Select the correct answer.
What is the solution to this system of equations?
3x + y= 17
x + 2y = 49
ОА.
It has no solution.
B.
It has infinite solutions.
O C.
It has a single solution: x= 15, y= 17.
OD
It has a single solution: x = -3, y= 26.

In this case we are dealing with an arithmetic sequence, we can represent this kind of sequences with the formula:

f(n) = f0 + d*n

Where f0 is the first term of the sequence and d is the difference between one term and the term that is previous to it.

In this case, f0 equals 7, since this is the value of the first term.

We can find d by taking two terms, let's take for example 1 and 4, by subtracting 4 from 1 we get:

d = 1 - 4 = -3

Then d equals -3 and the formula of the sequence is:

f(n) = 7 + (-3)n

f(n) = 7 - 3n

We can calculate the 75th term by replacing 75 for n, then we get:

f(75) = 7 - 3 * 75 = -218

Then f(75) equals -218

Answer:

Step-by-step explanation:

You want the radius and water depth in a spherical bowl in which the water level is 10 cm above the center of the sphere, and the circular surface has a diameter of 30 cm.

The geometry of the diameter of the water surface can be modeled as shown in the attachment. The radius of that surface forms one leg of a right triangle with the other leg being 10 cm. The hypotenuse of the triangle is the radius of the sphere, so we have ...

  r² = 15² +10² = 325

  r = √325 = 5√13 ≈ 18.03 . . . . . cm

The water depth is 10 cm more than the radius, so is ...

  d = 10 +r = 10 +5√13 ≈ 28.03 . . . . . cm

The radius of the bowl is about 18.03 cm; the depth of water is about 28.03 cm.

Answer:

There will be 5 zeros

Step-by-step explanation:

because the amoutnt of tens there are is the amount of zeros there are.

hope this helps

Answer:

There will be 5 zeros in the product because there are 5 10's in 5 * 10 * 10 * 10 * 10 * 10

An easier way is to just count how many zeros there are in the whole number and add them to the end.

Step-by-step explanation:

The dual for the given linear programming problems are as follows:

(i) Minimize Z' = 10a + 12b Subject to: a + 7b ≥ 3 2a + 3b ≥ 4 a + 9b ≥ 5 a, b ≥ 0.

(ii) Maximize Z' = 5a + 6b + 2c Subject to: 3a + 2b + c ≤ 1 4a + 6b + c ≤ 2 a + b ≤ 0 a, b, c ≥ 0.

In the first problem, we have a maximization problem with three variables (x, y, z) and two constraints. The dual formulation involves minimizing a new objective function with two variables (a, b) and four constraints. The coefficients of the variables and the constraints are transformed according to the rules of duality.

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

To find the dual, we introduce the dual variables a and b for the constraints:

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

In the second problem, we have a minimization problem with two variables (y1, y2) and three constraints. The dual formulation requires maximizing a new objective function with three variables (a, b, c) and four constraints. Again, the coefficients and constraints are transformed accordingly.

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

To find the dual, we introduce the dual variables a, b, and c for the constraints:

Maximize Z' = 5a + 6b + 2c

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

The duality principle in linear programming allows us to find a lower bound (for maximization) or an upper bound (for minimization) on the optimal objective value by solving the dual problem. It provides useful insights into the relationships between the primal and dual variables, as well as the economic interpretation of the problem.

Learn more about maximization

brainly.com/question/29787532

#SPJ11

The surface area of the box is 76 square inches.

The box in the given problem is a right triangular prism shaped box, it is 7 inches long and the triangular base measures 3 in x 4 in x 5 in. We need to determine the surface area of this box.

Therefore, let's first calculate the surface area of the base of the box. The base is a right-angled triangle. Its area can be calculated using the formula for the area of a triangle:

A = (1/2) x base x height = (1/2) x 3 x 4 = 6 square inches.

Now, we need to calculate the area of each of the three rectangular faces. Two of these faces are congruent rectangles and have dimensions 7 in x 3 in. The other face is a rectangle with dimensions 7 in x 4 in. Thus, the area of each of the congruent rectangles is:Area = length x width = 7 x 3 = 21 square inches. Therefore, the area of both rectangles is 21 + 21 = 42 square inches.Now, the area of the third rectangle is:Area = length x width = 7 x 4 = 28 square inches.So, the total surface area of the box can be found by adding the area of the base to the area of all three faces:S.A. = 6 + 42 + 28 = 76 square inches.

Therefore, the surface area of the box is 76 square inches.

To know more about triangle visit:

https://brainly.com/question/1058720

#SPJ11

Answer:

I believe it's 12 in.

Step-by-step explanation:

hope this helps you!

Answer:

its 38

Step-by-step explanation:

To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

To learn more about equal variances: -brainly.com/question/30777199

#SPJ11

To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

To learn more about equal variances: -brainly.com/question/30777199

#SPJ11

Answer: $210

Step-by-step explanation:

i’m over here doing the same work- $210 the answer.

13 number of free throws made and 4 number of two-point shots made.

Two or more expressions with an Equal sign is called as Equation.

Let x represents the number of free throws made (1 point each)

y represents the number of two-point shots made (2 points each)

Zoe made a total of 11 shots, this is written as:

x+y=11...(1)

She made a total of 15 points

x+2y=15..(2)

Subtract (2) from (1)

x+y-x-2y=11-15

-y=-4

y=4

Now plug y value in equation (1)

x+4=11

x=11-4

x=13

Hence 13 number of free throws made and 4 number of two-point shots made.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

Vertex

Step-by-step explanation:

The vertex is the point were two rays meet to form an angle.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

The number of people that Camilla should expect to go to Fiction and Literature is 87.

On Saturday, 344 people went to The Youth Wing, 471 people went to Social Issues, and 310 went to Fiction and Literature.

The percentage for those that went to fiction and literature will be:

= Number for fiction / Total number

= 310 / (344 + 471 + 310) × 100

= 310/1125 × 100

= 27.56%

Therefore when there are 300 visitors, the number of people in fiction will be:

= 27.56% × 300

= 87

There'll be 87 people.

Learn more about fractions;

brainly.com/question/17220365

#SPJ1

Answer:

Step-by-step explanation:

Perfect squares are numbers that their square root can be found easily without any remainder.

Given the following patterns;

1*1 = 1  and 1*1*1 = 1

It can be seen that 1 is 1 perfect square since 1*1 = 1² = 1

Also 1 is perfect cube since 1*1*1 = 1³ = 1 (cube of the value gives 1)

Similarly for the expression;

8*8 = 64

8² = 64 (since the square of 8 gives 64, then 64 is known to be a perfect square)

Also 4*4*4 = 64

i.e 4³ = 64 (This shows that the cube root of 64 is 4 making it a perfect cube since we can get a whole number for the cube root of 64)

The same is applicable for other expressions 729 = 27 × 27, and 9 × 9 × 9, 4,096 = 64 × 64, and 16 × 16 × 16

This values are easily expressed as a constant multiple of a number showing that they are both perfect squares and perfect cubes.

The answers are explained in the solution.

Given is a circle F,

The central angle = ∠GFH

The semicircle = arc GJI

The major arc = arc GJH

Since, the measure of semicircle is 180°, therefore,

The semicircle = arc GJI = 180°

We know that the measure of arc intercepted by the central angle is equal to the measure of the central angle.

Therefore, ∠GFH = 125°

Learn more about circles, click;

https://brainly.com/question/29142813

#SPJ1

Answer:

29+15=44

44÷7=6.28

y=6.28

Answer:I think you can say like the most bought music in class B is alternative and the lowest one is classical and so on

Step-by-step explanation:

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)

Answer: Mean = 21 , Variance = 6.3 , standard deviation =2.51

Step-by-step explanation:

Formula for the mean, variance and standard deviation of the binomial experiment :

\(Mean = np\\\\ Variance = np(1-p)\\\\ Standard\ deviation = \sqrt{variance}\)

, where n= sample size , p= population proportion.

As per given, p= 70%=0.7 , n=30

\(Mean = 0.7\times30=21\\\\Variance =(30)(0.7)(1-0.7)=(21)(0.30)=6.3\\\\ Standard\ deviation = \sqrt{6.3}\approx2.51\)

Hence, Mean = 21 , Variance = 6.3 , standard deviation =2.51

The ratio of the area of the triangle to the area of the square is \(\frac{1}{4}\).

State the formula for the triangle's area?

The formula for the area of a triangle can be calculated using the base and height of the triangle. The general formula is:

Area = \(\frac{(base\ *\ height) }{2}\)

In this formula, the base refers to the length of any side of the triangle, and the height refers to the perpendicular distance from the base to the opposite vertex.

Let's assume the square has side length s. Since the given points are the midpoints of two sides, they divide each side into two equal segments, each with length \(\frac{s}{2}\).

We can construct a triangle by connecting these two points and one of the vertices of the square. This triangle will have a base of length s and a height of \(\frac{s}{2}\).

The area of a triangle is given by the formula:

Area = \(\frac{(base\ *\ height) }{2}\)

Substituting the values, we have:

\(Area of traingle=\frac{(s\ *\frac{s}{2}) }{2}\\=\frac{(\frac{s^2}{2})}{2}\\=\frac{s^2}{4}\)

The area of the square is given by the formula:

Area of square =\(s^2\)

Now, we can calculate the ratio of the area of the triangle to the area of the square:

\(Ratio =\frac{ (Area of triangle)}{ (Area of square)} \\=\frac{(\frac{s^2}{ 4})}{s^2} \\\\= \frac{s^2 }{4 * s^2}\\\\=\frac{1}{4}\)

Therefore, the ratio of the area of the triangle to the area of the square is \(\frac{1}{4}\), expressed as a common fraction.

To learn more about the triangle's area  from the given link

https://brainly.com/question/17335144

#SPJ4

Answer: I'm gonna say (3,-2)

Step-by-step explanation: my best guess, bc they intersect

After 4 minutes of exposure to a disinfectant with a d-value of two minutes, the number of viable cells remaining in a culture containing 10,000,00 cells/ml will be 100,000 cells/ml.

As per the unitary method, We can also use a mathematical formula to calculate the number of viable cells remaining after a given time of exposure. The formula is as follows:

Nt = N0 x \(10^{-kt}\)

Where:

Nt = the number of viable cells remaining after a given time of exposure

N0 = the initial number of viable cells

k = the rate constant of the disinfectant

t = the time of exposure

Since the d-value of the disinfectant is 2 minutes, we can calculate the rate constant (k) as follows:

k = 0.693/d

Where:

d = the d-value of the disinfectant

k = 0.693/2 = 0.3465

Therefore, the formula for calculating the number of viable cells remaining after a given time of exposure is:

Nt = N0 x \(10^{-0.3465t}\)

When t = 4 minutes, we have:

Nt = 10,000,00 x \(10^{-0.3465 \times 4}\)

Nt = 100,000 cells/ml

To know more about unitary method here

https://brainly.com/question/28276953

#SPJ4

Point= (1, -1)

Hence, this is not the solution of the desired answer.

inequality is defined as declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or the algebraic expressions. Either queries or the declarations of fact in the form of theorems can be used to formulate and solve inequality problems.

Shaded Region represents y<2x-3

Given Point= (1, -1)

Hence, this is not the solution of the desired answer,

As it not defines the equality part.

As for example (2,-2) is the solution of the desired inequality and it satisfies the condition y<2x-3.

And given point (1, -1) is not the solution of the desired equation as it does not satisfy the inequality portion.

To learn more about Inequality, Visit:

https://brainly.com/question/28823603

#SPJ1

In total, the number of children, adult, and senior tickets sold are:

Children tickets = 35

Adult tickets = 45

Senior tickets = 70

Let's break down the problem step by step:

1. Let's assume the number of children tickets sold is x.

2. According to the problem, Danny sold 10 more adult tickets than children tickets. So, the number of adult tickets sold would be x + 10.

3. It is given that twice as many senior tickets were sold compared to children. So, the number of senior tickets sold would be 2x.

Now, to find the total number of tickets sold, we can add up the number of children, adult, and senior tickets:

Total tickets sold = Children tickets + Adult tickets + Senior tickets

Total tickets sold = x + (x + 10) + 2x

Total tickets sold = 4x + 10

We know that the total number of tickets sold is 150, so we can set up an equation:

4x + 10 = 150

Simplifying the equation:

4x = 150 - 10

4x = 140

x = 140/4

x = 35

Therefore, the number of children tickets sold is 35.

To find the number of adult tickets sold, we substitute x = 35 into the expression x + 10:

Adult tickets = 35 + 10 = 45

Thus, 45 adult tickets were sold.

To find the number of senior tickets sold, we substitute x = 35 into the expression 2x:

Senior tickets = 2 * 35 = 70

So, 70 senior tickets were sold.

In total, the number of children, adult, and senior tickets sold are:

Children tickets = 35

Adult tickets = 45

Senior tickets = 70

for more  such questions on total visit

https://brainly.com/question/9879870

#SPJ8

Answer:

0.08

Step-by-step explanation:

The simplification of the expression 4a + 3b - a + 3b + 6 is 3(a + 2b + 2)

Simplify 4a + 3b - a + 3b + 6

collect like terms

= 4a - a + 3b + 3b + 6

= 3a + 6b + 6

factorize

= 3(a + 2b + 2)

side a = 3x - 5

side b = 2x - 1

side c = x + 1

Perimeter = 31 cm

The perimeter of a triangle = side a + side b + side c

31 = (3x - 5) + (2x - 1) + (x + 1)

31 = 3x - 5 + 2x - 1 + x + 1

31 = 6x - 5

Add 5 to both sides

31 + 5 = 6x

36 = 6x

divide both sides by 6

x = 36/6

x = 6

Therefore, the value of x from the perimeter of the triangle is 6

Read more on perimeter of triangle:

https://brainly.com/question/24382052

#SPJ1

Answer:

1:2

Step-by-step explanation: