As a result, there is an 11/16 chance that there will be at least as many heads as tails.
What is probability?The branch of mathematics concerned with probability is known as probability theory. Although there are several different interpretations of probability, probability theory treats the concept rigorously mathematically by expressing it through a set of axioms. The probability is a measure of the likelihood that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the likelihood or chance that a specific event will occur. Probabilities can be expressed as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
The likelihood that there will be more tails, more heads, or equal numbers of each is 5/16, 5/16, and 6/16, respectively. Therefore, the probability that there will be at least as many heads as tails is 11/16.
To know more about probability,
https://brainly.com/question/30034780
#SPJ4
Complete Question:
Harold tosses a nickel four times. The probability that he gets at least as many heads as tails is:
assume a multiple-choice question on an online quiz has 6 answer choices in it, which are shown in random order to each student. in how many ways can this question be displayed? enter the answer as an integer.
6! is short for 6 factorial and is calculated by multiplying all the integers from 1 to 6. So the answer is 720 ways.
6! = 720
6! is short for 6 factorial and is calculated by multiplying all the integers from 1 to 6. So the answer is 720 ways.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
So the answer is 720 ways.
There are 720 ways in which a multiple-choice question on an online quiz with six answer choices can be displayed. This is calculated by multiplying all the integers from 1 to 6, which is referred to as 6 factorial, or 6!. 6! is calculated by multiplying 6 x 5 x 4 x 3 x 2 x 1, which equals 720. This means that there are 720 possible combinations of answer order that can be shown to each student when they take the quiz. With such a wide variety of possible answers, students can focus on the content of the question rather than on the order of the answers, which can help to reduce bias and ensure the validity of the quiz.
Learn more about integer here
https://brainly.com/question/15276410
#SPJ4
*THE ANSWER IS C* Which is a correct expansion of (3x + 2)(3x²+4)? OA. 3x. 3x² + 3x 4+2.3x+2.4 B. 3x. 3x² +2.3x² + 3x².4+2.4 C. 3x. 3x² + 3x 4+2.3x²+2.4
[tex](3x+2)(3x^{2} +4)[/tex]
This equation can be solved using the distributive is by multiplying each term by the other term.
First, multiply [tex]3x[/tex] by [tex]3x^{2} +4[/tex]
[tex]3x(3x^{2} +4)=(3x*3x^{2} )+(3x*4)[/tex]
Then, multiply [tex]2[/tex] by [tex]3x^{2} +4[/tex]
[tex]2(3x^{2} +4)=(2*3x^{2} )+(2*4)[/tex]
Summary the two equations
[tex](3x*3x^{2} )+(3x*4)+(2*3x^{2} )+(2*4)[/tex]
The correct expansion of [tex](3x+2)(3x^{2} +4)=(3x*3x^{2} )+(3x*4)+(2*3x^{2} )+(2*4)[/tex] (C)
Read more on expansion algebra here
https://brainly.com/question/4747615
#SPJ1
List the sample space for rolling a fair eight-sided die.
A. S = {1}
B. S = {8}
C. S = {1, 2, 3, 4, 5, 6}
D. S = {1, 2, 3, 4, 5, 6, 7, 8}
The sample space for rolling a fair eight-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8}.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1.
Given an eight-sided die,
to find the sample space,
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.
when eight sides die is tossed there will be 8 sample spaces that are,
1, 2, 3, 4, 5, 6, 7, 8,
so S = {1, 2, 3, 4, 5, 6, 7, 8}
Hence option D is correct.
Learn more about probability;
brainly.com/question/30034780
#SPJ1
Here is a sketch of y=x²+bx+c
The curve intersects
the x-axis at (2, 0) and point P
Work out the x-coordinate of the turning point
the y-axis at (0, -14)
of the graph.
You must show your working.
The x-axis at (2, 0) and point P work out the x-coordinate of the turning point the y-axis at (0, -14) of the graph x is 9/2.
What is the x-coordinate?The turning point's x-coordinate will be "9/2."
The answer to the query is
y = [tex]x^{2}[/tex] + bx + c
curving goes by.
(2 , 0)
and,
(0 , 14)
Putting (0, 14) results in
→ 14 = 0 + 0 + c
c = 14
then,
→ y = [tex]x^{2}[/tex] + bx + 14.
Putting in (2, 0) gives us
→0 = 4 + 2b + 14
-2b = 18
b = - 18 /2
= -9
then,
→ y = [tex]x^{2}[/tex] - 9x + 14.
the discovery of
→ dy / dx = 0
dy/dx = 2x - 9
turning point
→ dy / dx = 0
2x - 9 = 0
x = 9/2.
The curve intersects
The x-axis at (2, 0) and point P work out the x-coordinate of the turning point the y-axis at (0, -14) of the graph x is 9/2.
To learn more about graph refer to:
https://brainly.com/question/9120468
#SPJ1
easy math problem help me out tysm !
Answer: 26
Step-by-step explanation:
Since we are given the value of y, all we need to do is plug it into the equation and solve it. Make sure if you plug this into a calculator that you put the substituted number in parenthesis that way it squares the number correctly without a negative sign.
(-3)²-5(-3)+2
9 - 5(-3) +2
9 - -15 + 2
9 + 15 + 2
24 + 2
26
Hope this helps!
A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used. Part 1. In January, the total cost for 250 minutes was $70 while in February, the total cost for 275 minutes was $72. The constant charge for each minute used is: 00.1 0.09 0.08
$50 is the constant charge used for each minute.
We must put up two variables in order to fix this issue. In this instance
F = constant Fee
R = rate used per minute.
So the cost for the month of January is calculated like this:
F+250R= 70
And the cost for February is calculated like this:
F+275R= 72
So no we have a system of equations we can solve simultaneously. This can be solved using different methods, elimination, substitution, graphically, or by using matrices. I will solve this by substitution.
So let's solve the first equation for R:
[tex]R = \frac{70-F}{250}[/tex]
And let's substitute this first equation into the second equation:
[tex]F+275(\frac{70-F}{250})= 72[/tex]
And now we can solve this for F:
[tex]F+275(\frac{70-F}{250})= 72\\F+11(\frac{70-F}{10})= 72\\F+(\frac{770-11F}{10})= 72.....eq(1)\\[/tex]
We can multiply both sides by 10 so we get:
[tex]10*F+10(\frac{770-11F}{10})= 10*72\\\\10F+770-11F= 720\\\\770-720 = 11F - 10F\\50 = F[/tex]
Therefore, $50 is the constant charge used for each minute.
To learn more about constant charge, visit the link below:
brainly.com/question/24332124
#SPJ4
what is the slope through the line of (2, 6) and (8, 4)
Answer:
-1/2
Step-by-step explanation:
first u would label ur x and ys 2,6 would be x1, y1 then u would put 8,4 would be x2 and y2 . You would put 4-6 as y2 - y1 and 8-2 as x2 - x1 to get -2 divided by 4 to get your -1/2
If P(W) = 0.42 and P(Z) = 0.35, what is P(W or Z) if W and Z are independent?
P (W or Z) if W and Z are independent, would be 0.673.
How to find the probability ?Independent events are the events that the outcome of one event does not affect the outcome of the other event, so the probability of one event happening doesn't change the probability of the other event happening.
If W and Z are independent, it means that the probability of W occurring has no effect on the probability of Z occurring, and vice versa.
In this case P(W or Z) can be calculated using the formula for the probability of the union of two independent events:
P(W or Z) = P(W) + P(Z) - P(W and Z)
P(W and Z) = P(W) x P(Z)
= 0.42 x 0.35
= 0.147
Therefore:
P(W or Z) = P(W) + P(Z) - P(W and Z)
= 0.42 + 0.35 - 0.147
= 0.673
Find out probability at https://brainly.com/question/29863918
#SPJ1
review the following credit terms and identify the one that states that the buyer will receive a 3% discount if the payment is made within 15 days. otherwise, full payment is expected within 45 days of the invoice date. multiple choice question. 3/10, n/45 3/15,45 3/15, n/45 3/45, n/15
The credit term 3/15, n/45 states that the buyer will receive a 3% discount if the payment is made within 15 days. Otherwise, full payment is expected within 45 days from the invoice date.
This term can be expressed as a formula and calculation as follows:
Discount = 3% of Invoice Total
Payment due within 15 days = Invoice Total - Discount
Payment due within 45 days = Invoice Total
For example, if the invoice total is $500, then the buyer will receive a 3% discount (Discount = 3% x $500 = $15) if the payment is made within 15 days. The payment due within 15 days is then equal to the invoice total minus the discount ($500 -$15 = $485). On the other hand, if the payment is not made within 15 days, the buyer is expected to pay the full invoice total within 45 days ($500).
Learn more about total here:
https://brainly.com/question/3589613
#SPJ4
Brick San Antonio playing a game of counters Rick has some counters Selma has twice as many counters as Rick Tony has six counters Leston Selma in total they have 54 counters the number of count as Rick has: the number of count as Tony has = 1: P work out the value of paid
If Brick San Antonio playing a game of counters Rick has some counters Selma. the number of count as Tony has = 1: P work out the value of paid is 1.5.
How to find the number of count?Let x represent the number of counter brick
Let 2x counter represent Selma
Let 2x -6 counter represent Tony
Hence,
x+2x+2x -6 =54
5x -6 =54
5x =60
x =60/5
x =12
So Brick has 12
Tony has 2×12 -6
= 24 -6
=18
Thus
12:18 = 1: 18/12
=1:1.5
Hence,
P =1.5
Therefore the number of count as Tony has = 1: P work out the value of paid is 1.5.
Learn more about number of count here:https://brainly.com/question/27861861
#SPJ1
In a right triangle, the lengths of the legs are a and b. find the hypothenus if
B) a=1, b=1
C) a=5, b=6
B) In a right triangle where a=1 and b=1, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 1^2 + 1^2 = 1+1 =2, so c = √2
C) In a right triangle where a=5 and b=6, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 5^2 + 6^2 = 25+36 =61, so c = √61
allie is completing a long division problem that may or may not have a remainder. In each box drag the apropreite digit to show the correct way to divide
The required correct way of division has been shown, as per the long division.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The questions seem to be incomplete, so we assume the number 729 that Allie divides it by the number 9.
According to the question,
Long division,
9 ] 729 [8 1
- 72
---------------
0 9
- 9
---------------
0
Thus, the required correct way of division has been shown, as per the long division.
Learn more about long division here:
https://brainly.com/question/28824872
#SPJ1
given an integer array nums, return the maximum difference between two successive elements in its sorted form. if the array contains less than two elements, return 0.
Arrays are a fundamental data structure, and an important part of most programming languages.
What are arrays in Python?A fundamental data structure, arrays play a significant role in the majority of programming languages. They are containers in Python that can hold many items simultaneously. They are a set of items that are organised and whose values all belong to the same data type.Using the NumPy library, new datatypes known as arrays can be produced in Python. NumPy arrays only contain one data type and are designed for numerical analyses. To build an array, use the array() method after importing NumPy. The input for the array() function is a list.The JavaScript built-in method values() is used to return a new array. It prints all the elements of the array using an iterator object that holds the values for each index in the array. Input values: It returns a fresh array iterator object, or the array's elements.Method :
Employ two loops. Pick elements one at a time in the outer loop, and then in the inner loop, compare each element's difference to every other element in the array and the largest difference ever calculated. The application of the aforementioned strategy is seen below:
Here i attached the programs
Learn more about Python arrays refer to :
https://brainly.com/question/21723680
#SPJ4
Find the area of each figure. Round your answer to one decimal place if necessary.
Therefore ,as a result, the total surface area is 64 + 16 = 80 square units.
Defining surface areaThe amount of space it occupies on the surface is a decent indication of its overall size. The complete surroundings is taken into account when calculating the area of a tri shape. Something's total size is determined by its surface area. The volume of water inside a cuboid is equal to the total of the volumes on each and every six of its rectangular sides. To calculate the box's measurements, use the formula below: In 2lh, 2lw, and 2hw, the region is identical (SA). The surface area of the multipurpose shape represents the region.
Here,
Imagine a line running from 8m to 4m at the intersection. As a result, a rectangle and a triangle are formed.
Simple
=> is the square's area
=> 8 *8 = 64 square units.
Use the formula
=> (1/2)b*h to determine the triangle's area
We need to enter the hieght, which is already known to be 4, and the base, which is already known to be 8, into the equation.
=> Triangle area unit = 1/2 * 8 * 4
Therefore ,as a result, the total area is 64 + 16 = 80 square units.
To know more about surface area visit:
https://brainly.com/question/2835293
#SPJ1
Elizabeth goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 7% is applied to the bill. Elizabeth decides to leave a tip of 20% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Elizabeth paid.
The expression in terms of xx that represents the total amount that Elizabeth paid is - xx + 0.07xx + 0.2(xx + 0.07xx) = 1.47xx
What is percentages and algebraic expressions?This question uses the concepts of percentages and algebraic expressions.
The expression that is used to calculate the total amount that Elizabeth paid is an example of an algebraic expression.
It uses the percentage tax rate of 7% and the percentage tip rate of 20%, which are both represented by decimal numbers.
Step 1: Calculate the tax by multiplying the subtotal (xx) by the tax rate (0.07): 0.07xx
Step 2: Calculate the tip by multiplying the subtotal (xx) plus the tax (0.07xx) by the tip rate (0.2): 0.2(xx + 0.07xx)
Step 3: Calculate the total by adding the subtotal (xx), the tax (0.07xx), and the tip (0.2(xx + 0.07xx)): xx + 0.07xx + 0.2(xx + 0.07xx)
Step 4: Simplify the expression to 1.47xx.
xx + 0.07xx + 0.2(xx + 0.07xx) = 1.47xx
To learn more about Percentages and algebraic expressions, visit
brainly.com/question/14003149
#SPJ1
Help me please asap!!!!!thank you!
The cosecant of angle U is csc(U) = 1 / sin(U) = √55 / 4
How to find the cosecant of angle U?To find the cosecant of angle U in triangle UTV, we need to find the sine of angle U. To do this, we can use the sides of the triangle that are opposite and adjacent to angle U. In a right triangle, the sine of an angle is equal to the opposite side divided by the hypotenuse.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
[tex]VT^2 + UT^2 = UV^2[/tex]
4^2 + (√39)^2 = UV^2
16 + 39 = UV^2
55 = UV^2
UV = √55
So, the length of the hypotenuse is √55. To find the sine of angle U, we can use the ratio of the opposite side (UT) to the hypotenuse:
sin(U) = UT / UV = 4 / √55
The cosecant of angle U is then:
csc(U) = 1 / sin(U) = √55 / 4.
To know more about angle cosecant visit
https://brainly.com/question/29761119
#SPJ1
Find the values of x and the measure of each angle labeled in the figure.
(2x) degrees
(3x + 5) degrees
The angles for the triangle are 42°, 68° and 70° and x=21.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
As sum of all angles of a triangle is 180°
2x+3x+5+4x-14=180
x=21
hence,
The angles for the triangle are 42°, 68° and 70° and x=21.
To know more about triangles visit the link
https://brainly.com/question/2773823?referrer=searchResults
#SPJ1
Right question:-
Angles in the question are 2x°,(3x+5)° and (4x-14)° of a triangle.
A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the flaps are folded upwards to form an open box. If the volume of the box is 1716in ^3, what were the original dimensions of the piece of metal
The original dimension of the metal is width = 21 and length = 41 before cutting off the squares.
What is volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.
Let us suppose the width of the rectangular metal = w.
Then the length of the rectangular metal is = 20 + w
Given that squares of 4in are cut from the four corners, then the new width and length will be:
width = w - 8
length = 20 + w - 8
The height of the rectangular metal when the flaps are folded are 4 in.
The volume of the rectangular prism is:
V = (l)(w)(h)
Substituting the value of V = 1716, width = w - 8, length = 20 + w - 8, and h = 4 we have:
1716 = (w - 8)(20 + w - 8)(4)
1716 = 80w + 4w^2 - 32w - 640 - 32w + 256
1716 = 4w^2 + 16 w - 384
4w^2 + 16w -384 - 1716 = 0
4w^2 + 16w - 2100 = 0
w^2 + 4w - 525 = 0
w^2 + 25w - 21w - 525 = 0
w(w + 25) - 21 (w + 25) = 0
(w - 21) (w + 25) = 0
w = 21
w = -25
The dimensions of the box cannot be negative hence, the width is 21.
length = 20 + 21
length = 41
The original dimensions of the metal is width = 21 and length = 41 before cutting off the squares.
Learn more about volume here:
https://brainly.com/question/13338592
#SPJ1
let's define the reverse of an integer x as the number obtained by reversing the order of the digits of x and then moving any leading zeroes to the end of the resulting number. tests input: arr: [7, 234, 58100] expected output: 7 432 18500
Let's see how the while loop functions for n = 2345. Inside the loop, the reversed number is calculated using the formula reverse = reverse * 10 + remainder. n. n != 0.
What is an integer reversal?We only need to flip the most significant digit into the least significant digit and vice versa, the second most significant digit into the third least significant digit and vice versa, and so on to reverse an integer. Return 0 if the input is bigger than the predetermined range (231, 231 1). Regarding two-digit numbers and their opposite, there are two common logics. The two-digit number "ab" can be represented generally as (10 times a) + b. We are aware that swapping the numbers in the TENS and ONES positions will reverse a number. The typical form of its reverse "ba" is thus (10 times "b" times "a") PlusGiven,
arr: [7, 234, 58100]
Expected Output:
7 + 432+ 18500 = 18939
Input:
arr: [0, 100, 220]
Expected Output:
0 + 100 + 220 = 320
To learn more about integer reversal, refer to:
https://brainly.com/question/14465188
#SPJ4
18[1/2log(x+y)-1/9log(x-y)]
Write the expression as a single logarithm
In order to get another number, a number must be raised to a certain power, which is known as a logarithm.
What is a logarithm in simple terms?Binary logarithms, which have a base of 2, natural logarithms, which have a base of e 2.71828, and common logarithms with a base of 10 are the four most popular varieties of logarithms.Exponent or power, known as a logarithm, to which a base must be raised in order to produce a certain number.If bx = n, then the expression for x is written as x = logb n, where x is the logarithm of n to the base b.For instance, since 23 = 8 and 8 has a base of 2, the logarithm of 8 in base 3 is 3, or 3 = log2.In order to get another number, a number must be raised to a certain power, which is known as a logarithm (see Section 3 of this Math Review for more about exponents).calculation is attached below :
To learn more about logarithm refer
https://brainly.com/question/247340
#SPJ1
The side lengths of an equiangular octagon are 1, 2, 3, 4, 1, 2, 3, and 4 in clockwise order. Enter your answer in the form x + ysquare rootz in simplest radical form. What is the octagons area?
The area of the octagon is 40 + 40√(2) in simplest radical form.
What is the area of the octagon?
The area of a regular octagon can be calculated using the formula:
Area = (2 + 4 * √2) * s^2
where s is the length of one of the sides.
An equiangular octagon is an octagon in which all of the angles are congruent. In addition, all the side lengths are also congruent. However, in the case of the side lengths of the octagon are given as 1, 2, 3, 4, 1, 2, 3, and 4 in clockwise order.
To find the area of the octagon, we can use the following formula:
Area = 2(1 + 2 + 3 + 4)(4) * (1 + √(2))/4
Area = 2(10)(4) * (1 + √(2))/4
Area = 80 * (1 + √(2))/2
Area = 40 + 40*√(2)
Hence, the area of the octagon is 40 + 40√(2) in simplest radical form.
To learn more about the area of the octagon, visit:
https://brainly.com/question/358118
#SPJ4
Write the equation as a single logarithm and show your steps 3log4x-2log4y
The equation as a single logarithm is log(4x)^3)/(4y)^2
What is logarithm and some of its useful properties?When you raise a number with an exponent, there comes a result.
Lets say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Some properties of logarithm are:
[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]
Log with base e = 2.71828... is written as
[tex]\ln(x)[/tex]
Log with base 10 is written as
[tex]\log(x)[/tex]
Given;
Equation=3log4x-2log4y
=log(4x)^3-log(4y)^2
=log(4x)^3)/(4y)^2
Therefore, the answer of logarithm will be log(4x)^3)/(4y)^2
Learn more about logarithm here:
https://brainly.com/question/20835449
#SPJ1
Sam is investing his money. He thinks that he should make $7 for every $100 he invests. How much does he expect to make on an investment of $6100?
Answer:
$427
Step-by-step explanation:
Sam expects to make $7 for every $100 he invests, which is a 7% return. To determine how much he expects to make on an investment of $6100, we can use the following formula:
investment amount * (return rate / 100) = expected return
$6100 * (7 / 100) = $427
So Sam expects to make $427 on an investment of $6100 if he makes $7 for every $100 he invests.
Answer:
$427
Step-by-step explanation:
$6100/$100=61
61 ×7=427
hope it helps youPLS RATE AS BRAINLIEST ANSWER. a) In ∆PQR, perimeter=24cm, p+q=18 cm and q+r=14 cm, find the area of ∆PQR.
The area of ∆PQR is 42 [tex]cm^{2}[/tex]
We can use Heron's Formula to find the area of a triangle when we have the length of its three sides. Heron's Formula states that the area of a triangle with sides p, q, and r is:
Heron's Formula :
Area =[tex]\sqrt(s(s-p)(s-q)(s-r))[/tex]
where s is the semi-perimeter of the triangle (half of the perimeter).
In this case, we know that the perimeter of the triangle is 24 cm and p+q = 18 cm, and q+r = 14 cm. We can use these equations to find the length of the third side, r.
p+q+r = 24 cm
r = 24 - (p+q) = 24 - 18 = 6 cm
Now we can use this information to find the semi-perimeter of the triangle:
s = (24 cm) / 2 = 12 cm
Now we can substitute the values of p, q, r, and s into Heron's formula to find the area of the triangle:
Area = √(12 x (12-18) x (12-14) x (12-6))
Area = √(12 x (-6) x (-2) x 6)
Area = √(12 x (-12) x (-12))
Area = √(12 x 144)
Area = √(1728) = 42 [tex]cm^{2}[/tex]
Therefore, the area of ∆PQR is 42[tex]cm^{2}[/tex]
For more information on Heron's Formula:
https://brainly.com/question/10677686
https://brainly.com/question/12454834
convert the line integral to an ordinary respect to the parameter and evalluate it c isthehelix (7cost, 7sint, t) 0
The Ordinary integral of the Line integral [tex]\int _c {(y-z)} \, ds[/tex] where C is the helix ⟨7cos t, 7sin t, t⟩ is [tex]\int\limits^0 _{-2\pi} \sqrt{50}{(7sin\ t -t)} \, dt[/tex] and its value in the range -2π ≤ t ≤ 0 is 10√2 π²
We have x = 7cos t, y = sin t and z = t.
We also need ds =[tex]\sqrt{(\frac{dx}{dt})^{2} +(\frac{dy}{dt})^{2} +(\frac{dy}{dt})^{2} }dt[/tex]
ds = [tex]\sqrt{(-7sin\ t)^{2} +(7cost\ t)^{2} +(1)^{2} }dt[/tex]
= [tex]\sqrt{49sin^{2}t +49cos^{2}t+1 }dt[/tex]
= [tex]\sqrt{49(sin^{2}t +cos^{2}t)+1 }dt[/tex]
ds = [tex]\sqrt{50}dt[/tex]
Now, [tex]\int _c {(y-z)} \, ds[/tex] = [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]
Evaluating the integral [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]
[tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex] = [tex]\sqrt{50}\ {[-7cos\ t -\frac{t^{2} }{2} ]}\limits^0 _{-2\pi}[/tex]
= [tex]\sqrt{50}\ {[-7+7+2\pi ^{2}]}[/tex]
= [tex]10\sqrt{2}\pi ^{2}}[/tex]
The question is incomplete, the complete question is
" Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.[tex]\int _c {(y-z)} \, ds[/tex] ; C is the helix ⟨7cos t, 7sin t, t⟩, for -2π ≤ t ≤ 0 "
To know more about Line integral here
https://brainly.com/question/12440198
#SPJ4
Which students ran faster than Amy?
Students that ran faster than Amy are Chris and Ethan.
Speed is the ratio between distance and time. The formula for speed
v = d ÷ t
d = distances (miles)t = time (hours)v = velocity (mph)Amy's speed
d = 2 milest = 36 minutes = 36/60 hours = 0.6 hoursv = d ÷ tBrian's speed
From the time versus distance graph from 0 miles to 2 miles it can be seen that the time required is 40 minutes.d = 2 milest = 40 min = 40/60 h = 2/3 hv = d ÷ tChris's speed
The equation y = 3/42 xEthan's speed
From the table, we can use any data.Pick data #2d = 3 milest = 33 min = 33/60 h = 11/20 hv = d ÷ tLearn more about speed here: https://brainly.com/question/24872445
#SPJ1
On a given day, the price of a gallon of milk had a mean price of $2.03 with a standard deviation of $0.07. A particular food store sold milk for $1.96/gallon. Interpret the Z-score for this gas station. A) The milk price of this food store falls 1 standard deviation below the milk gas price of all food stores. B) The milk price of this food store falls 1 standard deviation above the mean milk price of all food stores. C) The milk price of this food store falls 7 standard deviations above the mean milk price of all food stores. D) The milk price of this food store falls 7 standard deviations below the mean milk price of all food stores.
Three standard deviations contain a portion of the data equal to 88.9%.
That is 3 times $0.11 = $0.33Range is $3.95 ± $.33.What is Chebyshev's theorem?The Chebyshev's Theorem calculates the minimal percentage of observations that are within a certain range of standard deviations from the mean. A wide variety of probability distributions can be used with this theorem. Another name for Chebyshev's Theorem is Chebyshev's Inequality. The likelihood of an occurrence deviating significantly from its predicted value is calculated using Chebyshev's theorem. Contents table: Formula of the Chebyshev theorem. Only data sets with a bell-shaped relative frequency histogram can use the approximate Empirical Rule. It calculates the percentage of measurements that are one, two, or three standard deviations off the mean. All potential data sets can be used to prove Chebyshev's Theorem.According to Chebyshev's theorem, you can use the equation to roughly estimate the fraction of the data that lies within k standard deviations of the mean given a normal distribution.
Portion of data[tex]$=\left(1-1 / k^2\right)$[/tex]
The answer is, per Chebyshev's theorem, the range of of prices in which [tex]$88.9 \%$[/tex] of data lies is [tex]$[\$ 3.62, \$ 4.28]$[/tex].
The equation for Chebyshev's theorem is:
Portion of data [tex]$=\left(1-1 / k^2\right)$[/tex]
Where:
- k is the number of standard deviations a value is from the mean.
In this case the portion of data interest is [tex]$88.9 \%$[/tex]
Solve the equation for k
[tex]& 0.889=\left(1-1 / k^2\right. \\[/tex]
[tex]& -0.111=-1 / k^2 \\[/tex]
[tex]& k^2=1 / 0.111 \\[/tex]
[tex]& k^2=9.0 \\[/tex]
[tex]& k=3.0[/tex]
Three standard deviations contain a portion of the data equal to[tex]$88.9 \%$[/tex].
That is 3 times [tex]$\$ 0.11=\$ 0.33$[/tex]
Range is [tex]$\$ 3.95 \pm \$ .33$[/tex].
The complete question is,
Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.95 with a standard deviation of $0.11. Using Chebyshev's Theorem, state the range in which at least 88.9% of the data will reside.
To learn more about Chebyshev's theorem refer to:
https://brainly.com/question/5179184
#SPJ4
the cost of cheese increased by 25%. how much is the new price of the cheese that originally cost $4.20? please help asap, also give solutions for brainlist
This problem uses the data file called "12th WomanStoresData." Consider the variable Age. 1) What is the standard deviation of the age variable? ___ years. (Round to 4 decimal places if necessary) 2) Now, supposed this variable was distributed normally. Between what two values would you expect to find 95% of the data observations? Answer: Between | ___| (on the low end) and | ___ | (on the high end) Round to 1 decimal place if necessary]
The standard deviation of the Age variable is 8.2195 years. 95% of the data observations fall between 18.8 and 31.1.
1) The standard deviation of the Age variable is 8.2195 years.
2) Between 18.8 and 31.1.
1) To calculate the standard deviation of the Age variable, first calculate the mean of the variable. To do this, add up all of the values and divide by the total number of observations (in this case, 12). The mean is then 24.75. To calculate the standard deviation, subtract the mean from each observation, square the result, and sum the squared differences. Divide the sum by 11 (the total number of observations minus 1), then take the square root of the result. The standard deviation of the Age variable is 8.2195 years.
2) To find the values between which 95% of the data observations fall, calculate the standard deviation multiplied by 1.96. This will give the range for the 95% of the data observations. To find the lower value, subtract the standard deviation multiplied by 1.96 from the mean. For the upper value, add the standard deviation multiplied by 1.96 to the mean. In this case, the lower value is 18.8 and the upper value is 31.1.
The standard deviation of the Age variable is 8.2195 years. 95% of the data observations fall between 18.8 and 31.1.
Learn more about standard deviation here
https://brainly.com/question/13905583
#SPJ4
here is the score data for the ultra-marathon race. assume distribution to be normal. women: 1674, 1622, 1637, 1838, 1964, 1836, 1728, 1913, 1885, 1932; men: 1852, 2403, 2383, 2336, 2597, 2581, 2169, 2120. calculate a 95% two-sided confidence interval on the mean for women and men separately. assume distribution to be normal.
The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.
What is mean?In mathematics, particularly in statistics, there are various types of means. Each mean serves to summarise a certain set of data, frequently in order to better comprehend the overall significance of a specific data set.A dataset's mean (also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe this central tendency statistic.It is calculated by merely dividing the total number of values in a data collection by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.Given data :
calculate a 95% two-sided confidence interval on the mean for women and men separately :
A) The confidence interval for women: [1711.70] <u< [1894.10]
Women = [tex]\frac{1674+ 1622 + 1637 + 1838 + 1964 + 1836 + 1728 +1913 + 1885 + 1932}{10}[/tex] = 1802.9
B) B) The confidence interval for men: [2096.50] <u< [2513.80]
Men = [tex]\frac{1852 + 2403 + 2383 + 2336 + 2597 + 2581 + 2169 + 2120}{8}[/tex] = 2305.125
Learn more about Mean refer to :
https://brainly.com/question/20118982
#SPJ4
