A store is having a sale on walnuts and chocolate chips. For 2 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $11. For 4 pounds of walnuts
and 8 pounds of chocolate chips, the total cost is $25. Find the cost for each pound of walnuts and each pound of chocolate chips.

The measure of angle C in the vertical angles is B. 28.3°.

Vertical angles are the angles formed when two lines intersect. The term "vertical" in this context refers to the fact that they share the same Vertex (corner point), rather than the usual meaning of up-down.

When two lines intersect, vertical angles are formed. Because the angles are opposite each other, they are sometimes referred to as vertically opposite angles. Real-world examples of vertical angles include a railroad crossing sign, the letter "X," open scissors pliers, and so on.

There angles are equal. Therefore, it'll be 28.3°.

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Answer: 28.3 GO GET UR A+ BROSKI

Step-by-step explanation:

They're virtical angles which mean

THEY'RE THE SAME BRO

so just do 28.3 :)

As per the confidence interval, the average weight gain for composites of this kind is smaller than 0.43% is 0.0006​

Confidence interval

In statistics, the probability that a population parameter will fall between two set values is known as Confidence interval.

Given,

Here the weight gains of a collection of n =21 samples of composite subjected to water diffusion were obtained. The sample mean is x=0.42% with a sample std. of S=0.04%

Here we need to find the 95% confident from the results of this experiment that the average weight gain for composites of this kind is smaller than 0.43% .

As per the given question, we have the following details,

=> x=0.337%,

=> s=0.025%,

=> n=18.

And then we use next test hypotheses 

=> H0​:μ≥0.36 versus HA​:μ<0.36.

And then first we will calculate t-statistic and then p-value to decide which hypotheses we will accept.

=> [(0.337−0.36)/ 0.025] x √18​

=> -3.903,

=> p = TDIST(∣t∣, n − 1 , 1)

=> p = TDIST(∣−3.903∣,17,1)=0.0006​

Therefore, p-value is smaller than 0.01, we reject H0​ and accept HA​.

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Therefore you can use midpoint to find the other endpoint  (x2,y2), then by rewriting the (x2,y2)= (2a-x1,2b-y1) .

The exact midpoint between two other plane points needs to be found on occasion. For example, you might seek out a line that splits a particular line segment into two equal halves. This central region is known as the "halfway."

Here,

If you are aware of one endpoint (x1, y1) and the midpoint (a, b), but are unaware of the second endpoint (x2, y 2), you can solve the problem by rewriting the

=> a=[tex]\frac{x1+x2}{2}[/tex]

=> 2a=x1+x2

=>2a-x1=x2

=> b=[tex]\frac{y1+y2}{2}[/tex]

=>2b=y1+y2

=> 2b-y1=y2

So, the unknown endpoint can be found by

(x2,y2)=(2a-x1,2b-y1)

Therefore you can use midpoint to find the other endpoint  (x2,y2), then by rewriting the (x2,y2)= (2a-x1,2b-y1) .

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Answer:One fourth

Step-by-step explanation:

In Experiment 1 the probability of each outcome is always the same. The probability of landing on each color of the spinner is always one fourth.

Answer:

Step-by-step explanation:

The average value of the function f(x) on [0, 2] is 3.03515625.

A function is a relationship between the inputs, such that each input is related to one and only one output. If it is related to more than one output, then the relation is not a function.

The question did not specify the value of f(x). Considering the value of f(x) as f(x)= [tex]x^4[/tex] on (0,2)

Now, partitioning the interval into four sub-intervals of equal length, we get,

2-0/4=2/4 or 1/2 or 0.5

Thus, we get the four intervals:

[0, 0.5], [0.5, 1], [1, 1.5], and [1.5, 2].

When finding the mid-points of the intervals, we get the mid-points as:

[0, 0.5] = 0.25

[0.5, 1] = 0.75

[1, 1.5] = 1.25

[1.5, 2] = 1.75

Now, finding the f(x) of each interval, by substituting the value of the mid-point in the place of x we get:

Thus, f(0.25) = [tex]0.25^4[/tex]

f(0.75) = [tex]0.75^4[/tex]

f(1.25) = [tex]1.25^4[/tex]

f(1.75) = [tex]1.75^4[/tex]

Now, find the average value of f(x) =[tex]x^4[/tex]  on [0, 2].

1/2[([tex]0.25^4[/tex]+[tex]0.75^4 +1.25^4+1.75^4[/tex])/2]

= 3.03515625

Thus,

The average value of the function f(x) on [0, 2] is 3.03515625.

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The value of x is 6.

What is system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations in mathematics. For instance, the system of three equations 3x + 2y - z = 1, 2x - 2y + 4z = -2, -x + y - z = 0 has the three variables x, y, and z.

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

Graphically, a system of linear equations that has no solution indicates two parallel lines-that is, two lines that have the same slope but different y-intercepts.

To have the same slope, the x-and y-coefficient must be the same.

To get from -2/3 to -8 you multiply by 12, so multiply  -1/2x by 12 as well to yield 6x.

Because the other x-coefficient is a, it must be that a = 6  and (D) is correct.

Note that, even though it is more work, you could also write each equation in slope-intercept form and set the slopes equal to each other to solve for a.

Hence, the value of x is 6.

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Answer:

............................

Answer:

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

40

a. The equation is, P = 15m + 10

b. The graph of P = 15m + 10 can be seen in the image attached below.

c. The total number of pages written in 5 months, is, 85.

A linear equation is a straight line graph, which can be expressed in slope-intercept form as y = kx + b, where;

a. To write the equation for the total number of pages P written after any number of months m, we have the following defined variables:

Unit rate or slope (k) = 15

Initial value or y-intercept (b) = 10

Number of pages, y = P

Number of months, m = x.

Substitute k = 15 and b = 10 into P = km + b:

P = 15m + 10

b. The graph of the P = 15m + 10 is shown below.

c. Substitute m = 5 into the equation, P = 15m + 10:

P = 15(5) + 10

P = 85

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The expected value means what we expect to lose -$1.05 if the 1st is correct and lose -$.63 for the 2nd if that is correct.

Alright so we need to know the equation for expected value. So this turns our to be a pretty simple equation being:

E(X)=ΣxP(X=x)

So since we have all of our information we just need to use the equation. So:

E(X)= -$5*125/216+ $5*75/216+$10*15/216+$24*1/216 = -$1.045

I did notice however that there might be a mistake on this question since you have the win if 2 dice are correct as only being $10 instead of what i would think of being 16. If that is the case then the expected value is below

E(X)= -$5*125/216+ $5*75/216+$16*15/216+$24*1/216 = -$.6300

So the expected value means what we expect to lose -$1.05 if the 1st is correct and lose -$.63 for the 2nd if that is correct.

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6/8 is an equivalent fraction to 3/4; 2/6 is equivalent to 1/3; 6/9 is equivalent to 2/3; 10/25 is equivalent to 2/5; 4/16 is equivalent to 1/4; the fraction of 1/3 is equivalent to 2/6; 8/16 is an equivalent fraction to 2/4.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. The fractions equivalent to each other have been mentioned above.

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The area on the graph that is not shaded is the region of feasibility. The shape is a triangle and the vertices of the feasible region are: (5,1.5), (.75,.75), (1.5,.5)

The system of inequalities below, We need to determine the shape of the feasible region and find the vertices of the feasible region

x+y<=2

3x+y>=3

x+3y>=3

x>=0

y>=0

Now, we would graph with the following inequalities

x+y>=2

3x+y<=3

x+3y<=3

x<=0

y<=0

Therefore, the area on the graph that is not shaded is the region of feasibility and the shape is a triangle, the vertices of the feasible region are: (5,1.5) (0.75, 0.75), (1.5,.5).

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Answer:

t = b + n

Step-by-step explanation:

for the 2 lines to be parallel then their slopes must be equal

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (x₁, a + n ) and (x₂, y₂ ) = (x₂, t ) ← 2 points on line k

m = [tex]\frac{t-(a+n)}{x_{2}-x_{1} }[/tex] = [tex]\frac{t-a-n}{x_{2}-x_{1} }[/tex]

repeat with

(x₁, y₁ ) = (x₁, a ) and (x₂, y₂ ) = (x₂, b ) ← 2 points on line j

m = [tex]\frac{b-a}{x_{2}-x_{1} }[/tex]

equating the 2 slopes gives

[tex]\frac{t-a-n}{x_{2}-x_{1} }[/tex] = [tex]\frac{b-a}{x_{2}-x_{1} }[/tex]

since the denominators are the same on both sides, then equate the numerators

t - a - n = b - a ( add a to both sides )

t - n = b ( add n to both sides )

t = b + n

Answer:

Step-by-step explanation:

Since we know the general circle equation is in the form

x^2 + y^2 = r^2, where r is radius

Now we are given the information that circle has the origin (0,0) and pass through point (-11,0), which mean the radius is 11 units.

Now we can write the circle equation as

x^2 + y^2 = 11^2

Answer:

the equation for the circle is:

X² +Y² = 11² = 121

a)  The probability that from 3 to 6 have blowouts is 0.7073

b)  The probability that fewer than 4 have blowouts is  0.4613

c)  The probability that more than 5 have blowouts is 0.1483

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given : In testing a certain kind of truck tire over rugged terrain, it found

that 25% of the trucks fail to complete the test run without a  blowout,

15 Truck Tested

To Find : probability that

(a) from 3 to 6 have blowouts:

(b) fewer than 4 have blowouts,

25% of the trucks fail to complete the test run without a  blowout,

=> probability of blow out p = 1/4

q  = 1 - p = 3/4

n = 15  

P(x)   = ⁿCₓpˣqⁿ⁻ˣ

probability that

(a) from 3 to 6 have blowouts:

= p(3) + p(4) + p(5) + P(6)

= ¹⁵C₃(1/4)³(3/4)¹² + ¹⁵C₄(1/4)⁴(3/4)¹² + ¹⁵C₅(1/4)⁵(3/4)¹⁰ + ¹⁵C₆(1/4)⁶(3/4)⁹

=0.7073

b) fewer than 4 have blowouts,

= P(0) + P(1)  + P(2)   + P(3)

= ¹⁵C₀(1/4)⁰(3/4)¹⁵ + ¹⁵C₁(1/4)¹(3/4)¹⁴ + ¹⁵C₂(1/4)²(3/4)¹³ + ¹⁵C₃(1/4)³(3/4)¹²

= 0.4613

c) more than 5 have blowouts

 Formula:

P(X>5) = 1 - P ( X≤ 5 )  = 1 - ( P(0) + P(1)  + P(2)   + P(3) + P(4) +P(5) )

Using the similar calculations , we get

P(X>5) =  1 - 0.8517 = 0.1483

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Answer:

Step-by-step explanation:

The final balance after 10 years is $33257.92.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The expression for the amount for compound interest is given as,

A = P(1 + r/100)ⁿ

After 6 years the amount can be calculated as,

A =  10000(1 + 10/100)⁶

  =  10000 × (11/10)⁶

  =  0.01 × 11⁶

  = 17715.61
As per the question $ 5000 is added at the end of 6 years.

So, the principal becomes 17715.61 + 5000 = 22715.61.

And, the remaining time is 10 - 6 = 4 years.
Now, the amount obtained after 10 years can be calculated as,

A = 22715.61(1 + 10/100)⁴

   = 22715.61 × 1.1⁴

   = 33257.92

Hence, the end of 10 years, the balance in Jarad's account is given as $33257.92.

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The values of the trigonometric functions sin(∅) and cos(∅) are -1/2 and [tex]\frac{\sqrt{3} }{2}[/tex] respectively.

The trigonometric functions and identities are the ratio of sides of a right-angled triangle. The sides of a right triangle are the perpendicular side, hypotenuse, and base, which are used to calculate the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulae.

if ∅ = [tex]\frac{11\pi }{6}[/tex] rad converting to degree

we know that [tex]\pi[/tex] rad = 180°

which means  ∅ in degrees = 11/6 x 180 which is 330°

sin(330) = -1/2

cos(330) = [tex]\frac{\sqrt{3} }{2}[/tex]

In conclusion, the function values of the sin(∅) and cos(∅) are -1/2 and  [tex]\frac{\sqrt{3} }{2}[/tex]

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The equation illustrates that the variable that represents the greatest number is E. This cannot be determined with the given information.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

From the information, the variable is given as 1/2m = 1/3n = 1/4p = 1/5q.

It should be noted that the greatest variable cannot be determined based on the information. In conclusion, the correct option is E.

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Answer:

g=7

Step-by-step explanation:

To solve this equation, we need to isolate the variable g on one side of the equation. We can do this by first dividing both sides of the equation by 2. This gives us:

g - 4 = 3

Next, we can add 4 to both sides of the equation to isolate the variable g on the left side of the equation. This gives us:

g = 7

Therefore, the value of g that satisfies the equation is 7.

Answer:

Yes, we can use both ASA Postulate or the AAS Theorem to prove the triangles congruent. ASA postulate says that if two angles and the included side of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

The equation which represents the counters inside the rectangle is,

12 ÷ 3 = 4.

What is equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

In the given diagram there is a rectangle containing 4 counters.

Each counter containing 3 red balls.

So, the total number of red balls are 4 x 3 = 12.

From this the equation which represents the counters inside the rectangle is,

12 ÷ 3 = 4.

Hence, the equation which represents the counters inside the rectangle is, 12 ÷ 3 = 4.

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To find the value of F1, we can start by writing out the given equations in a more standard form.

First, we can rewrite the equation "F1 + F2 = 100" as "F1 = 100 - F2".

Then, we can rewrite the equation "F1 - F2 = 20" as "F1 = 20 + F2".

If we set these two equations equal to each other, we get "100 - F2 = 20 + F2".

If we simplify this equation, we get "80 = 2 * F2".

