We can use the Law of Cosines to solve this problem. Let's call the starting point A, the point where the yacht turns B, and the final destination C.
Then we can use the given distances to find the length of each side of the triangle ABC, and the angles to find the angle opposite each side.
Using the angle opposite side AB as a reference angle, we can find the other angles as follows:
Angle BAC = 180° - (71° + 63°) = 46°
Angle ABC = 180° - (46° + 90°) = 44°
Now we can use the Law of Cosines:
[tex]AC^2 = AB^2 + BC^2 - 2ABBCcos(44°)[/tex]
[tex]AC^2 = (141)^2 + (213)^2 - 2(141)(213)*cos(44°)[/tex]
AC ≈ AC^2 = AB^2 + BC^2 - 2ABBCcos(44°)(rounded to the nearest hundredth)
Therefore, the distance from the starting point is approximately 281.21 miles.
To know more about Law of Cosines refer here
https://brainly.com/question/28547725#
#SPJ11
Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and
z are positive.
Maximize: f(x, y, z) = xyz
Constraint: × + y + z - 9 = 0
To use Lagrange multipliers, we need to define the Lagrangian function:
L(x, y, z, λ) = xyz + λ(x + y + z - 9)
Now, we need to find the partial derivatives of L with respect to x, y, z, and λ and set them equal to 0:
∂L/∂x = yz + λ = 0
∂L/∂y = xz + λ = 0
∂L/∂z = xy + λ = 0
∂L/∂λ = x + y + z - 9 = 0
From the first three equations, we can see that:
yz = -λ
xz = -λ
xy = -λ
Multiplying these equations together, we get:
(xyz)^2 = (-λ)^3
Substituting λ = -yz into the fourth equation, we get:
x + y + z - 9 = 0
Substituting λ = -yz into the first equation and solving for x, we get:
x = -λ/yz = (yz)^2/(-yz) = -y^2z^2
Similarly, we can solve for y and z:
y = -x^2z^2
z = -x^2y^2
Substituting these expressions into the constraint equation, we get:
(-y^2z^2) + (-x^2z^2) + (-x^2y^2) - 9 = 0
Simplifying and solving for xyz, we get:
xyz = sqrt(9/(x^2 + y^2 + z^2))
To maximize xyz, we need to minimize x^2 + y^2 + z^2. Therefore, we can set:
x^2 + y^2 + z^2 = 3
Substituting this into the expressions for x, y, and z, we get:
x = -y^2z^2
y = -x^2z^2
z = -x^2y^2
Substituting these expressions into xyz, we get:
xyz = sqrt(9/3) = 3
Therefore, the maximum value of f(x, y, z) = xyz subject to the constraint x + y + z - 9 = 0 is 3.
To solve this problem using Lagrange multipliers, we first set up the Lagrangian function L(x, y, z, λ) with the constraint function g(x, y, z) = x + y + z - 9.
L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z))
L(x, y, z, λ) = xyz - λ(x + y + z - 9)
Now we take the partial derivatives with respect to x, y, z, and λ, and set them equal to 0:
∂L/∂x = yz - λ = 0
∂L/∂y = xz - λ = 0
∂L/∂z = xy - λ = 0
∂L/∂λ = x + y + z - 9 = 0 (the constraint)
From the first three equations, we get:
yz = xz = xy
Since x, y, and z are positive, we can divide the first two equations:
y/z = x/z => y = x
x/z = y/z => x = y
So x = y = z. Now we can use the constraint equation:
x + x + x - 9 = 0 => 3x = 9 => x = 3
Thus, x = y = z = 3. Now we can find the maximum value of f(x, y, z):
f(3, 3, 3) = 3 * 3 * 3 = 27
So the maximum value of f(x, y, z) = xyz subject to the constraint x + y + z - 9 = 0 is 27, and this occurs at the point (3, 3, 3).
Learn more about Lagrange multipliers here: brainly.com/question/30776684
#SPJ11
Describe the end behavior of
f(x)= -x² -1
show steps
As the x-values go to either positive or negative infinity, the function decreases towards negative infinity.
Step 1: Identify the degree and leading coefficient.
In f(x) = -x² - 1, the degree is 2 (the highest power of x), and the leading coefficient is -1.
Step 2: Determine the end behavior based on the degree and leading coefficient.
Since the degree is even (2) and the leading coefficient is negative (-1), we know that both ends of the graph will point in the same direction.
Step 3: Identify the specific end behavior.
Because the leading coefficient is negative, the graph of the function will open downward. As x approaches positive infinity, f(x) will decrease towards negative infinity. Similarly, as x approaches negative infinity, f(x) will also decrease towards negative infinity.
