for any element g of G, we have shown that the left cosets of H cover all of G, satisfying the first condition.
Now, let H·x and H·y be two distinct left cosets of H. Suppose there exists an element z in both H·x and H·y.
Then, z = [tex]h_{1}[/tex]·x = [tex]h_{2}[/tex]·y for some [tex]h_{1}[/tex], [tex]h_{2}[/tex] in H.
Solving for x,
x = [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] · y.
Since H is a subgroup, [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] is also in H, and therefore x belongs to H·y.
Thus, H·x is contained entirely in H·y, and the two cosets cannot intersect.
This satisfies the second condition, and hence the left cosets of H constitute a partition of G.
A similar argument can be used to show that the right cosets of H also constitute a partition of G. This completes the proof.
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In how many distinct ways can the digits in the number 2,563,183,083 be arranged?
(If there are any zero digits then assume they can be placed in any position)
Out of 600 people sampled, 42 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.
Use GeoGebra to calculate! Give your answers as decimals, to three places
Answer:
So we can be 95% confident that the true proportion of people with kids in the population is between 0.044 and 0.096.
Step-by-step explanation:
To construct a confidence interval, we need to use the formula:
CI = p ± zsqrt((p(1-p))/n)
Where:
CI = confidence interval
p = sample proportion (in this case, 42/600 = 0.07)
z = the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval)
n = sample size (in this case, 600)
Plugging in the numbers, we get:
CI = 0.07 ± 1.96sqrt((0.07(1-0.07))/600)
Simplifying this, we get:
CI = 0.07 ± 0.026
Therefore, the 95% confidence interval for the true population proportion of people with kids is:
0.044 ≤ p ≤ 0.096
-3k - 7 ≤ 17 help!!!!!!!!!!!!!!!
Emilio puts $4,000.00 into an account to use for school expenses. The account earns 15% interest, compounded annually. How much will be in the account after 6 years?
Round your answer to the nearest cent.
Answer:
$10,359.73.
Step-by-step explanation:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money after the specified time
P = the principal amount (the initial amount of money)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, we have:
P = $4,000.00
r = 15% = 0.15
n = 1 (compounded annually)
t = 6 years
Substituting into the formula, we get:
A = 4000(1 + 0.15/1)^(1*6)
A = 4000(1.15)^6
A ≈ $10,359.73
Therefore, the amount in the account after 6 years, rounded to the nearest cent, is $10,359.73.
Which equation can be used to solve for x
Answer:
(a) 7(x +3.5x) = 56
Step-by-step explanation:
You want an equation to solve for x, the length of a morning run, if the evening run is 3.5 times as long, and these runs total 56 miles when done every day of the week.
Daily runThe morning run is given as x.
The evening run is 3.5 times as long, so is 3.5x
The total mileage each day is (x +3.5x).
Weekly totalIn 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:
7(x +3.5x) = 56
What’s the correct answer for problem 16???
The values of x and y of the given transverse lines are:
x = 44.25° and y = 7.25°
How to find the missing angle on the line?We know that there are different classification of angles such as:
Corresponding angles
Alternate angles
Opposite angles
Supplementary angles
Complementary angles
Now, we also know that sum of angles on a straight line is 180 degrees. Thus:
5x - 9y - 16 = 140
5x - 9y = 156 -----(1)
We also know that alternate angles are defined as two angles, that are formed when a line crosses two other lines, that lie on opposite sides of the transversal line and on the opposite relative sides of the other lines. If the two lines crossed are parallel, then the alternate angles are equal.
Thus:
3x + y = 5x - 9y - 16
2x - 10y - 16 = 0
2x - 10y = 16 ----(2)
Solving simultaneously gives us:
x = 44.25° and y = 7.25°
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In tetrahedron $ABCO,$ $\angle AOB = \angle AOC = \angle BOC = 90^\circ.$ A cube is inscribed in the tetrahedron so that one of its vertices is at $O,$ and the opposite vertex lies on face $ABC.$ Let $a = OA,$ $b = OB,$ and $c = OC.$ Show that the side length of the cube is
\[\frac{abc}{ab + ac + bc}.\]
[asy]
import three;
size(180);
currentprojection = orthographic(6,3,2);
real a, b, c, s;
triple A, B, C, O;
a = 6;
b = 3;
c = 2;
s = a*b*c/(a*b + a*c + b*c);
A = (a,0,0);
B = (0,b,0);
C = (0,0,c);
O = (0,0,0);
draw(O--A,dashed);
draw(O--B,dashed);
draw(O--C,dashed);
draw(A--B--C--cycle);
draw((0,0,s)--(s,0,s)--(s,0,0)--(s,s,0)--(0,s,0)--(0,s,s)--cycle,dashed);
draw((s,s,0)--(s,s,s),dashed);
draw((s,0,s)--(s,s,s),dashed);
draw((0,s,s)--(s,s,s),dashed);
label("$A$", A, SW);
label("$B$", B, E);
label("$C$", C, N);
dot("$O$", O, NW);
dot((s,s,s));
[/asy]
pls help me
Answer:
Step-by-step explanation:To solve this problem, we can use similar triangles. Let the side length of the cube be s, and let the midpoints of AB, AC, and BC be P, Q, and R, respectively. Then OP, OQ, and OR are the diagonals of the faces of the cube, and so they are equal to .Consider triangle AOB. By the Pythagorean theorem, we have , so . Since angle AOB is 90 degrees, we can use similarity to see that triangle OAP is similar to triangle OAB, so . Solving, we find that .Using similar triangles, we can find that . Since the sum of the squares of the lengths of the diagonals of a cube is equal to three times the square of the side length, we have
$$(0P2 + 0Q? + OR?) = 35388 Substituting the values we found for $OP$, $OQ$, and $OR$, we haveSimplifying and solving for , we find that . Thus, the side length of the cube inscribed in the tetrahedron is .
Please if you know the answer put the steps on thank you.
Answer:
1. # of people who predicted they would pass = 30
2. # of people who predicted they would fail = 20
3. # of people who predicted they would pass and actually passed = 27
4. # of people who predicted they would pass and actually failed = 3
5. # of people who predicted they would fail and actually passed = 11
6. # of people who predicted they would fail and actually failed = 9
Step-by-step explanation:
1. # of people who predicted they would
The total number of people who took the test is 50.The number of people who predicted they would pass is 30.The number of people who predicted they would fail is 20 (since 50 - 30 = 20)Let x be the number of people who predicted fail and actually passed the test. Since three times as many people who passed predicted pass than predicted fail, we know that 3x is the number of people who predicted pass and actually passed the test. Therefore, the total number of people who passed the test is x + 3x = 4x, and we know that 36 people passed the test, so 4x = 36, and x = 9.Since x is the number of people who predicted fail and actually passed the test, then the number of people who predicted fail and actually failed the test is 20 - x = 20 - 9 = 11.The number of people who predicted pass and actually passed the test is 3x = 3(9) = 27.The number of people who predicted pass and actually failed the test is 30 - 27 = 3.I also filled in the frequency table by extracting it from Brainly and drawing on it to show how the math works and fits in the table.
What’s the answer? Will give brainliest if correct
Explain reasoning
The statement that is not true is: C. The translation of a line is a pair of parallel lines.
What is transformation?In geometry, a transformation is a procedure that modifies a figure's position, size, or shape. Translation, rotation, reflection, and dilation are the four main categories of transformations.
Every point in a figure is translated by the same amount and in the same direction. A rotation revolves a figure around the centre of rotation, a fixed point. A figure is reversed over a line known as the line of reflection in a reflection.
In relation to a fixed point known as the centre of dilation, a dilation expands or contracts a figure by a specific scale factor.
