Answer:
117
Step-by-step explanation:
You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).
Cross productThe cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.
u×v = (12)(11) -(-3)(-5) = 132 -15
u×v = 117
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what’s the numbers that correspond to the corret number of solutions
The number of solutions for the given system of linear equations is: Infinitely many solutions.
Calculating the number of solutionsTo determine the number of solutions for the given system of linear equations:
3x - y = 4
6x - 2y = 8
We can use the algebraic method of solving the system of equations by substitution or elimination.
Let's use the algebraic method to determine the number of solutions:
3x - y = 4 (1)
6x - 2y = 8 (2)
We can simplify equation (2) by dividing both sides by 2:
3x - y = 4 (1)
3x - y = 4 (2')
Equations (1) and (2') are equivalent, which means that they represent the same line.
Therefore, the two equations represent the same line, and we have infinitely many solutions.
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Complete question
What’s the numbers that correspond to the corret number of solutions
0 solution, 1 solution, Many solutions
3x - y = 4
6x - 2y = 8
PLS HELP ASAP 90 POINTS Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.
Mangos Used Smoothie Size
Bri 1 7 oz
Kim 3 21 oz
Angela 4 28 oz
Which statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is 1:7, and the ratio of smoothie size to mangos used for Bri is 3:28.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 7:1, and the ratio of smoothie size to mangos used for Angela is 4:28.
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
Answer:
The correct statement is "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela".
The correct answer option is option A
How to solve ratio?
Mangos Used Smoothie Size
Angela 1 9 oz
Kim 3 27 oz
Bri 4 36 oz
Check the given options to determine which statement is correct;
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
Kim = 27 : 3 = 9 : 1
Angela = 9 : 1
True
The ratio of smoothie size to mangos used for Kim is 1:9, and the ratio of smoothie size to mangos used for Bri is 4:27.
Kim = 27 : 3 = 9 : 1
Bri = 36 : 4 = 9 : 1
False
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
Angela = 9 : 1
Kim = 27 : 3 = 9 : 1
False
The ratio of smoothie size to mangos used for Bri is 9:1, and the ratio of smoothie size to mangos used for Angela is 4:36.
Bri = 36 : 4 = 9 : 1
Angela = 9 : 1
False
Therefore, Kim and Angela has equal ratio of smoothie size to mangoes used.
A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 7 centimeters by 3 and three-fifths centimeters by 2 and two-fifths centimeters.
What is the surface area of the prism?
Answer:
The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width and h is the height.
In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of 2(7) (3.6) + 2(7) (2.4) + 2(3.6) (2.4), which simplifies to 50.4 + 33.6 + 17.28, or 101.28 square centimeters.
So, the surface area of this rectangular prism is 101.28 square centimeters.
Received message. The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is `2lw + 2lh + 2wh`, where `l` is the length, `w` is the width and `h` is the height. In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of `2(7)(3.6) + 2(7)(2.4) + 2(3.6)(2.4)`, which simplifies to `50.4 + 33.6 + 17.28`, or **101.28 square centimeters**. So, the surface area of this rectangular prism is **101.28 square centimeters**.
Step-by-step explanation:
On a computer screen, lengths and widths are measured not in inches or millimeters but
in pixels. A pixel is the smallest visual element that a computer is capable of processing. A
common size for a large computer screen is 1024 × 768 pixels. (Widths rather than heights are
conventionally listed first.) For the following, assume you’re working on a 1024 × 768 screen.
1. You have a photo measuring 640 × 300 pixels and you
want to enlarge it proportionally so that it is as wide as the
computer screen. Find the measurements of the photo after it
has been scaled up. Explain how you found the answer.
2. a. Explain why you can’t enlarge the photo proportionally so
that it is as tall as the computer screen.
b. Why can’t you correct the difficulty in (a) by scaling the
width of the photo by a factor of 1024 ÷ 640 and the
height by a factor of 768 ÷ 300
To enlarge the photo proportionally so that it is as wide as the computer screen, we need to find the scaling factor. The scaling factor is the ratio of the width of the computer screen to the width of the photo:
Scaling factor = 1024 ÷ 640 = 1.6
We can then use this scaling factor to find the new dimensions of the photo:
New width = 640 × 1.6 = 1024 pixels
New height = 300 × 1.6 = 480 pixels
Therefore, the new dimensions of the photo are 1024 × 480 pixels.
