John rides his bike 68 km south and then 6 km went. How far is he from his starting point?

For this equation: a=5, b=-13, c=6

5x^2−13x+6=0

Use the quadratic formula with a=5, b=-13, c=6.

x= [−(−13)± √(−13)2 −4(5)(6)] / 2(5)

x= (13±√49)/10

x=2 or x= 3/5

The equation is 6c - 55 = 455 and the regular cost of each chair is $85

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let c stands for the usual price for x chairs.

So c = mx + b

When a customer purchases a set of dining chairs, a one-time discount of $55 is applied to the total.

Given that a discount of $55 is applied to the total,

Therefore b = -55.

During the sale, Rhianna buys a set of 6 chairs and pays 455,

So 6c - 55 = 455

⇒ 6c = 510

⇒ c = 510/6

⇒ c = 85

Hence, the equation is 6c - 55 = 455 and the regular cost of each chair is $85

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Answer: whatever do I care

Step-by-step explanation: I don’t care

The required volume of the pyramid is, 22500 cubic cm.

Volume is referred to as the area occupied within an object's three-dimensional space.

Given that,

The length of cuboid = 90 cm

Width of cuboid = 50 cm

And height of cuboid = 225 cm

Let the height of the pyramid is x cm

Since the height of cuboid and pyramid = 240 cm

⇒ 225 + x = 240

⇒ x = 15 cm

Since the base of pyramid will be the same as the base of cuboid,

The volume of pyramid = 1/3 x base area x height

                                       = 1/3 x 90 x 50 x 15

                                       = 22500

The volume of the pyramid is 22500 cubic cm.

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Based on the given table, the probability of a student being in junior robotics is 16/50, and for robotics junior, it is 24/50.

In the table, the numbers represent the enrollment counts in the technology classes by year. To find the probabilities, we divide the enrollment count by the total number of students, which is 50.

14. The probability of a student being in junior robotics is 16/50, or 0.32, which can be simplified as 32%.

15. The probability of a student being in robotics junior is 24/50, or 0.48, which can be simplified as 48%.

16. The probability of a student being in game design given that they are a sophomore is 18/50, or 0.36, which can be simplified as 36%.

17. The probability of a student being a sophomore given that they are in game design is 18/50, or 0.36, which can be simplified as 36%.

18. Year and technology class enrollment are dependent events because the probability of being enrolled in a particular technology class depends on the student's year. The conditional probabilities in questions 16 and 17 indicate that the likelihood of being in a specific technology class changes depending on the student's year.

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Answer:

It is C

Step-by-step explanation:

The shape is a rectangle with a length of 22 units and a width of 20 units, then its area can be calculated by multiplying the length by the width: 22 × 20 = 440.

So the area of the rectangle is 440 square units

Answer:

The answer is 9 days

Step-by-step explanation:

First, we realise

-1.F = 1 day

-9.F = 9 days

The -1.F times 9 gives us one so the days times 9 as well.

Answer = 9

Answer:

Hey there!

We have that 4/5, or 80% of the 60 students passed the exam.

Thus, we have:

0.8(60)=48

48 students passed the exam.

Let me know if this helps :)

Answer:

(16 and 5 = gcf of 1) 12 and 3 = gcf of 3

Step-by-step explanation:

divid both to find the answer

Answer:

Step-by-step explanation:

y-intercept form: y =mx +b

Here m is slope and b is y-intercept

A) y = 4x + 5

Slope = 4

y-intercept = 5

B) y = 1/4x -2

Slope = 1/4

y-intercept = -2

Answer:

f(x)=3/2 x

Step-by-step explanation:

it starts at 0 and rise 3 and goes over 2

The answer is \(f(x)=\frac{3}{2}x\)

First, you must find 2 points.

(0,0)   (2,3)

Then, you must use the slope equation

\(\frac{3-0}{2-0}=\frac{3}{2}\)

The line crosses the y axis at 0, so there is no y intercept

\(f(x)=\frac{3}{2}x\)

Answer:

Step-by-step explanation:

5^-4 remember that a^-b=1/a^b

5^-4=1/5^4=1/625

9514 1404 393

Answer:

  168

Step-by-step explanation:

Below are shown the 7 different kinds of arrangements that can be made. Each of these can be permuted into 24 different arrangements by assigning colors in a different order than the one used here:

  {1, 2, 3, 4} ⇒ {green, blue, red, yellow}

Then the total number of possible correct colorings is 7·24 = 168.

__

These colorings were found using a computer program that identified all 168 viable colorings, then eliminated permutations. It started by identifying ways to color 2 rows, then adding rows based on that.

_____

You'll notice that the last on the attached list most closely matches the one in the problem statement.

Answer:

13.86

Step-by-step explanation:

\(8^2+x^2=16^2\\64+x^2=256\\x^2=192\\\sqrt{x^2} =\sqrt{192} \\x=13.86\)

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer:

196

Step-by-step explanation:

Answer:

$4.94

Step-by-step explanation:

Gummy worms cost $2.96 per lb, and she bought 4.25 lbs, so:

2.96 * 4.25 = $12.58 spent in gummy worms

Jaw breakers cost $4.95 per lb, and she bought 0.5 lbs, so:

4.95 * 0.5 = $2.48 spent in jaw breakers

Adding the gummy worms and the jaw breakers, she spent:

12.58 + 2.48 = 15.06 in Total

She gave the clerk $20.00, but she only spent only $15.06, so the clerk gave her back the difference:

20 - 15.06 = $4.94 is the change that she received

The final solution for the integral is:

∫(xe^(kx))/(1+kx)^2 dx = -xe^(1+kx)/(k(1+kx)) + (1/k)∫e^(1+kx)/(1+kx) dx + D

If k = 0, the term (1/k)∫e^(1+kx)/(1+kx) dx simplifies to e^x + E.

To find the integral ∫(xe^(kx))/(1+kx)^2 dx, we can use integration by parts. Let's denote u = x and dv = e^(kx)/(1+kx)^2 dx. Then, we can find du and v using these differentials:

du = dx

v = ∫e^(kx)/(1+kx)^2 dx

Now, let's find the values of du and v:

du = dx

v = ∫e^(kx)/(1+kx)^2 dx

To find v, we can use a substitution. Let's substitute u = 1+kx:

du = (1/k) du

dx = (1/k) du

Now, the integral becomes:

v = ∫e^u/u^2 * (1/k) du

 = (1/k) ∫e^u/u^2 du

This is a well-known integral. Its antiderivative is given by:

∫e^u/u^2 du = -e^u/u + C

Substituting back u = 1+kx:

v = (1/k)(-e^(1+kx)/(1+kx)) + C

 = -(1/k)(e^(1+kx)/(1+kx)) + C

Now, we can apply integration by parts:

∫(xe^(kx))/(1+kx)^2 dx = uv - ∫vdu

                         = x(-(1/k)(e^(1+kx)/(1+kx)) + C) - ∫[-(1/k)(e^(1+kx)/(1+kx)) + C]dx

                         = -xe^(1+kx)/(k(1+kx)) + Cx + (1/k)∫e^(1+kx)/(1+kx) dx - ∫C dx

                         = -xe^(1+kx)/(k(1+kx)) + Cx + (1/k)∫e^(1+kx)/(1+kx) dx - Cx + D

                         = -xe^(1+kx)/(k(1+kx)) + (1/k)∫e^(1+kx)/(1+kx) dx + D

Now, let's focus on the integral (1/k)∫e^(1+kx)/(1+kx) dx. This integral does not have a simple closed-form solution for all values of k. However, we can compute it separately for specific values of k.

If k = 0, the integral becomes:

(1/k)∫e^(1+kx)/(1+kx) dx = ∫e dx = e^x + E

For k ≠ 0, there is no simple closed-form solution, and the integral cannot be expressed using elementary functions. In such cases, numerical methods or approximations may be used to compute the integral.

Therefore, the final solution for the integral is:

∫(xe^(kx))/(1+kx)^2 dx = -xe^(1+kx)/(k(1+kx)) + (1/k)∫e^(1+kx)/(1+kx) dx + D

If k = 0, the term (1/k)∫e^(1+kx)/(1+kx) dx simplifies to e^x + E.

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Answer:

16 litres = 100% of the tank capacity

x litres = 75% of the tank capacity (since 3/4 is equivalent to 75%)

To solve for x, we can cross-multiply and simplify:

16 * 75 = 100x

1200 = 100x

x = 12

Therefore, 3/4 of the tank capacity when the tank holds 16 litres is 12 litres.

Answer:

= 12 liters.

Step-by-step explanation:

16*3/4 =48/4.

= 12

Answer:

If x is the one vertically opposite to 40, then x will be 40, due to vertically opposite angles.

To calculate the energy change associated with an electron transitioning from the n = 4 energy level to the n = 2 energy level, we can use the equation for the energy of an electron in an atom, which is given by:

Where E_n is the energy of the electron in the nth energy level, and eV is the unit of energy called the electronvolt.

Substituting the values of n = 4 and n = 2 into this equation gives us:

The energy change associated with the transition from n = 4 to n = 2 is given by

To convert this energy change from electronvolts to joules, we can use the fact that 1 eV is equal to 1.602176634 x 10^-19 joules.

Multiplying -2.55 eV by this conversion factor gives us an energy change of -2.55 eV * 1.602176634 x 10^-19 joules/eV = -4.13 x 10^-18 joules.

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Given, A = [-1 3; 2 -3; -1 3], b = [12; 9; 9], the least-squares solution of Ax=b is x = [1.4; 0.6].

To find the least-squares solution of A*x=b

(a) Construct the normal equations for x.

For a given matrix A with dimensions m x n and a column vector b with dimensions m x 1, the normal equations are as follows: AᵀAx = Aᵀb Where Aᵀ is the transpose of matrix A.

Now, let us construct normal equations for the given problem.

A = [-1 3; 2 -3; -1 3], b = [12; 9; 9]Normal equation is, AᵀAx = AᵀbSince, A is of dimension 3x2, AT will be of dimension 2x3.

Therefore, the normal equation will be of dimension 2x2.x = (ATA)−1ATb ⇒ x = inv(ATA)ATb

Let's calculate AT and ATA.AT = [-1 2 -1; 3 -3 3]ATA = [6 -12; -12 27](b) Solve for x.Substituting AT, ATA, and b in the equation we get,x = inv(ATA)ATb ⇒ x = inv([6 -12; -12 27]) * [-1; 3; -1; 3; -1; 3]⇒ x = [1.4; 0.6]

Therefore, the least-squares solution of Ax=b is x = [1.4; 0.6].

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The number of Hopper's steps that is equivalent to one of Skipper's jumps is given as follows:

2.45.

The situation can be modeled by a system of equations.

The variables for the system of equations are given as follows:

Hopper takes three jumps, he lands in the same place as Skipper does when she takes 4 jumps, hence:

3x = 4y.

x = 4/3y.

When Hopper takes six jumps and nine steps, he lands in the same place as Skipper does when she takes nine jumps, hence:

6x + 9z = 9y.

Replacing x = 4/3y on the second equation, we have that:

4(4/3y) + 9z = 9y.

9z = 9y - 16/3y

9z = 27/3y - 16/3y

9z = 11/3y

y = 27/11z

y = 2.45.

Meaning that 2.45 of Hopper's steps are equivalent to one of Skipper's jumps.

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Answer: m+1

Step-by-step explanation:

Answer:

the account will earn $4416.08

Answer:

\((2,8]\)

Step-by-step explanation:

Given

The attached piece wise function

Required

The domain

To do this, we simply consider the inequalities that bound the values of x.

The inequalities are:

\(2 < x < 4\)     \(4 < x < 8\)   and   \(x \ge 8\)

Combine the first two inequalities:

\(2 < x < 8\)    and   \(x \ge 8\)

For the inequality to be true, we must have:

\(2 < x \le 8\)

In interval notation, the inequality is:

\((2,8]\)

Number of seconds it takes the object to travel the entire length of the path is 15 seconds.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, the object travels 1/20 of the length of the path in 3/4 seconds.

1/20 is a tiny portion of the length that needs to be traveled.  

20/20 is the whole length.  

If 1/20 gets traveled in 3/4 of a second, multiply 3/4 by 20.

That is, 20(3/4) = 15 seconds

Therefore, number of seconds it takes the object to travel the entire length of the path is 15 seconds.

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The correct answer is Do Not Reject H0.a standard normal distribution table or calculator, we find that the p-value is approximately 0.478.

To test the claim made in the document, we can set up the following hypothesis test:

H0: The true proportion of female UVA undergraduates is 0.554 (claim made in the document).

H1: The true proportion of female UVA undergraduates is not 0.554 (contrary to the claim made in the document).

To conduct the hypothesis test, we can use the proportion test for a single population proportion. The test statistic is calculated using the formula:

z = (p - P) / sqrt(P(1 - P) / n)

Where:

p is the proportion of females in the sample

P is the proportion claimed in the document (0.554)

n is the sample size

Now, let's calculate the values:

p (proportion in the sample) = 57.9% = 0.579

P (proportion claimed in the document) = 55.4% = 0.554

n (sample size) = 200

Using these values, we can calculate the test statistic:

z = (0.579 - 0.554) / sqrt(0.554 * (1 - 0.554) / 200) ≈ 0.708

A. The value of the standardized test statistic: The value of the standardized test statistic is approximately 0.708.

To determine the rejection region, we need to find the critical value(s) for a two-tailed test at a 9% significance level. Since the test is two-tailed,

B. The rejection region for the standardized test statistic: The rejection region for the standardized test statistic is (-∞, -1.965) ∪ (1.965, ∞).

C. The p-value is approximately 0.478.

Comparing the p-value (0.478) to the significance level (9%), we can see that the p-value is greater than the significance level. Therefore, we fail to reject the null hypothesis.

D. Your decision for the hypothesis test: Based on the hypothesis test, we do not have sufficient evidence to conclude that the document's claim (55.4% female undergraduates) is false. Thus, we would not reject the null hypothesis (Do Not Reject H0).

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Answer:

B. 24 ft.

Step-by-step explanation:

25 would be the hypotenuse of a triangle and 7 is a leg, so

7^2 + x^2 = 25^2

49 + x^2 = 625

x^2 = 576

x = 24 ft

Answer:

The answer is B I took the test but used the person above me and it was right.

Step-by-step explanation: