ABCD is a square.

Square A B C D is shown. A diagonal is drawn from point A to point C. The measure of angle B A C is question mark.

What is the measure of angle BAC?
30°
45°
60°
90°

If mean is 98, standard deviation is 20.41, n=81 then sample mean will be  131.57445 which would have 10% of the possible mean less than it.

Given that mean is 98,standard deviation is 20.41,n=81 and significance level be 10%.

We are required to find the value of sample mean.

Because the value of n is greater than 30 so we will use z statistics in the problem.

We know that,

Z=(X-μ)/σ  in which μ is population mean, σ is standard deviation.

Confidence level=1-0.01=0.09 means 90%.

Z value for 90% confidence level be 1.645.

we have to put the value of Z=1.645 , μ=98,σ=20.41 to get the value of X.

1.645=(X-98)/20.41

1.645*20.41=X-98

33.57445=X-98

X=98+33.57445

X=131.57445

Hence if mean is 98, standard deviation is 20.41, n=81 then sample mean will be  131.57445 which would have 10% of the possible mean less than it.

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Answer: 15/2

Step-by-step explanation: if you fraction it, it'll be 60/8 so you can simplify it by 4. So 60÷4/8÷4 will be 15/2. So the answer is 15/2

Answer:

15/2 or 7 1/2.

Step-by-step explanation:

60 / 8      divide top and bottom by 4:-

= (60/4)  /  (8/4)

= 15/2.

The elements which must be contain in a body paragraph of a literary analysis are;

A strong body paragraph basically is characterized as a medium of stating facts regarding a viewpoint and these statements must be accompanied by supporting evidence and commentary.

On this note, the three elements which should be contained in a strong body paragraph are;

Remarks:

an introduction to a text

reasons that support a viewpoint

O a thesis statement

supporting evidence and commentary

Da summary of the main points

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Answer:

Option c is the correct answer

Step-by-step explanation:

distance of satrun - distance of jupiter

Step-by-step explanation:

[tex]12 {x}^{2} - 6( {a}^{2} + {b}^{2} )x + 3 {a}^{2} {b}^{2} = 0[/tex]

Using quadratic formula, we get

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( - 6) {}^{2}( {a}^{2} + {b}^{2}) {}^{2} - 4(12)(3 {a}^{2} {b}^{2} )} }{24} [/tex]

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( {a}^{2} + {b}^{2} ) {}^{2} - 144 {a}^{2} {b}^{2} } }{24} [/tex]

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( ({a}^{2} + {b}^{2}) {}^{2} - 4 {a}^{2} {b}^{2} }) }{24} [/tex]

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{6 \sqrt{ ({a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{24} [/tex]

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( {a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{4} [/tex]

Answer: x₁=6b²,  x₂=6a².

Step-by-step explanation:

[tex]12x^2-6*(a^2+b^2)+3a^2b^2=0\\D=(6*(a^2+b^2))^2-4*12*3a^2b^2\\D=6^2*(a^2+b^2)^2-144a^2b^2\\D=36*(a^4+2a^2b^2+b^4)-144a^2b^2\\D=36a^4+72a^2b^2+b^4-144a^2b^2\\D=36a^4-72a^2b^2+36b^4\\D=(6a^2)^2-2*6a^2*6b^2+(6b^2)^2\\D=(6a^2-6b^2)^2\\\sqrt{D}=\sqrt{(6a^2-6b^2)^2}=|6a^2-6b^2|=б(6a^2-6b^2).\\\displaystyle x_{1,2}=\frac{-(-6*(a^2+b^2))б(6a^2-6b^2)}{2} .\\x_1=\frac{6a^2+6b^2-6a^2+6b^2}{2} \\x_1=\frac{12b^2}{2} \\x_1=6b^2.\\x_2=\frac{6a^2+6b^2+6a^2-6b^2}{2} \\x_2=\frac{12a^2}{2} \\x_2=6a^2.[/tex]

based on the number of marbles in the bag, the number of marble groups possible is 7,140 groups.

the probability of selecting 2 red and 1 yellow is 1/68.

first, find the number of marbles:

= 7 + 8 + 9 + 7 + 5

= 36

the number of marble groups are:

= 36 ! / (3 ! x 33 !)

= 7,140 groups

the probability of picking 2 red and 1 yellow is:

= (( (7! / (2! x 5!)) x ( ( 5! / (1! x 4!))) / 7,140

= 1 / 68

= 1.47%

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The kite is flying 415.84 feet from the ground

The given parameters are:

Let the height be h.

So, we have the following sine function

sin(x) = h/L

Make h the subject

h = L * sin(x)

This gives

h = 725 * sin(35)

Evaluate

h = 415.84

Hence, the kite is flying 415.84 feet from the ground

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Answer:53.32

Step-by-step explanation:

$54 retail price

sales tax 8%

$54x8%= 4.32

sales tax is $4.32

$54+$4.32= $58.32

total with tax is $58.32

$58.32-$5= 53.32

Answer:

2.094 x 10¹⁰ I have to add more words soo

Answer:

Step-by-step explanation:

I would use the law of sins.

13/sin90 = 5/sin s

sin s  = (5 sin 90)/13

sin s = .3846.  

Now put in your calculator sin-1 .3846 and you will get the angle of 22.6 degrees rounded to the tenths place.

Answer:

22.6 = 113/5

Step-by-step explanation:

The amount of material needed for the entire kite is 48 square inches

The given parameters:

KI =6 inches

ET = 8 inches

KT=10 inches

Area of ΔKIT = 17 square inches

Start by calculating the area of the bottom triangle using:

A = 0.5 * Base * Height

This gives

A = 0.5 * 10 * 6

Evaluate

A = 30

The amount of material is

A = 30 + 17

A = 47

Hence, 48 square inches of material is used for the entire kite,  quadrilateral KITE

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Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]

The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:

X = 42:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (42 - 40)/2

Z = 1

Z = 1 has a p-value of 0.8413.

X = 38:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (38 - 40)/2

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

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Answer: 22

Step-by-step explanation:

The correct answer is all of the above.

Why is the range the most convenient measure of variability?

How do you find the range?

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There is a total of 90 handshakes.

There are 5 sets of triplets.

If we select one of the sets, each of the triplets will have one handshake with the other 12 people. So we have 36 handshakes at this point.

Now we only care for the other 4 sets.

We select one set again, each triple on that set will have one handshake with the other 9 people, so for the 3 triplets, we have a total of 27 new handshakes.

For the remaining 3 sets we do the same, this time we add 18 handshakes.

Finally, there are 2 sets of triplets, this time we add 9 new handshakes.

To get the total number of handshakes we need to add them all:

36 + 27 + 18 + 9 = 90

There is a total of 90 handshakes.

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The unknown sides and angles of the triangle are 18 cm and 39 degrees respectively.

The side and angle of a triangle can be found as follows:

using sine law,

Angle A = 180 - 68 - 59 = 53 degrees

19.5 / sin 59 = a / sin 53

19.5 sin 53 = a sin 59

a = 19.5 sin 53 / sin 59

a = 15.5733924459 / 0.8571673007

a = 18.1680280047

a = 18 cm

15 / sin ∅ = 20 / sin 57

15 sin 57 = 20 sin ∅

sin ∅ = 12.5800585192 / 20

sin ∅= 0.62900292595

∅ = sin ⁻¹ 0.62900292595

∅ = 38.9763828249

∅ = 39 degrees.

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Hey there!

12(w - 3)

= 12(10 - 3)

= 12(10) + 12(-3)

= 120 - 36

= 84

OR

12(w - 3)

= 12(10 - 3)

= 12(7)

= 84

Therefore, your answer should be:

84

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

8

Step-by-step explanation:

A cube is equal on all sides. Therefore the cubes must be 3cm x 3cm x 3cm. Therefore, each cube has an area of 27cm^3. The box that the cube has an area in is 3cm x 6cm x 12 cm which = 216cm^3. If you do [tex]216cm^3/27cm^3 = 8 cubes[/tex]

the probability that the sample mean will be smaller than m = 22 is 0.02275.

For the given question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Here sample size, n = 4

mean, μ = 30

standard deviation, σ = 8

The probability that the sample mean will be smaller than m = 22 is

z = [tex]\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

⇒ z =[tex]\frac{22-30}{\frac{8}{\sqrt{4} } }[/tex]

⇒ z = [tex]\frac{22-30}{\frac{8}{2} }[/tex]

⇒ z = [tex]-\frac{8}{4}[/tex]

⇒ z = -2

Refer the Z table for p value,

Thus for P(z < -2) is 0.02275.

Hence we can conclude that the probability that the sample mean will be smaller than m = 22 is 0.02275.

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Angles are formed when two or more lines intersect. Angles are majorly measured in degrees.

The required proof is as shown below:

Whenever a transversal passes through two parallel lines, angles are formed which have some similar properties.

             STATEMENTS                                           REASONS

1. AB ║DC                                                          Given.

2. < FDC ≅ < FBA                                              Alternate angle theorem.

3. <AFB  ≅ < DFC                                              Vertical opposite angle rule.

4. DF ≅ BF                                                         Given

5. ΔDFC  ≅ Δ BFA                                            Angle-Angle-Side property

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Answer:

The bars cost 1 each and the drinks cost 2 each.

Step-by-step explanation:

Let b = bars and d = drinks

4b + 3d = 10           6b + 2d = 10

There are a few ways to solve this.  If I want to eliminate the b's from both equations.  I would multiple the first equation all the way through by -6 and the second equation all the way through by 4.

4b+ 3d = 10

-6(4b + 3d) =(10)-6   Multiple all the way through by -6

-24b -18d = -60  A positive multiplies by a negative is a negative

6b + 2d = 10  

4(6b + 2d) = (10)4  Multiple all the way through by 4

24b + 8d = 40

Take the two bold equations from above and add them together

-24b - 18d = -60

24 b + 8d = 40  

          -10d = -20  Divide both sides by -10

d = 20 A negative divided by a positive is a negative.

Plug in 2o for d in either of the top two equations and get b = 1.

The center and radius of the circle is (b) center: (-5, 1) radius: 2

The circle equation is given as:

(x-5)^2 + (y+1)^2 = 4

The circle equation is represented as:

(x-a)^2 + (y-b)^2 = r^2

Where:

Center = (a,b)

Radius = 4

By comparison, we have:

(a, b) = (-5, 1)

r^2 = 4

This gives

(a, b) = (-5, 1)

r = 2

Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2

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Using the proportionality theorem, the length of the missing segment is 25 units.

According to the proportionality theorem, the middle segment in the diagram given divides the two sides it intersects proportionally.

Therefore, we would have:

x = missing segment

36/21 = (35 + x)/35

Cross multiply

35(36) = 21(35 + x)

1,260 = 735 + 21x

1,260 - 735 = 21x

525 = 21x

525/21 = x

x = 25

The missing segment is: 25 units.

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Answer:

2 sides and angle between them are congruent to the same 2 sides and angle on the other triangle

Step-by-step explanation:

The value of x from the given figure is 11

The sum of two complementary angles is 90 degrees.

The angles shown in the diagram are complementary such that;

20 + 5x + 15 = 90

5x + 35 = 90

5x = 90- 35

5x = 55

x = 55/5

x = 11

Hence the value of x from the given figure is 11

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Answer:

200 meters

Step-by-step explanation:

If the ratio is 5 inches to 20 meters that means for every 5 inches in the model there will be 20 meters on the real ship.

If the model is 50 inches long that means that there are 10 5 inch segments, multiply this 10 by the 20 meters in the ratio and you will get 200 meters as the final length for the ship.

Answer:

[tex]\sf -3xy\left(2x^2-3xy+4y^2\right)[/tex]

Step-by-step explanation:

[tex]\sf -6x^3y+9x^2y^2-12xy^3[/tex]

To factor the GCF of 6x³y + 9x²y2 - 12xy³ let's apply the exponent rule:-

[tex]\boxed{\sf a^{b+c}=a^ba^c}[/tex]

[tex]\boxed{\sf x^3y=xx^2y,\:x^2y^2=xxyy,\:xy^3=xyy^2}[/tex]

[tex]\sf -6xx^2y+9xxyy-12xyy^2[/tex]

Rewrite,

[tex]\sf 2\cdot \:3xx^2y+3\cdot \:3xxyy+4\cdot \:3xyy^2[/tex]

Now, factor out the common term [tex]\sf -3xy[/tex]:-

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