Answer: Symmetry Property of Equality
A local lighthouse is 170 feet tall. During a visit to the lighthouse Xavier, who is 6
feet tall, cast a shadow that was 1.8 feet long. How long, in feet, was the shadow
that the lighthouse cast?
Answer: 51 ft
Step-by-step explanation:
This is a Similar Triangles problem (geometry)
Draw 2 triangles with the sides correctly labeled.
Set up your ratios
170/6 = x/1.8
Solve for x
28.3 = x/1.8
x = 51 ft (length of shadow cast by the lighthouse)
A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 23 mg every six hours. Complete parts (a) and (b) below.
a. Following this dosage, how many 12.2 mg chewable tablets would be taken in a week?
b. This antihistamine also comes in a liquid form with a concentration of 12.2 mg/10 mL.. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person
take in a week?
a. A 100-pound person could take tablets in a week.
(Round to the nearest whole number
as needed.)
b. A 100-pound person could take mL in a week
(Round to the nearest whole number as needed.)
a) The number of 12.2 mg chewable tablets would be taken in a week is 53.
b) The liquid antihistamine should a 100-pound person taken in a week is 528ml
What is meant by ratio and proportion?An ordered pair of numbers a and b, denoted as a / b, is a ratio if b is not equal to 0. A proportion is an equation that equalizes two ratios.. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls.
Given that a typical dose for a 100-pound person is 23 mg every six hours.
100 pounds person - 23 mg - 6hrs
For 1 day it is 24 hrs
7 days-168hrs
Therefore,
a) For 6 hrs - 23 mg
168 hrs- ?
X=(23×168)/6
=644 mg
For 1 tablet -12.2 mg
=644/12.2
= 52.786≈53 tablets
The number of 12.2 mg chewable tablets would be taken in a week is 53.
b) If 12.2 mg equals to 10 ml then
644mg =(10/12.2)×644 ml
=527.87 ml≈528ml
The liquid antihistamine should a 100-pound person taken in a week is 528ml
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for lunch three days ago, i had four tacos , each with a different kind of filling. Three of my tacos contained a green salsa. My friend clara had three burritos on the same day, each with a different kind of filling. Clara is vegetarian so none of her burritos had meat. together, how many tacos and burritos did we have?
Answer:
The answer to your question is,
7
Step-by-step explanation:
mary invests 12500 in savings rate of 1.5 percent for 2 years
Answer:The question is very brief, im not sure if i understand what your asking
Step-by-step explanation:
in the fruit bowl there are 12 bananas 8 apples and 4 oranges. do for every one orange there are ___ bananas
For every 1 orange in the fruit bowl there are three bananas.
According to the question,
We have the following information:
In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.
Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:
4 oranges = 12 bananas
Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.
So, we have the following expression:
1 orange = 12/4 bananas
1 orange = 3 bananas
Hence, for every 1 orange in the fruit bowl there are three bananas.
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What sentence represents this equation?
8 3/4=17−x
The sentence that represents this equation 8 3/4 = 17 - x is B) 8 3/4 is the same as 17 decreased by a number.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, 8 3/4 is the same as 17 decreased by a number will be 8 3/4=17−x.
Therefore, the correct option is B.
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Complete question
What sentence represents this equation?
8 3/4 = 17 - x
A) A number is the same as the difference of 17 and 8 3/4.
B) 8 3/4 is the same as 17 decreased by a number.
C) 17 decreased by 8 3/4 is the same as a number.
D) 8 3/4 is the same as a number decreased by 17.
Kohler Corporation reports the following components of stockholders’ equity at December 31 of the prior year.
Common stock—$15 par value, 100,000 shares authorized, 50,000 shares issued and outstanding $ 750,000
Paid-in capital in excess of par value, common stock 70,000
Retained earnings 400,000
Total stockholders' equity $ 1,220,000
During the current year, the following transactions affected its stockholders’ equity accounts.
January 2 Purchased 6,000 shares of its own stock at $20 cash per share.
January 5 Directors declared a $2 per share cash dividend payable on February 28 to the February 5 stockholders of record.
February 28 Paid the dividend declared on January 5.
July 6 Sold 3,000 of its treasury shares at $24 cash per share.
August 22 Sold 3,000 of its treasury shares at $16 cash per share.
September 5 Directors declared a $2 per share cash dividend payable on October 28 to the September 25 stockholders of record.
October 28 Paid the dividend declared on September 5.
December 31 Closed the $428,000 credit balance (from net income) in the Income Summary account to Retained Earnings.
Required:
1. Prepare journal entries to record each of these transactions.
2. Prepare a statement of retained earnings for the current year ended December 31.
3. Prepare the stockholders’ equity section of the balance sheet as of December 31 of the current year.
1. The journal entries to record the transactions for Kohler Corporation are as follows:
Journal Entries:January 2 Debit Treasury Stock $90,0000
Credit Paid-in capital in excess $30,000 Cash $120,000
January 5 Debit Dividend $88,000
Credit Dividend Payable $88,000
January 5 Debit Retained Earnings $88,000
Credit Dividend $88,000
February 28 Debit Dividend Payable $88,000
Credit Cash $88,000
July 6 Debit Cash $72,000
Credit Treasury Stock $45,000
Credit Paid-inn Capital in excess $27,000
August 22 Debit Cash $48,000
Credit Treasury Stock $45,000
Credit Paid-inn Capital in excess $3,000
September 5 Debit Dividend $100,000
Credit Dividend Payable $100,000
September 5 Debit Retained Earnings $100,000
Credit Dividend $100,000
October 28 Debit Dividend Payable $100,000
Credit Cash $100,000
December 31 Debit Income Summary $428,000
Credit Retained Earnings $428,000
2. The preparation of the statement of retained earnings for the current year ended December 31 is as follows:
Kohler Corporation
Statement of Retained EarningsFor the current year ended December 31
Beginning balance $400,000
Dividends (88,000)
Dividends (100,000)
Income Summary 428,000
Ending balance $640,000
The preparation of the stockholder's equity section of the balance sheet as of December 31 of the current year is as follows:
Kohler Corporation
Stockholders' Equity Section of the Balance SheetAs of December 31 of the current year
Common stock—$15 par value, 100,000 shares authorized
50,000 shares issued and outstanding $ 750,000
Paid-in capital in excess of par value, common stock 70,000
Retained earnings 640,000
Total stockholders' equity $1,460,000
Transaction Analysis:January 2 Treasury Stock $90,0000 Paid-in capital in excess $30,000 Cash $120,000
January 5 Dividend $88,000 Dividend Payable $88,000 (50,000 - 6,000 x $2)
January 5 Retained Earnings $88,000 Dividend $88,000
February 28 Dividend Payable $88,000 Cash $88,000
July 6 Cash $72,000 Treasury Stock $45,000 Paid-inn Capital in excess $27,000 (3,000 x $24)
August 22 Cash $48,000 Treasury Stock $45,000 Paid-inn Capital in excess $3,000 (3,000 x $16)
September 5 Dividend $100,000 Dividend Payable $100,000 (50,000 x $2)
September 5 Retained Earnings $100,000 Dividend $100,000
October 28 Dividend Payable $100,000 Cash $100,000
December 31 Income Summary $428,000 Retained Earnings $428,000
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Given a quadratic function in vertex form:
a) A vertical stretch happens for values of a such that |a| > 1.
b) A vertical compression happens for values of a such that |a| > 0.
c) For a vertical stretch, the graph increases vertically, and for a vertical compression, the graph increases horizontally.
d) A reflection across the x-axis takes place when a < 0.
How to obtain the transformations?The definition of the quadratic function is given as follows:
f(x) = a(x - h)² + k.
The transformations to the function are given as follows:
Vertical stretch: multiplication of the function by a value with absolute value greater than 1, hence |a| > 1, increasing the graph vertically.Vertical compression: multiplication of the function by a value with absolute value less than 1, hence |a| < 1, increasing the graph horizontally.Additionally, for a reflection over the x-axis, the function is multiplied by a negative number, hence:
a < 0.
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Vonna scored 48 goals in her soccer kicking practice. If her success-to-failure rate was 3:2, how many times did she attempt a goal?
The number of attempts Vonna made is 80.
Given,
Vonna scored 48 goals in her scoccer kicking practice.
Her success to failure rate is 3:2
Vonna scored 48 goals" means that there were 40 successes,
= 48 goals
= 3:2
= 48:3
= 16
x = 6 positive integer
hence let 3x:2x
= 3(16) = 48
= 2(16) = 32
Total attempts = 48+32
= 80
Hence the total number of attempts Vonna made is 80.
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what is the kinetic energy of a 158 kg Green Sea Turtle swimming at 0.42 m/s? With work shown
Kinetic energy is defined as the work required to accelerate a body of a given mass from rest to its stated speed. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.
Mass - (Measured in Kilogram) - Mass is the amount of matter in a body, regardless of its volume or the forces acting on it.
Velocity - (Measured in Meters per Second) - Velocity is a vector quantity (has both magnitude and direction) and is the rate of change of an object's position with respect to time.
What is the kinetic energy of a 158 kg Green Sea Turtle swimming at 0.42 m/s? With work shownWe have that the data is:
m = 150 kgv = 0.42 m/sThe formula to calculate kinetic energy is:
Ec = m * v²/2
Since it only asks us to calculate the kinetic energy, it is not necessary to clear the formula.
[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*\left(0.42 \ \frac{m}{s}\right)^2 }{2} }}[/tex]
[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*0.1764 \ \frac{m^2}{s^2} }{2} }}[/tex]
[tex]\boldsymbol{\sf{Ec=13.9356 \ kg*\dfrac{m^2}{s^2} }}[/tex]
We work with the units, in this case with m^2 = m*m.
[tex]\boldsymbol{\sf{Ec=13.9356 \boxed{\boldsymbol{\sf{Kg*\frac{m}{s^2} }}}*m }}[/tex]
Newton's units are: Kg*m/s^2.
[tex]\boldsymbol{\sf{Ec=13.9356 \ N*m \longmapsto Joule \ units=N*m}}[/tex]
[tex]\boldsymbol{\sf{Ec=13.9356 \ J}}[/tex]
The kinetic energy (E) of a body with mass m = 158 kilograms and speed v = 0.42 m/s is equal to 13.9356 JBut if you need the rounded answer, then 13.94 Joules.
Organic sugar used to be sold at a bulk price of $5 per pound. The price was recently increased by 20%. What is the current price per pound?
please helpp
Answer:
$6
Step-by-step explanation:
5 x 0.20=1
5+1=6
Suppose that you borrow $17,000 for five years at 6% toward the purchase of a car. Find the monthly payments and the
total interest for the loan.
The monthly payment is $
The amount of the monthly payments is $368.34, and the total interest on the loan is $5,100.
The initial amount of money that we borrow is $17,000. We borrow this amount for a total of five years. The interest charged is 6%. We borrowed the money for the purchase of a car. We need to find the monthly payments and the total interest for the loan.
Let the total amount to be paid and the interest be denoted by the variables "A" and "I", respectively.
I = P*R*T
I = $17,000*0.06*5
I = $5,100
The total amount of money to be paid is the sum of the initial amount and the interest charged.
A = P + I
A = $17,000 + $5,100
A = $22,100
The total number of months in five years is 12*5 = 60.
The amount of the monthly payment is the ratio of the total amount to be paid to the total number of months.
M = $22,100/60
M = $368.34
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The equation of line L1, is y=5x+1
The equation of line L2, is 2y-10x+3=0
Answer:
y = 5x + 1
y = 5x + [tex]\frac{-3}{2}[/tex]
When the slopes are the same (5) the equations are parallel.
Step-by-step explanation:
You can look at the graph of the two equaions attached to see that there paralle.
2y - 10x +3 = 0 Add 10 to both sides of the equation
2y -3 = 10x Add three to both sides of the equation
2y = 10x -3 Divide all the way through by 2
y = 5x + [tex]\frac{-3}{2}[/tex]
Solve the following equation. 8x-6=10
Answer:
x = 2
Step-by-step explanation:
8x - 6 = 10 ( add 6 to both sides )
8x = 16 ( divide both sides by 8 )
x = 2
Answer:
x = 2
Step-by-step explanation:
8x-6 = 10
8x-6+6 = 10+6
8x = 16
8x/8 = 16/8
x = 2
2(g-1)=2g-1
A. No solution
B. 1 solution
C. Indefinitnely solution
Write, solve and graph a compound inequality: An architect is designing a rectangular park. The perimeter of the park must be at least 5,000ft and less than 8,000ft. If the width is 8 less than half the length, what are the possible lengths of the park?
The inequality of the scenario is 10000 ≤ l² - 16l < 16000 and the length is 1672 feet
How to determine the inequality?The statements from the question are given as:
Shape = Rectangular park
Minimum perimeter = 5000 square ft
Maximum perimeter = Less than 8000 square ft
Also, we have
Width = 8 less than half the length
This means that
w = 1/2l - 8
The perimeter of a rectangle is
perimeter = 2 * (l + w)
So, we have
P = lw
This gives
P = 2 * (l + 1/2l - 8)
P = 2 * (1.5l - 8)
Open the brackets
P = 3l - 16
Substitute the known values in the above equation So, we have the following equation
5000 ≤ 3l - 16 < 8000
The above represents the inequality
See attachment for the graph
From the graph, we have the solution to be
l = 1672 (approximately)
Recall that:
w = 1/2l - 8
So, we have
w = 1/2 * 1672 - 8
Evaluate
w = 828
Hence, the possible length is 1672 ft
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A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 60% pure antifreeze. The company wants to obtain 180 gallons of a mixture that contains 35% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?
The gallons of water and premium antifreeze solution that must be mixed are equal to 60 gallons and 120 gallons respectively.
How to determine the gallons of water and premium antifreeze solution?In order to calculate the gallons of water and premium antifreeze solution, we would assign variables to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the gallons of water.Let the variable y represent the premium 60% antifreeze.Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:
x + y = 180 ....equation 1.
0.60y = 0.40(180) ....equation 2.
From equation 2, we have:
0.60y = 0.40(180)
0.60y = 72
y = 72/0.60
y = 120 gallons of premium antifreeze.
For the gallons of water, we have the following:
x + y = 180
x = 180 - y
x = 180 - 120
x = 60 gallons of water.
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Which is the graph of f(x) = 3 sqrt 3
Answer: I think it’s the first one.
Step-by-step explanation:
Maxine's credit card has an APR of 21.99%. If her current monthly balance, before interest, is $2,586.50, what will her monthly interest charge be?
According to the given APR, the monthly interest charge is $47.46
APR
Basically, APR refers the refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors.
Given,
Maxine's credit card has an APR of 21.99%.
Here we have to find the monthly interest charge if her current monthly balance, before interest, is $2,586.50.
While we looking into the given question, we have identified the following,
APR = 21.99%
For one month the APR is calculated as,
APR = 21.99 / 12
APR = 1.8325%
When we convert this into decimal form then we get,
=> APR = 1.8325/100
=> APR = 0.01835
And the current monthly balance is $2,586.50,
So, the interest change for the month is
=>2,586.50 x 0.01835
=> 47.46
Therefore, the monthly interest charge is $47.46.
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Determine whether the series converges or diverges
Please, check the image
The series as represented in the task content is divergent and hence; diverges.
What convergence and divergence in series?It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.
It is noteworthy to know that;
If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.
Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.
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complete the missing numbers, please .
The cost of the sweater is $ 30 and
1 dollar = 17 pesos, $ 25 = 425 pesos and $ 3 dollar = 51 pesos.
Mathematical Operations:Mathematical Operations are activities or mathematical processes used to solve given problems. The most used mathematical activities are adding, subtracting, multiplying, and dividing.
The basic operations and their symbols are given below
Addition (+); Subtraction (-); Division (÷); and Multiplication (x).
Here we have
Priya exchanged 250 dollars for 4250 pesos
[Here we used division and multiplication to solve the problem ]
Then the value of 1 dollar in pesos = [tex]\frac{4250}{250}[/tex] = 17 pesos
⇒ 1 dollar = 17 pesos
⇒ 25 dollars = 25 × 17 = 425 pesos
⇒ 3 dollar = 3 × 17 = 51 pesos
Given the cost of the sweater = 510 pesos
The cost of the sweater in pesos = [tex]\frac{250}{4250} \times510[/tex] = 30
Therefore,
The cost of the sweater is $ 30 and
1 dollar = 17 pesos, $ 25 = 425 pesos and $ 3 dollar = 51 pesos
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Write an equation of the line passing through point P(0, -1) that is parallel to the line y = - 2x+3.
Answer:
[tex]y=-2x-1[/tex]
Step-by-step explanation:
If two lines are parallel, they have the same slope. In this case, it is -2
Using point-slope form, with a slope of -2 going to through point P(0,-1)
We have:
y+1=-2x
y = -2x - 1
:]
A manager samples the receipts of every sixth person who goes through the line. Out of 40 people, 3 had a mispriced item. If 750 people go to this store each day, how many people would you expect to have a mispriced item ?
Answer:
f
Step-by-step explanation:f
Your teacher will grade your responses to questions 4–8 to ensure you receive proper credit for your answers.
A carpenter cut the top section of a window frame with a 37º angle on each end. The side pieces each have a 50º angle cut at their top ends, as shown. Will the side pieces of the frame be parallel? Explain. Diagram not to scale.
SOMEONE PLEASE HELP ME!
Based on the given parameters about a carpenter cutting the top section of a window frame, the side pieces of the frame are not parallel.
How to show that the side pieces of the frame are parallel?Parallel lines are lines which are equally distant from one another at all points.
To show that the side pieces of the frame are parallel:
The interior angles are equal in measure and the sum of the interior angles must be equal to 180°
The two given side pieces of the window frame are also equal in measure.
If the sum of both side angles is equal to 180∘, then, the sides are parallel.
Adding one side of the interior angle:37∘ + 50∘ = 87∘
Adding both sides of the angle:2(37∘ + 50∘)
= 2(87∘)
= 174∘
Hence,
174∘ < 180∘
So therefore, the sides pieces of the window frame cut by the carpenter are not parallel.
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Determine an nth degree polynomial that satisfies the aforementioned conditions.
The polynomial of p(x) is -24 (x² + 15x + 54) with the satisfying's conditions degree 3.
Given,
An nth degree polynomial p meets the requirements listed below:
p is of degree 3.
-9 is a zero, with multiplicity 2, of p.
-6 is a zero, with multiplicity 1, of p.
p(-1) = -960
We have to determine an nth degree polynomial that satisfier the conditions.
Let the polynomial be p(x) whose zero are -9 and -6
a be the coefficient.
p(x) = a (x+9) (x+6)
p(x) = a(x² + 6x + 9x + 54)
p(x) = a(x² + 15x + 54)
Now, take x = -1
p(-1) = a (-1² + 15 x -1 + 54)
-960 = a ( 1 - 15 + 54)
-960 = a x 40
a = -960/40
a = -24
We get,
p(x) = -24 (x+9) (x+6)
p(x)= -24 (x² + 15x + 54)
Therefore, the polynomial of p(x) is -24 (x² + 15x + 54) with the satisfying's conditions degree 3.
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is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.25 . If the flight is on time, the probability that her luggage will make the connecting flight is , but if the flight is 0.8 delayed, the probability that the luggage will make it is only 0.65
The probability that Rebecca's first flight was delayed is 75%.
What is probability?Probability is the ratio or odds of an expected outcome occurring when there are many possible outcomes.
Probability is always a fractional value lying between 0 and 1. When the expected outcome is certain, the probability is said to be one. When it is uncertain, the probability is zero.
Like ratios, probability is depicted as decimals, fractions, or percentages when there is no 100% certainty or uncertainty.
The probability of Rebecca's first flight leaving on time = 0.25
The probability of Rebecca's first flight being delayed = 0.75 (1 - 0.25)
= 75%.
Thus, it is 75% likely that Rebecca's first flight will be delayed.
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Question Completion:Suppose you pick her up at the Denver airport and her luggage is not there. What is the probability that Rebecca's first flight was delayed?
If anyone could take some time and look at the photo and explain a little bit? Thank you I’m grateful for the help :)
Answer:
C= 31in
Step-by-step explanation:
First you must know the circumference equation. The circumference equation is C=2πr, with r being the radius. Since we are given the radius, we will fill in the radius given for r. So then we will fill in and solve:
C=(2)(π)(5in)
C=(10)(π)
C=31.4in...
C=31in
Hope this helps!
An account has a rate of 1.9%. Find the effective annual yield if the interest is compounded quarterly.
Answer:
1.914 %
Step-by-step explanation:
Compounded quarterly means 4 periods per year = n
interest in decimal form per period i = .019/4 = .00475
Formula
annual yield = ( 1+ i)^n -1
(1+ .00475)^4 -1 = .01914 = ~ 1.914%
Find the inverse of f(x) = 1/ x + 8
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~\cfrac{1}{x+8}\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{1}{y+8}} \implies y+8=\cfrac{1}{x}\implies {\large \begin{array}{llll} \stackrel{f^{-1}(x)}{y}=\cfrac{1}{x}-8 \end{array}}[/tex]
x -1 , 3, 7 , 11 and y 3, 6, 10, 15 is the relationship linear, exponential, or neither
Answer:
Yes i the relationship linear,exponential,or neither