Answer:
A unit cube is a cube whose each side is 1 unit long
Step-by-step explanation:
Examples: a cube whose each side is 1cm or each side is 1 in etc
3. Students performed in a play on a Friday and a Saturday. For both performances,adult tickets cost a dollars each and student tickets cost s dollars each.On Friday, they sold 125 adult tickets and 65 student tickets, and collected $1,200. OnSaturday, they sold 140 adult tickets and 50 student tickets, and collect $1,230.125a + 65 = 1,200140a + 50s = 1,230This situation is represented by this system of equations:a. What could the equation 265a + 115s = 2,430 mean in this situation?b. The solution to the original system is the pair a = 7 and s = 5. Explain why itmakes sense that this pair of values is also the solution to the equation265a + 115s = 2,430.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
students play:
125a + 65s = 1,200 ===> Friday
140a + 50s = 1,230 ===> Saturday
Step 02:
system of equations:
a.
a = adult tickets
s = students tickets
265a + 115s = 2,430
On this day, they sold 265 adults tickets and 115 students tickets, and collect $2,430.
b.
original solution:
a = 7
s = 5
265(7) + 115(5)= 2,430
1855 + 575 = 2430
2430 = 2430
It is verified that the original solution is also valid for this equation.
That is the full solution.
A bank features a savings account that has an annual percentage rate of r = 5.2% with interest compoundedsemi-annually. Dylan deposits $7,000 into the account.nakThe account balance can be modeled by the exponential formula A = P(1+ where A is the futurevalue, P is the present value, r is the annual percentage rate, k is the number of times each year that theinterest is compounded, and n is the time in years.(A) What values should be used for p, r, and k?PAT =k=(B) How much money will Dylan have in the account in 8 years?Answer = $Round answer to the nearest penny.(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effectiveannual percentage rate which includes all compounding in the year).APY =Round answer to 3 decimal places.
(A) Given that:
Present value, P = $7000
Annual percentage rate, r = 5.2% = 0.052
Number of compounding periods, k = 2
(B) Plug the values into the formula
[tex]A=P(1+\frac{r}{k})^{nk}[/tex]gives
[tex]A=7000(1+\frac{0.052}{2})^{2n}[/tex]Substitute 8 for n to find the amount of money after 8 years.
[tex]\begin{gathered} A=7000(1+\frac{0.052}{2})^{2\cdot8} \\ =7000(1.026)^{16} \\ =10554.94 \end{gathered}[/tex]In 8 years, Dylan will have $10554.94 in account.
(C) Find the annual percentage yield using the formula
[tex]\text{APY}=(1+\frac{r}{k})^k-1[/tex]Plug the values into the formula.
[tex]\begin{gathered} \text{APY}=(1+\frac{0.052}{2})^2-1 \\ =5.268\% \end{gathered}[/tex]The annual percentage yield for the savings account is 5.268%.
Construct sinusoidal functionsThe graph of a sinusoidal function intersects its midline at (0, -3) and then has a maximum point at (2, -1.5).Write the formula of the function, where x is entered in radians.
We have a sinusoidal function.
[tex]y=A\cdot\sin (b\cdot x+c)+d[/tex]Its midline is intersected at (0,-3) and has a maximum point at (2,-1.5).
As the midline intersects at y=-3, we know that function has an offset of 3 units down.
This offset is the value of the parameter d, so we have:
[tex]y=A\cdot\sin (b\cdot x+c)-3[/tex]The maximum value happens at point (2,-1.5). The maximum value happens when the pure sin function reaches the value 1, so we can write:
[tex]\begin{gathered} y_{\max }=A\cdot1-3=-1.5 \\ A-3=-1.5 \\ A=-1.5+3 \\ A=1.5 \end{gathered}[/tex]The amplitude is A=1.5, so we can write:
[tex]y=1.5\sin (b\cdot x+c)-3[/tex]We can find the values of the parameters b and c using the x-values of the the points (0,-3) and (2,-1.5):
[tex]\begin{gathered} (x,y)=(0,-3) \\ y(0)=1.5\sin (b\cdot0+c)-3=-3 \\ 1.5\cdot\sin (c)=-3+3 \\ 1.5\cdot\sin (c)=0 \\ \sin (c)=0 \\ c=0 \end{gathered}[/tex][tex]\begin{gathered} (x,y)=(2,-1.5) \\ y(2)=1.5\cdot\sin (b\cdot2)-3=-1.5 \\ 1.5\cdot\sin (2b)=-1.5+3 \\ 1.5\cdot\sin (2b)=1.5 \\ \sin (2b)=1 \\ 2b=\frac{\pi}{2} \\ b=\frac{\pi}{2}\cdot\frac{1}{2} \\ b=\frac{\pi}{4} \end{gathered}[/tex]The function becomes:
[tex]y(x)=1.5\sin (\frac{\pi}{4}x)-3[/tex]The graph of the function is:
Answer: y(x) = 1.5*sin(pi/4 * x)-3
I am stumped with the graph question attached. Please assist.
Answer:
[tex]\begin{gathered} 0.44x^{2}-2.67x+3 \\ or \\ \frac{1}{2.25}(x-3)^2-1 \end{gathered}[/tex]Explanation:
From the graph, we will observe that the vertex is at the point:
[tex]\begin{gathered} (h,k)=(3,-1) \\ \text{We will obtain the quadratic equation from the vertex form using the formula:} \\ f(x)=a(x-h)^2+k \\ \text{Inputting the values of ''h'' \& ''k'', we have:} \\ f(x)=a(x-3)^2-1 \\ \text{We have the x-intercept at point:} \\ (x,y)=(1.5,0) \\ f(1.5)=0 \\ \Rightarrow0=a(1.5-3)^2-1 \\ 0=a(-1.5)^2-1 \\ 0=a(2.25)-1 \\ 0=2.25a-1 \\ \text{Add ''1'' to both sides, we have:} \\ 1=2.25a \\ 2.25a=1 \\ \text{Divide both sides by ''2.25'', we have:} \\ a=\frac{1}{2.25}=0.44 \\ \text{We will substitute the value of ''a'' into the vertex equation, we have:} \\ f(x)=\frac{1}{2.25}(x-3)^2-1 \\ \text{Expand the bracket, we have:} \\ f(x)=\frac{1}{2.25}(x-3)(x-3)-1 \\ f(x)=\frac{1}{2.25}[x(x-3)-3(x-3)]-1 \\ f(x)=\frac{1}{2.25}[x^2-3x-3x+9]-1 \\ f(x)=\frac{1}{2.25}[x^2-6x+9]-1 \end{gathered}[/tex]We will obtain the quadratic function as shown below:
[tex]\begin{gathered} \frac{1}{2.25}[x^2-6x+9]-1 \\ \text{Expand the bracket, we have:} \\ 0.44x^2-2.67x+4-1 \\ 0.44x^2-2.67x+3 \\ or \\ \frac{1}{2.25}(x-3)^{2}-1 \\ \end{gathered}[/tex]What is 2/5 divided by 8/5
Answer: 1/4 or 0.25
Step-by-step explanation: multiply by the reciprocal, 2/5 ÷ 5/8 then change the symbol to multiplication 2/5 x 5/8 multiply and the answer is 1/4
A student worked 52 hr during a week one summer. The student earned $5.70 per hour for the first 40 hr and $8.55 per hour for overtime. How much did the student earn during the week? Enter your answer in the answer box
Total earnings during the week = $330.6
Explanations:The total number of hours worked during the week = 52 hr
Earnings per hour for the first 40 hours = $5.70
Earnings for the first 40 hours = $5.70 x 40
Earnings for the first 40 hours = $228
The number of hours worked as overtime = 52 - 40 = 12 hours
Earnings per hour for overtime = $8.55
Earnings for overtime = $8.55 x 12
Earnings for overtime = $102.6
Total earnings during the week= Earnings for the first 40 hours + Earnings for overtime
Total earnings during the week = $228 + $102.6
Total earnings durig the week = $330.6
Find the first four terms of the sequence given by the following.An= 42- 7(n-1), n=1, 2, 3...
In order to calculate the first four terms of this sequence, let's use the values of n = 1, 2, 3 and 4 in the expression for An:
[tex]\begin{gathered} n=1\colon \\ A_1=42-7(1-1)=42 \\ \\ n=2\colon \\ A_2=42-7(2-1)=35 \\ \\ n=3\colon \\ A_3=42-7(3-1)=28 \\ \\ n=4\colon \\ A_4=42-7(4-1)=21 \end{gathered}[/tex]Therefore the first four terms are 42, 35, 28 and 21.
Round 6,252 to the nearest hundred
To the nearest hundred, 6300 is round 6,252.
What formula is used to round numbers to the nearest hundred?100 closest to the whole number
Look at the tens digit to know how close a number is to 100. Round up when the tens digit is 5 or above. You should round down if the tens digit is 4 or fewer. 3281 has 8 as the tens digit.
