Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = 54000
r = Interest rate = 5.25% = 0.0525
n = Number of times the interest is compounded per year = 12
t = Number of years = 6
So:
[tex]\begin{gathered} A=54000(1+\frac{0.0525}{12})^{12\cdot6} \\ A\approx73943.18 \end{gathered}[/tex]Answer:
The balance is $73943.18
What are the center and the radius of the circle x2−2x+y2=0?A)The center is (1, 0), and the radius is 1.B) The center is (2, 0), and the radius is 2.C)The radius is 0, so the equation cannot represent a circle.D) The radius is negative, so the equation cannot represent a circle.
We want to know the center and the radius of the circle:
[tex]x^2-2x+y^2=0[/tex]We remember that the equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this case, we complete the square by adding 1 and substracting 1:
[tex]\begin{gathered} x^2-2x+1+y^2-1=0 \\ x^2-2x+1+y^2=1 \\ \text{Factoring the first three terms, we obtain:} \\ (x-1)^2+y^2=1 \end{gathered}[/tex]This means that the center is the point (1,0), and:
[tex]\text{Radius: }\sqrt[]{1}=1[/tex]A casting director wishes to find one male and one female to cast in his play. If he plans to audition 10 males and 14 females, in how many different ways can this be done?
There are 10 males and 14 females.
So the order doesn't matter and we cant repeat a person.
Given the before information, we are going to use combinations
[tex]c=\frac{n!}{r!(n-r)!}=[/tex]Where n is the total of people and r the election, so:
For males:
n=10
r=1
[tex]c=\frac{10!}{1!(10-1)!}=10[/tex]For females:
n=14
r=1
[tex]C=\frac{14!}{1!(14-1)!}=14[/tex]Finally, multiply both results:
10* 14 = 140
Therefore, there are 140 ways that the casting can be done.
The functions f and g are defined as follows.g(x) = 4x-2-Xf(x)=-3x-1Find f (5) and g(-3).Simplify your answers as much as possible.f(s) = 0:Х?&(-3) = 0
We need to find f(5) and g(-3)
First, we will solve f(5), for this, we have the following function:
[tex]\begin{gathered} f(x)=-3x-1 \\ f(5)=-3\cdot(5)-1 \\ f(5)=-15-1 \\ f(5)=-16 \end{gathered}[/tex]Second, we will solve g(-3), for this, we have the following function:
[tex]\begin{gathered} g(x)=4x^2-x \\ g(-3)=4(-3)^2-(-3) \\ g(-3)=4\cdot9+3 \\ g(-3)=36+3 \\ g(-3)=39 \end{gathered}[/tex]In conclusion, f(5) = -16 and g(-3) = 39
What other number is a part of this fact family? 3,4,
The other number that is a part of the fact family of 3,4 is 7.
According to the question,
We have the following information:
Two numbers of the fact family is 3 and 4.
Now, we know that in a fact family, if two numbers are given then the third number can be found by adding the two given numbers.
(More to know: fact family is often used to prove commutative property of addition. It can be used to find any number of other numbers of fact family are given.)
4+3 = 3+4 = 7
Hence, the other number that is a part of the fact family of 3,4 is 7.
To know more about fact family here
https://brainly.com/question/12557539
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I need help to graph the line this is a study guide check point it gives you the answer if you do not know it but I don’t want just the answer on how to do it I want the explanation of it being worked out
Given:
[tex]y=2x[/tex]To graph the given equation, we can plug in any values for x to get values for y as shown below:
Example 1:
Let x= 0
We plug in x= 0 into y=2x:
[tex]\begin{gathered} y=2x \\ y=2(0) \\ \text{Simplify} \\ y=0 \end{gathered}[/tex]Based on the above values of x and y, our point is (0,0).
Example 2:
We let x =2:
[tex]\begin{gathered} y=2x \\ y=2(2) \\ \text{Simplify} \\ y=4 \end{gathered}[/tex]It means that the point is (2,4).
Hence, the graph of y=2x is:
okay i just need the answer no explanation i just need to find the answer asap
Hello there. To solve this question, we need to pay attention to the data given by the question and set up an equation for the amount of rabbits in that colony.
In the year 2000 there were 1200 rabits in a colony, and it was observed that their population was increasing at a rate of 21% each year
For this type of question, we call f(x) the function that shows the population in a certain time x.
This function varies directly to the initial population and grows exponentially according to the rate .
Thus, we have that f(x) = P0 * (1+r)^x
In this case, P0 = 1200 and r = 0.21 (21% converted into decimals)
f(x) = 1200 * (1 + 0.21)^x
f(x) = 1200 * 1.21^x
This is the function that models the population of this colony for a year x.
To find how many rabbits you'll have in the year 2007, plug in x = 7
f(7) = 1200 * 1.21^7
Calculate the value
f(7) = 1200 * 3.797 = 4556
In which year will the population be equal to 5000
Making f(x) = 5000, we solve for x
5000 = 1200 * 1.21^x
Divide both sides of the equation by 1200
25/6 = 1.21^x
Take the natural log on both sides of the equation
ln(25/6) = ln(1.21^x)
Apply the logarithm power rule: log(a^b) = b * log(a)
ln(25/6) = x * ln(1.21)
Rewriting 1.21 as 121/100 = (11/10)², we get:
ln(25/6) = 2x * ln(11/10)
Divide both sides of the equation by a factor of 2ln(11/10)
x = ln(25/6)/(2ln(11/10)) approx. 7.4867 years
Rounding up to the next year, x = 8 years.
Simplify the expression to a polynomial in standard form: (3x + 10) (2x² - 2x + 3)
Step 1
Write out the question.
[tex]\begin{gathered} (3x+10)(2x^2\text{ - 2x + 3)} \\ =3x(2x^2-2x+3)+10(2x^2\text{ - 2x + 3)} \\ =6x^3-6x^2+9x+20x^2\text{ - 20x + 30} \\ =6x^3+14x^2^{}-11x+30^{} \end{gathered}[/tex]I need help to solve. This is my daily practice assignment
The scenario formed a right triangle with an adjacent side of 24.2 ft. and included an angle of 37°.
First, let's recall the three main trigonometric functions.
[tex]\text{ Sine }\Theta\text{ = }\frac{Opposite\text{ Side}}{\text{Hypotenuse}}[/tex][tex]\text{ Cosine }\Theta\text{ = }\frac{Adjacent\text{ Side}}{Hypotenuse}[/tex][tex]\text{ Tangent }\Theta\text{ = }\frac{Opposite\text{ Side}}{Adjacent\text{ Side}}[/tex]In the scenario, the height of the flagpole appears to be the Opposite Side of the right triangle formed.
Since the function that we will be equating involves the Opposite Side and Adjacent Side of a right triangle, we will be applying the Tangent Function to find the height of the flagpole.
We get,
[tex]\text{ Tangent }\Theta\text{ = }\frac{Opposite\text{ Side}}{Adjacent\text{ Side}}[/tex][tex]Tangent(37^{\circ})\text{ = }\frac{x}{24.2}[/tex][tex]\text{ Tangent (37}^{\circ})\text{ x 24.2 = x}[/tex][tex]\text{ 18.23600801249 = x}[/tex][tex]\text{ 18.2 ft. }\approx\text{ x}[/tex]Therefore, the height of the flagpole is 18.2 ft.
which of the following statements about the function f(x)=x2-2x-2 is true
Express f (x) = x^2 -2x in the form f(x) = (x - h ) ^2 - k
x^2 - 2x = +2
h = -b/2a and k = h^2
a = 1 , b= -2
h= -(-2)/ 2(1) = 2/2 = 1
k = h^2 = 1^2 = 1
So, x^2 - 2x = (x-1) ^2 - 1
To rewrite the complete equation
f(x) = (x - 1)^2 - 1 - 2
f(x) = (x - 1)^2 - 3,
[tex]f(x)=(x-1)^2-3[/tex]The minimum value is is -3
Option D is the answer
Car X weighs 136 pounds more than car Z. Car Y weighs 117 pounds more than car Z. The total weight of all three cars is 9439 pounds. How much does each car weigh?
Let x, y and z denote the weighs of car X, car Y and car Z, respectively.
We know that car X weighs 136 more than car Z, this can be express by the equation:
[tex]x=z+136[/tex]We also know that Y weighs 117 pounds more than car Z, this can be express as:
[tex]y=z+117[/tex]Finally, we know that the total weight of all the cars is 9439, then we have:
[tex]x+y+z=9439[/tex]Hence, we have the system of the equations:
[tex]\begin{gathered} x=z+136 \\ y=z+117 \\ z+y+z=9439 \end{gathered}[/tex]To solve the system we can plug the values of x and y, given in the first two equations, in the last equation; then we have:
[tex]\begin{gathered} z+136+z+117+z=9439 \\ 3z=9439-136-117 \\ 3z=9186 \\ z=\frac{9186}{3} \\ z=3062 \end{gathered}[/tex]Now that we have the value of z we plug it in the first two equations to find x and y:
[tex]\begin{gathered} x=3062+136=3198 \\ y=3062+117=3179 \end{gathered}[/tex]Therefore, car X weighs 3198 pound, car Y weighs 3179 pounds and car Z weighs 3062 pounds.
If f(x) = 2x² + 1 and g(x)=x²-7, find (f- g)(x).
ANSWER :
(f - g)(x) = x^2 + 8
EXPLANATION :
From the problem, we have :
[tex]\begin{gathered} f(x)=2x^2+1 \\ g(x)=x^2-7 \end{gathered}[/tex](f - g)(x) is the difference between the two functions
That will be :
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ =2x^2+1-(x^2-7) \\ =2x^2+1-x^2+7 \\ =x^2+8 \end{gathered}[/tex]help.par1. What is the product of 2/10 and 4/9?A. 6/19B. 4/45c. 9/20D. 11/14
To perform a product of fractions, we multiply the numerator with denominator and denominator with denominator:
[tex]\frac{2}{10}\cdot\frac{4}{9}=\frac{2\cdot4}{10\cdot9}[/tex]And solve:
[tex]\frac{2\cdot4}{10\cdot9}=\frac{8}{90}[/tex]And simplify:
[tex]\frac{8}{90}=\frac{4}{45}[/tex]The answer is option B. 4/45
A data set has a mean of 58 and a standard deviation of 17. All of the data values are within three standard deviations of the mean. Which of the following could be the minimum and the maximumvalues of the data set?Minimum 5: Maximum 106Minimum 5; Maximum 111Minimum 8: Maximum 111Minimum 2, Maximum 109
To answer this question, we can use the standard normal distribution, and use the z-scores for finding the minimum and maximum values in the distribution.
The z-score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]We have that the maximum and minimum are within three standard deviations. The z-scores are a measure of the standard deviations from the population mean. Then, the values are for minimum, z = -3, and for maximum, z = 3.
The population's mean is equal to 58 (mu), and the standard deviation is equal to 17.
We are going to find the raw score, x, for the minimum and maximum values 3 standard deviations below and above the mean. Then, we have:
Minimum
[tex]-3=\frac{x-58}{17}\Rightarrow-3\cdot17=x-58\Rightarrow x=-51+58\Rightarrow x=7[/tex]Maximum
[tex]undefined[/tex]In a normal distribution, what percentage of the data falls within 2 standarddeviations of the mean?
In a normal distribution, 68% of data will fall within two standard deviations of the mean
Justine is trying to read the most pages of all students in her Language Arts class by the end of the year. The table shows the pages Justine read, and the time she read them in.Which of the following would be the best equation for the function of the values for Justine's reading?A.h = 40pB.p = 7hC.40p = hD.p = 40h
Given
Hours (h) = 1, 2, 3, 4, 5, 6, 7
Pages (p) = 40, 80, 120, 160, 200, 240, 280
Procedure
[tex]\begin{gathered} \frac{\text{pages}}{\text{hours}}=\frac{40}{1}=\frac{80}{2} \\ \frac{p}{h}=40 \\ p=40h \end{gathered}[/tex]
The answer would be p = 40h
jackie made lunches for the family picnic. Dhe put 8 carrots sticks in each lunch and had no leftovers carrot sticks. which of the following shows how many corrot stick she might have started with?a. 26b. 38c. 44d. 48
Since putting 8 sticks in each lunch box doesn't give any leftover, that means that number of carrot sticks she had is a multiple of 8.
Pretty simply!
Let's see the multiples of 8.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, ....
Out of the choices, only 48 is a multiple of '8'.
Therefore,
D is correct
Rewrite the following into equivalent expressions using the GCF of both numbers and the distributive property.When complete, evaluate the expressions to check for equivalency.124 + 36
24 + 36
[tex]\begin{gathered} \text{factors of 24 = }\mleft\lbrace1,2,3,4,6,8,12,24\mright\rbrace \\ \text{factors of 36 = }\mleft\lbrace1,2,3,4,6,9,12,18,36\mright\rbrace \\ \text{GCF}=12 \\ 24=12\times2 \\ 36=12\times3 \\ (12\times2)+(12\times3) \\ 24+36=12(2+3) \end{gathered}[/tex]9. Simplify: 7 - 5m - 10m* O 7+ 15m O 7-15m O 7-5m O 7 +5m
1) Simplifying 7 -5m -10m we'll need to combine like terms. So
7 -5m -10m Combine Like terms
7 -15m
2) Given the options, the answer is 7 -15m
using exponential growthif the starting population of 5 rabbits grow at 200% each year, how many will there be in 20 years?
grow at 200% each year
so, population becomes twice in each year, then after 20 years:
[tex]\text{population}=5\times2^{20}=5\times1048576=5242880[/tex]answer: population is 5,242,880 after 20 years
Listed are the fractions of the total number of books Allisa put in a bookcase 2/5 history books 1/3 math books 1/10 art books Allisa will fill the remainder of the bookcase with science books Drag and drop the fractions into the boxes that show the fraction of the total number of books that are history, math, or art books in the bookcase and the fraction of the total number of books that will be science
Answer:
Books in Bookcase = 5/6
Science Books = 1/6
Explanation:
Given:
Total number of books Alissa put in a bookcase;
2/5 history books
1/3 math books
1/10 art books
We can go ahead and determine the fraction of the total number of books that are history, math, or art books in the bookcase by adding the given fractions together as seen below;
[tex]\frac{2}{5}+\frac{1}{3}+\frac{1}{10}=\frac{12+10+3}{30}=\frac{25}{30}=\frac{5}{6}[/tex]So the fraction of the total number of books that are history, math, or art books in the bookcase is 5/6
Let x represent the fraction of the total number of books that will be science.
We can go ahead and determine the value of x by subtracting the fraction of the total number of books that are history, math, or art books in the bookcase from 1;
[tex]x=1-\frac{5}{6}=\frac{6-5}{6}=\frac{1}{6}[/tex]So the fraction of the total number of books that will be science is 1/6
Which line is parallel to this one: y=2/3x-9A.y=3/2x+8B.y=2/3x-9C.y=2/3x-1D.y=-3/2x+7
to find the line parallel to th egiven line:
[tex]y=\frac{2}{3}x-9[/tex]the line parallel to the given equation is
[tex]y=\frac{2}{3}x-1[/tex]The graph is,
which equation describes the line with a slope of 2/3 that passes through the point
Option (a)
Given:
The value of slope is, m = -2/3.
Pass throught he point, (x1, y1) = (2,-3)
The objective is to find the equation of the line.
The general equation of straight line is,
[tex]y-y_1=m(x-x_1)[/tex]Now, substitute the given values in the above equation.
[tex]\begin{gathered} y-(-3)=-\frac{2}{3}(x-2) \\ y+3=-\frac{2}{3}(x-2) \end{gathered}[/tex]Hence, option (a) is the correct answer.
Find the area of the figure. zyd 13 / yd The area of the figure is yd?
