3 1/2 gal = how many qt?

The solution to the quadratic equation is x = 1

To find the values of p and q, we need to solve the following system of equations:

p + q = -6 (equation 1)

p * q = 1 (equation 2)

We need to find two numbers whose sum is -6 and whose product is 1. By examining the factors of 1, we see that the only possible values for p and q are -1 and -1 (since -1 * -1 = 1 and -1 + -1 = -2).

Now, we can rewrite the quadratic equation as:

x² + 6x + 1 = -4

(x + p)(x + q) = 0

(x - 1)(x - 1) = 0

Expanding (x - 1)(x - 1) gives us x² - x - x + 1 = x² - 2x + 1. As you can see, this expansion is equivalent to the original quadratic equation, x² + 6x + 1 = -4.

Therefore, we have successfully factored the left-hand side of the equation x² + 6x + 1 = -4 into two linear factors, which are (x - 1)(x - 1).

To solve the equation, we set each factor equal to zero and solve for x:

x - 1 = 0 or x - 1 = 0

Solving these equations, we find that x = 1 is the solution to the quadratic equation x² + 6x + 1 = -4.

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a. The probabilities of winning for the given selections is 0.0024

b. The probabilities of winning for the given selections is 0.0012

c. The probabilities of winning for the given selections is 0.0006

d. The probabilities of winning for the given selections is 0.0004

What is probability?

Probability is a measure or quantification of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 represents an event that is impossible or will never occur, and 1 represents an event that is certain or will always occur .The closer the probability value is to 1, the more likely the event is to occur, while the closer it is to 0, the less likely the event is to occur.

To calculate the probability of winning in the given state lottery scenario, we need to determine the total number of possible outcomes and the number of favorable outcomes for each selection.

In this lottery, four digits are drawn at random one at a time with replacement from 0 to 9. Since replacement is allowed, the total number of possible outcomes for each digit is 10 (0 to 9).

a. Probability of winning if you select 6, 7, 8, 9:

Total number of possible outcomes for each digit: 10

Total number of favorable outcomes: 4! (4 factorial) = 4 * 3 *2 * 1 = 24

The probability of  total number of favorable outcomes divided by the total number of possible outcomes:

Probability of winning = \(\frac{24 }{10^4}=\frac{ 24}{10000} = 0.0024\)

b. Probability of winning if you select 6, 7, 8, 8:

Total number of possible outcomes for each digit: 10

Total number of favorable outcomes: \(\frac{4!}{2!}\) (4 factorial divided by 2 factorial) = \(\frac{4 * 3 * 2 * 1}{ 2 * 1}= \frac{24}{2} = 12\)

Probability of winning = \(\frac{12 }{10^4} = \frac{12 }{10000 }= 0.0012\)

c. Probability of winning if you select 7, 7, 8, 8:

Total number of possible outcomes for each digit: 10

Total number of favorable outcomes: \(\frac{4!}{2! * 2!}= \frac{4* 3 * 2 * 1}{2* 1 * 2 * 1} = \frac{24}{4} = 6\)

Probability of winning =\(\frac{6 }{10^4} = \frac{6}{10000} = 0.0006\)

d. Probability of winning if you select 7, 8, 8, 8:

Total number of possible outcomes for each digit: 10 Total number of favorable outcomes: \(\frac{4!}{3! * 1!}= \frac{4 * 3 * 2 * 1}{3 * 2 * 1 * 1} = 4\)

Probability of winning = \(\frac{4 }{10^4} = \frac{4}{10000 }= 0.0004\)

Therefore, the probabilities of winning for the given selections are: a. 0.0024 b. 0.0012 c. 0.0006 d. 0.0004

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Answer:

99   (cm^2)

Step-by-step explanation:

Perpendicular to the AB segment at points D and C, the graph is divided into two triangles and a rectangle.

The area of the middle rectangle is equal to 8*9=72. The hypotenuse of the right triangle is 10cm, and one of the right sides is 9cm, so the other side is SQRT (10^2-9^2) = SQRT (19).

One side of the left triangle is 9cm long and the other side is 14-8-sqRT (19) = 6-sqRT (19) cm.

Then, add the area of the three parts.

72+9*sqrt（19）/2+9*（6-sqrt（19））/2=99    (cm^2)

After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

Answer:

the answer is a and c because both inequalities are true

The function in Excel that is used to compute the statistics required to create a histogram is the FREQUENCY function.

The FREQUENCY function is used to calculate how often values occur within a specified range or bin.

The output of the function is an array of values that represents the frequency distribution of the data, which can then be plotted to create a histogram.

To use the FREQUENCY function, we first need to define the bins or intervals that we want to use for our histogram.

These bins should cover the range of the data and should be of equal width.

Once we have defined our bins, we can use the FREQUENCY function to calculate the frequency of values that fall within each bin.

The syntax of the FREQUENCY function is as follows:

=FREQUENCY(data_array, bins_array)

The data_array argument is the array or range of data that we want to analyze, and the bins_array argument is the array or range of bins that we have defined.

The function returns an array of values that represents the frequency of values that fall within each bin.

Once we have the frequency distribution of our data, we can create a histogram by plotting the frequency values against the bin intervals.

Excel has built-in tools for creating histograms, which can be found under the "Data Analysis" menu.

By defining our bins and using the FREQUENCY function, we can quickly and easily analyze the distribution of our data and visualize it in a histogram.

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The ball's maximum height can be determined by analyzing the table of recorded heights at different times.

To find the maximum height, we look for the highest value in the table.

From the information provided, we do not have access to the table, so we cannot provide the exact maximum height. However, if you have the table, you can find the maximum height by identifying the highest value recorded.

Once you have the table, you can locate the highest point and determine the corresponding time.

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1. The number of computations (hashes) required for finding a collision at 80% and 10% probabilities is 1.8447 x 10^19.

2. It will take approximately 47,891 seconds (or 13.3 hours) to find a collision at 10% probability.

The number of computations (hashes) required for finding a collision at 80% and 10% probabilities depends on the size of the hash function output. Let's assume a hash function output size of 128 bits for this example.

For finding a collision at 80% probability, we need to use the birthday attack algorithm. The number of hashes required can be calculated using the following formula:

N = sqrt((2^(n+1))*ln(1/(1-p)))

where n is the size of the hash output in bits (n=128 in this case), p is the desired probability of finding a collision (p=0.8 in this case), ln is the natural logarithm, and sqrt is the square root function.

Substituting the values, we get:

N = sqrt((2^(128+1))*ln(1/(1-0.8))) = 2^64.3155 = 1.8447 x 10^19

Therefore, we need 1.8447 x 10^19 hashes to find a collision at 80% probability.

For finding a collision at 10% probability, we can use the following formula:

N = sqrt((2^(n+1))*ln(1/(1-p)))

Substituting the values, we get:

N = sqrt((2^(128+1))*ln(1/(1-0.1))) = 2^55.9724 = 4.7891 x 10^16

Therefore, we need 4.7891 x 10^16 hashes to find a collision at 10% probability.

If we have a computer that can process a trillion hashes per second, we can calculate the time required to find a collision at 10% probability as follows:

time = N / rate

where N is the number of hashes required to find a collision (N=4.7891 x 10^16), and rate is the rate of hashes that the computer can process per second (rate=1 trillion = 1 x 10^12).

Substituting the values, we get:

time = (4.7891 x 10^16) / (1 x 10^12) = 4.7891 x 10^4 seconds

Therefore, it will take approximately 47,891 seconds (or 13.3 hours) to find a collision at 10% probability with a computer that can process a trillion hashes per second.

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Answer:

Commutative property of multiplication; repeats, and has multiplication sign.

Step-by-step explanation:

5 * 2 = 2*5

When the square root of x is equal to 2, the value of x^2 + x^3 is 80. This can be found by squaring both sides of the equation √(x) = 2 to eliminate the square root.

This gives x = 4. Substituting this value into the expression x^2 + x^3 results in 80. Given the equation √(x) = 2, we can square both sides to get rid of the square root: (√(x))^2 = 2^2. Simplifying, we find x = 4. Now, we substitute this value into the expression x^2 + x^3: 4^2 + 4^3.

Evaluating this expression, we get 16 + 64, which equals 80. Therefore, when x is a real number such that √(x) = 2, the value of x^2 + x^3 is indeed 80.

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Functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

a) L(A) = 1 - 1: This function is not a linear operator because it does not preserve scalar multiplication. Multiplying A by a scalar c would yield L(cA) = c - c, which is not equal to cL(A) = c(1 - 1) = 0.

b) L(A) = 1 + 17: Similar to the previous case, this function is not linear since it fails to preserve scalar multiplication. Multiplying A by a scalar c would result in L(cA) = c + 17, which is not equal to cL(A) = c(1 + 17) = c + 17c.

c) L(1) = C1 + AC: This function is a linear operator since it satisfies both the preservation of addition and scalar multiplication properties. Adding matrices A and B and multiplying the result by scalar c will yield L(A + B) = C(1) + AC + C(1) + BC = L(A) + L(B), and L(cA) = C(1) + cAC = cL(A).

d) L(1) = C°1: This function is a linear operator since it satisfies the properties of linearity. Addition and scalar multiplication are preserved, and L(cA) = C(0)1 = c(C(0)1) = cL(A).

e) L(1) = 1?C: This function is not a linear operator as it does not preserve scalar multiplication. Multiplying A by a scalar c would give L(cA) = 1?(cC), which is not equal to cL(A) = c(1?C).

In summary, functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

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Answer:

b

Step-by-step explanation:

i know it

Answer:

b

Step-by-step explanation:

To find the particular solution, we need additional information such as the initial condition \(y(x_0) = y_0\), where \(x_0\) and \(y_0\) are known values.

To find the particular solution to a differential equation, we need to know the specific form of the differential equation. Without this information, it is not possible to determine the particular solution.

A differential equation is an equation that relates a function and its derivatives. The form of the differential equation determines the method used to solve it and find the particular solution.

For example, a simple linear first-order ordinary differential equation has the form:

\(\frac{dy}{dx} = f(x)\).

To find the particular solution, we need additional information such as the initial condition \(y(x_0) = y_0\), where \(x_0\) and \(y_0\) are known values.

The method of solution depends on the specific type of differential equation, which can include linear equations, separable equations, exact equations, etc. Each type of equation requires different techniques to find the particular solution.If you provide the specific form of the equation you want to solve or any additional information or context, I can guide you through the process of finding the particular solution. Otherwise, without the differential equation, it is not possible to determine the particular solution.

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By the concept of linear equation :

$1,500 was spent on flights,

$680 was spent on hotels,

$7,300 was spent on other purchases.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). For the purpose of resolving systems involving two linear equations, this form is also highly helpful.

Given:

Flights: 4 points per dollar

Hotels: 2 points per dollar

Other: 1 point per dollar.

Total spent = $9,480

Points earned = 14,660

Let

x = money spent on flights

y = money spent on hotels

z = money spent on other purchases.

Because the money spent on flights was $140 more than twice the money spent on hotels, therefore

x = 2y + 140          (1)

Total charges were $9,480, therefore

x + y + z = 9480    (2)

Total points earned was 14,660. Therefore

4x + 2y + z = 14660   (3)

Subtract (2) from (3).

4x + 2y + z - (x + y + z)

= 14660 - 9480

3x + y = 5180             (4)

Substitute (1) into (4).

3(2y + 140) + y = 5180

7y + 420 = 5180

7y = 4760

y = 680

From (1), obtain

x = 2y + 140

= 2(680) + 140

= 1500

From (2), obtain

z = 9480 - (x + y)

= 9480 - (1500 + 680)

= 7300

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Answer:

B

Step-by-step explanation:

Fip numbers and change both signs when reflecting over y=-x

Answer:

C

Step-by-step explanation:

The area of the field is 10,765.44 square meters.

Given that:

Diameter, d = 72 m

Width, W = 72 m

Length, L = 93 m

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the field is calculated as,

A = (π/4)d² + W·L

A = (3.14 / 4) x 72² + 72 x 93

A = 4,069.44 + 6,696

A = 10,765.44 square meters

The area of the field is 10,765.44 square meters.

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See below

Step-by-step explanation:

\(A = {9}^{2} = 81 \\ \\ A = {12}^{2} = 144 \\ \\ x = \sqrt{81 + 144} \\ \\ = \sqrt{225} \\ \\ = 15\\\\A = {15}^{2} = 225 \)

Answer:

C

Step-by-step explanation:

reflection across the x-axis.

Answer:

s(t)=200(1/2)^t/13

Step-by-step explanation:

Here's answer:

https://www.nysedregents.org/algebratwo/619/algtwo62019-mrs.pdf

The number of years it will take for  1/10 of this substance to remain is; 50 years

The half life formula is;

N(t) = N₀(¹/₂)^(t/t_1/2)

where;

N(t) is quantity of the substance remaining

N₀ is initial amount of substance

t is time elapsed

t_1/2 is half life

Thus;

S(t) = 200(¹/₂)^(t/15)

We want to find the time it will take 1/10 of the substance to remain. Thus;

1/10 = (200/200)(¹/₂)^(t/15)

1/10 = (¹/₂)^(t/15)

t/15 = In(1/10)/In(¹/₂)

t/15 = 3.32193

t = 49.88 ≈ 50 years

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Expectancy theory would best provide perspective on the question 'if i study for 12 hours, what is the probability that i'll get an on the exam?".

 Expectancy theory (expectancy theory of motivation) was put forward by Victor Vroom in 1964. Vroom put more emphasis on outcome factors, rather than needs as proposed by Maslow and Herzberg.

This theory states that the intensity of the tendency to perform in a certain way depends on the intensity of the expectation that performance will be followed by a definite outcome and on the attractiveness of the result to the individual.

Vroom argues that people will be motivated to do certain things to achieve goals if they believe that their actions will lead to the achievement of these goals.

There are three main assumptions of Vroom in expectancy theory.  These assumptions are as follows:

-Every individual believes that if he behaves in a certain way, he will get certain things.  This is called an outcome expectancy as a person's subjective assessment of the likelihood that a certain outcome will arise from that person's actions.

-Each outcome has value, or appeal to a particular person.  This is called valence (valence) as the value that people give to an expected result.

-Each outcome is associated with a perception of how difficult it is to achieve that outcome.  This is called effort expectancy as the possibility that one's efforts will result in the attainment of a certain goal.

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Answer:

x= -1 or x=3

Step-by-step explanation:

Answer:

S = k√(m2 ± n2). divide both sides by k. s/k = √(m2 ± n2). Take the square of both sides to remove the square root on the right-hand side.

Step-by-step explanation:

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The answer is B

Eplanation:

V = pi * r² * (h/3)

Then from here you just make h the subject of the formula:

h = (V * 3)/(pi * r²)

h = (393*3)/[3.14* (10/2)²]

h = 15.01910828 ft

which is rounded to 15 ft...B

:)

On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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Answer:

\(\boxed{\red{500 + x \leqslant 4500}}\\ x \leqslant 4500 - 500 \\ \blue{\underline{x \leqslant 4000}}\)

Answer:

Less

Step-by-step explanation:

Because we don’t know the value of x.

Answer:

She ran 28 miles cause if you add 17 and 11 you get 28! Hope this helped!

Step-by-step explanation:

Based on the given parameters, the simplified expression of (-5) to the power of -2 is 1/25

The mathematical statement is given as:

Simplify (-5) to the power of -2

This can be rewritten as:

(-5)^-2

Apply the power rule of indices to the above expression

1/(-5)^2

Evaluate the exponent in the above expression

1/25

Hence, the simplified expression of (-5)^-2 is 1/25; based on the given parameters

This means that the simplified expression of (-5) to the power of -2 is 1/25

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Answer:

both have equal.............

Answer: the answer is sas

Step-by-step explanation: i hoped that helped!