Wants to buy new boots that cost $68. The sales tax rate in her city is 5-%. What is the total cost for the boots

The required transformed coordinates of the quadrilateral as:A'(-10, 0),B'(-8, -6),C'(-3, -7), D'(0, -3).

The image matrix for the composite transformation of a rotation of 270º and a reflection over the line y=-x can be found by multiplying the transformation matrices for each operation.

The rotation matrix for 270º counterclockwise can be represented as:

[tex]$R_{270} = \begin{bmatrix}0 & -1 \1 & 0\end{bmatrix}$[/tex]

The reflection over the line y=-x can be represented as:

[tex]$F_{y=-x} = \begin{bmatrix}0 & -1 \-1 & 0\end{bmatrix}$[/tex]

To find the composite transformation matrix, we multiply the two matrices:

[tex]$M = F_{y=-x} \cdot R_{270} = \begin{bmatrix}0 & -1 \-1 & 0\end{bmatrix} \cdot \begin{bmatrix}0 & -1 \1 & 0\end{bmatrix} = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix}$[/tex]

To apply this transformation to the coordinates of the quadrilateral ABCD, we write each point as a column vector:

[tex]$A = \begin{bmatrix}-10 \0\end{bmatrix}$[/tex],

[tex]$B = \begin{bmatrix}-8 \6\end{bmatrix}$[/tex],

[tex]$C = \begin{bmatrix}-3 \7\end{bmatrix}$[/tex],

and

[tex]$D = \begin{bmatrix}0 \3\end{bmatrix}$[/tex]

We can then apply the composite transformation matrix M to each of these vectors:

[tex]$A' = M \cdot A = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-10 \0\end{bmatrix} = \begin{bmatrix}-10 \0\end{bmatrix}$[/tex]

[tex]$B' = M \cdot B = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-8 \6\end{bmatrix} = \begin{bmatrix}-8 \-6\end{bmatrix}$[/tex]

[tex]$C' = M \cdot C = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-3 \7\end{bmatrix} = \begin{bmatrix}-3 \-7\end{bmatrix}$[/tex]

[tex]$D' = M \cdot D = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}0 \3\end{bmatrix} = \begin{bmatrix}0 \-3\end{bmatrix}$[/tex]

We can then write the transformed coordinates of the quadrilateral as:

A'(-10, 0),

B'(-8, -6),

C'(-3, -7),

D'(0, -3)

Therefore, the image matrix of quadrilateral ABCD after the composite transformation is:

[tex]$ \begin{bmatrix}-10 & -8 & -3 & 0 \0 & -6 & -7 & -3\end{bmatrix}$[/tex]

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No, she have not enough time to fill the pool before he gets home. The garden hose with flow rate 24 gal/min will take 40 minutes to complete fill up the tank that is t ~ 40 minutes. So, she cannot complete fill up the pool before he come.

We have, the time in which Ines's younger brother will be home = an half hour = 1/2 hour

water flow rate of garden's hose = 24 gal/min

She want to fill up the pool. From the figure, depth of pool = 3 ft

Width of pool = 10 in.

1 inch = 0.0833 feet

So, 10 inches = 0.833 feet

outer diameter of pool = 9 ft

so, outer radius of pool = 4.5 ft

Now, inner diameter of pool/tank = outer diameter - 2(width)

= 9 - 2×0.833

= 9 - 1.666 = 7.334

Inner radius of pool = 7.334/2 = 3.667 ft

Water flow rate, Q = 24 gal/min

= 24/7.48 gal ( since 1 ft³ = 7.48 gal)

= 3.20 ft³

Using formula, Q = volume/ time

where t --> time to fill up the pool through hose

Volume of tank/pool = surface area × height (depth)

= π r² × h , where r is inner radius

= π (3.667)² × 3 ft³

= 126.71 ft³

So, Q = 126.71 ft³/t

=> t = 126.71 ft³/3.20 ft³

=> t = 39.59 min

Hence, required time is 39.59 ~ 40 minutes and she cannot complete before he come.

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Complete question:

Ines's younger brother will be home in a half hour. If her garden hose flows at a rate 24 gal/min, does she have enough time to fill the pool before he gets home? See the above figure

Explain. (Hint: 1 ft³ = 7.48 gal)

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Using the laws of exponents, the solution to the given problem is: 25

Some of the laws of exponents are:

1) Product of powers rule: This means that we add powers together when multiplying like bases.

2) Quotient of powers rule: This means that we subtract powers when dividing like bases.

3) Power of powers rule: This means that we multiply powers together when raising a power by another exponent.

4) Power of a product rule: This means that when any base is being multiplied by an exponent, distribute the exponent to each part of the base.

5) Negative exponent rule: This means that when there is a number being raised by a negative exponent, flip it into a reciprocal to turn the exponent into a positive

We are given the expression:

[tex]\frac{1}{5^{-2} }[/tex]

Using the negative exponent rule, we will have:

5² = 25

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The result will be the amount of interest earned or paid. Don't stress out too much - with a little practice, you'll become an expert at using this formula!

Sure, I'd be happy to help you with I=prt! This formula is used to calculate simple interest. "I" stands for the interest, "p" stands for the principal (the amount of money borrowed or invested), "r" stands for the interest rate (expressed as a decimal),

and "t" stands for the time period (usually expressed in years). To use the formula, simply multiply the principal by the interest rate and the time period (in years).

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Answer:

2200

Step-by-step explanation:

have a good day

The coordinates of the resulting point, P' as required to be determined in the task content is; (1, -6).

It follows from the task content that the coordinates of the image point P' formed when point P(-1, 6) is rotated 180° counterclockwise around the origin is to be determined.

On this note, since a rotation of 180° is such that we have;

(x , y) ======> (-x, -y).

Hence, when point P(-1, 6) is rotated 180° counterclockwise around the origin, the resulting image point, P' has coordinates; (1, -6).

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After answering the provided question, we can conclude that As a result, percentage the answer is A. 27.5%.

A percentage is a ratio or number expressed as a percentage of 100 in mathematics. The abbreviations "pct.," "pct," and "pc" are also used on occasion. Despite this, the percentage symbol "%" is commonly used to represent it. The % value is dimensionally empty. In essence, percentages are fractions with a denominator of 100. To indicate that a number is a percentage, a percent sign (%) should be placed next to it. For example, you receive a 75% on an exam if you correctly respond to 75 out of 25 pages (75/100). Divide the result by 100 after dividing the amount by the total when calculating percentages. The percentage is found by multiplying (value/total) by 100%.

To calculate the percentage of Monroe Middle School seventh-graders who participate in the school band, divide the number of students who play an instrument by the total number of seventh-graders and multiply the result by 100.

There are 33 seventh-graders in the school band, and there are 120 seventh-graders in total. Therefore:

percentage = (33 / 120) x 100% % = 27.5%

As a result, the answer is A. 27.5%.

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If your friend went to bed at 1:00am on Friday and woke up at 1:00pm on Friday, she slept for 12 hours.

To see why, you can count the number of hours between 1:00am and 1:00pm:

1:00am to 2:00am = 1 hour

2:00am to 3:00am = 1 hour

...

11:00am to 12:00pm = 1 hour

12:00pm to 1:00pm = 1 hour

The total number of hours between 1:00am and 1:00pm is 12 hours.

The equation of line perpendicular to y = -4x and passing through the point (12, 6) is y = 1/4 x + 3.

Using the slope method, determine the slope.

To find the y-intercept (b), use the slope and one of the locations.

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).

The given equation is y = -4x and we need to find the equation of the line which is passing through the point (12,6).

As y=-4x, therefore compared to the standard equation y = mx, hence the slope of the line is m = -4.

Therefore any line which is perpendicular and has a slope that is the negative reciprocal of the -4 is 1/4.

The modified equation becomes for the line that passes through (12, 6).

y-6 = 1/4 (x-12)

solving this equation we get,

y-6 = 1/4 x - 1/4 * 12

y-6 = 1/4 x - 3

y = 1/4 x -3 + 6

y = 1/4 x + 3

Therefore option 4 is correct, y = 1/4 x + 3

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The Saints had the best overall record for the season because they had a larger mean value of about 200 points, whereas the Saints had a larger median value of 12 points.

To determine which team had the best overall record for the season, we need to consider the total number of points earned by each team across all games. We can calculate the total points for each team by adding up the points earned in each game.

For the Saints:

Total points = 21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 200

For the Cowboys:

Total points = 10+3+8+6+24+12+21+3+10+28+28+7+7+13+3 = 183

Therefore, the Saints earned a total of 200 points, while the Cowboys earned a total of 183 points. Therefore, the Saints had the better overall record for the season.

To compare the central tendency of the points earned by each team, we can use either the mean or the median. However, in this case, the median is a better measure of center because it is less sensitive to extreme values than the mean.

Calculating the median for each team:

For the Saints:

Arrange the points earned in ascending order: 3 3 7 10 10 12 12 14 17 20 21 28 40

The median value is the middle value, which is 12.

For the Cowboys:

Arrange the points earned in ascending order: 3 3 6 7 8 10 10 12 13 21 24 28

The median value is the middle value, which is 10.

Therefore, the Cowboys have a median value of 10 points, while the Saints have a median value of 12 points. However, as we already determined, the Saints had a better overall record for the season based on the total points earned.

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28.26 is the volume of the fig.

Each thing in three dimensions takes up some space.

The volume of this area is what is being measured.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

Knowing an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

Hence, 28.26 is the volume of the fig.

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Annie made mistake in her trigonometric ratios. The opposite side of the right triangle should be 6 cm not 8 cm.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Annie tries to solve the angle ABC of the right triangle. The angle ABC can be found using trigonometric ratios as follows:

where

∅ = angle ABC

Therefore,

sin ∅ = opposite / hypotenuse

sin ∅ = 6 / 10

sin ∅ = 3 / 5

∅ = sin⁻¹ 0.6

∅ = 36.8698976458

∅ = 36.87 degrees

Therefore, she made mistake in her trigonometric ratios.

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Model reef can sustain 20% net fishing  because the species didn’t increase as much as it did with the other net fishing method.

Explanation:

What is reef fishing ?

Reef fishing is commonly called “Bottom Bouncing” where anglers using heavy 60-100lb handline and rod techniques to target such prized eating fish as Coral Trout, Red Emperor and Nannygai.

What is net fishing ?

A fishing net is a net used for fishing. Nets are devices made from fibers woven in a grid-like structure. Some fishing nets are also called fish traps, for example fyke nets.

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Answer:

10,
7777777777777777777777777777777777

Step-by-step explanation:

The dimensions of the can that use the least amount of material are a radius of approximately 4.38 cm and a height of approximately 3.11 cm.

To design a can that uses the least amount of material, we want to minimize its surface area. Since the can is shaped like a right circular cylinder, its surface area is given by:

A = 2πr² + 2πrh

where r is the radius of the base of the cylinder and h is its height.

We also know that the volume of the can is given by:

V = πr²h

We can use these equations to express h in terms of r, and then substitute this expression for h into the equation for surface area. Then we can differentiate the resulting equation with respect to r, set it equal to zero, and solve for r to find the value of r that minimizes surface area.

First, we solve for h in terms of r by rearranging the equation for volume:

h = V/(πr²)

Substituting this expression for h into the equation for surface area, we get:

A = 2πr² + 2πr(V/(πr²))

A = 2πr² + 2V/r

To minimize A, we differentiate with respect to r:

dA/dr = 4πr - 2V/r²

Setting this expression equal to zero and solving for r, we get:

4πr = 2V/r²

r³ = V/(2π)

Substituting the given value for V, we get:

r³ = 432/2π

r ≈ 4.38 cm

Now we can use the expression for h in terms of r to find the corresponding height:

h = V/(πr²) ≈ 3.11 cm

Therefore, the dimensions of the can that use the least amount of material are a radius of approximately 4.38 cm and a height of approximately 3.11 cm.

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Answer:

it is option no d at least

cuz it is what it is

Step-by-step explanation:

All three angels of a triangle have to sum to 180 degrees ....so there is only 90 degrees left for the other two  equal-sized angles (isosceles).....they must be 45° each

This inequality states that the total cost of buying x gumballs and y jawbreakers must be less than or equal to $3.00.

Let x be the number of gumballs that Bob buys, and let y be the number of jawbreakers that Bob buys.

The cost of buying x gumballs is $0.50 times x, or 0.50x. The cost of buying y jawbreakers is $0.30 times y, or 0.30y.

Bob has $3.00 to spend on candy, so we can write an inequality to represent the total cost of buying both types of candy:

0.50x + 0.30y ≤ 3.00

This inequality states that the total cost of buying x gumballs and y jawbreakers must be less than or equal to $3.00.

Note that this inequality assumes that Bob spends all of his money on candy. If Bob wants to save some money or spend it on something else, the inequality would need to be modified accordingly.

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According to the question we can conclude that the total mass of the jars is 2.561 g.

The mass is the amount of matter in an object. It is measured in grams, kg, ect. According to the law of conservation, mass in such an isolated system may only be changed through one form to another and cannot be created or destroyed.

To find the total mass of the jars, we simply need to add up the masses of jar one, jar two, and jar three:

Total mass of jars = mass of jar one + mass of jar two + mass of jar three

Total mass of jars = 0.62 g + 1.431 g + 0.5 g

Total mass of jars = 2.561 g

So the total mass of the jars is 2.561 g.

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To identify which lines intersect the line y = 3, you would need to provide a list of lines to choose from. In general, any line that is not parallel to y = 3 will intersect it. Lines parallel to y = 3 will have equations of the form y = c, where c is a constant value different from 3.

Answer:

x is the number of successes

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

There is a 17.18% probability that a randomly selected region had exactly two hits.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]

In which

x is the number of successes

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

In this problem we have that:

A total of 525 bombs hit the combined area of 561 regions. So the mean hits per region is:

[tex]P=\dfrac{525}{561}=0.9358[/tex]

Assume that we want to find the probability that a randomly selected region had exactly two hits.

This is P(X = 2).

[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]

[tex]P(X=2)=\dfrac{e^{-0.9358}\times(0.9358)^2}{(2)!}=0.1718[/tex]

There is a 17.18% probability that a randomly selected region had exactly two hits.

Answer:

4

Step-by-step explanation:

because it median, so it number  was the middle of the total

as we know there is total of 9

and we count to 5

so it 4 letters

Answer:

4

Step-by-step explanation:

arranging the name lengths from smallest to largest we have; 3,3,3,3,4,5,7,7,9

From the set of numbers,4 appears at the middle hence the median name length.

Answer:

Step-by-step explanation:

Answer:

[tex]a = \frac{1296}{5\pi} [/tex]

Step-by-step explanation:

Given:

C = 14,4 (circumference)

Find: A - ? (area)

Let's start by writing down both circumference and area formulas:

[tex]c = 2\pi \times r[/tex]

[tex]a = \pi \times {r}^{2} [/tex]

We can find the radius (r) from the 1st formula:

[tex]r = \frac{c}{2\pi} = \frac{14.4}{2\pi} =14 \frac{4}{10} \times \frac{1}{2\pi} = \frac{144}{10} \times \frac{1}{2\pi} = \frac{144}{20\pi} = \frac{36}{5\pi} [/tex]

Now, that we know the length of the radius, we can find the area:

[tex]a = \pi \times( { \frac{36}{5\pi} })^{2} = \frac{1296}{25 {\pi}^{2} } \times \frac{\pi}{1} = \frac{1296}{25\pi} [/tex]

bonjour,

a) on pourrait faire un produit en croix

8,3 m ----> 1s

combien de m en ----> 120s

120*8,3= 996m en 120s

soit 0,996 km (on décale de 3 rangs vers la gauche)

il parcoure donc 996m en 120secondes

b) pour parcourir 3km, de même faisons un produit en croix

(3 km = 3000m)

8,3 m ---> 1s

3000m ----> combien de secondes ?

3000*1/8,3= environ 361,45 secondes

transformons les en heures, minutes

361,45/60 = 6,02 minutes

0,02*60= 1,2

donc pour parcourir 3km, à cette vitesse, il mettra environ 6 minutes et 1 seconde.

c) posons un produit en croix :

vitesse en km/h

15km ----> 25 min

? -----> 60 min (1h)

60*15/25= 36

donc il a une vitesse de 36km/h

vitesse en km/mn

15km ----> 25 min

?km ------> 1 min

1*15/25 =0,6 km/mn

voilà j'espère t'avoir aidé

si t'as des questions n'hésite pas

The distance across the lake, given the distance of the tree and Cade would be 14.36 ft.

We can use the concept of similar triangles to solve this problem:

(Length of the tree's shadow) / (Distance from the tree to the edge of the lake) = (Length of Cade's shadow) / (Cade's height)

36.2 / 15 = 2.5 / 6.2

Now we can set up another proportion using the length of the tree's shadow and the length of the lake:

(Length of the tree's shadow) / (Length of the lake) = (Distance from the tree to Cade) / (Length of Cade's shadow)

Plugging in the values we know, we get:

36.2 / 15.6 = 15 / 2.5

6.2 * 2.32051282 = 14.36 ft

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The full question is:

The trees shadow is 36.2 feet long. The tree is 15 feet away from the edge of the lake. Cade is 6.2 feet tall and his shadow is 2.5 feet long, his shadow is measured at the exact time the trees shadow reaches the other side of the lake which is 15.6 feet long. What is the distance across the lake (water's edge to opposite side)​

Answer:

i) ABCDEF has an area of 98m

ii) Flower bed has an area of 6m

iii) The area of the grass is 92m

Hope this helps!

Step-by-step explanation:

The area of a triangle is  [tex]\frac{1}{2}[/tex] × L × H

The area for the triangle flower bed will be [tex]\frac{1}{2}[/tex] × 6m × 2m or 6m.

In order to find the entire area of ABCDEF, draw a segment FC to create a trapezoid and a rectangle. The rectangle has an area of 77m ( 7 × 11 ). The trapezoid has a formula of [tex]\frac{1}{2}[/tex] × ( b + b ) × h, this would be [tex]\frac{1}{2}[/tex] × ( 10 + 11 ) × 2.

The trapezoid has an area of 21, this added to the rectangle's area of 77 equals 98m as the total area of the garden.

Subtract the area of the flower bed ( 6 ) from the area of the garden, and you get an area of 92m. This is the area of grass.