Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 e3x − 1 − 3x x2

Assuming there are at least 12 of each kind of cupcake, number of ways can you choose 12 cupcakes is; 1399358844975 ways

We are given the quantity of each type of cupcake as follows;

Number of types of cupcakes = 5

Number of Chocolate Cupcakes = 12

Number of Vanilla Cupcakes = 12

Number of Lemon cupcakes = 12

Number of Strawberry Cupcakes = 12

Number of coffee cupcakes = 12

Thus, total number of cupcakes will be gotten by adding all the quantities given above of the different types of cupcakes and we will get; Total number of cupcakes = 12 + 12 + 12 + 12 + 12

Total number of cupcakes = 60

Now, since there is no order of selection, then the number of ways that you can choose 12 cupcakes will be gotten by using the combination formula which is; nCr = n!/(n!(n - r)!)

Thus, number of ways that you can choose 12 cupcakes =

60C12 = 60!/(12! * (60 - 12)!) = 1399358844975 ways

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Answer:

salary=120000

1/4×120000=30000= money spent

remainder=120000- 30000

= 90000

money spent on clothing =1/2×90000

=45000

Explanation: If his salary is $120,000 and 1/4 is used on food he has a remaining of $80,000. He uses 1/2 on clothing so he has a remainder of $40,000 so now we know that he used $40,000 on clothing

Answer: $40,000

Hope this helps you! :D

Answer: I believe the answer would be as follows:

8.431 grams

5.46 seconds

980 meters

900 miles

Step-by-step explanation:

it would first be which has the largest number after the decimal point, so if there’s three it goes first (0.12*3*). Then you would pick the one that is the smallest form of measurement, which would be meters in this case.

Hope this helped!

The first scatter plot is the only one that does not have a zero correlation.

In this problem, the last three graphs do not have the format of a line, that is, they have zero correlation, and the first scatter plot is the only one that does not have a zero correlation, as the points are in the format of a line.

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Answer:

x > 6

Step-by-step explanation:

2x - 7 > 5

2x > 5 + 7

2x > 12

x > 6

Answer: -49152

Step-by-step explanation: the pattern here is that each term is subtracting 3 times its absolute value. Going from -3 to -12 there is a difference of 9 which is 3 times to absolute value of -3. So, the sequence will continue like this : -192, - 768, -3072, - 12288, -49152.

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Take note that there is a vertical asymptote at x = -4. This means that our function has the form:

▪ [tex]\longrightarrow \sf{F (x)=\dfrac{A}{x + 4} }[/tex]

[tex]\leadsto[/tex] By comparing it with the given options, the correct option is A.

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \bm{A. \: \: F(x)= \dfrac{1}{x + 4} }[/tex]

Step-by-step explanation:

abx^2-aby^2+xya^2-xyb^2

abx^2+xya^2-aby^2-xyb^2

ax(bx+ya)-yb(ay+xb)

ax(bx+ya)-yb(xb+ay)

(ax-yb) (bx+ya)

The solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C

In solving for the values of 'x' we need to:

Given the expression;

1/x =x+3/2x^2

Cross multiply

x ( x+ 3) = 2x² ( 1)

Expand the bracket

x² + 3x = 2x²

collect like terms and equate all the variables to zero, we have ;

2x² - x² - 3x = 0

We then subtract the like terms, we getv

x²- 3x = 0

Now, let's find the common factor

Factor out 'x':

x ( x - 3 ) = 0

Equate each of the factors to zero and find the value of 'x' for each

So,

x = 0

And

x - 3 = 0

x = 3

Thus, the solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C

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The simplest form is 10.

We can find simplest as form:

Given, fractions are [tex]9\frac{1}{6}[/tex] and [tex]1\frac{1}{11}[/tex]

[tex]9\frac{1}{6}\times 1\frac{1}{11}[/tex]

[tex]\frac{55}{6}\times \frac{12}{11}[/tex]

[tex]=\frac{55\times 12}{6\times 11}[/tex]

=10

Hence, simplest form of given fraction is 10.

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Answer:

2.571428

Step-by-step explanation:

The mean absolute deviation of a dataset is the average distance between each data point and the mean.

Plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.

To plot the value(s) on the number line where the given function is equal to zero:

The equation is written as: y = (x+5)(x-1)

This is further written as:

The highest point occurs when x = 0, which is (5)(-1) = -5

Therefore, plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.

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The correct question is given below:

Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).

Answer:

distributive property

Step-by-step explanation:

The answers to the questions are as follows:

We have E = {1, 3,5, 7, 9, 11, 13, 15, 17, 19}

A= { 3, 7, 9, 11, 15}

B = {5, 7, 11, 13}

We have A n B = numbers that are contained in both of the sets

= 7, 11

a.) We have to count the total number in the dataset. That is the total number of odd numbers that are less than 20.