2a. We cannot enlarge the photo proportionally so that it is as tall as the computer screen because the aspect ratio of the photo is different from the aspect ratio of the computer screen. The aspect ratio of the photo is 640 ÷ 300 ≈ 2.13, while the aspect ratio of the computer screen is 1024 ÷ 768 ≈ 1.33. This means that if we enlarge the height of the photo to match the height of the computer screen, the width of the photo will be too wide to fit on the screen.
b. We cannot correct the difficulty in (a) by scaling the width of the photo by a factor of 1024 ÷ 640 and the height by a factor of 768 ÷ 300 because this would change the aspect ratio of the photo. The aspect ratio of the photo would become 1024 ÷ (640 × 1024 ÷ 640) ≈ 1.6, which is the same as the aspect ratio of the computer screen. However, the height of the photo would be scaled by a factor of 768 ÷ 300 ≈ 2.56, which would make the photo too tall to fit on the screen.
To enlarge the photo proportionally, we need to scale it up by the same factor in both dimensions. Since we want to scale it so that its width matches the width of the screen, we can find the scaling factor by dividing the screen width by the photo width:
scaling factor = screen width / photo width = 1024 / 640 = 1.6
Now we can use this scaling factor to find the new height of the photo:
new height = photo height x scaling factor = 300 x 1.6 = 480 pixels
Therefore, after the photo is scaled up proportionally, its measurements are 1024 x 480 pixels.
2a. We can't enlarge the photo proportionally so that it is as tall as the computer screen because its aspect ratio (the ratio of its width to its height) is different from the aspect ratio of the screen. The photo's aspect ratio is 640/300 = 2.13, while the screen's aspect ratio is 1024/768 = 1.33. Enlarging the photo so that its height matches the screen's height would require stretching the photo vertically, which would distort the image.
2b. Scaling the width of the photo by a factor of 1024/640 and the height by a factor of 768/300 would not correct the difficulty in part (a) because it would not change the aspect ratio of the photo. The aspect ratio of the photo would still be 2.13, which is different from the aspect ratio of the screen. The photo would still need to be stretched vertically to match the screen's height, which would distort the image.
James answered 14 lems correctly
an a 16-item quiz. what percentage did he answer correctly
Answer:
14/16 = 0.875
Consider the letters in the word SAMPLE. In how many ways can you arrange 5 of the letters?
Answer: 720
Step-by-step explanation: There are 6 choices for the first letter, 5 for the second, 4 for the third and so on. 6*5*4*3*2=720
Step-by-step explanation:
according to the law of combination
⁵C6 note 6 is a base numberCombining formula: 6!/(6-1)! 6!solving 6!/5! 6! :120waysa 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm
The shaded area of the portion as shown in the diagram is 78.04 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the shaded area of the portion, we use the formula below
Formula:
A = πr²-lw.................. Equation 1Where:
A = Area of the shaded portionr = Radius of the circlel = Length of the rectanglew = Width of the rectangleFrom the question,
Given:
r = 6 cml = 7 cmw = 5 cmSubstitute these values into equation 1
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Complete question: A 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm. Calculate the area of the shaded portion.
what is the slope of the line below?
Answer:
B. Y= 5x - 2
Step-by-step explanation:
The Y is negative, you can see the number -5 below the point, if you go to the top, that is, to 0 and count down, the lines are two and the X is positive 5, you can see where the number 5 is and the point is above.
I’ve had trouble on these even on my test and I still can’t figure it out. Can someone explain how to solve:
3x = y - 2
6x = 4 - 2y
Answer: Sure, here's how to solve the system of equations:
1. Start with the first equation: 3x = y - 2
Solve for y by adding 2 to both sides: y = 3x + 2
2. Substitute the value of y from the first equation into the second equation:
6x = 4 - 2y
6x = 4 - 2(3x + 2) (substitute y = 3x + 2)
6x = 4 - 6x - 4
12x = 0
3. Solve for x by dividing both sides by 12: x = 0
4. Substitute the value of x from step 3 into either equation to solve for y:
y = 3x + 2
y = 3(0) + 2
y = 2
Therefore, the solution to the system of equations is (x, y) = (0, 2).
hope this helpsss :D
Step-by-step explanation:
Julie was testing how far two new electric cars—model A and model B—could drive on a full charge. She obtained a sample of 5 55 new cars of each model, charged them fully, and drove them as far as she could along a controlled route. Here is a summary of the distances: Distance Model A Model B Mean 168 km 168 km168, start text, space, k, m, end text 172 km 172 km172, start text, space, k, m, end text Standard deviation 5.4 km 5.4 km5, point, 4, start text, space, k, m, end text 7.5 km 7.5 km7, point, 5, start text, space, k, m, end text Number of cars 5 55 5 55 Julie wants to use these results to test H 0 : μ A − μ B = 0 H 0 : μ A −μ B =0start text, H, end text, start subscript, 0, end subscript, start text, colon, space, end text, mu, start subscript, start text, A, end text, end subscript, minus, mu, start subscript, start text, B, end text, end subscript, equals, 0 versus H a : μ A − μ B ≠ 0 H a : μ A −μ B =0start text, H, end text, start subscript, start text, a, end text, end subscript, start text, colon, space, end text, mu, start subscript, start text, A, end text, end subscript, minus, mu, start subscript, start text, B, end text, end subscript, does not equal, 0. Assume that these are representative samples and all other conditions have been met. What is the P-value associated with these sample results? Choose 1 answer: Choose 1 answer: (Choice A) P -value < 0.01 P-value<0.01P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 01 A P -value < 0.01 P-value<0.01P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 01 (Choice B) 0.01 ≤ P -value < 0.05 0.01≤P-value<0.050, point, 01, is less than or equal to, P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 05 B 0.01 ≤ P -value < 0.05 0.01≤P-value<0.050, point, 01, is less than or equal to, P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 05 (Choice C) 0.05 ≤ P -value < 0.10 0.05≤P-value<0.100, point, 05, is le
The p value based on the information will be E. P - value ≥ 0.20
How to compute the valueOpen Minitab 17. Select 'Stat' -> 'Basic Statistics' -> '2 - Sample t... Select 'Summarized data' from the dropdown menu.
Enter 5 in both Sample size of sample 1 and sample 2, 168 and 172 in Sample mean of Sample 1 and Sample 2. 5.4 and 7.5 in Standard deviation of Sample 1 and Sample 2.
Click on 'Options' and Enter 'Confidence level' 95.0(or the given Cofidence level) , 'Hypothesized difference' 0.0 , 'Alternative hypothesis' 'Difference \\neq Hypothesized difference'. Also the box 'Assume equal variance' can be ticked as requirement.
Click on 'Ok' -> 'Ok'.
Output: -
P - value = 0.361 i.e., P - value ≥ 0.20
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A bag contains 19 blue, 28 purple, 21
red, and 29 orange balls. You pick
one ball at random. Find the
probability that it is purple or orange.
P(purple or orange) =
Simplify your answer completely.
Thus, the probability for the outcome of either purple or orange: P(purple or orange) = 57/97.
Explain about the term random selection:a choice that is made at random (entirely by chance, with no predictability). Every person in the population under study need to have an equal probability of getting chosen. Every person who is under investigation has an equal probability of being chosen at random for the sample.
Given bag with balls:
19 blue, 28 purple, 21 red, and 29 orange ballsTotal = 97 ballsprobability = favourable outcome / total outcome
P(purple) = 28/97
P(orange) = 29/97
Thus,
P(purple or orange) = 28/97 + 29/97
P(purple or orange) = 57/97
Thus, the probability for the outcome of either purple or orange ball : P(purple or orange) = 57/97.
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A company gives a 12% discount to his customers on retail price. If the total is over $10,000 after the discount, they give an additional 3% discount on the remaining balance. A customer’s total came to $13,500 (discounted price). How much did he save?
Answer:
Therefore, the customer saved $2,448.45.
Step-by-step explanation:
To answer this question, we need to use the percentage discount formula to find the original price and the amount saved.
Let x be the original price of the product. Then, after applying the 12% discount, the price becomes 0.88x. If the total is over $10,000 after this discount, then an additional 3% discount is applied on the remaining balance, which means the final price becomes 0.97 * 0.88x.
We are given that the final price is $13,500, so we can set up an equation and solve for x:
0.97 * 0.88x = 13,500 x = 13,500 / (0.97 * 0.88) x = 15,948.45
Therefore, the original price was $15,948.45.
The amount saved is the difference between the original price and the final price:
15,948.45 - 13,500 = 2,448.45
Solve the equation for x -4X+3=11
Answer:
x = -2
Step-by-step explanation:
-4x + 3 = 11
Subtract 3 from both sides:
-4x = 8
Divide both sides by -4:
x = -2
Find the midpoint of the segment formed by the points D(8, 6) and E(4, 10). A. (2, –2) B. (6, 8) C. (9, 5) D. (12, 16)
Answer:
B
Step-by-step explanation:
let the mid-point of DE be ( x , y )
x = (8+4)/2 = 6
y = (6+10)/2 = 8
the mid- point of DE is ( 6 , 8 )
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Answer:
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.
Step-by-step explanation:
To find the correct percentages, we need to calculate the percentage of visitors who used each mode of transportation out of the total number of visitors, which is the sum of all the numbers in the table:
Total number of visitors = 120 + 24 + 45 + 30 + 81 = 300
Percentage of visitors who walked = (120 / 300) x 100% = 40%
Percentage of visitors who used a bicycle = (24 / 300) x 100% = 8%
Percentage of visitors who used a car service = (45 / 300) x 100% = 15%
Percentage of visitors who used a bus = (30 / 300) x 100% = 10%
Percentage of visitors who used the subway = (81 / 300) x 100% = 27%
Therefore, the circle graph that correctly represents the data in the table is:
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.
Bree is replacing the wire on her farm paddock fences. She has measured a couple of the sides and drawn a sketch of the paddock shape. (pic below)
a. Find the two missing sides and calculate the perimeter of the paddocks
Perimeter?
b. The cost of fencing wire is $5 per meter. How much will the wire cost
Cost?
a. The perimeter of the paddock is 120 meters
b. The cost of the wire will be $600
a. To find the missing sides and calculate the perimeter of the paddock, let's analyze the given sketch.
The length of the missing side on the left can be determined by subtracting the known length of 10m from the total height of 20m. Therefore, the left side has a length:
20m - 10m = 10m.
The missing side on the right is equal in length to the known side of 40m.
Now we can calculate the perimeter by adding up all the side lengths:
Perimeter = 10m + 40m + 20m + 10m + 40m
= 120m.
b. To calculate the cost of the wire, we need to multiply the perimeter of the paddock by the cost per meter of fencing wire, which is $5/m.
Wire Cost = Perimeter × Cost per meter
= 120m × $5/m
= $600.
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Jordan is tracking a recent online purchase. The shipping costs state that the item will be shipped in a 24-inch long box with a volume of 2,880 cubic inches. The width of the box is seven inches less than the height.
The volume of a rectangular prism is found using the formula V = lwh, where l is the length, w is the width, and h is the height.
Complete the equation that models the volume of the box in terms of its height, x, in inches.
Is it possible for the height of the box to be 15 inches?
also the question has 3 boxes
Answer:
Sure, I can help you with that.
Given:
* The box is 24 inches long.
* The width of the box is seven inches less than the height.
* The volume of the box is 2,880 cubic inches.
To solve:
* Complete the equation that models the box's volume in terms of its height, x, in inches.
* Determine if the height of the box can be 15 inches.
Solution:
Let's define the following variables:
* $h$ = the height of the box (in inches)
* $w$ = the width of the box (in inches)
* $l$ = the length of the box (in inches)
We are given that l=24 and w=h−7. We can use these values to find the volume of the box:
[tex]V = lwh = 24(h - 7)h[/tex]
We can simplify this expression to get the following equation:
[tex]V = 24h^2 - 168h[/tex]
To determine if the height of the box can be 15 inches, we can substitute 15 for $h$ in the equation and see if we get a positive value for the volume.
[tex]V = 24(15)^2 - 168(15) = 2160 - 2490 = -330[/tex]
Since the volume is negative, the height of the box can't be 15 inches.
Therefore, the equation that models the box's volume in terms of its height, x, in inches is [tex]$V = 24x^2 - 168x$[/tex]. Consequently, the size of the box can't be 15 inches.
Answer:
Yes
Step-by-step explanation:
The only answer is height = 15 because the -8 will be rejected
Someone please help!! (20 POINTS!)
Answer: C
Step-by-step explanation: Rise/run so 1/1=1 but it's going down so it negative. -1
Where will X be after a rotation 90° clockwise about (-5,-1)?
Click on the grid to place the point.
The image point of the coordinate X after the rotation is (-1, 5).
Calculating the image point of the coordinate XWhen a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.
So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).
Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).
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Which of the following is a biconditional statement?
A) If x2 = 25, then x = 5 or x = –5
B) x = 5 if x2 = 25
C) x = 5 if and only if x + 5 = 10
D) If x ≠ 5 then x2 ≠ 25
Answer:
C) x = 5 if and only if x + 5 = 10
Step-by-step explanation:
You want to identify the biconditional statement among those that are given.
ConditionalA conditional statement is of the form ...
If P, then Q.
ConverseThe converse of the above conditional statement is ...
If Q, then P.
BiconditionalWhen both the statement and its converse are intended, the statement can be written as the biconditional ...
If and only if P then Q.
The given example of a biconditional statement is ...
x = 5 if and only if x +5 = 10.
__
Additional comment
This can be abbreviated ...
Iff P then Q
meaning "if P then Q, and if Q then P", or "if and only if P, then Q."
If 86
is added to a number, the result is 44
less than three times the number. Find the number.
Answer:
x = 65
Step-by-step explanation:
let the number be 'x'.
If 86 is added to a number, the result is 44 less than three times the number. Therefore the equation will be,
=> 86 + x = 3x - 44
Rearranging,
=> x - 3x = -44 - 86
=> -2x = -130
=> x = 130/2
=> x = 65
Match the situation with its probability.
The given probabilities are as follows:
Spinner landing on at least one A = 7/16Spinner landing on C and D in any order = 1/8Spinner landing on two Bs = 1/16Spinner landing on C on the second spin = 1/4What are the probabilities?The probabilities are determined using the formula below:
Probability = number of expected outcome / number of total outcomesSpinner landing on at least one A:
number of at least one A = 7
Spinner landing on at least one A = 7/16
Spinner landing on C and D in any order:
number of landing on C and D in any order = 2
Spinner landing on C and D in any order = 2/16
Spinner landing on C and D in any order = 1/8
Spinner landing on two Bs:
number of landing on two Bs = 1
Spinner landing on two Bs = 1/16
Spinner landing on C on the second spin:
Number of landing on C on the second spin = 4
Spinner landing on C on the second spin = 1/4
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A supermarket sells fruit snacks by the box. AEach box holds x pachages of strawberry snacks and y packages of cherry snacks. Nina bought 6 boxes.
Write two expressions for home many more strawberry packages than cherry packages nina bought. Then write what the few expressions being equivalent mean in terms of the situation
The two equivalent expressions are 6(x − y) and 6x − 6y.
What are the equivalent expressions?These expressions look different but their simplified forms are same expressions are called equivalent expressions.
The 1st expression shows subtracting the number of packages of cherry snacks from the number of packages of strawberry snacks in each box.
When we multiplying the difference by the number of boxes then, it will be: 6(x-y)
Now, total number of cherry snacks and subtracting it from the total number of strawberry snacks will be 6x - 6y. So, equivalent expressions means in terms of situation are 6(x − y) and 6x − 6y.
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A sequence can be generated by using gn = 2(gn-1), where g1 = 1/3 and n is a whole number greater than 1.
What are the first 5 terms of the sequence?
The first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
What are the first 5 terms of the sequence?From the question, we have the following parameters that can be used in our computation:
The sequence is generated by using gn = 2(gn-1)
Such that g1 = 1/3 and n is a whole number greater than 1.
Using the above as a guide, we have the following:
The sequence means that we multiply the current term by 2 to get the next term
So, we have the following representations
a(2) = 2 * 1/3 = 2/3
a(3) = 2 * 2/3 = 4/3
a(4) = 2 * 4/3 = 8/3
a(5) = 2 * 8/3 = 16/3
Hence, the first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
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Un elevador de taller mecánico tiene pistones de entrada y salida de 5 cm y de 60 cm de radio respectivamente. Con este dispositivo se mantiene levantado un auto de 2000 kg. ¿Cuál es la fuerza aplicada al pistón de entrada?
The force applied to the input piston is 136.25 N.
How to find the force applied to the intake piston?This problem can be solved using the principle of hydraulic systems, which states that pressure in a confined fluid is transmitted equally in all directions.
Thus, we can equate the pressure on the input piston to the pressure on the output piston, and solve for the force on the input piston. That is:
P₁ = P₂
F₁/A₁ = F₂/A₂ (Pressure = Force/Area)
F₂ = 2000 * 9.81 = 19620 N (F = mg)
A₁ = π * r₁² = π * 5² = 25π cm²
A₂ = π * r₂ ² = π * 60² = 3600π cm²
F₁ = F₂/A₂ * A₁
F₁ = (19620/3600π) * 25π
F₁ = 136.25 N
Therefore, the force applied to the input piston is 136.25 N.
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Question in English
A machine shop lift has input and output pistons of 5 cm and 60 cm radius respectively. With this device, a 2000 kg car is kept lifted. What is the force applied to the intake piston?
which expresion shows 7+21 written as a product of two factors
As we used the distributive property of multiplication to rewrite 7+21 as a product of 7 x (1+3) or 7 x 4.
However, you are asked to express this sum as a product of two factors. A factor is a number that is multiplied by another number to produce a product. Therefore, to express 7+21 as a product of two factors, we need to find two numbers that, when multiplied together, give us the sum of 7+21.
One way to approach this problem is to use the distributive property of multiplication, which states that a(b+c) = ab + ac. We can apply this property by rewriting 7+21 as 7+3*7, since 21 is equal to 3 times 7. Then, we can factor out the common factor of 7 from the expression to get:
7+37 = 7(1+3)
Now, we have expressed 7+21 as a product of two factors: 7 and (1+3), or simply 7 and 4. Therefore, the expression that shows 7+21 written as a product of two factors is:
7 x (1+3) or 7 x 4
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please helppp
here is the picture is about Row Ops
Multiplying row 1 of the matrix by 1 / 4 would give a resultant matrix of [ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ].
How to multiply the matrix row ?The question wants to multiply the first row of the matrix alone, with the fraction, 1 / 4.
First step is then to multiply the first row by the fraction of 1 / 4 :
( 1 / 4 ) x 2 = 1 / 2
( 1 / 4 ) x 0 = 0
( 1 / 4 ) x 3 = 3 / 4
The results acquired can then be input into the matrix which would then give a resultant matrix of :
[ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ]
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Write an equation in standard form
The equation of the quadratic with a directrix of x = 2 and vertex of (0 , 0) is: y² = -8x
The equation of the quadratic with a directrix of y = 4 and vertex of (1, 3) is: (x - 1)² = -4 (y - 3)
How to write the equation of parabola with directrix of x = 2 and vertex of (0, 0)Quadratic equation when the directrix is at x direction is of the form:
(y - k)² = 4P (x - h)
OR
standard vertex form, x = a(y - k)² + h where a = 1/4p
The vertex
v (h, k) = (0, 0)
P in this problem, is the distance between the vertex and the directrix
P = 0 - 2 = -2
substitution of the values into the equation gives
(y - k)² = 4P (x - h)
(y - 0)² = 4 x -2 (x - 0)
y² = -8x
Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (1, 3)
P in this problem, is the distance between the vertex and the directrix
P = 3 - 4 = -1
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - 1)² = 4 * -1 (y - 3)
(x - 1)² = -4 (y - 3)
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If Charlie invested $1,000 in an account paying 10% compounded monthly, how much will be in the account at the end of 10 years?
Answer:
Compound Interest Formula: A = P (1 + R/100)^t
P = Principle ($1,000)R = Rate (10%)T = Time (10 years)A = 1000 (1 + 10/100)^10
A = $2593.74
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what is 45 x 6 i need help
Answer:
270
Step-by-step explanation:
I am showing my mental math, hope this helps you:
45 x 6 is the same as 4 x 6 = 10s place value and 5 x 6 = 1s place value:
4 x 6 = 24
5 x 6 = 30
Therefore, the answer is:
2 (4 + 3) 0
270
The value of the expression 45 x 6 is 270.
We have,
To calculate the product of 45 multiplied by 6, you can follow these steps:
- Start by multiplying the units digits of the two numbers: 5 x 6 = 30.
- Write down the units digit of the result, which is 0, and carry over the tens digit, which is 3.
- Multiply the tens digit of the first number by the second number: 4 x 6 = 24.
- Add the carried-over value from step 2 to this result: 24 + 3 = 27.
- Write down the tens digit of the result, which is 7, and carry over the hundreds digit, which is 2.
- Multiply the hundred digit of the first number by the second number: 4 x 6 = 24.
- Add the carried-over value from step 5 to this result: 24 + 2 = 26.
- Write down the hundred digit of the result, which is 6.
- Combine the hundreds, tens, and units digits together: 6, 7, 0.
- The final product of 45 multiplied by 6 is 270.
So, 45 x 6 = 270.
Thus,
The value of the expression 45 x 6 is 270.
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