Final answer:
To determine the maximum number of adults and children that can attend the play without exceeding the bus capacity of 40 people and the $400 budget, set up and solve a system of equations representing the capacity and budget constraints. The solution is 8 adults and 32 children.
Explanation:
We are given a situation where a company charges $18 for each adult (a) and $8 for each child (c) for a bus trip to an upcoming play, with the constraints that the bus holds a maximum of 40 people and the available budget is $400. To find the maximum number of adults and children that can attend under these constraints, we need to set up a system of equations:
For the capacity constraint: a + c = 40
For the budget constraint: 18a + 8c = 400
We can solve this system using substitution or elimination. Let's use elimination. Multiply the first equation by -8 and add it to the second equation to eliminate c:
-8a - 8c = -320
18a + 8c = 400
Adding these two equations together gives us:
10a = 80
Thus, a = 8. Plugging a = 8 back into the first equation, we get c = 32.
The maximum number of adults and children that can attend the play is 8 adults and 32 children.
the value of x varies with y and when x=1/3 y=12 write an equationto represent the variation
Answer:
y = 36x
Step-by-step explanation:
Given that x and y vary directly then the equation relating the is
y = kx ← k is the constant of variation
To find k use the condition x = [tex]\frac{1}{3}[/tex], y = 12, then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{\frac{1}{3} }[/tex] = 12 × 3 = 36
y = 36x ← equation of variation
Given that point P partitions AB into a ratio of 3:2, and A is found at (-4, -3) and P is found at (3, 6), find the coordinates for B.
Answer:
The coordinates of B are (7.67,12)
Step-by-step explanation:
Let the coordinates of B are (h,k).
Now, point P(3,6) partitions AB into a ratio of 3 : 2 and A is found at (-4,-3).
We have to find B(h,k).
Now, from the formula of coordinate geometry we have,
[tex]3 = \frac{2(- 4) + 3h}{3 + 2}[/tex]
⇒ 3h - 8 = 15
⇒ 3h = 23
⇒ h = 7.67
And, [tex]6 = \frac{2(- 3) + 3k}{2 + 3}[/tex]
⇒ 3k - 6 = 30
⇒ 3k = 36
⇒ k = 12
Therefore, the coordinates of B are (7.67,12) (Answer)
What are multiples of nine
Step-by-step explanation:
We have,
Nine
To find, the multiples of nine = ?
The multiples of nine are:
1 × 9, 2 × 9, 3 × 9, 4 × 9, 5 × 9, 6 × 9, 7 × 9, .......
= 9, 18, 27, 36, 45, 54, 63, .....
∴ The multiples of nine are 9, 18, 27, 36, 45, 54, 63, .....
Thus, the multiples of nine are 9, 18, 27, 36, 45, 54, 63, ..... .
Find the value of x in the isoceles triangle shown below.
PLEASE HELPPPPP
Answer:
The measure of 'x' is 6 units.
Step-by-step explanation:
Given:
An isosceles triangle.
The two equal arms length = [tex]\sqrt{13}[/tex]
Measure of the altitude = [tex]2[/tex]
Note:The altitude to the base of an isosceles triangle bisects the base.
The altitude also forms 90 degree at the base.
So, the base length can also be seen as 'x' which we can also be written as [tex]x=\frac{x}{2} +\frac{x}{2}[/tex]
And [tex]\frac{x}{2}[/tex] is a part of the right angled triangle.
Where hypotenuse = [tex]\sqrt{13}[/tex]
Perpendicular length =[tex]2[/tex]
Base length = [tex]\frac{x}{2}[/tex]
Now,
From Pythagoras formula we know that:
[tex](hypotenuse)^2 =(perpendicular)^2+ (base)^2[/tex]
Plugging the values:
⇒ [tex](hypotenuse)^2 - (perpendicular)^2 = (base)^2[/tex]
⇒ [tex]\sqrt{ (hypotenuse)^2 - (perpendicular)^2} = (base)[/tex]
⇒ [tex]\sqrt{(\sqrt{13})^2-(2)^2} =\frac{x}{2}[/tex]
⇒ [tex]\sqrt{13-4}=\frac{x}{2}[/tex]
⇒ [tex]\sqrt{9} =\frac{x}{2}[/tex]
⇒ [tex]3=\frac{x}{2}[/tex]
⇒ [tex]3\times 2=x[/tex]
⇒ [tex]6 = x[/tex]
So the value of base 'x' = 6 units.
Option D is the rigth choice.
The cost of a rental car at a certain company is a $50 fee plus $0.40 for each mile driven up to 100 miles. For every
mile over 100 miles it is $0.50 per mile. What would the total cost be for renting the car and driving it 120 miles?
