Portfolio for Unit 5


Part 1: Car Wheel Project

Answer:

89

Step-by-step explanation:

\(3+75t-16t^{2} =h\\\\\)

we evaluate when t=2

\(3+75(2)-16(2)^2=h\\\\3+150-64=h\\\\h=89\)

so it's 89 feet

Answer:

89

Step-by-step explanation:

JUST TRUST ME

Answer:

20 men will paint the same wall in 3/4 hours.

Step-by-step explanation:

Given information is:

5 men paint a wall in 3 hours

Let x be the number of men

It is also mentioned that the rate will be same with x men. So we have to put both the rates/proportions equivalent to find the number of men.

So,

\(men * hours = men*hours\\5*3 = x*\frac{3}{4}\\15 = \frac{3}{4}x\\x = \frac{4}{3} * 15\\x = 20\)

Hence,

20 men will paint the same wall in 3/4 hours.

Answer:

Since QPR is an isoscelese triangle, QP and PR are congruent.

Therefore PR = 8

My guess for ST is z=1. So (5z = 5) and( 2z = 2). Then add 3 to 2 and you get 5. So ST = 5

Step-by-step explanation:

Hope this helps!!!

Please mark brainliest.

Answer:

There are various answers... x-6 or 10x-6-9x or (5x-3)2-9x or (-3+5x)2-9x

Step-by-step explanation:

We all just have to distributive or simplify

The general solution of the given differential equation expressed explicitly as a function of the independent variable, is:

w(x) = (1/16) * \(((3x + 2)^2 + 4Cx - 4x^2)^2\)

To obtain the solution, we can rewrite the given differential equation by separating the variables and integrating. First, we can divide both sides by √w and rearrange the terms:

√w dw = (3x + 2)/\(x^2\) dx

Then, with regard to the relevant variables, we integrate both sides. The integral of √w with respect to w can be computed using the power rule, while the integral of (3x + 2)/\(x^{2}\) with respect to x can be found using partial fractions. After integrating and simplifying, we obtain the general solution as:

w(x) = (1/16) * \(((3x + 2)^2 + 4Cx - 4x^2)^2\)

Here, C is the arbitrary constant that can take any real value.

This general solution represents a family of functions that satisfy the given differential equation. By choosing different values for the constant C, we can obtain specific solutions corresponding to different initial conditions or constraints imposed on the problem.

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The complete question is:

Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable.

\(x^2\)(dw/dx) = √(w)(3x+2)

Answer:

0.457

Steps bye step explanation:

True. In a continuous uniform distribution, all values within a specified interval are equally likely to occur. The mean or expected value of this distribution can be found by taking the average of the upper and lower limits of the interval.

This can be represented mathematically as (a+b)/2, where a and b are the lower and upper limits of the interval. For example, if we have a continuous uniform distribution on the interval [0,10], the mean value would be (0+10)/2 = 5.

This means that on average, we would expect a randomly selected value from this distribution to be around 5. It's important to note that the mean of a continuous uniform distribution is not affected by the shape or spread of the distribution, as all values have an equal chance of occurring.

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Answer: 74

Step-by-step explanation:

Answer:

74

Step-by-step explanation:

Got it right on the test.

Two buses leave a station at the same time and travel in opposite directions. After six hours, the two buses are 768 miles apart. We find that the speed of the first bus is 57 miles per hour, and the speed of the second bus is 71 miles per hour.

Let the speed of one bus be x miles per hour. Then the speed of the other bus is (x+14) miles per hour, as it travels 14 miles per hour faster.

We know that the two buses travel in opposite directions and are 768 miles apart after six hours. Using the formula:

Distance = Speed x Time

we can write two equations:

Distance covered by the first bus = x * 6

Distance covered by the second bus = (x+14) * 6

The sum of these distances is equal to 768 miles:

x * 6 + (x+14) * 6 = 768

Simplifying the equation, we get:

12x + 84 = 768

12x = 684

x = 57

Therefore, the speed of the first bus is 57 miles per hour, and the speed of the second bus is (57+14) = 71 miles per hour.

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Answer:

True

Step-by-step explanation:

B would be the midpoint because it is in the middle of both showing thats where both points connect.

Answer:

True

Step-by-step explanation:

You can either solve for x (which produces 0 as the result) or you can plug zero in for x into the original equation to verify that it produces a true statement.

Answer:

Step-by-step explanation:

True or false, 0 is a solution to

2x + 10 = 4x + 10

2x - 4x = 10 - 10

-2x = 0

x = 0/-2

x = 0

the equation is TRUE

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Answer:

1) 136

2) 136

3) 44

Step-by-step explanation:

trapezoid = 360 degrees

44 = the 3rd angle because they are equal

add the two angles(44 and 44) 44 + 44 = 88

that makes up half the shape

next 360 - 88 to find the last two

272 is the remaining measurements, split in half to find 1 and 2

272/2 = 136

The function is concave down on the interval ((2 -√(2))/2, (2 + √(2))/2), and concave up on the other two intervals. The inflection points are at x = (2 - √(2))/2 and x = (2 + √(2))/2.

To determine where the function is concave up or concave down, we need to find the second derivative and check its sign:

f(x) = x⁴ - 4x³ - 6x² - x - 7

f'(x) = 4x³ - 12x² - 12x - 1

f''(x) = 12x² - 24x - 12 = 12(x² - 2x - 1)

To find the intervals of concavity, we need to solve the inequality 12(x² - 2x - 1) > 0:

x² - 2x - 1 > 0

Using the quadratic formula, we find the roots of the quadratic equation:

x = (2 ± √(2))/2

These are the critical points where the concavity changes, so we can use them to divide the real line into three intervals:

(-∞, (2 - √(2))/2), ((2 - √(2))/2, (2 + √(2))/2), ((2 + √(2))/2, +∞)

Now we can test any value in each interval to determine the sign of the second derivative and any inflection points, and thus the concavity:

For x < (2 - √(2))/2:

f''(x) > 0, so f(x) is concave up.

For (2 - √(2))/2 < x < (2 + √(2))/2:

f''(x) < 0, so f(x) is concave down.

For x > (2 + √(2))/2:

f''(x) > 0, so f(x) is concave up.

Therefore, on the intervals((2 -√(2))/2, (2 + √(2))/2), the function is concave down, whereas on the other two intervals, it is concave up. Both at x = (2 - √(2))/2 and x = (2 + √(2))/2.

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After considering the given data we conclude that the correct answer which is the correct option is b which is 3/28, regarding the conditional probability.

We are given that an urn contains 3 green balls and 5 red balls. Let Rᵢ be the event that the i-th ball without replacement is red. We need to find \(P(R_3| R_2 \cap R_1).\)
Using the conditional probability formula, we have:
\(P(R_3| R_2\cap R_1) = P(R_3 \cap R_2 \cap R_1) / P(R_2 \cap R_1)\)
Since we are drawing balls without replacement, the probability of drawing a red ball on the first draw is 5/8. The probability of drawing a red ball on the second draw given that the first ball was red is 4/7. Similarly, the probability of drawing a red ball on the third draw given that the first two balls were red is 3/6 = 1/2. Therefore, we have:
\(P(R_3 \cap R_2 \cap R_1) = (5/8) * (4/7) * (1/2) = 5/56\)
To find P(R₂ ∩ R₁), we can use the law of total probability:
\(P(R_2 \cap R_1) = P(R_2 \cap R_1 | R_1) * P(R_1) + P(R_2 \cap R_1 | R_1') * P(R_1')\)
where R₁' is the complement of R₁ (i.e., the event that the first ball drawn is not red). Since we are drawing balls without replacement, the probability of drawing a red ball on the second draw given that the first ball was not red is 5/7. Therefore, we have:
\(P(R_2 \cap R_1) = (5/8) * (5/7) + (3/8) * (3/7) = 29/56\)
Substituting these values into the conditional probability formula, we get:
\(P(R_3| R_2 \cap R_1) = (5/56) / (29/56) = 5/29\)
Therefore, the answer is (b) 3/28.
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The complete question is
An urn contains 3 green balls and 5 red balls. Let R, be the event the i-th ball without replacement is red. Find P(R3| R2 \cap R₁).
a) 1/56
b) 3/28
c) 1/2
d) 5/8

Answer:

1 x 106

Step-by-step explanation:

Step-by-step explanation:

b) average velocity : ∆x/∆t = 100/9.8 ≈ 10.204 m/s

c) ∆x = v.∆t = 10.204 × 3 = 30.612 m

d) ∆t = ∆x/v = 80/10.204 = 7.84 s

Answer:

C

Step-by-step explanation:

Im going to be quick on this since your in a hurry, is AB is 3 and QR = 1  and their similar then BC would be 3 times the amount of RS which is 1.5 so the Answer is 4.5

Answer:

C

Step-by-step explanation:

　　＿＿＿　 AA

*～/■　■　⊂ P

　 |　■　■.（＿）

　 U U￣￣U U

Answer:

arithmetic sequence

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 10 - 19 = 1 - 10 = - 9

This means the sequence is arithmetic

Answer:

D.

Step-by-step explanation:

If you were to try to figure out how many miles Sandra walked per hour, you would set up your division as 13/3 miles over 1 hour, so therefore D is correct.

I hope I could help :)

Usually the one with the more vertical line would be steeper.

The probability of having two years with high sales in a row for Apple Inc. is 0.16 or 16%.

To find the probability of two independent events happening in succession, you multiply their individual probabilities together. In this case, the probability of high sales in a given year is 40%, or 0.4.

Step 1: Convert percentages to decimal form.
High sales: 40% = 0.4

Step 2: Multiply the probabilities of high sales for two consecutive years.
Probability of two high sales years in a row = 0.4 * 0.4

Step 3: Calculate the result.
Probability = 0.4 * 0.4 = 0.16

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Answer:

Hello! answer: 6

Step-by-step explanation:

6 people get to work in 20 minutes which is the only option which is less than 40 therefore 6 is the answer Hope that helps!

Answer:

14 remainder  2

Step-by-step explanation:

Step 1: Take the first digit of the dividend. ...

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next number (if present).

Step 5: Repeat the same process.

Answer:

14.334

Step-by-step explanation:

86/6=14.3333333….

Thus, the range of initial values for which the solution lies in the interval [3.99, 4] is ysubnot in (0, 4).

(a) As t goes to infinity, the denominator of the right-hand side approaches infinity while the numerator approaches 4ty. Thus, the solution approaches the equilibrium solution y=4.

(b) Using separation of variables and partial fractions, we can obtain the solution: y = 4 / (1 + 3e^(2t^2/2 + C)). Setting y = 3.99 and solving for t, we obtain t = sqrt[ln(3.99/0.01) / 2].

(c) We can rearrange the differential equation to obtain y'/(y(4-y)) = t/(1+t) and then integrate both sides. This gives ln|y/(4-y)| = C + ln(1+t) - t, where C is the constant of integration. To find the range of initial values for which the solution lies in the interval [3.99, 4], we need to solve the inequality 3.99 <= y <= 4 for y in terms of t. This gives the condition -∞ < t <= ln(999/1).

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Answer:

30%

Step-by-step explanation:

4320 - 288 = 4032

4032/12 =336 per copies

So, he sold them in 5760

5760 - 4032 = 1728

(1728/5760)*100 = 30%

Answer: \(30, 35\ mph\)

Step-by-step explanation:

Given

Truck can travel 150 miles while car can travel 175 miles in same time

If the speed of truck is 5 mph slower than the car

Suppose the speed of car is \(x\ mph\), speed of truck would be \(x-5\)

For same time

\(\Rightarrow \dfrac{150}{x-5}=\dfrac{175}{x}\\\\\Rightarrow 6x=7(x-5)\\\Rightarrow 6x=7x-35\\\Rightarrow x=35\ mph\)

Speed of truck is \(x-5=30\ mph\)

Speed of car \(x=35\ mph\)

Answer:

Step-by-step explanation:

Let's start by translating the given sentence into an equation:

2x + 29 ≥ -25

To solve for x, we can isolate x on one side of the inequality:

2x ≥ -25 - 29

2x ≥ -54

x ≥ -27

Therefore, the solution to the inequality is x ≥ -27.