[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ doubled }{\$ 1600}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases}[/tex]
[tex]1600 = 800e^{0.08\cdot t} \implies \cfrac{1600}{800}=e^{0.08t}\implies 2=e^{0.08t} \\\\\\ \log_e(2)=\log_e(e^{0.08t})\implies \log_e(2)=0.08t\implies \ln(2)=0.08t \\\\\\ \cfrac{\ln(2)}{0.08}=t\implies 8.66\approx t\qquad \textit{about 8 years and 241 days}[/tex]
A rectangular cedar chest measures 40 inches long by 22 inches wide by 20 inches high.
Part A
Find the volume of the chest.
Part B
A cushion is made to cover the top of the chest. Calculate the area of the chest that the cushion covers.
Part C
Explain any difference in the units for the volume and the area.
(A). The chest has a volume of 17,600 cubic inches. (B). The cushion covers 880 square inches of the chest. (C). Whereas area is measured in square units, volume is measured in cubic units.
What is the straightforward meaning of area?An object's area is determined by its shape. The amount of space a figurine or any other as double geometric shape takes up on a plane depends on its area.
(A). Chest volume is calculated as follows: 40 inches by 22 inches by 20 inches, or 17,600 cubic inches.
(B). The cushion's coverage area for the chest is 40 inches by 22 inches, or 880 square inches.
(C). The units for area are square units, while the units for volume are cubic elements (like as cubic feet or cubic meters) (such as square inches or square meters). This is so because area is the measure of space an item occupies in two dimensions, but capacity means the quantity of space an object occupies in three dimensions. As a result, area is expressed in feet or meters whereas volume is recorded in cubic units.
To know more about Area visit:
https://brainly.com/question/17335144
#SPJ1
Given R(x) is a rational function with VA at x=-1,-2,2,3,
Holes at (10,1) and (1,1), and there is no HA. What x-values
can R(x) not be? Put commas between your values and values i
The x-values that R(x) cannot be are -1, -2, 2, 3, 10, and 1.
R(x) cannot be at x=-1, -2, 2, 3 because these are the values of the function at these points. Additionally, R(x) cannot be at x=10 and x=1 because these are the holes of the function. Therefore, the x-values that R(x) cannot be are -1, -2, 2, 3, 10, and 1.
Learn more about function
brainly.com/question/21145944
#SPJ11
Which equation would calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown?
a cylinder with the diameter labeled 2.8 centimeters and the height labeled 3.7 centimeters
A. SA = 2π(1.4)2 + 2.8π(3.7)
B. SA = 2π(1.4)2 + 1.4π(3.7)
C. SA = 2π(2.8)2 + 2.8π(3.7)
D. SA = 2π(2.8)2 + 1.4π(3.7)
The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²
The surface area of a cylinder:
Surface area is the total area that the surface of an object occupies. It is a measure of how much area is covered by the exterior of an object. The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrhWhere r = radius of the base and h = height of the cylinder.
Here we have
Diameter of the cylinder = 2.8 cm
Radius of the cylinder = 2.8/2 = 1.4 cm
Height of the cylinder = 3.7 cm
Using the formula,
The surface area of a cylinder SA= 2πr² + 2πrh
The surface area of the cylinder
= 2π(1.4)² + 2π(1.4)(3.7)
= 2π(1.4)² + 2.8π(3.7)
Here, the total surface area of the cylinder will equal the amount of wrapping paper needed to completely cover the cylinder
Therefore,
The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²
Learn more about Cylinder at
https://brainly.com/question/22074027
#SPJ1
hi i think its A. SA = 2π(1.4)2 + 2.8π(3.7) hope this helped have a nice day! :)
the dimensions of a rectangle are 19 1/2 cm by 21 1/4 cm what is the area of the triangle
Answer: 207.1875
Step-by-step explanation:
side length a = 19.5 cm
side length b = 21.25 cm
diagonal p = q = 28.841159824112 cm
perimeter P = 81.5 cm
area of rectangle A = 414.375 cm2
area of rectangle divided into a triangle = 207.1875
hope this helps
Ian placed 263 stamps on 9 pages of his collection book. He wanted to place the same number
of stamps on each page with as few as possible left over. How many stamps are on each page?
How many were left to put in an envelope?
Enter the correct value to complete each sentence.
Blank stamps were placed on each page.
Blank stamps were put in an envelope.
Answer: To find the number of stamps on each page, we can divide the total number of stamps by the number of pages:
263 stamps ÷ 9 pages = 29.22 stamps per page (rounded to two decimal places)
Since we want to place the same number of stamps on each page with as few left over as possible, we can round down to the nearest whole number:
29 stamps per page
To find out how many stamps were left to put in an envelope, we can multiply the number of pages by the number of stamps per page, and then subtract from the total number of stamps:
263 stamps - (29 stamps per page x 9 pages) = 8 stamps left over to put in an envelope
Therefore, the completed sentences are:
29 stamps were placed on each page.
8 stamps were put in an envelope.
Step-by-step explanation:
do it to be the smartest (image attach)
Answer: a = 20°
Step-by-step explanation:
We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. We will write an equation to solve.
a = 180° - 90° - 70°
a = 20°
Answer:
20 degrees
Step-by-step explanation:
Straight Angle: 180 degrees
You know that there is a right angle which is 90 degrees. You can subtract 180 by 90 to get 90. Then you are given an angle measurement of 70 degrees. Subtract 70 from 90 to get 20.
20 is the measure of the missing angle
Suppose a researcher wishes to study how exercise and diet affect weight loss. The researcher collects data from 12 volunteers with similar weights and health conditions. All the partic- ipants are randomly assigned to one of the following three programs: Program I with diet only, Program II with exercise only, and Program III with combinations of diet and exer- cise. After three months, the weight loss (in pounds) of each participant is recorded and summarized as follows: Program 1: 2,0, 1, 1
Program II: 1, 2,1 Program III: 3, 2, 1, 4, 4 a) The researcher thinks that the three programs should not be equally effective. Please carry out a nonparametric test at a significant level of 0.05 to examine the effectiveness of the three programs. You can either do the calculation by hand or use R to get the results. b) The researcher also hopes to show that Progam III is more effective than Program I in weight loss. Please carry out a nonparametric test at a significant level of 0.05 to examine the effectiveness of the two programs. You can either do the calculation by hand or use R to get the results.
The researcher's study aims to examine how exercise and diet affect weight loss. The researcher collected data from 12 volunteers with similar weights and health conditions and randomly assigned them to one of three programs: Program I with diet only, Program II with exercise only, and Program III with a combination of diet and exercise. After three months, the weight loss of each participant was recorded and summarized. The researcher wishes to carry out nonparametric tests at a significant level of 0.05 to examine the effectiveness of the three programs and to compare the effectiveness of Program III to Program I.
a) To examine the effectiveness of the three programs, we can use the Kruskal-Wallis test, a nonparametric test that compares the medians of three or more groups. The null hypothesis is that the medians of the three programs are equal, and the alternative hypothesis is that at least one of the medians is different. We can use the R function kruskal.test() to carry out the test:
```
> weight_loss <- c(2,0,1,1,1,2,1,3,2,1,4,4)
> program <- factor(c(rep("I",4), rep("II",3), rep("III",5)))
> kruskal.test(weight_loss ~ program)
```
The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of the three programs.
b) To compare the effectiveness of Program III to Program I, we can use the Wilcoxon rank-sum test, a nonparametric test that compares the medians of two groups. The null hypothesis is that the medians of Program III and Program I are equal, and the alternative hypothesis is that the medians are different. We can use the R function wilcox.test() to carry out the test:
```
> weight_loss_I <- c(2,0,1,1)
> weight_loss_III <- c(3,2,1,4,4)
> wilcox.test(weight_loss_I, weight_loss_III)
```
The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of Program III and Program I.
Learn more about researcher
brainly.com/question/28555014
#SPJ11
Feb 23, 1:45:12 PM Factor the expression completely. 9-36x Answer: Submit Answer
The expression 9-36x can be factorized as 9(1-4x)
An expression's factors are things that are multiplied by other things. A number, variable, phrase, or any other lengthier expression may be used. For instance, 2, x, and y are the factors of 2xy.
To factor the expression 9-36x completely, we need to find the greatest common factor (GCF) of the two terms and then use the distributive property to factor it out.
The GCF of 9 and 36 is 9, so we can factor out 9 from both terms:
9-36x = 9(1-4x)
Now the expression is factored completely.
So the final answer is:
9-36x = 9(1-4x)
Learn more about expression at https://brainly.com/question/1548961
#SPJ11
roots in simplest form by completing the square: -5x^(2)-80x-140=0 Submit Answer
The roots in simplest form are x=-8+6i and x=-8-6i.
The question is asking you to find the roots of -5x^(2)-80x-140=0 in simplest form by completing the square.
To complete the square, follow the steps below:
1. Divide the coefficient of the x^2 term by 2 and add the result to both sides of the equation:
-5x^2/2 + 80x/2 + 140 = 0 + 5x^2/2
2. Square the coefficient of the x^2 term: (5x^2/2)^2
3. Add this result to both sides of the equation: 5x^2/2 + (5x^2/2)^2 + 80x/2 + 140 = 5x^2/2 + (5x^2/2)^2
4. Rewrite the equation as a perfect square on the left side of the equation: (5x^2/2 + 40x/2)^2 = (5x^2/2 + 40x/2)^2 + 140
5. Take the square root of both sides to solve for x:
5x^2/2 + 40x/2 = ± √140
6. Rewrite the equation as two equations in x:
x = -80 ± √140 / 10
7. Simplify:
x = -8 ± √14 / 1
Therefore, the roots of -5x^(2)-80x-140=0 in simplest form by completing the square are x = -8 ± √14 / 1.
To find the roots in simplest form by completing the square for the equation -5x^(2)-80x-140=0, we need to follow these steps:
1. First, we need to isolate the x terms on one side of the equation. We can do this by adding 140 to both sides of the equation:
-5x^(2)-80x=140
2. Next, we need to factor out the coefficient of the x^(2) term, which is -5:
-5(x^(2)+16x)=-140
3. Now we need to complete the square by adding the square of half of the coefficient of the x term to both sides of the equation:
-5(x^(2)+16x+64)=-140+320
4. Simplify the right side of the equation:
-5(x+8)^(2)=180
5. Divide both sides of the equation by -5:
(x+8)^(2)=-36
6. Take the square root of both sides of the equation:
x+8=±6i
7. Solve for x:
x=-8±6i
To know more about perfect square click on below link:
https://brainly.com/question/13521012#
#SPJ11
PLEASE HELP ASAP this math is kinda hard for me
The following are the correct convertion for the units of mass:
8000 mg converted to gram is 8 g
80 g converted to kilogram is 0.08 kg
0.8 kg converted to g is 800 g.
Units of mass measurementsGram (g) is the base unit of mass in the metric system. The milligrams (mg) and kilograms (kg) are derived units.
1 gram = 1000 milligrams (mg)
1000 grams = 1 kilogram (kg)
8000 mg = (8000/1000) g
8000 mg = 8 g
80 g = (80/1000) kg
80 g = 0.08 kg
0.8 kg = (0.8 × 1000) g
0.8 kg = 800 g.
In conclusion, 8000 mg converted to gram is 8 g, 80 g converted to kilogram is 0.08 kg, and 0.8 kg converted to g is 800 g.
Read more about mass here:https://brainly.com/question/229459
#SPJ1
Dividing Polynon Use synthetic division to divide the polynomi. (3x^(2)+7x+2)+(x+2)
The result of this synthetic division is the quotient (1 2/3 5/3)
To divide two polynomials using synthetic division, we need to write the dividend as a binomial of the form (x-r) and the divisor in its linear form. In this case, the binomial is (x+2) and the linear form is 3x2+7x+2.
Quotient:
3/3=1
2/3=2/3
Coefficients of dividend: 3 7 2
Quotient: 1 2/3
Product of quotient and binomial: (x+2)
(3x2+7x+2) - (x+2): 3x+5 2
Quotient:
3/3=1
2/3=2/3
5/3=5/3
The result of this synthetic division is the quotient (1 2/3 5/3).
Learn more about synthetic division here:
brainly.com/question/28824872#
#SPJ11
Complete the identity
The identity cos²θ/2 is (1 + cosθ)/2
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We can use the half-angle identity for the cosine function to solve this problem:
cos²θ/2 = (1 + cosθ)/2
Therefore, to find cos²θ/2 , we need to know the value of cosθ.
If the value of cosθ is known, we can substitute it into the half-angle identity to find cos²θ/2
Hence, the identity cos²θ/2 is (1 + cosθ)/2
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ1
HELPP! NEED NOW!!! ASAP!!
The volume of a rectangular prism is 208 cm³. If the area of one end is 16 cm², what is the length of the prism? (FOUND ANSWER)
The length of the rectangular prism is 13 centimetres.
How to find the side of a rectangular prism?The volume of a rectangular prism is 208 cm³. The area of one end is 16 cm². The length of the rectangular prism can be found as follows:
Therefore,
volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightHence, let's find the length
volume of a rectangular prism = lwh
208 = 16 × l
16l = 208
divide both sides by 16
l = 208 / 16
l = 13 cm
Therefore,
length of the prism = 13 cm
learn more on rectangular prism here: https://brainly.com/question/24460838
#SPJ1
RADICALS Solving an equation usir Solve x^(3)=-13 where x is a rea Simplify your answer as much a
To solve the equation x^(3) = -13, we need to take the cube root of both sides of the equation. The cube root of x^(3) is x, and the cube root of -13 is -2.3513 (rounded to 4 decimal places). Therefore, the solution to the equation is x = -2.3513.
Here are the steps to solve the equation:
1. Start with the equation x^(3) = -13
2. Take the cube root of both sides of the equation: (x^(3))^(1/3) = (-13)^(1/3)
3. Simplify the left side of the equation: x = (-13)^(1/3)
4. Calculate the cube root of -13: x = -2.3513 (rounded to 4 decimal places)
So the solution to the equation is x = -2.3513.
Note: The original question had some typos and irrelevant parts, so I ignored those and focused on the main equation to solve.
For more about equation:
https://brainly.com/question/29657992
#SPJ11
One solution to a quadratic function, g, is given.
9 - √2i
Which statement is true?
A. Function g has no other solutions.
B. The other solution to function g is -9 + √2i
.
C. The other solution to function g is -9 - √2i
.
D. The other solution to function g is 9 + √2i
.
Answer:
D. The other solution to function g is 9 + √2i
Step-by-step explanation:
The roots of a quadratic equation of the form ax² + bx + c = 0
are
[tex]x = -\dfrac{b}{2a} + \dfrac{\sqrt{b^2-4ac}}{2a}\\and\\x = -\dfrac{b}{2a} - \dfrac{\sqrt{b^2-4ac}}{2a}\\[/tex]
If one of the roots is 9 - √2i then
[tex]-\dfrac{b}{2a} = 9[/tex]
and
[tex]\dfrac{\sqrt{b^2-4ac}}{2a} = 2i[/tex]
So if one root is 9 - √2i then the other root must be 9 -+ 2i
This is answer choice D
True or false let be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that equals 8 is denoted by
The given statement " let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 will be denoted by P(X=8)" is true. Because In probability theory, P(X=8) denotes the probability that the random variable X takes on the value 8.
Probability is a measure of the likelihood or chance that a certain event or outcome will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
In this case, X represents the number of male births between 1:00am and 3:00am at a hospital in Orange County. So, P(X=8) represents the probability that exactly 8 male births occur during that time period.
To know more about probability here
https://brainly.com/question/11234923
#SPJ4
--The given question is incomplete, the complete question is
"True or false let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 is denoted by P(X=8)"--
given point A,P,Q construct D_a,k(R) if D_a,k(Q) = P
Points A and Q are connected by a line. To get the length of AR, measure the distance between A and Q and multiply that value by k. To find point R, mark off the length of AR along a ray that extends from point A in the direction of Q.
What serve ray lines?In mathematics, a ray is a segment of a line with a known starting point but no known endpoint. It can go on forever in that one direction. A beam cannot be measured since it lacks a terminal. fun facts A ray is similar to the sun's rays.
What is an example of a ray line?In geometry, a ray is a line that, starting from a single terminal, extends indefinitely in one direction (or point of origin). A ray is represented by a beam of sunlight travelling across space; while the sun is the ray's goal, it continues to travel forever.
To know more about line visit:-
brainly.com/question/2696693
#SPJ1
Complete question -
What is the value of the expression? −16+12 Responses −28 negative 28 −4 negative 4 4 4 28 28
The value of the expression −16 + 12 is −4.
What is subtraction?Subtraction is a basic arithmetic operation that involves finding the difference between two numbers. It is denoted by the minus sign (-) and is performed by subtracting the second number from the first number.
We can subtract fractions, decimals, and negative numbers by following the same principles of subtraction.
Here we have
The numerical expression −16 + 12
As we know
12 is 4 greater than 16 and 16 has a negative sign
Therefore,
The value of the expression −16 + 12 is −4.
Learn more about Subtraction at
https://brainly.com/question/637671
#SPJ1
write an expression by expanding -5(-2d + 6)
Answer:
See below.
Step-by-step explanation:
We are asked to "expand", rather distribute the expression.
We can Distribute due to the Distributive Property.
What is the Distributive Property?
The Distributive Property is a property that allows us to distribute the multiplier into numbers in the parentheses.
Let's distribute for this expression.
Distribute:
[tex]-5(-2d + 6)=(-5 \times -2d)+(-5 \times 6)= 10d -30[/tex]
Our distributed expression is 10d - 30.
If the height of the ice cream cone is H=12 what is the diameter of the opening of the cone
The diameter of the opening of the cone is approximately 8.92 units.
We can use the formula for the volume of a cone:
V = (1/3) × π × r^2 × H
where V is the volume, H is the height, and r is the radius of the base.
In this case, we are given the volume V = 196 and the height H = 12. We want to find the diameter of the opening, which is 2r.
First, we can rearrange the formula for the volume to solve for r
r = sqrt((3V) / (πH))
Plugging in the values, we get
r = sqrt((3 × 196) / (π × 12)) ≈ 4.46
So the radius of the base of the cone is approximately 4.46 units.
Finally, we can find the diameter of the opening:
d = 2r ≈ 8.92 units
Learn more about volume here
brainly.com/question/29171990
#SPJ4
The given question is incomplete, the complete question is:
The volume of the cone is 196 cubic units. If the height of the ice cream cone is H=12 what is the diameter of the opening of the cone?
On june 1, 2013, the number of hours of daylight in anchorage alaska was 18 1/4 hours what is the number of hours without daylight??
Answer:
On June 1, 2013, Anchorage, Alaska experiences 18 and 1/4 hours of daylight.
In a 24-hour day, there are 24 - 18 and 1/4 = 5 and 3/4 hours without daylight.
Therefore, the number of hours without daylight on June 1, 2013 in Anchorage, Alaska was 5 and 3/4 hours.
Answer:
24-18.4=5 and3/4
Step-by-step explanation:
Use the formula for simple interest, I = Pxrxt, to find the missing quantity. P = $4000; r = 8%; t = 3 years 01 = $1160 01 = $9600 01 = $960 01 = $96,000 Use the formula for simple interest, I = Pxrxt
To find the missing quantity, we will plug in the given values into the formula for simple interest and solve for the unknown variable. The formula for simple interest is I = Pxrxt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Given:
P = $4000
r = 8% = 0.08
t = 3 years
Plugging in the given values into the formula, we get:
I = $4000 x 0.08 x 3
Simplifying the equation, we get:
I = $960
Therefore, the missing quantity is the interest, I, which is equal to $960.
Know more about simple interest here:
https://brainly.com/question/25845758
#SPJ11
Why might a person open a savings account?
Will mark brainliest
A) Savings accounts are designed for a short term such as paying monthly bills.
B)Savings accounts provide high interest rates in exchange for taking on a great deal of risk.
C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.
D)Savings accounts provide a quick way to pay monthly bills.
Answer:
C) Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank. Savings accounts provide a safe and secure way to store money for use in the future. They also offer the opportunity to earn interest over time, which can be used to grow your savings. As a result, savings accounts are a great way to save for long-term goals such as retirement, a child's education, or a down payment on a home.
Answer:
C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.
Step-by-step explanation:
Savings accounts are designed to keep your money safe and to hold it for as long as you want. Ex for the future, such as collage or something you really want like a car. A saving account will will hold your money until you want to deposit it out of your account.
what is the ratio 28:20 simplified
Louis discovers that one variety of carp can grow 5 pounds during each year of its life. He
decides to purchase a very young carp of this variety that weighs 2 pounds.
Define variables and write an equation that represents the relationship between the amount o
time in years that Louis has the carp and the weight of the carp.
The equation which represents the relationship between the variables is; y = 5x + 2.
Which equation represents the situation?As evident in the task content;
To define the variables;
Let x = amount of time in years and
y = weight of the carp.
Since the carp grows 5 pounds each year and initially weighs 2 pounds.
By the slope-intercept form equation;
y = mx + c;
Where,
m = 5 pounds
c = 2 pounds
Therefore, the required relationship which represents the situation is; y = 5x + 2.
Read more on slope-intercept equation;
https://brainly.com/question/1884491
#SPJ1
In order to gaph the ine whote equition iay=52x+2, begin by ploeing the port Fromi ins pointi ne miove wits up the rese) and insts to the righe che runl. Fa in each blopk so thut the reseinng statement is true. In order to arach the ine whose equason isy=52x+3, begn by plotting the point: From this point, we mere units up (ehe fise) and unis to the right (the run). In ceder to graph the ine whose eqaston isy=52x+3, begin by ploting the poun From this point, we move Units up (the risel and unis to the tight (the nun).
This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.
In order to graph the line whose equation is y=5/2x+2, we need to begin by plotting the point (0,2) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.
Similarly, to graph the line whose equation is y=5/2x+3, we need to begin by plotting the point (0,3) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.
In both cases, the slope of the line is 5/2, which is the coefficient of x in the equation. The slope tells us how much the line rises or falls for every unit it moves to the right. In this case, the line rises 5 units for every 2 units it moves to the right. This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.
Learn more about plotting
brainly.com/question/15579115
#SPJ11
59. Standard Normal areas Find the proportion of observations in a standard Normal distribution that satisfies each of the following statements.
(a) z > -1.66
(b) -1.66
(a) The proportion of observations in a standard normal distribution that satisfies z > -1.66 is 0.0475, or approximately 4.75%.
(b) The proportion of observations in a standard normal distribution that satisfies -1.66 < z < 1.66 is 0.9050, or approximately 90.50%.
What is z-score?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.
Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
To find the proportion of observations in a standard normal distribution that satisfies each of the statements, we need to use a standard normal distribution table or calculator.
(a) z > -1.66
We need to find the area to the right of z = -1.66 on a standard normal distribution table or calculator. This is equivalent to finding the area to the left of z = 1.66 since the standard normal distribution is symmetrical.
Using a standard normal distribution table or calculator, we find that the area to the left of z = 1.66 is 0.9525. Therefore, the area to the right of z = -1.66 is:
1 - 0.9525 = 0.0475
So, the proportion of observations in a standard normal distribution that satisfies z > -1.66 is 0.0475, or approximately 4.75%.
(b) -1.66 < z < 1.66
We need to find the area between z = -1.66 and z = 1.66 on a standard normal distribution table or calculator.
Using a standard normal distribution table or calculator, we find that the area to the left of z = 1.66 is 0.9525 and the area to the left of z = -1.66 is 0.0475 (as calculated in part (a)). Therefore, the area between z = -1.66 and z = 1.66 is:
0.9525 - 0.0475 = 0.9050
Therefore, the proportion of observations in a standard normal distribution that satisfies -1.66 < z < 1.66 is 0.9050, or approximately 90.50%.
To learn more about the z score;
https://brainly.com/question/15016913
#SPJ1
Two weather stations are aware of a thunderstorm located at point c. The weather stations A and B are 34 miles apart. How far is weather station A from the storm?
The distance between weather station A and the storm is [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles, which can be calculated using the Pythagorean theorem.
What is the Pythagorean theorem?The Pythagorean Theorem is an equation in geometry which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse.
Weather station A is 34 miles away from the thunderstorm located at point c. To measure the distance between weather station A and the storm, we must calculate the hypotenuse of a right triangle. The right triangle is formed by the two points of the storm and weather station A, with the 34 miles between them forming the base of the triangle. The hypotenuse of the triangle is the distance between the two points, which can be calculated using the Pythagorean theorem. The equation for the Pythagorean theorem is a² + b²= c², where a and b are the sides of the triangle, and c is the hypotenuse.
Therefore, the distance between weather station A and the storm is [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles.
For more questions related to right triangle,
https://brainly.com/question/2869318
#SPJ1
Can anyone help me in my math homework 55 points I’ll send you 50 more if u can help
The ordered pairs are the solution to the inequality as follows:
6) (-1,3) and 7) (1,4).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per the question, we have:
5) (0,-1)
No, this ordered pair is not a solution to the inequality.
6) (-1,3)
Yes, this ordered pair is a solution to the inequality.
7) (1,4)
Yes, this ordered pair is a solution to the inequality.
8) (0,0)
No, this ordered pair is not a solution to the inequality.
9) (3,3)
No, this ordered pair is not a solution to the inequality.
10) (2, 1)
No, this ordered pair is not a solution to the inequality.
Thus, the ordered pairs are the solution to the inequality as follows:
6) (-1,3) and 7) (1,4).
Learn more about the inequalities here:
brainly.com/question/20383699
#SPJ1
$13.50 discounted 75%
Answer: 75% of $13.50 is 10.125
Step-by-step explanation:
Answer:
10.125
Step-by-step explanation:
13.50 x .75 = 10.25