***Important... Even though the question says 15m, the question owner says he meant to put 16m***
[tex]a^2+b^2=c^2\\\\16^2+30^2=34^2\\\\256+900=1156\\\\1156=1156[/tex]
True!
⭐ Answered by Hyperrspace (Ace) ⭐
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⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Forty-seven percent of fish in a river are catfish. Imagine scooping out a simple random sample of 25 fish from the river and observing the sample proportion of catfish. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.
The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
The standard deviation is 0.0998. The 10% condition is not met because there are less than 250 catfish in the river.
The standard deviation is 0.9002. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
The standard deviation is 0.9002. The 10% condition is not met because there are less than 250 catfish in the river.
We are unable to determine the standard deviation because we do not know the sample mean. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Answer:
Therefore the correct option is a.) The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Step-by-step explanation:
i) Let p = 0.47
ii) therefore q = 1 - 0.47 = 0.53
iii) sample size, n =25
iii) standard deviation = [tex]\sqrt{\frac{p \times q}{n} } = \sqrt{\frac{0.47 \times 0.53}{25} } = 0.0998[/tex]
Therefore the correct option is
a.) The standard deviation is 0.0998. The 10% condition is met because it
is very likely there are more than 250 catfish in the river.
The standard deviation of the sampling distribution of the sample proportion is 0.0998. To determine whether the 10% condition is met, the total population of catfish should be at least 10 times the sample size.
Explanation:The question asks about determining the standard deviation of the sampling distribution of the proportion of catfish in a river and if the 10% condition is met for the sampling distribution to be approximately normal. First, to calculate the standard deviation of the sampling distribution of the sample proportion (p-hat), we use the formula √[(p(1-p))/n], where p is the population proportion and n is the sample size. In this case, p = 0.47, so 1 - p = 0.53, and n = 25. The standard deviation is then √[(0.47*0.53)/25], which is approximately 0.0998.
Next, the 10% condition checks whether we can consider the population large enough that the sample size doesn't affect the population proportion notably when taking without replacement. This condition states that the sample size, n, should be no more than 10% of the population. If there are indeed more than 250 fish in the river (10 times the sample size), we can be confident that the 10% condition is met. If not, the condition is not met.
Therefore, the correct response would state the standard deviation and appropriately evaluate whether the 10% condition is met based on the estimated number of catfish in the river.
Sara bought a car for $15700 with interest rate of 5 3/7% and the contract is for 7 years.
How much interest will Sara owe? How much will the payments be with a seven year agreement?
1. How much interest will Sara owe?
She will owe 5,966 dollars
2. How much will the payments be with a seven year agreement?
Sara will pay 21,666 dollars
Explanation:The simple interest formula is as follows:
[tex]A=P(1+rt) \\ \\ \\ Where: \\ \\ A: \ is \ the \ Final \ Investment \Value \\ \\ P: \ is \ the \ Principal \ amount \ of \ money \ to \ be \ invested \\ \\ r: \ is \ the \ rate \ of \ interest \\ \\ t: \ is \ \ Number \ of \ Time \ Periods[/tex]
First, converting r percent to r a decimal
[tex]r = (5 \frac{3}{7})\%=(5+\frac{3}{7}))\%=\frac{38}{7}\% \\ \\ r=\frac{38/7}{100}=\frac{19}{350} \ per \ year[/tex]
Solving our equation:
[tex]A=15700 (1+\frac{19}{350}\times 7) \\ \\ A=15700(\frac{69}{50}) \\ \\ \boxed{A=\$21,666}[/tex]
So Sara will owe in interest the following amount of money:
[tex]I:Interest \\ \\ \\ I=21,666-15,700 \\ \\ \boxed{I=\$5,966}[/tex]
Finally, answering the questions:
1. How much interest will Sara owe?
She will owe 5,966 dollars
2. How much will the payments be with a seven year agreement?
Sara will pay 21,666 dollars
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Length 30.25
Volume7193.45
Width 14.5
What is the width?
Answer:
Height = 16.4 inches
Step-by-step explanation:
V = Length*Width*Height, so solving for the Height by dividing the Volume with the product of the Length and Width gives:
Height = Volume/Length*Width = 7193.45/(30.25*14.5) = 16.4 inches
3y + 2/5 = -1/5 what is y?
Answer:
3.6
Step-by-step explanation:
3y+2/5=-1/5
3y=-1/5-2/5
3y=-0.6
0.6/3=y
-3.6=y
y=-3.6
Plzzzzzzzz help will give brainliest!!!!!!!!
[tex]A = 100\pi cm^{2}[/tex]
Step-by-step explanation:
Given that an engineer is planning to install a new water pipe.
The diameter of the circular pipe is
d = 20 cm
Let us find the radius (r)
radius = diameter / 2
r = 20 / 2 = 10 cm
The area of circle (A) is given as:
[tex]A = \pi r^{2}[/tex]
[tex]A = \pi 10^{2}[/tex]
[tex]A = 100\pi cm^{2}[/tex]
Topic/Objective: Function Applications pp. 228-252
• Write the equation of a linear function and determine the rate of change of the function using a point on the line and the slope of the line.
Write the equation of a linear function and determine the rate of change of the function using two points on the line.
• Determine whether a function is linear or nonlinear using a graph.
• Determine whether a function is linear or nonlinear using a table.
• Determine whether a function is linear or nonlinear using an equation.
• Compare the properties of two linear functions that are represented differently.
Name
Class/Time
Date
Essential Question: How can we model relationships between quantities?
Questions/Voc. Terms/Properties
Define the vocabulary terms below:
Linear function
Nonlinear function
Increasing function
Decreasing function
Constant
How can linear models be interpreted?
How are independent and dependent variables represented on a coordinate plane?
What is the slope and y-intercept of the helicopter altitude from the graph?
What does 35 and 1.2 in the equation represent in the equation?
Describe the situation each equation represents for the water level in other tanks.
How can we represent the water level in a tank that’s empty at first but rises at a rate of 2.1 /s?
What is the process for solving problems involving constant rates?
What is the total cost for movie rental for 1 month? 5 months? 7 months? 1 year?
Is this a linear model? Explain.
What describes the relationship between the independent and dependent variables of the function?
What determines whether a function is linear or nonlinear?
How can we determine if a function is increasing or decreasing?
How can we determine whether a graph is increasing or decreasing?
How can functions be compared?
How can functions be represented?
How can we determine which line has a greater rate of change?
When interpreting a function graph, what key features can we look for?
How can we draw conclusions about an object’s speed?
Example Problems & Steps/Vocabulary Definitions/Property Descriptions
Write/type definitions beside each term below:
p. 228 Copy yellow box
p. 228 Copy purple box
pp. 228-229 Study graph and copy solutions below:
Example 1
A.
B.
pp. 229-230 Copy solution below:
Example 2
A.
p. 230 Copy solution below:
B.
p. 230 Copy solution below:
C.
pp. 231-231 Study table and graph and copy steps below:
Example 1
pp. 232-233 Study table and copy solution below:
Example 2
A.
Study rate of change between values and copy solution below:
B.
p. 234 See yellow box
pp. 234-235 Study tables & graph and copy solutions below:
Example 1
A. y = 2x - 1
B.
pp. 236 See pink box
pp. 236-237 Study graphs and write solutions below:
Example 2
A.
B.
C.
D.
p. 240 See yellow box
p. 240 See paragraph
Study functions pp. 240-244
p. 244 see graph and pink box
p. 246
p. 247 see pink box
Study pp. 247-252
Summary: Connections, Reflections, Analysis about what you learned (3 or more sentences, or you may use the following prompts - be specific):
Today my notes say…
I can use my notes to…
My notes mean…
Answer:
Are the following linear or nonlinear? Circle the correct response.
Step-by-step explanation:
The numder are hard to explain but
You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.
Answer:Your answer i
Step-by-step explanation:You can tell if a table is linear by looking at how X and Y change.
fine the equation of m= -5 (-1,3)
Answer:
The required equation to the given slope m=-5 and a point (-1,3) is 5x+y+2=0
Step-by-step explanation:
Given that the slope m=-5 and a point (-1,3)
Now we have to find an equation with the given slope and point :
Let [tex](x_1,y_1)[/tex] be the given point (-1,3)
The slope point formula is [tex]y-y_1=m(x-x_1)[/tex]
y-3=-5(x-(-1))
y-3=-5(x+1)
y-3=-5(x)-5(1) ( by using the distributive property a(x+y)=ax+ay here a=-5,x=x and y=1 )
y-3=-5x-5
y-3-(-5x-5)=-5x-5-(-5x-5) ( by using the distributive property a(x+y)=ax+ay here a=-1,x=-5x and y=-5)
y-3+5x+5=-5x-5+5x+5
y+2+5x=0
5x+y+2=0 which is the required equation
A circular playground has an area of about 1500 square feet. If the committee decides to double the radius, what is the approximate area of the new playground?
If the committee decides to double the radius, the approximate area of the new playground is; A_new = 6000 sq.ft
How to find the area of a Circle?We are given the area of a circular playground as;
A = 1500 ft²
Formula for area of Circle is;
A = πr²
Thus;
πr² = 1500
r = √(1500/π)
Now, they want to double the radius. Thus approximate area of the new playground is;
A_new = π * [2√(1500/π)]²
A_new = π * [4(1500/π)]
A_new = 6000 sq.ft
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Answer:
c
Step-by-step explanation:
time 4 learning and it was right people :)
How much cashews at $1.58 per pound must be mixed with walnuts that cost 78 cents per pound to make a mixture of 40 pounds of nuts that cost $1.50 per pound?
Answer:
Cashew= 36 pounds
Walnut= 4 pounds
Step-by-step explanation:
Given: Cost of Cashew= $1.58 per pound
Cost of walnut= $0.78 per pound
Total weight of mixture= 40 Pound
Cost of mixture= $1.50 per pound.
Lets assume the amount of cashew added in the mixture be "x".
∴ Amount of Walnut in the mixture will be [tex](40-x)[/tex]
Now, forming an equation to total cost and weight of mixture.
⇒ [tex]1.58\times x+0.78 \times (40-x)= 40\times 1.50[/tex]
Using distributive property of multiplication
⇒ [tex]1.58x+31.2-0.78x= 60[/tex]
⇒[tex]0.8x+31.2= 60[/tex]
Subtracting both side by 31.2
⇒[tex]0.8x= 60-31.2[/tex]
⇒[tex]0.8x= 28.8[/tex]
Dividing both side by 0.8
⇒[tex]x= \frac{28.8}{0.8}[/tex]
∴ [tex]x= 36\ pounds[/tex]
Hence, Amount of cashew added in the mixture of nuts is 36 pounds.
Next finding the amount of walnut added in the mixture.
subtituting the value of x
Amount of walnut in the mixture= [tex](40-x)[/tex]
⇒ Amount of walnut in the mixture= [tex](40-36)= 4\ pounds[/tex]
Hence, 4 pounds of walnut added in the mixture.
Final answer:
To make a 40-pound mixture of nuts that costs $1.50 per pound, mix 36 pounds of cashews, which cost $1.58 per pound, with walnuts costing $0.78 per pound.
Explanation:
Let's approach this mixture problem using the concept of weighted averages. We know we want to make a 40-pound mixture of cashews and walnuts that costs $1.50 per pound.
The cashews cost $1.58 per pound and the walnuts cost $0.78 per pound. To find out how many pounds of cashews to mix with walnuts, we can set up the equation:
Let x be the amount of cashews needed.
Since the total weight of the mixture is 40 pounds, the amount of walnuts needed would be 40 - x pounds.
Using the equation for the total cost of the mixture: 1.58x + 0.78(40 - x) = 1.50(40),
we solve for x:
1.58x + 31.2 - 0.78x = 600.8x = 28.8x = 36Therefore, to obtain a 40-pound mixture costing $1.50 per pound, a person should mix 36 pounds of cashews with walnuts.
The polynomial 4x^3 - 6x^2 + 8x – 12 can be grouped in different ways to factor by
grouping.
Try it both ways:
(4x3 – 6x>) + (8x – 12)
(4x3 + 8x) + (- 6x2 – 12)?
Answer:
(4x3-6x) + (8x-12)= 2x
(4x3+8x) + (-6x2-12)= 2(2x-3) (x^2+2)
Step-by-step explanation:
All you have to do is simplify.
Answer:
A,B,E
Step-by-step explanation:
Did on edgen
You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you
has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium.
How many seats does the auditorium contain? (Hint: Find the number of seats in the first
and last rows)
A. 2,604
B. 2,163
C. 2,422
D. 2,803
Answer: A. 2,604
Step-by-step explanation:
According to the given information the number of sets in rows following arithmetic progression (in short form AP).
Where , 23rd term is 65.
Common difference = 65-63=2
nth term in AP: [tex]a_n=a+(n-1)d[/tex]
For n= 23 , we have [tex]a_{23}=65[/tex] , d= 2
[tex]23=a+(23-1)2\\\\ 23= a+(22)2\\\\ 23=a+44\\\\ a=44-23=21[/tex]
Formula for the sum of first n terms in AP= [tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Since, There are 42 rows in the auditorium.
Then,
[tex]S_{42}=\dfrac{42}{2}[2(21)+(42-1)2]\\\\=21(42+82)\\\\=21(124)=2604[/tex]
Hence, the the auditorium contains 2,604 seats.
Thus , the correct answer is A. 2,604
We want to find the total number of seats in the auditorium, knowing that the number of seats is given by an arithmetic sequence.
The correct option is A: there are 2,604 seats in total.
We know that in the row before you (the number 22) there are 63 seats, in your row (number 23) there are 65 seats, and in the next row there are 67 seats, then we can write the 3 terms of a sequence:
[tex]a_{22}= 63\\a_{23} = 65\\a_{24} = 67[/tex]
Is simple to see that this is an arithmetic sequence, such that the difference between consecutive terms is 2, then the number of seats in the n-th row is given by:
[tex]a_n = a_{n-1} + 2[/tex]
or:
[tex]a_n = a_1 + (n - 1)*2[/tex]
Using this second equation, we can find the value of the first term of the sequence:
[tex]a_{23} = 65 = a_1 + 2*(23 - 1)\\\\65 - 44 = a_1 = 21\\[/tex]
Now, if we define d as the difference between consecutive terms in an arithmetic sequence, the sum of the first N terms is given by:
[tex]S(N) = N*(2*a_1 + (N - 1)*d)/2[/tex]
Here we have a total of 42 rows, so we use N = 42.
d =2
a₁ = 21
Then the total number of seats is:
[tex]S(N) = 42*(2*21 + (42 - 1)*2)/2 = 2,604[/tex]
This means that the correct option is A: there are 2,604 seats in total.
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Helene spends 12% of her budget on transport expenses. Write this percent as a fraction and as a decimal
Answer:
3/25 is the fraction .12 is the decimal
Step-by-step explanation:
Ron decided to use blocking to deal with extraneous factors in his
experiment. If 4 treatments are applied to one of his groups, how many
treatments should be applied to each of his other groups?
A. 3
B. 6
C. 5
D. 4
Is this no solution or infinite solutions?
2x+y=2
y=-2x-1
Answer:
infinite solutions
Step-by-step explanation:
find the area of the regular polygon, 6 sides, 12 in, rounded to the nearest tenth
Answer:
Step-by-step explanation:
6 ×12=72 rounded to the nearest tenth 5 or more add one more 4 or less let it rest
72 it would be 70 because 2 is not more than 5
_
Which statements are true about the multiplication and division properties of rational expressions? Check all that apply.
Answer: A, B, E
Step-by-step explanation:
Answer:
A, B, E.
Step-by-step explanation:
The closure property of multiplication states that the product of two rational expressions is a rational expression.
The commutative property only holds true for the multiplication of rational expressions.
The properties of rational expression multiplication and division are parallel to the properties of rational number multiplication and division.
7x5 answer plz i need help
Answer:
35
Step-by-step explanation:
7 x 7 = 35
what is 6(5−8v)+12=−54
Answer: v = 2
Step-by-step explanation:
30-48v+12 = -54
-48v = -54-30-12
[tex]\frac{-48v}{-48}[/tex] = [tex]\frac{-96}{-48}[/tex]
v = 2
Answer:
2
Step-by-step explanation:
6(5−8v)+12=−54
Divide through by 6, we have
5 — 8v + 2 = — 9
Collect like terms
— 8v = —9 — 2 — 5
—8v = — 16
Divide both side by the coefficient of v i.e —8
v = — 16/ —8
v = 2
Can anyone help me with a math paper via direct message
What is 4 tens and 6 tenths as a decimal
Answer 4.6
Step-by-step explanation:
solve this system of equations by using substitution
3x + 5y = 23
y= x + 3
Answer:
x=1
y=4
(1,4)
Step-by-step explanation:
TO SOLVE FOR X:
1. Substitute y=x+3 into the equation. This should look like this:
3x+5(x+3)=23
2. Use the distributive property.
3x+5x+15=23
3. Simplify:
8x+15=23
4. Subtract 15 from both sides. It should now lool like this:
8x=8
5. Divide both sides by 8.
x=1
TO SOLVE FOR Y:
1. Take x and substitute into original statement:
3(1)+5y=23
2. Simplify:
3+5y=23
3. Subtract 3 from both sides:
5y=20
4: Simplify:
y=4
CHECK ANSWER:
y=x+3
1. Substitute your answers
4=1+3
2. Simplify
4=4
3. Check for Truth. Is 4=4?
Yes. So your final answer is:
x=1
y=4
(1,4)
Complete the table for the given Rule:y=x-3
Answer:
1 = 2 - 3. is this what you mean?
A gym charges $25 per month plus $4 extra to swim in the pool for an hour. If a member only has $45 to spend each month, at most how many hours can the member swim? Write an equation and demonstrate this on a number line.
tickets for admission to a high school football game cost $3 for students and $5 for adults. During one game, $2995 was collected from the sale of 729 tickets. Write and solve a system of linear equations to find the number of tickets sold to students and the number of tickets sold to adults.
Answer:
404 tickets to adults have been sold .
325 tickets to students have been sold .
Step-by-step explanation:
A system of linear equations is a set of two or more first degree equations, in which two or more variables are related.
In this case, a system of two linear equations with two unknowns is solved.
To assemble the system of equations you must first define the variables, which in this case will be:
x: tickets for admission to a high school football game for students.y: tickets for admission to a high school football game for adults.On the one hand, you know that 729 tickets were sold, that is to say that tickets sold for students and adults must add 729. Expressed in an equation this is: x+y=729 equation (A)
On the other hand, you know that during a game, $ 2995 was raised for the sale of those 729 tickets. And you also know that tickets for a high school football game cost $ 3 for students and $ 5 for adults.
Then the proceeds from the sale of tickets for students is 3*x and for adults it is 5*y. And your sum must be $ 2995. Expressed in an equation this is:
3*x + 5*y=2995 Equation (B)
So the system of equations is:
[tex]\left \{ {{x+y=729} \atop {3*x+5*y=2995}} \right.[/tex]
There are several methods of solving a system of equations. In that case, the substitution method will be used, which consists of isolating an unknown element in one of the equations, which will be a function of the other unknown. In the other equation that has not been used, the same unknown is replaced by the expression previously obtained. In this case, the value of variable x in equation (A) will be isolated:
x+y=729 ⇒ x=729-y Equation (C)
Replacing this expression in equation (B) you get:
3*(729-y)+5*y=2995
Solving this equation:
3*729-3*y+5*y=2995
2187+2*y=2995
2*y=2995-2187
2*y=808
y=808÷2
y=404
Remembering that "y" is tickets for admission to a high school football game for adults. this indicates that 404 tickets to adults have been sold .
Replacing this value in equation (C), which is the previously isolated equation, you get:
x=729-y
x=729-404
x=325
Remembering that "x" is tickets for admission to a high school football game for students. this indicates that 325 tickets to students have been sold .
By setting up a system of linear equations, it's found that 325 student and 404 adult tickets were sold.
Explanation:The subject of this question is a linear system, specifically related to the ticket sales at a high school football game. Let's denote 's' as the number of student tickets sold, and 'a' as the number of adult tickets sold. We'll use the following two equations to reflect the given information:
s + a = 729 (This equation represents the total number of tickets sold.) 3s + 5a = 2995 (This equation represents the total cost of tickets sold.)
To solve the system of equations, one method is substitution or elimination. Using the elimination method, you could multiply the first equation by 3, getting 3s + 3a = 2187. Then, subtracting this from the second equation gives 2a = 808. Dividing by 2, we find that a = 404. Plugging this value into the first equation gives s = 729 - 404 = 325. Therefore, 325 student tickets and 404 adult tickets were sold.
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Is 1/4 greater than 1/3? Why?
Step-by-step explanation: Notice that the fractions that we're comparing in this problem have different denominators.
When fractions have different denominators, they're called unlike fractions. To compare unlike fractions, we must first get a common denominator.
The common denominator of 4 and 3 will be the least common multiple of 4 and 3 or 12. To get a 12 in the denominator of 1/4, we multiply the numerator and the denominator by 3 which gives us 3/12. To get a 12 in the denominator of 1/3, we multiply the numerator and the denominator by 4 which gives us 4/12.
Now we have the fractions 3/12 and 4/12.
The fraction with the greater denominator is larger so 4/12 is bigger which means that 1/3 is bigger.
1/4 is not greater than 1/3. In fact it is less than 1/3.
We have two fractions, 1/4 and 1/3.
We know that,
For a fraction, when the value of the denominator increases, the value of the fraction decreases.
So here the denominator of 4 is greater than 3.
So 1/4 is less than 1/3.
In other words, 1/4 can be defined as a part when 1 is divided in to 4 parts.
1/3 is one part when 1 is divided in to 3 parts.
So clearly, 1/4 < 1/3.
Hence 1/4 is less than 1/3.
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What do I have to do with this question? r=?, d=5m, C=15.70m
you add them then divide ur answer by 2
Solve 5x + 7 > 17.
{x | x < 2}
{x | x > 2}
{x | x < -2}
{x | x > -2}
Answer:
5x + 7 < 17
5x < 10
x < 2
answer is a
whats the root and vertex for y= 2x squared -5x-604
Vertex is calculated by -b/2a
So we have -(-5)/2(2)=5/4
The root is determined through the quadratic formula:
x=(-b+sqrt(b^2-4ac))/2a
x=(-(-5)+sqrt(-5^2-4(2)(-604)))/2(2)
x=(5+sqrt(25-4832))/4
x=(5+sqrt(-4807))/4
So the root is some imaginary number
Hope this helped!
Factor this: a^n+a^n+1
Answer:
1 + 2 a^n
Step-by-step explanation:
the table shows transactions in a checking account
A) Find the total of the transactions for each month
B) Find the mean total for the four months
Answer:
i) number of transactions for the month of January = 4
number of transactions for the month of February = 4
number of transactions for the month of March = 4
number of transactions for the month of April = 4
ii) Mean of four months = -495.7 /4 = -123.93
Step-by-step explanation:
i) number of transactions for the month of January = 4
number of transactions for the month of February = 4
number of transactions for the month of March = 4
number of transactions for the month of April = 4
ii) January February March April
-38.50 250.00 -14.00 -86.80
126.30 -135.20 99.00 -570.00
429.40 35.50 -82.70 100.00
-265.00 -62.30 -1.50 -280.10
Total 252.20 88.20 0.80 -836.9
Total of four months = 252.2 + 88.20 + 0.80 - 836.9 = -495.7
Mean of four months = -495.7 /4 = -123.93
Answer:
1) number of transactions for the month of January = 252.20
number of transactions for the month of February = 88.00
number of transactions for the month of March = 1.70
number of transactions for the month of April = -836.90
2. mean total of the four months -123.93
Step-by-step explanation:
Step-by-step explanation: