3. (a.) The 12th term of a linear sequence is 74 and the sum of the first three terms is 42, Find (i.) the first term and the common difference (ii.) the sum of the first 10th terms of the sequence. pls answer it is urgent pls​

The value of <RQZ has been calculated as 21 from the solution we have below.

We have

< PZQ= <PQZ

PQR - PRQ = 42

Let < PZQ = y⁰

PQZ = y⁰

Let PRQ = x⁰

< PQR = x + 42⁰

< QpZ + y + y = 180⁰

such that

QPZ + 2y = 180⁰

<QPZ = 180⁰ - 2y

<(QPZ + PQR + PRQ) = 180

Adding these equations, we would have

180 - 2y + x + 42 + x = 180⁰

180 would cancel out

We have

2x - 2y + 42 = 0

x- y +21 = 0

We have to add 21 to both sides of the equation

x- y + 42 = 21

(x + 42) - y = 21

(x + 42) = <PQR and y = < PQZ

Hence 21 = <RQZ

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The expression given in the task content can be evaluated and simplified to be equal to; sin²(x).

It follows from the task content that the result of the product given is to be determined.

Hence, the multiplication is as follows;

1 -cos(x) +cos(x) -cos²(x).

1 -cos²(x).

However, since sin²(x) + cos2(x) = 1; it therefore follows that;

1 -cos²(x) = sin²(x)

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The range of scores for 95% of the class is 63.8 to 86.6 using the empirical rule.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations.

The empirical rule specifically states that 68 percent of data will fall inside the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.

According to the question,

μ=75.2  and σ=5.7

So, according to the empirical rule, the range of scores for 95% of the class:

μ – 2σ =75.2-2*5.7=63.8

and μ + 2σ=75.2+2*5.7=86.6

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Answer:

37

Step-by-step explanation:

Let's use the rule GEMDAS (Grouping, Exponents, Multiply, Divide, Add, Subtract) from left to right. Therefore, we will simplify the equation in the parentheses. [tex]2^{3} = 8. (1-8= -7)[/tex]. -(-7) creates a double negative, deeming the 7 positive, because when there is two negatives the number will turn into a positive. [tex]7^{2}[/tex] = 49, -3 x 4= -12. Therefore the final form of the equation will be 49 - 12 = 37.

Let me know if there are mistakes.

The only wrong spot would be box 1 because the graph is not decreasing over the longest interval.

In the first graph, we see that the y-intercept which is the point where the curve crosses the y-axis is at y = -1. However, the interval for which it is decreasing is from x = -1 to x = 0.5.

For the second table, we see that the y-intercept is -1 and that as values of x keeps increasing, g(x) becomes more negative. Thus, it is decreasing on the longest interval.

For the third function which is;

h(x) = 3 + 4x³

The y-intercept is 3.

However, the higher the value of x, the greater the function.

Thus, the only wrong spot would be box 1 because the graph is not decreasing over the longest interval.

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The equation for the trend line in the scatter plot will be Y= 5x-1. Option B is correct.

In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.

When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.

The graphs are attached in the attachment.

The equation for the trend line in the scatter plot will be Y= 5x-1.

Hence, option B is correct.

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Step-by-step explanation:

sinA=sinA

sin2A

(sinA)2

Answer:

Choice A

Step-by-step explanation:

[tex] \rm \: a {}^{2} \{ \cdot \: \cfrac{1}{a {}^{ \frac{2}{3} } \ } \}[/tex]

Applying Distributive property;

Choice A is accurate.

Hello,

x⁴ + 12x³ - 64x² = 0

x²(x² + 12x - 64) = 0

x² = 0 or x² + 12x - 64 = 0

x = 0

∆ = b² - 4ac = 12² - 4 × 1 × (-64) = 400

x1 = (-b -√∆)/2a = (-12 - 20)/2 = -32/2 = -16

x2 = (-b + √∆)/2a = (-12 + 20)/2 = 8/2 = 4

S = {-16 ; 0 ; 4 }

→ factorizacion de x⁴ + 12x³ - 64x² : x(x - 4)(x + 16)

The solutions to this triangle are:

Using the law of cosine we would have

a²=b²+c²-2bc cos A

a² =100+49-2(10)(7)cos 52

This would give us

=149 -140 x (0.6157)

=62.82

We take the square root of 62.82 =

7.93 or 7.9

We have to use the sine law to find the other side

7.9/sin 52=10.057

10.06=7/sin C

such that

sin C = sin(0.6958)

=44.1°

10.06=10/sin B

cross multiply

sin B=10/10.06

= sin⁻¹0.9940

Then B = 83.7°

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Answer:

Step-by-step explanation:

[tex]if A+B=45\\tan(A+B)=tan(45)\\\dfrac{tanA+tanB}{1-tanA.tanB}=1\\ \implies tanA+tanB=1-tanA.tanB\\\frac{1}{cotA}+\frac{1}{cotB}=1-\frac{1}{cotA}\frac{1}{cotB}, \{tanX=\dfrac{1}{cotX} \}\\ cotA+cotB=cotA.cotB-1\\cotA.cotB-cotA-cotB=1.[/tex]

Answer:

b=136, c=44, d=44

Step-by-step explanation:

B is the same measure as A. C = D and A+B+C+D=360; C+D=88; C=44; D=44

Answer:

B. Yes, she used systematic random sampling

Explanation :

Systematic random sampling is method of sampling use in term of finding the the percent of a given population to find the final sample.

No, we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

Given mean of 15.5 minutes , standard deviation of 1.7 minutes, sample size of 90 and sample mean of 15.4 minutes.

We can do the following study for conclusion:

Firstly the null hypothesis is

[tex]H_{0}: x=15.5[/tex]

The alternate hypothesis is

[tex]H_{1}: x < 15.5[/tex]

since the value is less than this is a one tailed test.

Z=x bar-x/d/[tex]\sqrt{n}[/tex]

where x is sample mean and d is standard deviation.

Z=15.4-15.5/1.7/[tex]\sqrt{90}[/tex]

=-0.1/1.7/9.4868

=-0.560

Critical value of Z at 0.1 level of significance

Z=-1.28

We fails to reject the null hypothesis since -0.560>-1,28

Hence we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

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Question is incomplete. It should include:

mean of 15.5 minutes ,

standard deviation of 1.7 minutes,

sample size of 90

and sample mean of 15.4 minutes.

Answer:

Step-by-step explanation:

The formula for circumference is 2(3.14)r

So, we divide 141.3 by 6.28 and get 22.5

The radius is 22.5 feet.

True, a circle can be circumscribed about the quadrilateral described in the task content.

It follows from the task content that quadrilateral in discuss has angles; 95, 80, 85 and 100.

By convention, it follows that circles can be circumscribed about only cyclic quadrilaterals in which case their opposite angles are supplementary. Hence, since opposite angles of the quadrilateral are supplementary (i.e amount to 180). Then, True, the circle can be circumscribed about the quadrilateral.

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Answer:

4

Step-by-step explanation:

[tex] \frac{15}{20} = \frac{x + 2}{12 - x} \\ \\ 180 - 15x = 20x + 40 \\ \\ 35x = 140 \\ \\ x = 4[/tex]

The time taken by the stone to fall in air is 7 seconds and the time taken in water is 5 seconds.

Speed is the distance covered by an object in a fixed period of time. It is measured in m/sec.

The average speed in air is 16m/sec.

The average speed in water is 33m/sec.

The total time taken is 12 seconds.

Total distance covered =  Total time taken * speed at which it covered the distance

Let the time taken to fall in air is t

So, the time taken in water will be 12-t

The total distance is equal to

127 = 16*t + 3(12-t)

127 = 16t + 36 - 3t

127 - 36 = 16t - 3t

91 = 13t

t = 91/13 = 7 seconds

12-t = 12-7 =5 seconds

Therefore, the time taken by the stone to fall in air is 7 seconds and the time taken in water is 5 seconds.

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Answer:

f(-3) =8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer

f(x) has the same meaning as y. So you could rewrite the question as "What value of x gives y a value of 8"

The graph tells you that x = - 3 when y = 8.

f(-3) = 8

Answer:

0.1?

58

146,000?

22600

Step-by-step explanation:

So I assume first is 1st decimal place, so that would be the first after the decimal and then the number after has to be 5 or above, which it is. So then its just 0.1

This is easy, look at the decimal, its below .5, so 58.

Same thing for the rest, just look at the digit before.

The linear are said to be parallel.

Collinear points are the points that lie on the same straight line or in a single line.

Given:

slope= 3

If two non co-linear segments with a slope of 3 in a coordinate plane, which means that the two line segments are parallel to each.

So, the same slope symbolise the  concept of parallel line in same plane.

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Answer:

16a^2b^2

Step-by-step explanation:

An exponent that is over a whole entire fraction can be split up and put separately onto the numerator (top number) and denominator (bottom number) See image.

Then you can get rid of a negative exponent (make it positive) by moving the whole term across the fraction bar. The top moves to the bottom and the bottom moves to the top. See image.

In the term (4ab)^2, the exponent 2 can be passed out to the 4 and the a and the b. See image.

Answer: D

Step-by-step explanation:

Answer:

x = -4.5

Step-by-step explanation:

Solving the equation :

[tex]\left\vert -4+\frac{5}{2} \right\vert -\left( -x\right) =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-8}{2} +\frac{5}{2} \right\vert +x =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-8+5}{2} \right\vert +x =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-3}{2} \right\vert +x =-3[/tex]

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

[tex]\Longleftrightarrow x =-3-\frac{3}{2}[/tex]

[tex]\Longleftrightarrow x =-\frac{6}{2} -\frac{3}{2}[/tex]

[tex]\Longleftrightarrow x = -(\frac{6}{2} +\frac{3}{2} )[/tex]

[tex]\Longleftrightarrow x =-\frac{9}{2}[/tex]

[tex]\Longleftrightarrow x =-4.5[/tex]

A

this question did by quadratic formula means x = -b ± √b^ - 4ac / 2a by this formula first arrange the equation -5 x^ + 7 -2 and

a = -5

b = 7

C = -2

after that substitute in the formula

Answer:

19.6ft (nearest tenth)

Step-by-step explanation:

Please refer to the attached photo for better understanding.

Given Length of Wire = BC = 22ft

Given Distance from Grounded Wire to Base of Pole = AC = 10ft

Length of Pole = AB

We can use Pythagoras' Theorem to find Length of Pole, AB.

By Pythagoras' Theorem,

[tex]c^{2} =a^{2} +b^{2} \\BC^{2} =AB^{2} + AC^{2} \\22^{2} =AB^{2} +10^{2} \\484=AB^{2} +100\\AB^{2} =484-100\\AB=\sqrt{384} ft\\=19.6ft (nearest tenth)[/tex]

The image of the figure under reflections in line m and then line t is shown below.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the square DEFG will be given in the figure.

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Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Dilation does not preserve the size of a figure, it only preserves the shape and angle.

Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′

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[tex]x \geqslant - 3 \: \: \: \: \: \: x < 3[/tex]

Answer:

The answer is D intersection

Remember that AND indicates an intersection and OR indicates a union.

Step-by-step explanation:

Solve each inequality and then find the intersection.

Inequality Form: −3≤ x<3

Interval Notation:[−3,3)

The proportion that could be used to find the value of x is 3/x= x/11

The complete question is added as an attachment

From the attachment, the common side length between both right triangles is x

While the other sides are adjacent sides.

This means that the proportion is:

3/x= x/11

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