Make sense of problems. Determine the number , and explain how you came up with he solution

Answer:

The rule to be use is

SOC CAH TOA

But in this we use d CAH cox there's adjacent and hypothenos here

Step-by-step explanation:

The first triangle

hyp²=opp.²+adj²

62²=x²+3.5²

x²=62²-3.5²

x²=3844-12.25

x²=3831.75

Answer:

240ft

Step-by-step explanation:

You have to multiply length x width x height In this case its 12 x 4 x 5

The correct answer is option b, which is 20 out of 70 throws.

SOLUTION:

A six-sided loaded die is a die that has a non-uniform probability distribution of the faces.

the probability of a number from 1-5 is the same,

by using probability to solve this problem.

The total probability of getting any number from 1-5 is equal to 5 times the probability of getting 6,

the probability of getting 6 is twice the probability of getting any number from 1-5.

the probability of getting any number from 1-5 is (1/7)

the probability of getting 6 is (2/7).

Now, let's calculate the expected number of 6's when the die is thrown 70 times:

Expected value = Number of throws * Probability of getting a 6

Expected value = 70 * (2/7)

Expected value = 20

So, the expected number of times the die would show the number 6 in 70 throws is 20.

Therefore, the answer is option b, which is 20 out of 70 throws.

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Answer: 22 signs

Step-by-step explanation:

First find out how many feet are in a mile.

A mile = 5,280 feet

There are signs every 240 ft so the number of signs are:

= 5,280/240

= 22 signs

There is a sign at the beginning and one at the end both of which are already account for in the 22.

$200 of the first payment would represent interest.

To find out how much of the first payment would represent interest, let's first calculate the total amount of interest that will accrue over the entire repayment period. We can then divide that by the total number of payments and determine how much of each payment goes towards interest.

Given:

Loan Amount (Principal)= P = $10,000

Rate of Interest=R = 6% = 0.06

Number of Payments=n = 3 x 8 = 24 (Three installments per year for 8 years)

Using the formula for compound interest, we can calculate the total amount to be paid back:

A = P (1+r/n)^(n*t) Where,

P = Principal,

r = Rate of Interest,

n = Number of times interest is compounded per year,

t = Time (in years)

      Firstly, let's calculate the amount of interest to be paid over the entire repayment period. We can use the formula

  I = P*r*t, where

I is the amount of interest earned,

P is the principal amount,

r is the rate of interest per year

t is the time period in years.

I = P*r*t = $10,000 x 0.06 x 8 = $4,800

     This means that over the entire repayment period, the borrower will pay $4,800 in interest. We can now find out how much of the first payment represents interest.

   The borrower will make 24 payments, so we can divide the total interest by 24 to find out how much of each payment goes towards interest:

    $4,800 ÷ 24 = $200

Therefore, $200 of the first payment would represent interest.

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The equation of the locus of the moving point that maintains a distance of 4 units from the X-axis is y = ±4, representing two parallel horizontal lines.

To find the equation of the locus of a point that always maintains a distance of 4 units from the X-axis, let's analyze the given information.

Let P(x, y) be the moving point and Q(x, 0) be the fixed point on the X-axis. The distance between P and Q is denoted by PQ. According to the problem, PQ is always 4 units.

Using the distance formula, we have:

PQ² = (x - x)² + (y - 0)²

Since the x-coordinate of both P and Q is the same (x - x = 0), the equation simplifies to:

PQ² = y²

Substituting the value of PQ as 4 units:

4² = y²

16 = y²

Taking the square root of both sides:

\(\sqrt{16 } = \sqrt{y^2}\)

±4 = y

Therefore, the y-coordinate of the moving point P can be either positive or negative 4, giving us two possible solutions for the y-coordinate.

Hence, the locus of the moving point P that maintains a distance of 4 units from the X-axis is given by the equation:

y = ±4

This equation represents two horizontal lines parallel to the X-axis, with y-coordinates at +4 and -4. Any point (x, y) on these lines will always be at a constant distance of 4 units from the X-axis.

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In general, a change in the price of the product causes a movement along the demand curve; and a change in production cost and related factors causes a shift in the supply curve.

The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In a typical representation, the price will appear on the left vertical axis of the graph, and the quantity demanded on the horizontal axis.

The supply curve is a graphic representation of the relationship between product price and quantity of product which a seller is willing and able to supply. Product price is measured on the vertical axis of the graph, and the quantity of product supplied on the horizontal axis.

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Answer:

The answer is B, or the second choice.

Hope I helped! ☺

Answer:

the answer is -2, substitution took place tht is why w turned to -w

Step-by-step explanation:

-W=9 - 7

-W= 2.

W=-2

A woman is 10.296 km far from the starting point which is her house after she walks on 9 kilometers northward going to church.

A woman bikes 5 kilometer to the east going to school

After that she  walks on 9 kilometers northward going to church.

So she forms a right angle triangle ,

So the distance she is away from her home can be found out by Using Pythagoras theorem:

AB² = AC² + BC²

AB² = 5² + 9²

= 25 + 81

AB² = 106

AB = 10.296 km

Therefore, she is 10.296 km away from the starting point .

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Answer:

Explanation:

Here, we want to get the probability of picking two vowels in a row

The letters of a vowel are:

A , E , I , O , U

Let us sum up the number of tiles for all vowels:

We have that as the sum of the number of tiles of each of the vowels

Mathematically, we have that as:

9 + 12 + 9 + 8 + 4 = 42

The probability of picking a vowel is the number of vowel tiles divided by the total number of tiles

We have that as:

Now, we are not replacing the first vowel and we are going for another pick

The total number of vowel tiles is now 41 while the total number of tiles is 99

The probability of picking a vowel now will be:

Finally, we have the probability of picking two vowels in a row as the product of the two probabilities above

Mathematically, we have that as:

The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Answer:

27500

Step-by-step explanation:

meters are 100 times more than kilometers hope this helps:)

Relation r is defined on Z as Z follows m r n = 5|(m² − n²), for all integers.

This implies that  5|(m² − n²) is an integer.

Hence from the given set we can conclude that (m² − n²) ∈ (-5, 0, 5).

Here we have is 1 r (-6)

Here m= 1 and n = -6.

Therefore, (m² − n²)= {(1)² − (-6)²} = - 35

That implies (m² − n²) does not lie in the set (-5, 0, 5).

Hence, 1 r (-6) cannot be defined for the relation r on Z as Z follows m r n = 5|(m² − n²), for all integers.

A relation is defined between two sets is referred to the collection of ordered pairs, say x and y, containing one object from each set. And a relation defined on Z implies relation defined on set of integers.

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Option B "Perpendicular Lines"  is correct.

"Perpendicular Lines" are two lines that intersect at a right angle, forming 90-degree angles between them. Thus, Option B holds the truth.

Perpendicular lines are a fundamental concept in geometry and they are defined as two lines that meet at a right angle; forming four 90-degree angles. This means that the slopes of the two lines are negative reciprocals of each other. Perpendicular lines are important in many areas of mathematics and physics because they allow us to calculate angles, distances and other geometric properties.

Perpendicular lines are useful in many practical applications such as: architecture, engineering and construction. By understanding the properties of perpendicular lines, one can better understand the geometry of our world and solve real-world problems.

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

A compound statement is a group of two or more statements connected using words such as 'or', 'and', 'if then', 'if and only if'.

Then, we have:

This is a compound statement of conditional type where the first simple statement is the condition for the second simple statement.

Then, we have:

p: The dog is hungry.

q: She is barking.

p→q: The dog is hungry if she is barking.

Thus, this statement is a compound statement of conditional type.

We can see this statement as a conjunction of two simple statements:

• p: Bill reads books.

• q: Bill reads magazines.

Then, we have:

p ∧ q: Bill reads books and magazines.

Thus, this statement is a compound statement of conjunction type.

We can see this statement as a conjunction of two simple statements:

• p: There are wild animals on G Ranch.

• q: There are wild animals on L Ranch.

