The crime rate of a certain city is increasing by exactly 4% each year. If there were 350
crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2023.

Answer:

61

Step-by-step explanation:

the question is asking to find the number of element of set b that are not in set a

to find this one must know the common elements

the question has given the common elements to be 5

now subtract the number of elements in set b with the common elements

i.e. 66-5

=61

Answer:

$4,000.343

Step-by-step explanation:

Divided the months of the year and caculate the intrest.

Answer:

([tex]\frac{7}{2}[/tex],[tex]\frac{1}{2}[/tex])

Step-by-step explanation:

For this you use the midpoint formula

[tex](\frac{x_{2} +x_{1} }{2} ,\frac{y_{2} +y_{1} }{2} )[/tex]

the points would be (2,1) and (5,2)

The midpoint would be ([tex]\frac{7}{2}[/tex],[tex]\frac{1}{2}[/tex])

Answer:

Step-by-step explanation:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

⇒  The rate of change output value with respect to input value remains constant,

Hence, It represents a linear function because there is a constant rate of change.

The real-life problem will be:- The total number of chocolates is 24 and there are 3 boxes what will be the number of chocolates filled in each box. The number of chocolates in each box will be 8.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression is:-

[tex]24\times \dfrac{1}{3}[/tex] = 8

The real-life problem will be given the as:-The total number of chocolates is 24 and there are 3 boxes what will be the number of chocolates filled in each box. The number of chocolates in each box will be 8.

Hence the number of chocolates in each box will be 8.

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39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:

We can write a mixed fraction in a fraction:

6 1/2 = 13/2

8 1/2  = 33/2

7 3/4 = 31/4

8 1/12 = 97/12

8 5/12 = 101/12

Adding all the fractions:

[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]

[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]

[tex]=23+\dfrac{64}{4}[/tex]

= 39 hours

Thus, 39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

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Answer:

Graph of the given equation is a opening up parabola passing through origin (0,0) and (2,0) and having vertex (1,-1)

Step-by-step explanation:

parabola - it is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

vertex - The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.

the given equation can be resolved as:

[tex]g(x)=(x-1)^2-1\\g(x) = x^2 -2x +1 -1\\g(x) = x^2 - 2x[/tex]

now substituting x = 0,

[tex]g(x) = x^2 - 2x\\g(x) = (0)^2- 2(0)\\g(x) = 0[/tex]

therefore the equation satisfies the point (0,0)that is origin.

now putting g(x) = 0,

[tex]g(x) = x^2 - 2x\\0 = x^2- 2x\\2x = x^2\\2=x[/tex]

so when y coordinate is 0 x coordinate is 2,

therefore the equation also satisfies the (2,0)

general equation of a parabola is

[tex]f(x) = ax^2 + bx + c[/tex]

and the vertex of the parabola is given by  [tex]\frac{-b}{2a}{,}{f{(}\frac{-b}{2a}{)}}[/tex]

given equation of parabola [tex]g(x) = x^2 - 2x[/tex]

here a = 1 and b= -2

substituting in the vertex formula,

vertex of the parabola is [tex]{(}{1}{,}{f{(}{1}{)}}{)}[/tex]

[tex]f(1) = 1 - 2 = -1[/tex]

therefore the vertex is (1,-1).

so the parabola is passing through origin(0,0) and (2,0) with vertex (1,-1).

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The function is f(x) = log(x - 5).

A line or curve that acts as the limit of another line or curve.

The complete question is

Which function has an asymptote at x = 5 and an x-intercept of (6,0)? a. f(x) = log(x − 5) b. f(x) = log(x 5) c. f(x) = log x − 5 d. f(x) = log x 5

let us take,

f(x) = log(x - 5)

y = 0, then

0 = log(x-5)

x - 5 = [tex]e^{0}[/tex]

x - 5 = 1

x = 6

So, it can be conclude that the x-intercept is at (6, 0)

Hence, the function is f(x) = log(x - 5).

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They have no relation, except for the fact that they intersect.

We have given that,

The graphs of the two lines y= -4/5x + 2 and y = - 5/4x - 1/2

If the equations were instead y = +5/4x - 1/2 and

Vertical lines and horizontal lines are perpendicular to each other. The slope of the perpendicular line in this case would be the slope of a horizontal line which would be 0. The slope of the parallel line is undefined and the slope of the perpendicular line is 0.

y = -4/5x + 2, or

y = +4/5 + 2 and

y = -5/4x -1/2,

Then they would be perpendicular.

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Answer:54

Step-by-step explanation:

There are quicker ways to solve this but a simple and easy way to do this would be by dividing your number by the percent so 288/80 and with this, you would get your number for 1 percent or 3.6. Now you can multiply that number by the percent your need to find so 15. And 15 x 3.6 is = 54.

Answer:

see explanation

Step-by-step explanation:

using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

[tex]\sqrt{\frac{a}{b} }[/tex] ⇔ [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

then

[tex]\sqrt{500}[/tex]

= [tex]\sqrt{100(5)}[/tex]

= [tex]\sqrt{100}[/tex] × [tex]\sqrt{5}[/tex]

= 10 × 2.24

= 22.4

-------------------------------

[tex]\sqrt{0.5}[/tex]

= [tex]\sqrt{\frac{50}{100} }[/tex]

= [tex]\frac{\sqrt{50} }{\sqrt{100} }[/tex]

= [tex]\frac{\sqrt{50} }{10}[/tex]

= [tex]\frac{7.07}{10}[/tex]

= 0.707

The solution of the given equation 4(3x - 4) - 7( 2x + 3) = 3 is -20.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is;

4(3x - 4) - 7( 2x + 3) = 3

To solve;

4(3x - 4) - 7( 2x + 3) = 3

Solve the parentheses using the distributive property;

12x - 16 - 14x - 21 = 3

we need to get the like terms together;

12x - 14x -16 - 21 = 3

-2x - 37 = 3

Add 37 both sides, we get;

-2x = 40

Divide both sides by -2

x = -20

Hence, the solution of the given equation is -20.

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Eric spend 60 minutes for basketball and 35 minutes for volleyball.

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

Here, let Eric plays basketball for x minutes.

          and volleyball for y minutes.

Total time spend on playing basketball and volleyball everyday = 95 minutes.

Duration of Basketball 25 minutes more than volleyball

Now, according to question,

          x + y = 95        ..........(i)

          x - 25 = y          ...........(ii)

On solving equation (i) and (ii), we get

        x + x - 25 = 95

           2x = 95 + 25

           2x = 120

            x = 120 / 2

            x = 60

put value of x in equation (ii), we get

        60 - 25 = y

          y = 35

Yes, it is possible and clearly described in above calculation.

Thus, Eric spend 60 minutes for basketball and 35 minutes for volleyball.

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The regression equation is given by [tex]\overline{y}=50-0.01x[/tex]

We have given that,

The scatter plot shows the relationship between the mass of a tree and the total mass of the vegetation within 100 square meters of the tree.

The slope =change in y/change in x

We have given the two points (100,40) and (25000,2)

Therefore the slope of the given point is,

[tex]=\frac{25-40}{2500-1000} \\=-0.01[/tex]

The y-intercept is the value of y when x=0 this implies that y=50

Therefore the regression equation is given by

[tex]\overline{y}=50-0.01x[/tex]

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Answer: The second table.

Step-by-step explanation: The y coordinates are getting smaller over time, so I believe the second one would be the correct answer. I hope this helps!  :)

Answer:

2268x²-1944w+648

-9² = 81

81×4 =324

use the 324 to remove the bracket

Answer:

Since we want to find radius and the diameter is 28 we will divide by two = ²⁸/2 which gives a radius of 14

since the radius is 14cm. we move on to the volume .

WE SUBSTITUTE

⁴/3× ²²/7× 14 equals 58.2cm²

therefore radius; 14cm

volume; 58.2cm

The only true statement is A:

"The data show a negative linear relationship."

On the graph, we can see how the car's vale decreases almost linearly with the age of the car.

Where the response variable would be the one on the y-axis, which is the car's value.

For that linear behavior, we know that there is a correlation coefficient different than zero. So options B, C, and D are false.

Finally, we already saw the linear behavior (decreasing, so the slope is negative). Then we conclude that the only true statement is A.

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Answer: The height is 15

Step-by-step explanation:

Vcone =  pi * r^2 * h  / 3

Area of the base  =  pi*r^2  = 70   so...

350  = 70 * h / 3  

350  = (70/3) * h     multiply both sides by 3/70

350 (3/70)  = h  = 15 m

The reflected function is g(x) = √(-x).

And the correct option is the third one.

Remember that for a function f(x), a reflection across the y-axis gives:

g(x) = f(-x).

In this case, the original function was:

f(x) = √x

Then we have:

g(x) = √(-x).

So we can only evaluate this function in values of x such that:

x ≤ 0.

Then the correct option is:

"On a coordinate plane, a graph starts at (0, 0) and goes to the left through (negative 4, 2)."

As when we evalute g(x) in -4, we get:

g(-4) =  √(-(-4)) = √4 = 2

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Answer:

C

Step-by-step explanation:

Answer:

======================================================

Explanation:

Let's solve for y to get the equation into y = mx+b form, aka slope intercept form.

4x-8y= -6

-8y= -6-4x

y = (-6-4x)/(-8)

y = -6/(-8) + (-4x)/(-8)

y = 3/4 + (1/2)x

y = (1/2)x + 3/4

This is now in y = mx+b form

m = 1/2 = slope

b = 3/4 = y intercept

We'll ignore the y intercept and focus on the slope only.

-----------------

Rule: If the slope of a line is a/b, then the perpendicular slope is -b/a

Flip the fraction and flip the sign.

In this case, the original slope 1/2 has a perpendicular slope of -2/1 or simply -2.

The original slope multiplied with the perpendicular slope yields -1. So (1/2)*(-2/1) = -1

-----------------

Another rule: Two parallel lines always have equal slopes, but different y intercepts.

The original slope is 1/2, so the parallel slope is also 1/2.

Answer:

Area of the minor segment = 2.505324230749 cm²

Step-by-step explanation:

Area of the minor segment

= Area of the sector ABC - Area of the triangle ABC

……………………………………………………………………………………

• Area of the sector ABC

= Area of the whole circle ÷ 8

= (π×8²) ÷ 8

= 8π

______

•• Area of the triangle ABC

= (1÷2) × CA × CB × sin(45)

= (1÷2) × 8 × 8 × (√2/2)

= 16√2

______

Thus

Area of the minor segment

= 8π - 16√2

= 2.505324230749

Answer:

See below

Step-by-step explanation:

Longest is the down tube.....it is opposite the largest angle (95°) angle in the triangle .    This is a SCALENE triangle ( all sides of different length)

The longest tube that we have here is the down tube. The triangle that is formed id the scalene triangle

A scalene triangle is a type of triangle where all three sides have different lengths. In other words, no two sides of a scalene triangle are equal in length. Additionally, the angles of a scalene triangle are also different from each other.

The term "scalene" comes from the Greek word "skalenos," which means "uneven" or "unequal." This name reflects the defining characteristic of the scalene triangle, which is the absence of any equal sides or angles.

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The foci of the hyperbola represented by (0, –6) and (0, 6). Then the correct option is B.

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

The equation of the parabola is given below.

5y² – 4x² – 80 = 0

Then the equation can be written as

y² / 4 – x² / 5 – 4 = 0

  y² / 16 – x² / 20 = 1

Then the value of eccentricity will be

a² = 16 and b² = 20

Then we have

e = √[1 + (b² / a²)]

e = √[1 + (20 / 16)]

e = 1.5

Then the focus of the parabola will be

⇒ (0, ±ae)

⇒ (0, ± 4 x 1.5)

⇒ (0, ±6)

⇒ (0, –6) and (0, 6)

Then the correct option is B.

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Using translation concepts, the equation for the graph is given as follows:

b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have a cosine function(zero at pi/2, this is zero at the origin), shifted pi/2 units to the right and 1 unit up(as the standard amplitude is between -1 and 1, here is between 0 and 2).

Hence the rule is given by:

b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].

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We will see that we have a shift of 9 units to the left and 6 units upwards

For any given function H(x), we define a vertical shift of N units as:

g(x) = H(x) + N.

While a horizontal shift is written as:

g(x) = H(x + N).

Here we know that:

f(x) = 3*|x + 9| + 6

If the original function was:

H(x) = 3*|x|

Then we can write:

f(x) = H(x + 9) + 6

So we have a shift of 9 units to the left and 6 units upwards.

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The probability that both are smokers is 6903/180000

The given parameters are:

Male smoker = 177

Female smoker = 78

Total student = 78 + 522 = 600

The probability of a male smoker is

P(Male) = 177/600

The probability of a female smoker is

P(Female) = 78/600

The probability that both are smokers is

P(Smoker) =P(Male) *P(Female)

So, we have:

P(Smoker) = 177/600 * 78/600

Simplify

P(Smoker) = 177/600 * 39/300

Evaluate the product

P(Smoker) = 6903/180000

Hence, the probability that both are smokers is 6903/180000

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