What is the area, in square units, of trapezoid ABCD shown below?

The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.

This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.

a(n) = a(1) + d( n- 1)

d = 3

This is the formula of an arithmetic sequence.

an = a(1) + d( n- 1)

Substitute in the values of

a(1) = 7 and

d = 3

a(n) = 7 + 3 ( n- 1)

Simplify each term.

a(n) = 7 + 3n- 3

Subtract 3 from 7.

a(n) =  3n + 4

The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.

Substitute in the value of n to find the nth term.

a(55) = 3 (55) + 4

Multiply 3 by 55 .

a(55) = 165 + 4

Add 165 and 4.

a(55) = 169

Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.

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Answer:

3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.47, n = 460, \mu = 0.47, s = \sqrt{\frac{0.47*0.53}{460}} = 0.0233[/tex]

What is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Sample proportion lower than 0.47 - 0.05 = 0.42 or higher than 0.47 + 0.05 = 0.52.

Since they are equidistant from the mean of 0.47 they are equal. So we find one of them, and multiply by two.

Lower than 0.42:

pvalue of Z when X = 0.42. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.42 - 0.47}{0.0233}[/tex]

[tex]Z = -2.15[/tex]

[tex]Z = -2.15[/tex] has a pvalue of 0.0158

2*0.0158 = 0.0316

3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Answer:

np = 81  , nQ = 99

Step-by-step explanation:

Given:

X - B ( n = 180 , P = 0.45 )

Find:

Sampling distribution has an approximate normal distribution

Computation:

nP & nQ ≥ 5

np = n × p

np = 180 × 0.45

np = 81

nQ = n × (1-p)

nQ = 180 × ( 1 - 0.45 )

nQ = 99

[tex]Therefore, sampling\ distribution\ has\ an\ approximately\ normal\ distribution.[/tex]

Answer:

a) Fx=-5N  Fy=-5*sqrt(3) N   b) Fx= 5*sqrt(3) N    Fy=-5N

c) Fx=-5*sqrt(2) N    Fy=-5*sqrt(2)   N

Step-by-step explanation:

The arrow's F ( weight) component on axle x  is Fx= F*sinA  and on axle y is

Fy=F*cosA

a) The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(30)= -5 N      Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N

b) Now the x component  is co directed to axle x , and y component is opposite directed to axle y.

So x component is positive and y components is negative

So Fx = 10*sin(60)= 5*sqrt(3) N       Fy= -10*cos(60)= -10*1/2= -5 N

c)The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(45)= -5*sqrt(2)  N    

 Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N

Answer:

[tex]\boxed{11.78}[/tex]

Step-by-step explanation:

From observations, we can note that BC is the hypotenuse.

As the length of hypotenuse is not given, we can only use tangent as our trig function.

tan(θ) = opposite/adjacent

tan(67) = x/5

5 tan(67) = x

11.77926182 = x

x ≈ 11.78

Answer:

2

Step-by-step explanation:

5÷2 1/5 = 2

Answer:

2 3/11

Step-by-step explanation:

To find the original number, we need to divide 5 by 2 1/5.

5/ 2 1/5

Convert 2 1/5 to an improper fraction:

11/5

5/ 11/5

When dividing fractions, we can multiply the first number by the reciprocal of the second one to get the answer.

5*5/11

25/11

2 3/11

Answer:

stratified random sampling technique

The sampling technique described, where sixteen students are randomly selected from each grade level, is called "stratified random sampling."

We have,

Stratification involves dividing the population (in this case, the high school students) into distinct subgroups or strata based on certain characteristics

By selecting a random sample from each stratum (each grade level), the sampling technique aims to ensure that each subgroup is represented in the sample in proportion to its size within the population.

This approach allows for a more representative sample and provides insights into the eating habits of students across different grade levels.

Thus,

The sampling technique described, where sixteen students are randomly selected from each grade level, is called "stratified random sampling."

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Answer:

  6/(49π) ≈ 0.03898 m/min

Step-by-step explanation:

  V = πr²h . . . . formula for the volume of a cylinder

  dV/dt = πr²·dh/dt . . . . differentiate to find rate of change

Solving for dh/dt and filling in the numbers, we have ...

  dh/dt = (dV/dt)/(πr²) = (6 m³/min)/(π(7 m)²) = 6/(49π) m/min

  dh/dt ≈ 0.03898 m/min

Answer:

6

Step-by-step explanation:

We want to find the units digit of [tex]2^{4000}[/tex]. Let's first look for a pattern:

[tex]2^{1}=2[/tex]

[tex]2^{2}=4[/tex]

[tex]2^{3}=8[/tex]

[tex]2^{4}=16[/tex]

[tex]2^{5}=32[/tex]

[tex]2^{6}=64[/tex]

[tex]2^{7}=128[/tex]

[tex]2^{8}=256[/tex]

...and so on

Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!

