Given revenue function is:
[tex]R=3t^2-2t+5[/tex]Now revenue at t=(-1)
[tex]\begin{gathered} R=3(-1)^2-2(-1)+5 \\ R=3+2+5 \\ R=10 \end{gathered}[/tex]So the revenue at t=-1 is 10.
Make the following conversions.5 pounds 16 ounces toa. Ounces:? ozb. Pounds: ? lbNote : I have attempted 80 ounces in 1 pound as the answers and it is incorrect
In order to calculate these conversions, we need to know the following conversion rate:
1 pound is equal to 16 ounces.
Knowing that, let's convert:
a. to ounces:
[tex]5\text{ pounds 16 ounces }=5\cdot16\text{ ounces + 16 ounces}=80\text{ + 16 ounces }=96\text{ ounces}[/tex]b. to pounds:
[tex]5\text{ pounds 16 ounces }=5\text{ pounds + 1 pound }=6\text{ pounds}[/tex]P is inversely proportional to Q. If P = 24 when Q = 3, then write the inverse variation equation that relates P and Q.
Inverse proportionality is when the value of one quantity increases with respect to a decrease in another, they behave opposite in nature.
It is represented by the following expression:
[tex]P=\frac{k}{Q}[/tex]Since P=24 when Q=3, we can substitute and solve for the constant k:
[tex]\begin{gathered} 24=\frac{k}{3} \\ k=24\cdot3 \\ k=72 \end{gathered}[/tex]Then, the equation that represents the inverse variation would be:
[tex]P=\frac{72}{Q}[/tex]2(4-2x)-5=-2(x+5)+8x
The equation 2(4-2x)-5=-2(x+5)+8x has a value of 1.3 for x
How to determine the solution to the equation?From the question, the equation to solve is given as
2(4-2x)-5=-2(x+5)+8x
Rewrite the equation properly
This is represented by the following representation
2(4 - 2x) - 5=-2(x + 5) + 8x
Start by opening the brackets in the equation
So, we have the following equation
8 - 4x - 5 =-2x - 10 + 8x
Collect the like terms in the equation
So, we have the following equation
8x - 2x + 4x = 10 +8 - 5
Evaluate the like terms in the equation
So, we have the following equation
10x = 13
Divide both sides of the equation by 10
So, we have the following equation
x = 1.3
Hence, the solution to the equation for x is 1.3
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a rectangular rug has dimensions of 9'×12'find area of the rug
Explanation:
Area of the rectangular rug = length × width
dimension of rug = 9'×12'
length = 12', width = 9'
Area = 12 × 9
Area = 18
The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m^s. Find the dimensions.
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the formula for total surface area of cuboid
[tex]\begin{gathered} 2(lb+bh+lh) \\ \text{where l is the length} \\ b\text{ is the breadth} \\ \text{h is the height} \end{gathered}[/tex]STEP 2: Get the dimension of the sides
[tex]\begin{gathered} \text{ Since the dimensions of the cuboid are in the ratio 1:2:3} \\ the\text{ dimensions are given as:} \\ x,2x\text{ and }3x \\ \text{lenght}=x \\ \text{breadth}=2x \\ \text{height}=3x \end{gathered}[/tex]STEP 3: Substitute the dimensions into the formula to get the value of x
[tex]\begin{gathered} 2(lb+bh+lh)=88 \\ By\text{ substitution,} \\ 2((x\cdot2x)+(2x\cdot3x)+(x\cdot3x))=88 \\ \Rightarrow2(2x^2+6x^2+3x^2)=88 \\ \text{Divide both sides by 2} \\ \Rightarrow\frac{2(2x^2+6x^2+3x^2)}{2}=\frac{88}{2} \\ \Rightarrow2x^2+6x^2+3x^2=44 \\ 11x^2=44 \\ \text{Divide both sides by 11} \\ \frac{11x^2}{11}=\frac{44}{11} \\ x^2=4 \\ x=\sqrt[]{4}=2 \\ x=2m \end{gathered}[/tex]STEP 4: Get the other dimensions
[tex]\begin{gathered} \text{breadth}=2x \\ \text{substitute 2 for x} \\ \text{breadth}=2(2)m=4m \\ \\ To\text{ get height} \\ \text{height}=3x \\ \text{substitute 2 for x} \\ \text{height}=3(2)m=6m \end{gathered}[/tex]Hence, the dimensions are:
[tex]2m,4m,6m[/tex]Hoang has worked as a nurse at Springfield General Hospital for 6 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital?