Which method of teaching rounding is the simplest?The best technique to get children to round to the closest 10 is to model rounding using two-digit numbers. Ask your youngster to imagine a rounded number, then ask what comes before and after that amount, and only fill in those two numbers.
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Round 287.9412 to the nearest tenth. Do not write extra zeros.
To round the number 287.9412 to the nearest tenth.
First, we identify the tenth digit.
• The tenth digit is 9.
,• The digit after 9 is 4
Since the digit after 9 is less than 5, we simply cut off the numbers after 9.
Therefore:
287.9412 = 287.9 (correct to the nearest tenth).
Answer:
287.9
Step-by-step explanation:
There are three parts to this question. A) The number of people initially infected is? (round to the nearest whole number as needed)
a.
To find the initial number of people infected, let's calculate the value of f(t) for t = 0:
[tex]f(0)=\frac{102000}{1+5200e^0}=\frac{102000}{1+5200}=\frac{102000}{5201}=19.61[/tex]Rounding to the nearest whole number, the initial value is 20 people.
b.
Using t = 4, let's calculate the value of f(t):
[tex]f(4)=\frac{102000}{1+5200e^{-4}}=\frac{102000}{1+5200\cdot0.0183156}=\frac{102000}{96.24112}=1.059.84[/tex]Therefore the number of infected people is 1060.
c.
When t tends to infinity, the value of 5200e^-t will tend to zero, therefore we have:
[tex]\lim_{t\to\infty}f(t)=\frac{102000}{1+0}=102000[/tex]Therefore the limiting size is 102000 people.
Need help on this geometry assignment please
Step-by-step explanation:
The quotient of a number x and five
(translating english phrases to mathematical expressions)
The expression forming by the statement "quotient of a number x and 5" is x/5.
What do we mean by quotient?In this example, the number divided by (15) is known as the dividend, and the number divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, where the division produced the number 2, the result is the quotient. The dividend is 8 and the divisor is 4. An algebraic expression is referred to as a quotient expression or an algebraic fraction if division comes last in the evaluation process. An algebraic fraction or quotient expression is the expression 7x2+5x.So, the quotient of a number (x) and 5:
Where x is the number.then, the expression will be: x/5Therefore, the expression formed by the statement "quotient of a number x and 5" is x/5.
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The correct question is given below:
The quotient of a number (x) and five
the cost to rent a ski boat is $174.83 . Six friends each pay $34. How much change would a group of friends receive?
If $34 are paid six times, the group will pay in total:
$34 x 6 = $204
Since, the cost to rent a ski boat is $174.83, in order to find the change the group will receive we just need to substract it:
$204 - $174.83 = $29.17
Need help asap I will reward the first person who answers with a lot of points
Answer:
C 60 = x + 45
Step-by-step explanation:
They are vertically opposite angles so they are equal.
Solve log x = 4.Ox= 4Ox= 40Ox= 1,000Ox= 10,000Need help!!!
Let's recall that when do not see a base written, it means the base is 10.
Let's also recall that the log form and the exponential form are interchangeable.
[tex]\log _{a\text{ }}b\text{ = c }\Rightarrow\text{ }a^{c\text{ }}=\text{ b}[/tex]Therefore, we have:
[tex]\log _{10\text{ }}x\text{ = 4 }\Rightarrow10^4\text{ = x}[/tex][tex]The\text{ correct answer is x = }10^{4\text{ }}=\text{ 10,000}[/tex]The correct answer is D.
Which of the following is the simplified form of the expression 15z-9-3z-z+8?
Answer:
11z - 1
Step-by-step explanation:
After a dilation, triangle A(0,0), B(0,4), C(6,0) becomes triangle A’(0,0), B’(0,10), C’(15,0) what is the scale factor
Solution:
The triangle is dilated from
[tex]\begin{gathered} (1)A(0,0)\rightarrow A^1(0,0) \\ \text{There is no change in coordinate here, } \\ \text{This shows the center of dilation is at point (0,0)} \\ \\ (2)\text{ } \\ \text{From B(0,4) }\rightarrow B^1(0,10) \\ Scale\text{ factor is }\frac{10}{4}\text{ = 2.5} \\ Or\text{ } \\ (3)\text{ from C(6,0) to (15,0)} \\ Scale\text{ factor is }\frac{15}{6}\text{ = 2.5} \end{gathered}[/tex]The scale factor of the dilation is 2.5
Malik just returned from a spring break volunteer trip. He is shopping for a photo album that will showcase his photos from the trip. The albums range in photo capacity and orientation. Horizontally Vertically 50 photos 2 3 100 photos 2 7 150 photos 6 8 What is the probability that a randomly selected photo album holds exactly 50 photos or 150 photos? Simplify any fractions.
