The height of the water in the tank after 5 minutes is approximately 732.6 inches.
What is the equation for a cylinder's volume?V = πr²h, where V is a cylinder's volume, r is its radius, and h is its height, is the formula for calculating a cylinder's volume. The formula is created by first determining the area of the cylinder's base, which equals r2, and then multiplying that area by the cylinder's height to determine the volume. The volume of tanks, pipelines, and other cylindrical objects may be calculated using this formula, among many other uses.
The volume of a cylinder, which is:
V = πr²h
Given that, diameter is 15 feet, so the radius is 7.5 feet.
Also,
2 feet per second = 2 * 12 * 60 inches per minute = 1440 inches per minute
V = πr²h
Substituting the values:
V = π(7.5)^2(14405)
Here, 14405 is the amount of water that flows into the tank in 5 minutes.
Divide the volume of water by the area of the base of the cylinder
V/A = h
2,044,123/(π(7.5)^2) ≈ 732.6 inches
Hence, the height of the water in the tank after 5 minutes is approximately 732.6 inches.
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GIVING 100 POINTS PLEASE HELP I NEED IT DUE OR ELSE SHOW WORK AND ANSWER
Answer:1
Step-by-step explanation:
Can you please solve?
Answer:
19 and - 8
Step-by-step explanation:
( u ￮ w )(3)
evaluate w(3) then substitute the value obtained into u(x)
w(3) = - 2(3)² = - 2(9) = - 2 × 9 = - 18 , then
u(- 18) = - (- 18) + 1 = 18 + 1 = 19
-----------------------------------------------
( w ￮ u )(3)
evaluate u(3) then substitute the value obtained into w(x)
u(3) = - 3 + 1 = - 2 , then
w(- 2) = - 2(- 2)² = - 2(4) = - 2 × 5 = - 8
Selina is remodeling her home. She installed a low-flow toilet in her home that flushes 0.8 gallon each time. She replaced her showerhead with a low-flow showerhead that releases 1.5 gal/min. She flushes 12 times a day and showers for 10 minutes a day. On average, her appliances use 40.2 gal/day. Assuming no other appliance use, how much less water will she use than the average U.S. citizen?
The average U.S. citizen uses approximately 88 gallons of water a day.
What is Frequency?
Frequency is a measure of how often an event occurs within a given period of time. It is typically expressed as the number of occurrences of a given event per unit of time. Frequency can be used to measure a variety of phenomena such as the frequency of sound in a given environment or the frequency of a particular chemical element in a given sample.
Selina's low-flow toilet and showerhead will reduce her total water use to just 48.4 gallons per day, a savings of 39.6 gallons of water each day. This is a 44.8% reduction in her water consumption, saving her almost 40 gallons of water per day.
By making these improvements, Selina is helping to conserve a precious resource and limit her environmental impact. Not only is she helping to conserve water, but she is also saving money on her water bill. It is estimated that a typical household can expect to save about $170 annually by making these simple changes.
In addition to her low-flow fixtures, Selina can take additional steps to reduce her water consumption. She can install a water-efficient dishwasher, reduce the frequency of her laundry loads, and install a rain barrel to collect rainwater for gardening. By making these changes, she can reduce her water consumption even further and save even more money.
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K
The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total
amount due at time t.
P = $9000, r = 5.5%, t = 8 months
The future value is $
(Simplify your answer. Type an integer or a decimal.)
ew an example
Get more help.
Clear all
Check answer
orrect
Answer:
the future value or total amount due at the end of 8 months is $9,330.00
Step-by-step explanation:
To find the future value of a loan that is borrowed at a simple interest rate, we use the formula:
A = P(1 + rt)
where A is the future value or total amount due, P is the principal or initial amount borrowed, r is the simple interest rate as a decimal, and t is the time period in years.
In this case, the principal is $9000, the simple interest rate is 5.5% or 0.055 as a decimal, and the time period is 8 months or 8/12 = 2/3 years.
Substituting these values into the formula, we get:
A = 9000(1 + 0.055 × 2/3)
= 9000(1.0375)
= $9,330.00
Therefore, the future value or total amount due at the end of 8 months is $9,330.00
we know that a year has 12 months, so 8 months is really 8/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\to \frac{8}{12}\dotfill &\frac{2}{3} \end{cases} \\\\\\ A = 9000[1+(0.055)(\frac{2}{3})] \implies A = 9330[/tex]
The shape of the distribution of the time to get an oil change is 15 minute oil change factory is unknown. However records indicate that the mean time is 16.9 and the standard deviation is 4.7 minutes Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical
Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random
sample, at what mean oil-change time would there be a 10% chance of being at or below? This will be the goal
established by the manager.
There would be a 10% chance of being at or below minutes.
(Round to one decimal place as needed.)
The mean oil-change time for which there is a 10% chance of being at or below is approximately 15.92 minutes.
What is the mean oil-change time?We can start by using the Central Limit Theorem.
Data given:
The population mean is μ = 16.9 minutes
population standard deviation is σ = 4.7 minutes
sample size of n = 40 oil changes performed between 10 A.M. and 12 P.M.
The standard error of the mean (SE) is given by:
SE = σ / √n
SE = 4.7 / √40
SE = 0.743
To find the mean oil-change time for which there is a 10% chance of being at or below, we need to find the z-score associated with the 10th percentile of the standard normal distribution, which is -1.28 (using a standard normal distribution table or calculator).
We can use the formula for a z-score:
z = (x - μ) / SE
where x is the desired mean oil-change time.
Substituting the known values and solving for x, we get:
-1.28 = (x - 16.9) / 0.743
x = -1.28 * 0.743 + 16.9
x = 15.92
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An adult pass at the amusement park costs 1.6 times as much as a child’s pass.
How many dollars does an adult pass cost if a child’s pass costs:
By answering the supplied question, we may infer that the response is equation 1.6 x 30 Equals $48 for an adult pass if the price is $30.
so on.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Let's assume that a child's pass costs $x.
The issue states that the price of an adult pass is 1.6 times that of a kid pass. Thus, an adult pass costs:
$1.6 times
So, if a child's pass is expensive:
a) If an adult pass costs $10, then 1.6 x 10 equals $16.
b) $20, then 1.6 x 20 Equals $32 for an adult pass.
1.6 x 30 Equals $48 for an adult pass if the price is $30.
so on.
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Encuentre el valor de la expresión si a =2, b= -3 y c=-1 ; ab2 -c3
The equivalent expression value when {a} = 2, {b} = -3, {c} = -1 is 19.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is the algebraic expression as -
ab² - c³
For {a} = 2, {b} = -3, {c} = -1, we can evaluate the algebraic expression as -
ab² - c³
2(-3)² - (- 1)³
2 x 9 - (- 1)
18 + 1
19
Therefore, the equivalent expression value when {a} = 2, {b} = -3, {c} = -1 is 19.
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{Question in english -
Find the value of the expression if a =2, b= -3 and c=-1 ; ab2 -c3}
HELP ASAP NO ROCKY
-
-
-
-
NO LINKS
The graph of the function does not form a straight line. Option A
What is the equation of the straight line?The link between the x and y coordinates of the line's points is expressed mathematically as the line's equation. In general, a line's equation can be expressed in slope-intercept form, which is written as y = mx + b, where m denotes the line's slope and b its y-intercept (the point at which the line crosses the y-axis).
The equation in the form 5x^4 - 2 is exponential and it can not lead to a straight line.
