name the following polynomial expression.

\( {4x}^{2} + x - 3 \)
​

The probability P(E) is 13/15.

According to the statement

we have given that the S = {1, 3, 5, 7, 9}, E = {1, 5, 7}

And we have to find the probability P(E).

So, For this purpose

Recall the formula for the probability of an event E in case when all outcomes are equally likely:

P(E)= n(E) /n(S)

in which S is the sample space.

But we have the S = {1, 3, 5, 7, 9},

so, n(S) = Sum of all outcomes / number of outcomes

n(S) = 1+3+5+7+9 /5

n(S) = 25 /5

n(S) = 5 and

For n(E) = Sum of all outcomes / number of outcomes

n(E) = 1+5+7 /3

n(E) = 13 /3

n(E) = 13 /3

Substitute these values in the above written formula then

P(E)= n(E) /n(S)

P(E)=  (13/3)/ 5

P(E)= 13 /15

So, The probability P(E) is 13/15.

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Answer:3:24

Step-by-step explanation:

Answer:

The answer is 52. If you divide 13 by 0.25 which is 25% you get 52. And to check the answer 52 X 25% is 13.

Step-by-step explanation:

Answer:

abscissa and ordinate

Step-by-step explanation:

The first number of an ordered pair will represent the x-axis value.

What this is called is the abscissa

The second number of an ordered pair will represent the y-axis value

What this is called is the ordinate

Answer: X coordinate

Step-by-step explanation: You have a graph an on the left is the X coordinate and on the right is called the Y coordinate.

Answer:

A regular dodecagon has 12 sides and rotational symmetry. This means that if you rotate it by a certain angle about its center, it will look the same as before the rotation. The angle of rotation that would carry a regular dodecagon onto itself is equal to 360 degrees divided by the number of sides.

In this case, 360 degrees / 12 sides = 30 degrees.

So a regular dodecagon can be rotated onto itself by any multiple of 30 degrees. Out of the options you provided, only option 3 (330 degrees) is a multiple of 30 degrees. Therefore, an angle of rotation of 330 degrees would carry a regular dodecagon onto itself.

Answer:

$408

Step-by-step explanation:

Answer:

she is correct because if you reflect that over the Y axis

If you choose the lottery, you would be considered a risk taker.

By opting for the lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing, you are demonstrating a willingness to take a chance and accept the uncertainty associated with the potential outcomes. A risk taker is someone who is willing to engage in risky or uncertain situations for the possibility of gaining a favorable outcome. In this case, you are accepting the risk of potentially winning nothing in exchange for the chance to win a larger amount.

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The sum of given equation is 96/13.

Given equation is sum from n equals 1 to infinity of 12 times negative five eighths end quantity to the power of n that means

∑ n=1 to ∞ [12(-5/8)ⁿ]

This is in the form of geometric expression

that is an = ar^(n-1)

therefore we get

a = 12 and r = - 5/8

We have to find the sum.

Sum of infinity of the sequence is expressed as

Sum = a / (1-r)

where a  = first term of the series

and r = common ratio between two consecutive terms

Now we will substitute values of a and r in the above equation

Sum = \(\frac{12}{1-(-5/8)}\)

        = \(\frac{12}{1 + 5/8}\)

        = \(\frac{12}{13/8}\)

Sum = \(\frac{96}{13}\)

Hence the sum of given equation is 96/13.

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The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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Slope (m) of RH = 3/4

Distance of RH is d =5 units

Midpoint between points R and H is: M(1, 3.5)

Slope (m) = change in y / change in x = y2 - y1/x2 - x1, where:

R(3, 5) = (x1, y1)

H(-1,2) = (x2, y2)

Plug in the values

Slope (m) = (2 - 5) / (-1 - 3)

Slope (m) = (-3) / (-4)

Slope (m) of RH = 3/4

How to Find the Distance between two Points?

Distance formula used is: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

R(3, 5) = (x1, y1)

H(-1,2) = (x2, y2)

Plug in the values

RH = √[(−1−3)² + (2−5)²]

RH = √[(−4)² + (−3)²]

RH = 5 units

How to Find the Midpoint?

The midpoint formula used is: M[(x2 + x1)/2, (y2 + y1)/2)

R(3, 5) = (x1, y1)

H(-1,2) = (x2, y2)

Substitute the values

M[(-1 + 3)/2, (2 + 5)/2)

M(1, 3.5)

Therefore,

Slope (m) of RH = 3/4

Distance of RH is d =5 units

Midpoint between points R and H is: M(1, 3.5)

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Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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The completed statement is: (3a^2 - 5ab * b^2) - (-3a^2 * 2b^2 + 8ab) = 9a^2 + 6a^2b^2 - 5ab^3 - 8ab

To complete the statement and simplify the expression, let's carefully expand and combine like terms:

(3a^2 - 5ab * b^2) - (-3a^2 * 2b^2 + 8ab)

First, let's distribute the negative sign inside the second parentheses:

(3a^2 - 5ab * b^2) + (3a^2 * 2b^2 - 8ab)

Next, let's simplify each term:

3a^2 - 5ab * b^2 = 3a^2 - 5ab^3

3a^2 * 2b^2 - 8ab = 6a^2b^2 - 8ab

Now, we can rewrite the expression:

(3a^2 - 5ab^3) + (6a^2b^2 - 8ab)

To combine like terms, we add or subtract the  of similar terms:

3a^2 + 6a^2b^2 - 5ab^3 - 8ab

So, the simplified expression is:

9a^2 + 6a^2b^2 - 5ab^3 - 8ab

Therefore, the completed statement is:

(3a^2 - 5ab * b^2) - (-3a^2 * 2b^2 + 8ab) = 9a^2 + 6a^2b^2 - 5ab^3 - 8ab

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To make the augmented matrix correspond to a consistent system, we need to ensure that the third row is a linear combination of the first two rows. Let's denote the entries in the third row as a, b, and c, respectively. Then, the equation involving g, h, and k that makes the matrix consistent is:

-4g + 3h + 5k = a

7g - 5h - 9k = b

In a consistent system, all rows of the augmented matrix must be linearly dependent. This means that the third row should be a linear combination of the first two rows. By equating the corresponding entries in the third row to variables, we can find an equation involving g, h, and k that satisfies this condition.

In the given augmented matrix, the third row is represented by the variables g, h, and k. We denote the entries in the third row as a, b, and c, respectively. To create a consistent system, we need to find a relationship between these variables and the entries in the first two rows.

By comparing the entries in the first and second columns, we can set up the following equations:

-4g + 3h + 5k = a (equation 1)

7g - 5h - 9k = b (equation 2)

These equations ensure that the augmented matrix corresponds to a consistent system. If we substitute the values of g, h, and k into equations 1 and 2, the resulting values in the third row will satisfy the entries a and b, respectively.

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Answer:

11 Cups

Step-by-step explanation:

Carlos used 3 pints of lemon juice and 5 times more water than lemon juice. So, he uses 3 x 5 = 15 pints of water for the lemonade. The amount of lemonade is 15 + 3 = 18 pints. Now he pours it equally into 4 jugs which makes it 18 ÷ 4 = 4.5 pints in each jug. Now 1 pint fills 2.4 cups which means 4.5 pints will fill 4.5 x 2.4 = 10.8 cups which will apprroximately be 11 cups.

Answer:

6.96/12

= 0.58

Step-by-step explanation:

each donut costs $0.58. you can check the work by plugging 12 in for x.  (0.58x)

i hope this helps :)

Answer:

30% gain

Step-by-step explanation:

$30 for 10 = $3 each

$46.80 for 12 = $3.9 each

percentage change = (final price- initial price)/inital price  *100

3.9-3 = 0.9

0.9/3 = 0.3

0.3 x 100 = 30

so gain of 30%

Answer:

103 percent

just divide 20 by 15 and multiply the answer by 100 to convert to percentage form bro

The area of the sector created by a central angle of 60° in a circle with a diameter of 6 inches is approximately 4.7124 square inches.

To find the area of a sector of a circle, we need to know the central angle and the radius of the circle. In this case, we are given the central angle of 60° and the diameter of the circle, which we can use to find the radius.

The diameter is given as 6 inches, so the radius is half of that, which is 3 inches.

To calculate the area of the sector, we can use the formula:

Area of Sector = (θ/360°) * π * r²

where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius.

Plugging in the values:

Area of Sector = (60°/360°) * π * (3)²

Area of Sector = (1/6) * 3.14159 * 9

Area of Sector ≈ 4.7124 square inches

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Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

The length of one side of a square face of the cube is 5 inches.

A cube has six square faces, and the total surface area of a cube is the sum of the areas of all its faces.

Given that the net of the cube has a total surface area of 150 in², we can divide this by 6 to find the area of each square face.

150 in² / 6 = 25 in²

Since all the faces of a cube are congruent squares, the area of each face is equal to the side length squared. Therefore, we can set up the equation:

side length² = 25 in²

To find the length of one side of a square face, we take the square root of both sides:

√(side length²) = √(25 in²)

side length = 5 in

Consequently, the cube's square face's length on one side is 5 inches.

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Answer:es, theoretically you would expect to roll only eight 5s. 3. You survey 100 people in your school and ask them if they feel your school has adequate parking. Only. 30% of the sample feels the school has enough parking. If you have 728 students total in your school, how many would you expect out of all the student body that ...

Step-by-step explanation:

Let's analyze the given information and the statements provided.

We are told that the integers r, s, and t all have the same remainder when divided by 5. This means that these integers can be written in the form:

r = 5n + k

s = 5m + k

t = 5p + k

where n, m, and p are integers representing quotients and k is the common remainder.

Statement (1) r + s = t:

If r + s = t, we can substitute the expressions for r and s:

(5n + k) + (5m + k) = 5p + k

Combining like terms:

10n + 10m = 5p

Dividing both sides by 5:

2n + 2m = p

From this equation, we can see that p must be an even number. However, we cannot determine the exact value of t based on this equation alone. Statement (1) is not sufficient to answer the question.

