The cost of 78 apples is £27.30. (a) Find the approximate (b) Find the approximate cost of 49 apples. cost of 698 apples.​

By the principle of mathematical induction, we can conclude that f1(x) = f2(x) ∀ x ∈ X. Hence, f1 = f2.

Let f1(x) and f2(x) be two functions such that f1(1)=f2(1). We can then say that f1(x)-f2(x) = 0 for x=1. Since f1(i)=f2(i) for all i, we can state that f1(x)-f2(x) = 0 for all x. Therefore, f1(x) = f2(x) for all x, and f1=f2.

Let f1 and f2 be two functions, f1:X→Y, f2:X→Y, where X and Y are two sets.

If we assume that f1(1) = f2(1) and f1(i) = f2(i) for all i ∈ X, then it follows that

f1(x)=f2(x) ∀ x ∈ X.

To prove this, we will use mathematical induction. We will assume that the statement is true for some k ∈ X and prove that it is true for k+1.

Let us assume that f1(k) = f2(k).

Then,

f1(k+1) = f2(k+1)

Since f1(k+1) = f1(k) and f2(k+1) = f2(k), we can say that

f1(k) = f2(k)

Therefore, by the principle of mathematical induction, we can conclude that f1(x) = f2(x) ∀ x ∈ X. Hence, f1 = f2.

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Bob needs to run at a speed of at least 10.39 feet per second to catch the elevator.

To catch the elevator, Bob needs to reach the door before it fully closes, which means he needs to cover the distance of 4.3 - 0.6 = 3.7 feet in the time it takes the door to close. We can use the formula:

distance = rate x time

to find the time it takes for the door to close, and then use this time to find the speed that Bob needs to run. Let's set up the equation:

3.7 = 1.2t

where t is the time it takes for the door to close.

Solving for t, we get:

t = 3.7/1.2 = 3.08 seconds

Now we can use the formula again to find the speed that Bob needs to run:

speed = distance / time

speed = 32/3.08

speed = 10.39 feet per second (rounded to the nearest hundredth)

Therefore, Bob needs to run at a speed of at least 10.39 feet per second to catch the elevator.

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Answer:

The critical value for a 95% confidence level is 1.711.

Step-by-step explanation:

a=0.05

1-a=0.95

Degrees of freedom df =21-1=20

using the t-distribution table, the critical value for a 95% confidence level and df=20 is 1.711

Yes, the quadratic function f(x) and the linear function g(x) will intersect. The x-coordinate of the point of intersection could be positive, negative or zero, depending on the specific functions.

From the data given, it's not possible to determine the x-coordinate of the point of intersection.

A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.

Linear functions are usually written as y = mx + b and graphed as straight lines.

Begin with the y-intercept or b value, then use the slope to identify a second point on the graph. Quadratic functions are graphed as curved parabolas and have the formula y = ax2 + bx + c.

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There are 2 dimes in the purse that contains $2.20

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Let quarters be = x

The dimes be = 1/4 * x

25x+10x/4 = 220

(100x + 10x) /4 = 220

110x/4 = 220

110x = 220*4

110x = 880

x = 880/110

x = 8

The dimes be = 1/4 * x

The dimes be = 1/4 * 8

The dimes be = 2

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Answer:

6/7

Step-by-step explanation:

find the least common multiple of 7 and 5:

7,14,21,28,(35)

5,10,15,20,25,30,(35)

7x5=35 and 5x7=35

So multiply the denominator and numerator of 6/7 by 5, so 30/35

and multiply the denominator and numerator of 4/5 by 7, so 28/35.

30 is bigger than 28, so 30/35 is greater than 28/35.

Therefore, 6/7 is greater than 4/5

Answer:

$45

Step-by-step explanation:

We know

A merchant bought an item for $30 and sold it for 50% more.

50% of $30 = $15

What price did the merchants sell the item?

$30 + $15 = $45

So, the merchants sell the item for $45

If a bicyclist in motion increases his speed by 30 percent and then increases this speed by 10% , 43%. percent of the original speed is the total increase in speed

To find the total increase in speed, we first need to find the new speed after the first increase of 30%.

If the original speed is represented as 100%, then the new speed after the first increase is

100 + (30% of 100) = 100 + 30 = 130.