Step 4: Write the end behavior in a concise format.
The end behavior of f(x) = -x² - 1 can be written as:
As x → ±∞, f(x) → -∞.
In summary, the function f(x) = -x² - 1 has a downward-opening parabola due to its even degree and negative leading coefficient.
You can read more about negative infinity at https://brainly.com/question/30096822
#SPJ11
For exercise, a softball player ran around the bases 12 times in 15 minutes. At the same rate, how many times could the bases be circled in 50 minutes?
The bases could be circled 40 times in 50 minutes at the same rate.
To solve this problemFor this issue's solution, let's use unit rates.
In order to calculate the unit rate,
Considering that the player went 12 times around the bases in 15 minutes, the unit rate is 12/15, = 0.8 times per minute.
In a minute, the player would have circled the bases 0.8 times. By dividing the unit rate by the number of minutes, we can calculate how many times the bases could be circled in 50 minutes:
50 minutes x 0.8 times each minute = 40 times.
Therefore, the bases could be circled 40 times in 50 minutes at the same rate.
Learn more about unit rate here : brainly.com/question/29216897
#SPJ1
A particle moves along the x-axis with velocity given by v(t) = 3t2 + 6t for time t ≥ 0. If the particle is at position x = 2 at time t = 0, what is the position of the particle at t = 1?
The position of the particle at time t = 1 is x = 4 units.
What is the position of a particle that moves along the x-axis with velocity v(t) = [tex]3t^2[/tex] + 6t at time t = 1 if it is at position x = 2 at time t = 0?To find the position of the particle at time t = 1, we need to integrate the given velocity function v(t) with respect to time from 0 to 1:
x(t) = ∫v(t)dt (from t = 0 to t = 1)
= ∫([tex]3t^2[/tex]+ 6t)dt (from t = 0 to t = 1)
= ([tex]t^3 + 3t^2[/tex]) (from t = 0 to t = 1)
[tex]= (1^3 + 3(1^2)) - (0^3 + 3(0^2))[/tex]
= 4
Learn more about position
brainly.com/question/15668711
#SPJ11
Fred goes to Old Navy and buys two pairs of jeans for $17. 99 each, three shirts at $5. 99 each, and a pack of socks for $3. He has a coupon for 25% off his entire purchase. Sales tax is 6. 5%. What is the total cost after the discount and tax?
A: $43. 07
B: $39. 95
C: $45. 49
D: $60. 65
The total cost after discount and tax is $46.28.
To find the total cost after the discount and tax, we need to first find the subtotal before tax.
Fred bought two pairs of jeans for $17.99 each, so the cost of the jeans is $17.99 x 2 = $35.98.
He also bought three shirts at $5.99 each, so the cost of the shirts is $5.99 x 3 = $17.97.
The pack of socks costs $3.
The subtotal before discount is $35.98 + $17.97 + $3 = $57.95.
With the 25% off coupon, Fred gets a discount of $57.95 x 0.25 = $14.49.
The new subtotal after discount is $57.95 - $14.49 = $43.46.
Finally, we need to add the 6.5% sales tax.
The sales tax is $43.46 x 0.065 = $2.82.
The total cost after discount and tax is $43.46 + $2.82 = $46.28.
Therefore, the closest answer is C: $45.49.
Learn more about Profit and Loss: https://brainly.com/question/9281343
#SPJ11
If Franco's Pizza Parlor knows that the marginal cost of the 500th pizza is $3.50 and that the average total cost of making 499 pizzas is $3.30, then
a. average total costs are falling at Q = 500.
b. average variable costs must be falling.
c. average total costs are rising at Q = 500.
d. total costs are falling at Q = 500.
If Franco's Pizza Parlor knows that the marginal cost of the 500th pizza is $3.50 and that the average total cost of making 499 pizzas is $3.30, then Average total costs are rising at Q = 500. The correct answer is (c)
The marginal cost is the additional cost of producing one more unit. In this case, the marginal cost of the 500th pizza is $3.50.
The average total cost is the total cost of producing all units up to a certain level, divided by the number of units produced. In this case, the average total cost of making 499 pizzas is $3.30.
If the marginal cost of producing the 500th pizza is greater than the average total cost of making the first 499 pizzas, then the average total cost will increase when the 500th pizza is produced.
Therefore, the correct answer is (c) average total costs are rising at Q = 500.
Learn more about average total costs
https://brainly.com/question/13950634
#SPJ4
Q5. Compute the trapezoidal approximation for | Vx dx using a regular partition with n=6.
The trapezoidal approximation for | Vx dx using a regular partition with n=6 is approximately 0.1901.
How to find the trapezoidal approximation for a function?To compute the trapezoidal approximation for | Vx dx using a regular partition with n=6, we can use the formula:
Tn = (b-a)/n * [f(a)/2 + f(x1) + f(x2) + ... + f(xn-1) + f(b)/2]
where Tn is the trapezoidal approximation, n=6 is the number of partitions, a and b are the limits of integration, and x1, x2, ..., xn-1 are the partition points.
In this case, we have | Vx dx as the function to integrate. Since there are no given limits of integration, we can assume them to be 0 and 1 for simplicity.
So, a=0 and b=1, and we need to find the values of f(x) at x=0, 1/6, 2/6, 3/6, 4/6, and 5/6 to use in the formula.
We can calculate these values as follows:
f(0) = | V0 dx = 0
f(1/6) = | V1/6 dx = V(1/6) - V(0) = sqrt(1/6) - 0 = 0.4082
f(2/6) = | V2/6 dx = V(2/6) - V(1/6) = sqrt(2/6) - sqrt(1/6) = 0.2317
f(3/6) = | V3/6 dx = V(3/6) - V(2/6) = sqrt(3/6) - sqrt(2/6) = 0.1547
f(4/6) = | V4/6 dx = V(4/6) - V(3/6) = sqrt(4/6) - sqrt(3/6) = 0.1104
f(5/6) = | V5/6 dx = V(5/6) - V(4/6) = sqrt(5/6) - sqrt(4/6) = 0.0849
Now we can substitute these values in the formula and simplify:
T6 = (1-0)/6 * [0/2 + 0.4082 + 0.2317 + 0.1547 + 0.1104 + 0.0849/2]
= 0.1901
Therefore, the trapezoidal approximation for | Vx dx using a regular partition with n=6 is approximately 0.1901.
Learn more about the trapezoidal approximation.
brainly.com/question/29159712
#SPJ11
Prove that the value of the expression: (36^5−6^9)(38^9−38^8) is divisible by 30 and 37.
_x30x37
Don't answer if you don't know
To prove that the expression (36^5−6^9)(38^9−38^8) is divisible by 30, we need to show that it is divisible by both 2 and 3.
First, we can factor out a 6^9 from the first term:
(36^5−6^9)(38^9−38^8) = 6^9(6^10-36^5)(38^9-38^8)
Notice that 6^10 can be written as (2*3)^10, which is clearly divisible by both 2 and 3. Also, 36 is divisible by 3, so 36^5 is divisible by 3^5. Thus, we can write:
6^9(6^10-36^5) = 6^9(2^10*3^10 - 3^5*2^10) = 6^9*2^10*(3^10 - 3^5)
Since 2^10 is divisible by 2, and 3^10 - 3^5 is clearly divisible by 3, the whole expression is divisible by both 2 and 3, and therefore divisible by 30.
To prove that the expression is divisible by 37, we can use Fermat's Little Theorem. Fermat's Little Theorem states that if p is a prime number and a is any positive integer not divisible by p, then a^(p-1) is congruent to 1 modulo p, which can be written as a^(p-1) ≡ 1 (mod p).
In this case, p = 37, and 36 is not divisible by 37. Therefore, by Fermat's Little Theorem:
36^(37-1) ≡ 1 (mod 37)
Simplifying the exponent gives:
36^36 ≡ 1 (mod 37)
Similarly, 38 is not divisible by 37, so:
38^(37-1) ≡ 1 (mod 37)
Simplifying the exponent gives:
38^36 ≡ 1 (mod 37)
Now we can use these congruences to simplify our expression:
(36^5−6^9)(38^9−38^8) ≡ (-6^9)(-1) ≡ 6^9 (mod 37)
We know that 6^9 is divisible by 3, so we can write:
6^9 = 2^9*3^9
Since 2 and 37 are relatively prime, we can use Euler's Totient Theorem to simplify 2^9 (mod 37):
2^φ(37) ≡ 2^36 ≡ 1 (mod 37)
Therefore:
2^9 ≡ 2^9*1 ≡ 2^9*2^36 ≡ 2^(9+36) ≡ 2^45 (mod 37)
Now we can simplify our expression further:
6^9 ≡ 2^45*3^9 ≡ (2^5)^9*3^9 ≡ 32^9*3^9 (mod 37)
Notice that 32 is congruent to -5 modulo 37, since 32+5 = 37. Therefore:
32^9 ≡ (-5)^9 ≡ -5^9 ≡ -1953125 ≡ 2 (mod 37)
So:
6^9 ≡ 2*3^9 ≡ 2*19683 ≡ 39366 ≡ 0 (mod 37)
To know more about Fermat's Little Theorem refer here
https://brainly.com/question/30761350#
#SPJ11
Find an angle \thetaθ coterminal to -497^{\circ}−497 ∘
, where 0^{\circ}\le\theta<360^{\circ}0 ∘
≤θ<360 ∘
The correct answer for an angle coterminal to -497° within the interval 0°≤θ≤360° is 223°.
What are Coterminal angles?
Coterminal angles are angles that share the same initial and terminal sides when drawn in the standard position (starting from the positive x-axis) on the coordinate plane. In other words, coterminal angles are angles that differ by an integer multiple of 360° or 2π radians.
To find an angle coterminal to within the interval use the fact that to add or subtract a multiple of to an angle does not change its position on the unit circle.
To make the angle positive, add 360° repeatedly until an angle within the desired interval is obtained:
= -497° +360°
= -137°
adjust this angle to be within the interval 0°≤θ≤360°, and add another 360°:
= -137° + 360°
= 223°
The required angle is 223°.
Learn more about Coterminal angles here:
https://brainly.com/question/32053945
#SPJ12
An angle θ coterminal to -497 degrees, where 0 ≤ θ < 360 degrees, is 223 degrees.
Given that; the angle is, -497 degrees.
Now, for an angle coterminal to -497 degrees within the range 0≤θ<360 degrees, add or subtract multiples of 360 degrees until we get an angle within the desired range.
Now, add multiples of 360 degrees until we get a positive angle:
-497 + 360 = -137
Now we have an angle of - 137 degrees, but it is still not within the desired range of 0 ≤ θ < 360 degrees.
To adjust the angle, add 360 degrees to it:
-137 + 360 = 223
Now an angle of 223 degrees, which is within the desired range.
Therefore, an angle θ coterminal to -497 degrees, where 0 ≤ θ < 360 degrees, is 223 degrees.
To learn more about the angle visit:;
https://brainly.com/question/25716982
#SPJ12
Every line segment used to make this hospital logo is 3 meters long. What is the total area of the logo in square meters?
There were three ant hills in Mrs. Brown's yard. The first ant hill had 4,867,190 ants. The second ant hill had 6,256,304 ants, and the third ant hill had 3,993,102 ants. Choose the best estimate of the number of ants in Mrs. Brown's yard
The best estimate of the number of ants in Mrs. Brown's yard is 15,116,596.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
Mrs. Brown's yard has three ant hills, each with a different number of ants. To estimate the total number of ants in the yard, we simply add up the number of ants in each hill.
The first hill has 4,867,190 ants, the second has 6,256,304, and the third has 3,993,102. When we add these numbers together, we get a total of 15,116,596 ants in Mrs. Brown's yard. Of course, this is just an estimate, as there may be other ant hills or individual ants scattered around the yard.
However, this calculation gives us a good approximation of the number of ants in the yard based on the information given.
To estimate the total number of ants in Mrs. Brown's yard, we can add up the number of ants in each of the three ant hills:4,867,190 + 6,256,304 + 3,993,102 = 15,116,596.
Therefore, the best estimate of the number of ants in Mrs. Brown's yard is 15,116,596.
To learn more about arithmetic sequence from the given link:
https://brainly.com/question/15412619
#SPJ4
Write and expression for the calculation add 8 to the sum of 23 and 10
The expression for the calculation of adding 8 to the sum of 23 and 10 is 8 + (23 + 10)
How to find the expression?
To calculate expression parentheses the sum of 23 and 10, we add them together, which gives us 33. Then, we add 8 to that result, giving us a final answer of 41. So, the expression 8 + (23 + 10) equals 41.
This expression follows the order of operations, which states that we should first perform the addition inside the parentheses and then add the result to 8.
expressions are made up of numbers and symbols, and they represent a mathematical relationship or operation. In this case, the expression includes addition and parentheses, which tell us to perform the addition inside them first. The parentheses clarify which numbers should be added together first before adding 8.
To learn more about expressions parentheses
brainly.com/question/23978428
#SPJ11
A company manufactures to types of cabinets, type 1 and type 2. It produces 110 total cabinet’s each week.
Last week, the number of type 2 cabinets produced exceeded twice the number of type 1 cabinets produced by 20. If x is the number of type 1 cabinets produced and y is the number of type 2 cabinets produced, the system of equations that represent this situation is x + y = 110 and y = 2x+20
The number of type 2 cabinets produced last week is ____. This number exceeds the number of type 1 cabinets produced durin the week by ______.
The number of type 2 cabinets produced last week is 80. The number of type 2 cabinets produced last week exceeded the number of type 1 cabinets produced during the week by 50.
Using the system of equations given, we can solve for the number of type 1 and type 2 cabinets produced.
x + y = 110 represents the total number of cabinets produced, where x is the number of type 1 cabinets and y is the number of type 2 cabinets produced.
y = 2x + 20 represents the relationship between the number of type 1 and type 2 cabinets produced. This equation tells us that the number of type 2 cabinets produced exceeds twice the number of type 1 cabinets produced by 20.
To solve for y, we substitute the value of y from the second equation into the first equation:
x + (2x + 20) = 110
Simplifying this equation:
3x + 20 = 110
3x = 90
x = 30
Therefore, the number of type 1 cabinets produced last week is 30.
To find the number of type 2 cabinets produced, we substitute x = 30 into the second equation:
y = 2x + 20 = 2(30) + 20 = 80
The number of type 2 cabinets produced last week exceeds the number of type 1 cabinets produced during the week by:
80 - 30 = 50.
To learn more about equations click on,
https://brainly.com/question/30216070
#SPJ1
Solve for x WILL MAKE BRAINLIEST QUESTION IN PHOTI ALSO
The measure of x in the intersected chord is 16.
How to find the angle in an intersected chord?If two chords intersect in a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Using the chord intersection angle theorem,
5x - 7 = 1 / 2 (119 + 27)
5x - 7 = 1 / 2 (146)
5x - 7 = 73
add 7 to both sides of the equation
5x - 7 = 73
5x - 7 + 7 = 73 + 7
5x = 80
divide both sides of the equation by 5
x = 80 / 5
x = 16
learn more on chord here: https://brainly.com/question/24225997
#SPJ1
a gambler is going to play a gambling game. in each game, the chance of winning $3 is 2/10, the chance of losing $2 is 3/10, and the chance of losing $1 is 5/10. suppose the gambler is going to play the game 5 times. (a) write down the box model for keeping track of the net gain. (you already did this in a previous lab.) (b) now write down the box model for keeping track of the number of winning plays. (c) calculate the expected value and standard error for the number of winning plays. (d) would it be appropriate to use the normal approximation for the number of winning plays? why or why not?
The expected value and standard error for the number of winning plays is $3.1 and $ 2.21.
The population mean's likelihood to differ from a sample mean is indicated by the standard error of a mean, and simply standard error.
It reveals how much what the sample mean will change if a study were to be repeated with fresh samples drawn from a single population.
Chance of winning $3 = 2/10
chance of losing $2 = 3/10
chance of losing $1 = 5/10
Average of tickets. = - $2.50
SD of tickets = $1.80.
The box model for net gain has 2 tickets labeled $3, 3 tickets labeled $2, 5 tickets labeled
a) Expected value for the net gain.
The Expected value for net = ∑ x.p(x)
Here
can take value $1, $2 and $3
Here p(x) us the probability of winning respectively.
So, Now, Expected gain is,
(2 x 3 x 2/10) + (3 x -2 x 7/10) + (5 x -1 x 5/10)
= 12/10 - 18/10 - 25/10
= -31/10 = -$3.1.
b) Standard error of the net gain,
S.D = [tex]\sqrt{E(x^2) - [E(x)]^2}[/tex]
Now E(x²) = (2 x 3² x 2/10) + (3 x -2² x 7/10) + (5 x -1² x 5/10)
= 36/10 + 84/10 + 25/10 = 145/10
= $ 14.5
SD = [tex]\sqrt{14.5 - 3.1}\\[/tex]
SD = $ 2.21
c) Chance that the net gain is $15
P(X=15) = (z = 15-(-2.50)/1.80
= P(z=9.72) = 0.99.
Learn more about Expected value and standard error:
https://brainly.com/question/29732439
#SPJ4
Find the volume of the cone to the nearest whole number. Use 3. 14
for it.
Cone
Radius Height
Volume
varrh
Worms
3in.
6in.
Tree
Gum
The volume of the cone is 57 cubic inches. To find the volume of the cone, we use the formula: V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius of the cone, h is the height of the cone, and π is approximately 3.14.
Given that the radius of the cone is 3 inches and the height is 6 inches, we can substitute these values into the formula and solve for V: V = (1/3)π([tex]3^{2}[/tex])(6), V = (1/3)π(9)(6), V = (1/3)(3.14)(54), V = 56.52 cubic inches
Rounding to the nearest whole number, the volume of the cone is 57 cubic inches.
To know more about volume of cone, refer here:
https://brainly.com/question/29767724#
#SPJ11
Laura is driving to Los Angeles. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.85. See the figure below. Laura has 52 miles remaining after 41 minutes of driving. How many miles were remaining after 33 minutes of driving?