The area of the given parallelogram is:
A = b·h
b: base = 13 1/5 = (65 + 1)/5 = 66/5 = 13.2 yd
h: height = 27 1/2 = 13.5 yd
A = (13.2 yd)(13.5 yd) = 178.2 yd²
The product of two positive consecutive odd integers is 195. Create and solve an equation to find the value of the integers. What is the sum of the two integers?
Let's define the next variables:
x: the first odd integer
y: the next odd integer
Since they are consecutive:
x + 2 = y
The product of them is 195, then:
x*y = 195
Replacing the y from the first equation into the second one:
x*(x + 2) = 195
x*x + x*2 - 195 = 0
x² + 2x - 195 = 0
Solving with help of the quadratic formula:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-195)}}{2\cdot1} \\ x_{1,2}=\frac{-2\pm\sqrt[]{784}}{2} \\ x_1=\frac{-2+28}{2}=13 \\ x_2=\frac{-2-28}{2}=-15 \end{gathered}[/tex]Given that we are only interested in positive integers, the solution x = -15 is discarded.
Therefore, the integers are 13 and 15
The sum of them is 13 + 15 = 28
Hi. I think I am over thinking this question. Can you show me how this works step by step?
We know that:
MN = 7.3
DC = 8.7
M and N are midpoints of AD and BC respectively.
Since DC - MN = 8.7 - 7.3 = 1.4 and M and N are midpoints, we must have:
AB = 7.3 - 1.4 = 5.9
Find a_1 for the geometric sequence with the given terms. a_3 = 54 and a_5 = 486
ANSWER
[tex]6[/tex]EXPLANATION
We want to find the first term of the sequence.
The general equation for the nth term a geometric sequence is written as:
[tex]a_n=ar^{n-1}[/tex]where a = first term; r = common ratio
Let us use this to write the equations for the third term and the fifth term.
For the third term, n = 3:
[tex]\begin{gathered} a_3=ar^2 \\ \Rightarrow54=ar^2 \end{gathered}[/tex]For the fifth term, n = 5:
[tex]\begin{gathered} a_5=ar^4 \\ \Rightarrow486=ar^4 \end{gathered}[/tex]Let us make a the subject of both formula:
[tex]\begin{gathered} 54=ar^2_{} \\ \Rightarrow a=\frac{54}{r^2} \end{gathered}[/tex]and:
[tex]\begin{gathered} 486_{}=ar^4 \\ a=\frac{486}{r^4} \end{gathered}[/tex]Now, equate both equations above and solve for r:
[tex]\begin{gathered} \frac{54}{r^2}=\frac{486}{r^4} \\ \Rightarrow\frac{r^4}{r^2}=\frac{486}{54} \\ \Rightarrow r^{4-2}=9 \\ \Rightarrow r^2=9 \\ \Rightarrow r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Now that we have the common ratio, we can solve for a using the first equation for a:
[tex]\begin{gathered} a=\frac{54}{r^2} \\ \Rightarrow a=\frac{54}{3^2}=\frac{54}{9} \\ a=6 \end{gathered}[/tex]That is the first term.
Anza gave Angela directions to her house from school Angela was to head south for 2.2 miles and West for 3.5 miles then South again 45.8 miles use Mental Math to determine how far school is for on this house explain your reasoning
Solution
for this case we can do the following:
Could you help me find the slope of the line below
Explanation
[tex]m=\frac{6-(-4)}{6-1}=\frac{10}{5}=2[/tex]Answer
A. 2
what is 11.77 hr converted to hours and min
We are asked to convert 11.77 hours into hours and minutes. The first step is to divide the whole number from its decimal part, that is:
[tex]11.77\text{ hours=11 hours+ 0.77 hours}[/tex]Now we convert the decimal hours into minutes. To do that we use the conversion factor 1h = 60 minutes. We get:
[tex]0.77\text{hour}\frac{60\min}{1hour}=46.2\min [/tex]Therefore, 11.77 hours is approximately 11 hours and 46 minutes.
4x = 2 + 14, A = -3 b=3 C = -3 D = 4
4x = 2 + 14
4x = 16
4 is multiplying on the left, then it will divide on the right
x = 16/4
x = 4