The statement that is not true is: C. The translation of a line is a pair of parallel lines as translation is a transformation that moves every point of a figure the same distance in the same direction.
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Select all the correct answers.
If the measure of angle is which statements are true?
sin (0) = -
The measure of the reference angle is 30°.
cos (0) = √3
The measure of the reference angle is 45°.
tan (0) = -√3
The measure of the reference angle is 60°.
The measures of the trigonometric relations and reference angles are solved
Given data ,
Let the measure of the angle be θ = 2π/3
Now , from the trigonometric relation ,
The tangent of the function tan ( 2π/3 ) = -√3
And , the reference angle of the θ = 2π/3 is given by A = π/3
So , A = 60°
Hence , the reference angle is 60°
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Javier and Naida are discussing the elevation of Lima, Peru.
200
150 Lima
100
50+
0+Sea level
-50-
-100+
-150
-200
The elevation of Lima, Peru is 154 meters.
Javier: Lima is 154] meters from sea level.
Naida: Lima is 154 meters above sea level.
Whose statement is true?
Choose 1 answer:
Answer:
Naida's statement is true
Step-by-step explanation:
Since the elevation of Lima, Peru is a positive number, you can automatically tell that it is above sea level since sea level is zero
Can someone help me with this please
The measure of x is 36.
We have,
The angle opposite to equal sides is equal.
And,
The sum of the triangle.
27 + 90 + (x + 27)= 180
27 + 90 + x + 27 = 180
x = 180 - 144
x = 36
Thus,
The measure of x is 36.
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Express 1:0.2:0.75 in their simple form
Answer:
20 : 4 : 15
Step-by-step explanation:
1 : 0.2 : 0.75
1 : 2/10 : 75/100
1 : 20/100 : 75/100
(×100)
100 : 20 : 75
(÷5)
20 : 4 : 15
Please help will give a lot of points
Answer:
how many points will you give?
Step-by-step explanation:
How do I help my student understand this?
Cell 1 is in the "7th grade" row and "Pets" column. Have your student circle these labels or highlight them. Then it should be clear why choice E is the final answer.
Another way to rephrase it: the 35 people in cell 1 represent the number of 7th graders with pets.
Your friend has a bag of yellow and purple candy. He wants to use them to play a game with you.
Purple is worth 2 points and yellow is worth three points. Pick 9 candies from the bag
Create a system of equations where the combination of the candies gives you a total of 22 points. Make sure you label and define your variables.
The system of equations where the combination of the candies gives you a total of 22 points are:
x + y = 9
2x + 3y = 22
How can we create system of equations?To create the equations, we shall first define the variables:
x = the number of purple candies
y = the number of yellow candies
Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.
Then, we would make sure that the total number of candies selected is 9.
The first equation represents the total number of candies selected:
x + y = 9
The second equation represents the total number of points obtained:
2x + 3y = 22
Therefore, the system of equations is:
x + y = 9
2x + 3y = 22
This is a system of linear equations.
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What is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 96 words per minute?
Answer:
Step-by-step explanation:
We can calculate the t-statistic and the p-value as follows:
If we assume that the null hypothesis is true, then the t-statistic will follow a t-distribution with 19 degrees of freedom. We can compare the calculated t-statistic with the critical t-value at the 0.05 level of significance using a t-distribution table or statistical software.
If the calculated t-statistic is greater than the critical t-value, then we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the population mean reading rate is greater than 96 words per minute.
The p-value is the probability of obtaining a t-statistic as extreme or more extreme than the calculated t-statistic, assuming the null hypothesis is true. We can use the t-distribution table or statistical software to find the corresponding p-value.
If the p-value is less than the significance level of 0.05, then we can reject the null hypothesis at the 0.05 level of significance and conclude that the probability of obtaining a random sample of 20 second grade students with a mean reading rate of more than 96 words per minute is statistically significant.
