3^(7−2x) = (1/27)^(−8)
Solve the exponential equation for x

Answer:

got ya

Step-by-step explanation:

Sandy and Jessica travel the same distance of 16 miles on their bicycles. Therefore, 7.6923 miles = (7.6923 * 5280) feet= 40,582.4 feetSo, Jessica rode the bicycle at approximately 40,582.4 feet per hour.

Sandy and Jessica travel the same distance of 16 miles on their bicycles. Sandy rides her bicycle at the rate of 12 miles per hour.

Jessica reaches the place 45 minutes later. There are 5,280 feet in a mile.

Let's find Sandy's time first by using the formula:Speed = Distance / Time12 = 16 / Time

Time taken by Sandy to cover 16 miles = 16/12

Time = 1.33 hours, Now, we can find Jessica's time by adding 45 minutes = 0.75 hours to Sandy's time

Time taken by Jessica to cover 16 miles = Time taken by Sandy + 0.75= 1.33 + 0.75= 2.08 hoursNow, let's use the formula

Speed = Distance / Time

Speed = 16 / 2.08Speed = 7.6923 miles per hour1 mile = 5,280 feet

Therefore, 7.6923 miles = (7.6923 * 5280) feet= 40,582.4 feetSo, Jessica rode the bicycle at approximately 40,582.4 feet per hour.

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The equation S = -32p^2 + 960p represents the relationship between the price of the toy (p) and the total sales (S) in dollars. The price that will produce the highest total sales for the toy is $15.

The equation S = -32p^2 + 960p represents the relationship between the price of the toy (p) and the total sales (S) in dollars. In this case, we want to find the price that will result in the highest total sales.

To determine the price that produces the highest total sales, we need to find the vertex of the quadratic equation. The vertex represents the maximum point on the graph, which corresponds to the price that maximizes the total sales.

The vertex of a quadratic equation in the form of y = ax^2 + bx + c is given by the x-coordinate:

x = -b / (2a)

In this case, the equation is S = -32p^2 + 960p, where a = -32 and b = 960. Plugging these values into the formula, we get:

p = -960 / (2 * -32) = 960 / 64 = 15

Therefore, the price that will produce the highest total sales for the toy is $15.

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Answer:

Each result is equally likely.

The sample space has 36 different outcomes.

Explanation:

A number cube has 6 sides, and there are 2 number cubes so there are 36 possible outcomes because 6² = 36

Answer:

Each result is equally likely.

The sample space has 36 different outcomes.

Step-by-step explanation:

Answer:

9.625

Step-by-step explanation:

(3 1/2) x (2 3/4) = 9.625

Answer:

.........................

The value of the expression according to the order of operations is -11. Thus option D is correct.

According to the statement

We have to find that the value of the given expression.

So, For this purpose, we know that the

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.

From the given information:

The expression are :

(-2)-3-6

Now solve it with the order then

(-2)-3-6 = (-2)-3-6

(-2)-3-6 = -2-3-6

Now add the first two terms

then

(-2)-3-6 = -5-6

Now, Add next two terms

Then

(-2)-3-6 = -11.

The value becomes -11.

So, The value of the expression according to the order of operations is -11. Thus option D is correct.

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Answer:

yes yes

Step-by-step explanation:

The number of ways can arrange the songs on the CD will be 3,628,800.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Suppose Allen is going to burn a compact disk (CD) that will contain 10 songs.

Then the number of ways can arrange the songs on the CD will be given by 10 factorial.

⇒ 10!

⇒ 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

⇒ 3,628,800

Thus, the number of ways can arrange the songs on the CD will be 3,628,800.

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Answer:

100-500

Step-by-step explanation:

Both sides of a triangle cannot be shorter than the remaining side.  Thus, the side must be less than 500 units.  With the same rule, the side must be greater or equal to 100 units, as if it was less, then 200 + 99 < 300.

The compound inequality for the range of the possible lengths for the third side will be 100- 500.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.

Given:

side lengths of 200 units and 300 units.

The largest value of the third side will be

200+300=500

and, the smallest value will be

300-200=100

Hence, 100<X<500

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The summation for the indicated value of the variable is 23.

What is factorial?

The product of all positive integers less than or equal to n in mathematics is known as the factorial of a non-negative integer, indicated by the symbol n!. Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1.

Here, we have

Given

1(1!) +2(2!) +3(3!) + 4(4!)+......... m(m!)

By applying summation,

For m = 3, it will become,

= 1(1!) +2(2!) +3(3!)

Now we open factorization and we get

= 1(1) +2(2×1) +3(3×2×1)

= 1 + 4 + 18

= 23

Hence, the summation for the indicated value of the variable is 23.

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Therefore , the solution of the given problem of plotting data comes out to be it is heavily affected by outliers in the data set.

The most popular method for displaying data in a geographical format is to demonstrate the correlation between two additional factors. Digital or hand-drawn sketches are both acceptable. Starting at the starting the spot, move three separate parts upward and then two or more components in the right. The display of the reference system must show the numerals for positions 2, 3, and 4.

Here,

The usual distance between each data point and the data set's mean is measured by the mean absolute deviation, or MAD.

When the MAD value is low, the data points are typically near to the mean, and when the MAD value is high, the data points are farther apart from the mean.

The MAD in the displayed picture has been determined to be 6.8. This shows that, on average, the data values are 6.8 units away from the mean. The material is therefore fairly dispersed.

The MAD may not be the best measure of spread for distributions that are skewed or have heavy tails, however, because it is heavily affected by outliers in the data set.

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The first number which is 1.5 x 10⁹ is greater than the second number which is 7.5 × 107 by 1.425 ×10⁹.

Scientific notation is definitely as the expression of a very large number into a smaller number that is often written in a decimal form such as a × 10^b

When a number is written in a scientific notation form, what determines its quantity is 10^b.

From the given numbers;

1.5 x 10⁹ = 1,500,000,000

7.5 × 10⁷ = 75,000,000

The difference between the two figures = 1425000000 =

1.425 ×10⁹.

Therefore, first number which is 1.5 x 10⁹ is greater than the second number which is 7.5 × 107 by 1.425 ×10⁹.

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Answer:

I am pretty sure it is x>8 which is B.

Step-by-step explanation:

Answer:

9 seconds

Step-by-step explanation:

Answer:

9 secs

Step-by-step explanation:

450÷50=9

The probability of selecting all dimes when randomly choosing 2 coins from a set of 7 coins (3 dimes and 4 quarters) is 3/21, or approximately 0.1429.

To calculate the probability, we need to determine the number of favorable outcomes (selecting all dimes) and the total number of possible outcomes (selecting any 2 coins).

The number of favorable outcomes can be found by selecting 2 dimes from the 3 available dimes, which can be done in C(3,2) = 3 ways.

The total number of possible outcomes can be calculated by selecting any 2 coins from the 7 available coins, which can be done in C(7,2) = 21 ways.

Therefore, the probability of selecting all dimes is given by the ratio of favorable outcomes to total outcomes, which is 3/21.

Simplifying, we find that the probability is approximately 0.1429, or 14.29%.

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(a) This statement is false. The probability of getting heads or tails on a fair coin is always 50%, regardless of previous outcomes.  

(b) This statement is true. Drawing a face card and drawing a red card from a full deck of playing cards are mutually exclusive events.

(a) The statement is false. The outcome of each coin toss is independent of the previous tosses. Therefore, the chance of getting heads on the next toss is still 50%, regardless of the outcome of the previous eight tosses.

(b) The events of drawing a face card and drawing a red card are not mutually exclusive events. There are 12 face cards in a deck of playing cards, and 6 of them are red (2 jacks, 2 queens, and 2 kings). Therefore, the probability of drawing a face card and a red card from a full deck of playing cards is:

P(face card and red card) = P(face card) x P(red card|face card)
P(face card and red card) = (12/52) x (6/12)
P(face card and red card) = 3/52 or about 5.77%

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∵ 1/3 of 9 means multiply it by 9

3 is 1/3 of 9 cookies and lollipops

Answer:

1/3 of 9 is 3.

Step-by-step explanation:

Think of it like this: what number can be added to itself 3 times to get 9? The answer is 3! 3 + 3 + 3 = 9. So, 1/3 of nine is 3 because 9 split into 3 sections would be 1/3 + 1/3 + 1/3 = 1 and 3 + 3 + 3 = 9. So, 1/9 simplified is 1/3!

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Using the inverse binomial distribution, it is found that there is a 0.081 = 8.1% probability that the third caller is the first to correctly answers the question.

The number of callers that correctly answer the question is a binomial variable, however, we want the probability of the third caller being the first to answer the question correctly, hence it is a negative binomial variable.

Inverse binomial:

It is the number of trials until q successes of a binomial variable, with p probability of success.

The probability mass function is:

\(P(X = x) = C_{x+q-1,q-1}(1 - p)^xp^q\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

The probability that the third caller is the first to correctly answers the question is P(X = 3), hence:

\(P(X = x) = C_{x+q-1,q-1}(1 - p)^xp^q\)

\(P(X = 3) = C_{3,0}(0.9)^2(0.1)^1 = 0.081\)

0.081 = 8.1% probability that the third caller is the first to correctly answers the question.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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Answer:

4 X 2

8 unit²

Step-by-step explanation:

Given that:

Lot size = 10 X 5

Sport field = 6 X 2

Dimension of lot left :

(10 - 6) X (5 - 2)

4 X 2

Area left :

Length x width

4 * 2

= 8 units²

Answer:

seeing as no one is answering I will

Answer:

(- 11, - 4 )

Step-by-step explanation:

4x - 6y = - 20 → (1)

- 2x + 4y = 6 → (2)

multiplying (2) by 2 and adding to (1) will eliminate x

- 4x + 8y = 12 → (3)

add (1) and (3) term by term to eliminate x

0 + 2y = - 8

2y = - 8 ( divide both sides by 2 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

4x - 6(- 4) = - 20

4x + 24 = - 20 ( subtract 24 from both sides )

4x = - 44 ( divide both sides by 4 )

x = - 11

solution is (- 11, - 4 )

\(\frac{1}{2} | 261-161|\)The area of the quadrilateral whose vertices are A(1,1)B(7,−3),C(12,2) and D(7,21) is 49 square units

To find the area of the quadrilateral with vertices A(1, 1), B(7, -3), C(12, 2), and D(7, 21), you can follow these steps:

1. Divide the quadrilateral into two triangles: Triangle 1 (A, B, C) and Triangle 2 (A, C, D).

2. Calculate the area of each triangle using the   determinant method for the coordinates.

For Triangle 1 (A, B, C):
Area =   \(\frac{1}{2} | (1(-3)+7(2)+12(1) )- (-3(2)+1(12)+7(1)|\)
Area =\(\frac{1}{2} | (-3+14+12) - (-6+112+7)|\)
Area = \(\frac{1}{2} | (23-13)|\)
Area =\(\frac{1}{2} (10)\)

Area = 5 square units

For Triangle 2 (A, C, D):
Area =  \(\frac{1}{2} | (1(2)+12(21)+7(1))- (2(1)+21(7)+1(12)|\)
Area = \(\frac{1}{2} | (2+252+7)- (2+147+12)|\)
Area = \(\frac{1}{2} | 261-161|\)
Area = \(\frac{1}{2} (100)\)

Area = 44 square units

3. Add the areas of the two triangles to get the area of the quadrilateral:

Area of quadrilateral = Area of Triangle 1 + Area of Triangle 2 = 5 + 44 = 49 square units.

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The p-value can be found with the F-distribution table or statistical software. If the p-value is less than or equal to α, then answer is option (a),If the p-value is greater than α, then answer is option (b).

To determine the correct statistical decision based on the given F-statistic, F (3, 12) = 2.72, we need additional information such as the significance level (α) of the hypothesis test. The significance level is a predetermined threshold that is used to assess the statistical significance of the results.

The correct decision depends on whether the calculated p-value, which quantifies the strength of evidence against the null hypothesis, is less than or equal to the significance level (α).

To find the p-value, you would need the F-distribution table or statistical software.

Once you have the p-value, you can compare it to the significance level (α) to make a decision:

If the p-value is less than or equal to α, you would reject the null hypothesis, indicating a statistically significant mean difference.

If the p-value is greater than α, you would fail to reject the null hypothesis, suggesting that there is not a statistically significant mean difference.

Therefore, without the significance level or the p-value, it is not possible to determine the correct statistical decision.

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Answer:

x = -4 + 3 i or x = -4 - 3 i

Step-by-step explanation:

Solve for x:

(x + 4)/(x + 5) = (x - 5)/(2 x)

Hint: | Multiply both sides by a polynomial to clear fractions.

Cross multiply:

2 x (x + 4) = (x - 5) (x + 5)

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

2 x^2 + 8 x = (x - 5) (x + 5)

Hint: | Write the quadratic polynomial on the right hand side in standard form.

Expand out terms of the right hand side:

2 x^2 + 8 x = x^2 - 25

Hint: | Move everything to the left hand side.

Subtract x^2 - 25 from both sides:

x^2 + 8 x + 25 = 0

Hint: | Using the quadratic formula, solve for x.

x = (-8 ± sqrt(8^2 - 4×25))/2 = (-8 ± sqrt(64 - 100))/2 = (-8 ± sqrt(-36))/2:

x = (-8 + sqrt(-36))/2 or x = (-8 - sqrt(-36))/2

Hint: | Express sqrt(-36) in terms of i.

sqrt(-36) = sqrt(-1) sqrt(36) = i sqrt(36):

x = (-8 + i sqrt(36))/2 or x = (-8 - i sqrt(36))/2

Hint: | Simplify radicals.

sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:

x = (-8 + i×6)/2 or x = (-8 - i×6)/2

Hint: | Factor the greatest common divisor (gcd) of -8, 6 i and 2 from -8 + 6 i.

Factor 2 from -8 + 6 i giving -8 + 6 i:

x = 1/2-8 + 6 i or x = (-8 - 6 i)/2

Hint: | Cancel common terms in the numerator and denominator.

(-8 + 6 i)/2 = -4 + 3 i:

x = -4 + 3 i or x = (-8 - 6 i)/2

Hint: | Factor the greatest common divisor (gcd) of -8, -6 i and 2 from -8 - 6 i.

Factor 2 from -8 - 6 i giving -8 - 6 i:

x = -4 + 3 i or x = 1/2-8 - 6 i

Hint: | Cancel common terms in the numerator and denominator.

(-8 - 6 i)/2 = -4 - 3 i:

Answer: x = -4 + 3 i or x = -4 - 3 i

Answer:5

Step-by-step explanation:

Each circle has a weight of 6.25.

A circle is a shape consisting of all points in a plane that are a given distance from a given point, the center. The distance from the center to any point on the circle is known as the radius. A circle has no sides or corners, and all points along the circle are equidistant from the center.

The weight of each circle can be found by dividing 25 (the total weight) by 4 (the number of circles). Therefore, each circle has a weight of 6.25.

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