What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd

square yards

You are 44.0 meters from the center of town, at an angle of 23° North of East. You then walk 30.0 meters at an angle of 160° North of East. The total displacement is 55.6 meters at an angle of 57.7° North of East from the center of town.

We can solve this problem using vector addition. Let's break down the two displacements into their x and y components:

Displacement 1:

Magnitude: d1 = 44.0 m

Direction: θ1 = 23° North of East

x-component: d1x = d1*cos(θ1)

y-component: d1y = d1*sin(θ1)

Displacement 2:

Magnitude: d2 = 30.0 m

Direction: θ2 = 160° North of East

x-component: d2x = d2*cos(θ2)

y-component: d2y = d2*sin(θ2)

To find the total displacement, we add the x and y components of the two displacements:

x-component: dx = d1x + d2x

y-component: dy = d1y + d2y

The magnitude of the total displacement is:

d = √(dx^2 + dy^2)

The direction of the total displacement is:

θ = tan^(-1)(dy/dx)

Substituting the values we get:

d1x = 41.69 m

d1y = 18.62 m

d2x = -11.54 m

d2y = 28.45 m

dx = d1x + d2x = 30.15 m

dy = d1y + d2y = 47.07 m

d = √(dx^2 + dy^2) = 55.6 m

θ = tan^(-1)(dy/dx) = 57.7° North of East

Therefore, you are 55.6 meters from the center of town, at an angle of 57.7° North of East.

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Using vector addition, we find that a displacement of 44.0 m at 23° N of E added to 30.0 m at 160° N of E results in a displacement of 36.14 m at 45.79° from the +x-axis.

We can use vector addition to solve this problem. The first step is to represent the two displacement vectors as Cartesian vectors, using the angle measured clockwise from the +x-axis:

Vector 1: (44.0 m, 23° North of East)

x-component = 44.0 m * cos(23°) = 40.81 m

y-component = 44.0 m * sin(23°) = 17.51 m

Cartesian vector = (40.81 m, 17.51 m)

Vector 2: (30.0 m, 160° North of East)

x-component = 30.0 m * cos(160°) = -15.22 m

y-component = 30.0 m * sin(160°) = 7.73 m

Cartesian vector = (-15.22 m, 7.73 m)

To find the resultant vector, we can add the x- and y-components:

x-component = 40.81 m - 15.22 m = 25.59 m

y-component = 17.51 m + 7.73 m = 25.24 m

The magnitude of the resultant vector is:

magnitude = sqrt((25.59 m)^2 + (25.24 m)^2) = 36.14 m

To find the angle of the resultant vector, we can use the following equation:

angle = atan(y-component / x-component)

Substituting the values, we get:

angle = atan(25.24 m / 25.59 m) = 45.79°

Therefore, the distance from the center of town is 36.14 m, and the angle with respect to the +x-axis is 45.79°.

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The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.

Substitute x = 0 into the function T(x):

T(0) = -19 + 39e^(-0.45*0).

Simplify the expression:

T(0) = -19 + 39e^0.

Since e^0 equals 1, the expression simplifies to:

T(0) = -19 + 39.

Calculate the sum:

T(0) = 20.

Therefore, the initial temperature of the soda is 20 degrees Celsius.

To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):

Substitute x = 20 into the function T(x):

T(20) = -19 + 39e^(-0.45*20).

Simplify the expression:

T(20) = -19 + 39e^(-9).

Use a calculator to evaluate the exponential term:

T(20) = -19 + 39 * 0.00012341.

Calculate the sum:

T(20) ≈ -19 + 0.00480599.

Round the answer to the nearest degree:

T(20) ≈ -19 + 1.

Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.

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INCOMPLETE QUESTION

A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.

Answer:

Step-by-step explanation: 80

Answer: THE ANSWER IS 28%

worked it out on the calculator in the end

Step-by-step explanation:

Answer:

12.3 foot i think

Step-by-step explanation:

P.S. there will be no shadow of the boy if he is standing next to the statue because the shadow of the statue will cover him

just for fun

The total surface area of the cone with the given radius and slant height in terms of pi is 70πcm².

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The total surface area of a cone is given by its curved surface area plus area of its base.

Total surface area = curved surface area + area of base

Total surface area = πrl + πr²

Given that;

Total surface area = πrl + πr²

Total surface area = ( π ×  5cm × 9cm ) + ( π × (5cm)² )

Total surface area = 45πcm² + 25πcm²

Total surface area = 70πcm²

Therefore, the total surface area of the cone with the given radius and slant height in terms of pi is 70πcm².

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Answer:

70

Step-by-step explanation:

Answer: slope is -3/2

Step-by-step explanation:

(-2,5) (4,-4)

Use the slope formula y2-y1/x2-x1

5-(-4)/-2-4 = -3/2

Answer:

The slope of the line containing (-2,5) and (4,-4) is \(-\frac{3}{2}\)

Step-by-step explanation:

Trip of 700 km required 70 liter  gasoline

For go 200 km Distance total gasoline required = 20 liter

For go 1 km Distance total gasoline required = 20÷200

                                                                          =  0.1 liter

Total trip distance =700 km

Total gasoline required for  going 700 km = Total distance×Gasoline required for 1 km

 Total gasoline required for  going 700 km  = 700×0.01                                                          

                                                                         = 70 liters

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70 liters of gasoline will be used on a trip of 700 kilometers.

Given that,

200 kilometer is covered by 20 liters of gasoline.

For go 1 km Distance total gasoline required = 20÷200

                                                                          =  0.1 liter

Now,

Let x be the liters of gasoline required for a 700-km trip.

            ⇒ 20/200 = x/700

            ⇒ (200) (x) = (20) (700)

            ⇒ 200x = 14,000

            ⇒ 200x/200 = 14,000/200

              or,  x = 70

Therefore, the answer is :

70 liters of gasoline will be needed for a 700 kilometer of trip.

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Answer:

See below.

Step-by-step explanation:

Rectangle - c = √a²+b² = √6²+12² = 13.41641, or 13.42

Square - c = √a²+b² = √6²+6² = 8.48528, or 8.49

He is incorrect. 13.42 halved is 6.71, not 8.49.

-hope it helps

Answer:

Lani saved during 12 months

Using hypothesis tests the 90% confidence interval is the true mean number of minutes that Minnesotans watch a sporting event on TV each week falls within the range of 152.342 to 157.658 minutes.

We're given a random sample of 300 Minnesotans, where X = 155 minutes and s = 28 minutes. We want to find a 90% confidence interval for the true mean number of minutes that Minnesotans watch a sporting event on TV each week.

First, we need to calculate the standard error (SE) using the formula: SE = s / √(n), where n is the sample size. Plugging in our values, we get SE = 28 / √(300) = 1.617.

Next, we need to find the critical value for a 90% confidence level using a t-distribution table with degrees of freedom (df) = n - 1 = 299. For a 90% confidence level and 299 df, the critical value is approximately 1.645.

Now we can calculate the margin of error (ME) using the formula: ME = critical value × SE. Plugging in our values, we get ME = 1.645 × 1.617 = 2.658.

Finally, we can construct the confidence interval using the formula: CI = X ± ME. Plugging in our values, we get CI = 155 ± 2.658, which simplifies to (152.342, 157.658).

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Graph the line using the slope and y-intercept, or two points.

Slope:

4

y-intercept:

(0, 6)

Answer:

45

Step-by-step explanation:

Answer:

$45

$75 minus the 60 % is $30

$75 minis the $30 the customer would pay is $45. They saved $45.

The statement is False. The residuals will not necessarily add up to 0.

The residuals from a linear regression analysis are the differences between the observed values of the dependent variable and the predicted values of the dependent variable. Therefore, the sum of the residuals will depend on the data and the model used. If the model is a perfect fit, then the sum of the residuals will be 0. However, in most cases, the model will not be a perfect fit and the sum of the residuals will not be 0. Therefore, it is not true that the residuals from a linear regression analysis on any possible dataset (with more than 1 observation) will add up to 0.

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a. The angular velocity of the ball is 1.57rad/sec

b. The angular acceleration of the bicycle is 0.23 rad/sec²

angular is the rate of change of angular distance . it is measured in rad/sec. it is represented by w. Angular acceleration is the rate of change in angular velocity with time.

angular velocity = change in angle/ time

w = 2π/t

w = 2× 3.14/4

w = 6.28/4

w = 1.57 rad/sec

angular acceleration =( final angular velocity - initial angular velocity )/time

= (4.2 - 3.5)/3

= 0.7/3

= 0.23 rad/s²

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Answer:

First, the absolute value is a function that always has a positive output.

We can write the absolute value function as:

IxI = x if x > 0 (x is positive)

IxI = - x if x < 0. (x is negative)

But what happens if x = 0?

this is because 0 is equal to +0 and -0, then we have that:

I0I = 0 = +0 = -0.

So we can actually write the absolute value function as:

IxI = x if x ≥ 0 (x is positive)

IxI = - x if x ≤ 0. (x is negative)

Answer:

13

Step-by-step explanation:

The value of standard deviation of the sample is 11.29 grams.

To calculate the standard deviation of a sample, we need to use the following formula:

s = sqrt [ Σ(xi - x)^2 / (n-1) ]

where s is the standard deviation of the sample, Σ(xi - x)^2 is the sum of the squared deviations of each data point from the sample mean, n is the sample size and x is the sample mean

To calculate the standard deviation for the weights of the 5 mice, we first need to find the sample mean:

x = (56 + 59 + 78 + 56 + 77) / 5 = 65.2

Next, we can calculate the sum of the squared deviations:

Σ(xi - x)^2 = (56 - 65.2)^2 + (59 - 65.2)^2 + (78 - 65.2)^2 + (56 - 65.2)^2 + (77 - 65.2)^2

= 82.36 + 41.64 + 156.64 + 82.36 + 147.56

= 510.56

Finally, we can calculate the standard deviation:

s = sqrt [ Σ(xi - x)^2 / (n-1) ] = sqrt [ 510.56 / (5-1) ] = sqrt [ 127.64 ] = 11.29

Therefore, the standard deviation is 11.29 grams.

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Answer:

D

Step-by-step explanation:

the hypotenuse is 6

a2 + b2 = c2

3 + b2 = 6

3(2) is 9

6(2) is 36

36-9 = 27

√27 = 3√3

Answer:fixed cost=10

Independent variable=months paid

Dependent=hours on support

month=x,h=hour,10x+35h=total cost

97.50=10+35h

87.50=35h

h=2.5 hours

Step-by-step explanation:

showed work

We can conclude that the marketing manager's claim is true.

To determine whether the marketing manager's claim is true, we need to conduct a hypothesis test.

Let p be the proportion of all children aged 8-12 who have cell phones. The marketing manager claims that p > 0.5, while the national consumers group survey found that 39/54 or p' = 0.722 have cell phones.

The null hypothesis is that the true proportion of children with cell phones is less than or equal to 0.5:

H0: p ≤ 0.5

The alternative hypothesis is that the true proportion of children with cell phones is greater than 0.5:

Ha: p > 0.5

We will conduct a one-tailed hypothesis test with a level of significance of 0.05.

Under the null hypothesis, the sample proportion follows a binomial distribution with parameters n = 54 and p = 0.5. The standard error of the sample proportion is given by:

SE = √[p(1-p)/n] = √[0.5(1-0.5)/54] = 0.070

The test statistic is calculated as:

z = (p' - p) / SE = (0.722 - 0.5) / 0.070 = 3.14

The critical value for a one-tailed test with a level of significance of 0.05 is 1.645, using the standard normal distribution table.

Since the test statistic (z = 3.14) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than half of the children aged 8-12 have cell phones.

Therefore, we can conclude that the marketing manager's claim is supported by the data from the survey.

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Answer:

1 necklace will therefore cost 34/4 = $8.5

Step-by-step explanation:

She spent between $39 and $59. let us find the average of the amount she spent = 39+59 / 2 = $49.

At an average, she spent $49.

The price of a bracelet is $5 and each bracelet costs the same amount and she bought 3 bracelets = $5 x 3 bracelets each = $15... She spent $15 on the bracelets.

Thus $49 - $15 = amount spent on the 4 necklaces = $34.

4 necklaces cost $34, 1 necklace will therefore cost 34/4 = $8.5

The equation, in slope-intercept form, is y=-70x+350

Since x is the number of years since 1995, this means that at 1995,

x=0.

This also means that in 2000, x=5.

The values of the stuffed animals were 350 in 1995 and 0 in 2000.

The formula for slope is rise over run, so we can find the answer using this mathematical expression: y²-y¹/x²-x¹.

Plugging in our values, we get 0-350/5-0 which simplifies into -350/5. This further simplifies into -70. Our slope is -70.

The definition of y-intercept is the value of y when x=0. We know that x=0 at 1995 and the value for the stuffed animals was 350 at that time. This tells us that the y-intercept is 350.

Slope-intercept form is y=mx+b, so plugging in our information, we get y=-70x+350.

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The answer to the different parts is 32/81, (x+4) ^4/81 - 1,0.5299, -0.41 and 32.

(a) For this function to be a probability density function, it must satisfy the following conditions:

It must be non-negative for all values of x.

The area under the curve must be equal to 1 over the entire range of x.

Thus, we have:

∫f(x)dx = ∫c(x+4)^3dx = 1

Applying integration by substitution, let u = x+4, so that du/dx = 1 and dx = du. Then:

∫c(x+4)^3dx = c∫u^3du = c(u^4/4) = c(x+4)^4/4

Setting this equal to 1 and solving for c, we get

c(x+4)^4/4 ∣∣ 0 to infinity = 1

Substituting infinity, we get:

c(infinity) = 0, so we must use a limit to evaluate the integral at infinity. Let L be a large number, then:

c∫0 to L (x+4)^3dx = c[(L+4)^4/4 - 4^4/4] → cL^4 as L approaches infinity.

Thus, we have:

cL^4 = 4/[(L+4)^4 - 4^4]

Taking the limit as L approaches infinity, we get:

c = 32/81.

Therefore, c = 32/81 makes this a legitimate probability density function.

(b) The cumulative distribution function (c.d.f.) of X is given by:

F(x) = ∫f(t)dt from 0 to x

   = ∫32/81(t+4)^3dt from 0 to x

   = 32/81 [(x+4)^4/4 - 4^4/4]

   = (x+4)^4/81 - 1

(c) To find the probability that the time to failure is between 2 and 5 years, we evaluate the c.d.f. at x = 5 and x = 2, and take the difference:

P(2 ≤ X ≤ 5) = F(5) - F(2)

            = [(5+4)^4/81 - 1] - [(2+4)^4/81 - 1]

            = 4101/6561 - 625/6561

            = 3476/6561

            ≈ 0.5299

(d) To find the 60th percentile of the failure time, we need to find the value x such that F(x) = 0.6. Solving for x in the equation F(x) = (x+4)^4/81 - 1 = 0.6, we get:

(x+4)^4/81 = 1.6

Taking the fourth root of both sides, we get:

x+4 = 3.59

x = -0.41

Since the time to failure cannot be negative, we must interpret the 60th percentile as being 3.59 - 4 = -0.41 years from now, i.e., it has already failed with 60% probability.

(e) The expected value of X is given by:

E[X] = ∫xf(x)dx from 0 to infinity

   = ∫32/81(x+4)^4dx from 0 to infinity

   = 32

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The probability of obtaining the number of successes indicated in problems 51–58 is 0.42.

Probability is absolutely how in all likelihood something is to happen. every time we're unsure about the final results of an occasion, we can talk about the chances of sure results—how in all likelihood they may be. The analysis of occasions ruled by using probability is called facts.

The opportunity of an event may be calculated with the aid of the opportunity formula by means of truly dividing the favorable wide variety of results by way of the overall variety of feasible effects.

Probability is the department of mathematics regarding numerical descriptions of ways possibly an occasion is to occur, or how likely it's miles that a proposition is actual. The chance of an event is more than a few between zero and 1, in which, roughly talking, 0 shows the impossibility of the event and 1 suggests fact.

Cells x doute the no of surrell and

"p' denotes the probability of turrets

D= 5

H=pkin = 50-xo-5 = 250

σ = SD(X) = √√rbg

= √√5=x05x=5 = 14.№33

The probability of obtaining $45-26

= P(-5-250 < x-M 22605-250)

14.233

= P(-03864 < 2 2 0-7332)

8.4200

0.42

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First, we can find the total number of outcomes by adding all the numbers on the table:

then, let A be the event "a randomly selected oar was purchased in 2011" and let B be the event "a randomly selected oar was not made from ash wood". Then, their probabilities are:

then, the probability that event A or B happen is:

therefore, the probability is 87/97

Answer:

This is a negative slope.

Step-by-step explanation:

When plotting the numbers on a graph, the slope goes downhill from left to right.

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)

A substitute is a good or service that buyers can quickly swap out for another. For instance, a one-dollar bill can be used in place of another dollar bill.

In business and economics, a replacement, or substitutable good, is a good or service that consumers perceive as just being substantially the same as or reasonably similar to some other good. Consumers are given options and alternatives through substitutes, which also spur competition and lower prices in the market.

Here are a few examples of replacement goods:

1. A $1 bill can be exchanged for four quarters.

2. Coke against Pepsi

3. Regular vs. premium gas

4. Butter and lard

5. Tea and coffee

6. Apples and oranges

7. Comparing driving a car to riding a bike

8. Books in general and e-books

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The correlation coefficient of points is a negative correlation.

The given coordinates are (1, 9), (2, 7), (3, 6), (4, 1), (7, -2),(8, -5) and (10, -8).

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

• A scatter plot with increasing values of both variables can be said to have a positive correlation.

• A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.

The given coordinate points are plotted on graph.

From the graph (scatter plot) we can see that, the points have a negative correlation.

Therefore, the correlation coefficient of points is a negative correlation.

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Answer: The mean score for this class is 17.13.

Step-by-step explanation:

Add up all of the scores for the boys: 78 + 58 + 79 + 45 + 39 = 249

Add the mean score for the girls: 249 + 8 = 257

Add up the number of students in the class: 10 + 5 = 15

Divide the total score by the number of students to find the mean: 257 / 15 = 17.13

What do you understand by mean and how many methods are there to find it ?

Mean is a statistical term that refers to the average value of a set of data. There are two main methods for finding the mean:

Arithmetic mean: This is the most common method of calculating the mean. It is simply the sum of all the values in the set of data, divided by the number of values in the set.

Geometric mean: This method is used when the data set includes both positive and negative values. It is the nth root of the product of all the values in the set, where n is the number of values in the set.

There are also other methods for finding the mean, such as the harmonic mean, the weighted mean, and the trimmed mean, but these are less commonly used.

To find the mean score for the entire class, we need to add up all of the scores and divide by the total number of students. First, let's start by adding up all of the scores for the boys. We have: 78+58+79+45+39 = 249

Next, let's add the mean score for the girls, which is 8.

So the total is now: 249 + 8 = 257.

Now we need to divide this total by the number of students in the class to find the mean score. There are 10 boys and 5 girls in the class, for a total of 10 + 5 = 15 students.

Therefore, the mean score for this class is :

257/15 = 17.13.

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The mean score for this class is 17.13.

Add up all of the scores for the boys: 78 + 58 + 79 + 45 + 39 = 249

Add the mean score for the girls: 249 + 8 = 257

Add up the number of students in the class: 10 + 5 = 15

Divide the total score by the number of students to find the mean: 257 / 15 = 17.13

What do you understand by mean and how many methods are there to find it?

Mean is a statistical term that refers to the average value of a set of data. There are two main methods for finding the mean:

Arithmetic mean: This is the most common method of calculating the mean. It is simply the sum of all the values in the set of data, divided by the number of values in the set.

Geometric mean: This method is used when the data set includes both positive and negative values. It is the nth root of the product of all the values in the set, where n is the number of values in the set.

There are also other methods for finding the mean, such as the harmonic mean, the weighted mean, and the trimmed mean, but these are less commonly used.

To find the mean score for the entire class, we need to add up all of the scores and divide by the total number of students. First, let's start by adding up all of the scores for the boys.

We have: 78+58+79+45+39 = 249

Next, let's add the mean score for the girls, which is 8.

So the total is now: 249 + 8 = 257.

Now we need to divide this total by the number of students in the class to find the mean score. There are 10 boys and 5 girls in the class, for a total of 10 + 5 = 15 students.

Therefore, the mean score for this class is :

257/15 = 17.13.

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Answer:

Multiplication:

4.5x = 36 or ? · 4.50 = 36

Division:

Total cost  / cost per ticket = number of tickets or 36 ÷ 4.50 = ?