a horse trots in a circle at the end of a 4m rope. About how far does the horse trotted after completing ten circles?
In the figure, TR−→− and TV−→− are secants to circle A. mRV=99∘ mSU=45∘ What is the measure of ∠RTV ? Enter your answer in the box.
The surface area of a rectangular prism is 792 units2. The length of the prism is 2 times the width, and the width is 4 times the height. What is the volume of the prism?
Answer:
The real answer is 846 ^-^ I got it right
The volume of the rectangular prism is 105.57
What is the volume of a rectangular prism?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The volume of a rectangular prism=Length X Width X Height
Where l, h and w represent the length, height and width respectively.
Given that;
Length of the prism is 2 times the width L = 2w
the width is 4 times the height w = 4h
Now let’s plug these values;
the surface area equation, it becomes;
A = 2(2w(w) + w(w/4) + w/4(2w))
A = 2(2w^2 + w^2/4 + w^2/2)
A = 1/2(7w^2)
792 x2 = 7w^2
w = 15.04
The volume of a rectangular prism=Length X Width X Height
V = 2w x w x w/4
V x 2 = w³
V = 15.04³/2
V = 105.57
Thus, the volume is 105.57.
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The strength of the force of gravity depends ona.the masses of the objects and their speeds.
b.the masses of the objects and the distance between them.
c.the weight of the objects and their speeds.
d.the masses of the objects and their weights.
MAJOR HELP NEEDED!
Lea knows the following information about the 50 days where she tracked whether she wore a tie and whether she received a compliment on her outfit:
-There were 11 days where she neither wore a tie nor received a compliment.
-There were 30 days in total where she received a compliment.
-There were 16 days in total where she did not wear a tie.
Can you help Lea organize the results into a two-way frequency table?
We know that a two-way frequency table is constructed when we have to deal with two variables ( which is also known as a bivariate data)
Here we have two variables as wore a tie or not and the second variable is: Received compliment or not.
Hence, on the basis of the information provided to us in the question we see that the two-way frequency table is obtained as follows:
Wore tie Do not wore tie Total
Receive compliment 25 5 30
Do not receive compliment 9 11 20
Total 34 16 50
The considered data given about the frequencies of events can be used to fill the two-way frequency table. The values will be 25 and 5 in first row, and 9 and 11 in second row.
How to form two-way frequency table?Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ... , Y_n[/tex]
List them in title of the rows and left to the columns. There will be [tex]n \times k[/tex] table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex] (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
We're given that:
There were 11 days where she neither wore a tie nor received a compliment.There were 30 days in total where she received a compliment.There were 16 days in total where she did not wear a tie.If we take:
A = event of Lea wearing a tie on a day
A' = event of Lea not wearing a tie on a day
B = event of Lea getting a compliment on a day
B' = event of Lea not getting a compliment on a day
then, we're given that:
[tex]n(A' \cap B') = 11\\n(B) = 30\\n(A') = 16[/tex]
Also, total number of days = S = 50
On each of those 50 days, she either wore a tie or not.
If she didn't put on a tie on 16 out of 50 days, then she wore tie for 50-16=34 days.
Thus, we get n(A) = 34
Similarly, we get n(B') = 50 - n(B) = 50 - 30 = 20
[tex]\begin{array}{cccc}&A&A'&\rm Total\\B&n(B\cap A)&n(B\cap A')&n(B)=30\\B'&n(B' \cap A)&n(B' \cap A')=11&n(B')=20\\\rm Total & n(A)=34 & n(A')=16 & S=50 \end{array}[/tex]
Using the total of the third row, we get:
[tex]n(B' \cap A) + 11 = 20\\n(B' \cap A) = 9[/tex]
Similarly, now using second column's total, we get:
[tex]n(B \cap A) + n(B' \cap A) = 34\\n(B \cap A) + 9 = 34\\n(B \cap A) = 25[/tex]
Now using second row's total, we get:
[tex]25 + n(B \cap A') = 30\\n(B\cap A') = 5[/tex]
Thus, we get:
[tex]\begin{array}{cccc}&A&A'&\rm Total\\B&n(B\cap A)=25&n(B\cap A')=5&n(B)=30\\B'&n(B' \cap A)=9&n(B' \cap A')=11&n(B')=20\\\rm Total & n(A)=34 & n(A')=16 & S=50 \end{array}[/tex]
Thus, finally, we can say that:
Wore a tie, Didn't wore a tie
Got a compliment 25 5
Didn't got a compliment 9 11
Thus, the values will be 25 and 5 in first row, and 9 and 11 in second row.
