The answers are n(A ∪ Bc) = 10 and n(Ac ∩ Bc) = 6.
To solve this question we need knowledge of set theory, union and intersection.
(c) To find n(A ∪ Bc), we first need to find the complement of B, which is Bc = {5, 6, 7, 8, 9, d, e}. Now, we can find the union of A and Bc, which is A ∪ Bc = {1, 2, a, e, 5, 6, 7, 8, 9, d}. The number of elements in this set is n(A ∪ Bc) = 10.
(d) To find n(Ac ∩ Bc), we first need to find the complement of A, which is Ac = {3, 4, 5, 6, 7, 8, 9, b, c, d}. Now, we can find the intersection of Ac and Bc, which is Ac ∩ Bc = {5, 6, 7, 8, 9, d}. The number of elements in this set is n(Ac ∩ Bc) = 6.
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The display summarizes the favorite sports among 9th graders.
Circle graph titled favorite sports with five pieces. Baseball or softball is labeled 44 percent, basketball is labeled 20 percent, lacrosse is labeled 16 percent, soccer is labeled 12 percent, and field hockey is labeled 8 percent.
Which of the following describes the data set?
The data is univariate and categorical.
The data is univariate and numerical.
The data is bivariate and categorical.
The data is bivariate and numerical.
The function distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
The right response is: The information is categorical and univariate.
The only variable in the data set is the preferred sports among ninth graders. As it includes several categories or groupings, the variable is categorical (i.e., baseball or softball, basketball, lacrosse, soccer, and field hockey). The distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).
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The number e is the base of the ____________?
natural logarithm
decimal system
irrational number system
rational functions
Answer: C.
Step-by-step explanation:
Need help with these questions please
1. The height of the pyramid is 3.7 inches.
2. The length of the crossbar is 2√2 feet.
What is a pyramid?A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.
1. We know, The height, slant height, and half of the base length form a
right-angled triangle
Therefore, h² = 4² - (3/2)².
h² = 13.75
h = 3.7 inches.
2. We know, In a 45°, 45° and 90° triangle, It is an isosceles right-angled triangle, The hypotenuse is √2 times the two similar sides.
Therefore, From the given information, The length of the crossbar is
2√2 feet.
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NEED HELP ON THIS ASAP
The expression, h(x), in standard form that describes the length of the top surface of the rectangular boxes can be modelled by the function
[tex]h(x) = 6x + 66x^2 + 17[/tex].
What are expressions in standard form?A simplified way to write an expression is to use the expression in standard form. It entails expressing the expression in terms of its highest exponent, variables, and numerical coefficients. The use of standard form is intended to simplify the reading and comprehension of an expression. As opposed to writing an expression as, [tex]3x^2 + 4x +[/tex]7, it can be written in standard form as [tex]3x^2 + 4x + 7[/tex].
The two functions, f(x) and g(x), can be combined to form a single equation that expresses the length of the top surface of the rectangular boxes, which leads to the derivation of this expression.
The top surface's area is represented by the function f(x), which has the following form: [tex]f(x) = 66x^2 + 17x + 1[/tex]. With the formula g(x) = 6x + 1, the function g(x) denotes the width of the top surface. These two functions are combined to give us [tex]h(x) = 6x + 66x^2 + 17[/tex]. As a result, this expression describes how long the top surface of the rectangular boxes is.
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Rearrange the equation 2y = x into slope intercept form
Answer:
Step-by-step explanation:
y = [tex]\frac{1}{2}[/tex] x (divided both sides by 2)
This is slope intercept form (y=mx+b)
Slope = [tex]\frac{1}{2}[/tex] and intercept = 0
Identify the transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5. Select all that apply.
The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are: horizontal shift, vertical shift, and vertical stretch.
The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are:
- Horizontal shift: The parent function has been shifted to the right by 3 units. This is indicated by the subtraction of 3 from x in the equation.
- Vertical shift: The parent function has been shifted downward by 5 units. This is indicated by the subtraction of 5 from the entire equation.
- Vertical stretch: The parent function has been stretched vertically by a factor of (1)/(2). This is indicated by the multiplication of the entire equation by (1)/(2).
Therefore, the correct answers are horizontal shift, vertical shift, and vertical stretch.
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For the following decision problem where the objective is to maximize the expected return, find a. The optimal policy and expected return. b. The value of knowing X, but not Y, before D. c. The value of knowing Y, but not X, before D. d. The value of knowing both X and Y before D. e. Draw the influence diagram that corresponds to this decision tree.
a. The optimal policy and expected return can be found by working backwards from the end nodes of the decision tree. For each decision node, choose the action that results in the highest expected return. The expected return is calculated by multiplying the probability of each outcome by the corresponding return and summing the results. The optimal policy is to choose A if X is high, and B if X is low.
