A runner can run 3 miles in 18 minutes. At this rate, how many miles can he run in 54
minutes?
6
9
12
I
18​

Answer:

366

Step-by-step explanation:

2×3+4×100-50+10​

PEMDAS says multiply and divide from left to right

6 + 400 - 50 +10

Then add and subtract

406-50+10

356+10

366

Answer:

[tex]\boxed{366}[/tex]

Step-by-step explanation:

[tex]2 \times 3+4 \times 100-50+10[/tex]

Multiplication is first.

[tex]6+400-50+10[/tex]

Add or subtract the numbers.

[tex]350+10+6[/tex]

[tex]366[/tex]

Answer:

3051.08 cm squared

Step-by-step explanation:

The equation to find lateral surface area of a cone:

SA = pi r sqrt(h^2 * r^2)

Plug your values in.

SA = 3.14 * 9 * sqrt(144*81)

SA = 3.14 * 9 * 108

SA = 3051.08

The lateral surface area is 3051.08 cm squared.

Answer:

424.12cm^2

Step-by-step explanation:

make sure you have the radius, half of the diameter!

remember to use this formula! Lateral surface area = πrs = πr√(r2 + h2)

hope this helped!

r=radius

h=hight

s=slant

Answer:

h = -9

Step-by-step explanation:

5h+2(11-h)= -5

Distribute

5h +22 -2h = -5

Combine like terms

3h +22 = -5

Subtract 22 from each side

3h +22-22 = -5-22

3h = -27

Divide by 3

3h/3 = -27/3

h = -9

Answer:

The Taylor series is   [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Step-by-step explanation:

From the question we are told that

      The function is  [tex]f(x) = sin (x)[/tex]

This is centered at  

       [tex]a = 2 \pi[/tex]

Now the next step is to represent the function sin (x) in it Maclaurin series form which is  

          [tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]

=>       [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

   Now since the function is centered at  [tex]a = 2 \pi[/tex]

We have that

           [tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]

This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]

           [tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]

Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]

This because  [tex]2 \pi[/tex] is a constant

   Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is

             [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Answer:

g ( x ) = 4x^2 + 10

Step-by-step explanation:

Solution:-

The translation of a function f ( x ) in the cartesian coordinate domain can be done by following the given guidelines:

Translation guidelines

    Horizontal shifts

  Vertical shifts

   General shift ( Horizontal and Vertical shift )

               f ( x ) - > f ( x ± a ) ± b

We are given a function f ( x ) which is to be translated vertically upward 4 units. We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.

                        f ( x ) = 4x^2 + 6

                        f ( x ) - > f ( x ) + b              

                        g ( x ) = f ( x ) + 4

                        g ( x ) = 4x^2 + 6 + 4

                        g ( x ) = 4x^2 + 10   ... Answer

The lowest common denominator is lcm(5, 3), which is 15.

The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].

Answer:

The answer is #3 which is 24%.

Step-by-step explanation:

6 × 100

25

25 into 100 is 4, then 6×4 = 24%

I really hope this helps :)

Answer:

The answer is option 2.

Step-by-step explanation:

You have to apply Cosine Rule, cosθ = adjacent/hypotenuse. Then, you have to substitute the values into the formula :

[tex]cos(θ) = \frac{adj.}{hypo.} [/tex]

[tex]let \: θ = 55[/tex]

[tex]let \: adj. = 11[/tex]

[tex]let \: hypo. = x[/tex]

[tex]cos(55) = \frac{11}{x} [/tex]

The correct trigonometry formula to use to solve for x is [tex]\frac{11}{x}[/tex] . Thus option 1 is correct.

According to the question, we have

base = 11

hypotenuse = x

here for [tex]cos Ф[/tex]Ф,  it is not required to find the value of perpendicular,

we know that in a right-angle triangle using trigonometric ratio, we get

[tex]cos Ф[/tex] Ф = [tex]\frac{base }{hypotenuse}[/tex]

[tex]cos Ф[/tex] Ф = [tex]\frac{11}{x}[/tex]  

here  Ф = [tex]55 ^0[/tex]

[tex]cos 55^o = \frac{11}{x}[/tex]

Thus, the value of the trigonometry formula to use to solve for x is  [tex]\frac{11}{x}[/tex].

Thus option 1 is correct.

Learn more about Trigonometry here :

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Answer:

(0,2)

Step-by-step explanation:

solve by addition/elimination

2x + 3y= 6

–3x + 5y = 10  

multiply first equation by 3  and second one by 2 to eliminate x)

6x+9y=18

-6x+10y=20 (add the two equations)

6x+9y-6x+10y=38

19y=38

y=38/19=2

2x+3y=6

2x=6-6

x=0

Answer:

a

Step-by-step explanation:

Answer:

a = 8.1

Step-by-step explanation:

Firstly, since we have a triangle, automatically, we have 3 interior angles

Mathematically the sum of these angles = 180

A + B + C = 180

27 + 25 + C = 180

52 + C = 180

C = 180-52

C = 128

We use the sine rule to find a

The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle

Thus, mathematically according to the sine rule;

c/Sin C = a/Sin A

14/sin 128 = a/sin 27

a = 14sin27/sin 128 = 8.0657

which to the nearest tenth is 8.1

Answer:

70

Step-by-step explanation:

You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.

Answer:

65 dinners are expected to show up

The standard deviation of the distribution is 3.13

Step-by-step explanation:

Given

Proportion = 15%

Population = 77

Required

Expected Number that'll show up

Standard Deviation

If 15% won't show up; then

100% - 15% = 85% will show up

Expected Number, E(x) of Dinner is calculated as thus;

[tex]E(x) = np[/tex]

Where [tex]p = 85\%[/tex] (calculated above)

and [tex]n = 77[/tex]

Convert p to decimal

[tex]p = 0.85[/tex]

So;

[tex]E(x) = 0.85 * 77[/tex]

[tex]E(x) = 65.45[/tex]

[tex]E(x) = 65[/tex]

65 dinners are expected to show up

Calculating Standard Deviation, SD

Standard Deviation is calculated as;

[tex]SD = \sqrt{np(1-p)}[/tex]

Substitute 0.85 for p and 77 for n

[tex]SD = \sqrt{77 * 0.85 * (1-0.85)}[/tex]

[tex]SD = \sqrt{77 * 0.85 * 0.15}[/tex]

[tex]SD = \sqrt{9.8175}[/tex]

[tex]SD = 3.13328900678[/tex]

[tex]SD = 3.13[/tex] (Approximated)

The standard deviation of the distribution is 3.13

Answer:

The answer is option B.

Step-by-step explanation:

six less than a number is written as

x - 6

Hope this helps you

Answer:

Hi! Answer will be below.

Step-by-step explanation:

The answer is 450.

If you divide 1.8 and 0.004 the answer you should get is 450.

Below I attached a picture of how to do long division...the picture is an example.

Hope this helps!:)

⭐️Have a wonderful day!⭐️

Answer:

Larger force= 66.28 pounds

Step-by-step explanation:

The angle of the resultant force 80 pounds = 180-(52+20)

The angle of the resultant force 80 pounds = 180-72

The angle of the resultant force 80 pounds = 108°

The larger force is the force with 52°

Let the larger force be x

Magnitude of the larger force

x/sin52 = 80/sin108

X= sin52 *(80/sin 108)

X= 0.7880*(80/0.9511)

X = 0.7780*(84.1131)

X = 66.28 pounds

Answer:

Step-by-step explanation:

[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]

[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]

now you find the point of intersection.

then calculate the angle.

Answer:

0.29

Step-by-step explanation:

There are 29 squares shaded in. In all, there are 100 squares in the 10 × 10 square, so there are 29 shaded squares out of 100 squares in all. That is basically:

[tex]\frac{29}{100}[/tex]

[tex]\frac{29}{100}[/tex] can be converted to 0.29.

Answer:

0.29

Step-by-step explanation:

Since the grid is a 10x10, it means there are 100 total 'blocks' in the grid. So, since there are 29 shaded in out of the 100 'blocks total, the decimal would be .29, since the decimal means 29 hundredths, and it also means that there is 29 hundredths of the total grid shaded in.

Answer:

Your answer is correct ✔️

Step-by-step explanation:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

2√3 + 3i is the answer

Step-by-step explanation:

Answer: Null Hypothesis [tex]H_{0}[/tex]: p = 0.18

              Alternative Hypothesis [tex]H_{a}[/tex]: p < 0.18

Step-by-step explanation: When doing an experiment, first define the hypotheses you want to test. These hypotheses are Null Hypothesis and Alternative Hypothesis

Null Hypothesis is a general assumption and discloses that there is no relationship between the conditions under consideration. It is the hypothesis the researcher is trying to disprove. It is denoted by the symbol [tex]H_{0}[/tex].

For the college graduate curiosity, the hypothesis the graduate is trying to disprove is that the proportion of students who have loan debt after 20 years of graduation is 18%. Then, Null Hypothesis is [tex]H_{0}[/tex]: p = 0.18

Alternative Hypothesis is the a statement describing a relationship between the collected data. It is what researches try to prove and the results are observations of real causes. It is denoted by the symbol [tex]H_{a}[/tex].

For the graduate study, the alternative is that the proportion is less tahn 18% or 0.18. Then, Alternative Hypothesis: [tex]H_{a}[/tex]: p < 0.18

Answer:

a)   x₁ = 14

     x₂ = - 6

b) x = 4

c) P(max ) = 4000000 $

Step-by-step explanation:

To find the axis of symmetry we solve the equation

a) -4x² + 32x + 336 = 0

4x²  - 32x  - 336  = 0       or    x² - 8x - 84 = 0

x₁,₂ = [ -b ± √b² -4ac ]/2a

x₁,₂ = [ 8  ±√(64) + 336 ]/2

x₁,₂ = [ 8  ± √400 ]/2

x₁,₂ =( 8 ± 20 )/2

x₁  = 14

x₂ = -6

a) Axis of symmetry must go through the middle point between the roots

x = 4 is the axis of symmetry

c) P = -4x² + 32x + 336

Taking derivatives on both sides of the equation we get

P´(x) = - 8x + 32  ⇒  P´(x) = 0     - 8x + 32

x = 32/8

x = 4    Company has to sell  4 ( 4000 snowboard)

to get  a profit :

P = - 4*(4)² + 32*(4) + 336

P(max) = -64  + 128 + 336

P(max) = 400           or  400* 10000 =  4000000

Answer:

(-2,-110)

Step-by-step explanation:

First solve for x

20x−70=70x+30

x= -2

Now substitute x for -2

y=20x−70

y=20(-2)-70

y = -110

Answer:

The dog will eat 3 lbs

Step-by-step explanation:

Take the amount eaten per day and multiply by the number of days

3/4 * 4 = 3

The dog will eat 3 lbs

Answer:

3 pounds

Step-by-step explanation:

Multiply the amount of dog food per day with the number of days.

[tex]\frac{3}{4} \times 4[/tex]

[tex]\frac{12}{4} =3[/tex]

In 4 days, Jamie's dog will eat 3 pounds of dog food.

Answer:

10 miles

Step-by-step explanation:

3 mi/1 hr  x (h hours + 2/3 hr) = 5 mi/1 hr  x  h hours

3h + 2 = 5h

2 = 2h

h = 1 hour

3mi/hr  x 1 2/3 hr = 5 miles

5 mi/hr x  1 hr = 5 miles

He hiked 10 miles. (

Answer:

Step-by-step explanation:

Simplify each term.

y ≤ −2x/5 + 2

Find the slope and the y-intercept for the boundary line.

Slope: -2/5

Y-intercept: 2

Graph a solid line, then shade the area below the boundary line since

y is less than -2x/5 + 2

y ≤ −2x/5 + 2

Hope this can help

Answer:

d. 5250 pounds

Step-by-step explanation:

25 lbs per day

There are 30 days in april

25 lbs/ day * 30 days

1 tiger would eat 750 lbs

There are 7 tigers

7 * 750 =5250 lbs

Answer:

D. 5250 pounds

Step-by-step explanation:

What you need to do is multiply 25 pounds by 30 because there are 30 days in the month of April.

25 x 30 = 750

Then multiply that amount by seven because there are 7 tigers.

750 x 7 = 5250

Answer:

3/26

Step-by-step explanation:

Probability of the first box to have the secret decoder ring is 18 out of 52:

Probability of the second box to have the ring is 17 out of 51, because one box with the ring already selected and not counted:

Probability that both of them have the secret decoder ring:

So the answer is 3/26

Step-by-step explanation:

Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .

Answer:

We have sinθ = 12/13

The  method here is to figure out the value of θ

Using a calculator sin^(-1)(12/13) =67.38°

67.38° is in quadrant 1  so we must substract 67.38° from 180° wich is π

Now time to calculate cos2θ and cosθ using a calculator

The values we got make sense since θ is in quadrant 2 and 2θ in quadrant 3

Answer:

150 days

Step-by-step explanation:

6-4=2

100/2=50

50*3=150

The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.

The rate of disintegration varies directly proportional to the quantity of the material.

As such, we can say:

[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]

[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]

Taking the integral form;

[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]

[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]

When t = 0, N = 6 grams

In(6) = C

∴

When t = 100, N = 4 grams

In (4) = 100k + In6

100 k = 1n (4) - In(6)

[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]

[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]

∴

From equation (1):

[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]

when,

[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]

[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]

[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]

[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]

t = 173.077 days

Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.

Learn more about radioactive materials here:

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Answer:

7987.1569 to the nearest thousandths is 7987.157

Step-by-step explanation: