suppose a certain combination lock requires three selections of numbers, each from 1 through 25. (a) how many different combinations are possible? (b) suppose the locks are constructed in such a way that no number may be used twice. how many different combinations are possible?

The limit as a definite integral on the interval [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π , 4π] is [tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex].

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

[tex]$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$[/tex]

substitute the values in the above equation, we get

= [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π, 4π],

simplifying the above equation

[tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex]

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Three  pairs of fractions that have a sum of 5/6 are;

1/3 + 2/3 = 5/6

1/4 + 3/4 = 5/6

2/6 + 3/6 = 5/6

1/3 + 2/3 = 5/6: The fractions have a common bottom number of 3 because they both have the same bottom number.

Adding the top numbers: 1 plus 2 equals 3.

The total is three divided by three, which can also be written as one.

However, we need to show the total with a bottom number of 6 to match the original part. So, we make the top and bottom numbers twice as big to get 2/6. Hence , 1/3 + 2/3 = 2/6.

1/4 + 3/4 = 5/6:The fractions have the same bottom number, so their common denominator is 4.

When you add 1 and 3 together, you get 4.

The sum is four over four, and when simplified, it equals one.

Once again, we have to find a way to write the sum with a bottom number of 6 so that it is the same as the first number in the fraction. So, we take the top number and the bottom number and multiply them both by 3 to get the fraction 3/6. Hence, 1/4 + 3/4 = 3/6.

2/6 + 3/6 = 5/6:In this situation, the fractions already have the same bottom number which is 6.

Adding the top numbers together: 2 + 3 = 5.

The answer is 5/6, which is what we wanted to get.

Therefore each pair shows a different way to add numbers together, either by finding a number that both denominators can divide evenly into or by using numbers that already work well together.

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We can find the equation of any line passing through a given point and parallel or perpendicular to a given line by finding the slope of the given line and using slope-intercept form.

Given, the line passing through a given point and parallel and perpendicular to a given line

we have to find the equation of the lines

Let l1 be a line passing through a point (p , q) and parallel to a line l2.

suppose the equation of the line l2 be,

y = mx + c

the line l2 has slope m

Now to find the equation of the line l1,

(y - q)/(x - p) = m

On cross-multiplying, we get

y - q = m(x - p)

y = mx - pm + q

So, the equation of the line l1 be,

y = mx + (q - pm)

Similarly, we can find the equation of any line passing through a point and parallel to a given line.

Hence, we can find the equation of any line with the slope.

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The solution of the expression - 4 - 0.2x + 11 = - 0.8x + 10 is 28.33.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A numerical expression and we have to solve for x or find the value of x.

- 4 - 0.2x + 11 = - 0.8x + 10.

- 0.2x - 7 = - 0.8x + 10.

- 0.2x + 0.8x = 10 + 7.

0.6x = 17.

x = 17/0.6.

x = 28.33.

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Probability that the horse will not win the race is  d) 0.6250

What is a probability ?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

odds in favour of winning a race of 3:5

thus, 3 chances of winning to every 5 chances of losing.

So, if the race were held 8 times, one would be expected to win 3 races and lose 5 races.

Thus, the probability of winning the race is 3/8.

Probability that the horse will not win the race is 1- 3/8 = 1 - 0.3750 = d) 0.6250

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Answer:

60 or 90 degrees

Step-by-step explanation:

if one angle is 30 the other has to be 60 or 90 as they are common múltiples due the cosine rule and pythogras therom (mind my spelling).

The section A has total seats of, 25000, section B has got 14,700 and section C has got total 10,300 seats.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given equations in the question,

A + B + C = 50,000   (i)

42A + 24B + 18C = 1,588,200     (ii)

A = B + C    (iii)

Substitute value of A from (iii) to (i),

2B + 2C = 50000

B + C = 25,000   (iv)

Similarly, substitute value of (iii) in equation (ii),

42 (B +C) + 24B + 18C = 1588200

66B + 60C = 1588200

33B + 30C = 794100  (v)

Multiply 33 in equation (iv) and subtract from (v)

-3C = -30900

C = 10,300 seats.

Now,

B + C = 25000

B = 25000 - 10300

B = 14,700 seats.

And,

A = B + C

A = 10300 + 14700

A = 25000 seats.

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By taking out the distance, we know that the image of a 5.0 cm-tall nose is located at 39.29 cm.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

So, the equation to be used:

1 / f = 1 / p + 1 / q

The focal length of the metal salad bowl, which behaves like a mirror:

f = R / 2

f = 44/2

f = 22 cm

Suppose that the distance to the item is p = 50 cm, let's find the distance to the image:

1 / q = 1 / f  - 1 / p

1 / q = 1/22 - 1/50

1 / q = 0.0254

q = 39.29 cm

Therefore, by taking out the distance, we know that the image of a 5.0 cm-tall nose is located at 39.29 cm.

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Complete question:
You hold a spherical salad bowl 50 cm in front of your face with the bottom of the bowl facing you. The salad bowl is made of polished metal with a 44 cm radius of curvature.

Where is the image of your 5.0-cm-tall nose located?

Answer:

Yes.

Step-by-step explanation:

In order for a relation to be a function, Each y value must have a unique x value. If there is any point where a vertical line hits the relation in two places, it is not a function. This relation follows the rules of being a function, and therefore is a function.

Answer:

x=2

Step-by-step explanation:

7÷x=22÷6

cross multiply

7×6=21×x

21x=42

21x/21=42/21

x=2

56% interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

Given that,

Amira will put $580 into an account and let it sit there for 17 years.

We have to find what interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

We know that,

We have a formula

A=P(1+r/n[tex])^{nt}[/tex]

Here,

A=$840

P=$580

n=12

t=17

We get

840=580(1+r/12[tex])^{12\times17}[/tex]

840=580(1+r/12)²⁰⁴

42/29=(1+r/12)²⁰⁴

r=0.56

Therefore, 56% interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

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The equation of the line is y = 1/5(x + 37). The standard equation of a instantly line is y = mx + c, in which m is the gradient, and y = c is the cost in which the road cuts the y-axis.

This range c is known as the intercept at the y-axis. The equation of a instantly line with gradient m and intercept c at the y-axis is y = mx + c. The equation of a instantly line is y=mx+c y = m x + c m is the gradient and c is the peak at which the road crosses the y -axis, additionally referred to as the y -intercept.

Since equation have new line which is parallel  y = 1/5(x + 4), and 1/5 is most the gradient for the line y = 1/5(x + 4), this is the new line is 1/5.

Using the equation we can form a line in slope-point form,

[tex]\frac{y-y_{1} }{x-x_{1} } = m[/tex]

where (x₁, y₁) = (3, 8) and m = 1/5

Substituting the values for all variables into the equation, we have

[tex]\frac{y-y_{1} }{x-x_{1} } = m\\\frac{y-8 }{x-3 } = m\\[/tex]

Cross-multiplying. we have

5(y - 8) = x - 3

Expanding the bracket, we have

5y - 40 = x - 3

5y = x - 3 + 40

5y = x + 37

y = 1/5(x + 37)

So, the equation of the line is y = 1/5(x + 37)

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The proportion is 12 : 14 : : 18 : w and the value of w is 21

The number of shots in Game 2 is 21

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the 2 games be Game 1 and Game 2

Now , the equation will be

The number of points in Game 1 = 12

The number of shots in Game 1 = 14

And ,

The number of points in Game 2 = 18

The number of shots in Game 2 = w

So , the proportion equation is given as

Number of points in Game / number of shots in Game = number of points in Game / number of shots in Game 2

Substituting the values in the equation , we get

12 / 14 = 18 / w

Multiply by 14 on both sides of the equation we get

12 = ( 18 x 14 ) / w

Multiply by w on both sides of the equation , we get

12w = 18 x 14

Divide by 12 on both sides of the equation , we get

w = ( 18 x 14 ) / 12

On simplifying the equation , we get

w = 3 x 7

w = 21

Therefore , the value of w is 21

Hence , The proportion is 12 : 14 : : 18 : w and the value of w is 21

The number of shots in Game 2 is 21

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Therefore , the probability of at least two born on the same day of the week is  0.143

Probability is the possibility that an event will happen.This could mean that something is definitely going to happen, that it has a chance of happening, or that it is impossible. Mathematically, probability is quantified on a scale from 0 to 1.

Given:

group of 5 people at random.

We used the formula for the conditional probability

The conditional probability is,

P(A|B)=P(AUB)/P(A)

The complement rule of probability, which is the second, is

P(E) = 1 - P(e)

Calculate one by one

a) Since a week has seven days and the first person has seven possible birth dates, the likelihood of that person is:

P(1st person) = 7/7 = 1

The second person now gets the same possibilities as person 1, but he or she must match that person's day, therefore there is only one option out of seven that fits that criteria, as follows:

P(A|B) = 1/7

Then the probability is

P = 1 * 1/7 = 1/7 or 0.143

Therefore , the probability of at least two born on the same day of the week is  0.143

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Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

The rate of change of the distance below the sea level with respect to time is 11 feet per second.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

The table has a linear relationship.

We can choose two data from the table.

At time = 15,

Distance below the sea level = 545 feet.

At time = 27,

Distance between the sea level = 677

Now,

The rate of change of the distance below the sea level with respect to time.

Slope:

= (677 - 545) / (27 - 15)

= 132 / 12

= 11 feet per second

Thus,

The rate of change of the distance below the sea level with respect to time is 11 feet per second.

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The rate of change of distance for the submarine is given by 11 feet/sec.

In order to find the slope between two points (x₁, y₁) and (x₂, y₂), take the ratio of the difference of the respective coordinates as (y₂ - y₁)/(x₂ - x₁).

Given that,

The table for distance travelled versus time taken for a submarine.

In order to find the slope, take two values of distance and time from the given table as  380 feet at t = 0 and 545 feet at t = 15.

Now, the slope can be found as,

slope = (545 - 380)/(15 - 0)

         = 165/15

         = 11

Hence, the rate of change of distance below sea level with respect to time is given as 11 feet/sec.

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On solving the provided question, we got to know that -  to plot the graph, required equation is 3x +y -8 = 0

a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples -  2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥

We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.

To plot the graph,

we need to find the equation first.

and to find the equation -

[tex](y - y1) = m(x - x1)\\here,\\x1 = 1\\y1 = 5\\m- ( -3 )[/tex]

equation  -

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

-3x + 3 = y-5

3x - 3 = 5-y

3x +y -8 = 0

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A triangle has two sides of length 18.9 and 2.9. inequality which describes the possible lengths for the third side, x is 16 < x < 21.8

The triangle inequality theorem states that,

given two lengths of the sides of a triangle, the length of the third side of the triangle must be greater than the difference and less than the sum of the two given sides.

For the two sides a and b of the triangle, the third side c must follow as follows:

(a - b) < c < (a + b)

So let a = 18.9 and b = 2.9

let the length of third side of triangle be x then

(18.9 - 2.9) < x < (18.9 + 2.9)

=> 16 < x < 21.8

So , the third side of the triangle must follow the inequality 16 < x < 21.8

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Answer:

The answer is 1.86x10 6

Step-by-step explanation:

10x6 is 100k and the speed light travels is 186k so to get the answer you need to find the one that gets to 100k and then multiply it by 1.86

You can infer that the exponential model is a better fit for the data in the experiment, as it has smaller residuals than the quadratic model.

Residuals are the difference between the actual data points and the predicted values generated by the model. They are a measure of how well a model fits the data, and a lower residual indicates a better fit. Therefore, if the student's exponential model has smaller residuals than their quadratic model, it can be concluded that the exponential model is a better fit for the experiment data.

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Answer: Second graph from top.

Step-by-step explanation:

     Slope is written in change in y over change in x. In other words, "rise over run" so the slope of 4/5 means rise 4 units and move 5 units right. The graph that meets this requirement is the second graph, as shown in the attachment.

One-to-one is the following types of functions have inverse functions.

What is a simple definition of a function?

As a set of inputs with one output for each, a function is defined as a relationship between them. In plain English, a function is an association between inputs in which each input is connected to precisely one output.

                      A function is a type of rule that produces one output for a single input. One function, many. function onto (Surjective Function) into: perform. Function of a polynomial.

What does function entail when it does not?

A function is a relationship between a domain and a range where every value in the domain only has one possible value in the range. This notion is violated by relations that are not functions.

                            They contain at least one value in the domain that relates to two or more values in the range.

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Answer: 74

Step-by-step explanation:

Answer:

74

Step-by-step explanation:

Got it right on the test.

The required choice for inequality is Option 2.

What is inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.

Given, 3(8 – 4x) < 6(x – 5)

or, 24 - 12x < 6x - 30

or, 24 + 30 < 6x + 12x

or, 54 < 18x

or, 18x > 54

or, x > 3 means x is greater than positive 3 and pointing to the right.

Hence, the required choice for inequality is Option 2.

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Answer: b

Step-by-step explanation:

The dimensions of the rectangle are 6 and 3.5 ft.

Let the width of rectangle be x. So, the length of the rectangle will be 2x - 1. As per the known fact, the area of rectangle is given by the formula -

Area = length × breadth

Keep the values in formula to find the dimensions of the rectangle

x(2x - 1) = 21

Performing multiplication on Left Hand Side of the equation

2x² - x = 21

Rewriting the equation

2x² - x - 21 = 0

On factorizing we get, x = -3 and 3.5.

The dimensions of rectangle can not be negative, this, taking the value of x as 3.5. Now, the width of rectangle will be 3.5.

Length of rectangle = (2×3.5 - 1)

Length of rectangle = 7 - 1

Length of rectangle = 6

Thus, the length and width is 6 and 3.5 ft respectively.

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The complete question is -

the length of a rectangle 1ft less than double the width ,and the area of the rectangle is 21ft^2 find the dimensions

1. My friend took his master's degree in Spain :- Simple

2. Roses are red, but violets are blue. :- Compound

3. You are entitled to a 30% discount if you are a member.:- Compound

4. Boel was on time, but Tom was late.:- Compound

5. Either he watches a niovie or dines with his friends.:- Compound

6. If it is an acute angle, then it has less than 90.:- Simple

A simple sentence consists of just one clause. And it is consist of a subject and a verb.

A simple sentence has the most basic elements that make it a sentence: a subject, a verb, and a completes thought.

A compound sentence is made up of two or more independent clauses.

This compound sentence consist of two simple clauses connected by the coordinating conjunction 'and'.

Two independent clauses need to be connected with a coordinating conjunction or separated with a full stop or semicolon.

A simple sentence can also be refereed to as an independent clause.

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Answer:

The answer is 12

Step-by-step explanation:

8/x = 28/42

8/x = 2/3

(8) × 3 = (2) × (x)

2x = 24

2x/2 = 24/2

y = 12

y = 12Thus, The value of y is 12

Answer:

12

Step-by-step explanation:

use the theory of cross multiply

so 8•42=28x

        336=28x

             x=12

Answer:

∠D = 127°

Step-by-step explanation:

Let's define the properties of a parallelogram to understand how to solve for ∠D.

⭐The opposite angles in a parallelogram are congruent.

⭐The sum of the interior angles of a parallelogram is 360°.

First, let's solve for x knowing that the opposite angles are congruent.

∠A = ∠C

[tex]13x - 25 = 9x - 1[/tex]

[tex]13x - 9x = 25 - 1[/tex]

[tex]4x = 24[/tex]

[tex]x = 6[/tex]

∴ x = 6

Next, substitute x into ∠C.

∠C = 9x - 1

∠C = 9(6) - 1

∠C = 54 - 1

∴ ∠C = 53°

Finally, substitute ∠C into the equation 2(∠D) + 2(∠C) = 360° to solve for ∠D.

2(∠D) + 2(∠C) = 360°

2(∠D) + 2(53) = 360

2(∠D) + 106 = 360

2(∠D) = 254

∴ ∠D = 127°

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Answer:

m∠B = 121°

Step-by-step explanation:

[tex]10x-19=9x-5[/tex]  

[tex]10x=9x+14[/tex]  (add 19 on both sides)

[tex]x=14[/tex]  (subtract 9x on both sides)

[tex]9(14)-5 = 126-5=121[/tex]  

Answer: m∠B=121°

Step-by-step explanation:

The opposite angles of the parallelogram are equal

Hence,

(10x-19)°=(9x-5)°

10x-19=9x-5

10x-19-9x=9x-5-9x

x-19=-5

x-19+19=-5+19

x=14

Hence,

m∠B=(9(14)-5)°

m∠B=(126-5)°

m∠B=121°

Answer:

To represent the area of a stained-glass mosaic that sits under a parabolic arch, we can use the equation for a parabolic arch, which is of the form

y = a(x - h)^2 + k

where (h,k) is the vertex of the parabola. The width of the parabolic arch at the base is 8 feet, so the vertex of the parabola is located at (4,0). Therefore, the equation for the parabolic arch is

y = a(x - 4)^2

The height of the parabolic arch is 10 feet, so we can represent the area of the stained-glass mosaic as the region where y is between 0 and 10. This can be expressed as the inequality

0 ≤ a(x - 4)^2 ≤ 10

Solving this inequality for x gives us the solution

-2 ≤ x - 4 ≤ 2

which simplifies to

2 ≤ x ≤ 6

Therefore, the quadratic inequality that represents the area of the stained-glass mosaic is

2 ≤ x ≤ 6

Step-by-step explanation:

Answer:

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

According to given details we have:

The equation for the parabola is y = a(x - h)² + k, where (h, k) is vertex.

Substitute h = 4, k = 10:

We know y = 0 at x = 0, substitute to find the value of a:

So the parabola is:

We are looking for the area between the parabola and the x-axis, therefore we need two inequalities:

See attached for reference.

There are 28 males and 11 females in the class.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Let the number of males be x and the number of females be y. We know that x = y + 17 and x + y = 39.

Substituting the first equation into the second equation, we get:

y + y + 17 = 39

2y + 17 = 39

2y = 22

y = 11

The number of females is 11, and the number of males is x = y + 17 = 11 + 17 = 28.

Hence, there are 28 males and 11 females in the class.

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