18) Evaluate the following expression: A) 105 109-2 a) 1014 b) 102 c) 106 d) 1016 B) 104 x 10-10-2 a) 1011 b) 106 c) 106 d) 1016 C) 1030 ÷ 102 = ? a) 1011 b) 1027 c) 1010 d) 1016 D) 10-12 ÷ 10-4- a) 1011 b) 10%! c) 10-8 d) 10-16

It appears that you have some values for angles and sides in a triangle and you are trying to find the value of the side PO=OM.

PO/sin90 = (OM/sin(90-PX-16)) = (5(X+12))/sin90

PO = OM (since they are equal)

PO = 5(X+12)

This is the value of the side PO=OM in the triangle.

Regenerate response

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Answer:

The answer is 3w - g - 4

Step-by-step explanation:

(8w - 4g + 1) - (5w + 3g - 5)

8w - 4g + 1 - 5w + 3g - 5

Rearrange terms

8w - 5w - 4g + 3g + 1 - 5

Combine like terms

(8w - 5w) = 3w   ( -4g + 3g) = -g  (1 - 5) = - 4

Answer:

3w - g - 4

The magnetometers revealed that the basalt rocks along the mid-ocean ridges are aligned in alternating, symmetrical patterns. This is due to the Earth's geomagnetic field which constantly fluctuates in intensity and direction.

When molten basalt cools and sets, it orients itself in the direction of the Earth's field. As this field changes, the orientation of the rocks changes as well.

This creates the alternating, symmetrical pattern seen in the magnetometer readings. In addition, the seafloor spreading which occurs along the mid-ocean ridges can also contribute to the pattern of the rocks. As the seafloor spreads, new basalt rocks are formed and orient themselves by the Earth's field.

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The volume of the right triangular prisms are 1000cm³ and  14, 400mm³ respectively

The formula for determining the volume of a right triangular prism is expressed as;

V = 1/2 bhl

Where;

Now, substitute the values, we have;

Volume, V = 1/2 × 25 × 20 × 4

Multiply the values

Volume, V = 2000/2

Divide through

Volume = 1000cm³

For the second prism;

Volume = 1/2 × 16 × 50 ×36

Volume = 14, 400mm³

Hence, the values are 1000cm³ and  14, 400mm³

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The object falls from 115200 ft above the ground.

What is the quadratic equation?

A quadratic equation is any algebraic equation of the highest degree. The standard form of the quadratic equation in a variable is ax² + bx + c = 0, where a and b are coefficients, are constant, and is a non-zero numbers.

The acceleration of the object is given by the equation a = 32 - (v^2)/8 ft/s^2. Since the object is initially at rest, we can assume that v = 0 at the start of its fall.

To find the height from which the object fell, we need to use the equations of motion for uniformly accelerated motion. The equation for the distance traveled by an object under constant acceleration is:

d = 1/2 at^2 + vt + d0

where d is the distance traveled, a is the acceleration, t is the time, and d0 is the initial distance (which is zero in this case, since the object is initially at rest).

We know that the object is falling for one minute, and we can convert that to seconds by multiplying by 60. The acceleration is given by a = 32 - (v^2)/8, we know that v = 0, so a = 32 - (0^2)/8 = 32 ft/s^2.

Plugging in the values, we get:

d = 1/2 (32 ft/s^2) (60 s)^2

d = 32 x (3600)

d = 115,200 ft

This is the distance that the object fell. To find the height from which it fell, we simply have to take the distance and negate it.

So the height from which the object fell is:

-115,200 ft

Hence, the object falls from 115200 ft above the ground.

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The percentage represented by the shaded area will be 51.5%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Each big square below represents one whole.

In each big square, there are 100 small squares.

Then the number of blue small squares is 103. Then the percent represented by the shaded area is calculated as,

P = (103 / 200) x 100

P = 0.515 x 100

P = 51.5%

The percentage represented by the shaded area will be 51.5%.

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Answer:

4 balls for $2.50

Step-by-step explanation:

If 4 balls=$2.50

Then,$2.50+2.50= $6.25

$6.25 for 8 balls

Total comparisons required to order an array of 5 elements using the selection sort =29

Selection sort finds the smallest element and swaps it into the first position. The, from the remaining N-1 elements after the first one (which we know is the smallest), it finds the next smallest and swaps it into the 2nd position. And so on.

To find the smallest element from a group of N elements takes N-1 comparisons. Basically, compare item 1 to 2, remember the smallest. Compare item 3 to smallest and remember which ever is smaller, and so on. You end up doing 1 comparison for every element from 2 through N.

We have to find the smallest element N-1 times*, but each time we have a smaller list to look through.

So let’s turn to an array of 5 elements. To find the smallest element will take4 comparisons. Next time through we do 3 comparisons and so on:

Total comparisons = 4+3+2+1 = 10

For N elements it takes 1+2+3+…+N-1 = (N-1)N/2 comparisons.

You don’t have to run through an Nth time because after sorting N-1 items, the Nth item must be in the correct position already. Or, if you like, the Nth loop does N-N=0 comparisons so we can ignore it.

only counting comparisons of elements in the array. A loop is going to have to do a comparison of the loop variable to the length of the array every time it repeats. Usually those comparisons are disregarded because, unless the elements of the array are integers, the item comparisons take considerably more time than the index comparisons, and any way, it won’t increase the asymptotic complexity, only the constant of proportionality. If you want to count the index comparisons, you have one for every item comparison (because the inner loop does one item comparison per loop iteration) + 1 for each end of the inner loop (a loop that runs X times does X+1 comparisons) and then another N-1 for the outer loop + 1 for the loop end. For N = 5 there will be 10 + 4 + 4 + 1 = 19 index comparisons and 10 + 19 = 29 total comparisons.

total comparisons required to order an array of 5 elements using the selection sort =29

of course, if you write this in a language like java that does array bounds checking, you’ll add two more comparisons for each array access. And the compare function is probably a function call, so you’re increasing stack depth which potentially adds comparisons to make sure that doesn’t overflow… you know what? I think I’ll just stop there.

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The required solution to the given expression is 4x² + 5x - 4y - 3.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

y + 2x - 3 + 4x² + 3x - 5y

We have to determine the solution to the given expression.

As per the question, we have

y + 2x - 3 + 4x² + 3x - 5y

Rearrange the variables in the above expression,

4x² + 2x + 3x + y - 5y - 3

Combine likewise terms in the expression,

4x² + 5x - 4y - 3

Thus, the required solution is 4x² + 5x - 4y - 3.

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The question seems to be incomplete the correct question would be:

Find the solution to the below expression.

y + 2x - 3 + 4x² + 3x - 5y

The value of x=4.

Revenue is equal to the number of units sold times the price per unit. To obtain the revenue function, multiply the output level by the price function.

Given that,

R(x) = 200 х² + 8

differentiating we get,

R'(x)= 400x

Now,

400x=1600

i.e. x=4

Hence, The value of x=4.

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Since Ten students compared the amount (in dollars) they spent on books each week with the box plot showing the results, the median amount they spent each week is $50. The difference of the first and third quartiles of the data set is $45.

In Mathematics, a box plot is also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the box-and-whisker plot (box plot) shown above, the five-number summary for the given data set include the following:

For the difference, we have:

Difference = Third quartile - First quartile

Difference = 65 - 20

Difference = 45.

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Answer:

Step-by-step explanation:

0.00940718736

Answer:

13 divided by 16 is 0.8125, which is greater than 0 and less than 1. Therefore, 13/16 is located between 0 inches and 1 inch on the ruler.

Step-by-step explanation:

The percentage error, given the length of the pencil, can be found to be

The percentage error is simply the error of the length of the pencil, expressed as a percentage. The error in this case is the length of the pencil of 1 cm that is to be added or subtracted from the length of 20 cm.

The percentage error is:

= Length to be added to or subtracted from the pencil / Total length x 100 %

= 1 / 20 x 100 %

= 0. 05 x 100 %
= 5 %

In conclusion, the percentage error is 5 %.

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Answer:

See the explanation below.

Step-by-step explanation:

17) 40=x+45

x = -5

18) 70 = -2 + 8x

72 = 8x

x = 9

19) 19x - 3 = 17x + 11

2x = 14

x = 7

20) -2 + 14x = 12x + 14

2x = 16

x = 8

21) 11x - 3 + 18x + 9 = 180

29x + 6 = 180

29x = 174

x = 6

22) 6x - 4 + 14x + 4 = 180

20x = 180

x = 9

23) 68 + x + x + 128 = 180

196 + 2x = 180

2x = -16

x = -8

24) x + 87 + x + 107 = 180

2x + 194 = 180

2x = -14

x = -7

25) 70 + 12x - 10 = 180

60 + 12x = 180

12x = 120

x = 10

Answer: 1.25

2 1/2 (1/2)

2 1/2 (servings) x 1/2 (cups of milk)

The scatter plot shows any linear association. Option (B)

A scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.

A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure.

Advantages of scatter plot

From the above advantages, we can conclude on the answer which is Option (B)

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A function f(x) = -(x+4)^2 + 2 has vertex (-4,2) which is a maximum point and a function g(x) = (x-2)^2 - 2 has vertex (2,-2) which is a minimum point.

In this question we have been given two functions  f(x) = −(x + 4)2 + 2 and g(x) = (x − 2)2 − 2which  have been rewritten using the completing-the-square method.

We need to determine if the vertex for each function is a minimum or a maximum.

We know that, the vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants.

The graph of parabola is at (h, k).

So, the vertex of the quadratic function f(x)=-(x+4)^2+2 is (-4,2)

The vertex of quadratic function g(x) =(x-2)^2-2 is vertex (2,-2)

The graph of both the functions is shown below.

A vertex (-4,2) is a maximum point of function f(x) = −(x + 4)2 + 2  and a vertex (2,-2) is a minimum point of function g(x) = (x − 2)2 − 2

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The vertex of the equation is (x, y) = (2, 0). This also makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

The function f(x) = −(x + 4)2 + 2 is in vertex form and can be written as:

f(x) = −(x + 4)2 + 2 = −(x + 4)2 + 4 − 2

Using the completing-the-square method, the equation can be rewritten as:

f(x) = −(x + 4)2 + 4 − 2 = −(x + 4)2 + 4 − 4 + 2 = −(x + 4)2 + 4 = −(x + 4 + 2)(x + 4 − 2)

Now, we can determine the vertex of the equation. To do this, we can set the equation equal to 0.

0 = −(x + 4 + 2)(x + 4 − 2)

From this equation, we can solve for x to get the x-coordinate of the vertex.

x = −2

Now, we can plug this x-coordinate into the equation to get the y-coordinate of the vertex.

f(−2) = −(−2 + 4)2 + 4 = 0

Therefore, the vertex of the equation is (x, y) = (−2, 0). Since the y-coordinate of the vertex is 0, this means that the vertex is a minimum. This makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

We can use the same method for the function g(x) = (x − 2)2 − 2. First, we can rewrite the equation using the completing-the-square method.

g(x) = (x − 2)2 − 2 = (x − 2)2 − 4 + 2 = (x − 2)2 − 4 = (x − 2 + 2)(x − 2 − 2)

Set the equation equal to 0 and solve for x to get the x-coordinate of the vertex.

0 = (x − 2 + 2)(x − 2 − 2)

x = 2

Plug this x-coordinate into the equation to get the y-coordinate of the vertex.

g(2) = (2 − 2)2 − 4 = 0

Therefore, the vertex of the equation is (x, y) = (2, 0). Since the y-coordinate of the vertex is 0, this means that the vertex is a minimum. This also makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

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Answer:

a)  8.4

b)  8.5

c)  The mean and median will be one less (7.4 and 7.5).

Step-by-step explanation:

Given number of boxes in each stack:

To find the mean of the number of boxes in a stack, divide the total number of boxes by the number of stacks:

[tex]\implies \sf Mean=\dfrac{5+7+9+ 11+13+ 10+9+ 8+ 7+5}{10}=\dfrac{84}{10}=8.4[/tex]

The median is the middle value when all data values are placed in order of size.

To find the median of the number of boxes in a stack, first place the numbers in order of size:

As there is an even number of boxes (10), the median is the mean of the two middle values:

[tex]\implies \sf Median=\dfrac{8+9}{2}=\dfrac{17}{2}=8.5[/tex]

If one box is removed from each stack, the total number of boxes is 10 less than before.  Therefore:

[tex]\implies \sf Mean=\dfrac{84-10}{10}=\dfrac{74}{10}=7.4[/tex]

The number of boxes in each stack will be (in order of size):

Therefore, the median is 7.5.

So, if one box is removed from each stack:

The probability of having two black balls after the first draw is 1/6.

The probability of having two black balls after the second draw is 91/216.

Scenario 1: draw two black on the first draw

P(B,B) = (4/9)(3/8) = 12/72 = 1/6

The probability of ending up with two black by scenario 1 is 1/6.

Scenario 2: draw one black and one white; put back the white, and draw a black

P(B,W) = (4/9)(5/8) = 20/72 = 5/18

P(W,B) = (5/9)(4/8) = 20/72 = 5/18

P(one black and one white on first draw) = 5/18+5/18 = 5/9

When you put the white back, there are now 5 white and 3 black; the probability of drawing a black on the second draw is 3/8.

The probability of ending up with two black by scenario 2 is (5/9)(3/8) = 15/72. = 5/24

Scenario 3: draw two white; put both back and draw again, getting two black

P(W,W) = (5/9)(4/8) = 20/72 = 5/18

Since you put back both whites, the bag now contains the same balls it did at the beginning. The probability of drawing two black on the second draw is then 12/72 = 1/6, as before.

The probability of ending up with two black by scenario 3 is (5/18)(1/6) = 5/108.

Thus, The probability of having two black balls after the first draw is 1/6.

The probability of having two black balls after the second draw is the sum of the probabilities for the three scenarios: 1/6+5/24+5/108 = 36/216+45/216+10/216 = 91/216.

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The solution of the system of equations is x = 0.6 and y = 1.6.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given system of equations are,

2x + 3y = 6

7x - 2y = 1

Multiplying throughout the first equation with 7 and the second equation with 2, we get the system of equations as,

14x + 21y = 42

14x - 4y = 2

Subtracting the first equation with second,

21y + 4y = 40

25y = 40

y = 1.6

Substituting the value y = 1.6 in 2x + 3y = 6, we get,

2x + (3 × 1.6) = 6

x = 0.6

Hence the solution of the equations is the intersecting point (0.6, 1.6).

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The probability for green sedan and purple truck can be obtained as  1/3 and 1/6 respectively.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The probability can be found by looking at the diagram as,

P(Sedan) = 2/3

And,  P(Truck) = 1/3

P(green) = 1/2

P(purple) = 1/2

(a) The probability of green sedan is given as,

P(green sedan) = P(Green) × P(Sedan)

⇒ 1/2 × 2/3 = 1/3

(b) The probability of purple truck is given as,

P(purple truck) = P(purple) × P(truck)

⇒ 1/2 × 1/3 = 1/6

Hence, the required probabilities by spinning are given as 1/3 and 1/6 respectively.

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Answer :

2827.43 cm²

Step-by-step explanation:

1/5/2023

7:20PM

Answer:

2827.4 cm²

Step-by-step explanation:

A = 4πr²

A = 4π(15)² = 2827.4 cm²

a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.

b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.

a) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.

b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.

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The kinetic energy of the toy motorized airplane is 8 Joule.

Kinetic energy is the work or energy an object has due to it's motion. The standard unit of kinetic energy is Joule which is kg m²/s².

The formula for calculating Kinetic energy is,

KE = [tex]\frac{1}{2}[/tex] mv²

where m is the mass of the object and v is the velocity of the object.

Here, mass = 4 kg and velocity = 2 meter/second

KE = [tex]\frac{1}{2}[/tex] × 4 × 2²

     = 8 Joule

Hence the kinetic energy of the airplane is 8 Joule.

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Answer: 3. 5.4

Step-by-step explanation:

we can convert all of these numbers to decimal form. 3 = 3.00,1.05=1.05, 5.4 = 5.40, and 4.2= 4.20. As we can see here, 1.05 is clearly the smallest, 3.00 is the second smallest, and 5 is larger than 4 s o its 5.4

Answer:

a₄₀ = 35

Step-by-step explanation:

substitute n = 40 into the nth term rule, that is

a₄₀ = - 5 + 40 = 35

The value of the variable, S when  C = 6, n = 8, T = 1 and k = 18 is 1. 036

To make a variable the subject of formula, we have to make it stand alone on one end of the equality sign.

From the information given, we have the equation as;

C = n/Tk(1 + S²)

Now, let's cross multiply to make 'S' the subject of formula, we get;

C× Tk(1 + S²) = n

Divide both sides by the coefficient of S

1 + S² = n/CTk

collect '1' to the other side;

S² = n/CTk + 1

Take the square root of both sides

S = [tex]\sqrt{\frac{n}{CTk} + 1 }[/tex]

Now, substitute the values

S = [tex]\sqrt{\frac{8}{6* 1 * 18} + 1 }[/tex]

Multiply the values

S = [tex]\sqrt{1. 074}[/tex]

S = 1. 036

Thus, the value is 1. 036

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