You can infer from this problem that the shape of the wooden plank is a rectangle based on the dimensions given. The length of a rectangle is usually the longest side of the rectangle so you can conclude that the length of the rectangle is 12.5 cm. Therefore, the width is 8.5 cm.
What is the surface area of this figure?
Match the numbers in scientific notation with the corresponding numbers in standard notation.
232,000,000
0.00000431
2,320,000,000
0.000000000000431
2.32E9
2.32E8
4.31E-13
4.31E-6
The matching of the given numbers to there standard notation is given as follows:
232,000,000------ 2.32E8
0.00000431 ------ 4.31E-6
2,320,000,000 ----- 2.32E9
0.000000000000431 ----- 4.31E-13
Step-by-step explanation:We know that the standard notation of a number is given by:
There must be only one digit before the decimal and rest after that.
Also, it there is a shift of the decimal to the right then the power goes to negative and positive if shift is to the left.
1)
232,000,000
Here we have to take the decimal 8 digits from the left and the number in standard notation will be given by:
[tex]2.32\times 10^8[/tex]
which is written as: 2.32E8
2)
0.00000431
Here we have to shift the decimal 6 digits to the right.
Hence, the number is expressed as:
[tex]4.31\times 10^{-6}[/tex]
which is written as: 4.31E-6
3)
2,320,000,000
Here the decimal is to be put 9 digits from the left and hence the number is represented as:
[tex]2.32\times 10^9[/tex]
which is given by: 2.32E9
4)
0.000000000000431
Here we will shift the decimal 13 places to the right and hence the number is given by:
[tex]4.31\times 10^{-13}[/tex]
which is given by: 4.31E-13
Assignment: Compound Interest Investigation
Tyler has earned money by helping out on a neighbor's farm and now wants to put his earnings in a savings account. He is a bit confused on the different interest options available and how each will impact the amount he has after several years. Help Tyler better understand by showing him how his money will increase in an account that uses simple interest and one that uses compound interest over a specified period of time.
1. a. If Tyler deposits $1500 of the $3200 he has earned in an account that pays 4% interest compounded annually, how much will he have in his account after 5 years?
b. If Tyler deposits $1500 of the $3200 he has earned in an account that pays 4% simple interest, how much will he have after 5 years? Show all work.
c. Which account would yield a greater amount? What is the difference between the two amounts?
2. a. If Tyler deposits $2000 of the $3200 he has earned in an account that pays 8% interest compounded quarterly, how much will he have in his account after 1 year?
b. If Tyler deposits $2000 of the $3200 he has earned in an account that pays 8% simple interest, how much will he have after 1 year? Show all work.
c. Which account would yield a greater amount? What is the difference between the two amounts?
3. Tyler decides to deposit his earnings of $3200 in a savings account. Bank A offers an account with a simple interest rate of 3.5%. Bank B offers an interest rate of 3.4% compounded annually. After 3 years, in which bank will Tyler have the greatest total? Show all work.
a. Find the interest earned for Bank A.
b. Find the total amount for Bank B.
c. Which bank should Tyler choose if he wants to earn the greater amount? Explain your reasoning.
d. Which account would yield a greater amount? What is the difference between the two amounts?
Alexandra spent her birthday on a video game that cost $24, a controller for $13, and a memory card for $16. there total tax was $3. what is a subtraction equation for finding how much she gave alexandraif she received $4 in change
Give the required elements of the hyperbolas below.
1. x^2/9 - y^2/16 =1
a. 3
b. 4
c. 9
d. 16
2. 4x^2 - y^2 = 16
a. 1
b. 2
c. 4
d. 16
3. 2y^2 - 3x^2 =6
a. √ ̅2
b. √ ̅3
c. 2
d. 3
Final answer:
The hyperbolas' equations are analyzed to find the values of a² and b². For the first equation, a² is 9 and b² is 16; for the second, a² is 4 and b² is 16; and for the third, a² is 3 and b² is 2.