This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.

The answer is thus 6.

~ an aesthetics lover

Complete Question:

Find the directional derivative of g(x,y) = [tex]x^2y^5[/tex]at the point (1, 3) in the direction toward the point (3, 1)

Answer:

Directional derivative at point (1,3),  [tex]D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Step-by-step explanation:

Get [tex]g'_x[/tex] and [tex]g'_y[/tex] at the point (1, 3)

g(x,y) = [tex]x^2y^5[/tex]

[tex]g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486[/tex]

[tex]g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405[/tex]

Let P =  (1, 3) and Q = (3, 1)

Find the unit vector of PQ,

[tex]u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\[/tex]

[tex]|\bar{PQ}| = \sqrt{8}[/tex]

The unit vector is therefore:

[tex]u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }[/tex]

The directional derivative of g is given by the equation:

[tex]D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Answer:

1 cup per drink per student.

20 oz. left over

Step-by-step explanation:

given; 2 gallons for 100 students

1 cup holds 3 oz.

first, convert 2 gallons to oz.

1 gal = 160 oz.

2 gallons * 160 oz per 1 gal = 320 oz.

320 oz / 100 students = 3.2oz.

but 1 cup can only hold 3 oz.

therefore 3.2 - 3 = 0.2 oz * 100 = 20 oz. left over.

hope it helps.

Answer:

d. $125, $135, $150, $130

Step-by-step explanation:

$125, $135, $150, $130

Range of the above set of numbers:

$150 - $125 = $25

Mean of numbers:

$125 + $135 + $150 + $130 = $540

540 ÷ 4 = $135

Answer:

  p(mean < 2000) ≈ 0.81

Step-by-step explanation:

Your table gives the probability the value is between z=0 and z=0.88. You want the probability the value is between -∞ and 0.88, so you have to add the probability it is between -∞ and zero. You must add 0.5 to the table value.

  p(Z < 0.88) = 0.5 +0.3106 = 0.8106

_____

Comment on table values

You probably need to do some interpolation of your table values to get accuracy to 4 significant digits. All of the calculators I use give the probability for a Z-score of 0.88388 to be about 0.8116, not 0.8106.

When working with a "half" table, you need to be aware of what the table is giving you and what you're trying to use it for. A quick sketch of the problem may be helpful. (see below)

Answer:

  y

Step-by-step explanation:

The expression

  y = f(x)

tells you that y is the dependent variable, and that it depends on x, the independent variable. The independent variable is always the function argument. Any variable that depends on that is the dependent variable.

Answer:

Systematic Sampling

Step-by-step explanation:

Systematic sampling is a form of sampling in which the researcher applies probability sampling such that every member of the group is selected at regular intervals or periods. The researcher picks a random starting point and after an interval must have elapsed, another sample member is chosen. This sampling method is similar to that disclosed in the question because it has the key qualities.

For example, an interval is given after the 1000th soda is tested for quality.  This means that the interval for testing can accommodate 1000 sodas after which the first member is tested again. So, this is a Systematic sampling method.

Answer:

Q(x) = 4

R(x) = 0

Step-by-step explanation:

Q(x) = 2x + 2 ----- (1)

R(x) = x² - 1 -------- (2)

i) For (R * Q)(5)  and [(Q * R)], we have as follow:

[(x² - 1)(2x + 2)] (5)

= (2x³ + 2x² - 2x - 2)(5)

= x³ + x² - x - 1

When x = -1

x³ + x² - x - 1 = 0

∴ (x³ + x² - x - 1) ÷ (x + 1) = x² - 1

If x + 1 = 0

x = -1

and x² - 1 = 0

x = 1

From (1), when x= 1: Q(x) = 4

From (2), when x= 1 or -1: R(x) = 0

Answer:

x=4200, y=2700

Step-by-step explanation:

let x be first account

y the second

x+y=6900

0.03x+0.08y=342

solve by addition/elimination)

multiply first equation by 0.03

0.03x+0.03y=207  subtract from second

0.03x+0.03y-0.03x-0.08y=207-342

0.05y=135

y=2700, x=4200

Answer/Step-by-step explanation:

*The six raw data values in the second row are for teens are: 14, 15, 15, 15, 16, and 16

*There are 6 raw data values in the 20's represented in the 3rd row. They are: 25, 25, 27, 28, 28, and 28

*There are 3 raw data values in the 30's that are represented in the 4th row. They are: 35, 36, and 36.

*There are 0 raw data values in the 40's represented in the 5th row.

