Draw a diagram for this statement.
one sixth of the 48 vegetable plants were tomato plants.
use your diagram to determine how many of the vegetable plants were tomato plants

Answer:

The answer is 3093.

3093 (if that series you posted actually does stop at 1875; there were no dots after, right?)

Step-by-step explanation:

We have a finite series.

We know the first term is 48.

We know the last term is 1875.

What are the terms in between?

Since the terms of the series form a geometric sequence, all you have to do to get from one term to another is multiply by the common ratio.

The common ratio be found by choosing a term and dividing that term by it's previous term.

So 120/48=5/2 or 2.5.

The first term of the sequence is 48.

The second term of the sequence is 48(2.5)=120.

The third term of the sequence is 48(2.5)(2.5)=300.

The fourth term of the sequence is 48(2.5)(2.5)(2.5)=750.

The fifth term of the sequence is 48(2.5)(2.5)(2.5)(2.5)=1875.

So we are done because 1875 was the last term.

This just becomes a simple addition problem of:

48+120+300+750+1875

168      +   1050  +1875

          1218          +1875

                         3093

Answer:

Step-by-step explanation:

When a quantity changes exponentially by a fraction r in some time period t, the quantity is multiplied by 1+r in each period. That is the quantity (y) as a function of t can be described by ...

  y = y0·(1+r)^t

where y0 is the initial quantity (at t=0).

Here, the problem statement gives us two quantities and their respective rates of change.

Treatment A

  y0 < 300, r = -0.04, so the remaining amount is described by ...

  y < 300·0.96^t

__

Treatment B

  y0 ≤ 400, r = -0.062, so the remaining amount is described by ...

  y ≤ 400·0.938^t

__

When we graph these, we realize these inequalities allow the quantity of each substance to be less than zero. Mathematically, those quantities will approach zero, but not equal zero, so we can put 0 as a lower bound on the value of y in each case:

_____

Comment on these inequalities

We suspect your answer choices will not be concerned with the lower bound on y.

Answer:

y (arrow left) 300e-0.04t

y (arrow left underlined) 400e-0.062t

Step-by-step explanation:

Answer:

The correct option is D) How many visitors came to the museum each month last year?

Step-by-step explanation:

First, understand that what is the statistical question.

Statistical questions are those question which involves the collection of data. Which can be represented with the help of a chart or tables.

Now consider the provided options:

Options A, B and C are not a statistical question, because these questions do not require or involve the collection of data.

But the option D involves the collection of data because to find the number of visitors came to the museum each month, we need to collect the data.

Therefore the correct option is D.

Answer:

D.) How many visitors came to the museum each month last year?

i am taking the test rn :)

Answer:

197,8879 N.

Step-by-step explanation:

The magnitude of the horizontal force exerted on the statue can be calculated using trigonometric functions.

The question given says that Nancy is pushing the statue with a force of 120 N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180 N at a 40° angle with the horizontal.

With that information can be calculated the horizontal force exerted on the statue by Nancy, the horizontal force exerted on the statue by Harry and, adding that results, the total horizontal magnitude can be calculated.

The cosine function can be used to calculate the horizontal component of the forces exerted by Nancy and Harry, to determine the horizontal component of the force exerted on the statue.

F= (120 N cos 60°) + (180 N x cos 40°)

F= 197,8879 N

To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components. Nancy's horizontal force is 60N and Harry's horizontal force is 137.48N. The magnitude of the horizontal force exerted on the statue is 197.48N.

To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components.

Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal, so the horizontal component of her force is 120N * cos(60°) = 60N.

Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal, so the horizontal component of his force is 180N * cos(40°) = 137.48N.

To find the magnitude of the horizontal force exerted on the statue, we sum up the horizontal components of both forces: 60N + 137.48N = 197.48N.

