g Consider a brand of coffee. The weight of a pod of coffee this brand makes has mean 42.05 grams and standard deviation 0.025 grams. Using the central limit theorem and the normal distribution, what is the probability that the mean weight of 25 pods of coffee is less than 42.035 grams

Answer:

[tex]x=\frac{35}{9} .[/tex]

Step-by-step explanation:

[tex](3\sqrt{3})^{-x+1} =\frac{1}{3}*27^{x-5}\\( \sqrt{3^2*3}) ^{1-x}=\frac{1}{3} *((3)^3)^{x-5}\\(\sqrt{27} )^{1-x}=\frac{1}{3}*3^{3*(x-5)}\\ (\sqrt{3^3})^{1-x} =\frac{1}{3}*3^{3x-15}\\ 3^{\frac{3 }{2}*(1-x)}=\frac{1}{3}*3^{3x-15}\ |*3\\ 3*3^{\frac{3}{2}-\frac{3}{2}x}=3^{3x-15}\\ 3^{1+1,5-1,5}=3^{3x-15}\\ 3^{2,5-1,5x}=3^{3x-15}\ \ \ \ \Rightarrow\\2,5-1,5x=3x-15\\4,5x =17,5\ |*2\\9x=35\ |:9\\x=\frac{35}{9}.[/tex]

Since Jane wants to buys some lollipops, Jane has $13 dollars.

To answer the question, we need to solve simultaneous equations

Simultaneous equations are pairs of equations that contain two unknowns

Let

We know that If she buys 2 lollipops, she will have 3 dollars left, so we have that

y - 2x = 3  (1)

Also, If she wants to buy 3 lollipops, she will need 2 more dollars. So, we have that

y + 2 = 3x  (2)

So, the required simultaneous equations are

y - 2x = 3  (1)

y + 2 = 3x  (2)

From (1), x = (y - 3)/2

Substituting x into (2), we have

y + 2 = 3x  (2)

y + 2 = 3(y - 3)/2  

2(y + 2) = 3(y - 3)

2y + 4 = 3y - 9

2y - 3y = -9 - 4

-y = -13

y = -13/-1

y = 13

So, Jane has $13 dollars.

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The graph of the given quadratic function is shown below

From the question, we are to graph the given quadratic function.

The given quadratic equation is

y = −x² −8x −7

The graph of the given quadratic function is shown below

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Required probability is 0.8990

Given that,

p = 0.44

1 - p = 0.56

n = 736

[tex]\mu_\hat{p}} = p = 0.44\\\sigma_\hat{p}} = \frac{p*(1-p)}{n} = \sqrt(\frac{0.44*0.56)}{736} ) =[/tex]0.01830

Converting Normal distribution to standard normal because  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. Hence it's easy to work with standard normal distribution.

P(0.14<[tex]\hat{p}[/tex]<0.47) =  P((0.41-0.44)/0.01830) < [tex]\frac{\hat{p} - \mu _{\hat{p}} }{\sigma _{\hat{p}} }[/tex]<(0.47-0.44)/0.01830

Using normal algebra we get:

= P(-1.64 < z < 1.64)

= P(z < 1.64) - P(z < -1.64)

= 0.9495 - 0.0505

= 0.8990

Thus, required probability is 0.8990

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Answer:

11:16

Step-by-step explanation:

The loan amount is given as $76521

We first have to calculate the total amount of tuition

6970 x 4 + 11320 x 4

= 73160

[tex]73160 (1+\frac{\frac{4.5}{100} }{12} )^1^2[/tex]

= 73160 x (1 + 0.00375)¹²

= 76520.95

Hence the new loan amount after  agrace period of 1 year = $76521

b. PV = $76521

i = [tex]\frac{4.5/100}{12}[/tex]

= 0.00375

t = 10 years

[tex]PMT[\frac{1-(1+0.00375)^-^1^2^0}{0.0375} ]= 76521[/tex]

pmt = 793. 05

The monthly payment is  $793. 05.

In ten years the total payment is 793.05 x 10 x 12

= 95166

Difference = 95166 - 76521

= $18645

In ten years her ,monthly payment on the loan would be  $18645.

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Answer:

y = sin3x

Step-by-step explanation:

the equation is of the form y = sinbx

the period of the sine wave is

period = [tex]\frac{2\pi }{b}[/tex] ( b is the coefficient of x )

here period = [tex]\frac{\pi }{3}[/tex] × 2 = [tex]\frac{2\pi }{3}[/tex] , then

[tex]\frac{2\pi }{3}[/tex] = [tex]\frac{2\pi }{b}[/tex] ⇒ b = 3

y = sin3x ← equation of graph

Answer:

10 cm

Step-by-step explanation:

Hyp = [tex]\sqrt{6^{2}+8^{2} } =\sqrt{36+64} =\sqrt{100} =10[/tex]

Hope this helps

Step-by-step explanation:

310/100 × 72

= 223.2

using fraction × total

hope you understand.

pls like and follow :-):-)

The  equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

The given diagram shows two intersecting lines tangential to a circle at points A and C.

Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.

Mathematically;

<B = 1/2(arcADC - arcAC)

58 = 1/2(238 -x)

Hence the  equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Explanation } }:}[/tex]

" when rays parallel to optical axis/ principal axis fall on a concave mirror it passes through focus of mirror after reflection "

[tex] \qquad \large \sf {Conclusion} : [/tex]

The value of the median of the distribution is closest to 5.

A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The median is the number at the center of a dataset when the dataset is arranged in either ascending or descending order.

The numbers arranged in ascending order is : 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9

Median = 5

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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

(x + 1)² + (x + 3)² = (x + 5)² ← expand all factors using FOIL

x² + 2x + 1 + x² + 6x + 9 = x² + 10x + 25 , that is

2x² + 8x + 10 = x² + 10x + 25 ← subtract x² + 10x + 25 from both sides

x² - 2x - 15 = 0 ← in standard form

(x - 5)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 3 = 0 ⇒ x = - 3

however, x > 0 , then x = 5

Answer:

B. 5

Step-by-step explanation:

[tex] \sf{C = \sqrt{ A {}^{2} + B {}^{2} }}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(x + 3)}^{2} + {(x + 1)}^{2} }}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(x {}^{2} + 6x + 9)} + {(x {}^{2} + 2x + 1)}}}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(2x {}^{2} + 8x + 10)}}}[/tex]

[tex]\sf{(x + 5) {}^{2} = { {2x {}^{2} + 8x + 10}}}[/tex]

[tex]\sf{ {x}^{2} + 10x + 25= { {2x {}^{2} + 8x + 10}}}[/tex]

[tex]\sf{0= { {2x {}^{2} \red{ { - x}^{2} } + 8x \red{ - 10x} + 10 \red{ - 25}}}}[/tex]

[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]

[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]

[tex]\sf{0= (x - 5)(x + 3)}[/tex]

[tex] \sf{x_{1} - 5 = 0 }[/tex]

[tex] \sf{x_{1} = 0 + 5 }[/tex]

[tex] \sf{x_{1} = \boxed{5 }}[/tex]

[tex] \sf{x_{2} + 3 = 0 }[/tex]

[tex] \sf{x_{2} = 0 - 3 }[/tex]

[tex] \sf{x_{2} = \boxed{- 3 }}[/tex]

Option B. 5

Answer:

Double-displacement reaction

Step-by-step explanation:

In double-displacement reaction, aka. double-replacement reaction, the cation of one compound is swapped with the cation of another. They have the general structure:

AB + CD ---> AD + CB

In this case, the silver cation (Ag⁺) from AgNO₃ is swapped with the hydrogen cation (H⁺) of HCl.

The complete balanced equation is:

HCl + AgNO₃ ---> AgCl + HNO₃

The locus of the point represented by the equation y = 3•x + 2, indicates that the point (1, 5) is on the locus of the point.

The distance from the x-axis is the y-value

The distance from the y-axis is the x-value

Therefore;

The equation of the locus of the point is presented as follows;

When x = 1, y = 3 × 1 + 2 = 5

When x = 1, y= 5

Therefore;

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Step-by-step explanation:

Since [tex]cos(\theta) = -\frac{3}{4}[/tex] we can get some information from this. First of all [tex]cos(\theta)[/tex] is defined as [tex]\frac{adjacent}{hypotenuse}[/tex]. So the adjacent side is 3 and the hypotenuse is 4. Using this we can find the opposite side to find [tex]sin(\theta)[/tex] to calculate csc and cot of theta. So using the Pythagorean Theorem we can solve for the missing side. Also I forget to mention we have to calculate the sign of the adjacent side and the hypotenuse. Since you're given that the angle is in quadrant 2, that means the x-value is going to be negative, and the y-value is going to be negative. And the x really represents the adjacent side and the y represents the opposite. So the adjacent side is what's negative. and the opposite is positive

Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

[tex](-3)^2 + b^2 = 4^2[/tex]

[tex]9 + b^2 = 16[/tex]

[tex]b^2 = 7[/tex]

[tex]b = \sqrt{7}[/tex]

So now we can calculate [tex]sin(\theta)[/tex].

[tex]sin(\theta) = \frac{\sqrt{7}}{4}[/tex]

Now to calculate the exact value of csc you simply take the inverse. This gives you [tex]csc(\theta)=\frac{4}{\sqrt{7}}[/tex]. Multiplying both sides by sqrt(7) to rational the denominator gives you [tex]\frac{4\sqrt7}{7}[/tex].

Now to calculate cot(theta) you  find the inverse of tan. Tan is defined as [tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)}[/tex]. So all you do is take the inverse which is [tex]cot(\theta) = \frac{cos(\theta)}{sin(\theta)}[/tex].

Plug values in

[tex]cot(\theta) = \frac{-\frac{3}{4}}{\frac{4\sqrt{7}}{7}}[/tex]

Keep, change, flip

[tex]-\frac{3}{4} * \frac{7}{4\sqrt7}[/tex]

Multiply:

[tex]-\frac{21}{16\sqrt7}[/tex]

Multiply both sides by sqrt(7)

[tex]-\frac{21\sqrt7}{112}[/tex]

This is the value of cot(theta)

Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

Answer:

about 1920

step by step explanation:

40×50weeks=2000hours per year.

40×2weeks(the weeks off) = 80

2000-80= 1920hours per year

Answer:

-12.8 %

Step-by-step explanation:

-3200 / 25 000   x 100%  =  -  12.8 %

Answer:

Your answer is -12.8%

Step-by-step explanation:

To calculate the percent decrease, we:

Find the difference between the new value and the original

Divide the number by the original

Multiply by 100 and the % symbol.

The population of the town originally had 25,000. 3,200 people moved away. This means that the new population is 21,800.

21,800-25,000=-3,200

-3,200/25,000=-0.128

-0.128(100)=-12.8%

The towns population decreased by 12.8%.

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Answer:

(6,2)

Step-by-step explanation:

If you are looking for the coordinates then that is the correct answer.

Answer:

(6,2)

Step-by-step explanation:

Because the Y axis is vertical so you would move down and subtract 5 from the 7. Your X would stay the same. So the answer will be (6,2)

The area of the farm that is too rough to use is 157.86

An object's area is how much space it takes up in two dimensions. In other terms, it's the measurement of the number of unit squares that are completely around the surface of a closed shape.

Let the total area of the farm be x.

Area of the farm, too rough to use=x/4

Area of farm kept for poultry farms=2x/5

Remaining Area=221

Thus,

[tex]x-(\frac{x}{4}+\frac{2}{5}x)=221[/tex]

[tex]\\ x-\frac{13}{20}x=221\\[/tex]

[tex]\frac{7}{20}x=221\\[/tex]

x=631.43

Area of the farm too rough to use= 631.43/4

                                                        =157.86

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(a) The gradient is [tex]\frac{40}{5}=\boxed{8}[/tex], and represents the cost of buying one book in dollars.

