help please and thank u

To compute the average velocity over each time interval, we use the formula: average velocity = (h(t2) - h(t1))/(t2 - t1), where h(t) is the height function.

Using the given height function, h(t) = 34t - 4.9t^2, we calculate the average velocities:
1. [3, 3.01]:
Average Velocity = (h(3.01) - h(3))/(3.01 - 3) ≈ -17.147 m/s
2. [3, 3.001]:
Average Velocity = (h(3.001) - h(3))/(3.001 - 3) ≈ -17.194 m/s
3. [3, 3.0001]:
Average Velocity = (h(3.0001) - h(3))/(3.0001 - 3) ≈ -17.199 m/s
4. [2.99, 3]:
Average Velocity = (h(3) - h(2.99))/(3 - 2.99) ≈ -17.243 m/s
5. [2.999, 3]:
Average Velocity = (h(3) - h(2.999))/(3 - 2.999) ≈ -17.205 m/s
6. [2.9999, 3]:
Average Velocity = (h(3) - h(2.9999))/(3 - 2.9999) ≈ -17.200 m/s
To estimate the instantaneous velocity at t=3, observe the average velocities as the time intervals approach t=3:
As the intervals get closer to t=3, the average velocities appear to approach -17.2 m/s. Thus, the estimated instantaneous velocity at t=3 is:
V ≈ -17.2 m/s

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Answer:

Step-by-step explanation:

The integer is 45, since integers are only whole numbers and they're negative counterparts, so even if the fraction or decimal is negative, it is not an integer because it's not a whole number. Hope that helps!

Answer:

\(45/9\\45\\14/2\)

Step-by-step explanation:

An integer is a number that can be written without a fractional component.

\(-92.67=-278/3\)

\(-6/7=-6/7\)

\(45/9=5\)

\(45=45\)

\(14/2=7\)

Answer:

C. g(x) = x^2 + 3

Step-by-step explanation:

The greatest possible number of solutions is 2

From the question, we have the following parameters that can be used in our computation:

x^2 + y^2 = 9

9x + 2y = 16

The above is a system of equations with a linear equation and a circle equation

The maximum number of times the equations in the sytem can intersect when plotted is 2

This means that the solution is a maximum of 2

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Answer:

Adults tickets sold = 321

and children tickets sold = 227

Step-by-step explanation:

Let Adults tickets are represented by x

and children tickets are represented by y

If theater sold 548 movie tickets writing it in algebraic expression we get:

Adults ticket cost $6.50 and a child’s ticket cost $3.50. In all, $2881 was taken in. Writing it in algebraic expression we get:

We need to find value of x and y

Solving the system of equations and finding value if x and y.

and

Let:

Multiply eq(1) wit 3.50 and subtract both equations

So, value of x = 321

Now finding value of y by putting value of x in eq(1)

Value of y= 227

So, Adults tickets sold = 321

and children tickets sold = 227

Keywords: Word Problems

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

plug it in and 3 divided by 12 is 4

Answer:

127.39

Step-by-step explanation:

A=lw+l(w

2)2+h2+w(l

2)2+h2=6·6+6·(6

2)2+72+6·(6

2)2+72≈127.38928

Answer:

120 cm^2

Step-by-step explanation:

steps shown in the picture.

the cat is cute btw :D

Twelve students were randomly assigned to two groups: one group experienced sleep deprivation for 24 hours, while the other group had a normal amount of sleep.

a. The independent variable in this study is the sleep condition, which has two levels: sleep deprived and normal sleep. The dependent variable is the percentage of correctly recalled numbers, measured on a continuous scale.

b. The null hypothesis for this study would state that there is no difference in immediate memory capacity between the sleep deprived and normal sleep conditions. The alternative hypothesis would suggest that sleep deprivation affects immediate memory capacity, leading to lower performance in recalling numbers.

c. To conduct a statistical test at a significance level of p = 0.05, Excel can be used to perform a t-test or an analysis of variance (ANOVA) to compare the means of the two groups and determine if there is a significant difference in immediate memory capacity.

d. The statistical conclusion would involve evaluating the p-value obtained from the statistical test. If the p-value is less than 0.05, it would indicate that there is a significant difference in immediate memory capacity between the sleep deprived and normal sleep conditions.

e. The type of statistical error that could have been made in part C is a Type I error, where the null hypothesis is rejected when it is actually true. This means concluding that there is a significant difference in immediate memory capacity when, in reality, there is no difference.

f. To obtain the 95% confidence interval, the obtained statistic (e.g., mean difference, group means) can be used along with the standard error of the statistic. This interval provides a range of values within which the true population parameter is likely to lie.

g. The confidence interval obtained in part f allows us to estimate the plausible range of values for the effect or difference in immediate memory capacity between the sleep deprived and normal sleep conditions. It provides a level of uncertainty associated with the estimate.

h. The confidence interval does not directly determine if it supports the statistical conclusion. However, if the confidence interval does not include the null value (e.g., zero difference), it would provide additional evidence in support of the statistical conclusion. If the confidence interval includes zero, it suggests that the effect size may not be statistically significant.

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Let

y -----> candle heigh in centimeters

x ----> burning time in hours

In this problem we have the ordered pairs

(5,22.5) and (17,16.5)

step 1

Find out the slope

m=(16.5-22.5)/(17-5)

m=-6/12

m=-1/2 -----> is negative because is a decreasing function

step 2

Find out the equation in slope-intercept form

y=mx+b

we have

m=-1/2

point (5,22.5)

substitute

22.5=-(1/2)(5)+b

solve for b

b=22.5+2.5

b=25

therefore

y=-(1/2)x+25

step 3

For x=7 hours

substitute in the equation

y=-(1/2)(7)+25

y=-3.5+25

Answer:

$17.08

Step-by-step explanation:

Ok, so we know it takes 61-23 = 38 minutes of call to change the credit from $22.24 to $17.68.

Basically, it takes 43 minutes to lose 22.24 - 17.68 = $4.56

38 minutes - $4.56

5 minutes - $4.56 x 5 /38 = 0.6

I took 5 minutes because 5 + 61 = 66

Now, we know it takes 61 minutes for the person to have $17.68 remaining.

So, if we had 5 minutes, it becomes 17.68 - 0.6 = $17.08 remaining.

Pls mark as brainliest if possible. Cheers

Answer: x = 20

Step-by-step explanation:

The angles are corresponding angles so they are equivalent to each other. To solve for x, we set them equal and then solve for x.

65 = 3x + 5

60 = 3x

x = 20

Answer:

the other person has it right- it's x =20

We are are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.242895 in first simulation and between 0.1948 and 0.2732 in second simulation.

A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.

A 95% confidence interval gives us a range of values that we are 95% confident contains the true proportion of wins that the new game strategy will produce in the long run. To construct the confidence interval for each simulation, we can use the following formula:

CI = p ± 1.96 * sqrt(p * (1 - p) / n)

where p is the sample proportion of wins, n is the number of trials, and 1.96 is the z-score corresponding to a 95% confidence level.

For the first simulation, p = 212 / 1000 = 0.212 and n = 1000, so the confidence interval is:

CI = 0.212 ± 1.96 * sqrt(0.212 * (1 - 0.212) / 1000)

CI = (0.1812, 0.2428)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.2428.

For the second simulation, p = 235 / 1000 = 0.235 and n = 1000, so the confidence interval is:

CI = 0.235 ± 1.96 * sqrt(0.235 * (1 - 0.235) / 1000)

CI = (0.1948, 0.2732)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1948 and 0.2732.

In general, larger sample sizes lead to narrower confidence intervals. In this case, both confidence intervals overlap, indicating that the two simulations are consistent with each other. This gives us additional confidence in the estimated proportion of wins using the new strategy.

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Answer:

the confidence interval for the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

Step-by-step explanation:

got it right on the test :)

Answer:

77.44%

49.87%

Step-by-step explanation:

If 12% leaks everyday, on the first day 12% would leak, leaving 100 - 125 = 88% of air

on the second day, 12% of 88% would leak = 0.88 x 0.12 = 0.1056

Air left on the second day = 88% - 10.56% = 77.44%

After a week = (100 - 12%)^7 = 49.87%

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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To find \((f+g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\) together. Let's start by writing down the given functions:

The sum of the functions \(f(x) = 4x^2 + 3x - 2\) and \(g(x) = 6x^3 - 3x^2 - 4\) is \((f+g)(x) = 6x^3 + x^2 + 3x - 6\). This resulting function is a cubic polynomial with coefficients that reflect the combined terms of the original functions.

\(f(x) = 4x^2 + 3x - 2\)

\(g(x) = 6x^3 - 3x^2 - 4\)

Now, let's add them together:

\((f+g)(x) = f(x) + g(x)\)

\(= (4x^2 + 3x - 2) + (6x^3 - 3x^2 - 4)\)

To simplify the expression, we combine like terms:

\((f+g)(x) = 6x^3 + 4x^2 - 3x^2 + 3x - 2 - 4\)

\(= 6x^3 + (4x^2 - 3x^2) + 3x + (-2 - 4)\)

\(= 6x^3 + x^2 + 3x - 6\)

So, the sum of the functions \(f(x) = 4x^2 + 3x - 2\) and \(g(x) = 6x^3 - 3x^2 - 4\) is \((f+g)(x) = 6x^3 + x^2 + 3x - 6\).

In other words, the resulting function (f+g)(x) is a cubic polynomial with the highest degree term of \(6x^3.\) The other terms in the polynomial are \(x^2\), 3x, and a constant term of -6.

It's important to note that this sum is valid for all values of x within the domain of the original functions f(x) and g(x), unless otherwise specified. Therefore, \((f+g)(x) = 6x^3 + x^2 + 3x - 6\) is the expression representing the sum of the functions f(x) and g(x).

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Answer:

x = 25

∠A = 148°

Explanation:

the lines are parallel lines, meaning that there are alternate angles next to ∠A and ∠B. since the line is straight, the sum of the alternate angle as well as ∠A 180°. this is also true for ∠B, so we know that ∠A and ∠B are equal.

6x - 2 = 4x + 48

(add 2 to both sides) 6x = 4x + 50

therefore, 2x = 50 and x = 25.

now, we can find ∠A by substituting 25 into the equation:

6x - 2

= 150 - 2

= 148°

i hope this helps! :D

Answer:

Step-by-step explanation:

f(x)=x^2+1

f(x^2+1)

f(x^2+1):x^4+2x^2+2

f(f(x))=x^4+2x^2+2

2nd answer

Hope this helps!^^

The correct option is C. dy/dx - y = -2sin(x).

The function y = sin(x) + cos(x) is a solution to the differential equation dy/dx - y = -2sin(x).Solution:

Given function is y = sin(x) + cos(x)

Differentiate w.r.t x, we getdy/dx = cos(x) - sin(x)

putting the value in the differential equation

Y + dy/dx - 2sin(x) = cos(x) + sin(x) + cos(x) - sin(x) - 2sin(x)= 2cos(x) - 2sin(x)

Now, checking options one by oneOption A. Y + dy/dx = 2sin(x)

Putting the value of y and dy/dx in the given equation, we getsin(x) + cos(x) + cos(x) - sin(x) ≠ 2sin(x)

So, option A is incorrectOption B.

Y + dy/dx = 2cos(x)

Putting the value of y and dy/dx in the given equation, we getsin(x) + cos(x) + cos(x) - sin(x) = 2cos(x)

Hence, option B is also incorrectOption C.

dy/dx - y = -2sin(x)

Putting the value of y and dy/dx in the given equation, we getcos(x) - sin(x) - sin(x) - cos(x) = -2sin(x)

Thus, it satisfies the given differential equation.Therefore, the function y = sin(x) + cos(x) is a solution to the differential equation dy/dx - y = -2sin(x).

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Step-by-step explanation:

BE/BC=BD/BA

tHE TWO SIMILAR TRIANGLES ARE BED AND BC. tHE PROPORTION ABOVE REPRESENTS USE OF THE TWO SIMILAR TRIANGLES.

4/(4 + 10) = 5/(5+X) Cross Multiply

4(5+x) = 5(4+10)m

20 +4x=20 +50 subtract 20 from both sides

4x = 50 divide by 4

x =12.5

Answer:

224, 755

Step-by-step explanation:

you first have to find the differnce between 177 and 47 which equals to 133.

so you have to do 94+133

and 885-133

Answer:

82 + (12 + 3 + 4) -10 = 91

82 + (12 times 3 + 4) -10 = 156

82 + (12 divided by 3 + 4) -10 = 73.71

82 + (12 - (3+4)) -10 = 77

I wasn't sure what the space between the 12 and the 3 + 4 meant so I put the answers to what it could have possibly meant.

Answer:

See explanations below

Step-by-step explanation:

Given the simultaneous equations;

2x - 3y = 9... 1

2x + y = 13 ... 2

From 2;

y = 13-2x

Substitute into 1;

2x - 3(13-2x) = 9

2x -39 + 6x = 9

8x - 39 = 9

8x = 9+39

8x = 48

x = 6

Since y  = 13-2x

y = 13-2(6)

y = 13-12

y = 1

The soluton to the system of equation is (6, 1)

Given the equations;

99x + 101y = 499; .... 1 * 101

101x + 99 y = 501 ... 2 * 99

______________

9999x + 10,201y = 50,399

9999x + 9801y = 49,599

Subtract

10201y - 9801y = 50399-49599

400y = 800

y = 2

Substitute y = 2 into 1;

From 1;

99x + 101y = 499

99x + 101(2) =499

99x +202 = 499

99x = 499 - 202

99x = 198

x = 198/99

x =2

Hence the solution is (2,2)

For the equations;

49x - 57y = 172 .... * 57

57x - 49y = 252 __ * 49

____________________

2793x -3249y =  9804

2793x - 2401y = 12348

Subtract

-3249y+2401y = 9804-12348

-848y = -2544

y = 3

Substitute into 1;

49x - 57y = 172

49x - 57(3) = 172

49x - 171 = 172

49x = 171+172

49x = 343

x = 7

Hence the solution is (7, 3)

Yes, all requirements have been satisfied for drawing conclusions from statistics. would note a reduction in stress. whether the prerequisites for inference are present.

It is common practice to start with a statistical population or a statistical model that needs to be investigated when applying statistics to a problem in science, business, or society. The field of statistics is concerned with the collection, arrangement, organization, analysis, interpretation, and presentation of data.

The conditions for making judgments about a single proportion are Random: A random experiment or sample must have produced the data. For the sample distribution of pp with hat on top to be considered normal, there must be nearly equal numbers of expected successes and failures.

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Triangles

Looking at the image, It is safe to say there are two similar triangles having similar base and sides there.

Triangle BAC has the same base as Triangle DAC

Therefore, the vertices of the angle B is equivalent to the vertice of angle D

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Answer:

y = x³ - 12x² + 41x - 30