Find the lengths of the diagonals of rectangle WXYZ.
WY = 14x + 10
XZ = 11x + 22
The length of each diagonal is
units.

Therefore , the solution of the given problem of median comes out to be

a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.

Specify median.

The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.

Here,

Given : mean age is 36.

Standard deviation = 3.5

a) z - score = (34 - 28.3)/3.8 = 1.50

b) Interpretation:

An age of 34 is about 1.50 standard deviations above the mean.

c) Option B is correct.

Therefore , the solution of the given problem of median comes out to be

a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.

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Answer: The odds against an event occurring are the ratio of the probability that the event will not occur to the probability that the event will occur. To find the odds against an event, you can use the formula:

Odds against = (1 - probability of event occurring) / probability of event occurring

In this case, the event is that exactly 5 cars will pass over the bridge in a 4-minute period. The probability that this event will occur is 0.16. Therefore, the odds against this event occurring are:

Odds against = (1 - 0.16) / 0.16

= 0.84 / 0.16

= 5.25

So, the odds against exactly 5 cars passing over the bridge in a 4-minute period are 5.25 to 1.

It means that there are 5.25 times more likely that it will not happen compare to happen.

Step-by-step explanation:

Correct options are: A. Zeros: -2 and 1

E. x-Intercepts: (-2, 0) and (1, 0)

What are zeros & x-intercepts of quadratic function?

The zero of the function is where the y-value is zero.

The x-intercept is where the graph crosses the x-axis.

The zeros of a quadratic function are the values of x for which the function equals zero. In other words, they are the solutions to the equation f(x) = 0. For the given quadratic function, the zeros

are -2 and 1.

The x-intercepts of a function are the points at which the function crosses the x-axis. In other words, they are the solutions to the equation f(x) = 0 when y = 0. For the given function, the x-intercepts are (-2, 0) and (1, 0) which are the points on the x-axis where the function crosses it.

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Answer:

Step-by-step explanation:

a.Scale factor = distance on the plot / actual distance

b.3 feet = 12 inchs.

so scale factor = 5/12

Latitude 36°30′ was designated by the Missouri Compromise of 1820 as the northern limit for the legalization of slavery in the western territories.

By Stephen A. Douglas's Kansas-Nebraska Act of 1854, the Missouri Compromise's prohibition on slavery in the former Louisiana Territory north of the parallel 36°30′ north had been essentially removed. Latitude 36°30′ was designated by the Missouri Compromise of 1820 as the northern limit for the legalization of slavery in the western territories.

The expansion of slavery into the western lands was addressed by the Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas." The balance between "free" and "slave" states in the Union was a factor in each of them.

Slavery was proposed to be outlawed in the remaining Louisiana Territory above the 36° 30' latitude line in the Missouri Compromise. The Kansas-Nebraska Act of 1854 abolished this clause after it had been in effect for 34 years.

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The Missouri Compromise of 1820 established latitude 36°30′ as the northern boundary for the legalisation of slavery in the western territories.

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Answer:

96

Step-by-step explanation:

5 x 6 = 30

78 - 12 = 66

5 x 6 + 78 - 12

= 30 + 66

= 96

Answer:96

Step-by-step explanation:

The simplified value of x is 44 / 15 or 7 / 5 and value of y is -2

Simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Given that, simply the following

a) 2(y-1)/3-3(y-2)/4=1

b) 3x=44/5=2x+6

1) 2(y-1) / 3 - 3(y-2) / 4 = 1

Multiplying by 12 to both sides,

8(y-1) - 9(y-2) = 12

8y-8 - 9y+18 = 12

-y + 10 = 12

y = -2

2) 3x = 44 / 5 = 2x+6

3x = 44 / 5

Multiplying by 5 to both sides,

15x = 44

x = 44 / 15

or,

44 / 5 = 2x + 6

Multiplying by 5 to both sides,

44 = 10x + 30

14 = 10x

x = 7 / 5

Hence, the simplified value of x is 44 / 15 or 7 / 5 and value of y is -2

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It is not possible to find the height of an isosceles triangle when only the base is given. To find the height, you would need to know at least one other side length, in addition to the base.

The height of an isosceles triangle can be found using the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the two shorter sides. To use the Pythagorean Theorem, you must first know the length of at least two sides of the triangle. Since only the base is given, it is not possible to calculate the height of the isosceles triangle. In order to find the height, you would need to know either the length of the other two sides, or the angle of one of the two equal sides. Once you have this information, you can use the Pythagorean Theorem to calculate the height of the triangle.

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Answer: In order to calculate the value of 3h(2) + 4g(1), we would need to know the specific functions h(x) and g(x) that you are referring to. Without more information, it is not possible to determine the value of the expression.

Typically, piecewise functions are defined by several different expressions, each defined over a different interval of the input variable x. To evaluate a piecewise function at a specific value of x, we must first determine which interval that value of x falls into, and then use the corresponding expression for that interval to find the output value.

Are you able to provide the piecewise functions, or are you just using them as an example?

Also, in case if you want to describe the functions in words, please let me know.

Step-by-step explanation:

Answer: So the positive solution is:

ANSWER:    X = 5

(x = 5 ),  (x = - 2 )

Step-by-step explanation:

when 10 is subtracted from the square of a number the result is 3 times the number.

Find the positive solution.

Let:   x = number

Let x^2 = square of a number.

x^2 - 10x = 3x transpose

x^2  -  3x - 10 = 0

Apply Factoring: Fractions of  10  are   5  and 2

( - 5)(2)  =   - 10

- 5  + 2  =  - 3

( x - 5 )(x + 2) = 0

x - 5 = 0      x + 2 = 0

x = 5             x   =  - 2

So the positive solution is:

ANSWER:    X = 5

I hope that helps!!!!

The measure of the angle of the shaded sector with an area of 65 cm² is 74.5°

An equation is used to show the relationship between numbers and variables.

The area of a two dimensional shape is the amount of space it occupies.

The area of a sector in a circle is given by:

Area = (Ф/360) * π * radius²

Where Ф is the sector angle

Given that sector area is 65 cm², radius is 10 cm, hence:

Area = (Ф/360) * π * radius²

Substituting gives:

65 = (Ф/360) * π * 10²

Ф = 74.5°

The measure of the angle is 74.5°

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Answer: 110% of 120 minutes is equal to 132 minutes.

Step-by-step explanation:

To calculate percentiles:

Answer:

x + 5 = 10

Step-by-step explanation:

The sum of first 20 terms of the AP will be -206.25

As in AP, let us assume that the "a" be the first term and 'd' be the common difference.

So, the value of nth term can be determined by using formula: a_n=a+(n-1)d, where, n = number of terms, and d = common difference.

So, the value of 19th terms = a+(19-1)d = a+18d = -5 -----(i)

And the value of 15th term = a+(15-1)d = a+14d = -7(1/2) ----(ii)

Now subtracting (ii) from (i),

We will get,

4d = 2(1/2)

=>4d = 2.5

=>d = (2.5/4) = 0.625

Now putting value of "d" in (i)

We will get,

a+(18*0.625) = -5

a=-5-11.25 = -16.25

We have, the formula for finding the sum of terms:

Sum of terms can be determined by using formula:

Sum = (n/2) × [2a + (n-1)d]

Here, n = 20, a = -16.25, d = 0.625

We will get sum of first 20 terms as:

[tex](n/2)\times [2a + (n-1)d]\\(20/2) \times [2 \times -16.25+(20-1)0.625]\\[/tex]

10[-32.5+11.875]

=10(-20.625) =-206.25

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In the given pairs of polygons the scale factor of figure A to figure B is  2:4.

The scale factor is calculated using the following fundamental formula: Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.

The ratio of a smaller figure's side to its corresponding side in the bigger figure is the scale factor between the two figures.

As a result, the smaller figure's side length of 4 units and its side length of 10 units are equivalent.

Therefore:

Scale factor = 4:10

i.e. 2:5

Simplify

Scale of the smaller figure to the larger is equal to 2:4.

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A numerical equation using addition as the only operator, for instance, is 2 + 17.

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Answer:

No, the point isn't in the shaded area

Step-by-step explanation:

Answer:

SSS

Step-by-step explanation:

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle it is known was SSS congruence

The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numerical expression is given below.

⇒ 12 × [6.3 + 3 × (1.9)]

Simplify the numerical expression, then we have

⇒ 12 × [6.3 + 3 × (1.9)]

⇒ 12 × [6.3 + 5.7]

⇒ 12 × 12

⇒ 144

The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

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The fractions is simplified to 8ac²/ 5

A fraction can be described as the part of a whole element, number or variable.

There are different types of fractions, which includes;

Examples of improper fractions; 5/3, 7/5

Examples of proper fractions; 3/4, 5/6

Examples of mixed fractions; 3 1/2, 4 5/6

Examples of simple fractions; 1/2 , 1/ 4

From the information given, we have that;

[tex]\frac{32a^2bc^3}{20abc}[/tex]

This is simplified to;

32 × a × a × b × c × c × c/ 20 × a × b × c

Divide the common terms

8ac²/ 5

Hence, the fractions is 8ac²/ 5

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Using basic concept of proportion value and percentage from the total, The answer is there are 15 students in the club.

A percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, 50% means 50/100 or 0.50. It is commonly used to express rates and proportions. Percentages can be used to express a variety of information, such as discounts, increases, and proportions. For example, if a product is on sale for 20% off, that means the price has been reduced by 20/100 or 0.20 times the original price. If a company's profits have increased by 10%, that means they have gone up by 10/100 or 0.10 times the original amount.

A proportion is a mathematical relationship between two values that indicates that they are in a specific ratio to each other. Proportions can be expressed in a variety of ways, but one common way is to use the symbol ":" to separate the two values. In statistics, it is common to use proportions to express the relationship between different groups or categories in a population. In physics, proportions can be used to calculate different quantities in systems.

total = x

40% of x =6

40/100 * x =6

x=6*100/40

=15

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The correct option regarding the high tide and the low tide is given as follows:

B. high tide at 6 a.m. and 6 p.m., depth of 28 ft.

low tide at 12 midnight and 12 noon, depth of 20 ft.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

The amplitude for this problem is of 4, with a vertical shift of 24, hence the low and high tides are given as follows:

The function is reflected over the x-axis, due to the multiplication by the negative number, hence the low tide is at midnight.

The period of the function is given as follows:

2π/(π/6) = 12 hours.

Thus the low tide also happens at noon, meaning that option B is correct.

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Answer

x ≥ 40

Step-by-step explanation:

Since Josh only exercises more or equal to 40 min, this is how you would represent this problem.

A right cone is a cone whose apex is located along its center axis and whose axis is perpendicular to its base.

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Answer:

I used desmos to make the graph

Step-by-step explanation:

Hopefully this helps!

Answer:

Hypothesis - She is a spoiled brat who has rich parents. But where did they                                                                            get their wealth?

Conclusion - Her parents are hard workers who have made it up the ladder of wealth.

2. If the measure of an angle is 58*, then the angle is acute

Hypothesis - acute angles are from 1* to 89* which makes it the smallest angle. But why when the word acute means severe?

Conclusion - We know that anything below 90* is an acute angle.

This should be a start. I will finish in a sec...

Answer:

1.  Hypothesis:  Lola wants.  

    Conclusion:  Lola gets.

2. Hypothesis:  The measure of an angle is 58°.

    Conclusion:  The angle is acute.

3.  Hypothesis:  The segments are diagonals of a rectangle

    Conclusion:  The segments are congruent.

4.  Hypothesis:  You are a Filipino.

    Conclusion:  You are a God-fearing person.

5.  Hypothesis:  You are a good citizen.

    Conclusion:  You will obey rules and regulations.

Step-by-step explanation:

In a statement, the Hypothesis is the part after the "if", and the Conclusion is the part after the "then".

1.  If Lola wants, then Lola gets.

2.  If the measure of an angle is 58°, then the angle is acute.

3.  If the segments are diagonals of a rectangle, then the segments are congruent.

4.  If you are a Filipino, then you are a God-fearing person.

5.  If you are a good citizen, then you will obey rules and regulations.

The statistical model is not good, and this is true for a negatively skewed curve.

It is a statistical term implies that a curve is skewed at the left side.

In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.

In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.

In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.

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Answer:

3.5

Step-by-step explanation:

In this problem, the line's constant of proportionality is the same as its slope.

Slope is defined as rise / run (also notated as change in y / change in x).

Using the given point, we can deduce that the line's rise (change in y) is 3.5, and its run (change in x) is 1. Putting these values into the slope formula:

3.5 / 1 = 3.5

So, the constant of proportionality of this line is 3.5.

Domain

Range

Interval Notation

Let's organize what is given to us from the problem.

We are given a graph of a function.

We need to analyze the graph to determine the domain and range of the graph.

If we take a look at our x values, we see that our graph starts at x = 3 and continues infinitely.

∴ we can write the graph's x-values as [3, ∞), or x ≥ 3.

⇒ The domain of the graph is equal to x ≥ 3.

If we take a look at our y values, we see that our graph begins at y = 1 and also continues infinitely.

∴ we can write the graph's y-values as [1, ∞), or y ≥ 1.

⇒ The range of the graph is equal to y ≥ 1.

∴ the answer to the question is equal to:

A. D: x ≥ 3

    R: y ≥ 1

___

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Topic: Algebra I

Unit: Functions