(b) Draw the line through (0,0) and (20, 130).

(c) Since the gradient of the line representing company B is less (6.5 vs 8), it is better to buy books from company B because they are cheaper.

Step-by-step explanation:

x = 145°

we don't even need the upper parallel line with the 35° angle.

it is simply based on the fact that the angles on both sides of 2 intersecting lines have to be the same (just left-right mirrored).

Answer:

30000 milliliters

0.03 liters

Step-by-step explanation:

The volume of the box is 2.5 x 3.0 x 4.0 = 30 cc

There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml

There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters

The volume of the box is 30 mL or 0.03 L.

Volume is a metric magnitude that is defined as the extension in three dimensions of a region of space. Volume is defined as the amount of space occupied by the object or figure in three-dimensional space. Volume is measured in cubic units.

The volume of this prism depends on its three dimensions and is calculated as the multiplication of these dimensions,

Volume= Dimension 1× Dimension 2× Dimension 3

The volume of the box = 2.5 x 3.0 x 4.0 = 30 cc

There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml

There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters

Hence, the volume of the box is 30 mL or 0.03 L.

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Answer:

4/15

Step-by-step explanation:

Lets find a common denominator in order to find the total amount. There is a common denominator of 15 among 3 and 5. Therefore we will convert the fraction so they have the same denominator.

1/3 > 5/15

2/5 > 6/15

If Joy had read 5/15 of the book before reading at night, she already had the progress of being at 10/15 way through the book. At the end of the day, Joy had only 6/15 left of the book. To find the remainder, we subtract 10-6=4. This helps find the answer that Joy only read 4/15 of the book towards the end of the day.

Recall that the area of a trapezoid is equal to the average of its bases times its height.

For the trapezoids shown here, each base corresponds to the value of [tex]y=2x^2[/tex] when [tex]x[/tex] is one of the endpoints of some interval, while the height is the length of that interval.

On the interval [-2, -1], the trapezoids has bases 2(-2)² = 8 and 2(-1)² = 2, and "height" -1 - (-2) = 1. Then its area is (8 + 2)/2 × 1 = 5.

On the interval [-1, 0], one of the bases is 2(-1)² = 2 and the other is 2(0)² = 0, and the height is again 0 - (-1) = 1. Then the trapezoid's/triangle's area is (2 + 0)/2 × 1 = 1.

Then the total area under the curve [tex]y=2x^2[/tex] on the interval [-2, 0] is approximately 5 + 1 = 6.

Compare this to the actual value of the area given by the definite integral,

[tex]\displaystyle \int_{-2}^0 2x^2 \, dx = \frac{16}3 \approx 5.333\ldots[/tex]

Answer:

The bottom graph

Step-by-step explanation:

It shows that the kid starts 4 meters away and slowly decreases the distance for 8 seconds, pauses for 3, and moves back for 4.

Answer:

the 4th answer option

Step-by-step explanation:

the first one is looking good too, but the difference is to start at 4 meters away.

and the first graph starts at 9 meets away.

so, it is the 4th graph :

starting 4 meters away the person is coming slowly closer and closer for 8 seconds, then stands still for 3 seconds, and then walks away quickly for 4 seconds.

remember, the passing time is on the x-axis moving to the right (bigger and bigger numbers).

while the distance to the person is on the y-axis. and that value can get bigger and smaller.

Step-by-step explanation:

the whole forest is 4920 km².

4/5 if that was destroyed with salvageable wood :

4/5 × 4920 = 3,936 km²

there is 30 tons of salvageable wood per km², so in total :

3936 × 30 = 118,080 tons.

the wood can be removed at av rate of 53.5 tons per day.

how many days until cleaned up ?

as many days as 53.5 fits into the total amount of 118,080 :

118080 / 53.5 = 2,207.102804... days.

so, it will take about 2,207 days to remove all the salvageable wood.