What is the slope of the line in the following graph?

The piecewise function will be continuous in its domain if k = 49/48

Here we have a piecewise function and we want to find the value of k suc that the function is continuous on the domain.

To get that, both piecese of the function must ahve the same value in the jump, then we will get:

f(7) = f(7)

Replacing the functions we will get:

k·7²  = 7·7 + k

Let's solve that equation for k.

49k = 49 + k

49k - k = 49

48k = 49

k = 49/48

That must be the value of k such that the function is continuous in all its domain.

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Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.

On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.

With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.

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The population of interest is the group of students who submitted an application to the college in 2017.

A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.

The correct answer is C.

The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.

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Answer:

(1, 2) and (-1, -2). or. (±1, ±2)

Step-by-step explanation:

[tex]{ \sf{f(x) = \frac{4x}{ {x}^{2} + 1 } }} \\ [/tex]

- Simply, a critical number or critical point is gotten by differentiating the function.

From Quotient rule;

[tex]{ \sf{ {f}^{l}(x) = \frac{4( {x}^{2} + 1) - (2x)(4x)}{ {( {x}^{2} + 1)}^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{ {4x}^{2} + 4 - {8x}^{2} }{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{4(1 - {x}^{2}) }{ {( {x}^{2 } + 1) }^{2} } }}[/tex]

Then equate this derivative to zero;

[tex]{ \sf{0 = \frac{4(1 - {x}^{2} )}{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{4(1 - {x}^{2} ) = 0}} \\ \\ { \sf{4 - {4x}^{2} = 0}} \\ \\ { \sf{4 {x}^{2} = 4}} \\ \\ { \sf{x = \sqrt{1} }} \\ \\ { \sf{ \underline{ \: x = \pm 1 \: }}}[/tex]

Substitute for x in f(x)

For x = 1

[tex]{ \sf{f(1) = \frac{4(1)}{ {(1)}^{2} + 1} = \frac{4}{2} = 2 }} \\ [/tex]

For x = -1

[tex]{ \sf{f( - 1) = \frac{4( - 1)}{ {( - 1)}^{2} + 1 } = \frac{ - 4}{2} = - 2 }} \\ [/tex]

Therefore points are;

(1, 2) and (-1, -2)

The correct option b) [tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.

The graph οf a relatiοn is said tο reflect a functiοn if a vertical line drawn anywhere οn the graph οnly intersects the graph οnce. In the event when a vertical line can graph is nοt a representatiοn οf a functiοn if there are mοre than twο pοints οn it.

The graphs coordinate is at (-3, 3)

Lets put the value in all the given function to find the correct function

a. [tex]\rm y = \sqrt{x - 3} + 3[/tex]

Using (-3, 3) as x and y

[tex]\rm 3 = \sqrt{(-3) - 3} + 3[/tex]

[tex]\rm 3 = \sqrt{9} + 3[/tex]

[tex]\rm 3 \neq 3 + 3[/tex]

[tex]\rm y = \sqrt{x - 3} + 3[/tex] is not a function of graph.

b. [tex]\rm y = \sqrt{x+ 3} + 3[/tex]

Using (-3, 3) as x and y

[tex]\rm 3 = \sqrt{-3+ 3} + 3[/tex]

[tex]\rm 3 = \sqrt{0} + 3[/tex]

[tex]\rm 3 = 0 + 3[/tex]

[tex]\rm 3 = 3[/tex]

[tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.

The other two options are no the functions as cube root is used and the value of x wont satisfy there.

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The set of ordered pairs does not represent a function is the one in the third option.

{(-1,9), (-8, 5), (-1, 3), (-9, 1)}

A relation maps elements from one set, the domain, into elements of other set, the range.

Such that these mappings are of the form (x,y).

A function is a relation where each input is mapped into a single one output, then if you see a relation that has two points with the same value of x and different values of y, then that relation is not a function.

Particularly, if you look at the third option:

{(-1,9), (-8, 5), (-1, 3), (-9, 1)}

You can see that the first and second points have the same input and different outputs, then this is not a function, and that is the correct answer.

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Answer:

The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:

2, 4, 6, 8, 10

The average of these five integers is:

(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6

Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.

Answer:

No.

Step-by-step explanation:

Given two triangles on a coordinate plane, you can check whether they are congruent by using the distance formula to find the lengths of their sides. If three pairs of sides are congruent, then the triangles are congruent by the above theorem.

Over here, they aren't congruent by the SSS.

Answer:

We will use mathematical induction to prove the formula for the sum of arithmetic sequences:

For n=1, we have:

∑j=1^1(a + (j-1)d) = a

On the other hand, we have:

n/2(2a + (n-1)d) = 1/2(2a) = a

Thus, the formula holds for n=1.

Assuming the formula holds for n=k, we will prove that it holds for n=k+1.

We have:

∑j=1^(k+1)(a + (j-1)d) = (a + kd) + ∑j=1^k(a + (j-1)d)

Using the formula for n=k, we can write:

∑j=1^k(a + (j-1)d) = k/2(2a + (k-1)d)

Substituting this back into the first equation, we have:

∑j=1^(k+1)(a + (j-1)d) = (a + kd) + k/2(2a + (k-1)d)

Simplifying the right-hand side, we get:

∑j=1^(k+1)(a + (j-1)d) = 1/2(2a + (2k+1)d)

But (k+1)/2(2a + kd + d) = 1/2(2a + (2k+1)d), so the formula holds for n=k+1.

Therefore, by mathematical induction, the formula for the sum of arithmetic sequences is proved.

Selection bias can creep into a study if subjects are picked (intentionally or not) according to some criterion and not randomly.

Selection bias occurs when the selection of study participants is not random and is instead influenced by certain criteria. This can result in a non-representative sample that does not accurately reflect the population being studied, leading to inaccurate conclusions. For example, if a study on the effectiveness of a medication only enrolls participants who are already known to respond well to that medication, the results may overestimate its effectiveness in the general population. To minimize selection bias, researchers should use random sampling techniques and carefully consider the inclusion and exclusion criteria .

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answer: 175

Step-by-step explanation:

Answer:

71.9 degrees

Step-by-step explanation:

The find the value of x on the given diagram, we must first find the included angle between the two line segments labelled 94 mi and 119 mi in the triangle. To do this, we can use the Law of Cosines.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

The values to substitute into the formula are:

Solving for the angle C:

[tex]\begin{aligned}173^2&=119^2+94^2-2(119)(94)\cos C\\\\29929&=14161+8836-22372\cos C\\\\29929&=22997-22372\cos C\\\\6932&=-22372\cos C\\\\-\dfrac{6932}{22372}&=\cos C\\\\C&=\cos^{-1}\left(-\dfrac{6932}{22372}\right)\\\\C&=108.0502874...^{\circ}\end{aligned}[/tex]

As angles on a straight line sum to 180°, the value of x can be calculated by subtracting the found value of C from 180°:

[tex]x=180^{\circ}-108.0502874...^{\circ}[/tex]

[tex]x=71.9497125...^{\circ}[/tex]

[tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]

Therefore, the ship turned 71.9 degrees north of west when it changed direction.

Answer:

if u want total price then,

=Rs.35×80=Rs.2800

Answer:

Step-by-step explanation:

Let weight of fourth parcel be x

Mean = Sum of all values/total number of values.

8.5 = 7.7 + 7.6 + 8.2 + x/4

8.5 = 23.5 + x/4

8.5 × 4 = 23.5 + x

34 = 23.5 + x

34 - 23.5 = x

10.5 = x

Therefore, weight of the fourth parcel will be 10.5 kg

The measurement of angle PCD in equilateral triangle  is 67.38°.

Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.

Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.

Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.

Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.

Using the Pythagorean theorem in triangle $OCE$, we have

CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]

Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,

∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°

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Answer:

24 different lunches

Step-by-step explanation:

There are three choices for the beverage, two choices for the appetizer (soup or salad), and four choices for the sandwich. Therefore, using the multiplication principle of counting, the number of different lunches possible is:

3 choices for beverage x 2 choices for appetizer x 4 choices for sandwich = 24 different lunches.

a) The drawing of all data points on a 2D plane is illustrated below.

b) The angle in between the five other points is 27

c) The matrix outer product for X is R = XXT.

d) The matrix outer product can also be calculated via R is (2,27)

The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.

To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.

Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.

The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.

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The inventory turnover ratio can be calculated by dividing the cost of goods sold by the average inventory value. In this case, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.

The inventory turnover ratio measures the number of times a company sells and replaces its inventory during a period. It can be calculated by dividing the cost of goods sold by the average inventory value.

The inventory turnover ratio = Cost of goods sold / Average inventory value

In this case, the cost of goods sold is $600,000 and the average inventory value is $1,200,000.

Inventory turnover ratio = $600,000 / $1,200,000 = 0.5

Therefore, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.

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Complete question:

If the average aggregate inventory value is $1,200,000 and the cost of goods sold is $600,000, which of the following is inventory turnover?

A)60

B)10.4

C)2

D)0.5

E)None of these

As a result, both varieties of trees will be the same height after 9 years. We can change both equations to a = 9 to verify this: Height of the type A tree is 36 + 8(9) or 36 + 72 inches, whereas the height of the type B tree is 18 + 10(9) or 18 + 90 inches.

Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It utilised to compute height of towers, structures, mountains, etc., and distance between any two objects such celestial bodies others. ,sys,s tos.as to .... and.

Let's use "a" to denote the number of years after planting the trees.

A type A tree will reach the following height after "a" years:

Height of type A tree = 36 + 8a

After "a" years, the height of a type B tree will be:

Height of type B tree = 18 + 10a

We must set the two types of trees' heights equal to one another and solve for "a" to determine when they will reach the same height:

36 + 8a = 18 + 10a

Subtracting 8a from both sides, we get:

36 = 18 + 2a

Subtracting 18 from both sides, we get:

18 = 2a

Dividing both sides by 2, we get:

a = 9

Therefore, after 9 years, both types of trees will be the same height.

To check this, we can substitute a = 9 into both equations:

Height of type A tree = 36 + 8(9) = 36 + 72 = 108 inches

Height of type B tree = 18 + 10(9) = 18 + 90 = 108 inches

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Question:

You have two types of trees to plant in your yard: type A trees are 36 inches tall and grow 8 inches per year, while type B trees are 18 inches tall and grow 10 inches per year. At what point in time will the trees be the same height? How tall will the trees be at that time?

Two radicals are said to be radicals if they have the same indices and the radicand.

In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:

3√(pq) → pq is the radicand

√(a+b) → a + b is the radicand

4√15 → 15 is the radicand

A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.

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Complete question:

Type the correct words in the blanks:

Two radicals are said to be radicals if they have the same               and the radicand.

Answer: t = 1.8 seconds

Step-by-step explanation:

The function h(t) = 25t^2 - 81 gives the height of the rock (in feet) at time t seconds after it was dropped.

When the rock lands, its height is 0. So we can set h(t) = 0 and solve for t:

25t^2 - 81 = 0

Solving for t, we get:

t = ±√(81/25) = ±(9/5)

Since we are only interested in the time after the rock was dropped, we take the positive value:

t = 9/5 = 1.8 seconds

Therefore, the time between when the rock was dropped and when it landed is 1.8 seconds.

So the answer is: t = 1.8 seconds

Step-by-step explanation:

2x + ay + 2 = 0

the gradient or slope of the line is the factor m of x in the form

y = mx + b

so let's transform the given equation into that form :

ay = -2x - 2

y = (-2/a)x - 2/a

we know that m = 1.

so,

-2/a = 1

-2 = a

Answer:

D.

Step-by-step explanation:

Answer: 811 adult tickets and 868 child tickets

Step-by-step explanation:

35x +20y = 44,620

add 35+20

divide the sum by 44,620 and

the answer

In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.

Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.

Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:

P(accurate order) = 1246 / 1300 = 0.958 for McDonald's

P(accurate order) = 1020 / 1100 = 0.927 Taco Bell

P(accurate order) = 708 / 800 = 0.885 for Burger King

P(accurate order) = 940 / 1000 = 0.94 for Wendy's

P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929

As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

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Answer:

Greg bought a pack of X jumbo stickers during the back - to - school sale at Crafty's craft store. He ( uses 4  ( -4 ), ( you didn't give options ). There were 8 stickers left in the pack.

Hope this helps!

Step-by-step explanation:

The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%

What is Conditional probability?

Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."

The formula for conditional probability is:

P(A|B) = P(A and B) / P(B)

where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.

The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.

The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:

(number of Plastic #4 bottles correctly placed) / (total number of bottles)

So the probability is:

5/20 = 1/4 = 0.25

Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.

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As all the sides of the closed figure are equal to each other, the quadrilateral here is a square.

A square is a closed, two-dimensional (2D), object with four corners. With four sides and four vertices, a quadrilateral is referred to as a square. All four sides of a square are equal and parallel.

In other words, a square is a polygon or quadrilateral with four sides. An equiangular quadrilateral is a shape in which all of the angles are of equal size.

Here in the given figure, we can see a quadrilateral is given.

We can see that all the sides of the quadrilateral are given to be equal to each other.

We can conclude from the observation that the quadrilateral is a square as the sides are all equal to each other.

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The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.

Compare Alice's utility from each option and choose the one that maximizes her utility.

Let us consider each option,

If Alice offers Bob $0, her utility will be,

If XA > XB then

UA (XA , XB )= 0.3x3 + 0.72A

UA(10,0)

= 0.3(10)³ + 0.72(10)

= 307.2

If Alice offers Bob $5, Bob's utility will be,

UB(10,5)

= 0.314 + 0.72(5)

= 0.314 + 3.6

= 3.914

And Alice's utility will be,

UA(5,10)

= -0.32(5) + 1.3(10)

= 11.4

Total utility for both Alice and Bob will be,

UA(5,10) + UB(10,5)

= 11.4 + 3.914

= 15.314

If Alice offers Bob $2, Bob's utility will be,

UB(10,2)

= 0.314 + 0.72(2)

= 1.754

And Alice's utility will be,

UA(2,10)

= -0.32(2) + 1.3(10)

= 12.4

So the total utility for both Alice and Bob will be,

UA(2,10) + UB(10,2)

= 12.4 + 1.754

= 14.154

If Alice offers Bob $10, Bob's utility will be,

UB(10,10)

= 0.314 + 0.72(10)

= 7.514

And Alice's utility will be,

UA(10,10)

= 0.3(10)³ + 0.72(10)

= 307.2

So the total utility for both Alice and Bob will be,

UA(10,10) + UB(10,10)

= 307.2 + 7.514

= 314.714

Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.

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