A scrub nurse recorded the temperature in the operating theatre every two hours over a 12 hour period from noon to midnight. The results are shown in the following line graph

​

Answer:

[tex]6-8cos2x+2cos4x[/tex]

Step-by-step explanation:

We are given that

[tex]16sin^4 x[/tex]

We can write the given expression as

[tex]16(sin^2x \times sin^2 x)[/tex]

[tex]16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})[/tex]

By using the formula

[tex]sin^2\theta=\frac{1-cos2\theta}{2}[/tex]

[tex]4(1-cos2x)^2[/tex]

[tex]4(1-2cos2x+cos^2(2x)[/tex]

Using the identity

[tex](a-b)^2=a^2+b^2-2ab[/tex]

[tex]4(1-2cos2x+\frac{1+cos4x}{2})[/tex]

[tex]4-8cos2x+2+2cos4x[/tex]

[tex]6-8cos2x+2cos4x[/tex]

This is required expression.

Answer:

it opens up

goes up 4 but doesn't move left or right

Answer:

[tex] y = 3 [/tex]

Step-by-step explanation:

Given the above right angled triangle, we would use a trigonometric ratio formula to find y.

Given angle = 30°

Hypotenuse = 6

Opposite side = y

Solve for y using the trigonometric ratio formula as follows:

[tex] sin(X) = \frac{opposite}{hypotenuse} [/tex]

[tex] sin(30) = \frac{y}{6} [/tex]

Multiply both sides by 6

[tex] sin(30)*6 = \frac{y}{6}*6 [/tex]

[tex] 0.5*6 = y [/tex]

[tex] 3 = y [/tex]

[tex] y = 3 [/tex]

Answer:A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root. Example: √36 = 6 (because 6 x 6 = 36)

Answer:

Graph C.  See explanations below.

Step-by-step explanation:

Looking for graph corresponding to   d <= (w^2)/5

Take the third graph, which has a solid line (to correspond to the inequality <=, or less than or equal to).

For a dog's weight of 10 lb, the corresponding dose is 20 mg = 10^2/5

for 20 lb, dose = 80 mg (=20^2/5)

...

For 40 lb, dose = 320 mg (=40^2/5).

So this is the correct graph.

The fourth (d) is similar. But the dotted line eliminates the equality in

d <= w^2/5

so not correct.

Answer:

A and E

Step-by-step explanation:

If the answer was A, it would translate to:

I have done some stuff.

If the answer was D, it would translate to:

I have some stuff.

Both of the sentences are grammatically correct, so A and E are the answers.

Incorrect:

B. - I's do some stuff - doesn't make sense

C. - I's doing some stuff - doesn't make sense

D. - I's did some stuff - doesn't make sense

Answer:

x is approximately 53°

Answer:52.64°

Step-by-step explanation:

opp=31

hyp=39

sin x° =[tex]\frac{opp}{hyp}[/tex]

sin x°=31/39

sin x°=0.7949

x=[tex]sin^{-1} (0.7949)\\[/tex]

x=52.64

Answer:

The variables that can be used in the analysis are:

Dependent variable: person's height (Height)

Independent variable: person's dad's height (DadsHt)

Step-by-step explanation:

A linear regression model is used to predict the value of the dependent variable based upon the value of the independent variable.

The general form of a linear regression model is:

[tex]y=a+bx[/tex]

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variables in the model are changed.

The dependent variables are also known as response variables.

Independent variables are the variables that are being altered to see a proportionate change in the dependent variable. In a regression model there can be one or more than one independent variables.

The independent variables are also known as the predictor variables.

In this vase we need to form a regression model such that, a person's dad's height can be used to predict how short or tall the person will be.

That is, the dependent variable is the person's height and the independent variable is the person's dad's height.

The variables that can be used in the analysis are:

Dependent variable: person's height (Height)

Independent variable: person's dad's height (DadsHt)

Answer:

17.1

Step-by-step explanation:

The missing side is x

switch tan 25° and x

Answer:

29 ft x 58 ft

Step-by-step explanation:

Let x be the length of each side perpendicular to the wall, and y be the length of the side parallel to the wall.

The amount of wire available is:

[tex]116 = 2x+y\\y=116-2x[/tex]

The area of the region is:

[tex]A=xy=x(116-2x)\\A(x)=116x-2x^2[/tex]

The value of 'x' for which the derivate of the area function is zero will yield the maximum area:

[tex]A(x)=116x-2x^2\\A'(x) = 116-4x=0\\x=29\ ft[/tex]

The value of y is:

[tex]y=116-2*29\\y=58\ ft[/tex]

The dimensions of the region with the largest area are 29 ft x 58 ft.