Next, we find the new speed after the second increase of 10%.

The new speed after the second increase is

130 + (10% of 130) = 130 + 13 = 143.

Finally, we find the percent increase in speed compared to the original speed of 100%.

The percent increase in speed is

(143 - 100) / 100 * 100 = 43%.

Therefore, the total increase in speed is 43%.

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The median is 18.5, and it represents the typical age of the runners.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The given ages of 12 runners in a recent marathon are listed.

35, 17, 34, 14, 28, 20, 18, 15, 14, 19, 17, 31

Let us arrange the numbers in ascending order

14, 14, 15, 17, 17, 18, 19, 20, 28, 31, 34, 35

The middle most terms are 18 and 19

18+19/2

37/2

18.5

Hence, the median is 18.5, and it represents the typical age of the runners.

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In this city, the percentage of people who neither like watching football nor basketball is 20%.

This is calculated by subtracting the total percentage of people who like watching either football or basketball (80% + 70% - 30% = 120%) from the total population (100%).

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign (%). For example, 45% means 45 out of 100, or simply 0.45. To calculate the percentage of a number, divide the number by the total and multiply by 100. For example, to find the percentage of 12 out of 50, divide 12 by 50 and then multiply by 100, which equals 24%.

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Answer: Thus the mass of copper in solid form is m = 9860 kg / m^3.

Step-by-step explanation: solve it step by step

Answer:

2.5hrs

Step-by-step explanation:

We can start solving the problem by using the formula: distance = rate x time. If we call the time t in hours, we can write two equations:

49t = distance for the truck going south

62t = distance for the truck going north

We also know that the distance between the two trucks is the sum of the distances they have traveled, so:

distance = 49t + 62t = 111t

Now we can use the given information that the distance between the two trucks is 277.5 miles to find the value of t:

277.5 = 111t

t = 277.5 / 111

So the two trucks will be 277.5 miles apart after t = 2.5 hours.

The annual sales after the 7th year is 855,355.65

An exponential function is a type of function in math that involves exponents. A basic exponential function is of the form f(x) = bx, where b > 0 and b ≠ 1.

The standard expression for an exponential function is expressed as: y=a(1+r)^t

From the parameters in the question

Given the following parameters

a = 650000

r = 4% = 0.04

t = 7

Substitute the given parameters into the formula:

y=a(1+r)^t

y = 650000(1+0.04)^7

y= 650000(1.04)^7

y=855,355.65

Hence, the annual sales for the local restaurant after 7 years is 855,355.65

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The equation of the red line will be y = 5/3 x - 3 and The equation of the green line will be y = 0x + 1 i.e y = 1 .

What is Equation of a Straight line ?

Equation of a straight line as follows : y = mx + c

where m is the slope of line.

Start by seeing where the lines go. They cross (intersect) at (1, -1). We can use this to check later.

Now for slope: green is -4/2 = -2

pink is 4/2 = 2

Now we can create the equations

Let's make green = g(x) and pink = p(x)

if we use y = mx + b, then the green has a y-intercept (b) of +1

So g(x) = -2x + 1

pink has a y-intercept of -3, so p(x) = 2x - 3

Now let's plug n play: put our solutions x into each equation and confirm that it makes the y = -1

g(x) = -2x + 1 = -2(1) + 1 = -2+1 = -1

p(x) = 2x - 3 = 2(1) - 3 = 2-3 = -1

Therefore, The equation of the red line will be y = 5/3 x - 3 and The equation of the green line will be y = 0x + 1 i.e y = 1 .

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The 9-hour training schedule is broken up into his Wednesday clients' 6 hours and his Thursday clients' 7 hours.

Its core idea is thought to represent number's greatest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and treble. A fractional number can be checked to discover if it is a prime number. A statement having two spherical geometry and an equal sign in the middle is referred to as a mathematical equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Neither conditional equation or identities are categories for equations.

given

Make a system of equations where A represents the length of a Plan A session and B represents a Plan B session.

This Wednesday: 2A + 12B = 9 hours.

Thursday: 5A + 3B = 9 hours

Using addition, multiply the Thursday equation by -4 to find the solution:

2A + 12B = 9

(5A + 3B = 9) * -4

2A + 12B = 9

-20A -12B

= -36

The B's disappear if you combine the two equations:

1.5 hours from -18A to -27A.

the following into one of the initial equations:

12B = 6 B = 0.5 hours + 2(1.5) = 9

The 9-hour training schedule is broken up into his Wednesday clients' 6 hours and his Thursday clients' 7 hours.

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[tex]\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(11)\implies \cfrac{\log_{10}(11)}{\log_{10}(5)}\implies \stackrel{\textit{\Large both are equal}}{\boxed{\cfrac{\log(11)}{\log(5)}}\implies \cfrac{\log_{e}(11)}{\log_{e}(5)}\implies \boxed{\cfrac{\ln(11)}{\ln(5)}}}[/tex]

Answer:

1. Parabola

2. Quadratic Function

3. Minimum

4. Axis of Symmetry

5. Vertex

6. Maximum

7. domain and Range

8. Maxima and Minima

I cannot see #9 (assuming there is a #9), but the only remaining choice is Linear Function so  whatever the that #9 missing statement is has this as the definition

Step-by-step explanation:

The election board’s voter registration list is not a census because the eligibility to vote may affect some persons not to be counted also the body organizing the activities are not same

A census,, is a comprehensive count of the population that is conducted by the government. It is used to gather information about the size, distribution, and characteristics of the population for a variety of purposes, including apportioning congressional seats, drawing electoral districts, and allocating federal funds to states and localities.

Because voter registration and census are two different processes with different goals, they may not capture the same individuals. For example, not all adults are eligible to vote, such as non-citizens, felons, and those under the age of 18. Additionally, some eligible voters may choose not to register, while others may be missed by registration efforts. Therefore, the voter registration list may not be a complete or accurate representation of the adult population.

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According to the quadratic equation the solution of k is 48 ± 8√26.

In math the term called quadratic equation is known as the polynomial equation whose highest degree is two

As we all know that the value of the quadratic equation is written as,

=> (k - 4)x² - 3kx - 4(k -2) = 0.

Now we have identified that the given equation is in the form of ax² + bx + c = 0.

Here we have also identified the value of a = k - 4, b = -3k and c = 4(k-2)

And then we have to use the quadratic formula to identify the value of k,

Here it can be written as.

=> (-3k)² - (4 x (k - 4) x 4(k-2))

When we expand the term then we get,

=> 9k² - (16k² - 32k - 64k + 128)

When we simplify this one then  we get

=> -5k² + 96k - 128 = 0

Here we have to factorize the expression then we get the value of k as 48 ± 8√26.

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20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.

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

Given that, a pharmacist add to 10 cm³ of a 10% alcohol solution to strengthen it to a 70% solution.

Let x be the volume of pure alcohol (100%) in cm³ needed to be added.

x × 100% + 10 cm³ × 10% = 70% × (x + 10 cm³)

x × 1 + 10 × 0.1 = 0.7 × (x + 10)

x + 1 = 0.7x + 7

x - 0.7x = 7 - 1

0.3x = 6

x = 20 cm³

Therefore, 20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.

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An example of a relation that is a function is {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Relations and functions define a mapping between two sets (Inputs and Outputs) such that they have ordered pairs of the form (Input, Output).

An example of a relation that is a function:

{(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}

It is a function as every input has a single output.

So, 2,5,8,11,14 and 17 are the elements of the domain of the given relation.

Here domain ={2,5,8,11,14,17} and range ={1}

An example of a relation that is not a function

{(1,3),(1,5),(2,5)}

Since the element  1 corresponds to two different images i.e., 3 and 5 . So, this relation is not a function.

Therefore, an example of a relation that is a function is {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}.

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The equation model the depth (d) of the snow n days after the storm is d(n) = 15 * (0.8)^n

Let's call the initial depth of the snow (n = 0) as d0. d0 = 15 inches.

Every day, the snow depth decreases by 20%. So, the rate of change of the snow depth is -0.2.

Using this information, we can use the formula for exponential decay to find the depth of the snow (d) after n days:

d(n) = d0 * (1 - 0.2)^n

Substituting d0 = 15, we get:

d(n) = 15 * (0.8)^n

Therefore, the correct answer is as given above

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The solution to the given integral is 5ye10 - 5ye5 + c(y10 - y5).

To evaluate the given integral, we must first reverse the order of integration. This is done by switching the limits of integration for the two variables. In this case, the limits for the y variable are 10 and 5, and the limits for the x variable are 5 and 5. Thus, the integral can be rewritten as:

∫5∫10yex2dxdy

To evaluate this integral, we can use the following formula:

∫a∫bf(x,y)dxdy = ∫a∫bf(y,x)dydx

Using this formula, we can rewrite the integral as:

∫5∫10yex2dydx

We can now use the product rule to separate the integral into two separate integrals. First, we can integrate with respect to x:

∫5yex2dx

This integral can be solved using the fundamental theorem of calculus:

∫5yex2dx = 5ye5 - 5ye5 + c

Next, we can integrate with respect to y:

∫10(5ye5 - 5ye5 + c)dy

This integral can be solved by simply integrating the constants and the exponential:

∫10(5ye5 - 5ye5 + c)dy = 5ye10 - 5ye5 + c(y10 - y5)

Combining the two solutions, we get the following:

∫5∫10yex2dxdy = 5ye10 - 5ye5 + c(y10 - y5)

Therefore, the solution to the given integral is 5ye10 - 5ye5 + c(y10 - y5).

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The number of decorative pillows which the realtor arranged on each bed are 6 decorative pillows on each twin bed and 8 decorative pillows on each queen bed.

In order to write a system of equations that model this situation, we would assign variables to the number of decorative pillows on each twin bed and the number of decorative pillows on each queen bed respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into algebraic equation as follows:

3x + 2y = 34    ....equation 1.

x + 5y = 46    ....equation 2.

Multiplying equation 2 by 3 and subtracting from equation 3, we have:

3x + 2y = 34

3x + 15y = 138

-13y = -104

y = 8 decorative pillows on each queen bed.

x = 46 - 5y

x = 46 - 5(8)

x = 46 - 40

x = 6 decorative pillows on each twin bed.

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This statement is true. If a system of linear equations has two different solutions, it must have infinitely many solutions.

Linear equations are equations that involve only linear functions, or functions of the form f(x) = mx + b. These equations can be used to describe a variety of real-world phenomena, such as the motion of a particle along a straight line. Linear equations are generally solved by using the linear equation solving methods, such as substitution, elimination, and graphing. The solutions to a linear equation are the values of the variables that make the equation true.

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Answer:

it should be 24

Step-by-step explanation:

The statement that "there was only a 2.6% chance that the two groups were the same" is not accurate.

A p-value is a measure of the evidence against the null hypothesis, and represents the probability of observing a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

A low p-value (typically less than 0.05) is often taken as evidence against the null hypothesis, and in favor of the alternative hypothesis.

However, a p-value does not directly measure the probability that the null hypothesis is true. It only provides information about the evidence against the null hypothesis, and not about the probability of the difference between the two groups.

The conclusion that "there was only a 2.6% chance that the two groups were the same" is not a valid interpretation of the p-value.

It is also worth noting that p-values are not the only evidence to consider when making a decision about the null hypothesis. Other factors, such as the effect size, the sample size, and the quality of the study design, should also be taken into account.

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The scalar projection of b onto a is -7.33.

The scalar projection of a vector b onto a vector a is the magnitude of the component of b that is parallel to a. It is calculated by taking the dot product of the two vectors, and dividing it by the magnitude of a. Mathematically, this is represented by the equation:

(a⋅b)/|a|

In this example, the dot product of vectors a and b is equal to -66, and the magnitude of vector a is equal to 9. Therefore, the scalar projection of b onto a is equal to -7.33.

To calculate the scalar projection, we first need to calculate the dot product of a and b. To do this, we take the components of each vector and multiply them together. For vector a, this is done by taking -2 multiplied by -3, 8 multiplied by -10, and 3 multiplied by 5. We then add all of these products together to get the dot product of a and b, which is equal to -66.

Next, we calculate the magnitude of vector a, which is done by taking the square root of the sum of the squares of its components. For vector a, this is equal to the square root of (-2)^2 + (8)^2 + (3)^2, which is equal to 9.

Finally, we divide the dot product of a and b by the magnitude of a, which is -66 divided by 9, which is equal to -7.33. Therefore, the scalar projection of b onto a is -7.33.

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