The expected return is 0.7*30 + 0.3*10 = 24.
b. The value of knowing X, but not Y, before D is calculated by subtracting the expected return without knowing X from the expected return with knowing X.
The expected return without knowing X is 0.5*24 + 0.5*24 = 24.
The expected return with knowing X is 0.7*30 + 0.3*10 = 24.
Therefore, the value of knowing X is 24 - 24 = 0.
c. The value of knowing Y, but not X, before D is calculated by subtracting the expected return without knowing Y from the expected return with knowing Y.
The expected return without knowing Y is 0.5*24 + 0.5*24 = 24.
The expected return with knowing Y is 0.8*30 + 0.2*10 = 26.
Therefore, the value of knowing Y is 26 - 24 = 2.
d. The value of knowing both X and Y before D is calculated by subtracting the expected return without knowing X or Y from the expected return with knowing both X and Y.
The expected return without knowing X or Y is 0.5*24 + 0.5*24 = 24.
The expected return with knowing both X and Y is 0.7*0.8*30 + 0.7*0.2*10 + 0.3*0.8*10 + 0.3*0.2*30 = 25.2.
Therefore, the value of knowing both X and Y is 25.2 - 24 = 1.2.
e. The influence diagram that corresponds to this decision tree is shown below:
X -> D -> Y -> R
-> A -> R
-> B -> R
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In the diagram below, TU is parallel to
QR. If SU is 6 less than IS, QS = 55,
and SR = 44, find the length of IS.
Figures are not necessarily drawn to scale.
State your answer in simplest radical form, if necessary. In the diagram below, TU is parallel to
QR. If SU is 6 less than TS, QS = 55,
and SR = 44, find the length of TS.
Figures are not necessarily drawn to scale.
State your answer in simplest radical form, if necessary.
The length of TS is 30.
What are similar triangles?When on comparing the properties of two or more triangles, if a common relations holds, then they are said to be similar.
Note that similarity is NOT congruency.
In the diagram given in the question, let the length of TS be represented by x. So that;
TS/ QS = SU/ SR
But, we have;
TS = x
SU = TS - 6 = x - 6
So that;
x/ 55 = (x - 6)/ 44
44x = 55(x - 6)
= 55x - 330
330 = 55x - 44x
330 = 11x
x = 330/ 11
= 30
x = 30
Therefore, the length of TS is 30.
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2.) During recent seasons, Major League Baseball has been criticized for the length of games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following time to completion. (Note that the minutes have been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes is reported as 2.40 hours.) Can we conclude that the mean time for a game is less than 3.50 hours?
2.98 2.40 2.70 2.25 3.23 3.17 2.93 3.18 2.80
2.38 3.75 3.20 3.27 2.52 2.58 4.45 2.45
a) What is the critical value of t for this question at the .05 significance level?
b) What is the calculated value of t for this question at the .05 significance level? (You need to calculate the standard deviation for the sample.)
Enter the value as - x.xx
c) Can we conclude that games are less than 3.5 hours long based upon the calculated t-value compared to the critical t-value?
Choose 1 answer for question c.
c1) Reject the null because the calculated t-value is less than the critical t-value.
c2) We fail to reject the null because the calculated t-value is greater than the critical t-value indicating that games are longer than 3.50 hours.
a) The critical value of t for this question at the .05 significance level is -2.11.
b) The calculated value of t for this question at the .05 significance level is -1.47, given a standard deviation of 0.63.
c) We can reject the null hypothesis because the calculated t-value (-1.47) is less than the critical t-value (-2.11). This indicates that games are less than 3.50 hours long.
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Gilberto decides to give a T-shirt to each of his sponsors. Each shirt costs
him $4. 75. He plans to pay for each shirt with some of the money he raises
from each sponsor.
Write an equation that represents the amount of money Gilberto
The equation that represents the amount of money Gilberto has after buying T-shirts for n sponsors at a cost of $4.75 per shirt can be written as nx - 4.75n = n² - 4.75n.
Assume count that Gilberto has n sponsors, and he plans to buy a t-shirt for each sponsor at a fee of $4.75 in step with a t-shirt. Assume also count on that every sponsor contributes x greenbacks to Gilberto's fundraising marketing campaign.
The overall amount of money Gilberto raises from all n sponsors is n instances x or nx. If Gilberto makes use of some of this cash to buy t-shirts, he may have nx - 4. 75n bucks left over.
Therefore, the equation that represents the quantity of cash Gilberto has after shopping for t-shirts is:
nx - 4. 75n = (n - 4. 75)n
simplifying this equation, we get:
nx - 4. 75n = n² - 4. 75n
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Which statement is true about evaluating the expression 72÷12+9−5 on the basic calcul
On simplifying the given expression using simplification method BODMAS, we get the answer 10. Thus, in the calculator the calculation must be done from left to right.
What is simplification in mathematics?Simplification means using various operations to reduce the formula to a simpler form, and approximation simplifies the formula to the nearest, but not exactly correct, value.
What is BODMAS?BODMAS in simplification stands for Bracket, Ob, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction.
Solution using BODMAS and simplifying it:
72÷12+9−5 = (72/12) + 9 - 5
=6 + 9 - 5
= 15 - 5
⇒72÷12+9−5 = 10
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The population of bears in a national forest is changing according to the function N(t) = 850(0.96)*, where t is the time in years and N(C) is the number of bears.
Which statement explains how the bear population is changing?
A. The population is decreasing by 4% per year.
B. The population is increasing by 96% per year.
C. The population is increasing by 4% per year.
D. The population is decreasing by 96% per year.
The population function is N(t) = 850(0.96)^t.
The base of the exponential function is (0.96), which is less than 1. This means that the function is decreasing over time.
Therefore, the correct answer is:
A. The population is decreasing by 4% per year.
20 POINTSS!! HURRY!
Airplane A traveled 1662 miles in six hours.
For Airplane B, y =
922/
3
x represents its rate of speed over the same six hours.
Compare the two airplanes to determine which airplane traveled at a faster rate?
Group of answer choices
Airplane A
Airplane B
airplane A
To compare the rate of speed of Airplane A and Airplane B, we need to calculate the speed of Airplane B first.
The formula to calculate distance is:
distance = rate x time
For Airplane A, we know:
distance = 1662 miles
time = 6 hours
So, we can rearrange the formula to solve for the rate:
rate = distance / time = 1662 / 6 = 277 miles per hour
For Airplane B, we know:
y = 922/3
x = rate of speed over 6 hours
We can use the formula to solve for x:
distance = rate x time
922/3 = x * 6
x = (922/3) / 6 = 153.67 miles per hour
Comparing the rates of the two airplanes, we can see that Airplane A traveled at a faster rate with 277 miles per hour compared to Airplane B's rate of 153.67 miles per hour. Therefore, Airplane A traveled at a faster rate.
Michael sang 12 songs. Every song was 3/8 minutes long. For how much time did he sing in total? Write your answer in simplest form.
Answer:
Total time = (length of one song) x (number of songs)
Length of one song = 3/8 minutes
Number of songs = 12
Total time = (3/8) x 12
Total time = 36/8
Simplifying the fraction, we get:
Total time = 4 and 4/8 minutes
Total time = 4 and 1/2 minutes
Therefore, Michael sang for a total of 4 and 1/2 minutes.
Given that △ABC ≅ △XYZ which of the following are pairs of corresponding parts of the triangles?
1.
2.
__ __
3. ABandXY
__ __
4. ABandZY
5.
Given that △ABC ≅ △XYZ which of the following are pairs of corresponding parts of the triangles ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z and AB ≅ XY, BC ≅ YZ, AC ≅ XZ.
What are the triangle's matching sides and angles?Angles that are encompassed by a congruent set of sides from two comparable (or congruent) triangles are referred to as comparable angles in a triangle. In a triangle, corresponding angles are of the same measure.
What does a similar side look like?For instance, if one polygons has edges a, b, c, d, & e and the other has side v, w, x, y, & z, and if bc and w have comparable sides, then the side of the polygon that is next to b must match either v or x that are both next to w.
Corresponding angles: ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z.
Corresponding sides: AB ≅ XY, BC ≅ YZ, AC ≅ XZ.
Corresponding sides: AB ≅ XY.
Corresponding sides: AB ≅ ZY.
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Emilia's lemon cookie recipe calls for 1 1/8 cups of sugar. How much sugar would Emilia use to make 3 5/6 batches of cookies?
To find how much sugar would Emilia use to make about 3 5/6 batches of cookies.
1 1/8 cups of sugar
Next, we need to convert the mixed number to an improper fraction:
1 1/8 = (8 + 1) / 8 = 9/8
So, the amount of sugar needed for one batch of cookies is:
9/8 cups of sugar
To find the total amount of sugar needed for 3 5/6 batches, we can multiply the amount of sugar per batch by the number of batches:
(9/8 cups of sugar) x (23/6 batches) = 69/48 cups of sugar
thus, Emilia would need 69/48 cups of sugar to make 3 5/6 batches of cookies.
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k 4.1 Find the zeros of the polynomial function and state f(x)=-8(x-1)^(3)(x+5)^(2)x^(4) The smallest zero is with multiplicity
The zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4) are x = 1, x = -5, and x = 0. The smallest zero is x = -5 with multiplicity 2.
To find the zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4), we need to set the function equal to zero and solve for x:
0 = -8(x-1)^(3)(x+5)^(2)x^(4)
This equation will be true when any of the factors on the right-hand side are equal to zero. Therefore, we can find the zeros by setting each factor equal to zero and solving for x:
x-1 = 0 -> x = 1
x+5 = 0 -> x = -5
x^(4) = 0 -> x = 0
So, the zeros of the polynomial function are x = 1, x = -5, and x = 0.
The smallest zero is x = -5 with multiplicity 2, since it is the smallest value of x and the factor (x+5)^(2) has an exponent of 2.
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Im confused of what the answer should be
If you roll a fair number cube, what is the probability of landing on a 6? What is the probability of rolling a 7?
The probability of landing on a 6 is 1/6. The probability of rolling a 7 is zero.
What is probability?The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.
If you roll a fair number cube, The probability of landing on a 6 is 1/6.
As, all the possible outcome is 6 and favourable outcome is 1 (6), Probability = 1/6 or 16.66%
The probability of rolling a 7 is zero as there is only 6 possible out come and 7 is the 7th outcome which is not possible, therefore 0.
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Plot the points A(-2,-3), B(1, 12), C(3, -4) on the coordinate axes below. State the
coordinates of point D such that A, B, C, and D would form a rectangle. (Plotting
point D is optional.)
The opposite sides of the quadrilateral should be parallel and the diagonals should be equal. [For a rectangle]
First, let's find the slope of AB and its perpendicular slope.
Slope of AB = (y2 - y1)/(x2 - x1) = (12 - (-3))/(1 - (-2)) = 5
Perpendicular slope of AB = -1/5
The midpoint of AB is ((-2+1)/2, (-3+12)/2) = (-0.5, 4.5)
Let D be the point on line segment AC such that AD is perpendicular to AC. Since AB is parallel to DC, the slope of DC is also 5.
Slope of AC = (-4 - (-3))/(3 - (-2)) = -1/5
The equation of line AC is y = (-1/5)x - (13/5)
The equation of line DC passing through (3,-4) with slope 5 is y - (-4) = 5(x - 3)
Solving these two equations, we get D(2,-14/5).
Therefore, the coordinates of point D are (2, -14/5).
We can plot the points on the coordinate axes and verify that A, B, C, and D indeed form a rectangle.
Find the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly.
The final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $5386.42.
What is interest rate?Interest is the amount a lender or financial institution receives for lending money. Interest can also refer to a shareholder's level of ownership in a company, usually expressed as a percentage.
Interest rate indicates the cost of borrowing, or the reward for saving. So if you are a borrower, the interest rate is the amount charged to borrow money, expressed as a percentage of the total loan amount.
Solution according to the information given in the question :
Given, Principal(P) = $5,000
Compounding frequency(n) = 4
Time(in years)(T) = 5
Interest rate = 6%
Amount = P× (1 + r/n)^t
= 5,000 × (1 + 6/4×100)⁵
= 5,000 × (1 + 0.015)⁵
= 5,000 × (1.015)⁵
= 5000 ×1.077
= $5286.42
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packages of knives and packages of forks Two students evaluate the expression 17(4+15). Kode evaluates the expression by adding the product of 17 and 4 to the product of 17 and 15 . Elijah evaluates the expression by determining the product of 17 and 19.
Both methods are correct and either one can be used to evaluate the expression 17.
About distributive propertyBoth Kode and Elijah are using the distributive property to evaluate the expression 17(4+15).
The distributive property states that a(b+c) = ab + ac.
Kode's method:
17(4+15) = (17*4) + (17*15) = 68 + 255 = 323
Elijah's method:
17(4+15) = 17*19 = 323
Both students get the same answer of 323.
Therefore, both methods are correct and either one can be used to evaluate the expression 17(4+15).
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PLEASE HELP! I CANNOT DO THIS QUESTION.
Answer:
Step-by-step explanation:
16 is diameter so r= 16/2= 8
area of circle = 3.14*r^2
therefore 3.14*8^2
which is 3.14*64=200.96cm sq
Enjoy :)
The mean selling price of new homes was $114,000. The population standard deviation was $5,000. A random sample of 100 new home sales was taken without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie? a. $115,000 - $117,000 b. $116,000 - $118,000 c. $113,000 - $115,000 d. $114,000 -- $116,000
The mean selling price of new homes was $114,000. The population standard deviation was $5,000. A random sample of 100 new home sales was taken without doing the calculations, ranges the sample mean selling price is most likely to lie between C) $113,000 - $115,000.
The sample mean selling price is most likely to lie in the range of $113,000 to $115,000 because this range is within one standard deviation (i.e., $5,000) of the population mean of $114,000, and therefore it contains approximately 68% of the sample mean values. The other ranges are outside one standard deviation from the mean, and therefore, the probability of the sample mean being in those ranges is lower. However, it is important to note that the actual sample mean could fall outside this range as it is still subject to random variation.
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d. The height of the ball is represe x is time in seconds. Rewrite the -1(-6x^(2)+4x+2)
The height of the ball is represented by the equation -1(-6x^(2)+4x+2), where x is time in seconds.
We can rewrite this equation by distributing the -1 and simplifying.
First, we distribute the -1 to each term inside the parentheses:
-1(-6x^(2)+4x+2) = 6x^(2) - 4x - 2
Now, we can simplify by combining like terms:
6x^(2) - 4x - 2 = 6x^(2) - 4x - 2
Therefore, the rewritten equation for the height of the ball is:
h = 6x^(2) - 4x - 2
This equation shows the relationship between the height of the ball (h) and the time in seconds (x). As time increases, the height of the ball changes according to the equation.
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y>=-(7)/(6)x Alot points on the Boundary Ine. Select the Ene to swith between solif and dotted. Select a reglon to shade it.
The final solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.
To solve the inequality y>=-(7)/(6)x, we will first graph the boundary line and then shade the appropriate region.
1. Begin by graphing the boundary line y=-(7)/(6)x. This line has a slope of -(7)/(6) and passes through the origin (0,0).
2. Since the inequality includes the "greater than or equal to" symbol (>=), the boundary line should be solid to indicate that points on the line are included in the solution.
3. Next, we need to determine which region to shade. To do this, we can choose a test point that is not on the boundary line. A common test point is (0,1), which is above the boundary line.
4. Substitute the coordinates of the test point into the inequality to see if it is true or false: 1>=-(7)/(6)(0)
5. Since the inequality is true, the region that includes the test point is the solution. This means we should shade the region above the boundary line.
6. The final graph should have a solid boundary line with the region above it shaded.
The solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.
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Find the volume of the earth dug out from a pit 6. 5 m long 2. 4 M wide and 1. 5 m deep
The volume of the earth dug out from a pit = 23.4 m³
Let us assume that l represents the length of the pit, 'w' represents the width and 'h' be the height of the pit.
Here, the length of the pit(l) = 6.5 m
the width of the pit (w) = 2.4 m
height of the pit(h) = 1.5 m
We need to find the volume of earth dug out from a pit.
We know that pit is of the cuboid shape.
Using the formula of volume of cuboid,
V = l × w × h
V = 6.5 × 2.4 × 1.5
V = 23.4 m³
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Dakota is able to drive his car 32.5 miles per gallon of gasoline. Write and solve an inequality that could be used to determine the minimum number of gallons of gasoline Dakota would need to drive 117 miles to his brother's house. Then interpret the solution. Explain your reasoning.
According to the interpretation of the solution, Dakota's vehicle requires more than 3.6 gallons of fuel to travel the 117 miles to his brother's home.
What will be the interpretation of the equation?Dakota will use x gallons of gas to travel 117 miles to his brother's home.
The following inequalities can be used to determine how many gallons of fuel Dakota requires the most:
x ≥ 117/32.5
According to this inequality, x must be more than or equal to 117 miles, which is the required driving distance for Dakota, divided by 32.5 miles per gallon, the maximum fuel efficiency for his vehicle.
After finding x, we obtain:
x ≥ 3.6
Hence, in order to go 117 miles to his brother's home, Dakota would require at least 3.6 gallons of gasoline.
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Sanjayisasalesperson.Hesoldabarbecuegrillfor$421andearned3%commission. HowmuchcommissiondidSanjayearn?
Answer:
Step-by-step explanation:
rnw
I need help ASAP please it’s due tonight!
Step-by-step explanation:
Use the Pythagorean Identity
[tex] \cos {}^{2} ( \frac{x}{2} ) = 1 - \sin {}^{2} ( \frac{x}{2} ) [/tex]