Matthew and some friends are going to a concert. They hire a car service for $75 to drive them to a
restaurant for dinner and then the concert. They divide the $60 cost of the dinner equally. However, since
Matthew's dad provided concert tickets for the group, the friends agree that Matthew doesn't have to help pay
for the car service. The friends divide this cost equally among themselves. If each friend spends a total of $25,
how many friends went to the concert with Matthew?

Answer:

0.38

Step-by-step explanation:

imagine a circle, with C being the center, and 13 being the radius.

the triangle is then representing the trigonometric functions. remember, they are all multiplied by the radius as the circle is much higher than the norm circle (radius 1).

so,

5 = sin(C) × 13

sin(C) = 5/13 = 0.384615385... ≈ 0.38

The price of the pipette for company A and company B will be $480 and $420, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A research facility supervisor was keen on purchasing another pipette. Organization A was selling 2 pipettes for £300 not as much as Organization B was selling 3 pipettes for. For a solitary pipette, Organization A was more costly by £60 than Organization B.

Let 'x' be the price of the pipette of company A and 'y' be the price of the pipette of company B. Then the equations are given as,

2x = 3y - 300         ...1

x = y + 60                 ...2

From equations 1 and 2, then we have

2(y + 60) = 3y - 300

2y + 120 = 3y - 300

y = 420

Then the value of x is given as,

x = 420 + 60

x = 480

The price of the pipette for company A and company B will be $480 and $420, respectively.

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Answer: width is 13.5 cm

Step-by-step explanation:

9 x 2 +2x =45

45-18

2x=27

2x/2=27/2

x=13.5

width is 13.5 cm

Answer:

height = 4cm

Step-by-step explanation:

volume of right-circular cylinder = πr²h

h = r

so

πr²r or πr³

πr³ = 64π

r³ = 64

r = 4

h = 4

The value of the MN is 4 according to the assumption on the number line.

According to the statement

We have to find that the value of the MN with the help of the value of the x.

So, For this purpose, we know that the

A number line is a horizontal line that has equally spread number increments.

Now,

Assuming that L, M, and N are points on a number line with L < M < N,

According to the assumption, the equation become

2x + x+1 = 7

3x +1 =7

3x =6

x = 2.        

Now, the value of the MN become:

MN = 2x

MN = 2*2

MN = 4.

So, The value of the MN is 4 according to the assumption on the number line.

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114/9 > √150 that is, 114/9 is greater than √150

Given,

We have to compare √150 and 114/9 using  <, >, or =

Comparison between two numbers;

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than."

Here,

First we have to find the value of √150 and 114/9

That is,

The value of √150 = 12.25

The value of 114/9 = 12.66

Therefore,

We came to know that 114/9 is greater than √150 that is, 114/9 > √150

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The distance from the lighthouse is 64 ft and the distance from Maya to the lighthouse is 56 ft

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

Height of lighthouse = 48 ft

Height of Maya = 6 ft

Using the above parameters and the attached figure, we have the following equivalent ratio

48 : x = 6 : 8

Multiply the second ratio by 8

So, we have

48 : x = 48 : 64

This means that

x = 64

From the figure, we have

y + 8 = x

Recall that

x = 64

So, we have

y + 8 = 64

Evaluate

y = 56

Hence, the distance is 56 ft

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Answer:

P=-15

Step-by-step explanation:

P-12=-27  |+27

P+15=0

P=-15

To turn the specified limit, which is a Riemann sum, within the known interval, [2, 6], and variable, [tex]x_i[/tex], to a definite integral, the value, Δx is dx as n approaches infinity, to get;

[tex]\displaystyle \lim\limits_{n\to \infty}\sum\limits^n_{i=1}x_i\cdot \ln \left(1+x_i^2 \right) \Delta x, [2, \,6] = \int\limits^6_2 {x\cdot \ln \left(1+x_i^2 \right)} \, dx[/tex]

A Riemann sum is an approximation of an integral, which is the area of a region, by making use of the sum of simplified slices that make up the region.

A definite integral is a calculation used to find the area under a graph of a function by making use of very small or infinitesimal stripes of the region under the graph of the function.

The expression in the question is a Riemann sum

[tex]\lim\limits_{n \to \infty} \sum\limits_{i=1}^n x_i\cdot ln \left(1 + x_i^2 \right) \Delta x, [2, 6][/tex]

The Riemann sum can be converted into a definite integral, using the equation, [tex]\displaystyle{\lim\limits_{n \to \infty} \sum\limits_{i=1}^n f(x_i)\Delta x = \int\limits^b_a {f(x)} \, dx }[/tex]as follows;

The value of Δx is the value which values in the parenthesis are multiplying on the left, therefore; Δx is replaced with dx, as n → ∞

The limits of the Riemann sum in the question = [2, 6]

[tex]f(x_i) = x_i \cdot \ln\left(1 + x_i^2 \right)[/tex], therefore, [tex]f(x) = x \cdot \ln\left(1 + x^2 \right)[/tex]

Plugging in the the above values into the expression for the Riemann sum, we get the following definite integral;

[tex]\displaystyle{\lim\limits_{n \to \infty} \sum\limits_{i=1}^n x_i\cdot \ln \left(1 + x_i^2 \right) \Delta x, [2, 6] = \int\limits^6_2 {x\cdot \ln\left(1 + x^2\right)} \, dx[/tex]

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The values that make the inequality true are (a) 2.11 (c) 1.1 and (d) 1.63

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

0.3m ≥ 0.55-0.2m

Evaluate the like terms

0.5m ≥ 0.55

Divide both sides by 0.5

So, we have the following representation

m ≥ 1.1

This means that the true values are at least 1.1

In this case, they are 1.1, 1.63 and 2.1

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In the given equation, the coefficient of b is 183/23 and the constant coefficient is -30.

The given equation is 8b= b/23 +30.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 8b= b/23 +30

⇒ 8b-b/23 -30=0

⇒ 8b-b/23 -30=0

⇒ 183b/23 -30=0

Here, the coefficient of b is 183/23 and the constant coefficient is -30.

Therefore, in the given equation, the coefficient of b is 183/23 and the constant coefficient is -30.

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Answer:

y = 3/4x - 1

Step-by-step explanation:

4x + 3y = 7

3y = -4x + 7

y = -4/3x + 7/3

The slope of the given line is -4/3 so the slope of a line perpendicular to it is 3/4 (negative reciprocal).

y = 3/4x + b

Substitute x = 4 and y = 2:

2 = 3/4(4) + b

2 = 3 + b

b = -1

Thus the final equation is y = 3/4x - 1

Answer: It takes more five to reach that answer

Step-by-step explanation:

Answer: 20/100 or 1/5 (reduced)

Step-by-step explanation: To find the fraction, it is helpful to write a proportion. So. if we know every # will be out of 100, we can infer that it will be our whole (can also be represented by being written as 1 ) So now, if we move the decimal 2 places, we now have our fraction 20 out of 100. You can reduce this by dividing the 20 by 20 and the 100 by 20, to get 1/5. I hoped this helped.

The slope of the line that passes through the given two points is m = 26/25.

Consider a line that passes through the points (x1, y1) and (x2, y2).

So, the slope of the line is calculated by

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

The given line passes through points (1, 3) and (26, 29).

So, we can consider (x1, y1) = (1, 3) and (x2, y2) = (26, 29).

Then, the slope of the line is

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

   = (29 - 3)/(26 - 1)

   = 26/25

Therefore, the slope of the given line is 26/25.

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Answer:

Step-by-step explanation:

13

Answer: 13

Step-by-step explanation:

I hope it helps

The measurements of the figures that should be equal in order for the ratio of volumes between the volumes of the cone, sphere, and cylinder of 1:2:3 to be true is; The radius and the height

A ratio is a comparison between the magnitudes or measurements of items, expressing the number of times one item in the ratio is contained within another item in the ratio.

The formula for the volume of a cone, [tex]V_p[/tex] is, [tex]V_p[/tex] = (1/3)·π·r₁²·h₁

The formula for the volume of a sphere, [tex]V_s[/tex], is [tex]V_s[/tex] = (4/3)·π·r₂³

The formula for the volume of a cylinder, [tex]V_c[/tex], is [tex]V_c[/tex] = π·r₃²·h₃

The ratio of the volumes in the question is 1:2:3

Therefore; The volume of the sphere is twice the volume of the cone, and the volume of the cylinder is three times the volume of the cone, which indicates;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁...(1)

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁...(2)

Equation (1) indicates that we have;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁

Where, h₁ = 2·r₂, we get;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·(2·r₂) = (4/3)·π·r₁²·r₂

Therefore; r₁ = r₂, and the diameter of the sphere is equal to the height of the cone

The radius of the cone is equal to the radius of the sphere

Equation (2) indicates;

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁ = π·r₁²·h₁

Therefore;

r₃²·h₃ = r₁²·h₁

r₃ = r₁

h₃ = h₁

The radius of the cone = The radius of the cylinder

The height of the cone = The height of the cylinder

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Answer:

Hope the picture will help you

The solution is, 12000 pound was the ball's actual weight.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While on vacation in Missouri, Sue's family stopped to see the world's largest ball of nylon twine.

Before they got there, Sue predicted the ball would weigh 6,000 pounds.

Her prediction was 50% less than the actual weight of the ball.

let, the ball's actual weight = x

now, 50% of x = x/2

ATQ, x/2 = 6,000 pounds.

so, x = 12000

Hence, The solution is, 12000 pound was the ball's actual weight.

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x=7/6

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

Answer:

  yes

Step-by-step explanation:

You want to know if a function can have the characteristic that the limit at a point does not exist, but the function is defined at that point.

A function has no limit at a point if the limit from the left is different from the limit approaching from the right.

Consider the sign function ...

  [tex]\text{sign}(x)=\begin{cases}-1,&x < 0\\0,&x=0\\1,&x > 0\end{cases}[/tex]

The left limit as x → 0 is -1; the right limit as x → 0 is +1, so the limit as x → 0 "does not exist." However, the function is defined at x=0.

The function is defined everywhere, but the limit as x→0 does not exist.

The solution for this system of linear equations are x=-18 y=-71

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: 3x+2y=1

                  −x+5y=−23

[tex]\left[\begin{array}{ccc}3&2\\-1&5&\\\end{array}\right][/tex]  . [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]  = [tex]\left[\begin{array}{ccc}1\\-23\\\end{array}\right][/tex]

                      [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]   =   [tex]\left[\begin{array}{ccc}5&1\\-2&3&\\\end{array}\right][/tex] . [tex]\left[\begin{array}{ccc}1\\-23\\\end{array}\right][/tex]

                       [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-18\\-71\\\end{array}\right][/tex]

Hence, The solution for this system of linear equations are x=-18 y=-71

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Answer:

5.73

Step-by-step explanation:

I solved it by just multiplying and adding. I didn't use pemdas so it might be wrong and if it is I'm sorry..

Answer: 9

Step-by-step explanation:

Step-by-step explanation:

your question is strange.

first you tell us that 50 people like coffee, 25 like tea, and 13 like both.

and then you ask how many like coffee or tea or both.

is this a joke ? or do you rather mean how many like only coffee, or only tea, and how many don't like neither ?

since 13 people like coffee and tea, these 13 are also part of the group of 50 that like coffee, and of the group of 25 that like tea.

so, to get the number of people that like only one, we need to deduct the number of people, who like both from both groups.

the number of people that only like coffee is therefore

50 - 13 = 37

and the number of people that only like tea is

25 - 13 = 12

we know the number of people that like coffee and tea is 13.

together that are

37 + 12 + 13 = 62 people.

that means 70 - 62 = 8 people don't like neither coffee nor tea.

Answer: 62

Step-by-step explanation:

Those who like coffee only = 50 - 13 = 37. Those who like tea only = 25 - 13 = 12. Those who like either coffee, or tea, or both = 37 + 12 + 13 = 62.

In theory, the 70 people being surveyed could fall under any of the following four categories:

I have labelled the four categories 1, 2, 3 and 4 for convenient reference.

From the information provided in the question, category 1 contains 50 people, category 2 contains 25 people, while category 3 contains 13 people. We do not yet know how many people fall under category 4, but we shall calculate it.

We know from set theory that the four aforementioned categories are known formally as sets. A set is simply a group of objects or things that are similar in some way. Each of the objects in a set is called a member of that set. Two sets can intersect. The intersection of two sets is simply the collection of members that are in both of the two sets. Also, two sets can unite. The union of two sets is the collection of members that in either of the two sets.

For example, category 3 is the intersection of category 1 and 2. The question requires us to calculate the union of category 1 and 2.

Answer: y = -5/6x - 23/6

(Read the explanation first to make sure it's correct)

Step-by-step explanation:

A parallel line means that it has the same slope as the equation:

5x + 6y = 11

Let's first convert this standard form equation into slope-intercept form:

y = -5/6x + 11/6

So that means that our new line also has a slope of:

-5/6

So far, for our new equation we have:

y = -5/6x + b

Next, let's plug in the values of our point to the equation:

-3 = 5/6 + b

So b = -23/6

So the equation in slope-intercept form is:

y = -5/6x - 23/6

The factored form of the polynomial x + 9x + 20 is (x + 4)(x + 5). To obtain this form, we can use the factoring method known as "FOIL," which stands for "First, Outer, Inner, Last." This method involves multiplying the first terms, the outer terms, the inner terms, and the last terms of the two factors to obtain the original polynomial.

In this case, if we let the factors be (x + 4) and (x + 5), we can use FOIL to multiply them and obtain the following:

(x + 4)(x + 5) = (x * x) + (4 * x) + (x * 5) + (4 * 5)

This simplifies to:

(x + 4)(x + 5) = x^2 + 9x + 20

As we can see, the result is the original polynomial. Therefore, the factored form of x + 9x + 20 is (x + 4)(x + 5)

The value of the factored form of the polynomial are,

⇒ (x + 4) (x + 5)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The polynomial are,

⇒ x² + 9x + 20

Now, We can simplify as;

⇒ x² + 9x + 20

⇒ x² + 5x + 4x + 20

⇒ x (x + 5) + 4 (x + 5)

⇒ (x + 4) (x + 5)

Thus, The value of the factored form of the polynomial are,

⇒ (x + 4) (x + 5)

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Answer:10

Step-by-step explanation:3/5x10=6

Answer:

D) [tex]f^{-1}(x)=(x-3)^2+2[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{x-2}+3 \implies x=\sqrt{f^{-1}(x)-2}+3 \\ \\ x-3=\sqrt{f^{-1}(x)-2} \\ \\ (x-3)^2=f^{-1}(x)-2 \\ \\ f^{-1}(x)=(x-3)^2+2[/tex]

Note we take the positive case because the domain of the original function is the same as the range of the inverse, and the domain of [tex]f(x)[/tex] is [tex][2, \infty)[/tex].