trigonometric identities

9514 1404 393

Answer:

  b = 80 -6n . . . . boys who wear spectacles

Step-by-step explanation:

We know the ratio of boys who wear spectacles to those who don't is ...

  (4/5) : (1 -4/5) = 4 : 1

If we let b represent the number of boys who wear spectacles, then the number who don't is b/4. Then total number of boys is then b +b/4 = 5b/4. The number of girls in the classroom is this number less than 40.

Let's define a few groups:

Then the total of children who do not wear spectacles is ...

  n = b/4 +(1/3)(40 -5b/4)

  12n = 3b +(160 -5b) = 160 -2b . . . . multiply by 12

  2b = 160 -12n . . . . . . . . . . . . . add 2b-12n

  b = 80 -6n . . . . the desired relation, b = boys who wear spectacles

_____

Additional comment

The only values of n that make sense in this context are {8, 10, 12}, corresponding to {0, 15, 30} total girls and {40, 25, 10} total boys.

Answer:

6

Step-by-step explanation:

We need to evaluate :-

[tex]\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 ) [/tex]

Here the [tex]\Sigma[/tex] is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,

[tex]\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2) [/tex]

Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,

[tex]\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)[/tex]

Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,

[tex]\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}[/tex]

Hence the required answer is 6.

Answer:

-11

Step-by-step explanation:

I am going to assume that it is -x^2-5y^3.

-(4^2)-5(-1^3)

-16-5(-1)

-16+5

-11

Answer:

- 11

Step-by-step explanation:

If x = 4,  y = -1

then,

        - x^2 - 5y^3 = - (4)^2 - 5(-1)^3

                            = - 16 + 5

                            = - 11

Answer:

[tex]B)[/tex]

[tex](-1,1)(-3,3)\\\frac{3-1}{-3+1} =-1\\1=1+b\\b=0\\y=-x[/tex]

OAmayOHopeO

Answer:

The sample size necessary is of 168.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Based on a previous study, arrival delay times have a standard deviation of 39.6 minutes.

This means that [tex]\sigma = 39.6[/tex]

Find the sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento to within 6 minutes with 95% confidence.

This is n for which M = 6. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]6 = 1.96\frac{39.6}{\sqrt{n}}[/tex]

[tex]6\sqrt{n} = 1.96*39.6[/tex]

[tex]\sqrt{n} = \frac{1.96*39.6}{6}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*39.6}{6})^2[/tex]

[tex]n = 167.34[/tex]

Rounding up:

The sample size necessary is of 168.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The graph of g(x) is a vertically scaled version of the graph of f(x). The scale factor is 1/2, so vertical height at a given value of x is 1/2 what it is for f(x). This will make the graph appear shorter and fatter than for f(x).

The graph of g(x) is attached.

Answer:

A significant negative relationship exists between the variables

Step-by-step explanation:

Base on the information given in the question which goes thus : For every unit increase in x, y decreases by 12.8094. The value 12.8094 is the slope which is the rate of change in y variable per unit change in the independent variable. The sign or nature of the slope Coefficient gives an hint about the relationship between the x and y variables. The slope Coefficient in this case is negative and thus we'll have a negative relationship between the x and y variables (an increase in x leads to a corresponding decrease in y). This is a negative association.

Answer:

11/2

Step-by-step explanation:

[tex]\frac{\frac{3}{4} + \frac{5}{8} }{\frac{3}{4} - \frac{1}{2} }[/tex]

= 3/4 + 5/8 = 11/8 (take LCM)

3/4 - 1/2 = 1/4 (take LCM)

11/8 ÷ 1 /4

= 11/8 x 4

= 11/2

Answered by Gauthmath

Answer:

The 1st,Thrid, Fifth Option

Step-by-step explanation:

The first option is true. We can move the orginal square root function to get g(x).

The second option is false. Function g(x) which equals

[tex] \sqrt{x - 3} - 1[/tex]

Domain is all real numbers greater than or equal to 3.

The third option is true. Since minimum point we can get is 0 in a square root function. We have a vertical shift so our new minimum point is

[tex]0 - 1 = - 1[/tex]

We can take the sqr root of 0 so

So all real numbers that are greater than or equal to -1 is true.

The fourth option is false, we need to add 3 instead of subtract 3.

The fifth option is true, we can do that to get back to our original function

9514 1404 393

Answer:

  4/5

Step-by-step explanation:

The wording is ambiguous, as it often is when math expressions are described in English. We assume you intend ...

  [tex]\dfrac{3n+8}{n+7}=\dfrac{4}{3}\\\\3(3n+8)=4(n+7)\qquad\text{multiply by $3(n+7)$}\\\\9n+24=4n+28\qquad\text{eliminate parentheses}\\\\5n=4\qquad\text{subtract $4n+24$}\\\\\boxed{n=\dfrac{4}{5}}\qquad\text{divide by 5}[/tex]

The number is 4/5.

Answer:

[tex]2827.4 \dfrac{ft}{s}[/tex]

Step-by-step explanation:

[tex] A = \pi r^2 [/tex]

[tex] \dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt} [/tex]

[tex] \dfrac{dA}{dt} = 2 \times \pi \times 30~ft \times 15 \dfrac{ft}{s} [/tex]

[tex] \dfrac{dA}{dt} = 2827.4 \dfrac{ft}{s} [/tex]

Answer:

A) x = 0.

B) f is concave up for (-∞, 0).

C) f is concave down for (0, ∞).

Step-by-step explanation:

We are given the function:

[tex]f(x)=5+12x-x^3[/tex]

A)

We want to find the x-coordinates of all inflection points.

Recall that inflections points (may) occur when the second derivative equals zero. Hence, find the second derivative. The first derivative is given by:

[tex]f'(x) = 12-3x^2[/tex]

And the second:

[tex]f''(x) = -6x[/tex]

Set the second derivative equal to zero:

[tex]0=-6x[/tex]

And solve for x. Hence:

[tex]x=0[/tex]

We must test the solution. In order for it to be an inflection point, the second derivative must change signs before and after. Testing x = -1:

[tex]f''(-1) = 6>0[/tex]

And testing x = 1:

[tex]f''(1) = -6<0[/tex]

Since the signs change for x = 0, x = 0 is indeed an inflection point.

B)

Recall that f is concave up when f''(x) is positive, and f is concave down when f''(x) is negative.

From the testing in Part A, we know that f''(x) is positive for all values less than zero. Hence, f is concave up for all values less than zero. Our interval is:

[tex](-\infty, 0)[/tex]

C)

From Part A, we know that f''(x) is negative for all values greater than zero. So, f is concave down for that interval:

[tex](0, \infty)[/tex]

Answer:

B. 1✓3 in.

Search It ok

I see the answer :)

9514 1404 393

Answer:

  1. see below

  2. g(x) is f(x) translated left 2 and down 3

Step-by-step explanation:

1. The graphs are attached. F(x) is in red; g(x) is in blue.

__

2. The graph of g(x) = f(x -h) +k is the parent function translated by (h, k). Here we have (h, k) = (-2, -3), so g(x) is f(x) translated left 2 and down 3.

Answer:

A. y<-2x-1

Step-by-step explanation:

not C or D because it is a dashed line meaning the linear equation will either have the symbol ≥ or ≤.

when y is less than, you shade below

thus, the answer is A

Answer:

x = 16

Step-by-step explanation:

7(x + 2) = 6(x + 5)

First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.

7x + 14 = 6x + 30

Next, let's subtract "6x" from both sides of this equation!

x + 14 = 30

Now, we have to subtract "14" from both sides of the equation.

x = 16

Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.

7(16 + 2) = 6(16 + 5)

7(18) = 6(21)

126 = 126

Since our equations equal each other we know that our x-value is correct!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.

The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2

Explanation:

Interior angles are the angles that are inside the shape. The remote interior angles would be the 2 angles away from the exterior angle.

The exterior angle is the angle, made by the side of the shape and a line drawn out from an adjacent side.

I hope this helps!

Answer:

In LDR

In PDR

Exterior angle of a triangle is formed when one side of the triangle is extended .

Interior remote angles the angles in the triangle that do not lie on the extended side.

Answer:

The equation is x + 4 = 0.

Step-by-step explanation:

Point (-4 , 8)

A line parallel to the Y axis has slope is infinite.

The equation of line is

[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]

Complete Question

The quality control manager at a computer manufacturing company believes that the mean life of a computer is 91 months with a standard deviation of 10 months if he is correct. what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months? Round your answer to four decimal places. Answer How to enter your answer Tables Keypad

Answer:

[tex]P(-1.72<Z<1.72)=0.9146[/tex]

Step-by-step explanation:

From the question we are told that:

Population mean \mu=91

Sample Mean \=x =2.08

Standard Deviation \sigma=10

Sample size n=68

Generally the Probability that The  sample mean  would differ from the population mean

P(|\=x-\mu|<2.08)

From Table

[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]

T Test

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

[tex]Z=\frac{2.08}{\frac{10}{\sqrt{68} } }[/tex]

[tex]Z=1.72[/tex]

[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]

[tex]P(-1.72<Z<1.72)[/tex]

Therefore From Table

[tex]P(-1.72<Z<1.72)=0.9146[/tex]

Answer:

The minimum sample size required to create the specified confidence interval is 295.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Variance of 0.49:

This means that [tex]\sigma = \sqrt{0.49} = 0.7[/tex]

They want to construct a 95% confidence interval with an error of no more than 0.08. What is the minimum sample size required to create the specified confidence interval?

The minimum sample size is n for which M = 0.08. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.08 = 1.96\frac{0.7}{\sqrt{n}}[/tex]

[tex]0.08\sqrt{n} = 1.96*0.7[/tex]

[tex]\sqrt{n} = \frac{1.96*0.7}{0.08}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.7}{0.08})^2[/tex]

[tex]n = 294.1[/tex]

Rounding up:

The minimum sample size required to create the specified confidence interval is 295.

Answer:

j * .07 +j

Step-by-step explanation:

The tax on the jewelry is J* .07

Add the tax to the cost of the jewelry to get the total cost

j * .07 +j

Answer:

[tex]Cold = \frac{1}{6}\ mins[/tex]

Step-by-step explanation:

The correct given parameters are:

[tex]Both = \frac{1}{4}\ mins[/tex]

[tex]Hot = \frac{1}{12}\ mins[/tex]

Required

Time taken by the cold water faucet

We have:

[tex]Cold + Hot = Both[/tex]

Make Cold the subject

[tex]Cold = Both -Hot[/tex]

So, we have:

[tex]Cold = \frac{1}{4}-\frac{1}{12}[/tex]

Take LCM

[tex]Cold = \frac{3-1}{12}[/tex]

[tex]Cold = \frac{2}{12}[/tex]

Divide by 2

[tex]Cold = \frac{1}{6}[/tex]

Answer:

Step-by-step explanation:

If we are looking for the time(s) that the ball is at a height of 15, we simply sub in a 15 for the height in the position equation and solve for t:

[tex]15=-16t^2+23t+7[/tex] and

[tex]0=-16t^2+23t-8[/tex]

Factor this however you factor a quadratic in class to get

t = .59 seconds and t = .85 seconds.

This means that .59 seconds after the ball was thrown into the air it was 15 feet off the ground. Then the ball reached its max height, gravity took over, and began pulling it back down to earth. The ball passes the height of 15 feet again on its way down after .85 seconds.

Answer:

Step-by-step explanation:

Change the mixed numbers to improper fractions.

Answer:

i think 4 4 kilograms if im wrong sorry

Step-by-step explanation:

Answer:

we need a picture...

Step-by-step explanation: