7. A farmer plants 987 apple trees in
9 rows. Can each row have the same
number of trees? How do you know?​

Answer:

  a.  0

Step-by-step explanation:

You want the limit of (k(x) -h(x))/k(x) as x approaches 0 when k(x) = sin(x)/x {x≠0} and h(x)=x+1 {x<1}.

Since we're concerned about the limit as x → 0, we don't have to be concerned with the fact that the expression is undefined at x = 0.

The function h(x) is defined as h(0) = 1, so we can just be concerned with the value of ...

  lim[x→0] (k(x) -1)/k(x)

The limit of k(x) as x → 0 is 1, so this becomes ...

  lim[x→0] (k(x) -1)/k(x) = (1 -1)/1 = 0

At x=0, sin(x)/x is the indeterminate form 0/0, so its limit there can be found using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

  lim[x→0] sin(x)/x = lim[x→0] cos(x)/1 = cos(0) = 1

The fact that k(0) = 0 is irrelevant with respect to this limit.

__

Additional comment

We like to use a graphing calculator to validate limit values. The attachment shows the various functions involved. It also shows that as x gets arbitrarily close to 0 from either direction, the value of g(x) does likewise. This is all that is required for (0, 0) to be declared the limit. The lack of definition of g(x) at x=0 simply means the relation has a (removable) discontinuity there.

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Answer:

2/3 or 0.6

Step-by-step explanation:

Parallel lines problem:

Parallel lines have the same slope, so the answer should give a pair of lines whose slope is equal to that of line m, i.e., 2/3.

The only line that fits the bill is line p, whose slops is (8-6)/(12-9) = 2/3; none of the other lines has a slope of 2/3. Thus, b would be the correct answer here for the first image.

Congruent triangles problem:

Segment ZX and angle Y would be congruent to segment SQ and R, respectively, so the correct answer for the second image would be a.

Answer:

f(x) = 2(x + 3)² + 1 corresponds to graph C.

f(x) = -2(x + 3)² + 1 corresponds to graph D.

f(x) = 2(x - 3)² + 1 corresponds to graph A.

f(x) = -2(x + 3)² - 1 corresponds to graph B.

Step-by-step explanation: hope its right

Answer:

1256.64 square feet

Step-by-step explanation:

In this situation, 20 feet is the radius of the circle that is sprayed.

Use the area formula, A = \(\pi\)r²

Plug in 20 as the radius and solve:

A = \(\pi\)r²

A = \(\pi\)(20)²

A = 400\(\pi\)

This is approximately equivalent to 1256.64

So, the approximate area watered by the sprinkler is 1256.64 square feet

The answers to the given arithmetic problems are- (a) [3] + [4] 7 ] = 7, (b) [2] . ([2] + [7]) 2 ]] = 4, and (c) ([6] + [5]). ([3] + [7]) = 110.

Here, we are given three equations as follows, let us solve them one by one-

a. [ [3] + [4] 7 ]

Here [z] = remainder when z is divided by 8

Thus, [4] = 4

⇒ [ [3] + 4*7 ]

= [ 3 + 28 ]

= [ 31 ]

= 7

b.  [ [2] . ([2] + [7]) 2 ]

=  [ 2 . (2 + 7) 2 ]

= [ 2*9*2 ]

= [ 36 ]

= 4

c. ([6] + [5]). ([3] + [7])

= (6 + 5). (3 + 7)

= 11*10

= 110

The answers to the given arithmetic problems are- (a) [3] + [4] 7 ] = 7, (b) [2] . ([2] + [7]) 2 ]] = 4, and (c) ([6] + [5]). ([3] + [7]) = 110.

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Answer:

a) The differential equation for the velocity is given by

(dv/dt) = k(250 - v)

b) v(t) = 250 - e⁽⁵•⁵² ⁻ ᵏᵗ⁾

With units of km/h

Step-by-step explanation:

Acceleration, a ∝ (250 - v)

But acceleration is widely given as dv/dt

(dv/dt) ∝ (250 - v)

(dv/dt) = k(250 - v)

where k = constant of proportionality

(dv/dt) = k(250 - v)

b) (dv/dt) = k(250 - v)

dv/(250 - v) = k dt

∫ dv/(250 - v) = ∫ k dt

- In (250 - v) = kt + c (where c is the constant of integration)

v(0) = 0; meaning, at t = 0, v = 0

- In 250 = 0 + C

c = - In 250 = - 5.52

- In (250 - v) = kt - 5.52

In (250 - v) = 5.52 - kt

250 - v = e⁽⁵•⁵² ⁻ ᵏᵗ⁾

v = 250 - e⁽⁵•⁵² ⁻ ᵏᵗ⁾

With units of km/h

i hope this work for you

and sory if im wrang

The length of the longer ladder is 50 ft. Therefore, the answer is D.

Two ladders are leaning against the wall as shown below. The length of the longer ladder can be found as follows:

The triangles formed are right angle triangle. The triangles are similar to each other.

Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.

Therefore, using proportion,

15 / x = 3 / 10

cross multiply

150 = 3x

divide both sides by 3

x = 150 / 3

x = 50

Therefore,

length of the ladder = 50 ft

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The total number of boxes that can be loaded onto the trailer is 27.

Here we have to determine the maximum number of boxes.

That can be stored in a locker by the volume of one box.

From the given information volume of the box is Vb and the volume f the locker is Vl.

\(Volume=Length\times width\times height\)

Therefore we get,

\(V_b=4\times3\times2\\V_b=24ft^3\)

The volume of the locker is

\(V_L=12\times6\times 9\\V_L=684ft^3\)

Therefore the number of the maximum boxes are

\(\frac{VL}{V_b} =\frac{648}{24} \\=27\)

Therefore, The total number of boxes can be loaded onto the trailer are 27.

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To find the trigonometric substitution for ∫ (81+x^2)^−5 dx, we can use x = 9tanθ.
This substitution is useful because it allows us to rewrite the expression in terms of trigonometric functions, which we can then integrate using trigonometric identities.
Therefore, X(θ) = 9tanθ.

To find the indefinite integral of the given function using trigonometric substitution, you'll need to choose an appropriate substitution. For the integral ∫ (81+x^2)^−5 dx, we can use the substitution:

x(θ) = 9 * tan(θ)

This is because we can relate x^2 to a trigonometric identity. After substituting, you would proceed with integration, but since you asked to not integrate, I'll stop here. So the trigonometric substitution for this problem is:

x(θ) = 9 * tan(θ)

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Answer:

decision alternatives

Step-by-step explanation:

uhhh yea thats pretty much it -

The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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Confounding may invalidate the conclusions of the study as it can cause a bias that can make the effect of the explanatory variable look larger or smaller than it actually is.

This means that the relationship between alcohol drinking status and incidence of lung cancer is influenced by  After the classification of smokers and non-smokers, a separate analysis can be done to find the effect of alcohol drinking on lung cancer in both groups.

Explanatory and Confounding Variable in the study :In the given study, the explanatory variable is obesity and the response variable is coronary disease. Whereas, the confounding variable is hypertension and diabetes because these diseases are associated with obesity. The confounding variable can invalidate the conclusions of the study as it can affect the relationship between obesity and coronary disease .To eliminate the effect of the confounding variable, the study can be changed in the following ways.

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To find the marginal density of X/Y, we need to integrate the joint density function fXY(x, y) over the range of Y. By performing the integration, we obtain the marginal density of X/Y as a function of X. The resulting marginal density provides information about the distribution of the ratio X/Y.

The marginal density of X/Y can be obtained by integrating the joint density function fXY(x, y) over the range of Y. In this case, the joint density function is given by:

fXY(x, y) =

  24xy    if x >= 0, y >= 0, and x + y <= 1

  0       otherwise

To find the marginal density of X/Y, we integrate fXY(x, y) with respect to y, while keeping x as a constant. The integration limits for y can be determined based on the given conditions x >= 0, y >= 0, and x + y <= 1. Since y must be non-negative, the lower limit of integration is 0. The upper limit of integration can be determined by the constraint x + y <= 1, which implies y <= 1 - x.

Integrating fXY(x, y) over the range of y, we obtain the marginal density of X/Y as follows:

fX/Y(x) = ∫[0 to (1 - x)] 24xy dy

Evaluating the integral, we have:

fX/Y(x) = 24x * ∫[0 to (1 - x)] y dy

       = 24x * [(y^2)/2] evaluated from 0 to (1 - x)

       = 12x * (1 - x)^2

The resulting marginal density fX/Y(x) represents the distribution of the ratio X/Y. It provides information about the likelihood of different values of X/Y occurring. The shape of the distribution can be further analyzed to understand the characteristics of the random variable X/Y.

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The distance from -4 to 1 is 5 units.

The correct number line and expression to find the distance from -4 to 1 are:

Number line: -4 -3 -2 -1 0 1

Expression: |-4 - 1|

To find the distance, we subtract the smaller number (-4) from the larger number (1) and take the absolute value:

|-4 - 1| = |-5| = 5

Therefore, the distance from -4 to 1 is 5 units.

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The simplified form of the expression is -11/9

These are expressions written as fractions. Given the following fraction

\(\dfrac{\frac{5}{8} +\frac{3}{4} }{\frac{-2}{3}-\frac{5}{6} }\)

Find the LCM of the numerator and denominator

\(\dfrac{\frac{5}{8} +\frac{3}{4} }{\frac{-2}{3}-\frac{5}{6} }\\\dfrac{\frac{5+6}{8} }{\frac{-4-5}{6} } \\\dfrac{\frac{11}{8} }{\frac{-9}{8} }\)

Divide the result to have:

11/8÷-9/8

11/8 *  8/-9
-11/9

Hence the simplified form of the expression is -11/9

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

The ratio 9 to 12 is greater than 4 to 6

Step-by-step explanation:

9÷12=0.75

4÷6=0.67

0.75> 0.67

Answer:

n=15.1

Step-by-step explanation:

14.8=n-0.3

14.8+0.3=n

15.1=n

The require degenerative circle is (x - 5)² + (y - 1)² = 0. Option C is correct.

