The graph of the absolute value parent function, f(x) = Ixl, is stretched
horizontally by a factor of 5 to create the graph of g(x). What function is g(x)?

No issues with convergence here. If you actually expand the summand you can use the well-known Faulhaber formulas to compute the sum.

[tex]\displaystyle \sum_{i=1}^n 1 = n[/tex]

[tex]\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}2[/tex]

[tex]\displaystyle \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}6[/tex]

[tex]\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4[/tex]

and so on. You would end up with

[tex]\displaystyle L_n = \frac2n \times \frac{96-8796n^2+40283n^3-49458n^4}{n^3}[/tex]

As [tex]n\to\infty[/tex], we have [tex]L_n\to-98916[/tex].

Now, when [tex]i=1[/tex], the first term of the sum is

[tex]7(5+0)^3 - 6(5+0)^5[/tex]

so the left endpoint of the first subinterval is [tex]a=5[/tex].

At the other end, when [tex]i=n[/tex], the last term of the sum is

[tex]7\left(5+\dfrac{2(n-1)}n\right)^3 - 6\left(5+\dfrac{2(n-1)}n\right)^5[/tex]

which converges to

[tex]7(5+2)^3 - 6(5+2)^5[/tex]

so the left endpoint of the last subinterval converges to [tex]b=5 + 2 = 7[/tex].

From here it's quite clear that [tex]f(x)=7x^3-6x^5[/tex]. So, the Riemann sum converges to the definite integral

[tex]\boxed{\displaystyle \int_5^7 (7x^3 - 6x^5) \, dx}[/tex]

The length of the line AB as described by points A and B in the task content is; √125.

a) The length of AB as described is;

AB = √((7-2)² + (4-(-6))²)

AB = √(25 + 100) = √125.

b) The slope of AB is;

Slope, m = (7-2)/(4-(-6)) = 5/10

Slope = 1/2.

c). The coordinates of the midpoint of AB are;

x = (4+(-6))/2 = -1

y = (7+2)/2 = 4.5

The midpoint is; (-1, 4.5).

2) The radius of the circle as described with centre (0, 0) that passes through the point (5, –3) is;

Radius = √((5-0)² + (-3-0)²)

Radius = √(25+9) = √34 = 5.8

3) Hence, the equation of a circle with centre (0, 0) that passes through the point (5, –3) is;

(x-5)² + (x-3)² = 5.8².

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Answer:

15

Step-by-step explanation:

5x+13+11x-73=180°( co-interior angles sum is 180)

5x+11x+13-73=180°

16x-60=180

16x=180+60

16x=240

x=15

For a randomly chosen Monday, the probability there will be less than 340 column inches of classified advertisement is 0.8413.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with a population mean of 320 and a population standard deviation of 20 inches.

[tex]P(X < 340) = P(z < \dfrac{(340-320)}{20})[/tex]

                    =  P(z < 1)

                    = 0.8413

Hence, For a randomly chosen Monday, the probability there will be less than 340 column inches of classified advertisement is 0.8413.

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Answer:

30%

Step-by-step explanation:

[tex]\frac{145}{500} = 0.29[/tex] ≅ 0.30 or 30%

Answer:

m∠V = 28°

Step-by-step explanation:

In ΔUVW:

To find the measure of angle V, first find the value of x.

Interior angles of a triangle sum to 180°.

⇒ m∠U + m∠V + m∠W = 180°

⇒ (9x - 8) + (2x + 2) + (3x + 4) = 180

⇒ 9x + 2x + 3x - 8 + 2 + 4 = 180

⇒ 14x - 2 = 180

⇒ 14x = 182

⇒ x = 13

Substitute the found value of x into the expression for angle V:

⇒ m∠V = 2(13) + 2

⇒ m∠V = 26 + 2

⇒ m∠V = 28°

Therefore, the measure of angle V is 28°.

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Answer:

75% or 65%

Step-by-step explanation: that's what I did at lest

Step-by-step explanation:

The answer is D)

b^10/b^2

= b^10-b^2 = b^8

hope this helps.pls like and follow if you understand.

thanks:-):-)

Answer:

13. m∠MN + m∠NMP = m∠MP.

14. m∠NMP - m∠OMP = m∠NMO.

~

15. x = 3 + y and -2y + 3 < -1 : Given

16. x > y : x = 3 + y

17. -2y < -4 : -2y < -4

18. y > 2 : y > 2

19. x > 2 : x = 3 + y and y > 2

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

20/63

Step-by-step explanation:

Use Keep Change Flip so your question would become 4/3 multiplied by 5/21

Answer:

20/63

Step-by-step explanation:

[tex]\frac{4}{3} /\frac{21}{5} =\frac{(4)(5)}{(3)(21)} =\frac{20}{63}[/tex]

Hope this helps

The measure of ST based on the diagram regarding the circle is 56°.

Fron the information given, angle S is equal to 34°. Also, the triangle is inscribed in a circle.

Therefore, the measure of the angle will be:

= 180 - 90 - 34

= 56°

Therefore, the measure of angle ST is 56°.

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The required blank 1, blank 2 and blank 3 would be filled with 25 girls, 22 girls, 19 girls respectively.

Theatre company must cast 3 girls.
And has 25 resumes girls who wish audition.

permutation can be defined as study of combinations.

In the question we are asked to calculate the number of girls left after the director chooses.
At first director chooses 3 from 25.
At second director chooses 3 from 22.
At third director chooses 3 from 19.

Thus, the required  blank 1, blank 2 and blank 3 would be filled with 25 girls, 22 girls, 19 girls respectively.

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Answer:A person or thing that is different from other people or things.

Like me and you we might like different things like I like playing games you dont your the opposite of me.

A real world situation would be looking at maybe plants see how different they look or if they look the same study them and realize one is poison the other is fresh.

