Mr. Fink's economy car can travel 420 miles on a 12-gallon tank of gas. Determine how many miles he can travel on 8 gallons.

Answer:

a. 754cm³ (3 s.f.)

b. 415cm² (3 s.f.)

Step-by-step explanation:

Formulas (for easier reference):

Volume of cone: \(\pi\)r²\(\frac{h}{3}\)

Volume of hemisphere: \(\frac{2}{3}\)\(\pi\)r³

Surface area of cone without base: \(\pi\)rl

Surface area of hemisphere without base: 2\(\pi\)r²

We can just apply the formulas for the question:

Volume of toy = (\(\pi\) × 6² × \(\frac{8}{3}\)) + (\(\frac{2}{3}\) × \(\pi\) 6³)

                        = 96\(\pi\) + 144\(\pi\)

                        = 240\(\pi\)

                        = 754cm³ (3 s.f.)

Surface area of toy = (\(\pi\) × 6 × 10) + (2 × \(\pi\) × 6²)

                                = 60\(\pi\) + 72\(\pi\)

                                = 132\(\pi\)

                                = 415cm² (3 s.f.)

Answer:

 x = 4

Step-by-step explanation:

I hope this helps sorry if its wrong

Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer

Answer:

Step-by-step explanation:

If you are desperate, copy and paste the below answer. It should be correct but I don't know your syllabus.

8% C = 4      1% C = 4 ÷ 8 =0.5      100% C = 0.5 × 100 = 50

Hope this helps.

Answer:

36.656

Step-by-step explanation:

Calculate using trigonometry, Calculator may be required

Ok, so it's actually pretty easy

First of all, we know that all triangles' angles add up to 180 degrees

Here we can tell that we have one 90 degree angle and another 45 degree angle

Now, we can subtract both of these angles to then finalize that, the missing angle is equal to 45 degrees

Hope this helps :)

The expected value for the complete pairs of socks that make it out alive from the washing machine is calculated based on the probability of losing a sock and the number of pairs. The expected value for the complete pair of socks is 2.

Let's denote the random variable X as the number of complete pairs of socks that make it out alive. To calculate the expected value of X, we need to consider the probability of losing a sock and the total number of pairs.

In this case, there are 20 pairs of socks, which means there are a total of 40 socks. The washing machine eats four socks at random, which means there will be 36 socks remaining.

The probability of losing a sock can be calculated by dividing the number of socks lost by the total number of socks. In this scenario, four socks are lost out of 40 socks, so the probability of losing a sock is 4/40 = 1/10.

To calculate the expected value, we multiply the probability of losing a sock by the total number of pairs. In this case, the expected value is (1/10) * 20 = 2.

Therefore, the expected value for the number of complete pairs of socks that make it out alive from the washing machine is 2.

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Answer:

x=9

Step-by-step explanation:

If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.

x* (x+1) = 10*9

Distribute

x^2 +x = 90

Subtract 90 from each side

x^2 +x-90 =0

Factor

(x-9)(x+10) =0

Using the zero product property

x-9=0  x+10=0

x=9  x=-10

Since we cannot have a negative length

x=9

The circle is made up of 2 lines, this means that they will equal each other.

x(x + 1) = 10 * 9

~Simplify

x² + x = 90

~Subtract 90 to both sides

x² + x - 90 = 90 - 90

~Simplify

x² + x - 90 = 0

~Factor out

(x - 9)(x + 10) = 0

~Set both factors to equal 0

x - 9 = 0

x + 10 = 0

~Solve for x in [ x - 9 = 0 ]

x - 9 + 9 = 0 + 9

x = 9

~Solve for x in [ x + 10 = 0 ]

x + 10 - 10 = 10 - 10

x = -10

Since -10 is negative, we can't use it.

Therefore, x = 9

Best of Luck!

Answer:

you substitute x for 4 and so you multiply 9 x 4 which will give you 36 and then you have to add four times y so you substitute y for -3 and you add 36 - 12 which will give you 24

These issues are the lack of technological innovation and the increasing competition in the global market. Addressing these issues is crucial for the organization's sustainability and growth.

The lack of technological innovation is an issue because it hinders International Industries from staying competitive and meeting changing market demands.

Without innovation, the organization may fall behind in terms of product development, process efficiency, and customer satisfaction.

To address this issue, the organization should prioritize research and development efforts, invest in new technologies, and foster a culture of innovation. This can involve collaborating with external partners, conducting market research, and providing training and incentives to employees.

The increasing competition in the global market is another significant issue. With globalization, companies from different countries are entering the market, creating intense competition for International Industries. This can impact market share, pricing, and profitability.

To tackle this issue, the organization should focus on strategic positioning and differentiation. This can be achieved through product diversification, expanding into new markets, improving marketing strategies, and enhancing customer relationships.

