A machine is designed to dispense 20 mg of d-desoxyephedrine into each capsule of a medicine. 13
pills are tested, and it's found that they have a mean drug content of 20.2 mg, with a standard
deviation of 2.4 mg. To a 1% level of significance, can it be asserted that the standard deviation of
the process (in general) is over 2 mg?
[Assume that the drug contents of all the pills are normally distributed.]

Answer:

2x + 12y + 43 ≥ 40

17x + 12y + 8z ≥ 20

14x + 6y + z ≤ 50

x ≥ 0

y ≥ 0

z ≥ 0

Step-by-step explanation:

given:

Cost Eggs = $2

Cost of edema = $5

cost of  elbow Macaroni = $3

Lets eggs = x,

edamame = y

elbow macaroni = z

TC = 2x+5y+3z

Therefore;

2x + 12y + 43 ≥ 40

17x + 12y + 8z ≥ 20

14x + 6y + z ≤ 50

x ≥ 0

y ≥ 0

z ≥ 0

the first objective is to make sure the total cost is subject to the required nutritional requirements.

So the total cost function (TC) is denoted by the number of servings multiplied for each costs. Eggs cost $2, edamame $5, and macaroni $3.

The problem subjects that each meal contains at least 40g of carbohydrates (this is the condition).

to get this we need to add what each meal component adds to the total, eggs add 2g of carbs, edamame 12g, and macaroni 43g.

Same should be done for protein, we require at least 20 grams of protein,  Eggs add 17g, edamame adds 12g, and macaroni adds 8g.

and lastly we don't want more than 50 grams of fat,  Eggs add 14g, edamame add 6g and macaroni 1g.

Answer:

The answers are as follows:

5. \(12+3 = 3+12\)

7. \((6+4)+8 = 6+(4+8)\)

9. \((10*5)*7 = 10*(5*7)\)

Step-by-step explanation:

5. 12 and 3

Commutative property of addition states that the order of two numbers in addition doesn't matter; the result will be the same. If a and b are two numbers then the property will be:

a+b = b+a

For the given question, the commutative property will be:

\(12+3 = 3+12\)

Associative property deals with three numbers or variables. It states that when 3 numbers are being added or multiplied their order doesn't affect the result.

It can be stated as:

(a+b)+c = a+(b+c)

7. 6,4 and 8

The associative property will be:

\((6+4)+8 = 6+(4+8)\)

9. 10,5 and 7

\((10*5)*7 = 10*(5*7)\)

Hence,

The answers are as follows:

5. \(12+3 = 3+12\)

7. \((6+4)+8 = 6+(4+8)\)

9. \((10*5)*7 = 10*(5*7)\)

Answer:

From Thursday to Friday, the change in the depth was 19/16 inches

or as a mixed number, 1 3/16 inches

Step-by-step explanation:

From Monday to Thursday, the depth of a snowdrift changed by 2 3/8 inches

now, 2 3/8 = 2(8/8)+(3/8) = 16/8 + 3/8 = (16+3)/8

so, 2 3/8 = 19/8 inches = depth change from monday to thursday

From Thursday to Friday, the depth changed by half as much,

so,

depth change from Thursday to Friday = 1/2(depth change from Monday to Thursday)

depth change from thursday to friday = 1/2(19/8) = 19/16 inches

Weare given the function: g(x) = x^2 +1, and we are asked to find what is the value of g(1).

Then we simply repalce the independent variable "x" with "1" in the given expression, and evaluate:

g(x) = x^2 + 1

g(1) = (1)^2 + 1

g(1) = 1 + 1

g(1) = 2

The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

Learn more about sine of angles on https://brainly.com/question/22649800

#SPJ1

\(f(x) = 2x is linear.f(x) = 4^x is exponential.\) This is where at each level, each branch extends into 4 branches.

In the first prompt, the number of boxes in each row is increasing by a constant amount, so the function is linear. In the second prompt, the number of branches is increasing by a factor of 4 with each level, so the function is exponential.

A linear function is defined as one where the output increases by a constant amount for each increase in the input. An exponential function is defined as one where the output increases by a constant factor for each increase in the input. The first prompt corresponds to a linear function, while the second prompt corresponds to an exponential function.

Learn more about function

brainly.com/question/20476366

#SPJ4

The complete question is-

Is the function f(x) = 4^x, where x is the number of branches at level x in a tree diagram, linear or exponential? Explain your answer.

Answer:

1050 miles

Step-by-step explanation:

velocity=distance/time

Distance=450 miles

Time=3 hours

Velocity=150 miles/hours

if time is 7 and velocity is 150 distance is 7x150=1050 miles

The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

Learn more about volume or capacity at https://brainly.com/question/463363

#SPJ1

A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

Answer: Let's call the width of the rectangular playing field "w" and the length "l". From the problem, we know that:

l = 3w + 4 (the length is 4 yards longer than triple the width)

We also know that the perimeter of a rectangle is the sum of the lengths of all four sides, so:

P = 2l + 2w

We are given that the perimeter is 416 yards, so we can substitute that into the perimeter equation:

416 = 2(3w + 4) + 2w

Simplifying and solving for w:

16 = 6w + 8

8 = 6w

w = 8/6 = 4/3

We can now substitute that back into the equation for the length:

l = 3w + 4

l = 3(4/3) + 4

l = 4 + 4

l = 8

So the dimensions of the rectangular playing field are 4/3 yards wide and 8 yards long.

Step-by-step explanation:

We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

Learn more about thousand on https://brainly.com/question/29260004

#SPJ1

Answer:

1/13

Step-by-step explanation:

The number 7 cards= 4 of them

Total number of cards= 52

4/52 are 7's

Simplify 4/52>>>>2/26>>>>1/13

Hope this helped! Please give a brainly if you can <33

Answer:

y=5/1x or y=5x

Step-by-step explanation:

Answer:

-$35.00

Step-by-step explanation: I think

Answer:

Step-by-step explanation:

1. Divide the sides of the red triangle by 2. That will get your size

2. Translate 5 units down across the x-axis

3. Translate 6 unit to the right across the y-axis.

So your answer would be (5,6)/2= A prime

Hope this helped!

Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. The correct option is A.

Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.

The red figure is similar to the blue figure. The dilation factor is,

Dilation factor = Image/Pre-image = 2/4 = 1/2

Now, the position of the right-most vertice will be (0.5,1), if we see the transformation of this vertice, then after transformation, it will be at (4,-4).

Hence, the correct option is A.

Learn more about Dilation:

https://brainly.com/question/13176891

#SPJ2

Answer:

Step-by-step explanation:

ADE=DHG

FEH=IHE

ADE=DHE

ADC=EHI

BEF=IHE <This would be the correct answer if segment CDEF is parallel to segment GHI.

Answer:

ummm I think u want the answer x= 11 1/4

Answer:

x = 45/4

Step-by-step explanation:

4(x - 5) = 25

4x - 20 = 25

4x - 20 + 20 = 25 + 20

4x = 45

4x/4 = 45/4

x = 45/4

Answer:

Step-by-step explanation:

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

Answer:

90

Step-by-step explanation:

add the ratio 3+5 to get 8

amina received 3/8 of 240

perform the calculation 3/8×240

240/8=30. , 30×3=90

hi

because it lead to mathematical nonsense

3x-7  = 3x+5

3x-7 -3x-5 = 0

    -7-5 = 0

    -12 =0  

-12 = 0 is just not possible, so 3x-7 = 3x +5  has no solution.

The value of the vehicle 13 years after purchase is $13,695.24.

What is exponential decay?

Exponential decay is a mathematical process in which a quantity decreases over time in a manner proportional to its current value. This means that the rate of decay is proportional to the amount of the substance remaining, and as the amount of the substance decreases, the rate of decay also decreases.

We can use the formula for exponential decay to find the approximate value of the vehicle 13 years after the purchase:

\($V = V_0 e^{-rt}$\)

where V0 is the initial value of the vehicle, r is the annual depreciation rate (as a decimal), t is the number of years since purchase, and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

\($V \approx 29800 e^{-0.06*13}$\)

\($V \approx 29800 e^{-0.78}$\)

V ≈ 29800 x 0.4593

V ≈ 13695.24

Therefore, the approximate value of the vehicle 13 years after purchase is $13,695.24.

To know more about exponential decay visit:

brainly.com/question/2193799

#SPJ1

Answer:

15.87%

Step-by-step explanation:

Notice that the mean of 0.35 inches with a standard deviation of 0.01 gives you when you add (to the right of the distribution), exactly 0.36. Since you want to find the probability (or percentage) of the bolts that have diameter LARGER than 0.36 in, that means you want to estimate the area under the Normal distribution curve from 0.36 to the right). See attached image.

We can use the tables of Z distribution for that, or the standard normal tables:

P(x>0.36) = P(z>(0.36-0.35)/0.01) = P(Z>1) = 0.1587 = 15.87%

Answer:

2.9167

Step-by-step explanation:

i just calculated it i guess

We raise the fraction to the power of 4/3.

To evaluate the expression:

\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3},

we can simplify each term within the parentheses before multiplying them together.

Let's simplify each term step by step:

\left( \frac{16}{9} \right)^{2/3}:

To simplify this term, we raise the fraction to the power of 2/3.

\left( \frac{16}{9} \right)^{2/3} = \left( \left( \frac{2^4}{3^2} \right)^{1/3} \right)^2 = \left( \frac{2^{4 \cdot 1}}{3^{2 \cdot 1}} \right)^2 = \left( \frac{2^4}{3^2} \right)^2 = \left( \frac{16}{9} \right)^2 = \frac{16^2}{9^2} = \frac{256}{81}

\left( \frac{4}{3} \right)^{4/3}:

Similarly, we raise the fraction to the power of 4/3.

\left( \frac{4}{3} \right)^{4/3} = \left( \left( \frac{2^2}{3^1} \right)^{1/3} \right)^4 = \left( \frac{2^{2 \cdot 1}}{3^{1 \cdot 1}} \right)^4 = \left( \frac{2^2}{3^1} \right)^4 = \left( \frac{4}{3} \right)^4 = \frac{4^4}{3^4} = \frac{256}{81}

\left( \frac{9}{16} \right)^{2/3}:

We raise the fraction to the power of 2/3.

\left( \frac{9}{16} \right)^{2/3} = \left( \left( \frac{3^2}{2^4} \right)^{1/3} \right)^2 = \left( \frac{3^{2 \cdot 1}}{2^{4 \cdot 1}} \right)^2 = \left( \frac{3^2}{2^4} \right)^2 = \left( \frac{9}{16} \right)^2 = \frac{9^2}{16^2} = \frac{81}{256}

\left( \frac{3}{4} \right)^{4/3}:

We raise the fraction to the power of 4/3.

\left( \frac{3}{4} \right)^{4/3} = \left( \left( \frac{3^1}{2^2} \right)^{1/3} \right)^4 = \left( \frac{3^{1 \cdot 1}}{2^{2 \cdot 1}} \right)^4 = \left( \frac{3^1}{2^2} \right)^4 = \left( \frac{3}{4} \right)^4 = \frac{3^4}{4^4} = \frac{81}{256

For more questions on fraction

https://brainly.com/question/78672

#SPJ8

The percent increase in the average height of the corn plants during this one-week period is approximately 50%.

To calculate the percent increase in the average height of the corn plants, we need to find the difference between the final height and the initial height, and then express that difference as a percentage of the initial height.

Initial height = 16 1/2 in.

Final height = 24 7/10 in.

To find the difference, we subtract the initial height from the final height:

Difference = Final height - Initial height

Difference = 24 7/10 - 16 1/2

To perform the subtraction, let's convert the heights to a common denominator, which is 10:

Difference = (24 * 10 + 7) / 10 - (16 * 10 + 5) / 2

Difference = (240 + 7) / 10 - (160 + 5) / 10

Difference = (247 / 10) - (165 / 10)

Difference = 82 / 10

Difference = 8.2 in.

Now, let's calculate the percent increase:

Percent increase = (Difference / Initial height) * 100

Percent increase = (8.2 / 16.5) * 100

Percent increase ≈ 49.70

Rounding to the nearest whole percent, the percent increase in the average height of the corn plants during this one-week period is approximately 50%.

For more such questions on percent , Visit:

https://brainly.com/question/24877689

#SPJ11