you got this five numbers (1, 2, 3, 4). a) if you add a constant number to each, then the mean, the median and the mode changes. b if you add a constant number to each, then the range and the variance remain the same. c) if you multiply each number by a constant, then the mean, the median, the mode, the range change. the standard deviation remain the same. d) if you multiply the mean and the standard deviation by a constant, then both will change by the constant. e) b and c.

William Samuel Johnson felt that ,when men were born, they were equal.

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A linear function can be represented by an equation of the form y = mx + b, where m is the slope of the function and b is the y-intercept. The x-intercept is the point where the graph of the function intersects the x-axis, and the y-intercept is the point where the graph intersects the y-axis.

Given that the x-intercept of the linear function is −8 and the y-intercept is 4, an equation of the function can be written as:

y = mx + b

Substituting the values of the x-intercept and the y-intercept into this equation, we get:

y = m(-8) + 4

Since the y-intercept is 4, this equation can be rewritten as:

y = 4 + mx

This equation represents a linear function with a y-intercept of 4 and a slope of m.

Therefore, an equation of the linear function with an x-intercept of −8 and a y-intercept of 4 is y = 4 + mx.

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Given that the x-intercept of the linear function is −8 and the y-intercept is 4, an equation of the function can be written as:

y = mx + b

Substituting the values of the x-intercept and the y-intercept into this equation, we get:

y = m(-8) + 4

Since the y-intercept is 4, this equation can be rewritten as:

y = 4 + mx

This equation represents a linear function with a y-intercept of 4 and a slope of m.

Therefore, an equation of the linear function with an x-intercept of −8 and a y-intercept of 4 is y = 4 + mx.

The value of the function (f /g)(x) would be [tex](\frac{f}{g})(x)=x^2+6[/tex].

Option (A) is correct.

What are composite functions?

A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.'

Given:

                [tex]f(x)=7x^3-5x^2+42x-30\\\\g(x)=7x-5[/tex]

Now by using the definition of composite functions we can write

      [tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}\\\\(\frac{f}{g})(x)=\frac{7x^3-5x^2+42x-30}{7x-5}\\\\(\frac{f}{g})(x)=x^2+\frac{42x-30}{7x-5}\\\\(\frac{f}{g})(x)=x^2+6[/tex]

Hence, the value of the function (f - g)(x) would be [tex](\frac{f}{g})(x)=x^2+6[/tex].

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Answer:

Step-by-step explanation:

Ten bananas and ten pears will run you about £4.537.

Simultaneous equations are two equations with two unknown variables. From the given question;

If three bananas and two pears cost 95p and Five bananas and three pears cost £1.51, the equivalent equations will be:

3b + 2p = 0.95 * 3

5b + 3p = 1.51 * 2

Solve simultaneously;

6b + 6p = 2.85

10b + 6p = 3.02

Subtract

-4b = -0.17
b = 0.17/4

b = £0.0425

Since 3b + 2p = 0.95, hence

3(0.0425) + 2p = 0.95

0.1275 -0.95 = -2p

2p = 0.8225

p = 0.4112

The cost of  ten bananas and ten pears will be:

Cost = 10(0.0425) + 10(0.4112)
Cost  = 0.425 + 4.112
Cost = £4.537

Hence the cost of ten bananas and ten pears is approximately £4.537

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Yes, a discontinuous function is a function that is not continuous.

A function can have an asymptote if it approaches a horizontal or vertical line but never touches it. There are several types of functions that can have asymptotes, including rational functions, exponential functions, and logarithmic functions.

A continuous function in mathematics is a function without discontinuities, or any sudden changes in value. If we can guarantee arbitrarily small changes in the input of a function by limiting small enough changes, then the function is continuous.

A function is continuous if its graph can be drawn without lifting the pencil from the paper, or if the function's values remain "close" to one another as the input values change. A discontinuous function, on the other hand, has "breaks" or "jumps" in its graph, indicating that the function's values become "far" from one another as the input values change. An example of a discontinuous function is the absolute value function.

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If the graph of a function can be traced without removing the pencil from the paper or if the function's values stay "near" to one another while the input values change, the function is continuous. Contrarily, a discontinuous function's graph shows "breaks" or "jumps," suggesting that the function's values move "far" apart as the input values alter. The absolute value function is an illustration of a discontinuous function.

The coefficient of x² in (3x² – 5)( 4 +4x²) is -8.

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6.

First, let's multiply the terms in the given expression by opening the brackets.

⇒   (3x² – 5)( 4 +4x²)

Now, further multiplying we would get,

⇒   3x²(4 + 4x²) -5(4 + 4x²)

⇒    12x² +12x⁴-20-20x²

⇒  12x⁴ -8x²-20

As we can see that the term that is in multiplication with x² is -8. Similarly, the term that is coefficient of  x⁴ is +12.

Hence, the coefficient of x² in the equation  is -8.

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If the age requirements for academic progressions set by a school is satisfied, than yes it is possible for a 13 year old to be in 7th grade.

The age at which a child is ready to start schooling can vary depending on a number of factors, including the child's physical, social, and emotional development. In general, children who are at least 5 years old and are able to meet certain developmental milestones are typically ready to start school.

Because academic skills are directly tied to a pupil's capacity for academic success, they are sometimes seen as being more significant than age when deciding whether a student is prepared to proceed to a higher grade level. Age is not always a reliable indicator of a student's intellectual aptitude or preparation for a higher grade level. Even if they are younger than their peers, some children may be farther along in their studies and possess the abilities and knowledge required to succeed in a higher grade. Even if they are older than their friends, some kids may be falling behind in their academics and not yet ready to advance to a higher grade.

Depending on the school's age requirements and the student's academic standing, a 13-year-old may be in the 7th grade. A kid who is 13 years old might be in seventh grade since in many educational systems, pupils in this grade are between the ages of 12 and 13. It is usually recommended to verify with the school to clarify their age requirements because they might differ from one school system to another. The intellectual ability of a student may also play a role in establishing what grade they are in addition to their age.

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Answer:

(gf)(a)

=[g{f(a)}]

=g(3a-5)

=-4(3a-5)+5

=-12a+20+5

=-12a+25 is the right answer I think

but according to your options,

(gf)(a)

=g(a)×f(a)

=(-4a+5)(3a-5)

=-12a²+20a+15a-25

=-12a²+35a-25 which is option d.but I don't think it is the right process

Answer:

Step-by-step explanation:

The correct answer is option (D).

Given , g(a) = -4a + 5

f(a) = 3a-5

Here we have to find (gf)(a)

So,  we will replace  (gf)(a) with g(a).f(a)

= g(a).f(a) =( -4a+5 ).(3a-5)

= -4a*3a -4a*(-5)+ 3a*5+5*(-5)

= -12a2 + 20a + 15a - 25

Answer = -12a2 + 35a -25

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The relationship between the volume of a cone and a pyramid:

the volume of cone = volume of pyramid

if and only if the pyramid has circular base and both have equal radii and vertical heights

In this question we need to find the relationship between the volume of a cone and a pyramid.

We know that a pyramid is three dimensional shape with polygon base and trigular lateral faces which meet at vertex.

The formula for the volume of pyramid is,

V = 1/3 * base area * height

As we know a cone is nothing but a pyramid with circular base.

Consider a cone with radius r and vertical height h.

The formula for the volume of cone,

V = 1/3 × π × r² × h

V = 1/3 * area of circle * height

Therefore, the volume of a cone and a pyramid with circular base are equal.

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The special product formula for the 'square of a sum' is

(a + b)² = a² + 2ab + b².

(a + b)² = (a +b)×(a + b)

By applying Distributive law in multiplication, we know

(a + b)² = a×(a + b) + b×(a + b)

(a + b)² = a² + ab + ba + b²

(a + b)² = a² + 2ab + b²

For example, (3 + 2)²

We know that (3 + 2)² = 5² = 25

But let us try applying the special product formula

(3 + 2)² = 3² + 2×3×2 + 2²

(3 + 2)² = 9 + 12 + 4

(3 + 2)² = 25

So we can use this formula in cases where we don't know the square of a sum. Many applications can be seen like solving quadratic equations.

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Answer:

  ... centroid, or center of gravity.

Step-by-step explanation:

The point of concurrency of the medians of a triangle is always inside the triangle and is called the ______.

A median joins a vertex of a triangle with the midpoint of the opposite segment. It is a line segment that lies entirely within the triangle. Hence any two medians will meet at a point that is within the triangle.

The point of concurrency of medians is called the "centroid." If the triangle has uniform areal density, the centroid will be the center of gravity, the point at which the triangle could be balanced.

The centroid divides each median into parts in the ratio 1:2, where the longer part is the segment to the vertex, and the shorter is the segment to the midpoint of the side.

The simple interest earned on investing $880 at 5.25% for 2 years is $92.4

Simple interest is calculated using the formula;

SI = P × R × T

Where,

So,

SI = P × R × T

= 880 × 0.0525 × 2

= $92.4

Consequently, $92.4 is the simple interest earned on $880 at 5.25% for 2 years

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It is possible to compare the square roots of one hundred seventy and one hundred six eighths using the formulas sqrt(170) sqrt(106/8), and sqrt(170) = sqrt(106/8).

A number's square root is a value that yields the original number when multiplied by itself. The other way to square an integer is to find its square root. Squares and square roots are hence linked ideas.

Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.

For comparing them, we should always keep in mind that if square or cube roots of two numbers ('a' and 'b') are to be compared, such that 'a' is greater than 'b', then a2 will be greater than b2 and a3 will be greater than b3 and so on, i.e., nth

The square root of 170 is approximately 13.038404810405015, while the square root of 106/8 is approximately 3.2403703492039303. Therefore, the square root of 170 is greater than the square root of 106/8. This can be written as:

sqrt(170) > sqrt(106/8)

Alternatively, you can compare the two numbers using the less than (<) or equal to (=) symbols as follows:

sqrt(170) < sqrt(106/8)

sqrt(170) = sqrt(106/8)

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The square root of an integer is a quantity that, when multiplied by itself, equals the original value. Finding an integer's square root is another technique to square it. Thus, squares and square roots are related concepts.

The equation would be expressed as x=y or as x2 = y if x were the square root of y. In this case, the radical symbol for the number's root is "". By multiplying the positive integer by itself, the square of the number is represented. By taking the square root of the square of a positive number, the original number can be found.

The square root of 170 is approximately 13.038404810405015, while the square root of 106/8 is approximately 3.2403703492039303. Therefore, the square root of 170 is greater than the square root of 106/8. This can be written as:

sqrt(170) > sqrt(106/8)

Alternatively, you can compare the two numbers using the less than (<) or equal to (=) symbols as follows:

sqrt(170) < sqrt(106/8)

sqrt(170) = sqrt(106/8)

Two triangle is called SAS to each other when they have two similar side lengths along with identical angles between these two sides. SSS is called when both triangles have three similar side lengths.

Two triangles satisfy congruence theorem when they have equal corresponding side lengths and equal corresponding angles.

Triangles needed to satisfy at least one of 4 criteria. If two triangles have two similar side lengths having equal angles between these two sides. if two triangles have two equal angles along with one similar corresponding side length. If two triangles have identical 3 side lengths or two triangles which are right-angled having equal hypotenuse and an equal corresponding side.

hence, SAS and SSS are the indicator of congruent triangle.

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Without using calculator, the values are;

i. sec x = √5/2

ii. cosec x =  -√5

iii. cot x = -2

From the information given, we have that the trigonometric identity tangent takes the value;

tan x = - 1/2

Where;

Now, let's determine the hypotenuse side,

Hypotenuse square = opposite square + adjacent square

substitute the values

x² = (-1)² + (2)²

find the squares

x² = 1 + 4

x = √5

For secant,

sec x = hypotenuse/adjacent

sec x = √5/2

For cosecant,

cosec x = hypotenuse/opposite

cosec x = √5/-1 = -√5

For cot x,

cot x = Adjacent/opposite

cot x = 2/-1

cot c = -2

Hence, the values are √5/2, -√5 and -2

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The graph of the function y = x is shown and the data of the function is tabulated below.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
Let's assume the function,
f(x) = x or y = x
Now,
the graph of the function is shown,
and data is given as,
put x = 1,
so
y = 1
Similarly,

Other values can be obtained as y = 2, 3 , 4 for x = 2, 3, 4
Now the table is given as
x     y
1      1
2      2
3     3
4     4

Thus, the graph of the function y = x is shown and the data of the function is tabulated above.

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From the given expression , following represents the binomial :

Option d.  6 (a² + b).

As given in the question,

Given expressions  represents the different types of polynomial are explain as follow:

Simplify all the given options to get the binomial we have:

a. 7 × a + a

= 7a + a

= 8a it represents the monomial with single term.

b.  6a² + 7b + 2c

We cannot add these terms as all are having three different variables.

It represents the trinomial.

c. 4a × 3b × 2c

= 24abc it represents the monomial.

d.  6 (a² + b)

= 6a² + 6b represents the two terms, it is binomial.

Therefore, from the given set of expressions the option d.  6 (a² + b) represents the binomial.

The above question is incomplete , the complete question is :

Which of the following is a binomial?

(a) 7 × a + a

(b) 6a² + 7b + 2c

(c) 4a × 3b × 2c

(d) 6 (a² + b)

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Answer:

X=3

Step-by-step explanation:

7x-1=5x+5

do the same on both sides of the =

+1 to each side to get rid of the negative number

7x=5x+6

-5x from both sides

2x=6

divide by 2

x=3

Answer:

250 square feet

Step-by-step explanation:

1 1/2 = 3/2 = 1.5

1.5 pound bag = 375 square feet

Take 375 divided by 1.5 = 250 square feet

So, 1 pound of wildflower seeds will cover 250 square feet!

The solution to the system of equations, y = 7x - 3 and 7x - 6y = 18, is: (0, -3).

Given the system of equations:

y = 7x - 3 --> eqn. 1

7x - 6y = 18 --> eqn. 2

Using the substitution method, substitute y for (7x - 3) into eqn. 2:

7x - 6(7x - 3) = 18

7x - 42x + 18 = 18

-35x + 18 = 18

-35x = 18 - 18

-35x = 0

x = 0

To find the value of y, substitute x = 0 into eqn. 1:

y = 7(0) - 3

y = 0 - 3

y = -3

The solution is: (0, -3).

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Answer:

2 + (S ÷ 180)

Step-by-step explanation:

S is the sum of the measure of the interior angle measures for a polygon, while n is the number of sides.

We are given the equation S = 180(n - 2). In order to solve for n in terms of S, we must isolate the n on one side.

S = 180(n - 2) ⇒ divide both sides by 180

S ÷ 180 = n - 2 ⇒ add 2 to both sides

2 + (S ÷ 180) = n

Therefore, n = 2 + (S ÷ 180)

We need to use the concept of Plotting of Graphs.

A.(2018,62) and (2022,74) are the given points.

B. Slope=3

C. Height of Deshaun will increase 3 inches per year.

You must comprehend how the coordinate plane is organized and be aware of what to do with those (x, y) coordinates in order to graph points on the coordinate plane. Simply follow these instructions to learn how to graph points on the coordinate plane. You will graph a point in (x, y) form when you are graphing it on the coordinate plane. What you must understand is as follows:

The second coordinate is on the y-axis, while the x-axis runs left to right.

The y-axis is oriented vertically.

Positive numbers increase or move right (depending on the axis). Negative numbers move to the left or down.

Slope of a line segment=y2-y1/x2-x1 where (x1,y1) and (x2,y2) are the given points.

2018, Deshaun was 62 inches tall.

2022, Deshaun was 74 inches tall.

So assume the age on X-axis and Height on Y-axis.

A)Label the points we could use to find slope from this information:

  (2018,62) and (2022,74).

B) We know that,

    Slope=y2-y1/x2-x1

    ⇒Slope=(74-62)/(2022-2018)

    ⇒ Slope=12/4

    Slope=3.

C) As per the given slope, the height of Deshaun will increase 3 inches per year.

We need to use the concept of Plotting of Graphs.

A.(2018,62) and (2022,74) are the given points.

B. Slope=3

C. Height of Deshaun will increase 3 inches per year.

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The median for the next batch of observations is 5.

The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.

Here,

given set of observation,

=3,4,5,8,9

n=5

median=(5+1)/2

=3rd term

=5

The median for following set of observation is 5.

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A spinner simulation with an 8-section spinner and 7 trials would be appropriate.

