A rock-climbing wall at a local park has a right triangular section that slants toward the climber, as shown in the picture below. The height of the wall is 5 meters and the slanted section begins 1.2 meters up the wall at an angle of 14 degrees.

Answer:

Longest side = 10 inches

Medium side = 9 inches

Shortest side = 6 inches

Step-by-step explanation:

Let the longest side be L, the medium side be M and the shortest side be S

From the data,

L = S + 4        
(The longest side of a triangle is 4 inches longer than the shortest side)

M = S + 3

(The medium side is 3 inches longer than the shortest side)

Perimeter of the triangle

P = L + M + S

Substituting for L and M in terms of S:
P = (S + 4) + (S + 3) + S

P = S + S + S + 4 + 3
P = 3S + 7

We are given that perimeter P = 25 inches

So,

3S + 7 = 25

Subtract 7 from both sides
3S = 25-7 = 18

Divide by 3 both sides:
3S/3 = 18/3

S = 6

So shortest side is 6 inches

Longest side L = 6 + 4 = 10 inches

Medium side M = 6 + 3 = 9 inches

Answer:

x=78

Step-by-step explanation:

2/3(9+x)=-5(4-x)

6+2/3=-20+x

6=-20+1/3x

x=78

Answer:

x=6

Step-by-step explanation:

Distribute.

2/3 * 9 = 6

2/3 * x = 2/3x

Distribute other side.

-5*4 = -20

-5 * -x = 5x

Rewrite.

6 + 2/3x = -20 + 5x

Subtract 5x from both sides.

-13/3x + 6 = -20

Subtract 6 from both sides.

-13/3x = -26

Multiply -3/13 to both sides.

x=6

Answer:

Wouldn't it be answer B?

Step-by-step explanation:

The rest of the answers have addition which is not in the problem provided.

Answer:

There is a 0.2 chance or 20% change that he will choose a nonfiction book. PLease mark as helpful if it is! thanks

Answer:

2.94

Step-by-step explanation:

A = 6a²

6 × .7² = 2.94

.7 × .7 = .49

6 × .7 = 2.94

\( a = 6a {}^{2} \)

a is the side

area -6 x 0.7

Answer:

I think you meant to add a list of answers but didn't so here's the characteristics of a plane: Flat, two dimensional, extends infinitely, and is assembled about multiple points and lines.

Step-by-step explanation:

Answer:

If you are taking the FLVS test it is "Two endpoints"

Step-by-step explanation:

Just took the test

hope it helps :)

Answer:

$2600

Step-by-step explanation:

2/100×70000=1400

2/100×60000=1200

1400+1200=2600

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

The number of red balls to the number of green balls is 3 : 2

The distribution of the balls is given as:

6 red, 4 green, 2 yellow and 3 blue balls

The number of red balls to the number of green balls is represented as:

Ratio = Red : Green

So, we have:

Ratio = 6 : 4

Simplify

Ratio = 3 : 2

Hence, the number of red balls to the number of green balls is 3 : 2

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The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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The expression to represent the information will be 2(2m + 3n + 4p)

From the information given, Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens.

There are m number of games required.

There are n number of games that require 3 token.

Therefore, the expression to represent the information will be:

= 2(2 × m) + 2(3 × n) + 2(4 × p)

= 2(2m + 3n + 4p)

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Answer:

The other person who answered is incorrect!! The real answer is 2m + 3n + 4p

Step-by-step explanation:

have a good besti!!!!

-leeknowishawt

Answer:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

Step-by-step explanation:

The sum of x and y is 28. In other words, x plus y equals 28 and can be written as equation A:

x + y = 28

The difference between x and y is 6. In other words, x minus y equals 6 and can be written as equation B:

x - y = 6

Now solve equation B for x to get the revised equation B:

x - y = 6

x = 6 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 28

6 + y + y = 28

6 + 2y = 28

2y = 22

y = 11

Now we know y is 11. Which means that we can substitute y for 11 in equation A and solve for x:

x + y = 28

x + 11 = 28

X = 17

Summary: The sum of two numbers is 28 and their difference is 6. What are the two numbers? Answer: 17 and 11 as proven here:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

Answer:

17 +11 = 28

hope this helps

Answer:

A

Step-by-step explanation:

\($\frac{x-3}{x+5} \cdot \frac{3x}{x-5} $\)

\($\frac{3x(x-3)}{(x+5)(x-5)} $\)

\($\frac{3x^2-9x}{x^2-25} $\)

\(\dfrac{(3x^2-9x)}{(x^2-25)}\)

A rational function is defined as a polynomial divided by a polynomial.

Fractions is defined as a numerical value that represents a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

\((\dfrac{x-3}{x+5})(\dfrac{3x}{x-5} )\\\)

\(\dfrac{(x-3)(3x)}{(x+5)(x-5)}\)

Used formula a² - b² = (a + b)(a - b)

\(\dfrac{(3x^2-9x)}{(x^2-5^2)}\)

\(\dfrac{(3x^2-9x)}{(x^2-25)}\)

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The particular solution of Differential equation y" – 2y' + 2y = et sin x is yp = (1/2et - 1/2et cos(x))sin(x).

We assume the particular solution is of the form of given differential equation is

yp = (Aet + Bcos(t))sin(x) + (Cet + Dsin(t))cos(x)

where A, B, C, and D are constants to be determined.

