Find the number of different ways that an instructor can choose 4 students from a class of 31 students for a field trip.

Answer:

congruent, same length

Step-by-step explanation:

The three sides of an equilateral triangle are congruent.

They have the same length.

Note that where the above conditions exists with regard to the geometric ratios, the sum of the antecedents is approximately 445.31.

Let the three continuous geometric ratios be a, ar, and ar^2, where a is the first term and r is the common ratio. Then the equality can be written as:

a/ar + ar/ar² + ar² = 3/4

Simplifying this equation, we get:

1/r + r + r² = 3/4

Multiplying both sides by 4r², we get:

4r + 4r³ + 4r⁴ = 3r²

Rearranging, we get:

4r⁴ + 3r² - 4r = 0

We can factor this equation as:

r(4r³ - 4r² + 3) = 0

Since r cannot be zero, we must solve the cubic equation:

4r³ - 4r² + 3 = 0

Using a numerical method or a computer program, we can find that one real root of this equation is approximately 0.8202.

Now that we know the value of r, we can use the difference between the largest and minor consequent to find the value of a. The largest consequent is ar², and the minor consequent is a, so we have:

ar² - a = 120

Substituting r = 0.8202, we get:

a(0.8202)² - a = 120

Simplifying, we get:

a = 120 / (0.6721)

a ≈ 178.63

Finally, we can calculate the sum of the antecedents:

a + ar + ar² = 178.63 + (178.63)(0.8202) + (178.63)(0.8202)²

Summing these terms, we get:

a + ar + ar² ≈ 445.31

Therefore, the sum of the antecedents is approximately 445.31

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Translation:

If the sum of the ratios of an equality of 3 continuous geometric ratios is 3/4, calculate the sum of antecedents. Consider that the difference between the largest and minor consequent is 120

The extreme value of the function f(x) is the minimum value of the profit, which occurs when x = 15.

The given function f(x) represents the profit in thousands of dollars of selling x items. To find the meaning of the extreme value, we need to find the critical points of the function, which are the values of x where the derivative of the function is equal to zero or undefined.

The derivative of the given function is:

f'(x) = 12x - 180

Setting f'(x) = 0 to find critical points:

12x - 180 = 0

Solving for x, we get:

x = 15

So, x = 15 is the critical point of the function.

Now, we need to determine whether this critical point is a maximum or a minimum.

To do so, we can use the second derivative test. The second derivative of the given function is:

f''(x) = 12

Since f''(15) = 12 > 0, the critical point x = 15 is a minimum.

Therefore, the extreme value of the function f(x) is the minimum value of the profit, which occurs when x = 15. This minimum value represents the least amount of profit that can be earned by selling the items.

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Answer: 4:12

Step-by-step explanation: Since it is squares to total you have to put the amount of squares first. That would be 4. Then, you have to figure out the total which is just adding 4+8=12. That would be the total. Therefore, the answer would be 4 to 12.

The correct option is (c) i.e. The segments are parallel.

What are parallel lines?

Parallel lines are two lines in a two-dimensional space that never intersect, no matter how far they are extended in either direction. They always maintain the same distance between them and have the same slope. The symbol for parallel lines is "||".

In geometry, parallel lines are important because they create angles that are congruent or equal to each other when intersected by a third line, known as a transversal. This concept is used in many practical applications, such as in construction, engineering, and navigation.

The segments are parallel.

If the slopes of two lines are equal, it means that the lines are either parallel or they are the same line. In this case, since the two segments have zero slope, it means that they are horizontal lines. Horizontal lines are always parallel to each other, so we can conclude that the two segments are parallel.

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The correct answer is [tex](\frac{1}{10!} )[/tex] i.e. 0.00002756% , for this we have to learn probability.

Probability of an event which define as the possibility of any event to occur when we perform any event.

Probability is a method to determine how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make assumption about the likelihood or chance of an event happening, or how likely it is.

An event in probability theory is the result of a random experiment or a specified group of its results.

To achieve 10 balls in order we first choose a random ball, then the probability of that ball is i.e. P(1) =  [tex]\frac{1}{10}[/tex] .

Then choose Second ball whose probability is i.e. P(2) =  [tex]\frac{1}{9}[/tex] .