Explanation:
To identify the required elements for each of the hyperbolas, we need to look at the equations of the hyperbolas and determine the values of a and b, which are the square roots of the denominators of the x-squared and y-squared terms when they are in the standard form for a hyperbola, x²/a² - y²/b² = 1 for horizontal hyperbolas, and y²/a² - x²/b² = 1 for vertical hyperbolas.
1. For the hyperbola x²/9 - y²/16 = 1, the required elements are a² and b². Hence, a² = 9 and b² = 16, leading to the answers being c and d respectively.
2. The hyperbola 4x² - y² = 16 can be rearranged to x²/4 - y²/16 = 1. Here, a² = 4 and b² = 16, making the answers c and d respectively.
3. For hyperbola 2y² - 3x² = 6, it rearranges to y²/3 - x²/2 = 1. In this case, a² = 3 and b² = 2, so the answers are d and a respectively, since we are looking for a and b, not a² and b².
Which expression is equivalent to 15x+50
Final answer:
The equivalent expression to 15x+50, by factoring out the greatest common divisor, is 5(3x+10).
Explanation:
The question is asking for an equivalent expression to the linear algebraic expression 15x+50. By examining the coefficient and constant term, we note that both terms are divisible by 5. Therefore, we can factor out 5 to simplify the expression. The steps for simplification are as follows:
Find the greatest common divisor (GCD) of the coefficients, which in this case is 5.
Divide each term by the GCD.
Express the factored form using the distributive property.
By applying these steps:
The GCD of 15 and 50 is 5.
Dividing each term by 5 gives us 3x + 10.
Thus, we can write the expression as 5(3x + 10), which is equivalent to the original expression 15x + 50.
The plans for a shed call for a rectangular floor with a perimeter of 248ft. The length is three times rhe width. Find the length and width
length= 93 width=31
248=2L+2w
L=3w
248=2x3w+2w
248=6w+2w
248=8w (248/8=31)
31=w
L=3 x 31
L=93
check answer: 248= 2x93 + 2x31
248=186+62
248=248
Which ordered pair is the best estimate for the solution of the system of equations? y = −1/5x + 1 y = x + 4
Final answer:
The solution to the system of equations y = -1/5x + 1 and y = x + 4 is found by setting the equations equal to each other, solving for x, and then substituting back to find y. The solution is the ordered pair (-5, -1).
Explanation:
The student is asking to find the ordered pair that represents the best estimate for the solution to a system of linear equations. The given system of equations is: y = −1/5x + 1 and y = x + 4. To find the solution, we need to determine where the two lines intersect, which will give us the coordinates (x, y) of the solution.
To find the intersection, we can set the two equations equal to each other since they both equal y: −1/5x + 1 = x + 4. Then, we would solve for x:
Add 1/5x to both sides to get 1 = 6/5x + 4
Subtract 4 from both sides to get −3 = 6/5x
Multiply both sides by 5/6 to get x = −3 × (5/6)
Which simplifies to x = −5
Now we substitute x back into either of the original equations to find y. For instance, using the second equation y = x + 4, we find that:
y = (−5) + 4 = −1
Therefore, the ordered pair that is the solution to the system of equations is (-5, -1).
BRAINLIEST TO WHO GET IT RIGHT.
I know quadratic formula. I don’t understand how I would input the lines I’m given into that formula. Please help me, I already know what x equals.
I need help with number 3 please, thanks.
A number is between -5 and -14. What is the least possible integer value of the number?
Consider circle Y with radius 3 m and central angle XYZ measuring 70°. What is the approximate length of minor arc XZ? Round to the nearest tenth of a meter. meters
Use formula for the length of the arc:
[tex] \text{Arc Length} = (\theta\cdot \dfrac{\pi}{180^{\circ}}) \cdot r [/tex], where [tex] \theta [/tex] is central angle.
Substitute [tex] \theta [/tex] and r=3 into formula:
[tex] \text{Arc Length} = (\theta\cdot \dfrac{\pi}{180^{\circ}}) \cdot r=(70^{\circ}\cdot \dfrac{\pi}{180^{\circ}})\cdot 3=\dfrac{7}{6}\pi [/tex].
