A mountainer climbed 1000' at a rate of X feet per hour. He climbed in additional 5000' at a different rate. This rate was 10' per hour less than twice the 1st rate. Which expression represents the number of hours to mountainer climbed?

[tex]x^2 - y^2[/tex] when x = 1/2 and y = 1/4

[tex]\frac{1}{2} ^2 - \frac{1}{4} ^2\\\\=\frac{1}{4}-\frac{1}{16} \\\\= \frac{4}{16}-\frac{1}{16}\\ \\= 3/16[/tex]

The required monthly payment is given as follows:

$644.22.

The monthly payment is defined by the equation presented as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

The parameters are listed as follows:

For this problem, the values of these parameters are given as follows:

P = 120000, r = 0.05, n = 30 x 12 = 360.

Then:

r/12 = 0.05/12 = 0.004167.

Hence the monthly payment is obtained as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 120000\frac{0.004167(1.004167)^{360}}{(1.004167)^{360} - 1}[/tex]

A = $644.22.

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if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.

Least Common Multiple is the meaning of the abbreviation LCM.

The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

It can also be computed using two or more numbers.

Finding the LCM of a given collection of numbers can be done in a variety of ways.

Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.

The smallest number among all numbers is called the least common multiple of two or more numbers.

According to our question-

The number LCM is equal to 40.

4 × 5 × x = 40

20 × x = 40

20x=40

x=2

The larger number is equal to 4 x=4(2)=8.

The smaller value is =5x=5(2)=10.

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Complete question-

The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?

The difference between the number of passenger cars produced in Asia and the number produced in Eastern Europe/Russia is given as follows:

3 million.

The bar graph given by the image at the end of the answer shows the number of passenger cars produced in each of the regions.

From the graph, the numbers for each region are given as follows:

Then the difference between the number of passenger cars produced in Asia and the number produced in Eastern Europe/Russia is calculated as follows:

11 - 8 = 3 million.

The bar graph is given by the image shown at the end of the answer.

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Answer:

25 Questions

Step-by-step explanation:

This Question tests on the concept of Rationing using percentages.

Eg. 45% of 100 = 45, therefore 100% of 100 = 100.

Given information from the question:

56% = 14 Questions

1% = (14 ÷ 56) Questions

Total number of questions in the test = 100%

100% = (14 ÷ 56) × 100 Questions = 25

Answer:

[tex]\huge\boxed{\sf 25\ questions}[/tex]

Step-by-step explanation:

Let the total questions be x.

Given that,

56% of total questions = 14

Key: "of" means "to multiply", % means out of hundred.

[tex]\displaystyle \frac{56}{100} \times x = 14\\\\0.56 \times x = 14\\\\Divide\ 0.56\ to\ both\ sides\\\\x = 14/0.56\\\\x = 25[/tex]

So, there were 25 questions on the test.

[tex]\rule[225]{225}{2}[/tex]

Number of yellow marbles for every 18 green marbles = 30 yellow marbles

The unitary method entails figuring out the value of a single unit from which we can extrapolate the values of all the required units.

According to the given information

Applying the unitary method

Number of yellow marbles for every 3 green marbles = 5

Number of yellow marbles for every One green marbles = [tex]\frac{5}{3}[/tex]

Number of yellow marbles for every 18 green marbles = [tex]\frac{5}{3}[/tex] × 18

So

Number of yellow marbles for every 18 green marbles = 30 yellow marbles

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Answer:

y = 2x - 5

Step-by-step explanation:

slope = 1-(-3)/3-1

4/2 = 2

this is the m value, or value before x.

So far, this is what we have: y = 2x + b

To find b, we plug in one of the points we have, into the equation.

(in this case ill use (3, 1), where 3 is the x and 1 is the y)

So,

1 = 2(3) + b

1 = 6 + b

1 - 6 = b

-5 = b

Finally,

y = 2x - 5

Answer:

13

Step-by-step explanation:

w = -8 -5 =-13=13

Jenny needs to score 79 on final exam.

Total marks divide by total number subjects=Average

100+88+96+84+98+x=90*6

461+x=540

x=79

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"Define variables"

→ The number of student's tickets = a

→ The number of non-student tickets = b

→ the total cost represented = y

"Create an equation that models this situation"

→ y = $5 × a + $10 × b

"Rewrite the equation in slope intercept form"

→ y = $5 × a + $10 × b

→ y = 5a + 10b

→ 250 = 5a + 10b

The text messages that Rhonda can send and still pay less than a total of $70 is less than 80 messages.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the number of tests be represented by t.

The inequality will then be:

50 + 0.25t < 70

0.25t < 70 - 50

0.25t < 20

Divide

t < 20/0.25

t < 80

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The result is 6-13/3×t after simplification by multiplying first and added the like term.

The procedure of calculation which we use in arithmetic. We perform our mathematical calculation by using particular operational properties such as addition, subtraction, multiplication and division.

we can simplify any expression by using the properties of addition, subtraction, multiplication or division depending on the statement given.

in the above expression 7×(1/3)t- [10×(2/3)t-6]

we simplify it (7/3)t- (20/3)t+6

                      -(13/3)t+6

             hence, 6-13/3t

hence, the result is 6-13/3×t

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Answer:

19.25

Step-by-step explanation:

t = .55m

t = .55(35)

t = 19.25

I am not sure what you mean by 5 give the total cost in dollars T.  I am not sure where the comes from.

Answer:

$24.25

Step-by-step explanation:

Given equation:

[tex]T=0.55m+5[/tex]

where:

To find the total cost of renting a jet ski for 35 minutes, substitute m = 35 into the given equation and solve for T:

[tex]\implies T=0.55(35)+5[/tex]

[tex]\implies T=19.25+5[/tex]

[tex]\implies T=24.25[/tex]

Therefore, the total cost of renting a jet ski for 35 minutes is $24.25.

the answer is 14

simply multiply mika age by 2

since the difference is 7

meaning that mika is seven

and twice is 14

Answer:

265

Step-by-step explanation:

1590/6=265

265x1=265

Answer:

  8.2 m

Step-by-step explanation:

You want the length of the shadow whose tip is 34 m from the top of a 33 m building.

The described geometry can be modeled by a right triangle with one leg 33 m and hypotenuse 34 m. The Pythagorean theorem tells us the length of the other leg is ...

  a² +b² = c²

  b² = c² -a²

  b = √(c² -a²)

  b = √(34² -33²) ≈ 8.2 . . . . meters

The length of the shadow is about 8.2 meters.

__

Additional comment

The angle of elevation to the top of the building can be found from the trig relation ...

  Sin = Opposite/Hypotenuse

And the length of the shadow can be found from the relation ...

  Cos = Adjacent/Hypotenuse

If α is the angle of elevation, then ...

   sin(α) = 33/34   ⇒   α = arcsin(33/34)

and

  Adjacent = Hypotenuse × cos(α)

  Adjacent = 34·cos(arcsin(33/34)) ≈ 8.2 . . . . meters

where the "adjacent" side of the triangle is the side between the building and the tip of the shadow, along the ground.

The 16th term of the arithmetic sequence value is 103.

The 16th term of the arithmetic sequence whose common difference is d=7 and whose first term is a↓1=-2

An arithmetic sequence is defined as an=a1+d (n-1). In essence, this indicates that the term you're looking for, an, is equal to the first term, a1, plus the term difference, d, times the number of terms, n, minus one. For this issue, that essentially means that

an=a1+d(n-1)

The value of an at term sixteen is equal to -2 + 7*. (16-1)

PEDMAS is used to

a16= -2+7*15

a16= -2+105

a16= 103

Therefore, 103 will be the 16th term's value.

The 16th term of the arithmetic sequence value is 103.

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Probability to get at most 2 heads after flipping coin for 5 times is 1/2.

Probability is the ratio of good outcomes to all possible outcomes of an event is known as the probability.

The number of positive results for an experiment with n outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

With a fair coin, there are [tex]2^{5}[/tex] = 32 possible combinations of heads and tails after 5 flips.With 0 heads,5C0 = 5!/0!5! = 1 ways

get one head 5C1 = 5!/ 4!1! = 5 ways

To obtain precisely 2 heads,5C2 = 5!/ 2!3! = 10 ways

Obtain 3 heads,5C3 = 5!/ 3!2! = 10 ways

Total methods to gain at most 2 heads are 1+5+10 = 16.

Probability to get at most 2 heads is = ( total methods to gain at most 2 heads)/(total ways)

P(total methods to gain at most 2 heads) = 16/32 =1/2.

