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2 years ago

Solve for x.

Mathematics

1 answer:

Leto [7]2 years ago

3 0

Answer:

x < 4

Step-by-step explanation:

Step 1: Subtract 10 from both sides.

$-8x + 10 - 10 > -22 - 10$
$-8x > -32$

Step 2: Divide both sides by -8 and flip the inequality sign.

$\frac{-8x}{-8} > \frac{-32}{-8}$
$x < 4$

Therefore, the answer is x < 4.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

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There are two flavors of ice cream; strawberry and chocolate. the amount of strawberry ice cream is in the shape of a sphere. th

amid [387]

The complete question is
<span>There are two flavors of ice cream; strawberry and chocolate. the amount of strawberry ice cream is in the shape of a sphere. the amount of chocolate ice cream fills the rest of the cone. the dimensions of the sphere is 6cm and the cone is 12cm.

the figure is not drawn to scale

A. what is the volume, in cubic centimeters of the right circular cone ?show or explain how you got your answer.
B. the amount of strawberry ice cream is in the shape of a sphere. what is the volume in cubic centimeters of the strawberry ice cream?
C. what is the total volume in cubic centimeters of all the ice creams?
D.the amount of chocolate ice cream fills the rest of the cone. what is the volume in cubic centimeters of the chocolate ice cream?

we know that
the height of the cone is 12 cm
the diameter of a cone is 6 cm

Part A) </span>what is the volume, in cubic centimeters of the right circular cone? show or explain how you got your answer.

we know that
the volume of a cone=(1/3)*pi*r²*h
r=6/2----> 3 cm
h=12 cm
The volume of a cone=(1/3)*pi*3²*12------> 36*pi cm³-------> 113.04 cm³

the answer part A) is 36*pi cm³ (113.04 cm³)

Part B) the amount of strawberry ice cream is in the shape of a sphere. what is the volume in cubic centimeters of the strawberry ice cream?
volume of a sphere=(4/3)*pi*r³
r=3 cm
volume of a sphere=(4/3)*pi*3³-----> 36*pi cm³------> 113.04 cm³

the answer part B) is 36*pi cm³ (113.04 cm³)

Part C) what is the total volume in cubic centimeters of all the ice creams?
volume of the cone+volume of a hemisphere

36*pi+18*pi-----> 54*pi cm³-------> 169.56 cm³

the answer Part C) is 54*pi cm³ (169.56 cm³)

Part D) .the amount of chocolate ice cream fills the rest of the cone. what is the volume in cubic centimeters of the chocolate ice cream?
volume of a cone-volume of a hemisphere
36*pi-18*pi-----> 18*pi cm³-----> 56.52 cm³

the answer Part D) is 18*pi cm³ (56.52 cm³)

5 0

3 years ago

The length of a rectangle is four more than three times the width. If the perimeter of this rectangle is at least 70 square cent

FrozenT [24]

Answer:

Step-by-step explanation:

Let L represent the length of the triangle.

Let W represent the width of the triangle.

The length of a rectangle is four more than three times the width. This means that

L = 3W + 4

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

If the perimeter of this rectangle is at least 70 square centimeters, an inequality that can be solved to find the width of the rectangle is

2(L + W) ≥ 70

L + W ≥ 70/2

L + W ≥ 35

7 0

3 years ago

2. Use the following picture for this question:

Art [367]

Answer:

a. $24\sqrt{3}$ and 41.6

b. 52.1

Step-by-step explanation:

Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.

<u>Note:</u> the exact value of tan 60 is $\sqrt{3}$

Thus, we can write $Tan(60)=\frac{y}{24}\\y=24*Tan(60)\\y=24*\sqrt{3} \\y=24\sqrt{3}$

Approximate value (rounded to nearest tenth): $24\sqrt{3} =41.6$

Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.

Thus we can write and solve:

$Sin(53)=\frac{41.6}{x}\\x=\frac{41.6}{Sin(53)}=52.1$

4 0

3 years ago

Log x - log x -1² = 2log(x-1)

kap26 [50]

Answer:

Exact form

x= $\sqrt{10$ /10 + 1

Decimal

x=1.31622776

Step-by-step explanation:

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3 years ago

The following are score earned by 15 college students on a 20-point math quiz. (a) calculate the mean, median, and mode scores.

Softa [21]

Answer:

(a) 12.87; 14; 18; (b) median

Step-by-step explanation:

(a) Statistics

(i) Mean

The mean is the sum of all the data points divided by the number of points.

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(ii) Median

The median is the middle value in your list of observations.

0, 2, 3, 12, 12, 13, 14, 14, 15, 15, 18, 18, 18, 19, 20

Median = 14

(iii) Mode

The mode is the value that appears most often in your list of observations.

0, 2, 3, 12, 12, 13, 14, 14, 15, 15, 18, 18, 18, 19, 20

Mode = 18

(b) Most representative measure

The mean is dragged down by three low values. The median is the measure that is most representative of the data.

The histogram below shows the distribution of your data.

8 0

3 years ago