As a result, there is a about 74.53 degree elevation difference between the ladder and the ground.
what is angle ?A geometric shape known as an angle is created when two rays or line segments come together at a location known as the vertex. The sides of the angle are the rays or line segments. Angles are used to define the amount of rotation or inclination between two lines or planes and are commonly measured in degrees or radians. The most popular unit of measurement for angles is the degree, which is derived from the 360 equal divisions of a circle. Angles are measured in degrees using a protractor, and each component is referred to as a degree.
given
We may resolve this issue using trigonometric functions. The elevation angle between the ladder and the ground will be denoted by the symbol. Next, we have
opposite/hypotenuse of sin()
adjacent/hypotenuse = cos()
The building's height in this instance serves as the opposing side, and the length of the ladder serves as the hypotenuse. We thus have:
height/35 cos() = 9.7/35 sin()
By rearranging the first equation, we can find the height:
height equals 35*sin()
The second equation can then be changed to include the following expression:
cos(θ) = 9.7/35
cos(θ) = 0.2771
By taking the inverse cosine of both sides, we can now solve for :
θ = cos^(-1)(0.2771) (0.2771)
7.453 degrees
As a result, there is a about 74.53 degree elevation difference between the ladder and the ground.
To know more about angles visit:
https://brainly.com/question/14569348
#SPJ1
A baker me two batches of cookies the first batch contain 36 cookies in the second batch contain 48 cookies bakery divide the cookies into seven equal groups with non-leftover Right numerical expression using parentheses that show how to determine the total number of cookies the baker we should put into each
The total number of biscuits the baker should place into each, according to the declaration, is 12.
What does an arithmetic expression mean?The mathematical expressions consist of at least a couple of integers or issues, no fewer than one math procedure, and a sentence. It's achievable to multiply, divide, add, or remove with this algebraic method. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Arithmetic Operator)
The total number of cookies in both batches is:
36 + 48 = 84
To divide the cookies into seven equal groups, we need to divide the total number of cookies by 7:
84 / 7 = (12 x 7) / 7 = 12
So the baker should put 12 cookies into each of the seven groups.
A numerical expression that shows how to determine the total number of cookies the baker should put into each group with parentheses is:
(36 + 48) / 7 = (84) / 7 = 12
To know more about Expression visit:
https://brainly.com/question/1859113
#SPJ1
C. Steve is working on his electrical system. He knows the output of the system is equal to the
equation y = -x2 + 12x - 20. At what input will he reach his maximum output?
To achieve the maximum output from his electrical system, Steve should set the input to 6, the x-coordinate of the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex].
To find the input that will result in the maximum output of the electrical system, we need to find the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola is the point where the curve reaches its highest or lowest point, depending on whether the parabola opens upward or downward. In this case, the coefficient of [tex]x^2[/tex] is negative, which means the parabola opens downward, and the vertex represents the maximum point.
We need to find the vertex of the parabola given by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola with equation [tex]y = ax^2 + bx + c[/tex] is given by the formula x = -b/2a.
In this case, a = -1, b = 12, and c = -20, so the x-coordinate of the vertex is:
x = -b/2a = -12/(2*(-1)) = 6
Therefore, the input at which Steve will reach his maximum output is x = 6.
To learn more about parabola please click on below link
https://brainly.com/question/31142122
#SPJ1
newer automobiles have an odometer that measures speed in miles per hour and an instrument that measures fuel efficiency in miles per gallon. how could you use the readout from these two devices to calculate your fuel consumption in gallons per hour?
To calculate your fuel consumption in gallons per hour, divide the speed (in miles per hour) by the fuel efficiency (in miles per gallon). This will give you the gallons per hour (GPH).
For example, if your speed is 50 mph and your fuel efficiency is 30 mpg, your fuel consumption would be 1.67 GPH (50/30). You can then use this result to estimate your fuel costs and overall fuel consumption over a certain period of time.
To understand this concept better, it is important to know that speed (in mph) and fuel efficiency (in mpg) are inversely related. This means that as your speed increases, your fuel efficiency decreases, and as your speed decreases, your fuel efficiency increases.
So, if you want to maximize your fuel efficiency, you need to drive at the lowest possible speed. Additionally, the higher the fuel efficiency, the lower the fuel consumption in GPH.
In short, you can use the readout from your odometer and fuel efficiency meter to calculate your fuel consumption in GPH by dividing the speed (in mph) by the fuel efficiency (in mpg). This result can help you estimate your fuel costs and overall fuel consumption.
To know more about fuel efficiency click on below link:
https://brainly.com/question/27165872#
#SPJ11
A bicycle wheel has a diameter of 63.8 cm and a mass of 1.71 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 118 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 9.00-cm-diameter sprocket in order to give the wheel an acceleration of 4.46 rad/s2? N (b) What force is required if you shift to a 5.58-cm-diameter sprocket? N
In summary, the force required to give the wheel an acceleration of 4.46 rad/s2 when using a 9.00-cm-diameter sprocket is 8,550.54 N, and the force required when using a 5.58-cm-diameter sprocket is 13,764.83 N.
To answer (a) and (b), we need to determine the rotational inertia of the wheel, then calculate the torque and force required to accelerate the wheel with a given angular acceleration.
The rotational inertia of a wheel with all its mass concentrated on the outside radius can be calculated using the formula I = mr^2, where m is the mass of the wheel and r is its radius. In this case, the radius of the wheel is 63.8/2 cm (31.9 cm) and its mass is 1.71 kg, so the rotational inertia is I = [tex]1.71 * (31.9 cm)^2 = 17,214.939 cm^4.[/tex]
To calculate the torque and force required to accelerate the wheel, we use the equation T = I * alpha, where T is the torque, I is the rotational inertia, and alpha is the angular acceleration. Plugging in the values given in the question, we get[tex]T = 17,214.939 cm^4 * 4.46[/tex] rad/[tex]s2 = 76,954.848 Nm.[/tex]
To calculate the force required to accelerate the wheel, we use the equation F = T / r, where F is the force, T is the torque, and r is the radius of the sprocket. For the 9.00-cm-diameter sprocket, the force required is F = 76,954.848 Nm / 9 cm = 8,550.54 N. For the 5.58-cm-diameter sprocket, the force required is F = [tex]76,954.848 Nm / 5.58[/tex] cm = [tex]13,764.83 N.[/tex]
for such more questions on angular acceleration
https://brainly.com/question/21278452
#SPJ11
80x something will
=480
Answer:
400
Step-by-step explanation:
480-80=400
Answer
x=6
Step-by-step explanation:
80*x=480
80*6=480
a family has five children 3 boys and 2 girls. determine the experimental(empirical) probability that the next child is a boy.
The experimental (empirical) probability that the next child is a boy given that a family has five children: 3 boys and 2 girls is 0.6.
Given that the family has five children, 3 of whom are boys and 2 are girls. If we want to know the experimental probability that the next child is a boy, we need to find the ratio of the number of boys to the total number of children. Since the family has three boys and two girls, the total number of children is:
Total number of children = 3 + 2 = 5
Therefore, the probability of the next child being a boy is given by the ratio of the number of boys to the total number of children.
P(B) = Number of boys/Total number of children
P(B) = 3/5P(B) = 0.6
Therefore, the experimental (empirical) probability that the next child is a boy is 0.6.
To know more about probability refer here:
https://brainly.com/question/30034780
#SPJ11
in the new york state numbers lottery, you pay and pick a number from to . if your number comes up, you win , which is a profit of . if you lose, you lose . your probability of winning is .
The probability of winning the New York State Numbers Lottery is 1 in 1000.
When you pay for a ticket, you pick a number between 000 and 999. If your number is drawn, you win $500, meaning you made a profit of $490. If you don't win, you will lose the $1 that you paid for the ticket.
To calculate the probability of winning the New York State Numbers Lottery, you must first consider the total number of possible outcomes. Since you can pick a number between 000 and 999, there are 1000 possible outcomes. This means that your chance of winning is 1 in 1000, or 0.1%.
