The minimum value is 24
To find the minimum value of z=7x+3y, we must use the given constraints to determine the values of x and y.
First, solve 4x + 6y ≥ 24. Rearrange the equation to solve for x: x ≥ (24 - 6y) / 4.
Next, solve x + 6y ≥ 12. Rearrange the equation to solve for y: y ≥ (12 - x) / 6.
Using the two equations, determine the possible values of x and y:
If y = 0, then x = 6
If x = 0, then y = 2
Substitute the possible values of x and y into the equation z = 7x + 3y and find the minimum value:
z = 7(6) + 3(0) = 42
z = 7(0) + 3(2) = 24
Therefore, the minimum value of z is 24.
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Please answer number 15 and 16 show work
Algebra 2
The exponential function that models the percentage as a function of P is given as follows:
P(t) = 100(0.705)^t.
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the value of y when x = 0.b is the rate of change.The parameters for this problem are given as follows:
a = 100, as when x = 0, y = 100, from the second row of the table.b = 70.5/100 = 0.705, as when x increased by one, y was multiplied by 0.705.Hence the function that models the data in the table is defined as follows:
P(t) = 100(0.705)^t.
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Can someone explain how to do this? I'm confused. Anything helps.
Thank you so much!
Answer:
28 and 152 degrees
Step-by-step explanation:
Using sine inverse, the answer is 28 or 152 degrees.
Answer:48.87°
Step-by-step explanation:
3. In montht=0, a small group of rabbits escapes from a ship onto an island where there are no rabbits. The island rabbit population,P(t), in monthtis given byP(t)=1+24(0.85)′1000a) How many rabbits escaped from the ship? Explain how you arrived at your answer. b) EvaluateP(6)andP(24)and explain their meaning in the context of the problem. Use complete sentences. c) Use your calculator to graphP(t)for0≤t≤80. Obtain a printout of this graph, label each axis with both a variable and a word label, and label the scale on each axis. d) Describe the shape of the graph in mathematical words (increasing, decreasing, local maximum, local minimum). e) Use the graph to describe the manner in which the rabbit population has changed since the rabbits escaped. f) Does the graph suggest the growth in population you would expect among rabbits on an island. Explain g) Use the graph to estimate how long it will take before there are 500 rabbits. Show this on the graph vou drew. Write the conclusion in sentence.
a) The number of rabbits that escaped from the ship is 24.
b) P(6) = 1 + 24 (0.85)^6 = 91.7, and P(24) = 1 + 24 (0.85)^24 = 436.8.
c) The graph of P(t) for 0 ≤ t ≤ 80 is an exponential curve that increases steadily over time.
d) The graph of P(t) is increasing.
e) The graph shows that the population of rabbits has increased exponentially since they escaped from the ship.
f) Yes, the graph does suggest the growth in population that would be expected among rabbits on an island. This is due to the steadily increasing nature of the graph.
g) The graph suggests that it will take approximately 65 months for the rabbit population to reach 500. This can be seen on the graph, as the y-axis value reaches 500 around the 65th month.
a)This can be calculated by taking the initial population, 1, and multiplying it by the given rate of growth, 0.85, and raising that to the 1000th power.
b) The meaning of these numbers in the context of the problem is that P(6) represents the total rabbit population after 6 months, and P(24) represents the total rabbit population after 24 months.
c)It is labeled with the variable t on the x-axis and the word "Population" on the y-axis, with each axis scaled appropriately.
f) Yes, the graph does suggest the growth in population that would be expected among rabbits on an island. This is due to the steadily increasing nature of the graph.
g)The graph suggests that it will take 65 months for the rabbit population to reach 500. This can be seen on the graph, as the y-axis value reaches 500 around the 65th month.
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Evaluate the integral by changing to cylindrical coordinates. 7 −7 49 − y2 − 49 − y2 11 xz dz dx dy x2 + y2
The value of the triple integral is 49π ln(49) - 24.5π.
