Given: ABCD is a parallelogram and AC bisects BD.
Prove: AB is congruent to BC.

Given: ABCD Is A Parallelogram And AC Bisects BD.Prove: AB Is Congruent To BC.

Answers

Answer 1

Let's see

In ∆ABE and ∆CBE

BE=BE(Common side)AE=EC[Diagonals of a parallelogram bisect each other]<AEB=<BEC[90°]

So by

SAS congruence the triangles are congruent

AB=BC

Proved

Fact:-

It's already given AC is perpendicular to BD

It means diagonals are perpendicular to each other

According to general property of rhombus this parallelogram is also a rhombus.

So sides are equal hence AB =BC


Related Questions

Find x. special 15 A. 302–√ B. 206–√ C. 152–√ D. 106–√

Answers

The value of x in the triangle is (a) 30√2

How to solve for x?

The complete question is in the attached image.

From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function

[tex]\sin(45) = \frac{30}{x}[/tex]

Evaluate sin(45)

[tex]\frac 1{\sqrt 2} = \frac{30}{x}[/tex]

Solve for x

[tex]x = 30 * \sqrt 2[/tex]

Evaluate

[tex]x = 30 \sqrt 2[/tex]

Hence, the value of x in the triangle is (a) [tex]30 \sqrt 2[/tex]

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Find the value of x in circle O.
55 ?

Answers

Answer:

x = 55°

Step-by-step explanation:

given 2 inscribed angles intercept the same arc then they are congruent, so

x = 55°

A game club offers a special game to play. The tickets cost $5 for members and $10 for nonmembers. Write an expression to find the total cost of 6 member tickets and 4 nonmember tickets.
(6 + 5) + (4 + 10)
(6 * 5) + (4 * 10)
(4 * 5) + (6 * 10)
(6 + 5) * (4 + 10)

Answers

B. (6 * 5) + (4 * 10)


If there are six members that each cost five dollars, then you know a part of the equation is (6 * 5)

Likewise, if there are four non members that each spend ten dollars on tickets, the other part of the equation should be (4 * 10)

Then, to get the total amount of money spent, you would need to add these two mathematical statements together:


(6 * 5) + (4 * 10) is your answer

which of the following functions is graphed below ?

Answers

Answer:

B.) y = x² + 3, x < 4
          x + 4, x ≥ 4

Step-by-step explanation:

Remember, the x-values associated with closed dots are not included in the function. Therefore, only greater than/less than signs can be applied to these points.

The exponential function includes all x-values before x = 4. Therefore, the domain for the parabola is x < 4.

The linear function includes all x-values after and including x = 4. Therefore, the domain for the linear portion of the function is x ≥ 4.

Complete the diagram by identifying the missing angles. Use the length of the ladder you chose for the missing length.

Answers

Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.

What is the missing length about?

Note that: one has to derive b using the law of sine.

[tex]\frac{b}{sin (15)} = \frac{40}{sin 90}[/tex]

b  = [40  x  Sin (15)] / sin (90)

So:

Sin (15) = √3−1)/(2√2

= 0.2588190451

Then: Sin (90)  = 1

So,  b  = (0.2588190451 *40)/1

= 10.35/1

= 10.35

So one has to also derive for h

= [tex]\frac{b}{sin (15)} = \frac{h}{sin 75}[/tex]

Note that b = 10.35

Hence : h = 10.35 * [(√3 + 1) / 2√2] / [(√3−1)/(2√2)]

h  = 10.35 * 3.73

h = 38.62

Using  simple trigonometric analysis, we can say that:

∠ GJH = 90°; and

∠ GHJ = 10°

Therefore, to obtain Z

Z/ Sin (90) = h/Sin (10)

(Then make Z the subject of the formula)

Thus Z = h * Sin (90)/ Sin (10)

Z = 38.62 * 1/ 0.1736

Z = 222.47m

Therefore, Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.

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Question 3 of 10
For f(x) = 3x+1 and g(x)=x²-6, find (ƒ + g)(x).
OA. x² + 3x-5
OB. 3x² -17
O. C. 3x³-5
OD. x² + 3x +7

Answers

Answer:

A

Step-by-step explanation:

[f(x) + g(x)]=x²+3x-6+1

=x2+3x-5

The value of the composite function is A: x² + 3x - 5.

Option A is the correct answer.

We have,

To find (f + g)(x), you simply need to add the two functions f(x) and g(x) together.

So, (f + g)(x) = f(x) + g(x).

Given:

f(x) = 3x + 1

g(x) = x² - 6

Now, add the two functions:

(f + g)(x) = (3x + 1) + (x² - 6)

Now, combine like terms:

(f + g)(x) = 3x + 1 + x² - 6

Finally, rearrange the terms in descending order of powers of x:

(f + g)(x) = x² + 3x - 5

Thus,

The value of the composite function is A: x² + 3x - 5.

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Does this graph represent a function? Why or why not?

Answers

Answer:

no it does not pass the vertical line test choose D

Step-by-step explanation:

Correct answer is (A) doesn’t pass VLT (VERTICAL LINE TEST)

You invest $5,000 into an account where interest compounds continuously at 3.5%. How long will it take your money to double? Round answer to nearest year.

Answers

Answer:

20 years

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)

Given:

A = $10,000P = $5,000r = 3.5% = 0.035

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 10000=5000e^{0.035t}[/tex]

[tex]\sf \implies \dfrac{10000}{5000}=e^{0.035t}[/tex]

[tex]\sf \implies 2=e^{0.035t}[/tex]

[tex]\sf \implies \ln 2=\ln e^{0.035t}[/tex]

[tex]\sf \implies \ln 2=0.035t\ln e[/tex]

[tex]\sf \implies \ln 2=0.035t(1)[/tex]

[tex]\sf \implies \ln 2=0.035t[/tex]

[tex]\sf \implies t=\dfrac{\ln 2}{0.035}[/tex]

[tex]\implies \sf t=19.80420516...[/tex]

Therefore, it will take 20 years (to the nearest year) for the initial investment to double.

The ___-if analysis checks the impact of a change in a variable or assumption on the model. Multiple choice question. what goal pivot sensitivity

Answers

what-if analysis

What-if analysis is a technique used to determine how the expected performance is affected by changing the assumptions underlying the prediction. Use What-if analysis to compare different scenarios and their possible outcomes based on fluctuating conditions.

What-if analysis allows project managers to identify event options and impacts, as well as change assumptions. When used properly, project managers can make more informed decisions and more accurately predict the outcome of those decisions.

Sensitivity analysis determines how different values ​​of the independent variable affect a particular dependent variable under certain assumptions. In other words, sensitivity analysis examines how the causes of various uncertainties in a mathematical model contribute to the overall uncertainty of the model.

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Jamal simplified the expression startroot 75 x superscript 5 baseline y superscript 8 baseline endroot where x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0. startroot 75 x superscript 5 baseline y superscript 8 baseline endroot = startroot 25 times 3 times x superscript 4 baseline times x times y superscript 8 baseline endroot = 5 x squared y squared startroot 3 x endroot which describes the error jamal made?

Answers

The statement that describes the error that Jamal has made is option A: He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

What is the expression about?

An expression is often seen as a form of mathematical statement about a thing.

Note that from the expression:

[tex]\sqrt{75x^{5} y^{8} }[/tex]

[tex]\sqrt{25 x 3 x x^{4} x x x y^{8} }[/tex]

=   5x² y² [tex]\sqrt{3x}[/tex]

So, The statement that describes the error that Jamal has made is option A: He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

See options below

Which describes the error Jamal made?

A. He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

B. He should have written the square root of x Superscript 4 in the answer as x, not x squared.

C. He should have written the 5 inside of the radical in the answer.

D. He should have written the 3 outside of the radical in the answer.

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Answer:

A)

Step-by-step explanation:

Out of 300 students in a class, 60 percent students study physics, 35 percent students study chemistry and 20 percent do not study both of the subjects. how many students study both subjects

Answers

22 students study both subjects.

What is Venn diagram in math ?

In a Venn diagram, sets are represented by shapes; usually circles or ovals. The elements of a set are labeled within the circle.

N=55,n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(P∩C)=7,n(M∩C)=9,n(M∩P∩C)=4

Now, number of students who studying only Mathematics

n(M∩P)∩C =n(M)−n(M∩P)−n(M∩C)+n(M∩P∩C)    (by  Venn diagram) diagram=23−9−12+4=6

number of students who studying only Physics

n(P∩M )∩C  =n(P)−n(P∩M)−n(P∩C)+n(P∩M∩C)    (by Venn diagram)

                =24−12−7+4=9

Now, number of students  who studying only Chemistry

n(C∩M  )∩P =n(C)−n(C∩M)−n(C∩P)+n(M∩P∩C)    (by Venn diagram)

                    =19−9−7+4=7

So, how many students study only one of the three disciplines in detail                                                            6+9+7=22

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PLEASE HELP !!
Quadrilateral ABCD has vertices at A (0, 0), B (0, 3), C (5, 3), and D (5, 0). Find the vertices of the
quadrilateral after a dilation with scale factor 2.5.

Answers

According to the dilation formula, the location of the four vertices of the quadrilateral A'B'C'D' are A'(x, y) = (0, 0), B'(x, y) = (0, 7.5), C'(x, y) = (12.5, 7.5) and D'(x, y) = (12.5, 0).

How to determine the coordinates of the vertices of the dilated rectangle

Dilation are a kind of rigid transformations defined by the following formula:

P'(x, y) = O(x, y) + r · [P(x, y) - O(x, y)]     (1)

Where:

O(x, y) - Center of dilationr - Dilation factorP(x, y) - Original pointP'(x, y) - Resulting point

If we know that r = 2.5, O(x, y) = (0, 0), A(x, y) = (0, 0), B(x, y) = (0, 3), C(x, y) = (5, 3) and D(x, y) = (5, 0), then the resulting points are obtained:

A'(x, y) = (0, 0) + 2.5 · [(0, 0) - (0, 0)]

A'(x, y) = (0, 0)

B'(x, y) = (0, 0) + 2.5 · [(0, 3) - (0, 0)]

B'(x, y) = (0, 7.5)

C'(x, y) = (0, 0) + 2.5 · [(5, 3) - (0, 0)]

C'(x, y) = (12.5, 7.5)

D'(x, y) = (0, 0) + 2.5 · [(5, 0) - (0, 0)]

D'(x, y) = (12.5, 0)

Lastly, we proceed to graph the two figures.

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GO
What is the value of a in the equation 3 a+b=54, when b = 9?
O 15
O 18
O 21
O27

Answers

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the value of a in the equation 3a+b=54, if b=9?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Put in 9 for b.

[tex]\bf{3a+9=54}[/tex] | subtract 9 on both sides

[tex]\bf{3a=45}[/tex] | divide the entire equation by 3

[tex]\bf{a=15}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

       [tex]\bf{\bigcirc 15}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Answer:

a = 15

Step-by-step explanation:

3a + b = 54 ← substitute b = 9

3a + 9 = 54 ( subtract 9 from both sides )

3a = 45 ( divide both sides by 3 )

a = 15

The shape of a data-flow (DFD) diagramming process is a(n): A. rectangle. B. arrow. C. rounded rectangle. D. square. E. open box.

Answers

The shape of a data flow diagramming process is a  open box.

Given nothing and we have to tell the shape of a data flow diagramming process.

A data flow diagram expresses  the flow of information for any process or system. It uses symbols like rectangles, circles and arrows to show data inputs, outputs, storage points and the routes between each destination.

In this diagram the information is presented in rectangles and circles which are then joined through arrows.

It can present a process of coordination between departments.

Because there is no shape in which these rectangles , circles and arrows are present. That's why we have said that it is a open box.

Hence the shape of a data flow diagramming process is a open box.

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Select the correct answer.
A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?
A.
(-7, -1), 36 units
B.
(7, 1), 36 units
C.
(7, 1), 6 units
D.
(-7, -1), 6 units

Answers

The coordinates for the center of the circle and the length of the radius are  ( -7, -1 ) and 6 respectively.

Option D) is the correct answer.

What are the coordinates for the center of the circle and the length of the radius?

Given the equation;

x² + y² + 14x + 2y + 14 = 0

We subtract 14 from both sides

x² + y² + 14x + 2y + 14 - 14 = 0 -14

x² + y² + 14x + 2y = -14

Next, we complete the square for x² + 14

We have, ( x + 7 )² - 49

Next, we complete the square for y² + 2y

We have, ( y + 1)² - 1

We substitute these squares into the given equation

x² + y² + 14x + 2y = -14

( x + 7 )² - 49 + ( y + 1)² - 1 = -14

Collect like terms

( x + 7 )² + ( y + 1)² = -14 + 49 + 1

( x + 7 )² + ( y + 1)² = 36

( x + 7 )² + ( y + 1)² = 6²

Note that, the form of a circle is given as;

( x-h )² + ( y-k)² = r²

Hence, we match the values into the form and determine our center and radius.

( x-(+7) )² + ( y-(+1))² = 6²

( x-7 )² + ( y-1 )² = 6²

Hence Center = ( -7, -1 ) and radius = 6

The coordinates for the center of the circle and the length of the radius are  ( -7, -1 ) and 6 respectively.

Option D) is the correct answer.

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What is the area of the figure? Enter your answer in the box.

Answers

the answer is 30 because 3*4=12/2=6 and for the other triangle it is 8*6=48/2 =24 and 24+6=30

PLEASE HELP i need the answers and work for number 11 & 12

Answers

We can use the following identity:

(Xm, Ym) = X1+X2/2, Y1+Y2/2, where Xm and Ym are the midpoints of X and Y.

So, let's use it.

For question 11, X1 is -3, Y1 is 9, X2 is 3, and Y2 is -7.

Plugging in the points, we get:

-3 + 3 = 0 / 2 = 0 for x, and 9 + (-7) = 2 / 2 = 1 for y. Thus the midpoint is (0,1).

For question 12, X1 is -9, Y1 is -4, X2 is 1, and Y2 is 6. Plugging in the values we get:

-9 + 1 = -8 / 2 = -4 for x, and -4 + 6 = 2 / 2 = 1 for y. So the midpoint is (-4,1)

Answer:

Step-by-step explanation:

#11 (first photo): M = (0, 1)

basically, if you just count the units out (like i went from (-3,9) to (0,9) so i went 3 units to the right) and then do the same for the other point (making sure the number of units is equal so you would want to move 3 left) and then draw a line, you can then connect the other 2 points to create 2 triangles and where they intersect is the midpoint.

so in the picture, the bold green line is the original line, the purple line is the line created when you move units for both points, and the blue lines are the lines created when you fill in the blanks to make the triangles

#12 (picture 2): M = (-4, 1)

and the process is the exact same just change it for the points used

\A carpenter is making a wooden window frame that has a width of 1 inch.

A window with a one-inch frame is shown. The frame is comprised of a rectangle and a semicircle. The rectangle has side lengths of 12 inches and 48 inches. The semicircle has a radius of 6 inches. The frame is 1-inch wider than the window.

How much wood does the carpenter need to build the frame?

5.5 + 106 square inches
5.5 + 116 square inches
5.5 + 153 square inches
5.5 + 162 square inches

Answers

The area of wood needed for the frame is 5. 5 + 106 square inches. Option A

How to determine the area

The amount of wood needed for the window frame will be equal to area of window frame.

It is important to note that the upper part of window is semicircle

Area of the upper part = π [tex]\frac{R^2 - r^2}{2}[/tex]

where,

R = Outer radius,

r = Inner radius.

Area of upper part = π ×  [tex]\frac{6^2 - 5^2}{2}[/tex]

Area of upper part = 11π/2

Area of upper part = 5. 5π

To find the area of the lower part, it is important to note that the area of lower part of frame will be area of 3 different rectangles. Two are the same rectangles with length 48 inches and width 1 inch and one rectangle with length 10 inches (12-2) and width 1 inch.

Area of lower part = 2 × 48 × 1 + 10 × 1

Area of lower part = 96 + 10

Area of lower part  = 106 inches

Thus, the area of wood needed for the frame is 5. 5 + 106 square inches. Option A

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The graph shows temperatures at different altitudes. Which choice describes the relationship between temperature and altitude?

A)Positive Linear Relationship
B) Non-Linear Relationship
C)Negative Linear Relationship
D)No Relationship

Answers

Answer:

Negative linear relationship

Step-by-step explanation:

What’s the sum of square root of square root of -2

Answers

The sum of the square root of -2 and -18 is 4i√2

How to determine the sum of square root

From the information given,

The sum square root of -2

√-2 + √-18

√-2 = √(-1*2) =  √-1 * √2 = i√2   Note that the square root of -1 = i

√-18 = √(-1*18) =  √-1 * √1`8 = i√18  Note that the square root of -1 = i

But we have that

√18 = √(9*2)

Using surd form. we have

= √9 * √2= 3√2

Then,

√-18 = i√18= i(3√2) = 3i√2

Let's add the sum of square root, we have

√-2 + √-18 = i√2 + 3i√2 = (i + 3i)√2 = 4i√2

Therefore, the sum of the square root of -2 and -18 is 4i√2

The complete question is;

What is the sum of square root of -2 and square root of -18?

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A coin is flipped 15 times where each flip comes up either heads or tails. How many possible outcomes (a) contain exactly four tails

Answers

The combination of possible outcomes that we get exactly four tails is 1365.

According to the statement

The times for which coin is flipped (n) is 15

The number for which we get exactly the tails (r) is 4

So, use Combination formula which is written below

C(n,r)= n! / r!(n−r)!

Substitute the values in it

C(15,4)= 15! / 4!(15−4)!

C(15,4)= 15! / 4! * 11!

C(15,4)= 15*14*13*12*11! / (4*3*2*1) * 11!

C(15,4)= 32760 / 24

C(15,4)= 1365

So, the combination of possible outcomes that we get exactly four tails is 1365.

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Writing Exercises
361. Explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic equation?

Answers

Answer:

A quadratic equation can be solved using the quadratic formula, the factoring method, or completing the square. You expect to get either one or two answers.

Step-by-step explanation:

First, we have to understand how to solve a quadratic equation. There are three methods, the first of which is the quadratic formula. For any quadratic equation that takes the standard form of

[tex]f(x)=ax^2+bx+c[/tex]

you can solve for x by using the following formula:

x=(-b±√(b^2-4ac))/2a

Sometimes, however, the quadratic expression is factorable, meaning it can be converted into a product of two smaller expressions. For example:

[tex]x^2-4=(x-2)(x+2)[/tex]

As you can see, factoring gives you the roots easily (set each smaller expression to 0 and solve for x). If the quadratic is factorable, it would be easiest to use this method first.

Completing the square is another method that can be used to solve a quadratic function. It is often preferred because it converts the function into something factorable. In order to complete the square, you have to first ensure that the quadratic term's coefficient is 1. After that, you can take the linear term's coefficient, divide it by 2, and square it. Take the new term you found and add it to the equation. Because you are adding something to an equation, you must also subtract. Now, you can complete the square and factor. An example can be found below:

[tex]x^{2}-6=0\\\\(x^2-6+9)-9=0\\\\(x-3)^2-9=0\\\\(x-3-3)(x-3+3)=0\\\\x(x-6)=0\\\\x=0, x=6[/tex]

A quadratic equation can only have up to two solutions. You can imagine the graph of a quadratic. It looks like a parabola and only changes directions once. This means that it only crosses the x-axis two times. You can also look at the examples given and see that factoring only gives you two smaller expressions (leading to 2 roots). Sometimes, however, you might get a double root, leading to an equation with only one solution. This happens when the discriminant of the quadratic equation is 0. You can calculate this in advance to save yourself some time.

What is the ratio of cups of mixed nuts to the total number of cups of granola?
The ratio of cups of mixed nuts to cups of granola is 2 cups mixed nuts

Answers

The ratio of cups of mixed nuts to cups of granola is 2:11.

What is ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0

Given:

Rolled oats= 6 cups

Mixed nuts=2 cups

Sesame seeds=1/2 cup

Cranberries= 1 cup

Dried unsweetened coconuts=1

Honey =1/2 cup

As, the ingredients listed

Total cups of granola= Rolled oats + Mixed nuts + Sesame seeds + Cranberries + Dried unsweetened coconuts + Honey

=6 + 2 + 1/2 + 1 + 1 + 1/2

=11 cups

Hence, the ratio of cups of mixed nuts to cups of granola is 2:11.

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The complete question is

Granola 6 cups rolled oats 2 cups mixed nuts 1 2 cup sesame seeds 1 cup dried cranberries. What is the ratio of cups of mixed nuts to the total number of cups of granola? The ratio of cups of mixed nuts to cups of granola is to . 1 cup dried unsweetened coconut 1 2 cup honey

Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
335. (7w + 10x)(7w − 10x)

Answers

Answer:

The product is the difference of squares is [tex]$$(7w+10x)(7w-10x)=49{{w}^2}-100{{x}^2}$$[/tex]

Step-by-step explanation:

Explanation

The given expression is (7w + 10x)(7w-10x).We have to multiply the given expression.Square the first term 7w. Square the last term 10x.

[tex]$$\begin{aligned}&(7 w+10 x)(7 w-10 x)=(7 w)^{2}-(10 x)^{2} \\&(7 w+10 x)(7 w-10 x)=49 w^{2}-100 x^{2}\end{aligned}$$[/tex]

which one of these numbers could form a triangle?

Answers

Answer: non of those numbers

Step-by-step explanation:

all the numbers couldn't form a triangle

A manufacturer claims that a particular automobile model will get 50 miles per gallon on the highway. The researchers at a consumer-oriented magazine believe that this claim is high and plan a test with a simple random sample of 30 cars. Assuming the standard deviation between individual cars is 2.3 miles per gallon, what should the researchers conclude if the sample mean is 49 miles per gallon

Answers

A P-value of 0.0086 is sufficient evidence to refute the manufacturer's claim.

Suppose a particular vehicle gets 50 miles per gallon on the freeway and a simple random sample of 30 cars.

Let μ indicates the average number of miles per gallon of highway for a particular car model

Let [tex]\bar{x}[/tex] indicates the sample mean, σ indicates the population standard deviation and n indicates the sample size.

Given; [tex]\bar{x}[/tex]=49, σ= 2.3 and n = 30,μ₀ = 50

The significance level is α= 5%

Hypotheses: To test the null hypothesis: H₀: μ₀ = 50 Alternative hypothesis: H₁: μ <50

The test statistic can be written as:

[tex]z=\frac{\sqrt{n}(\bar{x}-50)}{\sigma}[/tex]

It follows a standard normal distribution under H₀.

Decision rule / rejection range: P-value <0.05 or because there is a test on the left

z <Ф⁻¹ (0.05) d. H. Z <-1.6449d. H.

[tex]\bar{x}[/tex] < μ₀+(σ÷√n )×-1.6449 = 49.3092725599558

Test statistic: Observations value of the test statistic,

[tex]\begin{aligned}Z_{stat}&=\frac{\sqrt{n}(\bar{x}-50)}{\sigma}\\ Z_{stat}&=\frac{\sqrt{30}(49-50)}{2.3}\\ Z_{stat}&=-2.3814\end[/tex]

critical value = Z critical = Z0.05 = -1.6449

P-value= P(Z < -2.3814)

P-value= P(Z < -2.3814)

P-value= (–2.3814)

P-value= 0.0086

Therefore, p-value = 0.0086 <0.05 and  test statistic observations Zstat critical value  [tex]\nleq[/tex] -1.6449, there is enough evidence to reject the null hypothesis.

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[tex]6/2-(81/3)^{2}[/tex]

Answers

The answer is -726
I hope this helps!

Answer:

-726

Step-by-step explanation:

So whenever you have a fraction raised to some power, you can distribute the exponent: [tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex] the reason for this can be explained, using the definition of an exponent. You can see: [tex](\frac{a}{b})^n[/tex] as [tex]\frac{a}{b} * \frac{a}{b} * \frac{a}{b}... \text{ n amount of times}[/tex] multiplying fractions simply multiplying the numerators by the other numerators, and the denominators by the other denominators. So you're going to have the fraction: [tex]\frac{a * a * a \text{ n amount of times...}}{b * b * b\text{ n amount of times...}}[/tex] which can be rewritten as an exponent, since this is the very definition of an exponent. This simplifies to: [tex]\frac{a^n}{b^n}[/tex].

Anyways now that you hopefully understand that, let's simplify the expression

The first step is to distribute the exponent to get the fraction:

[tex]\frac{6}{2}-\frac{81^2}{3^2}[/tex]

Now square both values to get

[tex]\frac{6}{2}-\frac{6,561}{9}[/tex]

The fraction simplifies to:

[tex]\frac{6}{2}-729[/tex]

the left fraction simplifies to 3, so you get

[tex]3-729[/tex]

This simplifies to

-726

Assignment: generating frequencies for compound events investigation fill out this table to show the sample space for a roll of two dice (six-sided number cubes). 1 2 3 4 5 6 1 2 3 4 5 6

Answers

Total 36 outcomes are possible on rolling two dices simultaneously

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment

A dice has 6 possibilities (1,2,3,4,5,6) , thus two when dices thrown together will have 36 outcomes in it's sample space. It's sample space is shown in picture attached below.

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What is the surface area of the composite figure?

Answers

Answer: 1226

Step-by-step explanation:

In a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event. What is the classical probability of the event

Answers

The classical probability of the given event is 1/4 or 0.25 or 25%.

The classical property of an event is the ratio of the total number of outcomes favorable to the event to the total number of outcomes in the experiment.

If we suppose an event A.

The total number of favorable outcomes to event A to be n.

The total number of possible outcomes in the experiment to be S.

Then, the classical probability of event A is given as:

P(A) = n/S.

In the question, we are informed that in a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event.

We are asked to find the classical probability of the event.

As we know, the classical probability of an event is the ratio of the number of favorable outcomes to the event to the total number of possible outcomes in the experiment.

Thus, the classical probability = 2/8 = 1/4 or 0.25 or 25%.

Thus, the classical probability of the given event is 1/4 or 0.25 or 25%.

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