Vince makes 75% of his free throws, so there is a 75% chance that he will make any given free throw. In order to simulate his free throw shooting and predict the probability that he will make 6 of his next 7 free throws, a spinner simulation with an 8-section spinner would be appropriate. The 8 sections would represent the possible outcomes of each free throw attempt: make or miss. The spinner would need to be spun 7 times to represent the 7 free throw attempts Vince will take. This simulation would allow Vince to see the probability of making 6 out of 7 free throw attempts based on his 75% success rate.

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The two main CPUs in laptops are called i3 and i5, and their names vary according to their level of efficiency.

In general, Core i5 CPUs perform better than Core i3 CPUs in terms of CPU performance. The Core i3 processors are all dual-core, in contrast to the dual-core and quad-core i5 CPUs. Along with cores and threads, you must also consider the processor generation.

In terms of CPU performance, Core i5 components often exceed Core i3 components. Dual-core and quad-core Core i5 CPUs are both available. When it comes to multimedia applications like video transcoding and photo editing, a true quad-core CPU will often beat a dual-core CPU.

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In the second year, the APR (Annual Percentage Rate) will increase quite substantially.

What is Introductory APR?

a temporary promotional interest rate that is lower than the card's standard APR, occasionally as low as 0% APR. Purchases, balance transfers, or both may be covered. After the introductory period has been over, your balance will be subject to the standard APR.

Any outstanding balances will begin to accrue interest once the promotional period is expired. Not just new charges, but also any amounts you charged or transferred to the credit card within the promotional APR period.

Your APR will transition from your promotional interest rate to a standard variable APR rate decided by your lender once it expires.

So, in this case, Trina's credit card has an introductory APR of 7.99-8.99%, but from the second year onwards the APR will increase.

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Following the conclusion of the promotional period, interest will start to be charged on any unpaid balances. Not only fresh charges, but also any sums you added to the credit card or transferred within the promotional APR period.

When the promotional period is up, your APR will change from the promotional interest rate to a standard variable APR rate chosen by your lender.

Thus, Trina's credit card in this instance has an introductory APR of 7.99–8.99%; but, in the second year, the APR will rise.

When given two values in algebra, it is simple to find the third value. The x value is 5.

x Multiplicand Equals Product

X = product / multiplicand

* x = 10

Product

The x value is 5.

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Step-by-step explanation:

The general quadratic equation [tex]ax^2+2hxy+by^2+2gx+2fy+c=0[/tex] represents pair of straight lines if its discriminant [tex]\Delta=0[/tex] and [tex]h^2-ab\geq0.[/tex] The discriminant of this equation is given by the determinant,

[tex]\Delta=\left|\begin{array}{ccc}a&f&g\\f&b&h\\g&h&c\end{array}\right|[/tex]

Here the given equation is,

[tex]\longrightarrow x^2+2xy+2y^2+2x+2y+1=0[/tex]

So,

[tex]a=1[/tex]

[tex]b=2[/tex]

[tex]c=1[/tex]

[tex]f=1[/tex]

[tex]g=1[/tex]

[tex]h=1[/tex]

Thus,

[tex]\longrightarrow\Delta=\left|\begin{array}{ccc}1&1&1\\1&2&1\\1&1&1\end{array}\right|[/tex]

Performing the operation [tex]R_3\to R_3-R_1[/tex] over this determinant,

[tex]\longrightarrow\Delta=\left|\begin{array}{ccc}1&1&1\\1&2&1\\0&0&0\end{array}\right|[/tex]

Now the 3rd row is completely so the discriminant is equal to zero.

[tex]\longrightarrow\Delta=0[/tex]

So our equation represents degenerate conics, which are,

pair of distinct straight lines intersecting each other at any point if [tex]h^2-ab > 0.[/tex]

pair of straight lines, either coincident or distinct but parallel to each other, if [tex]h^2-ab=0.[/tex]

a single point if [tex]h^2-ab < 0.[/tex]

We see that,

[tex]\longrightarrow h^2-ab=1^2-1\times 2=-1[/tex]

[tex]\longrightarrow h^2-ab < 0[/tex]

So our equation represents a single point.

Hence the equation does not represent pair of straight lines.