PLEASE HELP I have 30 minutes! What is the end behavior of this equation and how did you get it?
The limit of the function will be:
lim f(x) = ∞ as x → ∞
lim f(x) = 0 as x → -∞
How to explain the functionThe limit of f(x) as x goes towards infinity is infinite while the limit of f(x) approaches 0 when x tends to a negative value. Mathematically speaking,
lim f(x) = ∞ as x → ∞
lim f(x) = 0 as x → -∞
We can comprehend such behavior because the function's base is greater than 1 which explains how its growth accelerates as x increases and diminishes quickly as x declines towards zero.
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Can you help me with this question?
Answer:
C
Step-by-step explanation:
It mentions that they charge 1.20 per kg of lettuce
How to write Two times the sum of y and 5 is 24
Then solve
Answer:
Step-by-step explanation:
2(y+5)=24
What is 15% of 100
Please help
Answer:
Step-by-step explanation:15
Calculate, to the nearest cent, the Present Value of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time.
3 years, at 1.3% per year, compounded weekly (52 times per year).
PV=?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1000\\ P=\textit{original amount deposited}\\ r=rate\to 1.3\%\to \frac{1.3}{100}\dotfill &0.013\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]1000 = P\left(1+\frac{0.013}{52}\right)^{52\cdot 3} \implies 1000=P(1.00025)^{156} \\\\\\ \cfrac{1000}{(1.00025)^{156}}=P\implies 961.76\approx P[/tex]
A straw is placed inside a rectangular box that is g inches by 6 inches by 7 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answer:
The length of the straw will be 5.91607 inches long in radical form.
What is Length of diagonal in cuboid?
If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula
As per the question the length of the straw is equal to length of the diagonal of Rectangular box.
l= 3 inch , b= 5 inch , h= 1 inch
Let us consider the length of the straw be 'x'.
As, Diagonal of Cuboid is,
X= 5.91607 (in radical form)
Step-by-step explanation:
Hence, the length of the straw will be 5.91607 inches.
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(1/2 + 1/3) + [1/4 + (2/3)] ÷ 2/5 -4 x 5/6 ÷ 3/7
Answer:
Step-by-step explanation:
first, take 1/2+1/3 + 1/4+2/3
1/2+1/3=5/6 , 1/4+2/3=11/12
5/6+11/12=22/12
2/5-4=-18/5
-18/5*5/6=-3
22/12/3=22*3/12
=11/2
11/2/3/7=11/2*7/3
=77/6=12.8
Factor the expression. x^2-12x-45
Answer:
(x + 3)(x - 15)
Step-by-step explanation:
To factor the expression x^2 - 12x - 45, we need to find two numbers that multiply to -45 and add to -12. Let's use the method of decomposition to find these two numbers:
x^2 - 12x - 45
We need to find two numbers that multiply to -45 and add to -12. Let's try -15 and 3:
x^2 - 12x - 45 = x^2 - 15x + 3x - 45
Now we can group the first two terms and the last two terms:
x^2 - 15x + 3x - 45 = x(x - 15) + 3(x - 15)
We can see that both terms have a common factor of (x - 15), so we can factor this out:
x(x - 15) + 3(x - 15) = (x + 3)(x - 15)
Therefore, the expression x^2 - 12x - 45 can be factored as (x + 3)(x - 15).
Refer to the attachment ^-^
Hope Helpful ~
A sixth-grade class collected data on the number of letters in the first names (name lengths) of all the students in class. Here is the dot plot of the data they collected:
How many students are in the class?
Based on the data displayed in the dot plot, it can be concluded there are 25 students in this class.
How to know the number of students based on the dot plot?Dot plots represent data and trends but using dots. In these types of graphs, each individual is represented with a dot. For example, in the number 3, we can see there are 3 dots, which means three students have a first name made of three letters.
Therefore, you can get the total of students by counting all the dots. Based on this, there are 25 students in this class.
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