Answer: [tex] \text{Arc Length} =\dfrac{7}{6}\pi [/tex].
Answer:
its 3.7
Step-by-step explanation:
how do i solve this complex number (-3i)(-5i)(6+i)
What is the appropriation for the perimeter of a semicircle with a diameter of 64 meters? Use 3.14 to approximate pi
The weight of an object on earth is about 6 times as great as the objects weight on earths moon. What is the weight of an object on Earth’ s moon if it weight 42 pounds on Earth?
An object would weight 6 pounds on Callisto . What would it weight on Earth’s moon?
Ellen boughy a tray of plants for $8.15 there where 16 plants in the tray if i bought only one what would it cost
A(n) __________ is a rate that has a denominator of 1.
empty set
unit rate
contradiction
identity
Talia has 80 pounds of soil she wants to divide it into bucket so that each bucket weighs 4/5 lb how many buckets will she need
make a triangle with 5 smaller shapes
I'd appreciate someones help right about now Haha :)
I need help :/
What's the product of 713 and 82?
Terrance run 6 miles every half hour Jesse runs 2 miles every 15 minutes and Sandra runs at a rate of 8 miles in 45 minutes. How does Sandra unit rate compare to terrance and Jesse
To compare Sandra's unit rate with Terrance's and Jesse's, we must calculate their speeds in mph. Terrance runs at 12 mph, Jesse at 8 mph, and Sandra at 10.67 mph. Therefore, Sandra is faster than Jesse but slower than Terrance.
To compare Sandra's unit rate to Terrance's and Jesse's, we need to determine the speed at which each person runs in miles per hour (mph). The given information is:
Terrance runs 6 miles every half hour.
Jesse runs 2 miles every 15 minutes.
Sandra runs 8 miles in 45 minutes.
First, we calculate each person's running speed:
Terrance: 6 miles in 0.5 hours (30 minutes), so we multiply by 2 to find his speed per hour: 6 miles ÷ 0.5 hours = 12 mph.
Jesse: 2 miles in 0.25 hours (15 minutes), so we multiply by 4 to find his speed per hour: 2 miles ÷ 0.25 hours = 8 mph.
Sandra: 8 miles in 0.75 hours (45 minutes), so we divide her distance by the time in hours: 8 miles ÷ 0.75 hours = 10.67 mph.
Therefore, compared to Terrance and Jesse, Sandra's running speed is:
Faster than Jesse's (10.67 mph > 8 mph)
Slower than Terrance's (10.67 mph < 12 mph)
17 heartbeats in 15 seconds as a unit rate
Answer:
17 heartbeats in 15 seconds as a unit rate is-
1.13 over 1
hope it is clear to you
A rectangular quilt is 5 feet wide and 7 feet long. How many feet of lace are needed to cover the edges of the quit?
Mel slides down waterslide A, and Victor slides down waterslide B. After 2 seconds, Mel was 50 feet in the air, and after 5 seconds, she was 35 feet in the air. After 1 second, Victor was 60 feet in the air, and after 4 seconds, he was 50 feet in the air. Who was descending at a faster rate?
Mel: (2, 50) and (5, 35)
Victor: (1, 60) and (4, 50)
Mel’s rate of change is____.That means that her height in the air decreases _____ feet every second.
Victor’s rate of change is _____ . That means that his height in the air decreases _____ feet every second.
The height of Mel in the air is decreasing at a faster rate than victor's height in the air.
Mel's rate of change is -5 feet per second. That means that her height in the air decreases 5 feet every second. Victor's rate of change is -3.33 feet per second. That means that his height in air decreases 3.33 feet every second.Given information:
Mel slides down water-slide A and Victor slides down water-slide B.
After 1 second, height achieved by [tex]\rm{Mel}= 50\; \text{Ft}[/tex]
After 5 seconds, the height remained is 35 feet.
In another case,
The height achieved by Victor after 1 second is 60 feet.The height remained after 4 second is 50 feet.Now, the expression is used for evaluating the slope of the equation are formulated below:
[tex]\bold{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Where, [tex]m[/tex] is the slope and [tex]x[/tex] and [tex]y[/tex] are respective coordinates.
Hence, for Mel's case, apply the formula of slope and solve it further:
[tex]\begin{aligned}m_1&=\dfrac{35-50}{5-2} \\m_1&=-5 \end{aligned}[/tex]
So, the rate of change of Mel's height is 5 feet per second.
And for victor's case, slope will be:
[tex]m_2=\dfrac{50-60}{4-1} \\\\m_2=-3.33[/tex]
The rate of change of victor's height is 3.33 feet per second.
Mel's rate of change is -5 feet per second. That means that her height in the air decreases 5 feet every second.Victor's rate of change is -3.33 feet per second. That means that his height in air decreases 3.33 feet every second.For more information visit:
https://brainly.com/question/14914699
At a table tennis tournament, two games went on for a total of 32 minutes. One game took 12 mintues longer than the other. How long did it take to complete each game?
The total time for two game is 32 minutes. The time for each game can be determine using system equation.
The time for game is 10 minute and 22 minute respectively.
Given:
Total time to complete two game is 32 minutes.
Let [tex]x[/tex] is the time took to complete one game.
Write the system equation for the given condition.
[tex]\begin{aligned}\\ x+x+12=32\\2x=32-12\\x=10 \:\rm min\\\end{aligned}[/tex]
As per the question, one game took 12 minutes longer than other. So the time for second game is,
[tex]x+12=10+12=22 \:\rm minutes[/tex]
Thus, the time took to complete game is [tex]10\:\rm minutes[/tex] and [tex]22\:\rm minutes[/tex] respectively.
Learn more about Time here:
https://brainly.com/question/11613234
A 5-pound of flour costs $4.80. For this bag of flour, what is the cost of flour per ounce?
(1 pound = 16 ounces)
a. $0.06
b. $0.16
c. $0.60
d. $0.96
The cost of the flour per ounce will be $0.06 per ounce. Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A 5-pound of flour costs $4.80.
We know that in one pound, there are 16 ounces. Then the number of ounces in 5 pounds is calculated as,
⇒ 5 x 16
⇒ 80 ounces
Then the cost of the flour per ounce will be given as,
⇒ $4.80 / 80
⇒ $0.06 per ounce
The cost of the flour per ounce will be $0.06 per ounce. Then the correct option is A.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
The mean age of swimmers for all these teams is 10 Which team has the greatest MAD?
The answer is Jasons!
Answer:
Step-by-step explanation:
There are 3 data sets given as
I) x 7 8 9 10 11 12 13 Total
Frequ 1 2 1 2 2 0 2
Mean dev|x-10|*f 3 4 1 0 3 0 6 17
II) x 7 8 9 10 11 12 13 Total
Frequ 2 3 0 0 1 1 3
Mean dev|x-10|*f 6 6 0 0 1 2 9 24
III) x 7 8 9 10 11 12 13 Total
Frequ 0 0 4 4 1 0 1
Mean dev|x-10|*f 0 0 4 0 1 0 3 8
Thus we find the middle one Jason has the highest deviation.
Louis has three more quarters than dimes in his pocket, for a total of $1.80. Which equation could be used to determine the number of dimes, x, in his pocket?
Three pizzas of the same size were purchased for a party. After the guests finished eating pizza, 1/3 of the first, 1/4 of the second, 1/6 and of the third pizzas were leftover.
Part A If the leftover pieces are combined, what fraction of one whole pizza remains? Explain how you got your answer.
Part B What fraction of all three of the pizzas purchased for the party was eaten? Explain how you got your answer.
Part C Only six guests ate pizza at the party. If all of them ate the same amount, what fraction of one pizza did each person eat? Explain how you got your answer.