A company sells brass and steel machine parts.One shipment contains 3 brass and 10 steel parts and costs $48. A second shipment contains 7 brass and 4 steel parts and costs $54. Find the cost of each type of machine part.
For any value of n, list the numbers ln, rn, mn, tn and i in increasing order. (enter your answers as a comma-separated list. enter your answer using the variables rather than numerical values.)
The correct order is [tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex].
To list the values ln, rn, mn, tn and i in increasing order for any value of n, we need to understand the relationship between these variables.
The variables ln, rn, mn, and tn likely represent different measures, such as left endpoint, right endpoint, midpoint, and trapezoid point in numerical methods, while i often represents the imaginary unit iota in mathematics.
Commonly, if we assume these have increasing values when ordered, they would be listed as:
[tex]l_n[/tex][tex]m_n[/tex][tex]t_n[/tex][tex]r_n[/tex]iTherefore, the values in increasing order are:
[tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex]
How many ways are there to choose eight coins from a piggy bank containing 100 identical pennies and 80 identical nickels?
There are 9 ways to choose eight coins from a piggy bank.
Total number of ways =
(Combinations of 8 pennies) + (Combinations of 7 pennies and 1 nickel) + ... + (Combinations of 0 pennies and 8 nickels)
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9 ways
If "np is greater than or equal to 15" and "n(1-p) is greater than or equal to 15", what is the approximate shape of the sampling distribution of the sample proportion?
Answer:
The sampling distribution of the sample proportion will be approximately normally distributed with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
If np >= 15 and n(1-p) >= 15
Can be approximated to the normal distribution, with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
So
The sampling distribution of the sample proportion will be approximately normally distributed with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
What is f(2) if the linearization of f(x) at a = 2 is l(x) = 12x + 4?
What is the volume of a right circular cylinder with a radius of 3in and a height of 10in
Answer:
282.6 inches cubed
Step-by-step explanation:
The volume of the cylinder with radius 3 in and height 10 in is
[tex]V=\pi (3^2)(10)= \pi (9)(10)= 90\pi = 90(3.14) = 282.6 in^3[/tex]
Answer:
90 in3
Step-by-step explanation:
Last year, Rachel opened an investment account with $8200. At the end of the year, the amount in the account had decreased by 7.5%. How much is this decrease in dollars? How much money was in her account at the end of last year? What was the decrease in the amount? WHat was the year-end amount?
• Given the function, f(x) = x3 – 5x2 + 9x – 45, determine the number of roots and identify them.
Final answer:
The given function f(x) = x3 – 5x2 + 9x – 45 has rational roots ±1, ±3, ±5, and ±9.
Explanation:
To determine the number of roots and identify them for the function f(x) = x3 – 5x2 + 9x – 45, we can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation, then p must divide the constant term (in this case, 45) and q must divide the leading coefficient (in this case, 1). By trying all possible combinations of p and q, we can find the rational roots of the equation. In this case, the rational roots are ±1, ±3, ±5, and ±9.
The number of real roots is 1, and it is ( x = 5 ).
To determine the number of roots and identify them for the function[tex]\( f(x) = x^3 - 5x^2 + 9x - 45 \)[/tex], we can use various methods such as the Rational Root Theorem, Descartes' Rule of Signs, or graphing techniques. In this case, since the degree of the polynomial is 3, we know that there will be 3 roots in total.
We'll start by checking for rational roots using the Rational Root Theorem. According to this theorem, if a rational root [tex]\( \frac{p}{q} \)[/tex] exists for the polynomial [tex]\( f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 \), then \( p \)[/tex] is a factor of the constant term [tex]\( a_0 \) and \( q \)[/tex] is a factor of the leading coefficient [tex]\( a_n \)[/tex].
The constant term of [tex]\( f(x) \) is \( -45 \)[/tex]and the leading coefficient is ( 1 ). The factors of ( -45 ) are [tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]. The factors of \( 1 \) are \( \pm 1 \)[tex]\( 1 \) are \( \pm 1 \)[/tex].
By trying all possible combinations of these factors, we can find the rational roots of the polynomial. We'll then use synthetic division or polynomial long division to check if these roots are actually roots of the polynomial.
Let's proceed with the calculations:
1. Possible rational roots:
[tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]
2. Testing these roots using synthetic division or polynomial long division:
Testing [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = (1)^3 - 5(1)^2 + 9(1) - 45 = 1 - 5 + 9 - 45 = -40 \][/tex]
Testing [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = (-1)^3 - 5(-1)^2 + 9(-1) - 45 = -1 - 5 - 9 - 45 = -60 \][/tex]
Testing [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = (3)^3 - 5(3)^2 + 9(3) - 45 = 27 - 45 + 27 - 45 = -36 \][/tex]
Testing [tex]\( x = -3 \)[/tex]:
[tex]\[ f(-3) = (-3)^3 - 5(-3)^2 + 9(-3) - 45 = -27 - 45 - 27 - 45 = -144 \][/tex]
Testing ( x = 5 ):
[tex]\[ f(5) = (5)^3 - 5(5)^2 + 9(5) - 45 = 125 - 125 + 45 - 45 = 0 \][/tex]
[tex]\[ \Rightarrow \text{Root: } x = 5 \][/tex]
Testing ( x = -5 ):
[tex]\[ f(-5) = (-5)^3 - 5(-5)^2 + 9(-5) - 45 = -125 - 125 - 45 - 45 = -340 \][/tex]
Testing ( x = 9 ):
[tex]\[ f(9) = (9)^3 - 5(9)^2 + 9(9) - 45 = 729 - 405 + 81 - 45 = 360 \][/tex]
Testing ( x = -9 ):
[tex]\[ f(-9) = (-9)^3 - 5(-9)^2 + 9(-9) - 45 = -729 - 405 - 81 - 45 = -1260 \][/tex]
Testing ( x = 15 ):
[tex]\[ f(15) = (15)^3 - 5(15)^2 + 9(15) - 45 = 3375 - 1125 + 135 - 45 = 2340 \][/tex]
Testing ( x = -15 ):
[tex]\[ f(-15) = (-15)^3 - 5(-15)^2 + 9(-15) - 45 = -3375 - 1125 - 135 - 45 = -4680 \][/tex]
Testing ( x = 45 ):
[tex]\[ f(45) = (45)^3 - 5(45)^2 + 9(45) - 45 = 91125 - 10125 + 405 - 45 = 81060 \][/tex]
Testing ( x = -45 ):
[tex]\[ f(-45) = (-45)^3 - 5(-45)^2 + 9(-45) - 45 = -91125 - 10125 - 405 - 45 = -102705 \][/tex]
From these tests, we see that ( x = 5 ) is a root of the polynomial. The other roots are irrational or complex.
So, the number of real roots is 1, and it is ( x = 5 ).
TRUE or FALSE?
Two arcs of a circle are congruent if and only if their associated radii are congruent.
The area of a circle (A) is given by the formula A=pi*r2
where r is the circle's radius. The formula to find r is . If and , r is centimeters.
The area of a circle is calculated with the formula A = πr², where pi is the mathematical constant approximately equal to 3.14159 and r represents the circle's radius. Considering significant figures is crucial for maintaining precision, as demonstrated in rounding the calculated area of a circle with radius 1.2 m to 4.5 m², based on the initial data's precision.
Explanation:The area of a circle is calculated using the formula A = πr², where π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle. When calculating the area with a given radius, it's important to consider the significance of figures in your final answer. For instance, if a circle's radius is given as 1.2 meters (with two significant figures), and you calculate the area to be 4.5238934 square meters using a detailed value of pi, you need to round your final answer to maintain the precision of your initial data, resulting in an area of 4.5 m².
It's also valuable to note how ancient civilizations, like the Greeks, approximated mathematics related to circles and how such estimations have evolved into our modern understanding, where the concept of significant figures plays a critical role in ensuring accuracy across varying fields of study and applications.
Ms. Maple is a teacher whose salary is $22,570 for this school year, which has 185 days. In Ms. Maple’s school district, substitute teachers are paid $80 per day. If Ms. Maple takes a day off without pay and a substitute teacher is paid to teach her classes, how much less does the school district pay in salary by paying a substitute teacher instead of paying Ms. Maple for that day?
Final answer:
The school district pays $42 less by hiring a substitute teacher for a day instead of paying Ms. Maple, calculating by comparing Ms. Maple's daily salary to a substitute teacher's daily rate.
Explanation:
To calculate how much less the school district pays by hiring a substitute teacher instead of paying Ms. Maple for a day, we first need to determine Ms. Maple’s daily salary. This is done by dividing her annual salary by the number of working days in the school year.
Ms. Maple’s daily salary = $22,570 / 185 days = $122 per day.Substitute teacher’s daily salary = $80 per day.The difference between what the school district pays Ms. Maple and what it pays a substitute teacher for one day = Ms. Maple’s daily salary - Substitute teacher’s daily salary = $122 - $80 = $42.Therefore, the school district pays $42 less by hiring a substitute teacher for a day instead of paying Ms. Maple.
A rectangle is 5 centimeters long and 4 centimeters wide. What is its area?
Y=10x
Graph the function
How can you tell if the rule you have written for a set of points is correct?
6. Alice and Alma have to fill a workbook. Alice has already completed 3 pages and can do 7 pages per hour. Alma has completed 11 pages, but can only work at a rate of 3 pages per hour. Eventually Alice will catch up and the two will be working on the same page. How long will that take? How many pages will each of them have finished?
Alina has a spinner that has 5 equal sections: red, blue, green, purple, and orange. She spins the spinner 200 times. About how many times should Alina expect the spinner to land on either purple or orange?
Answer:
HI!
Your spinner has 5 colors, and if you spin it, the probability of landing in each color will be the same ( because the spiner has 5 equal sections).
So for every spin, the probability on landing on each color will be 20%.
If i spin it 200 times, then the 20% of 200 is 0.2*200 = 40.
It means that if you spin it 200 times, then each colour shows 40 times theoretically. The question is: how many times should Alina expect the spinner to land on either purple or orange?
you have 40 for purple and 40 for orange, then the total times that the spinner lands on either purple or orange is 80.
why does 16 to the power of 0 equal 1?
Find the length of the missing side. The triangle is not drawn to scale.
x = sqrt(17^2 + 15^2)
x = 8
missing side = 8
Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually. (Use the tables found in the textbook.)
Donte simplified the expression below. mc024-1.jpg What mistake did Donte make? He did not apply the distributive property correctly for 4(1 + 3i). He did not distribute the subtraction sign correctly for 8 – 5i. He added the real number and coefficient of i in 4(1 + 3i). He added the two complex numbers instead of subtracted.
From their house to their parents house, the Leightons have to drive 276 miles. if they have already driven 2/3 of the distance, how far have they gone?
Find the quadratic function whose zeros are 2 and -2 and has maximum value
Eli earned $98 at his job when he worked for 8 hours. what was his hourly pay rate in dollars per hour hour?Express your answer in simplest form
1. What is the area of this figure?
Enter your answer in the box.
? cm²
2. What is the measure of angle x?
Enter your answer in the box.
x = °
Answer:
The area if this figure is 35cm2
Step-by-step explanation:
Simplify the product. (5 − 6)(2 + 7)
Sarah spends 1/6 hour Vacuuming her moms car. She spends four times as long washing the car. Then she spends twice as long waxing the car as she does washing the car. What is the total amount of time Sarah spencer vacuuming washing and waxing her moms car
Answer:
C
Step-by-step explanation:
In 1999 there were 1647 daily and 7471 weekly newspapers published in the United States, as well as X other kinds of newspapers. The total number of newspapers was 700 greater then seven times the number of other kinds of newspapers. How many newspapers were published in 1999 that were not daily or weekly
I NEED THIS ANSWER !!!! 90 POInTS
I need help I would really thank whoever answers this for me
What is the weekly wage for a person who works 40 hours at an hourly rate of $9.75?
Final answer:
To find the weekly wage for someone working 40 hours at an hourly rate of $9.75, multiply the number of hours by the hourly rate, which equals $390.
Explanation:
The weekly wage for a person who works 40 hours at an hourly rate of $9.75 can be calculated by multiplying the number of hours worked per week by the hourly wage. Here's the calculation:
Hourly rate: $9.75Hours worked per week: 40 hoursWeekly wage = Hourly rate × Hours worked per weekWeekly wage = $9.75 × 40Weekly wage = $390Therefore, the answer required for the weekly wage for this person is $390.
Explain how to rename the fractions using division so they have the same denominator to compare. 4/5 and 6/10