pls help meeeeeee with this problem

a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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It costs $3.83 per package of gatorade.

11.49 = 3 packages. Divide 11.49 by 3 which results in $3.83.

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Answer:

The answer to the question provided is the answer is $3.80 (3.87 not rounded).

Step-by-step explanation:

All you really need to do is divide $11.49 by the 3 (packages)

Let's assume the number to be x.

According to the problem statement, the sum of a number and its reciprocal is 2 1/6 or 13/6.

So we can set up the equation:

x + 1/x = 13/6

Multiplying both sides by 6x, we get:

6x^2 + 6 = 13x

Bringing all the terms to one side, we get:

6x^2 - 13x + 6 = 0

We can solve for x using the quadratic formula:

x = [13 ± sqrt(13^2 - 4(6)(6))] / (2*6)

x = [13 ± sqrt(169)] / 12

x = [13 ± 13] / 12

So, x can be either 2/3 or 3/2. Therefore, the number is either 2/3 or 3/2.

Answer:

5

Step-by-step explanation:

The minimum value of x y is 0(-3) = 0. Hence, the correct answer is (B) 1.

The minimum value of the product x y for the equation y = 4x² - 3 can be found by using the formula of the vertex of a parabola which is given by (-b/2a, f(-b/2a)).

Here is the step-by-step solution:

Step 1: Write the equation in the form ax² + b x + c = 0. Thus, y = 4x² - 3 can be rewritten as 4x² + 0x - 3 = 0.Step 2: Identify the values of a and b. In this case, a = 4 and b = 0. Step 3: Use the formula of the vertex of a parabola to find the minimum value of x y.

The x-coordinate of the vertex is given by -b/2a and the y-coordinate is given by f(-b/2a).-b/2a = -0/2(4) = 0f(-b/2a) = f(0) = 4(0)² - 3 = -3

Therefore, the minimum value of x y is 0(-3) = 0. Hence, the correct answer is (B) 1.

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Answer:

y = 3x + 5

Step-by-step explanation:

The linear formula follows this general form: y = mx + c

Hence, to put 5-y=-3x in standard form, you would rearrange it

-y = -3x - 5

y = 3x + 5

Answer:

3x-y=-5

Step-by-step explanation:

standard form is Ax + By = C

5-y=-3x      move the y to the other side by adding it to the -3x

-3x+y=5     The x cant be negative so switch all the signs

3x-y=-5

Answer:

Step-by-step explanation:

To increase the difference between 456.674 and 234.458 by 345.856, we follow the following steps :

Step 1: Subtract 456.674 from 234.458 and,

Step 2:  Add 345.856 to the result.

so,  456.674 - 234.458 = 222.216

222.216 + 345.856 = 568.072

Therefore, the increased difference between 456.674 and 234.458 by 345.856 is 568.072

As a result, A is the appropriate response. Yes; there is only one output per set of inputs.

A function in mathematics is a formula that links every element of one set (referred to as the domain) to a single value of another set (called the range). To put it another way, a connection among multiple sets is called a function when every element in the domain is related to precisely one element in the range. There are many methods to depict a function, including calculations, tables, graphs, and projection diagrams. For instance, the function represented by the equation f(x) = x2 accepts any input value x and outputs the equivalent value x2. The scope, which in this instance is all real numbers, is the collection of all feasible input values.

given

Each input value (represented by the X) is paired with precisely one output value in the mapping diagram, which illustrates a function (represented by the o).

As a result, A is the appropriate response. Yes; there is only one output per set of inputs.

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Answer:

6.4 x 10¹¹

Step-by-step explanation:

(8 x 10⁵)(8 x 10⁵) = 6.4 x 10¹¹

Since He Sells 15 Iteam The He Meet His Goal Of L + S >= 12

As Far As The Other Inequlty

425*9 + 125*6 = $4575 (Goal Acheived)

The Answer Is Yes He Meets Both Of His Goals

The identity is verified since the expression containing sines simplifies to cos^2 α in the explanation below.

To verify the identity containing sines we can follow the given steps:

Step 1: Recognize that the given expression is in the form of a difference of squares, where (1 + sin α) and (1 - sin α) are the two factors.

Step 2: Use the difference of squares formula: (a + b)(a - b) = a^2 - b^2. In this case, a = 1 and b = sin α.

Step 3: Apply the difference of squares formula: (1 + sin α)(1 - sin α) = (1)^2 - (sin α)^2 = 1 - sin^2 α.

Step 4: Recall the Pythagorean identity for trigonometric functions: sin^2 α + cos^2 α = 1. We can rearrange this identity to find cos^2 α: cos^2 α = 1 - sin^2 α.

Step 5: Substitute the rearranged Pythagorean identity into the expression from Step 3: 1 - sin^2 α = cos^2 α.

So, we have verified the identity (1 + sin α)(1 - sin α) = cos^2 α.

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Answer:

A. 4.1

Step-by-step explanation:

3+4+ 5+ 3+ 4+ 5+ 6+ 7+ 1+ 2+ 3+ 4+ 5+ 6+ 4+ 8+ 4+ 3+ 2= 79

79/ 19 = 4.1

\(\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=11\\ \theta =60 \end{cases}\implies s=\cfrac{(60)\pi (11)}{180}\implies s=\cfrac{11\pi }{3}\implies s\approx 12~mm\)

Answer: 12mm

Step-by-step explanation:

Basically, you will find the circumference of the entire circle and then using that find the length of the arc.

So the circumference of the circle is its radius (11) times pi multiplied by 2.

2(11 x 3.14) = 69.08

Now a circle is always 360 degrees and the angle of the sector is 60 degrees.

So we have our circumference and we only need that small portion, so you take and make it a fraction and multiply by the circumference to find the length of that small portion:

60/360 x 69.08 = 11.51

Rounded = 12

Answer:

Measure of angle H is 110°.

Step-by-step explanation:

m∠G = (2x + 5)°

m∠H = (6x - 10)°

m∠I = (x + 10)°

Since, sum of interior angles of a triangle is 180°.

m∠G + m∠H + m∠I = 180°

(2x + 5) + (6x - 10) + (x + 5) = 180

(2x + 6x + x) + (5 - 10 + 5) = 180

9x = 180

x = 20

Therefore, m∠H = (6x - 10)°

                           = 6(20) - 10

                           = 110°

Therefore, measure of angle H is 110°.

The measure of the inscribed angle is equal to 90 degrees

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

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The volume of the solid is calculated to give 113.1 cubic centimeter

The volume of a solid say the capacity of the solid.

Foe a cylinder the volume is calculated by the formula

= π r² h

where:

r = radius

h = height

The volume of the smaller solid will be subtracted form the volume of th bigger solid

Volume of the smaller solid

= π * 2² * 3

= 12π

Volume of the bigger solid

= π (2 + 2)² 3

= π * 4² * 3

= 48π

The volume of the solid

= 48π - 12π

= 36π

= 113.1 cubic centimeter

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The mountain range would cause allopatric speciation, resulting in genetic divergence and the formation of two distinct populations of sheep adapted to their respective environments.



The mountain range separating the two populations of sheep would likely lead to allopatric speciation. Over time, the isolated populations would experience different selective pressures, leading to genetic divergence. Mutations, genetic drift, and natural selection would contribute to the accumulation of genetic differences.



The distinct environments on either side of the mountain range may drive adaptations specific to each population. As reproductive isolation develops, the two groups may become distinct species.

The mountain range acts as a geographical barrier, promoting allopatric speciation and resulting in two separate and genetically unique populations of sheep.

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Answer:

t ≤ − 4

Step-by-step explanation:

Answer: t ≤ -4

Step-by-step explanation:

rearrange the problem 24-(-6*t)≤0  Pull out like factors :24 + 6t  =   6 • (t + 4)

Divide both sides by 6    Subtract  4  from both sides t ≤ -4

When testing the difference between the means of two normally distributed populations using independent random samples with equal variances, the correct test statistic to use is the two-sample t-test.

The two-sample t-test compares the means of two independent samples to determine if there is a significant difference between them. It takes into account the sample means, sample sizes, and sample variances to calculate a t-value. The assumption of equal variances is important in this context.

The formula for the two-sample t-test depends on the specific context, such as whether the samples have equal or unequal variances. The appropriate formula can be selected accordingly. However, when the variances of the populations are assumed to be equal and the sample sizes are relatively large (as per the general guidelines), the pooled two-sample t-test is commonly used.

In summary, the correct test statistic to use for testing the difference between the means of two normally distributed populations using independent random samples with equal variances is the two-sample t-test.

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The maximum value of B is 80.

1. We are given the expression B = 5xy² and the constraint x + y² = 8.

2. We need to find the maximum value of B by optimizing the variables x and y.

3. To solve this problem, we can use the method of Lagrange multipliers.

4. Let's define the Lagrange function L(x, y, λ) as L(x, y, λ) = B - λ(x + y² - 8).

5. Taking the partial derivatives of L concerning x, y, and λ, we have:

  ∂L/∂x = 5y² - λ

  ∂L/∂y = 10xy - 2λy

  ∂L/∂λ = -(x + y² - 8)

6. Setting the partial derivatives equal to zero, we get the following equations:

  5y² - λ = 0    ...(1)

  10xy - 2λy = 0  ...(2)

  x + y² = 8     ...(3)

7. From equation (1), we can solve for λ in terms of y:

  λ = 5y²    ...(4)

8. Substituting equation (4) into equation (2), we have:

  10xy - 2(5y²)y = 0

  10xy - 10y³ = 0

  10y(x - y²) = 0

9. From the above equation, we have two possibilities:

  i) 10y = 0, which implies y = 0.

  ii) x - y² = 0, which implies x = y².

10. If y = 0, then from equation (3), we get x = 8.

11. If x = y², then substituting this into equation (3), we have:

   y² + y² = 8

   2y² = 8

   y² = 4

   y = ±2

   If y = 2, then x = (2)² = 4.

   If y = -2, then x = (-2)² = 4.

12. We have three potential solutions: (x, y) = (8, 0), (4, 2), and (4, -2).

13. Finally, substitute each of these solutions into the expression B = 5xy² and find the maximum value of B:

   B = 5(8)(0)² = 0

   B = 5(4)(2)² = 80

   B = 5(4)(-2)² = 80

14. Therefore, the maximum value of B is 80.

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Answer:

Step-by-step explanation:

Firstly, removing the 4 will cause the median to change.

Secondly,

   Range = highest number - lowest number

   With the outlier:

        Range = 33 - 4 = 29

   Without the outlier:

        Range = 33 - 22 = 11

The range has decreased.

Removing the outlier will not change the range and median, but it will increase the mean.

The range is the difference between the largest and smallest values in a data set. If you remove the outlier, which is 4 in this case, the smallest value will change, but the largest value will remain the same. Therefore, the range will stay the same.

The mean is the average of all the values in a data set. When you remove an outlier, it significantly affects the average because it is an extreme value. In this case, removing 4 as an outlier will increase the mean value.

The median is the middle value in a data set. Since the median is not affected by extreme values, removing the outlier will not change the median. In this case, the median will stay the same.

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If we take a simple random sample of size n=500 from a population of size 5,000,000, the variability of our estimate will be  (c) about the same as the variability for a sample  size n=500 from a population of size 50,000,000.

The variability of an estimate primarily depends on the sample size (n) rather than the population size. Since both scenarios have a sample size of 500, the variability will be approximately the same.

The correct answer is (d) slightly greater than the variability for a sample size n = 500 from a population of size 50,000,000. This is because the larger the population size, the smaller the sampling variability. In other words, if we take a sample of the same size from a larger population, there will be more variability due to the increased number of potential outcomes. However, the difference in variability between a population size of 5,000,000 and 50,000,000 is not significant enough to make a substantial impact on the estimate.

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7.  \(a2(a2)(a6)\)  is a monomial.

8. \(x(x2)(x2)(x7)\)  is a monomial.

9. \((y2z)(yz2)\) is a monomial.

10. (e² k²) (e³k) is a monomial.

11. (a²b⁴)(a²b¹) is a monomial.

12. (cd²)(c3d2) is a monomial.

13. (2x²)(3x⁵)  is a monomial.

14. (5a⁷)(a²b³) is a monomial.

15. (4xy³)(3x³y⁵) is a monomial.

16. (7a⁵b²)(a²b³) is a monomial.

17. (-5m³)(3m⁸) is a monomial.

18. (-2c⁴d)(-4cd) is a monomial.

19. (10²)³ is a monomial.

20. (P³)¹²  It is a monomial.

22. (-3y³) is a monomial.

A polynomial with only one term is called a monomial. An algebraic expression known as a monomial typically has one term, but it can also include several variables and a higher degree.

7. \(a2(a2)(a6)\)

    \(\\= a2+2+2+6 \\= a12\)

Yes. It is a monomial.

8. \(x(x2)(x2)(x7)\)

    \(= x1+2+2+7 \\= x12\)

Yes. It is a monomial.

9. \((y2z)(yz2)\)

   \(= y2+1 z1+2 \\= y3z2\)

Yes. It is a monomial.

10. (e² k²) (e³k)

   = (e2+3) (k2+1)

   = e5k3

Yes. It is a monomial.

11. (a²b⁴)(a²b¹)

   = a2+2 b4+1

   = a4b5

Yes. It is a monomial.

12. (cd²)(c3d2)

   = c1+3 d2+2

   = c4d4

Yes. It is a monomial.

13. (2x²)(3x⁵)

    = 2×3 x2+5

     = 6x7

Yes. It is a monomial.

14. (5a⁷)(a²b³)

    = 5a7+2b3

     = 5a9b3

Yes. It is a monomial.

15. (4xy³)(3x³y⁵)

    = 4×3 x1+3 y3+5

      = 12x4y8

Yes. It is a monomial.

16. (7a⁵b²)(a²b³)

   = 7a5+2 b2+3

    = 7a7b5

Yes. It is a monomial.

17. (-5m³)(3m⁸)

   = -5×3 m3+8

   = -15m11

Yes. It is a monomial.

18. (-2c⁴d)(-4cd)

    = 2×4 c4+1 d1+1

   = 8c5d2

Yes. It is a monomial.

19. (10²)³

   = \(10^6\)

Yes. It is a monomial.

20. (P³)¹²

   = \(P^{36}\)

Yes. It is a monomial.

22. (-3y³)

   = -3y3.

Yes. It is a monomial.

23. (3pr²)²

   = 9p²r4

Yes. It is a monomial.

24. (2b³c⁴)²

   = 4b6c8.

Yes. It is a monomial.

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we have the expression

we have that

Using the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer.

so

Answer:

400 employees

Step-by-step explanation:

Let the total no. of employees be x

From the information we get that,

30% of x= 120

Hence, 30/100x=120

x=120×100/30

x=400

Answer:

the answer is 56

Step-by-step explanation:

(70 × 80) ÷ 100 = 56

70% of 80 is 56

Answer:

x = 7, x = 2

Step-by-step explanation:

Given

x² = 9x - 14 ( subtract 9x - 14 from both sides )

x² - 9x + 14 = 0 ← in standard form

(x - 7)(x - 2) = 0 ← in factored form

Equate each factor to zero and splve for x

x - 7 = 0 ⇒ x = 7

x - 2 = 0 ⇒ x = 2

Answer:

three is greater than -8