Answers
First, we need to remember the cosine formula which is: cosine(theta)= adjacent/hypotenuse, now let's apply the formula to the triangle we have:
By using the formula we find that x=3√3 .
The answer is D.
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2. Consider drawing a card at random from a standard deck of cards,Part A: Determine the probability that the card is a spade, given that it is black,Part B: Determine the probability that the card is red, given that it is a heart,Part C: Determine the probability that the card is an ace, given that it is black.Part D: Determine the probability that the card is a queen given that it is a face card,
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Consider drawing a card at random from a standard deck of cards,
Part A: Determine the probability that the card is a spade, given that it is black,
Part B: Determine the probability that the card is red, given that it is a heart,
Part C: Determine the probability that the card is an ace, given that it is black.
Part D: Determine the probability that the card is a queen given that it is a face card,
we have 52 cards
A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)
so
Part A: Determine the probability that the card is a spade, given that it is black,
If the card is black, that means the possible outcomes are 26 cards
so
P=13/26
P=0.5Part B: Determine the probability that the card is red, given that it is a heart,
if the card is a heart, that means, the possible outcomes are 13
so
P=13/13
P=1because all the cards that are heart are red
Part C: Determine the probability that the card is an ace, given that it is black.
if the card is black the possible outcomes are 26
therefore
P=2/26
P=1/13Part D: Determine the probability that the card is a queen given that it is a face card
in exponential growth functions the base of the exponent must be greater than 1.how would the function change if the base of the exponent were1? how would the function change if the base of the exponents were between 0 and 1
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A projectile is fired vertically upwards and can be modeled by the function h(t)= -16t to the second power+600t +225 during what time interval will the project I’ll be more than 4000 feet above the ground round your answer to the nearest hundredth
Answers
Given:
[tex]h(t)=-16t^2+600t+225[/tex]To find the time interval when the height is about more than 4000 feet:
Let us substitute,
[tex]\begin{gathered} h(t)\ge4000 \\ -16t^2+600t+225\ge4000 \\ -16t^2+600t+225-4000\ge0 \\ -16t^2+600t-3775\ge0 \end{gathered}[/tex]Using the quadratic formula,
Here, a= -16, b=600, and c= -3775
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-600\pm\sqrt[]{600^2-4(-16)(-3775)}}{2(-16)} \\ =\frac{-600\pm\sqrt[]{360000^{}-241600}}{-32} \\ =\frac{-600\pm\sqrt[]{118400}}{-32} \\ =\frac{-600\pm40\sqrt[]{74}}{-32} \\ =\frac{-75\pm5\sqrt[]{74}}{-4} \\ t=\frac{-75+5\sqrt[]{74}}{-4},x=\frac{-75-5\sqrt[]{74}}{-4} \\ t=7.99709,t=29.5029 \end{gathered}[/tex]So, the interval is,
[tex]8.00\le\: t\le\: 29.50[/tex]im having a hard time understanding this could you please help me
Answers
Given -
The odds against winning a prize in the raffle = 9:1
To Find -
Probability of winning prize =?
Step-by-Step Explanation -
Total possible outcome = 9 + 1 = 10
Favourable outcome = 9
So,
Probability = Total outcome / Favourable outcome
Probability = 9/10 = 0.9
Final Answer -
Probability of winning prize = 0.9
Elena is traveling to visit her grandparents who live 125 miles away.
a. Elena stops for lunch 2/3 of the way. How far has Elena traveled?
b. Elena enters the city where her grandmother lives after 110 miles. Is she more or less than 9/10 of the way there?
PLS PLS PLS HELPP
Answers
Answer:
A. 83 1/3 miles
B. Less than 9/10 of the way there
Step-by-step explanation:
A.
2/3 of the way. "of" means to multiply, so multiply 2/3 and 125.
[tex]\frac{2}{3}[/tex] × [tex]\frac{125}{1}[/tex] = [tex]\frac{250}{3}[/tex]
Simplify by dividing 250 and 3.
250 ÷ 3
[tex]83 \frac{1}{3}[/tex] miles
B.
Multiply 125 by 9/10 then compare the answer to 110 to see if she is more or less than 110 miles.
[tex]\frac{125}{1}[/tex] × [tex]\frac{9}{10}[/tex] [tex]= \frac{1125}{10}[/tex]
Divide 1125 by 10
1125 ÷ 10 = 112.5
Since 9/10 of the distance is 112.5 miles, 110 miles is less than 9/10 of the way there.