The remaining distance after 33 minutes of driving = 58.8 miles.
Here, the slope of a linear function the remaining distance to drive (in miles) is -0.85
For this situation, we can write a linear equation as,
remaining distance = (slope)(drive time) + (intercept)
remaining distance = -0.85(drive time) + (intercept)
y = -0.85x + c ..........(1)
where y represents the remaining distance
x is the drive time
and c is the y-intercept
Here, Laura has 52 miles remaining after 41 minutes of driving.
i.e., x = 41 and y = 52
Substitute these values in equation (1)
52 = -0.85(41) + c
c = 52 + 34.85
c = 86.85
So, equation (1) becomes,
y = -0.85x + 86.85
Now, we need to find the remaining distance after 33 minutes of driving.
i.e., the value of y for x = 33
y = -0.85(33) + 86.85
y = -28.05 + 86.85
y = 58.8
This is the remaining distance 58.8 miles.
Learn more about the slope here:
https://brainly.com/question/30216543
#SPJ1
Frank keeps his pet iguana in a glass tank that is shaped like a rectangular prism.the height of the tank is 11 inches, the width is 34.5 inches, and the length is 25 inches.what is the best estimate for the volume of the tank in cubic feet?remember 12 inches = 1 foot.
The best estimate for the volume of the tank in cubic feet is 5.5 cubic feet.
The volume of the tank is:
V = l x w x h
where l is the length, w is the width, and h is the height.
Substituting the given values, we get:
V = 25 x 34.5 x 11 = 9547.5 cubic inches
To convert cubic inches to cubic feet, we divide by (12 x 12 x 12), since there are 12 inches in a foot and 12 x 12 x 12 cubic inches in a cubic foot:
V = 9547.5 / (12 x 12 x 12) cubic feet
V ≈ 5.5 cubic feet
Therefore, 5.5 cubic feet is the best estimate for the tank's cubic foot capacity.
Hence , the volume of the rectangular glass tank is 5.490 feet³
To learn more about volume click :
brainly.com/question/25422723
#SPJ11
Andrew went deep sea diving with some friends. If he descends at a rate of 4 feet per minute, what integer represents Andrews depth in ¼ of an hour?
The integer that represents Andrews depth in ¼ of an hour is 60 feet.
How to determine what integer represents Andrews depth in 1/4 of an hour?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation e.g. calculation of length and depth.
If Andrew descends at a rate of 4 feet per minute and we want to find his depth in ¼ of an hour.
1/4 of an hour = (1/4 * 60) minutes = 15 minutes
Thus, the integer that represents Andrews depth in ¼ of an hour will be:
(4 feet per minute) * (15 minutes) = 60 feet
Learn more about length on:
https://brainly.com/question/30592289
#SPJ4
Mrs. Sonora used 1/2 gallon of milk for a pudding recipe how many cups did she use for the recipe?
Answer: 8 cups
Step-by-step explanation: 16 cups in a gallon, Half of 16 is 8. (16 divided by 2 = 8)
if x varies directly as T and x=105 when T=400, find x when T=500
Answerx = 131.25
Step-by-step explanation:f x varies directly as T, then we can use the formula for direct variation:
x = kT
where k is the constant of proportionality.
To find k, we can use the given values:
x = 105 when T = 400
105 = k(400)
k = 105/400
k = 0.2625
Now that we have the value of k, we can use the formula to find x when T = 500:
x = kT
x = 0.2625(500)
x = 131.25
Therefore, when T = 500, x is equal to 131.25.
What is the area of the shaded part of the circle?
And also, I am so confused about how to do it so can someone help me pls?
The required area of the shaded part of the circle is 50.24 sq. cm
What is area of a circle?A circle of radius r has an area of r2 in geometry. Here, the Greek letter denotes the constant ratio of a circle's diameter to circumference, which is roughly equivalent to 3.14159.
According to question:Given data:
Radius of small circle = 6/2 = 3 cm
Radius of big circle = 10/2 = 5 cm
then.
Area of shaded part = area of big circle - area of small circle
Area of shaded part = π(5)² - π(3)²
Area of shaded part = 25π - 9π
Area of shaded part = 16π
Area of shaded part = 50.24 sq. cm
Thus, required area of the shaded part of the circle is 50.24 sq. cm
To know more about Circle visit:
brainly.com/question/12711347
#SPJ1
a fast food restaurant executive wishes to know how many fast food meals teenagers eat each week. they want to construct a 85% confidence interval with an error of no more than 0.06 . a consultant has informed them that a previous study found the mean to be 4.9 fast food meals per week and found the standard deviation to be 0.9 . what is the minimum sample size required to create the specified confidence interval? round your answer up to the next integer.
The minimum sample size which is need to to create the given confidence interval is equal to 467.
Sample size n
z = z-score for the desired confidence level
From attached table,
For 85% confidence level, which corresponds to a z-score of 1.44.
Maximum error or margin of error E = 0.06
Population standard deviation σ = 0.9
Minimum sample size required to construct a 85% confidence interval with an error of no more than 0.06,
Use the formula,
n = (z / E)^2 × σ^2
Plugging in the values, we get,
⇒ n = (1.44 / 0.06)^2 × 0.9^2
⇒ n = 466.56
Rounding up to the next integer, we get a minimum sample size of 467.
Therefore, the minimum sample size required to construct a 85% confidence interval with an error of no more than 0.06 is 467.
Learn more about sample size here
brainly.com/question/15120195
#SPJ4
A volleyball player’s serving percentage is 75%. Six of her serves are randomly selected. Using the table, what is the probability that at most 4 of them were successes?
A 2-column table with 7 rows. Column 1 is labeled number of serves with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0. 0002, 0. 004, 0. 033, 0. 132, 0. 297, 0. 356, question mark.
0. 297
0. 466
0. 534
0. 822
To solve this problem, we first need to understand what "at most 4 of them were successes" means. This includes the cases where there are 0, 1, 2, 3, or 4 successful serves out of the 6 selected.
We can use the table to find the probabilities for each of these cases.
For 0 successful serves, the probability is 0.0002.
For 1 successful serve, the probability is 0.004.
For 2 successful serves, the probability is 0.033.
For 3 successful serves, the probability is 0.132.
For 4 successful serves, the probability is 0.297.
To find the probability of at most 4 successful serves, we add up these probabilities:
[tex]0.0002 + 0.004 + 0.033 + 0.132 + 0.297 = 0.466[/tex]
So the probability of at most 4 successful serves is 0.466.
Therefore, the answer is 0.466 and it is found by adding up the probabilities for the cases where there are 0, 1, 2, 3, or 4 successful serves out of the 6 selected from the table.
To know more about probabilities refer here
https://brainly.com/question/30034780#
#SPJ11
A. Directions:translate each problem into algebraic expression or equation and identify the variable/s.
1. Julie weighs c kilogram. After going to gym for six months, she lost 2. 5 kilograms. Express her weight algebraically.
2. Peter is m centimeter tall. Jhon's height is 5 more than twice the height of Peter. How tall is Jhon?
3. Ador is thrice older than Emy. If Emy is d years old less than 9,how old is ador?
4. Jupiter is n years old now. How old is Jupiter 7 years from now?
5. Anna's sister is p years old. Anna is 4 years older than thrice the age of her sister. How old is Anna?
guys please help me please
lets assume.
Algebraic expression: c - 2.5. The variable is c, which represents Julie's initial weight in kilograms.
Algebraic equation: Jhon's height = 2m + 5. The variables are m, which represents Peter's height in centimeters, and the height of Jhon, which is represented by the equation.
Algebraic equation: Ador's age = 3(Emy's age - d). The variables are Ador's age and Emy's age, which is d years less than 9.
Algebraic expression: n + 7. The variable is n, which represents Jupiter's current age in years.
Algebraic equation: Anna's age = 3p + 4. The variables are p, which represents Anna's sister's age in years, and Anna's age, which is represented by the equation.
SO ANNA current age is P=3+4
and p=7
Anna's age = 3p + 4, where p is the age of Anna's sister in years, and Anna is 4 years older than thrice the age of her sister.
If Anna's sister is 10 years old, how old is Anna according to the equation?Algebraic expression: c - 2.5, where c is the weight of Julie in kilograms, and 2.5 is the weight she lost after six months of going to the gym.Algebraic equation: Jhon's height = 2m + 5, where m is the height of Peter in centimeters, and Jhon's height is 5 more than twice the height of Peter.Algebraic equation: Ador's age = 3(Emy's age - d), where Emy is d years less than 9, and Ador is thrice older than Emy.Algebraic equation: Jupiter's age 7 years from now = n + 7, where n is Jupiter's current age in years.Algebraic equation: Anna's age = 3p + 4, where p is the age of Anna's sister in years, and Anna is 4 years older than thrice the age of her sister.Learn more about Anna age
brainly.com/question/30473696
#SPJ11
A right triangle has legs that are 17 centimeters and 28 centimeters long.
What is the length of the hypotenuse?
Enter your answer as a decimal, Round your answer to the nearest hundredth.
Answer: 4.5
Step-by-step explanation:
When creating lines of best fit, do you believe that estimation by inspection of the equation is best or do you think it should be determined exactly? In what situations would it be best to use one over the other?
Your response should be 3-5 sentences long and show that you’ve thought about the topic/question at hand
In general, it is best to determine the equation of the line of best fit exactly rather than relying on estimation by inspection. This is because an exact equation allows for more precise predictions and calculations.
Estimation by inspection can be useful in situations where the data is relatively simple and a rough estimate is sufficient. However, in more complex datasets, it is important to use statistical methods to determine the line of best fit accurately.
It is also worth noting that in some cases, different methods of determining the line of best fit may be appropriate depending on the specific goals of the analysis.For example, in some cases, it may be more important to prioritize the accuracy of the slope of the line over the accuracy of the intercept. In such cases, certain methods, such as minimizing the sum of the squares of the vertical deviations, may be more appropriate than others.
To learn more about “estimation” refer to the https://brainly.com/question/28416295
#SPJ11
In ΔVWX, w = 4.7 inches, v = 2.4 inches and ∠V=8°. Find all possible values of ∠W, to the nearest 10th of a degree.
The value of W to the nearest tenth of degree is 15.8°
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Sine rule can be used to find unknown side or angle In a triangle.
w/sinW = v/sinV
4.7/sinW = 2.4 / sin8
2.4sinW = 4.7 sin8
2.4sinW = 0.654
sinW = 0.654/2.4
sinW = 0.273
W = sin^-1( 0.273)
W = 15.8° ( nearest tenth)
therefore the value of W is 15.8°
learn more about sine rule from
https://brainly.com/question/20839703
#SPJ1
Let a,b,c and d be distinct real numbers. Show that the equation (x-b)(x-c) (x-d) + (x-a)(x-c)(x - d) + (x-a) (x-b)(x-d) + (x - a)(x-b)(x-c) has exactly 3 distinct roul solutions (Hint: Let p(x)= (x-a)(x-b)(x-c)(x-d). Then p(x) = 0 has how many distinct real solutions? Then use logarithmic differentiation to show that p'(x) is given by the expression on the left hand side of (1). Now, apply Rolle's theorem. )
There exists at least one c in the open interval (a, b) such that f'(c) = 0.
There are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.
To prove that the given equation has exactly 3 distinct real solutions, let's follow the steps mentioned in the question.
First, consider the polynomial p(x) = (x-a)(x-b)(x-c)(x-d). Since a, b, c, and d are distinct real numbers, p(x) has 4 distinct real roots, namely a, b, c, and d.
Now, let's find the derivative p'(x) using logarithmic differentiation. Taking the natural logarithm of both sides, we have:
[tex]ln(p(x)) = ln((x-a)(x-b)(x-c)(x-d))[/tex]
Differentiating both sides with respect to x, we get:
[tex]p'(x)/p(x) = 1/(x-a) + 1/(x-b) + 1/(x-c) + 1/(x-d)[/tex]
Multiplying both sides by p(x) and simplifying, we have:
[tex]p'(x) = (x-b)(x-c)(x-d) + (x-a)(x-c)(x-d) + (x-a)(x-b)(x-d) + (x-a)(x-b)(x-c)[/tex]
Now, we apply Rolle's Theorem, which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the open interval (a, b) such that f'(c) = 0.
Since p(x) has 4 distinct real roots, there must be 3 intervals between these roots where the function p(x) satisfies the conditions of Rolle's Theorem. Therefore, there are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.
To learn more about Rolle's Theorem, refer below:
https://brainly.com/question/13972986
#SPJ11
The OLS estimator is derived by: Group of answer choices connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi making sure that the standard error of the regression equals the standard error of the slope estimator. Minimizing the sum of absolute residuals. Minimizing the sum of squared residuals
Minimizing the sum of squared residuals.
How is the OLS estimator derived?The OLS (Ordinary Least Squares) estimator is derived by minimizing the sum of squared residuals. This method aims to find the line of best fit that minimizes the vertical distance between the observed data points (Yi) and the predicted values on the regression line. The residuals represent the differences between the observed values and the predicted values.
By minimizing the sum of squared residuals, the OLS estimator ensures that the line fits the data as closely as possible. This approach is based on the principle of least squares, which seeks to find the parameters that minimize the overall discrepancy between the observed data and the predicted values.
Connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi or ensuring that the standard error of the regression equals the standard error of the slope estimator are not the steps involved in deriving the OLS estimator. The OLS method specifically focuses on minimizing the sum of squared residuals.
Learn more about estimator
brainly.com/question/16099852
#SPJ11