And then [tex]\frac{1}{8}, \frac{1}{7} ,\frac{1}{6} ,\frac{1}{5} .......... finally,\ \frac{1}{1}.[/tex]

[tex]P(1.......10\ in\ order)=\frac{1}{10!}[/tex]

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the fraction of people in the room with blue eyes is 9/50.

If approximately 18 out of every 100 people have blue eyes, then the fraction of people with blue eyes can be expressed as 18/100 or 0.18. To find the fraction of people with blue eyes in a room of 50 people, we need to multiply this fraction by the total number of people:

(0.18) x 50 = 9

So, there are approximately 9 people in the room with blue eyes. To express this as a fraction with a denominator of 50, we can write:

9/50

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The volume of the triangular prism is 115.5m³.

Given that,

Base = 7m.

Height = 3m.

Length = 11m.

Therefore, The area of the triangle on one side = [tex]\frac{1}{2} bh[/tex]

                                                                                = [tex]\frac{1}{2}[/tex] × 7 × 3

                                                                                = 21/2

                                                                                = 10.5 m².

The volume of the prism = area of the triangle × height

                                                           = 10.5 × 11

                                                           = 115.5 m³.

Therefore, the volume of the triangular prism is 115.5m³.

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The question is incomplete, the complete question would be

What is the volume of the triangular prism? A) 57. 75 m3 B) 115. 5 m3 C) 231. 0 m3 D) 462. 0 m3

Answer:

3rd and 5th options (check below)

Step-by-step explanation:

The gift card has $22.20

After payment he had $1.90 left

What was charged for the 4 tire patches? $22.90 - $1.90

How many tire patches did he pay for? 4

Let the patch be X, 4 patches will be 4X

4X = 22.20 - 1.90

The cost of the patches + the balance on the gift card is also 22.20

4x + 1.90 =22.20

If you Subract the cost of 4tire patches from 22.20, you will have 1.90 on the gift card

22.2 - 4X = 1.9

These are the three right equations

Answer:

60°

Step-by-step explanation:

Let m<R = x.

Let m<Q = 2x.

m<Q + m<R = 90

2x + x = 90

3x = 90

x = 30

m<Q = 2x = 2(30) = 60

Answer: 60°

Answer:

Add 3

Step-by-step explanation:

The pattern provided can be obtained by adding a constant number to the previous term. The common number is 3 because each term is 3 more than the previous term.

Therefore, you can add 3 to the previous term to get the next term.

A graph of each inequality is shown in the grid below.

A shape which the solution region represent is a rectangle.

In order to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

0.4r ≤ 120     .....equation 1.

r ≥ 4(360/5)    .....equation 2.

By evaluating the given system of inequalities, we have;

r ≤ 120/0.4

r ≤ 300

r ≥ 4(360/5)

r ≥ 4(72)

r ≥ 288

By combining the system of inequalities, we have:

288 ≤ r ≤ 300

Based on the graph shown in the image attached below, we can logically deduce that the solution to the given system of inequalities is within the shaded region between the solid lines, and the point of intersection of these solid lines on the graph.

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By making linear equations for given situation, the vendor sold 34 hot dogs and 84 sodas at the football game.

What is a linear equation, exactly?

A linear equation is an algebraic equation in which each term a constant or variable. In other words, a linear equation is an equation of the form:

y = mx + b

where y and x are variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).

Now,

Let x be the variable or number of hot dogs sold.

Then, according to the problem, the number of sodas sold is 50 more than the number of hot dogs sold. Therefore, the number of sodas sold can be represented as (x + 50).

We know that the total number of sodas and hot dogs sold is 118, so we can write an equation:

x + (x + 50) = 118

Simplifying and solving for x:

2x + 50 = 118

2x = 68

x = 34

Therefore, the number of hot dogs sold is 34, and the number of sodas sold is (x + 50) = 84.

So, the vendor sold 34 hot dogs and 84 sodas at the football game.

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Answer:

9/2

Step-by-step explanation:

To find the gradient of a line passing through two points, we can use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

Using the points (1, 4) and (-1, -5), we have:

m = (-5 - 4)/(-1 - 1)

= (-9)/(-2)

= 9/2

Therefore, the gradient of line L is 9/2.

Answer: 15, 18, 21 (next three terms), Rule: Skip counting by 3

First calculate the common difference between the terms, If [tex]a_{1}, a_{2}, a_{3}, a_{4}.....[/tex] are in sequence, the common difference is calculated by [tex](a_{2} -a_{1}), (a_{3} -a_{2}), (a_{4} -a_{3}) .......[/tex]

Since, the common difference are equal so its clear that the given sequence is an Arithmetic Expression.

The nth term of the AP is an  = a + (n-1)*d

1. Given: 3, 6, 9, 12, .....

  Answer: 15, 18, 21 (next three terms)

  Rule: Skip counting by 3

2. Given: 3, 5, 7, 9, .....

  Answer: 11, 13, 15 (next three terms)

  Rule: Skip counting by 1

3. Given: a, (a+b), (a+2b),.....

  Answer: (a+3b), (a+4b), (a+5b) (next three terms)

  Rule: nth term = a+(n-1)*b = a+nb-b

  if we need 4th term, put n=4 so that 4th term= a+4b-b = (a+3b)

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Answer:54

Step-by-step explanation:

7 squared + \sqrt{25 }

[tex]7^{2}=49\\and \ \\\sqrt{25}=5[/tex]

49+5=54

Answer:

54

Step-by-step explanation:

[tex]7 ^2 + \sqrt{25} \\= 49 + 5\\= 54[/tex]

Hope this helps!

Brainliest and a like is much appreciated!

Answer:

∠ 6 = 59°

Step-by-step explanation:

∠ 3 and ∠ 8 are same- side interior angles and sum to 180° , that is

∠ 3 + ∠ 8 = 180°

121° + ∠ 8 = 180° ( subtract 121° from both sides )

∠ 8 = 59°

∠ 8 and ∠ 6 are vertically opposite angles and are congruent , then

∠ 6 = 59°

The confidence interval then takes the form of x ± margin of error, which in this example is 28 ± 1.9, or (26.1, 29.9). This means that we are 90% confident that the true population mean of newborn girl's weights lies between 26.1 and 29.9 hg. the critical value t0.05/2, which is 1.699.

To construct a confidence interval with a 90% confidence level, we need to find the critical value t0.05/2. This critical value is found by using the t-distribution with a confidence level of 90% (0.90) and degrees of freedom equal to the sample size minus 1 (180 - 1 = 179). We can then use this critical value to calculate the margin of error of the confidence interval, which is equal to the critical value multiplied by the standard error (s/√n). In this example, that results in a margin of error of 1.699*(6.2/√180) = 1.9.

To construct a confidence interval with a 90% confidence level, we need to find the critical value t0.05/2. This critical value is found by using the t-distribution with a confidence level of 90% (0.90) and degrees of freedom equal to the sample size minus 1 (180 - 1 = 179). The t-distribution is used instead of the normal distribution because it is better suited to smaller sample sizes. We can then use this critical value to calculate the margin of error of the confidence interval, which is equal to the critical value multiplied by the standard error (s/√n). In this example, that results in a margin of error of 1.699*(6.2/√180) = 1.9. The confidence interval then takes the form of x ± margin of error, which in this example is 28 ± 1.9, or (26.1, 29.9). This means that we are 90% confident that the true population mean of newborn girl's weights lies between 26.1 and 29.9 hg.

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There are 5,642 fans at a concert. If there are 6 seats in each row, the  there are 940 rows each.

Numbers are mathematical objects used for counting, measuring and marking. The original examples are the natural numbers 1, 2, 3, 4, etc. Numbers can be represented by number words. More generally, individual numbers can be represented by symbols, called numerals; for example, "5" is the number representing the number five. Since only relatively few symbols can be memorized, base numbers are usually organized into a number system, which is an organized way of representing any number.

The most common numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of ten basic numeral symbols, called numerals. In addition to being used for counting and measuring, numbers are often used for labels (like phone numbers), orders (like serial numbers), and codes (like ISBNs) . In common usage, a number is not clearly distinguishable from the number it represents.

According to the question:

Number of chairs = 6 and

Number of rows =x

capacity of auditorium =  Number of chairs × Number of rows

⇒ 5642           = 6 × x

⇒ 6x = 5642

⇒ x = 5642/6

⇒ x = 940

round term = 940

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Answer:

A. Corresponding angles

B. Vertically opposite angles

C. Alternate angles

Step-by-step explanation:

Alternate angles are two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines. If the original two lines are parallel, the alternate angles are equal.

Vertically Opposite Angles are the angles opposite each other when two lines cross "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down. Example: a° and b° are vertically opposite angles.

Corresponding angles are the angles which occupy the same relative position at each intersection where a straight-line crosses two others. If the two lines are parallel, the corresponding angles are equal.

To find -2A, we simply multiply every element of A by -2. Therefore,

            6   -10   0

-2A  =  -6    4   -2

            2   -8   -14

A matrix is a rectangular array of numbers, arranged in rows and columns. Matrices are used in many areas of mathematics, science, and engineering to represent and manipulate data.

Matrices can have any number of rows and columns, but are typically denoted by the letter A with a subscript indicating the number of rows and columns. For example, a matrix with 2 rows and 3 columns might be denoted as [tex]A_{2x3}[/tex].

To find -2A, we need to multiply every element of matrix A by -2. In other words, we need to apply the scalar multiplication operation to every element in the matrix.

Scalar multiplication is a simple operation where we multiply each element in a matrix by a scalar, which is just a regular number. In this case, our scalar is -2.

To perform scalar multiplication on a matrix, we simply multiply each element of the matrix by the scalar. So, for each element in matrix A, we can write:

(-2) * aij

where i is the row number and j is the column number of the element.

We can use this formula to find each element of -2A. Let's look at the first element, a11:

(-2) * a11 = (-2) * 5 = -10

So the first element of -2A is -10. We can repeat this process for each element in the matrix to get the following result:

            6   -10   0

-2A  =  -6    4   -2

            2   -8   -14

And that's it! We have successfully found -2A by applying scalar multiplication to every element of matrix A.

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The solution for the formula V = πr² is A. r = √(V/(π)).

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

To solve for r in the formula V = πr², we need to isolate r on one side of the equation.

We can do this by dividing both sides of the equation by π and then taking the square root of both sides:

V/π = r²

√(V/π) = r

Therefore, the solution is A. r = √(V/(π)).

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The normal distribution is a mathematical model used to describe real-world data that occurs in many scenarios, including restaurant wait times. The normal distribution is characterized by a mean and a standard deviation; in this case, the mean wait time is 20 minutes, and the standard deviation is 4 minutes.

In order to find the maximum wait time for customers so that at most 1% of them would receive their meals for free, we can use the normal distribution graph.

The graph shows the probability of a customer waiting any given amount of time. The mean is the highest point on the graph, while the standard deviation can be seen as two "bumps" on either side of the mean. For this scenario, any customer who waits more than 25.5 minutes will be in the top 1% of wait times, and therefore, should receive their meal for free.

This provides a reasonable time limit for customers to expect their meal, while also helping to dispel any negative perceptions about the speed of service.

In terms of the company's profitability, offering free meals to the top 1% of customers does not present any significant risk. The 25.5 minute wait time is well above the average wait time of 20 minutes, so it's unlikely that the company will incur a significant loss due to this promotion.

To sum up, the maximum wait time to be advertised to customers so that 1% of them will receive their meals for free is 25.5 minutes. The normal distribution graph shows how this wait time is chosen, as it corresponds to the top 1% of wait times.

As the average wait time is much lower than this maximum wait time, this promotion is unlikely to cause the company any significant loss in profit.

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Answer: b

Step-by-step explanation: b is right

Check the picture below.

so if we just find the vertex of that parabolic path, we'd get how far up it went and how long it took

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+16}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 16}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (16)^2}{4(-16)}\right) \implies \left( - \cfrac{ 16 }{ -32 }~~,~~0 - \cfrac{ 256 }{ -64 } \right) \\\\\\ \left( \cfrac{ -1 }{ -2 } ~~~~ ,~~~~ 0 +4 \right)\implies \stackrel{seconds ~~ feet }{\left(0.5~~,~~4 \right)}[/tex]

well, as you see in the picture, the horse hits the ground again when h(t) = 0

[tex]\stackrel{h(t)}{0}=-16t^2+16t\implies 0=-16t(t-1)\implies t= \begin{cases} 0\\ 1 \end{cases}[/tex]

so at t=0 and t=1 it's touching the ground, at t=0 when it begins to jump at t=1 when it thumps back down, took that long.

Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.

The chance that a particular event will οccur is quantified by prοbability. It is a number between 0 and 1, where 0 denοtes that the event is hypοthetical and 1 denοtes that it will undοubtedly οccur. The number οf successful results multiplied by the entire number οf pοssible οutcοmes is used tο calculate an event's prοbability. Tο put it anοther way, prοbability is a way tο express the likelihοοd οf an event οccurring and tο quantify uncertainty.

given:

we can determine the likelihοοd οf receiving twο sοcks οf the same cοlοr.

We can select twο sοcks οf the same hue in any οf the fοllοwing ways:

In ₃C₂ = 3 οptiοns, we can select οur 2 gray sοcks.

There are ₃C₂ = 3 different methοds tο select 2 black sοcks.

Therefοre, there are a tοtal οf 3+3=6 methοds in which we can select 2 sοcks οf the same cοlοr.

There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.

The likelihοοd οf receiving twο sοcks οf the same cοlοr is as fοllοws:

6/15 = 2/5

Thus, the respοnse is c) 2/5.

b) The likelihοοd οf receiving twο pairs οf gray hοsiery is:

There are 3 οptiοns tο chοοse 2 pairs οf gray sοcks (₃C₂ = 3).

There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.

Cοnsequently, the likelihοοd οf receiving twο pairs οf gray hοsiery is:

3/15 = 1/5

Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.

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The point halfway between (–0.75, –1.25) and (–0.75, –0.25) is (–0.75, –0.75).To find the point halfway between (–0.75, –1.25) and (–0.75, –0.25), we will use the midpoint formula.

To find the point halfway between (–0.75, –1.25) and (–0.75, –0.25), we will use the midpoint formula. The midpoint formula is (x1 + x2) / 2, (y1 + y2) / 2. In this case, x1 and x2 are both –0.75, and y1 is –1.25 and y2 is –0.25. Plugging in the values and doing the math, we get (–0.75 + –0.75) / 2 = –0.75, and (–1.25 + –0.25) / 2 = –0.75. Therefore, the point halfway between (–0.75, –1.25) and (–0.75, –0.25) is (–0.75, –0.75).

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Answer:

15 packs of crayons and 20 packs of pens

Step-by-step explanation:

you have to the multiply the amount that comes in each pack together

The student's reading level is at the 4.01st percentile. Answer: 4.01.

Given that you are an elementary school teacher and you are evaluating the reading levels of your students. You find an individual that reads 50 word per minute. You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 85 words per minutes and a standard deviation of 20 words per minutes.The percentile of a given value represents the percentage of the distribution that falls below that value.To find the percentile rank of the student's reading level, we can use the Z-score formula:$$z = \frac{X - \mu}{\sigma}$$where X is the student's reading rate, μ is the mean reading rate for the grade level, and σ is the standard deviation of the reading rates for the grade level. Substituting the given values, we get:$$z = \frac{50 - 85}{20} = -1.75$$The negative sign indicates that the student's reading rate is below the mean rate for the grade level. Now we need to find the percentile of the Z-score -1.75.Using a standard normal table or calculator, we can find that the area to the left of -1.75 under the standard normal distribution is 0.0401. Therefore, the student's reading level is at the 4.01st percentile. Answer: 4.01.

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x = 2 is not a root of the given function.

We are required to use the Remainder Theorem to determine whether x = 2 is a root of the given function:????(x) = 3x³ − 4x² − 8.Remainder Theorem The Remainder Theorem states that when a polynomial function f(x) is divided by (x - a), the remainder equals f(a).In order to find whether x = 2 is a root of the function or not, we have to apply the Remainder Theorem. We can perform the division in the following manner: Solution The given polynomial function is: ????(x) = 3x³ − 4x² − 8.So, we can perform the division as shown below: On dividing f(x) by (x - a), the remainder is f(a). Hence, the remainder when the given function is divided by (x - 2) is -14.Therefore, x = 2 is not a root of the given function.

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