Answer:
1,400
Step-by-step explanation:
its the same thing as 7 times 200
10. Determine the line of regression and use it to find the best predicted new mileage rating of a ( point) four-wheel-drive vehicle given that the old rating is 19 mi/gal old 6 27 1 33 28 24 8 22 20 29 21 New 15 24 15 29 25 22 6 20 826 19 Oy 0.808 0.863x; 18.1 mi/gal Oy = 0.863 + 0.808x; 16.2 mi/gal oy 0.863 + 0.808x; 22.4 mi/gal y-0.808+ 0.863x; 17.2 mi/gal
The line of regression equation for the mileage rating of a ( point) four wheel drive vehicle is [tex]\hat y = 16.111 + 0.365x,[/tex] and the best predicted new mileage rating of a ( point) four-wheel drive vehicle when x = 19 mi/gal, is equals to the 23.046 mi/gal. So, option(b) is right one.
A linear regression line has an equation of the form [tex]\hat y = a + bx,[/tex]
where x is the independent variable and y is the dependent variable. The slope of the line is b, and a is the estimated intercept (the value of y when x = 0). We have a table form data of old and new rating of four-wheel-drive vehicles. We have to determine the line of regression. Now, we have to calculate the value of 'a' and 'b'. Let the old and new mileage rating of four-wheel-drive vehicles be represented by vaiables 'x' and 'y'. Using the following formulas, [tex]b =\frac{ S_{xy}}{S_{xx}}[/tex] where, [tex]S_{xx} = \sum x² - \frac{ (\sum x)² }{n} [/tex]
[tex]S_{xy} = \sum xy - \frac{ (\sum y \sum x) }{n}[/tex][tex]a = \bar y - b \bar x,[/tex]where , [tex]\bar x = \frac{\sum x }{n}[/tex]
[tex]\bar y = \frac{\sum y }{n}[/tex]Here, n = 11, [tex]\sum x[/tex] = 235
[tex]\sum xy[/tex] = 263, [tex]\sum x²[/tex] = 5733, [tex]\sum xy[/tex] = 5879, so
[tex]S_{xx}[/tex] = 5733 - (235)²/11
= 5733 - 5020.454 = 712.546
[tex]S_{xy}[/tex] = 5879 - (235×263)/11
= 260.364
Now, b = 260.364/712.546 = 0.365
a = (263/11) - 0.365 ( 235/11)
= 23.909 - 7.798
= 16.111
So, regression line equation is
[tex]\hat y = 16.111 + 0.365x,[/tex]
The best predicted value of y, when x = 19 mi/gal, [tex]\hat y = 19× 0.365 + 16.111[/tex]
=23.046 mi/gal
Hence, the best predicted value is
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Complete question:
10. Determine the line of regression and use it to find the best predicted new mileage rating of a ( point) four-wheel-drive vehicle given that the old rating is 19 mi/gal
old 6 27 17 33 28 24 8 22 20 29 21
New 15 24 15 29 25 22 6 20 82 6 19
a) y cap = 0.863 + 0.808x; 16.2 mi/gal
b) y cap = 16.111 + 0.365x; 23.04 mi/gal
c) y cap =0.808+ 0.863x; 17.2 mi/gal
d) y cap = 0.808 0.863x; 18.1 mi/gal
Which equation has a focus at (–6, 12) and directrix of x = –12?
1. ) ( y - 12)^2 = 1/12 ( x + 9 )
2. ) ( y - 12 )^2 = -1/12 ( x + 9 )
3. ) ( y - 12)^2 = 12 ( x+9 )
4. ) ( y - 12)62 = -12 (x + 9 )
Answer: C
None of the given options have a focus at (-6, 12) and directrix of x = -12,so none of the option is correct.
To find the equation with a focus at (-6, 12) and directrix of x = -12, we can use the general equation for a parabola with a vertical axis of symmetry:
(y - k)^2 = 4p(x - h)
where (h, k) is the focus and x = h - p is the directrix.
Given the focus (-6, 12) and directrix x = -12, we can determine the value of p:
p = h - (-12) = -6 - (-12) = 6
Now, we can plug in the values of h, k, and p into the equation:
(y - 12)^2 = 4(6)(x + 6)
Simplify the equation:
(y - 12)^2 = 24(x + 6)
Now, let's compare this equation to the given options:
1. (y - 12)^2 = 1/12 (x + 9)
2. (y - 12)^2 = -1/12 (x + 9)
3. (y - 12)^2 = 12 (x + 9)
4. (y - 12)^2 = -12 (x + 9)
None of the given options match the equation we found. Therefore, none of the given options have a focus at (-6, 12) and directrix of x = -12
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Find the divergence of vector fields at all points where they are defined.
div ( (2x^2 - sin(x2)) i + 5] - (sin(X2)) k)
The divergence of the given vector field at all points where it's defined is div [tex]F = 4x - 2x × cos(x^2).[/tex]
To find the divergence of the given vector field at all points where it's defined, we will use the following terms:
divergence, vector field, and partial derivatives.
The given vector field is[tex]F = (2x^2 - sin(x^2)) i + 5j - sin(x^2) k.[/tex]
To find the divergence of F (div F), we need to take the partial derivatives of each component with respect to their
respective variables and then sum them up. So, div [tex]F = (∂(2x^2 - sin(x^2))/∂x) + (∂5/∂y) + (∂(-sin(x^2))/∂z)[/tex].
Find the partial derivative of the first component with respect to x:
[tex]∂(2x^2 - sin(x^2))/∂x = 4x - 2x × cos(x^2)[/tex] (applying chain rule).
Find the partial derivative of the second component with respect to y:
∂5/∂y = 0 (since 5 is a constant).
Find the partial derivative of the third component with respect to z:
[tex]∂(-sin(x^2))/∂z = 0[/tex] (since there is no z variable in the component).
Sum up the partial derivatives:
[tex]div F = (4x - 2x × cos(x^2)) + 0 + 0 = 4x - 2x × cos(x^2).[/tex]
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Urgenttttt what is true about the series given: 25+5+1+...
the series converges to 31.25 the series diverges .
the series converges to 125
the series does not converge or diverge .
The statement "the series converges to 31.25" is true about the given series.
Given series is 25 + 5 + 1 + ....
We can clearly see that given series is infinite geometric series.
First term is a=25
common ratio is r = 5/25
= 1/5
We know that the formula of sum of an infinite geometric series is
S = a / (1 - r)
S = 25 / (1 - 1/5)
S = 25/(4/5)
S = (25*5)/4
S = 125/4
S = 31.5
Therefore, the sum of the infinite geometric series is 31.25.
Since, the sum of the series is a finite number, we can say that the series converges.
Therefore, the statement "the series converges to 31.25" is true about the given series.
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People were asked if they were considering changing what they eat.29% of the people asked said yes.of these, 23% said they were considering becoming vegetarian.what percentage of the people asked said they were considering becoming vegetarian?
Answer:
66.7%
Step-by-step explanation:
Let people asked bye x.
Then, people considering to change = 29% of x
People considering to become vegetarians = 23% of (29% of x)
= 23/100 * 29x/100
= 667x/10000
Percentage of people considering to become vegetarians = 667x/10
= 66.7%
Charity can make 36 cupcake in 45 minutes. If she continues at this rate, how many cupcakes can she make in 8 hours?
a. 280 cupcakes b. 384 cupcakes c. 360 cupcakes d. 300 cupcakes
The total number of cupcakes charity can make in 8 hours is 384
The total number of cupcakes she can make in 45 minutes is 36
Cupcakes she can make in 1 minute = 36/45
Cupcakes she can make in 1 minute = 0.8
Cupcakes she can make in 8 hours
We will convert hours into minutes
1 hour = 60 min
8 hour = 8 × 60 min
8 hour = 480 min
Cupcakes she can make in 8 hours that is 480 min = 480 × 0.8
Cupcakes she can make in 8 hours = 384
Total number of cupcakes she can make is 384
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Louise stops at the gift store to buy a souvenir of the statue of liberty. the original height of the statue is 151 ft. if a scale factor of 1in = 20 ft is used to design the souvenir, what is the height of the replica?
The height of the replica souvenir is approximately 7.55 inches.
To find the height of the replica souvenir of the Statue of Liberty, we'll use the given scale factor of 1 inch = 20 feet. The original height of the statue is 151 feet. Divide the original height by the scale factor:
151 ft / 20 ft/in = 7.55 inches
The height of the replica souvenir is approximately 7.55 inches.
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1. A company is testing a new energy drink. Volunteers are asked to rate their energy one hour
after consuming a beverage. Unknown to them, some volunteers are given the real energy
drink and some are given a placebo-a drink that looks and tastes the same, but does not have
the energy-producing ingredients. Show your work using the following list of random digits to
assign each participant listed either the real drink or the placebo.
69429 86140 11625 87049 23167
Volunteer
Abby
Barry
87524 24575 87254 97801 82231
Callie
Dion
Ernie
Falco
Garrett
Hallie
Indigo
Jaylene
Real or Placebo
2. The local water authority has received complaints of high levels of iron in the drinking water.
They decide to randomly select 20 houses from each subdivision of 100 houses to visit and test
their water. Describe how to use random numbers to select the 20 houses in each division.
3. A couple is willing to have as many children as necessary to have two girls.
a) Describe a simulation that can be performed to estimate the average number of children
required to have two girls.
If two fair dice are rolled, what is the probability that the total showing is either even or less than five? 5.
these are the choices:
a. 5/9
b. 17/36
c. 19/36
d. 11/18
If two fair dice are rolled, the probability that the total showing is either even or less than five is 17/36. The correct answer is B.
There are 36 possible outcomes when rolling two dice, since each die has 6 possible outcomes.
To find the probability that the total showing is either even or less than five, we can first find the probability that the total showing is even, and then add to that the probability that the total showing is less than five, excluding the outcomes where the total showing is even.
To find the probability that the total showing is even, we can consider the following possibilities:
both dice show even numbers (probability 1/4)
both dice show odd numbers (probability 1/4)
So the probability of rolling an even total is 1/4 + 1/4 = 1/2.
To find the probability that the total showing is less than five, excluding the outcomes where the total showing is even, we can consider the following possibilities:
the two dice show 1 and 1 (probability 1/36)the two dice show 1 and 2 (probability 1/18)the two dice show 2 and 1 (probability 1/18)the two dice show 1 and 3 (probability 1/12)the two dice show 3 and 1 (probability 1/12)the two dice show 2 and 2 (probability 1/9)the two dice show 1 and 4 (probability 1/9)the two dice show 4 and 1 (probability 1/9)the two dice show 3 and 2 (probability 1/6)the two dice show 2 and 3 (probability 1/6)the two dice show 1 and 5 (probability 1/6)the two dice show 5 and 1 (probability 1/6)the two dice show 4 and 2 (probability 1/6)the two dice show 2 and 4 (probability 1/6)So the probability of rolling a total less than five, excluding the outcomes where the total showing is even, is 1/36 + 1/18 + 1/18 + 1/12 + 1/12 + 1/9 + 1/9 + 1/9 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 11/36.
Therefore, the probability that the total showing is either even or less than five is 1/2 + 11/36 = 17/36.
So the correct answer is (b) 17/36.
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Evaluate the integral by making an appropriate change of variables. Sle 9e2x + 2y da, where R is given by the inequality 2[x] + 2 y = 2
Using the change of variables u = x and v = x + y, we transform the given region R into a rectangle S, and evaluate the integral as 9 (e^6 - 2e^4 + e^2 - 1).
We need to find a change of variables that maps the region R onto a rectangle in the uv-plane. Let's make the following substitutions
u = x
v = x + y
Then, the region R is transformed into the rectangle S defined by 0 ≤ u ≤ 1 and 0 ≤ v ≤ 2.
To find the limits of integration in the new variables, we can solve the equations 2[x] + 2y = 2 for x and y in terms of u and v
2[x] + 2y = 2
2u + 2v - 2[x] = 2
[x] = u + v - 1
Since [x] is the greatest integer less than or equal to x, we have
u + v - 1 ≤ x < u + v
Also, since 0 ≤ y ≤ 1, we have
0 ≤ x + y - u ≤ 1
u ≤ x + y < u + 1
u - x ≤ y < 1 + u - x
Now we can evaluate the integral using the new variables
∫∫R 9e^(2x+2y) dA = ∫∫S 9e^(2u+2v) |J| dudv
where J is the Jacobian of the transformation, given by
|J| = det [[∂x/∂u, ∂x/∂v], [∂y/∂u, ∂y/∂v]]
= det [[1, 1], [-1, 1]]
= 2
Therefore, the integral becomes
∫∫S 9e^(2u+2v) |J| dudv = 2 ∫0^1 ∫0^2 9e^(2u+2v) dudv
= 2 ∫0^1 [9e^(2u+2v)/2]_0^2 dv
= 2 ∫0^1 (9/2)(e^(4+2v) - e^(2v)) dv
= 2 (9/2) [(e^6 - e^2)/2 - (e^4 - 1)/2]
= 9 (e^6 - 2e^4 + e^2 - 1)
Therefore, the value of the integral is 9 (e^6 - 2e^4 + e^2 - 1).
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Refer to the data in exercise 2. should sarah use the mean or the median to show that she exercises for large amounts of time each day? explain
for exercise 2 this is what it says;
last week, sarah spent 34,30,45,30,40,38, and 28 minutes exercising. find the mean, median, and mode. round to the nearest whole number
The mean is 35 minutes and the median is 34 minutes.
let's first calculate the mean, median, and mode for Sarah's exercise times: 34, 30, 45, 30, 40, 38, and 28 minutes.
Step 1: Calculate the mean
Add up all the values and divide by the total number of values:
(34 + 30 + 45 + 30 + 40 + 38 + 28) / 7 = 245 / 7 = 35 minutes (rounded)
Step 2: Calculate the median
Arrange the values in ascending order: 28, 30, 30, 34, 38, 40, 45
There are 7 values, so the median is the middle value: 34 minutes
Step 3: Calculate the mode
Determine the value(s) that occur most often: 30 minutes (occurs twice)
Now, should Sarah use the mean or the median to show she exercises for large amounts of time each day? The mean is 35 minutes and the median is 34 minutes. Both values are close and represent the central tendency of the data. However, since the mean is slightly higher than the median, Sarah should use the mean (35 minutes) to show she exercises for a larger amount of time each day.
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Find the values of U and d for an arithmetic sequence with U20 = 100 and U25 = 115.
The values of U and d for an arithmetic sequence with U20 = 100 and U25 = 115 is U = 43 and d = 3.
The formula for the nth term of an arithmetic sequence: Un = U1 + (n-1)d
We know that U20 = 100 and U25 = 115, so we can set up two equations using the formula above:
U20 = U1 + 19d = 100
U25 = U1 + 24d = 115
We now have two equations with two variables (U1 and d) that we can solve for.
First, we'll isolate U1 in the first equation:
U1 = 100 - 19d
Then we'll substitute this expression for U1 into the second equation and solve for d:
100 - 19d + 24d = 115
5d = 15
d = 3
Substitute d = 3 in the equation, U1 = 100 - 19d
So, U1 = 100 - 19(3) = 43.
Therefore, the values of U and d for the arithmetic sequence are U= 43 and d = 3.
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Question
The figure is made up of a rectangle, 2 right triangles and a 3rd triangle.
What is the area of the figure?
Responses
46 in2
136 in2
34 in, 2
52 in2
The area of the polygon composed of rectangles and triangle is 52 in²
What is area?Area is the amount of space occupied by a two dimensional shape or object.
For the first right triangle:
base = 2 in, height = 6 in
Area of first right triangle = 1/2 * base * height = 0.5 * 2 in * 6 in = 6 in²
For the second right triangle:
base = 2 in, height = 6 in
Area of second right triangle = 1/2 * base * height = 0.5 * 2 in * 6 in = 6 in²
For the triangle:
base = (2 + 4 + 2) = 8 in, height = 4 in
Area of triangle = 1/2 * base * height = 0.5 * 8 in * 4 in = 16 in²
For the rectangle:
length = 4 in, width = 6 in
Area of rectangle = length * width = 4 in * 6 in = 24 in²
Area of polygon = 6 + 6 + 16 + 24 = 52 in²
The area of the polygon is 52 in²
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Calcula el trabajo realizado al elevar 75cm sobre el piso unas
pesas de 90 kg
The work done to lift a 90 kg weight by 75 cm is approximately 661.5 joules.
How to calculate work?Para calcular el trabajo realizado al elevar una pesa de 90 kg a una altura de 75 cm sobre el piso, necesitamos conocer la fuerza necesaria para levantar la pesa y la distancia que recorre la pesa para llegar a su altura máxima.
El trabajo se define como la energía necesaria para mover un objeto a través de una distancia determinada, y se calcula como el producto de la fuerza aplicada y la distancia recorrida.
En este caso, la fuerza necesaria para levantar la pesa es igual a su peso, que se calcula como su masa multiplicada por la aceleración debido a la gravedad (9.8 m/s²):
peso = masa x gravedad
= 90 kg x 9.8 m/s²
= 882 N
La distancia que recorre la pesa para elevarse 75 cm (o 0.75 m) es:
distancia = 0.75 m
Por lo tanto, el trabajo realizado al elevar la pesa es:
trabajo = fuerza x distancia
= 882 N x 0.75 m
= 661.5 J
Por lo tanto, se requiere un trabajo de 661.5 J para elevar una pesa de 90 kg a una altura de 75 cm sobre el piso.
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simplify, please, and thank you!
Answer:
(3x+4) ÷ (x+6)
Step-by-step explanation:
3x²-14x-24 = (3x+4) (x-6)
x²-36 = (x+6) (x-6)
= (3x+4) (x-6) ÷ (x+6) (x-6)
Eliminate the (x-6)
= (3x+4) ÷ (x+6)
In a recent Game Show Network survey, 30% of 5000 viewers are under 30. What is the margin of error at the 99% confidence interval? Using statistical terminology and a complete sentence, what does this mean? (Use z*=2. 576)
Margin of error:
Interpretation:
The margin of error at the 99% confidence interval is 1.39%. Interpretation: we can be 99% confident that the true proportion of viewers under 30 in the population falls within the range of 30% ± 1.39%.
To calculate the margin of error at the 99% confidence interval, we can use the formula:
Margin of error = z* × √(p × (1 - p) / n)
where z* is the critical value (2.576 for a 99% confidence interval), p is the sample proportion (0.30), and n is the sample size (5000).
Margin of error = 2.576 × √(0.30 × (1 - 0.30) / 5000) ≈ 0.0139 or 1.39%
The interpretation of this result is that we can be 99% confident that the true proportion of viewers under 30 in the population falls within the range of 30% ± 1.39%. In other words, if we were to conduct the survey multiple times, we would expect the proportion of viewers under 30 to fall within this interval 99 out of 100 times. This information is useful for understanding the level of uncertainty in the survey results and can help guide decision-making based on the findings.
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➡) Which ratios have a unit rate of 3? Choose ALL that apply. 2 cups : 2 3 cup 3³14 3- cups: 2 cups 4 2 3 cup: 1 cup 1 1 cup: cup 15 K 1 2 cups cup 2 15 2 5 6 1 cups: 22 2 cups
The ratios that have a unit rate of 3 include the following:
A. 15/2 cups: 2 1/2 cups
C. 2 cups: 2/3 cups
F. 2 1/2 cups: 5/6 cups
What is the unit rate?In Mathematics, the unit rate is sometimes referred to as unit ratio and it can be defined as the quantity of material that is equivalent to a single unit of product or quantity.
15/2 cups : 5/2 cups
15/2 ÷ 5/2 : 5/2 ÷ 5/2
15/2 × 2/5 : 1
3 : 1 (True)
1 cup: 1/4 cups
1 × 4 : 1/4 × 1
4 : 1 (False)
2/3 cups: 1 cup
2/3 × 3/2 : 1 × 3/2
1 : 3/2 (False)
3 3/4 cups: 2 cups
(4 × 3 + 3)/4 : 2
15/4 : 2
15/8 : 2/2
15/8 : 1 (False).
2 cups: 2/3 cups
2 × 3/2 : 2/3 × 3/2
3 : 1 (True).
2 1/2 cups: 5/6 cups
(2 × 2 + 1)/2 : 5/6
5/2 : 5/6
5/2 × 6/5 : 5/6 × 6/5
3 : 1 (True).
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Complete Question:
Which ratios have a unit rate of 3? Choose all that apply.
15/2 cups: 2 1/2 cups
1 cup: 1/4 cups
2/3 cups: 1 cup
3 3/4 cups: 2 cups
2 cups: 2/3 cups
2 1/2 cups: 5/6 cups
Garden plots in the Portland Community Garden are rectangles limited to 45 square meters. Christopher and his friends want a plot that has a width of 7.5 meters. What length will give a plot that has the maximum area allowed?
The length that will give a plot with the maximum area allowed is 6 meters.
To find the length that will give a plot with the maximum area, we need to use the formula for the area of a rectangle, which is A = lw, where A is the area, l is the length, and w is the width. In this case, we are given that the area is 45 square meters, and the width is 7.5 meters.
Substituting these values into the formula, we get:
45 = l(7.5)
To solve for l, we divide both sides by 7.5:
l = 45/7.5
Simplifying, we get:
l = 6
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ayuda porfa nose como se hace :'((((((((((((
esta es la fórmula: y=a(x-h)²+k
The quadratic function in vertex form is y = (8/9)(x - 5)^2 + 7
Calculating the quadratic function in vertex formThe vertex form of a quadratic function is given by:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
In this case, we are given that the vertex is (5, 7), so we can write:
y = a(x - 5)^2 + 7
To find the value of a, we can use one of the points on the parabola.
Let's use the point (2, 15):
15 = a(2 - 5)^2 + 7
8 = 9a
a = 8/9
Substituting this value of a into the equation above, we get:
y = (8/9)(x - 5)^2 + 7
Therefore, the quadratic function in vertex form is y = (8/9)(x - 5)^2 + 7
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Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a
20
%
20%20, percent chance of winning each game and that Cam has a
50
%
50%50, percent chance of winning each game.
Based on the information provided, the probability that Ben wins the board game is 30%.
What is the probability for Ben to win the board game?To calculate the probability of Ben winning the board game, let's start by checking the information provided:
Probability for Justin to win: 20% or 0.2
Probability for Cam to win: 50% or 0.5
Now, the total probability is always equivalent to 100% or 0.1. Based on this, let's calculate now the probability that Ben wins the game.
1 - (0.2 + 0.5)
1 - 0.7 = 0.3
Note: Here is the complete question:
Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a %20 percent chance of winning each game and that Cam has a %50 percent chance of winning each game. What is the probability that Ben will win the board game?
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The table shows the amount of time, in minutes, it takes to walk a given distance, in miles, along each path. complete the table to show the average walking rate, in miles per hour, for each path. path distance (mi) time (min) walking rate (mph) a 0.5 12 b 1.5 45 с 0.75 15
The average walking rate for Path A is 2.5 mph, path B's is 2 mph and path C's is 3 mph.
Average walking rate = distance/time
for path A = 0.5/12 = 0.0416 mpm
To convert miles per meter into miles per hour it we will multiply the equation by 60 because 1 hour has 60 min
so, for path A = 0.0416 × 60 = 2.5 mph
Similarly , for path B = (1.5/45) × 60 = 2 mph
For path C = (0.75/15)×60 = 3 mph
Table to show the average walking rate
Path Distance(mi) Time(min) Walking rate (mph)
A 0.5 12 2.5
B 1.5 45 2
C 0.75 15 3
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An artist buys 2 liters of paint for a project. When he is done with the project, he has 350 milliliters of the paint left over. The paint costs 2¢ per milliliter. How many dollars’ worth of paint does the artist use for the project?
The artist used a total of $0.33 worth of paint for the project.
The artist purchased 2 liters of paint, which is equivalent to 2,000 milliliters of paint. This amount of paint was used to complete a project, and after the project was finished, there were 350 milliliters of paint left over.
To determine how much paint was used for the project, we subtract the amount of leftover paint from the total amount of paint purchased, which gives us 2,000 - 350 = 1,650 milliliters of paint used for the project.
The cost of the paint is 2 cents per milliliter, which is equivalent to $0.02/100 milliliters or $0.0002 per milliliter. To determine the cost of the paint used for the project, we multiply the amount of paint used by the cost per milliliter.
Therefore, the cost of 1,650 milliliters of paint used for the project can be calculated by multiplying 1,650 milliliters by $0.0002 per milliliter, which gives us $0.33.
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A telephone pole has a wire attached to its top that is anchored to the ground. the distance from the bottom of the pole to the anchor point is
69 feet less than the height of the pole. if the wire is to be
6 feet longer than the height of the pole, what is the height of the pole?
A telephone pole has a wire attached to its top that is anchored to the ground then conclude the height of the pole is approximately 51.53 feet.
Let h be the height of the pole. The equation h = (h - 69) + 6 represents the given information. Solving it gives h = 75.
Let's denote the height of the pole as "h". Then, according to the problem, the distance from the bottom of the pole to the anchor point is 69 feet less than the height of the pole, which means it is h - 69. Additionally, the wire is to be 6 feet longer than the height of the pole, so its length is h + 6.
Now we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the wire) is equal to the sum of the squares of the lengths of the other two sides (in this case, the height of the pole and the distance from the bottom of the pole to the anchor point). So we have:
(h - 69)^2 + h^2 = (h + 6)^2
Expanding and simplifying, we get:h^2 - 138h + 4761 + h^2 = h^2 + 12h + 36
Rearranging and simplifying, we get:h^2 - 75h - 1602 = 0
We can solve for h using the quadratic formula:h = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -75, and c = -1602.
Plugging in these values, we get:h = (75 ± sqrt(75^2 - 4(1)(-1602))) / 2(1)
h ≈ 51.53 or h ≈ -31.53
Since the height of the pole cannot be negative, we can ignore the negative solution and conclude that the height of the pole is approximately 51.53 feet.
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Which correctly describes how to graph the equation shown below?
y=1/4x
Start with a point at (1, 4). Then go up 1 and 4 to the right.
Start with a point at (1, 4). Then go up 4 and 1 to the right.
Start with a point at (0, 0). Then go up 4 and 1 to the right.
Start with a point at (0, 0). Then go up 1 and 4 to the right.
The statement which correctly describes how to graph the equation shown above include the following: Start with a point at (0, 0). Then go up 1 and 4 to the right.
What is a translation?In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics and Geometry, the translation a geometric figure upward simply means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image;
g(x) = f(x) + N
g(x) = y = 1/4(x)
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Your answer should be in the form p(x) +k/x+2 where p is a polynomial and k is an integer of x^2 +7x+12/x+2
p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:
x + 5 + 2 / (x + 2)
To express the given expression x^2 + 7x + 12 / (x + 2) in the form p(x) + k / (x + 2), we will perform polynomial division.
1. Divide the numerator (x^2 + 7x + 12) by the denominator (x + 2):
(x^2 + 7x + 12) ÷ (x + 2)
2. Perform long division:
x + 5
________________
x + 2 | x^2 + 7x + 12
- (x^2 + 2x)
________________
5x + 12
- (5x + 10)
________________
2
3. Write the result:
p(x) + k / (x + 2) = x + 5 + 2 / (x + 2)
So, p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:
x + 5 + 2 / (x + 2)
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Find the linearization of the function f (x, y) = √x^2 + y^2 at the point (3, 4), and use it to approximate f (2.9, 4.1).
Therefore, the linearization predicts that f(2.9, 4.1) is approximately 4.142.
To find the linearization of the function f(x, y) = √x^2 + y^2 at the point (3, 4), we need to find the partial derivatives of f with respect to x and y, evaluate them at (3, 4), and use them to write the equation of the tangent plane to the surface at that point.
First, we have:
∂f/∂x = x/√(x^2 + y^2)
∂f/∂y = y/√(x^2 + y^2)
Evaluating these at (3, 4), we get:
∂f/∂x(3, 4) = 3/5
∂f/∂y(3, 4) = 4/5
So the equation of the tangent plane to the surface at (3, 4) is:
z - f(3, 4) = (∂f/∂x(3, 4))(x - 3) + (∂f/∂y(3, 4))(y - 4)
Plugging in f(3, 4) = 5 and the partial derivatives, we get:
z - 5 = (3/5)(x - 3) + (4/5)(y - 4)
Simplifying, we get:
z = (3/5)x + (4/5)y - 1
This is the linearization of f(x, y) = √x^2 + y^2 at the point (3, 4).
To approximate f(2.9, 4.1), we plug in x = 2.9 and y = 4.1 into the linearization:
z = (3/5)(2.9) + (4/5)(4.1) - 1
z ≈ 4.142
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Find the volume and surface area of the composite figure. Give your answer in terms of π.
The figure shows a compound solid that consists of a hemisphere with a right cone on top of it. The radii of both the hemisphere and the right cone are equal to 6 centimeters. The slant of the right cone is equal to 8 centimeters.
I WILL GIVE BRAINLIST,
To find the volume and surface area of the composite figure, we need to first find the individual volumes and surface and the right cone, and then add them together.
The volume of a hemisphere with radius r is (2/3)πr^3, and the surface area is 2πr^2.
The volume of a right cone with radius r, height h, and slant s is (1/3)πr^2h, and the surface area is πr^2 + πrs.
In this case, the radius r and slant s are both 6 cm, and the height h of the cone can be found using the Pythagorean theorem: h = √(s^2 - r^2) = √(8^2 - 6^2) = √28 ≈ 5.29 cm.
So, the volume of the hemisphere is (2/3)π(6 cm)^3 = 72π/3 = 24π cubic cm, and the surface area is 2π(6 cm)^2 = 72π square cm.
The volume of the right cone is (1/3)π(6 cm)^2(5.29 cm) = 62.83π/3 ≈ 20.94π cubic cm, and the surface area is π(6 cm)^2 + π(6 cm)(8 cm) = 36π + 48π = 84π square cm.
Therefore, the total volume of the composite figure is 24π + 20.94π = 44.94π cubic cm, and the total surface area is 72π + 84π = 156π square cm.
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an object that weighs 200 pounfs is on an invline planethat makes an angle of 10 degrees with the horizontal
The component of the weight parallel to the inclined plane is approximately 34.72 pounds, and the component perpendicular to the inclined plane is approximately 196.96 pounds.
To analyze the situation, we need to break down the weight of the object into its components parallel and perpendicular to the inclined plane.
Given:
Weight of the object = 200 pounds
Angle of the inclined plane with the horizontal = 10 degrees
First, we find the component of the weight parallel to the inclined plane. This component can be determined using trigonometry:
Component parallel to the inclined plane = Weight * sin(angle)
Component parallel to the inclined plane = 200 pounds * sin(10 degrees)
Component parallel to the inclined plane ≈ 200 pounds * 0.1736
Component parallel to the inclined plane ≈ 34.72 pounds
Next, we find the component of the weight perpendicular to the inclined plane:
Component perpendicular to the inclined plane = Weight * cos(angle)
Component perpendicular to the inclined plane = 200 pounds * cos(10 degrees)
Component perpendicular to the inclined plane ≈ 200 pounds * 0.9848
Component perpendicular to the inclined plane ≈ 196.96 pounds
Therefore, the component of the weight parallel to the inclined plane and the component perpendicular to the inclined plane is approximately 34.72 pounds and 196.96 pounds respectively.
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A store has two large vats of juice
containing a total of 28 gallons of juice.
One-eighth of container A is orange juice.
Three-fourths of container B is orange
juice. Together the two containers hold 11
gallons of orange juice. Which system of
equations can be used to determine a and
b, the total amounts of juice, in gallons, in
containers A and B?
F
H
+
b = 11
a
a + b 28
a + b = 28
320
b = 28
J
+ b = 28
4
a + b = 11
a + b = 11
The system of equations can be used to determine the gallons of juice in container A and the gallon of juice in container B is A + B = 28 and A + 6B = 88
Total amount of juice in both the vats is 28
Let the first container = A
second container = B
A + B = 28
Orange juice in A = 1/8 of A
Orange juice in B = 3/4 of B
Total orange juice in container A and B = 11
(1/8)A + (3/4)B = 11
A + 6B = 88
Hence the two equations will be A + B = 28 and A + 6B = 88
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Evaluate the integral (Use symbolic notation and fractions where needed. Use for the arbitrary constant. Absorb into C as much as possible.) 3x + 6 2 1 x 0316 - 3 dx = 11 (3) 3 27 In(x - 1) 6 + Sin(x-3) 6 +C Incorrect
To evaluate the integral of (3x+6)/(2x²-3)dx, we can use partial fraction decomposition:
(3x+6)/(2x²-3) = A/(x-√(3)/2) + B/(x+√(3)/2)
Multiplying both sides by the denominator and simplifying, we get:
3x+6 = A(x+√(3)/2) + B(x-√(3)/2)
Setting x = √(3)/2, we get:
3√(3)/2 + 6 = B(√(3)/2-√(3)/2) = 0
So B = -2√(3). Setting x = -√(3)/2, we get:
-3√(3)/2 + 6 = A(-√(3)/2+√(3)/2) = 0
So A = 2√(3). Therefore, we have:
(3x+6)/(2x^2-3) = 2√(3)/(x-√(3)/2) - 2√(3)/(x+√(3)/2)
Integrating each term, we get:
∫(3x+6)/(2x²-3)dx = 2√(3)ln|x-√(3)/2| - 2√(3)ln|x+√(3)/2| + C
where C is the arbitrary constant.
To evaluate the integral of the function 3x + 6 with respect to x, we will use the integral symbol and find the antiderivative:
∫(3x + 6) dx
To find the antiderivative, we will apply the power rule, which states that the integral of x^n is (x^(n+1))/(n+1), and the constant rule, which states that the integral of a constant is the constant times the variable:
(3 * (x^(1+1))/(1+1)) + (6 * x) + C
Simplifying the expression:
(3x²)/2 + 6x + C
Here, C is the arbitrary constant. So, the evaluated integral of 3x + 6 is:
(3x²)/2 + 6x + C
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