Then, we have:

p ∧ q: There are wild animals on G and L Ranch.

Thus, this statement is a compound statement of conjunction type.

Part a) Compound statement of conditional type.

Part b) Compound statement of conjunction type.

Part c) Compound statement of conjunction type.

The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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The total time taken by the elevator for the entire trip is 45 s + 15 s + 15 s + 15 s + 45 s = 135 seconds i.e., it takes the elevator 135 seconds to complete the entire trip.

The remote control car travels forward for 4 seconds at a speed of 2.0 m/s, then stops for 3 seconds, and finally travels backward for 3 seconds at a speed of 1.5 m/s.

The elevator travels from the lobby to the 36th floor in 45 seconds, stops for 15 seconds, descends to the 28th floor, stops for 15 seconds again, and returns to the lobby.

The total time taken by the elevator to complete this trip is calculated by adding up the times for each segment.

For the remote control car, it travels forward at 2.0 m/s for 4 seconds, covering a distance of 2.0 m/s * 4 s = 8 meters.

It then stops for 3 seconds, and finally travels backward at 1.5 m/s for 3 seconds, covering a distance of 1.5 m/s * 3 s = 4.5 meters.

Therefore, the total distance covered by the car is 8 m + 4.5 m = 12.5 meters.

For the elevator, it takes 45 seconds to go from the lobby to the 36th floor, and it stops for 15 seconds to let people off.

Similarly, it takes 15 seconds to go from the 36th floor to the 28th floor, and another 15 seconds to let people off.

Finally, it takes 45 seconds to return from the 28th floor to the lobby.

Therefore, the total time taken by the elevator for the entire trip is 45 s + 15 s + 15 s + 15 s + 45 s = 135 seconds.

In conclusion, it takes the elevator 135 seconds to complete the entire trip, including stops at different floors, based on the given information.

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Answer:

it should be c im pretty sure it's a quadratic function graph

Given that, the cartesian equation is x² = 2y.Let's substitute x = rcosθ and y = rsinθ to change this equation from Cartesian coordinates to polar coordinates.

r²cos²θ = 2rsinθr = 2tanθTherefore, the polar equation for the curve represented by the given Cartesian equation is r = 2tanθ.

The given cartesian equation is x² = 2y. Now, to change this cartesian equation to polar equation, we should substitute x = rcosθ and y = rsinθ in the cartesian equation. So, after the substitution we get, (rcosθ)² = 2rsinθ Simplifying this equation we get, r²cos²θ = 2rsinθ Dividing both sides by cos²θ we get, r² = 2rsinθ/cos²θ Simplifying we get, r = 2tanθTherefore, the polar equation for the curve represented by the given Cartesian equation is r = 2tanθ.So, the main answer is option (C) r=2tanθ. Therefore, the answer is (C) r=2tanθ.

Therefore, the polar equation for the curve represented by the given Cartesian equation is r=2tanθ.

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Answer: h(x) = 23

Step-by-step explanation:

Plug x in the equation

h(x) = 4(7) - 5

h(x) = 28 - 5

h(x) = 23

Given the expression:

Multiplying the coefficents 4 and -3 give -12

Multiplying the variables by summing the exponents

So,

So, the answer will be -12 x^5

Answer:

B

Step-by-step explanation:

Check the picture below.

Answer:

Equation should be: 15x + 5 = y

Step-by-step explanation:

I do not know the amount of money that he owed

For Example :

15(12) + 5 = y

180 + 5 = y

y = 185

Sorry if I'm incorrect

Answer:

C. \( y = 2x + 3 \)

Step-by-step explanation:

A linear equation written in the slope-intercept form is represented as \( y = mx + b \).

The y-intercept is b.

The variable b on a graph is the point where the line cuts across the y-axis, for which the value of x is zero.

Therefore, the y-intercept of the graph given is 3. At this point where the line intercepts the y-axis, you can observe that the value of x = 0.

Therefore, the linear function, \( y = 2x + 3 \) has the same y-intercept as the graph, which is 3.

Answer:

92 I think because in my class I heard my friend tell me