I really need help ​

The length of the garden will be 14.75 feet.

It was illustrated that the dad has 26 feet of fencing to go around the garden.

Also, the person wants the length of the garden to be 3 1/2 feet longer than the width.

Let the width be given as x.

Therefore the length will be x + 3.5

This will be illustrated as:

x + x + 3.5 = 26

2x + 3.5 = 26

Collect like terms

2x = 26 - 3.5

2x = 22.5

Divide

x = 22.5 / 2

x = 11.25

Therefore, the length will be:

= x + 3.5

= 11.25 + 3.5

= 14.75 feet.

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Jamie's annual interest rate is 5%.

To find Jamie's annual interest rate, we need to consider the relationship between the quarterly interest payments and the loan amount. Let's break it down step by step:

1. We know that Jamie's quarterly interest payments are $150. Since there are four quarters in a year, the total annual interest payments can be calculated by multiplying the quarterly payments by four: $150 * 4 = $600.

2. Now, let's determine the interest rate. We have the annual interest payment, but we need to express it as a percentage of the loan amount. The formula to calculate interest rate is (Interest Payment / Loan Amount)  100.

3. Substituting the values into the formula, we have ($600 / $12,000)

100 = 0.05  100 = 5%.

Therefore, Jamie's annual interest rate is 5%.

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The maximum error in the area is 33.933 sq cm. The relative error is 0.0148. The percent error will be 1.48%.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

1)  A = pi(r²)

dA = 2(pi)r(dr)

= 2(3.14)(27)(0.2) sq cm

= 33.93 sq. cm

2)  Relative error is the above divided by actual area

actual area=3.14*27*27

=2289.06 sq cm

Relative error=0.0148

3) % error -- convert the above to a % by appropriate shifting of decimal point

% error=0.0148*100

=1.48%

The area's largest inaccuracy is 33.933 sq cm. 0.0148 is the relative inaccuracy. There will be a 1.48% error percentage.

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The probability that the plant died because the neighbor forgot to water it is (1 - q) x (1 - %).

Let p = the probability that the plant will die without water, q = the probability that the plant will die with water, and r = the probability that the neighbor will remember to water the plant.

The probability that the plant died because the neighbor forgot to water it is equal to the probability that the plant would have survived had the neighbor remembered to water it, multiplied by the probability that the neighbor did not remember to water it.

P(plant died due to neighbor not watering) = P(plant survived with neighbor watering) x P(neighbor not remembering)

= (1 - q) x (1 - r)

= (1 - q) x (1 - % certain the neighbor will remember)

= (1 - q) x (1 - % certain)

= (1 - q) x (1 - %)

Therefore, the probability that the plant died because the neighbor forgot to water it is (1 - q) x (1 - %).

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the normal and shearing stresses will be 11.054 KiPs and 0 respectively.

What is shearing stress?

An object experiences deformation when an external force works upon it. if the force's direction is parallel to the object's plane. Along that plane, there will be a distortion. The object in this instance is under shear or tangential stress.

shear force(v) = 6sin 35 = 3.44 KiPs

Amal borce(P) = 6cot 35 = 4.91 kiPA

moment (m) =3.44 (16) - 4-91(8) = 15.72kiPA

for point a)

no mal stress (r) = P/a +m/I (y)

= 4.91 /(3.08) + (15 .72)/((0.8 * 33)/12) (-5 )

=2.04-13.1

11.054 KiPs

shear stress will be 0.

Hence the normal and shearing stresses will be 11.054 KiPs and 0 respectively.

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Answer:hour 1 500, hour 2 1000, hour 3 2000 , hour 4 4000

Step-by-step explanation:

After 1 hour 500 bacteria split into 500 bacteria.

After 2 hour 500 bacteria split into 1000 bacteria.

After 3 hour 500 bacteria split into 1500 bacteria.

After 4 hour 500 bacteria split into 2000 bacteria.

Given that,

In a biology lab, 500 bacteria reproduce by splitting.

Every hour, on the hour, each bacterium splits into two bacteria.

We have to find,

Find the number of bacteria after 4 hours.

According to the question,

Let us assume n = the number of bacteria at a given hour.

Total number of bacteria = 500

       So,  n(4)  = 4 × 500 = 2000 bacteria

       After 4 hour 500 bacteria split into 2000 bacteria.

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Based on the behavior of the terms, the series ∑n=1∞ (−1)nsin(9n) diverges.

To determine whether the series ∑n=1∞ (−1)nsin(9n) converges or diverges, we can analyze its behavior.

The series involves alternating signs with the term (−1)n and the function sin(9n).

For a series to converge, it must satisfy two conditions:

1.   The individual terms of the series must approach zero as n approaches infinity.

2.   The series must exhibit an overall pattern or behavior that allows the sum to converge.

Let's analyze the behavior of the terms in the series:

As n increases, the term (−1)n alternates between positive and negative values. The function sin(9n) oscillates between -1 and 1 as n increases.

Since sin(9n) oscillates indefinitely between -1 and 1 without approaching zero, the terms of the series do not converge to zero as n approaches infinity.

Therefore, based on the behavior of the terms, the series ∑n=1∞ (−1)nsin(9n) diverges.

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Answer:

  P(t) = 23400/(1 +e^(-35.1t))

Step-by-step explanation:

You want the solution of the logistic differential equation dP/dt = P(35.1-0.0015P) with initial condition P(0) = 936.

The generic solution to p' = p(a -bp) with p(0) = c is ...

  p = (a/b)/(1 +(a/(bc) -1)e^(-at))

For a = 35.1, b = 0.0015, c = 936, we have the coefficients ...

  a/b = 35.1/0.0015 = 23400

  a/(bc) -1 = 23400/936 -1 = 24

That means the solution equation is ...

  P(t) = 23400/(1 +24e^(-35.1t))

P(t) = e^(35.1t - 0.00075P² + C). The logistic differential equation you provided is dP/dt = P(35.1 - 0.0015P) with an initial condition P(0) = 936. To solve this equation, we will use the method of separation of variables.

First, separate the variables P and t by dividing both sides by P(35.1 - 0.0015P):

(1/P) dP = (35.1 - 0.0015P) dt.

Now, integrate both sides with respect to their respective variables:

∫(1/P) dP = ∫(35.1 - 0.0015P) dt.

The left side is a simple integration, resulting in ln|P| + C₁. The right side requires integration by parts, which yields 35.1t - 0.00075P² + C₂. Combining the constants of integration, we get:

ln|P| = 35.1t - 0.00075P² + C.

Now, exponentiate both sides to remove the natural logarithm:

P = e^(35.1t - 0.00075P² + C).

To find the constant C, use the initial condition P(0) = 936:

936 = e^(35.1(0) - 0.00075(936)² + C).

Solve for C, and then plug it back into the equation:

P(t) = e^(35.1t - 0.00075P² + C).

This equation represents the solution to the given logistic differential equation with the specified initial condition. Note that the actual values for C and the final equation form may require further calculations based on the integration steps.

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The calculated vectors are:

\(\vec{A}-\vec{B}\)=(3,-5,-4)

\(\vec{B}-\vec{C}\)=(-5,4,0)

\(-\vec{A}+\vec{B}-\vec{C}\)=(-6,4,3)

\(3 \vec{A}-2 \vec{C}\)=(-3,-2,-11)

Generally, the equation for is  mathematically given a

\(\vec{V}+\vec{W}=\left(V_1, V_2, V_3\right)+\left(W_1, W_2, W_3\right)\\\\\vec{V}+\vec{W}=\left(V_1+W_1, V_2+W_2, V_3+W_3\right) \text { }\)

\(\vec{V}-\vec{W}=\left(V_1, V_2, V_3\right)-\left(W_1, W_2, W_3\right)\\\\\vec{V}-\vec{W}=\left(V_1-W_1, V_2-W_2, V_3-W_3\right)\)

\(\alpha \cdot \vec{V}=\alpha \cdot\left(V_1, V_2, V_3\right)\\\\\alpha \cdot \vec{V}=\left(\alpha \cdot V_1, \alpha \cdot V_2, \alpha \cdot V_3\right)\)

\(\vec{A}-\vec{B}=(1,0,-3)-(-2,5,1)\\\vec{A}-\vec{B}=(3,-5,-4) \\\\&\vec{B}-\vec{C}=(-2,5,1)-(3,1,1)\\&\vec{B}-\vec{C}=(-5,4,0) \\\\&-\vec{A}+\vec{B}-\vec{C}=-(1,0,-3)+(-2,5,1)-(3,1,1)\\-\vec{A}+\vec{B}-\vec{C}=(-6,4,3) \\\\&3 \vec{A}-2 \vec{C}=3(1,0,-3)-2(3,1,1)\\3 \vec{A}-2 \vec{C}=(3,0,-9)-(6,2,2)\\3 \vec{A}-2 \vec{C}=(-3,-2,-11)\)

In conclusion,

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CQ

In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A rightarrow = (1,0, -3), rightarrow = (-2,5,1), and C rightarrow = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.

The derivative of the given function is approximately equal to x/((1-x²)^(3/2)(1-x²)).

In calculus, the derivative of a function is a measure of the rate at which the function changes with respect to its input variable. It represents the instantaneous rate of change of the function at a particular point.

To find the derivative of the given function, we can use the chain rule of differentiation. Let's start by expressing y in terms of the natural logarithmic function:

y = tanh⁻¹(√(1-x²))/2ln(e)

Using the chain rule, we have:

dy/dx = [1/(1-√(1-x²)²)] * (-1/2) * [1/ln(e)] * (-2x/((1-x²)^(3/2)))

Simplifying this expression, we get:

dy/dx = x/((1-x²)^(3/2)ln(e(1-x²)))

Now, we can simplify the expression further by using the identity:

ln(e(1-x²)) = 1-x²

Substituting this value in the above expression, we get:

dy/dx = x/((1-x²)^(3/2)(1-x²))

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The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer:

\(10^3\)

Step-by-step explanation:

An easy way to get exponents done if you're dealing with a multiple of 10, is to count the number of 0's present.

Since there are 3 0's in 1000, 10*10*10 = 1000 which just so happens to be the exponent needed

If we change the 0's to negative numbers then the average, median and SD. The average would b) decrease.

The average value calculated within a specific data set is referred to as the "mean.". This calculation can be used in any situation where knowing a data set's average value, such as its cost or income, may be deemed as useful.

By being aware of the average cost or income within a given data set, you can better position yourself to increase your profits or savings.

A normal distribution can have a mean that is negative in nature. When only some of the data points have negative values, this is both a possibility and a foregone conclusion;

however, if all of the data points have negative values as nature it should be noted that if a normal distribution has a negative mean, at least half of the data points in the distribution must also have a negative mean.

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Note that the full question is:

some of the girls with 0 weight gain actually lost weight. if we changed their 0's to negative numbers how would the average, median and sd change? the average would

a) increase

b) decrease

c) stay the same

Step-by-step explanation:

100+14.75%

100+14=114

=114.75%

Step-by-step explanation:

i probably didn't explain this too well, but I hope it helps

the answers are in blue

The length 20 inches of the icicle in feet is 1 2/3 feet

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

Jessica found an icicle 20 inches long.

This means that

Length = 20 inches

To convert inches to feet, we divide the length value by 12

So, we have

Length = 20/12 feet

Evaluate

Length = 1 2/3 feet

Hence, the length is 1 2/3 feet

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Step-by-step explanation:

$3.68 for 16 pens

$3.68 per 16 pens

($3.68) / (16 pens)  

$0.23 / (1 pen)

$0.23 / pen

$0.23 per pen

Answer: $0.36

Step-by-step explanation:

Because you divide $2.16 & 6 to get it.

Answer:

legend

Step-by-step explanation:

Answer:

1.0954.

Step-by-step explanation:

Standard error  =  std dev / √n

=  6 / √30

= 1.0954.

David can best improve his investigation by including a control group. A control group is a group that does not receive any treatment or intervention and is used as a benchmark to compare the results of the experimental group. In this case, the control group would be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well.

In scientific research, it is important to include a control group to ensure that the results of the experimental group are due to the treatment or intervention and not due to other factors. In this case, David is investigating the factors that affect plant growth, and he is manipulating the amount of water and fertilizer that the two elm trees receive. However, there could be other factors that affect plant growth, such as soil quality, sunlight exposure, temperature, and pests. If David only measures the height and trunk girth of the two elm trees that receive water and fertilizer, he cannot be sure if any changes in their growth are due to the treatment or due to other factors.

To improve his investigation, David can plant a third young elm tree near the other two and not give it any water or fertilizer. This third tree will serve as the control group, and David can measure its height and trunk girth every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

David can best improve his investigation by including a control group, which will serve as a benchmark to compare the results of the experimental group. The control group should be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

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Answer:

exact form:\(\frac{13}{28}\)

Decimal form:0.4642857143

Step-by-step explanation:

The probability a male's growth plate will fuse before age 17 is 0.1112, for this we have to learn probability.

Probability of an event is a number that shows what is the possibility of an event occur.

we have to take entire area under the standardized curve from and including the left tail up to the z-score for 17.

\(= \frac{(17 - 18.6 years)}{1.308333 years}\)

\(= \frac{(-1.6) }{1.308333}\)

\(= -1.22293\)

\(= approx. 1.22.\)

The area from the mean to +ve or -ve 1.22 is .3888

We have to subtract .3888 from area from the tail to the mean (.5000) to get area from the tail to 1.22.

So, the growth plates will fuse before age 17 \(= .5000-.3888 = 0.1112\)

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Answer:

3

Step-by-step explanation:

7*50=350

7-4=3

3*10=30

350+30=380

In order to justify their position candidate make assumption that the price effect would be larger than the quantity effect.

What is Price?

The amount of money required to obtain a certain thing is referred to as its price. Price is a measure of value in the sense that the amount people are willing to pay for a commodity signifies its value.

Concept:

Candidate A claims that raising the sales tax from 5% to 7% will enhance revenue. This suggests that the price effect is greater than the quantity effect because when taxes rise, prices rise and quantities fall; hence, tax revenue will rise only if the price effect is more than the quantity effect.

And Candidate B claims that the tax would harm merchants and customers, slow the economy, and reduce tax revenue, but only if the quantity effect outweighed the price effect.

As a result, Candidate A believes that the price effect will be greater than the quantity effect.

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Impulse, change in momentum, final speed, and momentum are all related concepts in the context of Newton's laws of motion. Let's go through each option and explain their relationships:

(a) Impulse delivered: Impulse is defined as the change in momentum of an object and is equal to the force applied to the object multiplied by the time interval over which the force acts.

Mathematically, impulse (J) can be expressed as J = F  Δt, where F represents the net force applied and Δt represents the time interval. In this case, you mentioned that the net force acting on the crates is shown in the diagram. The impulse delivered to each crate would depend on the magnitude and direction of the net force acting on it.

(b) Change in momentum: Change in momentum (Δp) refers to the difference between the final momentum and initial momentum of an object. Mathematically, it can be expressed as Δp = p_final - p_initial. If the crates start from rest, the initial momentum would be zero, and the change in momentum would be equal to the final momentum. The change in momentum of each crate would be determined by the impulse delivered to it.

(c) Final speed: The final speed of an object is the magnitude of its velocity at the end of a given time interval.

It can be calculated by dividing the final momentum of the object by its mass. If the mass of the crates is provided, the final speed can be determined using the final momentum obtained in part (b).

(d) Momentum in 3 s: Momentum (p) is the product of an object's mass and velocity. In this case, the momentum in 3 seconds would be the product of the mass of the crate and its final speed obtained in part (c).

To rank these quantities from greatest to least for each crate, you would need to consider the specific values of the net force, mass, and any other relevant information provided in the diagram or problem statement.

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Answer:

A

Step-by-step explanation:

Pick any two sides....their sum must be greater than the third side....

  a+b > c

  a+c > b

  c + b > a

The derivative dy/dx is given by dy/dx = (dy/dt)/(dx/dt). After differentiating y = √(2t - t^2) and x = cos^(-1)(1 - t) with respect to t, and substituting the derivatives into the formula, we get dy/dx = ((1/2) * (-2) * (2 - 2t)^(-1/2) - 2t) / (1/sqrt(1 - (1 - t)^2)). Further simplification depends on the specific value of t.

The derivative dy/dx is given by dy/dx = (dy/dt)/(dx/dt), where dy/dt is the derivative of y with respect to t and dx/dt is the derivative of x with respect to t. To find dy/dx, we need to differentiate y with respect to t and x with respect to t, and then substitute these derivatives into the formula.

Differentiating y = √(2t - t^2) with respect to t, we get dy/dt = (1/2) * (2 - 2t)^(-1/2) * (2 - 2t)' - (t^2)' = (1/2) * (-2) * (2 - 2t)^(-1/2) - 2t.

Differentiating x = cos^(-1)(1 - t) with respect to t, we get dx/dt = -(1/sqrt(1 - (1 - t)^2)) * (1 - t)' = -(-1/sqrt(1 - (1 - t)^2)) = 1/sqrt(1 - (1 - t)^2).

Now we can substitute dy/dt = (1/2) * (-2) * (2 - 2t)^(-1/2) - 2t and dx/dt = 1/sqrt(1 - (1 - t)^2) into the formula dy/dx = (dy/dt)/(dx/dt):

dy/dx = ((1/2) * (-2) * (2 - 2t)^(-1/2) - 2t) / (1/sqrt(1 - (1 - t)^2)).

Simplifying this expression further may be possible, but it cannot be determined without knowing the specific value of t.

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The two column proof is completed by

Statement                                            Justification

1. DE || KL                                        1. Given

2. < DFE ≅ < LF-K                            2. Vertical Angles Theorem

3. < DEF ≅ < LKF                            3. Alternate Interior Angles Theorem

4. Δ FDE ≅ Δ FLK                           4. AAS postulate

According to the AAS Postulate, triangles are congruent if two angles and the non-included side of one triangle are congruent with two angles and the non-included side of another triangle.

In the given problem the side is non included and the angels are congruent and hence completes the proof

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Answer:

Sienna will have done 6 laps while Lexi would have done 6

Step-by-step explanation:

Answer

it is 0.5

Step-by-step explanation: