The graph of y=|x| is a v-shaped graph that starts at the origin and continues infinitely in both the positive and negative x-directions. The graph of y=|x|+2 is the same v-shaped graph, but it has been shifted up two units so that it no longer intersects the x-axis. Finally, the graph of y=|x|-1 is a v-shaped graph that has been shifted down one unit so that it intersects the x-axis at (1,0) and (-1,0). All three graphs are symmetric with respect to the y-axis.
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = Sqrt 2 + t , y = 1 + 1 /2 t, where x and y are measured in centimeters. The temperature function satisfies Tx(2, 9) = 7 and
Ty (2, 9) = 1. How fast is the temperature rising on the bug's path after 2 seconds? (Round your answer to two decimal places.)
The temperature is rising at a rate of 7.5 degrees Celsius per second along the bug's path after 2 seconds.
What is differentiation?A derivative of a function with regard to an independent variable is defined as differentiation. In calculus, differentiation can be used to calculate the function per unit change in the independent variable.
We can use the chain rule of differentiation to find how fast the temperature is changing on the bug's path. Let T denote the temperature function, and let x and y be functions of time t given by x = sqrt(2) + t and y = 1 + t/2. Then the temperature function on the bug's path is given by T(x(t), y(t)), and we want to find dT/dt at t = 2.
Using the chain rule, we have:
dT/dt = dT/dx * dx/dt + dT/dy * dy/dt
We are given Tx(2, 9) = 7 and Ty(2, 9) = 1, so we can evaluate the partial derivatives at (x, y) = (2, 9):
dT/dx(2, 9) = 7
dT/dy(2, 9) = 1
To find dx/dt and dy/dt, we can take the derivatives of x and y with respect to t:
dx/dt = 1
dy/dt = 1/2
Now we can plug in the values:
dT/dt = 7 * 1 + 1 * 1/2
dT/dt = 7.5
Therefore, the temperature is rising at a rate of 7.5 degrees Celsius per second along the bug's path after 2 seconds.
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The cost in dollars to produce x shovels in a factory is given by the function C(x)=33x+430. The number of shovels that can be produced in h hours is given by the function N(h)=30h
7. Find the rule for C(N(h)).
8. Find the cost when h=12 hours
Okay, to find the maximum number of shovels that can be produced with $10,000, we need to do the following:
1) Set the cost function C(N(h)) = 10,000. So: 990h + 430 = 10,000
2) Subtract 430 from both sides: 990h = 9,570
3) Divide both sides by 990: h = 9.75 (round to 10 hours)
4) Substitute 10 hours into the function for number of shovels:
N(10) = 30(10) = 300 shovels
Therefore, the maximum number of shovels that can be produced with $10,000 is 300 shovels.
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18 students each collected the same number of Cans for a project. If the students collected a total of 306 cans, how many cans did each student Collect?
Using division operation, the number of cans collected by each of the 18 students is 17.
What is division operation?Division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
Division operation involves the dividend (the number being divided), the divisor (the number dividing the dividend), and the product called the quotient.
The total number of students engaged in the can collection project = 18
The total number of cans collected = 306
The number of cans collected by each, if each collected the same quantity = 17 (306 ÷ 18)
Thus, based on a division operation, the number of cans each student collected is 17.
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1.2 A Telkom account holder notices that her phone bills for three consecutive months were
significantly different. In May, her account was one and a half times more than her account in June.
Her account in July was R 50 more than her account in June. In total, she spent R 575 in cellular-
phone accounts in the three months. What was her account for each month?
The balance on the account of the Telkom account holder, every month was :
May - R 225June - R 150July R 200How to find the account balance ?We know that May was one and half times June :
M = 1. 5 x J
July was R 50 more than June :
L = J + 50
Total spent was R 575 :
M + J + L = R 575
Then we can solve by substitution:
( 1. 5 J ) + J + ( J + 50 ) = 575
3. 5 J + 50 = 575
3. 5 J = 525
J = 525 / 3. 5 = R 150
L would be:
= 150 + 50
= R 200
M would be:
= 1. 5 x 150
= R 225
The balances for the Telkom account holder is therefore May - R 225, June - R 150, and July R 200.
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help me solve this
Answer: ∠BEA
Step-by-step explanation:
Congruent: Same Angle Measure
Starting: ∠BHK
Congruent Angle: ∠BEA
John invested in a savings bond for 4 years and was paid simple interest at an annual rate of 4%. The total interest that he earned was $48. How much did he invest?
the principal or invested amount is $41.38
The computation of the invest amount is given below:
As we know that
Principal = Amount ÷ (1 + rate × time)
= $48 ÷ (1 + 0.04 × 4)
= $48 ÷ 1.16
= $41.38
Hence, the principal or invested amount is $41.38
Basically we have applied the above formula so that the same would be calculated
write 0.08 as a percentage.
Answer:
8%
Step-by-step explanation:
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34. The dimensions of Dawn's porch are shown.
Dawn's Porch
6 feet
A
B
6 feet
A. 32
2 feet
11 feet
What is the area, in square feet, of Dawn's porch?
B. 42
2 feet
C. 46
D. 50
Answer:
[tex]the \: answer \: for \: the \: question \: is \: 50[/tex]
Evaluate pqr - s2t, if p = -2, q = 5, r = -7, s = 0, and t = 4.
I need help fast!!
The answer of the given expression is 70.
What is the meaning of Evaluation?Evaluation refers to the process of assessing, examining, or appraising something to determine its worth, effectiveness, or quality. It involves the systematic and objective assessment of various aspects or criteria to form an informed judgment or opinion.
What is known by expression?An expression refers to a combination of numbers, symbols, and mathematical operations that represents a mathematical computation or relationship. It can be as simple as a single number or variable, or it can be more complex involving multiple terms, operations, and functions.
we have to find pqr-s2t:
if p=-2, q=5, r=-7, s=0, t=4
putting values in the expression we get
-2×5×(-7)-0×2×4= 70
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How many solutions can be found for the equation 3y + 5 − 2y = 1
We can solve the equation to find it's number of solutions, but we already know it only has 1 solution because it is a linear equation (y is raised to the first power).
[tex]3y + 5 - 2y = 11[/tex]
[tex]y + 5 = 11[/tex]
[tex]y = 6[/tex]
This confirms that there is only 1 solution.
4. You have been offered $3,000 in 4 years for providing $2,000 today into a business venture with a friend. If interest rates are 10%, is this a good investment for you?
Step-by-step explanation:
To determine if this is a good investment, we can use present value calculations to see what the $3,000 payment in 4 years is worth today:
Present value of $3,000 in 4 years at 10% interest rate = $3,000 / (1 + 0.10)^4 = $2,102.50.
If we invest $2,000 today and get a payment of $2,102.50 in 4 years, our net gain would be:
Net gain = $2,102.50 - $2,000 = $102.50
Therefore, investing $2,000 today with an interest rate of 10% and receiving $3,000 in 4 years would yield a net gain of $102.50.
While any gain is better than no gain, a return of $102.50 on an investment of $2,000 over a period of 4 years may not be considered a great investment. It's up to the individual to decide whether they feel that the potential gain is worth the initial investment and risk involved.
What integer is the square root of 115 closest to?
Answer:
10
Step-by-step explanation:
CAN SOMEONE HELP WITH THIS QUESTION?
Answer:
X2 = 1.697916 X3 = 1.431
Step-by-step explanation:
use Newton's formula of the method of approximating of zeros of a function : x_n+1. = x_n - f(x_n)/f'(x_n)
Teresa bought 6 CDs that were each the same price. Including sales tax, she paid a total of 84.60 . Each CD had a tax of 0.80 . What was the price of each CD before tax?
Answer:0.70
Step-by-step explanation:
A fair die with sides labeled 1 through 6 is rolled two times. The values of the two
rolls are added together. The sum is recorded as the outcome of a single trial of a
random experiment. Compute the probability that the sum is greater than 10.
A fair die is rolled twice, then the probability that the sum is greater than 10 is 1/12.
Finding the total number of possible outcomes when the dice is rolled twice:
A total of 6*6 = 36 outcomes are possible as there are 6 outcomes for the first roll and 6 outcomes for the second.
Making a list of all results that add up to greater than 10:
5 + 6 = 11
6 + 5 = 11
6 + 6 = 12
There are only three favorable outcomes.
So, the probability of getting a number greater than 10 =
[tex]\frac{no\ of\ favorable\ outcomes}{total\ number\ of\ possible\ outcomes}[/tex]
P(sum > 10) = 3/36 = 1/12
Therefore, there is a 1/12 probability that the sum of the two dice is greater than 10.
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #3
Answer:
The graph will be translated down 2 units.
The new horizontal asymptote is y=2 because the graph now crosses over the y axis at 2. This is at the point (0,2).
For a confidence level of 99% with a sample size of 19, find the critical t value.
10. A flagpole is supported by two identical wires. What is the distance (X) between the two wires?
Using the Pythagoras theorem, we can find the value of x to be = 10ft.
Option B is correct.
Define Pythagoras theorem?The right-angled triangle's three sides are related in line with the Pythagoras theorem, also referred to as the Pythagorean theorem. The hypotenuse of a triangle's other two sides add up to a square, according to the Pythagorean theorem, which states that.
Here in the question,
We have 2 right-angled triangles.
So, base of the large triangle, x
= √ (13² - 12²) + √ (13² - 12²)
= √ 5² + √ 5²
= 5 + 5
= 10ft.
Therefore, the length of the side, x = 10ft.
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Some states now allow online gambling. As a marketing manager for a casino, you need to determine the percentage of adults in those states who gamble online. How many adults must you survey in order to be 99% confident that your estimate is in error by no more than three percentage points? Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of adults who gamble online. n= (Round up to the nearest integer.)
The sample size for part (a) is 2401, and the sample size for part (b) is 1417 if the margin of error is no more than two percentage points and use a confidence level of 95%
We have,
It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.
The formula for finding the MOE:
MOE =Z_{score} * s/√n
Where Z_{score} is the z score at the confidence interval
s is the standard deviation
n is the number of samples.
We have:
MOE = 2% = 0.02 and
α = 1-0.95 = 0.05
Let's assume the value of p = 0.5, and q = 0.5
From the table:
Z_(0.05/2)
= Z_(0.025)
= 1.96
n = 2401
For part (b):
p = 18% = 0.18, and q = 0.82
so, we get,
n = 1417.5 = 1417
Thus, the sample size for part (a) is 2401, and the sample size for part (b) is 1417 if the margin of error is no more than two percentage points and use a confidence level of 95%
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Find the size of the following angles
Step-by-step explanation:
Q1. By linear pair, I know that 72* + unknown angle = 180*
therefore unknown angle = 180-72 = 108*
Now because this is a pentagon, the total of all interior angles of a polygon equals 540*
so 108* + 100* + 110* + 45* (Half of 90 , written as a semi-square) + Y* = 540
Y* = 540 - 363 = 177*
Q2. 360 - (80+70+110) = q
q = 360 - 220 = 140*
Q3. 160+160+ S* = 360*
360* - 320* = S*
S* = 40*
Hope it helps
Need help will give brainliest and 5 stars!
For this graph, for each vertical asymptote, write down the two limits that describe the graph of the function near the asymptote.
The limits on the vertical asymptotes of the function are given as follows:
[tex]\lim_{x \rightarrow -6^{-}} f(x) = \infty[/tex][tex]\lim_{x \rightarrow -6^{+}} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow -2^{-}} f(x) = \infty[/tex][tex]\lim_{x \rightarrow -2^{+}} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow 6^{-}} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow 6^{+}} f(x) = \infty[/tex]What are the vertical asymptotes of a function?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
On a graph, at the vertical asymptotes, the graph just approaches the point, it does not cross the point.
Hence the vertical asymptotes are given as follows:
x = -6, x = -2 and x = 2.
We must observe the limits to the left(denoted by the - sign) and to the right (denoted by the + sign) of each asymptote.
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Which function includes the minimum or maximum value of f as a number that appears as it is shown?
a) f(x)=(x+2)^{2}−16
b) f(x)=(x−2)(x+6)
c) f(x)=x^{2}+4x−12
d) f(x)=x^{2}+6x−2x−12
Hudson measure the volume of a sink basin by modeling it as a hemisphere. Hudson measures its circumference to be 91 3/4 inches. Find the sink's volume in cubic inches.
Round your answer to the nearest tenth if necessary.
Rounding to the nearest tenth, the sink's volume is approximately [tex]6328.2[/tex] cubic inches.
What is the Hudson measures?The circumference of a hemisphere is represented by the formula:
[tex]C = 2 \pi r[/tex]
here C is the circumference and r is the radius of the hemisphere.
it is given that the circumference C as [tex]91 3/4[/tex] inches. now convert into a decimal
[tex]91 3/4 inches = 91.75 inches[/tex]
we are having
[tex]91.75[/tex] inches [tex]= 2πr[/tex]
Solving for r, we get:
[tex]r = 91.75 / (2\pi) \approx 14.599[/tex] inches (rounded to three decimal places)
The volume of a hemisphere is represented by formula
[tex]V = (2/3)\pir^3[/tex]
Substituting our value of r, we get:
[tex]V = (2/3)\pi(14.599)^3 \approx 6328.2[/tex] cubic inches
Therefore, rounding to the nearest tenth, the sink's volume is approximately [tex]6328.2[/tex] cubic inches.
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NEED HELP PLEASE NOW
Answer:
im pretty sure its the first one that you chose :)
Step-by-step explanation:
I just want the answers, I’ve been on the same lesson since Thursday and no teacher from my school will help ♀️
The standard form of the equation, based on the foci and co - vertices would x ² / 250 + y ² / 25 = 1 .
How to write the standard form ?The foci and co-vertices must be known to compose the equation of an ellipse, which requires determining a, b, and c values. The major axis, minor axis and distance between the center and foci are related to these variables.
Their connection can be symbolized as follows: a for major axis, b for minor axis, and c for the length of the distance between the center and foci:
a ² = b ² + c ²
a ² = 5 ² + 15 ²
a ² = 25 + 225
a ² = 250
a = √ 250
The standard equation would be:
x ² / a ² + y ² / b ² = 1
x ² / 250 + y ² / 25 = 1
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QUICKLY HELP PLEASE ITS VERRY MUCH SO APPREICATED
The mean absolute deviation (MAD) of the data set include the following: A. 11.
How to calculate the mean absolute deviation?In Mathematics, MAD is an abbreviation for mean absolute deviation and the mean absolute deviation (MAD) of a data set can be calculated by using this formula;
MAD = 1/n ∑|x - μ|
Where:
n represents the number of data (observed values)μ represents the mean of the data set.x represents the individual data (values).By substituting the given parameters into the MAD formula, we have the following;
MAD = 1/10 [(325 - 290) + (310 -290) +(289-290)+(288-290)+(285-290)+(285-290)+(285-290) + (280-290) + (280-290) + (273-290)]
MAD = 1/10(35 + 20+1+2+5+5 +5 + 10 + 10 + 17).
MAD = 1/10(110)
MAD = 11
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URGENT!! I WILL GIVE
BRAINLIEST!!!!! AND ALSO 100 POINTS!!!!!
Answer: All of the slopes are the same.
draw a net for making a rectangular prism 5cm by 3cm by 1cm
Here is a net for making a rectangular prism with dimensions of 5 cm by 3 cm by 1 cm:
________
/ / |
/ / |
/_______ / |
| | |
| | |
| | |
| | /
| | /
|________|
The above net consists of six rectangles, where the first rectangle represents the base of the prism with dimensions of 5 cm by 3 cm, and the remaining five rectangles represent the sides of the prism.
What is a rectangular prism?A rectangular prism, also known as a rectangular cuboid, is a three-dimensional geometric shape that has six rectangular faces, where each face meets at right angles with its adjacent faces.
It is common in everyday objects such as boxes, books, and bricks, and they are used in various applications in mathematics, physics, engineering, etc.
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A full waterbed mattress is 6 ft by 5 ft by 2 ft. The mattress is to be filled with water that weighs 62.4 lb/ft^3. Find the weight of the water in the mattress to the nearest pound.
The waterbed mattress contains approximately ___ lb of water
The waterbed mattress contains approximately 3,744 lb of water.
How to calculate the weight of the water in the mattress?To calculate the weight of the water in the mattress, the volume of the mattress is first calculated using the given formula below:
The measurement of the waterbed mattress = 6ft by 5 ft by 2 ft
The volume of the waterbed = Length× width × height
That is = 6×5×2 = 60ft³
If 62.4 lb = 1 ft³
X lb = 60 ft³
Make X the subject of formula;
X = 60× 62.4 = 3,744lb
Therefore, the weight of water that the mattress will contain would be= 3,744lb
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The probability of winning a profit of twice your wager is 1/6, the probability of winning a profit equal to your wager is 1/3, and all other probabilities of winning are zero. What is your expected value for this game? Assume the wager is $1.
The expected value for the game is 2/3.
What is expected value?The average value we would anticipate to find if we repeated an experiment several times is the anticipated value of a random variable. It is calculated by averaging the outcomes of multiplying each potential result of the random variable by the associated probability. In other words, it's the weighted average of all potential possibilities, with the weights being the likelihoods that each outcome would actually happen. In several disciplines, including finance, economics, and engineering, predictions and judgements are made using the expected value, a fundamental idea in probability theory.
Let us suppose the profit = X.
Thus,
Probability of winning twice our wager = 1/6 thus, the expected value is:
(2)(1/6) = 1/3
No, for profit equal to wager we have:
(1)(1/3) = 1/3
The total expected value is:
E(X) = (1/3) + (1/3) + 0 = 2/3
Hence, the expected value for the game is 2/3.
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