Statement (2) 20 ≤ t ≤ 24:

This statement provides a range for the possible values of t. Since t has the same remainder when divided by 5 as r and s, it must be congruent to k modulo 5. From the given range, the only number that satisfies this condition is t = 20.

However, we need to consider the combined information from both statements to reach a conclusion.

By considering both statements, we find that the only value that satisfies both conditions is t = 20.

the value of t is 20.

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Answer:

(-3,16)

Step-by-step explanation:

(-5,12)

f (x) = ( (x+5) (x+5) ) + 12

f (x) = x^2 + 10x + 37

(-2,15)

f (x) = ( (x+2) (x+2) ) + 15

f (x) = x^2 + 4x + 19

Answer:

45 miles per hour = 66 feet/second

24 miles per hour = 35.2 feet/second

Train A will travel 3260.86 feet before they meet

Train B will travel 1739.13 feet before they meet

The train will meet in 49.41 seconds

Step-by-step explanation:

Here is the complete question:

Two trains are 5000 feet apart, heading toward each other, but on separate parallel straight tracks, Train A is traveling at 45 miles per hour and Train B is traveling at 24 miles per hour.

Change 45 miles per hour and 24 miles per hour into feet per second.

About how far will each train travel before they meet? Round your answers to the nearest hundredth.

In how many seconds will the trains meet?

Step-by-step explanation:

To change from miles per hour to feet per second, we will convert miles to feet and hour to second.

(NOTE: 1 mile = 5280 feet and 1 hour = 3600 seconds)

Hence,

For 45 miles per hour

45 miles per hour = 45 × 5280 feet / 3600 second

45 miles per hour = 66 feet/second

For 24 miles per hour

24 miles per hour = 24 × 5280 feet / 3600 second

24 miles per hour = 35.2 feet/second

To determine how far each train will travel before they meet,

Let the distance covered by Train A be x₁

the distance covered by Train B be x₂

and the time they meet be t

From

Speed = Distance / Time

Distance = Speed × Time

For Train A

Speed = 66 feet/second

∴ x₁ = 66t

For Train B

Speed = 35.2 feet/second

∴ x₂ = 35.2t

From the question, the two trains are 5000 feet apart.

Since the trains are 5000 feet apart, this means both trains will cover a total distance of 5000 feet.

∴x₁ + x₂ = 5000 feet

Then,

66t + 35.2t = 5000

101.2t = 5000

t = 5000/101.2

t = 49.407 seconds

t ≅ 49.41 seconds

But

x₁ = 66t

x₁ = 66 × 49.407

x₁ = 3260.86 feet

Hence, Train A will travel 3260.86 feet before they meet

For x₂

x₂ = 35.2t

x₂ = 35.2 × 49.407

x₂ = 1739.13 feet

Hence, Train B will travel 1739.13 feet before they meet

t is the time they meet

Hence, The train will meet in 49.41 seconds

Answer: y= -1-1 = (0,-1)   y= x + 3=(0,3)

Step-by-step explanation:

Answer:

See Below.

Step-by-step explanation:

Remember that:

Where c is the longest side, and a and b are the two remaining sides.

\(4^2\text{ is }\textbf{ less than (or $<$) } 3^2+3^2\)

\(\text{Therefore, }\Delta JKL \text{ is }\textbf{an acute triangle.}\)

(16 is less than 9 + 9 or 18.)

\(5^2\text{ is } \textbf{equal to (or $=$) } 3^2+4^2\)

\(\text{Applying the same method, $\Delta ABC$ is }\textbf{ a right triangle.}\)

(25 is equal to 9 + 16 = 25.)

Answer:

less then

acute

equal to

right

Step-by-step explanation:

To evaluate the given Boolean equation F = (a) AND NOT(b OR NOT(c)) for each set of variable values:

The Boolean equation F=(a) AND NOT(b OR NOT(c)) can be simplified as follows:

F = a AND (NOT b AND c)

The value of F depends on the values of a, b, and c.

Case A: a=0, b=0, c=0

In this case, F = 0 AND (NOT 0 AND 0) = 0 AND 0 = 0.

Case B: a=1, b=0, c=1

In this case, F = 1 AND (NOT 0 AND 1) = 1 AND 1 = 1.

Case C: a=1, b=1, c=0

In this case, F = 1 AND (NOT 1 AND 0) = 1 AND 0 = 0.

Case D: a=1, b=1, c=1

In this case, F = 1 AND (NOT 1 AND 1) = 1 AND 1 = 1.

Therefore, the correct answers are B and D.

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H= 20°

Explanation

as HJ is congruent to HK , here we have an isosceles triangle, The angles opposite to equal sides are equal in measure,so

Step 1

also, we know the sum of the internal angles in a triangle equals 180, so

Step 2

now, replace in angle H

therefore, the measurement fo H is

H= 20°

I hope this helps you

The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.