Answer:

CI =(0.333, 0.480)

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as shown;

CI = p±Z * √p(1-p)/n±0.5/n

Z is the z-score at 90% confidence

p is the sample proportion

n is the sample size

Given n = 144, p = 0.4 and z-score at 90%  CI = 1.645 (from z table)

Substituting this values;

CI = p ± 1.645*√0.4(1-0.4)/144 ±0.5/n

CI = 0.4 ± 1.645*√0.4(0.6)/144 ± 0.5/144

CI = 0.4 ±1.645 * √0.24/144 ± 0.00347

CI = 0.4 ±1.645 * 0.04087± 0.00347

CI = 0.4±0.06723±0.00347

CI =(0.333, 0.480)

Answer:

Step-by-step explanation:

In a pictogram, data can be arranged as follows:

Answer:

They will find 69 viruses in 8 hours.

Step-by-step explanation:

The number of viruses after t hours is given by the following equation:

[tex]V(t) = V(0)(1-r)^{t}[/tex]

In which V(0) is the initial number of viruses and r is the decay rate, as a decimal.

They start with 500 viruses

This means that [tex]V(0) = 500[/tex]

Decay rate of 22% per hour.

This means that [tex]r = 0.22[/tex]

So

[tex]V(t) = V(0)(1-r)^{t}[/tex]

[tex]V(t) = 500(1-0.22)^{t}[/tex]

[tex]V(t) = 500(0.78)^{t}[/tex]

How many viruses will they find in 8 hours?

This is V(8).

[tex]V(t) = 500(0.78)^{t}[/tex]

[tex]V(8) = 500(0.78)^{8}[/tex]

[tex]V(8) = 68.51[/tex]

Rounding to the nearest whole number

They will find 69 viruses in 8 hours.

Answer:

The researchers will find 86 viruses.

Step-by-step explanation:

Identify the value of each variable in the formula. Be sure to put the percent in decimal form. Be sure the units match—the rate is per hour and the time is in hours.

A =?

A0 =  500

R= -0.22/hour

t= 8 hours

Substitute the values in the formula.

A= A0e^rt

A= 500e^-0.22x8

Compute the amount.

A ≈ 86.02

Round to the nearest whole number.

A ≈ 86

Answer: C. p = p

Step-by-step explanation:

A tautology is a statement that is always true.

A. p = q

This is not always true. Counterexample: p = 1 & q = 2

B. p = q

This is the same as A (above)

C. p = p

This is ALWAYS true!

D. q = p

This is the same as A but in reverse order.

Answer:

212

Step-by-step explanation:

Answer:

212

Step-by-step explanation:

Answer: C. Interest will be charged

Step-by-step explanation:

Answer:

Step-by-step explanation:

Interest will be charged is your answer!

Answer:

the real deal is that you mistook if

cos(x)=y/z gives y=zcos(x)

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The given line passes through the points (-4, -3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, 3)?

a) y - 3 = -2(x + 4)

b) y - 3= - (x + 4)

c) y - 3 = (x + 4)

d) y - 3 = 2(x + 4)

Answer:

The equation of the line that is perpendicular to the given line and passes through the point (-4, 3) is

a) y - 3 = -2(x +4)

Step-by-step explanation:

First of all, we will find the slope of the given line.

We are given that the line passes through the points (-4, -3) and (4, 1)

[tex](x_1, y_1) = (-4,-3) \\\\(x_2, y_2) = (4,1) \\\\[/tex]

The slope of the equation is given by

[tex]$ m_1 = \frac{y_2 - y_1 }{x_2 - x_1} $[/tex]

[tex]m_1 = \frac{1 -(-3) }{4 -(-4)} \\\\m_1 = \frac{1 + 3 }{4 + 4} \\\\m_1 = \frac{4 }{8} \\\\m_1 = \frac{1 }{2} \\\\[/tex]

Recall that the slopes of two perpendicular lines are negative reciprocals of each other.

[tex]$ m_2 = - \frac{1}{m_1} $[/tex]

So the slope of the other line is

[tex]m_2 = - 2[/tex]

Now we can find the equation of the line that is perpendicular to the given line and passes through the point (-4, 3)

The point-slope form is given by,

[tex]y - y_1 = m(x -x_1)[/tex]

Substitute the value of slope and the given point

[tex]y - 3 = -2(x -(-4) \\\\y - 3 = -2(x +4)[/tex]

Therefore, the correct option is (a)

y - 3 = -2(x + 4)

The equation of the line in point-slope form is y - 3 = -2(x + 4)

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the y intercept.

The line passes through the point (-4, -3) and (4, 1). Hence:

Slope = (1 - (-3)) / (4 - (-4)) = 1/2

The slope of the line perpendicular to this line is -2 (-2 *  1/2 = -1).

The line passes through (-4, 3), hence:

y - 3 = -2(x - (-4))

y - 3 = -2(x + 4)

The equation of the line in point-slope form is y - 3 = -2(x + 4)

Find out more on linear equation at: https://brainly.com/question/14323743

Answer:

4/ 100000

hope it was useful for you

stay at home stay safe

pls mark me as brain.....m

keep rocking

Answer:

The daily rate is $33 and the per mile rate is $0.35

Step-by-step explanation:

4x + 440y = 286

3x + 190y = 165.5

We can solve this systems of equations by multiplying the second statement by [tex]-\frac{4}{3}[/tex] to try and eliminate the x variable.

4x + 440y = 286

-4x - [tex]\frac{760}{3}[/tex]y = -220[tex]\frac{2}{3}[/tex]

[tex]\frac{560}{3}[/tex] y= [tex]\frac{196}{3}[/tex]

560y = 196

y = 0.35

So, the rate per mile is 0.35. Now, with this info, let's find the daily rate by plugging it into the equation.

[tex]4x + 440\cdot0.35 = 286\\4x + 154 = 286\\4x = 132\\x = 33[/tex]

So, the daily rate is $33 and the mile rate is $0.35.

Hope this helped!

Answer:

the daily fee =33 dollars

and the mileage charge.=0.35

let d: be daily fee and m for mileage

cost of rental =(d*number of days)+ (m*number of mileage)

her first trip: 4d+440m=286

her second trip: 3d+190m=165.5

solve by addition and elimination

4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286

3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)

12d+1320m=858

12d+760m=662

subtract two equation to eliminate d

12d+1320m-12d-760m=858-662

560m=196

m=7/20=0.35 for on mileage

d: 4d+440m=286

4d=286-440(0.35)

d=(286-154)/4 33 dollars

Step-by-step explanation:

im sorry but i need more info or a picture or something to actually anwser the question...

Answer:

No solutions.

Step-by-step explanation:

You will only have solutions when the two lines meet. But since the slopes are the same, the two lines are parallel. Since the y-intercepts are different, that means that the two slopes will never intersect, which means that there are no solutions.

Hope this helps!

Answer: no solution

Step-by-step explanation: When lines have the same slope, the graphs of the two lines are parallel which means they never intersect.

Let's look at an example.

Below, you will see two equations.

Both of the lines have a slope of 1.

So, they must be parallel which means they don't cross.

So there is no solution.

Step-by-step explanation:

to find the sum of nth term

equation is

n/2 ( 2a + (n-1)d) where a is the 1st term and d is the common difference

5/2 ( 120 +( 4 × 31))

5/2 ( 120 + 124)

5/2 × 244

5 × 122 dividing 244 by 2

610

Answer: 610

Step-by-step explanation:

This sequence starts at 60 and increases by increments of 31.  Thus, to get the last two numbers, do 122+31=153, and 153+31=184.  Then add 60+91+122+153+184 to get 610.

Hope it helps <3

Answer:

A.

{-4 ≤ x ≤ 4}

{-4 ≤ y ≤ 4}

Step-by-step explanation:

We’ll domain is the amount of x values,

Range is the amount of y values

_______________________________

Domain:

Starts from -4 to 4

{-4 ≤ x ≤ 4}

I made the sign less than or equal to because the circle lines are solid.

Range:

This starts from -4 to 4 also.

{-4 ≤ y ≤ 4}

Thus,

answer choices A. is correct

Hope this helps :)

Hey there! I'm happy to help!

Note that this is not a function because some inputs can have more than one output, that's why they say relation, not function! :D

DOMAIN

The domain is all of the possible x-values of the relation.  We see that the lowest x-value is -4, while the highest is 4. If you plug in these two or any number in between, there will be at least one corresponding output.

This domain can be written as -4 ≤ x ≤ 4.

RANGE

The range is all of the possible outputs or y-values. We see that the minimum y-value is -4 and that the highest is 4. Therefore, we will just write it the same as the domain but use a different variable.

-4 ≤ y ≤ 4.

This matches with Option A.

I hope that this helps! Have a wonderful day!

Answer:

The answer is "[tex]y=\frac{c}{1+a}[/tex]".

Step-by-step explanation:

Given:

[tex]\bold{y=\frac{c}{1+ae^{-rx}}}[/tex]

For the y-intercept, the value x is =0

[tex]y=\frac{c}{1+ae^{-r \times 0}}[/tex]

[tex]y=\frac{c}{1+ae^{0}}[/tex]

[tex]\therefore e^0 = 1[/tex]

[tex]y=\frac{c}{1+a\times 1}}[/tex]

[tex]\boxed{y=\frac{c}{1+a}}[/tex]

Answer:

C. [tex] \frac{343}{18} pie [/tex]

Step-by-step explanation:

Given a circle of:

Radius (r) = 14

Measure of minor arc = 115°

We are required to find the length of DGE = length of major arc.

Length of arc is given as 2πr(θ/360)

Measure of the major arc DGE (θ) = 360 - 115 = 245°

Length of major arc DGE = [tex] 2*pie*14*\frac{245}{360} [/tex]

[tex] = 28*pie*\frac{49}{72} [/tex]

[tex] = \frac{28*49}{72} pie [/tex]

[tex] = \frac{7*49}{18} pie [/tex]

[tex] = \frac{343}{18} pie [/tex]

Length of arc DGE =

[tex] \frac{343}{18} pie [/tex]

Answer:

Sum of money = $600

Step-by-step explanation:

X = sum of money

Simple interest means that its the same percentage of interest for a given number of years.

The interest per annum is 5% for 3 years, so 5% x 3 = 15%

15% = 0.15 (as a decimal)

Now, we can put this into an equation:

0.15x = 90

x = 90 / 0.15

x = 600.

sum of money invested = $600

Answer:

See below.

Step-by-step explanation:

So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.

Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.

Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.

Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:

In other words, we will have:

[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.

Let's determine n first. We know that f(0)=64, thus:

[tex]f(0)=64=4(-2)^3\cdot n[/tex]

[tex]64=-32n, n=-2[/tex]

Now, let's expand:

Expand:

[tex]f(x)=(x+4)(x^2-4x+4)(x-2)(-2)[/tex]

[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]

[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]

[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]

This is the simplest it can get.

Answer:

8 servings

Step-by-step explanation:

Spice required for one serving, using the rice-to-spice ratio to calculate:

David can make servings according to amount of spice he has:

Answer: David will be able to make 8 servings

Answer: 8

Step-by-step explanation:

Answer:

1.    [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]

2.   [tex]cos(60)[/tex]

3.   [tex]cos(60) = \frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]cos(\alpha - \beta )[/tex]

[tex]cos(79)cos(19) + sin(79)sin(19)[/tex]

Solving for [tex]\alpha[/tex] and [tex]\beta[/tex]

In trigonometry;

[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]

Equate the above expression to [tex]cos(79)cos(19) + sin(79)sin(19)[/tex]

[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex] and [tex]cos(\alpha - \beta ) = cos(79)cos(19) + sin(79)sin(19)[/tex]

By comparison

[tex]cos\alpha\ cos\beta + sin\alpha\ sin\beta = cos(79)cos(19) + sin(79)sin(19)[/tex]

Compare expression on the right hand side to the left hand side

[tex]cos\alpha\ cos\beta = cos(79)cos(19) \\\\ sin\alpha\ sin\beta = sin(79)sin(19)[/tex]

This implies that

[tex]cos\alpha\ = cos(79)\\cos\beta = cos(19) \\\\ and\\\\sin\alpha\ = sin(79)\\sin\beta = sin(19)[/tex]

By further comparison

[tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]

Substitute [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex] in [tex]cos(\alpha - \beta )[/tex]

[tex]cos(\alpha - \beta ) = cos(79 - 19)[/tex]

[tex]cos(\alpha - \beta ) = cos(60)[/tex]

Hence, the expression is [tex]cos(60)[/tex]

Solving for the exact values;

Express [tex]cos(60)[/tex] as a difference of angles

[tex]cos(60) = cos(90 - 30)[/tex]

Recall that [tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]

So;

[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex]

------------------------------------------------------------------------------------

In trigonometry;

[tex]cos(90) = 0[/tex]; [tex]cos(30) = \frac{\sqrt{3}}{{2}}[/tex]; [tex]sin(90) = 1[/tex]; [tex]sin(30) = \frac{1}{2}[/tex];

---------------------------------------------------------------------------

[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex] becomes

[tex]cos(90- 30 ) = 0 * \frac{\sqrt{3}}{2} + 1 * \frac{1}{2}[/tex]

[tex]cos(90- 30 ) = 0 + \frac{1}{2}[/tex]

[tex]cos(90- 30 ) = \frac{1}{2}[/tex]

Hence;

[tex]cos(60) = \frac{1}{2}[/tex]