DONT SKIP PLZ
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-3, -1) and point (-2, -4) rounded to the nearest tenth?


3.2 units


2.9 units


3.4 units


4.1 units

Answer:

  7

Step-by-step explanation:

5 × 7 = 35

35 cans of cola can be grouped into 7 groups of 5 cans. For each of those 7 groups, James needs to buy one orange soda.

James should buy 7 orange sodas.

Answer:

C Trapezoid

Step-by-step explanation:

A trapezoid mostly has only one pair of parallel sides, not two

Answer: Trapezoid

Step-by-step explanation:

Answer:

These should be the question: a) What is the average seek time = 149.995 ms, b) average rotational latency = 4.16667ms , c) transfer time for a sector = 13.88us, and d) total average time to satisfy a request = 153.1805ms.

Step-by-step explanation:

A) average seek time.

Number of tracks transversed = 299.99ms

Seek time to access  the track = 0ms

= (0+299.99)/2 ==> 149.995ms

B) average rotational latency.

Rotation speed = 7,200rpm

rotation time = 60 / 7,200 = 0.008333s/rev

Rotational latency = 0.008333/2 = 0.004166sec

= 4.16667ms

C) Transfer time for a sector

at 7200rpm, a rev = 60 / 7200 = 0.00833s :    8.33ms

transfer time one sector = 8.333/600 ms

                                         = 0.01388ms  => 13.88us

D) average time to satisfy request

149 + 4.16667 + 0.013888

153.1805ms

Answer:

yp = -x/8

Step-by-step explanation:

Given the differential equation: y′′−8y′=7x+1,

The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)

First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;

y′′−8y′=0

The auxiliary equation will give us;

m²-8m = 0

m(m-8) = 0

m = 0 and m-8 = 0

m1 = 0 and m2 = 8

Since the value of the roots are real and different, the complementary solution (yc) will give us

yc = Ae^m1x + Be^m2x

yc = Ae^0+Be^8x

yc = A+Be^8x

To get yp we will differentiate yc twice and substitute the answers into the original DE

yp = Ax+B (using the method of undetermined coefficients

y'p = A

y"p = 0

Substituting the differentials into the general DE to get the constants we have;

0-8A = 7x+1

Comparing coefficients

-8A = 1

A = -1/8

B = 0

yp = -1/8x+0

yp = -x/8 (particular integral)

y = yc+yp

y = A+Be^8x-x/8

Step-by-step explanation:

Below is an attachment containing the solution

Answer: She would multiply the rate by the years to find the average rise in water levels, or 1.8 times 6.2 = 11.16. To find the difference between the water levels, she would subtract -13.64 from 11.16.

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

7+7=14

14/7=2

2+7=9..

Answer:

50

Step-by-step explanation:

not enough information

Answer:

a) 9(t - u)

Step-by-step explanation:

x = 10t + u

y = 10u + t

x - y = 10t + u - 10u - t

= 9t - 9u

= 9(t - u)

The required answer for the question is a) 9(t − u)

In mathematics , a set of simultaneous equations, also known as system of equations or an equation system, is a finite set of equations for which common solution are sought.

The given expression of x is given by,

x = 10t + u

If y be the 2-digit number formed by reversing the digits of x

then, the expression for y can be written,

y = 10u + t

Subtracting x with y we obtain,

x - y = 10t + u - 10u - t

Solving them we get

x - y = 9t - 9u

which can be written as,

x - y = 9(t - u)

Hence, the required expressions is equivalent to x − y =  9(t − u)

So the correct answer is a) 9(t − u)

More about simultaneous equation :

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Answer:

The range of the data = 99 -22 = 77min

The mean of the dataset is given as

The IQR  = 92 - 77 = 15 min

SIQR = IQR / 2 = 15 / 2 = 7.5 min

variance = 55.05 min

Step-by-step explanation:

First we need to arrange the data in ascending or descending order

22 ,58, 77, 84, 87, 87,91, 92, 99, 99 in ascending order

The range of the data is calculated by substracting the numbers at the extreme that is the lowest number subtracted from the highest number

range = 99 - 22 =  77min

The IQR stands for Inter-quartile range Q3 - Q1 where

Q1  is the middle value in the first half of the data set. i.e

Q1 is the middle of 22 ,58, 77, 84, 87 which is  77

Q1 = 77 min

Q3  is the middle value in the second half of the data set. i.e

Q3 is the middle of 87,91, 92, 99, 99 which is  92

Q1 = 92 min

Therefore IQR = Q3 - Q1 = 92min - 77min = 15 min

The SIQR stands for the semi-interquartile range. it is calculated by IQR / 2

SIQR = 15 / 2 = 7.5 min

To calculate the population variance we need to get the mean say X

The mean is the data point at the center. Since the dataset is even, there are two of them. which is 87 and 87

Therefore the mean is X = (87 + 87)/ 2 = 87

The variance = ∑[tex](X-x)^{2} /n[/tex]

where X is the mean = 87

x is a datapoint on the given dataset

n is the datasize = 10

variance =  [tex]((22-87)^{2} + (58-87)^{2} + (77-87)^{2} + (84-87)^{2} + (87-87)^{2} + (87-87)^{2} + (91-87)^{2} + (92-87)^{2} + (99-87)^{2} + (99-87)^{2} ) /10[/tex]

variance = [tex]((-65)^{2} + (-29)^{2} + (-10)^{2} + (-3)^{2} + (0)^{2} + (0)^{2} + (4)^{2} + (5)^{2} + (12)^{2} + (12)^{2} ) /10[/tex]

variance = [tex]((4225) + (841) + (100) + (9) + (0) + (0) + (16) + (25) + (144) + (144) ) /10[/tex]

variance = 5505/10

variance = 550.5 min

Answer:

Range =77

IQR=15

SIQR=7.5

Variance=550.5

Step-by-step explanation:

Range:

First find the lowest and the highest number in the data and then subtract high with the low to find the range. 99-22=77.

IQR:

Ascend the data from low to high like this:

22 58 77 84 87 87 91 92 99 99

Then break into two half

22 58 77 84 87 | 87 91 92 99 99

Find the median of all the two half

77 is rhe median in the first half and 92 is the median in the second half.

Then subtract them: 92-77=15 IQR

SIQR:

Divide the IQR/2

Hence 15/2=7.5.

Variance:

Find the mean of the data first i.e. 79.6

variance = 5505/10

variance = 550.5

Answer:

g(f(x)) = [tex]\sqrt{f(x)} +2=\sqrt{x+1} +2[/tex]

Domain = [-1,∞)

Step-by-step explanation:

Given f(x) = x+1 and g(x) = √x + 2

g(f(x)) is a composite function.

g(f(x)) = [tex]\sqrt{f(x)} +2=\sqrt{x+1} +2[/tex]

To find the domain of composite function we must get both domains right (the composed function and the first function used).

The domain of f(x) is all the real numbers.

The domain of g(f(x)) is the values of x provide that the square root is greater than or equal zero

So, x+1 ≥ 0

∴ x ≥ -1

So, the domain = [-1,∞)

The domain of the composite function g(f(x)) is x ≥ -2.

The domain of a function is the set of all possible input values for which the function is defined. To determine the domain of the composite function g(f(x)), we need to consider two things:

In this case, the domain of f(x) is all real numbers because there are no restrictions on the input values for f(x) = x + 1.

However, the domain of g(x) = √(x + 2) is limited by the requirement that the radicand (the expression inside the square root) must be greater than or equal to zero. So, x + 2 ≥ 0.

Solving this inequality, we get x ≥ -2.

Therefore, the domain of g(f(x)) is x ≥ -2, which can be written in interval notation as (-∞, -2] or [-2, ∞).

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Answer:

a) 1.92

b) 3.25

c) 1.5

d) -5.23

Step-by-step explanation:

We are given the following in the question:

4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3

a) mean of score change

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{23}{12} = 1.92[/tex]

b) standard deviation for this population

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

Sum of squares of differences = 126.92

[tex]\sigma = \sqrt{\frac{126.92}{12}} = 3.25[/tex]

c) median change score

[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]

Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

Median =

[tex]\dfrac{6^{th} + 7^{th}}{2} = \dfrac{1+2}{2} = 1.5[/tex]

d) change score that is 2.2 standard deviations below the mean.

[tex]x = \mu - 2.2(\sigma)\\x = 1.92-2.2(3.25)\\x = -5.23[/tex]

There are 1,296 different ways to make supreme choice pizza.

Step-by-step explanation:

Here, the total number of crusts available  = 6

The number of crust to be chosen = 1

So, the number of ways that can be done  = [tex]^6 C_1 = 6[/tex]  ways  ...... (1)

Similarly, the total number of meats available  = 4

The number of types meats to be chosen = 2

So, the number of ways that can be done  = [tex]^4 C_2 = 6[/tex]   ways ...... (2)

Similarly, the total number of vegetables available  = 9

The number of types vegetables to be chosen = 2

So, the number of ways that can be done  = [tex]^9 C_2 = 36[/tex] ways   ...... (3)

Now, combining (1), (2) and (3):

The number of ways one can choose 1 crust, 2 meat and 2 vegetables

= 6 ways x 6 ways x 36 ways  = 1,296 ways

Hence, there are 1,296 different ways to make supreme choice pizza.

Answer:

2(7-i)

Step-by-step explanation:

(8 +5i) + (6 - 7i)

Opening each bracket

8 +5i +6 -7I

8 +6 +5i-7i

14-2i

2(7-i)

Answer:

14 - 2 i

Step-by-step explanation:(8 + (5 * i)) + (6 - (7 * i)) =

Answer:

22.5

Step-by-step explanation:

All of the angles inside the triangle equals 180. Therefore, the equation is x+2x+5x=180. Then, you solve for x. The final equation should look like 8x=180 And that is how we get 22.5

Answer:

22.5

Step-by-step explanation:

The sum of the interior angles in a triangle is 180 degrees, so we have the equation $x+2x+5x=180$, so $x=\boxed{22.5}$.

Answer:

The p-value of the test is 0.1416.

The null hypothesis was not rejected concluding that μ = 100.

Step-by-step explanation:

The hypothesis is defined as:

H₀: μ = 100 vs. Hₐ: μ ≠ 100

The test is a two-tailed test.

The test statistic value is z = 1.47.

The significance level of the test is α = 0.10.

The p-value is computed as follows:

[tex]p-value=2\times P(Z<-1.47)=2\times0.0708=0.1416[/tex]

Decision rule:

If the p-value of the test is less than the significance level 0.10, then the null hypothesis is rejected and vice-versa.

The p-value = 0.1416 > α = 0.10.

The p-value is more than the significance level.

The null hypothesis was not rejected.

Conclusion:

The mean value is not different than 100.

To find the p-value for the test, calculate the area under the standard normal curve more extreme than the observed test statistic. The p-value is 0.1416, and we fail to reject the null hypothesis at α = 0.10.

To find the p-value for the test, we need to calculate the area under the standard normal curve that is more extreme than the observed test statistic. In this case, the test statistic is z = 1.47. Since it is a two-tailed test, we need to find the probability in both tails.

First, we find the area to the right of 1.47 by subtracting the cumulative probability from the mean to 1.47 from 1: P(Z > 1.47) = 1 - P(Z < 1.47) = 1 - 0.9292 = 0.0708.

Next, we double this probability to get the total p-value for both tails: p-value = 2 * 0.0708 = 0.1416. Since the p-value (0.1416) is greater than the significance level (α = 0.10), we fail to reject the null hypothesis. This means we do not have enough evidence to conclude that the population mean is not equal to 100.

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To find the central angle of an arc with a length of 8/5 in a circle with a circumference of 12, we set up a proportion with the full circle's 360 degrees and solve for the angle, resulting in a central angle of 48 degrees.

You want to find the central angle of an arc in degrees for a circle with a circumference of 12 units and an arc length of 8/5 units. Since the circumference of a circle is 2π times the radius (2πr) and corresponds to a full circle or 360 degrees, the angle for the entire circle is 360°. The arc length of 8/5 is a fraction of the total circumference, so to find the corresponding angle in degrees, set up the proportion:

(arc length) / (circumference) = (angle of arc) / (360 degrees)

Plug in the known values and solve for the angle of the arc:

(8/5) / 12 = (angle) / 360

Cross-multiply to solve for the angle:

360 * (8/5) = 12 * (angle)

angle = (360 * 8) / (5 * 12)

angle = 48 degrees

Therefore, the central angle of the arc is 48 degrees.

Step-by-step explanation:

The cost of cashews per pound  = $7

The cost of almonds per pound  = $5

Let x represent the number of pounds of cashews.

Let y represent the number of pounds of almonds

Now, the combined weight of the mixture is less than 6 pounds.

So, Weight of (Almonds + Cashews) < 6 pounds

or,  x + y < 6   ...... (a)

Now, cost of x pounds of cashews  = x ( Cots of 1 pound of cashews)

=  x (7)  = 7 x

Cost of y pounds of almonds  = x ( Cots of 1 pound of almonds)

=  y (5)  = 5 y

So, the combined price of x pounds of cashews and y pounds of almonds

= 7 x +  5 y

Also, given the total cost of the mixture is not more than $30.

⇒ 7 x +  5 y  ≤ 30 ..... (2)

Hence, form (1) and (2), the inequalities that represent the given situation are:

x + y < 6

7 x +  5 y  ≤ 30

Answer: The inequalities that represent constraints for this situation are

x + y < 6

7x + 5y ≤ 30

Step-by-step explanation:

Let x represent the number of pounds of cashews.

Let y represent the number of pounds of almonds.

The employee wants to make less than 6 pounds of the mixture. This is expressed as

x + y < 6

Cashews cost $7 per pound, and almonds cost $5 per pound. The employee wants the total cost of the nuts used in the mixture to be not more than $30. This is expressed as

7x + 5y ≤ 30

Option D: 13 units is the distance between the two points

Explanation:

Given that the points are [tex](-5,-2)[/tex] and [tex](8,-3)[/tex]

We need to find the distance between the two points.

The distance between the two points can be determined using the distance formula,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let us substitute the points [tex](-5,-2)[/tex] and [tex](8,-3)[/tex] in the above formula, we get,

[tex]d=\sqrt{(8-(-5))^2+(-3-(-2))^2}[/tex]

Simplifying the terms within the bracket, we have,

[tex]d=\sqrt{(8+5)^2+(-3+2)^2}[/tex]

Adding the terms within the bracket, we get,

[tex]d=\sqrt{(13)^2+(-1)^2}[/tex]

Squaring the terms, we have,

[tex]d=\sqrt{169+1}[/tex]

Adding, we get,

[tex]d=\sqrt{170}[/tex]

Simplifying, we have,

[tex]d=13.04[/tex]

Rounding off to the nearest tenth, we get,

[tex]d=13.0 \ units[/tex]

Hence, the distance between the two points is 13 units.

Therefore, Option D is the correct answer.

To determine the distance between two points, we apply the distance formula, substituting the x and y coordinates for each point into the equation. After simplifying, the resulting square root of 170 corresponds to a distance of 13.0 units when rounded to the nearest tenth. Thus, the distance between the given points is 13.0 units.

Let's apply the distance formula to the two points given: (-5, -2) and (8, -3). The distance formula, d = √[(x2 - x1)2 + (y2 - y1)2], allows us to calculate the distance between two points in a Cartesian coordinate system.

First identify the x and y coordinates for each point. For the point (-5, -2), x1= -5 and y1= -2. For the point (8, -3), x2= 8 and y2= -3.

Step 1: Substitute these values into the distance formula.

d = √[(8 - (-5))2 + ((-3) - (-2))2]

Step 2: Simplify inside the square root, which involves removing the brackets and calculating the squares of the differences of the coordinates.

d=√[(13)2 + (-1)2 ] = √[169 + 1] = √170

The final distance d is the square root of 170. Rounded to the nearest tenth, this equals 13.0 units.

Therefore, the distance between point (-5, -2) and point (8, -3) is 13.0 units.

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Answer:

23

Step-by-step explanation:

if you have $16.10, he could buy 23 bluebarry muffins. Because if yo do

16.10 / 0.70 you woould get 23, and if you put that in the equasion you would

get this, P=$0.70(23) .  23 * 0.70 = 16.1

The area of the slice is 13.0899 inch².

Explanation:

[tex]\(3^\frac{1}{2} \cdot 3^\frac{1}{2} = 3\)[/tex].

To simplify [tex]\(3^\frac{1}{2} \cdot 3^\frac{1}{2}\)[/tex], you can use the properties of exponents.

When you multiply two powers with the same base, you add their exponents:

[tex]\[a^m \cdot a^n = a^{m+n}\][/tex]

In this case, both exponents are [tex]\(\frac{1}{2}\)[/tex], so when you multiply them together, you add the exponents:

[tex]\[3^\frac{1}{2} \cdot 3^\frac{1}{2} = 3^{\frac{1}{2} + \frac{1}{2}}\][/tex]

[tex]\[= 3^1\][/tex]

= 3

So, [tex]\(3^\frac{1}{2} \cdot 3^\frac{1}{2} = 3\)[/tex].

When x is greater than or equal to 0 use the equation x +2

The x value is given as 3 in f(3)

Now replace x with 3 in the equation and solve:

F(3) = 3 + 2 = 5.

The answer is 5

Answer:

(a)12cm (b)5/13 (c)12/13 (d)5/12

Step-by-step explanation:

(a) In a right triangle, the length of the sides are govered by the Pythagoras Theorem.

[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

In the diagram

Hypotenuse=13cm; Opposite(With respect to angle A)=5cm

[tex]13^2=5^2+Adjacent^2\\Adjacent^2=169-25=144\\Adjacent=\sqrt{144}=12cm[/tex]

(b)sin A =[tex]\frac{opposite}{hypotenuse} =\frac{5}{13}[/tex]

(c)cos A=[tex]\frac{adjacent}{hypotenuse} =\frac{12}{13}[/tex]

(d)tan A=[tex]\frac{opposite}{adjacent} =\frac{5}{12}[/tex]

Answer:

The weight of peanuts in the mixture   = 8  kg

The weight of corns in the given mixture = 4 kg

Step-by-step explanation:

Let us assume the weight of peanuts in the mixture   = x kg

The weight if corns in the given mixture = y kg

Total weight = (x + y) kg

The combined mixture weight = 12 kg

⇒ x  + y = 12  ..... (1)

Cost of per kg if mixture  = $ 40

So, the cost of (x + y) kg mixture  = (x+y) 40 = 40(x+ y)   ..... (2)

The cost of 1 kg of peanuts =  $ 42

So cost of x kg of peanuts  = 42 (x)  = 42 x

The cost of 1 kg of corns  = $ 36

So cost of y kg of corns  = 36 (y)  = 36 y

So, the total cost of x kg peanuts  + y kg corns =  42 x +  36 y  .... (3)

From (1) and (2), we get:

40(x+ y)  = 42 x +  36 y

x +  y = 12 ⇒ y = 12 -x

Put this in  40(x+ y)  = 42 x +  36 y

We get:

40(x+ 12 -x)  = 42 x +  36 (12 -x)

480 = 42 x + 432 - 36 x

or, 480 - 432 = 6 x

or, x  = 8

⇒ y = 12 -x = 12 - 8 = 4

⇒  y = 4

Hence, the weight of peanuts in the mixture   = 8  kg

The weight of corns in the given mixture = 4 kg

Final answer:

The weight of peanuts in the mixture is 8  kg and the weight of corns in the given mixture = 4 kg

Explanation:

A mixture of peanuts and corn sells for P40 per kilo.

Let us assume the weight of peanuts in the mixture   = x kg

The weight of corn in the given mixture = y kg

Total weight = (x + y) kg

The combined mixture weight = 12 kg

= x  + y = 12  ..... (1)

Cost of per kg if mixture  = $ 40

So, the cost of (x + y) kg mixture  = (x+y) 40 = 40(x+ y)   ..... (2)

The cost of 1 kg of peanuts =  $ 42

So cost of x kg of peanuts  = 42 (x)  = 42 x

The cost of 1 kg of corn = $ 36

So cost of y kg of corn  = 36 (y)  = 36 y

So, the total cost of x kg peanuts  + y kg corns =  42 x +  36 y  .... (3)

From (1) and (2):

40(x+ y)  = 42 x +  36 y

x +  y = 12 ⇒ y = 12 -x

Put this in  40(x+ y)  = 42 x +  36 y

We get:

40(x+ 12 -x)  = 42 x +  36 (12 -x)

480 = 42 x + 432 - 36 x

or, 480 - 432 = 6 x

or, x  = 8

= y = 12 -x = 12 - 8 = 4

= y = 4

Answer:

21y^4= B*7y^3

B=(21y^4)/(7y^3)

B=3y

Using the principles of Pythagorean theorem, we can figure out that the radius of the circle inscribed by the given isosceles triangle is 5 units.

To solve this problem, we need to apply the principles of the Pythagorean theorem and radius calculation in a circle inscribed by a triangle.

To recall, the Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, if you have a right triangle, you can calculate the hypotenuse c with the formula: c = √a² + b².

In this case, the altitude to the base forms two right-angled triangles within the isosceles triangle. These triangles both have legs of 5 (altitude) and half the base.

We first need to calculate this half base. The half base can be calculated by using Pythagorean theorem where one leg of the right triangle is the altitude (5) and the other leg is half the base, and the hypotenuse is one side of the isosceles triangle (13). Solving this yields a half base of 12.

Now, with the whole base equal to twice this value, or 24, we have a right triangle where the hypotenuse of the triangle (the diameter of the circle) is also the side of the isosceles triangle (13) and one leg is the whole base of the isosceles triangle (24), and the other leg is the altitude from the center of the base to the top of the isosceles triangle which is also the radius of the circle we are looking for.

Applying the Pythagorean theorem here yields a radius of √(13² - 12²) which simplifies to 5. Therefore, the radius of the circle is 5 units.

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Answer:

Step-by-step explanation:

For a. you are asked to evaluate f(0).  This is a piecewise function with different domains for each piece of the function.  You can only evaluate f(0) in the function that has a domain that allows 0 in it.  In the first domain, it says

x < -3.  0 is not less than -3, so 0 is not in that domain, so you will not use that "piece" of the function to evaluate f(0).

In the next domain, it says that x is greater than or equal to -3 and less than 0.  Again, 0 is not included in that domain, so we can't use that "piece" of the function to evaluate f(0).

The last domain says that x is greater than OR EQUAL TO 0, so this is where we evaluate f(0):

f(0) = -0 - 4 so

f(0) = -4

When we want to evaluate f(2), we follow the same rules.  Find the piece of the function that allows 2 in its domain.  That's the middle piece:

f(2) = 2(2) - 6 so

f(2) = -2

Answer:

$327.25

Step-by-step explanation:

$435 - $50 = 385

15% = 15/100 = 0.15

$385 * 0.15 = 57.75

$385 - $57.75 = $327.25

The price, in dollars, of a $435 dollar refrigerator after both discounts is $327.25.

= $435 - $50

= 385

Since there is 15% discount

So here we have to do 15% discount of $385

i.e.

= $385 - 15% of $385

= $385 - $57.75

= $327.25

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Answer:

0.6517

Step-by-step explanation:

Given that in a certain game of chance, your chances of winning are 0.3.

We know that each game is independent of the other and hence probability of winning any game = 0.3 (constant)

Also there are only two outcomes

Let X be the number of games you win when you play 4 times

Then X is binomial with p = 0.3 and n =4

Required probability

= Probability that you win at most once

= [tex]P(X\leq 1)\\=P(X=0)+P(X=1)[/tex]

We have as per binomial theorem

P(X=r) = [tex]nCr p^r (1-p)^{n-r}[/tex]

Using the above the required prob

= 0.6517

Final answer:

To calculate the probability of winning at most once over four games with a win probability of 0.3, we calculate the binomial probabilities for winning 0 times and 1 time then add them, resulting in a total probability of approximately 0.6517.

Explanation:

The question involves calculating the probability of winning at most once in a game of chance played four times, where the chances of winning each game are 0.3. We use the binomial probability formula P(x) = C(n, x) * pˣ * q⁽ⁿ⁻ˣ⁾, where C(n, x) is the number of combinations, p is the probability of winning, q is the probability of losing (1-p), and n is the total number of games. In this case, n=4, p=0.3, and q=0.7. We need to find the probability of winning 0 times (P(0)) and 1 time (P(1)) and then add these probabilities together.

Adding these probabilities gives the probability of winning at most once as P(0) + P(1) = 0.2401 + 0.4116 = 0.6517. Therefore, the probability of winning at most once in four games is approximately 0.6517.

Answer:

She will earn $442.89 in one week after the changes.

And this is more than her previous weekly earnings.

Step-by-step explanation:

Given:

Alondra received a 14% hourly raise, but the number of hours worked decreased by 7.5%. If her wage was $10.50 an hour and she worked 40 hours per week before the changes.

Now, to find money she will earn in one week after the changes.

Her wage was = $10.50.

She worked per week = 40 hours.

So, her salary before changes:

[tex]10.50\times 40\\\\=\$420.[/tex]

Thus, the salary per week before changes is $420.

Now, to get her salary after 14% hourly raise:

[tex]10.50+14\%\ of\ 10.50\\\\=10.50+\frac{14}{100} \times 10.50\\\\=10.50+1.47\\\\=11.97[/tex]

Salary after hourly raise = $11.97 per hour.

Then, to get the number of hours worked decreased by 7.5%:

[tex]40-7.5\%\ of\ 40\\\\=40-\frac{7.5}{100} \times 40\\\\=40-3\\\\=37.[/tex]

Number of hours per week after hours of worked decreased  = 37 hours.

Now, to get the salary after changes:

Salary after hourly raise × number of hours per week after hours of worked decreased

[tex]=11.97\times 37[/tex]

[tex]=\$442.89.[/tex]

Salary after changes in one week = $442.89.

As, the previous salary was $420 in one week.

And after changes this salary is $442.89 in one week which is more than previous.

Therefore, she will earn $442.89 in one week after the changes.

And this is more than her previous weekly earnings.

Answer:

160 Chairs

Step-by-step explanation:

Convert 6 hrs to seconds, this gives you 21600 seconds. Convert 2 min and 15 sec to seconds, and this gives you 135 seconds per chair. Divide 21600 by 135. This gives you 160 Chairs produced in 6 hours.