It is important to remember that the New York State Numbers Lottery is a game of chance, meaning that there is no guarantee of winning.
However, if your number is drawn, you can win up to $500, which is a profit of $490. The odds of winning are 1 in 1000, and if you lose, you will only lose the amount you paid for the ticket.
To know more about probability click on below link:
https://brainly.com/question/30034780#
#SPJ11
according to the label on a box of ice cream bars, each bar contains 300 calories, and 175 of those calories come from fat. what is the percentage of calories from fat for one bar?
Answer:
58.3%
Step-by-step explanation:
Since 175 calories out of 300 come from fat, we can just do 175÷300 and multiply by 100 to get the percentage:
[tex] \frac{175}{300} \times 100 = 58.3\% \: (1dp)[/tex]
[tex]\Large\bold{SOLUTION}[/tex]
To find the percentage of calories from fat for one ice cream bar, we need to divide the number of fat calories by the total number of calories, and then multiply by 100 to get the percentage.
First, we know that each ice cream bar contains 300 calories, and 175 of those calories come from fat. So:
[tex]\sf 175\: fat\: calories \div 300\: total\: calories = 0.5833[/tex]
To convert this decimal to a percentage, we multiply by 100:
[tex]\sf 0.5833 \times 100 = 58.33\%[/tex]
Therefore, the percentage of calories from fat for one ice cream bar is 58.33%.
[tex]\rule{200pt}{5pt}[/tex]
andy has 15 coins made up of quarters and half dollars, and their total value is $5.00 how many quarters does he have
Andy has 15 coins made up of quarters and half dollars, and their total value is $5.00.
He has 10 quarters and 5 half dollars.
To find this answer, we can set up the following equation: 0.25Q + 0.50H = 5.00, where Q represents the number of quarters and H represents the number of half dollars. Solving for Q, we get Q = 10. Therefore, Andy has 10 quarters and 5 half dollars.
To solve this equation, we can use algebra to isolate the variable Q. We can start by subtracting 0.50H from both sides, giving us 0.25Q = 5.00 - 0.50H.
Next, we can divide both sides by 0.25, giving us Q = (5.00 - 0.50H) / 0.25. Therefore, we can substitute the values for 5.00 and 0.50H and solve for Q, giving us Q = 10.
To know more about equation click on below link:
https://brainly.com/question/29514785#
#SPJ11
Rotate the figure 180 degrees
The coordinates of the image after rotating the figure 180 degrees about the origin are T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Calculating the coordinates of the imageGiven that
T'(-4, 3). V'(-5, 5), W'(-2, 5). X(-1, 3)
Rotating a figure by 180 degrees is equivalent to flipping it over the horizontal and vertical axes simultaneously.
This means that the x-coordinate of each point will be negated, and the y-coordinate will be negated as well.
Therefore, to find the coordinates of the image of a point after rotating it by 180 degrees, you can use the following formula:
(x', y') = (-x, -y)
Using the above, the image is
T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Hence, the image is T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Read more about transformation at
https://brainly.com/question/4289712
#SPJ1
Complete question
Rotate the figure 180 degrees about the origin
T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
T'(3, 4). V'(5, 5), W'(5, 2), X '(3. 1) (Th
T'(-3, 4) V(-5. 5), W'(-5, 2). X'(-3, 1)
T'(-3, -4), V'(-5, -5). W(-5, -2), X '(-3, -1)
Alyssa has 4.5 liters of lemonade to pour into pitchers. Each pitcher holds 0.9 liter of lemonade. Alyssa pours an equal amount of lemonade into each pitcher. Alyssa draws the model below to show how many pitchers she fills. Is Alyssa’s model correct? Explain
HELP PLEASE AND SHOW HOW YOU DID IT
The volume of the cylinder with radius 19 yd and height 21 yd is 23,804.34 cubic yard
What is the volume of the cylinder?Volume refers to the unit of three-dimensional measure of space that comprises a length, a width and a height. It is measured in units of cubic centimeters in metric, cubic inches or cubic feet.
