From a rock ledge, the angle of elevation to the top of a tree is 22°. The angle of depression to the base of the tree is 12°.

a) Find the height of the rock ledge, to
the nearest metre.
b) Find the height of the tree, to the
nearest metre.

Answer:

The objective of the PACER is to run as long as possible while keeping a specified pace. Students run back and forth across a 20-meter space at a pace that gets faster each minute. A point is scored for each 20-meter distance covered. The test is easier in the beginning but progressively gets more difficult.

Step-by-step explanation:

The answer to the above question is B. Multiply the first equation by -2 and add the second equation.

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."

Given,

[tex]2x - 2y = 24\\4x + 7y=-40\-4x +4y = -96\\4x+7y = -40\\11y = -136\\y = -136/11[/tex]

The answer to the above question is B. Multiply the first equation by -2 and add the second equation.

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Answer:

To find the principal, P we can use the same formula, A=P(1+rn)nt. We have the balance of the account, A, after 6 years, $1,780.80. The interest rate, r, is 6.8% (or 0.68 as a decimal) and is compounded annually, so n=1. The time, t, is 6, since we know he opened his account 6 years ago. Plug in the known values into the formula and solve for the missing variable, P.

Step-by-step explanation:

1,780.80 = P (1+0.0681 divided 1^(6)

1,780.80= 1.484P

1,200=P         the principal amount Lex used to open his account 6 years ago

Answer:

7/12 (seven over twelve)

Step-by-step explanation:

1/3 -1/4 =4/12- 3/12=1/12

1/2+1/12=6/12+1/12=7/12

so the answer is 7/12

hopefully this helps

Answer:

The expression "d-7 / 2" can be written in words as

Step-by-step explanation:

The expression "d-7 / 2" can be written in words as "the quotient of d minus 7, divided by 2".

This is the operation of subtracting 7 from d and then dividing the result by 2.

Answer:

Step-by-step explanation:

10,14,18

Two equations that have the same solution as the given equation are;

2.3p – 10.1 =  6.49p – 4

230p – 1010 = 650p – 400 – p

Both sides of an equation will remain equal, when both sides are

multiplied by the same amount.

The given equation: 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Multiplying both sides of the original equation by 100 gives

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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Answer:

9.6 hours

Step-by-step explanation:

12×8 would equal the amount of hours it takes to complete the job in 12 days so you simply divide that number by 10 which will give you 9.6h

Answer:

6.67 hour per day

Step-by-step explanation:

If

=8 hours a day = 12 days

then

= ? = 10 days

= 10/12 × 8hours per

= 6.67 hours per day.

3/4 > 1/5
6/9 > 2/5
6/7 > 3/10
2/11 < 4/9

Answer:

3/4 > 1/5

6/9 > 2/5

6/7 > 3/10

2/11 < 4/9

Step-by-step explanation:

Manera facil de comparar fracciones:.

3/4    1/5

Multiplica el denominador (numero abajo) de cada fraccion por el numerador de la otra fraccion y escribe el producto arriba del numerador.

El numero mas grande esta arriba de la fraccion mas grande.

5 x 3 = 15 arriba  de 3/5

4 x 1 = 4 arriba de 1/5

Como 15 > 4, 3/4 > 1/5

30      18

6/9    2/5

6/9 > 2/5

 60     21

6/7    3/10

6/7 > 3/10

18       44

2/11   4/9

2/11 < 4/9

Answer:

7 cars

11 bikes

Step-by-step explanation:

18 cars would have 72 tires. This is 22 more tires than necessary. If we add a bike, we lose four tires (from the car) and add two (from the bike). This means we lose two tires. 22/2 is 11 so it would be 11 bikes and 7 cars.

11 bikes = 22 tires

7 cars = 28 tires

22+28=50 tires

Answer: q1=11 q2=15 q3=20

Step-by-step explanation:

The number of students that were in Mr Marco's class will be 9 students

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Here, the students in Mr Marcos art class use six jars of paint for their project each student uses 2/3 jars of paint

The number of students that were in Mr Marco's class will be:

= 6 ÷ 2/3

= 6 × 3/2

= 9 students

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Yogurt production is affected by the production technological conditions.

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Answer:

it too far i can't see it

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given  :

=> -x-y=-2

=>  5x + 7y= 28

So ,

=>x = 2-y

thus,

=> 5(2-y) + 7y =28

=> 10 -5y + 7y =28

=> 10 -2y = 28

=> -2y = 18

=> y =-9

and

=> x  = 2 - (-9)

=> x  = 11

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

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Answer:

[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex]  meters

[tex]r=10.24[/tex]  meters

Step-by-step explanation:

Here is the equation for the volume of a sphere

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

Lets solve for [tex]r[/tex].

Multiply both sides of the equation by [tex]\frac{1}{\frac{4}{3}\pi}[/tex].

[tex]\frac{1}{\frac{4}{3}\pi}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]

Simplify the left side.

Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].

[tex]\frac{1}{\frac{4\pi }{3}}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]\frac{3}{4\pi } (\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]

Cancel the common factor of [tex]\pi[/tex] by factoring it out of the first term.

[tex]\frac{3}{4} (\frac{4}{3}*r^3)=\frac{1}{\frac{4}{3}\pi}V[/tex]

Combine [tex]\frac{4}{3}[/tex] and [tex]r^3[/tex].

[tex]\frac{3}{4}*\frac{4r^3}{3}=\frac{1}{\frac{4}{3}\pi}V[/tex]

Multiply the numerators on the left side of the equation. Then multiply the denominators.

[tex]\frac{12r^3}{4*3}=\frac{1}{\frac{4}{3}\pi}V[/tex]

[tex]\frac{12r^3}{12}=\frac{1}{\frac{4}{3}\pi}V[/tex]

Cancel the common factor of 12.

[tex]r^3=\frac{1}{\frac{4}{3}\pi}V[/tex]

Simplify the right side.

Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].

[tex]r^3=\frac{1}{\frac{4\pi }{3}}V[/tex]

Multiply the numerator by the reciprocal of the denominator.

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

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

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

Now we have an equation to find the radius.

Substituting our number for volume gives us

[tex]r=\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]

Enter this into a calculator

[tex]\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]

You can leave the answer in simplest radical form or as a decimal.

[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex]

[tex]r=10.24[/tex]

A rating/review would be much appreciated. Hope this helps!

Answer:

0.95meters

Step-by-step explanation:

last year her was 0.45m tall

this past year he is 0.5m

Total = 0.45 + 0.5 = 0.95

Answer: 0.95

Step-by-step explanation: add 0.45+0.5=0.95

Answer:

  3.58

Step-by-step explanation:

You want to know the weekly growth factor if the daily growth factor is 1.2.

The weekly growth factor will be the growth factor over 7 days:

  (1.2)^7 ≈ 3.58

Every week, the number of locusts grows by a factor of 3.58.

__

Additional comment

The exponential model is ...

  number = (initial number)(growth factor)^t

The period of time associated with the growth factor is the units associated with t. Since 1 week = 7 days, the multiplier for 7 days is ...

  weekly growth factor = (daily growth factor)^7

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The nearest integer that is a solution, gotten through graphing of the quadratic function x² + 2x - 2 = 5, is x = -4

Quadratic equations when plotted on a graph follows a parabolic path.

To plot the functions there will be table of values that is used in making the graph. The table of values is solved as follows

x² + 2x - 2 = 5 rearranging the equation will result to x² + 2x - 7 = 0

For x = -20,  y = (-20)² + 2 * -20 - 7 = 353

For x = 0,  y = (0)² + 2 * 0 - 7 = -7

For x = 20,  y = (20)² + 2 * 20 - 7 = 433

x      y

-20  353

0      -7

20    433

The graph is plotted and attached. From the graph the solution is

x = -3.828, to the nearest integer = -4

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The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

when we have to solve an equation, it does not has an equal sign and inequalities.

When we have to solve an inequality equations usually are exact answers.

The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.

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The unbiased estimator of 1/p does not exist.

An estimate that deviates from the genuine population value is said to be biased. If the kind and extent of the bias are known, a biased sample may still be informative. When a sample's value matches the actual value of a population parameter, that is an unbiased estimator.

Given:

If the random variable X has the binomial.

1/p = 1 /{1-(1-p)} = 1 + (1-p) + (1-p)²/2! + ....

And let an unbiased estimator of 1/p exist.

[tex]\sum^n_k_=_0T(k)(^n_k)p^k(1-p)^k[/tex] = 1 + (1-p) + (1-p)²/2! + ....

The above series is finite on the LHS and infinite power series on the RHS.

That is contradiction.

The basic idea is that an unbiased estimator of 1/p would have to have the property that its expected value as a function of p would have to tend to infinity as p tends to 0.

But since Ep[U(x)] is bounded above by some function of n that is independent of p, no such estimator can exist.

Therefore, the unbiased estimator 1/p can not exist.

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Answer:

17/5÷23/8= 1  21/115

The answer is 1  21/115

No, 11^2 x 5^4 is not a factor of 11^3 x 5^4.

To see this, you can divide 11^3 x 5^4 by 11^2 x 5^4 and see that there is a remainder.

11^3 x 5^4 = (11 x 11 x 11) x (5 x 5 x 5 x 5)

= 121 x 625

= 75125

11^2 x 5^4 = (11 x 11) x (5 x 5 x 5 x 5)

= 121 x 625

= 75125

75125 / 75125 = 1 with a remainder of 0.

Therefore, 11^2 x 5^4 is not a factor of 11^3 x 5^4.

The product of the given numbers can be represented in a scientific notation form as = 6418 × 10^19 (approximately)

Multiplication can be defined as the repeated addition of a given value with the purpose of arriving to an expected value.

The multiplication of two given numbers is the same thing as the products of the given number and it's represented by the sign (X)

The product of 6,789,694,976 x 9,452,569,132 = 6418 × 10^19

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Total Liabilities  + Equity = $220,000.

Total Assets = $220,000.

What is Ratio Analysis and Balance Sheet?

The relationship between the two separate components is established through ratio analysis. Utilizing figures from the income statement, balance sheet, statement of cash flows, and other financial statements, it is used to assess the company's financial performance.

One of a company's financial statements that is created at the end of the year is the balance sheet. It establishes the balance of a company's assets, liabilities, and stockholder equity at the end of the fiscal year.

Here we are given in the Question,

Assets

Cash = $45,000

Inventory = $41,000

Property = $134,000

Liabilities

Notes  = $55,000

Wages  = $56,000

and

Equity

Stock = $50,000

Investment = $59,000

Total Liabilities  + Equity = ( Notes + wages ) + (stock + Investment)

Total Liabilities  + Equity = ( $55,000 + $56,000) + ($50,000 + $59,000)

Total Liabilities  + Equity = $220,000.

Total Assets = Cash + Inventory + Property

Total Assets = $45,000 + $41,000 + $134,000

Total Assets = $220,000

Therefore,

Total Liabilities  + Equity = Total Assets.

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Answer:

The area of a rectangle is given by the formula:

area = length * breadth

In this case, the length of the rectangle is (x+2) cm and the breadth is (x) cm, so the area is:

area = (x+2) cm * (x) cm

= x^2 + 2x cm^2

We know that the area of the rectangle is 15 cm^2, so we can set up the following equation:

x^2 + 2x cm^2 = 15 cm^2

We can solve for x by using the quadratic formula:

x = (-2 +/- sqrt(4 - 41(-15))) / (2*1)

= (-2 +/- sqrt(64)) / 2

= (-2 +/- 8) / 2

= (-4, 2)

We have two solutions for x, so we need to consider both of them to find the dimensions of the rectangle.

If x=-4, then the length of the rectangle is (x+2) cm = (-4+2) cm = (-2) cm and the breadth is (x) cm = (-4) cm. Since the length and breadth of a rectangle must both be positive, this solution is not valid.

If x=2, then the length of the rectangle is (x+2) cm = (2+2) cm = 4 cm and the breadth is (x) cm = 2 cm. These dimensions give us a valid rectangle with an area of 15 cm^2.

The perimeter of the rectangle is the sum of all four sides, so the perimeter is 2 cm + 2 cm + 4 cm + 4 cm = 12 cm.

Therefore, the value of x that gives us a rectangle with an area of 15 cm^2 and a perimeter of 12 cm is x=2.

Answer:

n = -4/9

Step-by-step explanation:

first get rid of n on left side

-2 = 9n + 2

Get rid of 2 on right side

-4 = 9n

Make 9n into n

-4/9 = n

ans: n = -4/9

hope this helps :)

The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that,

The function g(x).

The graph of a function never touches the x = 1 line

At x = -1 there will be a vertical asymptote.

At x = -2 there will be a horizontal asymptote.

The equation of the function g(x) will be:

g(x) = (2x + 4)/(x + 1)

The equation of rational function is g(x) = (2x + 4)/(x + 1)

Therefore,  g(x) = (2x + 4)/(x + 1) is correct.

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Answer:

5-3=2m

3x2=6m^2

Step-by-step explanation:

I can’t explain

LETTER B I DON’T KNOW THE ANSWER

As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.

Given that it has three sides and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon because it has three sides and three corners. The points at which the three sides of the triangle converge are referred to as its corners. Three triangle angles can be multiplied to get 180 degrees.

given

p is the midpoint of GI

GP = PI , PN = AP ( as mid point )

∠APG = ∠IPN ( as vertical opp. angle )

∠A = ∠N ( given )

so by ASA congruency ΔAPG = ΔIPN

As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.

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