A bakery sells pastries in boxes of 7 each. If the bakery has 27 pastries, how many boxes can be filled?​

The limit of the given function as x approaches 1 is 0.

To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:

1. Begin by substituting x = 1 into the numerator:

\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)

2. Now, substitute x = 1 into the denominator:

(1³ + 5)(1 - 1) = 6(0) = 0

3. Finally, divide the numerator by the denominator:

0/0

The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:

4. Take the derivative of the numerator:

\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)

5. Take the derivative of the denominator:

\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)

6. Substitute x = 1 into the derivatives:

Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)

Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6

7. Now, reevaluate the limit using the derivatives:

lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)

= 0 / 6

= 0

Therefore, the limit of the given function as x approaches 1 is 0.

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Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).

To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.

With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.

Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.

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Answer:

c

Step-by-step explanation:

Answer:

The 3rd graph

Step-by-step explanation:

The equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is 16 = 2 1/2 + 2 1/4b (option b)

To start with, we know that the farmer picks 16 quarts of berries. Out of those, 2 1/2 quarts cannot be used, which means the farmer has 16 - 2 1/2 quarts of berries that can be used to make jam.

Now, the recipe requires 2 1/4 quarts of berries to make one batch of jam. Let's represent the number of batches of jam the farmer can make with the remaining berries as "b".

Therefore, the equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is written as,

=> 16 = 2 1/2 + 2 1/4b

Hence the correct option is (b).

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The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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Answer:

don't believe the other guy he is a scaming bot don't click the link

Since, Z(0)>Z(0.1) that is 3.07>1.28. So reject H(0). So the option 1 and 3 is correct.

In the given question,

H(0): μ=18 ; H(a): μ>18

x = 19.1

Conclude whether to reject or not reject H(0), and interpret the results.

σ = 1.6

α  = 0.1 (significance level) .

The test statistic is

Z(0) = {x-μ(0)}/(σ/√n)

Z(0)= (19.1-18)/16/√20

Z(0) = 3.07

The critical value is Z(0.1) = 1.28.

As we can see that;

Z(0)>Z(0.1) that is

3.07>1.28

So reject H(0).

So the option 1 and 3 is correct.

Reject H(0), the test statistic Z(0)=3.07 is Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.

And

The test statistic falls within the rejection region.

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The right question is:

Select two responses below.

Select all that apply:

(1) Reject H(0). The test statistic Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.

(2) Fail to reject H(0). The test statistic Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.

(3) The test statistic falls within the rejection region.

(4) The test statistics is NOT in the rejection region.

The equation y² - y²x = 6  can be describe as a function of x as:

y = √(6/(x - x)).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y² - y²x = 6

Taking y² as common.

y²(1 - x) = 6

Divide both sides with (1 - x).

y² = 6/(1 - x)

Square root on both sides.

y = √(6/(x - x))

This is a function of x.

Thus,

y = √(6/(x - x)) is a function of x.

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Answer:

8(7 + 4) = 88

Step-by-step explanation:

56:

1 x 56

2 x 28

4 x 14

7 x 8

32:

1 x 32

2 x 16

4 x 8

Answer:

8(7+4)

Step-by-step explanation:

Answer:

no, it does not equal -6

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'll try to make this make as much sense as possible. If we have a cone with a liquid in it, this liquid takes up volume. Therefore, our main equation, at least at first, is to find the volume. This is because if we pump the liquid out of the tank, the thing that changes is the amount of liquid in the tank which is the tank's volume. The formula for the volume of a circular cone is

\(V=\frac{1}{3}\pi r^2h\)  and here's what we know:

r = 2 and h = 8. The formula for volume has too many unknowns in it, so let's get the radius in terms of the height and sub that in so we only have one variable. The reason I'm getting rid of the radius is because in the problem we are being asked how much work is done by pumping the liquid to the top of the tank, which is a height thing. Solve for r in terms of h using proportions:

\(\frac{r}{2}=\frac{h}{8}\) and solve for r:

\(r=\frac{2}{8}h =\frac{1}{4}h\) so we will plug that in and rewrite the equation:

\(V=\frac{1}{3}\pi(\frac{1}{4}h)^2h\) and simplify it til it's a simple as it can get.

\(V=\frac{1}{3}\pi(\frac{1}{16}h^2)h\) and

\(V=\frac{\pi}{48}h^3\) and since the volume is what is changing as we pump liquid out, we find the derivative of this equation.

