A boat traveled at a constant speed for six hours, covering a total distance of 58.5 km. To the nearest 10th of a kilometer per hour, how fast was it going?

Answer:

Step-by-step explanation:

Use Distributive Property: a*(b  -c) = a*b - a*c

2(3 -4k) = 2*3 - 2*4k

             = 6 - 8k

Answer:

  4.6 km

Step-by-step explanation:

You want to know how many kilometers east Santos walked to end up 5 km from his starting position after walking 2 km south.

The distance Santos is from his starting position will be the hypotenuse of a right triangle with one leg 2 km. Using the Pythagorean theorem, we can find the length of the other leg.

  c² = a² + b²

  5² = 2² + b²

  21 = b²

  b = √21 ≈ 4.583

Santos walked about 4.6 km east.

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The equation of the tangent line to the curve y = 6sin(x) at the point (π/6, 3) which can be written in the form y = mx + b is:

y = 3√3x - π√3/2 + 3, where m = 3√3 and b = -π√3/2 + 3.

To obtain the equation of the tangent line to the curve y = 6sin(x) at the point (π/6, 3), we need to determine the slope (m) of the tangent line and the y-intercept (b).

The slope of the tangent line is equal to the derivative of the function y = 6sin(x) evaluated at x = π/6.

Let's calculate it:

dy/dx = d/dx(6sin(x))

      = 6 * d/dx(sin(x))

      = 6 * cos(x)

Substituting x = π/6 into the derivative, we get:

m = 6 * cos(π/6)

 = 6 * cos(π/6)

 = 6 * (√3/2)

 = 3√3

Now that we have the slope (m), we can determine the y-intercept (b) using the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Plugging in the point (π/6, 3), we get:

y - 3 = 3√3(x - π/6)

Next, we can simplify and rewrite the equation in the form y = mx + b:

y = 3√3(x - π/6) + 3

 = 3√3x - π√3/2 + 3

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Answer:

  A: 8750(0.88^x)

  B: 9995(0.82^x)

Step-by-step explanation:

You want an exponential decay function for cars A and B given their cost and their "decay factor."

In general, an exponential function has the form ...

  value = (initial value)·(growth factor)^x

The growth factor is usually defined as ...

  growth factor = 1 + growth rate

where the "growth rate" is often expressed as a percentage or a fraction.

Your form for f(x) has a=(initial value) and b=(growth factor).

The value of x will be zero at the point where the initial value applies. It will increase by 1 unit for each interval in which the growth factor applies.

Car A

The initial value is presumed to be the Cost. What is called the "growth rate" above is the opposite of what is called the "Decay Factor" in this problem. That is ...

The exponential function is then ...

  f(x) = 8750·(0.88^x)

Car B

For this car, we have ...

The exponential function is then ...

  f(x) = 9995·(0.82^x)

Yes, X is a binomial variable.

A random variable is considered to be binomial if it meets the following conditions:

1. The trials are independent: In this case, the sampling of students for the flu test is an SRS (Simple Random Sample). Each student's selection is independent of the others.

2. The number of trials is fixed: The number of trials in this situation is 20. We are taking a sample of 20 students to test for the flu.

3. Each trial can have only two outcomes: In this case, the outcome of each trial (testing positive or not for the flu) has two possible outcomes: success (testing positive) or failure (not testing positive).

4. The probability of success is the same for each trial: The probability of testing positive for the flu is the same for each student in the sample since the total number of students with the flu (10) is fixed, and the sampling is random.

Since all these conditions are met, the number of students in the sample who test positive for the flu, X, follows a binomial distribution.

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Number of students that do two subjects are 12.

Number of students that do only exactly one subject are;

For Art;

⇒ 14

For Chemistry;

⇒ 11

For Bio;

⇒ 8

Number of students that do at least two of the subjects are 15.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.

All the students do at least one of the three subjects.

3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.

Here,

Total students = 48

So, Number of students that do two subjects are = 4 + 3 + 5

                                                                            = 12

And, Number of students that do only exactly one subject are;

For Art;

⇒ 24 - (3 + 4 + 3)

⇒ 14

For Chemistry;

⇒ 22 - (3 + 5 + 3)

⇒ 11

For Bio;

⇒ 20 - (3 + 4 + 5)

⇒ 8

Number of students that do at least two of the subjects are;

⇒ 3 + 3 + 4 + 5

⇒ 15

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Answer:

Find the rate of sales tax

R= 9000/120000

=0.075

=7.5%

So, the rate is 7.5%

The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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7. Pr(Y=1|X) = Φ(B1 + B2X) where Φ is the cumulative standard normal distribution function is True.

8. T-test used to see if an individual coefficient is statistically significant is True. The T-test is a statistical method that helps to determine if there is a significant difference between the means of two groups of data.

9. The LPM is heteroskedastic as it may produce forecasts of probabilities that exceed one or are less than zero is False. The term heteroscedasticity refers to the fact that the variances of the error terms in the regression model are not constant across all levels of the independent variable.
10. The interpretation of goodness-of-fit measures changes in the presence of heteroskedasticity is True.
11. If the Breusch-Pagan Test for heteroskedasticity results in a large p-value, the null hypothesis of homoskedasticty is not rejected.
12. The generalized least square estimators for correcting heteroskedasticity are called weighed least squares estimators is True.
13. An explanatory variable is called exogenous if it is not correlated with the error term. In the case of an exogenous variable, changes in the explanatory variable are independent of the error term.

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If we allow the number of edges between any two nodes to be more than two, we would need to use the adjacency matrix to accurately store that graph information.

The adjacency matrix is a matrix representation of a graph where the rows and columns represent the vertices and the values in the matrix represent the number of edges between two vertices.

In this case, we could have values greater than 1 in the matrix to represent multiple edges between two vertices.

On the other hand, the adjacency list data structure would not be able to accurately store this information, as it represents each vertex and its adjacent vertices in a linked list format.

It would be difficult to represent multiple edges between two vertices using this data structure.

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Answer:

they would have saved 35 dollars

Step-by-step explanation:

Ralph on his own would have paid  105 and jeff 140 but together with the discount they could save $35 by paying 210 in total with the discount.

Goran wants to find the average height of students in the 9th grade at Northside Highschool. So he will use the height of 50 students in the 9th grade to find the average height.

Explanation: pounds - currency/weight, ounces - volume of water, centimeter - height/length, grams - mass, inches - height

Solution:

(a)

1) centimeters

2) inches

(b) Solution: Randomly pick 50 students from the 9th grade and measure their heights.

Answer: 63 Stickers

Step-by-step explanation:

Given information:

Ratio = Slade : Corbett = 5 : 2

Corbett has 27 fewer stickers

Set variables:

Let x be the number of stickers Corbett has

Let x + 27 be the number of stickers Slade has

Set proportional equation:

\(\frac{2}{5}~ =~\frac{x}{x~+~27}\)

Cross multiply the system

\(2~(x~+~27)~=~5~*~x\)

Simplify by distributive property

\(2~*~x~+~2~*~27~=~5x\)

\(2x~+~54~=~5x\)

Subtract 2x on both sides

\(2x~+~54~-~2x~=~5x~-~2x\)

\(54~=~3x\)

Divide 3 on both sides

\(54~/~3~=~3x~/~3\)

\({x=18}\)

Add Corbett's and Slade's amounts together

Corbett = x = 18 stickers

Slade = x + 27 = 18 + 27 = 45 stickers

Total = 18 + 45 = \(\Large\boxed{63~Stickers}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

63 stickers

Step-by-step explanation:

Define the variables:

Given ratio:

Slade : Corbett = 5 : 2

Substitute the defined variables:

\(\implies \sf x : x - 27 = 5 : 2\)

\(\implies \sf \dfrac{x}{x-27}=\dfrac{5}{2}\)

Cross multiply:

\(\implies \sf 2x=5(x-27)\)

Expand:

\(\implies \sf 2x=5x-135\)

Subtract 5x from both sides:

\(\implies \sf -3x=-135\)

Multiply both sides by -1:

\(\implies \sf 3x=135\)

Divide both sides by 3:

\(\implies \sf x=45\)

Therefore, Slade had 45 stickers.

Substitute the found value of x into the expression for the number of stickers Corbett had:

\(\implies \sf 45-27=18\)

Therefore, Corbett had 18 stickers.

Total number of stickers = 45 + 18 = 63

Answer:

b, the probability that a customer buys a taco, a drink, or both is 45%

P(A or B) = 0.45 means that there is a 45% probability that a customer will buy a taco or a drink from the food truck.

In terms of this problem, P(A or B) = 0.45 represents the probability that a customer buys either a taco (event A) or a drink (event B).

When we say "P(A or B)," it refers to the probability of either event A or event B occurring. In this case, it means the probability of a customer buying a taco or a drink from the food truck.

The value of 0.45 indicates the numerical probability associated with the event A or B. It represents the likelihood that a randomly selected customer from the food truck will purchase either a taco or a drink.

Therefore, P(A or B) = 0.45 means that there is a 45% probability that a customer will buy a taco or a drink from the food truck.

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Answer:

The answer is 4a-12

Step-by-step explanation:

Hope this helped :>

Answer:

4a-12

Step-by-step explanation:

i hope this helps

1. Data input

P = 9500 dollars

r = 5.75% daily

A = 26100 dollars

n = 365

2. Equation

Answer:

-3.1

Step-by-step explanation:

2n+3=-3.2

2n=-6.2

n=-3.1

Answer:

n= -3.1

work is shown in the picture

Answer:  $42,236.97

Work Shown:

A = P*(1+r/n)^(n*t)

A = 25000*(1+0.06/1)^(1*9)

A = 42236.9739750673

A = 42236.97

Answer:

555.36

Step-by-step explanation:

5.34 times 104 = 555.36

Hope this helps! :D

The derivative of the function y = ∫0^(3sin(4t)) ex dt with respect to t is y'(t) = (3/4) (ex cos(4t)).

To use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function y = ∫0^(3sin(4t)) ex dt, we need to first understand what the theorem states.

Part 1 of the Fundamental Theorem of Calculus states that if a function f(x) is continuous on the closed interval [a, b], and if F(x) is any antiderivative of f(x), then the definite integral of f(x) from a to b is equal to F(b) - F(a), or ∫[a,b] f(x) dx = F(b) - F(a).

In other words, the theorem provides a way to calculate the definite integral of a function by evaluating the difference between two antiderivatives of the function.

Now, let's apply this theorem to the function y = ∫0^(3sin(4t)) ex dt. To do this, we need to first find an antiderivative of the integrand ex.

The antiderivative of ex is simply ex itself, so we have:
∫ ex dt = ex + C, where C is the constant of integration.

Now, we can use this antiderivative to find an antiderivative of the integrand in our original function y. Let u = 4t, so that du/dt = 4 and dt = du/4. Then, we have:

y = ∫0^(3sin(4t)) ex dt = ∫0^(3sin(u)) ex (du/4) = (1/4) ∫0^(3sin(u)) ex du
Let F(u) = ∫ ex du = ex + C, where C is a constant of integration. Then, we have:
y = (1/4) F(3sin(u)) - (1/4) F(0) = (1/4) (ex)|_0^(3sin(u)) = (1/4) (ex - 1)

Using the chain rule again, we have:
d/dt (3sin(u)) = 3cos(u) (du/dt) = 3cos(4t)

Substituting this expression back into the previous equation, we get:
y'(t) = (1/4) (ex) (3cos(4t)) = (3/4) (ex cos(4t))

Therefore, the derivative of the function y = ∫0^(3sin(4t)) ex dt with respect to t is y'(t) = (3/4) (ex cos(4t)).

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Answer:

A+c

Step-by-step explanation:

because common sense

Answer:

12% by 6° 2

Step-by-step explanation:

Thats the greater value

Just brainliest me

Answer:

g = \(\frac{4}{3}\)

Step-by-step explanation:

4 - \(\frac{1}{12}\) g - 2 = \(\frac{3}{2}\) g + 1 - \(\frac{5}{6}\) g

multiply through by 12 ( the LCM of 12, 2 and 6 ) to clear the fractions

48 - g - 24 = 18g + 12 - 10g

- g + 24 = 8g + 12 ( subtract 8g from both sides )

- 9g + 24 = 12 ( subtract 24 from both sides )

- 9g = - 12 ( divide both sides by - 9 )

g = \(\frac{-12}{-9}\) = \(\frac{12}{9}\) = \(\frac{4}{3}\)

Answer:

b

Step-by-step explanation:

point B has coordinates (0, 0 ) which is the origin

Answer:

A

Step-by-step explanation:

The transformation, the value of the table is B (-5,3) B 2.

We have given that,

Rectangle ABCD is translated (x + 2 y - 3) and then rotated 180° about the origin.

We have to complete the table to show the locations of A'. B', C', and D'  after both transformations.

A transformation is a function f, usually with some geometrical that maps a set X to itself, and f: X → X.

Therefore after the transformation, the value of the table is

B (-5,3) B 2.

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The value of x for the given equation is 16.

To find the value of x in the equation x + 10 = 26, we need to isolate x on one side of the equation by performing the same operation to both sides of the equation.

We can start by subtracting 10 from both sides of the equation:

x + 10 - 10 = 26 - 10

Simplifying the left-hand side gives:

x = 16

Therefore, the value of x is 16, as this is the solution that satisfies the equation x + 10 = 26.

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The complete question is below:

Find the value of x: for x +10 = 26

Answer:

16

Step-by-step explanation:

64 ÷ 4 = 16