murder rates. the data represent the murder rate per 100,000 individuals in a sample of selected cities in the united states. find the sample variance.

Answer & Step-by-step explanation:

To simplify the expression 3a + 6b - 8a + 9b, we can combine the like terms (terms with the same variable).

First, we can combine the 3a and -8a terms since they have the same variable 'a'. When we subtract 8a from 3a, we get -5a.

Then, we can combine the 6b and 9b terms since they have the same variable 'b'. When we add 6b and 9b, we get 15b.

Putting it all together, we get:

3a + 6b - 8a + 9b = -5a + 15b

Therefore, the simplified expression is -5a + 15b.

3a+6b-8a+9b

9b+6b-8a+3a

15b-5a

5(3b-a)

In linear equation, 24.9  tall is the tree .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

We can set up a proportion comparing the height of each object to the length of the shadow.

     h/15 = 21.1/12.7

     h = 1.66 * 15  

   h   = 24.9

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The steps to conduct a statistical survey are given below.

A statistical survey is any structured inquiry designed to obtain aggregated data, which may be qualitative or quantitative where the individual or corporate identities of the respondents are in themselves of little significance.

Given is to conduct a statistical survey.

The steps to conduct a statistical survey are given below -

Therefore, the steps to conduct a statistical survey are given above.

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{Question in english -

How to conduct a statistical survey}

The new basic feasible solution will have x\ as a non-basic variable and a new basic variable with a value not equal to zero.

When a problem is in canonical form and the associated basic feasible solution is degenerate, this means that one of the basic variables has a value of zero. If the pivot operation is then performed with the basic variable with a value of zero extracted from the basis, the new basic feasible solution will have x\ as a non-basic variable and a new basic variable with a value not equal to zero. This is because the pivot operation involves exchanging the extracted basic variable with one of the non-basic variables. Therefore, the new basic feasible solution will not be degenerate, as the new basic variable will have a value not equal to zero.

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Answer: A

Step-by-step explanation:

Flame length = l

Fire speed = s

In graph d, when l = 10, s does not equal 2.

It is eliminated.

In graph b, when l = 35, s=8, but in the graph, when l=30, s=8.

It is eliminated.

In graph c, when l=50, s=9, but in the graph when l=55, s=9.

It is eliminated.

The correct answer is a.

Answer:

4= 16 quarts

Step-by-step explanation:

Answer: 16 quarts

Step-by-step explanation:

1 gallon = 4 quarts

4 gallon = 4 x 4 = 16 quarts

This is a direct proportion

The value of the given expression is 1440

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

(x²yz^4)/z

Substitute the values for x,y and z

 ((-6)²*5*2^4)/2

= (36*5*16)/2

use 16/2 = 8

= 36*5*8

= 1440

The value of the given expression is 1440

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Answer:

To calculate the angle, you would need to use the tangent of an angle formula: tan(θ) = 107/260. Solving for θ yields an angle of 29.4 degrees. You would have to look up at an angle of 29.4 degrees to see the tip of the lighthouse.

The value of q = 25.96

This can be solved using the concept of triangle similarity.

Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner." Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed at a point where the three sides are joined end to end. The summation of the triangle's three angles equals 180 degrees. Triangles can be classified as equilateral, isosceles, or scalene depending on how long their sides are.

Consider, the triangle ABC and the mid-segment line becomes CD.

Now, from similarity

Δ DBA ≅ Δ ABC

AB² = BC. BD ............... (i)

Δ ADB ≅ Δ ABC

AD² = BD. CD ............. (ii)

thus, Δ ADC ≈ Δ ABC

AC² = BC. CD

Thus, q² = (17.5 + 21) × (17.5)

or, q² = 673.75

or, q = 25.96

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Answer: To calculate the amount of simple interest, we use the formula: I = P * r * t, where P is the principal amount (7500), r is the annual interest rate (5%) and t is the time in years (5).

So, the simple interest is: I = 7500 * 5 * 0.05 = 187.5

The total amount Susan will have to pay back to the bank is the principal amount plus the interest:

7500 + 187.5 = $76 87.5

Therefore, Susan will pay the bank back $76 87.5 after 5 years.

Step-by-step explanation:

The expression as product is sin(a)(4 + 2cos(a) - 4sin²(a))

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

sin(a)+sin(2a)+sin(3a)

By sine rule, we have

sin(a)+sin(2a)+sin(3a) = sin(a) + 2sin(a)cos(a) + sin(3a)

Factor out sin(a)

sin(a)+sin(2a)+sin(3a) = sin(a)(1 + 2cos(a)) + sin(3a)

Expanding sin(3a), we have

sin(a) + sin(2a) + sin(3a) = sin(a)(1 + 2cos(a)) + 3sin(a) - 4sin³(a)

So, we have

sin(a) + sin(2a) + sin(3a) = sin(a)(1 + 2cos(a) + 3 - 4sin²(a))

Evaluate the like terms

sin(a) + sin(2a) + sin(3a) = sin(a)(4 + 2cos(a) - 4sin²(a))

Hence, the product expression is sin(a)(4 + 2cos(a) - 4sin²(a))

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Step-by-step explanation:

Assuming it is a constant speed of 50km/h

So you travel 50km in one hour

So if you want to go 100km traveling at the constant speed of 50km it will take two hours as you are going 50km for one hour it will take two hours to go 100km.

Answer:

Step-by-step explanation:

σ = sqrt [ Σ ( xi - μ )^2 / N ]

where:

σ is the standard deviation

Σ is the sum of the values

xi is the value of the i-th observation

μ is the mean of the population

N is the number of observations

First, we need to find the mean of the population:

μ = (20 + 30 + 13 + 10 + 22 + 37) / 6

μ = 132 / 6

μ = 22

Next, we can calculate the deviations of each observation from the mean:

20 - 22 = -2

30 - 22 = 8

13 - 22 = -9

10 - 22 = -12

22 - 22 = 0

37 - 22 = 15

Then, we square each deviation:

(-2)^2 = 4

8^2 = 64

(-9)^2 = 81

(-12)^2 = 144

0^2 = 0

15^2 = 225

We add up the squared deviations:

4 + 64 + 81 + 144 + 0 + 225 = 518

We divide by the number of observations and take the square root:

σ = sqrt [ Σ ( xi - μ )^2 / N ]

σ = sqrt (518 / 6)

σ ≈ 10.72

Therefore, the standard deviation of the population is approximately 10.72 dollars.

Answer: 0.73

Step-by-step explanation: Because finding the absolute value only means finding how far away a number is from 0 on a number line, the answer is 0.73.

Answer:

i).7/18

ii).0/18

iii).0/18.

Step-by-step explanation:

Total bag of sweet = 18

Blue sweet = 5

Red sweet = 7

Green sweet = 6

i). Probability that Sue takes a red sweet = 7/18

ii). Does not take a Green sweet = 0/18

iii). takes a yellow sweet = 0/18.

In mathematics, the term "discrete" is often used to refer to objects or structures that are distinct and separate, rather than being continuous or flowing. In the context of this course, the term "discrete" is used to describe a particular branch of mathematics known as "discrete mathematics" or "discrete structures."

Discrete mathematics is concerned with mathematical structures that are countable and finite, rather than continuous or infinite. These structures are typically represented by sets, graphs, or other discrete objects, and can be used to model a wide range of phenomena, from computer algorithms to social networks.

One of the key features of discrete structures is that they are composed of individual, separate elements, rather than being continuous or flowing. For example, a set of integers is a discrete structure, because it consists of separate, distinct integers, rather than a continuous range of numbers. Similarly, a graph is a discrete structure, because it consists of separate vertices and edges, rather than a continuous line.

Because of their discrete nature, these structures can be analyzed and manipulated using a range of mathematical tools and techniques, such as combinatorics, graph theory, and probability theory. This makes discrete mathematics a fundamental part of many areas of computer science, engineering, and other fields that rely on mathematical modeling and analysis.

In contrast, continuous structures, such as real numbers or geometric shapes, are often analyzed using calculus or other techniques that deal with the infinite and continuous nature of these objects.

In summary, when we talk about "discrete structures" or "discrete mathematics," we are referring to mathematical objects and structures that are countable, finite, and composed of individual, separate elements. These structures can be analyzed and manipulated using a range of mathematical tools, and are a fundamental part of many areas of computer science, engineering, and other fields that rely on mathematical modeling and analysis.

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so we know the EQUATion of the line, now let's work out the inequality of it.

the shaded area is the "true" region or area, and the non-shaded is the "false" region, hmmm let's work our way from the "false" region.

first off, the line is solid, that means the line includes values in the inequality, meaning the shaded part extends to the borderline, so the inequality will be either ⩾ or ⩽, let's work it out from the "false" region, by picking out a point there, hmmm let's use say x = 6 and y = -4, so the point is (6 , -4) and let's plug it in the EQUATion.

[tex]y ~~ \square ~~ \cfrac{3}{4}x-3\hspace{5em}(6~~,~-4)\qquad \implies \qquad -4 ~~ \square ~~ \cfrac{3}{4}(6)-3 \\\\\\ -4 ~~ \square ~~ \cfrac{18}{4}-3\implies -4 ~~ \square ~~ \cfrac{9}{2}-3\implies -4 ~~ \square ~~ \cfrac{9-6}{2}\implies -4 ~~ \square ~~ \cfrac{3}{2} \\\\\\ -4 ~~ \square ~~ 1.5\qquad \textit{is -4 greater or less than 1.5?}[/tex]

well, clearly -4 is less than 1.5, however to  make that a false statement, we can say that -4 is more than 15, now, is not true, is "false" and since we're working from the "false" region, that is what we need, "more than", or ⩾

[tex]{\Large \begin{array}{llll} y\geqslant \cfrac{3}{4}x-3 \end{array}}[/tex]

now, bear in mind that we could have started from the "true" region, the shaded one, and pick a point in it like (0 , 0), if you test, that gives us something like 0 [ ] -3, to make that true, we make it 0 ⩾ -3, because that is true, 0 is really greater than -3, and working for the "true" region, that's what we need.

Answer: 6 minutes or 600 seconds. Thats how long it takes for him to ride his bike home

Step-by-step explanation: 7200 divided by 12 is 600

The amount of tax owed by a head-of-household taxpayer with a taxable income of $27,811 is given as follows:

$3,062.

The amount of tax is obtained identifying the correct position in the table in this problem.

The person in this problem is the head of the household, meaning that we should observe the last column of the table.

As income of $27,811 is between $27,800 and $27,850, hence, looking at the fourth-to-last row, the amount of tax owed by a head-of-household taxpayer with a taxable income of $27,811 is given as follows:

$3,062.

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The quadratic equation has the following three features:

B. 7 is the coefficient of one term of the expression.

C. x is a variable in the expression.

D. The expression has three terms.

In this question we have the case of a quadratic equation in standard form, whose features must be understood by direct inspection. At first sight we get the following conclusions:

Lastly, we get the following roots from the quadratic equation:

x² + 7 · x + 6 = 0

(x + 1) · (x + 6) = 0

x = - 1 or x = - 6

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Answer:

29.13

Step-by-step explanation:

5÷34+3÷64+5÷5

= 6.8+ 21.33+ 1

=29.13

Answer:

the person above me is right just did the math for u

Step-by-step explanation:

yea cuz we smart :))

As the acute angles of a right triangle are complementary, the measures of angle C and angle DAC add up to 90 degrees.

Given that it has three sections and three corners, a triangle qualifies as a polygon. It corresponds to the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle only with vertices A, B, and C. Once the points are not collinear, a unique plane and triangular in Geometric forms are discovered. Triangles are polygon because they have three parts and three corners. The points where its three sides of the triangle converge are referred to as the triangle's corners. Three pyramid angles are multiplied ta yield 180 °.

given

Provided that segment AD is an altitude, AD in triangle ABC is perpendicular to hypotenuse BC.

Triangle DAC is a right triangle, as it should be. As the acute angles of a right triangle are complementary, the measures of angle C and angle DAC add up to 90 degrees.

The same holds true for angles C and CBA's measurements.

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Answer:

p = -4

q = 9

Step-by-step explanation:

The vertex form of a parabola is:

y = a (x − h)² + k

Given that the leading coefficient is 1 and the vertex is (2,5):

y = (x − 2)² + 5

Distributing:

y = x² − 4x + 4 + 5

y = x² − 4x + 9

Alternatively, using calculus, if y = x² + px + q, then the derivative is:

dy/dx = 2x + p

The turning point occurs when the derivative is 0:

0 = 2x + p

0 = 2(2) + p

p = -4

Plugging in and solving for q:

y = x² − 4x + q

5 = (2)² − 4(2) + q

5 = 4 − 8 + q

q = 9

When the total amount raised by Slow Joe was subtracted from the total amount raised by Fast Freddy, the difference was $329.90. Therefore, Slow Joe raised $329.90 more than Fast Freddy.

Slow Joe raised $372.60 for charity.

Slow Joe raised $329.90 more than Fast Freddy.

Steps:

Slow Joe: 93.15 x 4 miles = 372.60

Fast Freddy: 93.15 x (4 x 0.2) = $37.26

Difference: 372.60 - 37.26 = $329.90

Slow Joe raised $372.60 for charity by riding 4 miles of the course for the 2021 Las Vegas Charity Bike-A-Thon. This was accomplished by Slow Joe's donators pledging a combined total of $93.15 for every mile Joe traveled from start to finish. In comparison, Fast Freddy raised $42.70 per mile for traveling 20% of the course. To calculate the difference between the two, Slow Joe's total was calculated by multiplying the amount per mile by the number of miles traveled (93.15 x 4 = 372.60). Fast Freddy's total was calculated by multiplying the amount per mile by the percent of the course traveled (93.15 x (4 x 0.2) = 37.26). When the total amount raised by Slow Joe was subtracted from the total amount raised by Fast Freddy, the difference was $329.90. Therefore, Slow Joe raised $329.90 more than Fast Freddy.

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As per arithmetic progression the value of 15th term is 0.

An arithmetic progression, or A.P., is a sequence of numbers in which the difference between consecutive terms is constant.

To start, let's call the common difference "d" and the first term "a". We can use the formula for the nth term of an A.P., which is Tn = a + (n-1)d, where Tn is the nth term and n is the position of the term in the A.P.

Using this formula, we can find the 6th term and 9th term. For the 6th term, T6 = a + (6-1)d = a + 5d. For the 9th term, T9 = a + (9-1)d = a + 8d.

Now, using the information given, we can create an equation: 6(a + 5d) = 9(a + 8d). Expanding both sides and simplifying, we get:

6a + 30d = 9a + 72d

Subtracting 9a from both sides, we get:

-3a + 30d = 72d

Subtracting 30d from both sides, we get:

-3a = 42d

Dividing both sides by -3, we get:

a = -14d

Now that we have found the value of "a", we can use the formula for the nth term again to find the 15th term. T15 = a + (15-1)d = -14d + 14d = 0.

So, the 15th term of the A.P. is 0.

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Answer:

Let's call the initial fee "x". The equation for the total cost of using a computer for t minutes at the internet cafe can be expressed as:

C = x + 0.60t

Knowing that the total charge to use a computer for 5 minutes would be $6, we can use this information to find the value of x:

C = x + 0.60 * 5

6 = x + 3

x = 6 - 3

x = 3

So, the equation representing the total cost of using a computer for t minutes at the internet cafe is:

C = 3 + 0.60t

Answer:81

Step-by-step explanation: AB=base 1 DC=base 2

Base1+Base2 divided by 2

The length of the midsegment of the trapezoid is 81 units.

The midsegment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

The length of the midsegment of a trapezium is half the sum of the top and bottom of the trapezoid.

Therefore, let's find LM, the midsegment of the trapezoid.

Hence,

LM = 1 / 2 (AB + DC)

AB = 34

DC = 128

LM = 1 / 2 (34 + 128)

LM = 1 / 2 (162)

LM = 81

Therefore,

LM = 81 units

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The slope of the ocean floor is: slope = (y2 - y1) / x

What is slope?

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

The slope of the ocean floor can be found by using the formula for the slope of a line:

slope = (change in y) / (change in x)

where the change in y is the difference in depth between the edge of the continental shelf and the beginning of the oceanic crust, and the change in x is the distance along the ocean floor between these two points.

Let's call the depth of the water at the edge of the continental shelf "y1" and the depth of the water at the beginning of the oceanic crust "y2". Then, the change in y is:

change in y = y2 - y1

Similarly, let's call the distance along the ocean floor between these two points "x". Then, the change in x is:

change in x = x

So, the slope of the ocean floor is:

slope = (y2 - y1) / x

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Answer:

Step-by-step explanation:

That’s the same as 10n + 4n = -56

= 14n = -56

= n = -56/14

n = -4

Answer:

n = -4

Step-by-step explanation:

10n + 56 = -4n

56 = -14n

n = -4

The height Sikdar calculated for Peak XV is approximately 29105.77 feet.

Let's first find the height of point A above the ground. We can use the tangent function:

tan(45) = height of A / d

height of A = d * tan(45)

height of A = 17409.7 * tan(45) = 17409.7 feet

h / (d - 17409.7) = height of A / d

h = (height of A * (d - 17409.7)) / d

h = (17409.7 * (17409.7 / tan(32) - 17409.7)) / (17409.7 / tan(32))

 = 29105.77 feet

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