Step-by-step explanation:

Answer:

  A. No.

Step-by-step explanation:

The job of science is to explain relationships in the real world. Scientists do this by making observations, forming theories regarding relationships, and conducting experiments to test those theories.

An observation of correlation may result in a theory that one of the correlated phenomena causes another. The correlation, by itself, does not demonstrate causation. Any number of other factors could be involved.

The radius of the circular vase is 6.37 * 10^-3 m.

The term pressure is defined as the ratio of force to area. Hence we can write;

P = F/A

F =  15 N

P = 750 N/m2

A = F/P

A = 15 N/750 N/m2

A = 0.02 m^2

Now;

A = πr^2

r = √A/ π

r = √ 0.02/3.142

r = 6.37 * 10^-3 m

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The part of the proof regarding the triangle that is incorrect is By the Congruent Complements Theorem AMB CMD.

From the information given, it should be noted that AMC is a right angle and also that BMD is a right angle.

Therefore, it illustrates that AMC and BMD are equal.

Therefore, by the Congruent Complements Theorem AMC and BMD are equal.

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Answer:

is it asking how many times u would get then number 5 when u roll or asking how you would expect for the first 5 rolls?

C

when doing substitution,you must make one a subject,which is y in this case.To make y the subject,you must move -2y to 4x to make the y positive,that leaves us with 2y+4x=5.Now move the 4x to 5 to make 2y=5-4x.Lastly,to make y the subject,divide both side by 2 to remove the 2 from the y, which leaves us with y=5-4x/2

By Green's theorem,

[tex]\displaystyle \int_C P(x,y)\,dx + Q(x,y)\,dy = \iint_D \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \, dA[/tex]

where [tex]D[/tex] is the interior of [tex]C[/tex]. It's easy to see that

[tex]D = \left\{(x,y) ~:~ 1 \le x \le 3 \text{ and } 1 \le y \le 4\right\}[/tex]

Now,

[tex]\dfrac{\partial Q}{\partial x} = \dfrac{\partial}{\partial x}(-x^2) = -2x[/tex]

[tex]\dfrac{\partial P}{\partial y} = \dfrac{\partial}{\partial y}(\ln(x) + y) = 1[/tex]

so that the line integral reduces to

[tex]\displaystyle \int_C (\ln(x)+y)\,dx - x^2\,dy = -\int_1^3 \int_1^4 (2x+1) \, dy\,dx = \boxed{-30}[/tex]

Answer:

Step-by-step explanation:

ABCD moves 2 quadrants, so has to move over 2 axes.

So, the only option that would work is A).

Hope this helps.

It would take about  8 hours 20 minutes for the 1000 mL of D5W to infuse completely.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the drop factor is 10 gtt/mL, hence:

Infuse rate = 20 gtt/min ÷ 10 gtt/mL = 2 mL/min

Time taken = 1000 mL / 2 mL per min = 500 min = 8 hours, 20 minutes.

It would take about  8 hours 20 minutes for the 1000 mL of D5W to infuse completely.

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Answer:

Step-by-step explanation:

900mL of RL is infusing at 80 gtt/min (80 macrodrops/min). Drop factor: 15 gtt/mL

From the values in the table,  we can say that the first graph is the correct one that shows some values for the given equation.

We are given the quadratic equation as;

y = x² - 1

From the given table;

At x = -2, y =  (-2)² - 1 = 3

At x = -1, y = 0

At x = 0, y = -1

At x = 1, y = 0

Now, from the values above, we can say that the first graph is the correct one that shows some values for the given equation.

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By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.

In order to determine the length of side BD, we would apply the law of sine because both side BD and side BC represent the opposite side and hypotenuse of right-angled triangle BCD respectively.

Mathematically, the law of sine is given by this mathematical expression:

sin(θ) = Opp/Hyp

Where:

Substituting the parameters into the formula, we have;

sin(θ) = BD/BC

sin(74) = BD/9.41

Cross-multiplying, we have:

BD = 9.41 × sin(74)

BD = 9.41 × 0.9613

BD = 9.05 cm.

By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.

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Answer:

m<A = 20°

Step-by-step explanation:

360  160 = 200

m<A = (1/2)(200° - 160°)

m<A = 20°

Answer:

[tex]k=2[/tex]

Step-by-step explanation:

The constant of proportionality is given as  [tex]k=\frac{y}{x}[/tex] .

Notice that when [tex]x=2[/tex] it follows that [tex]y=4[/tex].

Substitute [tex]x=2[/tex] and [tex]y=4[/tex] into the formula for the constant:

[tex]k=\frac{4}{2}=2[/tex] .

Therefore, the constant is equal to 2.

Answer:

(x' , y') = ( (x ± 1) , (y ± b) )

Step-by-step explanation:

(object vector) = (x', y')

(translation vector) = ( ±1 , ±b ) ==> Since horizontal movement (x) is right/ or left meaning ±1 , and vertical movement(y) is up or down meaning ±b

Notice that  :  (image vector) = (object vector) + (translation vector)

therefore        (x' , y') = ( (x ± 1) , (y ± b) )

The number of chocolate which goes into the small boxes is 100 chocolate

= 3x + 6x

= 9x

x + 3x + 9x = 1296

13x = 1296

x = 1296/13

x = 99.6923076923076

Approximately,

x = 100 boxes

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The equation based on the information given will be x⁴ + 8x² - 12.

It should be noted that from the information given, the expression to compute will be:

= g - g(x)²

This will be:

= 4 - (4 - x²)²

= 4 - (4 - x)(4 - x)

= 4 - (15 - 8x² + x⁴)

= x⁴ + 8x² - 12

The complete question is:

Use f(x) = 2x − 3 and g(x) = 4 − x² to evaluate the expression g - g(x)².

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