Question 1 (1 point)
m2IJK-570 and mZIJL-20°. Find mZLJK.
3
→K
O a MZLJK-77°
Ob mZLJK-37°
Oc mZLJK-40°
Od mZLJK=-37°

The area of the polygon is 12 square units.  In mathematics and everyday life, an estimate is an approximate calculation or guess that is close to the actual value but may not be exact.

To make an estimate or guess, you can square off the parallelogram and create a rectangle and add your squares (or multiply 3x4) to = 12": This part explains a method for estimating the area of a parallelogram. It suggests that if you take a parallelogram and "square it off" (convert it into a rectangle by drawing a perpendicular line), you can then find the area of the rectangle, which is easier to calculate. In this case, the dimensions of the rectangle are given as 3 units for the base and 4 units for the height, and the estimated area is 12 square units.

You can use the formula for the exact area using base x height (3x4) you get the same answer of 12 square units": This part emphasizes that the estimation method used in step 2 (multiplying 3 by 4) produces the same result as the exact formula for finding the area of a parallelogram, which is base times height. In this case, both the estimation and the formula give an area of 12 square units.

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The area of the convex polygon is 43/2 square units

The vertices are given as:

(0,5), (-1,2), (4,4), (-3,-4) and (2,0)

The area is then calculated as:

[tex]A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )[/tex]

So, we have:

[tex]A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)[/tex]

Evaluate

[tex]A = \frac12 * (|-43|)[/tex]

Remove the absolute bracket

[tex]A = \frac12 * 43[/tex]

This gives

[tex]A = \frac{43}2[/tex]

Hence, the area of the convex polygon is 43/2 square units

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Answer:

I guess the first one is correct........

The length of the arc is 15.70 km

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

The formula is given by

s = ϴ × r,

where

s is the arc length

r is the radius of the circle

θ is the central angle of the arc in radians

Given :- Radius = 10km

             Angle = 90 ° = [tex]\pi[/tex]/2 radians          (1 radian = 180°/[tex]\pi[/tex])

By using formula we get

Length of arc = 10 x[tex]\pi[/tex]/2 = 5[tex]\pi[/tex] km           ([tex]\pi[/tex] = 3.14)

                     = 15.70 km

Thus the length of the arc is 15.70 km

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Using the Fundamental Counting Theorem, it is found that:

a) 256 codes are possible.

b) The probability is [tex]\frac{1}{256}[/tex].

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

There are 4 keys, each with 4 options, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex].

Then the number of codes is:

[tex]N = 4^4 = 256[/tex]

And the probability is:

[tex]p = \frac{1}{256}[/tex].

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Answer: $18.51

Step-by-step explanation:
1015cm^3/7.95cm^3/g = 127.67g

127.67g/1000g = .128

.128*$.29 = $.037

$.037*500 = $18.51

Answer:

$1170

Step-by-step explanation:

1. We know that each steel part has a volume of 1015 cubic centimeters, and the machinist wants to make 500 of these. Then the total volume of the steel part the machinist will make will be 1015 x 500.

--> 1015 x 500

--> 507500 cubic centimeters.

2. The density of the steel part is 7.95 grams per one cubic centimeter. Then the total density of the 500 steel parts will be 507500 x 7.95.

--> 507500 x 7.95

--> 4,034,625 grams.

3. For every kilo of steel part, the cost is $0.29. We should first change the 4,034,625 gram to kilo. Since 1000 grams is a kilo, we divide 4,034,625 by 1000.

--> 4,034,625 grams / 1000 = 4034.625 kilograms.

Now we multiply 4034.625 by 0.29 to find the total cost.

--> 4034.625 x 0.29

--> 1170.04125.

Since the question specifically asked to round it to the nearest dollar, our final answer becomes $1170.