Answer:

a) The population proportion is 0.625

b) The confidence interval is (0.578 , 0.672)

Step-by-step explanation:

* Lets explain how to solve the problem

- The Fox TV network is considering replacing one of its prime-time

  crime investigation shows with a new family-oriented comedy show

- There are 400 viewers

∴ The sample size is 400

- 250 of them indicated they would watch the new show and

  suggested it replace the crime investigation show

∴ The number of success is 250

∵ The population proportion P' = number of success/sample size

∴ P' = 250/400 = 0.625

a) The population proportion is 0.625

* Lets solve part b

- Develop a 95 percent confidence interval for the population

  proportion

∵ The confidence interval (CI) = [tex]P'(+/-)z*(\sqrt{\frac{P'(1-P')}{n}}[/tex],

  where P' is the sample proportion, n is the sample size, and z*

  is the value from the standard normal distribution for the desired

  confidence level

∵ 95% z is 1.96

∴ z* = 1.96

∵ P' = 0.625

∵ n = 400

∵ [tex]\sqrt{\frac{P'(1-P')}{n}}=\sqrt{\frac{0.625(1-0.625)}{400}}=0.0242[/tex]

∴ CI = 0.625 ± (1.96)(0.0242)

∴ CI = (0.625 - 0.047 , 0.625 + 0.047)

∴ CI = (0.578 , 0.672)

b) The confidence interval is (0.578 , 0.672)

The probability that no more than [tex]25[/tex] were victims of e-mail fraud is [tex]\fbox{0.00169}[/tex].

Further explanation:

Given:

The probability of a user experience e-mail fraud [tex]p[/tex] is [tex]0.7[/tex].

The number of individuals [tex]n[/tex] are [tex]50[/tex].

Calculation:

The [tex]\bar{X}[/tex] follow the Binomial distribution can be expressed as,

[tex]\bar{X}\sim \text{Binomial}(n,p)[/tex]

Use the normal approximation for [tex]\bar{X}[/tex] as

[tex]\bar{X}\sim \text{Normal}(np,np(1-p))[/tex]

The mean [tex]\mu[/tex] is [tex]\fbox{np}[/tex]

The standard deviation [tex]\sigma[/tex] is [tex]\fbox{\begin{minispace}\\ \sqrt{np(1-p)}\end{minispace}}[/tex]

The value of [tex]\mu[/tex] can  be calculated as,

[tex]\mu=np\\ \mu= 50 \times0.7\\ \mu=35[/tex]

The value of [tex]\sigma[/tex] can be calculated as,

[tex]\sigma=\sqrt{50\times0.7\times(1-0.7)} \\\sigma=\sqrt{50\times0.7\times0.3}\\\sigma=\sqrt{10.5}[/tex]

By Normal approximation \bar{X} also follow Normal distribution as,

[tex]\bar{X}\sim \text{Normal}(\mu,\sigma^{2} )[/tex]

Substitute 35 for [tex]\mu[/tex] and 10.5 for [tex]\sigma^{2}[/tex]

[tex]\bar{X}\sim\text {Normal}(35,10.5)[/tex]

The probability that not more than [tex]25[/tex] were victims of e-mail fraud can  be calculated as,

[tex]\text{Probability}=P(\bar{X}<25)}\\\text{Probability}=P(\frac{{\bar{X}-\mu}}{\sigma}<\frac{{(25+0.5)-35}}{\sqrt{10.5} })\\\text{Probability}=P(Z}<\frac{{25.5-35}}{\sqrt{10.5} })\\\text{Probability}=P(Z}<-2.93})\\[/tex]

The Normal distribution is symmetric.

[tex]P(Z>-2.93})=1-P(Z<2.93)\\P(Z>-2.93})=1-0.99831\\P(Z>-2.93})=0.00169[/tex]

Hence, the probability that no more than [tex]25[/tex] were victims of e-mail fraud is [tex]\fbox{0.00169}[/tex].

Learn More:

1. Learn more about angles https://brainly.com/question/1953744

2. Learn more about domain https://brainly.com/question/3852778

Answer Details:

Grade: College Statistics

Subject: Mathematics

Chapter: Probability and Statistics

Keywords:

Probability, Statistics, E-mail fraud, internet, Binomial distribution, Normal distribution, Normal approximation, Central Limit Theorem, Z-table, Mean, Standard deviation, Symmetric.

Answer:

[tex]12x^8+15x^7-8x^6-10x^5[/tex]

Step-by-step explanation:

Start by using the FOIL method on your second and third terms.

[tex](3x^2-2)(4x^2+5x)\\12x^4+15x^3-8x^2-10x[/tex]

Next, multiply the first term ([tex]x^4[/tex]) against your result.

[tex]x^4(12x^4+15x^3-8x^2-10x)\\12x^8+15x^7-8x^6-10x^5[/tex]

For this case we must find the product of the following expression:[tex](x ^ 4) (3x ^ 2-2) (4x ^ 2 5x) =[/tex]

We must bear in mind that to multiply powers of the same base, the same base is placed and the exponents are added:

Multiplying the terms of the first two parentheses, applying distributive property we have:

[tex](x ^ 4 * 3x ^ 2-x ^ 4 * 2) (4x ^ 2 5x) =\\(3x ^ 6-2x ^ 4) (4x ^ 2 5x) =\\3x ^ 6 * 4x ^ 2 3x ^ 6 * 5x-2x ^ 4 * 4x ^ 2-2x ^ 4 * 5x =\\12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5[/tex]

Answer:

The product is: [tex]12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5[/tex]

To find the length of the rectangle with an area of 24 square centimeters and width of (a-5), solve the quadratic equation a^2 - 5a - 24 = 0, which gives a length a = 8 centimeters.

The question asks us to find the length a of a rectangle that has an area of 24 square centimeters, given that the width is a-5. Since area of a rectangle is found by multiplying the length by the width, we can set up the equation a*(a-5) = 24. To find the value of a, we need to solve this quadratic equation.

First, we expand the equation:

a² - 5a = 24

Then, we set the equation to zero:

a² - 5a - 24 = 0

Next, we factor the quadratic equation:

(a - 8)(a + 3) = 0

There are two possible solutions for a:

Since a length cannot be negative, we discard a = -3 and conclude that the length a of the rectangle is 8 centimeters.

Answer:

  f(x) = 4^x -3

Step-by-step explanation:

All of the listed functions are linear functions with a constant slope of 4. None of them goes through the point (0, -2).

__

So, we assume that there is a missing exponentiation operator, and that these are supposed to be exponential functions. If the horizontal asymptote is -3, then there is only one answer choice that makes any sense:

  f(x) = 4^x -3

_____

The minimum value of 4^z for any z will be near zero. In order to make it be near -3, 3 must be subtracted from the exponential term.

Answer:

positive

Step-by-step explanation:

Find the sign of (2-2x+y) for any point (x,y) in quadrant 2.

In quadrant 2, the x's are negative and the y's are positive.

So choose a negative value for x and a positive value for y and evaluate:

2-2x+y

Let's try (-4,5):

2-2(-4)+5

2+8+5

15 (positive)

Let's try(-1/2 , 10):

2-2(-1/2)+10

2+1+10

3+10

13 (positive)

Let's try in general Let (x,y)=(-a,b) where a and b are positive:

2-2(-a)+b

2+2a+b

Since a and b are positive, then 2+2a+b is positive because you are adding three different positive numbers.

Answer:

  (4, -3)

Step-by-step explanation:

-2u +v = -2(-1, 5) +(2, 7) = (-2(-1)+2, -2(5)+7)

  = (4, -3)

Answer:

320 bags

Step-by-step explanation:

Let's first assign some literals, to simplify the problem. The goal is to set everything up, in order to only use one symbol.

[tex]p [/tex]: number of bags with only peanuts.

[tex] a [/tex]: number of bags with only almonds.

[tex] r [/tex]: number of bags with only raisins.

[tex] x [/tex]: number of bags with only raisins and peanuts.

Now, the problem establish 3 useful equations. We can find equations equivalences for the next sentences.

"The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts"  is equivalent to [tex] r = 10p[/tex].

"The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts" is equivalent to [tex] a= 20x[/tex].

"The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds" is equivalent to [tex] p = \frac{1}{5} a [/tex].

We already know that [tex] a = 20x[/tex].  And because of that, we also know that

[tex]p = \frac{1}{5}a = \frac{1}{5}(20x) = 4x[/tex]

and to conclude this stage of the problem, we also know that [tex]r = 10p =10(4x) = 40x[/tex]

As there are only 3 items, it is possible to use a Venn diagram. As we can see in the diagram, the entire quantity of bags is going to be

[tex]210 + 4x + x + 40x = 210 + 45x[/tex]

But, we also know that there are 435 bags, then we only have to solve the equation:

[tex]210 + 45x = 435[/tex]

[tex]45x = 435 - 210[/tex]

[tex]45x = 225[/tex]

[tex]x = 225/45 [/tex]

[tex]x = 5 [/tex]

Substituting [tex]x = 5[/tex] we get

[tex]a = 20 x = 20(5) = 100[/tex]

[tex]p = 4 x = 4(5) = 20[/tex]

[tex]r = 40 x = 40(5) = 200[/tex]

Finally [tex] ans = 100 + 20 + 200 = 320 [/tex]

Answer:

3.9 mi/h

Step-by-step explanation:

If the boy is rowing perpendicular to the current, the two vectors form a right triangle.

AB represents the downstream current, BC is the speed across the river, and AC is the ground speed of the boat

AC^2 = 2.4^2 + 3.1^2 =5.76 + 9.61 = 15.37

AC = sqrt(15.37) = 3.9 mi/h

The boat's speed over the ground is 3.9 mi/h.

The ground speed is found to be approximately 3.92 miles per hour.

we use the Pythagorean theorem to solve this problem.

Step-by-step solution:

This demonstrates how mathematical principles can be applied to real-world scenarios, such as navigating a boat across a river with a current.

Answer:

193.04

Step-by-step explanation:

If one inch equals 2.54 centimeters, a 76-inch tall man is 193.04 centimeters.

1 inch = 2.54 centimeters

76 inches

2.54 x 76 = 193.04

Answer:

193.04 cm

Step-by-step explanation:

So let's line up our corresponding information.

1 inch=2.54 cm

76 in =x       cm

This is already setup for you to write a proportion:

[tex]\frac{1}{76}=\frac{2.54}{x}[/tex]

Cross multiply:

[tex]1(x)=76(2.54)[/tex]

Multiply:

[tex]x=193.04[/tex]

Answer:

  0.196 lbs

Step-by-step explanation:

The area of the cross section is the difference of the areas of circles with the different diameters. The volume of the pipe material is the product of its cross section area and its length:

  V = π(D² -d²)L/4 = π(0.82² -0.75²)36/4 ≈ 3.107 . . . in³

Then the weight of the material is this volume multiplied by the density.

  W = V·δ = (3.107 in³)(0.063 lb/in³) ≈ 0.196 lb

Finding the weight of the PVC pipe involves calculating the volumes of the outer and inner cylinders then finding the difference, which is multiplied by the weight per cubic inch of PVC.

The weight of a 36 inch piece of PVC pipe can be calculated using the formula for the volume of a cylinder and the given weight per cubic inch of PVC material. Firstly, calculate the volume of the outer cylinder, which we know the diameter and length (or height). The formula for the volume of a cylinder is πr²h, where r is the radius and h is the height. We need to halve the diameter to get the radius, which gives us 0.82/2 = 0.41 inches.

