Calculate the surface area of a triangular prism 10.8cm long and having a triangle bar face of dimensions 8.8cm by 5.7cm by 6.8cm​

The Rational Roots Theorem indicates that the set of possible rational roots for the polynomial x³ + 5·x² - 8·x - 20 = 0, is the option C

C. ±1, ±2, ±4, ±5, ±10, ±20

The Rational Roots Theorem states that if p/q is a rational root of a polynomial with integer coefficients, where p and q have only 1 as their common factor, then p must be a factor of the constant term and q must be a factor of the leading coefficient.

The Rational Root Theorem indicates that where the number p/q is a rational root of the polynomial, then p is a factor of the constant term -20, and q is a factor of leading coefficient 1

The factors of -20 are; ±1, ±2, ±4, ±5, ±10 and ±20

The factors of 1 is; 1

Therefore the possible values of p/q are; ±1, ±2, ±4, ±5, ±10 and ±20

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Answer:

Step-by-step explanation:

ACTUAL ANSWER

(-5¼)/(3/2)

= -{(20+1)/4}/(3/2) //CONVERTING INTO IMPROPER FRACTION

= (-21/4)/(3/2)

= (-21/4) x (2/3) // MULTIPLYING BY RECIPROCAL

 = (-21x2)/(4x3)

= -42/12

= -(7x6)/(2x6) TAKING 7 AS COMMON FACTOR

= -7/2

STEPS FOLLOWED BY ESMERELDA

(-5¼)/(3/2)

= -{(20+1)/4}/(3/2)

= -(21/4)/(3/2)

= -(21/4) x (3/2)

= -(21+3)/(4+2)

= - (24/6)

= -4

HENCE THE ERRORS COMMITTED BY HER ARE:-

1. ESMERALDA ADDED THE NUMERATORS

2. ESMERALDA ADDED THE DENOMINATORS

3. ESMERALDA DID NOT USE THE RECIPROCAL OF THE DIVISOE

The graph which shows the interval notation of the inequality 3 > - x > - 7 is option C.

3 > - x > - 7

Break the compound inequality into two and solve each

3 > - x

divide both sides by -1

-3 < x

- x > - 7

divide both sides by -1

x < 7

So the solution to the inequality is

-3 < x < 7

Therefore, it can be interpreted that x is greater than -3 and less than 7

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The range of the function h(x) with the restricted domain of {-2, 0, 2, 10} is {-27, -3, 21, 117}. Therefore, the correct response is {−27, -3, 21, 117}.

To find the range of the function h(x) = 12x - 3 with the restricted domain of {-2, 0, 2, 10}, we need to evaluate the function for each value in the domain and determine the corresponding range values.

For x = -2:

h(-2) = 12(-2) - 3 = -24 - 3 = -27

For x = 0:

h(0) = 12(0) - 3 = 0 - 3 = -3

For x = 2:

h(2) = 12(2) - 3 = 24 - 3 = 21

For x = 10:

h(10) = 12(10) - 3 = 120 - 3 = 117

The range of the function h(x) with the restricted domain of {-2, 0, 2, 10} is {-27, -3, 21, 117}. Therefore, the correct response is {−27, -3, 21, 117}.

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Answer:

The rational form of the ratio 2:3 is 2/5

Step-by-step explanation:

For those of us who don't know or don't remember what rational means, it just means fraction, and in this case is asking as to convert ratio 2:3 into a fraction.

-First thing is to add the ratio:

2+3=5

-Now, we are going to place 5 as the denominator of the fraction, and we are going to keep the 2 from the ratio (it will always be the first number of our ratio, for example, if the ratio is 6:1 we'd be keeping the 6), and place it on the numerator place:

2:3 = 2/5

-So, that would be pretty much it, by the way, I know that the question was upgraded, but I don't mind to have 5 points more.

Answer: 16.7%

Step-by-step explanation:

x/(root y) =x

root y is increased by 44%

x/(44+root y)=16.7%

Answer:

Step-by-step explanation:

2(97+69)=332(m)

Answer:

PQ=20

Step-by-step explanation:

1) 11+x+2+3x-1+10+2x=64

2) 6x+22=64

3) 6x=42

4) x=7

5) PQ = 3(7)-1 = 20

Answer:

OK, HERE IS YOUR ANSWER

Step-by-step explanation:

AI-generated answer

We are given a demand curve in the form of a graph, and we are asked to find the area of the triangle shown on the diagram. The formula for finding the area of a triangle is:

Area = 1/2 x base x height

In this case, the base of the triangle is the quantity in thousands of units per unit of time, and the height of the triangle is the price in dollars per unit.

The base of the triangle can be calculated as the difference between the quantities at the two endpoints of the demand curve. From the graph, we can see that the quantity at the left endpoint is 20, and the quantity at the right endpoint is 50. Therefore, the base of the triangle is:

Base = 50 - 20 = 30

The height of the triangle can be calculated as the difference between the prices at the two endpoints of the demand curve. From the graph, we can see that the price at the left endpoint is $90, and the price at the right endpoint is $70. Therefore, the height of the triangle is:

Height = 90 - 70 = 20

Now, we can use the formula to find the area of the triangle:

Area = 1/2 x base x height

Area = 1/2 x 30 x 20

Area = 300

Therefore, the area of the triangle shown on the diagram is $300. Hence, the correct answer is 300.

The area of the triangle in the demand curve diagram can be found using the formula for the area of a triangle which is 1/2 * base * height. From the points provided, we are able to calculate an area of 2450 dollars.

To answer this question, we need to understand how to calculate the area of a triangle which is represented by the equation: Area = 1/2 * base * height. From the diagram, we can find these values:

Base: The quantity 1,000s of units per unit of time which is the x-axis,

Height: Price per unit (dollars) which is the y-axis.

Assuming that the triangle's points intersect at 10 (on the y-axis) and 70 (on the x-axis) with a hypotenuse ending at 80 on the y-axis. The base would be 70 - 0 = 70, and the height would be 80 - 10 = 70.

Plugging these values into our formula, we get Area = 1/2 * 70 * 70 = 2450 dollars. So the area of the triangle is 2450 dollars.

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The probable question may be:

The diagram to the right illustrates a hypothetical demand curve representing the relationship between price (in dollars per unit) and quantity (in 1,000s of units per unit of time).

The area of the triangle shown on the diagram is $. (Enter your response as an integer.) 100 90- 80- 70-67 60 50- 40 30- 20-17 10- D 23 73 20 30 40 50 60 70 80 90 Quantity (1,000s of units per unit of time) 10 100

Answer:

Step-by-step explanation:

To find the slope and y-intercept of a linear function, we need to use the formula y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.

Given points in the linear function are not provided in the question, but if you are given two points on a line, you can find the slope of the line by using the slope formula:

slope = (change in y)/(change in x)

Assuming the given points of the linear function are (x1, y1) and (x2, y2), then the slope of the line is:

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

Once we have the slope of the line, we can use any point on the line and the slope to find the y-intercept, b, using the formula:

y = mx + b

b = y - mx

Therefore, we can find the slope and y-intercept of a linear function, given two points on the line.

Answer: -6

Step-by-step explanation:

1. Evaluate the expressions inside the innermost brackets and braces first:

 [tex]\((-2)^2 \cdot 2 - 6 = 4 \cdot 2 - 6 = 8 - 6 = 2\)[/tex]

  So, the expression becomes:

  [tex]\(14 - \{7 + 4 \cdot 3 - 2\}+ (2^2 + 6 - 5 \cdot 3) + 3 - (5 - 2^3 / 2)\)[/tex]

2. Continue evaluating the expressions inside the braces:

  [tex]\(7 + 4 \cdot 3 - 2 = 7 + 12 - 2 = 17\)[/tex]

  So, the expression becomes:

[tex]\(14 - 17 + (2^2 + 6 - 5 \cdot 3) + 3 - (5 - 2^3 / 2)\)[/tex]

3. Now, evaluate the expressions inside the parentheses:

[tex]\(2^2 + 6 - 5 \cdot 3 = 4 + 6 - 15 = -5\)[/tex]

 [tex]\(5 - 2^3 / 2 = 5 - 8 / 2 = 5 - 4 = 1\)[/tex]

  So, the expression becomes:

[tex]\(14 - 17 - 5 + 3 - 1\)[/tex]

4. Finally, perform the remaining operations:

[tex]\(14 - 17 - 5 + 3 - 1 = -3 - 5 + 3 - 1 = -6\)[/tex]

So, the result of the expression is -6.

The answer to four decimal places, the probability is approximately 0.6481.

To find the probability that a randomly chosen student is either female or received an "A," we need to calculate the sum of the probabilities of these two events occurring individually and subtract the probability of both events occurring simultaneously.

Let's start by calculating the probability of selecting a female student. From the given information, we know that there are 29 female students out of a total of 54 students. Therefore, the probability of selecting a female student is 29/54.

Next, we need to determine the probability of selecting a student who received an "A." Looking at the table, we can see that there are a total of 8 students who received an "A" grade out of 54. Hence, the probability of selecting a student who received an "A" is 8/54.

To find the probability of both events occurring, we need to consider the intersection of the two events, which is the set of female students who also received an "A." According to the table, there are 2 female students who received an "A." Therefore, the probability of selecting a female student who received an "A" is 2/54.

Now, we can calculate the probability of selecting a female student OR a student who received an "A" by summing the individual probabilities and subtracting the probability of both events occurring simultaneously:

Probability (Female OR "A") = Probability (Female) + Probability ("A") - Probability (Female AND "A")

= 29/54 + 8/54 - 2/54

= 35/54

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The presence of the Purple Party and the Chartreuse Party in the Houses of Parliament in Ghyronmia reflects the diversity of views and opinions in society. It creates a dynamic political environment that encourages debate, discussion, and better decision-making, and ensures that the interests of all sections of society are represented.

In Ghyronmia, a hypothetical small country, the Houses of Parliament have two political parties: the Purple Party and the Chartreuse Party. These two parties may have different political ideologies and values which reflect on their stances on various issues. The presence of different political parties in Parliament creates a dynamic political environment where different ideas are debated and discussed, and this leads to better decision-making and representation of different sections of society.
The Purple Party may represent a certain section of society that values conservatism, tradition, and stability. They may be more inclined to support policies that uphold traditional values, promote law and order, and preserve the status quo. On the other hand, the Chartreuse Party may represent a section of society that values progress, social justice, and reform.

They may be more inclined to support policies that aim to bring about change, promote equality, and challenge the status quo.
The presence of these two parties in Parliament means that different views and opinions are represented, and this creates healthy competition in the political sphere. It also ensures that decisions are not taken without due consideration and debate, and that policies are subject to scrutiny from different angles.

This, in turn, helps to prevent any one party or ideology from dominating the political discourse.

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a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer:

This is not the answer but if u have Spanchat you can go to the AI and ask him to fill in the table using this function rule, list x, and then put the equation and he'll give you the table

Step-by-step explanation:

[tex] \huge{ \tt{ \boxed{ \tt{answer}}}}[/tex]

★Refer the attachment mate!! Follow for more★

For the function g(x) graphed above, the limits should be identified as follows;

a. A. [tex]\lim_{x \to -4} g(x)=0[/tex]

b. A. [tex]\lim_{x \to -3} g(x)=-1[/tex]

c. B.  [tex]\lim_{x \to 0} g(x)[/tex] does not exist.

d. B.  [tex]\lim_{x \to 0} g(x)[/tex] does not exist.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables, graphs, or relations.

Part a.

By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that as x tends towards negative four, g(x) tends towards positive zero;

[tex]\lim_{x \to -4} g(x)=0[/tex]

Part b.

By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that as x tends towards negative three, g(x) tends towards negative one;

[tex]\lim_{x \to -3} g(x)=-1[/tex]

Part c and d.

By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that [tex]\lim_{x \to 0} g(x)[/tex] does not exist because the graph jumps and approaches both −1 and 1 as x → 0.

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Answer:

a.  0.00166

b. 0.00200

Overall B is correct because it has the prossibilty of getting more votes. 0.00200

Step-by-step explanation:

Answer:

a. The equation is separable, as we can write it as (1 - y²) dy = x² dx. Integrating both sides, we have (1/2)*ln|1 - y²| = (1/3)*x³ + C, where C is the constant of integration. Solving for y, we get an equation for the integral curves: y = ±sqrt(1 - exp(2/3*x³ + 2C)).

b. Rearranging the equation, we get (2/(y - 1)) dy/dx = (3x² + 4x + 2). This is separable, so integrating both sides, we have 2 ln|y - 1| = x³ + 2x² + 2x + C, where C is the constant of integration. Solving for y, we get y = 1 + Ce^(x³+2x²+2x)/2. Using y(0) = -1, we have -1 = 1 + C, so C = -2. Thus, the solution to the initial value problem is y = 1 - 2e^(x³+2x²+2x)/2. The solution exists for all values of x.

The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Part 1:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the margin of error is determined by the level of confidence and the standard error.

First, let's calculate the sample proportion:

Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)

Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)

Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).

Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.5066 ± 0.0350

Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)

Part 2:

The correct interpretation is:

C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.

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To order the fractions from least to greatest, we need to compare their values. The given fractions are 11/4, -2, and -1/8. The answer of the given question -2, -1/8, 11/4

Let's start by converting the mixed number -2 into a fraction. A mixed number consists of a whole number and a fraction. To convert it to a fraction, we multiply the whole number by the denominator of the fraction part and add the numerator. Then, we place the result over the original denominator. In this case, -2 can be written as -2/1.

Now we have the following fractions: 11/4, -2/1, and -1/8.

To compare these fractions, we can find a common denominator. The least common multiple (LCM) of the denominators 4, 1, and 8 is 8. So, we will rewrite the fractions using 8 as the common denominator:

11/4 = 22/8

-2/1 = -16/8

-1/8 remains the same

Now we have 22/8, -16/8, and -1/8. We can see that -16/8 is the smallest, followed by -1/8, and finally 22/8.

Therefore, in order from least to greatest, the fractions are:

-16/8, -1/8, 22/8

Simplifying further, we have:

-2, -1/8, 11/4

Note that we simplified the fractions, but the order remains the same. The fractions are ordered based on their numerical values, with the least value first and the greatest value last.

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The expression which represents the number of pieces of cargo is c/162.68 = x, where c is the weight of the cargo in pounds, and x is the number of pieces of cargo.

Given that the space shuttle carries c pounds of cargo, and each piece of cargo weighs 162.68 pounds. We have to determine which of the following expressions represents the number of pieces of cargo.

Let's assume that the number of pieces of cargo be x.

Therefore, the weight of x pieces of cargo will be 162.68x = weight of cargo. The expression which represents the number of pieces of cargo can be written as: c/162.68 = x

This is because the total weight of the cargo is c pounds, and we know that each piece weighs 162.68 pounds.

Therefore, to find the number of pieces, we can divide the total weight by the weight of each piece, which gives us the expression c/162.68 = x, where x is the number of pieces of cargo.

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To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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Answer:

y = 4x - 11

Step-by-step explanation:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:

1 = 4(3) + b

1 = 12 + b

-11 = b

Thus, the y-intercept is -11.

Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11

The answer is:

Work/explanation:

First, we will write the equation in point slope:

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

where m = slope;

(x₁,y₁) is a point on the line.

Plug in the data:

[tex]\sf{y-1=4(x-3)}[/tex]

Simplify

[tex]\sf{y-1=4x-12}[/tex]

Add 1 on each side

[tex]\sf{y=4x-12+1}[/tex]

[tex]\sf{y=4x-11}[/tex]

Answer:

Step-by-step explanation:

The sentence that represents the number of points in the problem is OD. The number of multiple-choice question points plus the number of short-answer question points is 60.

The problem states that the test is worth 60 points, and that multiple-choice questions are worth 2 points each and short-answer questions are worth 5 points each. If the test has 15 questions, then there must be some number of multiple-choice questions and some number of short-answer questions. The total number of points for the multiple-choice questions and the short-answer questions must add up to 60, so the answer is OD.

The other answer choices are incorrect. OA is incorrect because it says that the number of multiple-choice question points times the number of short-answer question points is 60. This is not possible, because the number of points for a question cannot be multiplied by the number of points for another question. OB is incorrect because it says that the number of multiple-choice question points plus the number of short-answer question points is 15. This is not possible, because the total number of points for the test is 60, not 15. OC is incorrect because it says that the number of multiple-choice question points minus the number of short-answer question points is 15. This is not possible, because the number of points for a question cannot be subtracted from the number of points for another question.

Answer:

$7/lb

Step-by-step explanation:

$70 / 10 lb = $7/lb

Answer:

$7 per pound of letuce

Step-by-step explanation:

We know

10 pounds = $70

1 pounds = ?

We cross multiply and get:

$7 per pound of letuce

So, the answer is $7 per pound of letuce

Answer:

f(x) = x² - 4x + 10

Step-by-step explanation:

the standard form of a quadratic function is

f(x) = ax² + bx + c ( a ≠ 0 )

given

f(x) = (x - 2)² + 6 ← expand the factor using FOIL

     = x² - 4x + 4 + 6 ← collect like terms

    = x² - 4x + 10 ← in standard form

Answer:

Slope = -7

Step-by-step explanation:

Take any two points from the table:

   (39 , 36) ⇒ x₁ = 39 & y₁ = 36

    (41 , 22) ⇒ x₂ = 41 & y₂ = 22

Substitute the points in the below formula:

                    [tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                                 [tex]\sf = \dfrac{22-36}{41-39}\\\\\\=\dfrac{-14}{2}\\\\=-7[/tex]