What is the area of a right triangle with a height of 6-yards and a base of 22 yards?
O 34 yds²
O 68³
yds²
O 132 yds²
O
137/ yds²

The correct statements  to conclude that a parallelogram is a rhombus are:  a.)  Segment AD ≅  Segment AB  e.)  Segment AB ≅  Segment DC

f.) ∠ABC ≅ ∠CDA

In two dimensions, a parallelogram is a geometric figure with parallel sides. It has two parallel sides that are  the same length, making it a four-sided polygon (sometimes called a quadrilateral). The sum of the adjacent angles of a parallelogram is 180 degrees. Parallelograms are a unique class of polygons.  

To conclude that a parallelogram is a rhombus, we must show that all four sides are congruent (of equal length). Therefore, statements that provide information about the sides of a parallelogram can help us make this conclusion.  

The correct statements  to conclude that a parallelogram is a rhombus are:

a.)  Segment AD ≅  Segment AB

e.)  Segment AB ≅  Segment DC

f.) ∠ABC ≅ ∠CDA

These statements tell us that opposite sides are congruent and opposite angles are congruent, which are properties of a rhombus. However, the expressions b, c and d do not give information about the sides, so it cannot be concluded from them that the parallelogram is a rhombus.

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A=200in² is the area of the shaded polygon so 200in² ➗ 30in

according to the given question Anna scored highest in the Afrikaans test.

When a relationship consistently has the same ratio, it is considered to be proportionate. For instance, the average amount of apples grown on each tree determines the number the trees within a fruit orchard plus the quantity of apples harvested. In mathematics, a linear relationship between two numbers or variables is referred by the term being proportionate. The other amount doubles when the initial amount does. The other variables also decline when one variable is brought down to 1/100th of its prior value.

given,

To determine whether Anna's results are proportionate, we need to compare the percentage scores she received in each test.

For the Afrikaans test, Anna's percentage score is (22/30) x 100% = 73.33%

For the mathematical literacy test, Anna's percentage score is (18/25) x 100% = 72%

Since Anna's percentage score for the Afrikaans test is higher than her percentage score for the mathematical literacy test, her results are not proportionate. Therefore, Anna scored highest in the Afrikaans test.

Note that if we were to compare the raw scores (22 vs. 18), it would seem like Anna performed better in the Afrikaans test. However, since the two tests have different total marks (30 for Afrikaans and 25 for mathematical literacy), comparing the raw scores directly does not give a fair comparison. Instead, we need to compare the percentage scores, which take into account the total marks of each test.

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Answer:

The length of the diagonal from P to Q is

[tex] \sqrt{ {9}^{2} + {12}^{2} + {8}^{2} } = \sqrt{289} = 17[/tex]

Answer:

In a bubble sort, on each pass through the list that must be sorted, the largest value "bubbles" to the end of the list. Therefore, after each pass, the end of the list is guaranteed to be sorted. This means that we can stop making pair comparisons one comparison sooner, which is option B.

Step-by-step explanation:

Bubble sort works by repeatedly comparing and swapping adjacent elements in the list if they are in the wrong order. During each pass through the list, the largest unsorted element "bubbles up" to its correct position. As a result, after the first pass, the largest element is in its correct position, after the second pass, the two largest elements are in their correct positions, and so on.

Therefore, with each subsequent pass, you can stop making pair comparisons one comparison sooner because the elements at the end of the list are already sorted.

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Answer: f(8) = -208

Step-by-step explanation:

     To solve, we will substitute 8 into the equation for x.

Given:

     f(x) = -3x² - 2x

Substitute 8 for x:

     f(8) = -3(8)² - 2(8)

Square:

     f(8) = -3(64) - 2(8)

Multiply:

     f(8) = -192 - 16

Subtract:

     f(8) = -208

The sum of the expression is simplified to give x² + 11x - 6/(x-3)(x+3)

Algebraic expressions are simply defined as expressions that consist of terms, factors, constants, variables and coefficients.

These mathematical expressions are also made up of arithmetic operations such as;

From the information given, we have the expression as;

x-2/x-3  + 10x/x² - 9

Find the lowest common factor, we have;

(x-2)(x+3) + 10x/(x-3)(x+3)

expand the bracket

x² + 3x - 2x - 6 +10x/(x-3)(x+3)

Now, add the like terms, we get;

x² + 11x - 6/(x-3)(x+3)

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the ratio of Nonfiction novels to all novels is: Nonfiction novels : Total novels  [tex]= 2 : 11[/tex]  So the correct answer is  [tex]2:11.[/tex]

The ratio of Nonfiction novels to all novels can be calculated by dividing the number of Nonfiction novels by the total number of novels.

The total number of novels is the sum of Nonfiction, mystery, and fiction novels:

Total number of novels = Nonfiction + Mystery + Fiction [tex]= 2 + 4 + 5 = 11[/tex]

The ratio of nonfiction novels to all novels is not a fixed value, as it depends on the specific set of novels being considered. However, it can be calculated if we have the appropriate data.

Therefore, the ratio of Nonfiction novels to all novels is: Nonfiction novels : Total novels  [tex]= 2 : 11[/tex] So the correct answer is 2:11.

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Answer:

Let's denote:

M: the set of students who like maths

S: the set of students who like science

n(M): the number of students who like maths

n(S): the number of students who like science

n(M ∩ S): the number of students who like both maths and science

n(M ∪ S): the number of students who like maths or science (or both)

We can use the principle of inclusion-exclusion to find n(M ∪ S):

n(M ∪ S) = n(M) + n(S) - n(M ∩ S)

From the problem statement, we know:

n(M) = 10

n(S) = 15

n(M ∩ S) = ? (unknown)

We also know that 10 students like neither maths nor science, which means that:

n(M ∪ S)' = 10

where (M ∪ S)' denotes the complement of M ∪ S, i.e., the set of students who do not like maths or science.

We can use the formula:

n(A') = N - n(A)

where N is the total number of students (N = 50).

n(M ∪ S)' = n((M ∪ S))' = N - n(M ∪ S) = N - (n(M) + n(S) - n(M ∩ S))

Substituting the known values:

n((M ∪ S))' = 50 - (10 + 15 - n(M ∩ S)) = 25 + n(M ∩ S)

Simplifying:

n(M ∩ S) = n((M ∪ S))' - 25 = 10

Therefore, we have:

n(M ∪ S) = n(M) + n(S) - n(M ∩ S) = 10 + 15 - 10 = 15

The ratio of the students who like maths or science is:

n(M ∪ S) / N = 15 / 50 = 3/10

So the required ratio is 3:10.

Step-by-step explanation:

Answer:  the tank filled with water weighs 4,710 pounds.

Step-by-step explanation: where:

π = 3.14 (surmised esteem of pi)

r = span = 2 feet

h = tallness = 6 feet

V = 3.14 x (2 feet)^2 x 6 feet

V = 75.36 cubic feet

Since one cubic foot of water weighs 62.5 pounds, the weight of the water within the tank can be calculated by increasing the volume of water by its weight:

Weight of water = volume of water x weight per cubic foot

Weight of water = 75.36 cubic feet x 62.5 pounds per cubic foot

Weight of water = 4,710 pounds

The equation of the given circle is;Option D; x² + y² = 9

The general formula for the equation of a circle is expressed as;

(x - h)² + (y - k)² = r²

Where;

We are told that;

Circle is at the origin with coordinates (0, 0)

r = 3

Substitute the known values in the above equation, so, we have the following representation

(x - 0)² + (y - 0)² = 3²

Evaluate the exponents and open the brackets

x² + y² = 9

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The equation of the circle is; Option D: x² + y² = 9

The general formula for expressing the equation of a circle is :

(x - h)² + (y - k)² = r²

Where;

(h, k) is the coordinate of the center of the circle

r is the radius of the circle

From the given image of the circle, we see that the center of the circle is at the origin. Thus, the coordinates of the center of the circle is (0, 0)

We also see that from the origin to the circumference is 3. Thus:

r = 3

Plugging in the relevant values into the circle equation, we have:

(x - 0)² + (y - 0)² = 3²

Simplifying further gives us:

x² + y² = 9

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The matrix of dependent coefficients and the vector column of independent variables of the system of linear equations are:

[tex]\vec A = \left[\begin{array}{ccc}1&-2&3\\-4&5&-6\\7&-8&9\end{array}\right][/tex]

[tex]\vec {b} =\left[\begin{array}{ccc}6\\8\\1\end{array}\right][/tex]

In this question we find a representation of a system of three linear equations with three variables {x, y, z}. This system can be described by following expression according to linear algebra:

[tex]\vec A \,\bullet \,\vec x = \vec B[/tex]

Where:

Please notice that operator "•" represents a dot product.

Then, the matrix of dependent coefficients and the vector column of independent variables are, respectively:

Matrix of dependent coefficients

[tex]\vec A = \left[\begin{array}{ccc}1&-2&3\\-4&5&-6\\7&-8&9\end{array}\right][/tex]

Vector column of independent variables

[tex]\vec {b} =\left[\begin{array}{ccc}6\\8\\1\end{array}\right][/tex]

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The cost of the treat would be 40 pennies.

In mathematics, an expression is a combination of symbols (such as numbers, variables, and operations) that represents a value.

Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables. They can also include functions, exponents, and other mathematical concepts.

Chloe started with 74 pennies and lost 10, so she has 74 - 10 = 64 pennies left. The treat costs 5/8 of her remaining pennies,

Calculate the cost by multiplying 5/8 by 64:

(5/8) x 64 = 40

Therefore, the treat costs 40 pennies.

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The new cost after the discount and tax are applied is $872.10, which is option (d).

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

First, let's calculate the amount of discount Angel will receive using the coupon code:

Discount = 15% of $950 = 0.15 x $950 = $142.50

Next, let's calculate the new price of the jacket after the discount is applied:

New price = $950 - $142.50 = $807.50

Now, let's calculate the amount of tax that will be applied to the new price:

Tax = 8% of $807.50 = 0.08 x $807.50 = $64.60

Finally, let's add the tax to the new price to get the total cost:

Total cost = $807.50 + $64.60 = $872.10

Therefore, the new cost after the discount and tax are applied is $872.10, which is option (d).

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The probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 8 + 7 + 6 = 21

probability of picking a blue ball = 7/21

probability of picking a green ball = 6/21

probability of picking a blue or green ball = 7/21 + 6/21

probability of picking a blue or green ball = (7 + 6)/21

probability of picking a blue or green ball = 13/21

probability of picking a blue or green ball = 0.6190

Therefore, the probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.

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The z-score associated with an observed age at first marriage of 25.50 is 0.35.

To calculate the z-score associated with an observed age at first marriage of 25.50, we use the formula:

z = (x - μ) / σ

where:

x = the observed age at first marriage (25.50)

μ = the mean age at first marriage (23.33)

σ = the standard deviation of age at first marriage (6.13)

Substituting the given values, we get:

z = (25.50 - 23.33) / 6.13

z = 0.35

Therefore, the z-score associated with an observed age at first marriage of 25.50 is 0.35.

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1)  The lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.

2)  CD = 2AD.

1) To prove that BMED is a trapezoid, we need to show that BM || ED.

Since O is the midpoint of AM, we have OB || MD (as OB and MD are both perpendicular to AM).

Also, since E is the midpoint of DC, we have DE || AC (as DE and AC are both perpendicular to BC).

Therefore, to show that BM || ED, it is enough to show that AC || OB.

We know that OB is a transversal to the parallel lines BM and AM, so we have:

∠OBD = ∠MBC (corresponding angles)

Similarly, we have:

∠OAD = ∠ABC (corresponding angles)

Since ∠MBC = ∠ABC (because [AM] is the median), we have:

∠OBD = ∠OAD

Therefore, the lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.

2) To prove that D is the midpoint of [AE], we need to show that AD = DE.

Since [AM] is the median, we have:

AD = MC

Also, since E is the midpoint of DC, we have:

DE = EC

So it is enough to show that MC = EC.

Since O is the midpoint of AM, we have:

OM = MA/2

But MA = MC + AC/2 (because [AM] is the median), so we have:

OM = (MC + AC/2)/2

= MC/2 + AC/4

Also, since E is the midpoint of DC, we have:

OE = EC/2

But AC = 2DC (because [AM] is the median), so we have:

OE = EC/2 = AC/4

Therefore, we have:

OM = OE

So triangle OME is isosceles, and we have:

∠OEM = ∠OME

But ∠OED = ∠OEM (because DE || AC), so we have:

∠OED = ∠OME

Therefore, triangles ODE and OME are similar, so we have:

OD/OM = OE/OE

= 1

Therefore, OD = OM.

But we also have:

OM = MA/2 = MC/2 + AC/4

= AD/2 + AC/4 (because [AM] is the median)

So we have:

OD = OM = AD/2 + AC/4

= AD/2 + DC/2 (because AC = 2DC)

= (AD + DC)/2

= AE/2 (because E is the midpoint of DC)

Therefore, we have shown that D is the midpoint of [AE].

Moreover, we have:

CD = AE/2 = AD + DC/2 = AD + AC/4 (because AC = 2DC)

= AD + MC/2 (because [AM] is the median)

= AD + AD/2 (because AD = MC)

= 3AD/2

So we have CD = 2AD.

3) To prove that OD = 4BD, we need to show that BD = (1/4)OM.

Since [AM] is the median, we have:

BM = MC

Also, since O is the midpoint of AM, we have:

OM = BM/2 + AM/2

= BM/2 + 2BM/2 (because [AM] is the median)

= 3BM/2

Therefore, we have:

BD = BM - MD

= MC - MD

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The drive-thru that typically has more wait time is

Burger Quick, because it has a larger median.

Option A is correct.

Because Burger Quick's box plot displays a higher interquartile range (from 9.5 to 24) than Super Fast Food (from 8.5 to 15.5), Burger Quick often has longer wait times.

Additionally, Burger Quick's median (15.5) is greater than Super Fast Food's median (12), demonstrating that Burger Quick's middle value of reported wait times is higher than Super Fast Food's middle value of reported wait times.

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Answer:

0.75

Step-by-step explanation:

P (Cherry or Orange)

0.27 + 0.20 = 0.47

P (Not Strawberry)

0.27 + 0.28 + 0.20 = 0.75

On solving the provided question we can say that as a result, the system of equations' solution is: x = 12.62 and y = 4/13

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions.

We wish to eliminate one of the variables, either x or y, by adding or subtracting the two equations to solve this system of equations using the elimination technique. To do this, multiply one or both equations by a constant factor such that one of the variables has the same coefficient in both equations but with opposite signs.

By multiplying the first equation by 5 and adding it to the second, we can remove x. This results in:

5x - 10y = 60

5x + 3y = -44

-13y = -4

y = 4/13

We may now plug this y value into one of the original equations to find x. Let's look at the first equation:

x - 2y = 12

x - 2(4/13) = 12

13x - 8 = 156

13x = 164

x = 12.62

As a result, the system of equations' solution is:

x = 12.62 and y = 4/13

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Answer:

(4x - 9)(3x + 2)(4x - 5)(3x - 1).

Step-by-step explanation:

Let's substitute y = (12x² - 19x):

So we have y² - 13y - 90, which can be factored as:

y² - 13y - 90 = (y - 18)(y + 5)

Substituting y back:

(12x² - 19x)² - 13(12x² - 19x) - 90 = [(12x² - 19x) - 18][(12x² - 19x) + 5]

= (12x² - 19x - 18)(12x² - 19x + 5)

= (4x - 9)(3x + 2)(4x - 5)(3x - 1)

The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.

It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.

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The mean would increase in value to about 45 when the teacher with the age of 45 is added to the data.

Option C is the correct answer.

