An expression is shown below.

−(2x−1)(3x+4)
Drag and drop numbers into the boxes to make the expression below equal to the expression above.

Zeroes of the equation are i3√3 and -i3√3.

A value (a number) at which the polynomial evaluates to zero is referred to as the "zero of a polynomial." For instance, the zeros of the polynomial x²-3x+2 are 1 and 2. A polynomial's zeros are frequently referred to as its "roots." Every polynomial has a unique multiset of zeros, which is an unordered list. The coefficients of a zero polynomial, which is a constant polynomial, are all equal to 0. The value of the variable that brings a polynomial to zero is referred to as its zero. As a result, any real integer is the zero of the zero polynomial.

Given Data

(x) = -x² - 27

To find zeroes,

m(x) = 0

0 = -x² - 27

x² = -27

As we know,

i² = -1

x² = i²(27)

x² = i (±3√3)

x = i3√3

x = -i3√3

Zeroes of the equation are i3√3 and -i3√3.

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Answer:

2.5

Step-by-step explanation:

2x = 5

x = 5/2 = 2.5

I hope im right!!

"Centripetal is the word used to describe a vector that always points toward the centre of a circular path."

The centripetal acceleration vector is an acceleration in the radial direction that is directed towards the centre of the circular line of motion. It runs perpendicular to the linear motion, or v.

The direction of the velocity shift for a ball travelling around a curve is in the direction of the curve's centre. Centripetal acceleration is the acceleration that is directed towards the centre of a curved or circular route.

Any force that changes the path of motion towards the centre of a circular motion is known as a centripetal force. The portion of the force that produces the centripetal force is the part that is perpendicular to the velocity.

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Answer:

x≈3.35, or the square root of 11.

Step-by-step explanation:

Use the pythagorian therom. 3²+1.5²=x²

(Half of 3 is 1.5 and the line splits it in half)

The total number of strings is given by the product of the two values mentioned above: C(13, 4) * 4^3.

To find the number of strings over the alphabet abcde of length 13 that have exactly four 'c's, we need to consider the placement of the 'c' characters. First, we choose the positions for the four 'c's out of the 13 positions, which can be done in (13 choose 4) ways, denoted as C(13, 4). For each choice of positions for the 'c's, we have three remaining positions to fill with the remaining four letters (a, b, d, e). The three positions can be filled in 4^3 ways.

Thus, the total number of strings is given by the product of the two values mentioned above: C(13, 4) * 4^3. Evaluating this expression, we find that the number of strings over the alphabet abcde of length 13 with exactly four 'c's is C(13, 4) * 4^3.

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A 24-hour collection provides a more comprehensive and reliable assessment of certain values.

A 24-hour collection is a better indicator of some values than a random specimen because it provides a more comprehensive and representative sample of the specific substance or parameter being measured.

It captures variations in levels throughout the day and allows for the detection of fluctuations that may not be captured by a single random specimen.

A 24-hour collection involves collecting samples over a full day, typically for substances such as urine or hormones. This method provides a more accurate representation of the average levels of the substance being measured. It takes into account the diurnal rhythm or cyclical variations that may occur throughout the day.

For example, hormone levels often fluctuate throughout the day, with different peaks and troughs at specific times.

By collecting samples at regular intervals over a 24-hour period, a more accurate picture of the average hormone levels can be obtained, allowing for a better assessment of hormonal imbalances or abnormalities.

In contrast, a random specimen may only capture a snapshot of the substance's level at a specific moment, which may not be representative of the overall pattern.

Fluctuations in levels throughout the day can be missed, leading to potential inaccuracies or misinterpretation of the data.

Therefore, a 24-hour collection provides a more comprehensive and reliable assessment of certain values by capturing variations and trends over time, making it a better indicator than a single random specimen.

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To find the probability distribution for Y, the number of errors detected by the auditor, we can use the binomial distribution formula. The binomial distribution is used when there are only two possible outcomes, success or failure, and each trial is independent.

In this case, the probability of success (detecting an error) is 5% or 0.05, and the probability of failure (not detecting an error) is 1 - 0.05 = 0.95.

a. To find the probability distribution for Y, we can use the formula for the binomial distribution:

P(Y = y) = (nCk) * p^k * (1-p)^(n-k)

where n is the number of trials (3 in this case), k is the number of successes (errors detected), p is the probability of success (0.05), and (nCk) is the combination formula.

For y = 0:
P(Y = 0) = (3C0) * (0.05)^0 * (0.95)^(3-0) = (1) * (1) * (0.95)^3 = 0.857375

For y = 1:
P(Y = 1) = (3C1) * (0.05)^1 * (0.95)^(3-1) = (3) * (0.05) * (0.95)^2 = 0.135375

For y = 2:
P(Y = 2) = (3C2) * (0.05)^2 * (0.95)^(3-2) = (3) * (0.05)^2 * (0.95)^1 = 0.007125

For y = 3:
P(Y = 3) = (3C3) * (0.05)^3 * (0.95)^(3-3) = (1) * (0.05)^3 * (0.95)^0 = 0.000125

So the probability distribution for Y is:
Y = 0 with probability 0.857375
Y = 1 with probability 0.135375
Y = 2 with probability 0.007125
Y = 3 with probability 0.000125

b. To construct a probability histogram for p(y), you can create a bar graph where the x-axis represents the number of errors detected (Y) and the y-axis represents the probability (P(Y = y)). Each bar will have a height corresponding to the probability.

c. To find the probability that the auditor will detect more than one error, we need to calculate the sum of the probabilities for Y = 2 and Y = 3:

P(Y > 1) = P(Y = 2) + P(Y = 3) = 0.007125 + 0.000125 = 0.00725

Therefore, the probability that the auditor will detect more than one error is 0.00725.

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Answer: -28

Step-by-step explanation:

\(|J|=(5)(-2)-(6)(3)=-10-18=-28\)

Answer: Use the equation for finding slope which Is Rise/Run

Step-by-step explanation:

Answer:

you could find slope by using the equation

y2 -y1/ x2-x1

meaning your coordinates

(2,1) and (1,3)

3-1/1-2

=2/-1

m=-2

Answer:

I believe it is 76 ft squared but I am not positive..

Using the Binomial probability distribution,

the probability that sheer guesswork will yield exactly 18 correct answers is ²⁷C₁₈(0.2)¹⁸(0.8)⁹

We have given that,

total number of multiple choice questions= 27

each question has number of possible answer

= 5

but only one is correct .

we have to find out the probability that sheer guesswork will yield 18 correct answer.

P(C) = probability of answering any question correctly = (1 / 5) = 0.2

P(W) = probability of answering any question wrongly = (4/ 5) = 0.8

Using the Binomial probability distribution,

P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Probability of answering exactly 18 questions correctly = P(X=18) = ²⁷C₁₈(0.2)²⁸(0.8)⁹

Hence, the probability value is ²⁷C₁₈(0.2)²⁸(0.8)⁹

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Answer:

m = 5

Step-by-step explanation:

if you input the equation into M aTh wA y, you get the answer in seconds

The equation in slope-intercept form is therefore:y = mx + b = -x + 4

To write the equation in slope-intercept form that corresponds with the given table, we need to use the slope-intercept formula which is:y = mx + b

where m represents the slope and b represents the y-intercept.The slope formula is given bym = (y2 - y1)/(x2 - x1)where (x1, y1) and (x2, y2) are two points on the line.

To get the equation in slope-intercept form, we need to find the slope and y-intercept from the given table. Then we'll substitute the values of m and b in the slope-intercept formula and solve for y.

Let's first identify two points from the table. We can use any two points on the line. Let's use (0, 4) and (2, 2) as they have nice values for calculations.Using the slope formula, we have:

m = (y2 - y1)/(x2 - x1) = (2 - 4)/(2 - 0) = -2/2 = -1

Substituting the value of slope (m = -1) and one of the given points (0, 4) in the slope-intercept formula,

we get:4 = -1(0) + b

Simplifying, we get:b = 4

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Answer:

Step-by-step explanation:

Answer:

what-

Step-by-step explanation:

Thus, the shaded region is the set of solutions for this system of inequalities, and the integers in this region are -4, -3, -2, -1, 0, 1, 2, and 3.

To solve the system of inequalities by graphing, we first need to rewrite each inequality in slope-intercept form, y < mx + b, where y is the dependent variable (in this case, we can use y to represent both 3-2a and 5a), m is the slope, x is the independent variable (in this case, a), and b is the y-intercept.

Starting with the first inequality, 3-2a < 13, we can subtract 3 from both sides to get -2a < 10, and then divide both sides by -2 to get a > -5. So the slope is negative 2 and the y-intercept is 3. We can graph this as a dotted line with a shading to the right, since a is greater than -5:

y < -2a + 3

Next, we can rewrite the second inequality, 5a < 17, by dividing both sides by 5 to get a < 3.4. So the slope is 5/1 (or just 5) and the y-intercept is 0. We can graph this as a dotted line with a shading to the left, since a is less than 3.4:

y < 5a

To find the integers that are in the set of solutions for this system of inequalities, we need to look for the values of a that satisfy both inequalities. From the first inequality, we know that a must be greater than -5, but from the second inequality, we know that a must be less than 3.4. So the integers that are in the set of solutions are the integers between -4 and 3 (inclusive):

-4, -3, -2, -1, 0, 1, 2, 3

To see this graphically, we can shade the region that satisfies both inequalities:

y < -2a + 3 and y < 5a

The shaded region is the set of solutions for this system of inequalities, and the integers in this region are -4, -3, -2, -1, 0, 1, 2, and 3.

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The slope of all the given options  are equal and it is equal to slope of given equation .

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

Given

Equation of a given line is x+2 y=6

Lets find out slope m by writing the equation in \($y= \mathbf{m}+\mathbf{b}$\) form

\($$\begin{aligned}& x+2 y=6 \\& 2 y=-x+6 \\& y=\frac{-1}{2} x+6\end{aligned}$$\)

The slope of the line is \($\frac{-1}{2}$\)

Now we find slope of each option using formula \($m=\frac{y_2-y_1}{x_2-x_1}$\)

Lets pick two points from the graph to find out slope

Pick (0,3) and (6,0)

\($$\begin{aligned}& m=\frac{y_2-y_1}{x_2-x_1} \\& m=\frac{0-3}{6-0}=\frac{-1}{2}\end{aligned}$$\)

Now pick two points from option \($\mathbf{B}$\) to find slope

(-10,-3) and (0,-8)

\(m=\frac{-8+3}{0+10}=\frac{-1}{2}$$\)

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Answer:

t= b/2 - 3d/2

Step-by-step explanation:

The company would need to reduce the standard deviation in the process to approximately 1.197 millimeters to meet the target defect probability of 1%.

To calculate the required reduction in the standard deviation, we first need to find the new tolerance interval that corresponds to a defect probability of 1%. We can use Table 9.1 in the textbook to do this.

First, we need to calculate the process capability index Cpk, which is given by:

Cpk = min[(USL - μ)/(3σ), (μ - LSL)/(3σ)]

where USL is the upper specification limit, LSL is the lower specification limit, μ is the process mean, and σ is the process standard deviation. Substituting the given values, we get:

Cpk = min[(23.2 - 23)/(3 × 0.15), (23 - 22.8)/(3 × 0.15)] = min[0.6667, 0.2222] = 0.2222

Table 9.1 provides the tolerance factor k for a given Cpk and defect probability p. We want to find k for Cpk = 0.2222 and p = 0.01. From the table, we find that:

k = 3.090

The tolerance interval is given by:

μ ± kσ

where μ is the process mean and σ is the process standard deviation. Substituting the given values, we get:

23 ± 3.090σ

To reduce the defect probability to 1%, we want this interval to cover at least 99% of the process output. Therefore, we need to solve the following equation for σ:

P[(23 - 3.090σ) ≤ X ≤ (23 + 3.090σ)] = 0.99

where X is the process output. Using Table 8 in the textbook, we can find the z-score corresponding to a tail probability of 0.005, which is 2.58.

Substituting the given values and solving for σ, we get:

0.99 = P[(23 - 3.090σ) ≤ X ≤ (23 + 3.090σ)]

= P[-2.58 ≤ Z ≤ 2.58] (where Z is the standard normal variable)

= 0.995 - 0.005

= 2 × 0.495 - 1

Therefore, we have:

2.58 = (23 + 3.090σ - 23)/σ

= 3.090

Solving for σ, we get:

σ = 3.090/2.58 ≈ 1.197 millimeters

Therefore, the company would need to reduce the standard deviation in the process to approximately 1.197 millimeters to meet the target defect probability of 1%.

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The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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The car's speed after the given amout of time is 19.8 m/s²

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration. A point or object going straight ahead is accelerated when it accelerates or decelerates. Any alteration in an object's velocity could take the form of a change in direction of motion or a speed increase or reduction. The moon orbiting the earth, an apple falling to the ground, and a car stopped at a stop sign are a few instances of acceleration.

Average Acceleration =Change in Velocity/ Time Taken

So Change in Velocity is 10-x m/s

Time taken is 7.25 s

Given accelaration 4.11 m/s²

Putting the values we get,

4.11 = (10-x)/7.25

⇒29.8 = 10-x

⇒x=19.8 m/s²

​

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The length of the day in Manila, Philippines, varies periodically and can be modeled by a trigonometric function. The formula is l(t) = (779.607 - 675.856) xcos((2π/365) x (t - 111111)) + (779.607 + 675.856) / 2.

To model the variation in the length of the day in Manila, a trigonometric function is used, considering the period of change as exactly 365365365 days. The shortest day occurs on December 21, with a length of 675.85675.85675, point, 85 minutes, while the longest day occurs on June 21, with a length of 779.60779.60779, point, 60 minutes.

To find the formula for the trigonometric function, we need to consider the general form of a cosine function, which includes an amplitude, angular frequency, and phase shift. Here, the amplitude is (779.607 - 675.856), the angular frequency is (2π/365), and the phase shift is (t - 111111), where t represents the number of days after January 1.

Therefore, the formula for the length of the day can be expressed as l(t) = (779.607 - 675.856) xcos((2π/365) x (t - 111111)) + (779.607 + 675.856) / 2. This equation represents the variation in the day length throughout the year in Manila, with the cosine function capturing the periodic nature of the changes.

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Answer:

66 feet

Step-by-step explanation:

5 1/2 times 12

Answer:

144

Step-by-step explanation:

9*3=27

27*4=108

6^2=36

108+36=144

Answer:

\(\Large \boxed{\sf 144 \ ft^2}\)

Step-by-step explanation:

Find the area of the 4 triangles and 1 square and add them.

Area of triangle = base × height × 0.5

Area of square = s²

\((9 \times 6 \times 0.5\times 4)+(6^2)=144\)

Answer:

There is NO mode.

The range is 6.

Step-by-step explanation:

Mode is the most frequent number and in this case there are no repetitive numbers.

Range is the Max Number minus the Minimum Number. So in this case 24-18 which equals 6.

using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.

To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.

Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:

A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168

B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165

C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168

D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165

Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.

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The  sum or a difference of logarithms are: a)= log-1  (b)  log₉11  2) a) log2072  (b)  log10077696  (3) s= 1

The logarithm of a product is the sum of the logarithms of the factors being multiplied, while the logarithm of the ratio or quotient of two numbers is the difference of the logarithms.  To write the sum or difference of logarithms as a single logarithm, one can use the addition rule, the multiplication rule of logarithm, or the third rule of logarithms that deals with exponents.

the given logarithms are

a. log(19/20)

Applying the law of logarithm to get

log(19-20)

= log-1

b. log9(3 x 8)

log₉3 + log₉8

log ₉(3+8)

= log₉11

2 The logarithm that has error include

a. log56 + log37 = log542

The logarithm is wrong

Applying the law of multiplication we have

log(56*37)

= log2072

b. 3 log216 = log2163

This logarithm is wrong because applying the power law of logarithm

log216³ = log10077696

3) S = 10 logl1 - 10logI0

Using the low of logarithm we have

s= log11¹⁰/log10¹⁰

log(11/10)¹⁰⁺¹⁰

log(1.1)⁰

Any number raised to power zero is 1

therefore s= 1

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