Answer:
$203
Step-by-step explanation:
Please mark brainliest
Find the area of the following figure. Round to the nearest hundred if necessary.
14 m
9.5 m
17 m
The area of the given figure is 133 m²
Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,
The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height
Therefore,
The area of the given figure = 9.5 x 14 = 133
Hence, the area of the given figure is 133 m²
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$16,000 is deposited into a savings account with an annual interest rate of 2% compounded continuously. How much will be in the account after 4 years? Round to the nearest cent.
The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.
Understanding Compound InterestRecall the compounding formula:
A = P * [tex]e^{rt}[/tex]
Where:
A = Final amount in the account
P = Initial principal (deposit)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (as a decimal)
t = Time in years
Given:
Initial principal (P) = $16,000
Annual interest rate (r) = 2% = 0.02
time (t) = 4 years.
Substitute these values into the formula, we get:
A = $16,000 * [tex]e^{0.02 * 4}[/tex]
Using a calculator, we can calculate:
A = $16,000 * [tex]e^{0.08}[/tex]
A = $16,000 * 1.0833
A = $17,332.8
Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.
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50 POINTS!!!
Math...Money...Interest...
Please give the correct answers and show the steps. I will report your account if I find an error. Thank you for your help.
Answer:
2.
Quarterly:
100000 = 60000(1 + 0.075/4)^4tt ≈ 6.87466382 yearsMonthly:
100000 = 60000(1 + 0.075/12)^12tt ≈ 6.83227061 yearsContinuously:
100000 = 60000e^0.075tt ≈ 6.811008 years3.
Twice a year:
300 = 100(1 + 0.1025/2)^2tt ≈ 10.99053398 yearsEight times a year:
300 = 100(1 + 0.1025/8)^8tt ≈ 10.78668624 yearsContinuously:
300 = 100e^0.1025tt ≈ 10.718169 yearsStep-by-step explanation:
The formula for compound interest is:
A = P(1+r/n)^nt
The formula for compounded continuously is:
A = Pe^rt
Where:
A = the future value of the investment
P = the principal balance
r = the annual interest rate (decimal)
n = number of times interest is compounded per year
t = the time in years
Using that we can plug the formula in for each question:
2.
Quarterly:
100000 = 60000(1 + 0.075/4)^4tCompounded quarterly means in a year, it is compounded 4 timesNote that the question is asking to find how much time it takes so t is the thing we need to solve fort ≈ 6.87466382 yearsMonthly:
100000 = 60000(1 + 0.075/12)^12tt ≈ 6.83227061 yearsContinuously:
100000 = 60000e^0.075tWe are now using the compounded continuous formulat ≈ 6.811008 years3.
Twice a year:
Since the question does not give us a starting amount but it gives us a goal of tripling the money, we can substitute any amount of money for P and A as three times PFor now, let's say P is 100 and A is 3 times 100 so A is 300300 = 100(1 + 0.1025/2)^2tt ≈ 10.99053398 yearsEight times a year:
We will continue to place hold P as 100 and A as 300300 = 100(1 + 0.1025/8)^8tt ≈ 10.78668624 yearsContinuously:
We will now use the compounded continuous formula300 = 100e^0.1025tt ≈ 10.718169 years.3185 degrees = minutes and seconds
The conversion of 3185 degrees to minutes and seconds is 19 minutes and 6.6 seconds
How to convert the 3185 degrees to minutes and secondsFrom the question, we have the following parameters that can be used in our computation:
Degrees = 0.3185
By definition, there are 60 minutes in a degrees
So, we have
Minutes = 0.3185 * 60
Evaluate the product
Minutes = 19.11
The decimal part of the product above represents the number of seconds
So, we have
Minutes = 19
Seconds = .11 * 60
Evaluate
Seconds = 6.6
Hence, .3185 degrees is 19 minutes and 6.6 seconds
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Select the matrix that represents the parallelogram
The correct matrix representation is; [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,
Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)
Given here the points are P₁(1, 3) and P₂(5, 2)
Thus, by the coordinates of the two vectors, we can represent the matrix ;
[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Hence, Option A) is the correct answer.
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Help me please answer is not A
Answer:
B) 16.47
Step-by-step explanation:
In order to find the mean of grouped data with intervals, we use the formula
(∑f * m) / (∑f)
where (∑f * m) is the sum of the product of each frequency (f) and the corresponding midpoint (m) for its interval and (∑f is the sum of each frequencyStep 1: First, we need to find the sum of the frequencies: ∑f = 2 + 3 + 8 + 4 = 17
Step 2: Next, we need to find the midpoint (m) of each interval. We do this by averaging the end points of each interval
m of first interval: (9.5 + 12.5) / 2 = 11
m of second interval: (12,5 + 15.5) / 2 = 14
m of third interval: (15.5 + 18.5) / 2 = 17
m of fourth interval: (18.5 + 21.5) / 2 = 20
Step 3: Now, we multiply the frequency for each interval by its corresponding midpoint and add them together to find the sum
f * m for first interval: (2 * 11) = 22
f * m for second interval: (3 * 14) = 42
f * m for third interval: (8 * 17) = 136
f * m for fourth interval: (4 * 20) = 80
Sum of f * m for each interval: 22 + 42 + 136 + 80 = 280
Step 4: Finally, we divide the sum of f * m for each interval by the sum of f to find the mean:
280 / 17 = 16.47058824 = 16.47
At Chairs and More, assemblers are paid according to the following differential piece rate scale: 1−25 chairs in a week, $10 each; 26−40 chairs, $13 each; and $17.50 each for every chair over 40. Salina Grant assembled 47 chairs in one week. Find her gross pay.
Salina Grant's gross pay for assembling 47 chairs in one week at Chairs and More is $567.50.
To calculate Salina Grant's gross pay, we need to determine the pay for each range of chairs assembled and sum them up.
Let's break down the calculation based on the given differential piece rate scale:
1-25 chairs: $10 each
Salina assembled 25 chairs in this range, so the pay for this range is
25 * $10 = $250.
26-40 chairs: $13 each
Salina assembled 15 chairs in this range, so the pay for this range is
15 * $13 = $195.
Chairs over 40: $17.50 each
Salina assembled 47 chairs in total, and since she already assembled 25 chairs in the first range and 15 chairs in the second range, the number of chairs in this range is
47 - 25 - 15 = 7 chairs.
The pay for this range is
7 * $17.50 = $122.50.
Now, let's sum up the pay for each range to find Salina Grant's gross pay:
$250 + $195 + $122.50 = $567.50
Therefore, Salina Grant's gross pay for assembling 47 chairs in one week at Chairs and More is $567.50.
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of tennis balls is shaped like a cylinder with the dimensions shown
r= 4 cm
What is the approximate surface area of the can? Use 3.14 for. Use the formula for the surface area of a cylinder SA= 2mth + 2rr²
527 cm²
100 cm²
628 cm²
525 cm²
21 cm
Previous
Next >
The formula for the surface area of a cylinder SA= 2mth + 2rr² is 525 cm².
To find the surface area of the cylindrical can, we need to use the formula:
SA = 2π[tex]r^2[/tex]+ 2πrh
where r is the radius of the circular base of the can, h is the height of the can, and π is a mathematical constant approximately equal to 3.14.
From the given dimensions, we know that the radius of the can is 4 cm. However, we do not have the height of the can. Therefore, we cannot accurately calculate the surface area of the can.
Based on the answer choices provided, we can approximate the surface area of the can by using the given value of r = 4 cm and an estimated value for the height.
For example, if we assume the height of the can is approximately 10 cm, then we can use the formula to calculate the surface area:
SA = 2π([tex]4^2[/tex]) + 2π(4)(10)
SA = 100.48 + 251.2
SA ≈ 351.68 [tex]cm^2[/tex]
≈525 cm²
This value is closest to the fourth answer choice of 350 [tex]cm^2[/tex]. However, it is important to note that this answer is an approximation based on estimated values, and may not be entirely accurate.The correct answer is 525 cm².
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NO LINKS!! URGENT HELP PLEASE!!
O is the center of the regular nonagon below. Find its area. Round to the nearest tenth if necessary.
Answer:
471.1 square units
Step-by-step explanation:
A regular nonagon is a 9-sided polygon with sides of equal length.
The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.
Therefore, the given diagram shows a regular nonagon with an apothem of 12 units.
The side length (s) of a regular polygon can be calculated using the apothem formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Given values:
a = 12n = 9Substitute the given values into the formula to create an expression for the side length (s):
[tex]12=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{9}\right)}[/tex]
[tex]12=\dfrac{s}{2 \tan\left(20^{\circ}\right)}[/tex]
[tex]s=24 \tan\left(20^{\circ}\right)[/tex]
The standard formula for an area of a regular polygon is:
[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]
Substitute the found expression for s together with n = 9 and a = 12 into the formula and solve for A:
[tex]A=\dfrac{9 \cdot 24 \tan(20^{\circ}) \cdot 12}{2}[/tex]
[tex]A=1296\tan(20^{\circ})[/tex]
[tex]A=471.705423...[/tex]
[tex]A=471.7\; \sf square\;units\;(nearest\;tenth)[/tex]
Therefore, the area of a regular nonagon with an apothem of 12 units is 471.1 square units, rounded to the nearest tenth.
Use angle diagram to name each one of the angles.
The angles in the parallel lines are solved
∠9 and ∠16 = alternative exterior angles
∠15 and ∠11 = supplementary angles
∠10 and ∠15 = alternate interior angles
∠12 and ∠15 = vertical angles
∠9 and ∠11 = corresponding angles
∠9 and ∠15 = none
∠13 and ∠14 = supplementary angles
∠14 and ∠11 = alternative interior angles
Given data ,
Let the two parallel lines be represented as a and b
where the transversal line is m
Now , from the given figure , we can deduct that
We can conclude some factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Now , the angles are
∠9 and ∠16 = alternative exterior angles
∠15 and ∠11 = supplementary angles
∠10 and ∠15 = alternate interior angles
∠12 and ∠15 = vertical angles
∠9 and ∠11 = corresponding angles
∠9 and ∠15 = none
∠13 and ∠14 = supplementary angles
∠14 and ∠11 = alternative interior angles
Hence , the angles are solved
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Please help I am struggling thank you, have a great day
Answer:
24
Step-by-step explanation:
For this problem, substitute the value -3 for x and solve. It would look like this:
[tex]4(-3)^2+2(-3)-6[/tex]
Using the order of operations (PEMDAS) we solve the exponent first.
[tex]-3^2=9[/tex]
Then solve the multiplication parts.
[tex]4(9)+2(-3)-6\\4*9=36[/tex]and [tex]2*(-3)=-6[/tex]
Finally subtract to get the answer.
[tex]36-6-6=24[/tex]
Could someone help me with this? Thank you
The values for the determinants of the matrices are:
|A| = -3
|B| = -2
|AB|= -6
How to determine the determinant of A, |A|?A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
If the matrix Z is given as:
[tex]Z = \left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]
The determinant will be:
|Z| = (a * d) - (b * c)
Thus:
|A| = (-1 * 3) - (0 * 0) = -3
|B| = (2 * (-1)) - (0 * 0) = -2
AB = A * B
[tex]AB = \left[\begin{array}{ccc}-1&0\\0&3\end{array}\right] * \left[\begin{array}{ccc}-2&0\\0&-1\end{array}\right][/tex]
Calculations for the product (multiply each row by each column):
[-1 * (-2)] + [0 * 0] = 2
[-1 * 0] + [0 * (-1)] = 0
[0 * (-2)] + [3 * 0] = 0
[0 * 0] + [3 * (-1)] = -3
[tex]AB = \left[\begin{array}{ccc}2&0\\0&-3\end{array}\right][/tex]
Thus,
|AB| = (2 * (-3)) - (0 * 0) = -6
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Two factory plants are making TV panels. Yesterday, Plant A produced 6000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 820 defective panels?
