Sketch the region that is common to the graphs of x ≥ 2,
y ≥ 0, and x + y ≤ 6, and find its area.

The value of the given algebraic expression is -63/8.

To evaluate an algebraic expression, we substitute the values of the variables in the expression, and then follow the rules of solving a numeral expression.

In the question, we are asked to evaluate the algebraic expression:

{(3a - b)/2c} + {(3a - c)/(c - b)}, given the values of a = 3, b = -2, and c = -4.

To evaluate the expression {(3a - b)/2c} + {(3a - c)/(c - b)}, given the values a = 3, b = -2, and c = -4, we substitute these values in the expression and solve as follows:

{(3(3) - (-2))/2(-4)} + {(3(3) - (-4))/((-4) - (-2))}

= {(9 + 2)/(-8)} + {(9 + 4)/(-4 + 2)}

= {-(11/8)} + {-(13)(2)}

= -(11/8) - (13/2)

= -(11/8) - (52/8)

= -(63/8).

Thus, the value of the given algebraic expression is -63/8.

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Answer:

Step-by-step explanation:

Answer:

0.4

Step-by-step explanation:

4/3(1.5/5)

4/3(0.3)

1.33333333333(0.3)

0.4

The solutions to the system of equations are given as follows: (1, -3) and (-4,2).

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The equations are given as follows:

From the second equation:

y = -2 - x.

Replacing in the first:

(x + 3)² + (y + 2)² = 17.

(x + 3)² + (-2 - x + 2)² = 17

x² + 6x + 9 + x² = 17

2x² + 6x - 8 = 0

2(x² + 3x - 4) = 0

2(x + 4)(x - 1) = 0.

Then the solutions for x are:

The solutions for y are:

Hence the solutions are:

(1, -3) and (-4,2).

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[tex]P(490 < X < 560)[/tex]= 0.3133

Given: μ = 560

σ = 90  

To find: P (490 < X < 560)

Normal distributions are symmetric, unimodal, and asymptotic. A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. It's always easy to solve questions in terms to standard normal

Hence, converting normal distribution to standard normal gives:

P(490 < X < 560)  = [tex]P(\frac{560-560}{90}[/tex]≤ [tex]\frac{X-\mu}{\sigma} < \frac{640-560}{90})[/tex]

                              = P(0 ≤ Z < 0.888)

                               = P (z<0.89) - P(z  ≤ 0)

Using standard normal table,

= 0.8133 - 0.5

P(490 < X < 560) = 0.3133

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Carol's speed is computed to be 6 miles/hour, solved using the equation (3x)/2 = 9.

We assume Carol's speed to be x miles/hours.

Carol's speed is given to be one-third of Alice's speed.

Then Alice's speed is three times Carol's speed, that is, Alice's speed = 3x miles/hour.

Alice's speed is given to be twice Bob's speed.

Then Bob's speed is half of Alice's speed, that is, Bob's speed = (3x)/2 miles/hour.

But, Bob's speed is given to be 9 miles per hour.

Therefore, we get the equation:

(3x)/2 = 9.

To find Carol's speed, we solve this equation as follows:

(3x)/2 = 9,

or, {(3x)/2}*2 = 9*2 {Multiplying both sides by 2},

or, 3x = 18 {Simplifying},

or, 3x/3 = 18/3 {Dividing both sides by 3},

or, x = 6 {Simplifying}.

Therefore, Carol's speed is computed to be 6 miles/hour, solved using the equation (3x)/2 = 9.

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Answer:

0.2

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

1 divided by 5 = 0.2

Answer:

8+16+2=28

Step-by-step explanation:

Answer:

210 yd²

Step-by-step explanation:

If we rotate the shape we get a right angle triangle with a hypotenuse of 29 yd :

The area of a right angle triangle is given by the formula :

A = [tex]\frac{ab}{2}[/tex]

Substituting the 2 values given in diagram gives us :

A = [tex]\frac{(20)(21) }{2}[/tex] = 420÷2 = 210

Our units will be yd² as we are dealing with area

Reciprocal the second fraction and perform multiplication instead addition.

What is fraction?

A number expressed as a quotient, in which a numerator is divided by a denominator.

Given:

Negative 2 and one-half divided by five-fourths = Negative five-halves divided by five-fourths = negative five-halves (five-fourths) = negative StartFraction 10 over 8 EndFraction.

As we see the calculations there is mistake which had amy made.

Amy should have reciprocal the second fraction before multiplication. As division is now allowed in fraction.

Also,  She perform addition instead of multiplication.

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8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]

11. The value of x is 4

From the question, we are to simplify the give expression

The given expression is

[tex]y^{3}\sqrt[5]{32x^{4} } - 7\sqrt[5]{x^{4}y^{15} }[/tex]

[tex]y^{3} (32x^{4} )^{\frac{1}{5} } - 7(x^{4}y^{15} )^{\frac{1}{5}[/tex]

[tex]y^{3} \times 32^{\frac{1}{5} } x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{\frac{15}{5}}[/tex]

[tex]y^{3} \times 2^{5 \times} ^{\frac{1}{5} } \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]

[tex]y^{3} \times 2 \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]

[tex]2 x^{\frac{4}{5} } y^{3} - 7 x^{\frac{4}{5}}y^{3}[/tex]

[tex]= - 5 x^{\frac{4}{5}}y^{3}[/tex]

11. [tex]\frac{1}{2}(5x+7 )^{\frac{2}{3} } =\frac{9}{2}[/tex]

Multiply both sides by 2

[tex]2 \times \frac{1}{2}(5x+7 )^{\frac{2}{3} } =2 \times \frac{9}{2}[/tex]

[tex](5x+7 )^{\frac{2}{3} } =9[/tex]

Multiply both sides by a power of 3/2

[tex](5x+7 )^{\frac{2}{3} \times {\frac{3}{2} } } =9^{\frac{3}{2} }[/tex]

[tex](5x+7 )=3^{2 \times} ^{\frac{3}{2} }[/tex]

[tex]5x+7 =3^{3}[/tex]

[tex]5x+7 =27[/tex]

[tex]5x =27-7[/tex]

[tex]5x = 20[/tex]

[tex]x = \frac{20}{5}[/tex]

x = 4

Hence,

8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]

11. The value of x is 4

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The equation of the line with a slope of -3 and passing through the point (3, 16) is y = -3x + 25

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of a line is:

y = mx + b

Where m is the slope and b is the y intercept.

Given that the line has a slope of -3 and passes through (3, 16), hence:

y - 16 = -3(x - 3)

y = -3x + 25

The equation of the line with a slope of -3 and passing through the point (3, 16) is y = -3x + 25

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Using proportions, it is found that the family would spend $36.75 on clothing.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The family has a budget of $525, and spends 7% of it in clothing, hence the amount is given by:

A = 0.07 x 525 = $36.75.

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The calculated distance of this throw is given as 41.23 meters.

In order to solve for this, we have to make use of the formula for calculating distance.

This is given as:

[tex]\sqrt{(x^{2}-x^{1} ) } (y^{2} -y^{1} )[/tex]

This is substituted as

sqr(50-10)²+(5-15)²

= √40² +√ -10²

= √1700

= 41.23

b. The points were created to find the distance by making use of yards from the goals and the yards from the sidelines.

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The probability of selecting a blue marble is 3/14. Hence, option D is the right choice.

The probability of any event is the chance of the occurrence of that event. It is given as the ratio of the number of favorable outcomes to the event to the total number of outcomes possible in the experiment.

If we consider an event A, the number of favorable outcomes to event A be n, and the total number of outcomes be S, then the probability of event A is given as:

P(A) = n/S.

Let us take the event of selecting a blue marble from the experiment of selecting a marble randomly from the bag be A.

The number of outcomes favorable to event A (n) = 3 {3 blue marbles}.

The total number of outcomes (S) = 14 {Total number of marbles in the bag = 4 red + 3 blue + 7 green = 14 marbles}.

Therefore, the probability of selecting a blue marble is,

P(A) = n/S = 3/14.

Hence, option D is the right choice.

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The x-value of the vertex of the given parabola is x = 5, so the correct option is b.

If we define the parabola by f(x), by looking at the table, we can read:

So, notice that:

f(2) = f(8).

Then the x-coordinate of the vertex is the midpoint between 2 and 8.

x = (2 + 8)/2 = 5

The x-value of the vertex of the given parabola is x = 5, so the correct option is b.

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Answer:

3*5*(x^3)*(y^2)

Step-by-step explanation:

Since we don't know what x and y are, we can leave them as they are. Now we just find the prime factorization of 15, which is 3*5.

The mean of the data about researcher counting of seconds each by stander helps a stranger struggling to pick up a heavy box fan varying amounts of time is 11.67 seconds.

Given if a researcher counting how many seconds each by stander helps a stranger struggling to pick up a heavy box fan varying amounts of time but is 10 seconds and 15 seconds equally as much in the data. all the restaurant under 10 seconds.

We have to calculate mean of the data.

Mean is the sum of numbers divided by total numbers included.

Mean=∑X/n

where n is the numbers.

Mean =(10+15+10)/3

=35/3

=11.67

Hence mean of the data about researcher's counting is 11.67.

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Answer:

31°

Step-by-step explanation:

Given Angle EFG = Angle EFH + Angle HFG (based on the diagram)

[tex]2x+52 = 21 + (x+31)\\2x+52 = 21+x+31\\2x+52=x+52\\2x-x+52=52\\x+52=52\\x=52-52\\x=0[/tex]

From here we can see the value of x is non-existent.

Substitute x to find Angle HFG.

x+31 = 0 + 31 = 31°

Part 1

The gradient of the line is [tex]\frac{11-1}{-3-2}=-2[/tex], so the equation is [tex]y=-2x+5[/tex].

This means the system is

[tex]y=-2x+5\\\\y=ax^2 +b[/tex]

Part 2

Substituting in the coordinates (-3,11) and (2,1) into the equation of the parabola,

[tex]11=9a+b\\\\1=4a+b[/tex]

Subtracting the equations, we get 10=5a, and thus a = 2

Substituting a = 2 back into the system, we get b = -7

Part 3

The equation of the parabola is [tex]y=2x^2 - 7[/tex], and the turning point is at [tex]x=0[/tex]. Therefore, the value of y is -7

Answer:

its answer is 36

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Since the variance is the square of the standard deviation, the variance here is 6.3.

A commonly used measure of dispersion is the standard deviation, which is simply the square root of the variance. Therefore, we just raise the standard deviation to the power of 2 to get the answer. We do as follows:

s = √v

(2.5)² = (√v)²

v = 6.25 = 6.3

So, Since the variance is the square of the standard deviation, the variance here is 6.3.

DISCLAIMER: The question was incomplete. Please find the full content below.

Question

Ms. Johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about the acceleration due to gravity. The program reports a mean of 31.5 and a standard deviation of 2.5. What is the variance of the data?

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Answer: D). 6.3

Step-by-step explanation:

Answer:

  (d)  x = (5±√53)/2

Step-by-step explanation:

The given quadratic equation is in standard form, so the coefficients are readily identified. The solution is given by the quadratic formula based on those coefficients.

The solution to the quadratic equation ax² +bx +c = 0 is given by the formula ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The given equation has coefficients a = 1, b = -5, c = -7, so the solutions given by the formula are ...

  [tex]x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(1)(-7)}}{2(1)}=\dfrac{5\pm\sqrt{25+28}}{2}\\\\\boxed{x=\dfrac{5\pm\sqrt{53}}{2}}[/tex]

Answer:

12 books

Step-by-step explanation:

Lets set aside $25 for dinner first.

Amount left = $230 - $25 = $205

Number of books able to buy = amount left ÷ cost per book

= $205 ÷ $17

= 12.058 books

Of course, you cant buy .058 books , that wont make sense, so you take the highest possible WHOLE number, which in this case, is 12 books.

Answer:

the answer is false .

Step-by-step explanation:

The solution to the given product is:

-6i*(6 - 2i) = -12 - 36i

Here we want to solve:

-6i*(6 - 2i)

Here the thing that you need to remember is that i² = -1.

Expanding the product, we get:

-6i*(6 - 2i) = (-6i)*6  + (-6i)*(-2i)

               = -36i + (6i)*(2i) = -36i + 12i² = -36i - 12

Then we conclude:

-6i*(6 - 2i) = -12 - 36i

That is the solution to the given expression.

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Answer: A: Whole Number B:Integer and C: Rational are all correct.

For the question: In the figure, AB is divided into equal parts. The coordinates of point A are (2, 4), and the coordinates of point B are (10, 6). Match each pair of coordinates to the corresponding point on AB.

Answer:The coordinates of the point are (6 , 5).

For the question: Imani and Abedi drive to work. Imani drives 66 miles in 1.5 hours. Abedi drives 56 km in 1 hour 15 min. Work out the difference between their average speeds in km/h. 1 mile = 1.6 km

Answer:25.6 km/h

I couldn't help you on all of them, but I helped you on some. Hope this helps :D

A triangle is a plane figure which has three sides and angles. Thus the sum of internal angles of a triangle is [tex]180^{o}[/tex]. Thus the answers to the missing values are:

7. x =  [tex]108^{o}[/tex]

8. x = [tex]133^{o}[/tex]

9. x = [tex]124^{o}[/tex]

10. x = [tex]62^{o}[/tex]

11.  x = [tex]74^{o}[/tex]

12. x = [tex]77^{o}[/tex]

13. a = [tex]35^{o}[/tex]

14. b = [tex]74^{o}[/tex]

15. c = [tex]66^{o}[/tex]

The sum of the internal angles of a triangle is [tex]180^{o}[/tex]. Thus in a given question, the required value for each missing value is:

7. Let the unknown inter nal angle ne represented by r, so that;

70 + 38 + r = [tex]180^{o}[/tex]

r = [tex]180^{o}[/tex] - 108

r = 72

So that,

x + a = [tex]180^{o}[/tex] (sum of angles on a staight line)

72 + a = [tex]180^{o}[/tex]

a = [tex]180^{o}[/tex] - 72

  = [tex]108^{o}[/tex]

a = [tex]108^{o}[/tex]

8. x = 39 + 94 (Sum of two opposite interior angles is equal to an exterior angle)

   x   = [tex]133^{o}[/tex]

9. x = 43 + 81 (Sum of two opposite interior angles is equal to an exterior angle)

    x  = [tex]124^{o}[/tex]

10. x + 19 = 81 (Sum of two opposite interior angles is equal to an exterior angle)

    x = 81 - 19

      x = [tex]62^{o}[/tex]

11. 41 + x = 115 (Sum of two opposite interior angles is equal to an exterior angle)

    x = 115 - 41

      x = [tex]74^{o}[/tex]

12. x = 41 + 36 (Sum of two opposite interior angles is equal to an exterior angle)

    x = [tex]77^{o}[/tex]

13. 33 + 112 + a =  [tex]180^{o}[/tex] (sum of angles on a staight line)

     a = [tex]180^{o}[/tex] - 145

        = [tex]35^{o}[/tex]

14. b + 71 + a = [tex]180^{o}[/tex] (sum of angles on a staight line)

     b =  [tex]180^{o}[/tex] - 106

       b  = [tex]74^{o}[/tex]

15. c + 71 + 43 = [tex]180^{o}[/tex] (sum of angles on a staight line)

      c = [tex]180^{o}[/tex] - 114

        c = [tex]66^{o}[/tex]

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The maximum value of allowable emissions in the year 2031 is equal to 3,502.

In order to determine the maximum value of allowable emissions in the year 2031, we would use an exponential function which also relates to compound interest as follows:

A = P(1 - r)^t

For the time, we have:

Time, t = 2031 - 2022

Time, t = 9

Substituting the given parameters into the formula, we have;

A = 4,200(1 - 0.02)^9

A = 4,200(0.98)^9

A = 4,200 × 0.8338

A = 3501.7 ≈ 3,502.

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Answer:

4.4

Step-by-step explanation:

The sum of the probabilities of all possible outcomes is 1.

As the die is loaded so that the number 4 occurs 3/10 of the time, and the other numbers occur with equal frequency, then the probability of numbers 1, 2, 3, 5, 6, 7 and 8 being rolled is 1/10.

Create a probability distribution table for X, where X is the score on the loaded 8-sided die:

[tex]\begin{array}{ | c | c | c | c | c | c | c | c | c |}\cline{1-9}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\cline{1-9} & & & & & & & &\\ \text{P}(X=x) & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{3}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10}\\& & & & & & & &\\\cline{1-9}\end{array}[/tex]

Add a product row and a totals column:

[tex]\begin{array}{ | c | c | c | c | c | c | c | c | c | c |}\cline{1-10}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 &\text{Total} \\ \cline{1-10} &&&&&&&&& \\ \text{P}(X=x) & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{3}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & 1\\ &&&&&&&&&\\ \cline{1-10} &&&&&&&&&\\\text{Product} & \frac{1}{10} & \frac{2}{10} & \frac{3}{10} & \frac{12}{10} & \frac{5}{10} & \frac{6}{10} & \frac{7}{10} & \frac{8}{10} & \frac{44}{10} \\ &&&&&&&&&\\\cline{1-10}\end{array}[/tex]

(The Product is row is the product of the score on the die and its probability).

The expected value (EV) is the sum of the product of each outcome and its probability.  

Therefore, the expected value (EV) of this die is 44/10 = 4.4