Mr. Trimke drove 280 miles in 5 hours. How long would it take to drive 420 miles

Answer:

Step-by-step explanation:

Let the first number be 'a' and the second number be 'b'. If the sum of the first and twice the second is 400 then;

a+2b = 400 ....

From the equation above, a = 400 - 2b ... 2

If the product of the numbers is a maximum then;

ab = (400-2b)b

let f(b) be the product of the function.

f(b) = (400-2b)b

f(b) = 400b-2b²

For the product to be at the maximum then f'(b) must be equal to zero i.e f'(b) = 0

f'(b)= 400-4b = 0

400-4b = 0

400 = 4b

b = 400/4

b = 100

Substituting b= 100 into the equation a = 400 - 2b to get a;

a = 400 - 2(100)

a = 400 - 200

a = 200

The two positive integers are 100 and 200.

Answer:

67/100

Step-by-step explanation:

Percent means out of 100.

67% = 67/100

Answer:

67/100

Step-by-step explanation:

Answer:

1.646×10¹¹ km³.

Step-by-step explanation:

From the question given, we obtained the following information:

Radius (r) = 3400 km

Volume (V) =.?

The shape of a planet is spherical in nature. Thus, we shall apply the formula for calculating the volume of a sphere to obtain the volume of Planet Mar as illustrated below:

Radius (r) = 3400 km

Pi (π) = 3.14

Volume (V) =.?

Volume of a sphere = 4/3 πr³

V = 4/3 × 3.14 × (3400)³

V = 4/3 × 3.14 × 3.9304×10¹⁰

V = 1.646×10¹¹ km³

From the calculations made above, the volume of Planet Mar is 1.646×10¹¹ km³

You would have an open circle. A way to remember it is that < and > is open and ≥ and ≤ mean closed circle. A way to also remember which way to go is remembering this cool strategy.

<ess than

>greater than

Less means left. Greater means right. So your graph would look like something along the lines of:

Answer:

a = 28 / √2

Step-by-step explanation:

Isosceles triangle therefor a = b

use pythagorean theorem

a² + a² = c²

2a² = 28²

a² = 28² / 2

Take the square root of both sides

a = 28 / √2

Answer:

a = \(\frac{28}{\sqrt{2} }\)

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = \(\frac{1}{\sqrt{2} }\) , then

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{a}{28}\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

a × \(\sqrt{2}\) = 28 ( divide both sides by \(\sqrt{2}\) )

a = \(\frac{28}{\sqrt{2} }\)

Answer:

2/7 or about 28% depending on what type of answer your teacher is looking for

Answer:

\(\Large \boxed{0.40 < 0.430 < 0.480 < 0.489}\)

Step-by-step explanation:

First you have to see the decimal places.

Than the number of digits there is.

So this is how we make it from least to greatest!

Since there is 3 numbers after the decimals in almost all of them...

Than let’s make ‘0.40’ into 3 numbers after the decimal too.

I am sure you have heard that if you add a ‘0’ to a decimal nothing will change right?

So let’s make 0.40 into 3 numbers after the decimal just like the other numbers!

Okay so first let’s add a zero to ‘0.40’... which now this turns into ‘0.400’

Now it will be more easier to compare least to greatest!

0.400 is the least, than comes 0.430, & than would be 0.480, & finally the greatest would be 0.489

Therefore the answer is 0.40 < 0.430 < 0.480 < 0.489.

The distance from the midpoint of the hypotenuse of any vertex is:

\(\sqrt{(0-a)^2 +(2b - b)^2} \\\)   = \(\sqrt{(2a - a)^2 +(0 -b)^2}\)

= \(\sqrt{a-0)^2 + (b -0)^2}\)

Right Angle Triangle:

A right triangle is a triangle with one of its angles 90 degrees. An angle of 90 degrees is called a right angle, so a triangle with a right angle is called a right triangle. In this triangle, we can use the Pythagorean law to easily understand the relationship of the various sides. The side opposite the right angle is the largest side and is called the hypotenuse.

In a right triangle we have:

                  (Hypotenuse)2 = (Base)2 + (Altitude)2

Mid point Theorem:

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half the length of the third side. This theorem is used in many places in real life. For example, if we don't have a measuring tool, you can use the midpoint theorem to cut a bar in half.

If we have a line segment whose endpoint coordinates are given by

(x₁, y₁) and (x₂, y₂), we can find the coordinates of the midpoint of the line segment using the following formula:

Let (xₙ , yₙ ) Coordinates of the midpoint of the segment. Then

(xₙ, yₙ) = ( (x₁+ x₂/2 , (y₁ + y₂)/2 )

This is known as the midpoint theorem.

According to the Question:

Suppose that we have two points (x₁ ,y₁)  and (x₂, y₂). The distance between them is given by:

D = \(\sqrt{(x_2-x_1)^2 + (y_2- y_1)^2 }\)

Hence the distance from the midpoint of the hypotenuse to any vertex is given by:

    \(\sqrt{(0-a)^2 +(2b - b)^2} \\\)

= \(\sqrt{(2a - a)^2 +(0 -b)^2}\)

= \(\sqrt{a-0)^2 + (b -0)^2}\)

Learn more about Hypotenuse:

https://brainly.com/question/14796372

#SPJ4

The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

for such more question on values

https://brainly.com/question/27746495

#SPJ8

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

For more such questions on GCF

https://brainly.com/question/902408

#SPJ8

Answer:

44.59 divided by 5.25= 8.49

Hope this helps!!

Answer:

44.5÷56 that how you answer

The amount that the taxpayer is owing in taxes is $2,691.05.

We have,

Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.

Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.

The tax payable will equals to:

= 15%*$11,757 + $927.50

= $1,763.55 + $927.50

= $2,691.05

Hence, The amount that the taxpayer is owing in taxes is $2,691.05.

Read more about tax payable

brainly.com/question/897877

#SPJ1

complete question:

Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?

Answer:

The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:

$442 * 0.9 = $397.80

The selling price of the same necklace at the competitor's store after 34% and 14% discount is:

$527 * 0.66 * 0.86 = $247.08

So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:

$397.80 - $247.08 = $150.72

To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:

($150.72 / $442) * 100 = 34.11%

Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.

Step-by-step explanation:

Answer:

it is right triangle so we have trigonometric ratio: tan(54)=3/x and from that we have x=3/tan(54)

Answer:

y  = (-4/3)x + 6

Step-by-step explanation:

The Y-intercept of the graph is 6. You can find the slope by following rise over run, or the change in y divided by the change in x. From (0,6) to (3,2), there is a negative 4 change in y and positive 3 change in x.

Answer:

Step-by-step explanation:

Rate:

Time:

Number of tops can be put in 270 min:

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

Read more on function and translation here: brainly.com/question/31559256

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Step-by-step explanation:

500 mg = 500 × 1 g / 1000 = 1/2 g = 0.5 g

so, the original target ratio is

0.5 g / 1 ml

the ratio has to be maintained when adding x ml of the sterile water to the 3 g.

3 g / x ml = 0.5 g / 1 ml

3 g / 0.5 g = x ml / 1 ml

3/0.5 = x

x = 6

only with x = 6 do we keep the target ratio.

so, we need to add 6 ml to the 3 g vial to make it a 500 mg/ml solution.

In the given origami of the two dimensional figure , the value of angle 2 is 70° and the value of angle 1 is 110 °

Parallel lines are straight lines that do not intersect at any point in geometry.

Parallel planes are three-dimensional pathways that never intersect. Parallel curves do not touch or intersect and have a fixed minimum distance.

From the figure we can see that m∠1 = 4x-30 as they are vertically opposite angles.

Again m∠1 = 3x+5 as they are corresponding angles from the pair of parallel lines.

now let us solve the linear equation to calculate the value of x.

3x+5 = 4x-30

or, -x = -35

or, x = 35

Now

m∠1 = 3x+5 = 110

Therefore m∠2 = 180 -110 = 70 ( straight angle formed whose sum is 180)

To learn more about origami visit:

https://brainly.com/question/8667656

#SPJ1

In the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

A sample space is a set of potential results from a random experiment.

The letter "S" is used to denote the sample space.

Events are the subset of possible experiment results.

Depending on the experiment, a sample area could contain a variety of results.

There are just two possible results when we toss a coin: either head or tail.

So, S = H, T, where H is the head and T is the tail, will be the sample space.

As a result, we are aware that there will be a total of 2n outcomes available if there are 'n' coins.

So, the coin has 2 outcomes which are H and T.

And the spinner has 8 outcomes which are 1 - 8.

Then, the sample space would be as follows:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

So, the sample space has a total of 16 elements.

Therefore, in the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

Know more about sample space here:

https://brainly.com/question/10558496

#SPJ1

The computation of the future value is $92,691.08

As we know that

Future value = Present value × (1 + interest rate)^number of years

where, the Present value is $24275

The Interest rate is 4.05%

And, the number of the year is 10 years

Now placing these values to the above formula;

So, the future value is;

Future value = Present value × (1 + interest rate)^number of years

= $24275× (1 + 0.0405)^10

= $24275× 1.448298166

= $92,691.08

Learn more about simple interest here;

brainly.com/question/1548909

#SPJ1

Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

Answer:

bru tell me why i cant see that

Step-by-step explanation:

Answer:

\(\frac{-10}{3}\)

Step-by-step explanation:

Cancel x+2 by multilying it with all terms.

x=2+4(x+2)

SImplify both sides

x=4x+10

Subtract 4 on both sides

−3x=10

Divide bot sides by -3

You get \(\frac{-10}{3}\)

Glad to help.

Step-by-step explanation:

1.

   First blank: total amount of outcomes

2.

   since there's four possible outcomes: (Head-Head, Head-Tail, Tail-Head, and Tail-Tail) Mason should expect to win 1/4 of the time, or roughly 50 times.

3.

   a) F

   b) F

   c) T

   d) T

   e) T

    f) T

4.

17/36, because 17 of the answers are greater than 10 and there are 36 total answers.

Sorry I didn't answer all of them, hopefully this still helps!

Goodluck with your schoolwork/homework!

--------------------------------------------------------------

Apologies in advance for any errors/bad explanations.

Answer:

$-33

Step-by-step explanation:

Andre still owes Billy money. If Andre paid Billy the 39 dollars he has, he would still owe Billy $33, which puts him $33 in the hole.