Answer:
16000
Step-by-step explanation:
You want to know the number of panels produced at plant B if that was 6000 more panels than at plant A, and the total number of defective panels was 820. The defect rate at plant A is 5%, and at plant B is 2%.
SetupLet b represent the number of panels produced at plant B. Then the number produced at plant A is (b-6000). The total number of defects is ...
0.05(b -6000) +0.02b = 820
SolutionSimplifying the equation, we have ...
0.07b -300 = 820
0.07b = 1120
b = 16000
Plant B produced 16000 panels.
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6 sin =5 solve to the nearest 0.1
Step-by-step explanation:
sin Φ = 5/6 = .8333
Arcsin ( sin Φ) = arcsin (.8333)
Φ = 56.4 degrees
how do i find find the distance
The value of distance of two points shown in figure is,
⇒ d = √20
We have to given that;
Two points on graph are,
(0, 1) and (2, - 3)
Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, The distance of two points shown in figure is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ d = √ (2 - 0)² + (-3 - 1)²
⇒ d = √4 + 16
⇒ d = √20
Thus, The value of distance of two points shown in figure is,
⇒ d = √20
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How do I solve this help me pls now I need it pls I’ll give lots of points help me I put a picture here
The radius of cylinder is 31.5 cm.
We have,
LSA of Cylinder. = 693 cm²
Height = 11 cm
We know the formula
Lateral Surface Area of Cylinder = 2πrh
So, LSA of cylinder = 639π
2πh= 693π
2rh = 693
r = 693 / 2h
r =693 / 2 x 11
t = 63/2
r = 31.5 cm
Thus, the radius of cylinder is 31.5 cm.
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Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $13.00
5 $17.50
7 $20.50
10 $25.00
15 $32.50
What does the y-intercept mean in this situation?
For every additional mile the cab travels, the total fee increases by $10.00.
For every additional mile the cab travels, the total fee increases by $1.50.
When the cab travels 0 miles, the total fee will be $1.50.
When the cab travels 0 miles, the total fee will be $10.00.
Answer:
When the cab travels 0 miles, the total fee will be $10.00.
Step-by-step explanation:
We Know
2 miles = $13.00
5 miles = $17.50
3 miles = 17.50 - 13.00 = $4.50
1 mile = 4.50 / 3 = $1.50
So, for every 1-mile go, the cost is increasing by $1.50; this is the slope.
What does the y-intercept mean in this situation?
It is the total fee that Tyrell pays when the cab goes 0 miles (when he first steps in the cap).
So, the answer is D. When the cab travels 0 miles, the total fee will be $10.00.
What is the x of 4(40)-10
A bag consists of 5 marbles. There is 1 yellow, 1 red marble, 1 clear marble, 1 green marble, and 1 blue marble. Which table shows the sample space for choosing 2 marbles from the bag with replacement? Answer by looking at the images below!
Table C shows the sample space for choosing 2 marbles from the bag with replacement. The probabity and there are 25 possible pairs.
The sample space for choosing 2 marbles from the bag with replacement consists of all possible pairs of marbles that can be chosen, where the order in which they are chosen does not matter.
Since there are 5 marbles in the bag and we are choosing 2 of them, there are 5 choices for the first marble and 5 choices for the second marble, for a total of [tex]5*5 = 25[/tex] possible pairs.
Table C shows the sample space for choosing 2 marbles from the bag with replacement. Each row and column in the table represents a different marble that can be chosen, and each cell represents a pair of marbles that can be chosen.
For example, the cell in row 2 and column 3 represents the pair of marbles consisting of the red marble and the clear marble. Tables A and B show the sample space for choosing 2 marbles from the bag without replacement. In this case, the order in which the marbles are chosen does matter, and each marble can only be chosen once.
Therefore, there are only 5 choices for the first marble, but only 4 choices for the second marble (since one marble has already been chosen), for a total of[tex]5 * 4 = 20[/tex] possible pairs.