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Answer:

14 4/5

Step-by-step explanation: 7 2/5 x 2 or 7 2/5

                                                                +7 2/5

                                                                  -------

                                                                   14 4/5

The total years taken to double the money according to Compounding will be 12.5  years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $900

Total amount = $1800

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/1200)^12t

T = A[tex](1+r/1200)^{12t}[/tex]

1800 = 900 (1+6/1200)^12t

2 = (1+1/200)^12t

2 = 1.005^12t

taking log on both sides

log 2 = 12t *log 1.005

0.3/0.002 = 12t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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Using translation concepts, the equation for the graph is b.

y = cos(x + π/2) + 1

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Suppose that we've got:

f(x) = a cos (bx - c) + d

Then, this function has:

Amplitude (the maximum distance of the graph from the middle line) = a

Period =[tex]\dfrac{2\pi}{b}[/tex]

Phase shift = [tex]\dfrac{c}{b}[/tex]

Maximum value: a + d

Minimum value: -a + d

In this problem, we have a cosine function

(zero at π/2, this is zero at the origin), shifted π/2 units to the right and 1 unit up.

Since the standard amplitude is between -1 and 1, here is between 0 and 2).

Hence the rule is given as follows:

b. y = cos(x + π/2) + 1

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Required equation of the parabola with origin as its vertex and directrix  

y = 1/2 is equal to x² = -2y.

As given in the question,

Let vertex of the parabola be ( h, k )

Vertex of the given parabola be at origin

⇒ ( h , k ) = ( 0 , 0 )

Directrix is y =1/2 above the vertex.

Focus is ( 0, -1/2)

Equation of the parabola is given by

Distance between focus to the vertex = distance between vertex to the directrix

( y - (1/2) )² = ( x - 0)² +  ( y - (-1/2) )²

⇒ y² - y + 1/4 = x² + y² + y + 1/4

⇒ -y = x² + y

⇒x² = -y - y

⇒ x² = -2y

Therefore, the equation of the parabola with vertex at origin and directrix y =1/2 is equal to x² = -2y .

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Answer:

17

Step-by-step explanation:

The standard form is y= 1/2x+ 4.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

(2,5) and (-4,2)

So, slope

= (2- 5)/ ( -4 - 2)

= -3 / (-6)

= 1/2

and, using slope- intercept form

y- 5 = 1/2( x - 2)

y-5 = 1/2x -1

y= 1/2x + 4

Hence, the standard form is y= 1/2x+ 4.

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Willka covers 4.5 m² in 1L paint and 45 m² in 10L in paint according to the table.

What are equivalent ratios?

We know that the equivalent ratio is defined as the ratio which is having the same proportion as given ratio.

Now, using the division property of the ratio, we will divide the given ratio with the same number both sides.

According to the given question:

If Willka covers 13.5 m² with 3L paint, to cover x m² she will need 1L paint

By equivalent ratios

13.5 : 3 = x : 1

x = 13.5 / 3

x = 4.5

Similarly to cover y m² she needs 10L paint

13.5 : 3 = y : 10

y = 13.5 x 10/3

y = 45

Therefore the answer for the blanks is 4.5 and 45.

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Answer: 13

Step-by-step explanation:

Minus 29 from 42 to get 13

Answer:

13

Step-by-step explanation:

If you subtract 20 from 42, you will get your answer. Then you plug it into the equation to make sure it's correct.

42-29=13

29+13=42

42-13=29.

-Hope this helped

Allison feeds 11 horses in a day.

Horses are herbivores and, as such, they need a very specific diet. They must consume lots of fiber to keep their extremely long and sensitive digestive tract working and they must eat little and often, almost all day long.

A horse's feed should consist primarily of grass or roughage. However, hay is insufficient to provide a complete nutritional profile. Important minerals and nutrients will be added by adding grains and concentrates, but calories will also be added. Roughage, feeds, and concentration types are listed below, from least to most "complete."

Given,

Allison feeds 2 quarter horses and 3 paint horses the same amount each day.

Therefore, she feeds 2*4+3 = 11 horses in a day.

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To each side, add 4 positive unit tiles.

What is a one-variable linear equation and what does it look like?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

The initial formula is:

3x - 4 = 2x + 5

Four positive unit tiles are added to each side, giving us:

3x - 4 + 4 = 2x + 5 + 4

3x = 2x + 9

which removes the independent elements off both sides of the equal sign and places them all on the right side (the +9 term), simplifying the initial equation. You'll see that the other choices don't produce this outcome.

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