The room temperature after 8 hours after the process begins would be 10°C.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided above, a linear equation that models the cooling machine is given by;
y = mx + c
y = -5x + 50
By substituting the given parameter (x = 8 hours), we have the following:
y = -5(8) + 50
y = -40 + 10
y = 10°C
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In ΔTUV, t = 22 inches, u = 79 inches and ∠V=51°. Find ∠U, to the nearest degree.
The measure of angle U is given as follows:
m < U = 66º.
What is the law of cosines?The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:
c² = a² + b² - 2abcos(C)
Hence the length of side v is obtained as follows:
v² = 22² + 79² - 2 x 22 x 79 x cosine of 51 degrees
v² = 4537.48
[tex]v = \sqrt{4537.48}[/tex]
v = 67.36.
By the law of sines, we have that:
sin(51º)/67.36 = sin(U)/79
Hence the measure of angle U is obtained as follows:
sin(U) = 79 x sine of 51 degrees/67.36
sin(U) = 0.9114
m < U = arcsin(0.9114)
m < U = 66º.
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NO LINKS!!!! URGENT HELP PLEASE!!!
Please help me with these problems
Answer:
[tex]\sf g(x) = f(x\; \boxed{+ 3}\;) \;\boxed{- 6}[/tex]
Step-by-step explanation:
A translation is a transformation that moves every point of a figure the same distance and in the same direction. This means that the size, shape, and orientation of the figure are preserved, but its position is changed.
From inspection of the given diagram, we can see that the size, shape and orientation of the graph of function g is the same as that of the graph of function f, but its position has changed. Therefore, the transformation is a translation.
We can use the vertex of both graphs to determine the translation.
The vertex of function f is the origin (0, 0).The vertex of function g is (-3, -6).Therefore, the graph of function f has been moved 3 units left and 6 units down to create the graph of function g.
When we move "a" units left, we add the value of "a" to the x-value of the function.
When we move "a" units down, we subtract the value of "a" from the function.
Therefore:
[tex]\sf g(x) = f(x\; \boxed{+ 3}\;) \;\boxed{- 6}[/tex]
Please help me find the equation to this in standard form equation ASAP
The equation of the line in the graph passing through the points (-2,1) and (6,7) is [tex]y = \frac{3}{4}x + \frac{5}{2}[/tex].
What is the equation of the line?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
From the graph, the line passes through point (-2,1) and (6,7).
First, we determine the slope:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{7 - 1}{6-(-2)} \\\\m = \frac{6}{6+ 2} \\\\m = \frac{6}{8} \\\\m = \frac{3}{4}[/tex]
Now, plug the slope m = 3/4 and point (-2,1) into the point-slope form:
( y - y₁ ) = m( x - x₁ )
[tex]y - 1 = \frac{3}{4}(x - (-2)) \\\\y - 1 = \frac{3}{4}(x + 2)\\\\y - 1 = \frac{3}{4}x + \frac{3}{2} \\\\y = \frac{3}{4}x + \frac{3}{2} + 1\\\\y = \frac{3}{4}x + \frac{5}{2}[/tex]
Therefore, the euation of the line is [tex]y = \frac{3}{4}x + \frac{5}{2}[/tex].
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Suppose you buy a book for $26 and use a $3 coupon. If the sales tax is 4.5%,
how much do you pay for the book?
A. $23.84
B. $24.04
C. $24.17
D. $27.17
Solve 125 + 20w− 20w = 43 + 37w− 20w
Answer:
[tex]w=\frac{82}{17}[/tex]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Decimal form: 4.82352941
having a great day and thx for your inquiry :)
PRACTICE 1 Shawna is a professional dog walker. She offers two different payment plans. She agrees to walk your dog twice a day for at least one mile per walk in each plan. Suppose you want to employ Shawna but need to choose between the two payment plans. X у Days Cost ($) The first plan charges a rate of $5 per day. A table of values represents the second plan, and you must purchase 20 days' worth of services per month. Consider a relationship where y represents the total cost of dog walking, in dollars, that you can express as a function of the number of days. a Identify which function has the greater rate of change and explain your reasoning. 20 24 85 102
pls i need help asap.
The first plan has a higher rate of change compared to the second plan based on the given information.
To identify which function has the greater rate of change, we need to compare the rate at which the cost increases for each function. Given the table of values, let's analyze the rates of change for both functions.
First Plan:
The first plan charges a rate of $5 per day, regardless of the number of days. In this case, the rate of change is constant at $5 per day, meaning the cost increases by $5 for each additional day.
Second Plan:
The table of values provided doesn't directly represent the second plan. We need the values for the number of days and their corresponding costs for the second plan to determine its rate of change.
However, since we're comparing the rates of change between the two functions, we can calculate the average rate of change for the second plan using the given values. Let's find the average rate of change between the first and last points:
Change in cost = 102 - 24 = 78
Change in days = 20 - 2 = 18
The average rate of change = Change in cost / Change in days
= 78 / 18
≈ 4.3333
The average rate of change for the second plan is approximately 4.3333 dollars per day.
Comparing the rates of change:
The rate of change for the first plan is $5 per day, while the average rate of change for the second plan is approximately $4.3333 per day. Therefore, the first plan has a greater rate of change.
In conclusion, the first plan has a higher rate of change compared to the second plan based on the given information.
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Calculator
A point is selected at random inside the given figure.
What is the probability the point will be in the region labeled A?
Enter your answer, as a fraction in simplest form, in the box.
P(A) =
Basic
5 in.
B
3 in.
A
C
4 in.
3 in.
D
4 in.
The probability the point will be in the region labeled A is 2/15 if point is selected at random inside the given figure.
Given that a point is selected at random from inside the given figure.
We are to find the probability that the point will be in the region labeled B.
From the figure, we note that the regions A, B and D are rectangles and the region C is a square.
The areas of all the regions are calculated as follows:
Area of region A is 5×(3+4) =35 sq in
Area of region B is 3×4 = 12 in
Area of region C is 4² = 16 sq in
Area of region D is 3×(4+5)= 27 sq. in
Therefore, the probability that the randomly chosen point will lie in the region B is given by P
P = 12/35+12+16+27
=12/90
=2/15
Hence, the probability the point will be in the region labeled A is 2/15
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The probability of being right-handed is 0.9. The probability that someone plays chess given that they are left- handed is 0.6. Research shows that one's dominant hand and playing chess are probabilistically independent.
Assuming that there are no ambidextrous people, what is the probability of someone being a right-handed chess player?
0.04
O 0.54
O 0.46
O 0.06
The probability of someone being a right-handed chess player is 0.962, or approximately 0.96
Now, We have to given that;
The probability of being right-handed (R) is 0.9 and the probability of playing chess (C) given that someone is left-handed (L) is 0.6.
And, We are also told that dominant hand and playing chess are independent, so this means that the probability of playing chess is the same regardless of whether someone is left-handed or right-handed.
Hence, the probability of someone being a right-handed chess player, we can use the following formula:
P(R and C) = P(R) x P(C)
We know that P(R) = 0.9,
and since playing chess is independent of handedness,
P(C) = P(C|L) + P(C|R) = 0.6 + P(C|R).
We want to find P(C|R), the probability of playing chess given that someone is right-handed.
We can use the fact that the probabilities must add up to 1 to solve for P(C|R):
P(C|R) = 1 - P(not C|R)
We know that;
P(not C|R) = 1 - P(C|R),
so we can substitute to get:
P(C|R) = 1 - (1 - P(C|R)) = 2P(C|R) - 1
Now we can substitute this back into the original formula and solve for P(R and C):
P(R and C) = P(R) x P(C) P(R and C) = 0.9 x (0.6 + P(C|R))
P(R and C) = 0.54 + 0.9P(C|R)
Finally, we use the fact that the probabilities must add up to 1 to solve for P(C|R):
P(C|R) = 1 - P(not C|R) P(C|R)
= 1 - P(no C and R) / P(R) P(C|R)
= 1 - P(R and not C) / P(R) P(C|R)
= 1 - (0.1 x 0.4) / 0.9
P(C|R) = 0.5333
Now we can substitute this back into the equation for P(R and C) to get:
P(R and C) = 0.54 + 0.9(0.5333...)
P(R and C) = 0.962
Therefore, the probability of someone being a right-handed chess player is 0.962, or approximately 0.96
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 32 liters per minute. There are 600 liters in the pond to start. Let W represent the total amount of water in the pond (in liters), and let T represent the total number of minutes that water has been added. Write an equation relating W to T Then use this equation to find the total amount of water after 13 minutes.
If owners of a recreation area are filling a small pond with water. The total amount of water after 13 minutes is 1016 liters.
What is the amount of water?Let the total amount of water in the pond = W
Let the total number of minutes that water has been added = T
The equation relating W to T Is:
W = 600 + 32T
Where:
600= initial amount of water in the pond
32T = additional water added over time
Now let find the total amount of water in the pond after 13 minutes
Substitute T = 13 into the equation:
W = 600 + 32(13)
W = 600 + 416
W = 1016
Therefore the total amount of water is 1016 liters.
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A student is saving money to go on a school field trip. The graph shows the relationship between the number of weeks the student has been saving, x, and the total dollar amount they have saved, y.
Answer:
The is is 1
Step-by-step explanation:
An insurance actuary tracks the customer mass and the dosage of a certain medicine prescribed to customers. An approximate least-squares regression line was used to predict the dosage, in milligrams; from a given costumer mass, in kilograms. Interpret the residual for the customer indicated in the scatter plot.
The residual measures the difference between the predicted and observed dosage, indicating if the customer received more or less medication than expected based on their mass.
The residual in this context refers to the difference between the predicted dosage of the medicine, based on the least-squares regression line, and the actual dosage observed for a specific customer. It indicates how much the actual dosage deviates from the expected dosage based on the customer's mass.
In the scatter plot, the residual for a particular customer represents the vertical distance between the observed data point (the actual dosage) and the regression line (the predicted dosage).
If the residual is positive, it means the observed dosage is higher than the predicted dosage, indicating that the customer received a higher dosage of the medicine than expected based on their mass.
Conversely, if the residual is negative, it means the observed dosage is lower than the predicted dosage, indicating that the customer received a lower dosage than expected based on their mass.
Interpreting the residual requires considering the magnitude of the deviation. A larger residual suggests a greater difference between the observed and predicted dosages, indicating a potentially significant variation from the regression model.
A smaller residual indicates a closer alignment between the observed and predicted dosages, suggesting that the regression model provides a more accurate estimation.
Overall, analyzing the residuals helps assess the effectiveness of the regression model in predicting the dosage of the medicine based on customer mass and identifies any outliers or discrepancies in the data that may need further investigation.
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Determine f(4) for A piecewise function f(x) = x^3 x<-3
2x^2-9 -3 ≤ x≤ 4
5x+4 x>4
PLEASE SHOW ALL WORK!!!!!!!!!!!!!!
23
24
41
64
thank you!
Find the distance between (-9, 8) and (-1,8).
The distance is how many units?
Here,
We know that,
[tex] \large \bf \: Distance= \sqrt{(x_2 - x_ 1) {}^{2} + (y_ 2 -y_1) {}^{2} } [/tex]
x1= -9x2 = -1 y1 = 8y2 = 8So ,
Putting the value of x and y in the given formula
We get,
[tex]\large\sf{ \: = \sqrt{ \{ \: - 1 - ( - 9) \} {}^{2} + (8 - 8) {}^{2} } \: }[/tex]
[tex]\large\sf{ = \sqrt{(8) {}^{2} + (0) {}^{2} } }[/tex]
[tex]\large\sf{ \: = \sqrt{64 + 0} }[/tex]
[tex]\large\sf{ = \sqrt{64} }[/tex]
[tex]\large\bf \blue { = 8 \: unit}[/tex]
Thus,
distance between (-9, 8) and (-1,8) is in 8 units.[tex] {\underline {\underline{ \rule{200pt}{8pt}}}}[/tex]
Jamal works at the recreation center 15 hours a week during the school year. He earns $8.75 an hour. in a typical month, he works 63 hours. Calculate his monthly taxes below.
Gross Monthly Income
Monthly Federal Income Tax (10%)
Monthly Social Security (FICA) (6.2%)
Monthly Medicare (1.45%)
Monthly State Tax (4%)
Monthly Local Tax (0.1 %)
Total Monthly Deductions
CA CA EA EA CA
S
Jamal's NMI =
Jamal's Net Monthly Income (NMI) is $431.40.
To calculate Jamal's Net Monthly Income (NMI)We need to calculate his gross income and all the monthly deductions first.
Gross Income = Hourly Rate x Total Hours Worked = $8.75/hour x 63 hours = $551.25
Monthly Federal Income Tax = Gross Income x Federal Tax Rate = $551.25 x 0.10 = $55.125
Monthly Social Security (FICA) = Gross Income x FICA Rate = $551.25 x 0.062 = $34.13625
Monthly Medicare = Gross Income x Medicare Rate = $551.25 x 0.0145 = $7.987625
Monthly State Tax = Gross Income x State Tax Rate = $551.25 x 0.04 = $22.05
Monthly Local Tax = Gross Income x Local Tax Rate = $551.25 x 0.001 = $0.55125
Monthly Federal Income Tax + Monthly Social Security (FICA) + Monthly Medicare + Monthly State Tax + Monthly Local Tax = Total Monthly Deductions
= $55.125 + $34.13625 + $7.987625 + $22.05 + $0.55125
= $119.85
Net Monthly Income (NMI) = Gross Income - Total Monthly Deductions
= $551.25 - $119.85
= $431.40
Therefore, Jamal's Net Monthly Income (NMI) is $431.40.
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Johnny uses a wheelbarrow to move planting soil to a delivery truck. The volume of planting soil that fits in the wheelbarrow measures
2
2 feet by
3
3 feet by
1.5
1.5 feet. The delivery truck measures
11
11 feet by
8
8 feet and is
6
6 feet tall. Johnny puts planting soil in the delivery truck until the truck is
70
70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is
70
70% full?
The minimum number of times Johnny needs to use to the wheelbarrow until the delivery truck is filled up to 70%, whereby the shape of the truck is a rectangular prism is about 41 times
What is a rectangular prism?A rectangular prism is a three dimensional geometric figure with three pairs of parallel facing sides, and perpendicular adjacent faces.
Whereby the wheelbarrow and the truck are rectangular prisms, we get;
The dimensions of the wheel barrow are;
2 feet by 3 feet by 1.5 feet
The dimensions of the truck are;
11 feet by 8 feet by 6 feet
The amount of soil John puts in the truck = 70% of the volume of the truck
Therefore;
The amount of soil John puts in the truck = 11 feet × 8 feet × 6 feet × 70%
11 feet × 8 feet × 6 feet × 70% = 528 ft³ × 70% = 369.6 ft³
The number of times to use the wheelbarrow, n, is therefore;
n = 369.6 ft³ ÷ (2 ft × 3 ft × 1.5 ft) ≈ 41.0
The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled is therefore 41 = 41 times
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Washington DC is the midpoint of Maine and South Carolina. If a town in SC is located at
(-2,-20) and a town in Maine is located at (18,42), what is the distance from the town in SC to Washington DC
The distance from the town in SC to Washington DC is,
⇒ 32.6 units
We have to given that;
Washington DC is the midpoint of Maine and South Carolina. If a town in SC is located at (-2,-20) and a town in Maine is located at (18,42),
Since, We know that;
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, We get;
The coordinate for Washington is,
⇒ (18 - 2)/2, (- 20 + 42) / 2
⇒ (8, 11)
The distance from the town in SC to Washington DC is,
⇒ d = √ (8 - (- 2))² + (11 - (- 20))²
⇒ d = √10² + 31²
⇒ d = √100 + 961
⇒ d = √1061
⇒ d = 32.6 units
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Net worth is the number of goods or services that can be purchased with
several units of currency.
O False
O True
Answer:
False
Step-by-step explanation:
Net worth is a combination of everything you own.
This includes the amount of money you have, or have ever made, plus your house, vehicle, belongings, etc.
Raquel informed her stockbroker that she wanted to buy a certain amount of stock. The broker informed her that because of the margin requirement of 55% she would need at least $825 in cash what is the dollar value of the stock that Raquel wants to purchase?
The dollar value of the stock that Raquel wants to purchase is $1,833.33.
If the margin requirement is 55%, then the amount of cash wanted is 45% of the total value of the inventory.
Consequently, we will set up the following equation like this:
0.45x = 825
Wherein:
x is the dollar value of the stock Raquel wants to purchase.
To solve for x, we are able to divide both aspects of the equation by way of 0.45:
x = 825 ÷ 0.45
x = $1,833.33
Therefore, the dollar value of the stock that Raquel wants to purchase is $1,833.33.
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pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\huge\mathcal{\fcolorbox{Aqua}{azure}{\red{➳Answer}}}[/tex]
Base of the Parallelogram=14m
Height of the Parallelogram=8m
∴ Are of the Parallelogram= Base × height
= (14×8) sq. m
=112 sq.m
Now,
Diameter of the circle (unshaded portion)=8m
Radius of the circle= Diameter/2 =8/2 m= 4m
So, radius=4m
∴ Area of the circle = πr²
=(22/7 × 4 × 4)sq.m
=352/7 sq.m
=50.2857 sq.m
=50.286 sq.m
∴ Are of the Unshaded portion= Are of the Parallelogram - Area of the circle
=(112-50.286) sq.m
= 61.714 sq.m (Ans)
∴The area of the shaded portion is 61.714 sq.m
Hope it helps you
[tex]\red{\rule{200pt}{5pt}}[/tex]
[tex]\bold{Thank ~you~:)}[/tex]
___________________________________
Given:-
Base of the Parallelogram=14m
Height of the Parallelogram=8m
∴ Are of the Parallelogram= Base × height
= (14×8) sq. m
=112 sq.m
Now,
Diameter of the circle (unshaded portion)=8m
Radius of the circle= Diameter/2 =8/2 m= 4m
So, radius=4m
∴ Area of the circle = πr²
=(22/7 × 4 × 4)sq.m
=352/7 sq.m
=50.2857 sq.m
=50.286 sq.m
∴ Are of the Unshaded portion= Are of the Parallelogram - Area of the circle
=(112-50.286) sq.m
= 61.714 sq.m (Ans)
∴The area of the shaded portion is 61.714 sq.m
___________________________________
Make the above person as brainlist :)
Thankyou :DHelp Quickly! Use the table. Estimate the total deer population for year 8.
A. about 1,815 deer
B. about 2,467 deer
C. about 1,934 deer
D. about 2,081 deer
2081 is the estimated population of the deer as per the given table.
We assume that the characteristics of the sample of the deer population match the characteristics of the population as a whole. This will be the case if the sample is random: each deer is equally likely to be included in the sample.
So, if 85 of the 110 marked deer show up in the sample, we assume that the sample is 85/110 of the entire population.
For a sample size of 1608 deer, that means the population is estimated to be ...
1608 = 85/110 × population
population = 1608 × 110/85 = 2081
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A person buys a phone for $88 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $118.96 per month. Write an equation that can be used to determine the total cost
C(t) of this phone plan for t months. Then, find the cost for 22 months, assuming that the number of minutes the person uses does not exceed 2000 per month.
Answer: The total cost will be equal to $2839.16. The expression to calculate the total cost is 119.92(m)+81=C(t).
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a person buys a phone for $81 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $119.92 per month.
The expression will be formed as below:-
119.92(m)+81=C(t)
119.92(23)+81=C(t)
2839.16=C(t)
Therefore, the total cost will be equal to $2839.16.
Enter the number that belongs in the green box
The number that belongs in the green box is 45.65
How to find the number that belongs in the green boxFrom the question, we have the following parameters that can be used in our computation:
The triangle
If the number that belongs in the green box is x, then we have
6.78/sin(29) = 10/sin(x)
Take the inverse of both sides
sin(29)/6.78 = sin(x)/10
This gives
sin(x) = 10 * sin(29)/6.78
Evaluate
sin(x) = 0.7151
Take the arc sin of both sides
x = 45.65
Hence, the number that belongs in the green box is 45.65
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simplify
2x^2+8-4x+3x-6x^2+7
Answer: -4x^2-x+15
Step-by-step explanation:
Combine like terms: 2x^2 and -6x^2 combine to -4x^2.
Combine like terms: -4x and 3x combine to -x.
Combine like terms: 8 and 7 combine to 15.
The simplified expression is -4x^2-x+15.
Mary pays income tax according to the graduated schedule shown below.
If taxable income
But not over-
The tax is:
is over-
10% of the amount over 50
$782.50 plus 15% of the amount over 7,825
$4,386 25 plus 25% of the amount over 31,850
$15.698.75 plus 28% of the amount over
77,100
SO
$7,825
$31,850
$77,100
$160,850
$349,700
$7,825
$31,850
$77,100
$160,850
$349,700
Mark this and return
no limit
$39,148.75 plus 33% of the amount over
160,850
$101.469 25 plus 35% of the amount over
349,700
If Mary's taxable income is $68,562, how much income tax does she owe, rounded to the nearest dollar?
a. $13,564
b. $17,140
c. $21,527
d. $12,349
Save and Exit
Next
3
Submit
We find that Mary owes $13,564 in income tax. So the correct option is (a) $13,564. Option a
Mary's taxable income falls between $31,850 and $77,100. This means we apply the tax rate relevant to this bracket, which is $4,386.25 plus 25% of the amount over $31,850.
First, we need to subtract $31,850 from Mary's income to find the amount that we need to apply the 25% tax rate to:
$68562 - $31850 = $36712
Next, we take 25% of this result:
0.25 * $36712 = $9178
Then we add the base tax for this bracket ($4,386.25) to this result to get the total tax:
$4386.25 + $9178 = $13564.25
Rounding this to the nearest dollar, we find that Mary owes $13,564 in income tax. So the correct option is (a) $13,564.
Option a
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1. A cube of sugar is 2 cm wide. Calculate the num- ber of cubes in a box 720 cm².2. Calculate the amount of air in a room 6 m long, 5 m wide and 3 m high.3. The area of one side of a cuboid is 360 cm². What is the length, if the width is 1.5 cm? 4What is the volume of a container if it contains 12 boxes each 2.5 cm by 3 cm by 4.5 cm?5. A tank contains 4 500/ of water. Find the depth of the tank if its base area is 300 m².
please help, I need the answer
The given equation is true when a and b are integers and x is not equal to 0.
The statement "xᵃ + xᵇ = x⁽ᵃ⁺ᵇ⁾ " is always true when a=b.
In this case, the exponents of x on both sides of the equation are equal, and the equation simplifies to xᵃ + xᵃ = x²ᵃ , which holds true.
When a=b, the exponents are the same, and the equation is satisfied.
However, the statement is not always true for all values of a and b. If a and b are not equal, then the equation does not hold true in general.
The statement is also not true when a=0 and b=0, as both sides of the equation become 1, but the equation becomes 1 + 1 = 1, which is not true.
Therefore, the statement "xᵃ + xᵇ = x⁽ᵃ⁺ᵇ⁾ " is always true when a=b, but not true in general for all values of a and b.
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8. How can we prove that cos = sin(90-) ? Write your proof below.
it can be seen in
с
A
0
B
We can conclude that cosθ = sin(90° - θ) for any right triangle with angle θ and its complementary angle (90° - θ).
To prove that cosθ = sin(90° - θ), we can use the properties of right triangles and their angles.
Consider a right triangle ABC, where angle A is θ, angle B is (90° - θ), and angle C is 90°.
According to the definition of trigonometric functions in a right triangle:
- cosθ = adjacent side (AB) / hypotenuse (AC)
- sin(90° - θ) = opposite side (AB) / hypotenuse (AC)
From the given definitions, we can see that both cosθ and sin(90° - θ) have the same ratio of side lengths, which is AB/AC.
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When calculating the cost of a good or service, you often have to consider price markups and discounts. Consider these two statements regarding a
discounted item:
• The list price of the item is 80 percent of the original price.
• The price of the item has been reduced by 80 percent.
Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent. Explain how a calculation for
change in percentage (increase or decrease) is different from a calculation that involves multiplying by percentages. Why is the wording of percentage
problems so important? Give examples to illustrate your point.
20 points:D
Answer:
Step-by-step explanation:
Let’s assume the original price of the item is “x.” Then, using the first statement, the list price of the item is 80% of the original price, or 0.8x. If there is a discount applied, let’s say “d,” then the discounted price would be (1-d)(0.8x).
Using the second statement, if the price of the item has been reduced by 80%, then the discounted price would be 0.2x. This can be expressed as (1 - 0.8)(x).
So, we have the following two equations:
(1 - d)(0.8x) = 0.2x
0.64x - 0.8dx = 0.2x
Simplifying this equation, we get:
0.44x = 0.8dx
d = 0.55
This means that the discount applied in the first statement is 55%, not 80%.
The calculation for change in percentage (increase or decrease) involves finding the difference between two values and expressing it as a percentage of the original value. This is different from multiplying by percentages, which involves finding a percentage of the original value and subtracting or adding it to the original value.
The wording of percentage problems is important because it can affect the way the problem is interpreted and the calculation that is used to solve it. For example, the phrase “increased by 50%” could be interpreted as multiplying the original value by 1.5, while the phrase “increased to 50%” could be interpreted as finding 50% of the original value and adding it to the original value.
Examples:
A shirt is on sale for 30% off its original price of $50. The discounted price is (1-0.3)($50) = $35.
A company’s revenue increased from $100,000 to $120,000. The percentage increase in revenue is ((120,000 - 100,000) / 100,000) x 100% = 20%.
Change 8000cm^3 to m^3
The problem asks to convert a volume of 8000 [tex]cm^3[/tex] to [tex]m^3[/tex] which is 0.008 [tex]m^3[/tex].
Unit conversion is the process of converting a quantity expressed in one unit of measurement into another equivalent quantity expressed in a different unit of measurement.
To do this conversion, we need to use the fact that 1 m = 100 cm (or equivalently, 1 cm = 0.01 m) and that volume is a cubic measure.
So, first we need to convert the volume from cubic centimeters to cubic meters. To do this, we can divide the volume in [tex]cm^3[/tex] by the number of [tex]cm^3[/tex] in 1 [tex]m^3[/tex].
1 [tex]m^3[/tex] = (100 cm)^3 = 1,000,000 [tex]cm^3[/tex]
Therefore,
8000 [tex]cm^3[/tex] / 1,000,000 [tex]cm^3/m^3[/tex] = 0.008 [tex]m^3[/tex]
Thus, the volume of 8000 [tex]cm^3[/tex] is equal to 0.008 [tex]m^3[/tex].
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State all possible conditions that must be true for j and k so that the product of the expression is negative -2jk
The product -2jk is negative if and only if either j or k is negative (but not both). Therefore, the possible conditions for j and k are:
j < 0 and k > 0
j > 0 and k < 0
For the expression -2jk to be negative, at least one of the factors j or k must be negative, since the product of two positive numbers is always positive, and the product of two negative numbers is positive as well. Therefore, the possible conditions for j and k are:
j is negative and k is positive.
j is positive and k is negative.
In other words, if j and k have opposite signs, their product will be negative. However, if both j and k are positive or both are negative, their product will be positive. It's important to note that there are infinite possibilities for j and k that satisfy these conditions, since j and k can take on any real value as long as one is negative and one is positive.
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