The expression we have to simplify is:
[tex]\frac{1\times10^3}{4\times10^5}[/tex]To divide expression such as the one we have, we use the following law of exponents:
[tex]\frac{a^m}{a^n}=a^{m-n}^{}[/tex]This tells us that when we have the same term in the numerator and denominator, to divide we subtract the exponents.
In this case, we will have:
[tex]\frac{1\times10^3}{4\times10^5}=\frac{1}{4}\times10^{3-5}[/tex]since 3-5=-2, we have:
[tex]\frac{1\times10^3}{4\times10^5}=\frac{1}{4}\times10^{-2}[/tex]We simplify 1/4 to its decimal value 0.25:
[tex]\frac{1\times10^3}{4\times10^5}=0.25\times10^{-2}[/tex]The negative exponent on the number 10, indicates the number of times we have to move the decimal point to the left.
Moving the decimal point two places to the left we get rid of the 10^-2, and the result is:
[tex]\frac{1\times10^3}{4\times10^5}=0.0025[/tex]Answer: 0.0025
Use the pattern from part a to find the sum of the squares of the first 16 Fibonacci numbers
GIVEN:
We are given a Fibonacci sequence as shown in the attached image.
Required;
To use the pattern derived to find the sum of the squares of the first 16 Fibonacci numbers.
Step-by-step solution;
We have a Fibonacci sequence whose first term is 1.
The sequence and the sum of the squares of a given number of terms is derived as follows;
[tex]\begin{gathered} 1^2+1^2=1\times2 \\ \\ 1^2+1^2+2^2=2\times3 \\ \\ 1^2+1^2+2^2+3^2=3\times5 \\ \\ 1^2+1^2+2^2+3^2+5^2=5\times8 \\ \\ 1^2+1^2+2^2+3^2+5^2+8^2=8\times13 \\ \\ 1^2+1^2+2^2+3^2+5^2+8^2+13^2=13\times21 \end{gathered}[/tex]Next, we determine the sequence from the 1st to 16th term as follows;
[tex]\begin{gathered} 1^2+1^2+2^2+3^2+5^2+8^2+13^2+21^2+34^2+55^2+89^2 \\ \\ +144^2+233^2+377^2+610^2+987^2=987\times1597 \end{gathered}[/tex]The sum of the squares of the first 16 terms therefore is
[tex]987\times1597=1,576,239[/tex]ANSWER:
[tex]1,576,239[/tex]Round the following percentages two decimal placesA. 16.981%B. 13.655%C. 0.569%D. 98.990%E. 98.999%
Given the percentages provided in the exercise, you need to follow these steps in order to round them to two decimal places:
1. Identify the digit in the Thousandths Place.
2. If the digit is greater than or equal to 5, you must round up. This means that you must add 1 unit to the digit in the Hundredths Place, and the other digits on the right become zero.
3. If the digit is less than 5, you must round down. This means that the digit in the Hundredths Place stays the same and the other digits on the right become zero.
Therefore, applying those steps, you get:
A.
[tex]16.981\text{\%}\approx16.98\text{\%}[/tex]B.
[tex]13.655\text{\%}\approx13.66\text{\%}[/tex]C.
[tex]0.569\text{\%}\approx0.57\text{\%}[/tex]D.
[tex]98.990\text{\%}\approx98.99\text{\%}[/tex]E.
[tex]98.999\text{\%}\approx99.00\text{\%}[/tex]Hence, the answers are:
A.
[tex]16.981\text{\%}\approx16.98\text{\%}[/tex]B.
[tex]13.655\text{\%}\approx13.66\text{\%}[/tex]C.
[tex]0.569\text{\%}\approx0.57\text{\%}[/tex]D.
[tex]98.990\text{\%}\approx98.99\text{\%}[/tex]E.
[tex]98.999\text{\%}\approx99.00\text{\%}[/tex]A manufacturer made a television set at a cost of $6,000.00 and sold it to a wholesaler at a profit of 10%.The wholesaler sold it to a retailer at a profit of 15%. The retailer marked the set to be sold at a profit of 25%.find the cost to the wholesaler, the selling price of the wholesaler and the marked price of the retailer
cost to the wholesaler:6600
selling price of the wholesaler : 7590
the marked price of the retailer is $ 9487.5
Explanation
Step 1
a)A manufacturer made a television set at a cost of $6,000.00 and sold it to a wholesaler at a profit of 10%
to find the new price, we can use the formula:
[tex]\text{new price= original price}\cdot(1+\frac{\text{ \% }}{100})[/tex]so,let
original price= 6000
%=10
replace
[tex]\begin{gathered} \text{new price= original price}\cdot(1+\frac{\text{ \% }}{100}) \\ \text{New}=6000\cdot(1+\frac{10}{100})=6000(1.1)=6600 \end{gathered}[/tex]so, the manufacturer sold the TV set for $6600
Step 2
b)The wholesaler sold it to a retailer at a profit of 15%
again we need apply the formula
this time, let
original price= 6600
% of profit=15
replace
[tex]\begin{gathered} \text{new price= original price}\cdot(1+\frac{\text{ \% }}{100}) \\ \text{New}=6600(1+\frac{15}{100})=6600(1.15) \\ \text{New}=7590 \end{gathered}[/tex]therefore,
the wholsaer sold it for $7590
Step 3
c)The retailer marked the set to be sold at a profit of 25%
hence,let
original= 7590
% of profit= 25%
replace and calculate
[tex]\begin{gathered} \text{new price= original price}\cdot(1+\frac{\text{ \% }}{100}) \\ \text{New}=7590\cdot(1+\frac{25}{100})=7590(1.25) \\ \text{New}=9487.5 \end{gathered}[/tex]therefore, the marked price of the retailer is $ 9487.5
I hope this helps you
How to solve for problem 21? Calculate the surface area of the hemisphere with the knowledge that the circumference of a great circle is 40.8 inches.
In order to get the surface area of a hemisphere, let's determine its radius first.
Based on the question, the circumference of a great circle is 40.8 inches. Since circumference = 2πr, then 40.8 inches = 2πr. From this, we can solve for the radius.
[tex]40.8=2\pi r[/tex]To solve for the radius, divide both sides of the equation by 2π. Use π = 3.14159
[tex]\frac{40.8}{2\pi}=r[/tex][tex]\frac{40.8}{2(3.14159)}\Rightarrow\frac{40.8}{6.28318}\Rightarrow6.4935[/tex]Therefore, the length of the radius is 6.4935 inches.
Now that we have the radius, let's calculate the surface area of the hemisphere. The formula is:
[tex]SA_{hemisphere}=3\pi r^2[/tex]Let's plug into the formula r = 6.4935 inches and π = 3.14159
[tex]SA_{hemisphere}=3(3.14159)(6.4935in)^2[/tex]Then, solve.
[tex]SA_{hemisphere}=(9.42477)(42.1655in^2)[/tex][tex]SA_{hemisphere}\approx397.4in^2[/tex]Therefore, the surface area of the hemisphere is approximately 397.4 square inches.
If y varies directly with X and Y 454 when 20. then which equation best represents this proportional relationship? A) y = 0.37xB) y = -0.37x C) y = -2.7xD) y = 2.7x
We need to find the constant of proportionality, so:
y(x) = ax
Where:
a = constant of proportionality
Using the data provided, if x = -20 ; y(-20) = -54, so:
-54 = a(-20)
Solve for a:
Divide both sides by (-20):
-54/-20 = -20a/-20
2.7 = a
a = 2.7
y = 2.7x
A) what is a linear system?B) what is the solution for a linear system?C) is it possible for a linear system not to have a solution? If so what can be deduced about the two lines?
PART A
A Linear system is a set of 2 simultaneous equations with 2 variables involved.
PART B
Graphically speaking, the solution of the system is the point were both lines meet (intersect).
PART C
Yes, it is possible for a inear system not to have a solution. This means that the lines never intersect, so we can deduct that they are parallel.
Convert 0.94 to fraction ( simply if possible)
to convert decimal to fraction.
[tex]\begin{gathered} \frac{94}{100} \\ =\frac{47}{50} \end{gathered}[/tex]the answer is 47/50
The perimeter of a regular pentagon is 10x + 15. what is the length of each side of the pentagon?
A regular pentagon has 5 equal sides. recall, perimeter is the sum of the distance around a shape. This means that the perimeter of the regular pentagon is the sum of the 5 equal sides. If the perimeter is 10x + 15, then,
length of each side = (10x + 15)/5
length of each side = 2x + 3
You have found the following ages (in years) of 5 gorillas. Those gorillas were randomly selected from the 29 gorillas at your local zoo:8, 4, 14, 16, 8,Based on your sample, what is the average age of the gorillas? What is the standard deviation? Round your answers to the nearest tenth.average age_______standard deviation_________
ANSWER:
Average age 10
Standard deviation 4.9
STEP-BY-STEP EXPLANATION:
To calculate average age of the gorillas:
[tex]average=\frac{\sum^n_i}{n}[/tex]Replacing:
[tex]\begin{gathered} average=\frac{8+4+14+16+8}{5} \\ average=\frac{50}{5} \\ average=10 \end{gathered}[/tex]The average age of the gorillas is 10
The formula for standard deviation is:
[tex]s^2=\frac{1}{n-1}\cdot\sum ^n_i(x_i-\bar{x})^2[/tex]Replacing:
[tex]\begin{gathered} s^2=\frac{1}{5-1}\cdot\mleft\lbrace(8-10)^2+(4-10)^2+(14-10)^2+(16-10)^2+(8-10)^2\mright\rbrace^{} \\ s^2=\frac{1}{4}\cdot(4+36+16+36+4) \\ s^2=\frac{96}{4} \\ s=\sqrt[]{24} \\ s=4.9 \end{gathered}[/tex]The standard deviation of gorillas is 4.9
Answer:
Step-by-step explanation:
dude I got it wrong bc I followed the comment before. The first answer is right
What is the standard form for g(x)= the square root of 6-x
The standard form of an Irrational function is given as:
[tex]\begin{gathered} y=\sqrt{a(x-p)}+q \\ \text{where:} \\ y\geqslant q\text{ and x}\geqslant p \end{gathered}[/tex]In the given function:
[tex]\begin{gathered} g(x)=\sqrt{6-x} \\ \text{Domain: }\left\lbrace x\in R\colon x\leqslant6\right\rbrace \\ \text{Range: }\left\lbrace y\in R,\text{ }y\geqslant0\right\rbrace \end{gathered}[/tex]Therefore, the standard form of g(x) is:
[tex]g(x)=\sqrt{-(x-6)}[/tex]SF(A-B) Sabe Capes Career Card 5 kapsa Sant Card 6 Card 5 I C Card 6 Card 7 C Card 7 Sport Card 8 Card 8
By considering the grid lines in the image, you would see that 1 box represents 1 unit.
1 box = 1 unit
For card 5:
The small circle spans 2 boxes
Size of small circle (A) = 2 units
The big circle spans 6 boxes
Size of big circle (B) = 6 units
The Scale Factor, SF (A-B) = 2 / 6 = 1 / 3
Therefore, SF (A-B) = 1 : 3
For card 6:
Size of A = 9
Size of B = 3
SF (A-B) = 9 / 3 = 3 / 1
SF (A-B) = 3 : 1
For card 7:
Size of A = 4
Size of B = 2
SF (A-B) = 4 / 2 = 2 / 1
SF (A-B) = 2 :1
For card 8:
Size of A = 5
Size of B = 5
SF (A-B) = 5 / 5 = 1 : 1
SF (A-B) = 1
The bakers want to sell their house for $145,500. After 2 months, the Bakers decided to mark down the price of their house 8% to sell more quickly. How much are the Bakers selling their Fouse for now?
The details provided are as follows;
The sales price of the house = 145500
Mark down price = -8%
This means the bakers were willing to sell their price not at a 100% price of 145500, but at a price which is -8% of 145500. We would start by calculating 8% of 145500 as follows;
How do I solve and graph this inequality?(2/3)x + 3 > 11
From the problem, we have the inequality :
[tex]\frac{2}{3}x+3>11[/tex]Substract both sides by 3
[tex]\begin{gathered} \frac{2}{3}x+3-3>11-3 \\ \frac{2}{3}x>8 \end{gathered}[/tex]Cross multiplication :
[tex]\begin{gathered} 2x>8(3) \\ 2x>24 \end{gathered}[/tex]Divide both sides by 2 :
[tex]\begin{gathered} 2x>24 \\ x>12 \end{gathered}[/tex]The solution is x > 12
To grahp this inequality, take note that the graph will be composed of a circle or endpoint and an arrow
If the inequality sign is < or >, the endpoint is an open circle.
If the inequality sign is ≤ or ≥, the endpoint is a closed or shaded circle.
Since the inequality symbol in the question is >, we will use an open circle.
The graph will look like this.
The endpoint is located at x = 12, and the direction is to the right since the sign is greater than ">"
Graph the inequality on the numberline and then write it in interval notation. 4-3y<-8
First, let's simplify the inequality
[tex]\begin{gathered} \frac{4}{3}y<-8 \\ \Rightarrow4y<-24 \\ \Rightarrow y<-6 \end{gathered}[/tex]The graph looks like this:
Notice that the white dot is placed above the -6, it is important to include it like that.
Now, as an interval:
[tex]\begin{gathered} y<-6 \\ \Rightarrow y\in(-\infty,-6) \end{gathered}[/tex]Using suitable identity evaluate the following : 98^3
941,192
Steps:
[tex](a-b)^3=a^3-b^3-3a^2b+3ab[/tex][tex]\begin{gathered} (98)^3=(100-2)^3 \\ (100-2)^{3\text{ }}=(100)^3-(2)^3-3\cdot(100)^2\cdot2+3\cdot100\cdot2^2\text{ } \\ (100)^3-(2)^3-3\cdot(100)^2\cdot2+3\cdot100\cdot2^2\text{ = 1,0}00,000\text{ - 3 - 60,000 +1,200} \\ \text{ 1,0}00,000\text{ - 3 - 60,000 +1,200 = 941,192} \end{gathered}[/tex]Can you help me solve this problem. Part b only
Answer:
C. (x, -y)
Explanation:
Given quadrilateral ABCD, we want to determine the coordinate describing the vertex when it is reflected over the x-axis.
When a point (x,y) is reflected across the x-axis, the transformation rule is given below:
[tex](x,y)\to(x,-y)[/tex]Given that (x,y) describes a coordinate of quadrilateral ABCD, the coordinates of A''B''C''D'' will be:
[tex](x,y)\to(x,-y)[/tex]The coordinate of the corresponding vertex is (x, -y).
Option C is correct.
Solve the formula for the indicated variable.W = XYZ for ZZ=
Answer:
Z = W/(XY)
Step-by-step explanation:
We have the following equation:
W = XYZ
To solve for Z, we switch XY to the other side of the equality, doing the inverse multiplication(it multiplies Z, so it switches dividing). Then
Z = W/(XY)
Is the solution for Z.
Find the equation of the line that passes through the two points ( -3,9) and ( -1/2,-7/2).Write your answer in standard form.
Given
The line passes through the points,
[tex](-3,9),(-\frac{1}{2},-\frac{7}{2})[/tex]To find the equation of the line and write in the standard form.
Now,
The equation of the line passing through two points is given by,
[tex]\frac{y_{}-y_1}{y_2-y_1}=\frac{x_{}-x_1}{x_2-x_1}[/tex]Since the points are
[tex](-3,9),(-\frac{1}{2},-\frac{7}{2})[/tex]Then, the equation of the line is,
[tex]\begin{gathered} \frac{y-9}{-\frac{7}{2}-9}=\frac{x-(-3)}{-\frac{1}{2}-(-3)} \\ \frac{y-9}{\frac{-7-18}{2}}=\frac{x+3}{\frac{-1+6}{2}} \\ \frac{y-9}{-25}=\frac{x+3}{5} \\ \frac{y-9}{-5}=x+3 \\ y-9=-5(x+3) \\ y-9=-5x-15 \\ y=-5x-15+9 \\ y=-5x-6 \end{gathered}[/tex]Hence, the equation of the line is,
[tex]y=-5x-6[/tex]And, the standard form of the line is,
[tex]5x+y+6=0[/tex]I will like help with the second question -3 1/2...
Answer:
Step-by-step explanation:
hope this helps
How long will it take for an investment of 1600 dollars to grow to 7600 dollars, if the nominal rate of interest is 8.3 percent compounded quarterly? FV = PV(1 + r/n )^ntAnswer= ________years. (Be sure to give 4 decimal places of accuracy.)
18.9669 years
Explanation:principal = $1600
future value = $7600
rate = 8.3% = 0.083
n = number of times compounded = quarterly
n = 4
time = ?
To determine the time it will take, we will apply the compound interest formula:
[tex]FV\text{ = P(1 +}\frac{r}{n})^{nt}[/tex]substitute the values into the formula:
[tex]\begin{gathered} 7600\text{ = 1600(1 +}\frac{0.083}{4})^{4\times t} \\ 7600=1600(1+0.02075)^{4t} \\ \\ \text{divide both sides by 1600:} \\ \frac{7600}{1600}=\frac{1600(1+0.02075)^{4t}}{1600} \\ 4.75\text{ = }(1+0.02075)^{4t} \\ \end{gathered}[/tex][tex]\begin{gathered} 4.75\text{ = }(1.02075)^{4t} \\ \text{take log of both sides:} \\ \log 4.75\text{ = log }(1.02075)^{4t} \\ \log 4.75\text{ = 4t log }(1.02075) \\ \\ \text{divide both sides by log }(1.02075)\colon \\ \frac{\log 4.75\text{ }}{\text{ log }(1.02075)}\text{=}\frac{\text{ 4t log }(1.02075)}{\text{ log }(1.02075)} \\ 75.8677\text{ = 4t} \end{gathered}[/tex][tex]\begin{gathered} \text{divide both sides by 4:} \\ \frac{75.8677}{4}\text{ = }\frac{4t}{4} \\ t\text{ = 18.9669} \end{gathered}[/tex]It will take 18.9669 years (4 decimal place)
A survey of a group of seventh graders and a group of teachers at a local middle school asked how many siblings they each have. The dot plots below show the results.
Students
A dot plot titled Students. A number line going from 0 to 9 labeled number of siblings. There are 2 dots above 0, 4 above 1, 7 above 2, 5 above 3, 2 above 4, and 0 above 5, 6, 7, 8, and 9.
Teachers
A dot plot titled Teachers. A number line going from 0 to 9 labeled Number of siblings. There is 1 dot above 0, 3 dots above 1, 2 above 2, 4 above 3, 5 above 4, 3 above 5, 1 above 6, 0 above 7, 1 above 8, and 0 above 9.
Which compares the modes of the data?
To obtain the information requested in the question, the following steps are necessary:
Step 1: Write out the values from the box plot as a sequence of numbers, as follows:
[tex]0,0,0,1,1,1,2,2,2,3,3,3,3,3,3,4,4,4,6[/tex]Step 2: Now, that we have the values written out as above, we can proceed to answering the questions, as follows:
a) To obtain the number of students that have at least 4 siblings (that is, more than 4 siblings), we count the number of times the numbers 4 and 6 occur.
By counting, we get: 5
Therefore, the number of students that have at least 4 siblings is: 5
b) To obtain the number of students that have no siblings (0 siblings), we count the number of times the number 0 occurs.
By counting, we get: 3
Therefore, the number of students that have at least 0 siblings is: 3
c) To obtain the mean (average) number of siblings, we proceed as follows:
[tex]average=\frac{sum\text{ of all the number of siblings}}{\text{total number of students}}[/tex]Therefore:
[tex]\begin{gathered} \text{average}=\frac{0+0+0+1+1+1+2+2+2+3+3+3+3+3+3+4+4+4+6}{20} \\ \text{average}=\frac{45}{20}=\frac{9}{4}=2.25 \\ \text{average}=2.25 \end{gathered}[/tex]Therefore, the mean (average) number of siblings is 2.25 (approximately 2)
Find the area of the shaded region. RQ=71.5 inches and PO=93.4 inches. Use 3.14 for π as necessary.A. 18,468 in²B. 2,836 in²C. 25,886 in²D. 62,345 in²
We must find the area of the bigger circle and then the area of the smaller circle.
Area of the bigger circle:
Using the formula for the area, we have:
[tex]\begin{gathered} A=\pi(PO)^2 \\ A=\pi(93.4)^2\text{ in}^2\text{(Replacing)} \\ A=27392\text{ in}^2\text{ (Raising the radius to the power of 2 and multiplying) } \end{gathered}[/tex]Area of the smaller circle:
[tex]\begin{gathered} _{}LO=PO-RQ\text{ (Finding the radius of the smaller circle)} \\ LO=(93.4-71.5)inches=21.9\text{ inches} \\ A=\pi(LO)^2\text{in}^2\text{ (Area of the smaller circle)} \\ A=\pi(21.9)^2\text{ in}^2\text{(Replacing)} \\ A=1506\text{in}^2\text{ (Raising the radius to the power of 2 and multiplying)} \\ \end{gathered}[/tex]Area of the shaded region:
The area of the shaded region is: Ab - As (Ab:Area of the bigger circle, As: Area of the smaller circle)
The area of the shaded region is: (27392 - 1506) square inches = 25886 square inches.
The answer is the option C.
Explain why you could use a base 2 or a base 4 to solve the problem above and get the same answer. Show your work and explain.
Step 1. The expression that we have is:
[tex]4^x=16^{x-2}[/tex]To prove that we get the same answer if we use a logarithm base 2 and a logarithm base 4, we will solve the equation using both and check that the result is the same.
Step 2. To solve using a base 2 logarithm, we apply it to both sides of the equation:
[tex]log_2(4^x)=log_2(16^{x-2})[/tex]Using the following property of logarithms:
[tex]log(x^m)=mlog(x)[/tex]The expression is simplified as follows:
[tex]xlog_2(4)=(x-2)log_2(16)[/tex]The base 2 logarithm of 4 and 16 is:
[tex]\begin{gathered} log_2(4)=2 \\ log_2(16)=4 \end{gathered}[/tex]Substituting these values into the equation:
[tex]\begin{gathered} x(2)=(x-2)(4) \\ Simplifying: \\ 2x=4x-8 \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 2x-4x=-8 \\ -2x=-8 \\ x=\frac{-8}{-2} \\ \boxed{x=4} \end{gathered}[/tex]Step 3. Now we repeat the process but this time we use the logarithm base 4.
The expression is:
[tex]4^{x}=16^{x-2}[/tex]Applying logarithm base 4 to both sides:
[tex]log_4(4^x)=log_4(16^{x-2})[/tex]Simplifying:
[tex]xlog_4(4)=(x-2)log_4(16)[/tex]The base 4 logarithm of 4 and 16 is:
[tex]\begin{gathered} log_4(4)=1 \\ log_4(16)=2 \end{gathered}[/tex]Substituting these values into our equation:
[tex]\begin{gathered} x(1)=(x-2)(2) \\ Simplifying\text{ and solving for x:} \\ x=2x-4 \\ x-2x=-4 \\ -x=-4 \\ \boxed{x=4} \end{gathered}[/tex]Answer: We have proven that we get the same result using a base 2 logarithm and a base 4 logarithm.
Use pictures and equations to show your work.At the end of the year, Mrs. Weeks bought an assortment of new balls toreplace some of the old ones. She had $150.00 to spend. Describe twodifferent ways that Mrs. Weeks could spend her money if she bought at leasttwo of each of the balls.Use coins or cut out the manipulatives on the next page to help you act outthe problem.
First, let's calculate the amount of money required to purchase two of each type of ball:
[tex]\begin{gathered} C=2(8+9+7+5)\\ \\ C=2\cdot29\\ \\ C=58 \end{gathered}[/tex]Now, to complete the remaining amount of money, we can choose more balls until the total cost reaches $150.
For example, let's add two more of each type of ball. So the total cost will be 116.
Then, to complete the remaining $34, let's create two possibilities of adding more balls:
- 2 baseballs and 4 softballs
- 3 basketballs and 1 baseball
Therefore two possibilities are:
4 footballs, 4 basketballs, 6 baseballs and 8 softballs;
4 footballs, 7 basketballs, 5 baseballs and 4 softballs.
Let's check if the total cost of each case is $150:
[tex]\begin{gathered} C_1=4\cdot8+4\cdot9+6\cdot7+8\cdot5=32+36+42+40=150\\ \\ C_2=4\cdot8+7\cdot9+5\cdot7+4\cdot5=32+63+35+20=150 \end{gathered}[/tex]Identify the constant in the following expression:-3m-7 A)7. B)-7. C)3. D)-3
For this case we have the following problem given:
[tex]3m-7[/tex]And e want to identify the constant of the expression given . We need to remember that the constant represent the number without any variabl so then for this case the answer would be -7
B)-7.
A diver stands on a platform 15 feet above a lake. He does a dive off the platform and lands in the water below. His height (h) above the lake after x seconds is shown on the graph below. After how many seconds did the diver land in the water?
Answer:
The diver lands on water after 3 seconds.
[tex]3\text{ seconds}[/tex]Explanation:
Given that the diver stands on a platform 15 ft above a lake.
As shown on the graph, at x=0, height h equals 15 ft.
The diver lands on water at h equals zero.
The time at h=0 is x=3 seconds.
Therefore, the time taken for the diver to land in water is;
[tex]\begin{gathered} x=3-0 \\ x=3\text{ seconds} \end{gathered}[/tex]What is the monthly rent? Can Jacob afford this rental if he makes 8,000 each month?
Solution
We are given the function
[tex]y=1.165x+615.23[/tex]Part A
We want to find the monthly rent for an apartment that has 1,500 sq.ft
We only need to put x = 1500 and then compute
[tex]\begin{gathered} y=1.165x+615.23 \\ \text{put x = 1500} \\ y=1.165(1500)+615.23 \\ y=1747.5+615.23 \\ y=2362.73 \end{gathered}[/tex]Therefore, the monthly rent is $ 2362.73
Part B
28% of the monthly gross income is on housing
If Jacob makes $ 8,000. We want to determine if Jacob can afford the rental
Jacob will spend 28% on housing
[tex]\begin{gathered} \frac{28}{100}\times8000 \\ =28\times80 \\ =2240 \end{gathered}[/tex]Jacob can only spend $2240 0n housing
Since the monthly rent ($2362.73) is greater than Jacob's recommendation percentage on housing ($2240), Therefore, Jacob CANNOT afford it.n
I need help answering this, having trouble It’s trig from my ACT prep guideI will send you another pic of the graph that goes along
Question:
Solution:
Step 1: graph the parent function f(x)=cos(x)
Step 2: We want to graph y = f(x+c) where c is π/2. To do this, shift the graph of y =f(x)=cos(x) to the left π/2 units:
So that, we can conclude that the correct answer is:
13. Identify the zeros of f(x)= - x - 3x + 4 = -(x + 4)(x - 1).Sketch a rough graph of f(x).
To find the zeros of the function we equal the function to 0
[tex]\begin{gathered} 0=-(x+4)(x-1) \\ 0=(x+4)(x-1) \end{gathered}[/tex]since this is a product, it can be 0 when one of the factors is equal to zero, for that reason:
[tex]\begin{gathered} x+4=0 \\ x=-4 \\ x-1=0 \\ x=1 \end{gathered}[/tex]the zeros of the function are x=-4 and x=1.
after that to do the sketch find the vertex which can be found by
[tex](h,k)=(-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]according to the function a=-1, b=-3 and c=4
the vertex is
[tex]\begin{gathered} h=-(\frac{-3}{2(-1)}) \\ h=-1.5 \end{gathered}[/tex]using the function find k
[tex]\begin{gathered} k=-(-1.5)^2-3(-1.5)+4 \\ k=6.25 \end{gathered}[/tex]the vertex is at (-1.5,6.25)
the graph should look like this
-r(a + b) if r = -2, a = 4, and b = -5
To evaluate the given equation using the given values for each variable:
-Substitute the corresponding values in the equation:
[tex]-(-2)(4+(-5))[/tex]- Eliminate parentheses:
Use the next sing rules:
[tex]\begin{gathered} +(+)=+ \\ +(-)=- \\ -(+)=- \\ -(-)=+ \end{gathered}[/tex][tex]\begin{gathered} =2(4-5) \\ \end{gathered}[/tex]- Solve operations in parentheses:
[tex]=2(-1)[/tex]- Solve multiplication:
[tex]=-2[/tex]Then, the solution is -2