If we divide both sides of the equation by 2, we get "40 = F2".

Substituting this value back into either of the original equations, we can find that "F1 = 100 - F2" or "F1 = 100 - 40" which gives us "F1 = 60".

Therefore, the value of F1 is 60.

The volume of the solid obtained by rotating the region bounded by the given curves about the X-axis is 340978 vu.

Given curve is,

y = [tex]x^{3}[/tex] , y = 8, x = 0 about x = 7

we know the formula for cylindrical shell is

V = πR²h

where R² = f(x)₂-f(x)₁ ,

            h = dx

here f(x)₂ = 8 and f(x)₁ = x³

⇒ V = π(8 - x³)²h

    V = π(64 - 16x³+x⁶)dx

integrating on both sides,

[tex]\int dV[/tex] =π [tex]\int ({64 - 16 x^{2} + x^{6} }) \, dx[/tex]

        = [tex]64 \int dx - 16 \int {x^{3} } \, dx + \int\ {x^{6} } \, dx[/tex]

    V = π(64x - 4x⁴+[tex]\frac{x^{7} }{7}[/tex])

    V = π(64 × 7 - 4(7)⁴ + [tex]\frac{7^{7} }{7}[/tex])

        = π(448 - 9604 + 117649 )

        = [tex]\frac{22}{7}[/tex](108493)

   V = 340978 vu

Therefore volume of the cylindrical shells to the region y = x³, y = 8, x = 0 about x = 7 is 340978 vu.

Cylindrical shells are essential structural elements in offshore structures, submarines, and airspace crafts. They are often subjected to combined compressive stress and external pressure, and therefore must be designed to meet strength requirements.

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The coefficient of x1 = 0.03 and the coefficient of  x2 = - 0.02.

The coefficient of x1 is  positive we can say there is a positive relationship  between x1 and y as the x1  value increases, the y value also increases

If the x1 value increases as 1 unit then the y  value increases as 0.03 unit while x2 keeps constant.

The coefficient of x2 is negative we can say there is a negative relationship between x2 and y as the x2 value increases y  value decreases.

If the x2 value increases as 1 unit then the y value decreases as 0.02 unit while x1 keeps constant.

A dichotomous variable is one that takes on one of just two potential qualities when noticed or estimated. The worth is most frequently a portrayal of a deliberate variable (e.g., mature: under 65/65 and over) or a quality (e.g., orientation: male/female).

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The structure of the Binary search tree as follows:

A

/ \

B  D

/   \

C    G

 \

  E

  \

   F

Step 1: Create an empty binary search tree.

Step 2: Insert the node "A" into the tree.

Step 3: Insert the node "B" into the tree, with "A" as its left child.

Step 4: Insert the node "C" into the tree, with "B" as its right child.

Step 5: Insert the node "D" into the tree, with "A" as its right child.

Step 6: Insert the node "E" into the tree, with "C" as its left child.

Step 7: Insert the node "F" into the tree, with "E" as its right child.

Step 8: Insert the node "G" into the tree, with "D" as its right child.

Step 9: The resulting binary search tree is as follows:

A

/ \

B  D

/   \

C    G

 \

  E

  \

   F

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The range is the set of all possible y-values that could come from the equation y = |x|.

Since the absolute value only results in 0 or positive numbers, the range cannot include any negative real numbers.  

    |3| = 3

    |0| = 0

    |-3| = 3

Therefore the range is not all real numbers, since all negative real numbers are excluded from the range.

The range is y ≥ 0.

The value for p is 9 and the equation is y = 9x.

What is the proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

We have,

x        y

4        36

8        72

12        108

A proportional relationship between x and y is p,

y = px

p = 36/4 = 9

p = 72/8 = 9

p = 108/12 = 9

Hence, the value for p is 9 and the equation is y = 9x.

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A meta - operation defines any form or protocol for the operation, but doesn't its implementation. Option (a) is correct.

Programmers reverence type of protocols. We think about protocols as some thing given to us from on excessive through the Cerfs, Postels, and Berners-Lees of the world. But the fact is that programmers construct protocols all of the time. Sometimes those are advert hoc and different instances they're constructed with the assist of a metaprotocol. Communication protocols in general, in addition to protection protocols, want a better degree of pliability to deal with evolution.

Many method will increase the extent of code sharing and reuse. I additionally observed that protection protocols are best-suitable for the utility of my framework due to the fact maximum protection protocols proportion a comparable set of capabilities and showcase not unusualplace sequences and styles withinside the manner they operate. Therefore, I proven the framework through making use of it to the implementation of numerous protection protocols: Needham-Schroeder Authentication Protocol, ISAKMP, and SSL.

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Answer: May I see the graph?

Step-by-step explanation: