A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. The length of the deck is to be expanded by 6 feet, and the width by 2 feet. If the area of the new rectangular deck is 68 ft2 larger than the area of the original deck, find the dimensions of the original deck.

The circumference of a circle with diameter 2ft is 2π ft and the area is π ft².

To find the circumference of a circle, you can use the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 2ft, so the circumference would be C = π(2) = 2π ft. To find the area of a circle, you can use the formula A = πr², where A is the area and r is the radius. Since the radius is half the diameter, the radius would be 2ft/2 = 1ft. Therefore, the area would be A = π(1)² = π ft².

Final answer:

The circumference of a circle with a diameter of 2 feet is approximately 6.28 feet, and the area is approximately 3.14 square feet using the formulas C = πd and A = πr².

Explanation:

To find the circumference and the area of a circle with a diameter of 2 feet, we can use the formulas for circumference and area. The diameter of the circle is given as 2 feet. Therefore, the radius (r) is half of the diameter, which is 1 foot.

The formula for the circumference of a circle is C = πd where C is the circumference, π (pi) is approximately 3.14159, and d is the diameter. Since the diameter (d) is 2 feet, the circumference is:

C = π × 2 feet ≈ 3.14159 × 2 feet ≈ 6.28318 feet

So the circumference is approximately 6.28 feet.

The formula for the area of a circle is A = πr² where A is the area and r is the radius of the circle. Using the radius 1 foot, we find the area as follows:

A = π × (1 foot)² ≈ 3.14159 × 1 foot × 1 foot ≈ 3.14159 square feet

So the area of the circle is approximately 3.14 square feet.

The dependent variable is the additional charge applied for each hour whereas the independent variable is the charge to be applied on the first hour

The dependent variable would be $1.45 for each additional hour. The cost depends on every hour so we can't really calculate it unless we have the hours given.

$3 is independent since it's only charged on the first hour. It doesn't depend on any other information.

Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.

Answer:

its

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

We are given that   a function

[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]

We have to find the minimum value of y.

We know that range of sin x is [-1,1].

[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]

[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]

[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]

[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]

[tex]-7\leq y\leq 3[/tex]

Maximum value of y=3

Minimum value of y=-7

Hence, the minimum value of given function =-7

x = average of next 5 quizzes

4 * 73 = first 4 quizzes

There will be a total of 4 +5 = 9 quizzes

Average of all quizzes = 88 = (4*73+5x)/9

9*88 = 9*(292 +5x)/9

792 = 292 + 5x

500 = 5x

X = 500/5 = 100

 Next 5 quizzes need to average 100

Answer:

v . w = <-20, -36, 15>

Step-by-step explanation:

r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>

To find the dot product of vectors we multiply the numbers

We need to multiply v  and w

vectors is in the form of <x,y,z>

Multiply all the x values

4 times -5= -20

6 times -6 = -36

-5 times -3 = 15

So v . w = <-20, -36, 15>

To find the area of sector AOB, use the formula A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, the area is approximately 0.139 m², rounded to the nearest tenth.

To find the area of sector AOB, we need to use the formula for the area of a sector: A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, we get A ≈ (1.11/360) * π * (4.5)^2.

Using a calculator, we can calculate the value to be approximately 0.139 m². Rounding to the nearest tenth, the area of sector AOB is 0.1 m².

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The areas of the sectors of circles 5 and 6 to the nearest tenth are 197.8 cm² and 6.3 ft² respectively.

The area of the sector of a circle can be expressed as:

Area = ( θ/360º ) × πr²

Where θ is the sector angle in degrees, R is the radius of the circle, and π is constant pi.

For question5)

Angle θ = 70 degrees

Radius r = 18 cm

Area =?

Area = ( θ/360º ) × πr²

Plug in the values:

Area = ( 70/360º ) × π × 18²

Area = 63π cm²

Area = 197.8 cm²

For question 6)

Angle θ = 180 degrees

Diameter d = 4ft

Radius r = 4/2 = 2ft

Area =?

Area = ( θ/360º ) × πr²

Plug in the values:

Area = ( 180/360º ) × π × 2²

Area = 2π ft²

Area = 6.3 ft²

Therefore, the area of the sector is 6.3 ft².

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Answer: 1.09

Step-by-step explanation:

Given : A basketball player makes 39% of her shots from the free throw line.

i.e. Proportion of her shots from the free throw line: p= 0.39

We assume that each of her shots can be considered independent .

She takes 5 shots.

i.e. Number of trials : n= 5

Let x = the number of shots that she makes.

Then , the standard deviation for x will be :-

[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{5(0.39)(1-0.39)}\\\\=\sqrt{1.1895}=1.09064201276\approx1.09064201276\approx1.09[/tex]

Hence, the standard deviation for x= 1.09

Final answer:

The standard deviation for the number of shots made by a basketball player who has a 39% success rate and takes 5 shots is approximately 1.09 shots, calculated using the binomial distribution formula.

Explanation:

To find the standard deviation for the number of shots made by a basketball player who makes 39% of her shots, we use the concept of a binomial distribution.

Given that each shot is independent and that she takes 5 shots, with x representing the number of shots made, we can calculate the standard deviation using the formula for a binomial distribution.

The formula for the standard deviation (σ) in a binomial distribution is σ = √[n × p × (1 - p)], where n is the number of trials (in this case, 5 shots), and p is the success probability per trial (in this case, 0.39 for making a shot).

Plugging in the values, we get σ = √[5 × 0.39 × (1 - 0.39)] = √[5 × 0.39 × 0.61] = √[1.1885] ≈ 1.09 shots.

Therefore, the standard deviation for the number of shots made is approximately 1.09 shots.

The difference between the total reading times of Noel and Tyra is 60 minutes. Therefore, the correct option is option C.

The difference in minutes between the total time Noel read and Tyra read can be calculated by adding up the individual reading times for each and then finding the difference.

Answer:  2.   [tex]\mathbf{2x^3y^5}[/tex]

Step-by-step explanation:

The given expression : [tex]12x^7y^9 + 6x^4y^7 - 10x^3y^5[/tex]

Term 1 : [tex]12x^7y^9[/tex]

Term 2 : [tex]6x^4y^7[/tex]

Term 3: [tex]- 10x^3y^5[/tex]

Lowest power of x = 3

Thus  , The highest common power of x = [tex]x^3[/tex]   (i)

Lowest power of y = 5

The highest  common power of y =[tex]y^5[/tex] (ii)

Greatest common factor of 12, 6 , -10= 2  [Because 2 is the largest number that divides all of them]   (iii)

From (i) , (ii) , (iii) , we have

Greatest common expression : [tex]2x^3y^5[/tex]

Hence, the correct answer is 2. [tex]\mathbf{2x^3y^5}[/tex]

Answer: Third graph represents the acceptable weights for the frozen yogurt options.

Step-by-step explanation:

Since we have given that

Number of ounces of frozen yogurt a machine fills cups with before the customer adds the toppings = 4

After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces.

So, it means the weight should be lie between 4 ounces and 7 ounces.

So, it can be written as [4,7].

4≤ x ≤7, here, x is the weight of frozen yogurt.

So, third graph represents the acceptable weights for the frozen yogurt options.

4 aces in a deck

 52 cards

 you have a 4/52 reduced to 1/13 probability of picking an ace.

 without replacing it there would be 51 cards left and 3 aces

 so second probability of picking an ace is 3/51 reduced to 1/17

 the probability of doing both = 1/13 x 1/17 = 1/221

Answer:

conf

Step-by-step explanation:

see picture for solution