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Lynette bought a new car for $34,000 . She paid a 20% down payment and financed the remaining balance for 60 months with an APR of 4.4% . Assuming she made monthly payments, determine the total cost of Lynette's car. Round your answer to the nearest cent, if necessary. Formulas
Answer:
The down payment Lynette made is:
Down payment = 20% of $34,000 = $6,800
The amount financed is:
Amount financed = Total price - Down payment
Amount financed = $34,000 - $6,800 = $27,200
To calculate the monthly payment, we can use the following formula:
Monthly payment = (Pr(1+r)^n) / ((1+r)^n - 1)
where:
P = amount financed
r = monthly interest rate
n = number of months
First, we need to calculate the monthly interest rate:
Monthly interest rate = APR / 12
Monthly interest rate = 4.4% / 12 = 0.0036667
Now, we can calculate the monthly payment:
Monthly payment = ($27,200 * 0.0036667 * (1+0.0036667)^60) / ((1+0.0036667)^60 - 1)
Monthly payment = $501.47
The total cost of the car is the sum of the down payment and the total of all the monthly payments over 60 months:
Total cost = Down payment + Monthly payment * 60
Total cost = $6,800 + $501.47 * 60
Total cost = $37,688.20
Therefore, the total cost of Lynette's car is $37,688.20.
Kathleen begins working and at age 32she invests $6000.0 into a retirement account that pays an APR of 6.4% compounded monthly. She expects to retire at age 65. What will be the size of Kathleen’s total interest when she retires?
By answering the above question, we may state that Hence, when interest Kathleen retires, her total interest will be $10,389.
what is interest ?Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to compute interest. The most typical technique to figure out interest is as a portion of the principle sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.
[tex]FV = PV x (r/n + 1)(n*t)[/tex]
where: $6,000 is the initial investment's present value, or PV.
6.4% is the yearly interest rate at zero.
n = 12 is the number of times interest is compounded annually (monthly)
33 years are equal to t. (from age 32 to age 65)
When we enter the values, we obtain:
FV = $6,000 x (1 + 0.064/12)(12*33) FV = $6,000 x (1 + 0.00533)396 FV = $6,000 x 2.7315 FV = $16,389 FV = $6,000 x 2.7315 FV = $16,389.0
As a result, Kathleen's retirement account will be worth $16,389.0 when she turns 65.
The difference between the future value and the initial investment is the total interest that Kathleen will earn:
Total interest is equal to $16,389 minus $6,000
Interest totaled $10,389.0.
Hence, when Kathleen retires, her total interest will be $10,389.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Based on the information, the statements about Josiah's solution that are true are:
He predicted that the number of rock songs on his MP3 player would be 300 songs.He did not multiply the numerator and denominator by the correct number to equal 1500.He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.How do we find this conclusion?Josiah used a proportion to predict the number of rock songs on his MP3 player. He started by setting up the proportion:
10/20 = x/1500He made a mistake when multiplying the numerator and denominator by 30. Instead, he should have multiplied them by 75, which is a common multiple of 20 and 1500. This would have resulted in:
10/20 = x/1500(10 x 75) / (20 x 75) = x/1500750/1500 = x/1500x = 750Therefore, the total number of rock songs on his MP3 player is 750, which is different from his prediction of 300. This means that he made an error in his calculation, and he should have multiplied by 75 instead of 30.
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How to solve (x-4)^2-9=0
Answer:
Step-by-step explanation:
(x-4)^2-9=0
Let's assume a=x-4 and b=3
We know that,
[tex]a^{2} -b^{2} =(a+b)(a-b)[/tex]
substituting values a, and b in above equation we get,
(x-4+3)(x-4-3)==
(x-1)(x-7)=0
x=1,7
Answer:
[tex]\displaystyle{x=7,1}[/tex]
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{\left(x-4\right)^2-9=0}[/tex]
Add 9 both sides:
[tex]\displaystyle{\left(x-4\right)^2-9+9=0+9}\\\\\displaystyle{\left(x-4\right)^2=9}[/tex]
Square root both sides:
[tex]\displaystyle{\sqrt{\left(x-4\right)^2}=\sqrt{9}}[/tex]
Cancel square root for left side and add plus-minus to right side:
[tex]\displaystyle{x-4=\pm \sqrt{9}}[/tex]
Evaluate the surd of 9:
[tex]\displaystyle{x-4=\pm 3}[/tex]
Add 4 both sides:
[tex]\displaystyle{x-4+4=\pm 3 +4}\\\\\displaystyle{x=\pm 3 +4}[/tex]
Two solutions can be either:
[tex]\displaystyle{x=3+4}[/tex] or [tex]\displaystyle{x = -3+4}[/tex]
Hence:
[tex]\displaystyle{x=7,1}[/tex]
What is the area of this figure?
