The sum of four consecutive integers is -62. What is
the least of the four integers?

[tex]30.87[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \frac{926}{30} \\ = 30 \frac{26}{30} \\ ( \: or \: ) \\ = 30.8666 \\ = 30.87 [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

I. Radius, r = 2.90 cm

II. Height, h = 4.10 cm

Step-by-step explanation:

Given the following data;

Volume of cone = 24 cm³

To find the height and radius of the cup that will use the smallest amount of paper;

Mathematically, the volume of a cone is given by the formula;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]  ......equation 1

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Substituting into the formula, we have;

[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]

Multiplying both sides by 3, we have;

[tex] 108 = \pi r^{2}h[/tex]

Making radius, r the subject of formula, we have;

[tex] r^{2} = \frac {108}{ \pi h} [/tex]

Taking the square root of both sides, we have;

[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]

Mathematically, the lateral surface area of a cone is given by the formula;

[tex] LSA = \pi rl [/tex]  ......equation 2

Where;

r is the radius of a cone

l is the slant height of a cone.

To find the slant height, we would apply the Pythagorean' theorem;

[tex] l = \sqrt {r^{2} + h^{2}} [/tex]

Substituting r into the above equation, we have;

[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]

Substituting the values of r and l into eqn 2, we have;

[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]

Simplifying further, we have;

[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]

[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]

Next, to find the value of h, we differentiate the above mathematical equation with respect to h;

[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]

Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;

[tex] \frac {dS}{dh} = 0 [/tex]

[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]

Rearranging the equation, we have;

[tex] \pi = \frac {216}{h^{3}} [/tex]

We know that π = 3.142

[tex] 3.142 = \frac {216}{h^{3}} [/tex]

Cross-multiplying, we have;

[tex] 3.142h^{3} = 216 [/tex]

[tex] h^{3} = \frac {216}{3.142} [/tex]

[tex] h^{3} = 68.75 [/tex]

Taking the cube root of both sides, we have;

Height, h = 4.10 cm

Lastly, we find the value of r;

[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]

[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]

[tex] r = \sqrt { \frac {108}{12.88}} [/tex]

[tex] r = \sqrt {8.39} [/tex]

Radius, r = 2.90 cm

The height and radius of the cup that will use the smallest amount of paper is;

Radius = 2.52 cm

Radius = 2.52 cmHeight = 3.58 cm

Let us first state some relevant formulas;

Volume of a cone is;

V = ⅓πr²h

Surface area of a cone is;

S = πrL

Where L is Slant height and has a formula;

L = √(h² + r²)

We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³

24 = ⅓πr²h

πr²h = 72

r = √(72/πh)

Putting √(72/πh) for r in the Slant height equation gives;

L = √(h² + (72/πh))

Thus;

S = π × √(72/πh) × √(h² + (72/πh))

Differentiating with respect to h gives;

dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)

At dS/dh = 0,we will have;

(π - 144/h³) = 0

Thus;

h³ = 144/π

h = 3.58 cm

Thus, from r = √(72/πh);

r = √(72/(π × 3.58))

r = 2.52 cm

Read more at; https://brainly.com/question/4405937

Answer:

A

Step-by-step explanation:

because this shapes angle would be out of 360 so you do 360-83-85-69=123 is the answer you get.

hope it make sense:)

Answer:

y < [tex]\frac{1}{4} x+3[/tex]

Step-by-step explanation:

(-4, 2) (4, 4)

4 - 2 = 2

4 - - 4 = 8

slope = 1/4

y intercept is 3 because the inequality goes up 3 units

Answer:

B)785.0 cubic inches

Step-by-step explanation:

amount of soup the pot can hold is equal to its volume

Volume of a cylinder is πr²h

π(5inches)²x 10inches

785.39816339744830

~785.0 cubic inches

Answer:

The first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.

Step-by-step explanation:

Since Paul signs up for a new cell phone plan, and he is offered a discount for the first five months, and after this period, his rate increases by $ 8.50 per month, and his total cost at the end of the year is $ 245.50, and Paul wrote the following equation to represent his plan: 5x + 7 (x + 8.50) = 245.50; To determine the value of X, the following calculation must be performed:

5X + 7 x (X + 8.50) = 245.50

5X + 7X + 59.50 = 245.50

12X + 59.50 = 245.50

12X = 245.50 - 59.50

12X = 186

X = 186/12

X = 15.50

Therefore, the first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.

Answer:

64

Step-by-step explanation:

You can figure it out by adding all the interior angles.

(180-75=105º)

(180-67=113º)

105+113+90=308º

The sum of interior angles is (n-2) × 180 so the sum in his case is

(5-2) ×180=540º

540º-308º=232º

However that is the sum of the two angles but since the angles are the same size, we can divide by 2

232º÷2=116º

We must remember that this is an interior angle so we now can calculate the value of y

180º-116º=64º

9514 1404 393

Answer:

  211

Step-by-step explanation:

Put the numbers where the variables are and do the arithmetic.

  b/2 +3c^2 = 38/2 +3(8^2) = 19 +3·64 = 211

Answer:

211

Step-by-step explanation:

given : b = 38 and c = 8

Evaluate :

= b/2 + 3c²

= 38 / 2 + 3 ( 8 )²

= 19 + 3 × 64

= 19 + 192

= 211

Hi there!  

»»————-　★　————-««

I believe your answer is:  

-6, -7, -8

[tex]\boxed{x<-5}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solve for 'x':}}\\\\-2x>10\\--------\\\rightarrow\frac{-2x>10}{-2}\\\\\rightarrow\boxed{x<-5}\\\\\text{The inequality sign is flipped because we divided by a negative value.}[/tex]

⸻⸻⸻⸻

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

fine ,it is a A ok,I am sorry for using rude words on you

9514 1404 393

Answer:

  30

Step-by-step explanation:

The sequence of square counts is ...

  170, 156, 142, 128

The differences from one row to the next are ...

  -14, -14, -14

We see that the differences are constant, so we know the sequence is an arithmetic sequence with first term 170 and common difference -14. This means the n-th term is ...

  an = a1 +d(n -1) . . . . . . for first term a1 and common difference d

  an = 170 -14(n -1)

For n=11, the number of squares is ...

  a11 = 170 -14(11 -1) = 30

There will be 30 squares in the 11th row.

Answer:

A.) y = -7/4x - 7

Step-by-step explanation:

The line's slope is -7/4 and its y-intercept is located at the point (0, -7).

Answer:

Base = 19

Height = 26

Step-by-step explanation:

Given :

Height, h = base, b + 7 feets

The area of triangle, A = 247 ft²

The area of a triangle is given by :

A = 1/2 * base * height

247 = 1/2 * b * (b + 7)

247 = 0.5 * b * (b + 7)

247 = 0.5b² + 3.5b

0.5b² + 3.5b - 247 = 0

Solving the quadratic equation ; using the quadratic equation solver, the roots are :

b = -26 or b = 19

Length of base can't be negative :

Hence,

Base, b = 19

Height, h = base + 7 = 19 + 7 = 26

Answer:

3/6=1/2

Step-by-step explanation:

There are 3 ways you can roll an even number on a 6-sided die: 2, 4, and 6

Therefore, the probability of rolling an even number is 3/6 or 1/2.

Answer:

20 is it's right answer I think ok

Answer:

hello

Step-by-step explanation:

a²+b²=c²

16²+b²=65²

256+b²=4225

b²=4225-256

b²=3969

[tex]b = \sqrt{3969}[/tex]

b=63

b=63 mi

have a nice day

Answer:

b = 63

Step-by-step explanation:

In a right angled triangle, hypotenuse squared is equal to the sum of the square of the other sides.

c² = a² + b² (where c is the hypotenuse, and a and b are the other two sides)

c =  65       , a = 16        b = ?

65² = 16² + b²

4225 = 256 + b²

4225 - 256 = b²

b² = 3969

b = [tex]\sqrt{3969}[/tex]

b = 63

check

c² = 16 ² + 63²

   = 256 + 3969

   = 4225

c = √4225

c = 65

9514 1404 393

Answer:

  103

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°, so the measure of x° is ...

  x° = 360° -127° -90° -40° = 103°

  x = 103

Answer:

The measure of x is 103 °.

Step-by-step explanation:

Concept :- As we know that sum angles of quadrilateral is 360 ° so, to find the measure of x.

Firstly add all the angles that we have given and subtract from 360 ° and we get the vue of x.

We know that The sum angles of quadrilateral is 360 ° , Hence, value of x =

x + 127 ° + 90 ° + 40 ° = 360 °

x + 257 ° = 360 °

Subtract 257 ° from 360 °

x = 360 ° - 257 °

x = 103 °

Therefore, The measure of x is 103 °.

Answer:

t think the answer is 1040.

Answer:

x

Step-by-step explanation:

f([tex]f^{-1}[/tex](x))

Lets work the brackets first!

[tex]f^{-1}[/tex](x)

To solve we are going to find the inverse of the function.

[tex]f^{-1}[/tex](x)

f ⇔ y

∴ y = x

Interchange x and y

x = y

Solve for y

y = x

∴ [tex]f^{-1}[/tex](x) = x

Now let's solve the rest of the equation.

f(x) = x

∴ f([tex]f^{-1}[/tex](x)) = x

I tried every combination. there seems to be something wrong with the informations you gave.

the second equation contains errors, and none of these 4 points can be solutions to the first equation alone

Answer:

y=-2x+7

Step-by-step explanation:

Hi there!

The form of slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

We are given the slope (-2) and a point (3,1)

We can immediately substitute -2 as the slope in the equation

y=-2x+b

Now we need to find b

Because the line will pass through the point (3,1), we can use it to solve for b

Substitute 3 as x and 1 as y

1=-2(3)+b

multiply

1=-6+b

add 6 to both sides to isolate b

7=b

Substitute 7 as b into the equation

The line is y=-2x+7

Hope this helps!

Answer:

[tex](f-g)(x)=x^2-4x-21[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=x^2-3x-28\text{ and } g(x)=x-7[/tex]

And we want to find:

[tex](f-g)(x)[/tex]

This is equivalent to:

[tex]=f(x)-g(x)[/tex]

Substitute:

[tex]=(x^2-3x-28)-(x-7)[/tex]

Distribute:

[tex]=x^2-3x-28-x+7[/tex]

Rearrange:

[tex]=(x^2)+(-3x-x)+(-28+7)[/tex]

Hence:

[tex](f-g)(x)=x^2-4x-21[/tex]

Answer:

Correct choice is B

Answer:

The answer is:

C. The median for town A, 20°, is less than the median for town B, 30°.

Step-by-step explanation:

Median is the middle (center) value.

Option (C) the median for town A, 20°, is less than the median for town B, 30°.

Box plot is a type of chart often used in explanatory data analysis. A graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

For the given situation,

The diagram shows the box plot of the daily low temperatures for a sample of days in two different towns.

From the box plot, the median of town A is 20° and the median of town B is 30°.

From the data,

⇒ [tex]20 < 30[/tex]

Hence we can conclude that option (C) the median for town A, 20°, is less than the median for town B, 30°.

Learn more about box plot here

https://brainly.com/question/12591498

#SPJ2

Answer:

-1

Step-by-step explanation:

f(4) = 2.5(4) -11

f(4) = 10 -11

f(4) = -1

Answer:

[tex]\displaystyle V = 2064.19 \ cm^3[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume of a Sphere Formula: [tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]

Step-by-step explanation:

Step 1: Define

Identify variables

r = 7.9 cm

Step 2: Find Volume