Secondly, we calculate the volume of the inner cylinder in the same way, except we use the inner diameter, which is 0.75 inches, halved gives us a radius of 0.375 inches. The volume of material used is then the volume of the outer cylinder minus the volume of the inner cylinder. Lastly, multiply the volume of material by the weight per cubic inch to get the total weight.

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Answer:

Option A) (-14, -4)

Step-by-step explanation:

we know that

If a ordered pair lie on the circumference of a circle , then the ordered pair must satisfy the equation of the circle

we have

[tex](x+10)^{2}+(y+1)^{2}=25[/tex]

Verify each ordered pair

case A) we have  (-14, -4)

substitute the value of x and the value of y in the equation and then compare the results

[tex](-14+10)^{2}+(-4+1)^{2}=25[/tex]

[tex](-4)^{2}+(-3)^{2}=25[/tex]

[tex]25=25[/tex] ----> is true

therefore

The ordered pair is on the circumference of the circle

case B) we have  (4,14)

substitute the value of x and the value of y in the equation and then compare the results

[tex](4+10)^{2}+(14+1)^{2}=25[/tex]

[tex](14)^{2}+(15)^{2}=25[/tex]

[tex]421=25[/tex] ----> is not true

therefore

The ordered pair is not on the circumference of the circle

case C) we have  (-14,4)

substitute the value of x and the value of y in the equation and then compare the results

[tex](-14+10)^{2}+(4+1)^{2}=25[/tex]

[tex](-4)^{2}+(5)^{2}=25[/tex]

[tex]41=25[/tex] ----> is not true

therefore

The ordered pair is not on the circumference of the circle

case D) we have  (-4,14)

substitute the value of x and the value of y in the equation and then compare the results

[tex](-4+10)^{2}+(14+1)^{2}=25[/tex]

[tex](6)^{2}+(15)^{2}=25[/tex]

[tex]261=25[/tex] ----> is not true

therefore

The ordered pair is not on the circumference of the circle

Answer:

[tex]W_{total} =  -56X + 68600[/tex]

Step-by-step explanation:

We wil define:

1) "x" as number of cans inside the truck.

2) "y" as number of bottles inside the truck.

We now that the amount of both cans and bottles inside the truck is "980". This quantity is equal to the sum of cans and bottles, so now we can write:

[tex]X+Y=980[/tex]

We will call this expression equation n° 1.

On the other hand, we know that the total weight is a sum of the weight of the cans and the weight of the bottles. The total weight of the cans, for example, is the result of  multiplying the numbers of cans in the truck with the weight of each can, like here: ([tex]W_{cans} = X * 14 oz[/tex]

So now we can write:

[tex]W_{total} = (X*14oz) + (Y*70oz)[/tex]

We well call this expression equation n° 2.

From equation n°1 we obtain "y", like this:

[tex]X + Y = 980\\Y = 980 - X[/tex]

And we replace it in equation n°2:

[tex]W_{total} = (X*14) + (Y * 70)\\\\W_{total}  = 14X + 70Y\\W_{total}  = 14X + 70(980-X)\\W_{total}  =  14X + 68600 - 70X\\W_{total} =  -56X + 68600[/tex]

Now we have the expression of the total weight considering the amount of cans in the truck.

*** IMPORTANT: there is a character similar to an "A" that i can't erase, maybe is a mistake from brainly. Do not consider it as part of the solution.

Using differentials, the estimated maximum percentage error in the calculated surface area is approximately 5.73%, considering the 6% error in weight and height measurements.

To estimate the maximum percentage error in the calculated surface area using differentials, we'll use the formula for the surface area of the human body:

[tex]\[ S = 0.1098w^{0.425}h^{0.725} \][/tex]

Given that the errors in measurement of  w  and  h  are at most 6%, we'll use differentials to estimate the maximum percentage error in the surface area.

