Solve the inequality.
8(x/4-6)>4
[10 points]

The volume of the baseball roundibg off to nearest whole number is 14 cube inches.

If radius of a sphere is r and the volume of that spherical figure is given by V then,

[tex]V=\frac{4}{3}\pi r^3[/tex]

So in the problem the object is a baseball which is a sphere for sure.

Given that the diameter of that baseball is 3 inches.

So the radius of that baseball is given by = 3/2 = 1.5 inches.

Hence the volume of that base ball is

[tex]=\frac{4}{3}\pi\times(1.5)^3 \approx 14.1372 \approx 14[/tex]

Thus the volume of the baseball rounding off to nearest whole number is given by 14 cube inches.

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Answer:

slope: 14

y intercept: (0,9)

Step-by-step explanation:

in the form y = mx + b, the slope is m: 14

to solve for the y intercept, we set x as 0: 14 * 0 + 9 = y interecept is 9.

The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.

It should be noted that a inference simply means the conclusion that can be deduced based on the information given.

In this case, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette.

Hence, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts. Therefore, ordering matters.

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Answer:

1960cm squared

Step-by-step explanation:

in case you're still confused ask where you're still confused and I'll offer my assistance.good day.

Answer:

160.14  mm^2

Step-by-step explanation:

Area of a circle = pi r^2

subtract the area of the smaller circle from the larger

  note that the smaller radius = 7 mm

pi ( 10^2  - 7^2 ) =

3.14 ( 51) = 160.14 mm^2

The area of the washer is approximately 160.14 square millimeters.

Use the concept of the circle defined as:

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

The line of reflection symmetry is formed by all lines that traverse the circle.

Additionally, every angle possesses rotational symmetry around the center.

Given that,

The outer radius of the washer: 10mm

Diameter of the hole: 14mm

π value to be used: 3.14

To find the area of the washer:

Subtract the area of the hole from the area of the outer circle.

The area of a circle is given by the formula A = πr²,

Where r is the radius.

For the outer circle:

The radius is 10mm, so the area of the outer circle = 10²π.

The area of the outer circle = 100π mm²

For the hole,

The diameter is 14mm,

So the radius of the hole = 7 mm.

The area of the hole = 7²π

The area of the hole = 49π mm²

To find the area of the washer,

Subtract the area of the hole from the area of the outer circle:

Area of washer = Area of the outer circle - Area of hole

Area of washer = (100π - 49π) mm²

Area of washer = 51π mm²

Area of washer ≈ 160.14 mm²

Hence,

The area of the washer is approximately 160.14 square millimeters.

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Answer:
I can help, its 45

Answer:

b. 0

c. 4

d. 2

e. [tex]\frac{76}{35}[/tex]

Step-by-step explanation:

b.) When translated it will become this expression 10 - [(2x15)/3] = 0

c.) It will become [tex]\frac{4(12-7)}{5}[/tex]

d.) This will transform to  [tex]\frac{(\frac{78-13}{5}) + 5}{9}[/tex]

e.) The first eq is [tex]\frac{4(7+3)}{8}[/tex], then after the changes it becomes [tex]\frac{4[\frac{(7+3)+9}{7}]}{5}[/tex]

Answer:

Step-by-step explanation:

let the number at unit place=x

ten's place=y

hundred's place=z

x,y,z are integers.

x+y+z=9

also digit=100z+10y+x

y=2z

x+2z+z=9

x+3z=9

x=1,3,5,7,9

for x=1

1+3z=9

3z=9-1=8

z=8/3 (rejected as z is an integer.)

when x=3

3+3z=9

3z=9-3=6

z=6/3=2

z=2

y=2z=2×2=4

so number=100×2+10×4+3=200+40+3=243

Using the Fundamental Counting Theorem, it is found that:

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For the 2 letters(26 outcomes each), and 3 numbers(10 outcomes each), we have that the parameters are:

[tex]n_1 = 26, n_2 = 26, n_3 = 10, n_4 = 10, n_5 = 10[/tex]

Hence the number of catalog numbers is:

[tex]N = 26^2 \times 10^3 = 676000[/tex]

The ID number is divisible by 5 if the last digit is either 5 or 0, hence [tex]n_5 = 0[/tex] and the probability is:

[tex]p = \frac{26^2 \times 10^2 \times 2}{26^2 \times 10^3} = 0.2[/tex]

There is a 0.2 = 20% probability that the ID number is divisible by 5.

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The volume of the cuboid is 183.96 m³

A cuboid is a plane shape with a six-faced solid called a hexahedron. The volume of a cuboid is Length × width × height

From the information given:

The volume of the cuboid is;

=  (7.3 × 6 × 4.2) m³

= 183.96 m³

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Using the given exponential function, we have that:

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, the function is:

[tex]A(t) = 523(0.5)^{\frac{t}{30}}[/tex]

Hence the initial amount is of 523 grams.

