In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 57 inches, and standard deviation of 7.3 inches.What is the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

The derivative of the function f(x) = √x-5 is 1/2√(x-5)

Given f(x) = √x-5

from the formula d/dx (√x) = 1/2√x

hence d/dx √x-5 = 1/2√x-5

or

d/dx √x-5 = 1/2 (x-5)¹/²

The formula for the derivative of root x is d(x)/dx = (1/2) x-1/2 or 1/(2x). The exponential function with x as the variable and base equal to 1/2 is the root x provided by x. Utilizing the Power Rule and the First Principle of Derivatives, we can get the derivative of root x.

Hence we get the value as 1/2 (x-5)¹/²

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b) There are 12 payments per year for 22 years; multiply 12 by 22 to get the total number of payments:

To find the total amount paid, multiply the number of payments by the payment amount:

c) Toward principal: $67,000

Toward interest: subtract the principal from the payment amount:

Let 91,608 be the 100%, use a rule of three to find the % corresponding to the principal and interest:

Explanation:

The total number of students is

Concept:

To figure out the probability that a student earns grade A,B or C

Will be calculated below as

The Probability of A is

The probabaility of B is

The probabaility of C is

Hence,

By substituting the values in the concept, we will have

Hence,

The final answer is

By applying Kepler's third law of planetary motion, the approximate revolution time for Jupiter is equal to 12 years.

Mathematically, Kepler's third law of planetary motion is given by this mathematical expression:

T² = a³

Where:

Note: Earth has 1 astronomical unit (AU) in 1 year of time.

For this direct variation, the value of the constant of proportionality (k) is given by:

T² = ka³

k = T²/a³

k = 1²/1³

k = 1.

When the semi-major axis or the distance of Jupiter from Sun is 5.2, we have;

T² = ka³

T² = 1 × 5.2³

T² = 140.608

T = √140.608

T = 11.858 ≈ 12 years.

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Kaitlin's family's trip from Washington D.C., to New York City of 227 miles at average rate of 55 miles per hour is 4 hours 8 minutes

information gotten from the question include

Washington D.C., to New York City is 227 miles

Kaitlin's family can drive an average of 55mi / h

Average speed is a function of ratio distance covered with time. this is represented mathematically as

average speed = distance covered / time

55 miles / h = 227 miles / time

time = 227 / 55

time = 4.127 hours

The trip take 4.127 hours

0.127 * 60 = 7.62 ≅ 8 minutes

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Given:

The sum of three numbers is 81, The third number is 2 times the second, The first number us 9 moe than the second.

Required:

We need to find all the numbers

Explanation:

Assume that a, b and c are the first, second and third numbers respectively.

By given ststement

substitute c and a in equation (i)

now put value of b in equation (ii) and (iii)

and

FInal answer:

first number a = 27

second number b = 18

third number c = 36

Given:

There are given the expression:

Explanation:

To find the value of x that is equal to 0, we need to perform LCM in the denominator and then find the value for x:

Then,

From the given expression:

Then,

According to the question, the values at least one denominator is equal to .

So,

Final answer:

Hence, the value of x is shown below:

Opposite angles in a quadrilateral inscribed in a circle add up to 180, therefore:

Answer:

b. 126

Here are the steps in multiplying scientific notations:

1. Multiply the coefficients first.

2. Multiply the base 10 by adding their exponents.

3. Connect the result in steps 1 and 2 by the symbol for multiplication.

Hence, the result is 6.6 x 10⁵.

Explanation:

To add mixed fractions we have to follow these steps:

1. Add the whole numbers together

2. Add the fractions

3. If the sum of the fractions is an improper fraction then we change it to a mixed number and add the whole part to the whole number we got in step 1.

In this case the sum of the fractions results in a proper fraction, so we can skip this step.

Answer:

The result is:

Answer: [2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x

Step-by-step explanation:

I think of a number, represented by the variable/pronumeral x.

I add 5 to it: x + 5

then double the result: 2(x + 5)

I then subtract 10 from this answer: [2(x + 5)] - 10

I then subtract the original number I thought of: [2(x + 5)] - 10 - x

Simplifying the expression will explain why you get the original number.

[2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x.  

To solve this question, we shall be using the principle of similar triangles

Firstly, we identify the triamgles

These are JKL and JMN

JKL being the bigger and JMN being the smaller

Mathematically, when two triangles are similar, the ratio of two of their corresponding sides are equal

Thus, we have it that;

Ok, so

Here we have the function:

Now we want to find the tripling-time for this population of deer.

If we make t=0, we will find the initial population of deer. This is:

Now, we want to find the time "t" such that this population is the triple.

This is:

We got this exponential equation:

As the base is the same, we could equal the exponents:

Therefore, tripling-time for this population of deer are 3 years.

1) rotation 90° clockwise over the origin and a reflection over the x-axis

2) rotation 90° counter clockwise over the origin and reflection over y-axis

The values of f(4) , f(0) and f(-5) are 16/7, -12 and -7/11 respectively.

We are given the function:-

f(x) = (x + 12)/(2x - 1)

We have to find the values of  f(4) , f(0) and f(-5).

Putting x = 4 in the given function, we can write,

f(4) = (4+12)/(2*4-1) = 16/7

Putting x = 0 in the given function, we can write,

f(0) = (0 + 12)/(2*0 - 1) = 12/(-1) = -12

Putting x = -5 in the given function, we can write,

f(-5) = (-5 + 12)/(2*(-5) - 1) = 7/(-10-1) = 7/(-11) = -7/11

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Answer

y = -3x - 13/4

Step-by-step explanation

Equation of a line in slope-intercept form

where m is the slope and (0, b) is the y-intercept.

Substituting into the general equation with m = -3 and the point (1/4, -4), that is, x = 1/4 and y = -4, and solving for b:

Substituting into the general equation with m = -3 and b = -13/4, we get:

The surface area of the figure is the sum of the area of the squares. Since they're all equal, is the amount of squares times the area of one square. We have a total of six squares, with a side length equal to 4 units. The area of a square is given by the product of its side length by itself, therefore, the total surface area of this figure is

The area of this figure is 96 ft².

Answer: 72 Square Meters sorry super late

Step-by-step explanation:

The company's sign has two(2) congruent trapezoids and two(2) congruent right angled triangle.

The area of the figure is:

The area of a trapezoid is given by the formula:

Thus, we have:

Area of a triangle is given by the formula:

Thus, we have:

Hence, the area of the company's sign is:

we multiply the first parenthesis by its coefficient

now multiply each value and add the solutions

The can is made up of aluminium.

So the area of the can must be equal to the area of the Aluminium sheet.

The can is in the form of a cylinder with diameter (d) 5.3 cm, and height (h) 12 cm.

Then its area is calculated as,

Thus, the area of the Aluminium sheet required is 244 square centimeters.

To find the coefficients we first need to make the multipliation on the left expression:

Then we have:

Two polynomials are equal if and only if their coefficients are equal, this leads to the following equations:

From the first one it is clear that the value of a is 2, from the last one we have:

Plugging the value of a in the second one we have:

Therefore, we conclude that a=2, b=1 and c=-1 and the correct choice is D.

we have the function

g(x)=(x/3)+2 ---------> interval (-infinite, 1)

g(x)=4x-2 ------> interval [1, infinite)

the given function is not one-to -one function, because don't pass the Horizontal Line Test.

Example

For the horizontal line

y=2

we have the values of

x=0 ---------> g(x)=(x/3)+2

and

x=1 -----------> g(x)=4x-2

that means

two elements in the domain of g(x) correspond to the same element in the range of g(x)

therefore

Part 3

An exponential growth function has the general form:

where r is the rate of growth, t is the time, and a is a constant. Notice that if calculate f(t) for t = 0, we have (1 + r)º = 1 (any number with exponent 0 equals 1). So, we obtain:

Thus, the constant a is the initial value of the function.

Now, the rate at which a bacteria grows is exponential. So, the function C(h) is given by:

Notice that we represented the time by the letter h instead of t.

Since C(0) = 10 and C(1) = 12, we can replace h by 1 to find:

Thus, the number of cells C(h) is given by:

Notice that this is valid for C(15) = 154:

Part 1

Then, using this formula, we find:

Part 2

Now, plotting the points, rounded to the nearest whole cell, on the graph, we obtain:

Part 4

Using a calculator, we obtain the following graph of the function C(h):

Comparing the graph to the plot of the data, we see that they match.

Part 5

After a full day, it has passed 24 hours. So, we need to use h = 24 in the function C(h):

Therefore, the answer is 795 cells.

Answer:

hey what don't u get? u didn't show the question

Inch is one of the units of measuring length.

Converting from inch to meters,

A 12-inch ruler converted to meters will be;

Converting the meter equivalent of the ruler into the sub-units of meters measurement,

From the conversions of metric units of length above, the 12-inch ruler measures 30.48cm which is closest to 30cm

Therefore, the ruler is closest to 30 centimeters

The popcorn we can order is either buttered or unbuttered.

Therefore, the probability of choosing buttered popcorn is 1/2

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Given expression:

[tex]2^{-2}[/tex]

[tex]\boxed{\textsf{Exponent rule}: \quad a^{-n}=\dfrac{1}{a^n}}[/tex]

Apply the exponent rule to the given expression:

[tex]\implies 2^{-2}=\dfrac{1}{2^2}[/tex]

Two squared is the same as multiplying 2 by itself, therefore:

[tex]\begin{aligned}\implies 2^{-2}&=\dfrac{1}{2^2}\\\\&=\dfrac{1}{2 \times 2}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]

Solution

[tex]2^{-2}=\dfrac{1}{4}[/tex]

Answer:

1/4

Step-by-step explanation:

Now we have to,

→ find the required value of (2)^-2.

Let's solve the problem,

→ (2)^-2

→ (1/2)² = 1/4

Therefore, the value is 1/4.

Given:

• Number of male who survived = 338

• Number if female sho survived = 316

• Number f children who survived = 57

• Number of male who died = 1352

• Number of female who died = 109

• Number of children who died = 52

• Total number of people = 2224

Let's solve for the following:

(a). Probability of the passenger that survived:

(b). Probability of the female.

We have:

(c). Probability the passenger was female or a child/

(d). Probability that the passenger is female and survived:

(e). Probability the passenger is female and a child:

(f). Probability the passenger is male or died.

Thus, we have:

(g). If a female passenger is selected, what is the probability that she survived.

(h). If a child is slelected at random, what is the probability the child died.

(i). What is the probability the passenger is survived given that the passenger is male.

ANSWER:

• (a). 0.320

• (b). 0.191

• (c). 0.240

• (d). 0.142

• (e). 0.009

• (f). 0.832

• (g) 0.744

• (h). 0.477

• (i) 0.2

Answer:

(3h+y)*(3h-y)

Step-by-step explanation:

We are given the following expression:

We want to find the LCD for:

9h²-y² and 3h + y.

3h+y is already in it's most simplified way.

9h²-y² , according to the notable product of (a²-b²) = (a-b)*(a+b), can be factored as:

(3h-y)*(3h+y).

The factors of each polynomial is:

3h + y and (3h-y)*(3h+y)

The LCD uses all unique factors(If a factor is present in more than one polynomial, it only appears once).

So the LCD is:

(3h+y)*(3h-y)

Which is option B.

Given,

The initial height of H feet.

The initial velocity of the object is Vo.

The equation of the path of projectile is,

This is the expression of the projectle path.

Hence, the path of the projectile object is y = h + xtan(theta) - x²/2V₀²cos²(theta)