Michelle has 3 kg of strawberries that she divided equally into small bags with 15 kg in each bag.
a. How many bags of strawberries did she make?

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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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 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:

a) 27. b) 27.3333 c) 40.75

Answer:

C

Step-by-step explanation:

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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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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Therefore , the solution of the given problem of parallel lines comes out to be parallel lines stay parallel option C is correct.

A parallelogram in Euclidean geometry is essentially a straightforward hexagon with two different groups & equal distances. When both sets of sides evenly share a horizontal path, a particular type of quadrilateral known as a parallelogram is created. There are four distinct types of parallelograms, three of them being incompatible. The four distinct forms are slightly parallelograms, rectangular shapes, squares, and parallelograms.

Here,

C. It is untrue that a line may be translated into two parallel lines.

A line can be translated into another line that runs parallel to the first line, but not into two parallel lines.

Every point on the line is rigidly transformed by a translation, which moves all of the points along the line uniformly and in one direction.

After a translation, parallel lines stay parallel.

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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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The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°

A common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.

For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.

Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:

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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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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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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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Answer: C

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

p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

According to the given information we are given that the first term of an arithmetic series is (21 + 1), which simplifies to 22. We are also given that the common difference of the series is 3. Therefore, the second term of the series is 22 + 3 = 25, the third term is 22 + 2(3) = 28, and so on.

To find the nth term of this arithmetic series, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is a common difference. We are given that the nth term is (141-5), so we can set up an equation and solve for n:

(141-5) = 22 + (n - 1)3

136 = 22 + 3n - 3

117 = 3n

n = 39

Therefore, there are 39 terms in the arithmetic series.

To find the sum of the first n terms of an arithmetic series, we can use the formula:

Sn = n/2(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We know that a1 = 22, an = (141-5), and n = 39, so we can substitute these values into the formula:

S39 = 39/2(22 + (141-5))

S39 = 19(136)

S39 = 2584

Therefore, the sum of the first 39 terms of the series is 2584.

Now, we need to write the sum of the first n terms of the series as p(gt - 1), where p, q, and r are integers.

We know that the common difference is 3, so we can write the nth term as:

an = a1 + (n - 1)d

an = 22 + (n - 1)3

an = 3n + 19

Substituting this into the formula for the sum of the first n terms, we get:

Sn = n/2(a1 + an)

Sn = n/2(22 + 3n + 19)

Sn = n/2(3n + 41)

[tex]Sn = 3/2 n^2 + 41/2 n[/tex]

Therefore, p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

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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.

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:

x²+14x+49

Step-by-step explanation:

(a+b)²=a²+2ab+b²

(x+7)²=x²+2×7×x+7²=x²+14x+49

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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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.

Answer:

The appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 is the t-statistic.

The t-statistic for testing the slope coefficient is calculated as follows:

t = (b1 - 0) / SE(b1)

where b1 is the estimated slope coefficient, and SE(b1) is the standard error of the estimated slope coefficient.

From the computer output, we see that the estimated slope coefficient for exercise time is -2.20, and the standard error of the estimated slope coefficient is 0.07.

Therefore, the t-statistic is:

t = (-2.20 - 0) / 0.07 = -31.43

This t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size. The sample size is not given in the output, so we cannot determine the exact degrees of freedom.

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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Answer:A

Step-by-step explanation:

If  u = - 3i + 2i,  v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.

To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:

3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j

Next, we can perform the scalar multiplication of u and the vector 6i + 14j:

5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)

Expanding the product, we get:

5(-18i² + 36ij + 42ij - 28j²)

Since i² = j² = -1, we can simplify this expression as:

5(18 + 70) = 440

Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.

The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.

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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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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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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.

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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Answer:

Step-by-step explanation: