the ____ numbering system is base 16; in other words, 16 numerals are used to express any given number

Answer:

d = 72

Step-by-step explanation:

1/3 d + 4 = 28

Subtract 4 from each side

1/3d +4-4 = 28-4

1/3d = 24

Multiply each side by 3

3 * 1/3d = 3 * 24

d = 72

Answer:

19.5/3=6.5 centimeters

Step-by-step explanation:

Total distance traveled by the luxury car on a gallon of gas is 24 miles

Let the distance traveled by luxury car with a 8 cylinder engine be x miles

And the distance traveled by midsize car with a 4 cylinder engine be y miles

Now as per the question,

Distance traveled by a midsize car with a 4 cylinder engine is 34 miles

Therefore, x = 34

Now, distance traveled by a midsize car with 4 cylinder engine is 10 miles more than a luxury car with 8 cylinder engine, therefore we can write

x - y = 10

But x = 34

Therefore, 34 - y = 10

                y = 34 - 10 = 24

Luxury car travelled 24 miles.

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Answer:

B

Step-by-step explanation:

Each tick = + or - 2 depending on which quadrant and axis

So the first line (the slanted one) intersects the y axis at (0,5) and continues until (2,5)

Then the line becomes straight (the y remains constant) from (2,5) (the points x value is 2) to (2,10) (the points x value is now 10)

The correct option is a) (x + y) (y + z). Given the output function F in sum-of-minterms form as F = (0, 1, 2, 3, 7), we need to determine the corresponding Boolean expression for the output function.

A 3x8 decoder has three input variables (x, y, z) and eight output variables, where each output variable corresponds to a unique combination of input variables. The output variables are typically represented as minterms.

Let's analyze the given output function F = (0, 1, 2, 3, 7). The minterms represent the outputs that are equal to 1. By observing the minterms, we can deduce the corresponding Boolean expression.

From the minterms, we can see that the output is equal to 1 when x = 0, y = 0, z = 0 or x = 0, y = 0, z = 1 or x = 0, y = 1, z = 0 or x = 0, y = 1, z = 1 or x = 1, y = 1, z = 1.

By simplifying the above conditions, we get (x + y) (y + z), which is the Boolean expression corresponding to the given output function F.

In summary, the correct option is a) (x + y) (y + z).

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Answer:

\(\sf \bf y = \dfrac{1}{3}x + 2\)

Step-by-step explanation:

Where m is slope and b is y-intercept.

To write in slope intercept form isolate y.

To isolate y, first add 'x' to both sides,

       -x + 3y = 6

              3y = x + 6

Now, divide the entire equation by 3,

            \(\sf \dfrac{3y}{3}=\dfrac{1}{3}x + \dfrac{6}{3}\\\\\\\)

             \(\sf \boxed{\bf y = \dfrac{1}{3}x + 2}\)

Answer:

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

The sum is 105

n+n+2+n+4=105

3n+6=105

minus 6 both sideds

3n=99

divide both sides by 3

n=33

n+2=35

n+4=37

The simplified frame of the expression \(3 \times \frac{7 {}^{2} }{3} \times \frac{8}{3} \times 7- \frac{1}{4} \) is 6511.5.

To disentangle the given expression, we got to apply the arrange of operations (PEMDAS) and streamline the terms utilizing the example and division rules.

PEMDAS stands for Enclosures, Exponents, Multiplication and Division, and Expansion and Subtraction. We ought to perform the operations in this arrange to streamline the expression.

We rearrange the type: \(7^2 = 49\)

We rearrange the division 8/3 by partitioning the numerator by the denominator: \( \frac{8}{3} = 2 \frac{2}{3} \)

We disentangle the division 7-1/4 utilizing the run the show that a negative example is comparable to the corresponding of the base raised to the positive type: 7-1/4 = 1/74.

To revamp the expression with the rearranged values:  \(3 \times 49 / (2 \frac{2}{3} \times 1/74)\)

To partition divisions, we increase by the corresponding of the second division:  \(3 \times 49 \times 74 / (2 \frac{2}{3} )\)

We have to be rearrange the blended number  \(2 \frac{2}{3} \) by increasing the total number by the denominator and including the numerator: \(2 \frac{2}{3} = \frac{8}{3} \)

We will disentangle the expression by canceling out common variables:

3 x 49 x 74 / (8/3) = 6511.5

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Answer:  c or d

Step-by-step explanation:

Answer:

\(m=\frac{5}{2}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-2, -4)

Point (2, 6)

Step 2: Find slope m

The length of the interior diagonal of the prism to the nearest hundredth is 10.39 inches.

The interior diagonal of a rectangular prism with sides measuring 8 inches, 6 inches, and 5 inches is 10.39 inches. To calculate this length, use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by connecting the midpoints of all three faces of the prism.

The three sides of the triangle will be the lengths of the edges of the prism, which in this case are 8 inches, 6 inches, and 5 inches. Using the Pythagorean theorem, a2 + b2 = c2, we substitute the sides in, and solve for c, which is the length of the interior diagonal:

82 + 62 = c2

64 + 36 = c2

100 = c2

c = 10.00

The length of the interior diagonal of the prism is 10.00 inches, but the question asked for the answer to the nearest hundredth, so the final answer is 10.39 inches.

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Answer:

25

Step-by-step explanation:

The sum of all of the angles inside of a triangle is 180 degrees. That means we know that:

\((x+26)+(x+14)+(4x-10)=180\)

We can then combine like terms:

\(6x+30=180\)

We want to get 6x alone, so we can subtract 30 from both sides:

\(6x=150\)

Then we want to get x alone, so we can divide both sides by 6:

\(x=25\)

Now we know that x is 25.

answer:19.8 should be the answer?

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Side - We know that the ticks mark the congruency of the two lines.

Angle - We know that the two angles are equal.

Side - The line in the middle is congruent to itself because of reflexive property.

The answer should be A, SAS

Answer:

∠ ABD = 49°, ∠ CBD = 28°

Step-by-step explanation:

∠ ABD + ∠ CBD = ∠ ABC , substitute values

3x + 22 + 5x - 17 = 77 , that is

8x + 5 = 77 ( subtract 5 from both sides )

8x = 72 ( divide both sides by 8 )

x = 9

Thus

∠ ABD = 3x + 22 = 3(9) + 22 = 27 + 22 = 49°

∠ CBD = 5x - 17 = 5(9) - 17 = 45 - 17 = 28°

Answer:

Step-by-step explanation:

6x-y=-5

-6x+y=5

Adding the 2 equations we have:

0 + 0 = 0

0 = 0

This means there are infinite solutions

- the equations are identical.

System B

x+3y=13

-x+3y=5

Adding:

6y = 18

y = 3.

x = 13 - 3(3) = 4.

The system has a unique solution

(x. y) = (4, 3).

Answer:

1)4 different kinds

There were 40 left

Ate 2 from each bag

2)The amount left in each bag

Step-by-step explanation:

I think these are the correct answers.

Hope this helps! :)

The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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Answer:

two ways in which the relationship negatively

The probability that at least one of the bulbs lasts 900 hours or more is approximately 0.992 or 99.2%.

To solve this problem, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

So, let's first find the probability that all three bulbs fail before 900 hours of use. Since each bulb's failure is independent of the others, we can multiply their individual probabilities of failure together:

0.2 × 0.2 × 0.2 = 0.008

This means that the probability of all three bulbs failing is 0.008.

Now, we can use the complement rule to find the probability that at least one bulb lasts 900 hours or more:

1 - 0.008 = 0.992

Therefore, the probability that at least one of the bulbs lasts 900 hours or more is approximately 0.992 or 99.2%.

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Answer:

Step-by-step explanation:

Invert and multiply the second fraction.

\(\frac{x^2 - 2x}{x^2 - 10x + 25} *\frac{x^2 - 25}{6x^2 - 12x}\)

All 4 parts of the two fractions can be factored into simpler factors.

\(\frac{x(x - 2)}{(x - 5)(x - 5)} * \frac{(x + 5)(x - 5)}{6(x - 2)}\)

Numerous cancelations can occur

Answer

\(\frac{x}{(x -5)} * \frac{(x + 5)}{6}\)

the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.

Corresponding angles are angles that are in the same position at each intersection where a straight line crosses two others. In the given list of angles, we can see that:

Angles 1 and 3 are corresponding angles, because they are on opposite sides of the line and are in the same position relative to the other lines.

Angles 5 and 7 are corresponding angles, for the same reason.

Angles 6 and 8 are corresponding angles, because they are alternate interior angles (they are on opposite sides of the transversal and inside the two lines).

Angles 7 and 2 are vertical angles, not corresponding angles.

Angles 6 and 3 are alternate interior angles, not corresponding angles.

Angles 1 and 6 are alternate interior angles, not corresponding angles.

Therefore, the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.

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The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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The relationship that is normally expressed as the quotient of one quantity divided by another is called a ratio

The relationship that is normally expressed as the quotient of one quantity divided by another is called a ratio. A ratio is a comparison of two numbers or measurements, and it can be written in different ways.

For example, if we have two quantities A and B, the ratio of A to B can be written as

A/B

A:B

"A is to B"

The ratio of A to B tells us how many times A is contained within B, or how many units of A we would need to have to match the amount of B.

Ratios are useful in many fields, such as finance, engineering, and science, where they are used to compare and analyze different quantities and their relationships.

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Answer:

15/4

Step-by-step explanation:

\(\ell=5/2 \\ \\ w=1 \\ \\ h=3/2 \\ \\ V=lwh=(5/2)(1)(3/2)=15/4\)

Answer:

3.75 so i believe the answer might be 15/4?

Step-by-step explanation:

im sorry if this is not the right answer

(A) The distribution consists of two clusters and a gap, which best describes the distribution.

So, in the given situation the distribution consists of two clusters and a gap, which best describes the distribution.

Therefore, (A) the distribution consists of two clusters and a gap, which best describes the distribution.

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The complete question is given below:

The diameter, in centimeters (cm), of each tree in a random sample of trees in a forest was measured. The histogram shown summarizes the diameters.

Which of the following is the best description of the distribution?

A. The distribution consists of two clusters and a gap.

B. The distribution is approximately normal.

C. The distribution is symmetric with a skew to the right.

D. The distribution is skewed to the left.

E. The distribution is uniform.

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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In the fixed case, the demand function for x is x = w/(2px) and the demand function for y is y = w/(2py). Plugging these demand functions back into the utility function yields the indirect utility function which equals V = min[w/(2px), w/(2py)].

Starting with the indirect utility function, then solving for 1 and letting E = w, we can rearrange the equation to get:

1 = min[E/(2px), E/(2py)]

Multiplying both sides of the equation by 2pxpy gives us:

2pxpy = min[E*py, E*px]

Dividing both sides of the equation by E gives us:

2pxpy/E = min[py, px]

This is the equation for the indirect utility function in the fixed proportions case.

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