The data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique. Which of the numbers below is the best measure of the central tendency of the data? {3, 3, 4, 4, 4, 5, 5, 5, 5, 30}

Answer:

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Step-by-step explanation:

Plato

The value of f(-3) for the given function f(x) = -4x² + 15 will be -21.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given function,

f(x) = -4x² + 15

Put x = -3

f(-3) = -4(-3)² + 15

⇒ -4 x 9 + 15

⇒ -36 + 15 = -21

Hence "The value of f(-3) for the given function f(x) = -4x² + 15 will be -21".

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I believe the equation you gave is wrong because the standard form of equation for C-14 decay is in the form of:

A = Ao e^-kt

So I think the right form of equation is (correct me if I’m wrong):

 P(t) = Po e^(-0.00012097t)

Where,

Po = initial value of C-14 at t = 0

t = time elapsed

Since it is given that:

P = (1 – 0.34) Po

P = 0.66 Po

Therefore, t is:

0.66 Po = Po e^(-0.00012097 t)

0.66 = e^(-0.00012097 t)

taking ln of both side:

ln 0. 66 = -0.00012097 t

t = - ln 0. 66 / 0.00012097

t = 3,434.86 years

Therefore the ivory tusk is about 3,435 years old.

The final amount is = $ 959.779

Compound interest is when you earn a hobby on both the cash we've got stored and the hobby we earn.

calculation:-

principal amount = $765.13

rate if interest = 12%

for 1st year:-

interest amount= $765.13*12/100

                            = $ 91.8156

final amount = $765.13 + $ 91.8156

                     = $ 856.9456

for 2nd year:-

principal amount = $ 856.9456

       12% interest on $ 856.9456 = $ 102.833472

final amount = $ 856.9456+$ 102.833472

                      = $ 959.779 answer

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To find what percent 187.05 is of 645, one can use the following formula:

[tex]\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \][/tex]

In this case, the Part is 187.05 and the Whole is 645. Plugging these values into the formula gives:

[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 \][/tex]

Now, calculate the fraction:

[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 = \left( 0.29155 \right) \times 100 \][/tex]

[tex]\[ \text{Percentage} = 29.155 \][/tex]

Therefore, 187.05 is approximately 29.155% of 645. To express this as a fraction, one can write:

[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \approx 29.155\% \][/tex]

To get the exact fraction, we can simplify:

[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \times \frac{20}{20} = \frac{374100}{12900} \][/tex]

Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 300, we get:

[tex]\[ \text{Percentage} = \frac{374100 \div 300}{12900 \div 300} = \frac{1247}{430} \][/tex]

So, the exact fraction representing the percentage is:

[tex]\[ \text{Percentage} = \frac{1247}{430} \times 100 \][/tex]

[tex]\[ \text{Percentage} = \frac{1247}{4.3} \][/tex]

[tex]\[ \text{Percentage} = 29.00 \% \][/tex]

Thus, 187.05 is exactly 29% of 645.

Answer : The correct option is, [(10 × 4 × 5) + (5 × 5 × 5)] cubic inches.

Step-by-step explanation :

As we know that,

Formula used for volume of cube is:

[tex]V=(a)^3[/tex]

or,

[tex]V=a\times a\times a[/tex]

where,

V = volume of cube

a = side of cube

Formula used for volume of cuboid is:

[tex]V=l\times b\times h[/tex]

where,

V = volume of cuboid

l = length of cuboid

b = breadth of cuboid

h = height of cuboid

The given figure is formed by the combination of two figure that is cube and cuboid.

Volume of cube = [tex](a)^3[/tex]

Given :

a = side of cube = 5 inch

Volume of cube = [tex]5\times 5\times 5[/tex] cubic inches

and,

Volume of cuboid = [tex]l\times b\times h[/tex]

Given :

l = length of cuboid = 10 inch

b = breadth of cuboid =5 inch

h = height of cuboid = 4 inch

Volume of cuboid = [tex]10\times 5\times 4[/tex] cubic inches

Total volume of figure = Volume of cuboid + Volume of cube

[tex](10\times 5\times 4)+(5\times 5\times 5)[/tex] cubic inches

Thus, the correct volume of the figure will be,

[tex](10\times 5\times 4)+(5\times 5\times 5)[/tex] cubic inches

The equation that can be used to determine t, the time it takes for the two cars to pass each other is:

60t + 55t = 150

Option C is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The equation that can be used to determine t, the time it takes for the two cars to pass each other is:

60t + 55t = 150

Here,

60t represents the distance covered by the first car in time t, and 55t represents the distance covered by the second car in time t.

When they meet, the sum of their distances would be equal to the total distance between them, which is 150 miles.

Therefore,

We can add their distances and set them equal to 150 miles to solve for t.

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The answer is 30 days.

The solution for this is to find the least common multiple. By getting the multiple of both numbers.

Multiples of 2:  2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40…..

Multiples of 15: 15,30,45,60,75……..

The Least Common Multiples of 2 and 15 is 30. So, Inez will do them both again in 30 days.

The least common multiple (LCM) of two numbers is the smallest number that is multiple by the both number.

Answer:20 !

Step-by-step explanation:

The answer is A. the time it takes for an airliner to fly from Los Angeles to New York city and B. the distance of an archer's shot from the centre of a target.

A normal distribution is a symmetrical continuous probability distribution in which values are usually clustered around the mean.

A & B should each have a range of values that cover most occurrences with outlying values that decrease in number as they move further away from the dominant value range, which is the definition of a normal distribution.

Therefore, The answer is A the time it takes for an airliner to fly from Los Angeles to New York City and B the distance of an archer's shot from the centre of a target.

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41+0.10x = 31+0.15x

10 +0.10x=0.15x

10=0.05x

x=10/.05

x= 200 text messages

check 200*0.10 = 20 +41 =61

200*0.15 = 30+31 = 61

 they equal each other so number of texts is 200

A customer must send 200 text messages for the cost of Plan A ($41 plus $0.10 per text) to be equal to the cost of Plan B ($31 plus $0.15 per text).

To find out how many text messages a customer must send for the cost of Plan A to be equal to the cost of Plan B, we can set up an equation based on the cost structures given. Let x be the number of text messages sent.

Cost of Plan A: $41 + $0.10x
Cost of Plan B: $31 + $0.15x

To find the point where both plans cost the same, we set the costs equal to each other:
41 + 0.10x = 31 + 0.15x

Solving the equation:
0.05x = 10
x = 10 / 0.05
x = 200

The customer must send 200 text messages for the costs of Plan A and Plan B to be equal.

The value of cosx if "tanx cscx = 2" is 1/2. The correct option is D)1/2

From the question, we are to determine the value of cosx

From the given information,

tanx cscx=2

Recall that,

[tex]tan(x )= \frac{sin (x)}{cos(x)}[/tex]

and

[tex]csc(x) = \frac{1}{sin(x)}[/tex]

Then,

Substitute these values into the given equation

tanx cscx = 2 becomes

[tex]\frac{sin (x)}{cos(x)} \times \frac{1}{sin(x)} = 2[/tex]

[tex]\frac{1}{cos(x)} = 2[/tex]

∴ [tex]cos(x) = \frac{1}{2}[/tex]

Hence, the value of cosx if "tanx cscx = 2" is 1/2. The correct option is D)1/2

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Final answer:

To eliminate the parameter 't' from the equations x = 5 cos t and y = 5 sin t, use the Pythagorean identity which leads to the non-parametric equation of a circle: x^2 + y^2 = 25.

Explanation:

To eliminate the parameter 't' from the parametric equations x = 5 cos t, y = 5 sin t, we can use the Pythagorean identity sin^2(t) + cos^2(t) = 1. Plugging in the given expressions for x and y:

(x/5) = cos(t)

(y/5) = sin(t)

We can square both sides of these equations and then add them together:

(x/5)^2 + (y/5)^2 = cos^2(t) + sin^2(t)

As cos^2(t) + sin^2(t) equals 1, the equation simplifies to:

(x/5)^2 + (y/5)^2 = 1

Thus, the eliminated parameter equation representing the same curve without the parameter 't' is:

x^2 + y^2 = 25

This is the equation of a circle with a radius of 5, centered at the origin.

Answer:

Step-by-step explanation:

Final answer:

By using the Pythagorean theorem on one of the right triangles formed by dividing the isosceles triangle, we find the height to be approximately 13.0 inches when rounded to the nearest tenth.

Explanation:

To find the height of an isosceles triangle with a base of 15 inches and congruent sides each 15 inches, we can use the Pythagorean theorem or note that the triangle can be split into two right triangles by a height dropping from the vertex opposite the base to the midpoint of the base.

The midpoint will divide the 15-inch base into two segments, each 7.5 inches. The height of the isosceles triangle is the same as the height of the right triangle.

Using the Pythagorean theorem (a² + b² = c²), we can find the height (h) knowing that the hypotenuse (c) is one of the congruent sides (15 inches) and one leg (a, half of the base) is 7.5 inches:

h² + (7.5 inches)² = (15 inches)²

h² + 56.25 inches sup>2 = 225 inches²

h² = 225 inches² - 56.25 inches²

h² = 168.75 inches²

h = sqrt{168.75 inches²}

h approx 12.99 inches, which rounds to 13.0 inches to the nearest tenth.

Therefore, the height of the isosceles triangle rounds to 13.0 inches.

83-79 =4

79-75 = 4

 the numbers are decreasing by 4

 so the next number would be 67-4 = 63