[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5500\\ P=\textit{original amount deposited}\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\dotfill &10 \end{cases} \\\\\\ 5500=Pe^{0.055\cdot 10} \implies \cfrac{5500}{e^{0.055\cdot 10}}=P\implies 3173.22\approx P[/tex]
NO LINKS!! Find the missing length indicated. The triangle is similar.
Answer:
143
Step-by-step explanation:
35/55 = 91/x
7/11 = 91/x so 143
Answer:
DB = 143 units
Step-by-step explanation:
In similar triangles, corresponding sides are always in the same ratio.
If ΔDCB ~ ΔDRS then:
[tex]\implies \sf DC : DR = CB : RS = DB : DS[/tex]
From inspection of the given diagram:
DC = 91DR = 35DS = 55Therefore:
[tex]\implies \sf 91 : 35 =DB : 55[/tex]
[tex]\implies \sf \dfrac{91}{35} =\dfrac{DB}{55}[/tex]
[tex]\implies \sf 55 \cdot \dfrac{91}{35} =55 \cdot \dfrac{DB}{55}[/tex]
[tex]\implies \sf 143=DB[/tex]
a service station on the interstate changes $2.29 per gallon of
gasoline and $1.89 per quart for oil. What would be a recourable
amount to pay for 10 gallons of gasoline and 2 quarts of oil ?
A) $20
B) $23
C) $25
D) $27
Answer:
D) $27
Step-by-step explanation:
You want an estimate of a reasonable amount to pay for 10 gallons of gas at $229 per gallon, and 2 quarts of oil at $1.89 per quart.
EstimateFor estimating purposes, we like to round numbers to 1 or 2 significant figures.
The cost of 10 gallons of gas is about 10 × $2.30 = $23.
The coast of 2 quarts of oil is about 2 × $2 = $4.
So, the total cost of the gas and oil is about $23 +4 = $27.
You expect the total to be near $27.
__
Additional comment
Part of estimating is estimating the error in your estimate. Here the error is $0.01 per gallon of gas, or $0.10 for 10 gallons. The error is $0.11 per quart of oil, so $0.22 for 2 quarts. The final estimate of $27 is $0.10 +0.22 = $0.32 too high. $27 is different from the next answer choice by $2, so is still the best answer choice.
Kim ran a 26-mile marathon.
She ran 1/7 of the marathon during
the first hour. How many miles did
Kim run during the first hour?
Answer:
3.714
Step-by-step explanation:
26 x ⅐ = 26 / 7
= 3.714 or [tex] 3 \frac{5}{7} [/tex]
I need help with this Question
Step-by-step explanation:
Just Substitute in place of X
Alex can earn $15 an hour mowing neighborhood lawns on weekends. If Alex decides to spend an hour mowing rather than watching a football game, his opportunity cost of mowinf lawns is:
a. The $15 he earns
b. The enjoyment he would have received from watching the football game during that time.
c. The $15 he earns minus the enjoyment he would have received from watching the football game during that time.
d. The $15 he earns plus the enjoyment he would have received from watching the football game during that time.
e. Nothing because he would have received $15 worth of enjoyment from watching the football game during that time
The opportunity cost of mowing the lawn is The $15 he earns minus the enjoyment he would have received from watching the football game during that time.
Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them. Making smarter decisions requires an understanding of the possible opportunities lost when a company or person selects one investment over another.
Opportunity Cost =FO−CO where:
FO=Return on best-forgone option
CO=Return on the chosen option
The formula for calculating an opportunity cost is simply the difference between the expected returns of each option.
To learn more about opportunity cost visit: brainly.com/question/13036997
#SPJ4
How many four-letter words can be formed by using the letters in facetious? There are nine letters
available, and each one can be used at most once per word.
Answer:
Step-by-step explanation:
To find the number of four-letter words that can be formed using the letters in facetious, you can use the combination formula:
nCr = n! / (r! (n - r)!)
In this case, n is the total number of letters available (9) and r is the number of letters per word (4). Therefore, the number of four-letter words that can be formed is:
nCr = 9! / (4! (9 - 4)!) = 9! / (4! 5!) = (9 x 8 x 7 x 6) / (4 x 3 x 2 x 1) = 126
Therefore, there are 126 four-letter words that can be formed using the letters in facetious.
Given: A AED and A BEC are isosceles, with congruent bases AD and BC Prove: ABCD is a rectangle
We have proved that ABCD is a rectangle.
What is the isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.
<EAD=<EDA ------------------∆AED is isosceles triangle.
<EBC=<ECB ------------------ ∆EBC is isosceles triangle.
AD= BC -------------------------Given
<AED=<BEC ------------------- Vertically opposite angle
<EAD=<ECB
2<EAD=180°- <AED
= 180°-<BEC
=2<ECB.
∆AED congruent to ∆BEC --------- By A-S-A Congruency.
AE=EC, DE=EB ----------Corresponding sides
ABCD is a parallelogram ----------- Diagonals bisect to each other.
AC=BD
AE+EC=DE+EB.
ABCD is a rectangle. ------------- Diagonals are equal.
Hence, we have proved that ABCD is a rectangle.
To learn more about the isosceles triangle, visit:
https://brainly.com/question/1475130
#SPJ1
In 1992, there were 285 alligators in Orange County, Florida. The number of alligators increased by 75% per year after 1992. How many alligators were there in Orange County, Florida in 2001?
The number of alligators was there in Orange country, Florida in 2001 is equal to 43872.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other words, it is a relationship where the worth of the entire is always considered 100.
As per the given information provided in the question,
Total number of alligators 1992 = 285
Percent increase of alligators every year = 75%
Total number of years from 1992 to 2001,
2001 - 1992 = 9 years
The population of alligators in 2001,
= 285 × (175/100)⁹
= 285 × (7/4)⁹
= 43871.98 or,
= 43872 alligators.
To know more about Percentage:
https://brainly.com/question/29306119
#SPJ1
6. What is the reflection image of (5, –3) across the line y = –x? (–3, 5) (–3, –5) (3, –5) (3, 5)
Check the picture below.
It is given § = {x: 1 ≤ x ≤ 10, x is an integer); P= {odd numbers); Q= {prime numbers) and R= {1,2,3,4,5} List the elements of each of the following sets. (a) (PNQ)UR (b) (RNP)'UQ (c) Q'N(PUR) (d) (PUQUR)' (POR)
The elements of the required sets would be:
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
What are sets?A set, denoted by the curly brackets , is a grouping of items, numbers, elements or objects.
A set of numbers, for instance, is 1, 2, 3, 4.
Solution:
P' = {2, 4, 6, 8, 10}
Q' = {1, 4, 6, 8, 9, 10}
R' = {6, 7, 8, 9, 10}
P∩Q = {3, 5, 7}
R'∪P' = {2, 4, 6, 7, 8, 9, 10}
P∪R = {1, 2, 3, 4, 5, 7, 9}
P∩R = {1, 3, 5}
P∪Q∪R = {1, 2, 3, 4, 5, 7, 9}
P'∩Q'∩R' = S - P∪Q∪R
= {6, 8, 10}
Now we can find the elements of the required sets:
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
Hence, the elements of the required sets would be
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
To learn more about sets from the given link
https://brainly.com/question/13458417
#SPJ1
PLEASE HELP NOW!!!!!
The percentage for blue balls will be 56% and the percentage for red balls will be 44%.
What is the percentage for the colors of the gumball?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this situation, there are 4000 balls and 2240 of then are blue while 1760 area red.
The percentage for blue balls will be:
= Number of blue balls / Total balls × 100
= 2240 / 4000 × 100
= 56%
The percentage for red balls will be:
= Number of red balls / Total balls × 100
= 1760 / 4000 × 100
= 44%
Learn more about percentages on:
brainly.com/question/24339661
#SPJ1
solve by completing the square
Answer:
Attached
Step-by-step explanation:
What is volume of a cone that has a radius of 6cm and height of 18c
Answer:
136
Step-by-step explanation:
The formula of the volume of a cone is v=b*h.First you need to find the diameter, simple, 6*2=12, you get the 12 because the diameter is always twice as large as the radius. Next you multiply 18*12 which gives you 136!
A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.
e. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
The true statement about J and K is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
The correct answer is option (c)
In this question, we have been given that a certain statistic will be used as an unbiased estimator of a parameter.
The sample size of J = 40.
and the sample size of K = 100.
We need to find the true statement about J and K.
By central limit theorem, both J and K will have same means.
An expression for standard deviation is:
s = σ/√n
From the above expression standard deviation is inversely proportional to the sample size n. This means, as the sample size increases, the standard deviation decreases.
Thus, the correct statement is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
Learn more about the certain limit theorem here:
brainly.com/question/898534
#SPJ4
The complete question is:
A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.
Which of the following must be true about J and K ?
a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.
b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.
c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.
e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.
A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet. What is the angle of elevation of the ramp to the nearest degree?
The angle of elevation of the ramp to the nearest degree will be 5.71°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that a ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet.
The angle of elevation will be calculated as,
tanθ = ( 1 / 10)
θ = tan⁻¹(1/10)
θ = 5.7°
Therefore, the angle of elevation of the ramp to the nearest degree will be 5.71°.
To know more about trigonometry follow
https://brainly.com/question/27674575
#SPJ1
what do 17, 19, 46 and 55 have in common?
Answer:
They are all prime numbers
Explanation:
17, 19, 46, and 55 are all prime numbers. A prime number is a whole number greater than 1 that is only divisible by 1 and itself. Since 17, 19, 46, and 55 are all prime numbers, they have no other factors besides 1 and themselves, which means they cannot be divided evenly by any other number.
x/4 -6 = -8 pls help i really dont understand this one
Answer:
x = -8
Step-by-step explanation:
Given equation,
→ (x/4) - 6 = -8
Now the value of x will be,
→ (x/4) - 6 = -8
→ x/4 = -8 + 6
→ x/4 = -2
→ x = -2 × 4
→ [ x = -8 ]
Hence, the value of x is -8.
A 6 -sided die with the numbers 1 to 6 on its faces is rolled and a ticket is drawn from a bag of 7 tickets labelled 1 to 7 . How many different ways can you roll a 1 on the die and draw a 7 from the bag of tickets?
The no. ways roll a 1 on the die and draw a 7 from the bag of tickets is 1 And the probaility is [tex]\frac{1}{42}[/tex]
What is Probability?Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to signify how many positive findings there are in an experiment with 'n' results. The following formula can be used to determine the likelihood of an event:
Probability (event) equals a favorable result/the total of outcomes divided by n.
The no. ways roll a 1 on the die and draw a 7 from the bag of tickets is 1
And the probaility is -
[tex]\frac{1}{6} X \frac{1}{7}[/tex]
[tex]= \frac{1}{42}[/tex]
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
Dividing power algebra two
By power algebra method,
a) [tex]\frac{16}{81}[/tex]
b) [tex]\frac{2xy}{3}[/tex]
c) [tex]\frac{16x^4}{y^8}[/tex]
d) [tex]\frac{3y^2}{x^3}[/tex]
What is dividing power property?According to the Quotient of Powers Property, you can maintain the base and subtract the exponents when dividing two exponents by the same base. Since you cannot divide by zero, this characteristic will always hold true as long as the base is not zero. For more information on this property, use the interactive below.
The Exponents Power Rule: am*n = (am)n. Multiply the exponent by the power to increase a number with an exponent to that power.
You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).
a) [tex](\frac{2}{3})^4[/tex] = [tex]\frac{2*2*2*2}{3*3*3*3}[/tex] = [tex]\frac{16}{81}[/tex]
b) [tex]\frac{2x^2y}{3x}[/tex] = [tex]\frac{2*x*x*y}{3*x}[/tex] = [tex]\frac{2xy}{3}[/tex]
c) [tex](\frac{2x}{y^2})^4[/tex] = [tex]\frac{2x*2x*2x*2x}{y^2*y^2*y^2*y^2}[/tex] = [tex]\frac{16x^4}{y^8}[/tex]
d) [tex]\frac{3xy^4}{x^3}[/tex][tex].\frac{y}{xy^3}[/tex] = [tex]\frac{3x*y*y*y*y}{x*x*x} . \frac{y}{x*y*y*y}[/tex] = [tex]\frac{3y^2}{x^3}[/tex]
To know more about power algebra refer to:
https://brainly.com/question/819893
#SPJ1
Solve 15x - 10y = -30 and 5x - 9y = 7 using elimination. Show Steps. Put answer in coordination form (x,y)
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The coordinates are (0, 3) or (34/5, 3)
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
15x - 10y = -30 _____(1)
5x - 9y = 7 ______(2)
Multiply 3 on (2)
15x - 27y = 21 _____(3)
Using the elimination method we get,
From (1) and (3) we get,
15x - 10y = -30
15x - 27y = 21
(-) (+) (-)
17y = 51
This means,
y = 51/17
y = 3
Now,
Put y = 3 in (1) we get,
15x - 10y = -30
15x- 10 x 3 = -30
15x - 30 = -30
15x = 0
x = 0
Put y = 3 in (2) we get,
5x - 9y = 7
5x - 9 x 3 = 7
5x - 27 = 7
5x = 7 + 27
5x = 34
x = 34/5
Thus,
The coordinates are (0, 3) or (34/5, 3)
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Mrs. magil asks her students to draw a right triangle with one angle measuring 63 degrees. Which equation can be used to determine a, the measure of the third angle in their triangle?