Let's denote:

- [tex]\( \Delta w \)[/tex] as the change in weight

- [tex]\( \Delta h \)[/tex] as the change in height

- [tex]\( \Delta S \)[/tex] as the change in surface area

Using differentials, we have:

[tex]\[ \Delta S \approx \frac{\partial S}{\partial w} \Delta w + \frac{\partial S}{\partial h} \Delta h \][/tex]

We need to find [tex]\( \frac{\partial S}{\partial w} \)[/tex] and [tex]\( \frac{\partial S}{\partial h} \):[/tex]

[tex]\[ \frac{\partial S}{\partial w} = 0.1098 \cdot 0.425w^{-0.575}h^{0.725} \][/tex]

[tex]\[ \frac{\partial S}{\partial h} = 0.1098 \cdot 0.725w^{0.425}h^{-0.275} \][/tex]

Given that the errors in measurement of  w  and  h  are at most 6%, we can express [tex]\( \Delta w \)[/tex] and [tex]\( \Delta h \)[/tex] as  0.06w  and  0.06h  respectively.

Now, substitute the values into the formula for [tex]\( \Delta S \):[/tex]

[tex]\[ \Delta S \approx (0.1098 \cdot 0.425w^{-0.575}h^{0.725})(0.06w) + (0.1098 \cdot 0.725w^{0.425}h^{-0.275})(0.06h) \][/tex]

[tex]\[ \Delta S \approx 0.005877w^{-0.575}h^{0.725} \Delta w + 0.004607w^{0.425}h^{-0.275} \Delta h \][/tex]

Now, let's compute the maximum percentage error:

[tex]\[ \text{Max percentage error} = \frac{\Delta S}{S} \times 100 \][/tex]

[tex]\[ \text{Max percentage error} = \frac{0.005877w^{-0.575}h^{0.725} \Delta w + 0.004607w^{0.425}h^{-0.275} \Delta h}{0.1098w^{0.425}h^{0.725}} \times 100 \][/tex]

[tex]\[ \text{Max percentage error} \approx \frac{0.005877(0.06w) + 0.004607(0.06h)}{0.1098w^{0.425}h^{0.725}} \times 100 \][/tex]

[tex]\[ \text{Max percentage error} \approx \frac{0.0003526w^{-0.575}h^{0.725} + 0.00027642w^{0.425}h^{-0.275}}{0.1098w^{0.425}h^{0.725}} \times 100 \][/tex]

[tex]\[ \text{Max percentage error} \approx \frac{0.0003526}{0.1098} + \frac{0.00027642}{0.1098} \times 100 \][/tex]

[tex]\[ \text{Max percentage error} \approx 3.21 + 2.52 \][/tex]

[tex]\[ \text{Max percentage error} \approx 5.73\% \][/tex]

Therefore, the estimated maximum percentage error in the calculated surface area is approximately 5.73%.

Answer:

The amount you need to invest in a year is $951.3

Step-by-step explanation:

Consider the provided information.

The future value can be calculated as:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where, A represents future value, P represents Principal value, r represents interest rate in decimal, n represents number of time interest is compounded and t represents time in years.

Now use the above formula to find the money needed to invest i.e P.

Substitute, n = 12 , t = 1, A = 1000 and r = 5% or 0.05 in the above formula.

[tex]1000=P(1+\frac{0.05}{12})^{12 \times 1}[/tex]

[tex]1000=P(1.00417)^{12}[/tex]

[tex]1000=P(1.0512)[/tex]

[tex]P=951.3[/tex]

Thus, the amount you need to invest in a year is $951.3

977.38 -_- ..........

Answer:

150%

Step-by-step explanation:

Best Tire : 50,000 miles

Better Tire : 20,000 miles

Difference : 50,000 - 20,000 = 30,000

The difference expressed as a percentage of the less expensive tire

= (30,000 / 20,000) x 100%

=150%

Final answer:

The domain for the base price of a car that Leonard can initially afford is [24,000, 30,000]. After buying car insurance worth $2,200, the domain changes to [24,000, 28,000], reflecting the reduced budget available for the car purchase.

Explanation:

Initially, Leonard can afford a car with a base price up to his budget of $33,000. Since car accessories cost one-tenth of the base price, we calculate the maximum base price he can afford as follows: Let x be the base price of the car. The total cost of the car, including accessories, would be x + (1/10)x = (1 + 1/10)x = (11/10)x. So, to stay within budget, (11/10)x ≤ $33,000. Solving for x gives us x ≤ $33,000 / (11/10) = $30,000.

Therefore, the domain representing the base price Leonard can afford is [24,000, 30,000].

After buying car insurance for $2,200, Leonard's budget for the car decreases. The new budget for the car including accessories is $33,000 - $2,200 = $30,800. Solving (11/10)x ≤ $30,800, we get x ≤ $30,800 / (11/10) = $28,000.

Now, the domain for the base price that Leonard can afford after the insurance payment is [24,000, 28,000].

Answer:

Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.

Step-by-step explanation:

For the given situation let the number of tv sets be x and number of dvd players be y.

Now we have to minimize the cost as it costs $75 to refurbish a tv set and $40 to refurbish a dvd player.

i.e. Minimize z=75x+40y

it gives subject to the constraints

4x+2y≥100......(1)(100 hours each week. It takes 4 hours to refurbish a tv set and 2 hours to refurbish a dvd player.)

x+y≥35.......(2)(weekly sales target is to refurbish at least 35 tv sets or dvd players.)

To plot equation (1) we need to find coordinates of points lying on line (1)

put x=0 gives 2y=100⇒y=50

put y=0 gives 4x=100⇒x=25

So we got points (0,50) and(25,0) for (1)..............(3)

Similarly for equation (2)

put x=0 gives y=35

put y=0 gives x=35

so we got points (0,35) and(35,0) for (2).................(4)

with the help of (3) and (4) we plot the following graph (assume x≥0 and y≥0)

The unbounded feasible region determined by constraints gives the corner points as A(0,50),B(15,20)and C(35,0).

from  we get the value of z is minimum at point B (15,20) .

hence we got our optimal solution at B (15,20), where x is the number of tv sets and y is the number of dvd players  .therefore Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.

Answer:

a. 226 pounds

b. 8 weeks

Step-by-step explanation:

To solve this problem, simply plug in the numbers for the variables it told you they correspond to. 12 is the number of weeks, and t represents the number of weeks, so we can plug 12 in for t.

[tex]W=-2(12)+250[/tex]

Simplify and you'll have your answer.

[tex]W=-24+250\\W=226[/tex]

For part B, 234 is the amount of pounds, and W represents the weight in pounds, so we can plug 234 in for W.

[tex]234=-2t+250\\-16=-2t\\8=t[/tex]

Answer:

  sin(2x) = 120/169

Step-by-step explanation:

A suitable calculator can figure this for you. (See below)

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You can make use of some trig identities:

Then your function value can be written as ...

  sin(2x) = 2sin(x)cos(x) = 2(sin(x)/cos(x))cos(x)² = 2tan(x)/sec(x)²

  = 2tan(x)/(tan(x)² +1)

Filling in the given value for tan(x), this is ...

  sin(2x) = 2(12/5)/((12/5)² +1) = (24/5)/(144/25 +1) = (120/25)/((144+25)/25)

  sin(2x) = 120/169

Answer: 2.632

Step-by-step explanation:

Given : The probability that the population has a particular genetic mutation = 1 % = 0.01

Let X be a random variable representing the number of people with genetic mutation in a group of 700 people.

Now, X follows the binomial distribution with parameters:

[tex]n=700;\ p=0.01[/tex]

The standard deviation for binomial distribution is given by :-

[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{700\times0.01(1-0.01)}\\\\=2.6324893162\approx2.632[/tex]

Hence, the standard deviation = 2.632

Answer:

1st problem: b) [tex]A=2500(1.01)^{12t}[/tex]

2nd problem:  c) [tex]A=2500e^{.12t}[/tex]

Step-by-step explanation:

1st problem:

The formula/equation you want to use is:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

t=number of years

A=amount he will owe in t years

P=principal (initial amount)

r=rate

n=number of times the interest is compounded per year t.

