Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10< x <22

Answer:

x = -4, 1

Step-by-step explanation:

Since we have a absolute value function here, we can tell there is goning to be multiple values.

First we will find x with the original function since we know |5| = 5.

Given f(x) = 5 = -2x-3,

[tex]2x-3 = 5 \\

-2x-3+3 = 5 + 3 \\

-2x = 8 \\

x = \frac{8}{ - 2} \\ = - 4[/tex]

Now we also know that |-5| = 5 as well (absolute value)

Given |-2x-3| = |-5|,

[tex] - 2x - 3 = - 5 \\ - 2x - 3 + 3 = - 5 + 3\\ - 2x = - 2 \\ x = \frac{ - 2}{ - 2} \\ = 1[/tex]

You can verifiy these 2 values by substituting them into the equation.

f(-4) = |-2(-4)-3|

= |8-3|

= |5|

= 5

f(1) = |-2(1)-3|

= |-2-3|

= |-5|

= 5

A modulus function is defined as a function that gives positive value for either a negative or positive argument. The values of x for given condition are -4 and 1.

A function in the form of f(x) = |x| is known as a modulus function. The graph of a modulus function is symmetric about y-axis.

The function is given as,

f(x) = |-2x-3|

which implies that f(x) = -2x - 3 for x > 0 and  f(x) = -(-2x - 3 )for x < 0

As per the question ,

Substitute the value of f(x) = 5, for both the cases to get the value of x as,

-2x - 3 = 5  and -(-2x - 3 ) = 5

=> x = -4 and x = 1.

Hence, the values of x obtained for the given condition are x =-4 and x = 1.

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We want to find a prime number greater than 10 and less than 19.

* What is a prime number?

Prime number is a number that cannot be divided by any number other than 1 and itself

There are so many possibilities:

Ellie's street address could be 11, 13 or 17

Hope it helps!

The first expression is Contingency.

The second expression is Tautology.

The third expression is Contingency.

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra.

A sentence is called a contingency if its truth table contains at least one 'T' and at least one 'F. '

A statement is called a contradiction if the final column in its truth table contains only 0's.

A tautology is a statement that is always true.

The first expression is Contingency.

The second expression is Tautology.

The third expression is Contingency.

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The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.

a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904

= $126,498.08.

b) For the annuity due case; the future value is;

= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07

= (1.07) × $2000(5.43-1)/0.07

= $135, 431.43.

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The solutions to the equation on the given interval are;

x = π/4, 3π/4, 5π/4, 7π/4.

Given that;

4(sin x)² - 2 = 0

Add 2 to both sides and divide both sides 4

4(sin x)² - 2 + 2  = 0 + 2

4(sin x)²  = 2

(4(sin x)²)/4  = 2/4

(sin x)²  = 1/2

Square both sides

√((sin x)²)  = ±√(1/2)

sin x = ±√(1/2)

sin x = ±(√2)/2

Next, we solve for x

Not that 180° = π

x = sin⁻¹ ( (√2)/2 ) = 45° = 180°/4 = π/4

x = π/4

Since the sine function is positive in the first and second quadrant, we subtract the reference angle from π to find the solution in the second quadrant.

x = π - π/4

x = 3π/4

Now, we find the period of sin x

2π / |b|

We know that, the distance between a number and zero is 1

2π / 1

2π

Hence, period of sin x function is 2π, values will repeat every 2π radians in both direction.

Since sine function is negative in third and fourth quadrant,

x = 2π + π/4 + π

x = 5π/4

Now, add 2π to every negative angle to get a positive angle

x = 2π + ( - π/4 )

x = 2π×4/4 - π/4

x = ((2π × 8) - π ))/4

x = (8π - π)/4

x = 7π/4

Therefore, the solutions to the equation on the given interval are;

x = π/4, 3π/4, 5π/4, 7π/4.

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Answer:

$100.8

Step-by-step explanation:

Discount=20% of 120 =24

Before tax: BP=120-24=96

After Tax BP=105% of 96=$100.8

It is a true statement that  it  is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.

A cubic equation is one in which the highest power of the variable present is 3. A quartic equation is one in which the highest power is 4. When we have a cubic or a quartic equation, the usual approach is to reduce the equation to a quadratic equation and solve by factorization.

Thus, it  is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.

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Answer:

t=5.5

Step-by-step explanation:

The ball hits the ground when h = 0.

[tex]-16t^2 + 88t = 0 \\ \\ 2t^2 - 11t =0 \\ \\ t(2t-11)=0 \\ \\ t=0, 5.5[/tex]

However, as the answer must be positive, t=5.5

The angle of X is 108°

Given,

XW ≅ YZ

∠Z = 72°

then ∠X = ?

Properties of trapezoid are:

We know that from the figure that ∠Z = ∠V & ∠W = ∠U

∵ Isosceles trapezoid rule

And sum of all the angles in a trapezoid = 360°

Now, 2 × 72 = 144

∴ 360 ₋ 144 = 216°

Now sum of other two angles = 216°

                              one angle = 216/2

                                               = 108°

Therefore the angle of ∠X is 108°

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Parallel lines have the same slope, so since the slope of the given line is -74, the slope of the line we want to find is also -74.

Substituting into point-slope form,

[tex]y+2=-74(x-4)\\\\y+2=-74x+296\\\\\boxed{y=-74x+294}[/tex]

Keiko have $31 in her wallet.

David have $25 in his wallet.

Tony have $50 in his wallet.

Keiko

Let x = the amount in Keiko’s wallet.

David

David has $6 less than Keiko .

x - 6

Tony

Tony has has two times what David has.

2(x - 6)

The total sum of their money = 106

Keiko

x + x - 6 + 2(x - 6) = 106

2x - 6 + 2x - 12 = 106

4x - 18 = 106

4x = 106 + 18

4x /4 = 124/4

x = 31

Therefore Keiko have $31 in her wallet.

David

x - 6

31 - 6 = 25

Therefore David have $25 in his wallet.

Tony

2(x - 6)

2(31 - 6)

2(25) = 50

Therefore Tony have $50 in his wallet.

To check your work out

31 + 25 + 50 = 106

The estimated total of 674, 692, 724, and 739 is: 2800.

To find the sum using clustering estimation technique first step is to round each number to the nearest 10s.

674 into 670

692 into 690

724 into 720

739 into 740

Second step is to add

Addition=670+690+720+740

Addition=2820

2820 to the nearest 100s is 2800.

Therefore the estimated total of 674, 692, 724, and 739 is: 2800.

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Answer: [tex]6.67m^3[/tex]

Step-by-step explanation:

For hemisphere...

diameter (d1) = 3m

radius (r1) = (3/2)m

The total volume of the hemisphere

[tex]v1=\frac{2}{3} \pi (r1)^3[/tex]

[tex]=\frac{2}{3} \pi (\frac{3}{2} )^3[/tex]

[tex]=\frac{9}{4} \pi[/tex]

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

For smaller cylinder

diameter (d2) = 0.75

radius (r2) = 0.75/2m

height (h2) = 0.80m

Volume of smaller cylinder

(V2) = [tex]\frac{1}{3} \pi (r2)^2h2[/tex]

[tex]=\frac{1}{3} \pi (\frac{0.75}{2} )^2*0.80[/tex]

[tex]=\frac{3}{80} \pi[/tex]

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

For bigger cylinder

Volume of bigger cylinder =

[tex]V3=\frac{1}{3} \pi (\frac{1.25}{2} )^2*0.70[/tex]

[tex]=\frac{35}{384} \pi[/tex]

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

Volume of water =  [tex](v1 - v2 - v3) =\frac{9}{4} \pi -\frac{3}{80} \pi -\frac{35}{384} \pi = 6.67 m^3[/tex]

The explicit formula for the arithmetic sequence is: [tex]P_n = 30 + 25n[/tex]

Using the formula, we have that [tex]P_{100} = 2530[/tex].

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

From the recursive formula, we have that:

[tex]a_1 = 30 + 25 = 55, d = 25[/tex]

Hence the explicit formula is:

[tex]P_n = 55 + 25(n-1)[/tex]

[tex]P_n = 30 + 25n[/tex]

Then, when n = 100:

[tex]P_{100} = 30 + 25(100) = 2530[/tex]

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Answer:

The parallel slope for this equation is going to be [tex]\frac{3}{4}[/tex] hope that helps and can you mark me as brainlist please.

Answer:

17

Step-by-step explanation:

f(5) means replacing any x in the equation with 5, so that would give you 3*5 + 2

in order of operations, 3*5 = 15 + 2 = 17

hope this helped! :)

Answer:

D

Step-by-step explanation:

well, you can simply put the arguments where belong and if you check choice D

5(1)–2(2)=1

so that will be the answer

Answer:

[tex]\sf C. \quad \dfrac{1}{9}[/tex]

Step-by-step explanation:

Addition Law for Probability

[tex]\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]

Given:

  [tex]\sf P(A)=\dfrac{1}{3}=\dfrac{3}{9}[/tex]

  [tex]\sf P(B)=\dfrac{2}{9}[/tex]

  [tex]\sf P(A \cup B)=\dfrac{4}{9}[/tex]

Substitute the given values into the formula and solve for P(A ∩ B):

[tex]\implies \sf P(A \cup B) = P(A)+P(B)-P(A \cap B)[/tex]

[tex]\implies \sf \dfrac{4}{9} = \sf \dfrac{3}{9}+\dfrac{2}{9}-P(A \cap B)[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{3}{9}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{3+2-4}{9}[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{1}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{3}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{3+2-4}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{9}[/tex]

The computation shows that the number of possible ways will be 12.

From the information given, Mary has four t-shirts-T₁, T2, T3, and T4, and three pairs of jeans-J1, J2, and J3.

Therefore, the number of possible ways that she can choose her outfit will be:

= 4 × 3 = 12

In conclusion, the correct option is 12.

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Using the Poisson distribution, it is found that:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

The average rate is of 3 no-hitters per season, hence:

[tex]\mu = 3[/tex].

The probability that an entire season elapses with a single no-hitter is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]

There is a 0.0498 = 4.98% probability that an entire season elapses with a single no-hitter.

Seasons are independent, hence:

If an entire season elapses without any no-hitters, there is a 0.0498 = 4.98% probability that there are no no-hitters in the following season.

The probability that there are more than 3 no-hitters in a single season is P(X > 3) given as follows:

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}3^{3}}{(3)!} = 0.2240[/tex]

Then:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.6472 = 0.3528[/tex]

There is a 0.3528 = 35.28% probability that there are more than 3 no-hitters in a single season.

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The profit for the Golfing Emporium is $160.

We know that profit is defined as the difference between the revenue and the cost.

Here, we know that on the sale, the Golfing Emporium sells the set of clubs at $780 (this is the already discounted price).

While when they buy the set, the pay $620 for it.

Then the profit is given by:

P = $780 - $620 = $160

The profit for the Golfing Emporium is $160.

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The value of 1000 represent the initial population of bacteria in the study and the difference of 1200 and 1000 mean difference between the initial populations in the studies.

Exponential functions are are written as y(x) = abˣ

Here

a is the initial population

b is the rate of growth or decrease

x is the time taken

The Given exponential function is

[tex]\rm b_1(t) = 1200( 1.8 )^t\\\\b_2(t) = 1000 (1.8)^t[/tex]

From the standard equation of Exponential function

(a) a = 1200 and 1000 is the initial population of the bacteria

(b)The difference of 1200 and 1000 means the difference between the initial populations in the studies

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Fundamental Theorem of Arithmetic is not a method for solving a system of equations.

A system of equations is a collection of two or more equations with a same set of unknowns.

The system of equation can be solved using the following method.

The graphing involves using graph to find the intersection of the system of equation.

Substitution method involves substituting one variable to another.

Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations

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B. The standard deviation is he square root of variance. The larger the standard deviation the more variation

Answer:

this is quite an easy problem.

Step-by-step explanation:

The problem appears to be asking for the class with the greatest variability of test 1, which merely means that you are looking for the graph that has the most distributed test scores. The graph that shows the largest difference in each test score will be your answer.

Using the mid-point concept, the best restaurant for them to meet is given by:

Greek restaurant at (–25, –15).

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

For the midpoint between his house and his mom's, the coordinates are given as follows:

Hence the Greek restaurant is the best option, as it is closest.

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Answer:

w x 6

Because W is a variable and we don't know what W so it the equation is gonna be a open sentance

Based on the Venn diagram, the elements in set A can be found to be 2, 3 ,5, 7,and 9.

The elements in set A would be those which are in A alone and in set B as well.

The numbers in set A alone are:

7, 3, 5, 9

The number in set B and A is 2.

The elements in set A is therefore:

2, 3 , 5, 7,and 9

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Answer: (-6:5)

Step-by-step explanation:

6/5 = 1.2

-1 * 6 = -6

-6/5 = -1.2

thus...

Ratio = (-6:5)

Step-by-step explanation:

ratio of ifran and Asim= I:A

2:3

rule of equation= TOTAL ratio=total amount

=(addition of the two ratios which are 2 and 3=5) and 1000

=5=1000

ratio of ifran(2)=? cross multiplication

=2×1000÷5

=400

=5=1000

ratio of Asim(3)=? cross multiplication

=3×1000÷5

=600

Answer:

Step-by-step explanation:

Irfan and Asim's ratio is 2:3, which means Irfan gets 2 parts while Asim gets 3. There are 5 parts in total, and this equals 10000. Let parts be p. [tex]5p=10000\\\\p=2000[/tex]

This means Irfan gets 2p = 4000 and Asim gets 3p = 6000.

Hope you have a nice day and you really should mark this as the brainliest :)

Observe that the [tex]n[/tex]-th term in the sum is

[tex]\dfrac{n^2 + n(n+1) + (n+1)^2}{n^3(n+1)^3} = \dfrac{3n^2 + 3n + 1}{n^3 (n+1)^3} \\\\ ~~~~~~~~ = \dfrac{(n+1)^3 - n^3}{n^3(n+1)^3} \\\\ ~~~~~~~~ = \dfrac1{n^3} - \dfrac1{(n+1)^3}[/tex]

Then the sum telescopes, and we have

[tex]\displaystyle \sum_{n=1}^{9} \frac{n^2 + n(n+1) + (n+1)^2}{n^3 (n+1)^3} = \sum_{n=1}^{9} \left(\frac1{n^3} - \frac1{(n+1)^3}\right) \\\\ ~~~~~~~~ = \left(\frac1{1^3} - \frac1{2^3}\right) + \left(\frac1{2^3} - \frac1{3^3}\right) + \cdots + \left(\frac1{8^3} - \frac1{9^3}\right) + \left(\frac1{9^3} - \frac1{10^3}\right) \\\\ ~~~~~~~~ = \frac1{1^3} - \frac1{10^3} \\\\ ~~~~~~~~ = 1 - \frac1{1000} = \boxed{\frac{999}{1000}}[/tex]

The sum of the series is 999/1000 .

A series is a sequence of expression in a certain pattern.

The series of n terms is given

[tex]\rm \frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}[/tex]

nth term of the series is given by

[tex]\rm T_n = \rm \dfrac{n^2 + n(n+1)+ (n+1)^2}{n^3*(n+1)^3}[/tex]

On simplification it can be written as

[tex]\rm T_n = \rm \dfrac{3n^2 + 3n+1}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{3n(n +1)+1}{n^3*(n+1)^3}\\\\\\T_n = \rm \dfrac{ (n +1)^3 - n^3}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{ 1}{n^3} - \dfrac{1}{(n+1)^3}[/tex]

The sum of terms from 1 to 9 is given by

∑  ( [tex]\rm \frac{ 1}{n^3} - \frac{1}{(n+1)^3}[/tex])

= [tex]\rm \dfrac{1}{1^3} - \dfrac{1}{2^3} + \dfrac{1}{2^3} - \dfrac{1}{3^3}+ .......... + \dfrac{1}{9^3} - \dfrac{1}{10^3}[/tex]

= (1/1³) - (1/10³)

= 999/1000

Therefore the sum of the series given is 999/1000

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