Converting between scientific notation and standard form in a real-world situation
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Answer:
[tex]\begin{gathered} a)9.54\times10^6\text{square miles} \\ b)0.0061\sec onds_{} \end{gathered}[/tex]Explanations:
a) The scientific notation is generally expressed as;
[tex]A\times10^n[/tex]A is any real numbers between 1 and 10
n is an integer
Given that the total surface area of North America is 9,540,000 square miles. This is expressed in scientific form as;
[tex]9,540,000=9.54\times10^6mi^2[/tex]From the scientific notation, A = 9.54 and n = 6
b) Given the scientific notation as shown:
[tex]6.1\times10^{-3}\text{seconds}[/tex]Writing in standard form means writing in the normal way we write numbers/decimals. Hence;
[tex]6.1\times10^{-3}=0.0061\text{seconds}[/tex]Eduardo's school is selling tickets to a play. On the first day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108. The school took in $114 on the second day by selling 10 adult tickets and 3 child tickets. What is the price each of one adult ticket and one child ticket?
Answers
The price of one adult ticket is $9 and the price of child ticket is $8
First day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108
Consider the price of adult ticket as x and child ticket as y
Then the equation will be
4x+9y = 108
Similarly the school took in $114 on the second day by selling 10 adult tickets and 3 child tickets
10x+3y = 114
Here we have to use the elimination method
Multiply the first equation by 10 and second equation by 4
40x+90y = 1080
40x+12y = 456
Subtract the equation 2 from equation 1
90y-12y = 1080-456
78y = 624
y = 624/78
y = $8
Substitute the value of y in any equation
10x+3y =114
10x+3×8 =114
10x +24 =114
10x = 90
x = 90/10
x = $9
Hence, the price of one adult ticket is $9 and the price of child ticket is $8
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The volume, V, of a cube with edge length s cm is given by the equation V=s3.Is the volume of a cube with edge length s=3 greater or less than the volume of a sphere with radius 3?If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere?Compare the outputs of the two volume functions when the inputs are 2?
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We have that the volume of sphere is
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot r^3 \\ \end{gathered}[/tex]and the volume of a cube is
[tex]V_c=s^3[/tex]so if s=r=3. The volume of the sphere is greater.
If they have the same volume, we get that
[tex]\begin{gathered} \frac{4}{3}\pi\cdot r^3=125\rightarrow \\ r^3=\frac{3}{4\cdot\pi}\cdot125\approx29.84\approx30 \\ r=\sqrt[3]{30}\approx3.10 \end{gathered}[/tex]when s=r=2 we have that
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot8=\frac{32}{3}\pi \\ V_c=8 \end{gathered}[/tex]so the volume of the sphere is greater
Solve fort 30 on t =(Type (Type an integer or a simplified fraction)
Answers
Multiply both sides by t:
[tex]\frac{12t}{10}=30[/tex]Multiply both sides by 10:
[tex]12t=300[/tex]Divide both sides by 12:
[tex]\begin{gathered} t=\frac{300}{12} \\ t=25 \end{gathered}[/tex]Yon buys tickets to a concert for himself and a friend. There is a tax of 6% on the price of the tickets andan additional booking fee of $20 for the transaction. Enter an algebraic expression to represent the priceper person. Simplify the expression if possible. Use variablet for the price of the 2 tickets in dollars.The algebraic expression is
Answers
Let the price of each ticket be represented by
[tex]=x[/tex]The price of two tickets will be
[tex]t=2x[/tex]The tax on the price of the tickets is 6% which be represented as
[tex]\begin{gathered} =\frac{6}{100}\times t \\ =\frac{6t}{100}=0.06t \end{gathered}[/tex]The price of the two tickets after tax will be
[tex]\begin{gathered} the\text{price of the two tickets+the tax on the two tickets} \\ =t+0.06t \\ =1.06t \end{gathered}[/tex]Therefore,
The price of the tickets after adding an additional booking fee of $20 will be given below as
[tex]=1.06t+20[/tex]Since,
We were asked to get the algebraic expression person, we would therefore divide the above expression by 2
[tex]\begin{gathered} =\frac{1.06t+20}{2}=\frac{1.06t}{2}+\frac{20}{2} \\ =0.53t+10 \end{gathered}[/tex]Hence,
The algebraic expression to represent the price per person using variable t is
=0.53t + 10
Please help me this is so confusing .which of the following, names a ray in the drawing?
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From the given figure, let's select the rays given in the option.
A ray can be said to be a straight line which starts from a point and goes to infinity at the other end.
From the given figure, the rays are:
• NK
,• NJ
,• NL
,• NM
Therefore, from the list the, the ray is NK.
ANSWER:
NK
Martin and Isabelle go bowling. Each game costs $10, and they split that cost. Martin has his own bowling shoes, but Isabelle pays $3 to rent shoes.Which graph shows a proportional relationship? Explain why.
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We have the following:
Martin's graph is good and correct, although it is not totally straight, but the relationship that it keeps is totally proportional.
On the other hand, Isabelle's graph, although it is totally straight, is wrong, because she must start from 3, which is the rental value of the shoes, and her graph starts at 0, therefore it is wrong, despite of which shows a proportional relationship.
Therefore the correct answer is Martin's graph.
Answer:
Step-by-step explanation:
Cylinder A has radius r, height h, and a volume of 10 pi cubic units. Cylinder B hastwice the radius and twice the height.hATBWhat is the volume of cylinder B?I2r2h
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Volume of a cylinder:
[tex]V=h*r^2*\pi[/tex]For cylinder A:
[tex]10\pi cm^3=h*r^2*\pi[/tex]For cylinder B:
[tex]V_B=2h*(2r)^2*\pi[/tex]Simplify the equation for volumen of cylinder B:
[tex]\begin{gathered} V_B=2h*4r^2*\pi \\ V_B=8*(h*r^2*\pi) \end{gathered}[/tex]in the equation for the volume of cylinder A you have the value of h*r^2*π:
[tex]\begin{gathered} V_B=8*(10\pi cm^3) \\ V_B=80\pi cm^3 \end{gathered}[/tex]Then, the volume of cylinder B is 80π cubic centimeters.Identity two angles that are marked congruent to each other on the diagram below.(Diagram is not to scale.)Mthth& congruent toSub Arwwer
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Congruency in this context is a term that describes a pair of angles as being identical.
In our shape, we have a parallelogram and
Grade 12 math can you please explain each step, what are you doing, why and the final result that contributes to the sketch.
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ANSWER and EXPLANATION
We want to sketch the graph of the given function:
[tex]y=\frac{2x^2-7x+5}{2x-1}[/tex]First, we have to check for the asymptotes of the function.
To find the vertical asymptote, we have to equate the denominator to 0 and solve for x:
[tex]\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}[/tex]That is the vertical asymptote.
To find the horizontal asymptote, we have to check the degrees of the numerator and denominator. Since the degree of the numerator is greater than the denominator's, there is no horizontal asymptote.
To find the slant asymptote, divide the numerator by the denominator and identify the quotient:
This implies that the slant asymptote is:
[tex]y=x-3[/tex]The asymptotes will provide the boundaries for the graph of the function as follows:
Now, we have to find some coordinate points that satisfy the function.
Let us solve for y for values of x = -2, -1, 0, 1, 2, 3:
[tex]\begin{gathered} \Rightarrow x=-2 \\ y=\frac{2(-2)^2-7(-2)+5}{2(-2)-1}=-5.4 \\ \Rightarrow x=-1 \\ y=\frac{2(-1)^2-7(-1)+5}{2(-1)-1}=-4.67 \\ \Rightarrow x=0 \\ y=\frac{2(0)^2-7(0)+5}{2(0)-1}=-5 \\ \Rightarrow x=1 \\ y=\frac{2(1)^2-7(1)+5}{2(1)-1}=0 \\ \Rightarrow x=2 \\ y=\frac{2(2)^2-7(2)+5}{2(2)-1}=-0.33 \\ \Rightarrow x=3 \\ y=\frac{2(3)^2-7(3)+5}{2(3)-1}=0.4 \end{gathered}[/tex]We also have to identify the x and y intercepts of the function.
For the x-intercept, solve for x when y = 0:
[tex]\begin{gathered} 0=\frac{2x^2-7x+5}{2x-1} \\ \Rightarrow2x^2-7x+5=0 \\ 2x^2-2x-5x+5=0 \\ 2x(x-1)-5(x-1)=0 \\ (2x-5)(x-1)=0 \\ x=\frac{5}{2};x=1 \end{gathered}[/tex]For the y-intercept, solve for y when x = 0:
[tex]\begin{gathered} y=\frac{2(0)^2-7(0)+5}{2(0)-1} \\ y=\frac{5}{-1} \\ y=-5 \end{gathered}[/tex]Let us draw the table of values:
Now, we can use the calculated points, the intercepts, and the asymptotes to sketch the graph of the function:
That is the sketch of the function.
Write a quadratic equation in standard form with the given roots. a. Write a quadratic equation with a double root of -5.
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a quadratic function has any root when replacing that number the equation is equal to zero
so
[tex](x+5)(x+5)[/tex]now solve the multiplication
[tex]\begin{gathered} (x\times x)+(x\times5)+(5\times x)+(5\times5) \\ x^2+5x+5x+25 \\ x^2+10x+25 \end{gathered}[/tex]What is the measure of the angle at the bottom of home plate?
Answers
We will ave the following:
*First: We will determine the sum of all internal angles of the polygon:
[tex](n-2)\cdot180\Rightarrow(5-2)\cdot180=3\cdot180[/tex][tex]=540[/tex]*Second: Now, that we know that the sum of all internal angles will be 540°, the following is true:
[tex]90+90+135+135+\alpha=540[/tex]Now, we solve for alpha [The angle]:
[tex]\Rightarrow\alpha=540-135-135-90-90\Rightarrow\alpha=90[/tex]So, the measure of the angle at the bottom is 90°.
What is the slope of this horizontal line from 10-13 minutes?
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We are asked to determien the slope of the line between 10 and 13 minutes. Since this is a horizontal line, it's slope is 0.
i need these answered , i am very confused The options for them are:constant rational square root exponential growth cube root linear absolute value cubic logarithmic quadratic
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Based on the question and the options provided, we have that:
[tex]7)\text{ The name of the parent function for g(x) = 3}\sqrt[]{x}\text{ is a square root}[/tex][tex]8)\text{ The name of the parent function for f(x) =}2^{x^{}}+5\text{ is exponential growth}[/tex][tex]9)\text{ The name of the parent function for f(x)=}\frac{5}{4}\sqrt[3]{x}\text{ is cube root}[/tex][tex]10)\text{ The name of the parent function for h(x) =}8x\text{ is linear}[/tex][tex]11)\text{ An example of an absolute value equation is: y = }\lvert x+5\rvert-3[/tex]Drew has a video game with five differentchallenges. He sets the timer to play his gamefor 10.75 minutes. He spends the same amountof time playing each challenge. How long doesDrew nlay the fifth challenge?
Answers
For each game, Drew spends 10.75 minutes, this means in total Drew spends
[tex]5\cdot10.75\text{ minutes}[/tex]this product gives
[tex]5\cdot10.75=53.75\text{ minutes}[/tex]then, in the fifth challenge Drew spends 53.75 minutes
3. Carlos Quintero, Treasurer of X Corp is analyzing an investment on two projects, C and D. The data to
consider are shown below
Initial Investment
Annual Rate of
Return
Pessimistic
Most Likely
Optimistic
Amount
$135,000
39%
27%
25%
Project C
Probability
.30
.45
.25
Amount
$145,000
25%
15%
30%
Project D
Probability
.35
.40
.25
A. Determine the rates of return for each of the two projects. (6 points)
Answers
The rates of return for each of the two projects for X Corp are as follows:
Project C = 30.1%Project D = 19.75%.What is the rate of return?The rate of return refers to the percentage gain or loss over the initial cost of the investment.
For this purpose, the rate of return is expressed as the percentage of the expected returns (which is a product based on the probability of different scenarios) over the initial investment cost.
Project C Project D
Amount Probability Amount Probability
Initial Investment $135,000 $145,000
Annual Rate of Return
Pessimistic 39% .30 25% .35
Most Likely 27% .45 15% .40
Optimistic 25% .25 30% .25
Returns from Project C:Pessimistic $15,795 ($135,000 x 39% x 30%)
Most likely $16,402.50 ($135,000 x 27% x 45%)
Optimistic $8,437.50 ($135,000 x 25% x 25%)
Total expected returns = $40,635
Rate of return = 30.1% ($40,635/$135,000 x 100)
Returns from Project D:Pessimistic $9,062.50 ($145,000 x 25% x 35%)
Most Likely $8,700 ($145,000 x 15% x 40%)
Optimistic $10,875 ($145,000 x 30% x 25%)
Total expected returns = $28,637.50
Rate of return = 19.75% ($28,637.50/$145,000 x 100)
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O GRAPHS AND FUNCTIONSWriting an equation for a function after a vertical and horizo
Answers
Given:
The point (0,0) lies on the graph f(x) and (4,-3) lies on the graph h(x).
To find:
We need to find the equation for the function h(x).
Explanation:
Consider the translation point which is translated horizontally a unit and vertically as b units.
[tex](x^{\prime},y^{\prime})\rightarrow(x+a,y+b)[/tex]The point (4,-3) can be written as follows.
[tex](4,-3)\rightarrow(0+4,0-3)[/tex]We get the function h(x) after f(x) translated horizontally 4 units right and vertically 3 units down.
The function can be written as follows.
[tex]h(x)=f(x-4)-3[/tex][tex]\text{Replace x=x-4 in f(x)=}\sqrt[]{x\text{ }}\text{ and substitute in the equation.}[/tex][tex]h(x)=\sqrt[]{x-4}-3[/tex]Final answer:
[tex]h(x)=\sqrt[]{x-4}-3[/tex]1: 9 11. The cost for a group of people to go to the movies is given by the expression 9a + 5b, where a is the number of adults and b is the number of children. What are the variables of this expression? of of A. 9 and 5 B. a and b C. 9a and 5b D. + and x
Answers
the variables are
a and bwhere
a -----> is the number of adults
b-------> is the number of children.
answer is option B
The Muffin Shop makes no-fat blueberry muffins that cost $.70 each. The Muffin Shop knows that 15% of the muffins will spoil. If The Muffin Shop wants 40% markup on cost and produces 800 muffins, what should The Muffin Shop price each muffin?
Answers
If The Muffin Shop wants a 40% markup on cost and produces 800 muffins, The Muffin Shop should price each muffin at $1.15.
How is the price determined?The total expected revenue is divided by the total unspoiled units sold to determine the selling price.
This is illustrated below.
Cost per unit of muffins = $0.70
The spoilage rate = 15%
Expected markup on cost = 40%
The total production units = 800 muffins
The total good units sold = 680 (800 x 1 - 15%)
Total cost for 800 units = $560 (0.70 x 800)
The markup on cost = $224 ($560 x 40%)
The total expected sales revenue = $784 ($560 + $224)
Seling price per unit = $1.15 ($784/680)
Thus, The Muffin Shop should price each muffin at $1.15 to meet its goals.
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15 = a/3 - 2
what is a?
Answers
Answer: a is 51
Step-by-step explanation:
Hope this help.
Answer:
a==51
Step-by-step explanation:
15=a/3-2
a/3-2+2=15+2
a/3=17
a=17*3
a=51
debbie and tom's bill for dinner was $58. They left a tip of $8.70. what percent of the bill was the tip?
Answers
The value of the bill was $58. The tip was $8.7. Percentage is expressed in terms of 100. To determine the percentage of the bill that was the tip, we would find the ratio of the tip to the bill and multiply by 100. It becomes
8.7/58 * 100
= 15%
The tip was 15% of the bill
Simplify (5x + 7) - (x + 2)
Answers
You have the following expression:
(5x + 7) - (x + 2)
in order to simplify the previous expression, eliminate parenthesis and take into account that if a parenthesis is preceeded by a minus sign, when you elminate th eparenthesis the sign inside change to the opposite, just as follow:
(5x + 7) - (x + 2) =
5x + 7 - x - 2 =
5x - x + 7 - 2 =
4x + 5
Hence, the simplified expression is 4x + 5
Solve 6 < x + 5 < 11
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we have the following:
[tex]\begin{gathered} 6Find fractional notation of 87.5%
Answers
To find the fractional notation, we have to transform 87.5% into a fraction. To do that, we just have to divide the percentage by 100.
[tex]\frac{87.5}{100}[/tex]Then, we multiply each part by 10.
[tex]\frac{87.5\times10}{100\times10}=\frac{875}{1000}[/tex]At last, we simplify the fraction by 125 to get 7/8.
[tex]\begin{gathered} \frac{875}{125}=7 \\ \frac{1000}{125}=8 \end{gathered}[/tex]Hence, the given percent, in fractional notation, is 7/8.A square room has a floor area of 49 square meters. The height of the room is 8 meters. What is the total area of all four walls?
Answers
The total area of all four walls is 224 square meters.
According to the question,
We have the following information:
A square room has a floor area of 49 square meters.
So, we have:
Area of square = 49 square meters
Side*side = 49
Side = [tex]\sqrt{49}[/tex] m
Side of the square = 7 m
Now, the side of the floor will be the width of the wall.
So, we have the width of the wall = 7 m.
The height of the room is 8 meters.
It means that the height of the wall is 8 m.
Area of 1 rectangular wall = length*width
Area of wall = 8*7
Area of 1 wall = 56 square meters
Now, the are of 4 walls will be (4*56) square meters or 224 square meters.
Hence, the total are of all four walls is 224 square meters.
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