You have found a store that is unique. All the shirts sell for a set price and all the pants are also priced the same in the entire store! You have purchased 3 shirts and 2 pants for $104.81 and your friend has purchased 2 shirts and one pant for $61.33. Set up and solve a system of linear equations. How much is one shirt?

Answer:

(x - 9)^2 + (y + 5)^2 = 50.

Step-by-step explanation:

To determine the equation of the circle with a center at (9, -5) and containing the point (10, 2), we need to find the radius of the circle first. The radius is the distance between the center and any point on the circle, such as (10, 2).

We can use the distance formula to find the radius:

r = √((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given values:

r = √((10 - 9)^2 + (2 - (-5))^2)

Simplifying:

r = √(1^2 + 7^2)

r = √(1 + 49)

r = √50

Simplifying further:

r = √(25 * 2)

r = 5√2

Now that we have the radius, we can write the equation of the circle in standard form:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values:

(x - 9)^2 + (y - (-5))^2 = (5√2)^2

Simplifying:

(x - 9)^2 + (y + 5)^2 = 50

Therefore, the equation of the circle with a center at (9, -5) and containing the point (10, 2) is:

(x - 9)^2 + (y + 5)^2 = 50.

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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(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:

(-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].

Answer:

Area of a Segment of a Circle = θ/360° × πr2 – ½ r2sinC

PLEASE MARK AS BRAINLIEST

Answer:

[tex]AB=2r\sin\left(\dfrac{m\overset\frown{AB}}{2}\right)[/tex]

Step-by-step explanation:

Label the center of the circle O.

If two line segments are drawn from the center of the circle to points A and B on the circumference, an isosceles triangle will be formed, where the legs OA and OB are the radius, r, and the base is chord AB.

If an angle bisector is drawn from the center of the circle to the midpoint of AB, the isosceles triangle is divided into two right triangles.

An equation can now be formed for the base of the right triangle (half the length of chord AB), by using the sine trigonometric ratio.

The angle is half the central angle AOB, the side opposite the angle is half the chord AB, and the hypotenuse is the radius, r. Therefore:

                [tex]\sin (\theta)=\dfrac{\sf opposite\;side}{\sf hypotenuse}[/tex]

[tex]\sin\left(\dfrac{m\angle AOB}{2}\right)=\dfrac{\frac{1}{2}AB}{r}[/tex]

Rearrange the equation to isolate AB:

[tex]\dfrac{1}{2}AB=r\sin\left(\dfrac{m\angle AOB}{2}\right)[/tex]

[tex]AB=2r\sin\left(\dfrac{m\angle AOB}{2}\right)[/tex]

Since the measure of an arc is equal to the measure of its corresponding central angle, this means that [tex]m\overset\frown{AB}=m \angle AOB[/tex]. Therefore, the equation to find the length of chord AB given the measure of arc AB is:

[tex]\boxed{AB=2r\sin\left(\dfrac{m\overset\frown{AB}}{2}\right)}[/tex]

Note: We would also need to know the length of the radius, r.

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).

Calculating 384 yd^2 and 1057 yd^2. expression, we find that the volume of the smaller solid is approximately 493.6 yd^3 when rounded to the nearest unit.

The surface areas of two similar solids are given as 384 yd^2 and 1057 yd^2. Let's denote the surface area of the smaller solid as SA_small and the surface area of the larger solid as SA_large.

We know that the surface area of a solid is proportional to the square of its linear dimension (length, width, or height) in similar solids. Therefore, the ratio of the surface areas is equal to the square of the ratio of their corresponding linear dimensions.

Using this concept, we can set up the following proportion:

(SA_small / SA_large) = (V_small / V_large)^2

Plugging in the given values, we have:

384 / 1057 = (V_small / 1795)^2

Simplifying further:

0.363 = (V_small / 1795)^2

Taking the square root of both sides:

√0.363 = V_small / 1795

V_small = √0.363 * 1795

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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.

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 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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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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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:

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

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.

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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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).

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.

The mean is the most sensitive to extreme scores, followed by the median, while the mode is the least affected. The mean is greatly influenced by outliers, the median is moderately influenced, and the mode is generally unaffected by extreme scores.

The mean, median, and mode are measures of central tendency used to describe the average or typical value in a dataset. They differ in their sensitivity to extreme scores, also known as outliers or extreme values.

Mean:

The mean is calculated by summing all the values in a dataset and dividing by the total number of values. It is highly sensitive to extreme scores because it takes into account the magnitude of each value. Even a single extreme score can significantly affect the mean. This sensitivity arises from the fact that the mean incorporates all values in the dataset. Therefore, outliers can distort the mean and pull it towards their direction

Median:

The median represents the middle value when the dataset is arranged in ascending or descending order. It is less sensitive to extreme scores compared to the mean. The median only considers the position of the values, not their actual values. Therefore, extreme scores have less impact on the median since it focuses on the relative position of values rather than their magnitude. As a result, outliers have minimal influence on the median.

Mode:

The mode represents the value(s) that appear most frequently in the dataset. Like the median, the mode is not significantly affected by extreme scores. Outliers can occur in a dataset without affecting the mode because the mode is determined by the most frequently occurring value(s), regardless of their magnitude. In datasets with multiple modes or no mode, extreme scores may not significantly impact the mode.

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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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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.

The graph of the function y = -2x + 3 is added as an attachment

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

So, the equation is

y = -2x + 3

The above function is a linear function that has been transformed as follows

Vertically stretched by a factor of -2

Shifted up by 3 units

Next, we plot the graph using a graphing tool by taking note of the above transformations rules

The graph of the function is added as an attachment

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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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f(g(x)) = x + 11 + 2√x and g(f(x)) = √(x² + 5) + 6. These are the simplified expressions for f(g(x)) and g(f(x)) using the given pair of functions.

To find f(g(x)), we substitute g(x) into the function f(x) and simplify:

f(g(x)) = f(√x + 6)

Since f(x) = x² + 5, we have:

f(g(x)) = (√x + 6)² + 5

= (x + 6 + 2√x) + 5

= x + 6 + 2√x + 5

= x + 11 + 2√x

Therefore, f(g(x)) simplifies to x + 11 + 2√x.

To find g(f(x)), we substitute f(x) into the function g(x) and simplify:

g(f(x)) = g(x² + 5)

Since g(x) = √x + 6, we have:

g(f(x)) = √(x² + 5) + 6

There is no further simplification possible for g(f(x)).

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Answer:

The Answer Will Be D

Step-by-step explanation:
The fuel economy of a car 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.We need to find the fuel economy of the car when it travels at an average of 20 miles an hour.f(20) = -0.009(20)² +0.699(20) +12f(20) = -0.009(400) +13.98f(20) = 9.6The fuel economy of the car when it travels at an average of 20 miles an hour is 9.6 miles per gallon.Therefore, the answer is option D. 22.38 miles per gallon.

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:

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