The lengths of the three sides of a triangle (in inches) are consecutive odd integers. If the perimeter is 5757 inches, find the value of the middle of the three side lengths.

Item b.)

To solve that item we must remember the general formula for exponential decay, it's

Then, let's modify it to fit our parameters

A is the initial value, in our case, the initial value is the dosage, 500mg, then A = 500

r is the rate, we have 5.2%, then the value of r will be 0.052

And f(t) will transform into D, changing the name.

Hence

We can also simplify the subtraction, we get

Item c.)

To solve that we will use our equation, we will input t = 6 hours and find the value of D.

The answer is 363 mg

When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.

It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.

On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.

In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.

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Answer:

Step-by-step explanation:

so all the angles of a triangle add up to 180 degrees

180-42-62= 76

so we know angle TUS is 76 degrees

the other triangle has an angle of 78 degrees which isn't 42, 62, or 76.

The triangles are not similar because similar shapes have congruent angles

Both triangles only have one pair of congruent angles (m∠TSU ≅ m∠RSQ), therefore, the triangles are not similar.

From the image given:

m∠TSU = m∠RSQ = 62°

m∠TUS = 180 - 42 - 62 = 76°

m∠QRS = 180 - 78 - 62 = 40°  

Thus, both triangles only have one pair of congruent angles (m∠TSU ≅ m∠RSQ), therefore, the triangles are not similar.

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Answer:

566

Step-by-step explanation:

785-219=566

Answer:

\(-2(1 - 4x) = 3x + 8\\\\-2 + 8x = 3x + 8\\\\-2 + 5x = 8\\\\5x = -10\\\\x = -2\)

The equation of the tangent line to the curve xe^y + ye^x = 1 is y = -(e + 1) x + 1 through the point (0, 1).

Given the equation of a curve.

xe^y + ye^x = 1

We have to find the equation of the tangent line to the curve.

First we have to find the derivative of the function that is, dy/dx.

Consider the equation,

xe^y + ye^x = 1

Differentiating on both sides using the product rule and the chain rule, we get,

[x e^y \(\frac{dy}{dx}\) + e^y] + [y eˣ + eˣ \(\frac{dy}{dx}\) ] = 0

Right hand side is 0 since the derivative of a constant is always 0.

Taking  \(\frac{dy}{dx}\) as common from 2 terms,

\(\frac{dy}{dx}\) (x e^y + eˣ) + e^y + y eˣ = 0

\(\frac{dy}{dx}\) (x e^y + eˣ) = - (e^y + y eˣ)

\(\frac{dy}{dx}\) = - (e^y + y eˣ) / (x e^y + eˣ )

Since the point is not given, assume the point for the tangent line to be (0, 1).

At this, point, the value of  \(\frac{dy}{dx}\) is the slope of the tangent line needed.

\(\frac{dy}{dx}\) at (0, 1) = - (e¹ + e⁰) / (0 e¹ + e⁰ )

                 = - (e + 1) / 1

                 = -(e + 1)

Equation of the tangent line is,

y - y' = m(x - x')

y - 1 = -(e + 1) (x - 0)

y - 1 = -(e + 1) x

y = -(e + 1) x + 1

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Answer:

a

Step-by-step explanation:

Answer:

see attached

Step-by-step explanation:

Answer:

The value of t = 18

Step-by-step explanation:

202 = 2t + 5 + t + 3t - 2 + 5t +1  Combine like terms

202 = 11t + 4  Subtract 4 from both sides

198 = 11\(\frac{11x}{11}\)x  Divide both sides by 11

\(\frac{198}{11}\) = 18

Is the question the value of t or the length of each side?

Each side

2t + 5

2(18) + 5

41

T

18

3T - 2

3(18) - 2

52

5T + 1

5(18) + 1

91

91 + 52 + 18 + 41 = 2002

Helping in the name of Jesus.

Answer:

3

22

0

Step-by-step explanation:

I'm pretty sure it is the answer but if it isn't then sorry

Answer:

Step-by-step explanation:

This is a piece-wise function.

The distance function depends on what time period is involved.

From t=0 to t=0.75, the distance function is: .3t

. . By the end of the 45 minutes, he has gone 2.25 miles.

From t=0.75 to t=2, the distance function is: .2.25+5t

. . By the end of the 75 minutes, he has gone another 6.25 miles, a total of 8.5 miles.

From t=2 to t=2.5, the distance function is: .8.5+0t=8.5

. . By the end of the 30 minutes, he hasn't moved; his total is still 8.5 miles.

From t=2.5 to 4, the distance function is: .8.5+3t

. . By the end of the 90 minutes, he has gone another 4.5 miles, a total of 13 miles.

The function would be written like this:

d(t) =   3t            0 ≤ t ≤ 0.75

        2.25+5t      0.75≤t<2

         8.5             2≤t≤2.5

         8.5+3t       2.5<t<4

Answer:

127.2

Step-by-step explanation:

The area of a semicircle is:

\(\frac{\pi r^{2} }{2}\)

So to figure it out we first find the diameter:

18÷2=9

Then we plug it into the equation

\(\frac{9^{2}\pi }{2} = \frac{81\pi}{2}\) Which we can put into a calculator to get 127.2345... so we round to 1 d.p to get our answer, 127.2 (the fifth digit, 3, rounds down)

The matrix can be diagonalized, and the correct choice is B. For P= ⎡⎣​3−110​11​⎤⎦, D= ⎡⎣​393​000​⎤⎦.

To diagonalize a matrix, we need to find its eigenvectors and use them to construct a matrix P, where the columns of P are the eigenvectors. The diagonal matrix D is formed by placing the eigenvalues on the diagonal.

First, we find the eigenvalues λ by solving the characteristic equation det(A - λI) = 0, where A is the given matrix and I is the identity matrix. By calculating the determinant, we have (33 - λ)(9 - λ) - (-3)(18) = 0, which simplifies to λ^2 - 42λ + 315 = 0. Solving this quadratic equation gives λ = 3 and λ = 9.

Next, we find the corresponding eigenvectors. For λ = 3, we solve the equation (A - 3I)v = 0, where v is the eigenvector. This leads to the eigenvector v = ⎡⎣​3−110​⎤⎦. For λ = 9, we solve (A - 9I)v = 0, which gives v = ⎡⎣​11​1​⎤⎦.

We construct matrix P by using the eigenvectors as columns: P = ⎡⎣​3−110​11​⎤⎦. The diagonal matrix D is formed by placing the eigenvalues on the diagonal: D = ⎡⎣​393​000​⎤⎦.

Therefore, the correct choice is B. For P= ⎡⎣​3−110​11​⎤⎦, D= ⎡⎣​393​000​⎤⎦.

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Answer:

(x + 4)^2 + (y - 1)^2 = 61.

Step-by-step explanation:

We need to find the square of the radius and the coordinates of the center.

Center = (-10 + 2)/2 , (-4 + 6)/2

= (-4, 1).

Length of the diameter

=  √((-10-2)^2 + (-4-6)^2)

= √(144 + 100)

=√244

So the radius = √244/2

and r^2 = 244/4 = 61,

So the equation of this circle is:

(x - (-4)^2 + (y - 1)^2 = 61

(x + 4)^2 + (y - 1)^2 = 61.

(x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given coordinates of the diameter of circle are  (-10,-4) and (2,6)

Diameter=√(x₂-x₁)²+(y₂-y₁)²

x₂=2,x₁=-10, y₁=-4, y₂=6

Diameter=√(2-(-10))²+(6-(-4))²

=√(12)²+(10)²

=√144+100

=√244

We know that Radius=Diameter/2

R=√244/2

Squaring both sides

R²=244/4

R²=61

So the equation of this circle is:

(x - (-4)² + (y - 1)² = 61

(x + 4)²+ (y - 1)² = 61.

Hence (x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

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The purpose of performing the overall F-test is to test whether at least one of the predictor variables is significant in a regression model.

This is option a.

The F-test is used to determine if the entire regression model is significant, rather than just one individual predictor variable. If the F-test is significant, it means that at least one of the predictor variables has a significant relationship with the dependent variable.

This can help us determine if the regression model is useful in predicting the dependent variable.

The F-test is an important step in regression analysis, as it can help us determine if our model is valid and useful for making predictions.

Hence Option A is correct.

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Answer:

n= 8

Step-by-step explanation:

Answer:

Les deux nombres doivent avoir une différence de 3. Algébriquement, ce serait x + (x + 3) = 129. 2x est alors égal à 126. X est égal à 63 et x + 3 est à 66. Ces nombres sont des multiples consécutifs de 3 dont la somme est de 129.

Step-by-step explanation:

The two numbers must have a difference of 3. Algebraically, it would be x + (x + 3) = 129. 2x then is equal to 126. X equals 63 and x + 3 is 66. These numbers are consecutive multiples of 3 whose sum is 129.

An angle of 0 radians is an angle along the positive x-axis of the unit circle. Its terminal point is (1, 0).

The tangent of 0 radians is defined as the ratio of the y-coordinate to the x-coordinate of the terminal point, which is 0/1 = 0.

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To find the percentage of values in a normal distribution between 18 and 23, we need to calculate the z-scores corresponding to these values and then use the 68-95-99.7 rule.

Given:

Mean (μ) = 18

Standard deviation (σ) = 5

Lower value (x1) = 18

Upper value (x2) = 23

To calculate the z-scores, we use the formula:

z = (x - μ) / σ

For the lower value (x1 = 18):

z1 = (18 - 18) / 5 = 0

For the upper value (x2 = 23):

z2 = (23 - 18) / 5 = 1

Now, we can use the 68-95-99.7 rule to find the percentage of values between z1 and z2.

The 68-95-99.7 rule states that:

- Approximately 68% of the values fall within 1 standard deviation of the mean.

- Approximately 95% of the values fall within 2 standard deviations of the mean.

- Approximately 99.7% of the values fall within 3 standard deviations of the mean.

Since our z-scores are 0 and 1, they fall within 1 standard deviation of the mean. Therefore, the percentage of values between 18 and 23 in the distribution is approximately 68%.

In conclusion, approximately 68% of the values in the normal distribution fall between 18 and 23, based on the given mean of 18, standard deviation of 5, and using the 68-95-99.7 rule.

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Answer:

728000 mosquitoes

Step-by-step explanation:

In attachment

Please giv brainliest, thanks!

Step-by-step explanation:

Find 100% of the price:

100 - 15 = 85% (Sale price)

85% = 136

1% = 136 divide 85 = 1.6

100% = 1.6 x 100 = 160

Ans: £160

Answer:

165

Step-by-step explanation:

\(A=\frac{1}{2}(11)(12+18)=165\)

The correct answers from the given lists are given as follows: Relation (a) a is (strictly) older than bA. irreflexiveB. asymmetricC. antisymmetricD. reflexiveE. transitive Relation (b) a and b have a common grandparentA.

irreflexiveB. antisymmetricC. symmetricD. reflexiveE. transitiveRelation (c) a has the same first name as bA. transitiveB. irreflexiveC. antisymmetricD. symmetricE. reflexiveRelation (d) a and b were born on the same dayA. transitiveB. reflexiveC. irreflexiveD. antisymmetricE. symmetric.

The given lists include different types of relations. Let's discuss the given relations one by one.(a) a is (strictly) older than b:This relation is irreflexive because a person can't be older than oneself. This relation is asymmetric because if a is older than b then it can't be possible that b is older than a.

This relation is antisymmetric because if a is older than b and b is older than a, then it means that a and b are the same person which is not possible. This relation is not reflexive because there is no one who is older than oneself. This relation is transitive because if a is older than b and b is older than c then a is also older than c.(b) a and b have a common grandparent:This relation is irreflexive because a person can't have a common grandparent with oneself. This relation is antisymmetric because if a has a common grandparent with b then it can't be possible that b has a common grandparent with a. This relation is symmetric because if a has a common grandparent with b then b also has a common grandparent with a. This relation is not reflexive because there is no one who has a common grandparent with oneself. This relation is transitive because if a has a common grandparent with b and b has a common grandparent with c then a also has a common grandparent with c.(c) a has the same first name as b:

This relation is transitive because if a has the same first name as b and b has the same first name as c then a has the same first name as c. This relation is irreflexive because a person can't have the same name as oneself. This relation is antisymmetric because if a has the same name as b then it can't be possible that b has the same name as a. This relation is symmetric because if a has the same name as b then b also has the same name as a. This relation is not reflexive because there is no one who has the same name as oneself.

(d) a and b were born on the same day: This relation is transitive because if a was born on the same day as b and b was born on the same day as c then a was born on the same day as c. This relation is reflexive because every person is born on the same day as oneself. This relation is irreflexive because no person is born on a different day than oneself. This relation is antisymmetric because if a was born on the same day as b then it can't be possible that b was born on the same day as a. This relation is symmetric because if a was born on the same day as b then b was also born on the same day as a.

The correct answers for each given relation are listed above.

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Answer:

Incorrect.

Step-by-step explanation:

6 + x = 19

Plug in when x = 12

6 + 12 = 19

18 = 19

It is incorrect, so 12 is not a solution.

Answer:

It is not a solution

Step-by-step explanation:

6 + x = 19

Substitute into the equation and see if it is true

6+12 = 19

18 =19

This is not true so it is not a solution

Answer:

Loll.

Step-by-step explanation:

That is inconsistent, therefore there is no solution

The bag that has more fruits is the second bag, because the ratio is greater.

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

Number of fruits in the first bag : (3/8) x 60 = 22.50

Number of fruits in the second bag :(7/17) x 60 = 24.71

Here is the complete question:

Tamika has two bags of trail mix. Each has a combination of 60 pieces of fruit and nuts. Ratio of fruit to nuts in the first bag:3 5 Ratio of fruit to nuts in the second bag:7 10 Which bag has more fruit? Use the ratios to justify your answer. The first bag, because the ratio is greater. The first bag, because the ratio is smaller. The second bag, because the ratio is greater. The second bag, because the ratio is smaller.

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Answer:

Any number bigger than 2/3

Step-by-step explanation:

btw, I didn't see the options but here's the explanation

When you multiply by a part of a whole, a fraction, you are getting smaller. When you multiply by a number bigger than one, your product gets bigger. So, any number bigger than 2/3 works just fine