*There are 21 raw data values in the entire data set. They are:

1, 2, 3, 7, 9, 14, 15, 15, 15, 16, 16, 25, 25, 27, 28, 28, 28, 35, 36, 36, and 50.

Answer:

170 children, 88 students, 85 adults

Step-by-step explanation:

x = children

y = students

z = adults

x + y + z = 343

5x + 7y + 12z= 2486

z = 1/2x

you can solve by elimination or substitution or both.

3 equations with 3 unknowns

By solving a system of equations, we conclude that:

Let's define the variables:

We know that the theater has a capacity of 343, then:

C + S + A = 343

We also know that there are half as many adults as there are children, then:

A = C/2

Finally, we know that the total profit is $2,468, then:

C*$5,00 + S*$7.00 + A*$12.00 = $2,468

So we have a system of 3 equations:

C + S + A = 343

A = C/2

C*$5,00 + S*$7.00 + A*$12.00 = $2,468

First, we can replace the second equation into the other two to get:

C + S + C/2 = 343

C*$5,00 + S*$7.00 + (C/2)*$12.00 = $2,468

Now we can rewrite the first equation as:

S = 343 - (3/2)*C

Now we can replace that on the first equation:

C*$5,00 + (343 - (3/2)*C)*$7.00 + (C/2)*$12.00 = $2,468

$2,401 + C*$0.50 = $2,468

C = ($2,468 - $2,401)/$0.50 = 134

And we know that:

A = C/2 = 134/2 = 67

And:

S =  343 - (3/2)*C =  343 - (3/2)*134 = 142

Then there are:

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Answer:

Less than 90

Step-by-step explanation:

All angles in a triangle add up to 180 degrees.

An obtuse angle is an angle that is greater than 90 degrees.

For simplicity's sake, let the obtuse angle be 91 degrees.

180-91=89

The remaining angles in an obtuse triangle are always acute.

Sorry for the trashy answer.

Answer:

Less than 90

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

8ʸ = 16ʸ⁺²

(2³)ʸ = (2⁴)ʸ⁺²

2³ʸ = 2⁴ʸ⁺⁸

3y = 4y + 8

y = -8

Answer:

A. -8

Step-by-step explanation:

edge 2021

Answer:

i think you have to take_16 to the right side.

Answer:

  B

Step-by-step explanation:

You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).

The shading is below the line because y-values are less than (or equal to) values on the line.

Choice B matches the attached graph.

Answer:

it is graph b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;

[tex]y = f(x_0) + f'(x_0)(x-x_0)[/tex]

[tex]x_n = x_n_-_1 - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}[/tex]

If [tex]x_0 = 1\\[/tex]

We will iterate using the formula;

[tex]x_1 = x_0 - \frac{f(x_0 )}{f'(x_0 )}[/tex]

Given f(x) = x³ + 5x +2

f(x0) = f(-1) = (-1)³ + 5(-1) +2

f(-1) = -1 -5 +2

f(-1) = -4

f'(x) = 3x²+5

f'(-1) = 3(-1)²+5

f'(-1) = 8

[tex]x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}[/tex]

f(-0.5) = (-0.5)³ + 5(-0.5) +2

f(-0.5) = -0.125-2.5+2

f(-0.5) = -0.625

f'(-0.5) = 3(-0.5)²+5

f'(-0.5) = 3(0.25)+5

f'(-0.5) = 0.75+5

f'(-0.5) = 5.75

[tex]x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913[/tex]

The estimated solution is -0.3913 (to 4dp)

Answer:

B) [tex]x^2-3x+15[/tex]

Step-by-step explanation:

[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]

A) [tex]x^2+15x+15[/tex]

B) [tex]x^2-3x+15[/tex]

C) [tex]13x^2 + 3x + 15[/tex]

D) [tex]x^4-3x + 15[/tex]

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▹ Answer

B. x² - 3x + 15

▹ Step-by-Step Explanation

7x² + 6x - 9x - 6x² + 15

Collect like terms

x² + 6x - 9x + 15

Subtract

x² - 3x + 15

Final Answer

x² - 3x + 15

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

the answer is 0.79 rounded to the nearest hundreth

Step-by-step explanation:

Answer:

b = (3V)/h

Step-by-step explanation:

You have to rearrange the equation so that it is equal to b.

V = hb/3

3(V) = (hb/3)(3)

3V = hb

(3V)/h = (hb)/h

b = (3V)/h

Answer:

D. [tex]3^3 - 4^2[/tex]

Step-by-step explanation:

Well if Alia gets 4 squared less than Kelly who get 3 cubed it’s natural the expression is 3^3 - 4 ^2