13.8 miles per hour x 3 hours = 41.4 miles ( what he already rode)
48 - 41.4 = 6.6 more miles to go
For the data in the table does y vary directly with x? X=16,32,48-Y=4,16,36
True or False?
When rainfall increases, the water level in the lake goes up. Rainfall is the independent variable in this situation.
Answer:
It is true, this person was wrong. True was the right answer on the test
Step-by-step explanation:
What is 120.571 in expanded form?
Find the value of x. Round the length to the nearest 10th the diagram is not shown to scale
Pablo bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $250 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 8.5% per year, and for the laptop it was 5% per year. The total finance charges for one year were $296 . How much did each computer cost before finance charges?
Find dy/dx by implicit differentiation and evaluate the derivative at the given point.xy = 12, (-4, -3)
When Irving was done, he checked his account balance and found he had a total of $95.06. How much money was in Irving’s account to begin with? a. $56.43 b. $151.49 c. $38.63 d. $142.36
3.5 x 10^4 write the following number in standard form (decimal).
Answer:
35,000
Step-by-step explanation:
you are lying 120 ft away from a tree that is 50 feet tall you look up at the top of the tree approxmaelty how far is your head from the top of the tree in a straight line
You have 900-grams of an an unknown radioactive substance that has been determined to decay according to
D(t)=900e−0.002415⋅t
where t is in years. How long before half of the initial amount has decayed?
It will take ____ years for half of the initial amount to decay. (Round to 1 decimal place)
It will take approximately 286.8 years for half of the initial amount (900 grams) to decay.
To find the time it takes for half of the initial amount to decay, we need to find the value of t when D(t) is half of the initial amount (900 grams).
Half of the initial amount = 900 grams / 2 = 450 grams
Now, set D(t) equal to 450 and solve for t:
[tex]450 = 900 * e^{-0.002415 * t}[/tex]
Divide both sides by 900:
[tex]e^{-0.002415 * t} = 0.5[/tex]
To find t, take the natural logarithm (ln) of both sides:
[tex]ln(e^{-0.002415 * t}) = ln(0.5)[/tex]
Now, use the property that [tex]ln(e^x) = x:[/tex]
-0.002415 * t = ln(0.5)
Now, solve for t:
t = ln(0.5) / -0.002415
Using a calculator, we get:
t ≈ 286.8 years
So, it will take approximately 286.8 years for half of the initial amount (900 grams) to decay.
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What is the rule for the following sequence of numbers: 2, 7, 17, 37, ?
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. suppose that a batch of 250 boards has been received and that the condition of any particular board is independent of that of any other board.
a. what is the approximate probability that at least 10% of the boards in the batch are defective?
b. what is the approximate probability that there are exactly 10 defectives in the batch?
The probability that at least 10% of the boards are defective can be approximated using a normal distribution, while the exact probability of having 10 defectives in the batch can be calculated using the binomial formula. For large samples, normal approximation can be used for convenience.
Explanation:To find the probability that at least 10% of the boards are defective, we can use the binomial distribution since each board's condition is independent of the other boards. The formula for binomial probability is P(X = k) = (n choose k) * pk * (1-p)(n-k), where n is the number of trials, p is the probability of success on each trial, and k is the number of successes. However, for large sample sizes and when the sample proportion is close to the population proportion, we can approximate the binomial distribution with a normal distribution.
To use the normal approximation, we calculate the mean and standard deviation with the formulas μ = n * p and σ = √(n * p * (1-p)). For the batch of 250 boards with 5% defective rate, μ = 250 * 0.05 = 12.5 and σ = √(250 * 0.05 * 0.95) ≈ 3.4641. We then convert the problem into a z-score and use standard normal distribution tables or software to find the probability that Z > (25 - 12.5)/3.4641.
To find the exact probability of having exactly 10 defectives in the batch, we use the binomial formula since the normal approximation is less accurate for exact probabilities. The calculation would be P(X = 10) = (250 choose 10) * 0.0510 * 0.95240.
Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 9. the hypotheses h0: μ = 73 and ha: μ < 73 are to be tested using a random sample of n = 25 observations.
Choose the equation below that represents the line passing through the point (−3, −1) with a slope of 4. (1 point) y = 4x − 11 y = 4x + 11 y = 4x + 7 y = 4x – 7 y − 3 = 4(x + 1) y + 3 = 4(x − 1)
At the beginning of the day the stock market goes up 30 1/2 points. At the end of the day, the stock market goes down 100 3/4 points. what is the change from the high to the end of the day?
The stock market changed by a net -70.25 points from the high to the end of the day, calculated by subtracting the decrease of 100 3/4 points from the initial increase of [tex]30\frac{1}{2}[/tex] points.
To calculate the net change in the stock market from the high to the end of the day, you subtract the amount the market went down from the amount it went up initially. First, convert the mixed numbers to improper fractions. 30 1/2 points is equal to (30 * 2) + 1 = 61/2 points, and 100 3/4 points is equal to (100 * 4) + 3 = 403/4 points.
Next, to find the change, you subtract the decrease from the initial increase:
61/2 - 403/4 = (61 * 4) / (2 * 4) - (403 * 2) / (4 * 2)
= 244/8 - 806/8
= (244 - 806) / 8
= -562/8
Finally, simplify the fraction:
= -70.25
So, the stock market changed by a net -70.25 points from the high to the end of the day. This means the market ended lower by 70.25 points from its highest point that day.
Are all rectangles similar
Find the surface area of the surface given by the portion of the paraboloid z=3x2+3y2 that lies inside the cylinder x2+y2=4. (hint: convert to polar coordinates after setting up the integral)
To find the surface area of the specified area in the paraboloid, convert the original cartesian coordinates to polar coordinates. Then set up and solve the appropriate double integral over the region defined by the circle in polar coordinates.
Explanation:To find the surface area of a paraboloid z=3x²+3y² inside the cylinder x²+y²=4, you first set up the integral and then convert to polar coordinates. As per the given paraboloid equation, we know that dz/dx = 6x and dz/dy = 6y. Therefore, the differential of surface area in polar coordinates can be given as √(1+(6r*cosø)²+(6r*sinø)²) rdrdø.
Next, integrate this over the area of a circle in polar coordinates, from r=0 to r=2 and ø=0 to ø=2π. The limits of 2 and 2π come from the given cylinder equation x²+y²=4, which represents a circle of radius 2 in polar coordinates.
The final integral in terms of r and ø should yield the desired surface area of the paraboloid which lies inside the cylinder.
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Use the equation v=10/p to determine the pressure when the volume is 12 liters
Find the slope of the line through p and q. p(5, −9), q(−5, 6)
Answer: slope = -1,5
Step-by-step explanation:
We can use slope formula to find the slope of a line that passes through two points (x₁ , y₁) and (x₂ , y₂)
m = ∆y/∆x = (y₂ - y₁)/(x₂ - x₁)
Given points are: p(x₁ , y₁) = (5 , −9) and q(x₂ , y₂) = (−5 , 6)
Substituting these two known points in the slope formula, we have:
m = (6-(-9))/(-5-5) = 15/-10 = -1,5
Therefore, the slope of this line = -1,5
Answer: slope = -1,5
SpymoreThe high temperature in Fairbanks, Alaska was 15.7 °F one day. That night, the temperature fell 38.4 degrees. What was the low temperature for the night? Enter your answer as a decimal in the box
Answer:
-22.7
Step-by-step explanation:
Since the temperature fell, that would means that it's was cooler outside.
Hotter = Temperature goes up
Colder = Temperature goes down
15.7 - 38.4 = -22.7
Answer:
-22.7
Step-by-step explanation:
did the test
Find the line of symmetry for the parabola whose equation is y = 2x 2 - 4x + 1.
Answer:
The axis of symm. is x = 1.
Step-by-step explanation:
When faced with a quadratic equation (or formula for a parabola), we can find the equation of the axis of symmetry using the following:
-b
x = -------
2a
Please use " ^ " to denote exponentiation: y = 2x^2 - 4x + 1.
Here, a = 2, b = -4 and c = 1.
Thus, the axis of symmetry of this parabola is
-(-4)
x = --------- = 1 or x = 1
2(2)
To evaluate the expression 25x-400, what would x need to be if the result must be at least 200?
Megan Mei is charged 2 points on a $120,000 loan at the time of closing. The original price of the home before the down payment was $140,000. How much do the points in dollars cost Megan? A. $4,200 B. $2,800 C. $8,200 D. $2,400
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given that
Amount of original price of the home before the down payment = $140000
Amount of loan at the time of closing = $120000
Megan Mei is charged 2 points on that amount means
[tex]2\%\ on\ \$120000\\\\=\frac{2}{100}\times 120000\\\\=0.02\times 120000\\\\=\$2400[/tex]
Hence, Option 'A' is correct.
write 25 x 10^6 in standard from
What is the slope and y intercept of y=-27.4x
7x300=7x blank hundreds
the lines below are parallel. if the slope of the green line is -3 what is the line of the red line
A jar contains 8 marbles numbered 1 through 8. an experiment consists of randomly selecting a marble from the jar, observing the number drawn, and then randomly selecting a card from a standard deck and observing the suit of the card (hearts, diamonds, clubs, or spades). how many outcomes are in the sample space for this experiment? how many outcomes are in the event "an even number is drawn?" how many outcomes are in the event "a number more than 2 is drawn and a red card is drawn?" how many outcomes are in the event "a number less than 3 is drawn or a club is not drawn?"
The number of outcomes in the sample space is 32. There are 16 outcomes for drawing an even number, 12 outcomes for drawing a number more than 2 and a red card, and 30 outcomes for drawing a number less than 3 or not drawing a club.
To determine the number of outcomes in the sample space for the described experiment, one can use the fundamental counting principle. In this case, there are 8 possible marbles that can be drawn and 4 possible suits from a card in a standard deck. So, the total number of outcomes in the sample space is the product of these possibilities, which is 8 marbles × 4 suits = 32 outcomes.
The event "an even number is drawn" corresponds to drawing one of the even-numbered marbles (2, 4, 6, or 8) and any of the 4 suits from the deck. There are 4 even-numbered marbles and 4 suits, resulting in 4 marbles × 4 suits = 16 possible outcomes.
For the event "a number more than 2 is drawn and a red card is drawn," we consider only marbles numbered 3 to 8 (6 possibilities) and the 2 red suits (hearts and diamonds) from the deck, resulting in 6 marbles × 2 red suits = 12 outcomes.
Finally, the event "a number less than 3 is drawn or a club is not drawn" includes two scenarios. The first is drawing marble number 1 or 2 (2 possibilities) and any of the 4 suits (8 outcomes). The second scenario includes drawing any of the 8 marbles and any of the 3 non-club suits (24 outcomes). Since the two scenarios are mutually exclusive, you add the outcomes: 8 + 24 = 32 outcomes. However, you must subtract the overlapping outcomes of drawing 1 or 2 with non-club suits (2 outcomes), resulting in 32 - 2 = 30 distinct possible outcomes for this event.
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