Please help with these 2 questions!!

To find the current when t = 0.5 s, we need to calculate the derivative of the charge function Q(t) with respect to time and evaluate it at t = 0.5. The current flowing through the wire is 5.5 amperes.

The derivative of Q(t) gives us the rate of change of charge with respect to time, which corresponds to the current flowing through the wire at any given time.

Differentiating Q(t) with respect to t, we get:

dQ/dt = 3t^2 - 4t + 6

Now, to find the current at t = 0.5 s, we substitute t = 0.5 into the derivative:

dQ/dt = 3(0.5)^2 - 4(0.5) + 6 = 1.5 - 2 + 6 = 5.5 A

Therefore, when t = 0.5 s, the current flowing through the wire is 5.5 amperes.

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Answer:

5x-20 =4x-20

5x-4x = -20+20

x= 0

a. The range of the data set is 14.

b. The sample variance is approximately 18.4857.

c. The sample standard deviation is approximately 4.3015.

a) To calculate the range, we subtract the smallest value from the largest value in the data set.

Range = Largest Value - Smallest Value

= 18 - 4

= 14

Therefore, the range of the data set is 14.

b) To calculate the sample variance, we need to find the average of the squared differences between each data point and the mean.

First, we find the mean (average) of the data set:

Mean = (13 + 15 + 8 + 18 + 12 + 11 + 4) / 7

= 81 / 7

≈ 11.5714

Next, we calculate the squared differences between each data point and the mean:

(13 - 11.5714)^2 ≈ 1.2429

(15 - 11.5714)^2 ≈ 11.9048

(8 - 11.5714)^2 ≈ 13.2857

(18 - 11.5714)^2 ≈ 41.0204

(12 - 11.5714)^2 ≈ 0.1875

(11 - 11.5714)^2 ≈ 0.3244

(4 - 11.5714)^2 ≈ 56.7449

Now, we calculate the average of these squared differences:

Sample Variance = (1.2429 + 11.9048 + 13.2857 + 41.0204 + 0.1875 + 0.3244 + 56.7449) / 7

≈ 18.4857

Therefore, the sample variance is approximately 18.4857.

c) To calculate the sample standard deviation, we take the square root of the sample variance:

Sample Standard Deviation = √(Sample Variance)

= √(18.4857)

≈ 4.3015

Therefore, the sample standard deviation is approximately 4.3015.

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Answer: measuring an angle can be done using a protractor and drawing an angle can be done with help of a scale and a compass or directly by a protractor

Step-by-step explanation:

Hope this helps you!!

Answer:

A protractor

Step-by-step explanation:

Just an easy answer!

Answer:

- \(\frac{2}{3}\) and \(\frac{3}{4}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = S(12, 9) and (x₂, y₂ ) = T(21, 3)

\(m_{ST}\) = \(\frac{3-9}{21-12}\) = \(\frac{-6}{9}\) = - \(\frac{2}{3}\)

Repeat with

(x₁, y₁ ) = S'(4, 3) and (x₂, y₂ ) = T'(7, 1)

\(m_{S'T'}\)  = \(\frac{1-3}{7-4}\) = - \(\frac{2}{3}\)

-----------------------------------------------------------

(x₁, y₁ ) = R(24, 18) and (x₂, y₂ ) = S(12, 9)

\(m_{RS}\) = \(\frac{9-18}{12-24}\) = \(\frac{-9}{-12}\) = \(\frac{3}{4}\)

Repeat with

(x₁, y₁ ) = R'(8, 6) and (x₂, y₂ ) = S'(4, 3)

\(m_{R'S'}\) = \(\frac{3-6}{4-8}\) = \(\frac{-3}{-4}\) = \(\frac{3}{4}\)

If the dividend is 872 and the quotient is 62 and remainder is 4, the divisor is equal to 14.

In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.

In Mathematics, dividend can be calculated by using this mathematical expression:

Dividend = divisor × quotient + residual

Substituting the given data points into the dividend formula, we have the following;

Dividend = divisor × quotient + residual

872 = divisor × 62 + 4

Divisor = (872 - 4)/62

Divisor = 868/62

Divisor = 14

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Complete Question;

If the dividend is 872 and the quotient is 62 and remainder is 4. What is the divisor?

Answer:

x represents the number of tickets per order and y represents the total cost of an order.

Answer:

4.3

Step-by-step explanation:

final velocity(v)= 26 m/s

time(t)= 6s

now,

Avg accleration = v/t

=26/6

=4.3

Answer:

65 passengers

At hour six, about 54 passengers will be on the boat.

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Sum of X = 15

Sum of Y = 195

Mean X = 3

Mean Y = 39

The sum of squares (SSX) = 10

The sum of products (SP) = 50

Regression Equation = ŷ = bX + a

b = SP/SSX = 50/10 = 5

a = MY - bMX = 39 - (5*3) = 24

ŷ = 5X + 24

When x = 6,

we get ŷ = 5(6) + 24 = 54

Therefore, the approximate number of passengers is 54.

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Answer:

option A is correct. this graph is a linear function

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. a is the constant term or the y intercept

Answer:

C.

Step-by-step explanation:

It is not a function at all because it does not have necessary properties of a function, it is just a graph

The expected value E(X) of a random variable X is -1.04

The expected value of a random variable is a measure of its central tendency. It represents the average value that would be obtained if the experiment or process that generates the variable is repeated many times.

To find the expected value of a discrete random variable X with probability distribution P(X), we multiply each possible value of X by its corresponding probability and then sum these products. Symbolically, this can be written as:

E(X) = Σ[x * P(X)]

In words, this formula says that we take each possible value of X, multiply it by its probability, and then add up these products to get the expected value.

In the given problem, we are given the probability distribution of X and asked to find its expected value. We can use the formula above to do this, by plugging in the values of x and P(X):

E(X) = (-9 * 0.16) + (-7 * 0.11) + (-5 * 0.14) + (-3 * 0.17) + (-1 * 0.10) + (1 * 0.32)

E(X) = -1.04

Therefore, the expected value of X is -1.04.

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The exponential function that would give the population after t years is given by:

\(P(t) = 100 \times 2^{\frac{t}{9}}\)

An exponential function is modeled by:

\(y = ab^{\frac{x}{n}}\)

In which:

Considering that the population starts with 100 individuals and doubles every 9 years, the parameters are given as follows:

a = 100, b = 2, n = 9.

Hence the function is given by:

\(P(t) = 100 \times 2^{\frac{t}{9}}\)

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Answer:100 x 2 t/9

Step-by-step explanation:

In order to determine if the ball reaches the 24 ft, replace h = 24 and solve the quadratic equation. If the solutions are real, then, the ball does reach 24ft.

Proceed as follow:

h = 16t² + 36t + 6

24 = 16t² + 36t + 6

16t² + 36t + 6 - 24 = 0

16t² + 36t - 18 = 0

use he quadratic formula, given by:

In this case, a = 16, b = 36 and c = -18

negative times do not have physical meanning, then, the available solution is

t = 0.42

Hence, you can conclude that the ball reaches 24 ft for a time of 0.42 seconds.

Answer:

0.009652 or 9.652×\(10^{-3}\)

Step-by-step explanation:

Answer:

Y = 3/4X - 3/2

Step-by-step explanation:

3X - 4y =6

3X - 6 =4Y

Y = 3/4X - 3/2

The value of Y for the expression 3x - 4y = 6 will be Y = 3/4X - 3/2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is 3x - 4y = 6. The value for y will be calculated as,

3X - 4y =6

Rearrange the above equation and solve for Y,

3X - 6 =4Y

Y = 3/4X - 3/2

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What is the answer?

here is the image

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image.

From the diagram:

Scale factor = A'B' / AB = 6/3 = 2

Center = (6, -6)

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

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Answer:

(C)(5,9.2)

Step-by-step explanation:

Given points Q(2, 5) and R(7, 12). We are to determine the coordinate of point P that lies along the directed line segment which partitions the segment in the ratio of 3 to 2.

For internal division of a line segment, the coordinate of the point which partitions the segment in the ratio m:n is given as:

\(\left(\dfrac{mx_2+nx_1}{m+n} , \dfrac{my_2+ny_1}{m+n}\right)\)

m:n =3:2

\((x_1,y_1)=Q(2,5)\\(x_2,y_2)=R(7,12)\)

Therefore:

\(P(x,y)=\left(\dfrac{3*7+2*2}{3+2} , \dfrac{3*12+2*5}{3+2}\right)\\=\left(\dfrac{25}{5} , \dfrac{46}{5}\right)\\P(x,y)=(5,9.2)\)

Answer:

on the value of the root may produce a value of the polynomial at the approximate root that is of the order of. For avoiding these problems, methods have been elaborated, which compute all roots simultaneously, to any desired accuracy. Presently the most efficient method is Aberth method.

Answer:

The answer for Q35 is : 176 cubic feet

Step-by-step explanation:

V = 16×3×2+16×5

= 96 + 80

= 176 cubic feet

The correct Numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.

The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:

9 x 4 + (3 − 2)

To solve this expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Evaluate the subtraction inside the parentheses:

3 − 2 = 1

Step 2: Rewrite the expression with the simplified value:

9 x 4 + 1

Step 3: Perform the multiplication:

9 x 4 = 36

Step 4: Add the products:

36 + 1 = 37

Therefore, the correct numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.

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C. A chain-style franchise is a type of franchise where the franchisee produces and sells a franchisor's product using the franchisor's name.

The franchisee operates under the franchisor's established system and business model, including marketing strategies, training programs, and support services. This type of franchise is also known as a product distribution franchise because the franchisee distributes the franchisor's product to customers within a specified territory.

In a chain-style franchise, the franchisor maintains control over the quality and consistency of the product, while the franchisee is responsible for the day-to-day operations of the business. Examples of chain-style franchises include fast-food restaurants, gas stations, and retail stores.

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The new interest rate for his mortgage would be  3.75%.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also gets additional income in terms of the recipient, known as interest, taking into account the time value of money.

Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.

A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)

New interest rate=4.5%-0.75%=3.75%

Thus, The new interest rate for his mortgage would be  3.75%.

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the order from smallest to largest is:

41, 56, 83.

Here we have 3 values, that are:

{83, 56, 41}

To list it from smallest to largest, we first need to write the smallest number, which we can identify is 41.

Then the middle number. Which is 56, that is larger than 41 and smaller than 83.

Finally, the largest number, which is 83.

Then the order is:

41, 56, 83.

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Question:

You are in a bike race. When you get to the first checkpoint, you are 2/5 of the distance to the second checkpoint. When you get to the second check point, you are 1/4 of the distance to the finish. If the entire race is 40 miles, what is the distance between the start and the first check point?

Answer: 4 miles

Step-by-step explanation:

Let distance between start to first checkpoint = x

First checkpoint to second checkpoint = 2/5 of x

Distance of start to checkpoint 1 = ( 2/5 of start to checkpoint 2)

Distance of start to checkpoint 2 = (1/4 of start to finish)

If start to checkpoint 2 = 1/4 of start to finish

Then,

Distance of start to checkpoint 1 = ( 2/5 * 1/4 of start to finish)

Distance of start to checkpoint 1 = 2/20 of start to finish = 1/10 of start to finish

Entire race = 40 miles = distance from start to finish

1/ 10 of 40

= ( 1/10) × 40

= 4 miles

Answer:

B = 34 C = 108 F = 94

Step-by-step explanation:

Answer:

B = 34   C = 108   F = 72

Step-by-step explanation:

It's not my answer look in the comments for the other answer :P

Answer:

15000 square feet.

Step-by-step explanation:

From the statement we have that it would be 2 times the length and 3 times the width due to the divisor, therefore, the perimeter would be equal to:

600 = 2 * l + 3 * w

300 = l + 3/2 * w

we solve for w:

l = 300 - 3/2 * w

in addition the area is equal to:

A = w * l

replacing:

A = w * (300 - 3/2 * w)

A = 300 * w - 3/2 * w ^ 2

We derive:

A '= 300 - 6/2 * w

A '= 300 - 3 * w

we equal 0:

300 - 3 * w = 0

w = 300/3

w = 100

replacing and we calculate l:

l = 300 - 3/2 * 100

l = 150

A = 100 * 150

A = 15000 ft ^ 2

The largest area would be 15000 square feet.

Step-by-step explanation:

the slope = (8-5)/(-6+2) = 3/-4 = -¾