If the cost, C. for manufacturing x units of a certain product is given by C = x2 + 35x + 35, find the number of units manufactured at a cost of $10,235.
Answer: 85 units
Step-by-step explanation:
x^2 +35x + 35 = 10235
-10235 on both sides
x^2 + 35x -10200
Now Factor
( x - 85 ) ( x + 120 )
Now plug in for x using 85 or -120
(85)^2 + 35(85) + 35
7225 + 2975 + 35 = 10235
So 85 is the right answer
Gabriella makes a profit of $.80 for every cup of coffee that she sells at her coffee shop she wanted to make a profit of at least $75 today on coffee if she’s sold 90 cups today which statement is correct
Answer:
Gabriela needs to sell 4 more cups of coffee to make a profit of $75.
She sells 90 cups and makes $0.80 profit on each cup. That equals $72 profit.
90 x $0.80= $72
She wants to make $75 profit.
$75 - $72 = $3 profit short for the day
$3/$0.80 = 3.75 cups of coffee short so to make her profit she must sell a total of 94 cups of coffee for the day or an additional 4 cups.
Step-by-step explanation:
A club is choosing 2 members to serve on a committee. The club has
nominated 3 women and 3 men. Based on chance alone, what is the
probability no women are chosen to be on the committee?
Answer: The probability that no women are chosen to be in the committee is 2/5 or 0.40.
Step-by-step explanation:
We have two positions, and we have 6 options for those positions, 3 are men, and 3 are women.
If we want to see the probability where no women are chosen, then this means that in the first selection a man is chosen.
If all the 6 nominees have the same probability of being chosen, then the probability that in the first selection a man is chosen is equal to the number of men divided the total number of nominees, this is:
p1 = 3/6 = 1/2.
Now the same happens for the second selection, but now we have 5 total nominees and 2 are men, so the probability now is:
p2 = 2/5
And the joint probability will be the product of the individual probabilities, then we have:
P = p1*p2 = (1/2)*(2/5) = 2/5.
The probability that no women are chosen to be in the committee is 2/5 or 0.40.
The probability that no woman is chosen to be on the committee is 0.40.
GivenA club is choosing 2 members to serve on a committee.
The club has nominated 3 women and 3 men.
The number of ways to select two persons from 6 will be:
[tex]\rm = ^6C_2[/tex]
Therefore,
The probability that no woman is chosen to be on the committee is;
[tex]= \dfrac{1}{2} \times \dfrac{2}{5}\\\\= \dfrac{1}{5}\\\\=0.40[/tex]
Hence, the probability that no woman is chosen to be on the committee is 0.40.
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9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle. Find the speed for the kayak. Use one of these facts to help. The steamboat's speed is 4 less than 8 times the speed of the kayak. The tall ship's speed is 1 more than 3 times the speed of the kayak. The yacht's speed is 5 less than 15 times the speed of the kayak. Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution)
10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef. It's 2:00 p.m. now, and your boat leaves the island at 7:30 p.m. Will you be able to kayak to the reef and back by then? If so, how long will you have to spend at the reef? If not, how late will you be for the return trip? Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)
Answer:
hi
Step-by-step explanation:
1. Circle the two boats you picked for your trip.
the yacht and the tall ship (aka the pirate ship)
2. Make sense of the problem.
what do you know?
The tall ship makes the trip in 10 hours. The yacht makes the trip in 2.5 hours. The tall ship is 30 knots slower than the yacht.
what do you want to find out?
How fast is each boat traveling in knots (nautical miles per hour)?
what kind of answer do you expect?
probably just some numbers like 10 miles per hour or 40 miles per hour
Writing some expressions
3. Write an expression for the distance going to the island. Let x be the speed of the boat you are taking to the island. Distance is equal to speed times time. (2 points)
the expression would be D = 10(x-30), d is the distance. it could also be simplified to 10x - 300
4. Write an expression for the speed of the boat coming back from the island in terms of the other boat's speed. Let x be the speed of the boat you are taking to the island. (2 points)
so the yacht's speed would be S = x knots, s is for speed.
5. Write an expression for the distance returning from the island. Use the expression for speed you found in question 4. Remember that distance is equal to speed times time. (2 points)
the distance returning from the island would be D = 2.5x.
6. Each ship travels the same distance. Set the distances equal to each other to get the equation for the speed of the ship you are taking to the island. (1 point)
10x - 300 = 2.5x
7. Solve the equation from question 6 for x. What does this tell you? (5 points: 1 point for showing your work, 3 points for solving for x, 1 point for explaining the answer)
10x - 300 = 2.5x
10x - 300 + 300 = 2.5x + 300
10x -2.5x = 300
7.5x = 300
x = 40
x is the speed of the yacht. (40 nautical miles per hour)
8. How fast does the second boat travel? Show your work. (2 points: 1 point for showing your work, 1 point for the answer)
the yacht travels at 40 nautical miles per hour and the tall ship travels at 100 (10x - 300) nautical miles per hour.
9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle.
Find the speed for the kayak. Use one of these facts to help.
The steamboat's speed is 4 less than 8 times the speed of the kayak.
The tall ship's speed is 1 more than 3 times the speed of the kayak.
The yacht's speed is 5 less than 15 times the speed of the kayak.
Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution)
the equation for the speed of the kayak is 40 = 15x - 5, which in this case, x is the speed of the kayak
40 = 15x - 5
40 + 5 = 15x -5 + 5
45 = 15x
x = 3
therefore, the speed of the kayak is 3 nautical miles per hour.
10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef.
It's 2:00 p.m. now, and your boat leaves the island at 7:30 p.m. Will you be able to kayak to the reef and back by then?
If so, how long will you have to spend at the reef?
If not, how late will you be for the return trip?
Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)
the distance to the island is 100 nautical miles, so the expression would be 100 = 20x -40, with x being the distance to the reef.
we can solve for x by doing:
100 = 20x -40
100 + 40 = 20x - 40 + 40
140 = 20x
140 / 20 = x
x = 7
so the distance from my starting point to the reef will be 7 nautical miles, and the distance from the island to the reef would be 93 nautical miles.in that case, I would be like a day and a half late, but if you are trying to say that the ship is waiting for me at the starting point of my "adventure", then I would not be late if I kayak from my starting point to the reef, in fact, I could stay at the reef for like 50 min, because:
7 / 3 = 2 1/3 hours.
2 1/3 x 2 = 4 2/3 hours or 280 min. (to the reef and back)
7:30 p.m. - 2:00 p.m. = 5 1/2 hours or 330 min. (how much time I have till the ship leaves)
330 - 280 = 50 min. (how many min I can spend at the reef)
This is for the people that want to find out how to find the distance to the island.
jamescodwell answered all the questions correctly btw.
Step-by-step explanation:
Distance travelled divided by trip time = speed
trip time multiplied by speed = distance travelled
So the steamboat makes the trip in 5 hours travelling at a speed of 20 knots.
5 * 20 = 100 The trip to the island is 100 nautical miles.
Yo does anyone know how to do this ?
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line.
(6, −7), (6, 1)
Answer: undefined; vertical line
Step-by-step explanation:
To find the slope, you use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]m=\frac{1-(-7)}{6-6} =\frac{8}{0}[/tex]
The slope is undefined because you cannot divide anything by 0.
The graph of the line is a vertical line at x=6. We know this because the points are both at x=6, with different y-values.
Someone please help me.
Answer:
1 is good number 2 is wrong number 3 is good
Step-by-step explanation:
your welcome im juss writting more so it wont say issa short question!!
f(x)=2x^7 find the domain and range
Answer:
Domain:
-∞<x<∞, or (-∞,∞) in interval notation
Range:
-∞<f(x)<∞, or (-∞,∞) in interval notation
Step-by-step explanation:
It’s infinite both ways, so:
Domain:
-∞<x<∞, or (-∞,∞) in interval notation
Range:
-∞<f(x)<∞, or (-∞,∞) in interval notation
PLSS HELPPP 20 POINTS
Which of the following is the best way of selecting a random sample from students at King
Middle School?
a) Use the student directory, toss a number cube, start from that name, and select every tenth person.
b) Select every student from one grade.
c) Use the student directory, pick one student's name by chance, and then pick another student's
name.
d) Pick every tenth person who arrives at school by bus.
Answer:
a
Step-by-step explanation:
just did it
Answer:the 2nd one is the answer it's easy I just did it :
The sum of three integers is 228. The second integer is 1 more than the first, and the third integer is 2 more than the first. Write an equation to determine the integers. Solve your equation. Show your work
Answer:
x=75
Step-by-step explanation:
first no.=x
second no.=x+1
third no.=x+2
now,
or,
x+x+1+x+2=228
or,
3x+3=228
or,
3x=228-3
or,
x=225/3
x=75 ans
10x2-10x+2 from 8x2+7-7
Step-by-step explanation:
10x2-10x+2
20-10x+2
22-10x
8x2+7-7
16+0
16
I'm confused so I add together cuz why not?
16+22-10x
28-10x
a preschool student finds a big bag of cookies and begins to take the cookies from the bag and hide them in her cubbyhole. after hiding 3 cookies, she decides to keep count of how many cookies are actually in her cubbyhole. first there are 3 cookies. after pulling out more cookies, she then has 5 cookies, then 7 cookies, and then 9 cookies. however, she only knows how to count to 10! assuming she continues to pull cookies from the bag at the same rate indicated by the sequence of cookies above, how would the preschool student continue the pattern? describe the arithmetic sequence in this context.
Answer:She will count the cookies by 2's
Step-by-step explanation:
Sally is shopping for diapers and sees a box with 216 diapers for \$39.98 and a box with 88 diapers for \$24.99 . Which option has the better deal the diapers?
Answer:
For me I think 216 diapers for 39.98 is the best option
Step-by-step explanation:
Get the price of one diaper in each offer
216 = $39.98
1= ?
1×39.98÷216=0.19
Option 2
88=24.99
1 =?
1×24.99÷88=0.28
So I prefer buying 1 diaper for$0.19 and get 216 of them for $39.98 rather than buying 1 diaper for $0.28 and get 88 of them for $24.99
Find an equation for the line with the given properties.
Parallel to the line 2x - y = - 4; containing the point (0,0)
y = 2x (Type your answer in slope-intercept form.)
Answer:
y = 2x
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
2x - y = -4
-y = -2x - 4
y = 2x + 4
Since the 2 lines are parallel, they have the same slope.
Step 2: Define variables
Slope m = 2
Origin (x-int and y-int) (0, 0)
Step 3: Write parallel linear equation
y = 2x + 0
y = 2x
What is the distance between the point in Maine and the point in Tennessee? Round to the nearest tenth.
Answer:
The distance between the point is 1806 unit
Step-by-step explanation:
Given that,
The distance between the point in Maine and the point in Tennessee.
Suppose, The points are (-801,670) and (990,900)
We need to calculate the distance between the point
Using formula of distance
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Put the value into the formula
[tex]d=\sqrt{(990-(-801))^2+(900-670)^2}[/tex]
[tex]d=1806\ unit[/tex]
Hence, The distance between the point is 1806 unit.
7. George went to the general store to buy provisions. He bought food items
worth $35. He had a $25 gift card for the store and he also paid $5 in cash.
How much debt does George have with the store?
I need it in ten minutes plz help
Answer:
He needs to pay $5
Step-by-step explanation:
$25 + $5 = $30 < how much he paid
$35 - $30 = $5 < how much more he needs to pay
Answer:
21
Step-by-step explanation:
21 yeet
brainlest plz is 21 if you dont brainlest you are gay
The sales tax on a used car priced at $4600 is $409.40. What is the sales tax rate?
Answer:
8.9%
Step-by-step explanation:
sales tax rate (in percentage) = 409.40÷4600*100=8.9%
Could the product of a positive integer and a negative integer be positive? Explain.
Answer: the product is always positive.
Step-by-step explanation: Rule 1: The product of a negative integer and a positive integer is a negative integer. Rule 2: The product of two positive integers or two negative integers is a positive integer. That means if you multiply two OF the same sign numbers, the product is always positive.
Answer: No because the product of a positive integer and a negative integer is always negative.
expressions that are equivalent to -8.
Answer:
f(1)=5x-13=-8
Step-by-step explanation:
5-13=-8
or
f(1)=5x-13=-8
Complete the recursive formula of the geometric sequence 56\,,-28\,,\,14\,,-7,...56,−28,14,−7,...56, comma, minus, 28, comma, 14, comma, minus, 7, comma, point, point, point. d(1)=d(1)=d, left parenthesis, 1, right parenthesis, equals d(n)=d(n-1)\cdotd(n)=d(n−1)⋅d, left parenthesis, n, right parenthesis, equals, d, left parenthesis, n, minus, 1, right parenthesis, dot
Answer:
Step-by-step explanation:
[tex]r=\frac{-28}{56}=-\frac{1}{2}\\a_{n}=\frac{-1}{2}a_{n-1}[/tex]
The recursive formula for the sequence is aₙ = (-1/2) * aₙ₋₁
What is a Geometric Series?A sequence of numbers such that the consecutive term is increasing or decreasing by a fixed ratio is called a geometric series.
The standard equation for geometric series is
Tₙ = a₁ rⁿ⁻¹
The formula above represents the explicit formula to determine the nth term of the sequence.
The recursive formula is used to determine the nth term when (n-1) th term is given.
The geometric sequence is,
56, -28, 14, -7,.................
The first term of the sequence is 56
The common ratio is determined by taking the ratio of the second term to the first term.
r = -28/56 = -1/2
The recursive formula is represented by,
aₙ = r * aₙ₋₁
aₙ = (-1/2) * aₙ₋₁
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Solve by completing the square x^2+6x+13=0
Answer:
x = -3 + 2 i or x = -3 - 2 i
Step-by-step explanation:
Solve for x:
x^2 + 6 x + 13 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 13 from both sides:
x^2 + 6 x = -13
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 9 to both sides:
x^2 + 6 x + 9 = -4
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x + 3)^2 = -4
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x + 3 = 2 i or x + 3 = -2 i
Hint: | Look at the first equation: Solve for x.
Subtract 3 from both sides:
x = -3 + 2 i or x + 3 = -2 i
Hint: | Look at the second equation: Solve for x.
Subtract 3 from both sides:
Answer: x = -3 + 2 i or x = -3 - 2 i
Perform the operation (7x3)+(- 2x3/8x2)
ILL GIVE YOU BRAINLIST !!! SHOW WORK
Answer:
45
Step-by-step explanation:
5z^x
Substitute each number for the right letter
5(-3)^2
5(9)
45
Write 4/9 as a decimal?
Answer: 0.44
Step-by-step explanation:
Kai had a gross weekly paycheck of $616 last week. Kai worked 6 hours for 4 of the days and 8 hours on 1 day. What is Kai's hourly rate of pay? a. $16.21 b. $19.25 c. $20.53 d. $25.67 Please select the best answer from the choices provided
The correct answer is B. $ 19.25
Explanation:
To calculate the hourly rate of pay, first, let's calculate the total number of hours Kai worked, and then divide the total earned into the number of hours.
6 hours x 4 days = 24 hours
8 hours x 1 day = 8 hours
24 hours + 8 hours = 32 hours
This shows Kai worked a total of 32 hours. Now to find the hourly rate of pay, follow this procedure:
$616 (total earned) ÷ 32 hours = $19.25 each hour
This means Kai earns $19.25 for each hour of work and therefore the hourly rate of pay is $19.25.
Answer:
B
Step-by-step explanation:
What is a complementary angle versus a supplementary angle?
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
Step-by-step explanation:
f(x)=-6x-8, what if f(-3)
Answer:
f(-3) = 10
Step-by-step explanation:
Simply plug in x as -3 to find f(-3):
f(-3) = -6(-3) - 8
f(-3) = 18 - 8
f(-3) = 10
Describe how each model can help you round a decimal.
You
Question 5: The following data give the numbers of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days.
74 73 74 77 75 68 73 69 69 69
70 71 73 72 72 71 62 63 66 65
65 64 68 67 67
Find the percentile rank of 73. % =
Answer:
The percentile rank of the data value 73 is 84.
Step-by-step explanation:
In this problem, you want to find the percentile rank of the data value 73 in the data set.
The percentile rank represents the percent of numbers in the data set that have value equal or less than 73.
Take note that there are 25 data values in this data set. It's helpful to sort them in ascending order.
Of these 25 data values, 21 are less than or equal to the data value 73. To find the percentile rank of 73, apply the formula:
percentile rank = (L/N)(100)
where L is the number of data values that are less than or equal to 73, and N is the size of the data set.
Substituting in values for this problem, we have:
percentile rank = (21/25)(100)
percentile rank = (0.84)(100)
Percentile ranks are always expressed as whole numbers.
Evaluating the multiplication above and rounding to the nearest whole number we have:
percentile rank = 84
Interpreting our answer, 84% of the numbers in the data set have values less than or equal to 73.
Solve for k.
k/4 + 8 = 12
Answer:
k = 16
Step-by-step explanation:
To solve this we must isolate k. Let's first simplify this equation by subtracting 8 from both sides:
k/4 = 4
Next, remove the fraction by multiplying both sides by 4:
k = 16