Question 4(Multiple Choice Worth 1 points)
(08.03 LC)

What are the exact solutions of x2 − 3x − 5 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a?

x = the quantity of negative 3 plus or minus the square root of 29 all over 2
x = the quantity of 3 plus or minus the square root of 29 all over 2
x = the quantity of 3 plus or minus the square root of 11 all over 2
x = the quantity of negative 3 plus or minus the square root of 11 all over 2

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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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]

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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Answer:

[tex] \boxed{\sf{x = \frac{5 \pm \sqrt{97} }{12} }}[/tex]

Step-by-step explanation:

[tex]\sf{5x = 6 {x}^{2} - 3 }[/tex]

[tex]\sf{0 = 6 {x}^{2} - 3 - 5x }[/tex]

[tex]\sf{0 = 6 {x}^{2} - 5x - 3 }[/tex]

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

[tex]\sf{x = \frac{ - ( - 5) \pm \sqrt{ { - 5}^{2} - 4(6)( - 3)} }{2(6)} }[/tex]

[tex]\sf{x = \frac{5 \pm \sqrt{ 25 + 72} }{12} }[/tex]

[tex]\sf{x = \frac{5 \pm \sqrt{97} }{12} }[/tex]

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:

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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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

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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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 correct answer is, b=4.

Given Information and To Find

It is given that in a right angled-triangle lmn,

∠m = 90°

∠l = x°

ln = 20 units

lm = 3b units

[tex]secx = \frac{5}{3}[/tex]

We have to find the value of b.

What is a right-angled triangle?

A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a right-angled triangle. Trigonometry's fundamental concept is the relationship between a right triangle's sides and other angles.

Applying Trigonometry

We know that in a right angled-triangle,

[tex]sec x=\frac{hypotenuse}{base}[/tex]

In this case, we have (refer to the diagram),

[tex]secx=\frac{ln}{lm}[/tex]

⇒ [tex]\frac{20}{3b} = \frac{5}{3}[/tex]

⇒ [tex]20(3) = 3b(5)[/tex]

⇒ [tex]15b = 60[/tex]

⇒ [tex]b=4[/tex]

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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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Using it's concept, the domain of the square root function shown in the graph is:

[tex]x \geq 0[/tex]

The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains the values of x.

Researching the problem on the internet, the graph is of the square root function, defined for [tex]x \geq 0[/tex], which is the domain of the function.

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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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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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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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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

[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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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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Squares are the results of multiplying a value by itself. The correct option is B.

Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.

The number 1764 in the form of prime factors can be written as,

1764 = 2×2×3×3×7×7×1

Therefore,

√1764 = 2×3×7 = 42

Hence, the correct option is B.

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Answer: d}2^2(3^2)(7^2)

Step-by-step explanation: I did the quiz

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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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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Hello,

[tex] \sqrt{50} = \sqrt{2 \times 25} = \sqrt{2 \times 5 {}^{2} } = 5 \sqrt{2} [/tex]

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

Answer:

56

Step-by-step explanation:

Let N be the total number of spins.

Probability of A on Red and B on Red = 0.5 x 0 .6 = 0.3 (top branch of tree)

Therefore with N spins, the estimated number of times spinner A and spinner B land on red is 0.3N and we are given this as 84

So 0.3N = 84
N = 84/0/3 = 280

The probability of spinner A on blue and spinner B on blue is 0.5 x 0.4 = 0.2 (lowest branch of tree)

For 280 spins, the estimated number of times that both spinners land on blue is given by 0.2 x 280 = 56

The probability that an individual will score of 50 or less is 0.06.

Given mean of 60 and standard deviation of 8.

We have to find the probability that individual will score 50or less.

Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula to calculate probability is as under:

Probability = number of items/total items.

We have to first find the z value from 50 to 60 which can be found as under:

z value=(50-60)/60

=-0.167

P value from 50 to 60 is 0.44

probability that the individual will score 50 or less is 0.5-0.44

=0.06

Hence the probability that the individual will score 50 or less is 0.06.

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Answer:

Step-by-step explanation:

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

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.

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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