Harper recorded the heights of plants, in inches, as shown in the table.
nd the mean of the data.
11 12 13 14 15 16 17 18 19 20 21
Heights of Plants (in.)

The prove of the statement is described below.

First of all ,

Labeling the given figure

And draw  a diagonal,

In the quadrilateral PQRS,

The side PQ is equal to the side RS.

Therefore,

PQ = RS

And also, the side PQ is parallel to the side RS.

Then,

PQ || RS.

Now, draw the diagonal PR.

We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.

By the rule of  Side-Angle-Side,

we can show that ∆ PQR ≅ ∆ RSP.

Therefore,

The side QR is parallel to PS

Then,

QR || PS.

Hence,

PQRS is a parallelogram.

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A) The inequality that the weight of a child who has outgrown the small T-shirt is w > 55. B) The inequality that the weight of a child who is not ready for the small T-shirt yet. Is y < 43

a. To describe the weight (w) of a child who has outgrown the small T-shirt, we can use the inequality:

w > 55

This inequality states that the weight of a child (w) must be greater than 55 pounds for them to have outgrown the small T-shirt.

b. To describe the weight (y) of a child who is not ready for the small T-shirt yet, we can use the inequality:

y < 43

This inequality states that the weight of a child (y) must be less than 43 pounds for them to not be ready for the small T-shirt yet.

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For calculating the percentage of discount, we can use the formula:

Percentage of discount = (Discount amount / Original price) * 100

We have given that the discounted price is Birr 51,000 and the discount amount is Birr 9,000,we need to find the original price.

Original price = Discounted price + Discount amount

Original price = 51,000 + 9,000 = 60,000 Birr

Now, we can calculate the percentage of discount:

Percentage of discount = (9,000 / 60,000) * 100 = 15%

Hence, the percentage of discount for the four-door model is 15%.

The probability of drawing the 2, 4, 6, and 8 of spades in that specific order is 0.0002.

The probability of drawing a specific card without replacement from a well-shuffled deck is 1/52 for the first card, 1/51 for the second card, 1/50 for the third card, and 1/49 for the fourth card.

We wish to draw the specific cards (2, 4, 6, and 8 of spades) in that specific order.

The probability will be:

Probability = (1/52) * (1/51) * (1/50) * (1/49)

probability = 0.0002.

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Answer:

SRTZ is not a parallelogram.

Slope of SZ:

[tex]m = \frac{ - 2 - 1}{1 - ( - 2)} = - 1[/tex]

Slope of RT:

[tex]m = \frac{0 - 3}{2 - 1} = - 3[/tex]

Since the slopes of SZ and RT are not equal, SRTZ is not a parallelogram.

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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Answer:

7/100 w postaci dziesiętnej to 0,07.

3 5/10 w postaci dziesiętnej to 3,5.

The graph of the polynomial function y = f(x) in the xy plane could be the first graph.

Given a polynomial function f.

Range of the polynomial function is the set of all the real numbers less than or equal to 4.

So y values are y ≤ 4

So the vertex of the function will be at y = 4 and other value are less than 4.

So parabola is downwards.

Two options are there with the parabola folded downwards.

Now the zeroes of f are at -3 and 1.

Zeroes of f are the values of x where the function touches the X axis.

Hence the correct graph is first one.

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Answer: sin(0) = 40.804/41

Step-by-step explanation:

The z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.

To compute the z-scores for each observation in the sample, we need to first calculate the mean and standard deviation of the data set.

Given the sample with observations: 16, 11, 13, 22, 15, and 19.

Calculate the mean (μ):

Add up all the observations and divide by the total number of observations.

Mean (μ) = (16 + 11 + 13 + 22 + 15 + 19) / 6 = 96 / 6 = 16.

Calculate the standard deviation (σ):

Subtract the mean from each observation.

Deviation = Observation - Mean

Square each deviation.

Squared Deviation = Deviation²

Calculate the average of the squared deviations.

Average Squared Deviation = (Squared Deviation1 + Squared Deviation2 + ... + Squared Deviation6) / 6

Take the square root of the average squared deviation.

Standard Deviation (σ) = √(Average Squared Deviation)

Let's calculate each step:

Deviation1 = 16 - 16 = 0

Deviation2 = 11 - 16 = -5

Deviation3 = 13 - 16 = -3

Deviation4 = 22 - 16 = 6

Deviation5 = 15 - 16 = -1

Deviation6 = 19 - 16 = 3

Squared Deviation1 = 0² = 0

Squared Deviation2 = (-5)² = 25

Squared Deviation3 = (-3)² = 9

Squared Deviation4 = 6² = 36

Squared Deviation5 = (-1)² = 1

Squared Deviation6 = 3² = 9

Average Squared Deviation = (0 + 25 + 9 + 36 + 1 + 9) / 6 = 80 / 6 = 13.33

Standard Deviation (σ) = √13.33 ≈ 3.65

Now that we have the mean (μ = 16) and standard deviation (σ ≈ 3.65), we can calculate the z-score for each observation.

The z-score (Z) for an observation (X) is calculated using the formula:

Z = (X - μ) / σ

Let's calculate the z-scores for each observation:

Z1 = (16 - 16) / 3.65 = 0 / 3.65 = 0

Z2 = (11 - 16) / 3.65 = -5 / 3.65 ≈ -1.37

Z3 = (13 - 16) / 3.65 = -3 / 3.65 ≈ -0.82

Z4 = (22 - 16) / 3.65 = 6 / 3.65 ≈ 1.64

Z5 = (15 - 16) / 3.65 = -1 / 3.65 ≈ -0.27

Z6 = (19 - 16) / 3.65 = 3 / 3.65 ≈ 0.82

So, the z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.

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Answer:

The correct answer is:

(A) enlargement

The value of x in trapezoid KFGJ is 40.

Given information:

KFGJ is a trapezoid.

KF = 20

JG = x

MN is midsegment of trapezoid KFGJ.

MN = 30

To find the value of x in trapezoid KFGJ, we can use the fact that the midsegment MN of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the bases.

In this case, MN is given as 30, and we know that KF is one of the bases with a length of 20. To find the length of the other base JG, we can use the formula for the midsegment of a trapezoid:

MN = (KF + JG) / 2

Substituting the given values, we have:

30 = (20 + x) / 2

To solve for x, we can multiply both sides of the equation by 2:

60 = 20 + x

Subtracting 20 from both sides:

x = 60 - 20

x = 40

Therefore, the value of x in trapezoid KFGJ is 40.

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Answer:

Step-by-step explanation:

Rachel already has 7 teaspoons of milk.

so 7 x 5 = 35

So Racheal will need 35 teaspoons of surger.

John will have to pay $12.24 in interest at the end of the loan.

To calculate the amount of interest John will have to pay at the end of the loan, we can use the formula for simple interest:

Interest = Principal * Rate * Time

Given:

Principal (P) = $4,300.00

Rate (R) = 13.75% per annum

Time (T) = 8 days

First, we need to convert the rate from an annual percentage to a daily rate. Since there are 365 days in a year:

Daily Rate = (Rate / 100) / 365 = (13.75 / 100) / 365 = 0.0003767

Now we can calculate the interest:

Interest = Principal * Rate * Time

= $4,300.00 * 0.0003767 * 8

= $12.24

Therefore, John will have to pay $12.24 in interest at the end of the loan.

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Answer:

5 m

Step-by-step explanation:

To convert 500 cm to m, you simply divide by 100 since there are 100 centimeters in 1 meter.

So, 500 cm ÷ 100 = 5 m

Answer: 42

Step-by-step explanation:

The best way to solve this is to set up an equation. In this problem, we can use "x" for Mikhail's age, so that Gabrielle's age becomes "x+13." Now, we can write, "x+x+13=97," because Mikhail's age (x) plus Gabrielle's age (x+13) is equal to 97. When we solve for x, we get x=42, so Mikhail's age is 42.

The length of arc length s is 1152π² or 11358.26.

We have,

The arc length of a circle can be calculated using the formula:

Arc Length = 2πrθ/360

Where:

π is a mathematical constant approximately equal to 3.14159.

r is the radius of the circle.

θ is the central angle subtended by the arc, measured in degrees.

The arc length of a circle can be written as:

s = angles/360 x 2πr _______(1)

Now,

r = 4 cm

Angle = (2/5)π

Now,

Substitute in (1).
s = angles/360 x 2πr

s = (2/5)π/360 x 2π x 4

s = 2π x 72 x 2π x 4

s = 4π² x 288

s = 1152π²

or

s = 11358.26

Thus,

The length of arc length s is 1152π² or 11358.26.

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These atomic formulas represent basic assertions or relationships between elements or sets.

In logic and mathematical logic, "atomic formulas" refer to the simplest, indivisible formulas that do not contain any logical connectives or quantifiers.

They are the building blocks from which more complex formulas are constructed.

In set theory, the atomic formulas are typically statements about membership or equality.

For example, "x belongs to y" (x ∈ y) and "x equals y" (x = y) are atomic formulas in set theory.

Using logical connectives (such as conjunction, disjunction, negation, implication, and equivalence) and quantifiers (such as "for all" (∀) and "there exists" (∃)), we can combine atomic formulas to form more complex formulas, enabling us to express a wide range of logical statements and mathematical properties.

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If  the sum of their ages 8 years ago was 48 then the present age​ of girl is 16 years.

Mrs. Sarfo is three times as old as her daughter, so her present age would be 3J years.

8 years ago, Joyce's age would have been J - 8, and Mrs. Sarfo's age would have been 3J - 8.

The sum of their ages 8 years ago was 48:

(J - 8) + (3J - 8) = 48

Simplifying the equation:

4J - 16 = 48

Adding 16 to both sides:

4J = 64

Dividing both sides by 4:

J = 16

Therefore, the present age of Joyce is 16 years.

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A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. A plane intersects the pyramid parallel to its base. The cross section is a rectangle  A plane intersects the pyramid perpendicular to its base and through the top vertex. The cross section is a triangle

A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. Let's explore the two scenarios you mentioned:

Plane parallel to the base: When a plane intersects the rectangular prism parallel to its base, the resulting cross section is also a rectangle. The shape of the cross section will have the same dimensions as the base of the rectangular prism.

Plane perpendicular to the base and through the top vertex: In this case, the cross section will be a triangle. The shape of the cross section will be determined by the intersection of the plane with the three sides of the rectangular prism. The base of the triangle will be formed by the side of the rectangular prism, while the other two sides will be formed by the edges connecting the top vertex of the pyramid to the corresponding vertices of the base.

It's important to note that a rectangular prism is different from a pyramid. A rectangular prism has six rectangular faces, while a pyramid has a polygonal base (in this case, a rectangle) and triangular faces converging to a single point called the apex or top vertex.

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Answer:

-12x⁸y⁵

Step-by-step explanation:

Exponent law:

         xᵃ * xᵇ = xᵃ ⁺ ᵇ

In exponent multiplication, if bases are same, add the exponents.

(4x⁵y³) (-3x³y²) = 4*(-3) * x⁵⁺³ * y³⁺²

                        = -12x⁸y⁵

Answer:

When the cab travels 0 miles, the total fee will be $10.00.

Step-by-step explanation:

We Know

2 miles = $13.00

5 miles = $17.50

3 miles = 17.50 - 13.00 = $4.50

1 mile = 4.50 / 3 = $1.50

So, for every 1-mile go, the cost is increasing by $1.50; this is the slope.

What does the y-intercept mean in this situation?

It is the total fee that Tyrell pays when the cab goes 0 miles (when he first steps in the cap).

So, the answer is D. When the cab travels 0 miles, the total fee will be $10.00.

1) sin θ + tan θ is equal to 5/6. 2) sin θ is 5/12. 3) sec θ + cosecc^2 θ = 12/√119 + 144/25 4) cot θ + sin θ is equal to 169/60.

1) To find sin θ + tan θ, we need to find the value of sin θ. Using the identity tan θ = sin θ / cos θ, we can rewrite tan θ as sin θ / cos θ.

tan θ = 5/12 = sin θ / cos θ

Since we are given that 0 < θ < 90, both sin θ and cos θ are positive.

Using the Pythagorean identity[tex]{sin^2}[/tex] θ + [tex]cos^2[/tex] θ = 1, we can solve for cos θ:

[tex]cos^2[/tex] θ = 1 - sin^2 θ

[tex]cos^2[/tex] θ = [tex]1 - (5/12)^2[/tex]

[tex]cos^2[/tex]θ = 1 - 25/144

[tex]cos^2[/tex] θ = 119/144

cos θ = √(119/144)

cos θ = √119/12

Now, we can find sin θ using the relationship [tex]sin^2[/tex] θ + [tex]cos^2[/tex]θ = 1:

[tex]sin^2[/tex] θ = 1 - [tex]cos^2[/tex] θ

[tex]sin^2[/tex]θ = 1 - (119/144)

[tex]sin^2[/tex]θ = 25/144

sin θ = √(25/144)

sin θ = 5/12

Finally, we can substitute the values of sin θ and tan θ into the expression sin θ + tan θ:

sin θ + tan θ = (5/12) + (5/12) = 10/12 = 5/6

Therefore, sin θ + tan θ is equal to 5/6.

2) The value of sin θ is already calculated as 5/12.

3) To find sec θ + [tex]csc^2[/tex] θ, we need to find the values of sec θ and csc θ.

Since sec θ is the reciprocal of cos θ, we can calculate sec θ as:

sec θ = 1/cos θ = 1/(√119/12) = 12/√119

csc θ is the reciprocal of sin θ, so:

csc θ = 1/sin θ = 1/(5/12) = 12/5

Now, we can substitute these values into the expression sec θ + [tex]csc^2[/tex]θ:

sec θ + [tex]csc^2[/tex]θ = (12/√119) + [tex](12/5)^2[/tex]= 12/√119 + 144/25

4) To find cot θ + sin θ, we need to calculate the value of cot θ.

cot θ is the reciprocal of tan θ, so:

cot θ = 1/tan θ = 1/(5/12) = 12/5

Now, we can substitute the values of cot θ and sin θ into the expression cot θ + sin θ:

cot θ + sin θ = 12/5 + 5/12

To add these fractions, we need a common denominator:

cot θ + sin θ = (12/5)(12/12) + (5/12)(5/5)

              = 144/60 + 25/60

              = 169/60

Therefore, cot θ + sin θ is equal to 169/60.

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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:    D.   <4 and <7

Step-by-step explanation:

Consecutive means one after the other

Interior means within the parallel lines

So we are looking for 2 to angles inside the parallelel lines that are 1 after the other on the same side

D.   <4 and <7

The domain and the range of the graph are Domain = [-10, -8] and Range = [-10, -1]

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

The graph

The above graph can be represented as a list of ordered pairs

The rule of a graph is that

Using the above as a guide, we have the following:

Domain = [-10, -8]

Range = [-10, -1]

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The relative frequency distribution is:

The correct option is A.

A relative frequency is the proportion of the total number of outcomes to the number of times a certain value of the data happens in the set of all outcomes.

The relative frequency distribution of the given data is constructed below:

Total number of students = 51 + 58 + 74 + 69 + 19

Total number of students = 271

The relative frequency of each class interval will be:

200-300; 51/271 * 100% = 18.82%

301-400; 58/271 * 100% = 21.40%

401-500; 74/271 * 100% = 27.30%

501-600; 69/271 * 100% = 25.46%

More than 600; 19/271 * 100% = 7.02%

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