Answer:
Explanation:
The total number of photo albums showcased:
[tex]\begin{gathered} =2+3+2+7+6+8 \\ =28 \end{gathered}[/tex]The number that holds exactly 50 photos = 2+3 = 5
[tex]P(\text{album holds 50 photos)=}\frac{5}{28}[/tex]The number that holds exactly 150 photos = 6+8 =14
[tex]P(\text{album holds 50 photos)=}\frac{5}{28}[/tex]T
Josh opens a savings account with a $300 deposit. He won't add or withdrawal any money. The
account earns 2% simple interest. What is the total amount that Josh will have on his savings at
the end of 5 years?
O $6
O $306
O $30
O $330
The most appropriate choice for simple interest will be given by-'
Amount of money Josh have at the end of 5 years = $330
Fourth option is correct
What is simple interest?
Simple interest ( SI) is the interest earned on a certain principal at a certain rate over a certain period of time,
If P is the principal, rate is r %, time is t years,
SI = [tex]\frac{p \times r \times t}{100}[/tex]
Adding Principal and simple interest will give the amount
Here,
Principal deposited by Josh= $300
Rate of interest = 2%
Time = 5 years
Simple interest = [tex]\frac{300 \times 2 \times 5}{100}\\[/tex]
= $30
Amount of money Josh have at the end of 5 years = $(300 + 30)
= $330
Fourth option is correct
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PLS HELP ME IN TEN MINS FOR 10 POINTS THANKS U which group of numbers to replace the ? In a tree diagram? [ A] -7/8, -2.5, -4 [B] 7/8 ,2.5 ,4 [C] -7, 8 ,-4 [D] NOT heren
According to the given image, the tree diagram begins with Real Numbers.
The second level is formed by subsets of Real Numbers which are Rational Numbers and Irrational Numbers.
The third level is formed by subsets of rational numbers which are Non-Integer Rational Numbers and Integer Rational Numbers.
This means the missing part must be filled with Integer Rational Numbers.
Therefore, the right answer is -7, 8, -4, because these numbers are rational integers.F (x) = 6x
Find x if f(x) = -24
Hey there!
[tex]f(x)=-6x\\whenf(x)=-24[/tex]
In order to find f(x), we need to substitute -24 for x:
[tex]f(x)=6(-24)\\x=-144[/tex]
Hope this helps!
Jeanine Baker makes floral arrangements. She has 13 different cut flowers and plans to use 4 of them. How many different selections of the 4 flowers are possible?
715 different selections of the 4 flowers are possible.
What is combination?Combinations are based entirely on grouping. Combinations can be used to determine how many different groups that can be created from the available items.
The scaling factor can be calculated if both the original dimensions and the new dimensions are known. There are two terms that must be grasped in order to use the scale factor. Scaling refers to the process of increasing or decreasing a figure's size. Scaling up refers to the process of increasing a figure's size.
Given:
n= 13,r= 4
Using Combination
[tex]^{13}c_4[/tex]
=13! / 4! (13 - 4)!
=13! / 4! 9!
= 13 x 12 x 11 x 10 x 9!/ 4! 9!
= 13 x 12 x 11 x 10 / 4 x 3 x 2
=13 x 11 x 5
= 715
Hence, 715 different selections of the 4 flowers are possible.
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A committee is to be formed consisting of 2 men and 5 women. If the committee members are to be chosen from 11 men and 12 women, how many different committees are possible?
through the given statement many 43,560 different committees are possible to be formed.
What is Probability?Probability is a measure of the likelihood of an event to occur.
Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.
Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).
The multiplication rule and the addition rule are used for computing the probability of A and B, as well as the probability of A or B for two given events A, B defined on the sample space.
Describe four Perspectives on Probability?Classical (sometimes called "A priori" or "Theoretical")Empirical (sometimes called "A posteriori" or "Frequentist")SubjectiveAxiomaticWe can choose 2 men from 11 men
That is 11C2 ways.
Similarly we can choose 5 women from 12 women
That is 12C5 ways.
Total ways in which we can choose 2 men and 5 women to form a committee = 11c2 * 12c5
= 55 * 792
= 43,560
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there is a .9987 probability that a randomly selected 27-year old male lives through a year. a life insurance company charges $154 for insuring that the male will live through the year. if the male does not survive the year, the policy pays out $100,000 as a death benefit
Using probability we know that the expected value of the insurance company is $141.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.So, the expected value of the insurance company:
Probability = 0.9987So, 1.0000 - 0.9987 = 0.0013Now, get the expected value as follows:
E(x) = 0.9987 × 154 + 0.0013(-9987)E(x) = 153.7998 + (-12.9831)E(x) = 153.7998 - 12.9831E(x) = 140.8167Rounding off: $141
Therefore, using probability we know that the expected value of the insurance company is $141.
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The complete question is given below:
There is a .9987 probability that a randomly selected 27-year-old male lives through a year. a life insurance company charges $154 for ensuring that the male will live through the year. if the male does not survive the year, the policy pays out $100,000 as a death benefit.
What is the expected value for the insurance company?
Exact value of addition and subtraction formulas / sin cos tan
Take into account that:
[tex]\frac{5\pi}{4}+\frac{\pi}{3}=\frac{15\pi+4\pi}{12}=\frac{19}{12}\pi[/tex]Then, for the given sine value, you can write:
[tex]\sin (\frac{19}{12}\pi)=\sin (\frac{5}{4}\pi+\frac{1}{3}\pi)[/tex]Now, consider that the sine of a sum is:
[tex]\sin (a+b)=\sin a\cdot\cos b+\cos a\cdot\sin b[/tex]Then, by applying the previous identity to the given expression, you obtain:
[tex]\sin (\frac{5}{4}\pi+\frac{1}{3}\pi)=\sin (\frac{5}{4}\pi)\cos (\frac{1}{3}\pi)+\cos (\frac{5}{4}\pi)\sin (\frac{1}{3}\pi)[/tex]Consider now that:
[tex]\begin{gathered} \sin (\frac{5}{4}\pi)=-\frac{\sqrt[]{2}}{2} \\ \cos (\frac{1}{3}\pi)=\frac{1}{2} \\ \sin (\frac{1}{3}\pi)=\frac{\sqrt[]{3}}{2} \\ \cos (\frac{5}{4}\pi)=-\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]Then, for the given expression of the question, you get:
[tex]\begin{gathered} \sin (\frac{5}{4}\pi+\frac{1}{3}\pi)=(-\frac{\sqrt[]{2}}{2})(\frac{1}{2})+(-\frac{\sqrt[]{2}}{2})(\frac{\sqrt[]{3}}{2}) \\ =-\frac{\sqrt[]{2}}{4}-\frac{\sqrt[]{2}\sqrt[]{3}}{4}=-\frac{(1+\sqrt[]{3})\sqrt[]{2}}{4} \end{gathered}[/tex]The pervious result is the answer to the given expression.
Find the unknown length in the right triangle.The unknown length b in the triangle is _____(Simplify your answer. Write an exact answer, using radicals as needed.)
The given triangle is a right triangle because one of its angles is 90 degrees. We would find b by applying the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the information given,
hypotenuse = 17
one leg = 7
other leg = b
Thus,
17^2 = 7^2 + b^2
289 = 49 + b^2
b^2 = 289 - 49 = 240
b = √240
b = 4√15
Convert the given rectangularcoordinates into polarcoordinates.(-5, -2) = (5.4, [?])Round your answer to the nearest tenth.Report theta in radians
Use the next relationships to convert rectangular coordinates to polar coordinates:
[tex]\begin{gathered} (x,y)=(r,\theta) \\ \\ r^2=x^2+y^2 \\ \\ tan\theta=\frac{y}{x} \end{gathered}[/tex]For the given rectangular coordinates:
[tex]\begin{gathered} (-5,-2) \\ x=-5 \\ y=-2 \\ \\ tan\theta=\frac{-2}{-5}=\frac{2}{5} \\ \\ \theta=\tan^{-1}(\frac{2}{5}) \\ \\ \theta=0.4 \end{gathered}[/tex]Then, the polar coordinates are (5.4, 0.4)What are two possible numbers that are 5 units from the number -6 on a number line?
Answer:
The 2 possible numbers are -11 and -1.
Step-by-step explanation:
Dude my sister posted this one
Answer:
do i need to do the right or wrong answer
im pretty sure that there is 12
Step-by-step explanation:
Rubio is grilling ground beef patties for his party. The nutritional label from the ground is shown. Based on the information in the label, about how many milligrams of cholesterol are recommended per day?
Answer:
259.26 mg of cholesterol per day.
Explanation:
From the label, we can say that 70 mg of cholesterol is equivalent to 27% of the daily value. So, we need to found the amount equivalent to 100%. So, we can use the following equation:
[tex]100\text{ \% }\times\frac{70\text{ mg}}{27\text{ \%}}=259.26\text{ mg}[/tex]Therefore, the answer is 259.26 mg of cholesterol per day.
