hannah is playing the lottery. she can pick 5 numbers between 1 and 32, with no numbers repeating. order of these numbers does not matter. she can also pick a bonus number between 1 and 20. what are her chances of picking all of the numbers, including the bonus, correctly?

As per the binomial distribution, the population size be at least 10 times the sample size is N

The term binomial distribution in math is defined as a probability distribution used in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions

Here we have given that we have to use a binomial distribution to approximate the count of successes in an SRS.

Here we know that if the 10 % condition is met, then a binomial distribution can be used to approximate the number of successes in a simple random sample.

Here we have also know that the 10% condition requires that the sample represents less than 10% of the population.

On the other hand the fact that the sample size is far too tiny in comparison to the population, then here it is reasonable to infer that the trials of occurrences are independent.

Therefore, the given situation suggests that the sample size n must be smaller than 10% of the population size N in this situation.

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The 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)

given that

95% confidence interval for the standard deviation of the lengths of pipes

a sample of 21 pipes

standard deviation of 14.6 inches

chi-squared(1 - a/2) < or = (n-1)s^2/(std. dev.)^2 < or = chi-squared(a/2)

in the above

a is alpha

std is standard deviation

a = (1-95/100) = 1 - 0.95 = 0.05

then, degree of freedom = 21 - 1 = 20

chi-squared(0.975) = 20.5

chi-squared(0.025) = 3.25

chi-squared for 20.5 = (21-1)×[tex](14.6)^{2}[/tex] / 20.5 = 103.98

chi - squared for 3.25 = (21-1)×[tex](14.6)^{2}[/tex] / 3.25 = 655.8

we need to square-root of the above values

chi-squared for 20.5 = [tex]\sqrt{103.98}[/tex] = 10.2

chi - squared for 3.25 = [tex]\sqrt{655.8}[/tex] = 25.6

the 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)

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Answer:

see below  : -0.0492

Step-by-step explanation:

-6*-6-3/10*-67=-33/670 = -0.0492

1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.

When limestone is subjected to the heat and pressure of metamorphism, marble is created as a metamorphic rock. Calcite (CaCO3) makes up the majority of its composition, but it also frequently includes other minerals such clay, mica, quartz, pyrite, iron oxides, and graphite.

When limestone undergoes a process known as metamorphism, which involves heat and tremendous pressure, marble is created. The marble's interconnecting calcite crystals are created when the calcite limestone recrystallizes after metamorphism.

Hence, 1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.

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The correct expression that represents the distance between the friends is 4 steps.

To calculate this

Joy walked 12 steps forward and Shaunte walked 8 steps backward. To find the distance between the two friends, we can add the number of steps they each took, so the expression would be:

12 + (-8) = 12 - 8 = 4

So the correct expression that represents the distance between the friends is 4 steps.

Note that the negative sign in front of Shaunte's steps indicates that she walked backward, and the positive sign in front of Joy's steps indicates that she walked forwards.

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The volume of the cylinder is 301.44 cm³. We use the radius that is half of diameter length in the formula for the volume of a cylinder.

The formula for the volume of a cylinder is

V = πr²h

Where

A cylinder has

Using π = 3.14, find the volume of the cylinder!

We find the radius of the cylinder.

r = ½d

r = ½(8) cm

r = 4 cm

The volume of the cylinder would be

V = πr²h

V = (3.14)(4)²(6)

V = 18.84 (16)

V = 301.44 cm³

Hence, the volume of a cylinder with the diameter of 8 cm and height of 6 cm is 301.44 cm³.

The correct option is (c).

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Answer:

301.44

Step-by-step explanation:

v=3.14 times radius squared times height

Diameter is the radius times 2

8 the diameter divided by 2 is 4

replace those

v=(3.14)4^2(6)

final answer is 301.44

The statement that when a point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x) is true. This can be calculated using the formula (x cos θ – y sin θ, x sin θ + y cos θ), where θ is the angle of rotation.

When point (x, y) is rotated 270 degrees about the origin, the coordinates of the resulting point can be calculated using the following formula: (x cos 270° – y sin 270°, x sin 270° + y cos 270°).

Plugging in the values, we get (y, -x). Therefore, the statement is true.

When rotating a point (x, y) around the origin, the coordinates of the resulting point can be calculated using the following formula: (x cos θ – y sin θ, x sin θ + y cos θ). Here, θ is the angle of rotation. In this case, when the point is rotated 270 degrees about the origin, the resulting point is (y, -x).

The statement that when a point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x) is true. This can be calculated using the formula (x cos θ – y sin θ, x sin θ + y cos θ), where θ is the angle of rotation.

