Answer: Since we know that the two variables are independent, we can use the addition rule of probability to find the probability of selecting a student who is either female or a psychology major:
P(female or psychology major) = P(female) + P(psychology major) - P(female and psychology major)
Since the variables are independent, we know that P(female and psychology major) = P(female) x P(psychology major) = 0 x 0.1 = 0.
Therefore:
P(female or psychology major) = 0 + 0.1 - 0 = 0.1
So the probability of randomly selecting a student who is either female or a psychology major is 0.1.
Step-by-step explanation:
Krish used to take thirty minutes to walk to his office. Recently, he bought a new cycle. Now he takes only seven-tenths of the time he used to take to reach office. How many minutes does he save by cycling to the office?
Answer:
Krish saves 9 minutes by cycling to his office.
Step-by-step explanation:
Krish used to take 30 minutes to walk to his office. After he bought a new cycle, he takes only 7/10 of the time he used to take to reach the office. Let's call the new time he takes to reach the office "t" (in minutes).
We can set up a proportion to find the value of t:
30 / 1 = t / (7/10)
To solve for t, we can cross-multiply:
30 * 7/10 = t
21 = t
So, Krish now takes 21 minutes to reach his office by cycle.
To find how many minutes he saves by cycling, we can subtract the new time from the old time:
30 - 21 = 9
Krish saves 9 minutes by cycling to his office.
se the equations shown in the table below to answer the following question.
Equation A -2x -6y=36 -4r
Equation B 2(3x-3y)=36
Equation C 4r-6y+36=-2r
Which two of the three equations create a system of equations with no solution?
Explain how you determined your answer.
Respond in the space provided.
Image shows 2 joined rectangular prisms. One is 10 in. in length, 6 in. in height, and 3 in. in width. The second is 4 in. in length, 3 in. in width, and 6 in. in height. Which expressions can be added to find the volume of the solid figure? A. 10 × 3 and 10 × 6 B. 10 × 3 × 6 and 4 × 3 × 6 C. 10 × 4 and 3 × 6 D. 10 × 3 × 3 and 10 × 3 × 6
The correct option to determine the value of volume of solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.
Explain about the rectangular prisms?One of the three-dimensional shapes that can be created with six pairs with parallel lines is a rectangular prism. Three-dimensional shapes in this category include cubes and cuboids. Prisms come in a variety of classifications based on the base.
Volume of rectangular prism = length * width * height
rectangular prism A:
length = 10 in.
Width = 3 in.
height = 6 in.
rectangular prism B:
length = 4 in.
Width = 3 in.
height = 6 in.
Thus,
volume of the solid = volume of rectangular prism A + volume of rectangular prism A
volume of the solid = 10*3*6 + 4*3*6
Thus, the correct option to determine the value of volume of the solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.
Know more about the rectangular prisms
https://brainly.com/question/24284033
#SPJ1
Round the decimal number to the nearest tenth: 285.429 can you show steps?
"To round the decimal number 285.429 to the nearest tenth, we need to look at the digit in the hundredths place, which is 2.
If the digit in the hundredths place is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is.
In this case, the digit in the hundredths place is 2, which is less than 5. Therefore, we leave the digit in the tenths place as it is, which is 2.
So, rounding 285.429 to the nearest tenth gives us:
285.4
Therefore, the rounded value of the decimal number 285.429 to the nearest tenth is 285.4." (ChatGPT, 2023)
Kareem is considering buying a guitar priced at $179.99 He has $200 cash with him. He uses predict whether he has enough money.
Add 10% and 1%
The current HST rate is 13%
a) Round the price of the guitar to a convenient
amount:
b) What is 10% of the rounded price
c) What is 1% of the rounded price
d) How many 1%s do you need?
e) What is the estimated tax?
f) Add the estimated tax to the rounded price.
Does Kareem have enough money with him? YES OR NO
Using the concept of percentage, we can deduce that Kareem does not have enough money with him
Does Kareem have enough money with him?To solve the questions given, we need to apply the concept of percentage on some.
a) Rounding the price of the guitar to a convenient amount, we get $180.
b) 10% of the rounded price is: 0.1 x $180 = $18.
c) 1% of the rounded price is: 0.01 x $180 = $1.80.
d) To get the estimated tax, we need to multiply the rounded price by the HST rate: 0.13 x $180 = $23.40. Dividing this by $1.80, we get approximately 13.
e) The estimated tax is $23.40.
f) Adding the estimated tax to the rounded price, we get $180 + $23.40 = $203.40.
Since Kareem has $200 cash with him, he does not have enough money to buy the guitar at the estimated price of $203.40. Therefore, the answer is NO.
Learn more on percentage here;
https://brainly.com/question/843074
#SPJ1
In a quadrilateral ABCD, AB is parallel to DC, and AD is parallel to BC. Find the perimeter of △COD if the diagonals of the quadrilateral intersect each other at point O and AC=40 in, BD=50 in, AB=25in.
Answer:
Step-by-step explanation:
In quadrilateral ABCD, we have:
AB is parallel to DC
AD is parallel to BC
AC = 40 in (given)
BD = 50 in (given)
AB = 25 in (given)
We can use the fact that opposite sides of a parallelogram are equal in length to find the length of CD:
CD = AB = 25 in
Next, we can use the fact that the diagonals of a quadrilateral bisect each other to find the length of AO and OC:
AO = BO = BD/2 = 50/2 = 25 in
OC = OD = AC/2 = 40/2 = 20 in
Now we can use the triangle inequality to find the perimeter of triangle COD:
CO + OD + CD > OC
CO + 20 + 25 > 20
CO + 45 > 20
CO > -25
CO + OC > CO
CO + 20 > 0
CO > -20
CO + CD > OD
CO + 25 > 20
CO > -5
Therefore, the possible range of values for CO is:
-20 < CO < -5
However, since lengths cannot be negative, we can take the absolute value of CO to get:
5 < CO < 20
So the perimeter of triangle COD is:
CO + OD + CD = CO + 20 + 25 = CO + 45
Substituting the possible range of values for CO, we get:
5 + 45 < CO + 45 < 20 + 45
50 < CO + 45 < 65
So the perimeter of triangle COD is between 50 in and 65 in.
Therefore, the perimeter of triangle COD is between 50 in and 65 in, but the exact value depends on the length of CO, which is between 5 in and 20 in.
Consider the equation: x2 18x +72 = 0
A) First, use the "completing the square" process to write this equation in the form (x + D)² =
and enter your results below.
x² 18x+72=0 is equivalent to:
=
Preview left side of eqn:
B) Solve your equation and enter your answers below as a list of numbers, separated with a com
where necessary.
Answer(s): 6,12
Using square process method, we can get the values of x to be 12 and 6.
Define square process?The formula a (x + m)2 + n = a (x + m)2 + n is the simplest to remember while learning how to complete the square technique.
The following formulas can be used to compute m and n in this situation: m = b/2a and n = c - (b2/4a).
From the question,
x² - 18x + 72= 0
⇒ x² - 18x = -72
Complete the square by adding the half of the square of the coefficient of x to both sides of the expression as shown:
⇒ x² - 18x + (18/2) ² = -72 + (18/2) ²
⇒ x² - 18x + 9² = -72 + 81
⇒ (x-9) ² = 9
⇒ x-9 = ± 3
So, values of x are:
x = 3 + 9
= 12
x = -3 + 9
= 6
Therefore, the values of x are 12 and 6.
To know more about square process, visit:
https://brainly.com/question/29180935
#SPJ1
Kyoko has $10,000 that she wants to invest. Her bank has several accounts to choose from. Her goal is to have $20,000 by the time she finishes graduate school in 7 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal assuming they compound daily? (Hint: solve the compound interest formula for the interest rate. Also, assume there are 365 days in a year)
The minimum annual interest rate for Kyoko to reach her goal, using daily compounding, is 9.903%.
How is the interest rate determined?The interest rate is computed using an online finance calculator that sets the following parameters.
The compounding period involved is 2,555 days for 7 years, based on the assumption that there are 365 days in a year.
N (# of periods) = 2555 days (7 years x 365 days)
PV (Present Value) = $10,000
PMT (Periodic Payment) = $-0
FV (Future Value) = $-20000
Results:
I/Y = 9.903% if interest compound 365 times per year (APR)
I/Y = 10.409% if interest compound once per year (APY)
I/period = 0.027% interest per period
Total Interest = $10,000.00
Learn more about compounding interest at https://brainly.com/question/24274034.
#SPJ1
julia needs to make 500 hamburgers for the a school function... hamburger patties are sold in packets of 12
how many packets of patties should she buy ?
Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:
12x = 500
x = 500/12
x = 41.67
x≅ 42
Julia needs to buy 42 packets
Find more on equation at: https://brainly.com/question/2972832
#SPJ1
This graph shows how the time required to complete an online shopping transaction is related to the number of products being purchased.
y
x
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
0
Time (seconds)
Products being purchased
Online shopping
What is the rate of change?
Write your answer as a decimal or integer.
seconds per product
Answer:
1 product
Step-by-step explanation:
Given the equation that shows how the time required to complete an online shopping transaction is related to the number of products being purchased as;
t = 24p + 27
t represents the time required to complete the transaction
p is the product purchased
If it takes 51 seconds to complete a transaction, to get the amount of product purchased, we will substitute t = 51 into the expression and find p as shown;
51 = 24p + 27
Substract 27 from both sides
51-27 = 24p + 27 - 27
24 = 24p
24p= 24
p = 24/24
p = 1
Hence only 1 product is being purchased
Solve for x to make A||B. A B- 45 x = [?] 6x + 15
Step-by-step explanation:
45+6x+15=180
60+6x=180
6x=180-60
6x/6=120/6
X=20
The value of x from the same side interior angles in a parallel lines is x = 20
What are angles in parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Given data ,
Let the parallel lines be represented as A and B
Now , the measures of angles are
p = 45°
And , q = ( 6x + 15 )°
where p and q are same side interior angles
And , the same side interior angles add up to 180°
On simplifying , we get
45 + 6x + 15 = 180
6x + 60 = 180
Subtracting 60 on both sides , we get
6x = 120
Divide by 6 on both sides , we get
x = 20
Hence , the angles in parallel lines are solved and x = 20
To learn more about angles in parallel lines click :
https://brainly.com/question/27400033
#SPJ2
It costs $1,400 to manufacture 100 designer shoes, and $4,100 to manufacture 400 designer shoes. If x represents the number of shoes, and y is the costs,
find the cost equation
What is the cost to manufacture 150 shoes
If the product sells for $19 per item; find the Revenue Function
Determine the number of items needed to break even.
Answer:
To find the cost equation, we can use the two data points given:
(100, 1400) and (400, 4100)
We can use the point-slope form of a linear equation, where the slope is the change in cost over the change in quantity:
slope = (4100 - 1400) / (400 - 100) = 2700 / 300 = 9
Using the point-slope form with the first data point:
y - 1400 = 9(x - 100)
y - 1400 = 9x - 900
y = 9x + 500
So the cost equation is y = 9x + 500.
To find the cost to manufacture 150 shoes, we can plug in x = 150 into the cost equation:
y = 9(150) + 500 = 1850
So the cost to manufacture 150 shoes is $1850.
To find the revenue function, we multiply the number of shoes sold by the price per shoe:
Revenue = price x quantity = 19x
To determine the number of items needed to break even, we need to find the quantity where revenue equals cost. Let C(x) be the cost function and R(x) be the revenue function. The break-even point occurs when:
C(x) = R(x)
9x + 500 = 19x
500 = 10x
x = 50
So the company needs to sell 50 designer shoes to break even.
Step-by-step explanation:
Answer:
Cost equation: y = 9x + 500
It costs $1,850 to manufacture 150 shoes.
Revenue function: R(x) = 19x
The number of items that need to be sold to break even is 50.
Step-by-step explanation:
Definition of variables
x is the number of designer shoes manufactured.y is the cost (in dollars) to manufacture the designer shoes.If it costs $1,400 to manufacture 100 designer shoes:
x = 100 when y = 1400.If it costs $4,100 to manufacture 400 designer shoes:
x = 400 when y = 4100.Assuming the relationship between the number of shoes and the cost to manufacture them is linear, the slope of the equation of the line the models the relationship can be found by dividing the change in y-values by the change in x-values of the two data points:
[tex]\implies \sf Slope\;(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4100-1400}{400-100}=9[/tex]
Substitute the found slope and one of the points into the point-slope form of a linear equation to create an equation that gives the total cost to manufacture the shoes in terms of the number of shoes (x):
[tex]\implies \sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-1400=9(x-100)[/tex]
[tex]\implies \sf y-1400=9x-900[/tex]
[tex]\implies \sf y=9x+500[/tex]
Therefore, the cost equation is y = 9x + 500.
To calculate the cost to manufacture 150 shoes, substitute x = 150 into the cost equation:
[tex]\begin{aligned}\implies \sf y&=\sf 9(150)+500\\&= \sf 1350+500\\&= \sf 1850\end{aligned}[/tex]
Therefore, it costs $1,850 to manufacture 150 shoes.
The revenue is the income a company generates before any expenses are subtracted. Therefore, the revenue function is simply the selling price of the item multiplied by the number of items sold.
Given the product sells for $19 per item, the revenue function is:
[tex]\implies \sf R(x)=19x[/tex]
The break even point is the point at which the total revenue equals the total cost, so there is neither profit nor loss.
To determine the number of items that should be sold to break even, equate the cost equation and the revenue function and solve for x.
[tex]\begin{aligned}\sf R(x)&=\sf y\\\implies \sf19x&=\sf 9x+500\\\sf 10x&=500\\\sf x&=50\end{aligned}[/tex]
Therefore, the number of items that need to be sold to break even is 50.
How do the joint frequencies differ from the marginal frequencies in a two-way frequency table? (1 point)
The joint frequencies are the sum of the row or column in a two-way frequency table. The marginal frequencies are the sum of the
row and column totals.
The joint frequencies are the sum of the row and column totals. The marginal frequencies are the sum of the row or column in a
two-way frequency table.
The joint frequencies are the cells where the categories for two variables in a two-way frequency table intersect. The marginal
frequencies are the sum of the row or column in a two-way frequency table.
The joint frequencies are the sum of the row or column in a two-way frequency table. The marginal frequencies are the cells where
the categories for two variables in a two-way frequency table intersect.
The joint frequencies are the cells where the categories for two variables in a two-way frequency table intersect, while the marginal frequencies are the sums of the row or column in a two-way frequency table.
Identifying the difference between the frequenciesJoint frequencies represent the frequency counts of each combination of categories for two variables, while marginal frequencies represent the frequency counts of each category for one variable, regardless of the other variable.
For example, in a two-way frequency table of gender and political affiliation, the joint frequency for "Male" and "Republican" would represent the number of individuals who are both male and Republican.
The marginal frequency for "Male" would represent the total number of males in the sample, regardless of their political affiliation. The marginal frequency for "Republican" would represent the total number of individuals who identify as Republican, regardless of their gender.
Understanding the difference between joint and marginal frequencies is important for analyzing the relationship between two variables and identifying any patterns or trends.
Read more about joint frequencies at
https://brainly.com/question/29264504
#SPJ1
At Brian’s Bookstore, 0.3 of the shelves hold mysteries, 25% of the shelves hold travel books, and 7/20 of the shelves hold children’s books. Which type of book covers the most shelf space in the store? Explain how you arrived at your answer
Answer:
Childrens books
Step-by-step explanation:
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To solve for which type of book covers the most space, we need to first convert 25% from a percentage to a fraction.
What is a percentage?A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
If percentages are fractions of 100, then 25% as a fraction would look like this:
25% = [tex]\frac{25}{100}[/tex]We can do the same to 0.3, although it isn't a percentage.
0.3 = 0.30 = [tex]\frac{30}{100}[/tex]Now, we need to convert the fractions ([tex]\frac{25}{100}[/tex], [tex]\frac{30}{100}[/tex], [tex]\frac{7}{20}[/tex]) to have a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
To make [tex]\frac{7}{20}[/tex] have a denominator of 100, we can multiply the 20 by 5 to get 100.
7 × 5 = 4520 × 5 = 100Now the fraction is [tex]\frac{35}{100}[/tex].
The three fractions given are:
[tex]\frac{30}{100}[/tex] (Mystery books)[tex]\frac{25}{100}[/tex] (Travel books)and [tex]\frac{35}{100}[/tex] (Children books)The larges given fraction is [tex]\frac{35}{100}[/tex] meaning that the children's books cover the most shelf space in the store.
What will be the reminder. When 362*461*2761will be divided by 6
Answer:
10
Step-by-step explanation:
362/6 = 60R2
461/6 = 76R5
2761/6 = 460R1
2x5x1 = 10
what is 19/100,also written into decimals
19/100 into decimals is 0,19
To solve this, we must knowTo write a fraction based on 10/100/1000... you must move the decimal point to the left the number of times equivalent to the number of zeros in the base.
In this case, base 100 has two zeros. Then move two squares to the left.
[tex]\begin{array}{l}\bf 19\\\sf {0}{,}\!\overset{\overset{2}{\curvearrowleft}}{1}\!\overset{\overset{1}{\curvearrowleft}}{9}\\\\\bf \dfrac{19}{100}=0{,}19\end{array}[/tex]
Did you see how easy the conversion was under these circumstances?
If you have any question about this solution, you can ask me in the comments :)
The diagram shows a parallelogram.
The area of the parallelogram is greater
than 10.5 cm²
a) Show that 2x² 25x + 33 < 0
The given inequality 2x² 25x + 33 < 0 has been proved by using properties of parallelogram.
The formula A = bh, where b is the parallelogram's base and h is its height, determines the area of a parallelogram.
Let's use x + 6 cm for the parallelogram's base and 2x + 3 cm for its height in the diagram. The parallelogram's area can therefore be represented as follows:
A = (x + 6)(2x + 3)
By extending this phrase, we get:
A = 2x² + 15x + 18x + 18
A = 2x² + 33x + 18
We now know that the parallelogram's area is more than 10.5 cm2. As a result, we can create the disparity shown below:
2x² + 33x + 18 > 10.5
By taking away 10.5 from both sides, we arrive at:
2x² + 33x + 18 - 10.5 > 0
By condensing the left side, we obtain:
2x² + 22.5x + 7.5 > 0
When we multiply both sides by 2, we obtain:
4x² + 45x + 15 > 0
By taking 3 away from both sides, we arrive at:
4x² + 45x + 12 < 0
As a result, we have demonstrated that 2x² 25x + 33 < 0.
To know more about Parallelogram visit:
brainly.com/question/19187448
#SPJ9
simplify 1/2-1/x-y+2/(x-y)
Answer: x^2-xy-2x^2y+2xy^2+2x+2y over 2x(x - y)
Step-by-step explanation:
because im that guy
18. A jar contains marbles of different colors. The probability of drawing a red marble at random is 210 .
What is the probability, and the likelihood, that the marble drawn is not red?
By answering the above question, we may state that The chance of probability drawing a non-red marble is just the probability of drawing a non-red marble. As a result, the probability is 209/210.
What is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
The likelihood of drawing a red marble is 210, which indicates that one red marble is drawn out of every 210 in the jar. This probability may be expressed as a fraction:
P(Red) = 1/210
The likelihood of drawing a non-red marble is the inverse of the probability of drawing a red marble:
P(Not Red) = 1 minus P(Red) = 1 minus 1/210 = 209/210
As a result, the chance of drawing a marble that is not red is 209/210.
The chance of drawing a non-red marble is just the probability of drawing a non-red marble. As a result, the probability is 209/210.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
tan(-A).sin (180°+A).sec (270°-A)=x. sin (-A)-cos²(90° + A).tan A. Find the value of x
Answer:
Step-by-step explanation:
We can simplify the expression on the left-hand side using trigonometric identities:
tan(-A) = -tan(A) (since tan(-θ) = -tan(θ))
sin(180°+A) = -sin(A) (since sin(180°+θ) = -sin(θ))
sec(270°-A) = -cos(A) (since sec(270°-θ) = -cos(θ))
cos²(90°+A) = sin²A (since cos²(90°+θ) = sin²θ)
Substituting these values, we get:
-x.sin(A).cos(A).tan(A) = x.sin(-A) - sin²A.sin(A)
-x.sin(A).cos(A).tan(A) = -x.sin(A) - sin³A
Now, we can simplify this equation by moving all the terms to one side:
-x.sin(A).cos(A).tan(A) + x.sin(A) + sin³A = 0
Factoring out sin(A), we get:
sin(A) (-x.cos(A).tan(A) + x + sin²A) = 0
Since sin(A) ≠ 0, we can divide both sides by sin(A):
-x.cos(A).tan(A) + x + sin²A = 0
Multiplying both sides by cos(A), we get:
-x.sin(A) + x.cos²(A) + sin²A.cos(A) = 0
Using the identity cos²(θ) + sin²(θ) = 1, we can write this as:
-x.sin(A) + x(1 - sin²A) + sin²A.cos(A) = 0
Simplifying and rearranging, we get:
x = sin(A)/(cos(A) - sin²(A))
Therefore, the value of x is given by the expression sin(A)/(cos(A) - sin²(A)).
Which shows the best estimate of the quotient of 523 +67?
O between 7 and 8
O between 8 and 9
O between 70 and 80
O between 80 and 90
PLEASE HURRY I WILL GIVE BRAINLIEST!!!!!
Which two objects are exerting more force on each other?
A. A
B. B
C. They are exerting the same amount of force. d
D. There is not enough information provided to answer the question.
Answer:
D
Step-by-step explanation:
..
Factor completely.
9 - 25x2
Answer:
-41 is the ANS.
Step-by-step explanation:
9-25*2
9-50
-41
lisa is going on a 5.632704 km hike. she has already hiked 4.425969 km. how many miles does she have left
Answer:
To convert kilometers to miles, we can use the conversion factor 1 km = 0.621371 miles.
First, let's convert the total distance of 5.632704 km to miles:
5.632704 km * 0.621371 miles/km = 3.497672 miles
Next, let's convert the distance already hiked, 4.425969 km, to miles:
4.425969 km * 0.621371 miles/km = 2.746203 miles
To find out how many miles Lisa has left, we can subtract the distance already hiked from the total distance:
3.497672 miles - 2.746203 miles = 0.751469 miles
So Lisa has 0.751469 miles left to hike.
Step-by-step explanation:
Question 1
Find the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made. The interest charge for unpaid balances is 18% per year.
Credit Card Balance = $5000
Credit Limit = $5000
Minimum Payment = $125.00
Assuming that there are no other transactions or fees on the credit card, here's how to calculate the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made:
1.) Unpaid Balance: The unpaid balance is the amount of the credit card balance that remains after making the minimum monthly payment. In this case, the minimum monthly payment is $125, so the unpaid balance would be:
$5000 - $125 = $4875
2.) Interest Charge: The interest charge for unpaid balances is 18% per year. To calculate the monthly interest rate, divide the annual rate by 12:
18% / 12 = 1.5%
3.) To calculate the interest charge for the month, multiply the unpaid balance by the monthly interest rate:
$4875 x 1.5% = $73.13
So the new interest charge for the month is $73.13.
4.) Purchasing Power: Purchasing power refers to the amount of credit that is available on the credit card after making the minimum monthly payment and accounting for any interest charges. To calculate the purchasing power, subtract the unpaid balance and interest charge from the credit limit:
$5000 - $4875 - $73.13 = $51.87
So the purchasing power on the credit card after the minimum monthly payment is made is $51.87.
Evaluate the given expression and show the steps, please.
Answer:
80
Step-by-step explanation:
The variable "n" is not defined, but rather "k" is used in the summation. Assuming that "n" was meant to be "k", the expression should be:
s4 = ∑ k=1 to 4 of 2(3^(k-1))
To evaluate this expression, we need to substitute each value of k from 1 to 4 into the expression 2(3^(k-1)), and then sum up the results.
Starting with k = 1:
2(3^(1-1)) = 2(3^0) = 2(1) = 2
Moving on to k = 2:
2(3^(2-1)) = 2(3^1) = 2(3) = 6
Next, k = 3:
2(3^(3-1)) = 2(3^2) = 2(9) = 18
Finally, k = 4:
2(3^(4-1)) = 2(3^3) = 2(27) = 54
Now we add up these four results:
s4 = 2 + 6 + 18 + 54 = 80
Therefore, the value of s4 is 80.
This question asks for the degree, leading coefficient, zeroes, factors, factors with multiplicity, and the final answer
Answer:
[tex]\textsf{Degree:}\quad 6[/tex]
[tex]\textsf{Leading\;coefficient:}\quad \dfrac{1}{3456}[/tex]
[tex]\textsf{Zeroes:}\quad -6, 2, 5, 8[/tex]
[tex]\textsf{Factors:}\quad (x + 6), (x - 2), (x - 5), (x - 8)[/tex]
[tex]\textsf{Factors\;with\;multiplicity:}\quad (x + 6)^3(x - 2)(x - 5)(x - 8)[/tex]
[tex]\textsf{Equation\;of\;function:}\quad f(x)=\dfrac{1}{3456}(x+6)^3(x-2)(x-5)(x-8)[/tex]
Step-by-step explanation:
ZeroesThe zeroes are the x-values of the points where the function crosses the x-axis, so the x-values when f(x) = 0.
Therefore, the zeroes of the given function are:
x = -6x = 2x = 5x = 8[tex]\hrulefill[/tex]
FactorsAccording to the factor theorem, if f(x) is a polynomial, and f(a) = 0, then (x - a) is a factor of f(x). Therefore, the factors of the function are the x-values that satisfy f(x) = 0.
Therefore, the factors of the given function are:
(x + 6)(x - 2)(x - 5)(x - 8)[tex]\hrulefill[/tex]
MultiplicitiesThe multiplicity of a factor is the number of times the factor appears in the factored form of the equation of the polynomial.
If the behaviour of the x-intercept is like that of a line, i.e. the curve passes directly through the intercept, its multiplicity is one.
Therefore, the factors (x - 2), (x - 5) and (x - 8) have multiplicity one.
The behaviour of the x-intercept at x = -6 is like that of a cubic function (S-shape). There, this zero has multiplicity 3: (x + 6)³.
[tex]\hrulefill[/tex]
DegreeSo far we have found the zeros, factors and their multiplicities, so we can write a factored form of the function:
[tex]\implies f(x)=a(x+6)^3(x-2)(x-5)(x-8)[/tex]
The degree of the function is the highest exponent value of the variables in the polynomial. Therefore, to find the degree of the function, simply sum the exponents of the factors:
[tex]\implies \textsf{Degree}=3 + 1 + 1 + 1 = 6[/tex]
Therefore, the degree of the function is 6.
[tex]\hrulefill[/tex]
Leading CoefficientFrom inspection of the given graph, the y-intercept is (0, -5).
Therefore, to find the leading coefficient (value of a), substitute (0, -5) into the equation and solve for a:
[tex]\begin{aligned}\implies f(0)=a(0+6)^3(0-2)(0-5)(0-8)&=-5\\a(216)(-2)(-5)(-8)&=-5\\-17280a&=-5\\a&=\dfrac{1}{3456}\end{aligned}[/tex]
Therefore, the leading coefficient of the function is 1/3456.
[tex]\hrulefill[/tex]
Equation of the functionPutting everything together, the function in factored form is:
[tex]f(x)=\dfrac{1}{3456}(x+6)^3(x-2)(x-5)(x-8)[/tex]
In standard form:
[tex]f(x)=\dfrac{1}{3456}x^6+\dfrac{1}{1152}x^5-\dfrac{1}{36}x^4-\dfrac{37}{432}x^3+\dfrac{17}{24}x^2+\dfrac{13}{8}x-5[/tex]
HELP ASAP PLEASE!!!!!!!!
The inverse function of f(x) = (x + 5)² on the domain x >= -5 is given as follows:
[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]
The domain of the inverse function is given as follows:
x >= 0.
How to obtain the inverse function?The function for this problem is defined as follows:
f(x) = (x + 5)² on the domain x >= -5.
The range of the function is y >= 0, as the vertex is at (-5,0) and the function is increasing over it's domain, hence the domain of the inverse function, which is the range of the original function, is given as follows:
x >= 0.
To obtain the inverse function, wee exchange x and y in the definition of the function, and then isolate y, hence:
x = (y + 5)²
[tex]y + 5 = \sqrt{x}[/tex]
[tex]y = \sqrt{x} - 5[/tex]
[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]
More can be learned about inverse functions at https://brainly.com/question/3831584
#SPJ1
An object is dropped from 44 feet below the tip of the pinnacle atop a 720-ft tall building. The height h of the object after t seconds is given by the equation h=16t^2+676 . Find how many seconds pass before the object reaches the ground.
Solving the quadratic equation we can see that the object will be 6.5 seconds falling down.
How many seconds pass before the object reaches the ground?We know that the height is modeled by the quadratic equation
h=-16t²+676
The object will reach the ground when the height is zero, so we need to solve:
-16t²+676 = 0
Solving this for t we will get:
16t² = 676
t² = 676/16
t = √(676/16)
t = 6.5
The object will be 6.5 seconds falling down.
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
Which logarithm bases can you use to solve for x in the exponential equation 4^3+x=25 ? (Select all that apply.) the plus x is part of the exponent.
log base 25
log base 4
log base x
log base 10
To solve the exponential equation 4^(3+x) = 25 for x, we need to use logarithms. We can use any base of the logarithm to solve this equation. However, some bases may be more convenient or easier to use than others. The possible bases of the logarithm that we can use to solve this equation are:
Log base 4: If we take the logarithm of both sides of the equation with base 4, we get:
log₄(4^(3+x)) = log₄(25)
(3+x)log₄(4) = log₄(25)
3+x = log₄(25)/log₄(4)
3+x = 2.3219
x ≈ -0.6781
Log base 25: If we take the logarithm of both sides of the equation with base 25, we get:
log₂₅(4^(3+x)) = log₂₅(25)
(3+x)log₂₅(4) = 1
3+x = 1/log₂₅(4)
3+x = 1/1.3219
x ≈ -1.6781
Log base x: If we take the logarithm of both sides of the equation with base x, we get:
logₓ(4^(3+x)) = logₓ(25)
(3+x)logₓ(4) = logₓ(25)
3+x = logₓ(25)/logₓ(4)
3+x = log₄(25)/log₄(x)
x = log₄(25)/log₄(x) - 3
Log base 10: If we take the logarithm of both sides of the equation with base 10, we get:
log₁₀(4^(3+x)) = log₁₀(25)
(3+x)log₁₀(4) = log₁₀(25)
3+x = log₁₀(25)/log₁₀(4)
3+x = 1.3979
x ≈ -1.6021
Therefore, we can use any of the above logarithm bases to solve for x in the given equation.