Hence total numbers in the set = 10

b. The probability that the number is in set AnB

= 7, 11

= 2/10

= 1/5

We can conclude that the probability that the number is in A intersect B = 1/5

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Answer:

[tex]\displaystyle{\sin \theta = \dfrac{2ab}{a^2+b^2}}\\\\\displaystyle{\cos \theta = \dfrac{a^2-b^2}{a^2+b^2}}\\\\\displaystyle{\csc \theta = \dfrac{a^2+b^2}{2ab}}\\\\\displaystyle{\sec \theta = \dfrac{a^2+b^2}{a^2-b^2}}\\\\\displaystyle{\cot \theta = \dfrac{a^2-b^2}{2ab}}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle{\tan \theta = \dfrac{2ab}{a^2-b^2}}[/tex]

To find other trigonometric ratios, first, we have to know that there are total 6 trigonometric ratios:

[tex]\displaystyle{\sin \theta = \sf \dfrac{opposite}{hypotenuse} = \dfrac{y}{r}}\\\\\displaystyle{\cos \theta = \sf \dfrac{adjacent}{hypotenuse} = \dfrac{x}{r}}\\\\\displaystyle{\tan \theta = \sf \dfrac{opposite}{adjacent} = \dfrac{y}{x}}\\\\\displaystyle{\csc \theta = \sf \dfrac{hypotenuse}{opposite} = \dfrac{r}{y}}\\\\\displaystyle{\sec \theta = \sf \dfrac{hypotenuse}{adjacent} = \dfrac{r}{x}}\\\\\displaystyle{\cot \theta = \sf \dfrac{adjacent}{opposite} = \dfrac{x}{y}}[/tex]

Since we are given tangent relation, we know that [tex]\displaystyle{y = 2ab}[/tex] and [tex]\displaystyle{x = a^2-b^2}[/tex], all we have to do is to find hypotenuse or radius (r) which you can find by applying Pythagoras Theorem.

[tex]\displaystyle{r=\sqrt{x^2+y^2}}[/tex]

Therefore:

[tex]\displaystyle{r=\sqrt{(a^2-b^2)^2+(2ab)^2}}\\\\\displaystyle{r=\sqrt{a^4-2a^2b^2+b^4+4a^2b^2}}\\\\\displaystyle{r=\sqrt{a^4+2a^2b^2+b^4}}\\\\\displaystyle{r=\sqrt{(a^2+b^2)^2}}\\\\\displaystyle{r=a^2+b^2}[/tex]

Now we can find other trigonometric ratios by simply substituting the given information below:

Hence:

[tex]\displaystyle{\sin \theta = \dfrac{y}{r} = \dfrac{2ab}{a^2+b^2}}\\\\\displaystyle{\cos \theta = \dfrac{x}{r} = \dfrac{a^2-b^2}{a^2+b^2}}\\\\\displaystyle{\csc \theta = \dfrac{r}{y} = \dfrac{a^2+b^2}{2ab}}\\\\\displaystyle{\sec \theta = \dfrac{r}{x} = \dfrac{a^2+b^2}{a^2-b^2}}\\\\\displaystyle{\cot \theta = \dfrac{x}{y} = \dfrac{a^2-b^2}{2ab}}[/tex]

will be other trigonometric ratios.

The probability of getting a Club given that the card is a Ten is 0.25.

According to the statement

we have given that the there is a deck of the 52 cards and we have to find the conditional probability that the card is a club and the given card is a 10 number card.

So, For this purpose we know that the

Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

And according to this,

The probability P is

P(Club) = 13/52 = 1/4

P(Ten) = 4/52 = 1/13

P(Club and Ten) = (1/4)(1/13) = 1/52

And we know that the

P(Club|Ten) = P(Club and Ten)/P(Ten)

And then substitute the values and it become

= (1/52)/(1/13) = (1/52)(13/1)

= 13/52 = 1/4

= 0.25

So, The probability of getting a Club given that the card is a Ten is 0.25.

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The equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at the point  (-6,8) is -6x+8y=100.

Given the equation of circle [tex]x^{2} +y^{2} =100[/tex]

and point at which the tangent meets the circle is (-6,8).

A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.

Linear equation looks like y=mx+c.

Tangent to a circle of equation [tex]x^{2} +y^{2} =a^{2}[/tex] at (z,t) is:

xz+ty=[tex]a^{2}[/tex].

We have to just put the values in the formula above to get the equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex]  at (-6,8).

It will be as under:

x(-6)+y(8)=100

-6x+8y=100

Hence the equation of tangent to the circle at the point  (-6,8) is -6x+8y=100.

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Answer:

Option 3

Step-by-step explanation:

Since the denominators are the same, you can just subtract the numerators.

Answer:

105.

Step-by-step explanation:

x/120 = 56/64   where x is the length of missing segment

64x = 120*56

x =  (120*56)/64

  =  105.

Answer:

The correct answer is the third option: y = 4x - 20

Step-by-step explanation:

To solve this problem, we should first find two points that are located along our line of best fit. We can see that the points (25,80) and (15, 40) are both located along the line. Next, we can calculate the slope using these two points.

slope = rise/run = Δy/Δx = (80-40)/(25-15) = 40/10 = 4

Therefore, the slope of the line of best fit is 4.

To find the y intercept, we can use our equation for slope and plug in one of our points.

y = mx + b

y = 4x + b

40 = 4(15) + b

40 = 60 + b

b = -20

Therefore, the y intercept is -20.

If we put both our slope and y intercept into one equation, we get:

y = mx + b

y = 4x - 20

The correct answer is the third option.

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There is a maximum value of 7/6 located at (x, y) = (5/6, 7).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 10.

Rearranging the constraint, we get:

6x + y = 10,

or, y = 10 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(10 - 6x) = 10x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 10 - 12x ... (i)

Equating to 0, we get:

10 - 12x = 0,

or, 12x = 10,

or, x = 5/6.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.

The value of y, when x = 5/6 is,

y = 12 - 6x,

or, y = 12 - 6*(5/6) = 7.

The value of f(x, y) when (x, y) = (5/6, 7) is,

f(x, y) = xy,

or, f(x, y) = (5/6)*7 = 7/6.

Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).

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Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

The least common multiple of two or more natural numbers is the least common multiple of all of them. This concept has historically been linked to natural numbers, but can be used for negative integers or complex numbers.

We calculate the least common multiple, by simultaneous decomposition, this method consists of extracting the common and non-common prime factors, therefore

L.c.m.(12,15,18)= 2² × 3² × 5 = 180 min

The least common multiple of 12, 15, and 18 is 180.

Convert the minutes to hours, for this we apply the rule of 3:

As the bells all together ring at 6 am, so we add

Answer: The bells are rung together again at 9 in the morning.

▪ [tex]\bold{\dfrac{2x-5}{x^{2} -2}}[/tex]

▪ [tex]\bold{\dfrac{dy}{dx}}[/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

» [tex] \tt{For \: \: y,}[/tex]

[tex]\longrightarrow\sf{y=v \dfrac{2x - 5}{ {x}^{2} - 2} }[/tex]

[tex]\longrightarrow\sf{\dfrac{dy}{dx} = \cfrac{ ( {x}^{2} - 2)(2) - (2x - 5)(2x)}{( {x}^{2} - {2}^{2} )}}[/tex]

[tex]\longrightarrow\sf{\cfrac{2 {x}^{2} - 4 - {4x}^{2} + 10x}{ ({x}^{2} - {2}^{2} )}}[/tex]

[tex]\longrightarrow{={ \boxed{\sf \cfrac{ - 2 {x}^{2} - 4 + 10x}{ ({x}^{2} - {2}^{2} )}}}}[/tex]

» [tex] \tt{At \: \: x = 2,}[/tex]

[tex]\longrightarrow\sf{ \dfrac{ - 2(2) {}^{2} + 10(2) - 4 }{( {2}^{2} - 2 {)}^{2} } }[/tex]

[tex]\longrightarrow\sf{\dfrac{ - 8 + 20 - 4}{4} }[/tex]

[tex]\longrightarrow\sf{ \dfrac{8}{4} }[/tex]

[tex]\longrightarrow{\sf = \boxed{\sf {2}}}[/tex] ✓

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

◆ The value of the given differential function at [tex]\sf{x=2}[/tex] is [tex]\sf{2.}[/tex]

Answer:

The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     [tex]\frac{1}{12}[/tex] turns

9 hours     ⇒     [tex]\frac{1}{12}[/tex]  × 9 = [tex]\frac{9}{12}[/tex]

                                     = [tex]\bf \frac{3}{4}[/tex] turns    (simplified)

∴ The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.

The answer is  [tex]\boxed{\frac{3}{4}}[/tex].

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.

The value of x from the given data is 2

Mean is the ratio of sum of numbers to the total samples. Given the following data

15,19,23,41, and Z

The mean is calculated as

Mean = 15+19+23+41+z/5

Since the mean the of the data is given as 20. Substitute

20 = 15+19+23+41+z/5

Cross multiply

20*5 = 15+19+23+41+z

100 = 15+19+23+41+z

100 = 98 + z

z = 100- 98

z = 2

Hence the value of x from the given data is 2

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To solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.

A quadratic equation is solved using the quadratic formula, [tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex], when the equation is in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.

In the question, we are asked for the first step in solving a² - 5 = -2.

We can see that the provided equation is quadratic in the variable a.

To solve, the equation, we first need to represent the given equation in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.

To represent it in the standard form, we add 2 to both sides of the equation, to get a² - 5 + 2 = -2 + 2, or, a² - 3 = 0, which is a standard quadratic equation in the variable a.

Thus, to solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.

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The events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)

The probability values are given as:

P(A) = 0.3

P(B) = 0.6

P(A or B) = 0.8

For mutually exclusive events, we have:

P(A or B) = P(A) + P(B)

Substitute the known values in the above equation

P(A or B) = 0.3 + 0.6

Evaluate the sum

P(A or B) = 0.9

From the given parameters, we have

P(A or B) = 0.8

Hence, the events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)

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Answer:

D

Step-by-step explanation:

edge 2023

The sum of P(A) and P(B) is not equal to P(A or B).

[4] Answer: (-4, 1)

[5] Answer: Infinite solutions

        See attached for the graphs.

Step-by-step explanation:

      The solution to a system of equations, when graphing, is the point of intersection. In other words, the point at which the lines intersect each other.

      In the case of problem 5, the equations are equal so they overlap. This means there are infinite solutions.