how do I simplify this (sinx)/(secx+1)

She can either have 24 people since there are more slices of pizza there will be extras

Answer:

[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]

Step-by-step explanation:

The area of the shaded region can be calculated as the area of the semicircle less the area of the right triangle.

The area of the right triangle can be calculated as:

[tex]A_t=\frac{b*h}{2} =\frac{LM*MN}{2}[/tex]

Where LM and MN have the same length because the internal angles are L=45°, M=90°, and N=45°. So the area is:

[tex]A_t=\frac{4*4}{2}=8[/tex]

The diameter of the circle can be calculated using the Pythagorean theorem as:

[tex]D=\sqrt{(LM)^2+(MN)^2} =\sqrt{4^2+4^4}=4\sqrt{2}[/tex]

So, the radius is [tex]r=2\sqrt{2}[/tex]

Finally, the area of the semicircle is:

[tex]A_c=\frac{\pi*r^2 }{2}=\frac{\pi*(2\sqrt{2})^2 }{2}=4\pi[/tex]

So, the area of the shaded region is:

[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]

Answer:

(1.5, -13.5)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Simply plug in our coordinates into the formula:

x = (17 - 14)/2

x = 3/2

y = (-11 - 16)/2

y = -27/2

Answer:

(-1.5, -13.5)

Step-by-step explanation:

To find the x coordinate of the  midpoint, add the x coordinates and divide by 2

( 17+-14)/2 = 3/2 =1.5

To find the y coordinate of the  midpoint, add the x coordinates and divide by 2

( -11+-16)/2 = -27/2= - 13.5

Answer:

The growth rate is of 0.085 = 8.5% a year.

Step-by-step explanation:

General growth equation:

[tex]B(t) = B(0)(1+r)^{t}[/tex]

In which B(t) is the population of butterflies after t years, B(0) is the initial population and r is the growth rate, as a decimal.

We have:

[tex]B(t)=137(1.085)^{t}[/tex]

Comparing to the general equation, we have that:

[tex]B(0) = 137, 1 + r = 1.085[/tex]

Growh rate:

1 + r = 1.085

r = 1.085 - 1

r = 0.085

The growth rate is of 0.085 = 8.5% a year.

Answer: y-2=1/2(x-(-7)) or y-2=1/2(x+7)

Step-by-step explanation:

The point-slope formula is y-y₁=m(x-x₁). Since we are given the point and the slope, we can directly plug them into where it is appropriate. The slope is 1/2. Slope is represented by m. We would plug in 1/2 into m. The point is (x₁,y₁). That format matches (-7,2).

y-2=1/2(x-(-7))

y-2=1/2(x+7)

Answer:

D.

Step-by-step explanation:

Answer:

83.0°

Step-by-step explanation:

Given ∆XYZ, with 3 known sides, to find angle X, apply the Law of Cosines, c² = a² + b² - 2ab*cos(C).

For convenience sake, this formula can be rewritten to make the angle we are looking for the subject of the formula.

Thus, we would have this following:

[tex] cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex]

Where,

C = X = ?

a = 8 ft

b = 16 ft

c = 17 ft

Plug in the stated values into the formula and solve for X

[tex] cos(X) = \frac{8^2 + 16^2 - 17^2}{2*8*16} [/tex]

[tex] cos(X) = \frac{320 - 289}{256} [/tex]

[tex] cos(X) = \frac{31}{256} [/tex]

[tex] cos(X) = 0.1211 [/tex]

[tex] X = cos^{-1}(0.1211) [/tex]

[tex] X = 83.0 [/tex] (to nearest tenth)

Answer:

its actually 83 not 83.0

Step-by-step explanation:

im only saying this bc i know people with type 83.0 in the box

Answer:

37.7

Step-by-step explanation:

Well use the formula for the volume of a cylinder which is,

,[tex]\pi r^2 h[/tex]

So the radius is 2 and the height is 3, so we plug those numbers into the formula,

(pi)(2)^2(3)

2^2 is 4 4*3 is 12

12*pi is about 37.7 rounded to the nearest tenth.

If you would like to check look at the image below.

Answer:

C h^2  / 680 = x

Step-by-step explanation:

C=680x/h^2

Multiply each side by h^2

C h^2=680x/h^2  * h^2

C h^2=680x

Divide each side by 680

C h^2  / 680=680x/680

C h^2  / 680 = x

Answer:

D

Step-by-step explanation:

1/3(9x + 27) > x + 33

3x + 9 > x + 33

2x > 24

x > 12

> means open circle

Answer:

The answer is D

Step-by-step explanation:

I took the plato test!

Answer:

C) 24/25

Step-by-step explanation:

did the quiz and got it right

The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]

The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.

In the first quadrant;

Thus, we have a positive x and y-axis.

Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)

The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]

Learn more about Trigonometric functions here:

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Answer:

Hey there!

The perimeter can be expressed as 140+140+68[tex]\pi[/tex]

This is equal to 493.52 m

Hope this helps :)

the bag is 200g

total weight with oranges is 1400g

deduct the bags weight from total weight

1400 - 200

1200g

this is the weight of the three oranges

so each orange would be

1200 ÷ 3

400g

Answer:

[tex] A = 50.7 [/tex] (to nearest tenth)

Step-by-step explanation:

Use the Law of Cosines to find the value of angle A as follows:

[tex] cos(A) = \frac{b^2 + c^2 - a^2}{2*b*c} [/tex]

Where,

a = 7 in

b = 5 in

c = 9 in

Plug in the values into the formula

[tex] cos(A) = \frac{5^2 + 9^2 - 7^2}{2*5*9} [/tex]

[tex] cos(A) = \frac{57}{90} [/tex]

[tex] cos(A) = 0.6333 [/tex]

[tex] A = cos^{-1}(0.6333) [/tex]

[tex] A = 50.7 [/tex] (to nearest tenth)

Answer:

47, 40, 33, 26 are the first four terms of the sequence.

Step-by-step explanation:

Expression representing the sequence is,

[tex]a_n=46-7(n-1)[/tex]

where n = number of term in the sequence

For n = 1,

[tex]a_1=47-7(1-1)[/tex]

    = 47

For n = 2,

[tex]a_2=47-7(2-1)[/tex]

    = 47 - 7

    = 40

For n = 3,

[tex]a_3[/tex] = 47 - 7(3 -1)

   = 47 - 14

   = 33

For n = 4,

[tex]a_4=47-7(4-1)[/tex]

    = 47 - 21

    = 26

Therefore, first four terms of the sequence are 47, 40, 33 and 26.

Answer:

The given data is:

30, 32, 11, 14, 40, 37, 16, 26, 12, 33, 13, 19, 38, 12, 25, 15, 39, 11, 37, 17, 27, 14, 36

We will fill the table with the relevant information:

Question 1: 21 - 25 (because the previous range stops at 20 and the following range starts at 26)

Question 2: III (write 3 as a tally)

Question 3: II (write 2 as a tally)

Question 4: 8 (write the tally as a number)

Question 5: 4 (write IIII as a number)

Answer:

$4800.25

Step-by-step explanation:

$42603 is a yearly salary.

There are 12 months in 1 year.

Monthly salary:

$42603/12 = $3550.25

Monthly travelling allowance: $1250

Total amount earned in 1 month:

$3550.25 + $1250 = $4800.25

ok its 45.15% trust me

Answer:

Step-by-step explanation:

This curve alone does  not give exact percentages with the exception of P(z=0) = .50 or 50%

A Pictorial where 'some' of the % have been added for helps more...  

However, most often one needs to use a table, calculator, or an Excel function ect to find exact Percentage,

P(x > 4000) = P(z = 0) =  .50  or 50 % |using above pictorial

Using Calculator etc:  Here, am using the Excel NORMSDIST function to find the Percentages:

P(z=3/5 - z=-3/5) =  .7257 - .2742 =.4515 or 45.15%

To write an inequality and show on a number line all numbers: greater than (−3) but less than or equal to 3

Let n be the number, then -3 < n ≤3 .

On number line we mark open circle at -3 (since it has a strictly less than sign) and a closed circle at 3  (since it has a less than and equal to sign) .

To the required inequality that shows all the numbers greater than (−3) but less than or equal to 3 : -3 < n ≤3 and the number line is represented below.

Answer:

0.0414 with an upper tailed test

Step-by-step explanation:

Claim: P1P1 = P2P2

The above is a null hypothesis

The alternative hypothesis for a two-tailed test would be:

P1P1 \=/ P2P2

Where "\=/" represents "not equal to".

Using a z-table or z-calculator, we derive the p-value (probability value) for the z-score 2.04

With an upper tailed test, the

2 × [probability that z>2.04] = 2[0.0207] = 0.0414

This is the p-value for the test statistic.

Focus is on the alternative hypothesis.

Answer:

[tex] c = 15.5 [/tex]

Step-by-step explanation:

Using the Law of Cosines, c² = a² + b² - 2ab*cos(C), let's find c.

Where,

a = 15 ft

b = 20 ft

C = 50°

Thus:

[tex] c^2 = 15^2 + 20^2 - 2*15*20*cos(50) [/tex]

[tex] c^2 = 625 - 600*0.6429 [/tex]

[tex] c^2 = 625 - 600*0.6429 [/tex]

[tex] c^2 = 625 - 385.74 [/tex]

[tex] c^2 = 239.26 [/tex]

[tex] c = \sqrt{239.26} [/tex]

[tex] c = 15.5 [/tex] (nearest tenth)

Answer:

c sorry gotta get points.

Step-by-step explanation:

Answer:

the probability that one parachute of the  five parachute is damaged is 0.156

Step-by-step explanation:

From the given information;

Let consider X to be the altitude above the  ground that a parachute opens

Then; we can posit that the probability that the parachute is damaged is:

P(X ≤ 100 )

Given that the population mean μ = 155

the standard deviation σ = 30

Then;

[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]

[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]

[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]

From standard normal tables

[tex]P(X \leq 100 ) = 0.0334[/tex]

Hence; the probability of the given parachute damaged is 0.0334

Let consider Q to be the dropped parachute

Given that the number of parachute be n= 5

The probability that the parachute opens in each trail be  p = 0.0334

Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334

The probability mass function is:

Q [tex]\sim[/tex] B(5, 0.0334)

Similarly; the event that one parachute is damaged is :

Q ≥ 1

P( Q ≥ 1 ) = 1 - P( Q < 1 )

P( Q ≥ 1 ) = 1 - P( Y = 0 )

P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )

P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = 1 -  0.8437891838

P( Q ≥ 1 ) = 0.1562108162

P( Q ≥ 1 ) [tex]\approx[/tex] 0.156

Therefore; the probability that one parachute of the  five parachute is damaged is 0.156

Answer:

Step-by-step explanation:

Hello,

Question 15

We can search x such that:

   [tex]x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }[/tex]

There is 1 solution.

Question 16

Again, we search x such that:

  [tex]x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }[/tex]There are two solutions.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]8cos^4}x = (3 + 4cos2x + cos4x)[/tex]

Step-by-step explanation:

Using the power reduction identity, we have that:

[tex]cos^{2}x = \frac{1}{2}(1 + cos2x)\\ \\cos^{4}x = (cos^{2}x)^2 = (\frac{1}{2}(1 + cos2x))^2\\\\cos^{4}x = \frac{1}{4} (1 + 2cos2x + cos^{2}2x)\\[/tex]

From the first line:

[tex]cos^{2}2x = \frac{1}{2}(1 + cos4x)[/tex]

Therefore:

[tex]cos^{4}x = \frac{1}{4} (1 + 2cos2x + \frac{1}{2}(1 + cos4x))\\\\cos^4}x = \frac{1}{4} (1 + 2cos2x + \frac{1}{2} + \frac{1}{2} cos4x)\\\\cos^4}x = \frac{1}{4} (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\=> 8cos^4}x = 8 * \frac{1}{4} (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\8cos^4}x = 2 * (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\8cos^4}x = (3 + 4cos2x + cos4x)[/tex]

Answer:

Step-by-step explanation:

The formula C = π2r

Is used for the circumference.

We know that the number π is defined as the quotient between the circumference of a circle and its diameter, so we can write:

C/d = π

And remember that the diameter is twice the radius, so we can write:

d = 2r

Then we can rewrite the equation for the circumference as:

C = π2r

Then we conclude that the correct option is B.

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Answer:

decreases.

Step-by-step explanation:

Type II error is one in which we fail to reject the null hypothesis that is actually false. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The power of Type II error is 1 - [tex]\beta[/tex]. As the power increases the probability of Type II error decreases.

Answer:

a) We reject H₀ we have enough evidence for that

b) 1.-The survey was made over a district, results will surely be different if the survey is carried out over a whole state ( considering urban and rural areas)

2.-In a district we find an equalized level of salaries, which could be associated with a similar level of habits

Step-by-step explanation:

We have to develop a proportion test. One tail-test

Population proportion mean (national proportion)  p₀  = 72 %

Sample information

sample proportion  271/300         p = 0,90      p = 90 %

We assume Confidence Interval  90 %     then α = 0,1

Test Hypothesis

Null Hypothesis                                 H₀     p   =  p₀

Alternative Hypothesis                       Hₐ    p   >  p₀

As  α = 0,1 and    

We look at z-table for z(c) and find     z(c) = 1,28

And we compute z(s)  as

z(s) = ( p - p₀ ) √  (p₀q₀/n

z(s) =  ( 0,9 - 0,72 ) /√(0,72)*(0,28)/300

z(s) =  0,18 / √0,1296/300

z(s) =  0,18/ 0,026

z(s) =   6,92

z(s) > z(c)      6,92 > 1,28

As z(s) is bigger than z(c), z(s) is in the rejection region, so we reject the null hypothesis. We have enough evidence to claim that the proportion in the district is bigger than the national one.

b)1. The survey was made over a district, results will surely be different if the survey is carried out over a whole state ( considering urban and rural areas)

2.-In a district we find an equalized level of salaries, which could be associated with a similar level of habits

Answer: 10

Step-by-step explanation:

Given : Total number of coins tossed = 10

Possible outcomes to toss a coin = Head or tail

Number of possible outcomes = [tex]2^{10}=1024[/tex]

Number of ways of obtaining exactly 1 heads = [tex]{10}C_1=\dfrac{10!}{1!9!}[/tex]     [using combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] ]

=10

Hence, the numbers of ways of obtaining exactly 1 heads= 10

Answer:

-1 is not in the domain of (f o g)(x)

Step-by-step explanation:

f(x) = sqrt(x - 9)

g(x) = -6x - 3

(f o g)(x) = f(g(x)) = sqrt(g(x) - 9)

(f o g)(x) = sqrt(-6x - 3 - 9)

(f o g)(x) = sqrt(-6x - 12)

Let x = -1:

(f o g)(-1) = sqrt(-6(-1) - 12)

(f o g)(-1) = sqrt(6 - 12)

(f o g)(-1) = sqrt(-6)

Since sqrt(-6) is not a real number, -1 is not in the domain of (f o g)(x).

Answer:

200 N/m

Step-by-step explanation:

Rearranging the formula F = kx, you find that k = F/x. For the first spring,

F = 36 N and x = 0.06 m (6 cm). So the spring constant, F/x, is 36N/0.06m = 600 N/m

For the second spring, F = 36 N and x = 0.09 m. F/x = 36N/0.09m = 400 N/m

The difference between these values is 200 N/m, and that's the answer.

Hi there! Thanks for your questions ;)

The answers are quite easily, go through the steps below so that you can catch it up yourself!!

= [tex]\rm{sin (x) = \dfrac{9}{20}}[/tex]

= [tex]\rm{0.45}[/tex]

= [tex]\rm{x = arcsin(0.45)}[/tex]

= [tex]\rm{h = 20 \times cos(x)}[/tex]

= [tex]\rm{20 \times cos(26.74)}[/tex]

Hope it is helpful!