1. The sides of a triangle are in the ratio 3:4:5 What is the length of each side if the perimeter
of the triangle is 90 cm?

The Probability of getting 35 or more sales for 1000 telephone calls is approximately 0.1771.Therefore, the correct option is A) 0.1770

To find the probability of getting 35 or more sales for 1000 telephone calls, we can use the binomial distribution.

The probability of a sale for each phone call is 0.03, and we have a total of 1000 phone calls. Let's denote the number of sales as X, which follows a binomial distribution with parameters n = 1000 and p = 0.03.

We want to find P(X ≥ 35), which is the probability of getting 35 or more sales. This can be calculated using the cumulative distribution function (CDF) of the binomial distribution.

Using a statistical software or calculator, we can calculate P(X ≥ 35) as follows:

P(X ≥ 35) = 1 - P(X < 35)

Using the binomial CDF, we find:

P(X < 35) ≈ 0.8229

Therefore

P(X ≥ 35) = 1 - P(X < 35)

= 1 - 0.8229

= 0.1771

The probability of getting 35 or more sales for 1000 telephone calls is approximately 0.1771.

Therefore, the correct option is A) 0.1770

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The probability of getting 35 or more sales for 1000 telephone calls is approximately 0.0475.

The number of sales X can be modeled as a binomial distribution with n = 1000 and p = 0.03.

Using the normal approximation to the binomial distribution, we can approximate X with a normal distribution with mean μ = np = 30 and variance σ^2 = np(1-p) = 29.1.

To find the probability of getting 35 or more sales, we can standardize the normal distribution and use the standard normal table.

z = (X - μ) / σ = (35 - 30) / sqrt(29.1) = 1.66

Using the standard normal table, we find that the probability of getting 35 or more sales is approximately 0.0475.

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Answer:

indeterminable, not enought info.

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(3^{y}\) + 1 = 1/9

3^y = -8/9

5^y/125^x = 125

5^y/5^3x = 125

5^(y-3x) = 5^3

y-3x = 3

Your question is incorrect as 3^x can never be negative.

But, now you know y - 3x = 3, so, use this to get the values when you reconsider the correct question.

Thanks

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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Answer:

In my view 1st answer is correct..

its the third choice

The equation y = 3/5 x is graphed on a coordinate plane and attached

The equation is graphed using some points for the input which is x values and solving to get the y values

This is called the table of values used to plot on the coordinate plane

The table of values for y = 3/5 x is formed as follows

For x = -10, y = 3/5 * -10 = -6

For x = -5, y = 3/5 * -5 = -3

For x = 0, y = 3/5 * 0 = 0

For x = 5, y = 3/5 * 5 = 3

For x = 10, y = 3/5 * 10 = 6

table of values

x     y

-10  -6

-5   -3

0     0

5     3

6     6

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Answer:

27

Step-by-step explanation:

Given that :

Dimension of poster board = 1 yd by 1 yd

Dimension of each poster sign = 1/3 yd by 1/9 yd

Number of poster signs that can be cut :

Area of poster sign = 1/3 * 1/9 = 1/27 yard²

Area of poster board = 1 yard²

Number of poster signs that can be cut :

Area of poster board / area of poster sign

1 yard² ÷ (1/27) yard²

1 ÷ 1/27

1 * 27/1

= 27 poster signs

Answer:7

Step-by-step explanation:

ball

Answer:

$24.

Step-by-step explanation:

Let's say Carlos has $c of money, and Mariame has $m of money.

c = 2.75m

c + m = 90

2.75m + m = 90

3.75m = 90

m = 24

c + 24 = 90

c = 66

So, Mariame has $24 and Carlos has $66.

Hope this helps!

Answer:

it should be the third option

Step-by-step explanation:

I hope this help

The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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The ground do the ropes intersect each other is at 4 ft.

AB and ED are the poles (perfectly vertical). BE and DA are the ropes that cross at C.

F is the point directly below C on the ground (line AE), which is perfectly flat and horizontal.

The vertical poles are part of parallel lines.

As a consequence, triangles ABC and DEC have congruent angles at B and E, and at A and D (alternate interior). Of course, ABC and DEC also have congruent angles at C (vertical angles).

Triangles ABC and DEC are similar, with corresponding sides in the ratio 2:1

\(\frac{AB}{DE}= \frac{BC}{EC}= \frac{AC}{DC}= \frac{2}{1}\)

In particular,

BC = 2EC and BE = BC + EC = 2EC + EC = 3EC

Right triangles ABE and FCE, with the same angle at E, are also similar, so

\(\frac{AB}{FC}= \frac{BE}{CE}= \frac{3EC}{EC3.1}\) --> AB = 3FC --> \(FC = \frac{AB}{3}= \frac{12 ft}{3} = 4ft\)

The ropes cross 4 ft above the ground.

Hence the answer is the ground do the ropes intersect each other is at 4 ft.

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Answer:

easy

Step-by-step explanation:

answer is

hiiiiiiiii

Answer:

independent is the time. time does change throughout the experiment.

Dependent is texting speed as it can vary.

hope this helps :)

The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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The principal mortgage amount is $220,000.

To compute the principal loan amount, we need to apply the compound interest formulation for a loan:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where M is the monthly reimbursement, P is the primary mortgage amount, i is the month-to-month interest charge, and n is the range of months.

First, we need to calculate the month-to-month interest charge:

i = 2.49% / 12 = 0.02075

Subsequent, we want to calculate the range of months:

n = 30 years x 12 months/year = 360 months

Now we are able to plug in the given values:

$986.50 = P [ 0.02075(1 + 0.02075)^360 ] / [ (1 + 0.02075)^360 – 1]

Solving for P, we get:

P = $221,114.07

Rounding to the nearest ten thousand dollars, the principal mortgage amount is $220,000.

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Answer:

She can buy 4 books

Step-by-step explanation:

If each notebook is $3, and she bought two, she'd be left with $32 because 40-6=32. Simply multiply 8 by 4 to get 32, which is the rest of her money. Hope this helps!

Answer:

13

Step-by-step explanation:

5x = 65

x = 65/5

x = 13

The length of minor arc CD is \(\( \frac{5\pi}{3} \)\) units.

1. Let's start by finding the measure of angles x and y. We know that the area of the circle is \(\(81\pi\)\), and since the area of a circle is given by the formula \(\(A = \pi r^2\\)), we can equate it to find the value of \(\(r\). So, \(81\pi = \pi r^2\).\)

  Solving this equation, we get \(\(r^2 = 81\)\), which gives us \(\(r = 9\)\).

2. Since points A, B, C, and D are on the circle, we can consider the angles formed by the lines connecting these points to the center of the circle.

3. Let's assume that the measure of angle x is \(\(a\)\) radians. As per the given information, the measure of angle y is \(\( \frac{5\pi}{9} \)\) radians greater than angle x. So, the measure of angle y is \(\(a + \frac{5\pi}{9}\)\) radians.

4. Since angles x and y are formed by lines from the center of the circle, the sum of their measures should be equal to \(\(2\pi\)\) radians. So we can write the equation \(\(a + (a + \frac{5\pi}{9}) = 2\pi\).\)

5. Simplifying the equation, we get \(\(2a + \frac{5\pi}{9} = 2\pi\).\)

6. Solving for \(\(a\)\), we find \(\(a = \frac{4\pi}{9}\).\)

7. Now that we have the value of angle x, we can find the measure of angle z. Again, since the sum of angles formed by lines from the center of the circle is \(\(2\pi\)\), we can write the equation \(\(a + (a + \frac{5\pi}{9}) + z = 2\pi\)\).

8. Substituting the known values, we have \(\( \frac{4\pi}{9} + (\frac{4\pi}{9} + \frac{5\pi}{9}) + z = 2\pi\)\).

9. Simplifying the equation, we get \(\( \frac{13\pi}{9} + z = 2\pi\)\).

10. Solving for \(\(z\)\), we find \(\(z = \frac{5\pi}{9}\)\).

11. Angle z represents the measure of the central angle that corresponds to minor arc CD.

12. The length of a minor arc in a circle is given by the formula \(\(s = r\theta\)\), where \(\(r\)\) is the radius of the circle and \(\(\theta\)\) is the central angle in radians.

13. Substituting the known values, we have \(\(s = 9 \cdot \frac{5\pi}{9} = \frac{5\pi}{3}\)\).

14. Therefore, the length of minor arc CD is \(\( \frac{5\pi}{3} \)\) units.

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Answer: she must sell 6 large photos and 6 small photos

Step-by-step explanation: and how I knew that is I multiplied 6 40 times and that gives you 240 and if you multiply 6 ten times that gives you 60 so 240 plus 60 is $300

The correct option for this question is option D. 2 more than the exponent.

An exponent is a number that indicates how many times a base number should be multiplied by itself.

For example, in the expression "x^3", the exponent is 3, and it means that the base number "x" should be multiplied by itself 3 times.

In other words, "x^3" is equivalent to "xxx". The base number is usually written in the base of the expression, and the exponent is written as a superscript.

The number of zeros in the product of 20 and 105 is 2 more than the exponent. This is because 20 has two zeros at the end and 105 has one zero at the end, for a total of 3 zeros. The exponent, in this case, is 1, because there is only one factor of 10 in the product (10 is being multiplied by itself once).

Therefore, the number of zeros in the product is 2 more than the exponent.

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Answer:

Hello! answer: y = 76

Because there vertical angles they Will have the same measure therefore y = 76 Hope that helps!

Answer:

Step-by-step explanation:

según el número de animales  

The expanded form of the expression is (-5)(-5)(-5)(-5) and it value as an integer is 625

Expressions are mathematical statements that comprise either numbers, variables, or both and have at least two words connected by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

The given expression is;

(-5)⁴

The expanded form of the expression is given as (-5)(-5)(-5)(-5) and the value as an integer is 625

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Answer:

a=300 and k=200

Step-by-step explanation:

Multiply the first equation by -10,and multiply the second equation by 1.

−10(a+k=500)

1(10a+3k=3600)

Becomes:

−10a−10k=−5000

10a+3k=3600

Add these equations to eliminate a:

−7k=−1400

Then solve−7k=−1400for k:

−7k=−1400 (Divide both sides by -7)

\(\frac{-7k}{-7} =\frac{-1400}{-7}\)

Now that we've found k let's plug it back in to solve for a.

Write down an original equation:

a+k=500

Substitute200forkina+k=500:

a+200=500

a+200+−200=500+−200(Add -200 to both sides)

a=300

Hope this helps :)

$65 is the expected annual cost associated with the managing potential shortages or surpluses of the product.

Given, a manufacturer of a particular bicycle model has the following costs associated with the management of this product's inventory.

If X units are demanded each year and X is less than 1000, the excess supply, 1000 − X units, must be stored until next year at a cost of $50 per unit. If X is greater than 1000 units, the excess demand, X − 1000 units, must be produced separately at an extra cost of $80 per unit.

We have to find the expected annual cost,

now, as P(X = 50) = 1/2

also P(X = 80) = 1/2

now, using the formula of expected value, we get

E(x) = 50×1/2 + 80×1/2

E(x) = 25 + 40

E(x) = 65

So, $65 is the expected annual cost associated with the managing potential shortages or surpluses of the product.

Hence, $65 is the expected annual cost associated with the managing potential shortages or surpluses of the product.

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The p-value for the given mentioned test, with the test static of -2.01  is calculated out to be  0.0456.

To calculate the p-value for this test, we first need to determine the appropriate null and alternative hypotheses.

Null hypothesis: The proportion of customers who wait longer than 5 minutes at the drive-through for this franchise is equal to the national value of 12%.

Alternative hypothesis: The proportion of customers who wait longer than 5 minutes at the drive-through for this franchise differs from the national value of 12%.

We can use a two-tailed Z-test to test this hypothesis, with a significance level of alpha = 0.05.

The test statistic is given as -2.01. Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution that is at least as extreme as the test statistic.

Using a standard normal distribution table or a calculator, we find that the area to the left of -2.01 is 0.0228. The area to the right of 2.01 is also 0.0228. Therefore, the total p-value is the sum of these two probabilities:

p-value = 0.0228 + 0.0228 = 0.0456

Therefore, the p-value for this test is 0.0456. This means that there is a 4.56% chance of obtaining a test statistic as extreme as -2.01, assuming that the null hypothesis is true. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportion of customers who wait longer than 5 minutes at the drive-through for this franchise differs from the national value of 12%.

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Answer:

your

Step-by-step explanation:

To describe a linear program for finding the largest axis-aligned square that lies entirely inside a polygon (p), we can define the decision variables, objective function, and constraints as follows:

Decision Variables:

Let x be the side length of the square.

Objective Function:

Maximize x. The objective is to find the largest possible side length for the square.

Constraints:

Square Within Polygon Constraint:

For each vertex (xᵢ, yᵢ) of the polygon p, we can define the following set of inequalities:

xᵢ ≤ x, for all vertices of the polygon.

These inequalities ensure that the square lies entirely within the polygon.

Square Symmetry Constraint:

To ensure that the square is axis-aligned, we can impose symmetry constraints. For example, if the coordinates of the center of the square are (c_x, c_y), then we can add the following constraints:

c_x ± (x/2) = constant, for fixed values of c_x.

c_y ± (x/2) = constant, for fixed values of c_y.

These constraints ensure that the sides of the square are parallel to the x and y axes.

Non-Negative Constraint:

x ≥ 0, to ensure a non-negative side length for the square.

By formulating and solving this linear program, we can find the optimal value for x, which represents the largest axis-aligned square that lies entirely within the given polygon p.

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