Shana bought 5 bags of popcorn and 2 bottles of soda.
What is an equation?
An equation is consist of two expressions. At least one of the expression contain a variable.
Given that, the cost unit bottle of soda is $3.
The cost of unit bag popcorn is $4.
Assume that she bought s number of soda bottle and p number of bags of popcorn.
Then the cost of s number of soda bottle is $3s.
The cost of p number of bags of popcorn $4p.
She spent $26 in total.
Therefore
3s + 4p = 26.....(i)
She bought 7 things from the shop.
Therefore,
s + p =7 .....(ii)
Solve equation (i) and (ii) by using elimination method:
Multiply equation (ii) by 3 and subtract it from (i)
3s + 4p = 26.
3s + 3p =21
(-) (-) (-)
_________
p = 5
Putting p = 5 in equation (ii)
s + 5 = 7
s = 2
To learn more about elimination method, click on below link:
https://brainly.com/question/26227916
#SPJ1
What is the antiderivative of 1/sinx?
The anti-derivative in other words integration of the inverse of sine function i.e 1/sinx is
x sin⁻¹x + √(1 - x²) + C.
Integration of a function is the inverse process of differentiation. The integral is just the inverse derivative. The inverse integral of sin is written as
x sin⁻¹x + √(1 - x²) + C.
where ∫ --> the sign of integration, dx --> that the integration of sine inverse with respect to x, C --> the constant of integration.
Integral of Sin Reverse proof by integration by parts :
The formula for integration by parts is ∫f(x)g(x)dx = f(x) ∫g(x)dx - ∫[d(f(x) ) /dx×∫g(x) dx] sin⁻¹x can be written as sin⁻¹x = sin⁻¹x.1.f(x) = sin⁻¹x, g(x) = 1
d(sin⁻¹x)/dx = 1/√(1 - x²)
Using these equations and facts,
∫sin⁻¹x dx = ∫sin⁻¹x.1 dx
= sin⁻¹x ∫1dx - ∫[d(sin⁻¹x)/dx × ∫1 dx] dx
= x sin⁻¹x - ∫[1/√(1 - x²) × x] dx
= x sin⁻¹x - ∫x/√(1 - x²) dx
= x sin⁻¹x + (1/2) ∫-2x/√(1 - x²) dx [multiplication and division by 2]
= x sin⁻¹x + (1/2) ∫(-2x)(1 - x²)-1/2 dx
= x sin⁻¹x + (1/2) [(1 - x²)-1/2 + 1/ (-1/2 + 1)] + C {using the formula ∫[f(x)]nf'(x)dx=[f(x)]n +1/(n + 1) +C}
= x sin⁻¹x + (1/2) [(1 - x²)1/2/ (1/2)] + C
= x sin⁻¹x + (1 - x²)1/2 + C
= x sin⁻¹x + √(1 - x²) + C
Therefore the inverse derivative of 1/sinc is x sin⁻¹x + √(1 - x²) + C.
To learn more about Integration , refer:
https://brainly.com/question/988162
#SPJ4
what number would you be rather guessing correctly? the number of rolls of a fair six-sided die will
The number of rolls of a fair six sided die will be 1/6.
A cube (plural "cubes") is a solid with marks on each face. Since the faces are usually all of the same shape, the dual of the Platonic solids and the Archimedean solids is a natural choice. You can "roll" a die by throwing it in the air and letting it rest on one of its faces. Dice are used in many games to choose random numbers to bet on, and are used in board and role-playing games to determine how many squares to move, the outcome of a competition, etc. Coins are a degenerate two-sided case of dice.
In probability theory, an outcome is the possible outcome of an experiment or trial. Each possible outcome of a given experiment is unique, and different outcomes are mutually exclusive (only one outcome occurs in each trial of the experiment). All possible outcomes of an experiment form an element of sample space.
According to the question,
When a dice is thrown, number of possible outcomes =
1, 2, 3, 4, 5, 6 = 6 = n
Here, 6 occurs one time, i.e. m = 1
Thus, Probability of getting a number 6 = 1/6
Learn more about Six sided die:
https://brainly.com/question/21563697
#SPJ4
what is the missing side length in this right triangle?round the answer to the nearest tenth.5.7 cm5.7 cm12.8 cm12.8 cm23.6 cm
The missing side length in the given right triangle is d) 23.6cm if the other two sides lengths are 14cm and 19cm respectively. So, correct option is d.
We know very well that if a triangle is a right angled it means that Pythagorean Theorem is applicable on it.
Pythagorean Theorem states that if a triangle is right angled then the sum of square of two sides which are originating from that angle which is 90 degree is equal to square of third side.
In other words,a²+b²=c² where a and b are two sides originating from 90 degree angle and c is the third side which is opposite of the 90 degree angle.
Now, we have a=14 and b=19cm,we need to find value of c.
So, putting the values, we get
=>14² + 19² =c²
=>c²=361+196
=>c² = 557
=>c=√557
=>c=23.6cm
Hence, missing side length is d)23.6cm
To know more about Pythagorean Theorem, visit here:
https://brainly.com/question/14930619
#SPJ4
(Complete question) is:
what is the missing side length in this right triangle if the other two sides length are 14cm and 19cm respectively ? round the answer to the nearest tenth.5.7 cm5.7 cm12.8 cm12.8 cm23.6 cm
13. a prospector thinks there is an even (50-50) chance that his property contains oil. any property suspected to have oil can go through two independent tests. the first test is 80% reliable; if there is oil on the property, it reports positive 80% of the time, and it reports negative 80% of the time whenever there is no oil. for the second test, it reports positive 75% of the time when there is oil, as well as reporting positive 50% of the time when there is no oil. what is the probability the property has oil, given that both tests report positive? assume event a: first test reports positive; event b: second test reports positive; event o: the property has oil.
The probability the property has oil, given that both tests report positive.
P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375
P(O|A∩B) = P(A∩B|O)P(O) / P(A∩B)
P(A∩B|O) = 0.8 * 0.75 = 0.6
P(O) = 0.5
P(A∩B) = P(A|O)P(O) + P(A|¬O)P(¬O)
P(A|O) = 0.8, P(¬O) = 0.5
P(A∩B) = 0.8 * 0.5 + 0.8 * 0.5 = 0.8
P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375
The probability theory is defined.The study of random events is the focus of probability theory, a subfield of mathematics. It is impossible to predict the outcome of a random event before it happens, although it could take any of numerous different forms. It is believed that chance played a role in how things turned out.
How does probability work?Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ4
a street light is at the top of a 16 foot tall pole. a 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 35 feet from the base of the pole?
By using property of similar triangle and speed, the answer is 4.2ft/sec
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
What is mean by similar triangle?Similar triangles always have comparable sides that are in the same ratio.
We can compare the ratio of sides of similar triangle for the calculations.
x= shadow length at 35feet away.
Using the property of Similar Triangle we get,
[tex]\frac {16}{35+x} = \frac {6}{x}[/tex]
x=21 feet
Velocity of shadow= 21/5
=4.2 feet/sec
To learn more about similar triangle visit:
https://brainly.com/question/25087910
#SPJ4
which triangle pairs are not necessarily congruent? select all that apply
The second triangle pairs are not necessarily congruent.
Option 2 is true.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
There are some triangles is shown in figure.
Now,
We know that;
Two triangles are congruent by theorem of SAS , ASA theorem.
So, When the ''two sides and one angle'' or ''two angle and one side'' are equal to another triangle then the triangles are congruent.
Here, In second option we have;
Only angles are equal, which make them similar not congruent.
Thus, We get;
The second triangle pairs are not necessarily congruent.
Learn more about the triangle visit:
brainly.com/question/17335144
#SPJ1
The Oakland Tigers are having team shirts made. One option is to pay Susan's Tees a $34 setup fee and then buy the shirts for $10 each. Another option is to go to City Printing, paying $23 for a setup fee and an additional $11 per shirt. The team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. What is the cost? How many shirts is that?
To find the cost of the shirts, we need to set up a system of equations. Let x be the number of shirts.
Option 1: 34 + 10x = Option 2: 23 + 11x
We can solve this system of equations by subtracting the equations:
34 + 10x - 23 - 11x = 0
11x - 23 = 0
11x = 23
x = 23 / 11
Therefore, the cost is the same when the team orders 23/11 = 2 shirts.
What is the smallest possible composite, positive, integer x and y such that [tex]\frac{x}{y}[/tex]=5
x=
y=
The smallest possible composite, positive, integer x and y such that x/y=5 are x=20, y=4.
What is a composite number?The result of multiplying two smaller positive integers is a positive integer known as a composite number. It is, in other words, an integer that is positive and has at least one divisor besides itself and 1. The composite numbers are exactly the numbers that are not prime and not a unit, since every positive integer is either composite, prime, or the number 1.
Because it is the result of the two smaller integers 2 and 7, for instance, the number 14 is a composite number. The integers 2 and 3 are also not composite numbers because they can only be divided by one another and themselves.
The smallest possible composite, positive, integers are
4 and 20
20/4=5
So, x=20 and y=4
Therefore, the smallest possible composite, positive, integer x and y such that x/y=5 are x=20 and y=4.
To know more about composite number, visit:
https://brainly.com/question/28199758
#SPJ1
A container Can hold a maximum of 17.5 pounds. There are two objects in the container. The first object weighs 2.65 pounds and the second object weighs 10.8 pounds . How many more pounds can container hold
Answer:
4.05 pounds
Step-by-step explanation:
You want to know the weight that can be added to 2.65 pounds and 10.8 pounds if the total is to be 17.5 pounds.
Additional weightThe available capacity is the difference between the capacity and the weight already in the container:
17.5 lb -2.65 lb -10.8 lb = 4.05 lb
The container can hold up to 4.05 more pounds.
Complete the coordinate proof of the theorem.
Given: ABCD is a square.
Prove: The diagonals of ABCD are perpendicular.
The coordinates of the square be
A (0, 0)
B (a, 0)
C (a, a)
D (0, a)
slope of line AC = 1
How to find the slope of ACSlope is the rate of change of the line AC this is solved by taking the ratio of change in y to change in x
A (0, 0) and C (a, a)
= (0 - a) / (0 - a)
= -a / -a
= 1
Slope of line BD = -1
the product of the slopes
= 1 * -1
= -1
therefore the diagonals of the ABCD are perpendicular since the product of the slope is -1
Learn more about perpendicular lines:
https://brainly.com/question/17565270
#SPJ1
i need help answering with steps
-40-2(3m+1/2) =7m-2
Answer:
Step-by-step explanation:
-Start by distributing the 2, -2(3m+1/2).
-Getting -6m-1, your equation should look like -40-6m-1=7m-2
-Combine -40 and -1 to get -41, and then add the -6m to the other side.
-The equation should look like -41=13m-2. Add the 2 to the -41 to get -39.
-Now, we have -39=13m. divide both sides by 13 to get m=-3.
Vickie made a recipe for 144 ounce of cented candle wax how many 1 cup candle mold can he fill with the recipe
The number of 1 cup candle mold which the can fill with 144 ounce of cented candle wax is 18.
As we know ,
1-cup= 8 ounces
On dividing ,
144 by 8 = 18
Therefore , the no of cups which can be filled is 18 .
One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations.
Any number divided by 0 has no specified result. The outcome in this situation can be expressed as infinite. For instance, 15/0 =, which is undefined.
Dividend :
The division procedure shown below is used to divide any expression.
Dividend is equal to Divisor Quotient + Remainder.
To learn more about division
https://brainly.com/question/21416852
#SPJ4
a = 1212(b1 b2)h find the area of the trapezoid.
The area of trapezoid with sides 125ft and 81ft with height 75ft is: 7,725ft².
What is the area of trapezoid?A trapezoid is a quadrilateral that is convex. There are at least two parallel sides to a trapezoid. The parallel sides are referred to as bases, while the non-parallel sides are referred to as legs.The bases are the two parallel sides, and height is always the perpendicular distance from one base to the opposite. The area of this parallelogram is equal to half of its height (half of the trapezoid's height) times its base (sum of the trapezoid's bases)Area of a trapezoid,
A = 1/2 x (b1 x b2)h
Here given,
b1 = 125ft
b2 = 81ft
h = 75ft
By substituting the values ,
A = 1/2 ( 125 + 81 ) x 75
A = 1/2 x 206 x 75
A = 0.5 x 206 x 75
A = 7,725 ft²
The complete question is "To answer the question, use the formula for the area of a trapezoid A=h((b1+b2)/2), where A is the area, b1 and b2 are the lengths of the bases, and h is the height. What is the area of grass on a trapezoidal field with a height of 75 feet and bases of 125 feet and 81 feet? HINT: Use the values given for h, b1, and b2.".
To learn more about trapezoid refer to :
https://brainly.com/question/1463152
#SPJ4
The area of trapezoid is 7725 ft²
What is a trapezoid?
In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English.
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. Unlike the specific situations below, a scalene trapezoid is a trapezoid that lacks equal-sized sides.
Given, the expression for the area a is given as
a = [(b₁ + b₂)/2]*h
where b₁ = 125ft, b₂ = 81ft, h = 75ft.
Substituting these values in the above area expression, we get,
a = [(125+81)/2]*75
a = 103*75
a = 7725 ft²
Thus, the area of trapezoid is 7725 ft²
To learn more about trapezoid refer to :
brainly.com/question/1463152
#SPJ4
How do you simplify the expression 1+tan^2θ?
The tangent theta is a Trigonometric function, the simplified value of 1 + tan²θ is sec²θ.
What is Trigonometry function ?Trigonometric functions are also called circular functions. They are easily defined as functions of triangle angles. This means that the relationships between the angles and sides of triangles are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant. Also read the triangle identity here.
We have given an expression, 1 + tan²θ
we know that , tanθ = sinθ /cosθ
sin²θ + cos²θ =1 and 1/cosθ = secθ
Now, 1 + tan²θ = 1 + sin²θ/cos²θ
taking LCM cos²θ
=> 1 + tan²θ = (cos²θ + sin²θ )/cos²θ
=> 1 + tan²θ = 1/cos²θ
=> 1 + tan²θ = sec²θ
Hence, the required expression is sec²θ.
To learn more about Trigonometric functions, refer :
https://brainly.com/question/25618616
#SPJ4
One-third of the seventh garde class bought tickets for the seventh grade dance. Then, 32 students bought tickets at the door. If there were 158 students at the dance, how many total students are there in seventh grade?
There are total 378 students in seventh grade.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the standard operations on numbers—addition, subtraction, multiplication, division, operation, and extraction of roots.
Main body:
The total number of students that are in the seventh grade are 378 students.
The number of students that had already bought tickets will be:
= 158 - 32 = 126 students.
Therefore, based on the information given, the equation to calculate the total students will be:
= (1/3 × x) = 126
x = 3 × 126
x = 378
Therefore, there are 378 students.
Read related arithmetic link on:
https://brainly.com/question/13378503
#SPJ1
A Blue spruce grows an average of 6 inches per year. A hemlock grows an average of 4 inches per year. If a blue spruce is 48 inches tall, and a Hemlock is 70 inches tall, when would you expect the trees to be the same height? What height will that be? Write and solve the system of equations for this problem.
In 12 years the two trees will be at the same height of 120 inches for the given condition of the equation.
What is an equation?
A mathematical statement called an equation demonstrates the equality of two mathematical expressions.
Based on the given condition of a question,
Let X be the required time duration, and then the equation will be
or, (48+6X)=(72+4X)
or, 48+6X=72+4X
or, 6X-4X=72-48
or, 2X=24
or, X=24/2
or, X=12 year
And height = 48 + 6*12 = 48 + 72 = 120 inches
Hence, In 12 years the two trees will be at the same height of 120 inches.
To learn more about an equation
https://brainly.com/question/24739899
#SPJ1
What number is 32% of 50?
Answer: 16
Step-by-step explanation:
32% of 50 = 16
Determine the coordinates of W(−7, 4) after a reflection in the line y=9
The coordinate of the reflection about the line y = 9 is thus (7, 4)
What is reflection?Reflection is a transformation in which an object is flipped over a line.
How to find the coordinates of W(−7, 4) after a reflection in the line y = 9?We know that to reflect W(-7, 4) over the line y = 9, the distance of the point W and its reflection from the line y = 9 must be the same.
The distance of point W(-7, 4) from the line y = 9 is d = 9 - (- 7) = 9 + 7 = 15
So, the x - coordinate of the reflection from the line y = 9 is x = 15 - 9 = 7
Since the y - coordinate of the point W, does not change, the coordinate of the reflection about the line y = 9 is thus (7, 4)
So, the coordinate of the reflection about the line y = 9 is thus (7, 4)
Learn more about coordinate of the reflection here:
https://brainly.com/question/17732634
#SPJ1
3. Write the equation of a line that is perpendicular to y =V3 x + 3 and goes through the point (-1, -2).
Step-by-step explanation:
is that root 3 x..........?
HELP PLEASE! ILL MARK BRAINILEST.
Answer:
Below
Step-by-step explanation:
Area of a triangle = 1/2 b * h
Triangle A = 1/2 (4 * 10) = 20 units^2 ( I got the '10' from answers below)
Triangle B must be b = 2 h = 2 (for area = 2)
Rectangle C must be 2 x 2 ( for area = 4)
Triangle D = 1/2 (2+2+6)*2 = 10 units ^2
Total = 20 + 2+4+ 10 = 36 units^2
Answer:
32
Step-by-step explanation:
Area of a triangle = 1/2bh
b = base
h = height
Area of a square = bh, where b=h
A: 1/2(2+2+6)(4) = 20
B: 1/2(2)(2) = 2
C: (2)(2) = 4
D: 1/2(6)(2) = 6
Total = A+B+C+D = 20+2+4+6 = 32
**the way the dimension "6" is labeled is a little confusing. I assumed 6 is the base of triangle D
Which of the following is a criteria for construction of triangles A AAA B SAS C ss D None?
A criteria for construction of triangle include the following: B. SAS.
What is a triangle?In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
Generally speaking, the side, angle, side (SAS) criterion is essential for the construction of any triangle such as the following:
Isosceles triangleObtuse triangleEquilateral triangleScalene triangleRight-angled triangleBased on the side, angle, side (SAS) criterion, a statement which is necessary to prove that two (2) triangles are congruent is that one of its side must be equal to another side because their angles are equal in measure or magnitude.
Read more on SAS similarity theorem here: brainly.com/question/11544842
#SPJ1
a city ordinance requires that more than 75% of its residents must agree to the construction of new public buildings (using tax dollars) before any such structures can be built. a proposal has been made to build a new recreational facility in the city, and sponsors of the proposal want to conduct a small survey to see if it would be approved if put to an official vote of all residents. a simple random sample of 150 residents revealed that 123 supported a change (and 27 did not). what is the value of the standardized test statistic for this significance test?
The value of the standardized test statistic for this significance test is 1.7265
Standardized test statistic
In statistics, the standardized test statistic means a way for you to compare your results to a “normal” population.
Given,
A city ordinance requires that more than 75% of its residents must agree to the construction of new public buildings (using tax dollars) before any such structures can be built. a proposal has been made to build a new recreational facility in the city, and sponsors of the proposal want to conduct a small survey to see if it would be approved if put to an official vote of all residents. a simple random sample of 150 residents revealed that 123 supported a change (and 27 did not).
Here we need to find the value of the standardized test statistic for this significance test.
While we looking into the given question we have identified the following values,
Random samples = 150
Supported values = 123
Not supported = 23
Aggreged percentage = 75%
So, the null and alternative hypotheses were as follows: H0: p = 0.75 and Ha: p ≠ 0.75.
Then the value of Standardized test statistic is calculated as,
=> (150 - 123) / (75 / √23)
=> 1.7265
To know more about Standardized test statistic here
https://brainly.com/question/16695849
#SPJ4
This graph shows the weights of some squashes at farmers' market: Weights of squashes W X 8 3 8 5 6 3 Pounds How much heavier is the heaviest squash than the lightest squash? Write your answer as proper fraction, mixed number, or whole number: pounds Submit dontt know thls yet > 9.52
1/2
what is whole number?
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.
According to question,
heaviest squash than the lightest squash are,
[tex]7/8-3/8=4/8[/tex]
[tex]=1/2[/tex]
To know more about whole number checkout https://brainly.com/question/29766862
#SPJ1
What is fg(x) given that f(x) equals x² + 7x and g(x) equals -2x² + 3x-5
Answer:
[tex] \huge{ \boxed{f(g(x)) = 4 {x}^{4} - 12 {x}^{3} + 15 {x}^{2} - 9x - 10 \\ }}[/tex]
Step-by-step explanation:
[tex]f(x) = {x}^{2} + 7x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ g(x) = - 2 {x}^{2} + 3x - 5[/tex]
To find f(g(x)), substitute g(x) into f(x). That is for every x found in f(x) replace it with g(x) and solve.
[tex]f(g(x)) = {( - 2 {x}^{2} + 3x - 5) }^{2} + 7( - {2x}^{2} + 3x - 5) \: \: \: \: \: \: \: \: \: \: \\ \\ = (4 x^4 - 12 x^3 + 29 x^2 - 30 x + 25) + (-14 x^2 + 21 x - 35) \\ = 4 {x}^{4} - 12 {x}^{3} + 29 {x}^{2} - 14 {x}^{2} - 30x + 21x + 25 - 35 \\ \\ = 4 {x}^{4} - 12 {x}^{3} + 15 {x}^{2} - 9x - 10[/tex]
We have the final answer as
[tex]f(g(x)) = 4 {x}^{4} - 12 {x}^{3} + 15 {x}^{2} - 9x - 10 \\ [/tex]
Solve the following system of equations using substitution (Enter your answer as an ordered pair, including the parentheses and comma.)
-3x+6y=12
2y=x+4
The system of equations has infinite solutions, both equations represent the same line.
How to solve the system of equations?
Here we have the following system of equations:
-3x+6y=12
2y=x+4
And we want to solve this by substitution, first, we can rewrite the first equation as:
-3x + 3*(2y) = 12
Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:
-3x + 3*(x + 4) = 12
Now we can solve this for x.
-3x + 3x + 12 = 12
12 = 12
So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
How do you write 145,000,000,000 in scientific notation?
The scientific notation is [tex]1.45*10^{11}[/tex]
Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We, therefore, employ scientific notations.
We need to move the decimal point 11 places to the left therefore the exponent for the 10s term will be positive:
[tex]145,000,000,000=145,000,000,000.0=1.45*10^{11}[/tex]
To learn more about scientific notation visit: brainly.com/question/18073768
#SPJ4
if a snowball melts so that its surface area decreases at a rate of 1cm2/min1cm2/min, find the rate at which the diameter decreases when the diameter is 10cm10cm.
The rate at which the diameter decreases is -0.16cm/min
Diameter:
In geometry, diameter refers the straight line that goes from one side to the other side of a circle, passing through the center.
Given,
Here we need to find if a snowball melts so that its surface area decreases at a rate of 1cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm. Finish solving the problem. Write an equation that relates the quantities.
Here we obtained the equation that relates the surface area S and the diameter D of a sphere given by
=> S = πD²
Now, we have differentiate the equation as,
=> dS/dt = d/dt (πD²)
=> dS/dt = π d/dt (D²)
=> dS/dt = 2πD dD/dt
Now, Solving for dD/dt, which is the unknown for this problem, we have
=> dD/dt = 1/2πD x dS/dt
Now, substituting the given values, the rate of change of the diameter when D=10 cm and dS/dt as (-1) is
=> dD/dt = 1/2 x π x 10 (-1)
=> dD/dt = -1/20π
=> dD/dt = -0.16cm/min
To know more about Diameter here.
https://brainly.com/question/5501950
#SPJ4
suppose steph curry is fouled while shooting a three-point goal and misses his shot. the probability of steph curry making a free throw is 90%. what is the probability that he makes the first and second free throw, but misses the third free throw?
The probability that he makes the first and second free throw, but misses the third free throw is 7.7 %.
Given :
suppose steph curry is fouled while shooting a three-point goal and misses his shot. the probability of steph curry making a free throw is 90%.
probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
P ( makes 2 then misses 1 ) = P ( make 1st ) and P ( make 2nd ) and P ( miss 3rd )
= 0.906 *0.906 * 0.094
= 0.077
= 7.7 %
Learn more about the probability here:
https://brainly.com/question/11234923
#SPJ4
which is the graph of y=2(x-3)^2 2
the probability that a restaurant passes its health department inspection is 0.94. the owners of 58 restaurants are surveyed to see if their restaurants passed inspection. For each binomial experiment described, find the mean, the variance and the standard deviation!
Mean = 54.52
V(X) = 3.2712
S.D = 1.8086
To calculate the mean (expected value) of a binomial distribution B(n, p) you need to multiply the number of trials n by the probability of successes p , that is: mean = n × p
Where, n= 58
p = 0.94
Therefore, mean = 54.52
To find the Variance of the given binomial distribution
Variance = np(1-p)
=58 X 0.94 ( 1- 0.94)
= 54.52 X 0.06
V(X) = 3.2712, when we know the variance and the mean then we can calculate the standard deviation easily
To find the standard deviation of the given binomial experiment = [tex]\sqrt{np(1-p)}[/tex]
= [tex]\sqrt{3.2712}[/tex]
S.D = 1.8086
To know more about binomial distribution
https://brainly.com/question/29732172
#SPJ4
