How does the frequency of f(x) = cos(2x) relate to the frequency of the parent function cos x?

Answer:

The standard form of the equation of y = -1/4x - 2 is x + 4y = -8 which is C

Answer:

Step-by-step explanation:

You can let c, b, s represent the investments in CDs, bonds, and stocks, respectively.

  c + b + s = 170000 . . . . . . total invested

  0.0325c +0.038b +0.067s = 7745 . . . . . . . annual income

  -c + b = 60000

You can solve this set of equations using any of a number of methods, including on-line calculators, graphing calculators, scientific calculators, Cramer's Rule, substitution, elimination, and more. The solution is ...

  c = 30,000

  b = 90,000

  s = 50,000

Maricopa's Success invested $30,000 in CDs, $90,000 in bonds, and $50,000 in stocks.

Answer:

Step-by-step explanation:

Substitute x = 1 and y = 1 to the both inequalities:

[tex]x-8y\leq9\\\\1-8(1)\leq9\\1-8\leq9\\-7\leq9\qquad\bold{TRUE}\\==================\\-7x+5y<4\\\\-7(1)+5(1)<4\\-7+5<4\\-2<4\qquad\bold{TRUE}[/tex]

Answer:

(1,1) does satisfy

x - 8y ≤ 9

- 7x + 5y < 4

Step-by-step explanation:

Well, first we need to plug in (1,1) into,

x - 8y ≤ 9

- 7x + 5y < 4

→ 1 - 8(1) ≤ 9

- 7(1) + 5(1) < 4

1 - 8 ≤ 9

-7 + 5 < 4

-7 ≤ 9

-2 < 4

Thus,

(1,1) does satisfy

x - 8y ≤ 9

- 7x + 5y < 4.

Hope this helps :)

Answer:

S(min) = 59,66 cm²

Step-by-step explanation:

The volume of a cylindrical can is:

V(c) = π*x²*h         where   x is radius of the base and h the height

V(c) = 50 cm³

50 =  π*x²*h      (1)

The surface area of the can (Sc) is  Surface area of the base (Sb) plus surface lateral area (Sl)

S(b) =  π*x²  

And  S(l) = 2*π*x*h

Then

S(c) =  π*x²  +  2*π*x*h

And  surface area as a function of x is

From equation (1)

h = 50 /π*x²   and plugging this value in the previous expression

S(x) =  π*x²  +  2*π*x*(50/π*x²)

S(x) =  π*x²  + 100/x

Taking derivatives on both sides of the equation

S´(x) = 2*π*x - 100/x²

S´(x) = 0     means       2*π*x - 100/x² = 0

π*x - 50/x²  = 0

π*x³ - 50  = 0

π*x³  = 50

x³ = 50 / 3,14

x³ = 15,92

x  = 2,51 cm

And  h =  50 / π* (2,51)²

h = 2,53 cm

Then minimum surface area of the can is:

S(min) = 19,78 + 39,88

S(min) = 59,66 cm²

Answer:

Step-by-step explanation:

Hello!

Out of 846 patients taking a prescription drug daily, 18 complained of flulike symptoms.

It is known that the population proportion of patients that take the drug of the competition and complain of flulike is 1.8%

Be the variable of interest:

X: number of patients that complained of flulike symptoms after taking the prescription drug, out of 846.

sample proportion p'= 18/846= 0.02

You have to test if the population proportion of patients that experienced flulike symptoms as a side effect is greater than 1.8% (p>0.018)

Assuming that the patients for the clinical trial were randomly selected.

The expected value for this  sample is np=846*0.02= 1658 (the expected value of successes is greater than 10) and the sample is less than 10% of the population, you can apply the test for the proportion:

The hypotheses are:

H₀: p ≤ 0.018

H₁: p > 0.018

α: 0.01

[tex]Z= \frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)

[tex]Z_{H_0}= \frac{0.02-0.018}{\sqrt{\frac{0.018*0.982}{846} } }= 0.437[/tex]

The p-value for this test is  0.331056

The decision rule is

If p-value ≤ α, reject the null hypothesis

If p-value > α, do not reject the null hypothesis

The p-value is greater than α, the decision is to reject the null hypothesis.

So at 1% significance level there is no significant evidence to reject the null hypothesis, you can conclude that the population proportion of patients that took the prescription drug daily and experienced flulike symptoms as a side effect is less or equal to 1.8%

I hope this helps!

Answer:

y ≤0

Step-by-step explanation:

y =- x^2

x^2 is always positive or 0

Make this negative

- x^2 is negative or 0

The range is negative or 0

y ≤0

Answer:

Step-by-step explanation:

y=-x^2

the range is(-∞,0]

y≤ 0 ( since the coefficient  a is negative it is open downward)

Answer:

Where is the table

Step-by-step explanation:

I cant answer without it

Answer:

x = 25

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent.

That is ∠ D and ∠ B are corresponding angles and congruent, thus

4x - 20 = 2x + 30 ( subtract 2x from both sides )

2x - 20 = 30 ( add 20 to both sides )

2x = 50 ( divide both sides by 2 )

x = 25

Answer:

[tex] db = 10 log_{10} (\frac{I}{I_o})[/tex]

With db =112 db, [tex]I_o =10^{-12} W/m^2[/tex] and solving for I the intensity we have:

[tex] \frac{db}{10}= log_{10} (\frac{I}{I_o})[/tex]

[tex] \frac{112}{10}= log_{10} (\frac{I}{10^{-12}})[/tex]

Now we can exponentiate with base 10 and we got:

[tex] 10^{11.2} = \frac{I}{10^{-12}}[/tex]

And solving we got:

[tex] I= 10^{-12} * 10^{11.2} = 0.158 \frac{W}{m^2} = 0.16 \frac{W}{m^2}[/tex]

Step-by-step explanation:

We knwo that the loudnes os 112 db and we want to find the intensity. So then we can use the following formula:

[tex] db = 10 log_{10} (\frac{I}{I_o})[/tex]

With db =112 db, [tex]I_o =10^{-12} W/m^2[/tex] and solving for I the intensity we have:

[tex] \frac{db}{10}= log_{10} (\frac{I}{I_o})[/tex]

[tex] \frac{112}{10}= log_{10} (\frac{I}{10^{-12}})[/tex]

Now we can exponentiate with base 10 and we got:

[tex] 10^{11.2} = \frac{I}{10^{-12}}[/tex]

And solving we got:

[tex] I= 10^{-12} * 10^{11.2} = 0.158 \frac{W}{m^2} = 0.16 \frac{W}{m^2}[/tex]

Answer: 40 ( to the nearest ten)

Step-by-step explanation:

Complete question :

The loudness of a jack hammer is 96 dB . Its sound intensity is about 0.004.

The loudness of a compactor is 94 dB . Its sound intensity is about 0.0025.

The sound intensity of the jack hammer is about 1.6 times the sound intensity of the compactor.

The loudness of a pile driver is 112 dB . About how many times the sound intensity of the jackhammer is the sound intensity of a pile driver? Round to the nearest ten.

Given that:

Sound intensity of jackhammer = 0.004

Sound intensity of compactor = 0.0025

Sound intensity of jackhammer is about 1.6 times the sound intensity of a compactor

Each factor of 10 in intensity corresponds to 10dB

Pile driver with loudness of 112dB ⇒ [tex]\frac{112}{10}=11.2[/tex]

Hence, 10^11.2 = 1.58489 × 10^11

Hence, sound intensity (I) in watts per m²

I = 1.58489 × 10^11 × 10^-12

I = 1.58489 × 10-1

I = 0.158489

Comparing the intensity of pile driver and jackhammer :

Intensity of piledriver / Intensity of jackhammer

[tex]\frac{0.158489}{0.004}[/tex]

= 39.622  ≅ 40 ( to the nearest ten )

Answer: 245 cu. cm.

Step-by-step explanation:

4/7-2/5=20/35-14/35=6/35

42 cm3 represents 6/35 of the total volume

how many 6/35's are in 35/35 ? (the total volume)

(35/35)/(6/35)=(35/35)*(35/6)=35/6=5 5/6

(5 5/6)*(42)=(35/6)*(42)=35*7=245 cm3 is the total volume

Answer:

12

Step-by-step explanation:

let

x= no. for English

y= no. for maths

z= no. for fine arts

a= no. for all subjects

x= 22

y= 21

z= 17

x+y+z= 39

x intersect y= 11

y intersect z= 8

x intersect z= 7

(4+a)+ (11-a)+ (7-a)+ (8-a)+ (2+a)+ (2+a)+ a= 39

34+a =39

a= 5

no.of teachers who teaches all & fine art only

= a + (2+a)

= 5+7

= 12

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:

D. [tex] y = \frac{8}{x} [/tex]

Step-by-step explanation:

The inverse variation between two variables usually takes the following equation form:

[tex] y = \frac{k}{x} [/tex]

In the equation form given above,

[tex] k [/tex] could be value of any real number

x is the explanatory variable (independet variable), while y is the response variable (dependent variable)

Therefore, [tex] y = \frac{8}{x} [/tex] , is an example of an equation that shows inverse variation between the x and y variables.

 The right option is D. [tex] y = \frac{8}{x} [/tex]

Answer:

9.40%

Step-by-step explanation:

Given:

Annual coupon rate = 11%

Time left to maturity = 11 years

Par value of bond = 1000

Present value of bond = 1153.60

Required: Find Yeild to Maturity (YTM)

To find the yield to maturity, use the formula below:

YTM = [Annual coupon+(Face value-Present value)/time to maturity]/(Face value+Present value)/2

where annual coupon = 1000 * 11% = 110

Thus,

[tex]YTM = \frac{\frac{110+(1000-1139.59}{9}}{\frac{(1000+1139.59)}{2}}[/tex]

YTM = 9.40%

Therefore the approximate YTM is 9.40%

Answer:

it opens up

goes up 4 but doesn't move left or right

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:

2.321428571%

Step-by-step explanation:

Given in the question,

P=$350

T=4years

I=$32.50

We know that

I=PTR/100

32.50=350*4*R/100

R=32.50*100/350*4

R=2.321428571%

So, the rate of interest is 2.321428571%

Answer:

352.8 ft

Step-by-step explanation:

m∠A = 180° − 102.9° − 18.6° = 58.5°

AB = c and BC = a.

Use law of sines:

c / sin C = a / sin A

c / sin 18.6° = 943 / sin 58.5°

c = 352.8

The correct answer is 45.5 km

Explanation:

The total distance from the locksmith to the hotel, located in the east of the graph is not directly given; however, this distance can be calculated by considering the partial distances given. This includes the distance from the locksmith to the furniture store (18.3 km), and the distance between the furniture and the hotel (27.2) as the total distance = distance from the locksmith to the furniture store + distance from the furniture store to the hotel. Thus, the total distance is 18.3 km + 27.2 km which is equal to 45.5 km.

Answer:

60 ounces

Step-by-step explanation:

A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint, that is, the white paint (w) to blue paint (b) ratio is 5:4. We can apply this ratio to different units such as ounces. This means that the mixture has 5 ounces of white paint to 4 ounces of blue paint. If a can of paint contains 75 ounces of white paint, the ounces of blue paint in the can are:

75 oz w × (4 oz b/5 oz w) = 60 oz b

Answer:

The probability is  [tex]P(X > x) = 0.0013499[/tex]

Step-by-step explanation:

From the question we are told that

     The mean is  [tex]\mu = 25[/tex]

      The standard deviation is [tex]\sigma = 5 \ minutes[/tex]

      The random number  [tex]x = 40[/tex]

Given that the time taken is  normally distributed  the probability is mathematically represented as

     [tex]P(X > x) = P[\frac{X -\mu}{\sigma } > \frac{x -\mu}{\sigma } ][/tex]

Generally the z-score for the normally distributed data set is mathematically represented as

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

So  

     [tex]P(X > x) = P[Z > \frac{40 -25}{5 } ][/tex]

    [tex]P(X > x) = 0.0013499[/tex]

This value is obtained from the z-table

Answer:

7

Step-by-step explanation:

2b - 5b is -3b so it leaves the equation with -3b + 7 + 3b

-3b + 3b cancells out to 0 so it leaves the final answer to 7

Answer:

Option A is correct

Step-by-step explanation:

From the question we are told that

  The  Null Hypothesis  is  [tex]H_o : p = 0.45[/tex]

   The alternative hypothesis [tex]H_a : p > 0.45[/tex]

   The  level of significance is  [tex]\alpha = 0.05[/tex]

    The  p-value is  [tex]p-value = 0.025[/tex]

Now looking at the given data we see that the the p-value is less than [tex]\alpha[/tex]

Generally when this occurs in a hypothesis test we reject the null hypothesis which mean that the result which we obtain is statistically significant.

Hence the alternative hypothesis is correct, which means that,

  There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 45%. which is option A

Answer:

A

Step-by-step explanation:

That is the radius. Since its half of the diameter.

Answer:

A.  Radius of the circle

Step-by-step explanation:

A line segment that has as endpoints the center of a circle and a point on the circle is called a radius.

Answer: A.  Radius of the circle

Answer:

The measure of each angle:

152.8°   and     27.2°

Step-by-step explanation:

Supplementary angles sum 180°

then:

a + b = 180°

a - b = 125.6°

then:

a = 180 - b

a = 125.6 + b

180 - b = 125.6 + b

180 - 125.6 = b + b

54.4 = 2b

b = 54.4/2

b = 27.2°

a = 180 - b

a = 180 - 27.2

a = 152.8°

Check:

152.8 + 27.2 = 180°

Answers:

Step-by-step explanation:

Let x and y be the measures of each angle.

x + y = 180°

x - y = 125.6°

180 - 125.6 = 54.4

Now we divide 54.4 evenly to get y.

y = 27.2°

To get x, we substitute y into the equation.

x = 27.2 + 125.6

x = 152.8°

To check, we plug these in to see if they equal 180°.

27.2 + 152.8 = 180° ✅

Answer:

i think it is E

Step-by-step explanation:

Answer:

N(n+1) = N(n)^2 - 1, n>=0, N(0) = 2

or equivalently

N(n) = N(n-1)^2 - 1, n>0, N(0) = 2

Step-by-step explanation:

Year 0 = 2 trees

year 1 = 2^2-1 = 3

year 2 = 3^2-1 =8

year 2 = 8^2-1 =63

...

Recursive formula

Let

n = integer year number

N(n) = number of trees to plant in year n

N(n+1) = N(n)^2-1, n>=0, N(0) = 2

or equivalently

N(n) = N(n-1)^2, n>0, N(0) = 2

Whats the options???

Answer:

[tex]B= 3.14 * 4^4 = 50.24cm^2\\h = 16cm\\V=B*h=50.24*16=803.84cm^3[/tex]

Step-by-step explanation:

The area of the base is the area of a circle with a radius equal to 4 cm. It means that the area can be calculated as:

[tex]B = 3.14 * r^2\\B= 3.14 * 4^4 = 50.24cm^2[/tex]

The height of the cylinder is shown in the picture, it is equal to 16 cm.

Finally, the volume of the cylinder can be calculated as:

[tex]V = B*h=50.24*16 = 803.84cm^3[/tex]

Where B is the base and h is the height of the cylinder.

Answer:

13

Step-by-step explanation:

10 + 16 = 26

26 divided by 2 = 13

The middle number is 13