Sean is travelling. He has a flight of 2 hours 30 minutes, a stopover of 45 minutes and then another flight of 4.75 hours. What is his total travel time? Give your answer in hours and minutes.

By solving the given equation f(x) = \(x^{2} +3x-40\), the zeroes are -3 and 5.

To solve the given equation we have to do the factorization.

What is factorization: Factorization is the method of writing numbers as the product of their factors or divisors.  In other words, we can say finding what to multiply together to get an expression.

To do the factorization, we have to follow the steps as shown below:

 \(x^{2} +3x-40\) \(= 0\)

\(-40 = 8 * -5\\\)                        [ multiplication of 8 and -5 is -40]

\(x^{2}+8x-5x -40\) \(= 0\)

\(x(x+8) -5(x+8)\) \(= 0\)

\((x-5)(x+8)\) \(= 0\)

\(x = 5\)   and  \(x = -8\)              [ The roots or zeroes]

From the above solution, we can conclude that the zeros of the given function \(x^{2} +3x-40\) are 5 and -8.

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Answer:

1 11/12

Step-by-step explanation:

Picture included)

Sorry about my handwriting

23/12 reduces to 1 11/12

Jason jumped farther by 23/ 12 feet.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Yolanda jumped 4 3/4 feet = 19/4 feet

and, Jason jumped 6 2/3 feet in a jumping contest. = 20/3 feet

First take the LCM of 3 and 4

LCM( 3, 4) = 12

Then, Yolanda jumped = 19/4 x 3/3 = 57/ 12

and, Jason jumped = 20/3 x 4/4= 80/ 12

Hence, Jason jumped farther by (80/12 - 57/12)= 23/ 12 feet.

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Answer:

f ( x ) = 3 x − 2   ,  x = 9 f ( x ) = x 2  ,  x = 12 f ( x ) = 7 x − 2  ,  x = 6

Step-by-step explanation:

x-3 = 8×4

x-3 = 32

x = 32+3

x = 35

Answer:

neither

Step-by-step explanation:

The lines are neither. They are perpendicular because when I graphed them, line 2 intersected line 1 at 5, -2.

Hope this helps! :)

Answer:

B

Step-by-step explanation:

i think

The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

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Answer:

Step-by-step explanation:

3 because at the bottem it is 3 away and top three away.

The major key with 2 flats is :

B♭ major

Answer:

The key of B♭ major has two flats

Step-by-step explanation:

An accidental sign consisting of two flat symbols ♭that lower a note by two half steps two semitones. The double flat symbol alters the pitch of the note to which it is attached as well as any subsequent occurrence of the same note identical line or space in the same measure.

Hope this helps

~Heaven~

Using Hooke's law the maximum value of |cos(8t)| is 1, so the maximum excursion is 1/6 meters.

To find the spring constant k, we use Hooke's law:

F = -ky

where F is the weight of the object, and y is the distance it is stretched from its rest position. At equilibrium, F = mg = 10 × 9.81 = 98.1 N. Thus,

98.1 = -k × 0.098

k = -1000 N/m

The equation of motion for the system is given by:

my'' + ky = F(t)

Substituting the given values, we get:

10y'' + (-1000)y = 100cos(8t)

y'' - 100y = 10cos(8t)

with initial conditions y(0) = 0 and y'(0) = 0.

The characteristic equation is r² - 100 = 0, with roots r = ±10i. The complementary solution is therefore y_c(t) = c1cos(10t) + c2sin(10t).

For the particular solution, we assume a form of yp(t) = Acos(8t) + Bsin(8t), and substitute it in the differential equation to get:

-64Acos(8t) - 64Bsin(8t) - 100(Acos(8t) + Bsin(8t)) = 10cos(8t)

Solving for A and B, we get A = -1/6 and B = 0. Thus, the particular solution is yp(t) = (-1/6) × cos(8t).

The general solution is therefore y(t) = c1cos(10t) + c2sin(10t) - (1/6)*cos(8t). Applying the initial conditions, we get c1 = 0 and c2 = 0, so the particular solution is simply y(t) = (-1/6) × cos(8t).

The maximum excursion from equilibrium can be found by taking the absolute value of y(t) and finding its maximum value. We have:

|y(t)| = (1/6) × |cos(8t)|

The maximum value of |cos(8t)| is 1, so the maximum excursion is 1/6 meters.

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The range of |f(x)| is [0, 9].

We are given that the range of the function f is [−2, 9]. We are required to find the range of |f(x)|.

Range of a function is defined as the set of all output values (y-values) that a function can produce. It is also called the codomain of the function.

The absolute value of a number is always positive or zero. Therefore, if the function has any negative values in the range, the absolute value of those negative values will be positive and their range will be the same as the positive range.

Therefore, the range of |f(x)| will be [0, 9]. This means that the range of |f(x)| is [0, 9] and is expressed in the interval notation as follows: [0,9].

Therefore, the range of |f(x)| is [0, 9].

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The transformations to the graph of the quadratic function are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.

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Answer:

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Step-by-step explanation:

abcdefghijklmnopqrstuvwxyz

Answer:

Step-by-step explanation:

Points given:

Use midpoint formula to find the coordinates of B:

Substitute known values and solve for x and y:

Point B is:

Answer:

3x²

Step-by-step explanation:

1 triangle is 1/2x²

2 triangles are x²

rectangle below is 2 squares

rectangle below is 2x²

x² + 2x² = 3x²

Answer:

-85.9

Step-by-step explanation:

Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.

To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.

Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)

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Answer: \(\triangle ABD \sim \triangle CBD\) by SAS

Step-by-step explanation:

\(\overline{BD} \cong \overline{BD}\) by the reflexive property, so \(\triangle ABD \cong \triangle CBD\) by SAS. Since all congruent figures are similar, this means that \(\boxed{\triangle ABD \sim \triangle CBD}\) by SAS.

The equation which can be used to determine the angle "A" is sin(A) / 3.2 = sin(110) / 4.6.

Given a triangle ABX.

It is required to find the equation which is used to determine the measure of the angle A.

Using the law of sine, the ratio between the sine of an angle of a triangle and the side length opposite it is a constant.

Here the angles are A, B, and X.

The side lengths opposite these are 3.2, 2.4, and 4.6 respectively.

Using the law of sines:

sin(X) / AB = sin(A) / BX

Here,

X = 110°

AB = 4.6

BX = 3.2

Substitute.

sin(110) / 4.6 = sin(A) / 3.2

Or,

sin(A) / 3.2 = sin(110) / 4.6

Hence, the correct option is C.

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The complete question is given below:

Answer:

a) 43.8 cm

I don't see a part b but let me know if you just forgot to include it and I can answer :)

Answer:

2.6 feet

Step-by-step explanation:

At each point, there is a loss of 20% (since it flies to 80%)

a) 8 - 20% of 8

= 8-1.6 = 6.4

b) 6.4 - 20% of 6.4

= 5.12

c) 5.12 - 20% of 5.12

4.096

d) 4.096 - 20% of 4.096

3.2768

e) 3.2768 - 20% of 3.2768

= 2.62144 feet

Answer:

a) 25

b) 64

Step-by-step explanation:

a) \(x^{2}\)

Substitute x for 5

= \(5^{2}\)

Simplify

=25

b) \((x+3)^{2}\)=

Substitute x for 5

=\((5+3)^{2}\)

Simplify

=\(8^{2}\)

=64

Answer:

\(\displaystyle \frac{x^2+3x+2}{1-x}<0\)

Step-by-step explanation:

Rational Inequality

We are given the solution of rational inequality:

(-2,-1) U (1,∞)

The first set suggests a limited zone than can be obtained by a quadratic equation of the form:

\((x-a)(x-b)<0\)

Where a and b are the roots of the equation, which coincide with the endpoints of the interval. Thus, to get the interval, we can use:

\((x+2)(x+1)<0\)

Operating:

\(x^2+3x+2<0\)

The second set is an open infinite interval, that can be modeled as a third binomial that changes signs in x=1 and is in the denominator, so x=1 is not included.

Thus, one possible inequality is:

\(\mathbf{\displaystyle \frac{x^2+3x+2}{1-x}<0}\)

The solution to the inequality (-2,-1)U(1, ∞) is (-2, ∞)

An inequality is an expression used to show the relationship between two or more numbers and variables.

A rational inequality is an inequality that contains a rational expression.

Given the inequality (-2,-1)U(1, ∞).

The solution to the inequality is (-2, ∞)

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The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.

Given readings:

25 psi pressure

13 psi vacuum

6.3 psi vacuum

7.8 psi vacuum

1.9 psi vacuum

2 psi pressure

7.8 psi pressure

Expressed as rational numbers with a common denominator:

25 psi = 25/1

13 psi = 13/1

6.3 psi = 63/10

7.8 psi = 78/10

1.9 psi = 19/10

2 psi = 2/1

7.8 psi = 78/10

Now, let's order these rational numbers from least to greatest:

1.9 psi = 19/10

6.3 psi = 63/10

7.8 psi = 78/10

7.8 psi = 78/10

13 psi = 13/1

25 psi = 25/1

2 psi = 2/1

Ordered from least to greatest:

19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1

Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

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Answer:

(1,6),(2,5),(3,4),(5,2) I think this is how you answer this question? If not then how?

Step-by-step explanation:

Given that the discharge current decreases to 27% of its initial value in 1.40 ms, we can use the equation of discharge current:

The capacitance of the capacitor is 0 F.

Part A:

Given that the discharge current decreases to 27% of its initial value in 1.40 ms, we can use the equation of discharge current:

I = I₀e^(-t/RC)

Here,

I₀ = initial current

R = resistance

C = capacitance

t = time

We are given that the current is 27% of the initial value, so the equation becomes:

0.27 = \(1e^(-1.40*10^-3/RC)\)

Simplifying the equation, we find:

RC =\(3.28* 10^-3 s\)   ----(1)

Part B:

The time taken to discharge a capacitor through a resistance R is given by:

t = RC ln (Vc/V₀)

where Vc = voltage across the capacitor at time t and V₀ = initial voltage across the capacitor.

Substituting the values, we have:

\(1.40*10^-3\) = C*90 ln (0/100)

Since a fully discharged capacitor has a voltage of 0, we set Vc = 0. Thus, the equation becomes:

\(1.40*10^-3\)= C*90 ln (0)

The natural logarithm of 0 is negative infinity. Therefore, the equation becomes:

\(1.40*10^-3\)= C*90*(-infinity)

Simplifying further, we find:

C = 0

Thus, the value of capacitance is 0 F.

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The probability that the coin is fair given that it lands heads is 0.3571.

Given that a coin is picked from the box and flipped, the probability of the coin being fair is 1/3.

The probability of the coin being biased towards heads and the coin being biased towards tails is 1/3.

Therefore, the probability that the coin is fair and lands heads is (1/3) x 0.5

= 0.1667.

The probability that the coin is biased towards heads and lands heads is (1/3) x 0.8

= 0.2667.

The probability that the coin is biased towards tails and lands heads is (1/3) x 0.1

= 0.0333.

Therefore, the total probability that the coin lands heads is 0.1667 + 0.2667 + 0.0333

= 0.4667.

Using Bayes' Theorem, the probability of the coin being fair given that it lands heads is:

P(fair|heads)

= P(heads|fair) * P(fair) / P(heads)

= 0.5 * 1/3 / 0.4667

= 0.3571.

Thus, the probability that the coin is fair given that it lands heads is 0.3571.

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Since we cannot determine the unknown variable, hence the equation 5(x + 4) - x = 4(x+5) -  1 has no solution

Equations with no solutions has two of its sides to be equal.

From the given option, we can check he equation

5(x + 4) - x = 4(x+5) - 1

Expand

5x + 20 - x = 4x + 20 -1

4x +20 = 4x + 19
4x - 4x = -1

Since we cannot determine the unknown variable, hence the equation 5(x + 4) - x = 4(x+5) -  1 has no solution

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