Answer: a = 180 - 63 - 90
Step-by-step explanation:
180 degrees in a triangle
90 degrees in a right triangle
180 = 63 + 90 + a
move 63 and 90 to the other side
a = 180 - 63 - 90
-2 = y - 9 solve for y
this is ur answer
[tex]2y = - 9 \\ y = ( - 9) - 2 \\ y = - 11[/tex]
what is the shortest side of a triangle when the numbers are 63,47,70
The shortest side of a triangle is just opposite of the angle 47°.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
All the angle of a triangle are,
⇒ 63°, 47°, 70°
Now,
Since, All the angle of a triangle are,
⇒ 63°, 47°, 70°
We know that;
The smallest side of a triangle is just opposite of the smallest angle.
Thus, The shortest side of a triangle is just opposite of the angle 47°.
Learn more about the triangle visit:
https://brainly.com/question/13569154
#SPJ1
How deep is a valley if it takes a rock 5.2 seconds to strike the bottom and it is traveling at 25 m/s?
Answer:
[tex]\huge\boxed{\sf h = 130\ m}[/tex]
Step-by-step explanation:
Given data:Time = t = 5.2 s
Velocity = v = 25 m/s
Required:Height = h = ?
Formula:h = vt
Solution:h = 25(5.2)
h = 130 m[tex]\rule[225]{225}{2}[/tex]
Answer:
The valley is 130 m deep.
Step-by-step explanation:
Formula we use,
→ Height = Time × Speed
Now the height will be,
→ Time × Speed
→ 5.2 × 25
→ 130 metres
Thus, valley is 130 m deep.
What is the correct answer ???????? only the answer
Answer: Open
Step-by-step explanation: the dot is only filled in when the inequallity is "greater than or equal to" or "less than or equal to"
Diego has 48 chocolate chip cookies, 64 vanilla cookies and 100raisin cookies for a bake sale. He wants to make bags that have all three cookie flavors and the same number of each flavor per bag.
A. How many bags can he make without having any cookies left over?
B. Find another solution to this problem
Answer:
Step-by-step explanation:
The number of bags he can make without having any cookies left over is 4 bags.
Number of chocolate chips = 48
Number of vanilla cookies = 64
Number of raisin cookies = 100
A park has two sprinklers that are used to fill a fountain. One sprinkler can fill the
fountain in 3 h, whereas the second sprinkler can fill the fountain in 6 h. How long will
it take to fill the fountain with both sprinklers operating?
It takes 2 hrs to fill the fountain with both sprinklers operating
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A park has two sprinklers that are used to fill a fountain
One sprinkler can fill the fountain in 3 h
second sprinkler can fill the fountain in 6 h
We need to find the time required to fill the fountain by two sprinklers.
Let t = time required with both sprinklers working
t/3+t/6=1
2t+t/6=1
3t/6=1
Apply cross multiplication
3t=6
Divide both sides by 3
t=2
Hence, it takes 2 hrs to fill the fountain with both sprinklers operating
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
The area of a circle is 0.2826 square inches. What is the circle's diameter?
Use 3.14 for .
Submit
inches
Answer:
0.6 inches
Step-by-step explanation:
The equation to find the area of a circle is:
[tex]{a} = \pi {r}^{2} [/tex]
however the problem requires you replace π with 3.14.
Using inverse operations you can find the variable r.
Step 1:
Plug in variables.
[tex]0.2826 = 3.14{r}^{2} [/tex]
Step 2:
Solve for r.
[tex]0.2826 \div 3.14 = 3.14 \div 3.14 \times {r}^{2} \\ \sqrt{0.09} = \sqrt{ {r}^{2} } \\ r = 0.3[/tex]
Step 3:
Find diameter from radius.
[tex]0.3 \times 2 = 0.6[/tex]
The diameter of the circle is 0.6 inches.
how do you solve 5/13y+25=0
Answer:
y = -100/13
Step-by-step explanation:
To solve this equation, we can first get all the terms containing the variable y on one side of the equation and all the constant terms on the other side. We can do this by subtracting 25 from both sides of the equation:
5/13y + 25 - 25 = 0 - 25
This gives us:
5/13y = -25
Next, we can divide both sides of the equation by 5/13 to get rid of the fraction:
(5/13y) / (5/13) = (-25) / (5/13)
This simplifies to:
y = -100/13
Therefore, the solution to the equation is y = -100/13.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
Given that an expression;
2.3p – 10.1 = 6.5p – 4 – 0.01p
Firstly we will simplify the above expression by removing decimals.
For that,
(23 / 10)p – (101 / 10) = (65 / 10)p – 4 – (1 / 100)p
Now we will take LCM,
{ (23 - 101) / (10) }p = {650p - 400 - p} / 100
230p – 1010 = 650p – 400 –p
Therefore The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p.
To learn more about the expression in mathematics;
brainly.com/question/24242989
#SPJ1