Ok let's take the information given and make an equations system with it.
I'm gonna use H for Hoang present working years and B for those of Bill. We know that right now Hoang has worked for 6 years longer than Bill, with this we can create the following equation:
[tex]H=B+6[/tex]We also have information from two years ago, at that time Hoang's working years doubled Bill's working years. One would feel tempted to write the equation H=2*B but you have to remember that this information is from the past and H and B stand for working years in the present. The correct way to approach this is change H and B by H-2 and B-2 so we consider that this information is from 2 years ago:
[tex]\begin{gathered} (H-2)=2\cdot(B-2) \\ H-2=2B-4 \\ H-2B=-2 \end{gathered}[/tex]So now we have constructed our equations system:
[tex]\begin{gathered} H=B+6 \\ H-2B=-2 \end{gathered}[/tex]Let's take the outcome of the first equation and use it in the second one:
[tex]\begin{gathered} H-2B=(B+6)-2B=-2 \\ B-2B+6=-2 \\ -B=-2-6=-8 \\ B=8 \end{gathered}[/tex]And going back to the first equation:
[tex]H=8+6=14[/tex]So Hoang has been working at the hospital for 14 years and Bill for 8 years.
The following are the annual salaries of 15 chief executive offers of major companies. The salaries are written in thousands of dollars.
The original data is:
405, 1108, 84, 315, 495, 609, 362, 428, 224, 338, 700, 790, 814, 767, 633
To find the required percentiles, we need to sort the dataset from lowest to highest.
84, 224, 315, 338, 362, 405, 428, 495, 609, 633, 700, 767, 790, 814, 1108
The total number of data is 15.
a) The 25th percentile is the element located at the position:
25/100 * 15 = 3.75
Rounding down, the position is 3, so the 25th perc
3-35. Fisher thinks that any two lines must have a point of intersection. Is he correct? If so, explain how youknow. If not, produce a counterexample. That is, find two lines that do not have a point of intersection and explainhow you know
Any two lines must have a point of intersection, with ONLY ONE exception : when the lines are parallel. That means they have exactly the same inclination or Slope.
As an example of two lines that hasnt point of intersection they are
y = 5x + 16
y = 5x + 11
We know both lines have no point of intersection because
both have the same slope or inclination m. By comparation with slope intercept equation
y = mx + b
then we see both have same inclination, and b is 11 in one line and 16 in the other line. This means both lines are parallel with one line going over the other line, without touching it in any point.
Write the product using exponents. I need help I’m not sure how to do this
Given:
The given expression is,
[tex]\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}[/tex]Required:
Write the product using exponent.
Answer:
Let us compute the product using exponents.
[tex]\begin{gathered} \frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5} \\ =(\frac{1}{5})^5 \\ =\frac{\left(1\right)^5}{\left(5\right)^5} \\ =\frac{1}{3125} \end{gathered}[/tex]Final Answer:
The product using exponents is given by,
[tex]\frac{1}{3125}[/tex]
Use the Pythagorean Theorem to find x, in simplest radical form. 20
The Pythagorean theorem states that the sum of the squares of the two sides of a right angle is equal to the square of the hypotenuse (longest side).
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where }c\text{ is the hypotenuse, and }a\text{ and }b\text{ are the other two sides of a right triangle.} \end{gathered}[/tex]Given: c = 20, a = 8, and b = x. Find x.
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8)^2+(x)^2=(20)^2 \\ 8^2+x^2=20^2^{} \\ 64+x^2=400 \\ x^2=400-64 \\ x^2=336 \\ \sqrt{x^2}=\sqrt[]{336} \\ x=\sqrt[]{16\cdot21} \\ x=4\sqrt{21}\text{ (final answer)} \end{gathered}[/tex]Hello, I need help completing this math problem. I will include a picture. Thank you so much!
From the given picture, we can see that the figure is a right triangle, so we can apply Pythagorean theorem, that is,
[tex]5^2+8^2=x^2[/tex]where x denotes the missing length. Then, our equation give us
[tex]\begin{gathered} x^2=25+64 \\ x^2=89 \end{gathered}[/tex]By taking square root to both side, we have
[tex]\begin{gathered} x=\sqrt[]{89} \\ x=9.4339 \end{gathered}[/tex]Therefore, by rounding this result to the nearest tenth, the answer is 9.4 ft
1. A jar contains 5 red marbles numbered 1 to 5 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability that the marble is blue or odd-numbered.
We will use the following formula:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B).[/tex]First, we compute the probability that we get a blue marble:
[tex]P(\text{Blue)}=\frac{6}{5+6}=\frac{6}{11}\text{.}[/tex]Now, we compute the probability of getting an odd-numbered marble:
[tex]P(\text{odd-num)}=\frac{6}{11}\text{.}[/tex]Finally, the probability that we draw a blue and odd-numbered marble is:
[tex]P(\text{blue and odd)=}\frac{3}{11}.[/tex]Answer: The probability that the marble is blue or odd-numbered is:
[tex]\begin{gathered} P(\text{blue or odd)=P(blue)+P(odd-num)-P(blue and odd)=}\frac{6}{11}+\frac{6}{11}-\frac{3}{11}=\frac{9}{11}. \\ P(\text{blue or odd)}=\frac{9}{11}\text{.} \end{gathered}[/tex]45 + 54 = 99 times ( ) + ( )
a) You have to find the greatest common factor for the values 45 and 54
To do so you have to determine the factors for each value and determine the highest value both numbers are divisible for.
Factors of 45 are
1, 3, 5, 9, 15, 45
Factors of 54 are
1, 2, 3, 6, 9, 18, 27, 54
The greatest common factor is 9, this means that you can divide both numbers by 9 and the result will be an integer:
[tex]\frac{45}{9}=5[/tex][tex]\frac{54}{9}=6[/tex]b) Given the addition
[tex]45+54[/tex]You have to factorize the adition using the common factor.
That is to "take out" the 9 of the addition, i.e. divide 45 and 54 by 9 and you get the result (5+6) but for this result to be equvalent to the original calculation, you have to multiply it by 9
[tex]45+54=9(5+6)[/tex]What is the value of x? A pair of intersecting lines is shown. The angle above the point of intersection is labeled left parenthesis 7 x minus 8 right parenthesis degrees. The angle directly opposite below the point of intersection is labeled left parenthesis 6 x plus 11 right parenthesis degrees. (1 point)
A –19
B 125
C 19
D 55
The value of x in the angles is 19.
How to find angles in intersecting lines?When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.
Therefore, let's find the value of x in the intersecting lines.
Hence,
7x - 8 = 6x + 11 (vertically opposite angles)
Vertically opposite angles are congruent and they share the same vertex point.
Hence,
7x - 8 = 6x + 11
subtract 6x from both sides of the equation
7x - 8 = 6x + 11
7x - 6x - 8 = 6x - 6x + 11
x - 8 = 11
add 8 to both sides of the equation
x - 8 + 8 = 11 + 8
x = 19
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Which statement is the converse of the conditional statement:
If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
• If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
O If point 8 is not the midpoint, then point B does not bisect line segment AC into two congruent segments.
Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.
O if point B
does not bisect line segment AC into two congruent segments, then point B is not the midpoint.
Point B is the midpoint if it divides line segment AC into two congruent segmentsIf point B is not the midpoint, then point B does not divide the line segment AC into two congruent segments, which is the statement opposite to the one that has been made.
Which statement is the converse of the conditional statement ?
A point that separates a segment into two congruent segments is the segment's midpoint.The segment is bisected by a point (or segment, ray, or line) that separates it into two congruent segments.Trisecting is the process of dividing a segment into three congruent segments using two points (segments, rays, or lines). A perpendicular bisector is a segment, ray, line, or plane that is perpendicular to another segment at its halfway. The x-coordinate of the midpoint M of the line segment AB is, as we can see from the formula, equal to the arithmetic mean of the x-coordinates of the segment's two endpoints.The midpoint's y-coordinate is also equal to the mean of the endpoints' y-coordinates. Even a unique postulate just for midpoints exists.Midpoint of a Segment Hypothesis.Any line segment will only have one midpoint, neither more nor less. Any line segment with equal measure is referred to as a congruent line segment.Congruent line segments, for instance, refer to the sides of an equilateral triangle since they all have the same length. Line segments that are congruent have the same length.There is a point in a line segment that will divide it into two congruent line segments.The middle is where you are now. A segment bisector runs through the middle of a line segment and divides it into two congruent portions.A segment bisector that intersects the segment at a right angle is called a perpendicular bisector.AB B C A C D E By applying algebraic techniques to solve the midpoint formula for one endpoint, the endpoint formula can be discovered.After performing the necessary algebra, (xa,ya)=((2xmxb),(2ymyb)) (x a, y a) = ((2 x m x b), (2 y m y b)) is the formula for the Endpoint A A of line AB A B.To learn more about mid point refer
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Please hurry!!!
Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference?
A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units.
Which describes the relationship between the distance and the difference?
The distance is always the opposite of the difference.
The distance is exactly the difference.
The distance is the absolute value of the difference.
The distance is not related to difference.
The third option that is the distance is the absolute value of the difference describes the relationship between distance and difference.
We know that the distance between two points is the difference of those two values.
But as the distance between two points can never be negative, we will write the absolute value of the difference as the distance between the two points.
Here we can see that,
a - b = -1 when distance = 1
a - b = 5 when distance = 5
a - b = 3 when distance = 3
Hence, the relationship between difference and distance is described by the third option.
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the difference of four times a number and seven is 13
ExplanatIon
Step 1
let x represents the number
hence,
four times a number =4*x=4x
the difference of four times a number and seven=4x-7
is can be written as equal or "="",so
the difference of four times a number and seven is 13
[tex]4x-7=13[/tex]Step 2
solve for x
[tex]\begin{gathered} 4x-7=13 \\ \text{add 7 in both sides} \\ 4x-7+7=13+7 \\ 4x=20 \\ \text{divide both sides by 4} \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]so, the number is 5.
I hope this helps you
Find the area of the triangle.
The area of the triangle given as in the attached image to the task content is; 1 ft².
What is the area of the triangle as indicated in the attached image?It follows from the task comtent that the area of the triangle given be determined.
Since the area of a triangle is given by the formula; Area = (1/2) × base × height.
Since the base of the triangle in discuss is 3 ft and it's height (altitude) as given in the task content is; (2/3) feet.
It follows that the area is;
Area = (1/2) × 3 × (2/3).
Area = 1 ft².
Ultimately, the area of the triangle is; 1 ft².
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Question 16
Given AEFHAGFH below, what is the measure of GFH?
F
21.6°
E<
(6x - 12)° H
G
1 pts
The most appropriate choice for congruency of triangles will be given by-
[tex]\angle GFH =68.4^{\circ}\\[/tex]
What is congruency of triangles?
Two triangles are said to be congruent if all the corrosponding sides and the corrosponding angles of the triangle are equal.
There are five axioms of congruency. They are -
SSS axioms, SAS axioms, ASA axiom, AAS axiom, RHS axiom.
Here,
[tex]\Delta EFH \cong \Delta GFH[/tex] [Given]
[tex]\angle E = \angle G = 21.6^{\circ}[/tex] [Corrosponding parts of congruent triangles are congruent]
[tex]\angle GFH[/tex] = 180 - (90 + 21.6) [Sum of the three angles of a triangle is 180°]
[tex]\angle GFH = 180 - 111.6\\\angle GFH =68.4^{\circ}\\[/tex]
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Given: B is the midpoint of AC. Complete the statementIf AB = 28, Then BC =and AC =
If B is the midpoint of AC, this means that point B divides the line AC exactly into 2 equal parts AB and BC, therefore,
[tex]AB=BC[/tex]Answer A
Thus, if AB = 28, BC = 28 too.
Answer B: Therefore, AC = 56
Which statement is true about the relation shown on the graph below?
We know that a function has a unique value of y for each value in x so the correct statement is:
c. it is not a function because there are multiple y values for a given x value
Use function composition to verify f(x)=-3x+5 and g(x)=5x-3 are inverses. Type your simplified answers in descending powers of x an do not include any spaces between your characters.Type your answer for this composition without simplifying. Use parentheses to indicate when a distribution is needed to simplify. g(f(x))=AnswerNow simplify the composition, are f(x) and g(x) inverses? Answer
Answer:
• (a)g[f(x)]=5(-3x+5)+5
,• (b)No
Explanation:
Given f(x) and g(x):
[tex]\begin{gathered} f(x)=-3x+5 \\ g(x)=5x-3 \end{gathered}[/tex](a)First, we find the composition, g[f(x)].
[tex]\begin{gathered} g(x)=5x-3 \\ \implies g\lbrack f(x)\rbrack=5f(x)-3 \\ g\lbrack f(x)\rbrack=5(-3x+5)+5 \end{gathered}[/tex](b)Next, we simplify g[f(x)] obtained from part (a) above.
[tex]\begin{gathered} g\mleft[f\mleft(x\mright)\mright]=5\mleft(-3x+5\mright)+5 \\ =-15x+25+5 \\ =-15x+30 \end{gathered}[/tex]Given two functions, f(x) and g(x), in order for the functions to be inverses of one another, the following must hold: f[g(x)]=g[f(x)]=x.
Since g[f(x)] is not equal to x, the functions are not inverses of one another.
What is 44 over 13 rounded to the nearest 10 tenths
we have that
44/13=3.38
rounded to the nearest tenths
3.38=3.4
the answer is 3.4A polynomial function is given.
Q(x) = −x2(x2 − 9)
(a) Describe the end behavior of the polynomial function.
End behavior: y → as x → ∞
y → as x → −∞
The end behavior of the polynomial is:
y → −∞ as x → ∞
y → −∞ as x → −∞
How is the end behavior?Here we have the polynomial:
Q(x) = -x²*(x² - 9)
Remember that polynomials with even degrees have the same behavior for the negative values of x than for the positive, in this case if we expand the polynomial we get:
Q(x) = -x⁴ + 9x²
The leading coefficient is negative, then the end behavior will tend to negative infinity in both ends, then we get:
y → −∞ as x → ∞
y → −∞ as x → −∞
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If the scale factor is 4, what is the measurement of x?24 m4 m20 m16 m
Let:
[tex]\begin{gathered} 6k=x \\ \end{gathered}[/tex]where:
k = scale factor
If the scale factor is 4, then:
[tex]\begin{gathered} 6(4)=x \\ 24=x \\ x=24 \end{gathered}[/tex]A)As the x-value Increases by one, the y-value decreases by 2.26.B)As the x-value increases by one, the y-value decreases by 53.769.C)As the x-value Increases by one, the y-value increases by 2.26.D)As the x-value Increases by one, the y-value Increases by 53.769. Which equation describes the line of best fit for the table below?
Option A
Explanations:The graph shows an inverse proportion.
As x increases, y decreases in value.
Finding the slope of the graph:
dy / dx = (y₂ - y₁) / (x₂ - x₁)
x₁ = 5, x₂ = 9, y₁ = 40, y₂ = 30
dy / dx = (30 - 40) / (9 - 5)
dy / dx = -10 / 4
dy / dx = -2.5
This means that as x increases by 1, decreases by 2.5
A is the only correct option.
The illustration below shows the graph of y as a function of x.complete the following sentences based on the graph of the function.* initially, as x increases, y (increases, decreases or stays constant).* the slope of the graph is equal to ___ for all x between x = 0 and x = 3.* starting at x = 3, the function value y (increases, decreases, or stays constant) as x increases.* the slope of the graph is equal to ___ for x between x = 3 and x = 5.* for x between x = 0 and x = 4, the function value y (≤, ≥, or =) 0.* for x between x = 4 and x = 8, the function value y (≤, ≥, or =) 0.
We will have the following:
*Initially, as x increases, y decreases.
*The slope of the graph is equal to -1 for all x between x = 0 & x = 3.
*Starting at x = 3, the function value y increases as x increases.
*The slope of the graph is equal to 3 for x between x = 3 & x = 5.
*For x between x = 0 & x = 4, the function value y ≤ 0.
*For x between x = 4 & x = 8, the function value y ≥ 0.
the difference between 58% of a number and 39% of the same number is 247. what is 62% of that number
Answer
62% of the number = 806
Explanation
We are told that that the difference between 58% of a number and 39% of the same number is 247.
We are then asked to compute 62% of the number.
Let the number be x.
From the first statement,
58% of x = 0.58 × x = 0.58x
39% of x = 0.39 × x = 0.39x
The difference between them is 247
0.58x - 0.39x = 247
0.19x = 247
Divide both sides by 0.19
(0.19x/0.19) = (247/0.19)
x = 1300
So, we can now calculate 62% of the number
62% of x = 0.62 × x = 0.62 × 1300 = 806
Hope this Helps!!!
8 nickels to 15 dimes what's the lowest terms
we have the quotient
8/15
remember that
8=2^3
15=3*5
8/15------> its irreducible
we have that
1 nickel=0.5 dimes
so
8 nickels=4 dimes
the ratio is
4/154/15Determine if u is a solution to 1 - 9u = 19u= -2, 7, 0, 6
-2
Replace u by -2, and check if the equality remains
1-9u = 19
1-9(-2) = 19
1-(-18)=19
1+18 = 19
19=19
-2 YES
7
1- 9(7) = 19
1-63 = 19
-62=19
NO
0
1-9(0) = 19
1= 19
NO
6
1-9(6) = 19
1-54=19
-53=19
NO
