∠PQR​​​ is a right angle. Find ​​​m∠PQS​ and ​m∠SQR​.

It would take Arron 3 hours to travel 18 miles upstream (against the river)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operations.

Speed is the ratio of total distance to total time taken.

Arron boat has a speed of 9 mph in still water and the speed of the river is 3 mph. Since he is travelling upstream, we subtract both speed:

He needs to travel 18 miles upstream at time t, hence:

(9 mph - 3 mph) = 18 miles / t

6t = 18

t = 3 hours

It would take Arron 3 hours

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Answer:

and c 20

Step-by-step explanation:

20 percent of t is 1

5 -1 =4

Answer: (-2, -1)

Step-by-step explanation:

Ok since we just have to find A", let's transform only point A.

Point A=(-1, 5).

Now let's translate it: (-1+3, 5-4). Point A' = (2, 1).

Now, we have to do a 180° rotation. The formula is (-x, -y).

Point A'' = (-2, -1)

The measure of the arc or angle indicated are:

(9). m∠KLN = 55°, (10). m∠LMN = 40°, (11). arc RT = 61°, (12). arc PR = 240°, (13). arc EG = 150° and (14). arc ? = 225°

(9). m∠KLN = 1/2(arc NK - arc MK) {secant tangent angle}

m∠KLN = 1/2(160 - 50)

m∠KLN = 110/2

m∠KLN = 55°

(10). m∠LMN = 1/2(140 - 60)

m∠LMN = 80/2

m∠LMN = 40°

(11). 60° = 1/2(181 - arc RT)

120° = 181 - arc RT {cross multiplication}

arc RT = 181 - 120

arc RT = 61°

(12). Angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference.

arc PR = 2(120)

arc PR = 240°

(13). arc EG = 2(75)

arc EG = 150°

(14). m∠TUV = 180 - arc TV {angle between two tangents}

arc TV = 180 - 45

arc TV = 135°

the larger arc ? = 360° - 135°

arc ? = 225°.

Therefore, the measure of the arc or angle indicated are:

(9). m∠KLN = 55°, (10). m∠LMN = 40°, (11). arc RT = 61°, (12). arc PR = 240°, (13). arc EG = 150° and (14). arc ? = 225°

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The value of the expression 0.36 × 4.2 - 0.008 ÷ 25.5 is approximately 1.5116863.

To evaluate the expression 0.36 × 4.2 - 0.008 ÷ 25.5, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, let's simplify the division: 0.008 ÷ 25.5 = 0.0003137 (rounded to six decimal places).

Now, we can substitute the simplified division back into the expression: 0.36 × 4.2 - 0.0003137.

Next, we perform the multiplication: 0.36 × 4.2 = 1.512.

Finally, we subtract the result of the multiplication from the simplified division: 1.512 - 0.0003137 = 1.5116863 (rounded to seven decimal places).

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The measure of angle A in the right triangle is 75.52°

The figure in the image is a right triangle.

Measure of angle A = ?

Adjacent to angle A = 2

Hypotenuse = 8

To solve for the measure of angle A, we use the trigonometric ratio.

Note: cosine = adjacent / hypotensue

Hence:

cos( A) = adjacent / hypotensue

cos( A ) = 2/8

cos( A ) = 1/4

Take the cos inverse

A = cos⁻¹( 1/4 )

A = 75.52°

Therefore, the measure of the angle is 75.52 degree.

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A quadrilateral is a polygon with four sides. All trapezoids have two pairs of parallel sides. Option (a) is correct.

A quadrilateral is a polygon with four sides, and there are several properties and characteristics that can be true about a quadrilateral. Some possible true statements about a quadrilateral include:

1. A quadrilateral has four angles.

2. A quadrilateral has four vertices.

3. The sum of the interior angles of a quadrilateral is always 360 degrees.

4. A quadrilateral can have sides of different lengths.

5. A quadrilateral can have parallel sides.

Compare each of the properties above to the given options.

Options:

a) All trapezoids have two pairs of parallel sides.

b) Only some rectangles have four right angles.

c) All squares are rectangles.

d) Some rhombuses are trapezoids.

We can conclude that option (a) is correct because it correspond to the property 5 of a quadrilateral.

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Answer:

(a) 44 (4 + 4 = 8), 62 (6 + 2 = 8)

(b) 165 (1 + 6 + 5 = 12)

Toheebah covered a distance of 9600 meters by running around the playground 12 times.To

The perimeter of a rectangle can be calculated by adding the lengths of all four sides. In this case, the playground has dimensions of 240 meters by 160 meters, so the perimeter is:

Perimeter = 2 * (Length + Width)

Perimeter = 2 * (240m + 160m)

Perimeter = 2 * 400m

Perimeter = 800m

Therefore, the perimeter of the playground is 800 meters.

To find the distance Toheebah covered by running around the playground 12 times, we multiply the perimeter by 12:

Distance covered = Perimeter * Number of laps

Distance covered = 800m * 12

Distance covered = 9600m

So, Toheebah covered a distance of 9600 meters by running around the playground 12 times.

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Answer: x=6.6

Step-by-step explanation:

The is a 30-60-90 triangle, which means it falls into the special right triangles category

That means that the hypotenuse (x) is the smaller leg (sqrt11) multiplied by 2.

Sqrt11 times 2 is 6.6332495807108

Rounded to the nearest tenth would turn out to be 6.6

1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.

2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.

3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.

1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.

2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.

3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.

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Step-by-step explanation:

There are   pi radians in 180 degrees

  you want   1/4 of 180 degrees   (45/180 = 1/4)  

    so this would be   1/4 pi radians  or   pi / 4   radians

45 *   pi / 180 = pi/4  

The trigonometric ratios are expressed as;

sin θ = 3/5

cos θ = 4/5

tan θ = 3/4

To determine the trigonometric ratios, we need to know the six identities.

These trigonometric identities are listed thus;

From the information given, we have that;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

We have that;

The hypotenuse is labeled as 5.

The adjacent leg is 4

The angle opposite the side labeled 3 is theta

Now, substitute the value to determine the ratios for each identity, we have that;

sin θ = 3/5

cos θ = 4/5

tan θ = 3/4

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Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.

We have,

To figure out how much wrapping paper Mrs. Horwitz needs, she should find the surface area of the rectangular prism box.

The surface area of a rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Given dimensions:

Length (l) = 13 in

Width (w) = 8 in

Height (h) = 11 in

Plugging these values into the formula, we get:

Surface Area = 2(13)(8) + 2(13)(11) + 2(8)(11)

Surface Area = 208 + 286 + 176

Surface Area = 670 in²

Therefore,

Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.

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The minor arcs of the circle C are given as follows:

The arcs of a circle can be classified as minor arcs or major arcs, depending on their angle measures, as follows:

The entire circumference of the circle is of 360º, hence we have that segment LN, connecting two points on the circumference of the circle through the center, represents the diameter of the circle, with an arc length of 180º.

Hence the minor arcs are all the arcs that are smaller than LN, given as follows:

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Answer:

I apologize, I am not able to provide visual drawings or diagrams. However, I can still provide a step-by-step guide to solve the problem.

To find the area of each shape, we need to use rectangles to determine the areas of right triangles that are inside the rectangles. Here are the steps:

1. Draw the given shape on geoboard paper.

2. Surround each triangle with a rectangle so that the vertices of the triangle are on the exterior of the rectangle.

3. Identify the right triangles that are inside the rectangles.

4. Use the formula for the area of a triangle, which is A = (base x height) / 2, to find the area of each right triangle.

5. Use the formula for the area of a rectangle, which is A = length x width, to find the area of each rectangle.

6. Add up the areas of the triangles and rectangles to find the total area of the shape.

Remember to label your answers with the correct units (square units).

The number of possible outcomes that Event E has is 33.

The 36 possible conclusions when rolling two dice is given in the image.

Now, we need to find the event where the sum of two rolled dice is greater than 3

Then, from the outcomes given above we can write those pair whose sum is greater than 3 as

1 + 3=4

1 + 4= 5

1+ 5 = 6

1 + 6 = 7

2+ 2 = 4

2 + 3 = 5

2 + 4 =6

2 + 5 = 7

2 + 6 = 8

3 +3=6

3 + 4 = 7

3 + 5 =8

3 + 6 =9

4 + 3 =7

4 + 4=8

4 + 5 = 9

5+ 5 = 10

5 + 6= 11

6 + 6 = 12

So, there are 33 outcomes whose sum is greater than 3.

The picture related sum greater than 3 is attached below.

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a) Area of rectangle = 28 cm²

b) Area of triangle = 14 cm²

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Length of rectangle = 4 cm

Width of rectangle = 7 cm

Since, WE know that;

Area of rectangle = Lenght x Width

Hence, We get;

Area of rectangle = 4 x 7

Area of rectangle = 28 cm²

And, By figure,

Heigh of triangle = 4 cm

Base of triangle = 7 cm

Hence,

Area of triangle = 1/2 x 4 x 7

Area of triangle = 14 cm²

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Step-by-step explanation:

The volume of a pyramid is 1/3 bh

First step is to find the base

The area of a triangle is 1/2 bh

We have both b and h of the base triangle

Area of base = 16.5 cm^2

Now we can sub. that in with the volume formula

1/3 16.5 x 9

1/3 x 148.5

49.49999999999995

Answer: We can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events.

In this case, we want to find the probability that a randomly selected senior is a varsity athlete or on the honor roll. We can define the events as follows:

A = the event that a senior is a varsity athlete

B = the event that a senior is on the honor roll

From the problem statement, we know:

P(A and B) = 10/200 = 1/20

P(A) = 70/200 = 7/20

P(B) = 68/200 = 17/50

Plugging these values into the formula:

P(A or B) = P(A) + P(B) - P(A and B)

= 7/20 + 17/50 - 1/20

= 21/50

Therefore, the probability that a randomly selected senior is a varsity athlete or on the honor roll is 21/50.

The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.

Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.

Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.

Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.

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The solution is: the dimensions of the flag in inches is:

40 inches by 55 inches.

The flag is rectangular in nature and the formula for calculating the perimeter of a rectangle is P = 2(L+W) where;

L is the length of the flag

W is the width of the flag

From the diagram, L = y and W = 11y/8

Since the perimeter = 190 inches, we will substitute the given parameters into the formula and firs calculate the value of y.

190 = 2(y+11y/8)

190 = 2y + 11y/4

multiply through by 4

760 = 8y+11y

760 = 19y

y = 760/19

y = 40

The length of the flag is 40 inches and the Width of the flag is 11(40)/8 = 55inches.

Hence, the dimensions of the flag in inches is 40 inches by 55 inches.

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complete question:

Item 15 Question 1 Write and solve an equation to answer the question. The perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag? Equation: =190 y= Question 2 Label the dimensions of the flag in inches.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Due to isosceles triangle , ∠ABC = ∠ACB = 7x

∠ACB + ∠ACD = 180  (  Linear pair I think )
7x + 110 = 180
7x = 70

x = 10°

Answer:

130 blackberries

Step-by-step explanation:

[tex]\displaystyle 600\biggr(\frac{78^\circ}{360^\circ}\biggr)=130[/tex]

Answer:

84

Step-by-step explanation:

28+54=84

Answer:84

Step-by-step explanation:

Hi! So to start/set up the problem, since Sophie brought 28 cards, that is how many she has so, so far we only have, 28+_=_.

The next step is to add 54 cards since she added that many. Now we have 28+54=_.

The last step is to calculate.  28+54=84.

Answer:

Step-by-step explanation:

To solve the given linear programming problem graphically, we'll plot the feasible region determined by the given constraints and then identify the optimal solution by maximizing the objective function Z = 10x1 + 20x2.

Step 1: Plotting the Constraints

We'll start by plotting the equations representing each constraint.

Constraint 1: 5x1 + 3x2 ≤ 30

To plot this constraint, we'll first find the points on the line 5x1 + 3x2 = 30. We can do this by setting x1 to 0 and solving for x2, then setting x2 to 0 and solving for x1.

Setting x1 = 0, we get: 3x2 = 30

x2 = 10

So, one point is (0, 10).

Setting x2 = 0, we get: 5x1 = 30

x1 = 6

So, another point is (6, 0).

Plotting these two points and drawing a line passing through them, we get a boundary line for the first constraint.

Constraint 2: 3x1 + 6x2 ≤ 36

Similarly, we find two points on the line 3x1 + 6x2 = 36.

Setting x1 = 0, we get: 6x2 = 36

x2 = 6

So, one point is (0, 6).

Setting x2 = 0, we get: 3x1 = 36

x1 = 12

So, another point is (12, 0).

Plotting these points and drawing a line passing through them, we get a boundary line for the second constraint.

Constraint 3: 2x1 + 5x2 ≤ 20

Again, we find two points on the line 2x1 + 5x2 = 20.

Setting x1 = 0, we get: 5x2 = 20

x2 = 4

So, one point is (0, 4).

Setting x2 = 0, we get: 2x1 = 20

x1 = 10

So, another point is (10, 0).

Plotting these points and drawing a line passing through them, we get a boundary line for the third constraint.

Step 2: Finding the Feasible Region

Now, we shade the region of the graph that satisfies all the constraints. The feasible region is the intersection of the shaded regions determined by each constraint.

Step 3: Maximizing the Objective Function

To maximize the objective function Z = 10x1 + 20x2, we look for the highest possible value within the feasible region. The optimal solution will be at one of the corner points of the feasible region.

We calculate the coordinates of each corner point formed by the intersection of the constraint lines and evaluate Z = 10x1 + 20x2 at each of these points. The corner point with the highest Z value will be the optimal solution.

By evaluating Z at each corner point, we can determine the optimal solution and its corresponding values of x1 and x2.

Note: Without specific numerical values for the corner points, I am unable to provide the exact coordinates and the optimal solution for this problem. However, by following the steps outlined above and evaluating the objective function at each corner point, you can identify the optimal solution for the given linear programming problem.

Hi. First of all, please give me 5 stars. There is the response:

To solve this problem graphically, we first plot the lines corresponding to the constraints, and then find the feasible region by shading the region that satisfies all constraints. Finally, we evaluate the objective function at each corner point of the feasible region to find the optimal solution.

The constraints can be rewritten in slope-intercept form as follows:

5x1 + 3x2 ≤ 30 => x2 ≤ (-5/3)x1 + 10

3x1 + 6x2 ≤ 36 => x2 ≤ (-1/2)x1 + 6

2x1 + 5x2 ≤ 20 => x2 ≤ (-2/5)x1 + 4

We plot these lines on a graph:

```

| / 5x1 + 3x2 = 30

6 +-------/------------

| / 3x1 + 6x2 = 36

| /

4 +----/--------------

| / 2x1 + 5x2 = 20

| /

2 +-/----------------

| /

|/

+------------------

0 2 4 6 8

```

Next, we shade the feasible region:

```

| /

6 +-------/-----RR-----

| / -----RR-----

| / -----RR-----

4 +----/-----RRR------

| / --RRRRRR------

| / -RRRRR--------

2 +-/----RRRR----------

| / R--------------

|/ R--------------

+------------------

0 2 4 6 8

```

The feasible region is the shaded area. There are 4 corner points: (0, 4), (4, 2), (6, 0), and (8/7, 26/21).

Finally, we evaluate the objective function at each corner point:

- (0, 4): Z = 10(0) + 20(4) = 80

- (4, 2): Z = 10(4) + 20(2) = 80

- (6, 0): Z = 10(6) + 20(0) = 60

- (8/7, 26/21): Z = 10(8/7) + 20(26/21) = 170/7

The optimal solution is (8/7, 26/21) with a maximum value of 170/7.

Answer:

---------------------------

There are total 20 numbers and half of them odd and half of them even.

Without replacement, the probability of an odd and then even number is:

Answer:

The correct answer is:

(A) enlargement

The missing probability is P(A|B) is 12/25 if P(B) is 1/4P and (A and B) is 3/25P.

P(B) = 1/4

P(A and B) = 3/25

The conditional probability is used to find the P(A|B):

P(A|B) = P(A and B) / P(B)

Conditional probability is defined as the number of possible outcomes from a given event based on the previous outcomes of the events.

By substituting the given values in the given probability, we get:

P(A|B) = (3/25) / (1/4)

Divide the fraction and multiply it with its reciprocal:

P(A|B) = (3/25) * (4/1)

P(A|B) = 12/25

Therefore, we can conclude that the missing probability is P(A|B) is 12/25.

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The complete question is:

Find the missing probability.

P(B)=1/4P

(AandB)=3/25P

P(A|B)=?

The correct statement regarding the bar graph is given as follows:

D. The light shined three times farther with brand “C” batteries than with brand “B” batteries.

A bar graph shows the output considering a given input.

Hence the bar graph in this problem shows the average lifetime for each battery type, given as follows:

Brand C has triple the length of Brand B, hence the correct statement is given by option D.

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