Please answer number number 3 please :)

The x-intercept of the function as an ordered pair is equal to (5, 0).

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this context, we would replace the y-value with zero (0) by substituting it into the given equation y = ∛x - 5 as follows;

y = ∛x - 5

0 = ∛x - 5

Taking the cube root of both sides of the function, we have the following:

0 = x - 5

x = 5

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Answer:

he ran 280 miles more than Michael

Step-by-step explanation:

438-158=280

At a price of $44, the quantity demanded is equal to q*, which is 30 units.

The market for good X is given with a price of $15 at q0 (10 units), a price of $21 at pa, a price of $31 at p* (30 units), a price of $44 at pb, a price of $57 at p1 (50 units), and a price of $70 at q2 (70 units). To calculate the quantity demanded when the price is $44, we first need to identify the price points on either side of $44. In this case, $31 and $57 are the two price points. We then look at the corresponding quantities at those two points, which are q* (30 units) and q1 (50 units). Since the demand curve is downward sloping, the quantity demanded at $44 (pb) will be between 30 and 50 units. Since 30 is the lower number, the quantity demanded at $44 will be q*, or 30 units.

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The tangent of the angle between vectors v and w is 2√(21) / 9

We can use the dot product and cross-product formulas to find the angle between two vectors.

The dot product of two vectors v and w is given by:

v · w = ||v|| ||w|| cos(θ)

where ||v|| and ||w|| are the magnitudes of the vectors v and w, and θ is the angle between them.

The cross product of two vectors v and w is given by:

v × w = ||v|| ||w|| sin(θ) k

where k is a unit vector in the direction of the cross product.

Since v × w = 6i - 7j + 9k and v · w = 9, we can find the angle between v and w as follows:

[tex]\theta = sin^{-1}\frac{||v \times w||}{||v|| \ ||w||} = sin^{-1}\frac{||6i - 7j + 9k||}{||v|| \ ||w||}[/tex]

We can find the magnitude of v × w by using the formula for the magnitude of a cross-product:

[tex]||v \times w|| = ||6i - 7j + 9k|| \\\\= \sqrt{6^2 + (-7)^2 + 9^2} = \sqrt{6^2 + 49 + 9^2}\\\\=\sqrt{84} = \sqrt(2^2 \times 3 \times 7) = 2\sqrt{(3 \times 7)[/tex]

We can find the magnitude of v and w using the given dot product formula:

v · w = ||v|| ||w|| cos(θ) = 9

||v|| ||w|| = 9 / cos(θ)

Since we know that ||v|| and ||w|| are positive, we can square both sides to obtain:

[tex](||v|| \ ||w||)^2 = \frac{9 }{cos(\theta))^2} \\\\||v||^2 \ ||w||^2 = \frac{81}{cos^2(\theta)}[/tex]

Finally, using the tangent formula, we can find tanθ:

tan(θ) = sin(θ) / cos(θ) = ||v × w|| / ||v·w|| = 2√(3 × 7) / 9 = 2√(21) / 9.

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Answer:

To figure out how many adults and children bought tickets, we can set up a system of equations using the information provided. Let x be the number of adults and y be the number of children. We know that:

x + y = 500 (because a total of 500 people bought tickets)

17.95x + 12.95y = 7355 (because the total revenue from ticket sales is $7355)

We can use the first equation to solve for one of the variables in terms of the other variable. For example, we can substitute y = 500 - x into the second equation:

17.95x + 12.95(500 - x) = 7355

This simplifies to:

17.95x + 6475 - 12.95x = 7355

5x = 1880

x = 376

so there are 376 adults bought tickets and 500-376=124 children bought tickets.

Step-by-step explanation:

Depending on the value of the definite integral of f(x) calculated between two limits, α and β, the area between two vertical lines can be positive, negative or zero.

The area between two vertical lines is given by the definite integral of a function f(x) calculated between two limits, α and β. In order to determine whether the area is positive, negative or zero, the values of the definite integral of f(x) calculated between two limits, α and β, must be known.

If the value of the definite integral of f(x) calculated between two limits, α and β, is greater than zero, then the area between the two vertical lines is positive. Mathematically, this can be expressed as:

Area = ∫βαf(x)dx > 0

Similarly, if the value of the definite integral of f(x) calculated between two limits, α and β, is less than zero, then the area between the two vertical lines is negative. Mathematically, this can be expressed as:

Area = ∫βαf(x)dx < 0

Lastly, if the value of the definite integral of f(x) calculated between two limits, α and β, is equal to zero, then the area between the two vertical lines is zero. Mathematically, this can be expressed as:

Area = ∫βαf(x)dx = 0

Therefore, depending on the value of the definite integral of f(x) calculated between two limits, α and β, the area between two vertical lines can be positive, negative or zero.

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the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ]  is the formula in terms of i and n for the gernal left endpoint x i-1

What is the formula for left endpoint approximation?

Rule: Left-Endpoint Approximation

On each subinterval [xi−1,xi] (for i=1,2,3,…,n), construct a rectangle with width Δx and height equal to f(xi−1), which is the function value at the left endpoint of the subinterval. Then the area of this rectangle is f(xi−1)Δx

In this problem you will calculate ∫302+4 by using the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ].

(a) The interval [0,3] is divided into equal subintervals of length Δ. What is Δ (in terms of )? Δ

(b) The right-hand endpoint of the th subinterval is denoted ∗. What is ∗ (in terms of and )

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Answer:

No solution

Step-by-step explanation:

1/3x-y=2  

x - 3y = 6​

Times the first equation by -3

-x + 3y = -6

x - 3y = 6

0 = 0

So, there is no solution.

Answer:

[tex]The[/tex] [tex]length[/tex] [tex]of[/tex] [tex]BC[/tex] [tex]is[/tex] [tex]\sqrt{55}[/tex] [tex](units)[/tex].

Step-by-step explanation:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 11 and DC = 5

Leg rule of geometric mean theorem:

[tex]\frac{hypotenuse}{leg}=\frac{leg}{part}[/tex]

[tex]\frac{AC}{BC}=\frac{BC}{DC}[/tex]

[tex]\frac{11}{x}=\frac{x}{5}[/tex]

Do cross multiplication.

[tex]11 * 5= x*x[/tex]

[tex]55=x^{2}[/tex]

Taking square root on both sides.

[tex]\sqrt{55} =\sqrt{x^{2} }[/tex]

[tex]\sqrt{55}=x[/tex], [tex]since[/tex] [tex]\sqrt{55}[/tex] [tex]cannot[/tex] [tex]be[/tex] [tex]reduced.[/tex]

The length of BC is [tex]\sqrt{55}[/tex].

The test statistic to test the claim that the standard deviation of all customer waiting times is greater than 3.5 minutes, 7.444

Standard deviation is a measure of the spread or dispersion of a set of data. It quantifies how much the individual data points in a set deviate from the mean (average) value of the set. In other words, it tells you how much the data is scattered around the mean.

The test statistic to test the claim that the standard deviation of all customer waiting times is greater than 3.5 minutes can be calculated using the following formula:

Z = (s / σ) x √n

where s is the sample standard deviation (4.8 minutes), σ is the population standard deviation (3.5 minutes), and n is the sample size (15).

Z = (4.8 / 3.5) x √15

  = 7.444

So the test statistic is 7.444.

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Step-by-step explanation:

the slope is always the ratio of

y coordinate difference / x circumstances difference

when going from one point on the line to another.

1.

x changes by +3 (from 2 to 5).

y changes by -6 (from -1 to -7).

the slope is -6/+3 = -2.

m = -2, b = 3 is the correct answer

2.

x changes by +2 (from -4 to -2).

y changes by +3 (from -2 to 1).

the slope is +3/+2 = 3/2.

m = 3/2, b = 4 is the correct answer.

FYI

because there is in both cases only one answer option with the correct slope, we did not need to check the y-intercept ...

Answer:

6(x-0)=-8

6x=-8

6x/6=-8/6

Hope this helps!!

Step-by-step explanation:

Answer: [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Let the number be x

6 times x = 6x

subtracted from 0

gives -8

∴ 0 - 6x = -8

0 + 8 = 6x

[tex]\frac{8}{6}[/tex] = x

[tex]\frac{4}{3}[/tex] = x

Answer: 3/4

Step-by-step explanation:

15/32 + 9/32 = 24/32 = 12/16 = 6/8 = 3/4

Answer:

I think its this, anns gym membership: y=$5x+$20
blakes gym membership: y= $3x+$30

i don’t understand the last question, I apologize if this is wrong.

The mode frequency can be a useful tool for understanding the distribution of the data and identifying any outliers or anomalies in the data set.

The mode frequency of the age variable refers to the most frequently occurring age in a given set of data. This measure of central tendency is particularly useful when working with categorical data, such as age ranges.

To calculate the mode frequency, one must first organize the data into a frequency distribution table, which lists all the different ages and the number of times each occurs. The age with the highest frequency is then considered the mode frequency.

For example, if there are 100 individuals in a data set and the ages range from 20 to 60, we would organize the data into age ranges, such as 20-29, 30-39, etc. Then we would count how many individuals fall into each age range and record this information in the frequency distribution table.

If the age range with the highest frequency occurs more than once, we have a multi-modal data set. On the other hand, if there is only one mode frequency, the data set is considered unimodal.

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Answer is Taking data:

                        28 78 74 89 72

                        50 55 66 26 84

                        59 64 88 23 27

                        70 63 42 37 29

The answer is width of class =13

As the data is not given in the question I'm guessing the data from the question I solved before

28 78 74 89 72

50 55 66 26 84

59 64 88 23 27

70 63 42 37 29

as taking the above data,

maximum value=89

minimum value=23

no : of classes scores are divided into=5 classes

As we know for finding the width of class:

width of class = (maximum value-minimum value)/ no ; of classes

width = (89-23)/5=66/5

width=13.2=13

Note : By using the above given formula you can calculate the width of any data just by taking the maximum and minimum values of data and the number of classes the data is divided into.

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The part of the function over the interval (-2,2) is nonlinear and decreasing.

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Answer:

m= -3/2

Step-by-step explanation:

To find slope

[tex]m \: = \frac{y2 - y1}{x2 - x1} [/tex]

We have our x1 and y1 of (2,5)

We have our x2 and y2 of (8,-4)

Now we plug in

= (-4-5)/(8-2)

= (-9)/(6)

Simplifying it would be

[tex]m = - \frac{3}{2} [/tex]

Answer: slope 'm' = -3 / 2

Step-by-step explanation: Using the formula m=(y2-y1)/(x2-x1), where 'm' is the slope of the line connecting the two points, we can plug in our x and y values:

x1 = 2

x2 = 8

y1 = 5

y2 = -4

Once we plug in our x and y values, we get the equation

m = (-4 - 5) / (8 - 2)

--> -9 / 6 (We can simplify this fraction to get or answer of -3 / 2)

An equation to represent the linear function comparing the number of months after the first month (x) to the number of total customers served (y),  400 + 70x

The number of customers served after 12 months, 1240

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

In the first month, the coffee shop served 400 customers

After that, the coffee shop served 70 customers each month

Suppose, coffee shop served x number of months after first month,

Total people served = 400 + 70x

The number of customers served after 12 months,

Total people served = 400 + 70x12

                                  = 400 + 840

                                  = 1240

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The surface area of an egg shell scales as the mass of the egg shell raised to 1.82694

The term surface area in math is defined as the area occupied by a three-dimensional object by its outer surface

Here we know that the area of a cube with edged is proportional to the second power d² while its volume is proportional to the third power d³.

Here we know that for any bounded solid object, here we have which encloses a region with some volume V and its enclosing surface has area A, where as the same kind of proportions can be derived in terms of a linear dimension d of the object, here for example the diameter of the object.

AS we all know that the surface area is directly proportional to the 3rd power of the mass of the egg, here we have A = km³ where A is the surface area, k a constant of proportionality, and m the mass.

For a chicken egg we have 28 = k(60)⁰°⁶⁷

Here by solving for k we get:

=> k = 28/60⁰°⁶⁷ ≈ 1.82694

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The system of equation (4) and (5) have no solution

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

7(5x + 2) = 5x + 2

Divide both sides by 5x + 2

7 = 1

This equation is false, meaning there is no solution for y that satisfies both equations.

Here, we have

2y = 6

y = -15

Since these are two different equations with the same variable, y, we can use substitution to find a solution.

Starting with the second equation, y = -15, we can substitute this value into the first equation:

2y = 6

2(-15) = 6

-30 = 6

This equation is false, meaning there is no solution for y that satisfies both equations.

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Complete question

4. How many solutions will this equation have? 7(5x + 2) = 5x + 2

5. Solve the given system of equations 2y = 6 and y = -15

The value of square feet means 1 acre be 43,560 square feet.

The US measurement system uses the acre as the unit of land area measurement. Every real estate transaction and listing worldwide has a connection to Square Feet.

The length and width of the land—which are often stated in feet—are multiplied to determine the acreage before converting the result to square feet. Following that, the square footage is converted to acres using a conversion ratio of 43560.

For standing or stored water, an acre-foot is the accepted unit of measurement. It is the volume of water necessary to cover an acre of ground that is 43,560 square feet in size and one foot deep. 325,851 gallons make up an acre-foot.

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Answer:

It's 3.5 hours. Or 3 hours and 30 minutes.

Step-by-step explanation:

If the painting of 3 small rooms takes as much time as the painting of 1 large and 1 small rooms then it takes the same amout of time to paint 1 large room and 2 small rooms.

7 hours = 1 large room

1 large room = 2 small rooms

1 small room is half the time of a large room

1/2 of 7 = 3.5

3.5 hours is 3 hours 30 minutes.

When it is third and long, the best move is typically to make a long pass to a wide receiver because it has the probability to gain the greatest yardage.

Throwing the ball far downfield is frequently the best move when the team has to gain a lot of yardage to continue the drive on third and long. The most yards may be gained by a deep pass to a wide receiver since it might extend the action past the original line of scrimmage. The prospect of a huge play, in which the receiver catches the ball and runs for a bigger gain, is also made possible. A deep pass might also throw the defense off because they might not be anticipating the offense to go for a long gain. But a deep pass can also be dangerous because it might result in a turnover if the receiver doesn't pay attention.

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The distance between the two planes 5x−4y−z=65x−4y−z=6 and 4y−5x z=−484y−5x z=−48 is sqrt(7/10).

What is vector ?

A vector is a mathematical object that has both magnitude (or length) and direction. Vectors can be used to represent physical quantities such as velocity, force, or displacement, where the magnitude represents the size of the quantity and the direction represents its orientation in space.

Let n1 and n2 be the normal vectors of the two planes, respectively.

The normal vectors are:

n1 = <5, -4, -1> and n2 = <5, -4, 1>.

The projection of n1 onto n2 is:

projn1 onto n2 = (n1 . n2 / ||n2||^2) * n2 = (n1 . n2 / ||n2||^2) * (n2 / ||n2||) = (n1 . n2 / ||n2||) * n2 / ||n2|| = (n1 . n2) * n2 / ||n2||^2.

The dot product of n1 and n2 is:

n1 . n2 = 5 * 5 + (-4) * (-4) + (-1) * 1 = 25 + 16 + 1 = 42.

The magnitude of n2 is:

||n2|| = sqrt(5^2 + (-4)^2 + 1^2) = sqrt(30).

Therefore, the projection of n1 onto n2 is:

(n1 . n2) * n2 / ||n2||^2 = 42 * <5, -4, 1> / 30 = <7/3, -4/3, 7/30>.

So , The distance between the two planes 5x−4y−z=65x−4y−z=6 and 4y−5x z=−484y−5x z=−48 is sqrt(7/10).

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Answer:

21[tex]e^{6}[/tex] and 30[tex]t^{6}[/tex][tex]v^{10}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

given

3e³ × 7e³

= 3 × 7 × e³ × e³

= 21 × [tex]e^{(3+3)}[/tex]

= 21[tex]e^{6}[/tex]

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

(10[tex]t^{4}[/tex][tex]v^{5}[/tex] )(3t²[tex]v^{5}[/tex] )

= 10 × 3 × [tex]t^{4}[/tex] × t² × [tex]v^{5}[/tex] × [tex]v^{5}[/tex]

= 30 × [tex]t^{(4+2)}[/tex] × [tex]v^{(5+5)}[/tex]

= 30[tex]t^{6}[/tex][tex]v^{10}[/tex]

The expected Net gain is -0.1001.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total possible selection = 10000

                  Net Gain             Probability

Win                8998                   1/ 10000

Lose                 2                     9999/10000

So, E(x) = 8998 x 1/10000 - 9999/10000

             = -1001 / 10000

so, the expected Net gain = -0.1001

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Answer:

The answer to the inequality is [tex]p\geq 4[/tex].

Step-by-step explanation:

Lets solve the inequality.

[tex]-2p\leq -8[/tex]

Divide both sides of the equation by -2.

There is an inequality rule that says when multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

First lets divide both sides by -2.

[tex]\frac{-2p}{2} \leq \frac{-8}{2}[/tex]

Simplify the left side by cancelling the common factor of −2.

[tex]p\leq \frac{-8}{2}[/tex]

Simplify the right side by dividing -8 by 2.

[tex]p\leq 4[/tex]

We need to flip the direction of the inequality sign.

[tex]p\geq 4[/tex]