David made an error when determining the product of (–2.5)(–8.3). Step 1: (–2.5)(–8.3) = (–8.3)(–2.5) Step 2: = (–8.3)(–2) + (–8.3)(–0.5) Step 3: = (–16.6) + (–4.15) Step 4: = –20.75 In which step did David make his first error? Step 1 Step 2 Step 3 Step 4
Answer:
Step 3.
Step-by-step explanation:
We need to tell the incorrect step in the given problem for the product of (–2.5)(–8.3)
Step 1. (–2.5)(–8.3) = (–8.3)(–2.5)
Step 2:
We can write -2.5 = -(2+0.5)
(–8.3)(-(2+0.5)) = (–8.3)(-2)+(-8.3)(-0.5)
= 16.6 + 4.15
Step 3.
= 20.75
He has done an error in step 3. It should be 16.6 + 4.15 instead of (–16.6) + (–4.15). As a result, he get incorrect answer.
Answer:
it is step 3
Step-by-step explanation: i just took the test mark me brainliest lol :>
In an certain species of newt, offspring are born either green or black. Suppose that 60% of these newts are born green. If we sample 183 of these newts at random, the probability distribution for the proportion of green newts in the sample can be modeled by the normal distibution pictured below. Complete the boxes accurate to two decimal places. Note: The left box is 2 standard deviations below the mean. The middle box is the mean. And, the right box is 2 standard deviations above the mean.
The probabilities for completed boxes are :Box 1: - 0.70Box 2: 0.60Box 3: 0.90
Why the boxes accurate to two decimal places?In a certain species of newt, offspring are born either green or black.
Suppose that 60% of these newts are born green.
If we sample 183 of these newts at random, the probability distribution for the proportion of green newts in the sample can be modeled by the normal distribution pictured below. The normal distribution is shown in the attached image.
The left box is 2 standard deviations below the mean. The middle box is the mean. And, the right box is 2 standard deviations above the mean.
We need to complete the boxes accurate to two decimal places.
The mean proportion of green newts in the sample is:µ = 0.60
The standard deviation of the distribution is given by:σ
= √(pq/n)Where p = proportion of success = 0.60q = proportion of failure = 1 - 0.60 = 0.40n = sample size = 183 Substituting the values in the above formula,
we get:σ = √(0.60×0.40/183) = 0.0509 (approx)
The required probabilities are:
P(X ≤ 0.50) = Φ[(0.50 - 0.60)/0.0509] = Φ[-1.96]
= 0.025P(0.50 < X < 0.70)
= Φ[(0.70 - 0.60)/0.0509] - Φ[(0.50 - 0.60)/0.0509]
= Φ[1.96] - Φ[-1.96] = 0.95 - 0.025
= 0.925P(X ≥ 0.70) = 1 - Φ[(0.70 - 0.60)/0.0509]
= 1 - Φ[1.96] = 1 - 0.975 = 0.025
Hence, the completed boxes are: Box 1: - 0.70 Box 2: 0.60 Box 3: 0.90
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The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places. (a) What is the probability that more than three aircraft arrive within an hour? Enter your answer in accordance to the item a) of the question statement (b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals? Enter your answer in accordance to the item b) of the question statement (c) Determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.27. Enter your answer in accordance to the item c) of the question statement
a) The probabilities for X = 0, 1, 2, and 3, and then summing them up, we find that P(X > 3) ≈ 0.019. b) The probability of zero successes is approximately 0.430. c) The length of an interval of time is 1.306 hours.
a) The time between arrivals of small aircraft is exponentially distributed with a mean of one hour. To find the probability that more than three aircraft arrive within an hour, we will use the Poisson distribution, where λ (lambda) represents the average number of arrivals per hour, which is 1 in this case. The probability formula is P(X > 3) = 1 - P(X ≤ 3), where X is the number of arrivals. Using the Poisson formula, we get:
P(X > 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
Calculating the probabilities for X = 0, 1, 2, and 3, and then summing them up, we find that P(X > 3) ≈ 0.019.
b) To find the probability that no interval contains more than three arrivals in 30 separate one-hour intervals, we can use the binomial distribution. The probability of success (an interval with more than three arrivals) is 0.019 from part a), and the probability of failure (an interval with three or fewer arrivals) is 1 - 0.019 = 0.981. Using the binomial formula with n = 30 (number of intervals) and p = 0.981, we find the probability of zero successes (i.e., no interval with more than three arrivals) is approximately 0.430.
c) To determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.27, we use the exponential distribution formula:
P(T > t) = e^(-λt), where T is the waiting time between arrivals, t is the time interval, and λ is the average number of arrivals per hour (1 in this case).
We want to find the value of t such that P(T > t) = 0.27. So:
0.27 = e^(-1 * t)
Taking the natural logarithm of both sides, we get:
ln(0.27) = -t
Solving for t, we find that t ≈ 1.306 hours.
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you buy a rare stamp for $50. each year the value of the stamp increases by 1.2%. write an equation that represents the value of the stamp, and then find the value of the value of the after 10 years
An equation that represents the value of the stamp is V(t) = V₀ * (1 + r)ˣ
The value of the stamp after 10 years would be approximately $56.34.
First, let's denote the initial value of the stamp as V₀ and the number of years as t. In this case, V₀ is equal to $50. The annual increase rate is given as 1.2%, which can be expressed as 0.012 in decimal form.
Now, we can start building the equation. Since the value of the stamp increases every year, we need to add the rate of increase to the previous year's value. Mathematically, this can be represented as:
V(t) = V₀ + (V₀ * r) + (V₀ * r) + ... + (V₀ * r)
Here, V(t) represents the value of the stamp after t years, and r represents the rate of increase (0.012 in decimal form).
Since the rate of increase remains constant at 1.2% each year, we can simplify the equation using exponential notation:
V(t) = V₀ * (1 + r)ˣ
Now we have an equation that represents the value of the stamp after t years, where V₀ is the initial value ($50), r is the rate of increase (0.012), and x is the number of years.
To find the value of the stamp after 10 years, we substitute t = 10 into the equation:
V(10) = $50 * (1 + 0.012)¹⁰
Calculating this equation will give us the value of the stamp after 10 years. Let's perform the calculation:
V(10) = $50 * (1.012)¹⁰
V(10) ≈ $50 * 1.1268250301
V(10) ≈ $56.34
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Solve the differential equations 2xy(dy/dx)=1 y^2. y(2)=3
The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).
To solve the given differential equation
2xy(dy/dx) = y²
We will use separation of variables and integrate to find the solution.
Start with the given equation
2xy(dy/dx) = y²
Divide both sides by y²:
(2x/y) dy = dx
Integrate both sides:
∫(2x/y) dy = ∫dx
Integrating the left side requires a substitution. Let u = y², then du = 2y dy:
∫(2x/u) du = ∫dx
2∫(x/u) du = ∫dx
2 ln|u| = x + C
Replacing u with y²:
2 ln|y²| = x + C
Using the properties of logarithms:
ln|y⁴| = x + C
Exponentiating both sides:
|y⁴| = \(e^{x + C}\)
Since the absolute value is taken, we can remove it and incorporate the constant of integration
y⁴ = \(e^{x + C}\)
Simplifying, let A = \(e^C:\)
y^4 = A * eˣ
Taking the fourth root of both sides:
y = (A * eˣ\()^{1/4}\)
Now we can incorporate the initial condition y(2) = 3
3 = (A * e²\()^{1/4}\)
Cubing both sides:
27 = A * e²
Solving for A:
A = 27 / e²
Finally, substituting A back into the solution
y = ((27 / e²) * eˣ\()^{1/4}\)
Simplifying further
y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)
Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is
y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)
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©Simplify fully
8x²y
4x
:))
Answer:2xy
Step-by-step explanation:
if one fifth to the mth power times one fourth to the 18th power equals 1 over 2 times 10 times 35 , then m =
if one fifth to the mth power times one fourth to the 18th power equals 1 over 2 times 10 times 35 , then m = 6340338097024.
Let us solve this question given:
if one fifth to the mth power times one fourth to the 18th power equals 1 over 2 times 10 times 35, then m =
Given,
One fifth to the mth power times one fourth to the 18th power equals 1 over 2 times 10 times 35.
Let us simplify both the sides of the equation and then solve it.1 / (2 × 10 × 35) = 1 / (2 × 5² × 7)1 / (2 × 10 × 35) = 1 / 700
Now, we know that 1 / 700 can be written as 7^-2 × 2^-2 × 5^-2
Substituting in the equation above,
One fifth to the mth power times one fourth to the 18th power equals 7^-2 × 2^-2 × 5^-2
Now, we can rewrite the given as mth power of one fifth times 18th power of one fourth equals 7^-2 × 2^-2 × 5^-2.Thus, m / 5^18 = 7^-2 × 2^-2 × 5^-2
This can be written as: m = 5^18 × 7² × 2²
The value of m = 6340338097024
The value of m = 6340338097024.
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Solve the following systems of equations using Gaussian Elimination. 2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13
Find the inner product of two vectors A = (2, -3,0) and B = = (-1,0,5)
The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).
Solving the given system of equations using Gaussian elimination:
2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13
Matrix form of the system is
[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13
Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1
Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4
Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5
Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5
Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6
The solution is (x,y,z) = (6,-5,5)
Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).
The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by
A·B = |A||B|cosθ
Given,A = (2, -3,0) and B = (-1,0,5)
Magnitude of A is |A| = √(2²+(-3)²+0²) = √13
Magnitude of B is |B| = √((-1)²+0²+5²) = √26
Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2
Cosine of the angle between A and B is
cosθ = A·B / (|A||B|)
cosθ = -2 / (√13×√26)
cosθ = -2 / √(13×26)
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I NEED AN ANSWER ASAP PLEASE
Step-by-step explanation:
the correct answer is option a 6a-7
The area of a circle is 4π cm². What is the circumference, in centimeters? Express your answer in terms of π pie
Answer:
The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius.
In this case, we are given that the area is 4π cm². Solving for the radius, we get:
4π = πr^2
r^2 = 4
r = 2
So the radius of the circle is 2 cm.
The formula for the circumference of a circle is:
C = 2πr
Plugging in the value for the radius, we get:
C = 2π(2) = 4π
Therefore, the circumference of the circle is 4π cm.
(q42) A bowl of soup is heated to a temperature of 190°F. It is then allowed to cool at a temperature of 50°F. The soup cools to 130°F in 20 minutes. Determine how long it will take for the soup to cool to 100°F.
It would take about 36 minutes for the soup to cool to 100°F.
What is Newton law of cooling?
The rate at which an object's temperature changes when it comes into contact with a medium that has a different temperature is described by Newton's law of cooling. According to this, an object's rate of heat uptake or loss is directly correlated with the temperature difference between the object and its surroundings.
We know that;
T(t) = T(s) + (T(o) - T(s))\(e^-kt\)
130= 50 + (190 - 50)\(e^-20k\)
130 - 50 = (190 - 50)\(e^-20k\)
80 = (190 - 50)\(e^-20k\)
80/140 = \(e^-20k\)
0.57 = \(e^-20k\)
ln(0.57) = ln \(e^-20k\)
-0.56 = - 20 k
k = 0.028
Then the time taken to cool to 100°F
100 = 50 + (190 - 50)\(e^-0.028t\)
50/140 =\(e^-0.028t\)
0.36 = \(e^-0.028t\)
t = ln(0.36)/-0.028
t = 36 minutes
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if you know the volume of a cone and that a cylinder has the same base ans height as the cone, how would you determine the volume of the cylinder?
A) add 3 to the volume of the cone
B) subtract 3 from the volume of the cone
C) multiply the volume of the cone by 3
D) divide the volume of the cone by 3
It's C, multiply the volume of the cone by 3.
Answer:
C
Step-by-step explanation:
Expand the following :
X( 2x-5)
2x (3x+4)
6x(x-2y)
The expressions are expanded to give;
1. 2x² - 5x
2. 6x² + 8x
3. 6x² - 12xy
What are algebraic expressions?Algebraic expressions are defined as expressions consisting of variables, coefficients, constants, terms and factors.
These expressions are also known to consist of mathematical operations, which includes;
BracketParenthesesAdditionSubtractionMultiplicationDivision, etcFrom the information given, we have that;
a. x (2x - 5)
expand the bracket
2x² - 5x
b. 2x (3x+4)
expand the bracket
6x² + 8x
c. 6x(x-2y)
expand the bracket
6x² - 12xy
Hence, the expressions are 2x² - 5x, 6x² + 8x and 6x² - 12xy
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Answer:
1) 2x² - 5x
2) 6x² + 8x
3) 6x² - 12xy
Step-by-step explanation:
1) x ( 2x - 5 )
To expand the above, multiply both terms inside the brackets by x.
2x² - 5x
2) 2x ( 3x + 4 )
To expand the above, multiply both terms inside the brackets by 2x.
6x² + 8x
3) 6x ( x - 2y )
To expand the above, multiply both terms inside the brackets by 6x.
6x² - 12xy
PLEASE HELP
Find the slope of the line passing through
the points (-3,-3) and (5. 5) using the
slope formula.
Answer:
slope = 1
Step-by-step explanation:
-3 | -3
5 | 5
_____
8 | 8
8/8= 1
How much would $100 invested at 6% interest compounded monthly be worth after 20 years? Round to the nearest cent.
Answer:$331.02
Step-by-step explanation:
you got it right on a p e x
a carpenter builds a frame from two 6-foot-long boards and two 8-footlong boards. given these side lengths, how can the carpenter ensure that the frame is a rectangle?
To ensure that the frame is a rectangle, the carpenter needs to make sure that opposite sides of the frame have the same length.
In other words, the two 6-foot-long boards must be opposite to each other and the two 8-foot-long boards must be opposite to each other.
This way, the carpenter can ensure that opposite sides of the frame are parallel and that the angles between these sides are right angles, which are characteristics of a rectangle.
Additionally, the carpenter could use a square or a measuring tape to check that the angles between the two sides of each length are 90 degrees. This will confirm that the frame is indeed a rectangle.
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Find the slope of the tangent line to the curve x(t) = cos^3(4t), y(t) = sin^3(4t) at the point where t = pi/6. 4 squareroot 3 squareroot 3 -squareroot 3 squareroot 3/3 -3 squareroot 3
The slope of the tangent line to the curve x(t) = cos^3(4t), y(t) = sin^3(4t) at the point is 1, -1.
To find the slope of the tangent line to the curve at a given point, we need to find the derivative of the curve and evaluate it at that point. So, let's find the derivative of the curve x(t) = cos^3(4t), y(t) = sin^3(4t):
x'(t) = 3cos^2(4t) * (-sin(4t)) * 4 = -12cos^2(4t)sin(4t)
y'(t) = 3sin^2(4t) * cos(4t) * 4 = 12sin^2(4t)cos(4t)
Now, let's evaluate these derivatives at t = pi/6:
x'(pi/6) = -12cos^2(2pi/3)sin(2pi/3) = -6sqrt(3)
y'(pi/6) = 12sin^2(2pi/3)cos(2pi/3) = 6sqrt(3)
So, the slope of the tangent line at t = pi/6 is:
y'(pi/6) / x'(pi/6) = (6sqrt(3)) / (-6sqrt(3)) = -1
Therefore, the answer is option 1, -1.
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3 friends ordered 2 pizzas of 6 slices each and ate equal amounts, how many slices did each person eat?
A 1
B 2
C 3
D 4
Answer:
Option D, 4
Step-by-step explanation:
2 pizzas x 6 slices per pizza = 12 slices of pizza
12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend
Option D, 4, is your answer
PLS HELP
If a cone has a volume of 75.36 cubic feet and a radius of 6 feet, what is the height of the cone? (Use 3.14 for .)
O2 feet
3.46 feet
06 feet
04 feet
the quotient of 45 and 5 form algebraic expression to verbal expression
please help me with this :D
what are the domain and range of the following quadratic
Answer:
ranalllldooo
Step-by-step explanation:
suiiiiiii
a pyramid has an isosceles , triangle base with sides 25,25 and 48 units . the height of the pyramid is 30 units . calculate The volume of the pyramid
A pyramid has an isosceles triangle base with sides of 25,25 and 48 units.
The height of the pyramid is 30 units. The volume of the pyramid is 13What is the volume?We have a pyramid with four sides and a square base. Two-thirds of the pyramid's sides make up its height. The volume of a pyramid is 1, and we need to determine which of them matches our volume. Third, multiplying the length by the width gives us our base's area, which is s times s, or s square.This tells us that our base's height is equal to two-thirds of its side because it is a square base.
That makes it 2 to times s, or 2 s over 3. So we incorporate that into our equations next. We have a volume that is equal to 1/s squared / 2 / s spanning 3 points.Therefore, a pyramid has an isosceles triangle base with sides of 25,25, and 48 units.
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How do you find 3/4 of 20
Fast response please!!
Answer:
15
Step-by-step explanation:
3/4(20/1) = (3*20)/(4*1)
60/4
15
Madison is entering a bicycle race for charity. Her mother pledges $0. 80 for every. 5 miles she bikes. If Madison bikes 12 miles, how much will her mother donate?
so Im not sure about how an equation for this would look but im assuming her mom doesnt pay unless a full 5 is completed, in that case her mom donates $1.6, in the case less than 5 is still donated for we make .16 * 12 which is $1.92
The diameter of a football is 12 cm. Calculate its volume.
Answer:
(4/3)*(22/7)*6*6*6
answer is 905.14
given that £1 = $1.62
how much is £650 in $
Answer:
$1053
Step-by-step explanation:
If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.
To do this multiplication, we can break 1.62 down simply into $1.00 +$0.6+$0.02
650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.
When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053
A weather forecast predicts that for each day from Monday to Friday this week, there is a $40\%$ chance of sun, a $25\%$ chance of getting 4 inches of rain, and a $35\%$ chance of getting 10 inches of rain. What is the expected value of the total number of inches of rain which will fall from Monday to Friday
Step-by-step explanation:
correct u know jsjsjsjsjajajaj shahha hshshs hsgshs hshshs hshshs hzhsvs hsvzvshsvss hshshs hshshs hshsh hshs
How do I match these?
Step-by-step explanation:
fgx= x+6
g(f(x)=√x²+6
am not sure about the rest
Solve the equation. m + (-22) = -25
Answer:
m=-3
Step-by-step explanation:
move the -22 to the other side by adding 22 on both sides:
m-22+22=-25+22
Simplify:
m=-3
Answer: m=-3
Hope this helps!