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The fraction of the tiled floor is made of darker tiles is = [tex]\frac{4}{9}[/tex]

Now, According to the question:

Let's know:

What is a fraction in math?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

The given data is;

A corner of a tiled floor is shown.

If the entire floor is tiled in this way and each of the four corners looks like this one.

To find fraction of the tiled floor is made of darker tiles.

Take the total darker portion is 16

All is = 6 x 6 = 36

The fraction of the tiled floor is made of darker tiles will be:

[tex]\frac{16}{36}=\frac{4}{9}[/tex]

The answer is:

= [tex]\frac{4}{9}[/tex]

Hence, The fraction of the tiled floor is made of darker tiles is = [tex]\frac{4}{9}[/tex]

Answer:

Its 24ft

Step-by-step explanation:

Make a linear function that, after t minutes, returns the circle's radius in inches. The circle's radius will have increased by inches, hence the radius increases by inches [3 points]. Create a linear function that returns the circle's radius.

The slope-intercept form of a linear function equation. As a result, it is written as f(x) = mx + b, where m is the slope & b is the y-intercept of a line.

Therefore, the distance to the safe zone is 24 * 4 + 70, which is 166.

The formula should be D=166-24t. She needs to go 166 meters, and since she is approaching the safe place at 24 meters per second, her distance to the safe zone is decreasing by 24 meters per second, making the calculation -24 meters per second rather than 24 meters per second.

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Answer:

A) Bald Eagle

Step-by-step explanation:

4,500 meters above sea level

3,000 metres below sea level

4,500m is more farther therefore Bald Eagle

Answer:

A) Curvier Beaked Whale

Step-by-step explanation:

Curvier Beaked Whale travel over 10,440 m or Costa Rica to Antartica.It is the longest mammal migration on Earth.

By using the logarithmic properties we can probe that,

(a) [tex]$\log _b \frac{x}{y}=\log _b x+\log _b y^{-1}$[/tex]

(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]

The logarithm is exponentiation's opposite function In mathematics. This means that the exponent which [tex]$b$[/tex] must be realized To produce a number [tex]$x$[/tex] is the logarithm of [tex]$x$[/tex] the base [tex]$b$[/tex]. For Instance, because[tex]$1000=10^{\wedge} 3$, Its logarlthm In base 10 is 3 , or $\log 10=3$.[/tex]

Given: [tex]$\log _b \frac{x}{y}$[/tex]

We have to prove,

(a) [tex]$\log _b \frac{x}{y}=\log _b x+\log _b y^{-1}$[/tex]

(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]

(a) Consider, [tex]$\log _b \frac{x}{y}=\log _a x+\log _b y^{-1}$[/tex]

L. H. S [tex]$=\log _b \frac{x}{y}$[/tex]

Using the Identity:  [tex]$\frac{1}{\nu}=y^{-1}$[/tex]

L.H.S [tex]$=\log _b x y^{-1}$[/tex]

Using Identity: [tex]$\log _b m n=\log _b m+\log _b n$[/tex]

[tex]$$\Rightarrow \text { L.H.S }=\log _b x+\log _b y^{-1}$$[/tex]

Hence, L.H.S = R.H.S

(b) Consider [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]

L.H.S [tex]$=\log _b \frac{x}{y}$[/tex]

Using the Identity

[tex]$$\begin{aligned}& \log _b \frac{m}{n}=\log _b m-\log _b n \\& \Rightarrow \text { L.H.S }=\log _b x-\log _b y \\& \text { L.H.S = R.H.S }\end{aligned}$$[/tex]

Hence, proved.

Hence, by using the logarithmic properties we can probe that,

(a) [tex]$\log _b \frac{x}{y}=\log _h x+\log _b y^{-1}$[/tex]

(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]

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Answer:

=C

=A

=D

=B

Step-by-step explanation:

Correct on Edge

The formula distance = speed x time must be used to calculate the duration of a marathon as a function of the runner's average speed.

 1: List the known data. For example, a marathon is 13.1 miles long, and an average runner moves at s miles per hour.

2 :Rearrange the equation to solve for time in Step 2: Time = Speed/Distance

3: Enter the known numbers for distance and speed into the equation: time = 13.1 miles per second.

4: If necessary, simplify the equation. The units of miles will cancel out because the time is measured in hours and the speed in miles per hour, therefore the ultimate unit of time will be hours.

  The final answer  is t = 13.1/s, which expresses the duration of a marathon (in hours) as a function of the runner's average speed (in miles per hour).

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The value of x is 19.

What is the slope intercept?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

We can start by using the information given in the problem to set up an equation. We know that:

m < 1 = 6x + 3

m < 2 = 117

We are also given that m < 1 and m < 2 represent different values.

Now we can substitute the second equation into the first equation:

6x + 3 = 117

To solve for x, we can subtract 3 from both sides:

6x = 114

Finally, we can divide both sides by 6:

x = 19

Hence, the value of x is 19.

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There are 16 possible combinations of two cards, where the first one is a red card and the second one is a face card.

There are 16 ways to select two cards, where the first one is a red card and the second one is a face card. The combinations are: Red Ace, Red King, Red Queen, Red Jack, Red 10, Red 9, Red 8, Red 7, Red 6, Red 5, Red 4, Red 3, Red 2, Hearts King, Hearts Queen, Hearts Jack, and Hearts 10.

There are 16 possible combinations of two cards, where the first one is a red card and the second one is a face card. These combinations include all of the red cards in a standard deck, as well as the King, Queen, Jack, and 10 of Hearts.

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The area of the given  isosceles triangle is 480 square units.

Isosceles triangle:

An isosceles triangle is a triangle with two sides of equal length. Let's do a little activity to understand this better. Take a square piece of paper and fold it in half. Draw a line from the folded top corner to the bottom edge (see image below). Open the sheet and you will see a triangle. Mark the triangle vertices as O, D, C. Then measure OD and OC. Repeat this activity at different scales and observe patterns. We can see that OD and OC are always the same. A triangle with two equal sides is called an isosceles triangle.

Given,

base (b) = 20 units and

height (h) = 120 units.

The formula to calculate the area is 1/2 × b × h square units.

By substituting the values, we get

⇒ Area = 1/2 × 20 × 120

            = 480 unit Squares

Therefore, the area of the given  isosceles triangle is 96 square units.

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The probability that one pile contains all the face cards is 0.047%.

A standard deck of cards has 52 cards, with 12 face cards (4 Kings, 4 Queens, and 4 Jacks). When the deck is randomly divided into four equal piles, each pile will have 13 cards.

To calculate the probability that one pile contains all the face cards, we need to consider the total number of ways that the 52 cards can be divided into four piles of 13 cards, and the number of ways that the 12 face cards can be in one of those piles.

The total number of ways to divide 52 cards into four piles of 13 cards is:

52! / (13! * 13! * 13! * 13!) = 22, 948, 036, 544

The number of ways to put 12 face cards in one pile and the other 40 cards in the remaining piles is:

(12! * 40!) / (12! * 13! * 13! * 13!) = 1, 077, 744

So the probability that one pile contains all the face cards is:

1,077,744 / 22,948,036,544 = 4.7*10^-5 or 0.00047 or 0.047%

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From the given data, we said that this business is not profitable. This can be solved using addition method.

Mathematically, addition is the process of merging several numbers together. The numbers that are being added are known as addends, and the outcome of the addition process, or the answer we ultimately obtain, is known as the sum. It is a fundamental mathematical operation that we employ on a daily basis. We add numbers in many different contexts. In arithmetic sums, the plus sign (+) is used to indicate addition.

The combination of at least two integers constitutes basic addition. Once a student has mastered counting, they may begin to study basic addition. By locating the addend at the top of the chart and tracing down to the row of the second addend, they may utilize an addition chart as a learning tool.

Given that,

Jennifer makes cupcakes to sell at the local farmers market along with her own cookbook which she recently finished creating.

On a recent Saturday, Jennifer sold all 473 cupcakes she made at a cost of $2.50 each, so total amount = 473 × $2.50 = $1182.5

Now, the cost of all ingredients:

= $97.82 + (27 × $18) + $2,200 + $200

= $2983.82

Now, we said that this business is not profitable.

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The probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.

The probability of a randomly selected student having at least two siblings can be calculated by adding the probabilities of having two and three or more siblings.

Using the given probabilities, the calculation is as follows:

P(at least 2 siblings) = P(2 siblings) + P(3 or more siblings)

= 0.121 + 0.039

= 0.160

Therefore, the probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.

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Answer:

Step-by-step explanation:

52.2 : 1 = x : 1.5

x = 52.2 × 1.5 : 1

78.3 miles

Coordinates of the given endpoints of the line segments ( 1, -3) and (5,-4) after translation of 3 units to the right and reflected over x-axis is given by :

a. Coordinates ( 4,3) and (8,4) , length of the given line segment does not get affected.

As given in the question,

Line segment of xy with endpoints (1, -3) and ( 5,-4).

Distance between endpoints are:

√( 5 -1)² + ( -4 + 3)²

= √17

Conditions given:

Line segment reflected over x-axis.

After reflection y-coordinates become positive.

Endpoints become : ( 1, 3 ) and ( 5, 4)

Translation of 3 units to the right.

New coordinates after translation:

(1 +3, 3) and ( 5+3 , 4)

= ( 4,3) and (8,4)

Distance between new endpoints are:

√( 8 -4)² + ( 4 - 3)²

= √17

Therefore, for the given endpoints of the line segment after reflection and translation as per given condition new coordinates are given by:

Option a. Coordinates ( 4,3) and (8,4) , length of the given line segment does not get affected.

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Answer: 14 mg

Step-by-step explanation:

5 mg/2.5 mL = 2 mg per mL

2 mg * 7 mL = 14 mg

Answer:

there are 14 milligrams in 7 mL.

Step-by-step explanation:

to find the number of milligrams in 7 mL, you can use the proportion:

(5 mg) / (2.5 mL) = (x mg) / (7 mL)

Where x is the number of milligrams in 7 mL. To solve for x, you can cross-multiply and divide:

(5 mg) * (7 mL) = (2.5 mL) * (x mg)

x = (5 mg) * (7 mL) / (2.5 mL)

x = 14 mg

Answer: A, [tex]\frac{-6}{17}[/tex]

Step-by-step explanation:

g(3) = 2([tex]3^{2}[/tex]) - 3(3) + 1 = 18 - 9 + 1 =10

f(10) = [tex]\frac{4-10}{7+10}[/tex] = [tex]\frac{-6}{17}[/tex]

A = 1.5x + 1400 is the equation for how much money was raised.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation.

The "=" sign and terms on both sides must always be present when writing an equation. both parties.

According to our question-

Let's stand in for

Adults = x, number of them

children = y is the number.

The total amount raised equals A

In the query, it is stated that:

400 people were fed during a pancake breakfast fundraiser that cost $5 for adults and $3.50 for kids.

Consequently, x + y = 400. Formula 1: y = 400 - x

Hence:

A is equal to $5 x and $3.50 y.

Where A = 5x + 3.50 and y = 400 - x (400 - x)

A = 5x + 1400 - 3.50x A = 1.5x + 1400

The formula for calculating how much money was raised is as follows:

A = 1.5x + 1400

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The information presented states that perhaps the sculpture is 21 feet in height.

A closed, two-dimensional triangle has three sides, three angles, and three vertices. A polygon also includes a triangle. Triangle ABC is shown in the image above. A triangle through one obtuse angle (more than 90°) and several acute angles is known as an obtuse trio (or obtuse-angled triangle). No Riemann triangle can contain more than one obscure angle because in Euclidean geometry, a rectangle angles must add up to 180°.

AB/DE = BC/EF

f/6 = 28.7/8.2

=> f/6 = 3.5

=> f = 3.5 *6 = 21 ft

Consequently, the memorial is 21 feet tall.

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The complete question is-

A monument casts a shadow 28. 7 feet long. A man who is 6 feet tall casts a shadow 8. 2 feet long. The triangle drawn with the monument and its shadow is similar to the triangle drawn with the man and his shadow. How tall is the monument? Complete the statement by providing the correct answer in number form.

Answer:

c) To feed 75 people, the cafeteria would need 14*75/6 = 21 cups of milk. Since 4 cups are in a quart and 4 quarts are in a gallon, the cafeteria would need 21/16 = 1.3125 gallons of milk, which is more than 1 gallon.

b) For the recipe to feed 75 people, the cafeteria needs 475/6 = 6 cups of flour. A 10 pound bag of flour contains 38 cups, so 6/38 = 0.158 of a 10 pound bag is needed. So the cafeteria needs 0.15810 = 1.58 pounds of flour, rounded to the nearest tenth of a pound.

d) The cafeteria has 1.52.2 = 3.3 pounds of sugar in the 1.5 kilogram bag. A cup of sugar weighs 0.5 pounds, so the cafeteria needs 140.5 = 7 pounds of sugar. The cafeteria has enough sugar as 3.3 pounds is more than 7 pounds.

The polynomial models the height of this ball will be D = (x² - 400) / 19.6 feet.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

At the same time, Min’s little brother throws a baseball from a height of 4 feet with an initial vertical velocity of 20 feet per second.

Let the final speed be 'x'. Then the equation is given as,

x² - (20)² = 2(9.8) · D

19.6D = x² - 400

D = (x² - 400) / 19.6

The polynomial models the height of this ball will be D = (x² - 400) / 19.6 feet.

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Answer:

Step-by-step explanation:

D. never

A parameter is a fixed value that represents a characteristic of a set population, such as the population mean or population proportion. It is a fixed value that is true for the entire population, it is calculated using all the data of the population. For example, the mean of the height of all adults in a country is a parameter. Since it is based on all the data, it is not an estimation, it is the true value of the population. Therefore, a parameter does not change, it is a fixed value for a set population.