___ units 2
The area of the figure is equal to:
A = 28[tex]unit[/tex]² + 7[tex]unit[/tex]² + 7[tex]unit[/tex]² =42[tex]unit[/tex]²
Provide an area example.You could also draw the shape on a grid and count the squares there: The rectangle has a 15 surface area. For instance, if the space is 15 m2 and each square is one meter in size (15 square meters).
Answer:
42[tex]units[/tex]²
Step-by-step explanation:
we know that
The area of the figure is equal to the area of a rectangle plus the area of two triangles
Find the area of rectangle
Observing the graph
The area of rectangle is equal to
A= bh = (2+5)(2+2)= 28[tex]unit[/tex]²
Find the area of the top triangle
A = 1/2bh = 1/2(2+5)(2+2) = 7[tex]unit[/tex]²
Find the area of the bottom triangle
A = 1/2bh = 1/2(2+5)(2+2) = 7[tex]unit[/tex]²
the area of the figure is equal to
A = 28[tex]unit[/tex]² + 7[tex]unit[/tex]² + 7[tex]unit[/tex]² =42[tex]unit[/tex]²
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3x + 6x help!!
Need this quicklllyh
Answer: 9x
Step-by-step explanation:
You combine like terms.
Which of the following is common both ADC and BCD
The segment CD is common on both ΔACD and ΔBCD.
What is a Triangle?Polygon, which has three sides and three vertices, is called a triangle.
The sum of all the angles of the triangle is 180°.
Given:
Two triangles ΔACD and ΔBCD in the given image.
To find the commonality between two triangles ΔACD and ΔBCD:
The sides of the triangle ΔACD are AC, CD, and AD.
The sides of the triangle ΔBCD are BC, CD, and BD.
From the diagram,
we can clearly see that the segment CD is common on both ΔACD and ΔBCD.
CD ≅ CD (reflexivity)
Therefore, the common segment is CD.
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find the 7th term in the sequence an= 1/2(3)^n-1
NEED IT SOONNNNNN
This should be the correct answer
Exact Form:
729/2
Decimal Form:
364.5
Mixed Number Form:
364 1/2
Test Prep While working at the school store, John sold a jacket for $40.00 and notebooks for $1.50 each. If he collected $92.50, how many notebooks did he sell?
Answer:
Step-by-step explanation:
1 jacket and 2 notebooks
(just my guess but you might get it right)
(also use desmos scientific calculator its a lot better)
Answer:
he sold 35 notebooks
Step-by-step explanation:
first you subtract 40.00 from 92.50 equaling 52.50 then you divide 52.50 by 1.50.
What is the spread of 2 1 4 3 5 1 1 2 using standard deviation
The spread of the numbers 2, 1, 4, 3, 5, 1, 1, 2 using standard deviation is approximately 1.768.
We must first determine the mean (average) of the numbers in order to use the standard deviation to determine the spread (i.e., variability) of the set of data.
By adding up all the numbers and dividing by the total number of numbers, the mean is calculated:
mean = (2 + 1 + 4 + 3 + 5 + 1 + 1 + 2) / 8
= 19 / 8
≈ 2.375
The difference between each number and the mean is then determined:
2 - 2.375 = -0.375
1 - 2.375 = -1.375
4 - 2.375 = 1.625
3 - 2.375 = 0.625
5 - 2.375 = 2.625
1 - 2.375 = -1.375
1 - 2.375 = -1.375\s2 - 2.375 = -0.375
Then, each of these discrepancies is squared:
(-0.375)^2 = 0.140625
(-1.375)^2 = 1.890625
(1.625)^2 = 2.640625
(0.625)^2 = 0.390625
(2.625)^2 = 6.890625
(-1.375)^2 = 1.890625
(-1.375)^2 = 1.890625
(-0.375)^2 = 0.140625
The variance is then calculated as the average of these squared differences:
variance is equal to 3.125 x (0.0140625 x 1.890625 x 2.640625 x 0.390625 x 6.890625 x 1.890625 x 0.140625).
Lastly, we calculate the standard deviation by taking the square root of the variance:
(3.125) 1.768 is the standard deviation.
As a result, using standard deviation, the range of the digits 2, 1, 4, 3, 5, 1, 1, 2 is almost 1.768.
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The spread οf the numbers 2, 1, 4, 3, 5, 1, 1, 2 using standard deviatiοn is apprοximately 1.768.
How to find the spread of numbers?We must first determine the mean (average) οf the numbers in οrder tο use the standard deviatiοn tο determine the spread (i.e., variability) οf the set οf data.
By adding up all the numbers and dividing by the tοtal number οf numbers, the mean is calculated:
mean = (2 + 1 + 4 + 3 + 5 + 1 + 1 + 2) / 8
= 19 / 8
≈ 2.375
The difference between each number and the mean is then determined:
2 - 2.375 = -0.375
1 - 2.375 = -1.375
4 - 2.375 = 1.625
3 - 2.375 = 0.625
5 - 2.375 = 2.625
1 - 2.375 = -1.375
[tex]1 - 2.375 = -1.375\s2 - 2.375 = -0.375[/tex]
Then, each οf these discrepancies is squared:
(-0.375)² = 0.140625
(-1.375)² = 1.890625
(1.625)² = 2.640625
(0.625)² = 0.390625
(2.625)² = 6.890625
(-1.375)² = 1.890625
(-1.375)² = 1.890625
(-0.375)² = 0.140625
The variance is then calculated as the average οf these squared differences:
variance is equal tο 3.125 x (0.0140625 x 1.890625 x 2.640625 x 0.390625 x 6.890625 x 1.890625 x 0.140625).
Lastly, we calculate the standard deviatiοn by taking the square rοοt οf the variance:
(3.125) 1.768 is the standard deviatiοn.
As a result, using standard deviatiοn, the range οf the digits 2, 1, 4, 3, 5, 1, 1, 2 is almοst 1.768.
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Select all expressions that represent a correct solution to the equation
6
(
�
+
4
)
=
20
6(x+4)=20
Therefore , the solution of the given problem of expression comes out to be D, E, and F are the appropriate answers as a result.
Explain expression.There is a need for mathematical operations like multiplying, splitting, combining, and now even deleting. If the equation were combined, it would be said that: A mathematical formula, some data, and an equation A declaration of truth is composed of values, elements, and mathematical operations like additions, subtractions, missteps, algebraic formulas, and divisions. It is possible to evaluate and analyse words and phrases.
Here,
The following is how the problem 6(x+4)=20 can be solved:
=>6(x+4) = 20
=> 6x + 24 = 20
=> 6x = -4
=> x = -4/6
=> x = -2/3
Let's verify which of the examples represents the right answer now:
=> A. (20−4)÷6 = 16/6 = 8/3 --> Incorrect
=> B. 16(20−4) = 16(16) = 256 --> Incorrect
=> C. 20−6−4 = 10 --> Incorrect
=> D. 20÷6−4 = (10/3) - 4 = (10-12)/3 = -2/3 --> Correct
=> E. 1/6(20−24) = -4/6 = -2/3 --> Correct
=> F. (20−24)÷6 = -4/6 = -2/3 --> Correct
D, E, and F are the appropriate answers as a result.
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The complete question is
Select all expressions that represent a correct solution to the equation 6(x+4)=20. copied for free from openupresources.Org Select all that apply: A. (20−4)÷6 B. 16(20−4) C. 20−6−4 D. 20÷6−4 E. 1/6(20−24) F. (20−24)÷6"
What do x equal in these?
Answer:
2.-♾️-61/14
3.-♾️-14
4.-♾️4
5.-♾️-10
Find the percent decrease from 498 to 0
As a consequence, the percentage decline from 498 to 0 is equal to 100% of the original value.
what is percentage ?As a fraction of 100, a figure can be expressed as a percentage. For instance, the decimal equivalent of 50% is 50/100 or 0.5. The comparison or representation of changes between two numbers is frequently done using percentages. For instance, a percentage increase or decline indicates how much something has changed from its starting point. Additionally, percentages are frequently used in daily contexts like interest rates, shopping discounts, and academic performance.
given
The formula below can be used to determine the percent reduction from 498 to 0:
(Original value - New value) / 100% of the original value equals the percent decline.
The initial number in this case was 498, and the updated value is 0.
Reduced percentage equals (498 - 0) / (498 x 100%)
% drop equals 100%
As a consequence, the percentage decline from 498 to 0 is equal to 100% of the original value.
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Given that a : b=11:32 and that b : c=8:9, find the ratio a : b : cGive your ratio in its simplest form with integer parts.
The ratio a : b : c in its simplest form with integer parts is therefore 11 : 32 : 36.
We are informed that
a : b = 11 : 32 ...(1)
b : c = 8 : 9 ...(2)
We must first determine the ratio between a, b, and c in terms of a common component in order to determine the ratio a: b: c. We may accomplish this by using the variable k and writing:
From equation (1), b = 32k
c = (9/8)
(According to equation (2))
The result of putting the first equation into the second equation is:
c = (9/8)(32k)\s= 36k
Hence, we have:
A = B + C = 32k + 36k
We can enter b = 32k into equation (1) to get:
a : (32k) : 36k = 11 : 32
When we multiply both sides by 32, we obtain:
32a : 32(32k) : 32(36k) = 11(32)
Simplifying:
32a : 1024k : 1152k = 352
When we multiply both sides by 32, we get:
a : 32k : 36k = 11 : 32 : 36
Hence, 11: 32: 36 is the ratio of a: b: c in its simplest form with integer parts.
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Question 1-25
Look at the recursive formula given for a sequence.
f(1) = 4
f(n) = f(n-1) +6
What is the fifth term in the sequence? Enter the answer in the box.
Answer:
[tex]1 - 25xy2256xx28( [/tex]
Of 109.6 million households, 19,508,800 watched the television show
CSI during the week of October 3, 2005. What percent of American
households watched CSI this week?
The percent of American households that watched CSI this week is 17.8%.
What is percent of a quantity?The percent is the part or fraction of a quantity taken from the whole quantity which is expressed in percentage. The quantity may be numbers, team, population etc.
Given that the total households are 109600000, of which 19508800 watched the television show CSI during the week of October 2, 2005.
Thus,
The percent of American households that watched CSI this week, N, can be determined as follows;
N = fraction/ whole * 100%
= 19508800/ 109600000 * 100%
= 17.8
N = 17.8%
The percent of American households that watched CSI this week is 17.8%.
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Graph the functions f(x)=−2x−6 and g(x)=−2x−6 on the same coordinate plane. What are the solutions of the equation −2x−6=−2x−6? Select each correct answer. Responses x=−1 x equals negative 1 x = 0 x, = 0 x = 1 x, = 1 x = 2 x, = 2 x = 3 x, = 3
The function has an infinite solution.
What is a function?A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values.
The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Since f(x) and g(x) are the same function, their graphs will be the same and all points on the line are solutions. All x values will be solutions. This means there are infinitely many.
You can see it algebraically too:
-2x-6 = -2x-6
-2x+2x-6 = -2x +2x -6
0-6 = 0-6
-6=-6 True. Infinite solutions.
Hence the function has an infinite solution.
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Suppose you play a game where you roll a fair six-sided die. If the die lands on an even number, you win $2, and if the die lands on an odd number, you lose $1. What is your expected value for one round of this game?
Show Work and Submit Full Answer
Answer:
1 buck
Step-by-step explanation:
Alright man im not a pro at this, so im not gonna have a professional explanation, but the final answer will be correct.
So listen up a dice has 6 sides labeled 1,2,3,4,5,6
3 of those are even
3 of those are odd
so you have a 50% chance of landing on an evan numbered side
and a 50% chance of landing on an odd-numbered side
So basically, if we play one round, there are 2 possibilities. We get even and win 2 bucks, or we get odd and lose a buck. We dont need to worry about probability as they are both 50%. Therfore, the value is 2-1 = 1 dollar. I found the value by subtracting the possbilities.
Use the graph to answer the question. Graph of polygon ABCD with vertices at 1 comma negative 1, 3 comma negative 5, 7 comma negative 5, 5 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at 1 comma negative 6, 3 comma negative 10, 7 comma negative 10, 5 comma negative 6. Determine the translation used to create the image. 5 units down 5 units up 1 unit down 1 unit up
The image was created by translating 5 units down, 5 units up, 1 unit down, and 1 unit up. ABCD and A'B'C'D' are two polygons on the graph.
The first polygon, ABCD, has vertices at (1,-1), (3,-5), (7,-5), and (8,-5). (5,-1). The vertices of the second polygon, A'B'C'D', are located at (1,-6), (3,-10), (7,-10), and (8,-10). (5,-6).
What exactly are vertices?Vertices are points in a geometric figure that define its shape. A vertex is defined mathematically as the intersection of two or more lines, edges, or curves.
We can compare the coordinates of the two polygons to determine the translation that was used to create the image. The first coordinate of the two polygons is (1,-1) and the second coordinate is (1,-1). (1,-6). The y-coordinate difference is 5 units, so the translation is 5 units down. The two polygons' second coordinate is (3,-5) and (3,-10). The y-coordinate difference is 5 units, so the translation is 5 units down.
The second polygon's third coordinate is (7,-5) and (7,-10). The y-coordinate difference is 5 units, so the translation is 5 units down. (5,-1) is the fourth coordinate of both polygons (5,-6). The y-coordinate difference is 5 units, so the translation is 5 units down.
The image was translated 5 units down, 5 units up, 1 unit down, and 1 unit up.
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the the percent change from 50 to 22
Answer:
227.27%
Step-by-step explanation:
QUESTION 18
Consider the following argument: If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's
nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it
isn't the case that Shaun eats popping candy while drinking a can of soda. What is the logical form of this argument?
O a. Affirming a disjunct
b. Denying the antecedent
O c. Affirming the consequent
d. Modus Tollens
Oe. Modus Ponens
If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it isn't the case that Shaun eats popping candy while drinking a can of soda. The logical form of this argument is denying the antecedent. The Option B is correct.
How is "denying the antecedent" a logical form in the statement?If we represent the argument in logical symbols, it would look like this:
P: Soda streams out of Shaun's nose when he eat candy Q: Soda does not streams out of Shaun's nose when he doesnt eat candyThe argument can be summarized as follows:
If P, then Q.
Not P.
Therefore, not Q.
This is the form of denying the antecedent, where the argument asserts that if P is true, then Q must also be true. However, the argument then proceeds to deny the antecedent by claiming that P is not true, and therefore, Q must not be true either.
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Complete the square
x^2 =−8x−7
super important
The solutions to the equation x²= -8x - 7 are x = -1 or x = -7.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
To complete the square for this equation x^2 = -8x - 7
Adding the square of half the coefficient of x (which is (-8)/2 = -4) to both sides of the equation:
x² + 8x + (-4)²= -7 + (-4)^2
This gives us:
x² + 8x + 16 = 9
Now we can write the left-hand side as a perfect square:
(x + 4)² = 9
Taking the square root of both sides gives us:
x + 4 = ±3
Solving for x, we get:
x = -4 ± 3
Therefore, the solutions to the equation x²= -8x - 7 are: x = -1 or x = -7.
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