A lighthouse flashes a beam of light once every 3/5 of a minute. How many times does it flash a beam of light in half an hour?

Answer:

f(10) =13

Step-by-step explanation:

f(x) =x/2+8,

Let x = 10

f(10) =10/2+8,

      = 5+8

       = 13

Question:

The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.

What is the value of h?

Answer:

A. 5

Step-by-step explanation:

Given

Solid Shape: Cone

Volume = 250/7

Diameter = Height

Required

Find the height of the cone

Provided that the diameter (D) and the height (h) are equal; This implies that

D = h ------ (1)

Also, Diameter (D) = 2 * Radius (r)

D = 2r

Substitute 2r for D in (1)

2r = h

Multiply both sides by ½

½ * 2r = ½ * h

r = ½h

Volume of a cone is calculated by;

Volume = ⅓πr²h

⅓πr²h = 250/7

Substitute ½h for r

[tex]\frac{1}{3} * \pi * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]

Take π as 22/7, the expression becomes

[tex]\frac{1}{3} * \frac{22}{7} * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]

Open the bracket

[tex]\frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7}[/tex]

Multiply both sides by 7

[tex]7 * \frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7} * 7[/tex]

[tex]\frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250[/tex]

Multiply both sides by 3

[tex]3 * \frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250 * 3[/tex]

[tex]22 * \frac{1}{4}h^2 * h = 750[/tex]

Multiply both sides by 4

[tex]4 * 22 * \frac{1}{4}h^2 * h = 750 * 4[/tex]

[tex]22 * h^2 * h = 3000[/tex]

[tex]22 * h^3 = 3000[/tex]

Divide both sides by 22

[tex]h^3 = \frac{3000}{22}[/tex]

[tex]h^3 = 136.36[/tex]

Take cube root of both sides

[tex]h = \sqrt[3]{136.36}[/tex]

[tex]h = 5.15[/tex]

[tex]h = 5[/tex] (Approximated)

Answer:

Fraction = 5/10 = 1/2

Decimal = 0.5

Step-by-step explanation:

Answer:

fraction-5/10 decimal-0.5

plz give brainiest

Step-by-step explanation:

Answer: kindly check Explanation.

Step-by-step explanation:

The function f(x) = 3x + 4 is a linear regression model. Orion's prediction was obtained by Substituting 25 for x to obtain the predicted variable

f(25) = 3(25) + 4 = 75 + 4 = 79.

However, with a correlation Coefficient of 0.39, which is a numerical value of range - 1 to +1 and is used to measure the statistical relationship between the dependent variable (number of gallons of ice-cream sold per day) and the independent variable (temperature).

The closer the correlation Coefficient (r) value is to +1 or - 1, the stronger the degree of correlation. Positive r values depicts positive relationship while negative r values depicts negative relationship. The closer the r value is to 0. The weaker the relationship and a r value of means there is no Relationship exists between the two variables.

With a correlation Coefficient of 0.39, we can Infer that that only a moderate positive relationship exists between temperature and gallons of ice cream sold per day.

Answer:

x = 9 (first odd number)

x + 2 = 11 (second odd number)

Step-by-step explanation:

Let

x =first odd number

x + 2=second odd number

given:

1/x - 1/(x + 2) = 2/99

Find the LCM

(x+2)-x / x(x+2)=2/99

x+2-x / x(x+2)=2/99

common denominator x( x + 2)

2 / x(x + 2) = 2/99

Take the reciprocal of both sides

1/2x(x + 2) = 99/2

multiply both by 2

x(x +2) = 99

Expand the left side

x^2 + 2x = 99

add 1 to both sides

x^2 + 2x + 1 = 100

express the left side as a square

(x + 1)^2 = 100

Square root of both sides

x + 1 = 10 or x + 1 = -10

taking the positive root only

x = 9 (first odd number)

x + 2 = 11 (second odd number)

check:

1/9 - 1/11 = 2/99

11/99 - 9/99 = 2/99

2/99 = 2/99

Step-by-step explanation:

The correct answer is the vertical change divided by the horizontal change between two points on a line. We can find the slope of a line on a graph by counting off the rise and the run between two points. If a line rises 4 units for every 1 unit that it runs, the slope is 4 divided by 1, or 4.

Answer:

Calculate the rise over the run/the change in y over the change in x

Step-by-step explanation:

In order to find the rate of change on a graph from a slope, you need to look at how many units up and how many units to the right. Find a solid point on the graph for both the x and y directions. Count how many units go up and how many go right. Divide how many units go up by how many go to the right and that is the rate of change on the graph.

Answer:

to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.

Step-by-step explanation:

Let the mortgage investment be X

The Bond to be Y

and the CDs to be Z

Thus;

X+Y+Z = 86000 ------- (1)

Y + Z = X       ------------(2)

10X + 9Y + 6Z = 7180 × 100 ------ (3)

So;we now have:

X+Y+Z = 86000 ------- (1)

Y + Z = X       ------------(2)

10X + 9Y + 6Z = 718000 ------ (3)

Let ; replace X with Y+Z in equation (1) and (3)

Y+Z + Y+Z = 86000

2Y + 2Z = 86000

Divide both sides by 2

Y+Z = 43000      ------ (4)

From equation (3)

10X + 9Y + 6Z = 718000

10(Y+Z) + 9Y + 6Z = 718000

10Y +10Z + 9Y +6Z = 718000

19Y + 16Z = 718000    -----(5)

Y+Z = 43000      ------ (4)

19Y + 16Z = 718000    -----(5)

Using elimination method; multiply (-16) with equation (4) and (5) ; so, we have:

 -16 Y -16 Z = -688000

 19Y + 16Z =    718000          

 3Y  + 0     =    30000            

3Y = 30000

Y = 30000/3

Y = 10000

From (4);

Y+Z = 43000  

So; replace Y with 10000; we have:

10000 + Z = 43000

Z = 43000 - 10000

Z = 33000

From (1) ;

X+Y+Z = 86000

X + 10000  + 33000 = 86000

X + 43000 = 86000

X = 86000 - 43000

X = 43000

Since we assume the bond to be Y and Y = $10000;

Thus; to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.

Answer:

Slope of Anya's line is m = 3

Step-by-step explanation:

Explanation:-

Given Anya graphed the line

                              (y−2)=3(x−1)

we know that  slope intercept form is

                                y = mx +c

now given Anya line

                           y−2=3(x−1)

            ⇒            y - 2 = 3x - 3

          ⇒             y = 3x - 3 + 2

         ⇒              y = 3 x - 1

Comparing slope -intercept form

                        y = mx +c

slope of Anya's line is m = 3 and y-intercept C = -1

Answer:

M=3

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

You can create a right triangle out of this information and then use right triangle trig to solve.

We are given the height of the triangle as the height of the tower which is 150m.

We are given the angle of inclination as the degree the tower makes with the ground which is 72.

From the angle of 72 degrees, which is also known as the reference angle, we have the side across from it (the height) and we are looking for the side adjacent to it (how far from the base of the tower the keys will land). Side opposite the reference angle over side adjacent to the reference angle is the tangent ratio:

[tex]tan(72)=\frac{150}{x}[/tex] and, solving for x,

[tex]x=\frac{150}{tan(72)}[/tex]

Make sure your calculator is in degree mode to solve this. Divide 150 by the tan(72) and find that

x = 48.7 m

Answer:

m < S = 55°

Step-by-step explanation:

Based on tangent theorem, a tangent line is said to be perpendicular to a radius of a circle when they intercept. The point at which they meet is said to be at 90°.

Therefore, in the ∆PQS, given, m < P = 90°.

m < Q = 35°

m < S = 180° - (90° + 35°) (sum of the angles in a triangle)

m < S = 180° - 125°

m < S = 55°

Answer:

A) 3,276 ways.

Step-by-step explanation:

In this case, choosing February 1, February 12, and February 20 would be the same thing as choosing February 12, February 1, and February 20. So, since order does not matter, we will use a combination to solve the question.

The formula for combinations is...

n! / [r!(n - r)!], where n = the number of days in February (28) and r = the number of days you are choosing (3).

28! / [3! * (28 - 3)!]

= 28! / (6 * 25!)

= (28 * 27 * 26) / 6

= (14 * 9 * 26) / 1

= 14 * 9 * 26

= 126 * 26

= A) 3,276.

Hope this helps!

Answer: 27cm²

Step-by-step explanation:

lets take the width as x and length as 3x( since length is 3 times the width)…

Perimeter of the rectangle is 24 cm( 2*(l+b))= 2×(3x+x):24

2×4x=24

8x=24

X( width): 24/8=3cm

Length= 3x: 3*3=9cm

Area of the rectangle: ( l*w)= 9×3: 27cm²

Answer:

Step-by-step explanation:

Answer:

y = (-x - 6)/2

Step-by-step explanation:

x + 2y = -6

2y = -x - 6

y = (-x - 6)/2

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]

Move constant to R.H.S and change its sign:

[tex]x = - \frac{21}{4} + \frac{1}{2} [/tex]

Take the L.C.M

[tex]x = \frac{ - 21 + 1 \times 2}{4} [/tex]

[tex]x = \frac{ - 21 + 2}{4} [/tex]

Calculate

[tex]x = - \frac{19}{4} [/tex]

Hope this helps...

Good luck on your assignment..

Step-by-step explanation:

-19/4 is the correct answer for your question

Answer:

A. -55

Step-by-step explanation:

f(x)=-2x^2+4x-7

f(-4)= -2(-4)^2+4(-4)-7

= -2(16)-18-7

= -32-16-7

= -55

Answer:

-55

Step-by-step explanation:

f(x) = −2x^2 + 4x − 7

Let x = -4

f(-4) = −2(-4)^2 + 4(-4) − 7

      = -2 (16) -16 -7

      = -32 -16 -7

      =-55

Answer:

-3, 5/2

Step-by-step explanation:

What are the roots of the function y = 4x2 + 2x – 30?

To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.

Factor out the GCF of : 2, so the equation becomes 0 = 2(2x2+x-15)

Next, factor the trinomial completely. The equation becomes: 0=2(x+3)(2x-5)

Use the zero product property and set each factor equal to zero and solve.

x+3=0      2x-5 = 0

x = -3, 5/2

The roots of the function are -3, 5/2.

Hope this helped!

The roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

y = 4x² + 2x - 30

To find the roots of the quadratic equation plug y = 0

4x² + 2x - 30 = 0

4x² + 12x - 10x - 30 = 0

4x(x + 3) - 10(x + 3) = 0

(x + 3)(4x -10) = 0

x + 3 = 0  or  4x - 10 = 0

x = -3 or x = 10/4 = 5/2

Thus, the roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.

Learn more about the function here:

brainly.com/question/5245372

#SPJ2

Answer:

Writing it in matrix form

- 2 - 4 - 5 - 155

1 1 6 101

2 2 - 3 37

I hope this helps you

Answer:

see below

Step-by-step explanation:

1.

1, H - 2, H - 3, H - 4, H - 5, H

1, T - 2, T - 3, T - 4, T - 5, T

2.

2,H is one out of 10 possible outcomes, so the probability is 1/10

Answer:

Dimensions of the bottle

x (radius of the base ) = 3,99 cm

h (heigh of the bottle ) = 3,99 cm

Surface area  = 149,99 cm²

Volume of the bottle = 199,45 cm³

Step-by-step explanation:

The bottle volume  must be  V(b) = 100 ml     or   V(b) = 100 cm³

The shape of the bottle is cylindrical

Surface area of bottle is

S = surface area of the base + lateral area

Area of the base = π*x ²         where x is radius of circle

Lateral area is  2*π*x*h           where h is the heigh of the bottle

V(b) = π* x²*h                             (1)        

π*x²  +  2*π*x*h  < 150 cm²  we work with the limit  150

π*x²  + 2*π*x*h  = 150

h   =  (150 - π*x²) /2*x*π

Plugging that value in equation (1)

V(x) = π*x² * (150 - π*x²) /2*x*π   ⇒    V(x) = 150*π*x²/2*x*π  - π²*x⁴/2*x*π

V(x) = 75*x - π*x³/2

Taking derivatives on both sides of the equation

V´(x) =  75  - 3*π*x²/2

V´(x) = 0           75 - 3*π*x² /2  = 0

x² = 75*2 /3*π       ⇒   x²  = 15,92      ⇒  x = 3,99 cm

And  h = ( 150 -π*x² )/2*π*x

h = ( 150 - 49,98 )/25,05

h  =  3,99 cm

Dimensions of the bottle

x (radius of the base ) = 3,99 cm

h (heigh of the bottle ) = 3,99 cm

Surface area  = 149,99 cm²

Volume of the bottle = 199,45 cm³

Answer:

the leanth of the track is 1/2 miles long.

Step-by-step explanation:

Im sorry that i couldn't complete all the questions, I had a family thing to go to so sorry.

Answer:

15

Step-by-step explanation:

mean means add all the numbers and divide them by how many there are

plot 1: 63 divided by 9 equals 7

plot 2: 330 divided by 15 equals 22

so now we need to subtract 22 minus 7 equals 15

hope this helps

Answer:

15

Step-by-step explanation: you have to add all of the numbers and then divide the answer by the number of numers you added

Answer:

D

Step-by-step explanation:

Assuming the figure to be a parallelogram, then

The consecutive angles are supplementary, that is

∠ D + ∠ C = 180°

145° + ∠ C = 180° ( subtract 145° from both sides )

∠ C = 35° → D

Answer:

138 : 269

Step-by-step explanation:

Last year, the number of bicyclists that showed up was 1345.

This year, there were 690 bicyclists.

The ratio of the number of bicyclists that showed up for the past two years is the ratio of those that showed up this year to those that showed up last year:

690 : 1345

Let us put it in simplest terms:

138 : 269

Answer:

B. 642.22 units squared

Step-by-step explanation:

Knowing that QP ║ MN and ∠QLP = ∠MLN, then ΔQLP ~ ΔMLN.

That means corresponding sides and heights have the same ratios.

We know that QP = 25, which corresponds to MN = 34. Also, the height of ΔQLP, LS, corresponds to the height of ΔMLN, LR = LS + SR = LS + 10. Let's say LS = x.

We can now write:

QP / MN = LS / LR

25 / 34 = x / (x + 10)

Cross-multiply:

34 * x = 25 * (x + 10)

34x = 25x + 250

34x - 25x = 250

9x = 250

x = 250/9 ≈ 27.78 units

So, LS = 27.78 units and LR = LS + SR = 27.78 + 10 = 37.78 units.

The area of a triangle is denoted by A = (1/2) * b * h, where b is the base and h is the height.

Here, the base of ΔLMN is MN = 34, and the height is LR = 37.78. Plug these in:

A = (1/2) * b * h

A = (1/2) * 34 * 37.78 ≈ 642.22 units squared

The answer is thus B.

~ an aesthetics lover

Answer:

Length= 58

width= 26

Step-by-step explanation:

Answer:

  16

Step-by-step explanation:

(f - g)(5) = f(5) -g(5)

From the tables, ...

  f(5) = 29

  g(5) = 13

Your desired function is ...

  f(5) -g(5) = 29 -13 = 16

Answer and Step-by-step explanation:

The domain of a function is the values the invariable can assume to result in a real value for the variable. In other words, it is all the values x can be.

Since it's related to area, the values of x has to be positive. The domain must be, then:

[tex]-6x^{2} + 105x - 294 = 0[/tex]

Solving the second degree equation:

[tex]\frac{-105+\sqrt{105^{2} - 4(-2)(-294)} }{2(-6)}[/tex]

x = 3.5 or x = 14

The domain of this function is 3.5 ≤ x ≤ 14

The maximum area is calculated by taking the first derivative of the function:

[tex]\frac{dA}{dx} = -6x^{2} + 105x - 294[/tex]

A'(x) = -12x + 105

-12x + 105 = 0

-12x = -105

x = 8.75

A(8.75) = [tex]-6.8.75^{2} + 105.8.75 - 294[/tex]

A(8.75) = 165.375

The maximum area of the garden is 165.375 square units.

The Range of a function is all the value the dependent variable can assume. So, the range of this function is: 0 ≤ y ≤ 165.375, since this value is the maximum it will reach.

A(x) = 100

[tex]100 = -6x^{2} + 105x-294[/tex]

[tex]-6x^{2} + 105x - 394 = 0[/tex]

Solving:

[tex]\frac{-105+\sqrt{105^{2}-4(-6)()-394} }{2(-6)}[/tex]

x = 5.45 or x = 12.05

The values of x that produces an area of 100 square units are 5.45 and 12.05