Jose's ball is stuck on the roof of his home, which is 8 feet high. He wants to use a ladder to climb up and get his ball. If he sets the base of the ladder 6 feet away from his home, what is the minimum length that the ladder can be? Explain how you solved this question using context and at least three sentences. Hint: Draw your the scenario and label given values.

Answer:

17.5x + 55 < 12.5x + 95

Step-by-step explanation:

Answer:

17.5x+55 < 12.5x+95

Step-by-step explanation:

Let x be the maximum number of months Katy is enrolled

Charge of School A must be less than Charge of School B

School A < School B

17.5x+55 < 12.5x+95

look at the picture

Answer:

60

Step-by-step explanation:

180-120=60 so the answer is 60

9.

x, y and z are three different numbers.

x + y + z = 100

The mean of x, and y is 40.

The mean of y and z is 35.

the means of x, y is that like similar to coordinator

Answer:

y-187.50= 1.50(x-125)

this is in point slope, but in slope intercept it would be y=1.50x+0

Step-by-step explanation:

Answer:

\(y-187.50=1.50(x-125)\)

Step-by-step explanation:

Slope = $1.50

\(x=125\)

\(y=$187.50\)

(a) The number of pathways in the plane from point (0, 0) to point (110, 111) when each step consists of walking one unit up or one unit to the right is known as the number of ways to go to a point in a grid using just right and up moves.

This is a classic combinatorial problem known as a binomial coefficient. The binomial coefficient C(110+111, 110) = C(221, 110) = 221!/(110!111!) is the number of ways to travel from (0, 0) to (110, 111).

(b) The number of paths from (0, 0) to (210, 111) where each step consists of walking one unit up or one unit to the right and the path must pass through (110, 111) is the product of two binomial coefficients.

First, as calculated in section 1, the number of pathways from (0, 0) to (110, 111) is C(110+111, 110) = C(221, 110). Second, there are C(210+211, 210) ways to get from (110, 111) to (210, 111). (210, 211). (421, 210). C(221, 110) * C is the total number of paths found by multiplying these two binomial coefficients (421, 210).

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Answer:

It should be PT and NO

Hope this helps!

We need to find the function f(n) whose terms are the same as the series in question. We can then integrate this function from n=1 to infinity and determine if the integral is convergent or divergent. If it is convergent, then the series is convergent. If it is divergent, then the series is also divergent.

To determine whether a series is convergent or divergent using the integral test, we need to first check if the series satisfies three conditions:

1) The terms of the series are positive.

2) The terms of the series are decreasing.

3) The series has an infinite number of terms.

Assuming these conditions are satisfied, we can use the integral test which states that if the integral of the function f(x) from n=1 to infinity is convergent, then the series with terms a_n = f(n) is also convergent. Conversely, if the integral is divergent, then the series is also divergent.

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Answer:

287

Step-by-step explanation:

The probability of getting:

a) 2 apples is 5/33

b) 1 apple and 1 orange 35/132 .

Here, we have,

given that,

A fruit basket contains 5 apples and 7 oranges.

Paul picks a fruit at random from the basket and eats it.

He then picks another fruit at random to eat.

so, we get,

total number of fruits = 12

now, we have,

a) P( pick 1 apple) = 5/12

then, P( pick another 1 apple) = 4/11

so, we get,

P( picking 2 apples) = 5/12 * 4/11 = 20/132 = 5/33

b) P( pick 1 apple) = 5/12

then, P( pick 1 orange) = 7/11

so, we get,

P( picking 1 apple and 1 orange) = 5/12 *  7/11 = 35/132

Hence, The probability of getting:

a) 2 apples is 5/33

b) 1 apple and 1 orange 35/132 .

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Wherever you see the letter \(x\) in the equation, you write \(4\), \(0\) or \(-4\) and perform arithmetic operations. Good luck!

The length of the diagonal side is 82, or answer (d) in its simplest radical form.

The Pythagorean Theorem must be utilized in order to determine the length of the diagonal side of a square with a length of 8 feet. You can use the formula a2 + b2 = c2, where a and b are the sides of the triangle and c is the hypotenuse, since the diagonal side of the square is. Because a and b are both 8 feet, you can use those numbers to solve for c:

82 + 82 = c2 64 + 64 = c2 128 = c2 The length of the diagonal side is 82, or answer d in its simplest radical form.

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The value of x along the perpendicular bisector of line PR is 7.

The perpendicular bisector of a line is a line that intersects the given line at a 90-degree angle (i.e., perpendicular) and also passes through the midpoint of the line segment.

In other words, if you have a line segment, the perpendicular bisector is a line that cuts it exactly in half, and at the same time, creates two equal angles where it intersects the line segment.

The value of x is calculated as follows;

line PT = Line RT

x - 1 = 6

x = 6 + 1

x = 7

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The value of x in the secant intersection is 16 units.

Secant is a line that intersects a curve at a minimum of two distinct points. Therefore, the product of secant segment is equals to the product of the other secant segment and its external segment.

Hence, using the rule for secant intersection,

let's find x

8 × (8 + 4) = (x - 10)x

8(12) = x² - 10x

96 = x² - 10x

x² - 10x - 96 = 0

x² - 16x + 6x - 96 = 0

x(x - 16) + 6(x - 16) = 0

(x + 6)(x - 16) = 0

Therefore,

x = -6 and x = 16

Therefore, we can only use positive number.

Hence,

x = 16 units

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Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2 , thus

y = 2x + c ← is the partial equation

To find c substitute (3, 5) into the partial equation

5 = 6 + c ⇒ c = 5 - 6 = - 1

y = 2x - 1 ← equation of line

Answer:

10 cm

Step-by-step explanation:

Volume = length x width x height

360 cm³ = 6 cm x 6 cm x h

Simplifying this expression:

360 cm³ = 36 cm² x h

h = 360 cm³ / 36 cm²

h = 10 cm

Answer:

10

Step-by-step explanation:

length ×width×height =360cm³

6×6=36cm³

360÷36=10

Answer:

.l,´mfkf jh h

Step-by-step explanation:

Answer:

-13 to the fifth power.

Answer:

x= 75*2

x= 3/4*200

(The options arent very clear)

Step-by-step explanation:

The equation is

x= 75/100 *200

= 75*2

or 3/4 * 200

Answer:

The answer is B.

Step-by-step explanation:

1. To make 5 L of a 40% sweet tea concentrate, you need to mix approximately 2.22 L of the 90% sweet tea concentrate with 2.78 L of water.

2. For 400 ml of 790 mM calcium chloride, you would need approximately 34.97 grams of anhydrous calcium chloride.

3. To achieve a final concentration of 20 μM hydrogen peroxide in 10 ml of cells, you would need to add approximately 6.67 μL of a 30 mM stock solution of hydrogen peroxide.

4. To prepare 0.80 liters of culture media, you would need to mix 16 ml of the 50X liquid salt solution with 784 ml of water.

C1V1 = C2V2 where C1 is the initial concentration (90%), V1 is the initial volume (unknown), C2 is the desired concentration (40%), and V2 is the final volume (5 L). Rearranging the equation, we have:

V1 = (C2V2) / C1

Plugging in the values, we get:

V1 = (0.4 * 5 L) / 0.9

V1 ≈ 2.22 L

So, you'll need to mix approximately 2.22 L of the 90% sweet tea concentrate with 2.78 L of water to obtain 5 L of a 40% sweet tea concentrate for your cookout.

To calculate the amount of anhydrous calcium chloride needed for 400 ml of 790 mM calcium chloride, you can use the formula:

mass = molarity × volume × molecular weight

First, convert the molarity from mM to M (mol/L):

790 mM = 0.79 M

Then, calculate the mass using the formula:

mass = 0.79 M × 0.4 L × 110.99 g/mol

mass ≈ 34.97 g

Therefore, you would need approximately 34.97 grams of anhydrous calcium chloride for 400 ml of 790 mM calcium chloride solution.

To determine the amount of a 30 mM stock solution of hydrogen peroxide (H2O2) needed to achieve a final concentration of 20 μM in 10 ml of cells, you can use the formula:

C1V1 = C2V2

Where C1 is the initial concentration (30 mM), V1 is the initial volume (unknown), C2 is the desired concentration (20 μM), and V2 is the final volume (10 ml). Rearranging the equation, we have:

V1 = (C2V2) / C1

Plugging in the values, we get:

V1 = (20 μM × 10 ml) / 30 mM

V1 ≈ 6.67 μL

Therefore, you would need to add approximately 6.67 μL of the 30 mM stock solution of hydrogen peroxide to your 10 ml of cells to achieve a final concentration of 20 μM.

To prepare a stock solution of medium for your culture cells, you'll need to dilute the liquid salt solution and add the required amount of fetal bovine serum (FBS). Since the liquid salt solution is supplied at a 50X concentration and you need a 1X concentration, you'll need to dilute it 50-fold. For a final volume of 0.80 liters, you'll need to mix 0.016 liters (or 16 ml) of the 50X liquid salt solution with 0.784 liters (or 784 ml) of water.

Next, you'll need to calculate the volume of FBS required to achieve a final concentration of 15%. To calculate this, you can use the equation:

V_FBS = (C_FBS × V_total) / C_FBS%

Where V_FBS is the volume of FBS, C_FBS is the desired concentration (15%), V_total is the final volume (0.80 liters), and C_FBS% is the concentration of the supplied FBS (75%). Plugging in the values, we get:

V_FBS = (0.15 × 0.80 liters)

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The area swept clean by the wiper blade is 221.128 square inches.

To find the area swept clean by the wiper blade, we can calculate the area of the sector of a circle that the blade moves through.

The radius of the circle that the blade moves through is the length of the arm, which is 19 inches.

The angle that the blade moves through is 105 degrees.

To calculate the area of the sector, we need to convert the angle to radians:

105 degrees * (π/180) = 1.8326 radians (rounded to 4 decimal places)

The area of the sector is then:

(1/2) * r^2 * θ = (1/2) * (19^2) * 1.8326 = 325.628 square inches (rounded to 3 decimal places)

However, the area swept clean by the wiper blade is not the full area of the sector, as the blade itself has a width of 11 inches. Therefore, we need to subtract the area of the triangle formed by the blade and the two radii of the sector that intersect at the blade's pivot point.

The length of one of the radii is the length of the arm, which is 19 inches. The length of the other radius is 19 - 8 = 11 inches since the blade is mounted 8 inches from the pivot point.

Using the formula for the area of a triangle:

(1/2) * base * height = (1/2) * 11 * 19 = 104.5 square inches

Therefore, the area swept clean by the wiper blade is:

325.628 - 104.5 = 221.128 square inches (rounded to 3 decimal places)

So the area swept clean by the wiper blade is approximately 221.128 square inches.

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In this question, the gradual, long-term movement in time series data is referred to as temporal variation.

The correct answer is a. temporal variation. Temporal variation describes the systematic and long-term changes that occur in time series data over an extended period. It is characterized by a gradual shift or trend in the data points, indicating an underlying pattern or direction.

Temporal variation can be observed in various contexts, such as economic indicators, population growth, weather patterns, and stock market trends. It reflects the impact of factors that change over time, such as demographic shifts, technological advancements, economic cycles, or environmental conditions.

It is important to differentiate temporal variation from other types of movements in time series data. Cyclical movement refers to regular fluctuations that occur within a specific time frame, while exponential smoothing and linear regression are statistical techniques used to analyze and forecast time series data. Therefore, the correct term to describe the gradual, long-term movement in time series data is temporal variation.

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By permutation without repetition, there are 524160 possible different special pizzas.

The possible special pizzas can be calculated with permutation without repetition. The formula of permutation without repetition can be written as

P = n! / (n - k)!

where P is all of the possible combinations, n is the number of objects or elements, and k is how many numbers should be chosen.

From the question above, we know that :

n = 16

k = 5

By substituting the parameters, we can determine all of the possible different pizzas

P = n! / (n - k)!

P = 16! / (16 - 5)!

P = 16! / 11!

P = 16 x 15 x 14 x 13 x 12 x 11! / 11!

P = 524160

Hence, there are 524160 possible different special pizzas

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Answer:.

Step-by-step explanation:

The value of x for the given right triangle is 2 units.

According to the question,

We have the following information:

We have a right triangle where the measurements of its sides are given and one angle is given.

We can use trigonometric function to find the value of x for this triangle.

So, we have the following expression:

Sin 60 = √3/x

Putting the value of sin 60:

√3/2 = √3/x

Using the cross multiplication method:

√3x = 2√3

Dividing by √3 on both the sides:

x = 2 units

Hence, the value of x for the given right triangle is 2 units.

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Answer:

\(m=\frac{3}{2}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-5, -4)

Point (-1, 2)

Step 2: Find slope m

The car will take approximately 5.87 seconds to reach a velocity of 27 m/s. During this time, it will travel approximately 81.53 meters.

To determine the time it takes for the car to reach a velocity of 27 m/s and the distance it travels during that time, we can use the equations of motion. Assuming the car starts from rest, we can use the following equations:

1. v = u + at

2. s = ut + (1/2)at^2

where:

v = final velocity (27 m/s)

u = initial velocity (0 m/s, since the car starts from rest)

a = acceleration (4.6 m/s^2)

t = time taken

s = distance traveled

First, let's calculate the time it takes for the car to reach a velocity of 27 m/s using Equation 1:

27 = 0 + 4.6t

Simplifying the equation, we have:

4.6t = 27

Dividing both sides by 4.6, we find:

t = 27 / 4.6

t ≈ 5.87 seconds

Therefore, it will take approximately 5.87 seconds for the car to reach a velocity of 27 m/s.

Next, let's calculate the distance traveled by the car during this time using Equation 2:

s = (0)(5.87) + (1/2)(4.6)(5.87)^2

Simplifying the equation, we have:

s = (1/2)(4.6)(5.87)^2

s ≈ 81.53 meters

Therefore, the car would travel approximately 81.53 meters during the time it takes to reach a velocity of 27 m/s.

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The statement that is correct concerning the concept of materiality is , Materiality is a matter of professional judgment , the correct option is (d) .

The Materiality is defined as a concept used in auditing and accounting to determine the significance of an item or amount in financial statements.

It is a matter of professional judgment based on the auditor's assessment of the size, nature, and circumstances of the item or amount in relation to the financial statements as a whole.

Materiality is not determined by specific guidelines established by the AICPA or any other accounting or auditing standards-setting organization.

Therefore , The correct statement is represented by Option(d) .

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The given question is incomplete , the complete question is

Which one of the following statements is correct concerning the concept of materiality?

(a) Materiality is determined by reference to guidelines established by the AICPA

(b) Materiality depends only on the dollar amount of an item relative to other items in the financial statements

(c) Materiality depends on the nature of an item rather than the dollar amount

(d) Materiality is a matter of professional judgment.

From the problem, we have :

We need to think of a square number that if we multiply it by 9, the result is 64.

That would be 64/9

The square root of 64/9 is 8/3.

Let u = 3x/8

8u = 3x

x = 8u/3 (This value is the same as we've got above 8/3)

du = 3/8 dx

dx = 8/3 du

Subsitute x = 8u/3 and dx = 8/3 du

Extract the square root of 64 which is equal to 8.

Note that the identity :

It follows that :

Bring back u = 3x/8, the answer is :

Answer:

Minor Arc AC = 360 - 235 = 125°

\(mABC = \frac{Major \ arc - Minor \ arc}{2} = \frac{235 - 125}{2} = \frac{110}{2} = 55\)