Given that,  
The equation for the degenerative circle is to be determined.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.

The degenerative circle is a circle whose radius is zero, from the option,
Option C has the equation of the circle with radius zero.

Thus, the required degenerative circle is (x - 5)² + (y - 1)² = 0.

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Step-by-step explanation:

Initially, there's only 1 letter.

Tania sends the letter to 4 friends.

Each friend sends a letter to 4 more friends (4 × 4 = 16).

Each of those friends sends to 4 more friends (16 × 4 = 64).

The pattern is 1, 4, 16, 64, etc.

This is a geometric sequence.  The first term is 1 and each term is 4 times the previous term.

a₁ = 1

aₙ = 4 aₙ₋₁

The explicit formula is:

aₙ = 1 (4)ⁿ⁻¹

Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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From the calculations using the data provided, the acceleration of the ball is 10 m/s^2

We know that the acceleration is the rate at which there is an increase or a decrease in the velocity of a body. In this case, we are told that A ball is released from rest and falls 125 meters in 5 seconds.

We have the following;

Distance of the object = 125 meters

Time taken =  5 seconds

Given that;

s = ut + 1/2at^2

u = 0 m/s because it was released from rest

s = 1/2at^2

a = 2s/t^2

a = 2(125)/(5)^2

a = 250/25

a = 10 m/s^2

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If water is being pumped into the trough at 2 cubic feet per minute, then the water level rising (in feet per minute) when h is 1.6 foot deep is 0.1 feet cubic per minute.

Suppose that we have a function y = f(x), and wish to find the rate of change of y with respect to a third variable t, where we do not have y expressed explicitly in terms of t. We use the chain rule in differentiation to find this rate of change in a process called implicit differentiation.

                     dy/dt = dy/dx × dx/dt

If base is equal to the height, by similar triangles:

Volume v = base x height x length/2

                = bhl/2

                = h²12/2

                = 6h².

Therefore,  

dv/dt = 12hdh/dt

         = 2 ft³/min

 Now,

dh/dt = 2/(12h)

when h = 1.6,

dh/dt = 2/(12 × 1.6) ≈ 0.1 ft³/min

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Answer:

See below

Step-by-step explanation:

Using the table of 150 students, we can configure probabilities.

18 students participate in tennis, so the probability of a student participating in tennis is 18/150, or 3/25 simplified.

45 students participate in football, so the probability of a student participating in football is 45/150, or 3/10 simplified.

12 students participate in gymnastics, so the probability of a student participating in gymnastics is 12/150, or 2/25 simplified.

9 students participate in volleyball, so the probability of a student participating in volleyball is 9/150, or 3/50 simplified.

Answer:

11 is the median of the entire data set

6 is the median of the lower half and 16 is the median of the upper half data scores...

Subtract 16 from 6 gives 10 so the answer is C) 10

=============================================================

Explanation:

The first step is to sort the data from smallest to largest. Luckily, that's already been done for us.

Next, we find the median. This is the middle most number of the set. In this case, the median is 11 since we have 3 values below it (2,6,7) and 3 values above it (15,16,17).

Let

L = {2,6,7}

U = {15,16,17}

where L and U are the lower and upper sets respectively.

In other words, anything in set L is lower than the median while anything in set U is above the median. The median itself (11) is not part of either set.

Notice how 6 is the midpoint of set L, while 16 is the midpoint of set U.

This means Q1 = 6 and Q3 = 16

Therefore,

IQR = Q3 - Q1

IQR = 16 - 6

IQR = 10

which is why choice C is the final answer.

SOLUTION

We want to use the information in the diagram to prove that

Now, we have been given for number 1

2.

3.

4.

5.

6.

7.

8.

9. and 10. is good (correct)

11.

12.

13.

14.

The vector z in the component form is z = < 21 , 24 , -27 >

Given data ,

A vector in component form is typically written as an ordered pair or triplet, where each component represents the magnitude of the vector along a specific coordinate axis.

Now , the vector u = < -1 , 3 , 1 >

v = < 4 , -3 , -1 >

w = < 10 , 5 , -10 >

Now , the value of vector z = < 3w - 2v + u >

z = 3w - 2v + u

z = 3w - 2 * < 4 , -3 , -1 > + < -1 , 3 , 1 >

Using scalar multiplication, we get:

z = < 30 , 15 , -30 > - < 8 , -6 , -2 > + < -1 , 3 , 1 >

Adding vectors, we get:

z = < 30 - 8 - 1 , 15 - (-6) + 3 , -30 + 2 + 1 >

z = < 21 , 24 , -27 >

Hence , the vector z in component form is z = < 21 , 24 , -27 >

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Answer:

23

Step-by-step explanation:

The circumference of the circle to the nearest hundredth is 21.98 inches.

The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.

The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.

The circumference of the circle can be found as follows:

circumference of a circle = 2πr

where

Therefore,

diameter of the circle = 7 inches

radius of the circle = 7 / 2 = 3.5 inches

Hence,

circumference of a circle = 2 × 3.14 × 3.5

circumference of a circle = 21.98 inches

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