To evaluate this triple integral using cylindrical coordinates, we need to express the limits of integration in terms of cylindrical coordinates. We can convert the Cartesian coordinates to cylindrical coordinates as follows:
x = r cos(θ)
y = r sin(θ)
z = z
The region of integration is a cylinder centered at the origin with radius 7 and height 14 (from -7 to 7 in the y-direction). Therefore, the limits of integration are:
0 ≤ r ≤ 7
0 ≤ θ ≤ 2π
-7 ≤ z ≤ 7
Substituting these limits of integration and the Cartesian-to-cylindrical conversion into the integral, we get:
∫∫∫ 7 −7 (49 - [tex]y^2 - r^2[/tex]) / ([tex]x^2 + y^2)[/tex] dz dx dy
= ∫[tex]0^7[/tex]∫[tex]0^2π[/tex] ∫-7^7 (49 - [tex]r^2[/tex]sin^2(θ) - r^2) / (r^2cos^2(θ) + r^2sin^2(θ)) dz r dθ dr
= ∫0^7 ∫0^2π ∫-7^7 (49 - r^2) / r^2 dz r dθ dr
= ∫0^7 ∫0^2π [ln|49-r^2|] from -7 to 7 dθ dr
= ∫0^7 2π ln|49-r^2| dr
This integral is now a single-variable integral that can be evaluated using integration by substitution or by parts. Let u = 49 - r^2 and du = -2r dr. Then:
∫0^7 2π[tex]ln|49-r^2|[/tex] dr = ∫49^0 -πln|u| du/-2
= π/2 [u ln|u| - u] from 49 to 0
= π/2 [49 ln(49) - 49] = 49π ln(49) - 24.5π
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At a bank, ECS2.60 is equivalent to US$1.00. For every US$1.00 exchanged, ECS0.10 is deducted as an exchange fee. How much EC dollars will Leon receive if he exchanges US$100.00? (A) (B) (C) (D) $ 90.90 236.34 $ $ 250.00 $ 260.00
Leon will receive ECS250.00 dollars if he exchanges US$100.00 at this bank.
How determine how much EC dollars Leon will receive if he exchanges US$100.00?If ECS2.60 is equivalent to US$1.00, then the exchange rate from US dollars to EC dollars is 1:2.60.
To find out how much ECS dollars Leon will receive for US$100.00, we first need to convert US$100.00 to EC dollars using the exchange rate:
US$100.00 * 2.60 = ECS260.00
So, Leon will receive ECS260.00 for US$100.00 before any exchange fees are deducted.
The exchange fee for every US$1.00 exchanged is ECS0.10. Therefore, the exchange fee for US$100.00 will be:
US$100.00 * ECS0.10 = ECS10.00
To find out how much Leon will receive after the exchange fee is deducted, we need to subtract the fee from the initial amount:
ECS260.00 - ECS10.00 = ECS250.00
Therefore, Leon will receive ECS250.00 if he exchanges US$100.00 at this bank.
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Change 42 kilograms into stones
42 kilograms are equal to 6.6 stones.
What is Unit?A unit is a common element used to quantify similar physical quantities.
As per the given data:
1 kilogram = 2.2 pounds
1 stone = 14 pounds
For converting 42 kilogram to stones:
42 kilogram = 2.2 × 42 pounds
= 92.4 pounds
1 pound = (1/14) stone
= 92.4 × (1/14) stones
= 6.6 stones
Hence, 42 kilograms are equal to 6.6 stones.
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Consider the following vectors v1 = 1 , v2 = 2 , and v3 = -1 . For what values (s) -1 1 3
2 1 h
of h is the set. {v1, v2, v3] linearly dependent? Work must be shown for this question. h = -4
h = 4
all real number h ≠ 4 all real number h ≠ -4
The set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.
The set of vectors {v1, v2, v3} is linearly dependent if there exists a set of real numbers a, b, and c such that a*v1 + b*v2 + c*v3 = 0 and at least one of a, b, or c is not equal to zero. In this case, we can write the equation as:
a*1 + b*2 + c*(-1) = 0
We can rearrange this equation to solve for h:
h = -a - 2*b + c
Now we can plug in the values for v1, v2, and v3:
h = -1 - 2*2 + (-1)*(-1)
h = -4
Therefore, the set of vectors {v1, v2, v3} is linearly dependent when h = -4.
Alternatively, we can also use the determinant of the matrix formed by the vectors to determine when the set is linearly dependent. The determinant of the matrix is given by:
| 1 2 -1 |
| -1 1 3 | = (1)(1)(h) + (2)(3)(-1) + (-1)(-1)(2) - (-1)(1)(-1) - (2)(-1)(1) - (1)(3)(2)
| 2 1 h |
Simplifying this equation gives:
h - 6 - 2 + 1 + 2 - 6 = 0
h - 11 = 0
h = 11
Therefore, the set of vectors {v1, v2, v3} is also linearly dependent when h = 11.
So the set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.
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Write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. Display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places. All numbers are to be right justified. The columns of the table should have appropriate headings.
To write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5, you can use the following code:
#include <iostream>This program will print a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. The table will display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places, with all numbers being right justified. The columns of the table will have appropriate headings.
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Please help, I don't know how to do this!!!
the height of the antenna is approximately 24 meters.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
From the diagram, we see that we need to find the distance d and the height h. We can use the tangent function to find these values.
First, let's find d:
tan(θ) = h / (d + 1.51)
Rearranging, we get:
d = (h / tan(θ)) - 1.51
Next, let's find h:
tan(θ') = h / d
Substituting the expression for d that we found above, we get:
tan(θ') = h / ((h / tan(θ)) - 1.51)
Multiplying both sides by (h/tan(θ1)) - 1.51 and simplifying, we get:
h = (29 * tan(θ') * tan(θ)) / (tan(θ') - tan(θ))
Now we can plug in the values for the angles and solve for h:
h = (29 * tan(31°) * tan(17°)) / (tan(31°) - tan(17°))
h ≈ 24
So the height of the antenna is approximately 24 meters.
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Kehlani is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 24 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 20^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 41^{\circ} ∘ . If her eyes are 1.51 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
The antenna's height is 12.1 meters, as stated throughout the announcement.
What does building type mean?Building type refers to a grouping of buildings according to their purpose, location, and style that serves as the standard for evaluating and categorizing variants. Buildings must be categorized as either support, civic, commercial, industrial, or residential. Any kind of fella construction is a structural. It could be anything: a dam or a bridge, for instance. In contrast, a building is a closed construction with walls and a roof. Once more, the more precise phrase is "building," although "structure" is far more generic.
Based on the graph.
[tex]$$\begin{aligned}& \overline{O H}=\overline{C D}=1.51 \mathrm{~mm} . \\& \overline{O C}=24 \mathrm{~m} . \\& \angle O C A=20^{\circ} . \quad \angle O C B=41^{\circ} .\end{aligned}$$[/tex]
In RT [tex]$\triangle A O C_,$[/tex]
[tex]$$\begin{aligned}& \tan 20^{\circ}=\frac{A_0}{O C}=\frac{A_0}{24} \\& \text { So } A_0=\tan 20^{\circ} \times 24=8.74 \mathrm{~m}\end{aligned}$$[/tex]
In Rt ΔOBC.
[tex]$$\begin{aligned}\tan 41^{\circ} & =\frac{O B}{O C}=\frac{O B}{24} \\O B & =\tan 41^{\circ} \times 24=20.86 \mathrm{~m} .\end{aligned}$$[/tex]
[tex]A B=O B-O A=20.86-8.74=12.12 \mathrm{~m} \approx 12.1 \mathrm{~m} .[/tex]
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Answer:
12.1
Step-by-step explanation:
I got the question right
Find the measure of the central angle indicated. Lines that appear to be diameters, are diameters.
The measure of the central angle indicated is 60°.
Define central angle?The central angle of a circle is the angle that an arc takes up in the centre. The radius vectors are what make up the angle's arms.
The formula for calculating a central angle is: Central Angle = Arc length (AB) / Radius (OA) = (s 360°) / 2r, where "s" stands for arc length and "r" for circle radius.
Now here in the given diagram,
Let x equal the desired angle.
The central angle that we need to find is:
Now x = 360-120-(90+90)
⇒ x = 360-300
⇒ x = 60°
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What is the expression written using each base only once? 48 x 43 O A 411 O B. 1211 O C. 424 O D. 6411
The expression written using each base only once is 4¹¹ , the correct option is (a).
The expression 4⁸×4³ can be simplified using the rule of exponents,
The rule of exponents states that when we multiplying two exponential expressions with the same base, the exponents gets added.
which means that, nᵃ×nᵇ = nᵃ⁺ᵇ;
In this case the expression is: 4⁸×4³ , it has common base as "4",
So, by the rule of exponents, the power(exponents) gets added up ;
The expression "4⁸×4³" can be rewritten as 4⁸⁺³, which is equal to 4¹¹,
Therefore, Option(a)4¹¹, is the expression written using each base only once.
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The given question is incomplete, the complete question is
What is the expression written using each base only once? 4⁸×4³
(a) 4¹¹
(b) 12¹¹
(c) 4²⁴
(d) 64¹¹.
How do you find the scale factor of a shape. For common core? And what is the sequence of transformations?
The process to find the scale factor of a shape and the concept of sequence of transformations is explained below.
In order to find the scale factor of a shape, we need to compare the corresponding side lengths of the original shape to the corresponding side lengths of the new shape after a dilation.
The scale factor is the ratio of any two corresponding side lengths.
The sequence of transformations is defined as the order in which different transformations are applied to a shape.
For example, if we have a triangle and we first translate it, then rotate it, and then dilate it, the sequence of transformations would be : translate → rotate → dilate.
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The given question is incomplete, the complete question is
How do you find the scale factor of a shape? And What is the sequence of transformations?
The table below shows how much Eloise spent on ribbon at two different shops. What is the difference in the price of 300cm of ribbon between shop A and shop B? Give your answer in pounds (£).
The difference in price of both the shops is £0.25.
What is price?
Price is the amount of money one pays for a good or service. It is determined by a variety of factors, such as supply and demand, the cost of production, and the availability of resources. Prices are also affected by government regulations, taxes, inflation, and other economic and market forces. The price of a product or service is an important factor in determining whether consumers will purchase it or not.
Shop A | Shop B
200 cm | £0.50 | 300 cm | £0.75
The difference in the price of 300cm of ribbon between shop A and shop B is £0.25. Eloise spent £0.50 on 200cm of ribbon at shop A, and £0.75 on 300cm of ribbon at shop B. Therefore, the difference in price is £0.25.
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Mary has 7.2 yards of cloth. She uses 3.25 yards. She claims that she has 4.5 yards of cloth left. Do you agree?
How do u do this question
yes or no. Mary has 3.95,4.5, or 10.45 yards left.
Answer:
Step-by-step explanation:
jkhnb and then efhrfehnb c3454k3
8. An escalator in a mall must lift customers to a height of 22 ft. If
angle between the escalator stairs and the ground floor will be 30°, what will be the
length of the escalator?
The length of the escalator, considering the trigonometric ratios, is of
38.1 ft.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the angle of 30º, we have that:
The adjacent side is the length.The opposite side is of 22 ft.Hence the length of the escalator is obtained with the tangent as follows:
tan(30º) = 22/l
l = 22/tangent of 30 degrees
l = 38.1 ft.
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What is the maximum of the sinusoidal function?
Enter your answer in the box.
The maximum of the sinusoidal function is 4
How to determine the maximum of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph of the sinusoidal function
In the graph of the sinusoidal function, we can see that
The maximum is at y = 4
Also, we can see that
The minimum is at y = 1
Hence, the maximum is 4
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A Box Contains 16 Silver Counters, 8 Brown Counters And 20 Pink Counters. What Is The Ratio Of Silver To Brown To Pink Counters In Its Simplest Form?
Answer:
4 : 2 : 5
Step-by-step explanation:
To find the ratio of silver to brown to pink counters in simplest form, we need to divide the number of each type of counter by their greatest common factor.
The greatest common factor of 16, 8, and 20 is 4.
So, we divide each of the numbers by 4:
Silver counters: 16 ÷ 4 = 4
Brown counters: 8 ÷ 4 = 2
Pink counters: 20 ÷ 4 = 5
Therefore, the ratio of silver to brown to pink counters in simplest form is:
4 : 2 : 5
or
2 : 1 : 2.5 (if we prefer to express the ratio in decimal form)
hdlppppppppppp asapppp 50 points
Answer:
5
Step-by-step explanation:
a chain is attached to a pulley whose radius is 26 cm and
rotates at 38 RPM. Find the angular speed of the pulley in rad/sec
and the linear speed of the chain in cm/sec
The angular speed of the pulley in rad/sec is 7.95 rad/sec, and the linear speed of the chain in cm/sec is 495.6 cm/sec.
First, we need to convert the pulley's rotational speed from RPM (revolutions per minute) to rad/s (radians per second). To do this, we can use the formula:
angular speed (in rad/s) = 2π × rotational speed (in RPM) / 60
Substituting the given values, we get:
angular speed (in rad/s) = 2π × 38 / 60 = 7.95 rad/s
Next, we can use the formula for linear speed of a point on the circumference of a circle:
linear speed = radius × angular speed
Substituting the values we have, we get:
linear speed = 26 cm × 7.95 rad/s = 206.7 cm/s
However, this is the linear speed of the pulley's circumference. Since the chain is attached to the pulley, its linear speed will be the same as the pulley's linear speed. Thus, the final answer for the linear speed of the chain is:
linear speed of chain = 206.7 cm/s × 2.4 = 495.6 cm/s
Here, 2.4 is the gear ratio of the chain to pulley.
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what is the slope intercept for
(5,1) and (2,16)
So the slope-intercept form of the equation of the line passing through the two given points is:
y = -5x + 26
What distinguishes a linear equation?If an equation is expressed in the form y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the line passing through the two given points (5,1) and (2,16), we can use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (5,1) and (x2, y2) = (2,16)
m = (16 - 1)/(2 - 5) = -5
So the slope of the line is -5.
To find the y-intercept b, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (5,1) and the slope m = -5, we get:
y - 1 = -5(x - 5)
Simplifying this equation, we get:
y = -5x + 26
So the slope-intercept form of the equation of the line passing through the two given points is:
y = -5x + 26
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A probability distribution table is as follows Х 1 2 3 P(x) 1/6 2/3 1/6 The value of E(x^2) is____
a. 13/3
b. 4
c. 1
d. 16/3
The correct answer to this question is a. 13/3.
To find the value of E(x^2), we need to multiply each value of x by its corresponding probability and then sum the results. This can be written as E(x^2) = (1^2)(1/6) + (2^2)(2/3) + (3^2)(1/6).
Simplifying the equation gives us:
E(x^2) = (1/6) + (8/3) + (9/6) = (1/6) + (16/6) + (9/6) = (26/6) = 13/3
Therefore, the value of E(x^2) is 13/3.
In conclusion, the correct answer to this question is a. 13/3.
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Can you do Step by Steps for this problem, please.
Answer:
36.9
Step-by-step explanation:
sinJ=[tex]\frac{21}{35}[/tex]
J= [tex]sin^{-1}[/tex][tex]\frac{21}{35}[/tex]
J= 36.9
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -1, 1-i f(x) = 0 = Х 3 ?.
The polynomial f(x) of degree 3 with real coefficients and the given zeros is f(x) = x³ - x² + 4x + 2.
To find a polynomial f(x) of degree 3 with real coefficients and the given zeros, we need to use the fact that if a polynomial has a complex root, then its conjugate is also a root. This means that if 1-i is a root, then 1+i is also a root.
So, our polynomial f(x) has the following roots: -1, 1-i, 1+i.
We can write the polynomial as the product of its factors:
f(x) = (x - (-1))(x - (1-i))(x - (1+i))
Simplifying the factors:
f(x) = (x + 1)(x - 1 + i)(x - 1 - i)
Multiplying the factors:
f(x) = (x + 1)(x² - 2x + 2)
Expanding the polynomial:
f(x) = x³ - 2x² + 2x + x² - 2x + 2
Simplifying the polynomial:
f(x) = x³ - x² + 4x + 2
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The difference between the digits of a two-digit number is 1. The number itself is one more than five times the sum of its digits. If the unit digit is greater than the tens digit, find the number
Answer:
The number is → 56
Step-by-step explanation:
tens digit [tex]\Rightarrow x[/tex]
unit digit [tex]\Rightarrow y[/tex]
"The difference between the digits of a two-digit number is 1...", " ...the unit digit is greater than the tens digit..."
[tex]y-x=1 \qquad \textbf{ec.1}[/tex]
"The number itself is one more (unit) than five times the sum of its digits..."
[tex]10x+y=5(x+y)+1\\ 10x+y= 5x + 5y+1\\5x= 4y+1 \qquad \textbf{ec.2}[/tex]
we clear "y" in equation 1:
[tex]y=1+x \qquad \textbf{ec.3}[/tex]
then we substitute in equation 2:
[tex]5x=4(1+x)+1\\5x=5+4x\\\boxed{x=5}[/tex]
Finally, we substitute in equation 3:
[tex]y=1+5\\\boxed{y=6}[/tex]
With this we have solved the exercise.
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
How much of a 40% antifreeze solution must a mechanic mix with an 80% antifreeze solution if 16 gallons of a 50% antifreeze solution are needed?
The mechanic must mix 12 gallons of a 40% antifreeze solution with 4 gallons of an 80% antifreeze solution to create 16 gallons of a 50% antifreeze solution.
To find out how much of a 40% antifreeze solution must be mixed with an 80% antifreeze solution to create 16 gallons of a 50% antifreeze solution, we can use the following equation:
40% x + 80% y = 50% (16)
Where x is the amount of 40% antifreeze solution and y is the amount of 80% antifreeze solution.
We can also use the fact that the total amount of solution must equal 16 gallons:
x + y = 16
Now we can solve for one variable in terms of the other. Let's solve for x in the second equation:
x = 16 - y
And substitute this value of x into the first equation:
40% (16 - y) + 80% y = 50% (16)
Simplifying:
[tex]6.4 - 0.4y + 0.8y = 8[/tex]
0.4y = 1.6
y = 4
Now we can substitute this value of y back into the equation for x:
x = 16 - 4
x = 12
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pls help me
Let f(t) = 10 and g(t) = 65t. The distance, in miles, that a car is from a city can be modeled by f(t) + g(t), where t represents time, in hours. Riordan claims that the car is 150 miles from the city after 2 hours of driving, since (10 + 65) = 75(2) = 150. Decide if Riordan is correct. If he is correct, enter 150 below. If he is incorrect, enter the correct distance. miles
Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:
d(t) = f(t) + g(t) = 10 + 65t
So, after 2 hours of driving, the distance that the car has traveled from the city is:
d(2) = 10 + 65(2) = 10 + 130 = 140 miles
Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.
Step-by-step explanation:
Consider the following time series data: month 1 2 3 4 5 6 7 value 24 13 20 12 19 23 15 a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-week moving average for this time series. Compute mse and a fore- cast for month 8. C. Use a 5 0. 2 to compute the exponential smoothing values for the time series. Compute mse and a forecast for month 8. D. Compare the three-week moving average forecast with the exponential smoothing forecast using a 5 0. 2. Which appears to provide the better forecast based on mse? e. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller mse than what you calculated for a 5 0. 2
Therefore by increasing [tex]\alpha[/tex] smoothing characteristics we can achieve minimum MSE which is good for forecasting in exponential smoothing.
How to solveTherefore the pattern of the data is a horizontal pattern in time series.
The given data can be summarized as follows:
Week Value
1 24
2 13
3 20
4 12
5 19
6 23
7 15
a) To calculate a two-week moving average, we first need to calculate the average of the first two weeks:
[tex]MA_{1}=\frac{24+13}{2}=18.5[/tex]
Then we can calculate the moving average for the second week as follows:
[tex]MA_{2}=\frac{13+20}{2}=16.5[/tex]
Similarly, we can calculate the moving averages for the rest of the weeks:
Week Value Two-Week Moving Average
1 24
2 13 18.5
3 20 16.5
4 12 16.0
5 19 15.5
6 23 21.0
7 15 19.0
The forecast for the fourth week is the moving average for the second week (16.5), and the forecast for the fifth week is the moving average for the third week (16.0), and so on. The forecast error is the difference between the forecast value and the actual value.
Week Value Two-Week Moving Average Forecast Forecast Error
1 24
2 13 18.5
3 20 16.5
4 12 16.0 16.5 -4.5
5 19 15.5 16.0 3.0
6 23 21.0 15.5 7.5
7 15 19.0 21.0 -6.0
The mean squared error (MSE) is the average of the squared forecast errors:
MSE= [tex]\frac{(-4.5)^{2}+3^{2}+7.5^{2}+(-6)^{2}}{4}=33.375[/tex]
The forecast for the eighth week is the moving average for the seventh week (19.0).
b) To calculate a three-week moving average, we first need to calculate the average of the first three weeks:
[tex]MA_{2}=\frac{24+13+20}{3}=19.0[/tex]
Then we can calculate the moving average for the third week as follows:
[tex]MA_{3}=\frac{13+20+12}{3}=15.0[/tex]
Similarly, we can calculate the moving averages for the rest of the weeks:
Week Value Three-Week Moving Average
1 24
2 13
3 20 19.0
4 12
Read more about time series plot here:
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List the root (s) and multiplicity for each term: (2x+3)^(4)(x-10)^(2)(2x+1)^(6)
The root(s) and multiplicity for each term are:
- Root: x = -3/2, Multiplicity: 4
- Root: x = 10, Multiplicity: 2
- Root: x = -1/2, Multiplicity: 6
The root(s) and multiplicity for each term are as follows:
- The term (2x+3) has a root of x = -3/2 and a multiplicity of 4. This means that the value of x = -3/2 makes the term (2x+3) equal to zero and that this root appears 4 times in the equation.
- The term (x-10) has a root of x = 10 and a multiplicity of 2. This means that the value of x = 10 makes the term (x-10) equal to zero and that this root appears 2 times in the equation.
- The term (2x+1) has a root of x = -1/2 and a multiplicity of 6. This means that the value of x = -1/2 makes the term (2x+1) equal to zero and that this root appears 6 times in the equation.
In summary, the root(s) and multiplicity for each term are:
- Root: x = -3/2, Multiplicity: 4
- Root: x = 10, Multiplicity: 2
- Root: x = -1/2, Multiplicity: 6
Learn more about root(s)
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Someone please help me on this
Answer:
x=6
Step-by-step explanation:
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