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measure of Angle PRT = 90 degrees

A circle with center T exists -- Given

Point R is on the the circle. -- THIS IS AN ASSUMPTION BASED ON THE PICTURE (if you have more information that makes this not true, the rest of this logic fails).

Line segment TR is the radius of the circle. -- Definition of radius

Line PR is tangent to the circle. -- PR touches at exactly one point: R

Angle PRT has a vertex as point R. -- definition of angle PRT

Since PR is tangent to the circle, TR is perpendicular to PR -- consequence of lines perpendicular to circles

Perpendicular lines form right angles. -- Consequence of two congruent angles that form a straight angle pair.

The measure of a right angle is 90 degrees. -- definition of right angle

Therefore, the measure of angle PRT is 90 degrees.

The given probabilities are as follows:

The probabilities are determined using the formula below:

Spinner landing on at least one A:

number of at least one A = 7

Spinner landing on at least one A = 7/16

Spinner landing on C and D in any order:

number of landing on C and D in any order = 2

Spinner landing on C and D in any order = 2/16

Spinner landing on C and D in any order = 1/8

Spinner landing on two Bs:

number of  landing on two Bs = 1

Spinner landing on two Bs = 1/16

Spinner landing on C on the second spin:

Number of landing on C on the second spin = 4

Spinner landing on C on the second spin = 1/4

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The p value based on the information will be E. P - value ≥ 0.20

Open Minitab 17. Select 'Stat' -> 'Basic Statistics' -> '2 - Sample t... Select 'Summarized data' from the dropdown menu.

Enter 5 in both Sample size of sample 1 and sample 2, 168 and 172 in Sample mean of Sample 1 and Sample 2. 5.4 and 7.5 in Standard deviation of Sample 1 and Sample 2.

Click on 'Options' and Enter 'Confidence level' 95.0(or the given Cofidence level) , 'Hypothesized difference' 0.0 , 'Alternative hypothesis' 'Difference \\neq Hypothesized difference'. Also the box 'Assume equal variance' can be ticked as requirement.

Click on 'Ok' -> 'Ok'.

Output: -

P - value = 0.361 i.e., P - value ≥ 0.20

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Answer:

Step-by-step explanation:

To compare these two values, we first need to convert the mixed number 7 3/8 to an improper fraction. To do so, we multiply the whole number (7) by the denominator of the fraction (8), then add the numerator (3), and put the result over the denominator:

7 3/8 = (7 x 8 + 3) / 8 = 59/8

Now we can rewrite the inequality as:

(59/8) × (4/5) < 59/8

To simplify the left-hand side of the inequality, we multiply the numerators and denominators:

(59/8) × (4/5) = (59 × 4) / (8 × 5) = 236/40 = 59/10

So the inequality becomes:

59/10 < 59/8

To compare these fractions, we need to find a common denominator. The least common multiple of 8 and 10 is 40, so we can convert both fractions to have a denominator of 40:

59/10 = (59 x 4) / (10 x 4) = 236/40

59/8 = (59 x 5) / (8 x 5) = 295/40

Now we can see that 236/40 < 295/40, which means that:

59/10 < 59/8

Therefore, the inequality 7 3/8 × 4/5 < 7 3/8 is true.

The two equivalent expressions are 6(x − y) and 6x − 6y.

These expressions look different but their simplified forms are same expressions are called equivalent expressions.

The 1st expression shows subtracting the number of packages of cherry snacks from the number of packages of strawberry snacks in each box.

When we multiplying the difference by the number of boxes then, it will be: 6(x-y)

Now, total number of cherry snacks and subtracting it from the total number of strawberry snacks will be 6x - 6y. So, equivalent expressions means in terms of situation are 6(x − y) and 6x − 6y.

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Answer:

x = 65

Step-by-step explanation:

let the number be 'x'.

If 86 is added to a number, the result is 44 less than three times the number. Therefore the equation will be,

=> 86 + x = 3x - 44

Rearranging,

=> x - 3x = -44 - 86

=> -2x = -130

=> x = 130/2

=> x = 65

As we used the distributive property of multiplication to rewrite 7+21 as a product of 7 x (1+3) or 7 x 4.

However, you are asked to express this sum as a product of two factors. A factor is a number that is multiplied by another number to produce a product. Therefore, to express 7+21 as a product of two factors, we need to find two numbers that, when multiplied together, give us the sum of 7+21.

One way to approach this problem is to use the distributive property of multiplication, which states that a(b+c) = ab + ac. We can apply this property by rewriting 7+21 as 7+3*7, since 21 is equal to 3 times 7. Then, we can factor out the common factor of 7 from the expression to get:

7+37 = 7(1+3)

Now, we have expressed 7+21 as a product of two factors: 7 and (1+3), or simply 7 and 4. Therefore, the expression that shows 7+21 written as a product of two factors is:

7 x (1+3) or 7 x 4

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Daniel incorrectly applied the square root to both terms on the left side of the equation and he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.

Let's first look at the first equation that Daniel solved incorrectly:

25x²-16=9

Daniel's solution:

√(25x² )-√16=√9

5x-4=±3

5x=±7

x=±7/5

What Daniel did wrong here is that he incorrectly applied the square root to both terms on the left side of the equation.

Instead, he should have simplified the left side first, using the fact that √(a²) = |a|, before applying the square root. So the correct solution is:

25x²-16=9

25x²=25

x²=1

x=±1

Now let's look at the second equation that Daniel solved incorrectly:

z³-2=6

Daniel's solution:

z³=8

∛(z^3 )=∛8

z=±2

What Daniel did wrong here is that he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.

In fact, z³ = 8 has three roots: z = 2, z = -1 + i√3, and z = -1 - i√3. So the correct solution is:

z³-2=6

z³=8

z=2

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The length of c in the triangle is 4.2 units.

The side of a triangle can be found using cosine law as follows:

Hence,

c² = a² + b² - 2ab cos C

where

Therefore,

c² = 7² + 8² - 2(7)(8) cos 32°

c² = 49 + 64  - 112 cos 32°

c² = 113 - 112(0.84804809615)

c² = 113 - 94.9813867695

c² = 18.019

square root both sides of the equation

c = √18.019

c  = 4.24487926801

c = 4.2 units

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According to the information, the router cannot cover the kitchen area.

To calculate if the router covers the kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router. So, we have to calculate the square root of 850 ft^2.

From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.

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The value of 3.1 divided by 6 leaving 7 digits after the decimal point without rounding is 0.5166666

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

3.1 divided by 6

When represented as an expression, we have

3.1 divided by 6 = 3.1/6

The above expression can be calculated using a calculator

Using a calculator, we have

3.1/6 = 0.51666666666

This means that

3.1 divided by 6 = 0.51666666666

Leaving 7 digits after the decimal point without rounding, we have

3.1 divided by 6 = 0.5166666

Hence, the value of 3.1 divided by 6 is 0.5166666

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The probability that a randomly selected test score will fall in the interval 360 to 380 is the option (3), 0.24.

To calculate the probability that a test score falls between 360 and 380, we need to standardize these values by subtracting the mean and dividing by the standard deviation.

This gives us:

z(360) = (360-350)/18 = 0.56

z(380) = (380-350)/18 = 1.67

We can then use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores.

The probability is approximately 0.24.

Therefore, the answer is option (3), 0.24.

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The probability that fewer than 18 people from this sample were between the ages of 25 and 34 is 0.1089 (or 10.89%).

Using the normal approximation to the binomial distribution, the mean (μ) of the sample is:

μ = np = 90 x 0.26 = 23.4

The standard deviation (σ) of the sample is:

σ = √(np(1-p)) = √(90 x 0.26 x 0.74) = 4.37 (rounded to 4 decimal places)

To find the probability that fewer than 18 people from this sample were between the ages of 25 and 34, we need to calculate the z-score:

z = (x - μ) ÷ σ = (18 - 23.4) ÷ 4.37 = -1.24

Using a standard normal table or calculator, we find that the probability of a z-score less than -1.24 is 0.1089.

0.1089 = 10.89%

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Answer:

The correct answer is (C) 310.

Multiplying the given expression by 36 gives:

(32)(38) + (35)(35) - (33)(37)

= 1216 + 1225 - 1221

= 1220

So the equivalent expression is 1220.

Option (C) 310 is not equivalent to 1220.

Answer:

The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width and h is the height.

In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of 2(7) (3.6) + 2(7) (2.4) + 2(3.6) (2.4), which simplifies to 50.4 + 33.6 + 17.28, or 101.28 square centimeters.

So, the surface area of this rectangular prism is 101.28 square centimeters.

Received message. The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is `2lw + 2lh + 2wh`, where `l` is the length, `w` is the width and `h` is the height. In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of `2(7)(3.6) + 2(7)(2.4) + 2(3.6)(2.4)`, which simplifies to `50.4 + 33.6 + 17.28`, or **101.28 square centimeters**. So, the surface area of this rectangular prism is **101.28 square centimeters**.

Step-by-step explanation:

By summing all the fractions that was left, we have 3 cups of flour left. The correct option is (B).

The "x" represents the quantity while the fractions represents the value.

To get the cups of flour left, we first multiply the number of "x" with the fraction and then add the resulting fractions together.

Cups left = 1 (1/8) + 1(3/8) + 2(1/2) + 2(3/4)

= 1/8 + 3/8 + 1 + 3/2

Find the LCM

= [tex]\frac{1 + 3 + 8 + 12}{8}[/tex]

= 24/8

Cups left = 3 cups

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The image point of the coordinate X after the rotation is (-1, 5).

When a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.

So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).

Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).

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The exact values are;

sin⁡θ = -5/√29

cos⁡θ = 2/√29

sec⁡θ =√29/2

csc⁡θ = -√29/5

cot⁡θ = -2/5

We are given that

tan⁡θ=-5/2 and sin⁡θ>0

First quadrant: I, 0°<θ<90°

We can find the first quadrant between 0° and 90° , the values from 0 to the positive numbers for the x-axis and the y-axis, the functions sine, cosine and tangent will always have positive values.

sin⁡θ = -5/√29

cos⁡θ = 2/√29

sec⁡θ =√29/2

csc⁡θ = -√29/5

cot⁡θ = -2/5

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Answer:

Step-by-step explanation:

-4+8-3-7+1-6-2+5

4-10-5+3

-6-2

-8

Step-by-step explanation:

the negative sign changes to a positive sign so

( -12)+ (-10) -(-7)+(-7)

= -22

The shaded area of the circle is around 65.44 square meters in size.

To find the area of the shaded region, subtract the area of sector FGH from the area of sector FEGH.

The area of sector FEGH is:

A1 = (1/2) r² θ₁

where r = radius of the larger circle and θ₁ = angle subtended by the arc EH.

Since EH = 30 m and the radius of the larger circle = 18 m (half of 10 + 8):

θ₁ = (EH arc length) / r = 30/18π radians

So,

A₁ = (1/2) (18)² (30/18π) = 270/π m²

The area of sector FGH is:

A₂ = (1/2) r² θ₂

where θ₂ = angle subtended by the arc GH.

Since GH is 8 m and the radius of the larger circle is 18 m:

θ2 = (GH arc length) / r = 8/18π radians

So,

A₂ = (1/2) (18)² (8/18π) = 64/π m²

Therefore, the area of the shaded region is:

A = A₁ - A₂ = (270/π) - (64/π) = 206/π ≈ 65.44 m²

Hence, the area of the shaded region is approximately 65.44 square meters.

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By ASA (Angle-Side-Angle) congruence, triangle ABC is congruent to triangle DEF.

Instructions to draw the routes:

Draw the x-axis and y-axis to create a coordinate plane.

Mark the starting point of Zari's run as (0,0) on the coordinate plane.

From (0,0), move 2 units north to reach (0,2).

From (0,2), move 4 units east to reach (4,2).

From (4,2), move directly back to the starting point (0,0) using the shortest route.

Mark the starting point of Taye's run as (0,0) on the coordinate plane.

From (0,0), move 2 units west to reach (-2,0).

From (-2,0), move 4 units south to reach (-2,-4).

From (-2,-4), move directly back to the starting point (0,0) using the shortest route.

Instructions to prove that the two triangles are congruent using ASA:

Label the vertices of Zari's triangle as A (0,0), B (4,2), and C (0,0).

Label the vertices of Taye's triangle as D (0,0), E (-2,-4), and F (0,0).

Show that angle A and angle D are congruent because they are both right angles (90 degrees).

Show that segment AB and segment DE are congruent because they both have a length of 4 units.

Show that segment AC and segment DF are congruent because they both have a length of 2 units.

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Answer:

the formula: Speed = Distance / Time.

Let's break down the problem into two parts:

a) Find the average speed of the motorist.

Let's assume the average speed of the motorist is "v" km/h.

The distance the motorist traveled in 1 1/2 hours is given by: Distance = Speed × Time = v × (3/2) km.

The distance the cyclist traveled in 1 1/2 hours (opposite direction) is given by: Distance = Speed × Time = 45 × (3/2) km.

Since they passed each other, the sum of their distances should be equal to the distance between Town A and Town B.

So, we can set up the equation: v × (3/2) + 45 × (3/2) = Distance between Town A and Town B.

b) Find the distance between Town A and Town B.

When the motorist reached Town B 2 hours later, the cyclist was 30 km away from Town A.

We can set up the equation: Distance between Town A and Town B = v × 2 + 30.

Now, let's solve the equations:

v × (3/2) + 45 × (3/2) = v × 2 + 30.

Simplifying the equation, we have: (3v + 135)/2 = 2v + 30.

Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 3v + 135 = 4v + 60.

Subtracting 3v from both sides of the equation, we have: v = 75.

Therefore, the average speed of the motorist is 75 km/h.

To find the distance between Town A and Town B, we substitute the value of v into the equation:

Distance between Town A and Town B = v × 2 + 30 = 75 × 2 + 30 = 150 + 30 = 180 km.

Therefore, the distance between Town A and Town B is 180 km.

The value of x in the equation y = 9 sec(2x) at [0, π/4) ∪ (π/4, π/2] is x = 1/2[sec₋¹(y/9)]

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

y = 9 sec(2x)

The interval of x is also given as

[0, π/4) ∪ (π/4, π/2]

This means that the values of x is from 0 to π/2, however, the function is undefined at x = π/4 i.e. there is a hole at x = π/4

Next, we set the equation to y

So, we have

9 sec(2x) = y

Divide both sides by 9

sec(2x) = y/9

Take the arc sec of both sides of the equation

2x = sec₋¹(y/9)

Divide both sides by 9

x = 1/2[sec₋¹(y/9)]

Hence, the value of x is x = 1/2[sec₋¹(y/9)]

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The number of solutions for the given system of linear equations is: Infinitely many solutions.

To determine the number of solutions for the given system of linear equations:

3x - y = 4

6x - 2y = 8

We can use the algebraic method of solving the system of equations by substitution or elimination.

Let's use the algebraic method to determine the number of solutions:

3x - y = 4 (1)

6x - 2y = 8 (2)

We can simplify equation (2) by dividing both sides by 2:

3x - y = 4 (1)

3x - y = 4 (2')

Equations (1) and (2') are equivalent, which means that they represent the same line.

Therefore, the two equations represent the same line, and we have infinitely many solutions.

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Complete question

What’s the numbers that correspond to the corret number of solutions

0 solution, 1 solution, Many solutions

3x - y = 4

6x - 2y = 8

Answer:

B. Y= 5x - 2

Step-by-step explanation:

The Y is negative, you can see the number -5 below the point, if you go to the top, that is, to 0 and count down, the lines are two and the X is positive 5, you can see where the number 5 is and the point is above.

Answer:

C

Step-by-step explanation:

Answer: C

Step-by-step explanation: Rise/run so 1/1=1 but it's going down so it negative. -1

Squaring a number implies increasing it by itself. In case the number being squared is negative, the result will continuously be positive. Increasing a number by 2 implies multiplying it, which is not linked to squaring a number.

To square a number, one must raise it to the power of two, that is different from carrying out its multiplication with itself. One way of squaring a value is shown by taking the number 3 and raising it to the power of 2.

3² = 3 x 3 = 9

By the same way , if we raise -2 to the power of 2, the result will be a positive value of four.

Raising numbers to the power of two is a frequent mathematical procedure use in numerous academic fields such as algebra, geometry, physics, and statistics.

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Answer: 720

Step-by-step explanation: There are 6 choices for the first letter,  5 for the  second,  4 for the third and so on. 6*5*4*3*2=720

Step-by-step explanation:

according to the law of combination

Answer:A

Step-by-step explanation: