Answer:
So,
let the amount of each transaction be x.
3x= 115.25+77.73
x= 192.98÷
x= 64.327
each transaction was of 64.327
Step-by-step explanation:
since the amount left is -77.73 then three equal transaction will also include 115.25+77.73= 1 92.98
192.98 was the total amount used
y=(x-5)^2 quadratic function and state the functions domain and graph
there are about 6*10^24 molecules in a litre of water. it is estimated that a person drinks about 2.2 *10^3 litres of water a year. how many molecules of water does a person drink in a year?
Based on the concept of multiplication, the amount of molecules consumption of water does a person drink in a year is 1.32 x 10²⁸.
Molecules:
A molecules is the group of two or more atoms linked together by sharing electrons in a chemical bond
Given,
There are about 6 x 10²⁴ molecules in a liter of water. it is estimated that a person drinks about 2.2 x 10³ liters of water a year.
Here we have to find the amount of molecules consumption of water does a person drink in a year.
To find the total amount of molecules consumption for the year we have to use the following formula,
Total molecules consumption per year = amount of water x molecules.
Here we know the values of the following,
Water consumption per year = 2.2 x 10³ liters
Molecules of one liter water = 6 x 10²⁴
Apply the values on the formula, then we get,
=> total molecules consumption = (2.2 x 10³) x (6 x 10²⁴)
=> (2.2 x 6) x (10³ x 10²⁴)
=> 13.2 x 10³⁺²⁴
=> 13.2 x ²⁷
It can be further simplified as,
=> 1.32 x 10²⁸
Therefore, the amount of molecules consumption of water does a person drink in a year is 1.32 x 10²⁸.
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Find the equation of the line whose slope is 1/6 passing through the point (-9, 3)
The equation of the line whose slope is 1/6 passing through the point (-9, 3) is -x - 6y - 27 = 0
What is slope formula ?To determine a line's inclination or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.
Given slope of equation m =[tex]\frac{1}{6}[/tex]
A point on line (x₁,y₁) = (-9,3)
(y-y₁)= m (x-x₁)
(y-3) = [tex]\frac{1}{6}[/tex] ( x − (-9))
y-3= [tex]\frac{1}{6}[/tex] (x+9)
6(y-3) = x+9
6y - 18 = x +9
-x - 6y - 27 = 0
This is the equation of line
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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 50.2 . You would like to be 90% confident that your estimate is within 1.5 of the true population mean. How large of a sample size is required?
The required sample size of the given estimate is 3030.65.
Given that,
The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
For the 90% confidence the value of the z = 1.645
Now the sample size is given as,
n = [z × σ/1.5]²
Substitute values in the above equation,
n = [1.645×50.2/1.5]²
n = 3030.65
Thus, the required sample size of the given estimate is 3030.65.
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Kim's room is an 11 ft by 12 ft rectangle. How many square feet of carpeting does she need to buy to cover the entire floor?
In order to calculate the area of carpet needed to cover the entire floor, we just need to calculate the area of the room.
The area of a rectagle is calculated by the product of its dimensions, so we have:
[tex]\text{Area}=11\cdot12=132\text{ ft2}[/tex]So the area of carpet needed is 132 square feet.
Julie plans to put a fence around her square shaped backyard. The length of one side measures 2n-3feet. Write a simplified expression to represent the perimeter of the backyard.
We have the following:
Since it is a square, the sides are equal, and the perimeter is the sum of all the sides, therefore it would be
[tex]\begin{gathered} p=4\cdot l \\ l=2n-3 \\ \text{replacing} \\ p=4\cdot(2n-3) \\ p=8n-12 \end{gathered}[/tex]The answer is 8n - 12
pls solve this question properly
Answer:
∡BOA ≅ ∡DOC
Step-by-step explanation:
Given a circle O with congruent chords BA and DC, you want the relation between angles BOA and DOC.
CongruenceAll of the radii of circle O are congruent. That means BO≅AO≅DO≅CO. The chords BA and DC are marked as congruent. This means ∆BOA and ∆DOC are congruent by the SSS postulate.
Corresponding parts of congruent triangles are congruent, so ...
∡BOA ≅ ∡DOC
express 952 in scientific notation and please show the work
We are asked to express 952 in scientific notation
The scientific notation is given by
[tex]952=9.52\times10^2[/tex]The number 952 has the decimal point at the end, so we move this decimal point to the left until there is only one digit is left (9 in this case) and then count the number of times we moved.
In this case, we moved 2 times so the exponent (power) is 2
The sign of exponent is positive when we move to the left (like in this case)
The sign of exponent is negative when we move to the right.
Find the critical value (tα/2) for a 90% confidence interval if the sample size is 15. Round your answer to three decimal places.
tα/2 =
The critical value of tα/2 for a 90% confidence interval for the sample size 15 is 1.761.
Given, sample size=15
Confidence interval= 90%.
To find the critical value we have to first find alpha, by subtracting 90 from 100.
= 100%-90%
=1-0.9
=0.1
α=0.1
α/2=0.05
Next, we have to find the degrees of freedom(df) by using the formula n-1.
=15-1
df=14
Calculate tα/2 by using t-distribution with degrees of freedom 14 and α/2 = 0.05 as right-tailed area.
From the table we get the critical value for tα/2 as 1.761.
Therefore, the critical value for a 90% confidence interval with sample size 15 is 1.761.
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Bill bought a table on sale for $558. This price was 28% less than the original price,What was the original price?
For the new price to be 28% less than the original price then, therefore, the original price is definitely more than the new price
Let the original price be
[tex]x[/tex]the new price given is
[tex]\text{ \$558}[/tex]It means that the percentage decrease is
[tex]28\text{ \%}[/tex]The formula for percentage decrease is
[tex]\text{percentage decrease=}\frac{\text{original price-new price}}{\text{original price}}\times100\text{ \%}[/tex]By substitution, we will have
[tex]\begin{gathered} 28=\frac{x-\text{ \$558}}{x}\times100 \\ 28x=100x-55800 \\ 55800=100x-28x \\ 72x=55800 \\ \frac{72x}{72}=\frac{55800}{72} \\ x=\text{ \$775} \end{gathered}[/tex]Therefore,
The original price = $775
according to City high school's alumni records 375 students graduated in college in 2001 are these graduates 176 were female 100 and 47 of whom were accepted into college of the male graduate 100 were accepted to college.A) what is the probability that a 2001 graduate of City high School was accepted into collegeB) what is the probability that 2001 graduate of City high School was not a female C)what is the probability that a 2001 graduate of City high School was accepted into college or maleD) what is the probability of being a female given you were accepted into college.
We are asked to determine probabilities from a population of high school graduates. Let's remember that probability is defined as the quotient of desired events and the number of total events.
a) what is the probability that a 2001 graduate of City High School was accepted into college
To determine the probability we need to find the quotient of the number of students that were accepted into college and the total number of students. The total number of students accepted into college is 145 female plus 100 males, therefore, the probability is:
[tex]P(a)=\frac{145+100}{375}=\frac{245}{375}=0.653[/tex]Therefore, the probability is 65.3%.
b)what is the probability that 2001 graduate of City high School was not a female
To do this we will use the fact that the sum of the probabilities that a student is a female plus the probability that the student is not a female must be equal to 1.
[tex]P(\text{female)}+P(\text{not female)=1}[/tex]Therefore, solving for the probability that the student is not a female we get:
[tex]P(\text{not female)=1-P(female)}[/tex]The probability that the student is female is the quotient between the number of female students and the total number of students, therefore:
[tex]\begin{gathered} P(\text{not female)=1-}\frac{176}{375} \\ \\ P(\text{not female)=1-0.461} \\ P(\text{not female)=0.539} \end{gathered}[/tex]Therefore, the probability that the student is not a female is 53.9%.
c) what is the probability that a 2001 graduate of City high School was accepted into college or male
To determine this probability we need to have into account that the probability of event A or event B happening is the sum of both probabilities minus the probability of both events happening at the same time, therefore:
[tex]P(\text{accepted or male)=P(accepted)+P(male)}-P(\text{accepted and male)}[/tex]Replacing the probabilities we get:
[tex]P(\text{accepted or male)=}0.653+\frac{375-176}{375}-\frac{100}{375}[/tex]Solving the operations:
[tex]\begin{gathered} P(\text{accepted or male)=0.653+0.53-0.267} \\ P(\text{accepted or male)=0.916} \end{gathered}[/tex]Therefore, the probability that a student is accepted or male is 91.6%
d) what is the probability of being a female given you were accepted into college.
The probability of event A given event B is given by the following formula:
[tex]P(A\parallel B)=\frac{P(AandB)}{P(B)}[/tex]In this case, we have:
[tex]P(female\parallel accepted)=\frac{P(\text{female and accepted)}}{P(accepted)}[/tex]Replacing the probabilities:
[tex]\begin{gathered} P(female\parallel accepted)=\frac{\frac{147}{375}}{0.653} \\ \\ P(female\parallel accepted)=\frac{0.392}{0.653} \\ \\ P(\text{female}\parallel accepted)=0.6 \end{gathered}[/tex]Therefore, the probability is 60%.
Calculate the area of each figure. Which figure has the greatest area?
a) Area of the parallelogram = b x h
= 9 cm x 7 cm
= 63 cm^2
Usain Bolt is considered to be the fastest person on earth. He holds the record for the fastest 100 m (meters), ,which he ran in 9.58 s (seconds), in 2009. We'll assume that Bolt ran the race at a constant speed.
Which of the following equations, where t represents time in seconds and d represents distance in meters, describe a speed greater than Bolt's record-breaking speed in 2009?
Choose all answers that apply!
A. d=10t
B. d=10.2t
C. d=10.4t
D. d=10.45t
Khan Academy - Rates & proportional relationships
The graph y= f(x) is shown. Translate it to get the graph of y = f(x-2)
The translation of two units right of the graph of y = x is graphed at the end of the answer.
TranslationTranslation is a transformation to the graph of a function or of a figure that keeps everything such as orientation and inclination stable, changing only the position of the graph.
The translations are movements to left, right, up or down, and each movement is represented as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.In this problem, the definition of the translation is given as follows:
y = f(x - 2).
Hence a = 2, and the function is shifted right 2 units.
Considering function y = x, the translated function is:
y = f(x - 2) = x - 2.
(each instance of x in the function is replaced by x - 2).
The graph of the two functions is shown at the end of the answer, which x - 2 being a shift right of 2 units of f(x).
Missing InformationThe function is not given, hence we suppose that it is of y = x.
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Since 12:00 am., a cold front has caused the tempurature in a particular city to decrease at a constant rate. At 2:00 a.m., the tempurature was 54 degrees Farenheit, and at 5:00 a.m., the tempurature was 45 degrees Fahrenheit. Which of the following statements is correct?
A. The tempurature at 12:00 a.m. was 57 degrees Fahrenheit.
B. The tempurature at 12.00 a.m was 60 degrees Fahrenheit.
C. The tempurature at 12:00 a.m was 63 degrees Fahrenheit.
D. The tempurature is decreasingn at a rate of 9 degrees Fahrenheit per hour.
Answer: B.
Step-by-step explanation: First, you find the difference between 2 and 5 =( 3 ), and 54 and 45 ( -9 ). Meaning the unit rate is -3. (-9/3 = -3)
The difference between 12:00 am and 2:00 am is 2 hours meaning 2 x 3 is 6. 54 + 6 = 60 meaning at 12:00 am it was 60 degrees Fahrenheit.
Please help with math question
Answer:
x-intercept is at (18, 0)
y-intercept is at (0, 360)
A restaurant frequently offers a special prix fixe meal and has been charging $140 per person for the event. At that price, they’ve been averaging 50 customers each time. Their marketing firm has convinced them that they’ll gain a customer for every dollar they lower the cost of the event, and conversely lose a customer for every dollar they raise the cost. Their fixed cost per event is $2600 and preparing each customer’s meal costs an additional $40. What are the break-even points in terms of customers served? Write the exact answer. Do not round. Separate multiple answers with a comma.
The milestones at which we will be profitable in terms of the number of consumers serviced are going to be (20, $170), and (130, $60).
How to calculate the break-even point?In several aspects of commerce and finance, a break-even point is an important concept to understand. In the context of finance and accounting, it is a reference to the level of output at which the total production income matches the entire production expenses.
When it comes to financing, the moment at which an investment is considered to have broken even is known as the "break-even point."
When the market price of an underlying asset hits the level at which a buyer will not incur a loss, this is referred to as the break-even point in the options trading market.
In contrast, the point at which a buyer will not incur a loss.
The following will serve as examples of the model:
n - n1 = m(p - p1)
n - 50 = -1(p - 140)
n = -p + 190
Where
Revenue = price * quantity
Revenue = p * n
Revenue = (190 - n) * n
[tex]Revenue= 190n - n^2[/tex]
Cost = 40n +2600
At break-even, revenue = cost
[tex]190n - n^2 = 40n + 2600[/tex]
[tex]n^2 - 150n + 2600 = 0.[/tex]
n = 20 p = 170
n = 130 p = 60
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Which of the following statements is false?A. A rhombus is a quadrilateral.B. A quadrilateral is a polygon with four angles.C. In quadrilateral PQRS, ∠P and ∠S are opposite angles.D. The diagonals of a rhombus are perpendicular and bisect each other.
We have the following statements and results.
A. A rhombus is a quadrilateral.
True. A rhombus is a quadrilateral all of which sides have the same length.
B. A quadrilateral is a polygon with four angles.
True. A polygon is a plane figure with at least three straight sides and angles, and typically five or more.
C. In quadrilateral PQRS, ∠P and ∠S are opposite angles.
False. If we have a quadrilateral PQRS, that means that ∠P and ∠S are consecutive angles, not opposite.
D. The diagonals of a rhombus are perpendicular and bisect each other.
True. It is true that the diagonals of a rhombus are always perpendicular and bisect each other.
Answer.
Statement C is false.
What is the value of sec 3pi/2 in simplest form with a rational denominator?
The given expression is
[tex]sec\frac{3\pi}{2}[/tex]Since sec is the opposite of cosine, then
[tex]sec\frac{3\pi}{2}=\frac{1}{cos\frac{3\pi}{2}}[/tex]Since the value of cos(3pi/2) is 0, then
[tex]\begin{gathered} cos\frac{3\pi}{2}=0 \\ \\ sec(\frac{3\pi}{2})=\frac{1}{cos\frac{3\pi}{2}}=\frac{1}{0} \end{gathered}[/tex]Since 1/0 is an undefined value, then
The answer is undefined
Use 3.14 for pi or the pi button and round to the nearest hundredth. The volume of the cone?
Given:-
[tex]r=4.5,h=9[/tex]To find the volume of cone.
So the volume formula for cone is,
[tex]v=\pi r^2\frac{h}{3}[/tex]Substituting we get,
[tex]\begin{gathered} v=3.14(4.5)(4.5)(\frac{9}{3}) \\ v=3.14(4.5)(4.5)(3) \\ v=190.755 \end{gathered}[/tex]So the required solution is 190.76
what is 10 divided by 3 1/3
Answer:
10 divided by 3 1/3 is;
[tex]3[/tex]Explanation:
We want to divide 10 by 3 1/3;
[tex]10\div3\frac{1}{3}[/tex]Firstly, let us convert the mixed fraction to improper fraction;
[tex]\begin{gathered} 10\div\text{ }\frac{3(3)+1}{3} \\ =10\text{ }\div\text{ }\frac{10}{3} \end{gathered}[/tex]Then we can proceed to divide;
[tex]\begin{gathered} 10\text{ }\div\text{ }\frac{10}{3} \\ 10\times\frac{3}{10} \\ =\frac{30}{10} \\ =3 \end{gathered}[/tex]Therefore, 10 divided by 3 1/3 is;
[tex]3[/tex]Juan's father deposited $1500 in the bank as a graduation gift for juan. The bank pays a compound interest rate of 12% compounded annually. What is Juan's balance after 4 years
. 2 1 3 LAU 5 16 7 DO If angle 1 is x+74 and angle 8 is 2x - 1, what are the measures of angle and 87
Consider that the Alternate Exterior Angles are always equal for a transversal passing through two parallel lines.
The given diagram depicts two incline parallel lines and the vertical line acts as a transversal to them.
Now, angle 1 and angle 8 are alternate exterior angles so they must be equal,
[tex]\begin{gathered} m\angle1=m\angle8 \\ x+74=2x-1 \\ 2x-x=74+1 \\ x=75 \end{gathered}[/tex]So the measure of the angles is given by,
[tex]\begin{gathered} m\angle1=x+74 \\ m\angle1=75+74 \\ m\angle1=149 \end{gathered}[/tex]Thus, both the angles measure 149 degrees.
What is the functional value of the ceiling function: f(1.5)
f is the ceiling function
f(1.5) = 2
if 6 bushels of apples is equal to 24pecks of apples,what is the ratio of bushels of bushels to pecks?
Explanation:
6 bushels = 24 pecks
1 bushel = ??
[tex]\frac{6}{24}=\frac{1}{4}[/tex]Answer:
The ratio of bushels to pecks is 1/4
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The required solution of the inequality on the number line is represented as x>20 .
Any monotonically rising function can, by definition, be applied to both sides of an inequality without destroying the inequality connection (provided that both of the expressions are in the domain of that function).
–3(2x – 5) < 5(2 – x)
-6x+30 < 10-5x
-6x+5x<-20
-x<-20
x>20 (x∈R)
The inequality relation is flipped when a monotonically decreasing function is applied to both sides of an inequality. In the equations for the adding inverse and multiple inverse for positive numbers, a monotonically decaying function is utilized.
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Find the APR (rounded to the nearest tenth of a percent) for the loan. Purchase a living room set for $3,600 at 8 % add- on interest for 3 years.
The annual percentage rate (APR) for the loan of $3,600 at 8% add-on interest for 3 years is 15.6%.
What is the annual percentage rate?The annual percentage rate is the nominal or effective interest rate charged on a loan for a year, unlike the Monthly Percentage Rate (MPR), which is a monthly rate.
The annual percentage rate can be calculated by using the formula:
APR = 2Nr/N + 1
N = number of payments
r = the add-on interest rate
N = 3 years = 36 months (12 x 3)
r = 8% or 0.08 (8/100)
APR = (2 x 36 x 0.08)/(36 + 1)
= 5.76/37
= 0.15.57
= 15.57%
= 15.6%
Thus, with an 8% interest rate for 3 years, the APR is 15.6%.
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Julie is given two points, (x,y) and (w,z). Which process can she use to find the distance between the points?
One option is to use the distance formula.
In this case, this is what Julie would be working with:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(x-w)^2+(y-z)^2}\\\\[/tex]
If Julie knew the values of x, y, w, and z, then she could find a numeric result for the distance (d).
Can I get help in #5 ? I don’t get it
Step 1
The selection formula is;
[tex]\begin{gathered} ^nc_r=\frac{n!}{r!(n-r)!} \\ n=10 \\ r=5 \end{gathered}[/tex][tex]=\frac{10!}{5!(10-5)!}=\frac{3628800}{120(120)}=252\text{ groups}[/tex]Answer; 252 groups
Hi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.Good evening g, thanks for helping meHi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.The problem is 7.Can you please help and thanks 7. The two lines y=4x+5 and y= 4x-2 are parallel because their slopes are equal (both equal to 4).What happens when you try to algebraically solve for their intersection point?
No solution
Explanation:y = 4x + 5
y = 4x - 2
Solving algebraically:
equate both equations
y = y
4x + 5 = 4x - 2
collect like terms:
4x - 4x = - 2 - 5
0 = -7
When the right hand side is not the same as the left hand side equation, it is a no solution.
Their intersection point gives no solution