Volume of a cylinder = π × r ²× h
Where,
π = 3.14
Radius, r = 19 yd
Height, h = 21 yd
So,
Volume of a cylinder = π × r² × h
= 3.14 × 19² × 21
= 3.14 × 361 × 21
= 23,804.34 cubic yard
Ultimately, 23,804.34 cubic yard is the volume of the given cylinder.
Read more on volume of a cylinder:
https://brainly.com/question/9554871
#SPJ1
You have been keeping track of the outside temperature for a class project.
At noon, the temperature was 80°F
.
At 5:00
p.m., the temperature was 64°F
.
What was the percent change between the temperature at noon and the temperature at 5:00
p.m.?
Answer:
20%
Step-by-step explanation:
80 - 64 = 16
16 ÷ 80 = 0.2
0.2 × 100 = 20%
when we use the estimated regression equation to develop an interval that can be used to predict the mean for all units that meet a particular set of given criteria, that interval is called a
The interval is known as a prediction interval when it is created using the estimated regression equation to forecast the mean for all units that satisfy a specific set of supplied criteria.
A prediction Interval is a statistical interval that provides a range of values within which a future observation is likely to fall. It takes into account both the variability of the data and the uncertainty in the estimates of the regression coefficients.
In contrast, a confidence interval is a statistical interval that provides a range of values within which a population parameter is likely to fall. It is used to estimate the true value of a population parameter based on a sample of data.
Therefore, a prediction interval is specific to the individual unit being predicted, while a confidence interval is specific to the population parameter being estimated.
To learn more about prediction interval, refer:-
https://brainly.com/question/13708942
#SPJ4
A salesperson earns a commission of $448 for selling $2800 in merchandise. Find the commission rate. Write your answer as a percentage.
Answer:
16%
Step-by-step explanation:
translation
x% times 2800 = 448
x% = 448 divided by 2800
x% = 0.16 = move decimal 2 spaces to the right = 16%
To find the commission rate we just have to divide the total commission by the total amount of merchandise sold. The commission was $448 and the amount of merchandise sold was $2800.
[tex]\dfrac{448}{2800}=0.16[/tex]
Then, to rewrite a decimal as a percentage, we just need to multiply the number by 100.
[tex]0.16=\dfrac{0.16\times100}{100} =\dfrac{16}{100} =16\%[/tex]
The commission rate is 16%.
Inc pairs of numbers with a sum of 207, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms. Answer
The value of both numbers in fractions will be 207/2 and 207/2.
Given that:
Equation: x + y = 207
The two numbers' product is:
P = xy
P = x(207 - x)
P = 207x - x²
Differentiating P with regard to x. Then we have
dP/dx = 0
207 - 2x = 0
x = 207/2
Then the other number is calculated as,
x + y = 207
207/2 + y = 207
y = 207/2
More about the maxima and minima links are given below.
https://brainly.com/question/12870695
#SPJ12
Given g(x)=4x-7
, find g(3)
.
g(3)=
Answer: Simplifying this equation, we get the ANSWER 5
Step-by-step explanation: Since g(x) = 3, we can plug this into the given equation 4x-7.
now we rewrite the given equation, which is now 4(3)-7
Now we find 4(3), simplifying/multiplying that, we get 12.
We minus 12 by 7 which is 5
Which characteristic BEST describes 5.1 in the polynomial 5.1xy−4x+y−1.5?
The characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.
What is polynomial?
A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.
In a polynomial expression, a coefficient is the numerical factor that is multiplied by a variable or variables raised to a certain power. In the expression 5.1xy - 4x + y - 1.5, the coefficient 5.1 is multiplied by the variables x and y, raised to the first power. Therefore, the term 5.1xy consists of the coefficient 5.1 and the variables x and y.
In contrast, the other terms in the polynomial do not have a coefficient that contains a decimal or a fraction. The term -4x has a coefficient of -4, the term y has a coefficient of 1, and the constant term -1.5 has a coefficient of -1.5.
Thus, the characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.
To learn more about polynomial from the given link:
https://brainly.com/question/29073508
#SPJ1
which function produces a range of (-11,-5,1,7,13) given a domain of (-2,0, 2, 4, 6)?
01(x)==+2
Of(x) = -52 +3
01(z)-38 +4
01 (2)-32-5
1 of 10
M
P
(318
0
The function f(x) = 3x - 5 has the defined set of range and domain of the function.
Which function have the given set of range and domain?The range {−11,−5,1,7,13} and the domain {−2,0,2,4,6} of the function
Taking the first function;
f(x) = 3x - 5
When x = -2, f(x) = 3(-2) - 5 = -11
When x = 0, f(x) = 3(0) - 5 = -5
When x = 2, f(x) = 3(2) - 5 = 1
When x = 4, f(x) = 3(4) - 5 = 7
When x = 6, f(x) = 3(6) - 5 = 13
Therefore, the function f(x) = 3x - 5 produces the given range when the domain is {−2,0,2,4,6}.
Learn more on range of a function here;
https://brainly.com/question/7954282
#SPJ1
complete question :
Which function produces a range of {−11,−5,1,7,13} given a domain of {−2,0,2,4,6}
f(x) = 3x − 5
f(x) = −3x + 4
f(x) = x + 2
f(x) = −5x + 3
the apothem of a regular polygon is 7. and the polygon's perime- ter is 56. find the polygon's area.
Answer:
A = 196 units²
Step-by-step explanation:
the area (A) of a regular polygon is
A = [tex]\frac{1}{2}[/tex] perimeter × apothem
here perimeter = 56 and apothem = 7 , then
A = [tex]\frac{1}{2}[/tex] × 56 × 7 = 28 × 7 = 196 units²
Consider the system of equations
below. What is the solution of the
system?
y=4x-8
4x + 2y = 20
Answer:
x = 3, y = 4
Step-by-step explanation:
Substitute 4x - 8 in for y and then solve for x:
4x + 2(4x - 8) = 20
Then, 4x + 8x - 16 = 20 --> 12x = 36 --> x = 3.
Once you have x, you can solve for y.
y = 4x - 8 = 4(3) - 8 = 12 - 8 = 4
So, x = 3, y = 4
please help!! the answers are not 9, 18, 54, or 6
Answer:
If x = 3 and y = 2.3^3, then we can evaluate y using exponents:
y = 2.3^3 = 2.3 × 2.3 × 2.3 = 12.167
So, y = 12.167 when x = 3.
Next, if we want to solve the equation y = 2[?] using order of operations, we need to evaluate what is inside the brackets first. We know that y = 12.167, so we can substitute that value into the equation:
y = 2[?]
12.167 = 2[?]
To solve for the missing value inside the brackets, we need to divide both sides by 2:
12.167 ÷ 2 = ?
6.0835 = ?
Therefore, the solution is y = 2(6.0835), or y = 12.167, which we already found earlier.
the length of a rectangualr park is twice its width. the aprk is surrounded by a 3foot wide path. write a quadratic function to represent the total area of the park and its path
The quadratic function to represent the total area of the park and its path is given by: f(x) = 2x² + 18x + 36.
In this problem, we are given that the length of a rectangular park is twice its width, and it is surrounded by a 3-foot wide path.
We are required to write a quadratic function to represent the total area of the park and its path.
The rectangular park can be represented as follows:
Length = 2x (twice the width)
Width = x
Therefore, the total length of the park including the 3-foot wide path can be represented as (2x + 2*3),
and the total width of the park including the 3-foot wide path can be represented as (x + 2*3).
The area of the park is given by the product of its length and width.
Thus, the area of the park can be represented as follows: Area of the park = (2x + 6)(x + 6)
To represent this as a quadratic function,
we can simplify the above expression using the distributive property.
Area of the park = 2x² + 6x + 12x + 36 = 2x² + 18x + 36.
For similar question on quadratic function.
https://brainly.com/question/29293854
#SPJ11
If the ratio of the number of cats to dogs at an
animal shelter is 9 to 5, which of the following is
the possible number of cats to dogs at the animal
shelter?
Answer:
If the ratio of the number of cats to dogs at the animal shelter is 9 to 5, this means that for every 9 cats at the shelter, there are 5 dogs.
We can express this ratio as:
number of cats : number of dogs = 9 : 5
To find the possible number of cats to dogs, we need to look for pairs of numbers that have a ratio of 9:5. Here are some possible pairs:
9 cats : 5 dogs
18 cats : 10 dogs
27 cats : 15 dogs
36 cats : 20 dogs
45 cats : 25 dogs
54 cats : 30 dogs
...
We can see that there are infinitely many possible pairs of numbers that have a ratio of 9:5. To narrow down the possibilities, we need more information such as the total number of animals at the shelter or the number of cats or dogs at the shelter.
Spaceship Earth is a major tourist at Epcot. It is a sphere whose volume is
approximately 65, 417 m³. What is the approximate circumference of Spaceship
Earth? Use π = 3. 14. Round to the nearest whole number. Thank you in advance!
The approximate circumference of this Spaceship is equal to 157 meters.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this mathematical expression:
Volume = 4/3 × πr³
Where:
r represents the radius.
By substituting the given points into the volume of a sphere formula, we have the following;
65,417 = 4/3 × 3.14 × r³
r³ = 65,417/4.1867
Radius, r = ∛15,624.96
Radius, r = 25 meters.
How to determine the circumference of this Spaceship?Mathematically, the circumference of a sphere can be calculated by using this mathematical expression:
Circumference of a sphere, C = 2πr
Circumference of a sphere, C = 2 × 3.14 × 25
Circumference of a sphere, C = 157 meters.
Read more on volume of a sphere here: brainly.com/question/20394302
#SPJ1
the chance of getting a rare disease is .03 per person. out of 1,000 people, how many of them are expected to get the disease?
Answer:
I believe the answer would be 30 people.
Step-by-step explanation:
To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.
Match the following terms with the descriptions. a. total purchase price b. unit pricing c. comparison shopping d. coupons e. rebates f. markdown g. markdown rate h. sale price 14. A technique that allows shoppers to compare prices 15. The total selling price plus the sales tax - 16. Discount 17. Regular selling price minus the markdown 18. Locating the best value for your money
a. Total purchase price: 15.The total selling price plus the sales tax.
b. Unit pricing: 18. Locating the best value for your money
c. Comparison shopping: 14. A technique that allows shoppers to compare prices
d. Coupons: 16. Discount
e. Rebates: 16. discount
f. Markdown: 17. regular selling price minus the markdown.
g. Markdown rate: 16. Discount
h. Sale price: 18. Locating the best value for your money
What is selling price?Selling price is the amount of money a customer pays for a product or service. It is the amount that a customer pays for the product or service after any discounts, taxes, or fees have been applied.
a. Total purchase price: The total selling price plus the sales tax. This amount is the total cost the customer pays for the good or service, including any taxes and fees.
b. Unit pricing: The cost per unit of a good or service. This allows shoppers to compare the cost of similar items and make an informed decision about which item offers the best value.
c. Comparison shopping: A technique that allows shoppers to compare prices, quality, and other factors when making a purchase.
d. Coupons: A form of discount that can be used when making a purchase. Coupons are often found in newspapers, magazines, or online and can be used to reduce the total purchase price.
e. Rebates: A form of discount where customers receive money back after making a purchase. Rebates are often found in the form of a check or a prepaid debit card.
f. Markdown: The regular selling price minus the markdown. The markdown is the amount that is discounted from the regular selling price.
g. Markdown rate: The percentage of the regular selling price that is discounted. This rate is used to calculate the amount of the markdown.
h. Sale price: The discounted price of a good or service. This is the amount the customer pays after any discounts or coupons have been applied.
