Emily collected a sample of geodes and measured their masses. Her sample is Normally distributed with a mean of 0.8 kilograms and standard deviation of 0.04 kilograms.
Complete the statements based on the Normal distribution.
About
__% of Emily’s geodes have a mass between 0.76 and 0.88 kilograms.

To find the rate at which the light projected onto the wall is moving along the wall, we can use trigonometry and calculus. Let's denote the angle between the rotating light and the wall as θ.

Given:

Distance from the light to the wall, r = 15 feet

Rate of rotation, dθ/dt = 1 rotation every 4 seconds

We need to find the rate at which the light's projection moves along the wall, which is represented by dx/dt.

Using trigonometry, we know that the tangent of the angle θ is equal to the ratio of the distance along the wall (dx) to the distance from the light to the wall (r).

tan(θ) = dx / r

Differentiating both sides of the equation with respect to time t, we get:

sec^2(θ) * dθ/dt = dx/dt

Since we are given that the angle θ is 15 degrees, we can substitute the values and solve for dx/dt.

sec^2(15°) * (1 rotation / 4 seconds) = dx/dt

Simplify and calculate the value to find the rate at which the light's projection moves along the wall in feet per second.

For such more question on tangent

https://brainly.com/question/4470346

#SPJ8

Neither the addition property of equality nor the subtraction property of equality can be demonstrated by themselves. They are properties that must be satisfied by the operations of addition and subtraction respectively, in order for equality to hold.

The addition property of equality states that if two quantities are equal.

(a = b), then their sum with any other quantity (c) will also be equal (a + c = b + c). The subtraction property of equality states that if two quantities are equal (a = b), then their difference with any other quantity (c) will also be equal (a - c = b).

In other words, both properties say that when two quantities are equal, then the result of adding or subtracting the same quantity from both will also result in equal quantities.

To know more about Addition:

https://brainly.com/question/29464370

#SPJ4

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

For such more question on frequency

https://brainly.com/question/254161

#SPJ8

Answer:

Step-by-step explanation:

To find Bianca's walking speed, we need to divide the distance she walks by the time it takes her to walk that distance. We can do this by converting both the distance and time to the same unit of measure.

Since 1 hour is equal to 60 minutes, 1/3 of an hour is equal to 1/3 * 60 minutes = 20 minutes. Now that we have the distance in miles and the time in minutes, we can divide the distance by the time to find Bianca's walking speed.

5/6 of a mile is equal to 5/6 * 1 mile = 0.83 miles. So, Bianca's walking speed is 0.83 miles / 20 minutes = 0.0415 miles per minute. To convert this to miles per hour, we can multiply by the conversion factor of 60 minutes per hour. This gives us a walking speed of 0.0415 miles/minute * 60 minutes/hour = 2.49 miles per hour. So, Bianca's walking speed is 2.49 miles per hour.

0.1920 mL of the anesthetic should be given to the patient.

First, we need to convert the patient's weight from kilograms to pounds:

58 kg x 2.20462 lb/kg = 128.01 lbs

Next, we can calculate the total amount of anesthetic to be given to the patient:

15 mg/10 lbs x 128.01 lbs = 19.20 mg

Finally, we can divide the total amount of anesthetic by the concentration of the anesthetic in each mL:

19.20 mg / 100 mg/mL = 0.1920 mL

So, 0.1920 mL of the anesthetic should be given to the patient.

Learn more on Calculation of Dosage: https://brainly.com/question/29056148

#SPJ1

There were 8 slices in the whole pizza.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.  Let us assume the number of slices in the whole pizza is "x".

Since Jim ate two slices which is 25% of the pizza, we will set up the equation:

2 = 0.25x

To solve for "x":

2 / 0.25 = x

x = 8.

Read more about equation

brainly.com/question/29174899

#SPJ1

Remove the parentheses and combine the like terms:

7 - -9 = 7+ 9 = 16

6i - -8i = 6i +8i = 14i

The answer is 16 + 14i

To calculate the number of different meals available when selecting an appetizer, an entrée, and a dessert, we need to multiply the number of choices for each course.

Using the multiplication principle of counting, we can find the total number of meal options as follows:

Total number of meal options = number of appetizer choices x number of entrée choices x number of dessert choices

Total number of meal options = 5 x 13 x 4

Total number of meal options = 260

Therefore, there are 260 different meals available when you select an appetizer, an entrée, and a dessert from the given choices.

Answer:

A square pyramid has 5 faces: 1 square base and 4 triangular faces.

The area of the base is:

A = s^2

where s is the length of the base edge.

In this case, s = 1 m, so:

A = 1^2 = 1 m^2

The area of each triangular face is:

A = 1/2 * b * h

where b is the base of the triangle (which is equal to the length of one side of the square base) and h is the height of the triangle (which is given as 1 m).

In this case, b = 1 m and h = 1 m, so:

A = 1/2 * 1 * 1 = 0.5 m^2

The total surface area of the pyramid is the sum of the area of the base and the area of the four triangular faces:

SA = A_base + 4 * A_triangles

SA = 1 + 4(0.5)

SA = 1 + 2

SA = 3 m^2

Therefore, the surface area of the pyramid is 3 square meters.

Answer:

b

Step-by-step explanation:

< less than

> greater than

= equal to

1,372 is less than 3,496 true

1,372 is greater than 3,496 false

2,583 is less than 4,194 true

3,496 is greater than 1,372 true

Answer:

Step-by-step explanation:

15-10=5 degrees

In order to determine f(-3), we just need to use the value of x = -3 in the equation of f(x) and determine its value.

So we have:

So the value of f(-3) is 1.

Answer:

20m/s

Step-by-step explanation:

Given, s=400m

t=20s

Required, v=?

v=s/t

=400m/20s

=20m/s

Firm shown in the graph will produce q0, but all the firms in the market will produce a total of Q0.

A perfect market, sometimes known as an atomistic market, is described in economics by numerous idealizing requirements, together known as perfect competition, or atomistic competition. A competitive market is one in which no one customer or producer has sway over the market. Its reaction to supply and demand varies with the supply curve, which represents the quantity of a commodity. Perfect competition, monopolistic competition, oligopoly, and monopoly are the four types of economic market systems.

Here,

The business on the graph will create q0, but the market as a whole will yield Q0.

To know more about competitive market,

https://brainly.com/question/29407851

#SPJ4

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

Learn more on the variance of a set of data here: https://brainly.com/question/30701163

#SPJ1

Answer:

B 80,000

Step-by-step explanation:

Answer:

$242.3

Step-by-step explanation:

She earns $17500 per year. Multiply that number by 0.28 to get how much she withholds for taxes and other deductions. Subtract that number from 17500. You get 12600. Since there are 52 weeks in a year, divide 12600 by 52 to get how much she earns each week minus the 28 percent.

The number you get from this is $242.3, which is the net pay of each paycheck.

Answer:

$242.31/wkly

Step-by-step explanation:

$17,500.00 × 28% = $4,900.00

$17,500.00-$4,900 = $12,600.00

$12,600.00 ÷ 52/(weeks in a year) = $242.31 a week

$12,600 ÷ 12/month = $1,050.00

$1,050 ÷ 4/weeks = $262.50

Answer:

The probability of getting two numbers whose sum is 10 is 25%.

Step-by-step explanation:

Given that a single die is rolled twice, and there are 36 equally-likely outcomes, to find the probability of getting two numbers whose sum is 10 the following calculation must be performed:

1 = +9

2 = +8

3 = +7

4 = +6

5 = +5

6 = +4

7 = +3

8 = +2

9 = +1

9/36 = 0.25

Therefore, the probability of getting two numbers whose sum is 10 is 25%.

Answer:

D. 286.5 in.^2

Step-by-step explanation:

3 X 7.5+ 3 X 11.5 + 3 X 7.5+ 11.5 X 3 + 7.5 X 11.5 + 7.5 X 11.5=

22.5 + 34.5 + 22.5 + 34.5 + 86.25 + 86.25=

total surface area= 286.5 in.^2

Answer:

Option (4)

Step-by-step explanation:

Let x = \(\sqrt[4]{7}\)

\(\sqrt[4]{7}\times \sqrt[4]{7}\times \sqrt[4]{7}\times \sqrt[4]{7}\) = (x)(x)(x)(x)

                                 = \(x^{1+1+1+1}\)

                                 = x⁴

Now we substitute the value x = \(\sqrt[4]{7}\)

x⁴ = \((\sqrt[4]{7})^4\)

x⁴ = 7

Therefore, Option (4) will be the answer.

Answer:

undefined

Step-by-step explanation:

division by zero is undefined

Division Property of zero

For any nonzero real number a

The quotient of "a" and 0 is undefined. That is a/0 is undefined

The solution:

Exercise 1:  x = -1 and 3.

Exercise 2:  x = 2 and 4.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The graphs of the two quadratic equation.

So, Exercise 1,

-x² + 2x + 3 = 0.

From the graph,

-1 and 3 are the zeros of the equation.

The solution of the equation is,

x = -1 and 3.

Exercise 2,

x² - 6x + 8 = 0.

From the graph,

2 and 4 are the zeros of the equation.

The solution of the equation is,

x = 2 and 4.

Therefore, the solutions of the both the equation are given above.

To learn more about the quadratic equation;

https://brainly.com/question/17177510

#SPJ1

Answer:

y = (-mi/h)x + b

y = total distance left to cover

-mi/h = speed at wich he is covering ground

b = the total distance to cover from start to finish

Step-by-step explanation:

Slope Intercept form without other variables filled is shown like this with mx being the slope and b being the y intercept

y = mx + b

all we need to do is fill in known variables with hours multiplied by x represented as m...

y = (-mi/h)x + b

note the negative symbol, this shows that the higher that miles an hour (mi/h) aka speed is, the more distance he will cover REDUCING the distance to cover faster meaning the line will slope DOWNWARD

b would be the the total distance that he has started with, meaning on the point where the line crosses the y axis, the number it crosses at will represent how much he has started with

Answer: 2/1/3

Step-by-step explanation:

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

for such more question on temperature

https://brainly.com/question/14820864

#SPJ8

Answer:

$190.08

Step-by-step explanation:

Take 27% of the total $704 spent in July:

0.27($704) = $190.08

He spent an estimated $190.08 on clothing in July.

Answer:

Step-by-step explanation:

I THINK 140