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The stem-and-leaf plot shows the number of home runs hit by the top major league baseball players in the 2000 season. stem leaf 3 0 0 0 0 1 1 1 1 1 1 1 2 2 2 3 3 4 4 4 5 5 5 6 6 6 7 7 8 8 9 4 0 1 1 1 1 2 2 3 3 3 4 4 7 7 9 5 0 3⏐0 ? 30 what is the probability that one of these players picked at random hit more than 35 home runs
1. Astronomers measure large distances in light-years. One light year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light years from Earth. In scientific notation, approximately how many miles is it?
A. 5.88 x 10^13 miles
B. 5.76 x 10^14 miles
C. 5.88 x 10^12 miles
D. 9.8 x 10^12 miles
2. A 1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?
A. $4,979.11
B. $14,920.54
C. $112,992.00
D. $15,494.70
Final Answer:
The answers are:
1. B. 5.76 x 10¹⁴ miles
2. D. $15,494.70
Explanation:
Let's solve each of these questions step by step.
Question 1:
First, we'll calculate the distance to the star in miles, given its distance in light years.
One light year is approximately 5.88 x 10¹² miles.
The star is 9.8 x 10¹ light years from Earth.
To find the distance in miles, we multiply the distance in light years by the length of one light year in miles:
Distance in miles = (5.88 x 10¹² miles/light year) * (9.8 x 10¹ light years)
To multiply these numbers in scientific notation, we multiply the coefficients (5.88 and 9.8) and then add the exponents of 10 (12 and 1).
Coefficient multiplication: 5.88 * 9.8
Using a calculator or doing the multiplication by hand, we find that 5.88 * 9.8 is approximately 57.624.
Exponent addition: 12 + 1 = 13
So the distance in miles is approximately 57.624 x 10¹³ miles.
However, in scientific notation, the coefficient should be between 1 and 10. Therefore, we need to adjust the coefficient from 57.624 to 5.7624 and increase the exponent by 1 to keep the same value.
Distance in miles = 5.7624 x 10¹⁴ miles
To make it approximately and match the answer choices, we can round the coefficient to 5.76.
Distance in miles ≈ 5.76 x 10¹⁴ miles
The closest answer to our computed value is:
B. 5.76 x 10¹⁴ miles
Question 2:
Next, let's use the compound interest formula to find the balance in the account after 33 years.
The compound interest formula is:
[tex]A = P (1 + r/n)^{(nt)[/tex]
where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
We're given:
P = $1,600.00
r = 7% annual interest = 0.07 (as a decimal)
n = 2 (since interest is compounded semiannually)
t = 33 years
Plugging these values into the formula gives us:
[tex]A = 1600.00 * (1 + 0.07/2)^{(2*33)[/tex]
Let's break it down:
Interest rate per compounding period: 0.07/2 = 0.035
Number of compounding periods: 2*33 = 66
Now substitute these values:
A = 1600 * (1 + 0.035)⁶⁶
We calculate (1 + 0.035)^66 using a calculator:
(1 + 0.035)⁶⁶ ≈ (1.035)⁶⁶ ≈ 9.682
So the final balance is:
A ≈ 1600 * 9.682 ≈ 15491.2
The closest answer to our computed value is:
D. $15,494.70
Hence, the answers are:
1. B. 5.76 x 10¹⁴ miles
2. D. $15,494.70
What would the total bill be of painting the costs $44.80 with the tax rate of 6%?
Write an equation for the line whose data is in the table below
X:1 2 5
Y: 4 6 12
Suppose rebecca needs a dog sitter so that she can travel to her sister's wedding. rebecca values dog sitting for the weekend at $200. susan is willing to dog sit for rebecca so long as she receives at least $150. rebecca and susan agree on a price of $175. suppose the government imposes a tax of $10 on dog sitting. the tax has made rebecca and susan worse off by a total of
The tax has only made Susan worse off by $10 or 5.7% because Rebecca is the one who is going to pay for the dog sitting and not Susan (who is going to have an income of $165 after-tax).
Further Explanation:
Income Tax: It is the additional payment that an individual needs to pay on the amount of income he/she generates. Here $10 is the tax on the income which Susan is going to generate by dog sitting the dog of Rebecca.
Here, it can be seen that Susan is the one who is earning from the transaction and not Rebecca. So, Rebecca is should not bear any tax payable to the government since both of them agree to a price of $175 so that is the only amount which Rebecca is going to pay for dog sitting. Also, if Susan herself pays the whole amount of tax, it still would not bother her because her expectation from dog sitting was $150 which is still lesser than what she expected in the first place.
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2. Learn more about the personal tax
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3. Learn more about the role of money
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Answer details:
Grade: Senior School
Subject: Taxation
Chapter: Tax imposed on various services.
Keywords: Income tax, payment of tax, dog sitting during the wedding, dog sitter, worse off condition of Rebecca and Susan.
1. Based on the information given, can you determine that the quadrilateral must be a
parallelogram? Explain.
Given: (BE) ̅ (ED) ̅ and (AE) ̅ (EC) ̅
2. The parallelogram has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.
Solving Q1: Given BE = ED and AE = EC.
Considering triangles ΔAED and ΔCEB;
1. AE = EC (given)
2. ∠AED = ∠CEB (vertical angles)
3. ED = EB (given)
ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)
∠DAE = ∠BCE and AD = BC (using CPCTC)
⇒ AD║BC (Converse of Alternate Interior angles theorem)
Similarly consider triangles ΔABE and ΔCDE;
1. AE = CE (given)
2. ∠BEA = ∠DEC (vertical angles)
3. BE = DE (given)
ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)
∠ABE = ∠CDE and AB = CD (using CPCTC)
⇒ AB║CD (Converse of Alternate Interior angles theorem)
Since we have AB║CD, AB = CD and AD║BC, AD = BC.
Therefore, quadrilateral ABCD is a parallelogram.
****************************************************************************************************
Solving Q2: The parallelogram has the angle measures shown in the diagram.
It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.
Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.
Using Angle-Side-Angle congruence of triangles, both the triangles would be congruent too.
Using CPCTC, we can say opposite sides of quadrilateral would be congruent.
Therefore, all sides in given quadrilateral are equal.
Hence, Given quadrilateral is a Rhombus.
A seller buys an item from a manufacturer for $9,500 he increases cost by %5 percent.What is the markup value?
markup = original cost x percentage markup
Answer: $475
Step-by-step explanation:
Given : A seller buys an item from a manufacturer for $9,500 he increases cost by %5 percent.
i.e. The original cost of item = $9,500
Mark up percentage = 5% = 0.05
The formula given to find the mark up value is :_
[tex]\text{Mark up}=\text{Original cost * percentage mark up}\\\\\Rightarrow\ \text{Mark up}=9500\times0.05=\$475[/tex]
Hence, the mark up value = $475
ALL I NEED YOU GUYS TO DO IS TO EXPLAIN THIS IN THE MOST FANCY WAY POSSIBLE!!!! THIS IS JUST FOR FUN, I WILL MARK BRAINLIEST FOR THE FANCIEST ANSWER!!!!
WHAT IS 5x5?!?!?!?!?!
It's 25 easy how I got my answer I looked on my fingers and put 5 fingers up and i did it 5 times and got 5.10.15.20.25 that's 5 times
All the events for the volunteer committee need to be finished;____, parents' day needs to be completed.
Choose the transitional word or phrase that best fits the blank.
A. In essence
B. Similarly
C. Finally
D. In particular
Rachel is selling T-shirts. It costs her $5 each week to advertise her T-shirts. She buys each T-shirt for $3.50 and sells each one for $8.00. Write an equation to model the amount of profit, P, she makes from selling x T-shirts in one week.
P = 3.50x − 5
P = 8x − 3.5
P = 5x + 3.5
P = 4.5x − 5
please help 1. another term for adding money to an account is
A) additional
B) submission
C) contribute
D) payment
2. which situation allows you to have the most saved
A) having a set amount set aside for savings each time you are paid
B) having a set minimum or percentage for saving whichever is greater
C) having a percentage set aside for savings
D) having a percentage set aside for savings when your pay is higher and hours are more
1. Another term for adding money to an account is - contribute
One should contribute to his account. This phrase means, one should add money to his account. Contribution is addition of money in account.
2. Which situation allows you to have the most saved ?
A) having a set amount set aside for savings each time you are paid- this can be the most possible answer. Technically a person should save 20% to 25% of his income and this amount increases with income. So, each time when you are paid, set aside the savings amount.
Let set C = {even numbers between 1 and 99} and set D = {numbers between 1 and 150 that are evenly divisible by 10}.
What is C ∩ D?
@ganeshie8,
The tangent ratio compares the length of what to the length of what
Which expressions are equivalent to the one below? Check all that apply. 9x
Answer:
C.),F.),andD.) Are correct
Step-by-step explanation:
Option: C, D and F are the correct options.
C. [tex](\dfrac{36}{4})^x[/tex]
D. [tex]9\cdot 9^{x-1}[/tex]
F. [tex]\dfrac{36^x}{4^x}[/tex]
Step-by-step explanation:We are asked to find the expression which is equivalent to:
[tex]9^x[/tex]
C)
[tex](\dfrac{36}{4})^x[/tex]
We know that:
[tex](\dfrac{36}{4})^x=9^x[/tex]
Since, 36/4=9
Hence, option: C is correct.
D)
[tex]9\cdot 9^{x-1}=9^{1+x-1}[/tex]
Since,
[tex]a^m\cdot a^n=a^{m+n}[/tex]
Hence,
[tex]9\cdot 9^{x-1}=9^x[/tex]
Hence, option: D is correct.
F)
[tex]\dfrac{36^x}{4^x}[/tex]
We know that:
[tex]\dfrac{36^x}{4^x}=(\dfrac{36}{4})^x[/tex]
Since, we know that:
[tex]\dfrac{a^n}{b^n}=(\dfrac{a}{b})^n[/tex]
Hence, we have:
[tex]\dfrac{36^x}{4^x}=9^x[/tex]
Since, 36/4=9
Hence, option: F is the correct answer.
How many solutions does the system have?
X+y=5
X+y=6
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
x + y = 5
x + y = 6
5 ≠ 6
The system of equations has many solutions.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 is an equation.
2x + 4 - 5x is an equation.
We have,
x + y = 5 _____(1)
x + y = 6 ______(2)
Now,
Solving (1) and (2) we get,
5 = 6
This is not true.
This means that,
We have many solutions.
If we get,
x = y
0 = 0
n = n ( n can be any value)
The system of equations will have no solutions.
Thus,
x + y = 5
x + y = 6
5 ≠ 6
The system of equations has many solutions.
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BRAINLIESTTTT!!!
If Mary pitches a baseball with the initial height of 6 feet and a velocity of 73 feet per second, how long will it take for the ball to hit the ground? :)
The system shown is____.
equivalent
independent
inconsistent
If you rewrite the problem 14(22) as 14(20+2) so that you can use mental math, which of the following properties will you use?
*nevermind I got it*
The sum of three consecutive even integers is 222. find the three integers.
1. What is the value of x?
sin(x+22)°=cos(2x−7)°
2.Given cosx=1213 and sinx=513
.
What is ratio for tanx
?
leave answer as a fraction in simplest form
the sine and cosine are co-functions
So
sin (theta) = cos (90 - theta)------> This implies that the angles sum to 90°
therefore
( x + 22) + (2x - 7) = 90 simplify
3x + 15 = 90 subtract 15 from both sides
3x = 75 divide both sides by 3
x = 25
The answer Part 1) is x=25°
Part 2) Given cos x=12/13 and sin x =5/13
What is ratio for tanx ?
we know that
tan x = sinx / cos x
tan x = (5/13) / (12/13) = (5/13) * (13/12) = 5/12
the answer Part 2) is 5/12
The picture below shows a portion of a river dam:
Which of the following can be used to calculate the height of the river dam? (6 points)
220 cos 40°
220 divided by tan 40 degrees
220 sin 40°
220 divided by cos 40 degrees
Answer:
220cos40
Step-by-step explanation:
cos40=x/220
(220)cos40=x/220(220)
220cos40=x
PLEASE PLEEAASE HELP!! You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly? Type your answer below using complete sentences,
The difference between 3.6 and a number is 2.95, as shown below. What number should go in the box to complete the subtraction problem?
Numerical Answers Expected!
If possible, choose k so that the following function is continuous on any interval:
f(x)= (5x^4-20x^3)/(x-4) , x≠4
f(x)= K , x=4
k=?,
Using continuity concepts, it is found that K = 320 makes the function continuous.
------------------
A function f(x) is said to be continuous at x = a if:
[tex]\lim_{x \rightarrow a^{-}} = \lim_{x \rightarrow a^{+}} = f(a)[/tex]
------------------
The piece-wise function given is:
[tex]f(x) = \frac{5x^4 - 20x^3}{x-4}, x \neq 4[/tex]
[tex]f(x) = K, x = 4[/tex]
------------------
The definition for x different of 4 can be simplified, as follows:
[tex]f(x) = \frac{5x^4 - 20x^3}{x-4} = \frac{5x^3(x - 4)}{x - 4} = 5x^3[/tex]
Thus, the simplified definition is:
[tex]f(x) = 5x^3, x \neq 4[/tex]
[tex]f(x) = K, x = 4[/tex]
------------------
For the lateral limits, x is close to but not exactly 4, so the first definition is used.
[tex]\lim_{x \rightarrow 4^-} = \lim_{x \rightarrow 4} 5x^3 = 5(4)^3 = 5 \times 64 = 320[/tex]
[tex]\lim_{x \rightarrow 4^+} = \lim_{x \rightarrow 4} 5x^3 = 5(4)^3 = 5 \times 64 = 320[/tex]
------------------
For continuity, it is needed that:
[tex]f(4) = 320[/tex]
Thus:
[tex]K = 320[/tex] makes the function continuous.
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Three survey markers are located on a map at points H, I, and J. A triangle is formed by connecting these markers by string so that HI = 150 feet, HJ = 245 feet,and IJ = 365 feet.
Which statement is true about the measures of the angles of TriangleHIJ?
f m∠I is the largest
g m∠H is the largest
h m∠H is the smallest
j m∠I is the smallest
The measure of the side IJ is the longest one so the largest angle is ∠H. Then the correct option is B.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Three survey markers are located on a map at points H, I, and J. A triangle is formed by connecting these markers by string so that HI = 150 feet, HJ = 245 feet, and IJ = 365 feet.
If the side is the largest one then its opposite angle will be the largest one.
The measure of the side IJ is the longest one so the largest angle is ∠H. Then the correct option is B.
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