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The complete question is:
A bag contains five green marbles, three blue marbles, two red marbles, and two yellow marbles. One marble is drawn out randomly.
a) Are the four different colour outcomes equally likely? Explain.
b) Find the probability of drawing each colour marble i.e., P(green), P(blue), P(red) and P(yellow)
c) Find the sum of their probabilities.
During the repair, the mechanics will need to
connect a cable between chairs B and J, and then
continue that cable to chair G. What is the angle
formed by the cable?
The angle formed by the cable between chairs B and J, and then
continue chair G is
75 degrees
How to determine the angleThe angle is determined with the knowledge of the total angle in a circle which is 360 degrees. Also, intercepted arc = 2 * inscribed angle
Assuming each chair is equal distance apart, then they will subtend equal angle.
The number of chairs for A to L is 12
angle per chair = 360 / 12 = 30 degrees
number of chairs from B to G = 5 and angle intercepted arc = 30 * 5 = 150 degrees
Inscribed angle = 1/2 * intercepted arc
Inscribed angle = 1/2 * 150
Inscribed angle = 75 degrees
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The price of a computer is $999.00. The sales tax rate is 7%. What is the sales tax on this computer in dollars and cents?
The sales tax on the computer is $69.93.
How to determine the sales taxTo calculate the sales tax on the computer, we need to multiply the price of the computer by the sales tax rate. Here's how you can do it:
Price of the computer: $999.00
Sales tax rate: 7% (which can be expressed as 0.07)
Sales tax = Price of the computer * Sales tax rate
Sales tax = $999.00 * 0.07
To find the sales tax in dollars and cents, we can perform the calculation:
Sales tax = $999.00 * 0.07
Sales tax = $69.93
Therefore, the sales tax on the computer is $69.93.
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You are given a map with a number scale 1:60 you must measure a length on the map of 10cm
The measure of a length of 10cm on the scale is 1/6 units
How to determine the measure of a length on the map of 10cmFrom the question, we have the following parameters that can be used in our computation:
Scale = 1 : 60
For a length of 10 cm, we have
Actual length = 10 cm
This means that
Scale ; 10 cm = 1 : 60
Express as fraction
So, we have
Scale/10 cm = 1/60
When evaluated we have
Scale = 1/6 units
Hence, the measure of a length of 10cm on the scale is 1/6 units
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How many variables are in the expression.
8d²+2bc+ 10ab
1
2
3
4
There are 4 variables in the expression 8d² + 2bc + 10ab
How to determine the number of variables in the expressionFrom the question, we have the following parameters that can be used in our computation:
8d²+2bc+ 10ab
Express properly
So, we have
8d² + 2bc + 10ab
Consider an expression ax + by where the variable is a and b are constants
The variables in the expression are x and y
Using the above as a guide, we have the following:
The variables in the expression 8d² + 2bc + 10ab are a, b, c and d
This means that there are 4 variables in the expression
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: 127
Step-by-step explanation:
360 - 70 - 36 = 254
254/2 = 127
D = 127
please help me thank you so much
Answer:
1)
7+9-15 = add 7 and 9, then subtract 15
2)
15-(7+9) = The sum of 7 and 9 subtracted from 15
3)
15-(7+9) = subtract 7 from 15, then add 9
Step-by-step explanation:
Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient
side length of titles are 2ft. Rachel tiled the whole floor with 6 rows of 4 tiles
what is the area of the kitchen floor
The area of the rectangular shaped kitchen floor is A = 96 feet²
Given data ,
The side length of each tile is 2ft, then the area of each tile is:
Area of a tile = side x side = 2ft x 2ft = 4 sq ft
Since there are 6 rows of tiles, each row has 4 tiles, therefore the total number of tiles is:
Total number of tiles = 6 x 4 = 24 tiles
So, the total area covered by the tiles is:
Total area covered by tiles = Area of a tile x Total number of tiles
= 4 sq ft/tile x 24 tiles
= 96 sq ft
Hence , the area of the kitchen floor is 96 feet²
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Suppose theta is an angle in the third quadrant and cos theta = 5/7. What is the value of sin(theta)
3√8
√24
24
2√12
The value of sinθ is √24/7 meanwhile the correct answer is not in the option provided or perhaps option (b) is meant to be √24/7 instead.
Understanding Quadrant in TrigonometryIn the third quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) of the angle are negative.
Given that
cosθ = 5/7
we can determine the value of sinθ using the Pythagorean identity:
sin²θ + cos²θ = 1
sin²θ + (5/7)² = 1
sin²θ + 25/49 = 1
Now, let's solve for sinθ:
sin²θ = 1 - 25/49
sin²θ = 49/49 - 25/49
sin²θ = 24/49
Taking the square root of both sides, we find:
sinθ = √(24/49)
Simplifying further:
sinθ = √24 / √49
sinθ = √24 / 7
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Idaho gets out and closes the door behind her. She is in a room with one exit, and the lock requires a key. There's a table with a briefcase that is also locked. It has a three-digit combination. The first part of the combination is on a wheel with all 10 digits. The second wheel has only 5 digits, and the third has 3 digits. How many combinations are possible?
Answer:
150
Step-by-step explanation:
To determine the number of possible combinations for the briefcase, we need to multiply the number of options for each wheel.
The first wheel has 10 digits, so there are 10 possibilities.
The second wheel has 5 digits, so there are 5 possibilities.
The third wheel has 3 digits, so there are 3 possibilities.
To calculate the total number of combinations, we multiply the possibilities for each wheel:
10 × 5 × 3 = 150
Therefore, there are 150 possible combinations for the briefcase.
Answer: 150
Step-by-step explanation:
I’m not completely sure, but this is going by my logic. The first one has ten digits and any of those ten digits could go with 1 digit from the 5 wheel, and 1 digit from the 3 wheel, so (I think) you have to multiply 10x5x3 to get the amount of possible combinations.
But, if this is wrong, please correct me! I love puzzles and just though this would be fun to try and figure out, I don’t want to spout out any mis or disinfo to anyone
But, in the case my answer’s right, hope this helped :D
Question 1 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
OA. x=-8, y = 2
OB. More than 1 solution
OC. No solution
OD. x= 12, y = 3
3y-12x = 18
2y-8x = 12
The system of equations has infinitely many solutions, which corresponds to option (OB).
We can use the graphing function on a calculator to find the solution to the system of equations:
[tex]3y - 12x = 18\\\\2y - 8x = 12[/tex]
To do this, we can rearrange each equation to solve for y in terms of x:
[tex]3y = 12x + 18\\\\y =4x + 6[/tex]
For the second equation.
[tex]2y = 8x + 12\\\\y = 4x + 6[/tex]
We can see that the two equations have the same slope (4) and y-intercept (6). Therefore, the two equations represent the same line, and any point on that line will satisfy both equations.
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A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 270 degrees counterclockwise, the new coordinates would be:
After rotating the triangle counterclockwise by 270 degrees, the new coordinates of the vertices would be (3, -1), (-4, 2), and (3, 5).
How to Find the New Coordinates of a Triangle after a Rotation?To rotate a point counterclockwise around the origin by 270 degrees, we can use the following transformation rules:
[tex]New_x = -y[/tex]
[tex]New_y = x[/tex]
Let's apply these rules to each vertex of the triangle and find the new coordinates:
For the first vertex (-3, 1):
[tex]New_x = -1[/tex]
[tex]New_y = -(-3) = 3[/tex]
So, the new coordinates for the first vertex after rotating counterclockwise by 270 degrees are (3, -1).
For the second vertex (2, 4):
[tex]New_x = -4[/tex]
[tex]New_y = 2[/tex]
The new coordinates for the second vertex after rotating counterclockwise by 270 degrees are (-4, 2).
For the third vertex (5, -3):
[tex]New_x = -(-3) = 3[/tex]
[tex]New_y = 5[/tex]
The new coordinates for the third vertex after rotating counterclockwise by 270 degrees are (3, 5).
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