Additionally, the organization should constantly monitor and analyze the competitive landscape to identify opportunities and adapt accordingly.

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Answer:

-9/11 > -5/8

Step-by-step explanation:

For the line segment AB with coordinates A( 4,5) and B(12, 9) divided by point P in the ratio AP : PB = 3 : 1 then coordinates of P are ( 10,8).

As given in the question,

Given:

Line segment AB with coordinates A( 4,5) and B(12, 9)

Line segment AB divided by point P in the ratio AP : PB = 3: 1

Let (x ,y) be the coordinates of point P .

Coordinates of A(4,5) = ( x₁, y₁)

B(12,9) = (x₂ , y₂)

Ratio m : n = 3 : 1

Coordinates of point P is given by:

x = (mx₂ + nx₁)/ ( m+ n)

  = [3(12) + 1(4)] / (3+1)

  = ( 36 +4)/ 4

  = 40 /4

  = 10

x = (my₂ + n y₁)/ ( m+ n)

  = [3(9) + 1(5)] / (3+1)

  = ( 27 +5)/ 4

  = 32/4

  = 8

P(x ,y) = P(10, 8)

Therefore, For the line segment AB with coordinates A( 4,5) and B(12, 9) divided by point P in the ratio AP : PB = 3 : 1 then coordinates of P are ( 10,8).

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Answer:

It's definitely not the first one or the second one, not sure about the third one but the last one is equivalent to it.

3/4 x . 8 = 6

2-1=1

Answer:

1/3 = 1 serving

2/3 =2 servings

1 cup= 3 servings

so if one cup is 3 servings we can multiply 3 x 6 for an answer of 18 servings

The table that represents the function y = -2x + 4 is: the second table.

Considering the third table representing a function given:

x | y

0   4

1    2

2   0

Find the slope (m) using the two points (1, 2) and (2, 0):

Slope (m) = change in y / change in x = (0 - 2) / (2 - 1)

m = -2/1

m = -2.

The y-intercept (b) = 4.

Substitute m = -2 and b = 4 into y = mx + b:

y = -2x + 4

Therefore, the second table represents the function y = -2x + 4.

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A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.

Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.

\( \bar{AB}\)

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The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.

Given the following data: Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min.

Its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.

The pile is 10 ft high.

To determine how fast the height of the pile is increasing, we need to differentiate the formula for the volume of a cone with respect to time.

We know that the volume of a cone is given by: \(V = (1/3)πr²h\)

We are given that the base diameter and the height of the cone are always equal, so we can write: r = (d/2)and h = d

where d is the diameter of the base of the cone.

The volume of the cone is given by: V = (1/3)π(d/2)²d

Simplifying, we get:\(V = (1/12)πd³\)

Differentiating both sides with respect to time, we get:

dV/dt = (1/4)πd² (dd/dt)

We are given that dV/dt = 30 ft³/min, and we want to find dd/dt when h = 10 ft.

Substituting V = (1/3)π(10/2)²(10)

= (1/3)π(25)(10)

= (250/3)π and d = 10,

we get:

30 = (1/4)π(10²)(dd/dt)

Simplifying, we get:

dd/dt = 12/π

The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.

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Clare plans to fold up the sides of a poster board that is 30 inches by 25 inches of box. The volume V(x)=4x³-110x²+750x.

Given that,

Clare plans to fold up the sides of a poster board that is 30 inches by 25 inches and trim the corners to create an open-top box. The open-top box's volume, "V(x)," in cubic inches, depends on the square cuts' side length, "x," in inches.

Length =30 inch

Width=25 inch

The box's size changes when x is taken out of the container.

Length=30-2x

Width=25-2x

Height=x

Because x is eliminated from both ends, we subtract 2x.

The volume is then determined as follows:

V(x)=length×width×height

V(x)=(30-2x)×(25-2x)×x

V(x)=(30-2x)×(25x-2x²)

V(x)=750x-110x²+4x³

V(x)=4x³-110x²+750x

Therefore, the volume V(x)=4x³-110x²+750x.

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Answer:

2/3

Step-by-step explanation:

Word problems: Since they encourage students to apply their knowledge of many topics to "real-life" situations, word problems are a crucial component of the core modules.

Additionally, they help pupils get familiar with terms like "more," "fewer," "subtract," "difference," "totally," "equal," "sharing," "multiplied," and "reduced."

A word problem is a description of a situation in real life when a computation is necessary to solve a problem.

It is important for students to learn how to answer word problems because it allows them to apply mathematical ideas to a variety of real-life situations.

Students must therefore be conversant with the vocabulary associated with the mathematical symbols they are used to in order to comprehend the word problem. In this tutorial, let's learn more about word problems in depth.

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Answer:

we will write 972 in standard form

Step-by-step explanation:

Standard form of a given number 972 is equals to 9.72 × 10².

" Standard form is defined as the mathematical expression, number, any equation , quantity with certain rules defined for it."

According to the question,

Given number = 972

Standard form of writing a number is

Given number should be express as a decimal number between 1.0 to 10.0

multiply by power of 10.

Standard form of 972 =  9.72 × 10²

Hence , standard form of a given number 972 is equals to 9.72 × 10².

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The scale factor of the dilation used to transform trapezoid MNOP to RSTU obtained by the  ratio of the corresponding sides is 1.5

A dilation transformation is one in which the lengths of the sides of the original figure are multiplied by a constant known as the scale factor of the dilation.

Part of the question includes the diagram of the trapezoids.

Please find attached diagrams of two similar trapezoids that can be used to illustrate the problem created with MS Word.

The corresponding sides of the trapezoids are;

Side OP in trapezoid MNOP is the corresponding side to side ST in trapezoid RSTU

The ratio of the corresponding side in the trapezoids indicates the scale factor of the dilation as follows;

The scale factor, s.f. used to transform trapezoid MNOP to trapezoid RSTU obtained from the ratio of the corresponding sides is; s.f. = ST/OP

ST = 15

OP = 10

Therefore; s.f. = 15/10 = 1.5

The scale factor of dilation used to transform trapezoid MNOP to trapezoid RSTU, s.f. is 1.5

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Answer: 3344c^2m^2

Step-by-step explanation:

After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.

What is proportion?

 Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.

Here 16 oz medium size has 260 calories.

Then

=> \(\frac{size of coffee}{ calories}\)

=>\(\frac{16}{260}=\frac{20}{x}\)

=>x=\(\frac{20*260}{16}\)

=> x = 325

Hence 325 calories will she get if she drinks the larger 20 oz. size.

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Answer:

hello your question is incomplete attached below is the missing part

answer : Path C

Step-by-step explanation:

when a positively charged particle is launched past the fixed negatively charged particle in the attached diagram the most likely  Path that will be formed is "C".  and this is

Given that the launched charge is positive hence the field lines will point radially away from the point charge ( fixed negative charge )

Answer:

You can get the answer of 1,2,3,4,5 or 6. Each are 1/6 likely to be rolled.

Step-by-step explanation:

The die has 6 sides. If you were to roll the die 6 times you have the chance to roll the side with 1. The chances of rolling a 1 are 1/6.

Answer:

29.4

Step-by-step explanation:

42*0.7

Answer:

C) 29.4

Step-by-step explanation:

Plug in 42 for t in the equation:

f(t) = 0.7t

t = 42

f(42) = 0.7 * (42)

Multiply:

f(42) = 0.7 * 42

f(42) = 29.4

C) 29.4 is your answer.

~

Timothy is currently 7 years old and Adele's current age is 12 years old.

To solve this age problem involving Adele and Timothy, we can set up two equations based on the information given. Let A represent Adele's current age and T represent Timothy's current age. The problem states:
Adele is 5 years older than Timothy: A = T + 5
In three years, Timothy will be 2/3 of Adele's age: (T + 3) = (2/3)(A + 3)
First, let's rewrite equation 1 in terms of T: T = A - 5
Now, substitute this expression for T into equation 2:
(A - 5 + 3) = (2/3)(A + 3)
Simplify the equation:
A - 2 = (2/3)(A + 3)
Multiply both sides by 3 to eliminate the fraction:
3(A - 2) = 2(A + 3)
Expand:
3A - 6 = 2A + 6
Now, solve for A:
A = 12
So, Adele's current age is 12 years old. To find Timothy's age, we can use the equation T = A - 5:
T = 12 - 5 = 7
Thus, Timothy is currently 7 years old. Therefore, the correct answer is not among the given options, as Adele's current age is 12 years.

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Answer:

(-4,-9)

Step-by-step explanation:

vertex form: y=a(x-h)^2+k

hk=vertex of x and y

inside parentheses=horizontal (opposite signs)

that’s why it’s -4 instead of 4 for h (x) while -9 stays the same since it’s not inside the parentheses

Answer:

2 positive unit tiles is needed

Step-by-step explanation:

Given the expression x^2 – 3x – 10, the partial factorization is as shown;

x^2 – 3x – 10

=  x^2 +2x – 5x – 10

= x(x+2)-5(x+2)

= (x-5)(x+2)

Note that negative values are represented as tiles labelled below (negative tiles) while positive values are tiles labelled above (positive tiles)

From the second line we can see that first term 1 is labeled + x squared, second is labelled +2x (two positive tiles above), then the 5 tiles below + x squared are labeled negative x, and the 10 tiles below the + x tiles are labeled negative.

Hence base on the partial factorization and the underlined statement, we can see that 2 positive unit tiles is needed to complete the factorization

Answer:

B i think

Step-by-step explanation: