Answer:
16 children attended the play
Step-by-step explanation:
Since one adult brought four children. The cost of their tickets should be:
($4×1) + ($2×1)
= 4+8
= $12
Since the remaining adults brought 2 children each, it means that each of the remaining adults will pay the cost of three tickets (1 for themselves and 2 for their children) which is:
($4×1) + ($2×2) = $4 + $4 = $8.
Since total cost of tickets for adults and children = $60, we will subtract $12 from $60 in order to know the cost of the tickets for the remaining adults and their children.
$60 - $12 = $48
Each of the remaining adults paid $8 as ticket cost for themselves and their kids. If the adults that brought only 2 kids paid a combined $48, then the number of adults that brought 2 kids each
= $48/$8
= 6 adults.
If each of these 6 adults brought 2 kids each, then the number of children that they brought = 2 × 6 = 12
We now add this to the four children of the first adult
12 + 4 = 16
Therefore the number of children that attended the play = 16
The problem is solved by setting up and solving equations, determining that 16 children attended the play.
Explanation:The subject of this problem is setting up and solving equations. The given information can be translated into equations. Four children and one adult make up one group. For this group, the total cost is $4 (for the adult) + $2 * 4 (for the children) = $12. For the remaining adults and children, we know each adult brought 2 children and the cost would be $4 (for the adult) + $2 * 2 (for the children) = $8 per group. We know the total cost was $60. So, subtract the $12 from the first group, which leaves $48. As we know each of the remaining groups cost $8, we divide $48 by $8 to find that there were 6 more groups. Each of these groups consists of 1 adult and 2 children, so there were 6 * 2 = 12 children in these groups. Added to the original 4 children, that makes 16 children in total.
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A bag contains 31 red blocks, 49 green blocks, 24 yellow blocks, and 21 purple blocks. You pick one block from the bag at random. Find the indicated theoretical probability.
P(green or red)
Answer:
16/25 or 0.64 or 64%
Step-by-step explanation:
Please kindly check the attached file for explanation
Answer: The probability of picking a green block or red block is 0.64 (or 64%)
Step-by-step explanation: The total number of blocks can be derived as;
31 (R) + 49(G) + 24(Y) + 21(P) = 125
With 125 blocks in total, there are 125 possibilities and the possibility of picking any of the four colors shall be be determined as a fraction of the entire possible outcomes.
The probability of picking a green ball when picked at random is given as;
P(Green) = Number of required outcomes ÷ Number of all possible outcomes
P(Green) = 49/125
(Note that there are 49 green blocks and a total of 125 blocks of all four colors)
Also the probability of picking a red ball when picked at random is given as;
P(Red) = Number of required outcomes ÷ Number of all possible outcomes
P(Red) = 31/125
The probability of picking a green block or a red block is given as P(green or red)
P(Green or Red) = 49/125 + 31/125
P(Green or Red) = 80/125
P(Green or Red) = 16/25
P(Green or Red) = 0.64
Therefore the probability of picking a green or red block at random is 0.64 or 64%
gnostic Test
25
Taryn is hosting a party at a restaurant. The restaurant is charging her $160 to rent the space and $19 per guest. If Taryn wants to
spend less than $635, which inequality could be used to solve for x, the number of guests Taryn can invite?
A. $19x + $160 < $635
OB. $19x < $160
C. $19x < $635
OD. $19x - $160 < $635
Reset
Submit
Answer:It would be A. $19x + $160 < $635
Step-by-step explanation:
What is the volume of the die?
Answer:
3375
Step-by-step explanation:
Because you need to do length x width x height
Two ducklings wander away from the nest while their mother is away. The first duckling's displacement (distance and direction) from the nest is (12,5) The second duckling's displacement is (13,-8) How much farther did the second duckling wander than the first duckling?
The magnitude of the first duckling's displacement is 13 units, and for the second duckling it is approximately 15.3 units. The second duckling wandered 2.3 units farther than the first.
Explanation:The student is asking about the displacements of two ducklings from their nest and how much farther one wandered than the other. To compare the displacements of the two ducklings, we calculate the magnitudes of their displacements using the Pythagorean theorem.
For the first duckling's displacement, with coordinates (12,5), the magnitude is
sqrt(122 + 52) = sqrt(144 + 25) = sqrt(169) = 13 units.
For the second duckling's displacement, with coordinates (13,-8), the magnitude is
sqrt(132 + (-8)2) = sqrt(169 + 64) = sqrt(233) = approximately 15.3 units.
The second duckling wandered farther by the difference in magnitudes, which is 15.3 units - 13 units = 2.3 units. Therefore, the second duckling wandered 2.3 units farther than the first duckling.
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3h=15 solve the equation
Answer:5
Step-by-step explanation:PLS GIVE ME BRAINLIEST
Value of h is 5 for 3h=15.
An equation is a mathematical statement that shows that two mathematical expressions are equal. It is used to calculte the values of the variable such they satisfy the expression on both the side of the equal symbol. The equation may involve one variable, two variables, three variable,s and so on.
Given equation:
3h=15
This is an equation in one variable, which can be solved by transposition.
To calculate the value of h
On dividing 3 both sides,
3h/3=15/3
h=5
Thus , for equation 3h=15, value of h is 5
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Maya decided to paint some of the rooms in her hotel. She found out that a room required 3/2 cans of paint. If Maya buys 9 cans of paint, how many rooms can she paint?
Answer:
She can paint 6 rooms.
Step-by-step explanation:
Given:
Maya decided to paint some of the rooms in her hotel. She found out that a room required 3/2 cans of paint.
If Maya buys 9 cans of paint.
Now, to find the rooms she can paint.
So, we use unitary method to get the number of rooms:
If, [tex]\frac{3}{2}[/tex] cans of paint is needed to paint 1 room.
Then, 1 can of paint is needed to paint = [tex]\frac{1}{\frac{3}{2}} =\frac{2}{3}[/tex] room.
Thus, 9 cans of paint is needed to paint = [tex]\frac{2}{3} \times 9[/tex]
[tex]=\frac{18}{3} \\\\=6\ rooms.[/tex]
Therefore, she can paint 6 rooms.
20 POINTS HELP ASAP
Indicate the formula for the following conditions P^c(n,r)=
Answer:
The answer is C(n,r) = n!/[(n-r)!r!]
The formula for the following conditions is [tex]C(n,r) = \dfrac{n!}{[(n-r)!r!]}[/tex]
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
A total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in a total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, a total number of choices, in that case, would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called the permutation of k items chosen out of m items (all distinct).
The formula for the following conditions is [tex]C(n,r) = \dfrac{n!}{[(n-r)!r!]}[/tex]
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Identify the zeros if the quadratic function.
A) x=2 and x=5
B) y=2 and y=5
C) x=-2 and x=-5
D) y=-2 and y=-5
Answer:
C) x=-2 x=-5
Step-by-step explanation:
When you look at the X-axis you can see that is crosses at the points (-5,0) and (-2,0)
Answer:
The zeros are x=-2 and x=-5.
Dance lessons cost $198.75 for 15 classes
What is the cost per class? What would the cost
be for 25 classes?
Answer:
331.25
Step-by-step explanation:
First you want to find how much each class cost. So first you want to divide $198.75 by 15 and you will get 13.25. Once you do that you will multiply 13.25 by 25 to get 331.25. Your welcome.
HELP. It’s LOG form. Since were out of school I forgot how I did this and it’s due so it would be a life saver.
Answer:
see below
Step-by-step explanation:
exponent to log: [tex]a^b[/tex] = c ---> logₐc = b
ie. question 6
log ₁₀(3x+1) = 2 -----> [tex]10^{2} = 3x+1[/tex]
that will get you through questions 1 to 3, 5 to 6, and 8
in question 4, all you have to do is know that 2^2 = 4 and 2^3 = 8, by setting the bases equal, you can manipulate the exponents to get 2x+8 = 3x-3
for questions 7 and 9,
remember that:
logₐc + logₐd = logₐ(cd)
logₐc - logₐd = logₐ([tex]\frac{c}{d}[/tex])
remember change of base is [tex]log_{a} b = \frac{log_xb}{log_xa}[/tex], this will be useful if you need your calculator since calculators only have base 10 and maybe if your calculator is good enough natural base e
A small town in kansas with a population of 2300 people 80 years ago. Now, the town has experienced significant growth and has a population of about 3234956 people. Approximately how many times larger is the current population in the Kansas town than it was 80 year's ago?
Answer:
It has grown by 1406.50%
Step-by-step explanation:
Take 3234956 and divide it by 2300 and you get your percentage from population then to now
Please make me the Brainliest Answer
evaluate 3/2 y - 3 + 5/3 z
when y = 6 and z= 3
Answer:
Step-by-step explanation:
Substitute the numbers in for y and z.
3/2(6)+5/3(3)-3
9+5-3
14-3=11
answer: 11
A 10 foot ladder is leaning against the wall. The bottom of the ladder is 4 feet from the base of the wall. Which is closest to the distance from the top of the ladder to the base of the wall
Answer: 9.16 feet
Step-by-step explanation:
Hi, to answer this question, since we have formed a right triangle (see attachment) we have to apply the Pythagorean theorem:
a2 +b2 = c2
Where c is the hypotenuse of a right rectangle (the longest side) and a and b are the lengths of the other 2 sides.
In this case the hypotenuse us the ladder.
So, replacing with the values:
4^2 + b ^2 = 10^2
16 + b^2 = 100
b^2 = 100-16
b^2 = 84
b = √84
b= 9.16 feet
how many solutions does the system have
4x−2y=8
2x+y=2
Under the elimination method, we normalized the systems of equations, resulting in the equation: 0=1. Since this is not possible, the system has no solutions.
Explanation:To determine the number of solutions for the system of equations, we can use the method of substitution or elimination. Let's use elimination:
First, we normalize the equations by dividing the first equation by 4 and the second equation by 2. This gives us:Because 0 does not equal 1, we can conclude that the system of equations has no solutions.
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3/15 divided by 4/9
please help me my dudes
Answer:
9/20
(9 over 20)
Step-by-step explanation:
Answer:
9/20 or 0.45
Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of 4/9: 9/4
Now, multiply it with the dividend
So, 3/15 ÷ 4/9 = 3/15 × 4/9= 3 × 9/15 × 4
3 × 9
15 × 4
=
27 /60
After reducing the fraction, the answer is
9 /20 or 0.45
PLEASE HELP I WILL MAKE BRAINLIST
In a certain Algebra 2 class of 28 students, 21 of them play basketball and 8 of them play baseball. There are 2 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer: 11%
Step-by-step explanation: What I did is i added 21 8 and 2 together and subtracted them by the amount of students which is 28. Then with that number/ 3 I divided by 28 which gave me the percentage .10714. I then rounded and ended with 11%. Im pretty sure this is the right answer if anyone thinks they know im wrong please say
Answer:
THE CORRECT ANSWER IS 3/28
Step-by-step explanation:
I am unable to solve this problem. Tap for examples... if prices increase at a monthly rate of 2.4%, by what percentage do they increase in a year?
Answer:
[tex]28.8\%[/tex].
Step-by-step explanation:
We have been given that prices increase at a monthly rate of 2.4%. We are asked to find the percentage at which prices will increase in a year.
We know that 1 year equals 12 months.
To find the increase in one year, we will multiply monthly increase rate by 12 as:
[tex]\text{Yearly increase rate}=12\times 2.4\%[/tex]
[tex]\text{Yearly increase rate}=28.8\%[/tex]
Therefore, the prices will increase at a rate of [tex]28.8\%[/tex] in a year.
I deliver truck is transporting box of two sizes large and small large box weigh 50 pounds each and a small box weighs 35 pounds each they’re 150 bucks an hour if the truck is you’re a total of 4775 pounds in boxes how many of each type of boxes of carrion
Answer:
95 and 136 respectively
Step-by-step explanation:
4775/50=95R25
4775/35=136R15
Suppose that $6500 is placed in an account that pays 3% interest compound each year. Assume that no withdrawals are made from the account
Find the amount in the account at the end of 1 year
Find the amount in the account at the end of 2 years
Answer:
1 year:
The amount is $6695 and the interest is $195
2 years:
The amount is $6895.85 and the interest is $395.85.
The balance in the account at the end of 1 year would be approximately $6695 and at the end of 2 years would be approximately $6899.85 with an initial investment of $6500 with a 3% interest rate compounded annually.
Explanation:The subject of this question is compound interest. When an amount of money is placed in an account with a certain interest rate, the amount grows over time. In this case, the initial investment is $6500 and the interest is compounded annually at a rate of 3%.
To calculate the total amount in the account after a certain period, you can use the following formula:
A = P(1 + r/n)^(nt)
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time in years.
Applying this formula to the problem: for the end of first year, t=1, we will have:
A=6500(1 + 0.03/1)^(1*1) ≈ $6695
For the end of 2 years, t=2, we will get:
A=6500(1 + 0.03/1)^(1*2) ≈ $6899.85
Therefore, the balance in the account at the end of 1 year would be approximately $6695 and at the end of 2 years would be approximately $6899.85. Assume there are no withdrawals from the account during this period.
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The following are the ages (years) of 5 people in a room:
20, 21, 13, 22, 18
A person enters the room.
The mean age of the 6 people is now 18.
What is the age of the person who entered the room?
Answer:
The person is 14 years old
Step-by-step explanation:
1. Multiply 6 times 18 which is 108
2. Add all numbers together in list which is 94
3. Subtract 94 from 108 which is 14
4. To check answer add 94 plus 14 and divide by 6 and you will get the median which is 18, now you know this answer is correct.
A tangent line intersecting with a radius always creates a
A tangent line intersecting with a radius always creates a right angle.
A tangent line intersects with a circle at only one point.
This point is referred to as the point of tangency.
When a radius is drawn to intersect with the tangent line at the point of tangency, then the angle at that point of intersection is a right angle i.e. the measure of the angle is 90 degrees.
This is so because both lines (i.e. the radius and the tangent line) are perpendicular lines.
Hence, the text that completes the statement is right angle.
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Mitchell received a stipend at the beginning of the semester to buy textbooks. During the semester, he spent $429.17 on textbooks. He had $77.85 of the stipend left at the end of the semester How much was Mitchell's stipend? A. $584.87 B. $351.32 C. $390.25 D. $507.02
Final answer:
(Option D)Mitchell's stipend was $506.02.
Explanation:
To find out how much Mitchell's stipend was, we can subtract the amount he spent on textbooks from the amount he had left at the end of the semester.
Let's assume Mitchell's stipend was X dollars.
He spent $429.17 on textbooks, so the remaining amount would be X - $429.17.
We know that he had $77.85 left, so we can set up the equation:
X - $429.17 = $77.85
Now, we can solve for X:
X = $77.85 + $429.17 = $506.02
So, Mitchell's stipend was $506.02. This corresponds to answer (Option D).
Use the quadratic formula to solve 2x^2 + 2x - 12?
Answer:
If you plug it all in you will get x=2 x=-3
Step-by-step explanation:
The quadratic formula is
-b+/-[tex]\sqrt[/tex]-b^2-4ac all over 2(a)
your equation 2x^2+2x-12
you can label it
a=1 b=2 c=-12
If you plug it all in and solve you will get x=2 x=-3
The values of x would be 2 and 3 which are determined by using the quadratic formula to solve the given quadratic function.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
We have been given that quadratic function as
2x² + 2x - 12
Compare the given function to the standard quadratic function f(x) = ax² + b x + c.
We get a = 2, b = 2 and c = -12
Using the quadratic formula to solve the above quadratic function
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values of a = 2, b = 2 and c = -12 in the quadratic formula,
[tex]x = \dfrac{-2\pm\sqrt{2^2-4\times2\times-12}}{2\times2}[/tex]
[tex]x = \dfrac{-2\pm\sqrt{4+96}}{4}[/tex]
[tex]x = \dfrac{-2\pm\sqrt{100}}{4}[/tex]
[tex]x = \dfrac{-2\pm10}{4}[/tex]
x = (-2+10)/4 and x = (-2-10)/4
x = (8)/4 and x = (12)/4
x = 2 and x = 3
Therefore, the values of x would be 2 and 3 which are determined by using the quadratic formula to solve the given quadratic function.
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What is the volume of a rectangular prism with length 12, width 6m and height 5m
Answer:
360
Step-by-step explanation:
12x6x5 is 360. The volume formula is V=L*W*H
A washer and a dryer cost $713 combined. The washer costs $37 less than the dryer. What is the cost of the dryer
Answer:
375
Step-by-step explanation:
713 - 37 = 676
676 divided by 2 = 338
That would be the washer but we need to add the 37 again for the dryer
338 + 37 = 375
Find the value of 4x^2– 2y when x = 3 and y = 2.
Answer:
The answer is 32.
Step-by-step explanation:
Remember that order of operation is very important in this problem.
Substitute x for 3 and y for 2 in the equation.
When solving the first term, we must note that we have to square the 3 first before we multiply it by 4. So, 4(3)^2 is basically 36. To simplify the second term you just have to do 2*2, which is 4. 36-4=32, which is the answer.
Final answer:
The value of the expression 4x² - 2y when x = 3 and y = 2 is 32, found by substituting the values of x and y into the expression and simplifying.
Explanation:
To find the value of 4x² - 2y when x = 3 and y = 2, we need to substitute these values into the expression.
Start by substituting x with 3: 4(3)² = 4(9) = 36.Next, substitute y with 2: -2(2) = -4.Now, combine these results: 36 - 4 = 32.So, the value of the expression 4x² - 2y when x = 3 and y = 2 is 32.
Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph slower than Cynthia's. At the end of one hour, they are 70 miles apart. Find Cynthia's average speed. (Round your answer to the nearest tenth.)
Answer:
54.2 mph
Step-by-step explanation:
Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...
70² = c² +(c -10)²
4900 = 2c² -20c +100 . . . . eliminate parentheses
c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form
(c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form
c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical
c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution
Cynthia's average speed was 54.2 miles per hour.
4 of 5
© Natasha can type 2600 words in 40 minutes.
Henry can type 4900 in 70 minutes.
Mark can type 3750 words in 50 minutes.
Who types at the fastest rate of words per minute?
Answer:
Mark types the fastest rate of words per minute at 75 words per minute
Step-by-step explanation:
In this question, we want to know which of the three typists has the fastest typing rate.
To calculate this, what we need to do is to divide the total number of words they can type by the number of minutes taken to type those words.
For Natasha, we have; 2600 words / 40 minutes = 65 words per minute
For Henry, we have 4900 words/70 minutes = 70 words per minute
For Mark, we have 3750 words/50 minutes = 75 words per minute
We can see that Mark with 75 words per minute has the fastest typing rate
Si un cono lo obtienes haciendo girar un triángulo rectángulo cuya base es de 10cm y su altura es de 16cm ¿cuánto mide el radio de la base del cono?
Answer:
10 cm.
Step-by-step explanation:
In order to better understand this question, I will attach an allusive image to the question.
Keep in mind that in this case the base of the triangle is equal to the radius of the base of the cone since the triangle rotates on its own axis, therefore the measurement of the base corresponds to 10 cm, therefore the radius measures 10 cm.
Which two of the following are applications of the Logarithmic model? *
20 points
College GPA
Richter Scale
Acidity/Alkilinity
Compound Interest
Amortization Schedule
Question:
a. College GPA
b. Richter Scale
c. Acidity/Alkalinity
d. Compound Interest
e. Amortization Schedule
Answer:
The correct two options are;
b. Richter Scale
c. Acidity/Alkalinity
Step-by-step explanation:
Here we have
b. The Richter Scale, given by the following relation;
[tex]M = log(\frac{I}{I_0} )[/tex]
M = Earth quake magnitude
I = Earthquake intensity
I₀ = Earthquake intensity of magnitude 0
Comparing two Earthquakes, A and B, we have
[tex]M_A - M_B = log(\frac{I_A}{I_B} )[/tex]
c. Acidity/Alkalinity are determined by the pH of the solution, which is the negative logarithm of the hydrogen ion concentration
pH = -log₁₀ [H⁺].