Need help with number 3 inequalities with variables on both sides

The sum of the first 30 terms of the arithmetic series is 1560

From the question, we are to determine the sum of the first 30 terms of the series

Using formula,

[tex]S_{n} = \frac{n}{2}(a + l)[/tex]

Where [tex]S_{n}[/tex] is the sum of the nth term

n is the number of terms

a is the first term

and [tex]l[/tex] is the last term

From the given information,

n = 30

a = 3

[tex]l[/tex] = 101

Thus,

[tex]S_{30} = \frac{30}{2}(3+ 101)[/tex]

[tex]S_{30} = 15(104)[/tex]

[tex]S_{30} = 15 \times 104[/tex]

[tex]S_{30} = 1560[/tex]

Hence, the sum of the first 30 terms of the arithmetic series is 1560

Learn more on Sum of an Arithmetic progression here: https://brainly.com/question/24295771

#SPJ1

Answer:

1. (x + 8)(x + 3)

2. (x - 9)²

Step-by-step explanation:

Given trinomials:

1. [tex]x^2+11x+24[/tex]

2. [tex]x^2-18x+81[/tex]

..................................................................................................................................................

When factoring trinomials of the form ax² + bx + c:

..................................................................................................................................................

1) x² + 11x + 24

Step 1: Multiply the leading coefficient (1) and the last term (24).

[tex]\implies 1 \times 24 = \boxed{24}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (11).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:24 & \sf Sum\:of\:factors\\\cline{1-2} 1, 24\ \| -1, -24 & 25\ \| -25 \\\cline{1-2} 2, 12\ \| -2, -12 & 14\ \| -14 \\ \cline{1-2} 3, 8\ \| -3, -8 & 11\ \| -11 \\\cline{1-2} 4, 6 \ \| -4, -6 & 10\ \| -10 \\\cline{1-2}\end{array}[/tex]

[tex]\implies 3x+8x=11x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2+3x+8x+24[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2+3x)}^x+\overbrace{(8x+24)}^8\ \ \textsf{[ Factor out $x$ and $8$. ]}[/tex]

[tex]\implies x\overbrace{(x+3)}^{\textsf {Factor out}}+8(x+3)[/tex]

[tex]\implies \boxed{(x+8)(x+3)}[/tex]

The factored form of the given trinomial is [tex](x+8)(x+3)[/tex].

..................................................................................................................................................

2) x² - 18x + 81

Step 1: Multiply the leading coefficient (1) and the last term (81).

[tex]\implies 1 \times 81 = \boxed{81}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (-18).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:81 & \sf Sum\:of\:factors\\\cline{1-2} 1, 81\ \| -1, -81 & 81\ \| -81 \\\cline{1-2} 3, 27\ \| -3, -27 & 30\ \| -30 \\ \cline{1-2} 9, 9\ \| -9, -9 & 18\ \| -18 \\\cline{1-2}\end{array}[/tex]

[tex]\implies (-9x)+(-9x)=-18x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2-9x-9x+81[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2-9x)}^x+\overbrace{(-9x+81)}^{-9}\ \ \textsf{[ Factor out $x$ and $-9$. ]}[/tex]

[tex]\implies x\overbrace{(x-9)}^{\textsf {Factor out}}-9(x-9)[/tex]

[tex]\implies (x-9)(x-9)[/tex]

[tex]\implies \boxed{(x-9)^2}[/tex]

The factored form of the given trinomial is [tex](x-9)(x-9)\ \textsf{or}\ (x-9)^2[/tex].

The are of the triangle is mathematically given as

a=62.4in^2. This is further explained below.

Generally, the equation for the area is  mathematically given as

a= 0.5(base X height)

Therefore

a= 0.5 (10.4 x 12)

a=62.4in^2

In conclusion, The area of the triangle is

a=62.4in^2

Read more about area

https://brainly.com/question/27683633

#SPJ1

The time, date and the day when the journey finished is 2:30 pm on Thursday 9th January

68 hours = 68/24

= 2 days and 20 hours

6;30 pm on Monday 6th January + 2 days and 20 hours

= 2:30 pm on Thursday 9th January

Learn more about time:

https://brainly.com/question/25800303

#SPJ1

N-acetyltyrosine ethyl ester may likely have a higher Vmax.

Km is inversely proportional enzyme affinity for substrate. The lower the Km, the higher the enzyme affinity for substrate and vice versa.

Vmax is the maximum velocity of the reaction when the enzyme is fully saturated with substrate.

Based on the Km values, chymotrypsin has higher affinity for N-acetyltyrosine ethyl ester, thus, N-acetyltyrosine ethyl ester may likely have a higher Vmax.

In conclusion, the Vmax is the maximum velocity of an enzyme-catalyzed reaction.

Note that the complete question is given below:

The Km for the reaction of chymotrypsin with N-acetylvaline ethyl ester is 8.8 x 10-2 M, and the Km for the reaction of chymotrypsin with N-acetyltyrosine ethyl ester is 6.6 x 10-4 M.

Which of the following substrates is likely to give a higher value for Vmax?

Learn more about Km and Vmax at: https://brainly.com/question/16108691

#SPJ1

Total possible outcomes are 312

We need to find that if you roll a 6-sided die and draw a card from a deck of 52 cards,what are total possible outcomes

Probability is a measure of the possibility that an event will occur. Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it. Probability can range from 0 to 1, where 0 means an event is impossible and 1 means a certain event

An outcome is the result of an event that depends on probability. Probability refers to the likelihood that something will happen, and an event can have more than one possible outcome.

Enumeration of possible outcomes is the process of determining the number of possible outcomes for an event. There are various methods to carry out this process. The best way to calculate the number of possible outcomes of an event depends on the type of event and the structure of the event

If a 6-sided die and draw a card from a deck,

then each side has total possible outcome 52

so, total number of possible outcomes for 6 - sided dice are 52 * 6

= 312

Hence total number of possible outcomes are 312

Learn more about possible outcomes here:

https://brainly.com/question/28052707

#SPJ4

The null hypothesis be is =15 and the alternative hypothesis be  is ≠15

According to the statement

Mean length of time on death row is 17.4 years

Standard deviation of 6.3 years.

Now we determine the hypothesis with mean time 15 years then

P value outcome is 0.00015

So, The null hypothesis be  is =15 and the alternative hypothesis be is ≠15

Learn more about HYPOTHESIS here https://brainly.com/question/12416923

#SPJ4

The reasonable value for the range of the given function is: A. 75.

The range of a function is the output that a corresponding input value would give as a relation.

In this scenario, the grade you get is a function of number of hours you study. Range is the grade (output), while the domain is hours of study (input).

The given possible range values in the options are, 75, 1.25, -30, 1/2.

A reasonable value of a a grade cannot be a negative number, neither can it be 1.25, nor 1/2.

Therefore, the reasonable value of the range is: A. 75.

Learn more about the range of a function on:

https://brainly.com/question/7644636

#SPJ1

An analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.

Therefore, an analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.

Know more about a parameter here:

https://brainly.com/question/2292917

#SPJ4

Answer:

-1728:512

Step-by-step explanation:

(-12)³ = -1728

8³ = 512

ratio is -1728:512

Answer:

the side length of hypotenuse is 16.28

Step-by-step explanation:

[tex]a^{2}+b^{2}=c^{2}[/tex]

= [tex]11^{2}+12^{2}= C^{2}[/tex]

= [tex]121+144=c^{2}[/tex]

= [tex]265= c^{2}[/tex]

= [tex]\sqrt{265} = c[/tex]

= [tex]c = 16.28\\[/tex]

Answer:

A = 42.5° (nearest tenth)

B = 47.5° (nearest tenth)

C = 90°

a = 11

b = 12

c = √(265) = 16.3 (nearest tenth)

Step-by-step explanation:

Information:

Side a is opposite angle A.

Side b is opposite angle B.

Side c is opposite angle C.

From inspection of the triangle:

To find the missing side length, use Pythagoras Theorem:

Pythagoras Theorem

a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle).

Substitute the given values of a and b into the formula and solve for c:

⇒ 11² + 12² = c²

⇒ 121 + 144 = c²

⇒ c² = 265

⇒ c = √(265)

To find one of the missing angles, use the Sine Rule.

Sine Rule

[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Substitute the given values into the formula:

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin B}{12}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]

Solve for angle A:

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{1}{\sqrt{265}}[/tex]

[tex]\implies \sf \sin A=\dfrac{11}{\sqrt{265}}[/tex]

[tex]\implies \sf A=\sin^{-1} \left(\dfrac{11}{\sqrt{265}}\right)[/tex]

[tex]\implies \sf A=42.51044708...^{\circ}[/tex]

Therefore, A = 42.5° (nearest tenth)

Interior angles of a triangle sum to 180°:

⇒ A + B + C = 180°

⇒ 42.5° + B + 90° = 180°

⇒ B + 132.5° = 180°

⇒ B = 47.5°

Learn more about angles in triangles here:

https://brainly.com/question/27648540

https://brainly.com/question/28033514

The equation which can be used to determine x, the number of players the team can bring to the

tournament is 1353 = 943.50 + 31.50x and x = 13 players

1353 = 943.50 + 31.50x

1353 - 943.50 = 31.50x

409.50 = 31.50x

x = 409.50 / 31.50

x = 13 players

Learn more about equation:

https://brainly.com/question/13763238

#SPJ1

The area of the shaded region is B. 52 square inches.

It should be noted that the shaded region is in the shape of a rectangle.

Length = 18 - 4 - 1= 13 inches

Width = 6 - 2 = 4 inches

The area is:

= Length × Width

= 13 × 4

= 52 inches²

Learn more about area on:

brainly.com/question/25292087

#SPJ1

Answer:

In math, calculus deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two basic types of calculus are differential calculus and integral calculus.

Step-by-step explanation:

hope it helps

sorry if I'm wrong

The additional information needed to determine that ABCD is a parallelogram is: A. AB ≅ CD.

One of the criteria for proving that a quadrilateral is a parallelogram is that one of the pairs of opposite sides are congruent and also parallel to each.

We are already given that side AB is parallel to side CD, therefore, the additional information we would need to prove that quadrilateral ABCD is a parallelogram is: A. AB ≅ CD.

Learn more about parallelogram on:

https://brainly.com/question/3050890

#SPJ1

Answer:

y= -1/3x + 1

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y= -1/3x + 1

Answer:

(C)=22.5

Step-by-step explanation:

Hi! ❄

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

First, let's subtract by 23 both sides.

[tex]\sf{\dfrac{3}{2}c=15}[/tex]

Now we multiply the equation by 2.

[tex]\sf{3c=30}[/tex]. See how on the left hand side, the 3/2c*2 turned into 3c? That's because multiplication and division are operations that undo each other.

And Now we just divide by 3 both sides.

[tex]\sf{c=10}[/tex]

Hope this made sense !!

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

[tex]\star\tiny\pmb{calligraphy}\star[/tex]

The lateral area of the given pyramid is 108 cm².

Any three-dimensional figure's lateral surface area is its side surface area.

In the question, we are asked to find the lateral area of the given pyramid, whose base is a regular hexagon, with a side length of 3 cm, and the slant height of the pyramid is 12 cm.

To determine the lateral area, we determine the area of one lateral face, and then multiply it by the number of lateral faces in the pyramid.

The number of lateral faces = sides of the base = 6 {Since the base is a regular hexagon}.

Area of a lateral face = (1/2)*base*height {Since its a triangle},

or, area of a lateral face = (1/2)*3*12 {Since the base is the side length of the base, and the height is the slant height},

or, area of a lateral face = 18 cm².

Thus, the lateral area of the pyramid = 6 * 18 cm² = 108 cm².

Thus, the lateral area of the given pyramid is 108 cm².

Learn more about lateral areas at

https://brainly.com/question/12736338

#SPJ4

The coterminal angles are given as follows:

a) 0º.

b) 120º.

The coterminal angle of a negative angle between 0 and -360º = -2pi is found adding 360º = 2pi to the angle, hence:

-2pi + 2pi = 0, which is the answer to item a.

The coterminal angle is found taking the remainder of the division of the angle by 360º.

The remainder of the division of 480º by 360º is of 120º, hence the coterminal angle of 480º is of 120º.

More can be learned about coterminal angles at https://brainly.com/question/23093580
#SPJ1

Answer:

10%.

Step-by-step explanation:

There are a total of 40 numbers.

Number of permutations of 3 numbers from 40

= 40 P 3

= 40! / (40-3)!

= 59,280.

The total of even numbers is (38 - 2) / 2 + 1 = 19.

Number of permutations of 3

=  19P 3

=  5814

So Prob(all even) = 5814/59280

= 0.098077

= 9.8%

= 10% to nearest whole number.

A simple main effect analysis looks at the mean difference at each level of the independent variable.

Given With a simple main effect, the analysis examines.

Simple effects are also called the main effects of design of experiments. The main effect can be defined as the effect of the explanatory variables measured on a particular criterion or response variable of the study. It's easy to say that what happens within the level of the explanatory variables is the difference. In a factorial experiment, the simple main effect is that one independent variable is at a specified level of another. The main effect of one independent variable is averaged across the levels of the other independent variable. For a simple main effect, the results are analyzed as if a separate experiment was performed at each level of the other independent variables.

Therefore, a simple main effect analysis looks at the mean difference at each level of the independent variable.

Learn more about analysis from here brainly.com/question/15179003

#SPJ4

===================================================

Explanation:

If it increases by 5%, then we use the multiplier 1.05

Think of it like saying 100% + 5% = 1 + 0.05 = 1.05

Similarly, an increase of 20% means we involve 1.20

Combine those multipliers to get: 1.05*1.20 = 1.26

This is a net increase of 26%

Interestingly, we get fairly close to 25% which is what many students might go for (since 5 + 20 = 25). This is a beginner's trap.

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

An example:

Let's say the temperature is 20 degrees Celsius (68 degrees Fahrenheit)

An increase of 5% means it moves to 1.05*20 = 21 degrees C

A 20% increase means we go to 1.20*21 = 25.2 degrees C

The shortcut would be to do a 26% increase to get 1.26*20 = 25.2 to help confirm we have the correct combined increase.

Answer:

6 hours.

Step-by-step explanation:

Speed = distance / time.

Carla travels  3 * 12 = 36 miles before Zari leaves the shop.

So Zari travels x miles in the same time as Carla travels x- 36 miles.

So 18 = x/t and 12 = (x - 36)/t

From first equation x = 18t so we have the equation

12 = (18t - 36/t

18t - 36 = 12t

6t = 36

t = 6 hours.

Answer:

104 miles.

Step-by-step explanation:

5 inches is 2 * 2.5 inches so the distance required is 2*52 = 104 miles.

Answer:

[tex]\frac{\sqrt{3} }{6}[/tex]

Step-by-step explanation:

using the 30- 60- 90 triangle for exact values , then

tan60° = [tex]\sqrt{3}[/tex] , and

cot60° = [tex]\frac{1}{tan60}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]

cos60° = [tex]\frac{1}{2}[/tex]

cot60° cos60°

= [tex]\frac{1}{\sqrt{3} }[/tex] × [tex]\frac{1}{2}[/tex]

= [tex]\frac{1}{2\sqrt{3} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= [tex]\frac{1}{2\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= [tex]\frac{\sqrt{3} }{6}[/tex]

The answer is [tex]\boxed {\frac{1}{2\sqrt{3}}}[/tex]

The needed trigonometric values :

Hence, the value of the expression is :

p→r

The law of syllogism, also known as transitivity reasoning, is a legitimate kind of deductive reasoning that adheres to a predetermined pattern. The transitive property of equality states that if a = b and b = c, then a = c. so we can conclude that The law of syllogism is almost  similar to the transitive property.

now if we want to define general case then we can say tha

a→b

and

b→c  => a→c

now according to statements given in the problem

p→q and q→r ⇒ p→r

which completes the syllogism.

hence ,  p→r is the required answer.

learn more about syllogism here:

https://brainly.com/question/5142648

#SPJ4

14) theorem

15) sides

16) separately

17) equilateral

18) supplementary