Please help me with this please

Please Help Me With This Please

Answers

Answer 1

The measure of the angles are 60 degrees each

How to determine the measure of the angles

From the question, we have the following parameters that can be used in our computation:

AOB = 138 degrees

Also, we have:

The line OX bisects the angle AOB

Using the above as a guide, we have the following:

AOX = AOB/2 = 138/2 = 69

Also, we have

XOB = AOB/2 = 138/2 = 69

Hence, the angles are 69 degrees each

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Related Questions

The grass in the photo above can be found in the __________ ecosystem.

Answers

The tropical savanna environment is home to the grass in the picture above.

What is Southeast Asia's ecosystem like?

The two primary types of forests are deciduous or monsoon rainforests and tropical evergreen rainforests, which have leaves all year round (these loose their leaves during the dry season). Human activity causes deforestation because it endangers the local ecosystem's ability to sustain life.

What is the ecosystem of the rainforest?

Rainforests are a type of forest habitat that have a dense canopy, great species variety, and high rainfall rates. The Amazon is made up of a variety of ecosystems and plant life, including savannas, deciduous woods, seasonal forests, and rainforests.

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3. Explain how "a" affects the graph of a parabola. (f(x) = ax²)

Answers

The effect of "a" in the graph of parabola is value from the quadratic function.

How to determine the standard equation of the parabola?

In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:

y = a(x – h)2 + k or x = a(y – k)2 +h

Where:

(h, k) - The vertex of the parabola.

p - Least distance between the vertex and the focus of the parabola.

Given that;

The equation of parabola is f(x) = ax².

Now, Let's look at the graph of f(x) = x^2 + 3x + 1, which is below. The b-value in this equation is 3.

We see that our graph is indeed a parabola. Our parabola is curving up. The x-value of the vertex, the tip of the parabola, is -3 / 2 or -1.5. We can actually calculate this x-value by evaluating the expression -b / 2a, where a and b are the values from the quadratic function.

Therefore, the role of a in parabola is stated.

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Last week's and this week's low temperatures are shown in the table below Low Temperatures for 5 Days This Week and Last Week Low Temperatures This Week (F) Low Temperatures Last Week (F) Which measures of center the mean of this wer O the mean of the range of this O the mean absolute deviat the mean absolute devi 10 ariability are greater than 5 degrees? Select three choices temperatures temperature

Answers

The measures of the center or variability that are greater than 5 degrees are :

a) the mean of this week’s temperaturesb) the mean of last week’s temperaturesc) the range of this week’s temperatures

How to find the center of variability ?

The mean of the data on temperature this week and the last is :

= ( 4 + 10 + 6 + 9 + 6 ) / 5

= 7 degrees Fahrenheit 4+ 10+ 6+9+ 6

The mean of the data on temperature last week and the last is :

= ( 13 + 9 + 5 + 8 + 5 ) / 5

= 8 degrees Fahrenheit

The range of this week's temperature is :

= 10 - 4

= 6 degrees Fahrenheit

All these measures of center are above 6 degrees.

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The full question is:

Temperatures for 5 Days This Week and Last Week

Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.

a) the mean of this week’s temperatures

b) the mean of last week’s temperatures

c) the range of this week’s temperatures

d)the mean absolute deviation of this week’s temperatures

e) the mean absolute deviation of last week’s temperatures

Subtract 5m + 11 and m + 8

Answers

The expression (m + 8) - (5m + 11) simplifies to -4m - 3.

How to subtract the expresisons

From the question, we have the following parameters that can be used in our computation:

Subtract 5m + 11 and m + 8

To subtract (5m + 11) from (m + 8), we need to distribute the negative sign to each term inside the first set of parentheses:

(m + 8) - (5m + 11)

Open the brackets

= m + 8 - 5m - 11

Evaluate the like terms

= -4m - 3

Hence, (m + 8) - (5m + 11) simplifies to -4m - 3.

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2 Δ Δ Δ Δ Δ
Δ.
57. If t is any real number, which of the following
statements must be true?
A. -t <0
B. -t C. -t=t
D. ts|-t
E. (-t)2 = -12
58. Let a and h be positive real num

Answers

When t is any real number, the true statements will be:

A. -t < 0:

B. -t = 0

E. (-t)^2 = -t^2

How to get the true statements

If t is any real number, then the following statements are true:

A. -t < 0: This statement is true if t > 0, and false if t <= 0.

B. -t = 0: This statement is true if t = 0, and false if t ≠ 0.

C. -t = t: This statement is false for all real numbers t, since the negative of any non-zero real number is not equal to the original number.

