Simplify the following expression.
44[(9 + 3) + 72 - 6 * 2.5 - 19] - [42 - 3(77 + (3.5 2)) - 9]

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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A two-sample z-test for a difference in population proportions is the appropriate method for analyzing the results.

Z-test is a statistical test often utilizes to find the difference in mean. It is coupled with variances and sample size to find the appropriate results. It is a hypothetical test where normal distribution is seen.

z-test holds numerous advantages such as it indicates difference in small size groups making it more usable. Moreover, it is also reliable in non-normal distribution of data and is efficient while taking multiple groups in a single analysis. The question has two different popular proportion and hence the two sample z-test will suitable to compare the means.

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Answer:

27

Step-by-step explanation:

13 + 14 = 27

Answer: -13+-14

Step-by-step explanation: the Absolute value is the opposite value of something like 24-57 the absolute value of that would be -24-(-57)

Our vertex has an x-coordinate of 0, so the axis of symmetry for our function is x = 0. Now, let's consider the zeros of our function. Graphically, the zeros of a function are the x-coordinates of the points where the function crosses the x-axis. This occurs where y = 0.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

B 100%

Step-by-step explanation:

Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Answer:

After 5 minutes, the submarine is at 240 ft below sea level.

Step-by-step explanation:

-300 + 16z

After 5 minutes, z = 5.

-300 + 16(5) = -300 + 80 = -240

After 5 minutes, the submarine is at 240 ft below sea level.

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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We can deduce that option A is likely to be true based on the given graph of rolling dice median data.

The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median.

The graph illustrates that the median value of the rolls is closer to the center of the possible outcomes (numbers 3, 4, and 5) than the extremes (numbers 1 and 6).

This implies that when rolling a dice several times, the median is less likely to fall between the numbers 1 and 6.

However, because rolling the dice is a random process, there is always a degree of uncertainty in predicting the outcomes.

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The image of the function after the translation is g(x) = log(x + 1) + 4

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

f(x)=logx

How to determine the equation of g(x)?

From the graph, the given parameters are:

f(x) = log(x)

From the graph, we can see that:

The graph of f(x) is translated left by 1 unit

The graph of f(x) is translated up by 4 units

This transformation is given as

g(x) = f(x + 1) + 4

Mathematically, this transformation can be represented as

(x, y) = (x + 1, y + 4)

When represented as a function, we have

g(x) = f(x + 1) + 4

Substitute the equation f(x) = log(x)

f(x + 1) = log(x + 1) + 4

So, we have the following equation

g(x) = log(x + 1) + 4

Hence, the equation of g(x) is g(x) = log(x + 1) + 4

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Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

The probability that Aakesh will select a blue marble from each bag is 4/45.

To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.

Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:

P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag

P(Blue from first bag) = 2 / 5

Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:

P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag

P(Blue from second bag) = 2 / 9

To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:

P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)

P(Blue from both bags) = (2 / 5) * (2 / 9)

P(Blue from both bags) = 4 / 45.

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Answer:

138,920 m²

Step-by-step explanation:

A square pyramid has 1 square base and 4 lateral triangular faces.

Area of square pyramid is given as BASE Area (BA) + ½*Perimeter of Base (P) × Slant height

Area of pyramid = \( b^2 + \frac{1}{2}*4(b)*l \)

Where,

b = base length = 230 m

l = slant height = 187 m (height of the triangular sides)

Surface area = \( 230^2 + \frac{1}{2}*4(230)*187 \)

\( = 52900 + 2(230)*187 \)

\( = 52900 + 86020 \)

\( = 138920 \)

Surface area of the pyramid = 138,920 m²

Answer:

hope i helped thank you

Step-by-step explanation:

Answer:

1 kg = 1000 grams

15,000 grams = 15kg

Answer:

False

Step-by-step explanation:

Should be 3 x 10 = 6 x 5

Answer:

Yes it is correct.

Proportional relationships are relationships between two variables where their ratios are equivalent.

if you divide 4/16 with 4 you will find 1/4

good luck

There is not enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes.

To determine whether there is enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes, we can conduct a one-sample t-test with the following hypotheses:

Null hypothesis: The true mean time in changing a muffler is equal to 13 minutes.

Alternative hypothesis: The true mean time in changing a muffler is less than 13 minutes.

Use the formula to calculate the test statistic,

\(t = \dfrac{(x - \mu)} { \dfrac{s} { \sqrt{n}}}\)

where x is the sample mean, μ is the hypothesized population mean (13 minutes), s is the sample standard deviation, and n is the sample size (6).

Plugging in the numbers, we get:

t = (12.3 - 13) / (2.3 / √6) = -0.72

Using a t-distribution table with 5 degrees of freedom (n - 1), we find that the critical value for a one-tailed test with α = 0.05 is -2.571. Since our calculated t-value (-0.72) is greater than the critical value, we fail to reject the null hypothesis.

Therefore, there is not enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes.

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Answer: negative 2 (-2)

Step-by-step explanation:-6+4=-2

Answer:

−2

Step-by-step explanation:

−6 − (−4)

= −6 − (−4)

= −6 + 4

= −2

Answer:

To determine the velocity of the roller coaster as it moves down, we use the kinematic equation which is expressed as 2gy = vf^2 - v0^2 where g is the gravitational acceleration, y is the elevation of the roller coaster, vf and vo are the final and initial velocity. We calculate as follows:

2gy = vf^2 - v0^2

Since it starts at rest, v0 is zero.

2gy = vf^2

vf = √2gy

vf = √2(9.8)(101)

vf = 44.5 m/s ----> option B

Step-by-step explanation:

Answer:

we need to solve the volume of a figure in order to know the amount of substance in an object

we need volume in many area such as labs when mixing chemicals or vaccines

Step-by-step explanation:

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Hello!

To find the equation of the line that passes through the points (0, -8) and (4, -3), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

First, we can find the slope of the line by using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, -8) and (x2, y2) = (4, -3). Substituting these values, we get:

m = (-3 - (-8)) / (4 - 0) = 5/4

So the slope of the line is 5/4. Now we can use the point-slope form of the equation with either of the given points. Let's use the point (0, -8):

y - (-8) = 5/4(x - 0)

Simplifying this equation, we get:

y + 8 = 5/4x

Subtracting 8 from both sides, we get the final equation:

y = 5/4x - 8

So the equation of the line that passes through the points (0, -8) and (4, -3) is y = 5/4x - 8.

Answer: B

Step-by-step explanation:

It is $29.35 for each of the tickets that they buy for adults, so to figure out how much it is for all the adult tickets, it would be $29.35 times x. Same for the children tickets except it is times y and the amount of money is different.

Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

DOMAIN X CAN BE ALL REAL NUMBERS.

RANGE: Y IS ALL THE REAL NUMBERS GREATER THAN 0.