Answer:

5

Step-by-step explanation:

Formula for finding slope:

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

Slope of line passing through (-5,5) and (-4,10)

=

[tex] \frac{5 - 10}{ - 5 - ( - 4)} \\ = \frac{ - 5}{ - 5 + 4} \\ = \frac{ - 5}{ - 1} \\ = 5[/tex]

Answer:

Slope = 5

Step-by-step explanation:

    (-5,5)   ;   x₁ = -5    & y₁ = 5

    (-4, 10)  ;   x₂ = -4  & y₂ = 10

             [tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                         [tex]\sf =\dfrac{10-5}{-4-[-5]}\\\\ =\dfrac{10-5}{-4+5}\\\\=\dfrac{5}{1}\\\\= 5[/tex]

Using the binomial distribution, there is a 0.265 = 26.5% probability that at least two of them have the same number.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are:

p = 1/65 = 0.0154, n = 65.

The probability that at least two of them have the same number is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

P(X < 2) = P(X = 0) + P(X = 1)

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{65,0}.(0.0154)^{0}.(0.9846)^{65} = 0.3647[/tex]

[tex]P(X = 1) = C_{65,1}.(0.0154)^{1}.(0.9846)^{64} = 0.3703[/tex]

So:

P(X < 2) = P(X = 0) + P(X = 1) = 0.3647 + 0.3703 = 0.735.

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.735 = 0.265[/tex]

0.265 = 26.5% probability that at least two of them have the same number.

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Answer:

Step-by-step explanation:  use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.

Considering the definition of an inequality, the inequality that expresses the previous relationship is 12 < x ≤ 12.2

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that to fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm.

It means that the length has to be strictly greater than 12 cm but less than or equal to 12.2 cm. In other words, length of frame must be longer than 12 cm means that x>12, while ength of frame not longer than 12.2 cm means x≤12.2

Finally, the inequality that expresses the previous relationship is

12 < x ≤ 12.2

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Using proportions, it is found that 66 men can leave so there will still be enough food.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the situation described, the rule of three is given as follows:

4200 men - 32 days - 12 hectogram per person.

x men - 42 days - 16 hectogram per person.

Considering that the amount per person and the number of people is inverse proportional, we have that:

[tex]\frac{4200}{x} = \frac{32}{42} \times \frac{16}{12}[/tex]

[tex]\frac{4200}{x} = \frac{512}{504}[/tex]

Applying cross multiplication:

512x = 504 x 4200

x = 504 x 4200/512

x = 4134.

The amount of men that can leave is:

4200 - 4134 = 66.

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The volume of the oblique prism is 16261 cubic units

The given parameters are:

Height = 23

Base area = 707

The volume is calculated as:

V = base area * height

So, we have:

V = 707 * 23

Evaluate

V = 16261

Hence, the volume of the oblique prism is 16261 cubic units

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The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)

Heptagons are polygons with seven sides, seven vertices, seven interior angles and seven central angles. Herein we know the value of the sum of six interior angles and we need to know the measure of the seventh interior angle. We can determine the measure of the seven interior angles by using the following expression:

θ = (n - 2) · 180°, where n is the number of sides of the polygon.     (1)

If we know that n = 7, then sum of the internal angles in the heptagon is:

θ = (7 - 2) · 180°

θ = 900°

And the measure of the final interior angle is found by subtraction:

θ₇ = 900° - 776°

θ₇ = 124°

The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)

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Answer:

- There are more points above the line than below

- This is not a line of best fit

Step-by-step explanation:

       If we count the data points above and below the line, we can see there are about 4 below and 11 above. This means there are more points above the line than below. Since there are more points above the line than below, this is not a line of best fit.

Answer:

B 4 1/3

Step-by-step explanation:

The resulting equation written in standard form is 16x² - 22x + 6 = 0.

Quadratic Equation in Standard Form: ax² + bx + c = 0

a, b and c are known values. a can't be 0.

"x" is the variable or unknown (we don't know it yet).

The "solutions" to the Quadratic Equation are where it is equal to zero.

They are also called "roots", or sometimes "zeros"

We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)

Calculation for the given equation-

Now, y=-16x²+24x+6

Substitute, y = 12+2x in y = -16x²+24x+6.

=> 12+2x = -16x²+24x+6

=> 16x²-24x-6+12+2x = 0

=> 16x²-22x+6 = 0

Therefore, the quadratic equation given in the standard form is 16x²-22x+6 = 0.

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The complete question is-

The two equations are given below;

Y = 12 + 2x   linear equation

Y = -16x² + 24x + 6  quadratic equation

If you substitute 12 + 2x for y in the second equation how is the resulting equation written in standard form?

From the given graph, we can see by tracing that f(4) is -3.5

The given graph is a graph of a quadratic function with a parabola opening upwards.

According to the question, we are to find the value of y where the value of x is 4. From the given graph, we can see by tracing that f(4) is -3.5

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The answers to all the parts are given below.

The height equation is:

h(t) = - 16t^2 + 100t + 10

A) To find the maximum height, we must find the time where the velocity is 0, so we must derive it with respect to the time.

v(t) = - 2 * 16 * t + 100 = 0

t = 100/(2*16) = 3.125s

Now we put this time in our height equation:

h(3.125s) = -16*3.125^2 + 100*3.125 + 10 = 166.25 ft.

B) The lowest height of the potato will be h = 0ft when the potato hits the ground.

C) the lowest time that works for that function is t = 0s when the potato is fired by the gun.

D) the maximum time can be found when the potato hits the ground, after that point the equation does not work anymore, let's find it,

h(t) = 0 = -16t^2 +100t+10

we can solve it using Bhaskara's equation:

[tex]t=\frac{-100+-\sqrt{100^{2} +4*16*10} }{-2*16} =\frac{-100+-103.2}{-32}[/tex]

So the two solutions are:

t = 6.3s

t = -0.1s

We need to choose the positive time, as we already discussed that the minimum time that works for the equation is t = 0s.

so here the answer is t = 6.3s

E) the domain is  0s ≤ t ≤ 6.3s

The range is 0ft ≤ h ≤ 166.25 ft.

Therefore, the answers to all the parts are shown.

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a. Mean is 70.8, median is 70, and mode is 60

b. Mean describes the data best

c. Mean can be a misleading central measure in case of outliers

Calculating Mean, Median and Mode

Mean = Total sum of pries / Total number of sunglasses

Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25

Mean = 70.8

Median = (n/2 + 1)th term

Here, n is the number of sunglasses.

Median = (25/2 + 1)th term

Median =13th term

Median = 70

Mode = Most occurring data

Mode = 70

Why is mean the best central measure to describe the data?

When your data distribution is continuous and symmetrical, such as when your data are normally distributed, the mean is typically the best measure of central tendency to utilize. Thus, mean describes the average price of the sunglasses here

Mean Being Misleading

In case there are outliers, the mean of the data gets highly affected. Hence, it can be misleading for analyzing average price of the data.

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Answer:

2y+6

Step-by-step explanation:

first, pull out the 2 from the top to separate the equation

second, factor out y

third, cancel out the common factor of y-1

fourth, remove the parenthesis from 2(y+3)

answer = 2y+6

Answer:

  a.  1 dag

Step-by-step explanation:

The list of SI prefixes is attached. Each has an abbreviation that can be used with the abbreviation for the SI unit of interest.

A factor of 10 is signified by the prefix deka-, abbreviated "da". Then 10 grams is 1 dekagram, or 1 dag.

The expression which can be used to represent the total amount llean earned last week is 75 + 18x

An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)

= 75 + (18 × x)

= 75 + 18x

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A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution

x1 = x2 = .... = xk =0. Then the set  {v1,v2,...,vk} is linearly dependent otherwise.

So putting in the formula we get

x1u1 + x2u2 + x3u3 = 0

x1u1 + x2u2 = -x3u3

au1 + bu2 = u3               ∵ (-x1/x3 = a & -x2/x3 = b)

On putting in the values

a(3,-1) + b(4,5) = (-4,7)

(3a+4b,-a+5b) = (-4,7)

On comparing we get

3a + 4b = -4 -(1)

-a + 5b = 7  -(2)

on solving these equations we get

b = 17/19 and a= -48/19

which is non trivial.

Thus the following form linearly dependent sets of vectors.

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Answer:

Step-by-step explanation:

20% of a number is 17 . find the number

divide 17 by 20 and you find 1%, multiply by 100 and you get 100%

x = 17 : 20 * 100

x = 0.85 * 100

x = 85

The probability that a male is selected, then a female is 0.26

The probability that a female is selected, then a male is 0.26

The probability that two males are selected is 0.18

The probability that two females are selected is 0.30.

The probability that no males are selected is 0.30.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a male is selected, then a female = (11/25) x (14 / 24) = 0.26

The probability that a female is selected, then a male = (14/25) x (11 / 24) = 0.26

The probability that two males are selected = (11/25) x (10/24) = 0.18

The probability that two females are selected = (14/25) x (13 / 24) = 0.30

The probability that no males are selected =  (14/25) x (13 / 24) = 0.30

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The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The point A = (1 - 4, -3 - 2) = (-3, -5)

The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)

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Answer:

I'm pretty sure it is √10, 3.12, 3.24, 31

Step-by-step explanation:

I don't know if you messed up but I got a question similar that is the length 31 in your quesion is actually 3 1/4 in my question. but i did the math and 31 is still the greatest number.

Answer:

(4,-3)

Step-by-step explanation:

Multiplying the bottom equation by -6, we get -6x+12y=-60.

Adding this to the first equation gives 15y=-45, and thus y=-3.

So, it follows that 6x+3(-3)=15, and thus x=4.

Answer:

88.5

Step-by-step explanation:

3.5 * 8 = 28, this is how much was spent on copies printed. If 800 copies cost $64 and 28 of that was on the 3.5 fee per 100, then the flat rate must be:

64-28 = 36.

Now, let's do 1500. For 1500 copies, you will get charged $3.5 15 times. This amounts to 52.5, then adding the fixed fee of 36 dollars, you get

88.5

The sample standard deviation of sample 1 is 11.54,  of sample 2 is 10.21,  of sample 3 is 11.25,  of sample 4 is 14.15.

Given

Data point      sample 1     sample 2           sample 3                sample 4

1                          37                38                       16                             19          

2                          15                31                        21                             10

3                          43                12                       45                             45

4                          25                19                        32                            37

5                          21                 28                       25                             22

We have to find the sample standard deviation of each sample.

We have to first mean of each sample.

Sample mean of 1=141/5=28.2

Sample mean of 2=128/5=25.6

Sample mean of 3=139/5=27.8

Sample mean of 4=133/5=26.6

Sample standard deviation=[tex]\sqrt{}[/tex]∑[tex](x-x bar)^{2}/n-1[/tex]

∑[tex](x-x bar)^{2}[/tex] is calculated in the figure.

Sample standard deviation of sample 1=[tex]\sqrt{532.8/4}[/tex]

=[tex]\sqrt{133.2}[/tex]

=11.54

Sample standard deviation of sample 2=[tex]\sqrt{417.2/4}[/tex]

=[tex]\sqrt{104.3}[/tex]

=10.21

Sample standard deviation of sample 3=[tex]\sqrt{506.8/4}[/tex]

=[tex]\sqrt{126.7}[/tex]

=11.25

Sample standard deviation of sample 4=[tex]\sqrt{801.2/4}[/tex]

=[tex]\sqrt{200.3}[/tex]

=14.15.

Hence the sample standard deviation of sample 1 is 11.54, sample standard deviation of sample 2 is 10.21, sample standard deviation of sample 3 is 11.25, sample standard deviation of sample 4 is 14.15.

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