SOLUTION
1. From the question the machine stamps 36 caps in 10 seconds
In 5 minutes it will cap
[tex]\begin{gathered} 5\text{ minutes = 5 }\times\text{ 60 seconds } \\ =300\text{ seconds } \\ 36\text{ }\rightarrow\text{caps in 10 seconds } \\ x\text{ }\rightarrow\text{caps in 300 seconds } \\ \text{cross multiplying we have } \\ 36\times300=10\times x \\ 10800=10x \\ x=\frac{10800}{10} \\ x=1080 \end{gathered}[/tex]So in 5 minutes, it would stamp 1080 bottle caps
2. Minutes it would take to stamp 24,408 bottle caps?
[tex]\begin{gathered} 1080\text{ }\rightarrow\text{caps in 5 minutes } \\ 24,408\rightarrow caps\text{ in }x\text{ minutes } \\ \text{cross multiplying we have } \\ 1080\times x=24,408\times5 \\ 1080x=122040 \\ x=\frac{122040}{1080} \\ x=113\text{ minutes } \end{gathered}[/tex]Hence it would take 113 minutes to stamp 24,408 bottle caps
ratios 1 to 32 spoonful of 32 sprinkles
If for each sundae the shop uses 4 spoonfuls of sprinkles, if we want to know how many sundaes the shop did with 32 spoonfuls we must divide 32 by 4, if we do it we get
[tex]32\div4=8[/tex]Therefore, the shop did 8 sundaes! we can count it to make sure:
4 spoonfuls - 1 sundae
8 spoonfuls - 2 sundaes
12 spoonfuls - 3 sundaes
16 spoonfuls - 4 sundaes
20 spoonfuls - 5 sundaes
24 spoonfuls - 6 sundaes
28 spoonfuls - 7 sundaes
32 spoonfuls - 8 sundaes
Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship.A child’s age and the number of hours spent napping-positive-negative-no correlation
We know that a a childresn spend more hours napping when they are youngers therefore we have a negative correlation
A businesswoman buys a new computer for $4000. For each year that she uses it the value depreciates by $400. The equation y=-400x+4000 gives the value y of the computer after x years. What does the x-intercept mean in this situation ? Find the x-intercept. After how many years will the value of the computer be $2000 ?
We have the following:
The intersection with the x-axis is when the value of y is 0, that is, the computer already has a value of 0 and has no commercial value.
we found it like this
[tex]\begin{gathered} 0=-400x+4000 \\ 400x=4000 \\ x=\frac{4000}{400} \\ x=10 \end{gathered}[/tex]which means that in 10 years, the computer does not represent a commercial value
to calculate the number of years that have passed when the computer has a value of 2000, y = 2000, therefore we replace
[tex]\begin{gathered} 2000=-400x+4000 \\ 400x=4000-2000 \\ x=\frac{2000}{400} \\ x=5 \end{gathered}[/tex]This means that in a total of 5 years the value of the computer will be $ 2000
Which of the following is a solution to the equation c + ( 4 -3c) - 2 = 0?A. -1B. 0C. 1D. 2
Given data:
The given equation is c+(4-3c)-2=0
The given equation can be written as,
c+4-3c-2=0
-2c+2=0
-2c=-2
c=1
Thus, the value of c is 1, so option C) is correct.
Divide the polynomial by the binomial. (Simplify your answer completely.)
(q² + 5q + 20) / (q + 8)
Answer:
It's already in its simplest form.
Step-by-step explanation:
Factorising QuadraticsI'm writing a book/document on this topic but it's not finished. I suspect there is an error in this question because it's practically impossible to factorise it into integers.
The quadratic polynomial in the numerator has imaginary roots because 5 squared is less than 20 times 4.
ax² + bx + c;
if ( b² < 4ac ) { 'solution is imaginary' }
The quadratic equation will explain the above.
Assume that Jim Bruce and Valerie are 3 of the 17 members of the class, and that of the class members will be chosen randomly to deliver their reports during the next class meeting. What is the probability that Jim Bruce and Valerie are selected in that order?
The probability that Jim, Bruce and Valerie are selected in that order is P = 1/680
Given,
Number of students in a class = 17
Jim, Bruce and Valerie are 3 of the 17.
Three of students from the class are randomly chosen to deliver their reports during the next class meet.
We have to find the probability that Jim, Bruce and Valerie are selected in that order;
Here,
The total number of possible selection;
S = ⁿCr
Where, n = 17 and r = 3
Then,
S = ¹⁷C₃
S = 17! / 14! x 3!
S = 680
Therefore,
The probability that Jim, Bruce and Valerie are selected in that order is P = 1/680
Learn more about probability here;
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Derek has $20 to spend on used books, but he can not spend all $20.Hardcover books cost $5 each and paperbacks cost $2 each. Create aninequality which determines the number (x) of hardcover books and the number(y) of paperback books he can buy.
Given:
The amount to spend on books, T=$20.
The cost of a handcoverbook, m=$5.
The cost of a paperback, n=$2.
Let x be the number of handcover books and y be the number of paperback books.
It is said that the complete amount of $20 cannot be spend.
So, the inequality to determine x and y can be written as,
[tex]\begin{gathered} T>mx+ny \\ 20>5x+2y \end{gathered}[/tex]So, the inequality is 20>5x+2y.
Find the equation of the line with slope = 5 and passing through (-7,-29). Write your equation in the form
y = mz+b.
Answer:
[tex]y =5x+6[/tex]
Step-by-step explanation:
In the equation, [tex]y=mx+b[/tex], the "m" represents the slope, and the b represents the y-intercept.
We know the slope is 5, so we already know part of the equation: [tex]y=5x+b[/tex]
To solve for the "b" part or y-intercept, we can simply plug in a known point on the line, which was given to be (-7, -29)
This gives us the following equation:
[tex]-29 = 5(-7) + b\\\text{simplify}\\-29 = -35 + b\\\text{add 35 to both sides}\\6=b[/tex]
Answer: y = 5x + 6
Step-by-step explanation:
1. Do point-slope formula {(y - y1) = m(x - x1})
(y - 29) = 5(x - 7)
Distribute
(y - 29) = 5x - 35
Subtract 29 on both sides
Cancel out y - 29 - 29
y = 5x + 6
The figure ABCD is a rectangle. AB = 2 units, AD = 4 units, and AE = FC = 1 unit.Find the area of triangle ABE.
Area of triangle ABE can be calculated using the formula 1/2 x b xh
From the question,
base b = AE = 1
height h =AB = 2
substitute the values into the formula
[tex]A=\frac{1}{2}\times1\times2[/tex]Area = 1 square unit
Gary is saving money to buy a ticket to a New York Jets game that costs $225. Healready has saved $18. What is the least amount of money Gary must save each week, sothat at the end of 9 weeks he has enough money to buy the ticket? (Only an algebraic- solution will be accepted.)
lillyvong13, this is the solution:
Cost of the ticket to a New York Jets game = $ 225
Savings up to now = $ 18
Difference = 225-18 = 207
Number of weeks = 9
Let x to represent the amount of money Gary must save each week for buying the ticket, as follows:
x = 207/9
x = 23
Gary must save $ 23 at the end of 9 weeks to have enough money to buy the ticket
A basic cellular package costs $20/month for 60 minutes of calling with an additional charge of $0.20/minute beyond that time. The cost function C(x) for using x minutes would beIf you used 60 minutes or less, i.e. if if x≤60, then C(x)=20 (the base charge). If you used more than 60 minutes, i.e. (x−60) minutes more than the plan came with, you would pay an additional $0.20 for each of those (x−60) minutes. Your total bill would be C(x)=20+0.20(x−60). If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use?
The maximum number of calling minutes you can use for $50 is 210 minutes.
To solve this, we have the function cost C(x) that depends on the amount of acalling munutes (x)
We want this cost to be $50 or lower. This means:
[tex]\begin{gathered} CostFunction\colon C(x)=20+0.2(x-60) \\ Maximum\text{ value of 50:}C(x)\le50 \end{gathered}[/tex]Then we can create an inequality:
[tex]50\ge20+0.2(x-60)[/tex]And now we can solve for x:
[tex]\begin{gathered} 50\ge20+0.2(x-60) \\ \frac{50-20}{0.2}\ge x-60 \\ 150+60\ge x \\ x\le210\text{ minutes} \end{gathered}[/tex]Thus, with $50 we can talk up to 210 minutes.
To be sure of the result, let's plug x = 210 in the function and it should give us a cost of C(210) = 50:
[tex]\begin{gathered} x=210\Rightarrow C(210)=20+0.2(210-60) \\ C(210)=20+0.2\cdot150 \\ C(210)=20+30=50 \end{gathered}[/tex]This confirms the result.
y=x-6y=x+2 how to solve this problem
No solutions
Explanation
[tex]\begin{gathered} y=x+6\text{ Eq(1)} \\ y=x+2\text{ Eq(2)} \end{gathered}[/tex]
Step 1
replace Eq(1) in Eq (2)
[tex]\begin{gathered} y=x+2\text{ Eq(2)} \\ x+6=x+2 \\ \end{gathered}[/tex]Step 2
subtract x in both sides
[tex]\begin{gathered} x+6=x+2 \\ x+6-x=x+2-x \\ 6=2 \end{gathered}[/tex]6=2 is false, it means there is not solution for both equations,
it's Hamilton path and Hamilton circuitweighted graph / graph theoryyou have to add each angle up and find the answer for each row 12 grade math
What you need to do in order to solve this is add the values that are defined by the begining and end points declared in there:
[tex]A\text{ B D E C A}[/tex]that means the distance defined by AB, BD, DE, EC & CA:
[tex]4+8+11+10+8\text{ = 41}[/tex]And in the same manner all of the other series of distances.
Find the sum of the first 39 terms of the following series, to the nearest integer.2,7, 12,...
The sequence 2,7,12,... given is an arithmetic progression. This is because it has a common difference.
Given:
first term, a = 2
common difference, d = second term - first term = 7 - 2 = 5
d = 5
n = 38
The sum of an arithmetic progression is given by;
[tex]\begin{gathered} S_n=\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ S_{38}=\frac{38}{2}\lbrack2(2)+(38-1)5\rbrack \\ S_{38}=19\lbrack4+37(5)\rbrack \\ S_{38}=19\lbrack4+185\rbrack \\ S_{38}=19(189) \\ S_{38}=3591 \end{gathered}[/tex]Therefore, the sum of the first 39 terms of the series is 3,591
Pic includes all informatin
Answer: 8squares
Step-by-step explanation:
f(x) = -2x² + 2x
Find f(-8)
Answer:
f(-8)= -112
Step-by-step explanation:
-2(-8)^2 + 2(-8)
-2(-64) + 16
-128 + 16
= -112
hope this helped
have a good day :)
Identify the augmented matrix for the system of equations and the solution using row operations.
Given:
The system of equation is given as,
[tex]\begin{gathered} 7x-4y=28 \\ 5x-2y=17 \end{gathered}[/tex]The objective is identify the augmented matrix for the system of equations and the solution using row operations.
Explanation:
The required augmented matrix will be,
Performing the Gauss-Jordan elimination with the following operation,
[tex]R_2=R_2-\frac{5R_1}{7}[/tex]By applying the operation to the augmented matrix,
To find y :
On equating the second row of the matrix,
[tex]\begin{gathered} \frac{6y}{7}=-3 \\ y=\frac{-3}{\frac{6}{7}} \\ y=\frac{-3\times7}{6} \\ y=\frac{-7}{2} \end{gathered}[/tex]To find x :
On equating the first row of the matrix,
[tex]\begin{gathered} 7x-4y=28 \\ 7x=28+4y \\ x=\frac{28+4y}{7} \end{gathered}[/tex]Substitute the value of y in the above equation.
[tex]\begin{gathered} x=\frac{28+4(\frac{-7}{2})}{7} \\ x=\frac{28-14}{7} \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]Thus the value of solutions are,
[tex]\begin{gathered} x=2 \\ y=-\frac{7}{2}=-3.5 \end{gathered}[/tex]Hence, option (3) is the correct answer.
to find the height of a tree, a group of students devised the following method. A girl walks toward the tree along it's shadow until the shadow of the top of her head coincide with the shadow of the top of the tree. if the girl is 150 cm tall, her distance to the foot of the tree is 13 meters, and the length of her shadow is 3 m, how tall is the tree?
Answer: 8m
Explanation:
Given:
To find the height(h) of the tree, we can use ratio since they are similar triangles.
Triangle 1
Triangle 2
So,
[tex]\begin{gathered} \frac{1.5}{3}\text{ = }\frac{h}{16} \\ \text{Simplify and rearrange} \\ h=\text{ }\frac{1.5}{3}(16) \\ \text{Calculate} \\ h=\text{ 8 m} \end{gathered}[/tex]Therefore, the height of the tree is 8m.
I will give brainliest. By the way, two people need to answer for someone to give brainliest.
For the direct variation equation y=223x, what is the constant of proportionality?
A: 2
B: 2 2/3
C: 2/3
D: 3
The equation y=7x gives the relationship between the number of road projects, x, and the number of weeks it takes a crew of workers to complete all the projects, y. What is the constant of proportionality? What does it mean in this context?
A: The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete 1 road project.
B: The constant of proportionality is 7. It takes the crew of workers 7 days to complete all of their road projects.
C: The constant of proportionality is 7. It takes the crew of workers 7 days to complete 1 road project.
D: The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete all of their road projects.
Write a direct variation equation to find the number of miles a jet travels in 3 hours if it is flying at a rate of 600 mph.
A: 600 = 3x
B: 3 = 600x
C: y = 600/3
D: y = 600 x 3
Jamal earns $125,000 a year as a systems analyst. He wants to know how much he will earn if he continues at the same rate of pay for 7 years. Which equation will help him find this amount?
A: x = 125,000/5
B:125,000 = 7x
C:125,000 = 7/x
D: y = 125,000 x 7
Answer: I think B and for the second one I think C
Step-by-step explanation: The constant of proportionality is 7. It takes the crew of workers 7 days to complete 1 road project. That means they have to take at least 7 days which is correct.
can you please help me on e. f. and g.
His temperature was 100.1 degree farad initially which is around 6 pm. At 7 pm it became 101 degree farad.
[tex]\begin{gathered} \text{slope = }\frac{y_2-y_1}{x_2-x_1}=\frac{101-100.1}{7-6}=\frac{0.9}{1}=0.9 \\ m=0.9 \end{gathered}[/tex]y = mx + b
where
m = slope
b = y - intercept
let find the y intercept
[tex]\begin{gathered} 101=0.9(7)+b \\ 101-6.3=b \\ b=94.7 \end{gathered}[/tex]Therefore, the equation is
[tex]y=0.9x+94.7[/tex]e. let us draw a graph
His temperature will be critical above 22 minutes past 9 pm.
f . He should go to emergency room.
g.
[tex]\begin{gathered} y=0.9x+94.7 \\ 98.6=0.9x+94.7 \\ 98.6-94.7=0.9x \\ 3.9=0.9x \\ x=\frac{3.9}{0.9} \\ x=4.33333333333 \end{gathered}[/tex]His temperature will be normal around past 4 pm which is 98.6 degree farad.
I need some help with this! I know about the trig identitys and stuff like that, but I just get a little confused on how to apply sometimes.
we have that
Let
x ------> the distance in miles from a point on the ground (the red line)
In the right triangle of the figure
sin(6.5)=7,000/x
solve for x
x=7,000/sin(6.5)
using a calculator
x=61,835.70 ft
Convert to miles
Remember that
1 mile=5,280 ft
so
61,835.7 ft=61,835.7/5,280=11.71 miles
therefore
the answer is 11.71 milesI need help please quickly I need help
10(2 + 3) - 8 · 3.
20+50-8 times 3
70 -24
46 is answer
Answer:
10(5)-24 ----) 50-24 -----) 26
Step-by-step explanation:
answe is 26
Find extreme values of function f(x) = x³ - (3/2)x² on interval [- 1,2]
we have the function
[tex]f(x)=x^3-\frac{3}{2}x^2[/tex]Find out the first derivative of the given function
[tex]f^{\prime}(x)=3x^2-3x[/tex]Equate to zero the first derivative
[tex]\begin{gathered} 3x^2-3x=0 \\ 3x(x-1)=0 \end{gathered}[/tex]The values of x are
x=0 and x=1
we have the intervals
(-infinite,0) (0,1) (1,infinite)
Interval (-infinite,0) -----> f'(x) is positive
interval (0,1) ---------> f'(x) is negative
interval (1,infinite) -----> f'(x) is positive
that means
x=0 is a local maximum
x=1 is a local minimum
Find out the y-coordinates of the extreme values
For x=0 -----> substitute in the function f(x) ---------> f(x)=0
For x=1 ------> substitute in the function f(x) ------> f(x)=-0.5
therefore
The extreme values are
local maximum at (0,0)local minimum at (1,-0.5)-2 decimal 3/% because if you divide the principal in half its 1% of 3
Metric area unit conversion with decimal valuesTammy has a rectangular poster. The poster is 1.2 meters long and 0.9 meters wide. What is the area of the poster in square centimeters? Do not round youranswer.cmcm²cm³
We are asked to find the final area in square centimeters.
We must first convert the measurements of the poster into centimeters:
1.2m = 120cm
0.9m = 90cm
Area = length * width
= 120*90
= 10800 square centimeters.
Hello, I need assistance with this question within the image posted below.
A(-4, 0) and B(4, 0)
Explanation:A parabola is symmetrical about the y-axis, if the vertex is of the form (0, y). The y-axis is the line of symmetry. That is, the point x = 0.
If the parabola is symmetric about the y-axis, points A and B should fall on opposite sides of the y-axis.
For the parabola to be symmetric about the y-axis, the possible points to move A and B to are A(-4, 0) and B(4, 0)
74. Noam wants to put a fence around his rectangular garden. His garden measures 35 feet by 50 feet. Thegarden has a path around it that is 3 feet wide. How much fencing material does Noam need to enclose thegarden and path?A. 97 ftB. 194 ftC. 182 ftD. 146 ft
Given:
The length of the rectangular garden, l=50 feet.
The breadth of the rectangular garden, b=35 feet.
The width of the path around the garden, w=3 feet.
The figure can be drawn as,
So, the length of the fence, L=l+2w.
The breadth of the fence, B=b+2w
The perimeter of the fence can be calculated as,
[tex]\begin{gathered} P=2(L+B) \\ =2(l+2w+b+2w) \\ =2(l+b+4w) \\ =2(50+35+4\times3) \\ =2(50+35+12) \\ =2\times97 \\ =194\text{ ft} \end{gathered}[/tex]Therefore, the perimeter of the fence is 194 ft.
Option B is correct.
7) The water park is a popular field trip destination. This year the senior class at High School A and thesenior class at High School B both planned trips there. The senior class at High School A rented andfilled 1 van and 14 buses with 309 students. High School B rented and filled 4 vans and 14 buseswith 354 students. Each van and each bus carried the same number of students. Find the number ofstudents in each van and in each bus.C) Van: 19 Bus: 29 D) Van: 15, Bus: 21
Given
The water park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and 14 buses with 309 students. High School B rented and filled 4 vans and 14 buses with 354 students. Each van and each bus carried the same number of students.
Answer
Let students in Van be x
And students in bus be y
A/Q
x + 14y = 309 (1)
4x + 14y = 354 (2)
Subtracting (1) and (2)
3x = 45
x = 15
Put in eq (1)
15 + 14 y = 309
14y = 309 - 15
14 y = 294
y = 21
St
Leila runs at 12 mph find the number of miles she can travel if she runs for 2 hours
20 POINTS ANSWER I WILL MARK BRAINLIEST!!!!!!!!!!
Answer: 24 mph
Step-by-step explanation:
If she can run 12 mph/ 12 miles per hour
She runs for 2 hours
12 · 2 = 24
Juan and María López wish to invest in a no-risk saving account. they currently hace $30,000 in an account bearing 5.25% annual interest, compounded continuously. the following choices are available to them.A. Keep the Money in The account they currently have B. invest the Money in an account earning 5.875% interest compounded annually c. invest the Money in an account earning 5.75% compounded semi annually d. invest Money in an account earning 5.5% annual interést compounded quarterly
The general formula for the amount in savings account compounded annually is given as;
[tex]\begin{gathered} A=P(1+\frac{r}{100n})^{nt} \\ \text{Where A=Amount} \\ P=\text{Initial deposit} \\ r=\text{rate} \\ n=n\text{ umber of times it is compounded annually} \\ t=\text{time} \end{gathered}[/tex]A. The equation for the value of the investment as a function of t in the current account they have is;
[tex]A(t)=\text{ \$30000(1+}\frac{5.25}{100})^t[/tex]B. The equation for the value of the investment in an account earning 5.875% interest compounded annually is;
[tex]A(t)=\text{ \$30000(1+}\frac{5.875}{100})^{t^{}}[/tex]C. The equation for the value of the investment in an account earning 5.75% compounded semi-annually; that is twice in a year is;
[tex]\begin{gathered} A(t)=\text{ \$30000(1+}\frac{5.75}{100(2)})^{2t} \\ A(t)=\text{ \$30000(1+}\frac{5.75}{200})^{2t} \end{gathered}[/tex]D. The solution for the value of the investment in an account earning 5.5% annual interest compounded quarterly; that is four times in a year;
[tex]\begin{gathered} A(t)=\text{ \$30000(1+}\frac{5.5}{100(4)})^{4t} \\ A(t)=\text{ \$30000(1+}\frac{5.5}{400})^{4t} \end{gathered}[/tex]Brenda is preparing food for a picnic. She must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich
For 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.equation modelling : Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is Brenda who must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, and 45 minutes to make a dozen cookies.
If she makes [x] sandwiches and [y] dozen cookies, then the total time she would take to make them can be written as -
t = 4x + 3y
For 6 sandwiches and 3 dozen cookies, we can write -
t(6, 3) = 4 x 6 + 3 x 3 = 24 + 9 = 33 minutes
t(6, 3) = 33 minutes
Therefore, for 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.
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{Complete question is given below -
She must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, x, and 45 minutes to make a dozen cookies, y.}