D. t|-t: This statement is false for all real numbers t, since the absolute value of any real number is non-negative.

E. (-t)^2 = -t^2: This statement is true for all real numbers t, since squaring a real number gives a non-negative result. Note that the negative sign in front of the square is distributive and can be moved inside the square.

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Joseph selects a card from a standard deck of 52 cards and then replaces it afterwards. He decides to record the total number of red cards that he selects and calculates the proportion of red cards that he has selected so far after each pick. He then constructs a graph to visualize his results. Which of the following statements is FALSE?O The theoretical probability for selecting a red card in each pick is 0.5. O For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far. O This is an example of the law of large numbers. O The relative frequency of selecting a red card changes with the increase in number of selections.

Answers

He then constructs a graph to visualize his results,  For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far is FALSE.

Probability refers to potential. A arbitrary event's circumstance is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to read the liability of colorful events. The degree to which commodity is likely to be is principally what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

We are only interested in finding red card so we can't differentiate between diamond or hearts at any time. Hence,

The false statement is:

For a given number of selections, we can use Josephs graph to find the number of diamonds that he has picked so far.

Option B is correct.

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Kelsey orders several snow globes that each come in a cubic box that measures 14
foot on each side. Her order arrives in the large box shown below. The large box is completely filled with snow globes.

Answers

The number of snow globe in box is  x³/ 2744.

What is Volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

length of one small cube = 14 foot.

Volume of small cube = l³

                                     = 2744 ft³

let the edge of one large cube be x.

So, volume of large cube= x ft³

Thus, number of globes in larges box

= Volume of large box/ Volume of small box

= x³/ 2744

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PLEASE HELP ASAP WILL GIVE BRAINLIEST

Answers

The value of the length /MK/ is 10 units

How to find the length?

Recall that in an isosceles reangle, two sides are equal and the base angles are equal

We can use the cosine rule to find the length MK

N² = K²+M² - 2KMCosN

This implies that /MK/² = 5²+5²-2*5*5*cos110

⇒25+25-50*-0.9990

= 50+49.95

=99.95  this can be approximated to 100

the /MK/ = √100= 10 units

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The Lopez family is looking to rent a large truck for their upcoming move. With Felipe's
Moving, they would pay $90 for the first day plus $1 per additional day. With Springdale
Rent-a-Truck, in comparison, the family would pay $40 for the first day plus $6 per additional
day. Before deciding on which company to use, Mrs. Lopez wants to find out what number of
additional days would make the two choices equivalent with regards to cost. How many
additional days would that be?
Write a system of equations, graph them, and type the solution.

Answers

The system of equation is written as follows

y = 90 + x

y = 40 + 6x

With regards to cost the choices will be equivalent in 10 day

How to write the system of system of equations

Assuming additional day is x

Felipe's Moving, they would pay $90 for the first day plus $1 per additional day:

= 90 + x

Rent-a-Truck, the family would pay $40 for the first day plus $6 per additional day.

= 40 + 6x

Equating both costs gives

90 + x = 40 + 6x

90 - 40 = 6x - x

50 = 5x

x = 10

in 10 days the cost will be same

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The answer to this problem

Answers

Answer:

A. (f+g)(x)=-2x^2-2x+8

Step-by-step explanation:

You combine like terms by adding

write an absolute value inequality for each length x with the given tolerance
1. a length of 4.2 cm with a tolerance of 0.01 cm
2. a length of 3.5 cm with a tolerance of 0.2 cm
show work pls

Answers

The absolute value inequalities for the different lengths are

1) 4.19 ≤  x ≤  4.21

2) 3.3 ≤  x ≤  3.7

What is an absolute value inequality?

The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|.

An expression using absolute functions and inequality signs is known as an absolute value inequality. One example of an absolute value inequality with a larger than symbol is the statement |x + 3| > 1.

1)  length x = 4.2 cm with a tolerance of 0.01 cm

Absolute value inequality is:

|x - 4.2| ≤ 0.01

This can be written as:

x - 4.2 ≤ 0.01

           x ≤ 4.21

x - 4.2 ≥ - 0.01

            x ≥ 4.19

2)  length x =  3.5 cm with a tolerance of 0.2 cm

Absolute value inequality is:

|x - 3.5| ≤ 0.2

This can be written as:

x - 3.5 ≤ 0.2

           x ≤ 3.7

x - 3.5 ≥ - 0.2

            x ≥ 3.3

Therefore the absolute value inequalities for the different lengths are

1) 4.19 ≤  x ≤  4.21

2) 3.3 ≤  x ≤  3.7

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Find the value of x that makes AABC~ADEF.
B
8
12

A x+7 C
X =
D
24
E
48
3(x+3)
F

Answers

Answer:e

Step-by-step explanation:t

PLEASE ANSWER!!!

Russell surveys 200 randomly selected seventh-graders in his school and finds that 30 attend summer camp. If there are 780 seventh-graders in his school,
about how many are expected to attend summer camp?

Answers

Answer:

To estimate the number of seventh-graders who attend summer camp, we can use the sample proportion of 30 out of 200 students.

Let's call the population proportion of seventh-graders who attend summer camp "p".

The sample proportion can be estimated as:

p = 30/200 = 0.15

To estimate the number of seventh-graders in the entire school who attend summer camp, we can multiply the population size by the sample proportion:

Estimated number of seventh-graders attending summer camp = p * population size = 0.15 * 780 = 117

So, about 117 seventh-graders in the school are expected to attend summer camp.

Answer:

117 seventh-graders in the school are expected to attend summer camp.

Step-by-step explanation:

A city bowling league is holding a tournament in which the top 8 bowlers with the highest three-game totals are awarded cash prizes. First place will win $1250, second place $1132, third place $1014, and so on.
(a) Write a sequence a, that represents the cash prize awarded in terms of the place n in which the bowler finished
(b) Find the total amount of prize money awarded at the tournament.

Answers

The sequence will be aₙ=$1250-118ⁿ⁻¹ where n= place at which a bowler finished.

What exactly is a sequence?

A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. To figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.

Now,

given award money for 1, 2, 3 places is given as $1250, $1132 and $1014

that means for the sequence, first term is 1250 and difference between the next terms will be 118 (less)

So, the sequence will be aₙ=$1250-118ⁿ⁻¹

where

n=place at which a bowler is placed.

Hence,

           The sequence will be aₙ=$1250-118ⁿ⁻¹.

 

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the function of G takes a student's first name for its input and gives the number of letters in the first name for its output

Describe the meaning of G(jada)=4

Find the value of G(Diego).

Answers

Answer:

Step-by-step explanation:

The meaning of the function notations are

G(Jada) = 4 means that the first name Jada has four letters

C(11-15)= chemistry means that the Monday class for 11-15 is chemistry

How to interpret the function notations?

The meaning of the function G

From the question, we have the following parameters that can be used in our computation:

Function G gives the number of letters in the first name for its output.

Next, we have

G(Jada) = 4

Using the meaning of the function, we have

G(Jada) = 4 means that the first name Jada has four letters

The meaning of the function C

From the question, we have the following parameters that can be used in our computation:

Function C gives a student's Monday class for its output.

Next, we have

C(11-15)= chemistry

Using the meaning of the function, we have

C(11-15)= chemistry means that the Monday class for 11-15 is chemistry

A certain antihistamine is often prescribed for allergies. A typical dose for a 100​-pound person is 22 mg every six hours. This antihistamine also comes in a liquid form with a concentration of 12.3 ​mg/ 6mL. Following the prescribed​ dosage, how much liquid antihistamine should a 100​-pound person take in a​ week?

Answers

On solving the provided question, we can say that equation is 532/13.5 = 39.4 doses.

What exactly is an equation?

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2.

the equation is the week * 7 (weekdays) * 24 (hours/day) * 19/6 (MILIGRAMS/HOURS)

532 mg per week (532/13.5 = 39.4 doses)

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Find the value of x for the following

Answers

Answer: x = 10

Step-by-step explanation:

4x+89=129

(2 parallel straight lines have congruent angles)

then solve for x.

Step 1: Subtract 89 from both sides of the equation.

4x = 40

(We want to isolate the variable x on one side of the equation. To do this, we need to get rid of the number 89 that is currently on the right side of the equation. To do this, we subtract 89 from both sides of the equation.)

Step 2: Divide both sides of the equation by 4.

x = 10

(To isolate the variable x further, we need to get rid of the coefficient 4 that is currently in front of x. To do this, we divide both sides of the equation by 4.)

A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, determine the velocity of the truck immediately after the collision.

Answers

Answer: The momentum of the truck before the collision is given by the formula:

p_i = m_i * v_i, where m_i is the mass of the object and v_i is its velocity.

The momentum of the truck before the collision is:

p_i (truck) = 3000 kg * 10 m/s = 30000 kg m/s

The momentum of the car before the collision is:

p_i (car) = 1000 kg * 0 m/s = 0 kg m/s

The total initial momentum of the system is the sum of the initial momenta of the truck and car:

p_i (total) = p_i (truck) + p_i (car) = 30000 kg m/s + 0 kg m/s = 30000 kg m/s

After the collision, the final momentum of the system is the sum of the final momenta of the truck and car:

p_f (total) = p_f (truck) + p_f (car)

Let's call the velocity of the truck after the collision v_f (truck). The final momentum of the truck is:

p_f (truck) = 3000 kg * v_f (truck)

The final momentum of the car is:

p_f (car) = 1000 kg * 15 m/s = 15000 kg m/s

Using the conservation of momentum, we can write an equation:

p_f (total) = p_i (total)

30000 kg m/s = p_f (truck) + p_f (car)

30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s

30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s

v_f (truck) = (30000 kg m/s - 15000 kg m/s) / 3000 kg = 7.5 m/s

So, the velocity of the truck immediately after the collision is 7.5 m/s.

Step-by-step explanation:

1/4x
10. Last night, 4 friends went out to dinner at a restaurant. They split the bill evenly. Each friend paid $12.75 for his or her meal and each left the same amount for a tip, t. The total dinner bill including the tip was $61. What equation could you use to describe the situation?

Answers

Answer:

Step-by-step explanation:

Let's call the number of friends "f". Since each friend paid $12.75 for their meal, the cost of the meals can be represented as f * 12.75. And since each friend left the same amount for a tip, the cost of the tips can be represented as t * f.

The total cost of the dinner including the tip was $61, so we can write the following equation:

f * 12.75 + t * f = 61

Expanding the left side of the equation:

12.75f + t * f = 61

Combining like terms:

13.75f + t = 61

Solving for t:

t = 61 - 13.75f

So, the equation that describes the situation is t = 61 - 13.75f.

Mike is working on solving the exponential equation 37^x= 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation
Hint Use the change of base formula: logby=
log y over log b

Answers

Answer:

should" (and any subsequent words) was ignored because we limit queries to 32 words.

50x2\10 es para orita urge

Answers

Answer:

= 10.

Step-by-step explanation:

=

[tex]50 \times \frac{2}{10} \\ = 5 \times 2 \\ = 10.[/tex]

The answer becomes for the given expression is: 10.

What is multiplication?

Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in mathematics refers to the continual addition of sets of the same size. One of the fundamental mathematical processes is multiplication. The result of multiplying two or more integers together is known as the product. The first number used in a multiplication operation between two numbers is referred to as the multiplicand.

Given that,

= 50 × (2/10)

= 50 × (1/5)

= 10

Thus, for the given expression the answer becomes: 10

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1 The difference between the simple interest and compound interest on a sum put out for 2 years at 5% was 6.90 .find the sum​

Answers

so we're assuming the compounding period is annual, so hmmm let's call our sum "P", how much is it at simple and compound interest anyway?

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P[1+(0.05)(2)] \implies \boxed{A = 1.10P} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annual, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P\left(1+\frac{0.05}{1}\right)^{1\cdot 2} \implies \boxed{A = 1.1025P}[/tex]

now, the larger one will be the compound interest one, so, let's subtract the simple interest one from it to get 6.90

[tex]1.1025P~~ - ~~1.10P~~ = ~~6.90\implies 0.0025P=6.90 \\\\\\ P=\cfrac{6.90}{0.0025}\implies {\Large \begin{array}{llll} P=2760 \end{array}}[/tex]

3. The number of pages
in my book is less
than 96 and greater
than 90.
Who could I be?
2
I have 3 letters in my
'name.
Who am I?
4.

Answers

The number of pages in the book is given by the inequality 90 < A < 96 , where A is the number of pages

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of pages in the book be A

And , it is more than 90 and less than 96

So , the value of A is { 91 , 92 , 93 , 94 , 95 }

On simplifying , we get

90 < A < 96 , where A is the number of pages

Hence , the inequality is 90 < A < 96

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9. Find the sum of the first multiples of 5.​

Answers

Answer:

75

Step-by-step explanation:

Use the arithmetic progression formula:  S =n/2(2a + (n-1)d)

a = 5, d = 5, n = 5

S = 5/2((2(5) + (5-1)(5)) = 75

Please Explain and solve this problem. What trigonometric function would you use based upon the given information in the triangle shown below? ASAP

Answers

To solve the problem we would use tangent as a trigonometric function and find the unknown value.

What are trigonometric functions?

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

From the given triangle we observe that the given values are:

Angle B, side a and side b.

To find any of the unknows in the three we use the trigonometric function tangent.

Tan α = opposite side / adjacent side

For the given figure:

Tan B = b / a

Hence, to solve the problem we would use tangent as a trigonometric function and find the unknown value.

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Box plot pls answer what is the outlier and a box plot represents the data excluding the outlier

Answers

Answer: The outlier is $95 and the plot is D.

Step-by-step explanation:

          An outlier is the data value that's much larger or much smaller than the other data values. Here, that is $95.

          Excluding this value, our smallest is $15 and the largest is $60. We plot a dot at both of these points.

          The middle dot is the median. To find this, we will arrange the values in order and find the middle value. (We are excluding $95.) After doing this process, we see the middle dot is at 39.

    $15, $20, $38, $60, $45, $40, $35, $50

    $15, $20, $35, $38, $40, $45, $50, $60

    ----, ----, ----, $38, $40, ----, ----, ----

                    [tex]38 + 40 = 78, \;\;78 / 2\;\;\boxed{= 39}[/tex]

          This means we have dots at 15, 39 and 60, leading us to answer D.

I need to know why the medians differ relative to the data set and the best measure of center?

Answers

Explanation:

In this case the median value is more representative of the 'center' of the population. The median is a better measure when the data set is skewed, has fat tails as compared to a normal didtribution, or has outliers. Otherwise you should use the arithmetic mean.


Find the perimeter of the figure.

Answers

Answer:

≈29.93 [units].

Step-by-step explanation:

according to the attachment the required perimeter is:

P=2*6+4.25*2+3.1415*3=12+8.5+9.4245=29.9245 [units].

In one lottery game, contestants pick six numbers from 1 through 23 and have to match all six for the big prize (in any order).
You'll get twice your money back if you match four out of six numbers. If you buy five tickets, what's the probability of matching four out of six numbers?

If you buy five tickets, the probability of matching four out of six numbers is…?

(Enter your answer as a fraction in lowest terms.)

Answers

The answer is 0.360, or approximately 36/100.

What is probability?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

The probability of matching four out of six numbers in a single ticket can be calculated as follows:

There are C(23, 6) = 8,145 possible combinations of six numbers from 1 through 23.

There are C(23, 4) = 1,531 possible combinations of four numbers from 1 through 23.

So, the probability of matching four out of six numbers in a single ticket is 1,531/8,145 = 19/102.

If you buy five tickets, the probability of matching four out of six numbers in at least one of them is 1 - (1 - 19/102)⁵ , which can be calculated as:

1 - (1 - 19/102)⁵ = 1 - 0.848⁵ = 1 - 0.640 = 0.360

Therefore, The answer is 0.360, or approximately 36/100.

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*Please help, I will mark brainest*
A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 532,000 gallons. Tank card with three different carrying capacities are available: 7,000 gallons, 14,000 and 28,000. How many of each type of tank car should be leased?

Fill in the blank: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1=_t+(_), x2=_t+(_) & x3=t

Answers

Answer:

Let's call the number of 7,000 gallon tank cars "x1", the number of 14,000 gallon tank cars "x2", and the number of 28,000 gallon tank cars "x3".

We can write the following constraints based on the total carrying capacity of the fleet:

7,000x1 + 14,000x2 + 28,000x3 = 532,000

x1 + x2 + x3 = 25

x1, x2, x3 >= 0 (since we can't have a negative number of tank cars)

This is a linear programming problem, which can be solved using simplex method or the graphical method.

By using the graphical method, we find that there are multiple optimal solutions. For example, one solution is x1 = 11, x2 = 7, and x3 = 7. This means that the manufacturer should lease 11 7,000 gallon tank cars, 7 14,000 gallon tank cars, and 7 28,000 gallon tank cars to meet the total carrying capacity requirement of 532,000 gallons.

So, the answer to the question is: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1 = 11 + 7t, x2 = 7 + 7t, and x3 = 7 + 7t.

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