Find the measure of the angle indicated in bold.

Using the Venn Diagram principles, the number of customers at the supermarket who purchased both shirts and pants is 26.

A Venn Diagram shows a pictorial or graphical representation of the relationship (similarities and differences) between data sets.

In a Venn Diagram, overlapping circles or other shapes can be used to depict the logical relationships between two or more data sets or items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, using the formula of Venn Diagram, we can conclude that at this supermarket with 118 customers, 26 customers purchased both shirts and pants.

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The unit cost C depends on the number of engines made. If x engines are made, then the unit cost is given by the function:

C(x)=0.2x²+ 248x +21,748 is $12917, which is the minimum unit cost.

Unit cost, also known as the break-even point, is the lowest price at which a company must sell a product to avoid losses. For example, a product with a breakeven unit cost of $10 per unit must sell above that price. Revenues above this price constitute the company's profit.

The calculates the unit cost of production as the break-even point. This cost constitutes the base price that the company uses to determine its market price.

In general, a unit must sell for more than its unit cost to generate a profit. For example, a company manufactures 1,000 units of a product that costs $4 each and sells them for $5 each. The profit is $5 minus $4, or $1 per unit of income. If a unit is priced at $3 per unit, there is a loss because $3 minus $4 (cost) is a loss of $1 per unit.

By the definition of average cost, we know it is the ratio of the total cost to the number of manufactured products. The total cost here is also termed as unit cost, which is equal to the sum of fixed cost and variable cost.

Hence, Average cost = Total cost/Number of units

                                    =  (Fixed cost + Variable cost)/Number of units.

According to the Question:

The minimum unit cost is $12197.

Take the derivative and set = 0  solve for x

C'(x) = 2x -360 = 0

x = 180 engines

C(180)  = (180)² -360(180) + 44,597

           = 44,597 - 32400

           = $12,197  minimum cost.

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1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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A relation represents a function when each input value is mapped to a single output value.

On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.

Tracing a vertical line for any x > -3, the vertical line would cross the graph at two points, meaning that the relation is not a function.

As for the domain and the range, we have that:

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Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

To show that the Directed Disjoint Paths Problem is NP-complete, we can use a reduction from the well-known NP-complete problem of Hamiltonian Path, which is defined as follows: given a graph G and a starting node s, does G contain a simple path that visits every node exactly once and ends at s?

We can reduce the Hamiltonian Path problem to the Directed Disjoint Paths Problem as follows. Given a graph G and a starting node s for the Hamiltonian Path problem, we can construct a new graph G' as follows:

Now, consider the k pairs of nodes (s1,t1), (s2,t2), ..., (sk,tk) in G', where si and ti are the corresponding nodes in G' for the ith node in G. We can see that G contains a Hamiltonian path from s to s if and only if G' contains k node-disjoint paths from si to ti for all i.

Since the Hamiltonian Path problem is NP-complete, and we have shown that it can be reduced to the Directed Disjoint Paths Problem in polynomial time, it follows that the Directed Disjoint Paths Problem is also NP-complete.

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Answer:

The equation of the circle is \((x + 4)^2 + (y - 10)^2 = 64\), third option is correct.

Step-by-step explanation:

Equation of a circle:

The equation of a circle with center \((x_0,y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

Center at (-4, 10)

This means that \(x_0 = -4, y_0 = 10\).

Radius of 8:

This means that \(r = 8\). So

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

\((x - (-4))^2 + (y - 10)^2 = 8^2\)

\((x + 4)^2 + (y - 10)^2 = 64\)

The equation of the circle is \((x + 4)^2 + (y - 10)^2 = 64\), third option is correct.

Answer:

It might be 1/3 but I'm not 100% sure

The required scale factor  of ABC to DEF is 1/3.

Scale factor of ABC to DEF to determine.

The scale factor is defined as the ratio of modified change in length to

Here, Triangle ABC is similar to triangle DEF. So, the ratio of the same sides describe the scale factor.
Scale factor = EF/BC
                   = 7/21
                   = 1/3

Thus, the required scale factor  of ABC to DEF is 1/3.

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Answer:

see below

Step-by-step explanation:

To graph this equation, start at the origin (0,0) since there is not y-intercept.

Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.

Because the rise (up and down, numerator) is 1, we know that we will go up one unit.

The run (side to side, denominator) is 4, so we will go to the right 4 units.

This makes the first point (4, 1).

Continue doing this until you get an idea of the line and connect the points to get the graph

Answer:

Info down in Explaination

Step-by-step explanation:

To graph this equation, start at the origin (0,0) since there is not y-intercept.

Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.

Because the rise (up and down, numerator) is 1, we know that we will go up one unit.

The run (side to side, denominator) is 4, so we will go to the right 4 units.

This makes the first point (4, 1).

Continue doing this until you get an idea of the line and connect the points to get the graph

Answer:

Here to get the points thanks for recommending this ur so nice.

Step-by-step explanation:

\( - 13 = \frac{w}{9} - 6 \\ - 13 + 6 = \frac{w}{9} \\ - 7 = \frac{w}{9} \\ w = - 63\)

so only -63 is the solution, the rest three are NOT solution for this equation.

Answer:

(9,16)

Step-by-step explanation:

We Know

The equation y = 3x - 2

Find the y coordinate (9, ?)

We just simply put 9 in for x and solve for y

y = 3(9) - 2

y = 18 - 2

y = 16

So, the coordinate are (9,16)

The set of values that we are permitted to enter into our function is referred to as the domain of a function. The x values for a function f make up this collection (x). A function's range is the range of values that it can accept as input. When we enter an x value, the function outputs this set of outcomes.

(a) f - {1 2 3 4 5} -> {1 2 1 2 1}

This function is neither injective nor surjective. It is not injective because f(1) = f(3) = f(5) = 1, and it is not surjective because 2 is not in the range.

(b) f - {1 2 3 4 5} -> {1 2 3 1 2}

This function is neither injective nor surjective. It is not injective because f(1) = f(4) and it is not surjective because 3 is not in the range.

(c) f(x) = { x if x < 3, x - 3 if x > 3}

This function is both injective and surjective, and hence bijective. It is injective because each element in the domain maps to a unique element in the codomain, and it is surjective because every element in the codomain is mapped to by at least one element in the domain. Hence, this function is bijective.

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Tο summarize, here are the classificatiοns fοr each functiοn:

(a) f(x) = {1 2 1 2 1} is neither injective nοr surjective.

(b) f(x) = {1 2 3 1 2} is neither injective nοr surjective.

(c) f(x) = { x if x < 3 x -3 if x > 3 } is neither injective nοr surjective.

In mathematics, a functiοn definitiοn is a statement that defines a relatiοnship between input values (called the dοmain) and οutput values (called the cοdοmain οr range). A functiοn takes an input value and prοduces a unique οutput value based οn a certain rule οr algοrithm.

(a) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 1 and 2 are mapped tο 1, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 3 is never used.

(b) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 1 and 2 are mapped tο the οutput 1, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 3 is never used.

(c) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 3 and 4 are mapped tο the οutput 0, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 1 is never used.

Hence,

Tο summarize, here are the classificatiοns fοr each functiοn:

(a) f(x) = {1 2 1 2 1} is neither injective nοr surjective.

(b) f(x) = {1 2 3 1 2} is neither injective nοr surjective.

(c) f(x) = { x if x < 3 x -3 if x > 3 } is neither injective nοr surjective.

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The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given trinomial,

a² + 2a - 3 = 0

a² + 2a = 3

Add 1 on both sides,

a² + 2a + 1 = 3 + 1

(a + 1)² = 4

(a + 1)² - 4 = 0

As per the given trinomial,

a² - 2a - 8 = 0

a² - 2a = 8

Add 1 on both sides,

a² - 2a + 1 = 8 + 1

(a - 1)² = 9

(a - 1)² - 9 = 0

As per the given trinomial,

p² + 16p - 22 = 0

p² + 16p = 22

Add 64 on both sides,

p² + 16p + 64 = 22 + 64

(p + 8)² = 86

(p + 8)² - 86 = 0

Hence "The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively".

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The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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Answer:

C

Step-by-step explanation:

Both triangles have three angles of the same value.

Remember that the angles in all triangles add up to 180°.

Let's use that to find out the unknown angles.

For the first triangle:

180 - 82 - 43 = 55°

55° is also in the second triangle.

Let's check with the second triangle:

180 - 82 - 55 = 43°

43° is also in the first triangle.

Therefore, both triangles are similar as the angles in both triangles are the same - 82°, 43° and 55°.

Hence, C.

Answer:

2/5 or 0.4.

Step-by-step explanation:

6/15 = 2/5

the number of pancake does it make from 3 1/3 cups of pancake is 30 pancakes.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Here it is given that :

2/3 of a cup of pancake mix makes 6 pancakes

2/3  pancake mix = 6 pancakes

multiply 3/2 both side :

1 pancake mix = 6x3/2 pancakes

1 pancake mix = 9 pancakes

Now to find the number of pancake does it make from 3 1/3 cups of pancake mix multiple 3 1/3 both side That is :

3 1/3  pancake mix = 9 x 10/3 pancakes

3 1/3  pancake mix = 30 pancakes

Therefore, the number of pancake does it make from 3 1/3 cups of pancake is 30 pancakes.

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Answer:

2x-7y

8x+2y

Step-by-step explanation:

Answer:

creating shapes,angles and lines

Answer:

hello! :)

Three ways math is in math is that everything in dancing has to do with patterns, dancers memorize patterns in the steps in their dances. The larger number of dancer, the more possible relations of lines, shapes and patterns arise from their interacting bodies

Answer:

  x ≈ 21.7

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(37°) = 17.3/x

  x = 17.3/cos(37°)

  x ≈ 21.7

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

52 bags.

Step-by-step explanation:

Your question is how many full bags are available in terms of 38 gram packs from less than 2000 grams sum.

Now:

2000

 38

=

52.63

Since you only need full (38 grams) paks, your answer is 52 bags.

What is the leftover amount?

L

=

2000

−

(

52

×

38

)

=

2000

−

1976

=

24

grams.

Your leftover part is 24 grams.

Answer:

∠Q≅∠F

Step-by-step explanation:

Two triangles are said to be congruent if all the three sides of the triangles are equal and all the three angles are equal.

Given that: In triangle DEF, DE=8 in., DF=23 in., and ∡D=16°. In triangle PQR, PQ=23 in., PR=8 in., and ∡P=16°.

Hence we can say that ΔDEF is congruent to ΔPQR. According to the side-angle-side (SAS) triangle congruence theorem: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Therefore:

DF = PQ, DE = PR, EF = RQ, ∠D = ∠P, ∠E = ∠R and ∠F = ∠Q

The unknown angle measures are d = 76, c = 53, a = 51 and b = 76

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

The lines

The sum of angles on a line is 180

So, we have

b = 180 - 51 - 53

b = 76

By vertical angle theorems, we have

d = 76

c = 53

a = 51

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Answer:

y = -5/2x

Step-by-step explanation:

y = mx + b

y = -5/2x

Answer:

Answer:

Solution given:

\((x_1,y_1)=(-4,10)\)

\((x_2,y_2)=(-6,15)\)

now

slope:\(\frac{y_2-y_1}{x_2-x_1}=\frac{15-10}{-6+4}=\frac{5}{-2}\)

Slope: -5/2