Taking the first and second derivative of yp with respect to t:

yp' = Aet sin(x) - Bsin(t)sin(x) + Cet cos(x) + Dcos(t)cos(x)

yp'' = Aet sin(x) - Bcos(t)sin(x) - Cet sin(x) + Dsin(x)cos(t)

Substituting these into the differential equation and simplifying, we get:

(et sin x) = (A - C)et sin(x) + (B - D)cos(x)sin(t)

Since et sin x is not a solution to the homogeneous equation, the coefficients of et sin x and cos(x)sin(t) on both sides of the equation must be equal. Therefore:

A - C = 1 and B - D = 0

Solving for A, B, C, and D, we get:

A = 1/2, B = 0, C = -1/2, D = 0

So the particular solution is:

yp = (1/2et - 1/2et cos(x))sin(x)

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Answer:

1) dividend

2) divisor

3) quotient

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

7x - 4 < 24

Step-by-step explanation:

8 + 4x - 12 + 3x < 24

3x + 4x - 12 + 8 < 24

7x - 4 < 24

Hope this helps!

Have a nice day!

If you find my answer helpful

Pls consider marking my answer as Brainliest! It would mean a lot!

Answer:

8 + 4x - 12 + 3x < 24

3x + 4x - 12 + 8 < 24

7x - 4 < 24

Step-by-step explanation:

Answer:

The domain of a function is the set of numbers for which the function is defined.

Here, this function has values of number from -1 to +3

therefore, it's domain is [-1,3]

The range is the set of results of a function

here, this function ranges between -5 to +4

therefore, its range is [-5,4]

I am 1 Brainly away from Virtuoso, help if you find this answer helpful

Answer:

There are 10 credits per semester.

Step-by-step explanation:

Given that: A college student takes the same number of credits each semester.

They had 8 credits when they started, and after 5 semesters, they had total 58 credits.

Now, In which rate they are earning credits per semester,

for that use the formula:

\(rate=\frac{change of credits}{total no of semeters}\)

rate=50/5

The change in credits is 58-8 = 50, since the

student earned 50 credits in 5 semesters.

So the rate at which they are earning credits per semester is:

Rate = 10 credits per semester.

Hence, there are 10 credits per semester.

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Explanation

To find the answer, we will have to find the equations that define the two functions

For the first graph

For the second graph (The purple)

Thus, the answer is

The number of students who offered Accountancy only is 10.

Let's represent the number of students who offered Mathematics as M, the number of students who offered Accountancy as A, and the number of students who offered Economics as E.

From the given information:

M = 30 (Number of students who offered Mathematics)

A = 20 (Number of students who offered Accountancy)

E = 40 (Number of students who offered Economics)

We are also given the following conditions:

M ∩ A > A ∩ E by 2

M ∩ E = 0

We know that the total number of students is 80, so:

M + A + E = 80

Now, let's solve for the number of students who offered Accountancy only.

We can start by substituting the given values into the equation:

30 + 20 + 40 = 80

Now, we need to find the value of A ∩ E (Number of students who offered both Accountancy and Economics).

Since none offered both Mathematics and Economics, we can subtract M from A:

A - M = A ∩ E

20 - 30 = A ∩ E

-10 = A ∩ E

Since A ∩ E cannot be a negative number, we know that A ∩ E = 0.

Now, let's use the first condition: M ∩ A > A ∩ E by 2.

Substituting the values, we have:

M ∩ A - A ∩ E = 2

M ∩ A - 0 = 2

M ∩ A = 2

Now, we can substitute the values of M ∩ A and M into the equation M + A + E = 80:

30 + A + 40 = 80

A + 70 = 80

A = 10

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Answer:

3

Step-by-step explanation:

4x3=12

12-1=11

Answer:

No

Step-by-step explanation:

3 × \(\frac{2}{5}\) = \(\frac{6}{5}\) = 1 \(\frac{1}{5}\) cups required to triple her recipe

she only has 1 cup

so does not have enough to triple her recipe

Answer:

No

Step-by-step explanation:

If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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The domain is:

D: {-4, 5, 6, 8}

The range is:

R: {-4, 3, 5}

And yes, the relation is a function.

For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).

Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}

The domain is the set of the first values of each pair, so we have:

D: {-4, 5, 6, 8}

The range is the set of the second values of each pair:

R: {-4, 3, 5}

Now, is this a function?

Yes, it is a function, because each input is mapped into only one output.

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Answer:

21/100

Step-by-step explanation:

By looking at the table, we can find the box that has information on people who have dogs but do not walk. The number is 21. The total number of people is 100. To find probability, divide 21 by 100.

21/100

This fraction is in its simplest form and cannot be simplified any further.

Answer:

1.6x-y=5--->equ.(i)

3x+4=y--->equ.(ii)

substitution method

6x-y=5

y=5+6x--->equ (iii)

Replace y=5+6x into equ--->(ii)

3x-5+6x=4

3x+6x=4+5

9x=9

divide both side by 9

9x/9=9/9

x=1

Replace x=1 into equ (iii)

6(1)-y=5

6-y=5

y=5+6

y=11

then your x and y is

x=1,y=11

The output value of (f∘g)(x) is:  \((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)

The domain of (f∘g)(x) is (-∞, -3) U (-3, ∞).

In this scenario, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations (multiplication) in simplified form as follows;

\(f(x) = \frac{x-6}{x +3}\)

g(x) = 4x - 15

Next, we would write the numerators and denominators in factored form as follows;

(x - 6)(4x - 15)

4x² - 15x - 24x + 60

4x² - 29x + 60

Now, we can derive the corresponding composite function of f(x) and g(x);

\((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x + 3 ≠ 0

x ≠ -3

Domain = (-∞, -3) U (-3, ∞).

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