A bag contains 4 blue and 6 white tokens. Two tokens are drawn from the bag one after another, without replacement. Find the probability that: the first is blue and the second is white.
Answers
Concept; Probability
Step1: The total number of tokens is
[tex]6\text{white +4 Blue}=\text{ 10 tokens}[/tex]let the probability of blue be P(B) and the probability of red be P(R)
The probability that the first is Blue is
[tex]\begin{gathered} P(B)=\frac{number\text{ of blue }}{total\text{ number of tokens}}=\frac{4}{10}=\frac{2}{5} \\ \end{gathered}[/tex]The probability the second is white without replacement is
[tex]P(R)=\frac{number\text{ of white}}{total\text{ token}}=\frac{6}{9}=\frac{2}{3}[/tex]Hence the combined probability of Blue and Red is
[tex]P(BR)=\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}[/tex]Therefore the probability that the first is blue and the second is white is 4/15
Related Questions
a person had $14,000 infested in two accounts, one paying 9% simple interest and one paying 10% simple interest. how much was invested in each account if the interest at the one year is $1339?
Answers
Given:
a.) A person had 14,000 infested in two accounts.
b.) One paying 9% simple interest.
c.) One paying 10% simple interest.
Let,
x = the amount invested at 9% simple interest
y = the amount invested at 10% simple interest
1.) We know the total amount of money invested is $14,000. We get,
x + y = 14,000
2.) We know that the total interest for the year for the two accounts is $1432. We get,
0.09*x + 0.1*y = 1,339
Let's equate the two equations,
x = 14,000 - y (Substitute for x)
0.09*(14,000 - y) + 0.1*y = 1,339
1,260 - 0.09y + 0.1y = 1,339
0.1y - 0.09y = 1,339 - 1,260
0.01y = 79
0.01y/0.01 = 79/0.01
y = 7,900
Therefore, $7,900 was invested at the rate of 10% simple interest.
Let's determine x, substituting y = 7,900 in x + y = 14,000.
x + y = 14,000
x + 7,900 = 14,000
x = 14,000 - 7,900
x = 6,100
Therefore, $6,100 was invested at the rate of 9% simple interest.
Ken charges his neighbors $17.00 to wash their car. How many cars must he wash next summer if his goal is to earn at least$1800?
Answers
Let x be the minimum number of cars Ken has to wash to reach his goal, then we can set the following linear equation:
[tex]17x=1800.[/tex]Solving the above equation for x, we get:
[tex]x=\frac{1800}{17}.[/tex]Rounding up to the nearest whole number we get:
[tex]x\approx106.[/tex]Answer: [tex]106.[/tex]Help please this is due later on.
Answers
Answer:
[tex] \csc(θ) = \frac{1}{ \sin(θ) } [/tex]
Help please I will give brainliest
Answers
The unknown angle in the triangle is as follows;
∠H = 38 degrees.How to find angles in a triangle?The angle H can be found using the exterior angle theorem.
The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In other words, an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Hence,
∠DFG = ∠G + ∠H
∠DFG = 14x + 1
∠G = 89°
∠H = 5x - 7
14x + 1 = 89 + 5x - 7
14x + 1 = 89 - 7 + 5x
14x - 5x = 89 - 7 - 1
9x = 81
divide both sides by 9
x = 81 / 9
x = 9
Therefore,
∠H = 5(9) - 7 = 45 - 7 = 38 degrees.
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100 POINTS Which statement about this figure is true?
It has no rotational symmetry.
It has rotational symmetry with an angle of rotation of 90°.
It has reflectional symmetry with four lines of symmetry.
It has point symmetry
before you answer, just know it does have rotational symmetry, just not 90° so A and B are out. i'm just stumped about C and D
Answers
Answer:
It has reflectional symmetry with four lines of symmetry.
Step-by-step explanation:
======================================================
Explanation:
Choice A is false since it does have rotational symmetry. See choice B.
Choice B is close, but the "90 degrees" needs to be "45 degrees". Each 45 degree rotation of the figure has the "before" and "after" be the same.
Choice C is one of the answers. There's a vertical line of symmetry, and a horizontal one as well. Then there are two diagonal lines of symmetry. Each goes through the center. A line of symmetry is a mirror line to allow us to reflect one half over this line to get the other half.
Choice D is another answer. It has point symmetry since we can pick any point on the figure and reflect it over the center point, to land on a corresponding image point on the opposite side of the figure. For example, the northern most point reflects over the center to land on the southern most point.
In the triangle below, suppose that mV = (x - 2)",mW = (x - 2)°, and m ZX=(4x+4)*Find the degree measure of each angle in the triangle.(x - 2)(4x + 4)m ZV =Х5?m ZW =001Xm 2x =(x - 2)°
Answers
SOLUTION
Consider the image given below.
From the image above,
[tex]\begin{gathered} \angle V=(x-2)^0 \\ \angle W=(x-2)^0 \\ \angle X=(4x+4)^0 \end{gathered}[/tex]To find the measures of each angle, we need to obtain the value of small x in the diagram.
Applying the rule: Sum of angle in a triangle is 180 degrees
[tex]\angle V+\angle W+\angle X=180^0[/tex]Then substitute the given expression, we have
[tex]\begin{gathered} (x-2)^0+(x-2)^0+(4x+4)^0=180^0 \\ Then \\ x-2+x-2+4x+4=180^0 \end{gathered}[/tex]Collect like terms and add
[tex]\begin{gathered} x+x+4x-2-2+4=180^0 \\ 6x-4+4=180^0 \\ \text{then} \\ 6x=180 \end{gathered}[/tex]Divide both sides by 6, we have
[tex]\begin{gathered} \frac{6x}{6}=\frac{180}{6} \\ hence \\ x=30 \end{gathered}[/tex]hence, x=30
Then substitute the value of x to obtain the measure of each angles.
[tex]\begin{gathered} \angle V=(x-2)^0 \\ \text{Then x=30} \\ \angle V=30-2=28^0 \end{gathered}[/tex]Since the triangle is an issoceles triangle, then
[tex]\angle W=28^0[/tex]Hence
[tex]\begin{gathered} \angle X=(4x+4)^0 \\ \angle X=(4\times30+4)^0=(120+4)=124^0 \\ \text{hence} \\ \angle X=124^0 \end{gathered}[/tex]Therefore
Answer : ∠V= 28°, ∠W=28°, ∠X=124°
For the cented functions g(x) = x + 3 and h(x) = (x-4, find the composition gºh and specify its domain using interval notation,
Answers
Answer
Part A
(g o h)(x) = x - 1
Part B
Domain of (g o h) = (-∞, ∞)
Explanation
Part A
We are given that
g(x) = x² + 3
h(x) = √(x - 4)
We are then asked to find (g o h)(x)
To do that, we need to note that (g o h)(x) means we write g(x), but instead of x, we write h(x). That is,
(g o h)(x)
= g(h(x))
= [h(x)]² + 3
= [√(x - 4)]² + 3
= x - 4 + 3
= x - 1
Part B
To find the domain
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists.
And for (g o h)(x) = x - 1, we know there will be an answer for all real number values of x. Hence,
Domain = (-∞, ∞)
Hope this Helps!!!
Given the frequency table, what percentage of the students that like rap are also in grades 9–10? Round to the nearest whole percent.
A. 16%
B. 38%
C. 40%
Answers
The percentage of students that like rap that are also in grades 9–10 = 32%.
What is a frequency table?A frequency table is the type of table that shows the number of occurrence of different types of variables of an experiment.
From the frequency table given;
In grade 9 - 10;
Rap students = 40 students
Rock students = 30 students
Country students = 55 students
The total students in grade 9 - 10 = 125
Therefore, the percentage of rap students in grade 9 - 10;
= 40/125×100/1
= 4000/125
= 32%
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The domain of the given function is ____ (use integers of fractions for any numbers in the expression.)f(z) = 5z²- 6z+2 —————- 6z² +5
Answers
Given:
[tex]f(z)=\frac{5z^2-6z+2}{6z^2+5}[/tex]Required:
To find the domain of the given function.
Explanation:
Now consider
[tex][/tex]Por C?AnswerExample0 How many ways can 4 candy bars be chosenfrom a store that sells 30 candy bars?С27,4052 How many ways can 13 students line up for lunch?113 How many ways can you make a 3-letterarrangements out of the letters in the wordTRAPEZOID.4 How many ways can you choose 2 books from ashelf of 40 books-5 How many ways can 12 swimmers finish in first,second, and third place?.L11---How many ways can Mrs. Sullivan choose twostudents from 27 to help put away calculators atthe end of class?----1-111
Answers
1) How many ways can 4 candy bars be chosen from a store that sells 30 candy bars?
In this case we can combine 30 types of candy bars in a set of 4 bars.
This can be calculated as a combination of 30 in 4 with no repetition:
[tex]\begin{gathered} C(n,r)=\frac{n!}{(n-r)!r!} \\ C(30,4)=\frac{30!}{(30-4)!4!}=\frac{30!}{26!4!}=\frac{30\cdot29\cdot28\cdot27}{4\cdot3\cdot2\cdot1}=\frac{657720}{24}=27405 \end{gathered}[/tex]Answer: 27,405 possible combinations (C).
2) How many ways can 13 students line up for lunch?
In this case we have a permutation of 13 in 13 with no repetition.
We can calculate this as:
[tex]\begin{gathered} P(n,r)=\frac{n!}{(n-r)!} \\ P(13,13)=\frac{13!}{(13-13)!}=\frac{13!}{1}=6227020800 \end{gathered}[/tex]Answer: 6,227,020,85)00 possible permutations (P).
3) How many ways can you make a 3-letter arrangements out of the letters in the word TRAPEZOID.
In the word we have 9 letters with no repetition, so we have to calculate a permutation (as order matters) of 9 letters in 3 places.
We can calculate this as:
[tex]P(9,3)=\frac{9!}{(9-3)!}=\frac{9!}{6!}=9\cdot8\cdot7=504[/tex]Answer: 504 possible permutations (P).
4) How many ways can you choose 2 books from a shelf of 40 books.
In this case, the order does not matter, so it is a combination of 40 in 2.
This can be calculated as:
[tex]C(40,2)=\frac{40!}{(40-2)!2!}=\frac{40!}{38!2!}=\frac{40\cdot39}{2\cdot1}=\frac{1560}{2}=780[/tex]Answer: 780 possible combinations (C)
5) How many ways can 12 swimmers finish in first, second, and third place?
In this case, the order does matter, so we have a permutation of 12 in 3:
[tex]P(12,3)=\frac{12!}{(12-3)!}=\frac{12!}{9!}=12\cdot11\cdot10=1320[/tex]Answer: 1320 permutations (P)
6) How many ways can Mrs. Sullivan choose two students from 27 to help put away calculators at the end of class?
The order does not matter between the two students, so it is a combination of 27 in 2:
[tex]C(40,2)=\frac{27!}{25!2!}=\frac{27\cdot26}{2\cdot1}=351[/tex]Answer: 351 combinations (C)
Which is not a statistical question? * 1 point how much did the corn plants grow last week? what is the height of the tallest corn plant? how much water did the corn plants get each day last month? how tall are the corn plants?
Answers
The option that is not a statistical question is D. how tall are the corn plants?
What is a statistical question?A statistical question is one that may be answered by gathering data and for which the data will vary. Questions answered with a single data point are not statistical questions since the data utilized to answer the question is not variable.
A statistical question is one that can be answered by gathering varying amounts of data. A statistical inquiry is one that yields varying responses and outcomes (data). It must be collected on more than one person and there must be room for the facts to vary.
Therefore, based on the information illustrated, the correct option is D. It was too general and not specific
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How do I find the slope and Y-intercept of the line x+2y=-2
Answers
slope = -1/2
y-intercept = (0, -1)
Explanation:Given:
[tex]x\text{ + 2y = - 2}[/tex]To find:
the slope and the y-intercept
To determine the slope we will use the linear function formula:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex]We need to rewrite the given equation in the form above so as to get the slope
[tex]\begin{gathered} x\text{ + 2y = -2} \\ 2y\text{ = -x - 2} \\ y\text{ = -}\frac{x}{2}\text{ - }\frac{2}{2} \\ y\text{ = }\frac{-x}{2}-1 \end{gathered}[/tex]From the above, m = -1/2
Hence, the slope is -1/2
The y-intercept is the value of y when x = 0
To get the y-intercept, we will substitute x with 0:
[tex]\begin{gathered} y\text{ = }\frac{-0}{2}\text{ - 1} \\ y\text{ = 0 - 1} \\ y\text{ = -1} \\ \\ The\text{ y-intercept in ordered pair \lparen x, y\rparen:} \\ when\text{ x = 0, y = -1} \\ y-\text{ intercept = \lparen0, -1\rparen} \end{gathered}[/tex]explain the ideas (natrual rights,role of the government) and the complaints set forth in the declaration of independence
Answers
Answer:
1. Fact that all individuals are created equal and are endowed by their creator with certain unalienable rights is a clear statement in the Declaration of Independence.
2. Aim of having a government is to safeguard these rights, the people have the right and the duty to alter, abolish, or over through that government.
3. The Decoration of Independence lists the grievances that the government has failed to resolve and reconcile with the colonies.
4. The decree was made to become an autonomous nation and the motives for asserting independence are listed in the grievances.
Is this function continuous or discrete? How far can you get on 20 gallons? What is the domain and range of this function? How many gallons to get 500 miles? Where do the labels on the graph go?
Answers
EXPLANATION
The equation of the function can be represented as shown as follows:
[tex]G(m)=12m[/tex]-This function is discrete.
-If we have 20 gallons, we can obtain the number of miles by plugging in the value into the equation, as shown as follows:
[tex]20=12m[/tex]Dividing both sides by 12:
[tex]\frac{20}{12}=m[/tex]Simplifying:
[tex]\frac{5}{3}=m[/tex]We can make 1.67 miles with 20 gallons.
-The domain of the function are all the Real Numbers and the Range are also the Real numbers.
-Finally, drawing the graph of the function:
The points of the table are the following:
Gallons Miles
2 24
4 48
6 72
8 96
-We can get the number of gallons needed to, make 500 miles by plugging the value 500 into the equation, as shown as follows:
[tex]500=12m[/tex]Isolating m:
[tex]\frac{500}{12}=m[/tex]Simplifying:
[tex]41.7=m[/tex]The number of gallons to make 500 miles is equal to 41.7 gallons
Finally, labeling the graph:
in recent years the state of alaska issued license plates consisting of 7 characters. the first three characters are the letters of the alphabet excluding i, o, and x. the last four characters are the numeral digits. how many different license plates can be issued using this configuration (with repetition)?
Answers
121670000 different license plates are possible.
A license plate consists of 7 characters.
The first 4 characters are numerals from 0 to 9.
each character can be in 10 ways
so possible ways = 10 * 10 * 10 * 10 = 10000
The last 3 characters are letters excluding I, O, and X.
Each character can be in 26 - 3 = 23 Ways
Possible ways = 23 *23 * 23 = 12167
Number of possible different license plates = 10000 * 12167
= 121670000
What is car registration ?
Motor vehicle registration is the registration of a motor vehicle with a public authority, whether compulsory or otherwise. The purpose of registering a motor vehicle is to establish a link between the vehicle and the owner or user of the vehicle. This link may be used for taxation or criminal investigations.
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Fernando has been saving money to buy an e–book reader. A store has just marked
down the price of its readers by 40%. Each reader comes with a mail-in rebate for
$25.
If the reader used to cost $150, what will Fernando's final price be after the markdown
and rebate?
Complete each step to solve the problem.
1. How much money will Fernando save because of the 40% markdown? Show your
work.
2. The total amount off includes the markdown and rebate. What is the total amount
off?
3. What will the final price of the reader be? Show your work.
Answers
Answer: 65$
Step-by-step explanation:
1. 40% of 150 is 60 so 60$ off of 150 is 90
2. total amount off is 85$. 60 is the 40% off and additional 25 for the rebate
3. final price will be 65$. 90-25=65
A local movie theater sells tickets at different prices for an adult and for a child. The price of an adult’s ticket is $10.50 and the price of a child’s ticket is $6.50 . If the theater sells a total of 65 tickets for a total price of $594.50 in an afternoon, how many child tickets did the theater sell?
Answers
Answer:
6.50 × 65 tickets.
Answer = $422.5
The theater sells 43 adult tickets and 22 child tickets.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let us assume,
The number of adult tickets sold is x
The number of tickets sold for children is y
Since the total number of tickets sold is 65,
x + y = 65 .....(i)
Charge per adult ticket=$10.50,
So the amount collected by selling adult tickets is 10.50×x
Charge per child ticket=$6.50,
So the amount collected by selling tickets for children is 6.50×y
We know that the total amount earned by the theater is $594.50
So, 10.5x +6.5y = 594.50 ......(ii)
After solving equations (i) and (ii), we get the values of x and y as
x = 43 and y = 22
Therefore, the theater sells 43 adult tickets and 22 child tickets.
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A number is selected randomly from a container containing all the integers from 10 to 50. Find P(Prime|between 11 and 30).A. 7/10B. 1/2C. 1D. 3/10
Answers
Given:
Numbers in the container: All integers from 10 to 50
Let's find P(Prime numbers| numbers between 11 and 30).
Here, we are to find the conditional probability.
Apply the formula:
P(Prime|between 11 and 30) = P(prime numbers and between 11 and 30) ÷ P(numbers between 11 and 30).
Where:
• Prime numbers between 11 and 30 = 11 , 13 , 17 , 19 , 23 , 29 =6 numbers
,• Intergers from 10 to 50 = 41 integers.
To find the probability, we have:
[tex]\begin{gathered} P(Prime|between11and30)=\frac{\frac{6}{41}}{\frac{20}{41}} \\ \\ =\frac{6}{41}\ast\frac{41}{20} \\ \\ =\frac{6}{20} \\ \\ =\frac{3}{10} \end{gathered}[/tex]Therefore, we have:
P(Prime|between 11 and 30) = 3/10.
ANSWER:
D. 3/10
What is the first step in evaluating the expression shown below? (12.9-3.1) x 6.2-2 + 43 00:00 Multiply 3.1 and 6.2. 00:00 Add 2 and 43 Subtract 3.1 from 12.9. Subtract 2 from 6.2.
Answers
We have to indicate the steps to follow in order to evaluate:
(12.9-3.1) x 6.2-2 + 43
So FIRST: we solve for the operation indicated inside the parenthesis
12.9 - 3.1 = 9.8 (we subtract 3.1 from 12.9)
This is the answer you need to select.
im not sure ols help
Answers
Answer: √141
Step-by-step explanation:
a^2=c^2-b^2
The hypotenuse is larger in this question so we subtract them.
25^2-22^2=625-484=141
√141
Answer:
x = √141
or
x = 11.87
Step-by-step explanation:
is a right triangle, we solve it with the Pythagorean theorem ("In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides".)
x² = 25² - 22²
x² = 625 - 484
x² = 141
x = √141
or
x = 11.87
Point Pis on line segment OQ.Given OQ = 4s – 10, OP = 23, and PQ = I,determine the numerical length of OP.
Answers
P
OQ = 4S - 10
OP = 23
PQ = 1
Equation
OQ = OP + PQ
Substitution
4S - 10 = 23 - 1
Simplification
4S = 22 + 10
4S = 32
S = 32/4
S = 8
Determine OP
OQ = 4(8) - 10
OQ = 32 - 10
OQ = 22
a street light is at the top of a ft. tall pole. a man ft tall walks away from the pole with a speed of feet/sec along a straight path. how fast is the tip of his shadow moving when he is feet from the pole?
Answers
[tex]\frac{dx}{dy} = \frac{5}{3}. 4\frac{ft}{s} = \frac{20}{3}\frac{ft}{s}[/tex] is moving at the speed of the shadow
x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. I assume the man and pole are standing straight up, which means the two cases are similar.
[tex]\frac{y-x}{y} = \frac{6}{15}[/tex]
15(y-x) = 6y
9y = 15x
[tex]\frac{5}{3}x\\[/tex] = y
differentiate both sides with respect to t or time.
[tex]\frac{dx}d{y} = \frac{5}{3}\frac{dx}{dt}[/tex]
you know [tex]\frac{dx}{dy} = 4\frac{ft}{s}[/tex] because the man is walking that speed away from the pole. you want to find [tex]\frac{dx}{dy}[/tex] , how fast the tip of the shadow is moving.
that means
[tex]\frac{dx}{dy} = \frac{5}{3}. 4\frac{ft}{s} = \frac{20}{3}\frac{ft}{s}[/tex]
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A hot air balloon is cruising at an altitude of 150 meters above the ground when it begins its descent. The balloon descends at a rate of 5.5 meters per minute. Write an equation to model when the balloon will reach an altitude of 95 meters above the ground. Use n to represent the unknown
Answers
150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that,
A hot air balloon is cruising at an altitude of 150 meters above the ground when it begins its descent.
The balloon descends at a rate of 5.5 meters per minute.
We need to write an equation to model when the balloon will reach an altitude of 95 meters above the ground.
The equation is 150 - 5.5n= 95
Hence 150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.
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A cylindrical drinking glass has radius 3 cm and height 8 cm. (i) Calculate the volume of water the glass holds when it is filled to the top.Give the units of your answer. Answer(a)(i); Water is poured into a number of these glasses from a jug containing 1.5 litres Each glass has a horizontal line 2 cm from the top. Calculate how many of these glasses can be filled up to the line from the jug
Answers
The volume of the glass is 454.16cm² and the number of glasses filled upto a horizontal line of 2 cm from top is 4
A cylindrical drinking glass has radius 3 cm and height 8 cm.
The volume of a cylinder is 2πr²h
= 2 (3.14) 3² x 8
= 452.16cm³
The jug contains 1.5 litres of water
1 litre = 1000cm³
1.5 litre = 1500cm³
The volume of glass if it is filled upto a horizontal line 2 cm from the top.
volume = 2πr²h
= 2 (3.14) 3² x 6
= 339.12cm³
Number of glasses filled = 1500/339.12 = 4.42
4 glasses can be filled up to the line from the jug
Therefore, the volume of the glass is 454.16cm² and the number of glasses filled upto a horizontal line of 2 cm from top is 4
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An observation deck extends 200 feet out above a valley. The deck sits 150 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given by h=-16t^2 +150. How long will it take for the object to be 6 feet above the valley floor?
Answers
If equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds
The equation of the height h = -16[tex]t^2[/tex]+150
Where h is the height
t is the time taken
We have to find the time taken for the object to be 6 feet above the valley floor
The height = -150+6
= -144
Substitute the values in the equation
-16[tex]t^2[/tex]+150 = -144
-16[tex]t^2[/tex] = -144-150
-16[tex]t^2[/tex] = -294
[tex]t^{2}[/tex] = 18.375
t = 4.28 seconds
Hence, if equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds
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Alec has a cherry tree in his yard. When he first planted it, the tree was 40 feet tall. Now it is 76 feet tall. What is the percent of increase in the height of the tree?
PLEASE HELP
Answers
Answer:
90%
Step-by-step explanation:
To find the percent of increase in the height of the tree, we need the change of the height and the original height (40 feet)
The change of height = 76 - 40 = 36 feet
Now, we need to divide the change by the original height to find the percent of increase.
36/40 = 9/10
9/10, which is then 90%.
Montraie drove 220 miles in 5 hours. If he continued at the same rate, how long would it take to travel 88 miles?
Answers
The time taken for Montraie to travel a distance of 88 miles is 2 hours.
How long would it take for Montraie to travel 88 miles?Speed is simply referred to as distance traveled per unit time.
It expressed mathematically as;
Speed = Distance ÷ time.
Given the data in the question;
Distance covered = 220 milesTime elapsed = 5 hoursSpeed = ?First, we determine the speed of Montraie.
Speed = Distance ÷ time.
Speed = 220 miles ÷ 5 hours
Speed = 44 miles per hour.
Now, time spent in traveling a distance of 88 miles will be;
Speed = Distance ÷ time
Time = Distance / Speed
Time = 88 miles / 44 miles per hour
Time = 2 hours
Therefore, the elapsed time is 2 hours.
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If Montraie drove 220 miles in 5 hours. If he continued at the same rate, then it takes 2 hours to travel 88 miles.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that,
Montraie drove 220 miles in 5 hours.
We need to find how long it would take to reach 88 miles.
Let us form a equation based on given data.
Let x be the time to reach 88 miles.
We need to find value of x.
220/5=88/x
Apply cross multiplication
220x=440
x=440/220
x=2
Hence it takes 2 hours to travel 88 miles with same rate.
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a collection of nickels, dimes, and quarters consist of 70 coins with a total of $ 8.00 . if there are 2 times as many dimes as quarters, find the number of each type of coins.
Answers
The number of each type of coins are as follows:
q = 15 quarters.
d = 30 dimes.
n = 25 nickels.
How to determine the number of each type of coins?In order to solve this word problem, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let d represent the number of dimes.
Let q represent number of quarters.
Let n represent number of nickels.
Let T represent total number of coins.
Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.
Translating the word problem into an algebraic equation, we have;
Dimes; d = 2q .....equation 1.
Nickels; (70 - (q + 2q)) = (70 - 3q) .....equation 2.
Total coins; T = n + d + q
0.5(70 - 3q) + 2q(0.1) + q(0.25) = 8.00
Multiplying all through by 100, we have:
5(70 - 3q) + 2q(10) + q(25) = 800
350 - 15q + 20q + 25q = 800
350 + 30q = 800
30q = 800 - 350
30q = 450
q = 450/30
q = 15 quarters.
For the number of dimes, we have:
Dimes, d = 2q
Dimes, d = 2(15)
Dimes, d = 30 dimes.
For the number of nickels, we have:
Nickels, n = (70 - 3q)
Nickels, n = (70 - 3(15))
Nickels, n = (70 - 45)
Nickels, n = 25 nickels.
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help, please! ♡ (photo attached)
Answers
The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.
How to simplify a rational equation by algebra properties
In this case we find a rational equation whose numerator and denominator are polynomials, which must be simplified by using algebra properties. The complete procedure is now shown:
(9 · x - 6)² / (2 · x⁴ + 4 - 2 · x⁴ - 1) Given
(81 · x² - 108 · x + 36) / (3) Perfect square binomial / Associative, commutative and modulative properties / Existence of additive inverse /Definition of subtraction
27 · x² - 36 · x + 12 Addition and subtraction of fractions with same denominator / Associative and commutative properties / Definition of division
The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.
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Formula to work out the surface area of half a cylinder
Answers
Formula to work out the Total surface area of half-cylinder = [tex]\pi rh + \pi r^{2} + 2rh[/tex]
To find:
Formula to work out the surface area of half a cylinder
Solution:
The surface area of a semi-cylinder can be calculated by adding half the curved area of the cylinder to the area of the two semi-circles and the area of the rectangular section below. The formula for the surface area of a semi-cylinder is given by: Total surface area of
Total surface area of a half-cylinder = (1/2) × curved area of cylinder + 2 × area of semi-circle + area of base of cylinder.
total surface area of a half-cylinder = [tex]\pi rh+\pi r^{2} +2rh[/tex]
where r = radius of cylinder
[tex]\pi[/tex] = 3.14 or 22.7 cm
h = height of cylinder
(Or) We can find Total surface area of half cylinder as, Total surface area of half cylinder ÷ 2
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