3. The fuel economy of a car, measured in miles per gallon, is modeled by the function f(s) = -0.009s² +0.699s +12 where s represents the speed of the car, measured in miles per hour. What's the fuel economy of the car when it
travels at an average of 20 miles an hour?
O A. 20 miles per gallon
O B. 26.63 miles per gallon
4
O C.-10.02 miles per gallon"
O D. 22.38 miles per gallon
O Mark for review (Will be highlighted on the review page)

Answer:

y = - 3

Step-by-step explanation:

the midline is a horizontal line positioned midway between the maximum and minimum values of the graph.

maximum = - 1 and minimum = - 5

then

(- 1 + (- 5)) ÷ 2 = (- 1 - 5) ÷ 2 = - 6 ÷ 2 = - 3 so equation of midline is

y = - 3

Given statement solution is :-You should mix 20 milligrams of Medication A this week when using 26 milligrams of Medication B.

To determine how many milligrams of Medication A should be mixed this week, we need to maintain the same proportion as last week.

Last week's proportion:

Medication A : Medication B = 100 mg : 130 mg

To find out the amount of Medication A for this week's prescription, we can set up a proportion using the known ratio:

Medication A / Medication B = Last week's Medication A / Last week's Medication B

Let's plug in the values:

Medication A / 26 mg = 100 mg / 130 mg

To solve for Medication A, we can cross-multiply and then divide:

Medication A * 130 mg = 100 mg * 26 mg

Medication A * 130 mg = 2600 mg*mg

Medication A = 2600 mg*mg / 130 mg

Medication A = 20 mg

Therefore, you should mix 20 milligrams of Medication A this week when using 26 milligrams of Medication B.

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(i) The probability that none of the 11 patients will have the mild side effect can be calculated using the binomial distribution.

In this case, the probability of an individual patient having the side effect is 6% or 0.06, and the probability of not having the side effect is 1 - 0.06 = 0.94.

The probability that none of the 11 patients will have the side effect can be calculated as:

P(X = 0) = (0.94)^11 ≈ 0.5147

So, the probability that none of the patients will have the mild side effect is approximately 0.5147 or 51.47%.

(ii) The probability that at least one patient will have the mild side effect can be calculated as the complement of the probability that none of the patients will have the side effect.

In other words, it is 1 minus the probability of none of the patients having the side effect.

P(at least one patient has the side effect) = 1 - P(X = 0) = 1 - 0.5147 ≈ 0.4853

So, the probability that at least one patient will have the mild side effect is approximately 0.4853 or 48.53%.

(i) To find the probability that none of the patients will have the mild side effect, we use the binomial distribution formula.

The probability of success (having the side effect) is given as 0.06, and the probability of failure (not having the side effect) is 1 - 0.06 = 0.94.

We raise the probability of not having the side effect to the power of the number of trials (11 patients) to find the probability that none of them will have the side effect.

(ii) To find the probability that at least one patient will have the mild side effect, we use the complement rule.

The complement of none of the patients having the side effect is at least one patient having the side effect.

By subtracting the probability of none of the patients having the side effect from 1, we find the probability of at least one patient having the side effect.

These probabilities are important in assessing the likelihood of experiencing the mild side effect when using the new drug.

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The price of coffee in 2009 would have been approximately $5.15.

To find the price of coffee in 2009, we need to use the index number for that year. According to the table, the index number for 2009 is 103.0.

We can set up a proportion to solve for the price in 2009:

Price in 2015 / Index in 2015 = Price in 2009 / Index in 2009

Let's denote the price in 2009 as x:

$4.48 / 89.8 = x / 103.0

Now we can solve for x:

x = ($4.48 / 89.8) * 103.0

x ≈ $5.15

Therefore, the price of coffee in 2009 would have been approximately $5.15.

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Answer:

-5

Step-by-step explanation:

Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

Answer:

$2,400

Step-by-step explanation:

This is a very simple problem. Simply type the following into a calculator: 0.15*16000, and you should get 2400.

We have to turn the percentage into a decimal less than one because 15% represents 15/100.

Answer:

(-3,7)

Step-by-step explanation:

[tex]3 > -x > -7[/tex] is the same as [tex]-3 < x < 7[/tex] when we divide everything by -1 and flip the signs. Therefore, the interval would be [tex](-3,7)[/tex].

The matrix[tex]A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.[/tex]

To find the inverse of a matrix, we can use the formula:[tex]A^(-1) = (1/det(A)) * adj(A)[/tex]

Where A^(-1) represents the inverse of matrix A, det(A) is the determinant of A, and adj(A) denotes the adjugate of A.

Given the matrix A with 2 rows and 2 columns:

A = | 4  4 |

      | 2  1 |

To find A^(-1), we need to calculate the determinant of A and the adjugate of A.

The determinant of A (det(A)) is calculated as:

det(A) = 4 * 1 - 2 * 4 = -4

The adjugate of A (adj(A)) is obtained by swapping the diagonal elements and changing the sign of the off-diagonal elements:

adj(A) = |  1  -4 |

             | -2   4 |

Finally, we can find A^(-1) using the formula mentioned earlier:[tex]A^(-1) = (1/det(A)) * adj(A)A^(-1) = (1/-4) * | 1 -4 |[/tex]

                       | -2   4 |

Simplifying the expression:

A^(-1) = | -0.25  1 |

              |  0.5  -1 |

Therefore, the matrix A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.

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Path A-B-C-E represents the distance traveled, which is 18 meters.

Path A-G-C-E represents the displacement, which is 17 meters.

From the given figure, we can identify the paths and calculate the distance and displacement.

Path A-B-C-E represents the distance traveled, and path A-G-C-E represents the displacement.

Let's calculate the lengths of both paths:

Distance traveled (Path A-B-C-E):

Length of AB = 9m

Length of BC = 3m

Length of CE = 6m

Total distance traveled = Length of AB + Length of BC + Length of CE

= 9m + 3m + 6m

= 18m

Therefore, the distance traveled along path A-B-C-E is 18 meters.

Displacement (Path A-G-C-E):

Length of AG = 5m

Length of GC = 6m

Length of CE = 6m

Total displacement = Length of AG + Length of GC + Length of CE

= 5m + 6m + 6m

= 17m

Therefore, the displacement along path A-G-C-E is 17 meters.

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The options that apply are:

A. A list of all questions from the lessons

B. Description of what you need to know or apply

C. Concepts tested

D. Reference column.

The options that are typically included in a table for each unit are:

- A list of all questions from the lessons: This helps in organizing and categorizing the questions based on the specific unit or topic.

- Description of what you need to know or apply: This provides an overview or summary of the key concepts, knowledge, or skills that are covered in the unit.

- Concepts tested: This section highlights the specific concepts or skills that will be tested or assessed in relation to the unit. It helps students understand the focus areas and what they need to prioritize in their learning.

- Reference column: This column may include additional information such as page numbers, section titles, or references to specific resources or materials that are relevant to the unit. It serves as a guide for further exploration or reference.

A brief quiz, on the other hand, is not typically included in a table for each unit. Quizzes are usually separate assessments that are administered to evaluate understanding and mastery of the unit's content.

So, the options that apply are:

- A list of all questions from the lessons

- Description of what you need to know or apply

- Concepts tested

- Reference column

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Answer:

W.T.H is this

Step-by-step explanation:

This ain't the way to past <s<h>t>

>>>>>>>>>(X₁V₂) O A. A=(₁-₂)(53-51) B. A=(3-₁)(3-1) CO. A=(₁-₁)(2-51) O D. A=(√₂-₁)(²3-11) O E. A=(√₂-₁)(52-51) (Xg. Ya)​?????????????????

XD u a noobie of life kid get better lol

Answer:

F

Step-by-step explanation:

i could be incorrect but SSA isn't a valid congruency statement and if you were trying to prove them congruent that wouldn't work

Answer: There will be a total of 18 books per box.

Step-by-step explanation:

Here,

Total number of boxes = 7

Total number of books = 126

Let n be the total number of books per boxes.

Now,

n = 126 / 7 = 18

Therefore, the total number of books per boxes is 18.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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The slope-intercept form of the equation of the line that passes through (-2, -1) and is perpendicular to y + 15 = x + 10 is y = -x - 3.

To find the slope-intercept form of the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.

The given line equation is y + 15 = x + 10. To rewrite it in slope-intercept form (y = mx + b), we isolate y:

y = x + 10 - 15

y = x - 5.

From this equation, we can see that the slope of the given line is 1.

To find the slope of the line perpendicular to this, we take the negative reciprocal of 1, which is -1.

Now that we have the slope (-1) and a point (-2, -1) that the line passes through, we can use the point-slope form of a line to find the equation.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Plugging in the values (-2, -1) and -1 for x1, y1, and m respectively, we get:

y - (-1) = -1(x - (-2))

y + 1 = -1(x + 2)

y + 1 = -x - 2.

To rewrite this equation in slope-intercept form (y = mx + b), we isolate y:

y = -x - 2 - 1

y = -x - 3.

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Answer:step 4

Step-by-step explanation: I just took the test pookies

a) The equation of the line perpendicular to the tangent line at (2,6) is y = (-1/8)x + 7/4.

b) The smallest slope on the curve is at (-sqrt(4/3), 10 - 4sqrt(4/3)).

c) The tangent lines to the curve where the slope is 8 are y = 8x - 10 and y = 8x + 14.

a) To find the equation of the line perpendicular to the tangent line at the point (2,6), we first need to determine the slope of the tangent line. The derivative of the curve y=x^3-4x+6 is y' = 3x^2 - 4. Evaluating the derivative at x = 2 gives y'(2) = 3(2)^2 - 4 = 8.

Since the line perpendicular to the tangent line has a slope that is the negative reciprocal of the tangent line's slope, the slope of the perpendicular line is -1/8. Using the point-slope form of a linear equation with the given point (2,6), we have y - 6 = (-1/8)(x - 2). Simplifying, we get y = (-1/8)x + 7/4 as the equation of the perpendicular line.

b) To find the smallest slope on the curve, we can take the derivative and set it equal to zero. Differentiating y=x^3-4x+6, we have y' = 3x^2 - 4. Setting y' equal to zero, we get 3x^2 - 4 = 0. Solving for x, we find x = ±sqrt(4/3). The smallest slope occurs at the point where x = -sqrt(4/3) since the curve is concave up at this point. Evaluating y at this x-value, we have y = (-sqrt(4/3))^3 - 4(-sqrt(4/3)) + 6, which simplifies to y = 4 - 4sqrt(4/3) + 6 = 10 - 4sqrt(4/3).

c) To find the equations of the tangent lines where the slope of the curve is 8, we set the derivative equal to 8 and solve for x. 3x^2 - 4 = 8. Simplifying, we get 3x^2 - 12 = 0. Factoring, we have 3(x^2 - 4) = 0, which gives us x = ±2. Evaluating y at these x-values, we find y = 2^3 - 4(2) + 6 = 2 and y = (-2)^3 - 4(-2) + 6 = -2.

Therefore, the equations of the tangent lines to the curve where the slope is 8 are y = 8x - 10 and y = 8x + 14.

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Answer:

f(-3) = -29

f(-5) = -45

f(-6) = -53

Step-by-step explanation:

8x-5 , x [tex]\leq[/tex] -5

f(-5)

= 8(-5) - 5

= -40-5

=-45 ( less than -5 , so we can use)

-[tex]x^{2}[/tex] , x > -5

= -[tex](-5)^{2}[/tex]

= -(25)

= -25 (greater than -5, we can't use)

if u have any question let me know.

Answer:

35/12

Step-by-step explanation:

9 2/3 = 29 / 3

6 3/4 = 27 / 4

We have to find the common denominator. In this case, it is 12

29/3 x 4/4 = 116/12

27/4 x 3/3 = 81/12

Now we can subtract both fractions.

116/12 - 81/12 = 35/12

So, the answer is 35/12

Answer:

35/12 or 2 11/12

Step-by-step explanation:

9 2/3 = 29/3

6 3/4 = 27/4

29/3 - 27/4 = 35/12

The weight of the new player is 9 kg.

Given -

Mean weight of the team before including the new player = 86.5 kg

Mean weight of the team after including the new player = 86 kg

Number of players in the team before including the new player = 18

To find -

The weight of the new player

Solution -

Let's denote the weight of the new player as 'x' kg.

To solve the problem, we'll use the formula for the mean:

Mean = (Sum of all values) / (Number of values)

The sum of weights of the original 18 players = 86.5 kg * 18

The sum of weights of all 19 players = (86 kg * 18) + x kg

According to the problem, the mean weight before including the new player is 86.5 kg, and the mean weight after including the new player is 86 kg. So, we can set up the following equation:

(86.5 kg * 18) = (86 kg * 18) + x kg

Now, let's solve the equation to find the weight of the new player:

(86.5 kg * 18) = (86 kg * 18) + x kg

1557 kg = 1548 kg + x kg

9 kg = x kg

Therefore, the weight of the new player is 9 kg.

Answer:

268.8

Step-by-step explanation:

Let the sides of the base triangle be:

a = 8.8 cm

b = 5.7 cm

c = 6.8 cm

Let h be the length

h = 10.8 cm

The surface area is given by:

[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}[/tex]

Where

[tex]s = \frac{a + b + c}{2} \\\\= \frac{8.8 + 5.7 + 6.8}{2} \\\\=\frac{21.3}{2} \\\\= 10.65[/tex]

[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}\\\\= (8.8 + 5.7 + 6.8)*10.8 + 2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\= 21.3*10.8 +2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\=230.04 + 2\sqrt{ 10.65(1.85)(4.95)(3.85)}\\\\=230.04 + 2\sqrt{ 375.48}\\\\= 230.04 + 2*19.38\\\\=230.04 +38.76\\\\=268.8[/tex]

The maximum amount of juice blend he can make is 2 blends.

Ratio of oranges to apples required to make the blend = 5 : 2

Quantity of oranges available = 26 litres

Quantity of apples available = 9 litres

Number of blend made with oranges = 26 litres / 5

= 5.2

Approximately to the nearest whole number

= 5

Number of blend made with apples = 9 litres / 2

= 2.5

Approximately to the nearest whole number is

2

Since, the quantity of apple concentrate available can only make 2 blend of juice, it can be concluded that maximum amount of juice blend he can make is 2

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Answer:

Ok, Here is your answer

Step-by-step explanation:

To find the percentage of players who played well on the baseball team, we need to divide the number of players who played well by the total number of players and then multiply by 100.

Number of players who played well = 6

Total number of players = 11

Percentage of players who played well = (6/11) x 100%

= 54.55%

Therefore, the answer is 54.55%. Hence, option D, 54.55%, is the correct answer.

Answer:

5.4 ft²

Step-by-step explanation:

To find the surface area of the cone-shaped megaphone, use the surface area of a cone formula.

[tex]\boxed{\begin{minipage}{7cm}\underline{Surface area of a cone}\\\\$S.A.=\pi r^2+\pi rl$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius of the circular base.\\ \phantom{ww}$\bullet$ $l$ is the slant height of the cone.\\\end{minipage}}[/tex]

The radius of a circle is half its diameter.

Therefore, if the diameter of the cone's circular base is 1.2 ft, then its radius is r = 0.6 ft.

Given values:

Substitute the values into the formula and solve:

[tex]\begin{aligned}\textsf{Surface area}&=3.14 \cdot0.6^2+3.14 \cdot 0.6 \cdot 2.25\\&=3.14 \cdot 0.36+3.14 \cdot 0.6 \cdot 2.25\\&=1.1304+1.884 \cdot 2.25\\&=1.1304+4.239\\&=5.3694\\&=5.4\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the surface area of the cone-shaped megaphone is 5.4 ft² (rounded to the nearest tenth).

Answer:

Let's assume the woman invested x dollars in the account that pays 11% per year.

Since she invested a total of $8000, the amount invested in the account that pays 12% per year would be (8000 - x) dollars.

Now, let's calculate the interest earned from each investment:

Interest from the 11% account: 0.11x

Interest from the 12% account: 0.12(8000 - x)

According to the given information, the total interest earned in the first year is $910. Therefore, we can set up the following equation:

0.11x + 0.12(8000 - x) = 910

Let's solve this equation to find the value of x:

0.11x + 0.12 * 8000 - 0.12x = 910

0.11x - 0.12x = 910 - 0.12 * 8000

-0.01x = 910 - 960

-0.01x = -50

Dividing both sides by -0.01:

x = (-50) / (-0.01)

x = 5000

Therefore, the woman invested $5000 in the account that pays 11% per year.

The amount invested in the account that pays 12% per year would be 8000 - 5000 = $3000.

So, she invested $5000 in the 11% account and $3000 in the 12% account.

Using the Law of Cosines with angle 103° and adjacent sides 9 and 6, the remaining side is approximately 12.26 units long.

To find the remaining sides of the triangle, we can use the Law of Cosines. Let's assume that the angle of 103 degrees is opposite side c, and the adjacent sides are a = 9 and b = 6.

The Law of Cosines states:

[tex]c^2 = a^2 + b^2[/tex] - 2ab * cos(C)

Plugging in the known values:

[tex]c^2 = 9^2 + 6^2[/tex] - 2 * 9 * 6 * cos(103°)

Simplifying the equation:

[tex]c^2[/tex] = 81 + 36 - 108 * cos(103°)

Now we need to evaluate cos(103°).

Using a scientific calculator or trigonometric table, we find that cos(103°) ≈ -0.3090.

Substituting the value of cos(103°) back into the equation:

[tex]c^2[/tex] = 81 + 36 - 108 * (-0.3090)

Simplifying further:

[tex]c^2[/tex] = 117 + 33.2724

[tex]c^2[/tex]≈ 150.2724

Taking the square root of both sides:

c ≈ √150.2724

c ≈ 12.26

Therefore, the remaining side (opposite the angle of 103 degrees) is approximately 12.26 units long.

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A. The relation R is reflexive. B. This relation is not symmetric. C. The relation R is neither an equivalence relation nor a partial ordering relation on the set N = {1, 2, 3, 4, ...}.

Di. R is not a partial ordering relation, a Hasse diagram cannot be drawn. ii. There are no equivalence classes to find.

To determine whether the relation R is an equivalence relation or a partial ordering relation on the set N = {1, 2, 3, 4, ...}, examine its properties.

a. Reflexivity:

For a relation to be reflexive, every element in the set should be related to itself. In the given definition of R, we have x = y¹, where y¹ represents the first power of y. Since any number raised to the power of 1 is equal to itself, the relation R is reflexive.

b. Symmetry:

For a relation to be symmetric, if x is related to y, then y should also be related to x. In the given definition of R, we have x = y¹. This relation is not symmetric because if x = 2 and y = 3, then x = y¹ is not satisfied.

c. Transitivity:

For a relation to be transitive, if x is related to y and y is related to z, then x should be related to z. In the given definition of R, we have x = y¹. This relation is not transitive because if x = 2, y = 3, and z = 4, then x = y¹ and y = z¹ are satisfied, but x = z¹ is not satisfied.

Based on the above analysis, we can conclude that the relation R is neither an equivalence relation nor a partial ordering relation on the set N = {1, 2, 3, 4, ...}.

d. Since the relation R is neither an equivalence relation nor a partial ordering relation on the set N = {1, 2, 3, 4, ...}, the Hasse diagram cannot be drawn, as it is applicable only for partial ordering relations.

i. Given that R is not a partial ordering relation, a Hasse diagram cannot be drawn.

ii. Since R is not an equivalence relation, there are no equivalence classes to find. Equivalence classes are relevant only for equivalence relations, where elements are grouped together based on their equivalence under the relation.

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