A triangle with interior angles measuring a, b, and c degrees and exterior
angle measuring d degrees is shown above. If d measures 140°, what is the
sum of a and b?

 50 is  your sample size have to be, at minimum in standard deviation.

What is standard deviation?

We want n * p  and n * ( 1 - p ) both atleast 10.

                        0.2  * n ≥  10

                           n ≥    10/0.2

                              n ≥   50

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Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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The equation total amount of flour (f) for making n number of cakes is given by f = 3n

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

Let f represent the total amount of flour and n represent the number of cakes. Hence:

f = kn

where k is the constant of proportionality.

The baker uses 3 pounds of flour to make cupcakes. Hence:

3 = k(1)

k = 3

f = 3n

The equation is given by f = 3n

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Answer:

We have to use addition or subtraction property of equality to determine the value of variable involve.

Step-by-step explanation:

Example with variable term:

3x=4-x

Add x on both sides of equation:

3x+x=4-x+x

4x=4

x=1

Example with contact involve:

5y+7=12

Subtract 7 from both sides

5x+7-7=12-7

5x=5

x=5/5

x=1

Answer:

22.4

Step-by-step explanation:

set up the equation

6x+157= -x+45

157=5x+45

112=5x

22.4=x

Answer:

x-intercept is (10,0)

y-intercept is (0, -8)

Step-by-step explanation:

Our equation is 4x - 5y = 40

Let's find x-intercepts first

X-intercepts is when the y = 0

So we put 0 in for the y, and we have the equation

4x =40

x =10

So our x-intercept located at (10,0)

Now find the y-intercepts

Y-intercepts is when the x = 10

So we put 0 in for the x, and we have the equation

-5y = 40

y= -8

So our y-intercept is located at (0,-8)

Answer:

Step-by-step explanation:

Y-int: (0, -8)

X-Int: (10, 0)

To find the y and x intercepts you have to plug in the 0 for the variable. You'd get 4(0)-5y=40 you get this by plugging in the 0 for x and then you solve. 4 x 0 is 0 so you'd get -5y=40 divide -5 on both sides and get y=-8 meaning that is the y-intercept.

You'd do the same when you look for the x-int. Just that you'd plug in a 0 for y instead of x. Which is 4x-5(0)=40. -5 x 0 is 0. So you'd have 4x=40 divide both sides by 4 and you'd get x=10 meaning that is the x intercept.

Remember that when looking for the y- intercept there should always be a zero in front meaning the x-value, and when looking for the x-intercept there should always be a  zero in the back meaning the y-value.

(Hopefully you were able to understand how I got the x and y intercepts for this equation)

The order of visit for DFS and BFS will differ based on the structure of the graph or tree and the starting node. DFS will typically visit nodes in a deeper order, while BFS will visit nodes in a breadth-first order.

Both  algorithm depth-first search and algorithm breadth-first search are used to traverse or search a graph or tree data structure. The difference between them lies in their traversal strategy.
Depth-first search (DFS) starts at a root node and explores as far as possible along each branch before backtracking. It follows a content-loaded algorithm, meaning that it prioritizes exploring deeper into the structure before considering other branches. In terms of visit order, DFS starts at the root node, then moves to its first child node, and continues to explore its descendants until it reaches a leaf node. Once it has visited all descendants of the current node, it backtracks to the previous node and repeats the process until it has visited all nodes.
On the other hand, breadth-first search (BFS) starts at the root node and explores all the neighboring nodes at the current depth level before moving on to the next depth level. It follows a breadth-first algorithm, meaning that it prioritizes exploring all nodes at a given depth level before moving on to deeper levels. In terms of visit order, BFS visits all nodes at a given depth level before moving on to the next level.

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Answer:

After 15 years the population will be 7,625

Step-by-step explanation:

3.5% of 5,000 = 175

175 x 15 = 2625

2625 + 5,000 = 7625

The population after 15 years should be  8,376

Since the population is 5,000 and it grows 3.5 years and the time period is 15 years

So, the population after 15 years is

\(= 5,000 \times (1 + 3.5\%)^{15}\\\\\)

= 8,376

Therefore, we can conclude that The population after 15 years should be  8,376

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Answer:

20

Step-by-step explanation:

TO find the answer, use multiplication.

When one part of a fraction multiplies, you multiply the other number with it. 22x3 is 66, so divide 60 by 3. You get 20. n=20. Hope it helps.

You can use ratio. 60:66 is n:22. 22 goes into 66 3 times,  and 20 goes into 60 3 times too, so 20:22 is equivalent to 60:66

(please give brainliest)

n=20

I used cross multiplication

Answer:

OCD473

Step-by-step explanation:

The length of the segment joining the points which are given is  \(\sqrt{10}\)

To measure the distance between these two given points

The given coordinates are

Let P = P(5,-3) and Q = Q(8,-2)

By using the distance formula we get;

the distance formula is used to calculate the length of the segment when points are given as in this question

thus the distance formula is :

\(\sqrt{(x2-x1)^2 + (y2 - y1)^2}\)

here x2 = 8 and x1 = 5

and y2 = - 2 and y1 = - 3

thus on substituting the values we get

\(\sqrt{(8-5)^2 + ( -2 +3)^2}\)

= \(\sqrt{3^2 + 1^2}\)

= \(\sqrt{10}\)

Thus the length of the segment is  \(\sqrt{10}\) units

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Answer:83 -->17-->103-->43-->7-->1

Have a good day

Answer:

Step-by-step explanation:

solution -4x+6

Answer:19/3

Step-by-step explanation:

Answer:19/3

Step-by-step explanation:

9. A rule to describe this transformation is a rotation of 180° about the origin.

10. A rule to describe this transformation is a reflection over the x-axis.

11. A rule to describe this transformation is a rotation of 180° about the origin.

12. A rule to describe this transformation is a rotation of 90° clockwise around the origin.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Question 9.

Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is as follows:

(x, y)            →            (-x, -y)

U (-1, 4)       →           U' (1, -4)

Question 10.

By applying a reflection over or across the x-axis to vertices D, we have:

(x, y)           →            (x, -y)

D (4, -4)       →           D' (4, 4)

Question 11.

By applying a rotation of 180° counterclockwise about the origin to vertices E, we have::

(x, y)            →            (-x, -y)

E (-5, 0)       →           E' (5, 0)

Question 12.

By applying a rotation of 90° clockwise about the origin to vertices C, we have::

(x, y)            →            (-y, x)

C (2, -1)       →           C' (1, 2)

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

  6 h

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance / speed

The total time for the two segments of her ride will be the sum of the times for each of the segments.

__

  t1 = (9 miles)/(3 mi/h) = 3 h

After riding 9 miles of the 15-mile distance, Dana had 15 -9 = 6 miles to go.

  t2 = (6 miles)/(2 mi/h) = 3 h

The total time required for the distance of 15 miles is ...

  t1 +t2 = (3 h) +(3 h) = 6 h

It took 6 hours for Dana to cover the distance.

The equation of the line parallel to 2x + y - 4 = 0 and passing through the point (-2, 2) is y = -2x - 2.

The equation of line in slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

2x + y - 4 = 0

Covert to slope-intercept form:

y = -2x + 4

The slope of the line is -2

Since the parallel line has the same slope, we can use the point-slope form of a line to find the equation.

Now, plug the slope m = -2 and point (-2,2) into the point-slope form and simplify:

( y - y₁ ) = m( x - x₁ )

( y - 2 ) = -2( x - (-2) )

y - 2 = -2x - 4

y = -2x - 4 + 2

y = -2x - 2

Therefore, the equation of the parallel line is y = -2x - 2.

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The number of ways integer points can be assigned to the 12 problems, given that the total points is 100 and each problem is worth at least five points, can be calculated using a combinatorial approach.

To determine the number of ways, we can use the concept of stars and bars, which is a combinatorial technique used to distribute indistinguishable objects into distinguishable groups. In this case, the stars represent the total points (100) and the bars represent the dividers between the problems.

Since each problem is worth at least five points, we can consider a minimum of five points already assigned to each problem. This means we need to distribute the remaining points (100 - 12*5 = 40 points) among the 12 problems.

Using the stars and bars approach, we have 40 stars (representing the remaining points) and 11 bars (representing the dividers between the 12 problems). The number of ways to arrange these stars and bars is equivalent to the number of ways to assign points to the problems.

The answer, therefore, can be calculated using the formula for combinations with repetition: C(n + k - 1, k - 1), where n is the number of stars (40) and k is the number of bars (11).

Hence, the number of ways to assign integer points to the problems is C(40 + 11 - 1, 11 - 1) = C(50, 10).

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Answer:

0.14

Step-by-step explanation:

If winning holds a probability of 0.5 and a draw holds a probability of 0.3, then that means that losing has a probability of 0.2 (1 - 0.5 - 0.7 = 0.2). Therefore, to find the probability of Vishi losing exactly one of the two games we need to multiply the probability of him losing one game by the probability of him winning or tying the second game like so...

0.2 * (0.5 + 0.3) = x

0.2 * 0.7 = x

0.14 = x

Finally, we can see that the probability of Vishi losing exactly one of the two games is 0.14

There are three expressions having quotient 6 are:

4 2/3 ÷ 7/9

9 ÷ 3/2

12/7 ÷ 2/7

There are three expressions having quotient 9 are:

4 1/2 ÷ 1/2

21 ÷ 7/3

72/7 ÷ 8/7

The splitting of a large group into smaller groups such that every group will have an equal number of items.

We have,

Finding quotient for each expression.

1.

4 2/3 ÷ 7/9

= 14/3 ÷ 7/9

= 14/3 x 9/7

=6

2.

9 ÷ 3/2

= 9 x 2/3

= 6

3.

4 1/2 ÷ 1/2

= 9/2 x 2/1

= 9

4.

21 ÷ 7/3

= 21 x 3/7

= 9

5.

12/7 ÷ 2/7

= 12/7 x 7/2

= 6

6.

72/7 ÷ 8/7

= 72/7 x 7/8

= 9

Thus,

Expression having quotient 6:

- 4 2/3 ÷ 7/9

- 9 ÷ 3/2

- 12/7 ÷ 2/7

Expression having quotient 9:

- 4 1/2 ÷ 1/2

- 21 ÷ 7/3

- 72/7 ÷ 8/7

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In general, the tallest and shortest plant heights can vary widely depending on the species of plant being considered.

For example, some species of trees can grow over 300 feet tall, while certain species of mosses may only grow a few millimeters in height. The specific environmental conditions, such as the availability of water, sunlight, and nutrients, can also impact the growth and height of plants. Therefore, without more specific information, it is difficult to provide a more precise answer.

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1. a) The prime factorization of 64 is 2^6 and the prime factorization of 72 is 2^3 × 3^2. The common factor is 2^3, so the GCF of 64 and 72 is 8.  b) The GCF of 2a^2 and 12a is 2a.  c) The GCF of 4x^2 and 6x is 2x.

2. a) Factored form: 3(x - 4), GCF = 3  b) Factored form: 5(13y - x), GCF = 5  c) Expanded form: 3x^2 + 12x + 9, GCF = 3

3. a) 3(p - 5), check: 3p - 15 b) 3(7x - 3)(x + 2), check: 21x^2 - 9x + 18 c) 6(y + 1)(y + 5), check: 6y^2 + 18y + 30

4. A trinomial expression with a GCF of 3n is 3n(x^2 + 4x + 3). Factoring the expression, we get 3n(x + 3)(x + 1).

Let us discuss this in detail.

1. a) The GCF of 64 and 72 is 8.
  b) The GCF of 2a^2 and 12a is 2a.
  c) The GCF of 4x^2 and 6x is 2x.

2. a) 3x - 12 is in expanded form, GCF = 3.
  b) 5(13y - x) is in factored form, GCF = 5.
  c) 3x^2 + 12x + 9 is in expanded form, GCF = 3.

3. a) Factoring 3p - 15 gives 3(p - 5), Check: 3(p - 5) = 3p - 15.
  b) Factoring 21x^2 - 9x + 18 gives 3(7x^2 - 3x + 6), Check: 3(7x^2 - 3x + 6) = 21x^2 - 9x + 18.
  c) Factoring 6y^2 + 18y + 30 gives 6(y^2 + 3y + 5), Check: 6(y^2 + 3y + 5) = 6y^2 + 18y + 30.

4. A trinomial expression with a GCF of 3n could be 3n(x^2 + y^2 + z^2). Factoring this expression gives 3n(x^2 + y^2 + z^2), which is already in factored form.

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We are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.

Given that, n=550 (Sample size, Number of trials), p=0.6 (Sample proportion) and 1−α=0.9 (Confidence level).

The confidence interval is one of the most used for estimating population parameters in statistics. It is common to perform an interval with a known confidence level to find a range of values that show us information about the population.

Using the standard error of the sample proportions \(ME=z_{\alpha /2}.\sqrt{\frac{p(1-p)}{n} }\)

\(=z_{0.9/2}.\sqrt{\frac{0.6(1-0.6)}{550} }\)

\(=z_{0.45}.\sqrt{\frac{0.6(0.4)}{550} }\)

= 0.1736 × √(0.24/550)

= 0.1736 × 0.0208

= 0.00361

Confidence interval = 0.6±0.00361

= (0.6+0.00361, 0.6-0.00361)

= (0.6036, 0.5963)

Therefore, we are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.

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The relationship between the number of trees per acre and the average yield per tree is nonlinear, and Paula needs to balance the trade-off between the number of trees and the average yield per tree when deciding how many trees to plant in the new section of the orchard.

A. The relationship between the number of trees per acre and the average yield per tree is nonlinear. This is because the reduction in yield is not constant and varies based on the number of trees per acre. As per the given information, if Paula plants more than 30 trees per acre, the average yield of 600 peaches per tree will decrease by 12 peaches for each additional tree over 30.

This indicates that the decrease in yield is not linearly proportional to the increase in the number of trees per acre. Instead, the decrease in yield per tree increases as the number of trees per acre increases. Thus, the relationship between the number of trees per acre and the average yield per tree is nonlinear.

B. If Paula plants six more trees per acre, the average yield in peaches per tree will decrease by 12 peaches for each additional tree over 30. Therefore, the average yield per tree would be 588 peaches. On the other hand, if Paula plants 42 trees per acre, there will be 12 additional trees over 30 per acre.

Therefore, the average yield per tree would decrease by 12 peaches for each of these additional trees, which would result in an average yield of 564 peaches per tree. Thus, Paula needs to consider the trade-off between the number of trees and the average yield per tree when deciding how many trees to plant in the new section of the orchard. She should plant the number of trees that maximize her overall yield, considering both the number of trees per acre and the average yield per tree.

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Answer: graph is in picture

Graph the line using the slope and y-intercept, or two points

Slope: −1/2

x y

0. −2

2. −3

—————-————————————

the x- and y-intercepts :

x-intercept(s): (−4, 0)

y-intercept(s): (0, −2)

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Answer:

✅The point (4, 6) can be represented by the ratio, 4:6, and means 4 yards of strings made 6 bracelets.

✅The point (6, 9) can be represented by the ratio, 6:9, and means 6 yards of strings made 9 bracelets.

Step-by-step explanation:

The relationship between the number of yards of string used (x) and the number of the bracelets made (y) is a proportional relationship as shown by the given graph. The number of bracelets made is dependent on the number of strings used.

In terms of this situation, the two points on the graph mean the following:

✅The point (4, 6) can be represented by the ratio, 4:6, and means 4 yards of strings made 6 bracelets.

✅The point (6, 9) can be represented by the ratio, 6:9, and means 6 yards of strings made 9 bracelets.

Answer:

12

Step-by-step explanation:

12