[tex]10[/tex] pupils mean in age from sum [tex]150[/tex] to [tex]15[/tex] years.
What does the math mean?The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from the scaling factor) of a dataset. This indicator of central tendency is usually referred to as the "average".
How is the mean determined?Just dividing the total number of values inside a data collection by the sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table may be utilized in the computation. Often, average is referred to as mean or mathematical mean. Mean is only a way of summarizing the sample's average.
Mean age [tex]=[/tex] (sum of ages) / (number of students)
Mean age [tex]= 150 / 10[/tex]
Mean age [tex]= 15[/tex]
Therefore, the mean age of the [tex]10[/tex] students is [tex]15[/tex] years.
To know more about mean visit:
https://brainly.com/question/31105204
#SPJ1
Ethan invested £500 in the bank for 2 years. He earned £40 simple interest in total. What was the simple interest rate per annum?
Answer:
4%
Step-by-step explanation:
The formula for simple interest is I = Prt, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.
In this case, we know that:
P = £500 (the principal amount)
I = £40 (the interest earned)
t = 2 years (the time the money was invested)
We can rearrange the formula to solve for r:
r = I / Pt
Substituting the given values, we get:
r = 40 / (500 x 2)
r = 0.04 or 4%
Therefore, the simple interest rate per annum is 4%.
solve the inequalities. show each solution as an interval on the number line. 41-x<17
The inequality in the expression [tex]41-x < 17[/tex] is the less than inequality
The solution to the inequality is [tex]x > 24[/tex]
How to solve the inequality?The inequality is given as:
[tex]41-x < 17[/tex]
Subtract 41 from both sides of the inequality
[tex]41 - 41 -x < 17 - 41[/tex]
Evaluate the difference
[tex]-x < -24[/tex]
Multiply both sides by -1
[tex]-1 \times -x < -24 \times -1[/tex]
Evaluate the product
[tex]x > 24[/tex]
all the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday. 24% of the students purchased their lunch. 190 students brought their lunch from home. How many students are in the sixth grade?
In the percentage , the total number of students in sixth grade is 250.
What is percentage?
Percentage is Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.
Here we know that total number of students is 100%.
Students purchased their lunch = 24%
Students brought their lunch from home = 190
Then percentage of students brought their lunch from home is
=> (100%-24%) = 190
=> 76% = 190
Then Total number of students in sixth grade is,
76% = 190
100% = x
=> x = [tex]\frac{190\times100\%}{76\%}[/tex] = 250.
Hence the total number of students in sixth grade is 250.
To learn more about percentage refer the below link
https://brainly.com/question/24877689
#SPJ1
if f ( x ) = f ( g ( x ) ) , where f ( 5 ) = 7 , f ' ( 5 ) = 5 , f ' ( 0 ) = 3 , g ( 0 ) = 5 , and g ' ( 0 ) = 3 , find f ' ( 0 ) .
If f ( x ) = f ( g ( x ) ) , where f ( 5 ) = 7 , f ' ( 5 ) = 5 , f ' ( 0 ) = 3 , g ( 0 ) = 5 , and g ' ( 0 ) = 3 ,f'(0) = 15
We start by using the chain rule to find the derivative of f(x) with respect to x:
f'(x) = f'(g(x)) * g'(x)
Next, we evaluate this equation at x = 0, and use the given values to solve for f'(0):
f'(0) = f'(g(0)) * g'(0)
f'(0) = f'(5) * 3 (since g(0) = 5 and g'(0) = 3)
Now, we need to find f'(5) using the given information. We can start by using the definition of the derivative:
f'(5) = lim h->0 [f(5+h) - f(5)] / h
We know that f(5) = 7, so we can simplify this expression:
f'(5) = lim h->0 [f(5+h) - 7] / h
Using the fact that f(x) = f(g(x)), we can substitute g(x) for x:
f'(5) = lim h->0 [f(g(5+h)) - 7] / h
Now, we can use the mean value theorem to approximate f(g(5+h)):
f'(5) = lim h->0 [f'(g(c)) * g'(5+h)] / 1
where 5 < c < 5 + h. Since f'(5) = 5 and g'(5) = 3, we can simplify this expression:
f'(5) = lim h->0 [5 * 3] / 1 = 15
Therefore, we have found that f'(0) = f'(5) * 3 = 5 * 3 = 15.
For more questions like Equation click the link below:
https://brainly.com/question/29657983
#SPJ11
a visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an island. the island is 7 miles due south of the shoreline. the visitor plans to travel from the cottage to the island by running and swimming. if the visitor runs at a rate of 5 mph and swims at a rate of 3 mph, how far should the visitor run to minimize the time it takes to reach the island?
The visitor should run 1.2 miles to minimize the time it takes to reach the island.
Consider the following figure.
Let us assume that x (CD) represents the distance covered when visitor runs at a rate of 5 mph
So, the time taken by visitor would be:
t₁ = x/5
Let the distance covered 10 - x when visitor swims at a rate of 3 mph
From figure consider right triangle ABC.
Using Pythagoras theorem,
BC² = 7² + (10 - x)²
BC = [tex]\sqrt{49 + (10-x)^2}[/tex]
Now the times taken by visitor when he swims at a rate of 3 mph,
t₂ = [tex]\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]
so, the total time would be:
t = t₁ + t₂
[tex]t=\frac{x}{6}+\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]
Differentiating with respect to x we get,
[tex]\frac{dt}{dx}=\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}[/tex]
consider dt/dx = 0
[tex]\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}=0[/tex]
If we solve above equation for x we get, x = 11.2 and x = 8.8
The distance the visitor should run to minimize the time would be:
10 - 8.8 = 1.2 miles
Therefore, the required distance is 1.2 miles
Learn more about the Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ4
The exchange rate at the post office is £1= 1.17 euros
How many euros will you get for £280?
Answer:
The exchange rate at the post office is £1= 1.17 euros
How many euros will you get for £280?
Step-by-step explanation:
280 * 1.17 = 327.6
find the volume: height - 4 1/2 width - 3 1/3 length - 5
HELP!!!
Answer:
= 75 cubic units
Step-by-step explanation:
Volume = height * width * length
Then:
volume = 4 1/2 * 3 1/3 * 5
4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2
3 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3
Then:
volume = 9/2 * 10/3 * 5/1
volume = (9*10*5) / (2*3*1)
volume = 450 / 6
Volume = 75 cubic units
Thomas has some leftover paint that he would like to sell. he mixes 4 3 8 gallons of blue paint with 6 5 8 gallons of white paint. then, he pours this light-blue mixture into 1 4 gallon containers. to find out how many of these 1 4 gallon containers he can fill, which two equations would you need?
Thomas can fill 35 of these 1/4 gallon containers with the light-blue mixture.
To find out how many 1/4 gallon containers Thomas can fill with the light-blue mixture, we need to divide the total volume of the mixture by the volume of one container.
The total volume of the mixture can be found by adding the volumes of blue and white paint that Thomas mixed
Total volume = 4 3/8 gallons + 6 5/8 gallons
To add these mixed numbers, we need to find a common denominator, which is 8
Total volume = (4 x 8 + 3) / 8 gallons + (6 x 8 + 5) / 8 gallons
Total volume = 35/8 gallons
Now we can set up the two equations
Total volume = number of containers x volume per container
We know the total volume is 35/8 gallons, and the volume per container is 1/4 gallon, so we can write
35/8 = (1/4) x number of containers
Number of containers = total volume / volume per container
We can rearrange the above equation to solve for the number of containers
Number of containers = total volume / volume per container
Number of containers = 35/8 / 1/4
Number of containers = 35/8 x 4
Number of containers = 35
Learn more about total volume here
brainly.com/question/13436458
#SPJ4
The given question is incomplete, the complete question is:
Thomas has some leftover paint that he would like to sell. he mixes 4 3/8 gallons of blue paint with 6 5/8 gallons of white paint. then, he pours this light-blue mixture into 1/4 gallon containers. find out how many of these 1/4 gallon containers he can fill?
Quadrilateral PQRS is a parallelogram. What is m∠KSP?
The measure of angle m∠KSP is 14⁰.
What is the special property of a parallelogram?
A special property of a parallelogram is that opposite angles are equal in measure. This means that if you take any two angles of a parallelogram that are opposite each other, they will have the same degree measure.
The measure of angle m∠KSP is calculated as follows;
The measure of angle P and R = ¹/₂[ 360 - (76 x 2)] (sum of angles in quadrilateral )
The measure of angle P and R = 104
The measure of QPK = 180 - (76 x 2) (sum of angles in a triangle )
The measure of QPK = 28⁰
Angle P consists of QPK plus KPS
KPS = 104 - QPK
KPS = 104 - 28
KPS = 76
The measure of angle m∠KSP is calculated as;
KSP = 180 - (90 + 76) ( sum of angles in a triangle)
KSP = 14⁰
Learn more about angle of parallelogram here: https://brainly.com/question/20526916
#SPJ1
Answer:
38
Step-by-step explanation:
We know that Q and P are supplementary because they are parallelograms.
So,
180 - < Q = < P Use substitution
180 - 76 = < P Solve
180 - 76 = 104
104 = < P
Since we know that < QPK and < KPS are congruent and are apart of < P we can multiply < P by 1/2 to find either < QPK or < KPS.
So,
1/2(104) Simplify using distributive property
52
If a shape is a triangle, then it’s interior angles all add up to 180.
< KPS + < PKS + < KSP = 180 Use substitutions
52 + 90 + < KSP = 180 Move variables to one side
< KSP = 180 - 52 - 90 Simplify
< KSP = 38
And there’s your answer: 38
exercise 4.36. how many randomly chosen guests should i invite to my party so that the probability of having a guest with the same birthday as mine is at least 2/3?
You should invite at least 23 guests to your party to have at least a 2/3 chance of having a guest with the same birthday as yours.
For your party, you need to invite at least 23 randomly chosen guests in order to have a probability of 2/3 or higher of having a guest with the same birthday as yours. This is known as the birthday paradox and it is based on the probability of two people having the same birthday. To calculate the number of guests needed for the probability of having at least one match, you can use the following formula:
P(at least one match) = 1 - (365/365)^n
where n is the number of guests you invite.
So, to solve for n, you would rearrange the equation to:
n = ln(1-P) / ln(365/365)
When P = 2/3, this equation gives us n = 23.
To learn more about probability visit : https://brainly.com/question/13604758
#SPJ11
What does the differences between the price after value added tax (VAT) and price after discount of any article give us?
Answer:
The difference between the price after value added tax (VAT) and the price after discount of an article gives us the actual amount of money saved by the customer.
The price after VAT is the price of the item including the tax imposed by the government, whereas the price after discount is the price of the item after any promotional or discounted price reduction. By subtracting the price after discount from the price after VAT, we can determine the actual amount saved by the customer, which is the discount amount minus any VAT paid on the original price.
For example, if an item originally cost $100 with a 10% VAT, the price after VAT would be $110. If the item was discounted by 20%, the price after discount would be $80. The difference between the price after VAT and the price after discount would be $30, which is the actual amount saved by the customer ($20 discount minus $10 VAT paid on the original price).
Step-by-step explanation:
To calculate the actual amount saved by the customer, we need to follow these steps:
Determine the original price of the item. For example, let's say the original price of the item is $100.
Calculate the VAT amount paid on the original price. To do this, multiply the original price by the VAT rate as a decimal. For example, if the VAT rate is 10%, then the VAT amount would be:
VAT amount = original price x VAT rate
VAT amount = $100 x 0.1
VAT amount = $10
So, the VAT amount paid on the original price of $100 is $10.
Determine the discounted price of the item. For example, let's say the item is discounted by 20%, so the discounted price is:
Discounted price = original price - (original price x discount rate)
Discounted price = $100 - ($100 x 0.2)
Discounted price = $80
So, the discounted price of the item is $80.
Calculate the actual amount saved by the customer. To do this, subtract the discounted price from the price after VAT. For example:
Actual amount saved = price after VAT - discounted price
Actual amount saved = $110 - $80
Actual amount saved = $30
So, the actual amount saved by the customer is $30, which is the discount amount minus the VAT paid on the original price.
The arithmetic mean of the numbers -2,3,0,-15,5,-20,-4 .Could you explain the solution in steps? Thanks in advance!
Answer:
Step-by-step explanation:
The mean is found by adding the numbers and dividing by how many numbers there are.
[tex]Mean=\frac{-2+3+0-15+5-20-4}{7} =\frac{-33}{7} =-4\frac{5}{7}[/tex]
17.Two paddocks in the shapes shown below are to be fenced with wire. If the same total
amount of wire is used for each paddock, what are the dimensions of each paddock in
metres?
you know that i have gave wrong Ans
explanation: because i need points
Answer:
Step-by-step explanation:
where’s the figure ?
Which algebraic rule describes the reflection of FG.
Answer: A. (x,y)----->(x,-y)
because their x coordinates are all -6. But their y coordinates are 6 and -6.
a ticket for an evening movie costs 1.5 times more than a ticket for a matineé movie. enter an equation that can be used to find the price of a ticket to a matineé movie, m, if the cost of a ticket to an evening movie is $13.50.
The equation for the cost of ticket 13.50 = 1.5m is and the price for a matinee movie ticket is $9.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Let's use "m" to represent the price of a ticket to a matinee movie.
From the given information, we know that the cost of a ticket to an evening movie is 1.5 times more than a ticket for a matinee movie.
This means that -
Cost of an evening movie ticket = 1.5 × Cost of a matinee movie ticket
We also know that the cost of a ticket to an evening movie is $13.50.
Substituting this value into the equation above, we get -
$13.50 = 1.5m
To solve for "m", we can divide both sides of the equation by 1.5 -
$13.50 / 1.5 = m
m = $9
Therefore, the price of a ticket to a matinee movie is $9.
To learn more about equation from the given link
https://brainly.com/question/28871326
#SPJ1
I need help on these three pages please asap. Thank you!
Step-by-step explanation:
Example 1:
Given pair: (3;2)
{2x + 3y = 12,
{x - 4y = -5;
Make x the subject from the 2nd equation:
x = -5 + 4y
Replace x in the 1st equation:
2 × (-5 + 4y) + 3y = 12
-10 + 8y + 3y = 12
11 y = 12 + 10
11y = 22 / : 11
y = 2
y = 2x = -5 + 4 × 2 = -5 + 8 = 3
The answer: (3;2)
The given pair is the solution of the system of equations
.
Example 2:
Given pair: (0; -4)
{x + y = -4,
{x - 5y = 20;
x = -4 - y
(-4 - y) - 5y = 20
-4 - y - 5y = 20
-6y = 20 + 4
-6y = 24 / : (-6)
y = -4
y = -4x = -4 - (-4) = -4 + 4 = 0
The answer: (0; -4)
The given pair is the solution
.
Example 3:
Given pair: (3;3)
{x + 2y = 9,
{4x - y = 15;
x = 9 - 2y
4(9 - 2y) - y = 15
36 - 8y - y = 15
-9y = 15 - 36
-9y = -21 / : (-9)
[tex]y = 2 \frac{1}{3} [/tex]
[tex]x = 9 - 2 \times 2 \frac{1}{3} = 9 - 2 \times \frac{7}{3} = 9 - \frac{14}{3} = \frac{13}{3} = 4 \frac{1}{3} [/tex]
The given pair is not the solution
.
Example 4:
Given pair: (1; -2)
{2x - 3y = 8,
{3x + 2y = -1;
2x = 8 + 3y / : 2
x = 4 + 1,5y
3(4+1,5y) + 2y = -1
12 + 4,5y + 2y = -1
6,5y = -1 - 12
6,5y = -13 / : 6,5
y = -2
y = -2x = 4 + 1,5 × (-2) = 4 - 3 = 1
The given pair is the solution
.
Example 5:
Given pair: (1;5)
{5x - 2y = -5,
{3x - 7y = -32;
-2y = -5 - 5x / : (-2)
y = 2,5 + 2,5x
3x - 7(2,5 + 2,5x) = -32
3x - 17,5 - 17,5x = -32
-14,5x = -32 + 17,5
-14,5x = -14,5 / : (-14,5)
x = 1
x = 1y = 2,5 + 2,5 × 1 = 5
The given pair is the solution
.
Example 6:
Given pair: (-1; -3)
{3x + y = -6,
{2x = 1 + y;
y = -6 - 3x
2x = 1 + (-6 - 3x)
2x = 1 - 6 - 3x
2x + 3x = 1 - 6
5x = -5 / : 5
x = -1
x = -1y = -6 - 3 × (-1) = -6 + 3 = -3
The given pair is the solution
A study on students drinking habits wants to determine the true average number of alcoholic drinks all FSU graduate students have in a one week period. We know from preliminary studies that the standard deviation is around 1.79. How many students should be sampled to be within 0.5 drinks of population mean with 95% probability?
A. 50
B. 49
C. 24
D. 25
how could you use your graphing calculator to determine that a polynomial function is not the correct factorization of another polynomial function. explain
By answering the presented question, we may conclude that If the two graphs are identical, F(x) may polynomials be a valid factorization of G(x), but more study is required to establish this.
what are polynomials?A polynomial is a mathematical statement composed of variables and coefficients that be combined using only addition, subtraction, multiplication, and non-negative integer exponents. The phrase 2x3 + 5x2 - 3x + 1 is a polynomial, for example, where x is the variable and the coefficients of the various components are 2, 5, -3, and 1. Polynomials may include one or more variables, but each term must have the same variable (s). The degree of a polynomial is the highest exponent of its variable (s). In the above example, the degree of the polynomial is 3. Polynomials are used in many areas of mathematics, including algebra, calculus, and numerical analysis.
If you believe that one polynomial function is not the right factorization of another, you may use your graphing calculator to confirm this by graphing both functions and comparing their graphs.
Then, in your calculator, insert the polynomial function that you believe is the right factorization. Let us refer to this function as G. (x).
Graph the function G(x) on your calculator by hitting the "graph" button or the equivalent button.
Examine the two graphs. If the two graphs disagree, F(x) does not represent the right factorization of G. (x). If the two graphs are identical, F(x) may still be a valid factorization of G(x), but more study is required to establish this.
To know more about polynomials visit:
https://brainly.com/question/11536910
#SPJ1
Question content area top
Part 1
If the simple interest on $ for years is $, then what is the interest rate?
Hence, the interest rate is 0.03 percent, or 3%. it is expressed as a percentage .
what is interest ?The amount of money earned or charged on a principal sum of money over time is referred to as interest in mathematics. In financial transactions like loans, investments, and savings accounts, it is frequently utilized. Simple interest is calculated for the full time period as a fixed percentage of the principal amount. For instance, after a year, you would owe $50 in interest if you borrowed $1,000 at a simple interest rate of 5% per year.
given
We can use the following formula for simple interest to determine the interest rate given the principal, period, and simple interest:
I = P * r * t
where r is the interest rate expressed as a decimal, P is the principal, I is the simple interest, and t is the amount of time in years.
This formula can be changed to account for the interest rate:
r = I / (P * t)
In this instance, the principal, period, and simple interest are all provided. These values can be plugged in to find the interest rate:
r = I / (P * t)
r = 600 / (4000 * 5)
r = 0.03
Hence, the interest rate is 0.03 percent, or 3%. it is expressed as a percentage .
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
Can anyone help with how the answer is 2/5 for k?
Answer:
k = 2/5
Step-by-step explanation:
Given a diagram with triangles ONM and OAB such that M is the midpoint of OB, A lies on AN with AN = 2·OA, and P is the point of intersection of NM and AB, you want the ratio AP/AB.
ProportionPlease refer to the attached diagram.
Point C is located at the midpoint of AN, which makes OA≅AC≅CN, or AN is 2/3 of ON. Segments AD and CE are parallel to AN, so divide OM into thirds. The length DM is 2 of those thirds, and the length MB is equal to OM, so is 3 of those thirds. That is, the ratio DM/DB is (2/3)/(2/3+3/3) = 2/5.
Triangle BAD is similar to triangle BPM, so the ratio AP/AB is also 2/5.
consider the quadratic equation x^2-10x=-29. A: is x=5+2i a solution to the equation? how can you be sure without solving?
B: without solving, predict another solution to the equation. verify your prediction by checking it.
C: where does the parabola y=x^2-10x+29 intersect the x-axis? Explain.
A.
by simply putting the suggested solution into the equation and see if it stays true. if yes, it is a solution.
(5 + 2i)² - 10(5 + 2i) = -29
25 + 20i - 4 - 50 - 20i = -29
21 - 50 = -29
-29 = -29 true
yes, it is a solution.
B. for a parabola the 2 solutions are usually symmetrical around the center line.
so, I suspect 5 - 2i to be a solution too.
(5 - 2i)² - 10(5 - 2i) = -29
25 - 20i - 4 - 50 + 20i = -29
21 - 50 = -29
-29 = -29 true
yes, it is a solution too.
C.
nowhere.
with 2 complex solutions there are no real number solutions left. and that means there is no intersection with the x-axis.
every quadratic equation must have 2 and only 2 solutions. a solution is normally an intersection with the x-axis (the x- value when y = 0).
On a circular playground the distance from its center to the edge of the playground is 38 feet. What is the approximate circumference of the playground (use 3.14 for pi)
Answer:
238.64
Step-by-step explanation:
center to edge is a radius
2pi(radius) = circumference, so 6.28(38) = circumference = 238.64
Write the equation of the ellipse using the given information, The ellipse has foci (2,0) and (-2,0) and major vertices (4,0) and (-4,0)
Answer:
The equation of the ellipse is:
(x^2)/16 + (y^2)/4 = 1
Step-by-step explanation:
An ellipse is a set of points on a plane, the sum of whose distances from two fixed points (called foci) is constant. The distance between the foci of an ellipse is denoted by 2c, and the distance between the center of the ellipse and one of its vertices is denoted by a.
In this problem, the foci are located at (2,0) and (-2,0), so the distance between the foci is 2c = 4, which means that c = 2. The major vertices of the ellipse are located at (4,0) and (-4,0), so the distance between the center and one of the vertices is a = 4.
The formula for the equation of an ellipse centered at the origin is:
(x^2)/(a^2) + (y^2)/(b^2) = 1
where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex. Since the center of this ellipse is at the origin and the major axis lies on the x-axis, we know that b = a, so we can substitute a for b in the equation:
(x^2)/(a^2) + (y^2)/(a^2) = 1
To find a, we use the fact that c^2 = a^2 - b^2:
a^2 - b^2 = c^2
a^2 - a^2 = 4
b^2 = 4
b = 2
Now we can substitute a = 4 and b = 2 into the equation:
(x^2)/(16) + (y^2)/(4) = 1
This is the equation of the ellipse.
Find y, 3y + 7y - 84 = 180
Answer:
26.4
Step-by-step explanation:
You can add Y together because they have the same variable making it 10y
The equation is now 10y - 84 = 180
Add 84 to 180 since on the left side it was -84 (Imagine it crossed a magic bridge and become the opposite of what it is)
The equation is now 10y = 264
Divide the equation by 10 because 10 crossed a "magic bridge" to the other side and became division instead of multiplication
The equation is now solved = 26.4
We can cross check this by adding it to the first equation
3(26.4) + 7(26.4) - 84
which gives us 180
Hope this helps
Answer: y=26.4
Step-by-step explanation:
First we need to simplify 3y+7y .... that would be 10y.
Now we have 10y-84=180. We can add 84 to both sides of the equation
So now we have 10y= 180+84 = 10y= 264
Divide both sides by 10= y= 26.4
Now we can check this answer by inputting 26.4 to all the y values in the equation.
(3*26.4) +(7*26.4) - 84=180
79.2 + 184.8 -84=180
180=180 so we know 26.4 is the correct answer
Find the median and mean of the data set below: 19 , 20 , 40 , 3 , 17 , 5 , 22
Answer:
Median: 19
Mean: 18
Step-by-step explanation:
Numbers: 19, 20, 40, 3, 17, 5, 22
Number in order from least to greatest: 3, 5, 17, 19, 20, 22, 40
The median is the number in the middle of a data set.
The median is: 19
The mean is the average of a set of data.
The mean is: [tex]\frac{3 + 5 + 17 + 19 + 20 + 22 + 40}{7}[/tex] = 18
So, Median is 19
Mean is 18
One angle of a triangle measures 85°. The other two angles are in a ratio of 9:10. What are the measures of those two angles?
Answer:
Let x be the first unknown angle, and y be the second unknown angle.
We know that the sum of the three angles in a triangle is 180 degrees, so:
85 + 9kx + 10kx = 180
where k is a constant representing the ratio of the other two angles.
Simplifying the equation, we get:
19kx = 95
Dividing both sides by 19k, we get:
x = 5/k
Since the ratio of the other two angles is 9:10, we know that:
y = 9kx = 9k(5/k) = 45
So the measures of the two unknown angles are:
x = 5/k and y = 45
We cannot find the exact measures of x and y without more information, but we know that x and y are in a ratio of 9:10 and their sum is 180 - 85 = 95 degrees. We can set up the following equation to solve for k:
5/k + 45/k = 95
50/k = 95
k = 50/95
Using this value of k, we can find the measures of x and y:
x = 5/k = 5/(50/95) = 9.5
y = 9kx = 9(50/95)(9.5) = 47.37
Therefore, the measures of the two unknown angles are x = 9.5 degrees and y = 47.37 degrees (rounded to two decimal places).
Step-by-step explanation:
The area of square C is 100 square units and the area of square B is 64 square units. What would be the area of square A? CA? 64 units A B. C. D. 100 units² 2 units 6 units 36 units 64 units 164 units
We don't have enough information to determine the exact side length of either square A or square C, so we cannot directly calculate their areas. However, we can use the relationship between the areas of the squares to make some conclusions.
Since the area of square B is 64 square units, we know that its side length is √64 = 8 units.
Similarly, since the area of square C is 100 square units, we know that its side length is √100 = 10 units.
Square A is composed of square B and four identical triangles. We know the area of square B is 64 square units, so we need to determine the area of the four triangles to find the area of square A.
Each triangle has a base of 8 units (which is also the length of one side of square B) and a height of half the length of one side of square A. Let's call this length x.
The area of one triangle is (1/2) * 8 * x = 4x square units.
The total area of the four triangles is 4 times the area of one triangle, which is 16x square units.
Therefore, the area of square A is 64 + 16x square units.
We still don't know the exact value of x, but we can make some observations. Since square A is larger than square B, we know that x > 4. And since the triangles make up exactly half of square A (the other half being square B), we know that the area of square A is twice the area of the four triangles. Therefore:
64 + 16x = 2(16x)
64 + 16x = 32x
64 = 16x
x = 4
So the length of each side of square A is 8 + 2x = 16 units, and its area is 64 + 16x = 128 square units.
The length of CA is just the length of one side of square C, which is 10 units.
the demand over lead time is normally distributed with a mean of 80. the reorder point for a 95% service level is 119. what is the standard deviation of demand over the lead time
The standard deviation of demand over the lead time is 23.72.
The demand over lead time is normally distributed with a mean of 80. The reorder point for a 95% service level is 119. To calculate the standard deviation of demand over the lead time, we need to use the following formula:
z = (x - μ) / σ, where z is the number of standard deviations from the mean, x is the reorder point for a 95% service level, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
To solve for σ, we need to first find the z-score for a 95% service level, which can be obtained from the standard normal distribution table.
The z-score for a 95% service level is 1.645.
Substituting the given values in the formula, we get:
1.645 = (119 - 80) / σ
Solving for σ, we get:σ = (119 - 80) / 1.645
σ = 23.72
Therefore, the standard deviation of demand over the lead time is 23.72.
To learn more about standard deviation visit : https://brainly.com/question/475676
#SPJ11
Explanation and steps please.
Tel Chords intersecting Theorem 3, Solve for X?
Answer:
x = 10
Step-by-step explanation:
You want to find the value of x, where a chord of segment lengths 9 and x crosses a chord of segment lengths 6 and 15.
Intersecting chordsThe product of the segment lengths is the same for intersecting chords:
9x = 6·15
x = 90/9 . . . . divide by 9
x = 10
please help my math assignment dues pleaseee
The time period required is 31.91 months(Approx)
The monthly payments based on the given information would be $129.88
How to solve
Putting into a financial calculator;
PV=-1245
PMT=50
I/Y=(19/12)=1.58333333%
Solving for N;we get N=31.91
Hence time period required=31.91 months(Approx)
b.Putting into a financial calculator;
PV=-2456.80
N=(2*12)=24
I/Y=(23.99/12)=1.99916667%
Solving for PMT;we get PMT=129.88
Hence monthly payments=$129.88(Approx)
Read more about interest rates here:
https://brainly.com/question/2294792
#SPJ1