For more questions related to discounts
https://brainly.com/question/7459025
#SPJ1
a radioactive material decays according to the formula , where a is the final amount, is the initial amount and t is the time in years. find k, if 700 grams of this material decays to 550 grams in 8 years.
the decay constant for this material is approximately 0.0445.when t = 8 years, the amount of the material remaining is 550 grams.
The formula for radioactive decay is given by:
a = [tex]e^(-kt)\\[/tex] * A
where a is the final amount,A is the initial amount, t is the time in years, and k is the decay constant.
We can use the given information to solve for k as follows:
When t = 0, a = A. So, we have:
A = [tex]e^(0 * k)[/tex] * A
Simplifying this gives:
1 = e^0
Therefore, we can see that k = 0 at the start of the decay process.
Now, when t = 8 years, the amount of the material remaining is 550 grams. Therefore, we have:
550 = [tex]e^(-8k)[/tex] * 700
Dividing both sides by 700 and taking the natural logarithm of both sides, we get:
ln(550/700) = -8k
Simplifying this gives:
k = ln(700/550)/8
Using a calculator, we can evaluate this expression to get:
k ≈ 0.0445
Therefore, the decay constant for this material is approximately 0.0445.
Learn more about amount here
https://brainly.com/question/8082054
#SPJ4
The size of a computer screen is determined by the length of its diagonal. Each student in Mrs. W's math class
was asked to measure the diagonal of his or her Chromebook. Jason's measurements was 13 inches. The
computer's actual diagonal length is 14 inches. Calculate the percent error for Jason's measurement.
The percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.
What is percent error?Percent error is a measure of the difference between an actual value and an estimated or measured value, expressed as a percentage of the actual value. It is used to evaluate the accuracy of measurements or calculations.
According to question:To calculate the percent error for Jason's measurement, we first need to find the absolute error, which is the difference between his measurement and the actual value:
Actual value minus measured value equals absolute error.
Absolute error = |14 - 13|
Absolute error = 1 inch
Next, we can use the formula for percent error:
(Absolute error / Actual Value) x 100% equals the percent of error.
Percent error = (1 / 14) x 100%
Percent error = 0.0714 x 100%
Percent error = 7.14%
Therefore, the percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.
To know more percent error visit:
https://brainly.com/question/30545034
#SPJ1
random sample of size is selected from a population with . a. what is the expected value of (to decimals)? .40 b. what is the standard error of (to decimals)? .048 c. show the sampling distribution of . (to decimals) (to decimals) d. what does the sampling distribution of show? - select your answer -
Random sample of size is selected from a population:
expected value of the sample proportion is 0.40standard error of the sample proportion is 0.0024.sampling distribution follows a normal distribution = 0.40sampling distribution p ∼ N ([tex]p, \frac{p(-p)}{n}[/tex]) as n → ∞.The sample statistic that is calculated for the sample values serves as the foundation for the sampling distribution. To estimate the population percentage, the sample proportion, a sample statistic, is computed from the sample values.
In statistics, a simple random sample is a subset of individuals selected at random from a larger population with an equal probability of selection.
Given that we have,
n = 100
p = 0.40
a) The expected value of the sample proportion is defined as:
E(p) = p = 0.40
b) The standard error of the sample proportion is defined as:
[tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]
= [tex]\sqrt{\frac{0.40(1-0.40)}{100} }[/tex]
S.E = 0.0024.
c) The sample proportion's sampling distribution follows a normal distribution, with an expected value of 0.40.
E(p) = 0.40
d) According to the central limit theorem, as the sample size approaches infinity, the sample statistic (sample percentage) tends to the population parameter (population proportion).
so,
p ∼ N ([tex]p, \frac{p(-p)}{n}[/tex]) as n → ∞.
Learn more about Random sample:
https://brainly.com/question/29523732
#SPJ4
Complete question:
A random sample of size 100 is selected from a population with p = 0.40 .
a. what is the expected value of p (to decimals)? .
b. what is the standard error of p (to decimals)?
c. show the sampling distribution of p
d. what does the sampling distribution of show?