A. $40
B. $50
C. $90
D. $100
E. $110
Answer:
D
Step-by-step explanation:
50 + .40(100) = 90
.50(20) = 10
90 + 10= 100
Answer:
D: 100
So the first multiply 0.4 times 100 which you would get 40 now add the 50 dollar fee to 40 which you would get 90 dollars. Now for the 20 miles remaining multiply 0.5 times 20 which you would get 10. Now add everything together 90+10 which would equal 100.
How is the sum expressed in sigma notion? Multiple choice
Answer:
The given sum expressed in sigma notation is
[tex]\sum\limits_{i=1}^{5}4^{i-4}[/tex]Therefore [tex]\sum\limits_{i=1}^{5}4^{i-4}=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]Step-by-step explanation:
Given series is [tex]\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]
The given sum expressed in sigma notation is
[tex]\sum\limits_{i=1}^{5}4^{i-4}[/tex]Now verify that the sigma notation [tex]\sum\limits_{i=1}^{5}4^{i-4}[/tex] is correct or notNow expand the series [tex]\sum\limits_{i=1}^{5}4^{i-4}=4^{1-4}+4^{2-4}+4^{3-4}+4^{4-4}+4^{5-4}[/tex] [tex]=4^{-3}+4^{-2}+4^{-1}+4^{0}+4^{1}[/tex] ( using the properties [tex]a^{-m}=\frac{1}{a^m}[/tex] and [tex]a^0=1[/tex] )[tex]=\frac{1}{4^3}+\frac{1}{4^2}+\frac{1}{4^1}+1+4[/tex][tex]=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]Therefore [tex]\sum\limits_{i=1}^{5}4^{i-4}=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]Hence verified
Answer:
Option 2
Step-by-step explanation:
1/64 = 4^-3
1/16 = 4^-2
1/4 = 4^-1
1 = 4^0
4 = 4^1
What the answer to this is
Answer:
1 and 2 or A
Step-by-step explanation:
it is only what macks seans
Write 4,570,000 in scientific notation
Answer:
4.57 x 10(little 6 lol )
Step-by-step explanation:
4.57 x 10^6
(use the caret symbol [^] to type or write)
4.57E+6
(Scientific E-notation)
4570000
(Real Number)
Please help fast!! A, B, C or D?
Answer:
the answer would be is 6
Answer:
a
Step-by-step explanation:
Allie and Sarah decided that they want to purchase renters insurance for the apartment they share. They made a list of all of the items to be covered by the insurance policy, along with their estimated values. If the items to be covered total more than $3000, the insurance company charges an annual premium of 23% of the total value of the items. If the items to be covered total $3000 or less, the insurance company charges an annual premium of 20% of the total value of the items. Using the list of items Allie and Sarah provided, determine their monthly renters insurance premium. Allie's Stuff Sarah's Stuff TV ($250) Stereo ($75) Stereo ($150) Bicycle ($250) CD's ($225) CD's ($130) DVD's ($385) DVD's ($300) Bicycle ($400) IPOD ($80) Microwave ($30) Computer ($675) Laptop Computer ($950) a. $65.00 b. $74.75 c. $325.00 d. $780.00
Answer:
The answer is b. $ 74.75
Step-by-step explanation:
First, we need to gather the data from the question.Data:
Let x be the value of items to be insured.
1. if the items are more than $ 3 000 it means that x is greater than $ 3000 and the annual premium will be 23 % of the total value.
2. if the items are less or equal to $ 3 000, it means that x ≤ $ 3 000 ( in other words, x is less than or equal to $ 3 000)
Second, we find the total worth of all the items. Adding up all the values gives $ 3900 which is more than $ 3 000. Therefore, rule 1 applies.The annual premium for the goods will be:
annual premium = 23 % × $ 3900
= $ 897
However, the premium is supposed to be paid monthly. Divide the total premium by 12 to get:
$ 897/12 = $ 74.75
This is option c.
a boat costs $16600 and decreased in value by 14% per year. How much will the boat be worth after 11 years?
The worth of boat after 11 years is $ 3159.3013
Solution:
Given that,
Boat costs $16600 and decreased in value by 14% per year
To find: Worth of boat after 11 years
The formula for decreasing function is given as:
[tex]y = a(1-r)^t[/tex]
Where,
y is the value after "t" years
t is the number of years
a is the initial value
r is decreasing rate in decimal
From given,
a = 16600
t = 11
[tex]r = 14 \% = \frac{14}{100} = 0.14[/tex]
Substituting the values we get,
[tex]y = 16600(1-0.14)^{11}\\\\y = 16600(0.86)^{11}\\\\y = 16600 \times 0.1903\\\\y = 3159.3013[/tex]
Thus the worth of boat after 11 years is $ 3159.3013
What is the domain of the function y = StartRoot x EndRoot + 4
Answer:
third option !!!! 0 less-than-or-equal-to x less-than infinity
Step-by-step explanation:
The domain of the function y = √x + 4 is all real numbers x such that x ≥ 0, because the square root of a negative number is not a real number in the set of real numbers.
Explanation:The given function is y= x +4. The square root function x is defined only for non-negative values of x. This is because the square root of a negative number is not a real number in the real number system.
Therefore, for the given function to be defined, the expression inside the square root (x) must be greater than or equal to zero. Mathematically, this condition is expressed as:x≥0
This inequality ensures that the square root is always defined for any real number x in the domain of the function.
So, the domain of the function y= x +4 is all real numbers x such that x≥0. In interval notation, this can be expressed as [0,∞).
The slope of a line is -3 and the y-intercept is (0,4). What is the equation of the line in slope-
intercept form?
Answer:
y=-3x+4
Step-by-step explanation:
y-y1=m(x-x1)
y-4=-3(x-0)
y-4=-3(x)
y-4=-3x
y=-3x+4
Solve: 2(23 + a) = 34
Answer:
a = −6
Step-by-step explanation:
Step 1: You should divide both sides by 2.
[tex]23+a=\frac{34}{2}[/tex]
Step 2: then simplify [tex]\frac{34}{2}[/tex] into 17.
23 + a = 17
Step 3: next, you need to subtract 23 from both sides.
a = 17 − 23
Step 4: lastly, Simplify 17 − 23 to −6 and you're done!
a = −6
Answer:
a = -6
Step-by-step explanation:
2 (23 + a) = 34
46 + 2a = 34
2a = 34 - 46
2a = - 12
a = - 12/2
a = - 6
What are the x-intercepts of the graph of the equation y = x² + 4x - 5 ?
5 and 1
-5 and 1
-5 and 0
5 and -1
Answer:
The x-intercepts of the graph of the equation y = x² + 4x - 5 is -5 and 1
Step-by-step explanation:
Given:
y = x² + 4x-5
To Find:
x-intercepts
Solution:
Finding the value of the x by using quadratic formula
x = [tex]\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
On substituting the values ,
x = [tex]\frac{-4 \pm \sqrt{(4)^2 -(4(1)(-5))}}{2(1)}[/tex]
x = [tex]\frac{-4 \pm \sqrt{16 -(-20)}}{2}[/tex]
x = [tex]\frac{-4 \pm \sqrt{36}}{2}[/tex]
x = [tex]\frac{-4 \pm6 }{2}[/tex]
[tex]x = \frac{-4-6}{2}[/tex] [tex]x = \frac{-4+6}{2}[/tex]
[tex]x = \frac{-10}{2}[/tex] [tex]x = \frac{2}{2}[/tex]
x = -5 x = 1
2 Points
A radio wave has a wavelength of 357 m. What is this wavelength in scientific
notation?
Step-by-step explanation:
[tex]357 \: m = 3.57 \times {10}^{2} \: m[/tex]
The wavelength of the radio wave in scientific notation is 3.57 x 10^2 m.
Explanation:The wavelength of a radio wave is given as 357 m. Since this is already a simple number, converting it to scientific notation would be 3.57 x 102 m. Here, '3.57' is the significant part of the number (the significand) and '2' is the power to which 10 is raised (the exponent). In scientific notation, we aim to express numbers between 1 (inclusive) and 10 (exclusive).
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
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ans
Directions: Type your answer in the box without the dollar sign.
Brian purchased 4 items that were $1.00 each. The sales tax rate is 5.5%. How
much was Brian's total bill including sales tax?
The correct answer is $4.22.
Is states that Brian purchased 4 items that were $1.00.
That means he has spent a total of $4.00.
5.5% of $4.00 is 0.22.
Add that together and it gives you the sum/answer of $4.22.
Triangle XYZ undergoes a single
transformation to form the image,
triangle X'Y'Z'. The image is congruent
to the original figure. Which of the
following best describes the possible
transformation that took place?
O A. a reflection only
O B. a rotation only
OC. a translation only
O D. a reflection, rotation, or a
translation
Answer:
D
Step-by-step explanation:
When something is forgoing a transformation that stays congruent, if it is rotating, it is simply turning a given amount of degrees: if it is translating, it is simply move up/down or right/left on the x and y axis; and finally, if it reflects, it is simply being inverted across either the x or y axis. None of these transformations result in changing the shape and/or size of the triangle.
Final answer:
The possible transformation that could have taken place is either a reflection, a rotation, or a translation, as they all preserve the congruency of the original triangle. Option D is correct.
Explanation:
If triangle XYZ is transformed to form triangle X'Y'Z' and the image is congruent to the original triangle, then the transformation could be a reflection, a rotation, or a translation. Congruent transformations are those that preserve the size and shape of a figure. Since the original triangle is congruent to its image after the transformation, we can conclude that the transformation is one that preserves congruency. Reflections across a line, rotations about a point, and translations (which slide a figure) all preserve the size and shape of the figure, and hence the triangles would remain congruent after any of these transformations.
May had 66 books. She gave 3 books to 11 friends. Then, she got 51 more. How many books does May have now?
Answer:
81
Step-by-step explanation:
Answer:
84
Step-by-step explanation:
So 3 and 11 make 33 and subtract that from 66. That gives you 33. Add 51 and you get 84.
Mr. Walker needs to purchase another pair of Crocs. He got an email coupon for 20% off an de free shipping at Shoebye.com. The pair he regularly $49.00 at Shoebuy. He also sees the same shoes on sale at Crocs.com for $35.00 plus $4.30 shipping and handling. Which is the better buy? Show your work to prove your answer.
Answer: Shoebuy.com
Step-by-step explanation:
20% of $49.00 is $9.8. When you subtract $9.80 from $49, you end up with $39.2. Now to look at Crocs.com, in order to get the total, add the price of the shoes, $35 and the shipping cost, $4.30, you'll end up with $39.30. Because Shoebuy is $.10 less than Crocs.com, it is the better choice.
After calculating the total costs, purchasing the Crocs from Shoebye.com with the 20% discount and free shipping comes out to be cheaper by $0.10 than buying them on sale at Crocs.com with added shipping and handling.
Explanation:Mr. Walker is trying to determine the better buy for a new pair of Crocs. The comparison involves a 20% discount and free shipping at Shoebye.com versus sale price with additional shipping and handling at Crocs.com.
Calculation at Shoebye.com:
Original price: $49.00
Discount (20% of $49): $9.80
Discounted price: $49 - $9.80 = $39.20
Shipping: $0 (free)
Total cost at Shoebye.com: $39.20
Calculation at Crocs.com:
Sale price: $35.00
Shipping and handling: $4.30Total cost at Crocs.com: $35.00 + $4.30 = $39.30
Comparing both totals, Shoebye.com's offer of $39.20 is slightly better than Crocs.com's offer of $39.30. Thus, purchasing from Shoebye.com would save Mr. Walker $0.10.
Find the 59th term of the arithmetic sequence 29,37,45
Answer:
[tex]T_{59}= 493[/tex]
Step-by-step explanation:
Given:
Arithmetic sequence
29, 37, 45............
n = 59
We need to find the 59 term of the arithmetic sequence.
Solution:
Using formula for nth term of arithmetic sequence.
[tex]T_{n}= a + (n-1)d[/tex] -------------(1)
Where:
a = first term of the sequence.
d = Common difference.
first find the the common difference of .
[tex]d = a_{2}-a_{1}[/tex]
[tex]d=37-29[/tex]
d = 8
Substitute a = 29, d = 8 and n = 59 in equation 1.
[tex]T_{59}= 29 + (59-1)8[/tex]
[tex]T_{59}= 29 + 58\times 8[/tex]
[tex]T_{59}= 29 + 464[/tex]
[tex]T_{59}= 493[/tex]
Therefore, 59th term of the arithmetic sequence [tex]T_{59}= 493[/tex]
Answer:
the 59th term of the arithmetic sequence is T=493
Step-by-step explanation:
Here is prove
solve the system of equations by graphing. x+y=-9 4x+y=-19
For this case we have the following system of equations:
[tex]x + y = -9\\4x + y = -19[/tex]
We multiply the first equation by -4:
[tex]-4x-4y = 36[/tex]
We have the following equivalent system of equations:
[tex]-4x-4y = 36\\4x + y = -19[/tex]
We add the equations:
[tex]-4x + 4x-4y + y = 36-19\\-3y = 17\\y = - \frac {17} {3}[/tex]
We find the value of the variable "x":
[tex]x = -9-yx = -9 - (- \frac {17} {3})\\x = -9 + \frac {17} {3}\\x = \frac {-27 + 17} {3}\\x = - \frac {10} {3}[/tex]
Thus, the solution of the system is:
[tex](x, y): (- \frac {10} {3}, - \frac {17} {3})[/tex]
See the graphic in the attached image
ANswer:
[tex](x, y): (- \frac {10} {3}, - \frac {17} {3})[/tex]
See the graphic in the attached image
Answer: D
Step-by-step explanation:
Edge 2021
67% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
To calculate probabilities in a binomial experiment, use the binomial probability formula. For exactly five successes, use P(X=k) = C(n,k) * p^k * (1-p)^(n-k). For at least six successes, sum the probabilities of getting exactly six to ten successes. For less than four successes, sum the probabilities of getting zero to three successes.
Explanation:To find the probability of selecting a certain number of U.S. adults with very little confidence in newspapers, we can use the binomial probability formula. For (a) exactly five, we can calculate the probability using the formula P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials (10), k is the desired number of successes (5), p is the probability of success (0.67), and C(n,k) is the number of combinations. Plugging in the values, we find P(X=5) = C(10,5) * (0.67)^5 * (1-0.67)^(10-5).
For (b) at least six, we need to calculate the probability of getting six or more successes. We can find this by summing the probabilities of getting exactly six, seven, eight, nine, and ten successes: P(X>=6) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10).
For (c) less than four, we need to calculate the probabilities of getting zero, one, two, or three successes: P(X<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3).
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Please help me... Has to be in my 1pm today and I have no idea... out of my league but I need to pass to get into the course I want
Answer:
AB = -4i -7j
CD = -5i + 4j
Step-by-step explanation:
i.) vector AB = -4i -7j
where i is the unit vector in the x direction and j is the unit vector in the y direction.
vector AB is 7 units down and 4 units west
ii)vector CD = -5i + 4j
vector CD is 5 units west and 4 units up
How many unique ways are there to arrange the letters in the word THAT?
Answer:
12
Step-by-step explanation:
its 12
because its 12
Answer: 12
Step-by-step explanation:
There are 16 ounces in 1 pound Chanda picked 9 pounds of cherries from her tree this year find the number of ounces of cherries
Answer:
16 x 9 = 144 144 is the answer.
Step-by-step explanation:
Simplify.
14y+112+2−134y−12
I would appreciate it if i get an answer quickly, please and thank you.
Answer:
answer is 148y + 102
Step-by-step explanation:
First add like terms 14y + 134y = 148y
then add the whole numbere 112 + 2 = 114
then subtract 114 - 12 = 102
and you get 148y + 102
David bought 3 dvds and 4 books for $40 at a yard sale. Anna bought 1 dvd and 6 books for $18. How much did each dvd and book cost?
Answer: d=$12, b=$1
d represents DVDs
b represets books
Step-by-step explanation:
Whenever you have 2 examples of 2 different things (such as books and dvds), make a systems of equations.
Step 1: Write a system of equations
3d+4b= 40
d+6b= 18
Step 2: Eliminate any letter. I'll just choose d.
To elimiate d, you have to make them both equal to the biggest d variable. In other words, make both d terms equal to 3d. To do this, miultiply the 2nd equation by 3, and keep the 1st one the same.
3d+4b=40
3d+18b= 54
Now, elimiate d, by doing 3d-3d= 0. Now use subtraction to solve for b since we used this to get 3 and 3 to 0.
4b-18b=40-54
-14b= -14
b= -14÷-14
b= 1
Each book costs 1 dollar.
Step 3: Plug in b=1 to find how much each dvd costs (plug into any equation)
3d+4b=40
3d+4(1)=40
3d+4=40
3d=40-4
3d=36
d=36÷3
d=12
Each dvd is $12
Step 4: Checks--plug d=12 and b=1 into any equation
3d+4b=40
3(12)+4(1)=40
36+4=40
40=40
It's correct ✅
Also i know this was answered really late but id appreciate if i could get brainliest as i worked pretty hard for this :) Hope i could help the best i could :D
Determine the slope of a line that is perpendicular to the line y = -2x + 7
Select one:
O A. Slope = -1/2
O B. Slope = 2
O C. Slope = 1/2
O D. Slope = -7
Answer:
C)
Step-by-step explanation:
Perpendicular means negative reciprocal of the current slope.
And the negative reciprocal of -2 is 1/2.
What are the roots of the equation x^2 + -9=0
Answer:
x = 3 or x = -3
Step-by-step explanation:
If x^2 - 9 = 0 we transfer 9 to the right side of the equation and it's change negative sign to positive while doing so
now we have x^2 = 9 the square of a number must be equal to a positive number in real numbers
but the root can be either negative or positive so we say x = 3 or x = -3