Step 1
State the compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where;
[tex]\begin{gathered} A=\text{ amount} \\ P=Prin\text{cipal}=\text{\$3000} \\ r=\text{ rate= }\frac{\text{6}}{100}=0.06 \\ n=\text{ number of periods of compounding= 4} \\ t=\text{ time = 6 years} \end{gathered}[/tex]Step 2
Find the amount as required
[tex]\begin{gathered} A=3000(1+\frac{0.06}{4})^{6\times4} \\ A=3000(1+0.015)^{24} \\ A=3000(1.015)^{24} \\ A=\text{\$}4288.508436 \\ A\approx\text{ \$}4288.51 \end{gathered}[/tex]Hence the amount compounded quarterly for 6 years based on a principal of $3000 and a 6% annual interest rate = $4288.51
Write an expression to determine the surface area of a cube-shaped box, S A , in terms of its side length, s (in inches).
The cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
What is a cube?A three-dimensional object with six equal square faces is called a cube. The cube's six square faces all have the same dimensions.
A cube is become by joining 6 squares such that the angle between any two adjacent lines should be 90 degrees.
A cube is a symmetric 3 dimension figure in which all sides must be the same.
The cube has six equal squares.
It is known that the surface area of a square = side²
Therefore, the surface area of the given cube is 6 side².
Given cube has side length = s
So,
Surface area = 6s²
Hence the cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
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A local road has a grade of 5%. The grade of a road is its slope expressed as a percent. What is the slope? What is the rise? What is the run?
a) Since the grade is given by the slope, and the grade has a 5%.
We can rewrite it as a fraction, like this:
[tex]\frac{5}{100}=\frac{1}{20}[/tex]Note that we have simplified this to 1/20 by dividing the numerator and the denominator (bottom number) by 5
So, the slope is:
[tex]\frac{1}{20}[/tex]b) The "rise" is the difference between two coordinates on the y-axis and the "run" is the subtraction between two coordinates on the x-axis. Let's remember the slope formula and the Cartesian plane:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1}{20}[/tex]So the "rise" for this grade is 1 foot and the run is 20 feet.
3) Hence, the answers are:
[tex]\begin{gathered} a)\text{ }\frac{1}{20} \\ b)\text{ }Rise\colon\text{ }1\text{ Run: 20} \end{gathered}[/tex]#24Graph the function and tell wether or not it has a point of discontinuity at x = 0. If there is a discontinuity, tell wether it is removable or non removable.
We have the function:
g(x) = x/(x - 2)
Notice that if x = 2 the denominator equals zero and then we have a vertical asymptote at x = 2. Furthermore, if x = 0, g(0) = 0.
The graph of g(x) is shown below:
As you can notice, there is no a discontinuity at x = 0.
Chloe's car used 15 gallons to travel 570 miles. How many gallons of gas would she need to travel 380 miles?
Answer:
10
Step-by-step explanation:
I divided 570 by 15 to see how many miles she can travel per gallon of gas which came out to be 38.
After that i divided the 380 by the 38. 380÷38 is 10.
Answer:
Need:
10 gallons
Step-by-step explanation:
Proportions:
15 gallons ⇒ 570 miles
A gallons ⇒ 380 miles
A = 15gallons * 380miles / 570miles
A = 10 gallons
I got this connected from the tutor I need to know how to do the factorial in this formula to bio normal distribution formula The symbol that looks like an!
Binomial distribution formula:
[tex]P(x)=\frac{n!}{(n-x)!x!}*p^{`x}*q^{n-x}[/tex]For the gien situations:
* n=15, p=0.4, find P(4 successes)
[tex]\begin{gathered} n=15 \\ p=0.4 \\ q=1-p=1-0.4=0.6 \\ x=4 \end{gathered}[/tex][tex]P(4)=\frac{15!}{(15-4)!4!}*0.4^4*0.6^{15-4}[/tex][tex][/tex]Given the base band height of a triangle, calculate the area A using the formula for the area of a triangle: A ) bh
Solution
For this case the area is given by:
[tex]A=\frac{1}{2}bh[/tex]Then we can replace b = 5ft and h = 20 ft and we got:
[tex]A=\frac{1}{2}(5ft)(20ft)=50ft^2[/tex]What’s is the volume and surface area of the figure shown ?
• The total surface area of a cylinder is given by:
[tex]SA=2πr\left(r+h\right)[/tex]where r = 1.75 cm
h = 3 cm
Hence:
[tex]SA=2\times\pi\times1.75\times(1.75+3)=57.7\text{ }cm^2[/tex]• The volume of a cylinder is given by:
[tex]V=πr^2h[/tex]Hence:
[tex]V=\pi\times(1.75)^2\times3=28.9\text{ }cm^3[/tex]ANSWER
surface area = 57.7 cm²
volume = 28.9 cm³
The proof below may or may not be correct. If the proof is incorrect, determine the first step number that is not justified and the reason it is not justified.
The first step number that is not justified and the reason it is not justified:
From the attached image
[tex]<\text{ECF}\congStep 1: is said to be correct cause all the range are equivalent and parallel
Step 2: is said to be correct AECF is a parrelologram because it is a quadilateral with two opposite equal sides
Step 3: is correct
[tex]\begin{gathered} \Delta BEC\cong\Delta\text{ECF}\ldots\text{..} \\ \text{parallel lines cut by a transverse form congruent alternate interior angle.} \end{gathered}[/tex]Step 4: is correct
[tex]<\text{BEC}\congStep 5: is correct [tex]<\text{BEC}\congStep 6 : is not correct , because corresponding parts of the congruent triangle are not congruent.
Step 7: is correct , because its a rhombus.
Which of the following sets of ordered pairs lies on the y-axis of a coordinate grid?
Solution
for this case the point that lies on the y axis need to satisfy that the x coordinate must be:
x= 0
then the best solution would be:
(0, -4)
Find the slope and y-intercept of the graph of the linear equation. Give the y intercept in point form in the space provided. Use the equation editor to enter the slope if there are fractions. 5x - y = -5
The general equation of a line is:
y = mx + b
Here, y refers to how far up and x refers to how far along.
m is slop, that is the change in y to the change in x
and b is y intercept or the point where the value of x is zero.
So,
The given equation is:
5x - y = -5
The simplest step is to map the given equation with the standard equation (y = mx + b).
So,
- y = -5 -5x
Multiplying both sides by -1, we get
y = 5 + 5x
or
y = 5x + 5
Now, if we map this form with the standard equation (y = mx + b), we get
m = 5 and b = 5
Therefore, the slope (m) is equal to 5.
Also, y-intercept (b) is equal to 5.
Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
(-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5 as it's definition states "a relationship between two expressions or values that are not equal to each other".
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b. a ≤ b means that a is less than or equal to b. a ≥ b means that a is greater than or equal to b.
What is interval notation?When using interval notation, we first write the set's leftmost number, then a comma, and finally its rightmost number. Depending on whether those two numbers are a part of the set, we then enclose the pair in parentheses or square brackets (sometimes we use one parenthesis and one bracket!).
Here,
3x+4≤5
3x≤1
x≤1/3
(-∞,1/3]
As it's definition states "a relationship between two expressions or values that are not equal to each other" (-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5.
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can you help me solve this in expanded form. 156 X 687 = ?
Given data:
The given expression is 156x687.
The given expression can be written as,
[tex]\begin{gathered} (100+50+6)(600+80+7)=60000+8000+700+30000+4000+350+3600+480+42 \\ =107172 \end{gathered}[/tex]Thus, the value of the given expression is 107172.
For the polynomial below, 3 is a zero.f(x) = x^3+ 3x^2-11x-21Express f(x) as a product of linear factors.f (x) = ?
EXPLANATION
Given the polynomial f(x) = x^3 +3x^2 -11x -21
Separating the expression into groups as shown as follows:
4. A teacher can only make 3000 copies in a month. If a teacher-has-made 2700 copies so far this month, what percentage of her copies has she used?
In order to determine the percentage, let x as the percentage. Then, you can write:
[tex]\frac{x}{100}\cdot3000=2700[/tex]factor x/100 is the percentage in decimal form. The product of this factor and 3000 equals 2700.
Solve for x and simplify:
[tex]x=\frac{2700}{3000}\cdot100=90[/tex]Hence, teacher has used 90% of the copies.
A rectangular prism has a legth of 5 1/4 m, a width of 4m, and a height of 12 m.How many unit cubes with edge lengths of 1/4 m will it take to fill the prism? what is the volume of the prism?
Volume of a cube with edge lengths of 1/4m:
[tex]\begin{gathered} V_{cube}=l^3 \\ \\ V_{cube}=(\frac{1}{4}m)^3=\frac{1^3}{4^3}m^3=\frac{1}{64}m^3 \end{gathered}[/tex]Volume of the rectangular prism:
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \\ V=5\frac{1}{4}m\cdot4m\cdot12m \\ \\ V=\frac{21}{4}m\cdot4m\cdot12m \\ \\ V=252m^3 \end{gathered}[/tex]Divide the volume of the prism into the volume of the cubes:
[tex]\frac{252m^3}{\frac{1}{64}m^3}=252\cdot64=16128[/tex]Then, to fill the prism it will take 16,128 cubes with edge length of 1/4 mIn which quadrant does 0 lie if the following statements are true:sin 0 > 0 and sec 0 < 0Quadrant IQuadrant IIQuadrant IIIQuadrant IV
Given the conditions in the question:
1. sin θ > 0, therefore, it must be positive. From that, we can conclude that y must be on the positive side, therefore, located at the top of the coordinate plane.
2. sec θ < 0, therefore, it must be negative. From that, we can conclude that x must be on the negative side, therefore, located at the left side of the coordinate plane.
Therefore, the quadrant that the θ belongs to is in the top and left of the coordinate plane and that is Quadrant II.
Does the following table show a proportional relationship? 8 h 3 9 6 36 9 81 O Yes No
Proportional relationships are relationships between two variables where their ratios are equivalent.
From the table given;
g:h are respectively;
[tex]\begin{gathered} 3\colon9=1\colon3 \\ 6\colon36=1\colon6 \\ 9\colon81=1\colon2 \end{gathered}[/tex]Since the ratios above are not equivalent, their relationship is not proportional.
Hence, the correct option is B
INT. ALGEBRA: You have a coupon for $20 off the purchase of a calculator. At the same time, the calculator is offered with a discount of 20%, and no further discounts apply. For what price on the calculator do you pay the same amount for each discount?
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
The answers available are SSS SAS CPCTC and definition of congruence
Solution
The diagram below will be of help
From the above, we have two sides to be equal and an angle to be equal
Therefore, the answer Side, Angle, Side (SAS)
Im in algebra 2 but we are also learning geometry the question asks to find the length of each arc
The length of the arc = 8π/3 mi
Explanation:The length of an arc is given by the fomula:
[tex]L=\frac{\theta}{360}\times2\pi r[/tex]The radius, r = 8 ml
[tex]\theta=60^0[/tex][tex]\begin{gathered} L=\frac{60}{360}\times2\pi\times8 \\ \\ L=\frac{16\pi}{6} \\ \\ L=\frac{8\pi}{3} \end{gathered}[/tex]The length of the arc = 8π/3 mi
Give the point-slope form of the equation of the line that is perpendicular to y= -4x/5+10 and contains P(5,6)
You have to write the equation of a line perpendicular to
[tex]y=-\frac{4}{5}x+10[/tex]That crosses the point (5, 6)
A caracteristic of a line permendicular to another one is that its slope pf the perpendicular line is the negative inverse of the slope of the first line.
So for example if you have two lines:
1_ y=mx+b
and
2_ y=nx+c
And both lines are perpendicular, the slope of the second one will be the negative inverse of the slope of the first one, that is:
[tex]n=-\frac{1}{m}[/tex]The slope of the given line is m=-4/5
The negative inverse is
[tex]-(\frac{1}{-\frac{4}{5}})=-(-\frac{5}{4})=\frac{5}{4}[/tex]Now that you know the slope of the perpendicular line, use it along with the given point (5, 6)
in the slope-point formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{5}{4}(x-5) \end{gathered}[/tex]Which of the following is a solution to the equation c + ( 4 -3c) - 2 = 0?A. -1B. 0C. 1D. 2
Given data:
The given equation is c+(4-3c)-2=0
The given equation can be written as,
c+4-3c-2=0
-2c+2=0
-2c=-2
c=1
Thus, the value of c is 1, so option C) is correct.
45% of 240 is what number?
We are asked to determine the 45% of 240. To do that we need to multiply 240 by 45/100, that is:
[tex]240\times\frac{45}{100}=108[/tex]therefore, 45 percent of 240 is 108
Use a graph to predict the value of jewelry in 7 years.
Solution:
Given that the initial cost price of the jewelry is $2,200.
The rate at which it decreases each year is 12%.
Thus, the exponential decay function is;
[tex]\begin{gathered} y(t)=2200(1-0.12)^t \\ \\ \text{ Where }t\text{ is the time in years.} \end{gathered}[/tex]The graph of the function is;
From the graph;
CORRECT OPTION:
[tex]\approx899.09[/tex]Find a.Round to the nearest tenth:a10 cm150°12°с=a = [ ? ]cmLaw of Sines: sin A=sin Bbasin cСEnter
Answer:
24.0 cm
Explanation:
To find the value of a, we will use the Law of sines, so
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]So, replacing A = 150°, B = 12°, and b = 10 cm, we get:
[tex]\frac{\sin150}{a}=\frac{\sin 12}{10}[/tex]Now, we need to solve for a. First, cross multiply
[tex]10\cdot\sin 150=a\cdot\sin 12[/tex]Then, divide by sin12
[tex]\begin{gathered} \frac{10\cdot\sin150}{\sin12}=\frac{a\cdot\sin 12}{\sin 12} \\ \frac{10\cdot(0.5)}{0.208}=a \\ 24.0=a \end{gathered}[/tex]Therefore, a = 24.0 cm
There are 73 students in a classroom, and the desired ratio of students to computers is 6 to 1. How many computers are needed to achieve the desired ration?
Answer: 12
Explanation:
Given:
Total number of students in a classroom = 73
Ratio of students to computers = 6:1
To find the number of computers needed to achieve the desired ration, we use the ratio:
[tex]\begin{gathered} \frac{\text{Total number of students}}{\text{Total number of computers}}=\frac{6}{1} \\ We\text{ plug in what we know} \\ \frac{\text{7}3}{\text{Total number of computers}}=\frac{6}{1} \\ \text{Simplify and rearrange} \\ \text{Total number of computers = 73(}\frac{1}{6}) \\ \text{Calculate} \\ T\text{otal number of computers = }12.16\text{ =12} \\ \end{gathered}[/tex]Therefore, the number of computers needed is 12.
Circumference? (you must include units) Round to the tenthsas needed.
The circumference formula is given by:
[tex]L=2\pi r[/tex]Where r is the radius of the circle. From the problem, we have r = 10.9 ft. Then, using the formula:
[tex]\begin{gathered} L=2\pi\cdot10.9 \\ \\ \therefore L=68.5\text{ ft} \end{gathered}[/tex]The circumference is 68.5 ft
My name is nessalovetrillo i am prepping and studying to test out of my algebra class this is for a study guide Please see attached picture
Given:
S={(5,6),(-2,-9),(-9,6)}
To find the domain and range:
The domain is,
{-9, -2, 5}
The range is,
{-9, 6}
Which value of n makes the following equation true?√n=4020408O 16
Solution
- The solution steps are given below:
[tex]\begin{gathered} \sqrt{n}=4 \\ \text{ Square both sides} \\ n=4^2 \\ n=16 \end{gathered}[/tex]Final Answer
The answer is 16
A real estate agent has 18 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling more than 4 properties in one week. Round your answer to four decimal places.
The probability of selling more than 4 properties in one week is 0.985.
What is probability?A probability formula can be used to calculate the likelihood of an occurrence by simply dividing the favorable number of possibilities by the entire number of possible outcomes.
The binomial distribution is a discrete probability distribution in probability theory and statistics that gives only two possible outcomes in an experiment: success or failure.
In this case, the real estate agent has 18 properties. Therefore, n = 18. p = 50% = 0.5.
The probability will be:
= P(X > 4)
= 1-0.0154 by using Excel command
= 0.985
The probability is 0.985.
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