We have,

Given ages: 24, 32, 33, 35, 41, 42, 42, 43, 44, 51, 52, 53

Mean without the additional teacher

= (24 + 32 + 33 + 35 + 41 + 42 + 42 + 43 + 44 + 51 + 52 + 53) / 12

= 37.5

New ages: 24, 32, 33, 35, 41, 42, 42, 43, 44, 51, 52, 53, 45

Mean with the additional teacher

= (24 + 32 + 33 + 35 + 41 + 42 + 42 + 43 + 44 + 45 + 51 + 52 + 53 + 45) / 13

= 582/13

= 44.77

= 45

Therefore,

The mean would increase in value to about 45 when the teacher with the age of 45 is added to the data.

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Answer: 1.7(repeating) OR 1.78

Step-by-step explanation:

Divide 4 by 2.25 (2 1/4)

Answer:

2((6(14) + 6(5) + 14(5)) = 2(84 + 30 + 70) =

2(184) = 368 square centimeters

The probability of drawing two red balls in a row from one of the two boxes, given that the first ball drawn is red, is 1/7.

The first step in solving this problem is to determine the probability of selecting the red box versus the other box. Since we have two boxes and each one has an equal chance of being selected, the probability of selecting the red box is 1/2.

Now we can put all of these probabilities together to determine the overall probability of drawing two red balls in a row from one of the two boxes.

We know that the probability of selecting the red box is 1/2, the probability of drawing a red ball on the first try is 4/7, and the probability of drawing a red ball on the second try, given that we've already drawn one red ball, is 1/2.

To find the overall probability, we simply multiply these three probabilities together:

(1/2) x (4/7) x (1/2) = 1/7

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The probability that the second ball will be red, given that the first ball is red, is 3/7.

To find the probability that the second ball will also be red given that the first ball is red, we need to consider two cases.

Case 1: Selecting a box with 4 red balls and 3 purple balls.

Case 2: Selecting a box with 4 green balls and 3 red balls.

Now, we calculate the overall probability by adding the probabilities of the two cases: (4/7) * (3/6) + (3/7) * (2/6) = 12/42 + 6/42 = 18/42 = 3/7.

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The length of NI is 8.5 cm.

The area of a kite can be found using the formula: Area = (d1 * d2)/2, where d1 and d2 are the lengths of the diagonals.

Substituting the given values, we get:

Area = (12 * 15)/2

Area = 90 square cm

Therefore, the area of the kite is 90 square cm.

In a parallelogram, opposite angles are equal. So, we have:

Angle A = Angle C (opposite angles)

Angle B = Angle D (opposite angles)

Also, sum of adjacent angles in a parallelogram is 180 degrees. So, we have:

Angle A + Angle B = 180 degrees

(x+30) + (3x-90) = 180

4x - 60 = 180

4x = 240

x = 60

Therefore, Angle A = x + 30 = 90 degrees, and Angle B = 3x - 90 = 90 degrees.

Let the shorter base of the trapezoid be x. Then, the longer base is x+6 (as given in the problem).

The median of a trapezoid is the average of the two bases. So, we have:

Median = (x + x + 6)/2 = 19

2x + 6 = 38

2x = 32

x = 16

Therefore, the shorter base of the trapezoid is 16 m and the longer base is 22 m.

In an isosceles trapezoid, opposite angles are supplementary. So, we have:

Angle C + Angle L = 180 degrees

4x + 3 + 5x - 15 = 180

9x - 12 = 180

9x = 192

x = 21.33

Therefore, the value of x is 21.33.

In a trapezoid, the median is the average of the two bases. So, we have:

AB = 18 (given)

Median = (SP + NI)/2

But SP = NI (opposite sides of a trapezoid are equal)

So, Median = 2SP/2 = SP

Therefore, SP = Median = 19/2 = 9.5 cm

Also, AB = SP + NI

18 = 9.5 + NI

NI = 8.5 cm

Hence concluded that the length of NI is 8.5 cm.

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Number of clients who do not play either the piano or the guitar is 22

To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.

Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments

Substituting the given values, we get

|A ∪ B| = 46 + 58 - 17

|A ∪ B| = 87

Therefore, the number of clients who do not play either instrument is:

109 - 87 = 22

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Answer: 3,456

Step-by-step explanation: