Find the approximate sum of the series shown below.

Answer:

D. 80    :)

Step-by-step explanation:

The solution is : The value of segment LM is 9x + 5.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

Consider the image below.

A perpendicular bisector is a line segment that bisects another line segment into two equal parts and is perpendicular to this line segment.

So from the diagram below we know:

KL = LM

line a is ⊥ to KM

∠NLK = 90°

Since the angle measure of ∠NKL is not provided we cannot determine the value of x.

So, the value of segment LM is 9x + 5.

To learn more on angle click:

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Complete question:

Line a is a perpendicular bisector of line segment K M. It intersects line segment K M at point L. Line a also contains point N. Line segment K L is 9 x +5. Line segment K N is 14 x minus 3. What is the length of segment LM? units

Answer:

A=1,728

Step-by-step explanation:

To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.

The width is 12, the hight is 12, and the depth is 12 so you can write

A=12*12*12

Multiply 12 by 12

A=144*12

Multiply 12 by 144 to get your final total area

A=1,728

Hope this helps, feel free to ask follow-up questions if confused.

Have a good day! :)

Answer:  i) θ = 30°, 60°, 210°, & 240°

              ii) θ = 20° &  200°

Step-by-step explanation:

i) sin (2θ) = cos 30°

[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]

To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above.   θ = 30°, 60°, 210°, 240°

If you need ALL of the solutions (more than one rotation), add 180n to the solutions.   θ = 30° + 180n   &   60° + 180n

*********************************************************************************************

ii) cos α = sin (50 + α)

Use the Identity: cos α = sin (90 - α)

Use Transitive Property to get:   sin (50° + α) = sin (90° - α)

50° + α = 90° - α

50° + 2α = 90°

        2α = 40°

          α = 20°

To find all solutions for one rotation, add 360/2 = 180 to the solution above.

α = 20°, 200°

If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n

Answer: 0.0548

Step-by-step explanation:

Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.

Let [tex]\overline{X}[/tex] represents the sample mean GPA for each student.

Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:

[tex]P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z<1.6)\\\\=1-0.9452=0.0548[/tex]

hence, the required probability is 0.0548.

Step-by-step explanation:

f(x)=2x²+3x+9

g(x) = - 3x + 10

In order to find (f⋅g)(1) first find (f⋅g)(x)

To find (f⋅g)(x) substitute g(x) into f(x) , that's for every x in f (x) replace it by g (x)

We have

(f⋅g)(x) = 2( - 3x + 10)² + 3(- 3x + 10) + 9

Expand

(f⋅g)(x) = 2( 9x² - 60x + 100) - 9x + 30 + 9

= 18x² - 120x + 200 - 9x + 30 + 9

Group like terms

(f⋅g)(x) = 18x² - 120x - 9x + 200 + 30 + 9

(f⋅g)(x) = 18x² - 129x + 239

To find (f⋅g)(1) substitute 1 into (f⋅g)(x)

That's

(f⋅g)(1) = 18(1)² - 129(1) + 239

= 18 - 129 + 239

We have the final answer as

Hope this helps you

Answer:

Range of wages is £140 to £525.

Mean wage = £226

Step-by-step explanation:

Given:

Weekly wages paid to the staff are :

£245, £140, £525, £163, £195, £174 and £140.

To find:

Range of these wages = ?

Mean wage = ?

Solution:

First of all, let us learn about the range of wages and mean wage.

Range of wages has a minimum pay and a maximum pay.

Here, if we have a look £140 is the minimum pay and

£525 is the maximum pay.

So, range of wages is £140 to £525.

Mean wage means the average of all the wages given to the staff.

Mean is defined as the formula:

[tex]\text{Average/Mean =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]

Here, Sum of all observations mean sum of the wages of all the staff members.

Number of observations mean the number of staff members i.e. 7 here.

Applying the formula:

[tex]\text{Average/Mean =} \dfrac{\text{245+140+525+163+195+174+140}}{\text{7}} \\\Rightarrow \text{Average/Mean =} \dfrac{\text{1582}}{\text{7}}\\\Rightarrow \text{Average/Mean =} 226[/tex]

So, the answer is:

Range of wages is £140 to £525.

Mean wage = £226

Answer:

Im not 100% sure, but I think it is:

No

No

No

Yes

Answer:

slope is undefined

Step-by-step explanation:

x = 4 is the equation of a vertical line parallel to the y- axis.

The slope of a vertical line is undefined

Answer:

Undefined

Step-by-step explanation:

If the line is strait up like x = 4 that means it is undefined.

Answer:

460

Step-by-step explanation:

Answer:

460

Step-by-step explanation:

Answer:

RS = 8

Step-by-step explanation:

Given:

Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16

Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8

To find the measure of RS, we need to find the value of x.

Thus, recall the "Two Secant Theorem"

According to the theorem,

(RS + RQ)*RQ = (PU + PQ)*PQ

Thus,

[tex] (3x - 5 + 8)*8 = (7 + 9)*9 [/tex]

[tex] (3x + 3)*8 = (16)*9 [/tex]

[tex] 24x + 24 = 144 [/tex]

Subtract 24 from both sides

[tex] 24x + 24 - 24 = 144 - 24 [/tex]

[tex] 24x = 120 [/tex]

Divide both sides by 24

[tex] \frac{24x}{24} = \frac{120}{24} [/tex]

[tex] x = 5 [/tex]

Plug in the value of x into (3x - 5) to find the measure of RS

RS = 3(5) - 5 = 15 - 7

RS = 8

━━━━━━━☆☆━━━━━━━

▹ Answer

12

▹ Step-by-Step Explanation

[tex]7/\frac{7}{12} \\\\= 7 * \frac{12}{7} \\\\= \frac{84}{7} \\\\= 12[/tex]

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

x = 50

Step-by-step explanation:

Since the triangle has 2 congruent sides then it is isosceles, thus the base angles are congruent, that is x and x

The sum of the angles in a triangle = 180°, thus

x + x + 80 = 180

2x + 80 = 180 ( subtract 80 from both sides )

2x = 100 ( divide both sides by 2 )

x = 50

Answer:

Option (4)

Step-by-step explanation:

By the Angle of intersecting secants,

"If two lines intersect outside a circle, then the measure of the angle between these lines or secants will be one half of the difference between the intercepted arcs."

From the picture attached,

Angle between the secants = ∠1

Measure of intercepted arcs are a° and b°.

By this theorem,

m∠1 = [tex]\frac{1}{2}(a-b)[/tex]

Option (4) will be the answer.

Answer:

4.12 kg

Step-by-step explanation:

Regular cakes:

1 dozen normal sponge cakes: 264 g plain flour

Vegetarian cakes:

1 dozen cakes: 264 g plain flour

4 eggs are replaced by 4 * 30 g of flour = 120 g flour

total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g

Proportion for regular cakes:

12 cakes to 264 g flour = 100 cakes to x grams flour

12/264 = 100/x

12x = 26400

x = 2200

2200 g flour for 100 regular cakes

Proportion for vegetarian cakes:

12 cakes to 384 g flour = 60 cakes to y grams flour

12/384 = 60/y

12y = 384 * 60

12y = 23040

y = 1920

1920 g flour for 60 vegetarian cakes

Total flour needed:

2200 g + 1920 g = 4120 g

4120 g * 1 kg/(1000 g) = 4.12 kg

Answer: 4.12 kg

Answer:

332.88 million

Step-by-step explanation:

you do the thing

Answer:

5

Step-by-step explanation:

Answer:

A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Step-by-step explanation:

We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.

For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.

Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;

                     P.Q.  =  [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~  [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15

[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06

[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11

[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09

[tex]n_1[/tex] = sample of 25-mil film = 8

[tex]n_2[/tex] = sample of 20-mil film = 8

[tex]\mu_1[/tex] = population mean speed for the 25-mil film

[tex]\mu_2[/tex] = population mean speed for the 20-mil film

Also,  [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005

Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.

So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;

P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98  {As the critical value of t at 14 degrees of

                                             freedom are -2.624 & 2.624 with P = 1%}  

P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98

P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] <  ) = 0.98

P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98

98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]

= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]

 = [-0.042, 0.222]

Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.

Answer:

It is less  than 3000 ft^3 by 450 ft^3

Step-by-step explanation:

The volume of the bin

V = l*w*h

V = 17*15*10

V =2550 ft^3

If it less than 3000 ft^3

V = 3000- 2550 =450 ft^3

If is less by 450 ft^3

Answer:

Let’s first multiply all the numbers given

Since it wants the volume we need to use the formula

LxWxH

17x15x10=2,550

Part A: yes the bin is under 3,000

Part B: by 450 more because if you subtract 3,000 and 2,550 you will get 450

Hope this helps! :)

Answer:

Short answer A,B,D

Step-by-step explanation:

The ideas from the excerpt would be most appropriate to include in a summary are;

Summary is known to be a form of quick or short review of what has happened in a specific passage.

The summary  is regarded as a statement that present the main points of a passage as seen above.

Learn more about novels from

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Answer:

[tex]\boxed{7^{\frac{3}{2} } \times 4}[/tex]

Step-by-step explanation:

[tex]4 (\sqrt{7} )^3[/tex]

Square root can be written as a power.

[tex]4(7^{\frac{1}{2} })^3[/tex]

Multiply the exponents.

[tex]4(7^{\frac{3}{2} })[/tex]

Answer:

A (7^3/4)

Step-by-step explanation:

ed 2020

Answer:

C. y-intercept: (0, -18); vertex point: ( [tex]-\frac{2}{3}[/tex], [tex]-20\frac{1}{4}[/tex]); x-intercepts: (3, 0) and (-

6,0)

Step-by-step explanation:

Hope it helped

Answer:

C. y-intercept: (0, -18); vertex point: ( - 2/3, - 20 1/4); x-intercepts: (3, 0) and (-

6,0)

Step-by-step explanation:

It's a positive parabola, so that means it opens upward. Crossing the x-axis at -6 and 3 it's minimum is -20 and crosses the Y-axis at -18.

Answer:

Infinite Solution!

Step-by-step explanation:

First, We simplify the right side.

Distribute -4, -4x-20=-4x-20

Now we add +4x to both sides, now the equation stands as -20=-20

We know when the solution is same #= same #. We have infinite solution!

Answer:

The answer is below

Step-by-step explanation:

Given that mean (μ) = 266 days, standard deviation (σ) = 16 days, sample size (n) = 16 women.

a) The mean of the sampling distribution of Xbar ([tex]\mu_x[/tex]) is given as:

[tex]\mu_x=\mu=266\ days[/tex]

The standard deviation of the sampling distribution of Xbar ([tex]\sigma_x[/tex]) is given as:

[tex]\sigma_x=\frac{\sigma}{\sqrt{n} } =\frac{16}{\sqrt{16} }=4[/tex]

b) The z score is a measure in statistics used to determine by how much the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

For x > 270 days:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{270-266}{\frac{16}{\sqrt{4} } }=1[/tex]

The probability the average pregnancy length exceed 270 days = P(x > 270) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587 = 15.87%

Answer:

x = √(-1) = i

Since the value of √(-1) is not real.

The system has no real solution.

Step-by-step explanation:

The solution to the system of equations is at the point where they intercept each other.

y1 = y2

For the given equation;

y=x^2-2x and y=-2x-1

To get the where they intercept, we will equal both equations;

y=x^2-2x = -2x-1

x^2 - 2x = -2x - 1

x^2 - 2x + 2x + 1 =0

x^2 +1 = 0

x^2 = -1

x = √(-1) = i

Since the value of √(-1) is not real.

The system has no real solution.

Answer:

The GCF is the largest expression that is factor of all expressions

Answer:

The GCF of two expressions is the greatest expression that is a factor of both the expressions.

Step-by-step explanation:

For example 7x² and 14x.

7x² = 1, 7, x, x

14x = 2, 7, x

The greatest common factor of the two expressions is 7x.

Answer:

3.22222......  = [tex]\frac{29}{9}[/tex]

Step-by-step explanation:

In this question we have to convert the number given in recurrent decimals into fraction.

Recurrent decimal number is 3.22222.......

Let x = 3.2222.........   -------(1)

Multiply this expression by 10.

10x = 32.2222........... -------(2)

Now subtract the expression (1) from (2),

10x = 32.22222.....

   x = 3.22222.......

9x = 29

x = [tex]\frac{29}{9}[/tex]

Therefore, recurrent decimal number can be written as [tex]\frac{29}{9}[/tex] which is in the form of [tex]\frac{p}{q}[/tex].

Answer:

$14.4

Step-by-step explanation:

From the question;

There are 300 strands of light each containing 150 light bulbs. Altogether, there are;

300 x 150 light bulbs = 45000 light bulbs.

Also;

Each bulb consumes 4 watts of power. Since there are 45000 light bulbs, the total power consumed by all the bulbs is;

45000 x 4 watts = 180000watts

Next convert the total power consumed to kW by dividing by 1000. i.e

180000watts = 180kW

Therefore, total power consumed is 180kW

He lights up for 5 hours a day for 30 days. This means that the total number of hours he lights his home for those 30 days is:

30 x 5 hours = 150 hours.

Now since power in his area sells for $0.08/kWh, this means that;

1kWh costs $0.08

Then;

180kWh will cost [180kWh x $0.08 / 1kWh] = $14.4

Therefore, he will end up paying $14.4 to light his home for the holidays.

Answer:

60°C

Step-by-step explanation:

This is a great example of a problem that looks really complicated, but can be broken down and easily understood!

First, we want to know the temperature the instant it is removed from the heat source. In that case, the time that has elapsed after it has been removed is 0, so we're looking for:

[tex]T(0)=55e^{-0.1(0))}+15=55e^{0}+15[/tex]

Now, any number raised to to the power of zero is 1, so this becomes:

[tex]T(0)=55(1)+15=60[/tex]

For more information on why any number raised to the zero power is 1, I highly recommend researching if it interests you. One of the most intuitive ways is to think of the pattern of exponents:

[tex]3^{3}=3*3*3=27[/tex]

[tex]3^{2}=3*3=9[/tex]

[tex]3^{1}=3[/tex]

You might notice that with each decrease in power, it can be read as dividing the expression by three, so following that pattern gives:

[tex]3^{0}=\frac{3}{3}=1[/tex]

And if we follow the division pattern, we do end up going into negative exponents correctly:

[tex]3^{-1}=\frac{1}{3^{1}}[/tex]

[tex]3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}[/tex]

[tex]3^{-3}=\frac{1}{3^3}=\frac{1}{27}[/tex]

surface area of a equilateral by hand a 140.4 cm and 9cm

Answer:

b^2

------

2a

Step-by-step explanation:

-6ab^3          10b

-------------- * -----------

5a                   -24 ab^2

Rewriting

-6ab^3          10b

-------------- * -----------

 -24 ab^2      5a

Canceling like terms

b                  2b

-------------- * -----------

 4                a

Canceling the 2 and 4

b                  b

-------------- * -----------

 2                a

b^2

------

2a

Answer:

b²/2a

Step-by-step explanation:

[(-6ab³)/5a]*[(10b)/(-24ab²)]

-60ab^4/-120a²b²= ( when divide ,subtract the exponents)

b²/2a