The amount after 50 years will be given by:

[tex]A(50) = 523(0.5)^{\frac{50}{30}} = 165[/tex]

The amount after 50 years will be of 165 grams.

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Answer:

Since there are 20 chickens in one supermarket, and 25 chickens in the other supermarket, there are 45 chickens to choose from.

The percentage increase China's population from 1970 to 1995 is: 56.25%.

Percentage increase = (Final Value - Original Value)/Original value × 100.

Given the following:

Original value = 0.8 billion

Final Value = 1.25 billion

Final Value - Original Value = 1.25 - 0.8

Final Value - Original Value = 0.45

Percentage increase = 0.45/0.8 × 100 = 56.25%.

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Answer: Option (2)

Step-by-step explanation:

[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].

Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].

So, the answer is Option (2).

Answer:

Step-by-step explanation:

First, let's start by removing the parentheses and simplifying the expression.

3.125 + - 3.9 - 2.46

Adding a negative number is the same as subtracting it, so we can remove the + sign.

3.125 - 3.9 - 2.46

From there, we can do simple subtraction and get:

-3.235

The question asks the value of f(x) when x = 4 in the equation

x = 4 is less than or equal to 4, so we use the first equation in the piecewise functions => {4x when x≤4}

Solving for f(x):

4(4)=16

16 is the answer!

Hope it helps!

The regression equation is (d) log(y) = 0.064x + 1.706

The table of values is given as:

x   2   3   4   5   6

y   73  77  85  101  133

Calculate the logarithm of the y values.

So, we have:

x          2   3   4   5   6

log(y)   1.86  1.89  1.93  2  2.12

Next, we enter the above values in a regression calculator.

From the calculator, we have the following summary:

The regression equation is then represented as:

log(y) = bx + a

Where:

b = SP/SSX = 0.64/10 = 0.064

a = MY - bMX = 1.96 - (0.064*4) = 1.706

So, we have:

log(y) = 0.064x + 1.706

Hence, the regression equation is (d) log(y) = 0.064x + 1.706

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Answer: D. log(y) = 0.064x + 1.706

Step-by-step explanation: I got it right on my test

Answer:

3 is the mode

Step-by-step explanation:

Work Shown:

[tex]a^2+b^2 = c^2\\\\5^2+b^2 = 13^2\\\\25+b^2 = 169\\\\b^2 = 169-25\\\\b^2 = 144\\\\b = \sqrt{144}\\\\b = 12\\\\[/tex]

I used the pythagorean theorem.

The solution to the inequality is (-4, ∞)

The second inequality is given as:

8 - y < 12

Subtract 8 from both sides

-y < 4

Rewrite as:

y > -4

In interval form, we have:

y = (-4, ∞)

Hence, the solution to the inequality is (-4, ∞)

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Answer:

3x^2+3x/2-9

Step-by-step explanation:

collect like term

The attached figure represents the complete flowchart.

The given statement is:

∠1 ≅ ∠2

To prove

∠3 ≅ ∠4

By vertical angle theorem, we have:

∠2 ≅ ∠4

By transitive property of congruence, we have:

∠2 ≅ ∠3

By transitive property of congruence, we have:

∠1 ≅ ∠3

By vertical angle theorem, we have:

∠3 ≅ ∠4

See attachment for the complete flowchart.

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Answer:

In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?

Choose the most logical value for the variable to represent.

x= Diana's age now

This question is impossible to fully answer without further context. (Who is Dianna? Why do we need her age?)

However, it can be noted that [tex]x[/tex] is easily the most common variable name whenever you have a missing value in an equation. Generally, it is understood by mathematicians that [tex]x[/tex] and most other letters denote an unknown value, something to either use in solving the equation or something to find on its own.

Step-by-step explanation:

so, what do we need to do ?

just solve these equations and find Sam's age (and Harry's) ?

x = 3y

x = 10 + 2y

so, we simply use the first equation in the second :

3y = 10 + 2y

y = 10

x = 3y = 3×10 = 30

Sam is currently 30 years old, Harry is 10.

Answer:

constant (unchanged) ratio of two variable quantities

Step-by-step explanation:

y = k x ( or y = k x )

y = 15 when x = 24, find x when y = 25. find the constant of variation.

The circumference of the larger circle is about 12.57 inches. The circumference of the smaller circle is about 3.14 inches. So, the total length of gold leaf on a tag is approximately 15.71 inches.

The circumference will be:

= 2πr

= 2 × 3.14 × 2

= 12.57 inches.

The circumference of the smaller circle will be:

= 2πr

= 2 × 3.14 × 0.5

= 3.14

The total length will be:

= 12.57 + 3.14

= 15.71 inches.

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The amount going to her savings accounts is $192

The given parameters are:

Drawings = 24

Rate = $12

The total amount earned from selling the drawings is:

Total = 24 * $12

Evaluate

Total = $288

She buys books with 1/3.

This means that she saved 2/3

So, we have:

Savings = 2/3 * $288

Evaluate

Savings = $192

Hence, the amount going to her savings accounts is $192

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