\(\frac{dV}{dt}=\frac{\pi}{48}*3h^2\frac{dh}{dt}\) and of course this simplifies as well:

\(\frac{dV}{dt}=\frac{\pi}{16}h^2\frac{dh}{dt}\)

Work is equal to the amount of force it takes to move something times the distance it moves. In order to find the force it takes to move this liquid, we need to multiply the amount (volume) of liquid times the weight of it, given as 1000 kg/m³:

F = \(1000(\frac{\pi}{16}h^2\frac{dh}{dt})\) and the distance it moves is 8 - h since the liquid has to move the whole height of the tank in order to move to the top of the 8-foot tank. That makes the whole integral become:

\(W=\int\limits^8_0 {1000(\frac{\pi}{16}h^2(8-h)) } \, dh\) and we'll just simplify it down all the way:

\(W=62.5\pi\int\limits^8_0 {8h^2-h^3} \, dh\) and you're done (except for solving it, which is actually the EASY part!!)

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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The solution for the expression is (35y - 22)/(5y-8)(10y+1). The solution has been obtained by solving the algebraic expression.

What is algebraic expression?

An algebraic expression is one that uses variables, constants, and algebraic operations (addition, subtraction, etc.).

The four primary categories of expressions are as follows:

We are given

⇒(2/5y -8)+ (3/10y+1)

⇒(2(10y+1) + 3(5y -8))/(5y-8)(10y+1)

⇒(20y + 2 + 15y - 24)/(5y-8)(10y+1)

⇒(35y - 22)/(5y-8)(10y+1)

Hence, the solution for the expression is (35y - 22)/(5y-8)(10y+1).

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Answer:

# of broken crayons    # of boces

           1-5                            1

          6-10                          4

          11-15                          5

          16-20                        3

          21-25                         1

Step-by-step explanation:

1-5: 4 (1 number)

6-10: 6, 6, 8, 9 (4 numbers)

11-15: 12, 13, 14, 14, 15 (5 numbers)

16-20: 17, 17, 19 (3 numbers)

21-25: 24 (1 number)

Answer:

Number of broken crayons Number of boxes

1-5 = 4

6-10 = 9

11-15 = 14

16-20 =19

21-25 =24

Step-by-step explanation:

To find the number of boxes compared to the number of broken crayons you have to find 5 consecutive (hence there being five boxes to fill in) numbers with a constant rate of change. Start with the largest number possible that you can pick and then find the second largest so 24 and 19 the rate of change is 5. Compared to 17 and 19 the rate of change is 2 so it doesn’t have the same rate of change but if you try 19-5 you get 14 which is an option if you subtract 14-5 you get 9 which is another option 9-5 is 4 the lowest number you could possibly pick and they all have a constant rate of change of 5 so the answer is correct.

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:

(1,2) and (x-2)-3 should be on the graph

Step-by-step explanation:

The camera must turn at a rate of about 53.67 degrees/s to follow the ball at an angle of 15 degrees.

In this issue, we are given the underlying speed of the football and the distance of the television camera from the way of the football. We really want to find the rate at which the camera should go to follow the ball at a specific point theta=15 degrees. We can utilize geometry to take care of this issue. The point between the way of the ball and the line associating the camera and the ball is given by 90 - 15 = 75 degrees. Utilizing the cosine capability, we can find the part of the speed of the football opposite to the camera, which is 56*cos(15) = 53.17 ft/s. Presently, utilizing the digression capability, we can find the rate at which the camera should go to follow the ball, which is (53.17/92)*tan(75) = 0.937 radians/s or roughly 53.67 degrees/s. In this manner, the camera should turn at a pace of around 53.67 degrees/s to follow the ball at a point of 15 degrees.

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The complete question is:

A football is thrown horizontally (very little arc) at 56 ft./s parallel to the sideline. A TV camera is 92 ft. from the path of the football. Find de/dt, the rate at which the camera must turn to follow the ball when θ = 15°. football TV camerao 92 ft.

Orbital period of the planet is 2√2 earth years

According to Kepler's third law, the square of a planet's orbital period is proportional to the cube of its semi major axis.  

T² α a³

where, T is orbital period and a is length of semi-major axis.

Given,

Distance between the sun and the planet

= twice the distance of sun and earth

Let distance between sun and earth a₁ = d

then distance between planet and sun a₂= 2d

Orbital period of earth T₁ = 1 earth year

By Kepler's third law

T² α a³

(T₁/T₂)² = (a₁/a₂)³

(1/T₂)² = (D/2D)³

1/T₂² = 1/8

T₂ = 2√2 earth years

Hence, 2√2 earth years is the orbital period of other planet.

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The exponential formula that shows population is y = y₀ (1.031)ˣ.

An exponential function is a function which can be defined as y = y₀ aˣ, Where 'x' is a variable and 'a' is a constant.

Given that,

The growth of population is exponential.

Also,

The initial population y₀ = 3190.

And after 4 year the population y = 3605.

Use exponential formula

y = y₀ aˣ     (1)

Where x = time

Substitute the values in the formula,

3605 = 3190 a⁴

3605/3190 = a⁴

1.13009  = a⁴

a = 1.031

Substitute the value of a in equation (1),

y = y₀ (1.031)ˣ

The required formula is y = y₀ (1.031)ˣ.

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Answer: The slope is $70

Step-by-step explanation: Slope is rate of change, so define your values.

-$100 is the initial fee

-$70 is charged per month

per month is the constant rate of change

70 is the slope

hope this helps

Answer:

-1040 feet

Step-by-step explanation:

Since the altitude decreases at 40 feet per second, we can find the change in altitude by multiplying -40 by the number of seconds:

So, multiply -40 by 26:

-40(26)

= -1040

So, the change in altitude will be -1040 feet

Answer:

$61.29 per day.

Step-by-step explanation:

Checking account balance on February 1st: $443

Checking account balance on February 7th: $872

Difference in balances: $872 - $443 = $429

Number of days between February 1st and February 7th: 7 days

Rate of change = Difference in balances / Number of days

Rate of change = $429 / 7 days

To find the rate of change per day, divide the difference in balances by the number of days:

Rate of change = $429 / 7 days ≈ $61.29 per day

Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.

Answer:

the value of m will be 20

Answer:

I think 1.identity property of addition is answer

We can divide the number by prime numbers until we get a prime at last. Then we multiply the prime factors to get the number.

The process is shown below:

Thus, we can write 2 x 3 x 7 as the prime factorization of 42.

The volumes of the figures are 65.94 m³, 3052.08 cm ³, 100.48 in³, 314 mm³, 602.88 ft³, 1766.25 m³, 381.51 ft³, 50.24 m³ and  9.42 in³

Figure 1: Cone

The volume is calculated as

V = 1/3πr²h

So, we have

V = 1/3 * 3.14 * 3² * 7

V = 65.94 m³

Figure 2: Sphere

The volume is calculated as

V = 4/3πr³

So, we have

V = 4/3 * 3.14 * *(18/2)³

V = 3052.08 cm ³

Figure 3: Cylinder

The volume is calculated as

V = πr²h

So, we have

V = 3.14 * 2² * 8

V = 100.48 in³

Figure 4: Cone

The volume is calculated as

V = 1/3πr²h

So, we have

V = 1/3 * 3.14 * (10/2)² * 12

V = 314 mm³

Figure 5: Cylinder

The volume is calculated as

V = πr²h

So, we have

V = 3.14 * (8/2)² * 12

V = 602.88 ft³

Figure 6: Sphere

The volume is calculated as

V = 4/3πr³

So, we have

V = 4/3 * 3.14 * 7.5³

V = 1766.25 m ³

Figure 7: Sphere

The volume is calculated as

V = 4/3πr³

So, we have

V = 4/3 * 3.14 * (9/2)³

V = 381.51 ft ³

Figure 8: Cylinder

The volume is calculated as

V = πr²h

So, we have

V = 3.14 * 2² * 4

V = 50.24 m³

Figure 9: Cone

The volume is calculated as

V = 1/3πr²h

So, we have

V = 1/3 * 3.14 * 1² * 9

V = 9.42 in³

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Answer:

here is ur answer....OPTION "D"

Step-by-step explanation:

Answer:

35.6

Step-by-step explanation:

By the Pythagorean Theorem:

\( {x}^{2} + {91.3}^{2} = {98}^{2} \)

\(x = \sqrt{ {98}^{2} - {91.3}^{2} } = 35.6\)

Answer:

-2/3 is slope and y-intercept is 5