In the Michigan lottery game, LOTTO 47, the state selects six balls randomly out of 47 numbered balls. The player selects six different numbers out of the first 47 positive integers. Prizes are given for matching all six numbers in any order (the jackpot) and matching five numbers ($2500). A ticket costs $1.00 and this dollar is not returned to the player. Find the probabilities of matching

Answer: 6.1

Step-by-step explanation:

1) If the discriminant is greater than 0, the quadratic equation has 2 real solutions. Here D is grater than 0 . the quadratic equation has two real, distinct (different) roots.

2) If the discriminant of a quadratic equation is 4, then there are two real roots.

3) A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

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The interior angle of a regular octagon is 135 degrees.

An octagon is a polygon that has 8 sides. Therefore, a regular octagon is a octagon with all it sides and angles equal to each other.

Therefore, the sum of angles in an octagon is each interior angle multiply by the number of sides.

Therefore,

n = number of sides = 8

Hence,

interior angle = (n - 2)180 / n

interior angle = (8 - 2)180 / 8

interior angle = 6 × 180 / 8

interior angle = 1080 / 8 = 135°

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Answer:

75%

Step-by-step explanation:

9 divided by 12 is 0.75, so 9 is 75 percent of 12.

I hope this helps, have a good day!

Answer:

The field is 1 and 4/10 mile long.

Step-by-step explanation:

If I understand the question:

(1/2) + (9/10) =

(5/10) + (9/10) = (14/10)

(14/10) is 1 and 4/10

The field is 1 and 4/10 mile long.

For the eradication of malignancies like the aggressive type of human brain tumour known as glioblastoma multiforme (GBM), 3D platforms are crucial for tracking tumour growth and assessing treatment candidates.

Glioblastoma (GBM), commonly known as a grade IV astrocytoma, is an aggressive brain tumour that grows quickly. The local brain tissue gets invaded, but it typically does not spread to distant organs. GBMs can develop from lower-grade astrocytomas or develop from new brain tumours.

Some characteristics of GBM are-

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Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

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The cost of one pen is Rs 15.

It is given that Ruby paid with a 500 rupee note and got Rs 90 back.

This means that she spent 410 rupees.

Therefore the cost of 24 books and 5 pens is Rs 410.

Let the cost of books be x and the cost of pens be y.

Therefore, we can form the following equations:

24x + 5y = 410                   (1)

12x + 10y = 280                   (2)

We have to find the value of y.

Multiply the second equation by 2:

24x + 20y = 560                   (3)

Now subtract the first equation from the third equation:

24x + 20y - 24x - 5y = 560 - 410

15y = 150

y = 15.

The variable y represents the cost of one pen.

This means that the cost of one pen is Rs 15.

Therefore, we have found that the cost of one pen is Rs 15.

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I got you, bro

Answer:

(x+4)(x+18)

Explanation

Let's factor x2+22x+72

x2+22x+72

The middle number is 22 and the last number is 72.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 22

Multiply together to get 72

Can you think of the two numbers?

Try 4 and 18:

4+18 = 22

4*18 = 72

Fill in the blanks in

(x+_)(x+_)

with 4 and 18 to get...

(x+4)(x+18)

Answer:

(x+4)(x+18)

Answer:

(x+4)(x+18)

Step-by-step explanation:

Using the factorisation method :

We need 2 numbers that multiply to give +72 and add to give +22 :

To find these numbers we write out all the factors of 72 :

1, 72

2 , 36

3 , 24

4 , 18    ----> These must be the numbers as 4+18 = 22

Now we split +22x into +4x and +18x :

x² + 4x + 18x + 72

Factor the first 2 terms together and the last two terms :

x(x+4) + 18(x+4)

Keep 1 bracket and terms outside the brackets collect them into one:

(x+4)(x+18)

This is our final answer

Hope this helped and have a good day

The height of the center of the frame has to be 15ft.

Slope of the tarp is given as 2/5

The height is said to be 10 feet

The width is given as 25

25/2 = 12.5

AB/BC = 2/5

AB/12.5 = 2/5

cross multiply to find AB

5AB = 25

AB = 5

The height = 10 feet + 5 feet

= 15 feet

Hence the center of the frame has to be 15 feet.

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The probability in all given conditions is 1/4.

According to the statement

Number of coin tossed = 3

Total outcomes = 8

Now, we have to find the probabilities on different conditions.

Probability = A head on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

Probability = alternating tale and head / total outcomes

Probability = 2/8

Probability = 1/4.

Probability = A No tails on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

So, The probability in all given conditions is 1/4.

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See below for the table of -csc theta

The function is given as:

-csc theta

Rewrite properly as:

[tex]-\csc(\theta)[/tex]

This is calculated as:

[tex]-\csc(\theta) = -\frac{1}{\sin(\theta)}[/tex]

Set [tex]\theta[/tex] to 0, 30, 45, 60 and 90

[tex]-\csc(0) = unde fined[/tex]

[tex]-\csc(30) = -2[/tex]

[tex]-\csc(45) = -\sqrt 2[/tex]

[tex]-\csc(60) = -\frac{2\sqrt 3}{3}[/tex]

[tex]-\csc(90) = -1[/tex]

So, the table of -csc theta is

Angle      -csc theta

0              undefined

30            -2

45            -√2

60             -2/3 √3

90             -1

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Answer:

160 ft

Step-by-step explanation:

We have

2(length + width)= perimeter

than,

let, width =x

now,

2(x+60+x) = 520

or, 2x+60 = 260

or, 2x = 200

or, x = 100

so length is 100+60 = 160

By definition of a binomial random variable,  the probability that the machine will be working is 0.82045.

First of all, you should know that the Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

On the other hand, a random variable is a function that associates a real number, perfectly defined, to each sample point.

A random variable is discrete if the numbers it gives rise to are integers.

Finally, a binomial distribution is a discrete probability distribution that describes the number of successes in performing n independent experiments on a random variable.

The expression to calculate the binomial distribution is:

P(X=x)=([tex]n\\ x[/tex]) pˣ qⁿ⁻ˣ

Where:

Remember that:

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

where the exclamation mark represents the factorial symbol, that is, the product of all positive integers from 1 to n.

A machine has 28 identical components which function independently. The probability that a component will fail is 0.19.

The following random variable is defined:

x= the number of components will stop working.

Being n the total number of pieces (in this case, 12 pieces) and p the probability of success (the piece fails, in this case 0.19), the expression to be used is expressed as:

P(X=x)=([tex]12\\ x[/tex]) 0.19ˣ (1-0.19)¹²⁻ˣ

P(X=x)=[tex]\frac{12!}{x!(12-x)!}[/tex] 0.19ˣ (0.81)¹²⁻ˣ

Since the machine will stop working if more than three components fail, you need to know the probability that the machine will be working if 3 or less than 3 components fail. In other words, it may be that 0, 1, 2 or 3 pieces are broken and the machine continues to work:

P(X≤3)= P(X=0) + P(X=1) + P(X=2) + P(X=3)

Then:

P(X≤3)= [tex]\frac{12!}{0!(12-0)!}[/tex] 0.19⁰ (0.81)¹²⁻⁰ + [tex]\frac{12!}{1!(12-1)!}[/tex] 0.19¹ (0.81)¹²⁻¹ + [tex]\frac{12!}{2!(12-2)!}[/tex] 0.19² (0.81)¹²⁻² + [tex]\frac{12!}{3!(12-3)!}[/tex] 0.19³ (0.81)¹²⁻³

Solving:

P(X≤3)= [tex]\frac{12!}{0!12!}[/tex] ×1×(0.81)¹² + [tex]\frac{12!}{1!11!}[/tex] 0.19×(0.81)¹¹ + [tex]\frac{12!}{2!10!}[/tex] 0.19²×(0.81)¹⁰ + [tex]\frac{12!}{3!9!}[/tex] 0.19³×(0.81)⁹

P(X≤3)= 1×1×(0.81)¹² + 12×0.19×(0.81)¹¹ + 66×0.19²×(0.81)¹⁰ + 220×0.19³×(0.81)⁹

P(X≤3)= (0.81)¹² + 2.28×(0.81)¹¹ + 2.3826×(0.81)¹⁰ + 1.50898×(0.81)⁹

P(X≤3)= 0.82045

Finally, the probability that the machine will be working is 0.82045.

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Answer:

Vertex - (2, -1)

Axis of Symmetry - x = 2

X intercept - (3,0) (1, 0)

Y intercept (0, 3)

Domain - (negative infinity, positive infinity)

Range - [-1, infinity)

Step-by-step explanation:

I graphed with desmos and found it.

Answer:

(x-4)=0 or (x+2)=0 is correct

Step-by-step explanation:

(x+1)(x-3)=5

x^2 -3x +x -3=5

x^2-2x-8=0

x^24x+2x-8=0

(x+2)(x-4)=0

so,

(x-4)=0 or (x+2)=0

The solutions to the expression are:

x - 4 = 0 or x + 2 = 0.

Option C is the correct answer.

We have,

To determine which of the following statements is true:

(x + 1) = 0 or (x - 3) = 0

(x + 1) = 5 or (x - 3) = 5

(x - 4) = 0 or (x + 2) = 0

We can solve the given equation (x + 1)(x - 3) = 5 by expanding the equation and setting it equal to 0:

(x + 1)(x - 3) - 5 = 0

Expanding the equation:

x² - 3x + x - 3 - 5 = 0

x² - 2x - 8 = 0

Now we can factor the quadratic equation:

(x - 4)(x + 2) = 0

From this factorization, we find two possible solutions:

x - 4 = 0 --> x = 4

x + 2 = 0 --> x = -2

Therefore,

The correct statement is:

(x - 4) = 0 or (x + 2) = 0

i.e

x - 4 = 0 or x + 2 = 0.

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The number of gallons of the 35% acid solution eli should add is; 0.125 gallons

From the given table, since Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution, then we can say that;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

where g is number of gallons

Now,  for us to determine how many gallons of the 35% acid solution eli should add, we will solve the word problem earlier to get;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

⇒ 0.05 + 0.35g = 0.15g + 0.075

⇒ 0.35g - 0.15g = 0.075 - 0.005

⇒ 0.2g = 0.025

g = 0.025/0.2

g = 0.125 g

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The ratio of all the corresponding sides of the triangle are equal to each other.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangles are said to be similar if they have the same shape and the same corresponding angles.

Also, the ratio of all the corresponding sides of the triangle are equal to each other.

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The solution for the questions is mathematically given as

a)

t-distribution.

b)

the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952, 7.3048 )

c) the value of the [tex]\mu_0[/tex] is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_0; otherwise, reject H _0.

d)

you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

Generally, the equation for is mathematically given as

a.

In this case, the standard deviation of the population is unknown.

As a result, we make use of the t-distribution.

b)

We wish to generate a confidence interval with a 98 percent likelihood for the mean.

Because of this,

[tex](\bar{X}-t_{n-1,\alpha/2}\frac{s}{\sqrt{n}},\bar{X}+t_{n-1,\alpha/2}\frac{s}{\sqrt{n}})[/tex]

[tex](6.85-t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}},6.85+t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}})[/tex]

[tex](6.85-t_{147,0.01}\frac{2.12}{12.1655},6.85+t_{147,0.01}\frac{2.12}{12.1655})[/tex]

(6.3952,7.3048)

Therefore, the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952 , 7.3048 )

c )

If the value of the mu _0 is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_o; otherwise, reject H_0.

d . Here, we want to determine the sample size

Therefore,

[tex]n=t_{n-1,\alpha/2}^2\frac{s^2}{E^2}[/tex]

[tex]n=t_{148-1,0.05/2}^2\frac{2.12^2}{0.5^2}[/tex]

[tex]n=t_{147,0.025}^2\frac{2.12^2}{0.5^2}[/tex]

[tex]n=2.6097^2\frac{2.12^2}{0.5^2}[/tex]

n=122.4364

In conclusion, you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

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Since the given lines a and b are neither parallel, nor do they intersect each other. Also, they lie on two different planes, P and Q respectively, and thus, are co-planar. hence, a and b can be called skew lines.

Definition of Skew Lines

Skew lines in 3D geometry, are, by definition, a pair of lines that are neither parallel nor intersect each other. Such lines are therefore not coplanar, according to the conclusion.

Skew lines tend to occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. Skew lines go on forever in both directions.

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Answer:

Step-by-step explanation:

Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.

The radius of the cone's base in the unit is 9*7x².

Given:

To find:

Solution:

As we know, the volume of the cone formula is

V = πr²h/3

So, lets us compare the above formula with the given expression;

πr²h/3 = 3*7x³

Here, h is represented as x, we get;

πr²x/3 = 3*7x³

πr²/3 = 3*7x²

r²= 9*7x²

Hence, the radius of the cone's base, in units, is 9*7x².

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The required system of equations that can be used to determine the total number of ounces in the jug of water (x), and the total number of ounces in the bottles of juice (y) is

[tex]x - y = 192[/tex]

[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]

To write an equation,

It is given that,

The difference between the jug of water and the bottle of juice that Kira is drinking is 192 ounces

Kira has consumed a total of 42 ounces, which is 3/32 of the bottle of juice and 9/64 of the jug of water.

Consider,

The total number of ounces in the jug of water = x

The total number of ounces in the bottle of juice = y

Applying these variables in the above sentences,

[tex]x-y=192[/tex]

[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]

Therefore, these two equations are used to determine the total number of ounces in the jug of water and the bottle of juice.

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If fish are sold at [tex]10[/tex] for $[tex]864[/tex].  the cost to the nearest dollar of [tex]16[/tex]fish is $ [tex]1382[/tex]

How can we find the cost of the [tex]16[/tex] fish ?

The cost of the selling [tex]10[/tex] fish = $[tex]864[/tex]

So the cost of the [tex]1[/tex] fish is

[tex]= \frac{864}{10} \\=86.4[/tex]

So the cost of the selling [tex]16[/tex] fish

[tex]= 16* 86.4\\=1382 $[/tex]

$[tex]1382[/tex] is the selling cost of [tex]16[/tex] fish.

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Skew lines and parallel lines do not intersect

As a general rule, skew lines are lined that are not on the same plane; they are not parallel to each other and they do not intersect

Using the above definition as a guide, the skew lines in the figure are:

Parallel lines and skew lines are different in the following ways:

Parallel lines and skew lines are alike in the following way:

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Answer:

Step-by-step explanation:

Comment

The radius is 33 feet. The height is really a radius. The diameter consists of 2*r

r = diameter / 2

diameter = 66 feet

r = 66 /2 = 33

So you have 2 ways of finding the radius.

Solution

Area of a full circle = pi r^2

Area of a full circle = pi * 33^2

Area of a full circle = 1089 pi    

Area of a semicircle = area of a full circle / 2

Area of a semicircle = 1089 * pi /2

Area of a semicircle = 544.5 * pi

Answer

Exact answer in terms of pi is 544.5 * pi

Approximate answer using 3.14 for pi = 3.14*544.5 = 1709.73

Answer:

Area=

πr2

2

Step-by-step explanation:

3.14159⋅(33)2

2

=1710.5958

Answer:

Answer should be 15

Step-by-step explanation:

25 divided by 15 is 1.6666666667 so if use that multiply 9 you'll get 15.

Answer:

Step-by-step explanation:

A^2 + B^2=C^2

30^2 -25^2= 16.5

answer= 16.5

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

Explanation:

Triangle ABC is similar to triangle DEF. The order of the lettering is important because it tells us how the letters pair up.

Based on that, we can determine how the segments pair up

We want to find how long EF is, which means we'll involve BC = 17 since it is paired with it.

The diagram shows that AC = 14 and DF = 3, which is another pair we'll use

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

The key takeaway is that

Those two facts lead to the steps below

[tex]\frac{AC}{DF} = \frac{BC}{EF}\\\\\frac{14}{3} = \frac{17}{EF}\\\\14*EF = 3*17\\\\14*EF = 51\\\\EF = \frac{51}{14}\\\\EF \approx 3.642857\\\\EF \approx 3.6\\\\[/tex]

The proportion in step 1 is valid due to the similar triangles, and because of the corresponding side pairs mentioned. In step 3, I cross multiplied.

Answer:

3.6 cm

Step-by-step explanation:

Similar Triangle Theorem

If two triangles are similar, the ratio of their corresponding sides is equal.

Given triangles:

Therefore the corresponding sides are:

To find the measure of side EF, use the Similar Triangle Theorem:

[tex]\implies \sf AC:DF=BC:EF[/tex]

[tex]\implies \sf \dfrac{AC}{DF}=\dfrac{BC}{EF}[/tex]

[tex]\implies \sf \dfrac{14}{3}=\dfrac{17}{EF}[/tex]

[tex]\implies \sf EF=17 \cdot \dfrac{3}{14}[/tex]

[tex]\implies \sf EF=\dfrac{51}{14}[/tex]

[tex]\implies \sf EF=3.642857...[/tex]

[tex]\implies \sf EF=3.6\:cm\:\:(nearest\:tenth)[/tex]

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Answer:

d. x =0 or x = -6

Step-by-step explanation:

x(x + 6) = 0

This is telling us that either x is 0 or x is -6, because:

1) when x = 0, 0*(0+6)=0, and

2) when x = -6, -6*(-6+6) = 0;  -6(0) = 0

Answer:

H. 15 ft by 15 ft

Step-by-step explanation:

area of square = side²

225 ft² = side²

side = √(225 ft²)

side = 15 ft

Answer: H. 15 ft by 15 ft