the diameters of ball bearings are distributed normally. the mean diameter is 58 millimeters and the standard deviation is 6 millimeters. find the probability that the diameter of a selected bearing is greater than 52 millimeters. round your answer to four decimal places.

Answers

Answer 1

The probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413. This can be calculated using the formula for probability of a normal distribution:

P(x > 52) = 1 - P(x ≤ 52)

P(x ≤ 52) = (52 - 58) / 6 = -1

P(x > 52) = 1 - P(-1) = 1 - 0.1587 = 0.8413.

Therefore, the probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413.

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Related Questions

in how many ways can a class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer and a secretary g

Answers

The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040

A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.

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The interest rate of an auto
loan is 4%. Express this
number as a decimal.

Answers

Answer: 0.04

Step-by-step explanation:

In order to get 4% as a decimal, you must divide 4 by 100.

4/100 = 0.04

Thus, the answer to your question is 0.04

what is the value of y in the solution to the system of equations below.
y=-x+6
2x-y=-9

Answers

Answer:

I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.

for the first equation y=-x+6, y intercept is (0,6)

for equation two 2x-y=-9, y intercept is (0,9)

In both of the equations the x value is 1.

Solving for y without graphing. Y=9+2x

and x=-1

Step-by-step explanation:substitute i

HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5

It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.

After heating up in a teapot, a cup of hot water is poured at a temperature of
201°F. The cup sits to cool in a room at a temperature of 73° F. Newton's Law
of Cooling explains that the temperature of the cup of water will decrease
proportionally to the difference between the temperature of the water and the
temperature of the room, as given by the formula below:
T = Ta + (To-Ta)e-kt
Ta
the temperature surrounding the object
To the initial temperature of the object
t = the time in minutes
=
T =
the temperature of the object after t minutes
k = decay constant
The cup of water reaches the temperature of 189°F after 3 minutes. Using
this information, find the value of k, to the nearest thousandth. Use the
resulting equation to determine the Fahrenheit temperature of the cup of
water, to the nearest degree, after 6 minutes.

Answers

The temperature of the cup of water is approximately 180°F after 6 minutes.

How to find temperature and time?

Using the given formula, we can write:

T = Ta + (To - Ta) * e^(-kt)

where Ta = 73°F (the temperature of the room), To = 201°F (the initial temperature of the water), and T = 189°F (the temperature of the water after 3 minutes).

We can solve for the decay constant k as follows:

(T - Ta) / (To - Ta) = e^(-kt)

ln[(T - Ta) / (To - Ta)] = -kt

k = -ln[(T - Ta) / (To - Ta)] / t

Substituting the given values, we get:

k = -ln[(189°F - 73°F) / (201°F - 73°F)] / 3 minutes

k = -ln[116 / 128] / 3 minutes

k ≈ 0.0434 minutes^-1 (rounded to the nearest thousandth)

Now we can use this value of k to find the temperature of the water after 6 minutes:

T = Ta + (To - Ta) * e^(-kt)

T = 73°F + (201°F - 73°F) * e^(-0.0434 minutes^-1 * 6 minutes)

T ≈ 180°F (rounded to the nearest degree)

Therefore, the temperature of the cup of water is approximately 180°F after 6 minutes.

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suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward a distance of 6 units. what are the coordinates of your position? (x, y, z)

Answers

The coordinates of your position If we start at the origin, we are moving only along the x-axis  of  a distance of 7 units in positive direction and then only in the negative y-axis direction and  z-coordinate is zero are (7,-6,0).

The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.

The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).

The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).

Therefore, the coordinates of our position are (7, -6, 0)

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What’s -9.1 times 3.75

Answers

-9.1 x 3.75 = -34.125

answer = -34.125
the answer to ur question is -34.125

Can anyone please help with this math problem? Thanks!

Answers

Answer: Yes Sofia will have enough money

=======================================================

Explanation:

Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.

The area of the rectangle is 16*7 = 112 square meters.

The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be

sum of the exterior sides = perimeter

6+7+16+7+6+x = 54

42+x = 54

x = 54-42

x = 12

The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.

area of the trapezoid = 0.5*height*(base1+base2)

area = 0.5*5.66*(16+12)

area = 79.24 square meters

----------------

Recap so far

area of the rectangle at the bottom = 112 square metersarea of the trapezoid up top = 79.24 square meters

The total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.

Let's convert that to square decimeters.

Recall that 1 decimeter = 10 centimeters

Multiply both sides by 10

1 decimeter = 10 centimeters

10*(1 decimeter) = 10*(10 centimeters)

10 decimeters = 100 centimeters

10 decimeters = 1 meter

Then,

[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]

The entire lawn is 19124 square decimeters.

----------------

We have one final block of calculations to determine the total price.

x = number of rolls

1 roll covers 90 square decimeters

x rolls cover 90x square decimeters

90x = 19124

x = 19124/90

x = 212.489 approximately

Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).

In short, Sofia needs 213 rolls.

1 roll costs $4.50

213 rolls will cost 213*4.50 = 958.50 dollars.

This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).

Sofia will have enough money to pay for all of the grass.

Will make you brainlist!

Answers

Answer:

x = -2 ,  y = 2

Step-by-step explanation:

label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find x

hope this helps :)

Solve: 3√x-√9x-17 =1 ​

Answers

The solution to the equation (3√x) - √(9x-17) = 1 is x = 9.

What is the solution to the given equation?

Given the equation in the question (3√x) - √(9x-17) = 1.

To solve for x in the given equation:

(3√x) - √(9x-17) = 1

We can start by isolating the square root term on one side of the equation. Adding √(9x - 17) to both sides, we get:

(3√x) = √(9x - 17) + 1

Squaring both sides of the equation, we get:

(3√x)² = (√(9x - 17) + 1)²

9x = -16 + 2√(9x - 17) + 9x

Solve for 2√(9x - 17)

2√(9x - 17) = 16

36x - 68 = 256

Add 68 to both sides

36x - 68 + 68 = 256 + 68

36x = 324

x = 324/36

x = 9

Therefore, the solution is x = 9.

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A straw that is 15cm long leans against the inside of a glass. The diameter of a glass is
5cm, and has a height of 8cm. How far past the edge of the glass would the straw extend?
Round your answer to the nearest tenth.

Answers

The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.

the dog eats 8 ounces of dog food each day his owner bought 28 pound bag at the 8 ounces cost $3.50 so how much did the owner spend for 28 bag​

Answers

Answer:

$196

Step-by-step explanation:

1 lb = 16oz

28 lbs x 16 = 448 ozs (in 28 lb bag)

448/8 = 56 (8 oz portions)

56 x $3.50= $196

Smoothie Activity

6. Using the relative frequency table, create a segmented bar graph by employee type using technology or by hand. If using Excel technology the columns may need to be switched after inserting the chart. Click on the chart and the "Chart Design" ribbon will pop up. Then select "Switch Row/Column." (10 points)

Answers

By answering the presented question, we may conclude that I used the following procedures to produce this graph.

What is graphs?

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I made the segmented bar graph using these percentages.

The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.

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Find the value of the expression x+|x| if x=7, 10, 0, -3, -8. write the expression without the absolute value symbol for these values of x: x≤0

Answers

The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.

What does the expression mean?

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).

For x =7,x+|x| =7+|7| =14

For x =10,x+|x|= 10+|10| =20

For x = 0,x+|x| =0+|0| =0

For x = -3, x + |x| = -3 + |-3| = 0

For x = -8, x + |x| = -8 + |-8| = 0

The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.

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Use the following function to find d(0)
d(x)=-x+-3
d(0)=

Answers

When the function d(x) = -x +(-3), then the value of d(0) is -3

In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.

In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.

To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:

d(0) = -(0) - 3

The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as

d(0) = -3

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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation

Answers

Hence, 28 toy soldiers are the correct answer.

In mathematics, how is a group defined?

A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.

Let's refer to the quantity of toy soldiers as "x".

We are aware that x is within the range of 27 and 54 thanks to the problem.

x can be divided by 4 without any remainders.

The residual is 6 when x is divided by 7.

The leftover after dividing x by five is three.

These criteria allow us to construct an equation system and find x.

Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:

x = 4k, where k is some integer.

Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:

x ≡ 6 (mod 7)

This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:

4k ≡ 6 (mod 7)

We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:

4(1) ≡ 6 (mod 7)

4 ≡ 6 (mod 7)

It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.

k = 2:

4(2) ≡ 6 (mod 7)

1 ≡ 6 (mod 7)

k = 3:

4(3) ≡ 6 (mod 7)

5 ≡ 6 (mod 7)

k = 4:

4(4) ≡ 6 (mod 7)

2 ≡ 6 (mod 7)

k = 5:

4(5) ≡ 6 (mod 7)

6 ≡ 6 (mod 7)

k = 6:

4(6) ≡ 6 (mod 7)

3 ≡ 6 (mod 7)

k = 7:

4(7) ≡ 6 (mod 7)

0 ≡ 6 (mod 7)

We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:

x = 4(7) = 28

This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.

28 toy soldiers are the correct response.

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Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. The hotel served 180 gallons of orange juice last year. This year, the hotel served 70% more orange juice than it did the previous year. How much was served this year?

Answers

The hotel served 306 gallons of orange juice this year.

To find the amount of orange juice served this year, we need to add 70% more of the amount served last year to the amount served last year. Let's denote the amount served last year as "x". Then we can set up the equation:

Amount served this year = x + 0.7x

Simplifying this equation gives us:

Amount served this year = 1.7x

We know from the problem that the amount served last year was 180 gallons. Plugging this into our equation, we get:

Amount served this year = 1.7(180)

Simplifying this equation gives us:

Amount served this year = 306

Therefore, the hotel served 306 gallons of orange juice this year.

In summary, we used the information given in the problem to set up an equation and solve for the amount of orange juice served this year. We first found the amount served last year, and then added 70% more of that amount to get the total amount served this year.

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In a 7-sided figure, three of the angles are equal
and each of the other four angles is 150 greater
than each of the first three. Find the angles.

Answers

The sum of the angles of an N-sided convex figure is (n-2)*180 - a simple proof of which is just to decompose the figure into triangles, each of which has all of its vertices the same as three of the vertices of the original figure. (Cut a quadrilateral into two triangles along a diagonal, for instance).

So, a 7-sided figure has angles totaling 5*180 = 900. Now set up a simple equation:

3x + 4(x+15) = 900

7x + 60 = 900

7x = 840

x = 120

The figure has three angles of 120 degrees, and four angles of 135 degrees.

an inner city revitalization zone is a rectangle that is twice as long as it is wide. the width of the region is growing at a rate of 32 m per year at a time when the region is 220 m wide. how fast is the area changing at that point in time?

Answers

The area is changing at a rate of 28,160 m²/year at that point in time.

The area of the rectangular region is given by:

A = lw

Where l is the length of the rectangular region and w is the width of the rectangular region.

The width of the rectangular region is given to be 220 m. Therefore, we have the width w = 220 m. The length l of the rectangular region can be found knowing that it is twice as long as it is wide. Therefore, the length of the rectangular region is given by:

l = 2w

l = 2 x 220

l = 440

Therefore, the length l of the rectangular region is 440 m.

At the given point in time, the width of the rectangular region is growing at a rate of 32 m per year. Therefore, we have the rate of change of the width dw/dt to be 32 m per year. We need to find how fast the area of the rectangular region is changing at that point in time. Therefore, we need to find the rate of change of the area of the rectangular region dA/dt.

A = lw

dA/dt = w dl/dt + l dw/dt

dA/dt = 220 d/dt(2w) + 440 dw/dt

dA/dt = 220 x 2 dw/dt + 440 dw/dt

dA/dt = 880 dw/dt

Substitute the value of dw/dt to get:

dA/dt = 880 x 32

dA/dt = 28,160 m²/year

Therefore, the area of the rectangular region has a rate of change of 28,160 m² per year at that point in time.

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Help please & thanks

The function f(t)=−5t^2+20t models the approximate height of an object t seconds after it is launched. Which of the following equations correctly shows the quadratic formula being used to determine the number of seconds it will take for the objects to be at a height of 18 feet after launch?

Answers

The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex]  tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

What is trigοnοmetric equatiοns ?

Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.

Accοrding tο the given infοrmatiοn:

The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.

Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].

Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].

In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

Plugging in the values οf a, b, and c, we get:

[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]

Simplifying this expressiοn, we get:

[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

[tex]t = 2 \± 0.632[/tex]

Therefοre, the twο pοssible values οf t are:

t = 2 + 0.632 = 2.632 secοnds

t = 2 - 0.632 = 1.368 secοnds

Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

t = 2 ± 0.632

Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

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Calculate the amount of interest on $4,000. 00 for 4 years, compounding daily at 4. 5 % APR. From the Monthly Interest Table use $1. 197204 in interest for each $1. 00 invested

Answers

The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.

To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:

A = $4,000.00(1 + 0.045/365)^(365*4)

A = $4,000.00(1.0001234)^1460

A = $4,889.68

The final amount is $4,889.68, which means that the interest earned is:

Interest = $4,889.68 - $4,000.00 = $889.68

We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:

$1.197204 / $1.00 = 1.197204

Interest earned = $889.68 x 1.197204 = $1,064.08

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Ñamandu es un genio dibujó un cuadrado de x cm cada lado en la parte superior del cuadrado partió en tres partes iguales quedando el corte expresado de esta manera x bajo 3 unió el primer punto de corte con el vértice del lado paralelo trazando un segmento a lo que llamó y Descubre que figuras se forman y entra el perímetro de cada figura formado

Answers

The figures created are a square and a right triangle, and the perimeter of the entire figure is (13x/3) + x × sqrt(10).

When Namandu divides the top side of the square into three equal parts, he creates two segments of length x/3 each. By connecting the first point of division with the vertex of the parallel side, he creates a right triangle with legs of length x/3 and x, and hypotenuse of length y.

Using the Pythagorean theorem, we can solve for y:

y^2 = (x/3)^2 + x^2

y^2 = x^2/9 + x^2

y^2 = (10x^2)/9

y = x×sqrt(10)/3

Now we can find the perimeter of each figure that is created

Perimeter of the original square = 4x

Perimeter of the right triangle = x + x/3 + y = x + x/3 + xsqrt(10)/3

Perimeter of the entire figure = 4x + x + x/3 + xsqrt(10)/3 = (13x/3) + x×sqrt(10)

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What is the answer I keep getting 32

Answers

Answer:

2 9/14

Step-by-step explanation:

How do you do this I need help please

Answers

Answer:

30,000 grams

Step-by-step explanation:

multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g

Answer:

hi I'm really sorry I can't help

ABCD is a quadrilateral in which BD = 15 cm., perpendiculars from A and Con BD are 6 cm and 8 cm respectively. Calculate the area of the quadrilaterals​

Answers

The area of the quadrilateral is 161.24 cm².

How to deal with quadrilateral?

We can see that we can divide the quadrilateral into two triangles: ABD and CBD. We know that the height of ABD is 6 cm and the height of CBD is 8 cm. We also know that BD is 15 cm. To find the area of each triangle, we need to find the base of each triangle. We can do this using the Pythagorean theorem.

For triangle ABD:

AB² = AD² + BD²

AB² = (6 cm)² + (15 cm)²

AB² = 261 cm²

AB = [tex]\sqrt(261) cm[/tex]

For triangle CBD:

BC² = CD² + BD²

BC² = (8 cm)² + (15 cm)²

BC² = 289 cm²

BC = 17 cm

Now we can find the areas of the triangles:

Area of ABD =[tex]\frac{1}{2}[/tex] * AB * 6 cm

Area of ABD = [tex]\frac{1}{2}[/tex] * [tex]\sqrt(261) cm[/tex] * 6 cm

Area of ABD = 93.24 cm^2

Area of CBD = [tex]\frac{1}{2}[/tex] * BC * 8 cm

Area of CBD = [tex]\frac{1}{2}[/tex] * 17 cm * 8 cm

Area of CBD = 68 cm²

Finally, we can find the area of the quadrilateral by adding the areas of the triangles:

Area of ABCD = Area of ABD + Area of CBD

Area of ABCD = 93.24 cm² + 68 cm²

Area of ABCD = 161.24 cm²

Therefore, the area of the quadrilateral is 161.24 cm².

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Qual o resultado do problema 3528÷98?

Answers

Answer:

36

Step-by-step explanation:

Find the distance between each pair of points.
a. M= (0,-11) and P=(0,2)
b. A= (0,0) and B= (-3,-4)
c. C= (8,0) and D=(0,-6)

Answers

Answer:

To calculate the distance between each pair of points given, we can use the distance formula which is derived from the Pythagorean theorem. The formula is:

distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]

Using this formula, we can calculate the following distances:

a. Distance between M and P = 13 units

b. Distance between A and B = 5 units

c. Distance between C and D = 10 units

One number is 13 less than another number. Let x represent the greater number. What is the sum of these two numbers?

Answers

Answer:

2x - 13

Step-by-step explanation:

If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:

x + (x - 13) = 2x - 13

a data set consists of the data given below plus one more data point. when the additional point is included in the data set the sample mean of the resulting data set is 32.083. what is the value of the additional data point?

Answers

The value of the additional data point is  [tex]$19.17$[/tex].

What is the value of the additional data point?

Let us first find the mean of the given data:

[tex]Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6[/tex]

Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is

[tex]$(39+45+43+42+44+x)$[/tex].

Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:

[tex]32.083 = \frac{(39+45+43+42+44+x)}{6}[/tex]

Multiplying both sides of the equation by 6 we get:

[tex]6 \times 32.083 = (39+45+43+42+44+x)[/tex]

We have the value of [tex]$39+45+43+42+44$[/tex] which is [tex]$213$[/tex].

Therefore, substituting all the values, we get:

[tex]193.83 + x = 213[/tex]

On subtracting [tex]$193.83$[/tex] from both sides, we get the value of

[tex]x. x = 213 - 193.83 = 19.17[/tex]

Therefore, the value of the additional data point is [tex]$19.17$[/tex]

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6. 4 The point Q (3, -1) has been translated from P by the vector (3) What are the coordinates of the point P?​

Answers

The coordinates of the point P is (-1,2) .

What is translation?

In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.

Finding the coordinates of the point P :

The coordinates of point P can be found by subtracting the vector from point Q.

To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).

Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:

3 - 4 = -1

Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:

-1 - (-3) = 2

Therefore, the coordinates of point P are (-1, 2).

So, the correct answer is (C) (-1, 2).



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Charles is 10 years old what is the best estimate of the length of his shoe ​

Answers

Answer:

Size 3 ‍♀️

Step-by-step explanation:

In the US, the average shoe size for 10-Year-Old is USA Size 3.

-Jul 12, 2020

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