A ketchup company regularly receives large shipments of tomatoes. For quality control purposes, they take a sample of tomatoes from each shipment. If the sample shows convincing evidence that more than 8\%8%8, percent of the tomatoes in the entire shipment are bruised, then the company will request a new shipment of tomatoes. So the company tests H0 : p = 0.08 versus Ha ​: p > 0.08H, where p is the proportion of tomatoes in the entire shipment that are bruised.
One day, a supervisor takes a random sample of 600 tomatoes from a shipment and finds that 53 of the tomatoes are bruised, which results in a test statistic of z ≈ 0.75. Assuming that the necessary conditions are met, what is the approximate P-value associated with the significance test for this shipment?

Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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Answer:

The sister is 10 and Mike is 20

Step-by-step explanation:

10 x 2 = 20

10 +20 = 30

Let Mike's sister age be x

Then Mike age ATQ = 2 × age of his sister = 2x

Now According to the Question (ATQ):-

\(Mike \: age + his \: sister \: age = 30 \\ 2x + x = 30 \\ 3x = 30 \\ \cancel{3}x = \cancel{30} ^{ \: \: 10} \\ x = 10\)

So Mike age = 2x = 2×10 = 20

Mike's sister age = x = 10

Just put the value in the equation ATQ :-

\(Mike \: age + his \: sister \: age = 30 \\ 20 + 10 = 30 \\ 30 = 30 \\ LHS = RHS\)

Answer:

Step-by-step explanation:

The number of tickets sold (q) at some price p is apparently ...

  q = 150 + 25(20 -p)/2 = 150 +250 -12.5p

  q = 12.5(32 -p)

The revenue is the product of the price and the number of tickets sold:

  r = pq

  r = 12.5p(32 -p) . . . . revenue equation

__

The maximum of revenue will be on the line of symmetry of this quadratic function, which is halfway between the zeros at p=0 and p=32. Revenue will be maximized when ...

  p = (0 +32)/2 = 16

The theater should charge $16 per ticket.

__

Maximum revenue will be found by using the above revenue function with p=16.

  r = 12.5(16)(32 -16) = $3200 . . . . maximum revenue

_____

Additional comment

The number of tickets sold at $16 will be ...

  q = 12.5(32 -16) = 200

It might also be noted that if there are variable costs involved, maximum revenue may not correspond to maximum profit.

Answer: \($m=-\frac{1}{22}$\)   \($b=\frac{15}{22}$\)

Step-by-step explanation:

To find the equation of the tangent line to the curve \($xy^3+xy= 14$\) at the point \($(7,1)$\) we need to first find the derivative of the equation with respect to x using implicit differentiation.

Taking the derivative of both sides with respect to x:

\($\frac{d}{dx}(xy^3+xy)=\frac{d}{dx}(14)$\)

Using the product rule and chain rule:

\($y^3+x(3y^2\frac{dy}{dx}+y)=0$\)

Simplifying and solving for \($\frac{dy}{dx}$\)

\($\frac{dy}{dx}=-\frac{y}{3y^2+1}$\)

Now we can substitute x=7 and y=1 into this equation to find the slope of the tangent line at the point (7,1):

\($m=\left.-\frac{y}{3y^2+1}\right|_{(7,1)}=-\frac{1}{22}$\)

So the slope of the tangent line is \($-\frac{1}{22}$\)

To find the y-intercept, we can use the point-slope form of the equation of a line:

\($y-1 = m(x-7)$\)

\($y=mx+(1-7m)$\)

Therefore, the equation of the tangent line to the curve \($xy^3+xy=14$\) at the point (7,1) can be written as:

\($y=-\frac{1}{22}x+\frac{15}{22}$\)

So \($m=-\frac{1}{22}$\) and \($b=\frac{15}{22}$\)

ANSWER

EXPLANATION

We want to solve the system of equations using the linear combination method:

This method involves the combination of the two equations to form one simplified equation with only one variable.

From the given equations, we see that the coefficients of y in both equations are equal. Hence, we can combine them by finding the difference between the two equations.

Let us subtract the first equation from the second equation:

Now, simplify by dividing both sides by 3:

To find the value of y, substitute the value of x into the first equation and solve for y:

Hence, the solution to the system of equations is:

Complete question :

shopkeeper sells one machine for 990 re at a profit of 10% and another machine for 1960 at a loss of 2%. What is his gain or loss percent

Answer:

1.72%

Step-by-step explanation:

Given that :

MACHINE 1:

Sales price = 990

Profit percent = 10%

The cost price of the machine (x) :

10% profit of x :

(100 + 10)% of x = 990

110% of x = 990

1.1x = 990

x = 990/1.1

x = 900

MACHINE 2:

Sales price = 1960

Loss on sale = 2%

Cost price (x) :

(100 - 2)% of x = 1960

98% x = 1960

0.98x = 1960

x = 1960/0.98

x = 2000

Total amount realized from sale = (990 + 1960) = 2950

Total cost of production = (2000 + 900) = 2900

Profit Made = (2950 - 2900) = 50

% profit:

(Profit / cost of production) * 100

(50 / 2900) * 100%

0.0172413 * 100%

profit % = 1.72

The profit made is 50

Cost price of first machine will be:

= 100/(100 + 10) × 990

= 100/110 × 990

= 100 × 9

= 900

Cost price for second machine will be:

= (100 - 2) × x = 1960

= 98% × x = 1960

= 0.98x = 1960

x = 1960/0.98.

x = 2000

The total cost price = 900 + 2000 = 2900

Total selling price = 990 + 1960 = 2950

Therefore, profit will be:

= Selling price - Cost price .

= 2950 - 2900

= 50

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The mean absolute deviation (MAD) of the data set is equal to 180.625.

The mean absolute deviation of a data set is to find the average distance of each observation of the data set and the mean of the data set.

Mean absolute deviation = 1/n ∑ absolute value of (xi - x bar)

x bar =average value of the given data set

n= total number of data set

xi = data value in a given set

According to the question,

x bar = sum of all the data set / total number of the data set

x bar = 2052/16 = 128.25

Substitute the value in the formula, we have

Mean absolute deviation = 2890/16 = 180.625

Hence, the Mean absolute deviation of the data set is equal to 180.625.

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As per the given data, the Mean absolute deviation (MAD) of the data set is equals to 17.5

The term Mean absolute deviation in math is defined as the average distance of each observation of data set  and the mean of the data set.

Here we have given the following data.

=> 13, 0 , 14 , 36, 18, 9

Then the mean of the data is calculated as,

=> (13 + 0 + 14 + 36 + 18 + 9)/6

=> 90/6

=> 15

Now, we have to the Substitute the value in the formula, we have

And then the Mean absolute deviation is calculated as,

=> (90 + 15)/6

=> 105/6

=> 17.5

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Answer:

510 minutes.

Step-by-step explanation:

i hope this helped you! :)

510 MINUTES!! :)

Hope this helped!

Answer:

The tip would be $6.00

Step-by-step explanation:

To tip 20% you move the decimal point to the left once to get 3.1. then you round to the nearest whole number which is 3. Finally, you double 3 which is 6.

I hope this helped! Have a nice day!

Answer:

stucco Waco spa with success windup stucco extra Arden grasp recap year ready 354

Answer:

the last one is not part of the proof, because it's not SSS it's SAS.

Answer:

D

Step-by-step explanation:

it is incorrect the answer is SAS

Answer:

1650

Step-by-step explanation:

30 percent of 5500 is 1650

Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

Answer:

The cost per ounce of the small cup is $0.269

Step-by-step explanation:

To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.

Cost per ounce = Cost of the cup ÷ Number of ounces in the cup

Cost of the cup = $2.69

Number of ounces in the cup = 10 oz

So,

Cost per ounce = $2.69 ÷ 10 oz

Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)

Therefore, the cost per ounce of the small cup is $0.269.

Answer:

Step-by-step explanation:

Given : A right triangle

To do : Solve for x

Solution,

\(cos \: 55 = \frac{x}{20} \) ( by definition of cos function, adjacent / hypotenuse )

\(0.5736 = \frac{x}{20} \)

multiply both sides of the equation by 20

\((0.5736) \times 20 = x\)

Calculate the product

\(11.471 = x\)

Swipe both sides of the equation

\(x = 11.471\)

Round answer to nearest hundredth

\(x = 11.47\)

Hope this helps...

Best regards!!

The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².

To calculate the perimeter and area of the square, we can use the formulas:

Perimeter = 4 * side length

Area = side length * side length

Substituting the given side length of 4√5mm into the formulas, we have:

Perimeter = 4 * 4√5mm = 16√5mm

Area = (4√5mm) * (4√5mm) = 16 * 5mm = 80mm²

Therefore, the perimeter of the square is 16√5mm, and the area of the square is 80mm².

Please note that the values are based on the provided side length of 4√5mm. If there are any changes to the side length, the perimeter and area will differ accordingly.

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The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².

I took the test on plato.

Answer:

I THINK rachel will be 12

Step-by-step explanation:

Step-by-step explanation: 9.1 x 102 = 928.2.

We use pythagoras theorem

Let y represent the other leg

The measure of the other leg is 16.70 cm

For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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Answer:

Step-by-step explanation:

1  13/24

The y-intercept is 40.5 the machine starts with 40.5 ounces of diet soda.

Option B is the correct answer.

We have,

From the graph plot,

We see that,

The y-intercept is when x = 0.

This means,

At 0 hours, the amount of diet soda is 40.5.

Now,

y = 40.5 means the machine starts with 40.5 ounces of diet soda.

Thus,

The y-intercept is 40.5 the machine starts with 40.5 ounces of diet soda.

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The number of seats in the first, second and third aircraft are 561 seats,  497 seats and 842 seats respectively

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Let F, S and T represent number of seats in the first, second and third aircraft respectively

We can set up three equations to represent the situation:

F = 64 + S   --- (1)

T = 2S - 152 --- (2)

F + S + T = 1900 --- (3)

Put (1) and (2) in (3):

F + S + T = 1900

(64 + S) + S + (2S - 152) = 1900

64 + S + S + 2S - 152 = 1900

4S - 88 = 1900

4S = 1900 + 88

4S = 1988

S = 1988/4

S = 497 seats

F = 64 + S

F = 64 + 497 = 561 seats

F + S + T = 1900

561 + 497 + T = 1900

1058 + T = 1900

T = 1900 -1058 = 842 seats

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Answer:

47 years old

Step-by-step explanation:

21, 23, 30, 32, 32, 25, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53, 55

First eliminate the one on the very end of the left side

23, 30, 32, 32, 25, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53, 55

Eliminate 55

23, 30, 32, 32, 25, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53

Eliminate 23

30, 32, 32, 25, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53

Keep going until you get two numbers left or one number...

In this case, we are left with two numbers: 46 and 48.

To find the median age, we must find the average of these two numbers.

\(\frac{(46+48)}{2}\)

\(\frac{94}{2} = 47\)

The median age is 47 years old.

9514 1404 393

Answer:

  LW = 17.5

Step-by-step explanation:

In this geometry, all of the right triangles are similar. This means the ratio of long side to short side is the same for all of the triangles:

  WA/YA = YA/LA

  WA = YA²/LA = 7.0²/3.5 = 14.0

Then the length of LW is ...

  LW = LA +AW = 3.5 +14.0

  LW = 17.5

Step-by-step explanation:

the process is shown in the picture.

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question