Which phrase best represents the following?
"Six times the quantity of four plus a number"
0 64 + n)
O 6n + 4
0 6(4) + n
O 4n + 6

Using Arithmetic progression, There were 4,13,22,31 pupils chosen out of the applicants.

The professor desires to choose four students at random.

A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

The fourth student was chosen at random, followed by every ninth student.

The fourth student is chosen first.

Using the following term formula, which is

=>a + d(n-1) (n-1)

The second student is the one after that.

=>4 + 9(2-1) (2-1)

=>4 + 9(1) (1)

=>4 + 9

=> 13

The third pupil will be

=>4 + 9(3-1) (3-1)

=>4 + 9(2) (2)

=>4 + 18

=> 22

The fourth pupil will be

=>4 + 9(4-1) (4-1)

=>4 + 9(3) (3)

=> 4+ 27

=> 31

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Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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When using the `foreach` function, the signs of the first and second derivatives of the function appear to be negative over the given interval. What is the `foreach` function?The `foreach` function in PHP is utilized for iterating over arrays or objects. The `foreach` function works by stepping through each value of an array, and one iteration can be done for each of the array's elements, which can include key-value pairs. It is mainly utilized to execute a block of code for each element of an array.What is a derivative?A derivative is a calculus concept that refers to the slope of a function at a certain point. It is usually the rate at which a function's value changes as its input variable changes. Derivatives are widely utilized in many fields, including physics, engineering, and economics.How to determine the signs of the first and second derivative?We can determine the signs of the first and second derivative by finding the derivative of the given function f(x). Once we find the derivative of the function, we can put the values in a table like the following:X    1   1.1   1.2   1.3   1.4   1.5f(x) 7.1 6.1 5.0 3.8 2.5 1.1 We can calculate the first derivative of f(x) by the following formula:f'(x) = f(x + 1) - f(x)We can calculate the second derivative of f(x) by the following formula:f"(x) = f'(x + 1) - f'(x)Based on the table above, we can determine that the signs of the first and second derivatives of the function are negative over the given interval.

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The signs of the first derivative of the function F(x) over the given interval are not consistent, so it is difficult to determine whether it appears to be positive or negative.

The first derivative of a function represents the rate of change of the function at a given point, while the second derivative represents the curvature or concavity of the function at that point.

To determine the signs of the first derivative of F(x) over the given interval, we need to find the slope of the tangent line at each point. We can do this by calculating the difference between consecutive y-values and dividing by the corresponding difference in x-values.

For example, the slope between (1, 7.1) and (1.1, 6.1) is (6.1 - 7.1)/(1.1 - 1) = -1, which indicates a negative slope. However, the slope between (1.2, 5.0) and (1.3, 3.8) is (3.8 - 5.0)/(1.3 - 1.2) = -12, which indicates a much steeper negative slope.

We can repeat this process for each pair of consecutive points to find the sign of the first derivative at each point. However, since the signs of the slopes are not consistent over the given interval, we cannot determine whether the first derivative appears to be positive or negative.

In other words, the function may be increasing or decreasing at different rates over different portions of the interval, which makes it difficult to make a general statement about the sign of the first derivative.

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Answer:

its 22 degrees

Step-by-step explanation:

GOODLUCK

a. uniformly distributed.  When the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is said to be uniformly distributed.

In a uniform distribution, the probability density function is constant within the interval, meaning that all values within the interval have an equal chance of occurring.

The uniform distribution is characterized by a rectangular-shaped probability density function, where the height of the rectangle represents the probability and the width of the rectangle represents the interval. This distribution is often used when there is no specific bias or preference for any particular value within the interval.

On the other hand, the normal distribution (b) follows a bell-shaped curve, the exponential distribution (c) describes the time between events in a Poisson process, and the Poisson distribution (d) is used to model the number of rare events occurring in a fixed interval of time or space.

Therefore, the random variable is uniformly distributed (a) when the probability is proportional to the length of the interval.

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Answer:

3 + 7x = 7x + 3

Step-by-step explanation:

Simplifying

7x + 3 = 7x + 3

Answer:

Angle A = 45 degrees

Step-by-step explanation:

7x+3 + 7x+3 +90 = 180

14x + 96 = 180

14x = 84

x = 6

Angle A = 7x+3. --> 7(6) + 3 --> 45

Angle A = 45 degrees

Answer:

A. They can be searched using keywords.

Answer:

15708 cubic inches

Step-by-step explanation:

The formula for a cylandir is V=πr^2h, substitute in your known factors and multiply by 20 for the 20 pails used and you get your answer.

The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

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Answer:

£ 8

Step-by-step explanation:

basic equation:

£40 * 1/5

£ 40/5

£ 8

Answer:

Solution:

\( = \frac{1}{ \cancel5} \times \cancel{40} \: {}^{8} £\)

\( = 1 \times 8£\)

\( = 8£\)

Answer:

The height of the pile is increasing at a rate of 16.72 feet per minute. To solve this problem, we need to use the volume formula for a right circular cone: V=pi/3 r²h. We know that the volume is 20 cubic feet per minute, the height is 14 feet and the radius of the base is 14 feet. So we can calculate the rate of change of the height by rearranging the formula to give v/(pi/3r²). So for our example, v/(pi/3*14²)=20/(pi/3*14²)=20/(3.14*196)=20/613.44=16.72 feet per minute.

Answer:

Step-by-step explanation:

You want the repeating decimal cost ...

  \(\$3.\overline{23}\)

written as a fraction and as a mixed number.

One can convert the repeating decimal to a fraction by multiplying it by a power of 10 equal to the number of repeating digits.

This cost number (C) has 2 repeating digits (23), so we want to multiply it by 10^2:

  \(100C=10^2\times3.23\overline{23}=323.\overline{23}\)

Now, we can subtract the original cost to cancel the repeating decimal fraction:

  \(100C -C = 323.\overline{23}-3.\overline{23}=320\)

Dividing by the coefficient of C, we have the fraction we want:

  \(C=\boxed{\dfrac{320}{99}}\)

This is expressed as a mixed number by figuring the quotient and remainder.

  \(\dfrac{320}{99}=\boxed{3\dfrac{23}{99}}\)

Using geometric sequence concepts, it is found that the sum of the first 10 terms is of 4068.6.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

The sum of the first n terms is given by:

\(S_n = \frac{a_1(q^n-1)}{q - 1}\)

In this problem, the sequence is:

\(\frac{16}{25}, \frac{8}{5}, 4, 10,...\)

Hence:

\(a_1 = \frac{16}{25}, q = \frac{10}{4} = 2.5\)

Then, the sum of the first 10 terms is:

\(S_{10} = \frac{\frac{16}{25}(2.5^{10}-1)}{2.5 - 1} = 4068.6\)

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I'll do problem 6 to get you started

x = number of people training all 3 sports.

This is because all 3 sports are needed for the triathlon

There are 35 swimmers total. 9 of which are also cyclers (but not runners), and there are 13 swimmers who are also runners (but not cyclers)

That leaves 35-9-13-x people who are swimmers only. I'll leave this expression un-simplified so you can see where the numbers are coming from. Take note of where I'm placing this in the venn diagram below.

There are 32 cyclers. Of this group, 9 are swimmers (but not runners) and 11 are runners (but not swimmers). That leaves 32-9-11-x people who are cyclers only.

There are 38 runners. Of this group, 13 are swimmers (but not cyclers) and 11 are cyclers (but not swimmers). That leaves 38-13-11-x people who are runners only.

All of these values are honestly hard to keep track of. This is why a visual approach using a Venn Diagram is recommended. See the diagram below.

The idea is that every value in the diagram then adds up to the 58 total attendees. This helps form the equation needed to solve for x.

Such an equation is possible because each attendee participates in at least one of the sports mentioned. No values will be outside of all three circles at the same time.

(35-9-13-x)+(32-9-11-x)+(38-13-11-x)+(9)+(13)+(x)+(11)=58

-2x+72 = 58

-2x = 58-72

-2x = -14

x = -14/(-2)

x = 7

Answer:

0

Step-by-step explanation:

y2 - y1 / x2 - x1

-7 - 10 / -8 - (-8)

-17/0

= 0

Answer:

1: sin B, cos B, and tan B = 36.87°

2: x = 11.7

Step-by-step explanation:

Question 1: As toy can see they all have the same angle answer just different methods of finding it

Question 2:

adjacent is the closest side to the angle

opposite is the side across from the angle

hypotenuse is always the longest side

x = 11.7025

Hope it helps :)

If you have any questions or anymore help lmk, happy to help with any school work!!

Have a nice day, you’ll make it thru <3

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Answer:

After 20 days, the two runners will have run the same number of miles

Step-by-step explanation:

The problem can be solved by using equations. However, we'll approach the solution by using pure reasoning and logic, besides calculations.

The first runner has already run 15 miles this month and plans to run 2 1/2=2.5 miles per day for the rest of the month.

The other runner has not yet run and plans to run 3 1/4 = 3.25 miles per day for the rest of the month. Since his running rate is greater than the other runner, they will both eventually have the same number of miles.

The difference in their running rates is 3.25 - 2.5 = 0.75 miles per day. Since the current difference between them is 15 miles, the second runner needs to run for 15 / 0.75 = 20 days.

After 20 days, the two runners will have run the same number of miles

Answer:

10,305.99 cm^3

Step-by-step explanation:

V=4/3πr^3=4/3·π·13.5^3≈10305.9947

Answer:

523.5988in³

Step-by-step explanation:

input Data :

Length = 5 in

Objective :

Find what is volume of the sphere for given input data?

Formula :

Volume =

4πr3

3

Solution :

Volume =

4 x 3.1416 x 53

3

=

4 x 3.1416 x 125

3

=

1570.7963

3

Volume = 523.5988 in³

Answer:

b is the answer

Step-by-step explanation:

The truth value of proposition 2a, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], given that a and b are true and x and y are false, is TRUE.

In the provided scenario where a and b are true while x and y are false, proposition 2a, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], is evaluated to be true. Let's break it down to understand why.

The proposition is in the form of an implication (⊃), where the antecedent is [(x ⊃ a) • (b ⊃ ∼ y)] and the consequent is [(b ∨ y) • (a ⊃ x)]. To determine the true value, we need to examine both the antecedent and the consequent.

In the antecedent, we have two conditions connected by a conjunction (∧): (x ⊃ a) and (b ⊃ ∼ y). Since x and y are false, the condition (x ⊃ a) is vacuously true because false implies anything. Similarly, (b ⊃ ∼ y) is also true because b is true, and ∼ y (not y) is true since y is false. Therefore, the antecedent is true.

Moving on to the consequent, we have two conditions connected by a conjunction (∧): (b ∨ y) and (a ⊃ x). In this case, b is true, so (b ∨ y) is true regardless of the truth value of y. Additionally, a is true, and since x is false, (a ⊃ x) is false. Therefore, the consequence is false.

Now, when we evaluate the entire proposition, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], we find that a true antecedent implies a false consequent, which results in a true overall proposition. Hence, the truth value of proposition 2a is TRUE in the given scenario.

In conclusion, proposition 2a holds true when a and b are true, and x and y are false. Understanding the evaluation of logical propositions like these can help in reasoning and problem-solving tasks.

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How to find input and output from the co-ordinates on the graph?

Here the co-ordinate having x=2 is

So the output is 0

Every pair have ( x , y ) which means x is input and y is output .

Here , input is 2 (x)

then , let output be y ( indicate with 0 )

So , the co- ordinates are ( x , y ) = ( 2 , 0 ) .

We would need to add 8 more sets of 3 candies to 23 candies in order to have the same amount as Casey.

To find this, we can divide the total amount of candy Johnny has (23) by the amount of candy Casey has (3) and round up to the nearest whole number:

(23) / (3) = 7.666...

Since we can't have a fraction of a set of candies, we must round up to the nearest whole number, which is 8.

So, to have the same amount of candy as Casey, we would need to add 8 more sets of 3 candies to Johnny's 23 candies.

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Answer:

$3.35

Step-by-step explanation:

$50.25 ÷ 15 gallons = $3.35 a gallon

Answer:

≈5.15 [cm].

Step-by-step explanation (English version):

1) Capacity - V - 1000 cm³;

height - h - 12 cm;

radius - r - ?

2) the initial formula is:

V=π*r²*h, where π=3.1415;

then final formula of the required r is:

\(r=\sqrt{\frac{V}{\pi *h}};\)

3)   \(r=\sqrt{\frac{1000}{3.1415*12}} =\sqrt{26.5266} =5.15[cm].\)

Answer:

3.6%

Step-by-step explanation:

The probability that the person has a tattoo is 230 out of 995.

We randomly select a person who responded to this survey. The calculation that gives the probability that the person has a tattoo is 230 out of 995.

Probability is a measure of the likelihood of a particular event occurring, typically expressed as a fraction or percentage.

The probability of an event occurring is calculated by dividing the number of favorable outcomes by the number of possible outcomes.

Therefore, the calculation that gives the probability that the person has a tattoo is 230 out of 995.

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Answer:

g=2 i hope this helps

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have a good day.

Answer:

−16n² −4n −4

Step-by-step explanation:

=(4)(−4n²+−n+−1)

=(4)(−4n²)+(4)(−n)+(4)(−1)

=−16n² −4n −4

The dimensions of the rectangle has a width = 12cm and length = 5cm.

In calculating the area of a rectangle, we multiply its length and width.

Let us use the letter x to represent the width, so that the length = x - 7

hence we calculate for the unknown x as follows;

x(x - 7) = 60

expand and equate to zero to derive a quadratic equation

x² + 7x - 60 = 0

by factorisation;

x² - 12x + 5x - 60 = 0

x(x - 12) +5(x -12) = 0

(x + 5)(x - 12) = 0

thus for x + 5 = 0

x = -5

and for x - 12 = 0

x = 12

Therefore, x = 12 is true for the quadratic equation and also for the width = 12 and length = 5cm for the rectangle.

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Answer: It is 160

Step-by-step explanation:

I just completed the test

Therefore , the solution of the given problem of surface area comes out to be the right response is option c 160 in².

Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.

Here,

the base's outermost boundary is:

=> Perimeter = 4s

To locate s,

=> Base  Area = s² = 64 in².

To solve for s, we obtain:

=> √(64 in²) = 8 in

We can now determine the perimeter:

=> perimeter: 4s

=> (4 * 8 inches)/(32 inches)

Finally, we can enter the numbers into the surface area formula as follows:

=>  Base Area + (1/2) x Perimeter x Slant Height

=> Surface Area Surface Area = 64 in² + (1/2) x 32 in x 6 in

=> Surface area = 64 in² + 96 in².

160 in² is the surface area.

Consequently, the cone has a surface area of 160 in².

The right response is (c) 160 in².

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