We are given:

P=2500

r=12%=.12

n=12 (since there are 12 months in a year and the interest is being compounded per month)

[tex]A=2500(1+\frac{.12}{12})^{12t}[/tex]

Time to clean up the inside of the ( ).

[tex]A=2500(1+.01)^{12t}[/tex]

[tex]A=2500(1.01)^{12t}[/tex]

----------------------------------------------------

2nd Problem:

Compounded continuously problems use base as e.

[tex]A=Pe^{rt}[/tex]

P is still the principal

r is still the rate

t is still the number of years

A is still the amount.

You are given:

P=2500

r=12%=.12

Let's plug that information in:

[tex]A=2500e^{.12t}[/tex].

Answer:

a = 2 and b = 2

Step-by-step explanation:

It is given a matrix multiplication,

To find the value of a and b

It is given that,

| 3  2 |  *  | -2 |    =   | a |

|-1  0 |     |  4 |         | b |

We can write,

a = (3 * -2) + (2 * 4)

 = -6 + 8

 = 2

b = (-1 * -2) + (0 * 4)

 = 2 + 0

 = 2

Therefore the value of  a = 2 and b = 2

Answer:

a=2 and b=2.

Step-by-step explanation:

The given matrix multiplication is

[tex]\begin{bmatrix}3&2\\ -1&0\end{bmatrix}\begin{bmatrix}-2\\ 4\end{bmatrix}[/tex]

We need to resulting vector matrix of this matrix multiplication.

[tex]\begin{bmatrix}3\left(-2\right)+2\cdot \:4\\ \left(-1\right)\left(-2\right)+0\cdot \:4\end{bmatrix}[/tex]

[tex]\begin{bmatrix}2\\ 2\end{bmatrix}[/tex]

It is given that [tex]\begin{bmatrix}a\\ b\end{bmatrix}[/tex] is resulting matrix.

[tex]\begin{bmatrix}2\\ 2\end{bmatrix}=\begin{bmatrix}a\\ b\end{bmatrix}[/tex]

On comparing both sides, we get

[tex]a=2,b=2[/tex]

Hence, a=2 and b=2.

Answer:

  none of the above

Step-by-step explanation:

The applicable relationship is ...

  C = 2πr

Solving for r, we get

  r = C/(2π) ≈58. (367 cm)/(2·3.14159) ≈ 58.41 cm . . . . no matching choice

_____

When the problem does not include a correct answer choice, I usually suggest you ask your teacher to show you the working of it.

18cm I hope this helps

Given that [tex]P(Q)=\dfrac{3}{5},P(R)=\dfrac{1}{3}[/tex]

Also,

[tex]P(Q\wedge R)=P(Q)\cdot P(R)=\dfrac{3}{5}\cdot\dfrac{1}{3}=\dfrac{1}{5}[/tex]

We can conclude that,

[tex]P(Q\vee R)=P(Q)+P(R)=\dfrac{3}{5}+\dfrac{1}{3}=\boxed{\dfrac{14}{15}}[/tex]

The answer is B.

Hope this helps.

r3t40

The greatest common factor (or GCF) is, as the name says, the greatest factor a set of numbers have in common. We can find this by listing out all the possible factors (multiples) of each number:

For 28:

1, 2, 4, 7, 14, 28

For 42

1, 2, 3, 6, 7, 21, 42

(note you don't need to list out all the factors, I just did it for visual purposes)

As you can see, 28 and 42 have 3 factors in common, with 7 being the greatest.

Therefore, the answer would be C: the GCF is 7.

Hope this helps! :)

Answer:

it is 14... have a blessed and amazing day

Step-by-step explanation: