The number of crimes that occurred in a certain city per 1000 people had decreased from 46.1 in 1920 to 45.3 in 1940. Find the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 1940.

A. The distribution of x is normal with mean 2 mm and standard deviation 0.008 mm.

B. The bounds are given as follows:

C. The probability that the sample mean is outside the interval 2 ± 3 x is given as follows: 0.003 = 0.3%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the population are given as follows:

[tex]\mu = 2, \sigma = 0.04[/tex]

Hence, for a sample of 25, the standard error is given as follows:

s = 0.04 / square root(25) = 0.008 mm.

The interval for item b is within three standard errors of the mean, hence:

The Empirical Rule states that 99.7% of the measures are within three standard errors of the mean, hence the probability that the sample mean is outside the interval 2 ± 3 x is given as follows: 0.003 = 0.3%.

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The inequalities that can be used to represent the situation are:

Inequalities are mathematical statements showing that two or more mathematical expressions are unequal.

With inequalities, two or more values are compared to show that they are not equivalent.

Inequalities can be represented as follows:

The cost of small candles per unit = $3.50

The cost of large candles per unit = $5.00

The number of small candles = x

The number of large candles = y

The number of candles Jimmy needs to buy ≥ 20

The total amount Jimmy can spend on the candles ≤ $80

3.50x + 5y ≤ $80

x + y ≥ 20

Thus, with these inequalities, the total cost of small and large candles must not exceed $80 and the number can be 20 or more.

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Show the two inequalities representing the situation.

Ling is now 17 feet off the ground if she is climbing a rock wall.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

She begins by climbing 12 feet. Then she descends 3 feet to take a different path. She climbs another 8 feet from there.

Ling started 12 feet off the ground and climbed down 3 feet, so she is now 12 - 3 = 9 feet off the ground.

Then she climbed up another 8 feet, so she is now 9 + 8 = 17 feet off the ground.

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The value of the function 3f(1)−4g(−2) is -19.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that f(x) =7x−4 and g(x) =11−x². The value of the expression 3f(1)−4g(−2) will be calculated as,

3f(1) = 3 x ( 7 - 4 ) = 9

4g(−2) = 4 x [ 11 - (-2)² ] = 4 x -7 = -28

Substitute the values and solve,

E = 3f(1)−4g(−2)

E = 9 - 28

E = -19

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The diagonal intersection and the midpoint of both diagonal lies on the same point.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

As per the given parallelogram,

The midpoint of diagonal through J(4,-2) and H(-2,2) will be as,

x = (4 - 2)/2 = 1

y = (-2 + 2)/2 = 0

So it will be (1,0)

The midpoint of diagonal through K(-2,-3) and I(4,3) will be as,

x = (-2 + 4)/2 = 1

y = (-3 + 3)/2 = 0

So it will also be (1,0).

Since both midpoints are the same thus it will be the intersection point.

Hence "The midpoint of both diagonals and the diagonal intersection is located at the same location".

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These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

the triangle's circle's center. It is the point where the "perpendicular bisectors," or lines parallel to the centre of both sides, cross.

The intersection of any two perpendicular bisectors of any two triangle sides is known as the circumcenter of a triangle ABC.

The equation y=1 is the perpendicular bisector of sides B(3,0) and C(3,2). Because AB's midpoint is at 3,1 and its slope is unknown. The perpendicular bisector has zero slope. The equation for such a line is y=y1.

The equation for the perpendicular bisector of A(0,0) and B is also x=1.5 (3,0). The reason is that AB has a midpoint of zero slope and (1.5,0). The perpendicular bisector's slope won't be clearly defined. The equation for such a line is x=x1.

These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

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The line QS represents nothing from the given options, option D is correct.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Given a ΔTQR

a line from Q intersects at TR at point S and divides angle Q to 30° and 34°,

The line QS is not a median, because a median divides the side into two equal halves, and the figure does not show that  ST is equal to SR.

The line QS is not an attitude because the figure has not specified the angle of S in line TR, if given that the ∠QSR = ∠QST = 90° then QS will be called altitude.

The line QS is also not an angle bisector because an angle bisector divides the angle into two equal parts but the given angles are not equal.

Hence option D is correct.

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

Explanation:

Let,

These equations are valid because segment AP bisects the angle CAB, i.e. it splits it into two equal pieces. Similarly, segment BP bisects angle ABC.

Then we can say,

Let's focus on triangle CAB. The three interior angles add to 180 degrees. This is true of any triangle.

(angleCAB)+(angleCBA)+(angleACB) = 180

(2x) + (2y) + (44) = 180

2x+2y+44 = 180

2(x+y+22) = 180

x+y+22 = 180/2

x+y+22 = 90

x+y = 90-22

x+y = 68

Normally we would try to isolate one variable, but I'll stop here. We'll use this later in the next section.

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

Now focus your attention on triangle PAB.

The three interior angles add to 180.

(anglePAB)+(angleABP)+(angleAPB) = 180

(x)+(y)+(z) = 180

x+y+z = 180

(x+y)+z = 180

68+z = 180 .... replace "x+y" with 68

z = 180-68

z = 112 degrees is the measure of angle APB.

Answer:

its (-644) because 4 multiplication 23 and multiplication 7 is 644 and a minus will be written

Answer:644

Step-by-step explanation:

i got it right

Answer:

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

Given ratios:

Simplify the second ratio by dividing both parts by 3:

The ratio becomes:

We get same ratios so they are equivalent.

Answer:

  82 m²

Step-by-step explanation:

You want the area of the triangle with sides b = 13 m, c = 17 m, and the angle between them, A = 48°.

The relevant formula for the area is ...

  Area = 1/2(bc)sin(A)

  Area = 1/2(13 m)(17 m)sin(48°) ≈ 82.1175 m²

The area of the triangle is about 82 square meters.

The value of angle x in the straight line is 41 degrees.

The sum of angles on a straight line is 180 degrees. In other words, angles on a straight line add up to 180°. Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line.

Therefore, let's find the angles x.

Using sum of angles on a straight line,

x + 139 = 180

subtract 139 from both sides of the equation

x + 139 - 139 = 180 - 139

Hence,

x = 41 degrees

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The following graph will represents the possible number of orange fish, k, and blue fish, that they can put in the tank.

Here we have given that owners of an aquarium have recently built a new tank that can hold up to 110 fish.

And here we also know that owners wish to fill it with orange fish and blue fish. The orange fish are smaller, so they want at least 20 more orange fish than blue fish.

Let us consider that x refers the orange fish and y refers the blue fish.

Then the total number of fish in the tank is written as,

=> x + y = 110

Here we have the condition that at least 20 more orange fish than blue fish.

Then the inequality for the situation is written as.

=> x > 20

So, when we plot these on the graph then we get the graph like the following.

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Answer:

[tex]\huge\boxed{\sf Option \ 1}[/tex]

Step-by-step explanation:

Here, 6x + 6 is a linear expression since all the terms are raised to power 1 only.

[tex]\rule[225]{225}{2}[/tex]

Predicting when Old Faithful will spurt next can be done by timing the previous eruption. the next eruption is expected to occur at 12:59. p.m

Generally, The eruption that begins at 11:32 a.m. will end at 11:36 a.m.

So, the next eruption will occur approximately 12.5t + 33 minutes after 11:36 a.m., which is 12.5 * 4 + 33 minutes after 11:36 a.m., or 83 minutes after 11:36 a.m.

Therefore, the next eruption is expected to occur at 12:59. p.m. (11:36 a.m. + 57 minutes).

To calculate this, you would first add the minutes (83) to the number of minutes in the starting time (36). This sum, 119, is greater than 60, so you need to carry over 1 hour from the minutes to the hours.

This leaves 19 minutes, which is less than 60, so the result is 12:19. However, you also need to add 1 hour to the starting time to account for the carried over hour, giving you a final result of 12:59.

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The value of m is 32, the measure of the angle ∠ MLE is 16° and the measure of ∠ ELB is 74°.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Given:

The measure of ∠ MLE = 1 / 2 m, ∠ ELB = 2 (m + 5)

Calculate the value of m as shown below,

∠ MLE + ∠ ELB  = 90  (As given on figure)

1 / 2 m + 2 (m + 5) = 90

1 / 2 m + 2 m + 10 = 90

m + 4 m + 20 = 180

5 m = 180 - 20

m = 160 / 5

m = 32

Hence, ∠ MLE = 32 / 2 = 16°, and ∠ ELB = 2 (32 + 5) = 74°

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The complete question is attached below.

The Pair 1 and Pair 3 polygons are congruent. Therefore, the correct option is D.

The definition of a congruent polygon is a polygon that is the same shape, has the same length of sides, and has the same interior angles as the polygon it is being compared to. Congruent shapes must all be the same type of shape in order to fulfill the requirement.

Pair 1:

Here, the shapes are same and have same length.

So, the polygons are congruent.

Pair 2:

Here, the shapes are same but they have different lengths

So, the polygons are not congruent.

Pair 3:

Here, the shapes are same and have same length.

So, the polygons are congruent.

Pair 4:

Here, the shapes are same but they have different lengths

So, the polygons are not congruent.

Therefore, option D is the correct answer.

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It can change be 6 5/8 as a percentage is 662.5%.

The percentage is defined as a ratio expressed as a fraction of 100.

To change a mixed fraction to a percent, you first need to convert the fractional part (in this case, 5/8) to a decimal. To do this, divide the numerator (5) by the denominator (8). In this case, 5/8 simplifies to 0.625.

Next, add the whole number (6) to the decimal from step 1 (0.625) to get 6.625.

Finally, multiply this sum by 100 and add the percent sign %, so 6.625 * 100 = 662.5%

So, 6 5/8 as a percent is 662.5%.

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Based on the function, an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient is f(x) = (x+1)^2 -25. (Option D)

The function is f(x) = (x + 6)(x – 4). Solving the function

f(x) = (x + 6)(x – 4)

= x (x – 4) + 6(x – 4)

= x^2 – 4x + 6x – 24

= x^2 + 2x – 24

= x^2 + 2x + 1– 25

= (x + 1)^2 – 25

When x = -1, the value of f(x) = (-1 + 1)^2 – 25 = -25

Hence, the equation for which the minimum value of f appears as a constant or coefficient is (x + 1)^2 – 25.

Note: The question is incomplete. The complete question probably is f(x) = (x + 6)(x – 4). Which of the following is an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient? A) f(x) = x^2-24 B) f(x) = x^2+2x-24 C) f(x) = (x-1)^2 -21 D) f(x) = (x+1)^2 -25

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The number of ways that he can reach the bottom step in 5 jumps will be 792.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

Running down the stairway is someone. He could hop over some steps since he is in a hurry. When a staircase has 12 steps (including the top one, where he begins, and the last one, where he ends).

The number of ways will be given as,

¹²C₅ = (12!) / [(12 - 5)! x 5!]

¹²C₅ = (12 x 11 x 10 x 9 x 8 x 7!) / [7! x 5 x 4 x 3 x 2 x 1]

¹²C₅ = 11 x 9 x 8

¹²C₅ = 792

The number of ways that he can reach the bottom step in 5 jumps will be 792.

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Black and very dark greys are difficult for LCDs to produce. They consequently typically have lower contrast than CRTs and have less colour saturation for low intensity hues.

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Answer:

Associative Property

(2•x)•5=2•(x•5)

this equation represents the Associative Property.

hope that helps...

Answer:cDADVFBDGFZDGSHHDBHDG

Step-by-step explanation:

The length of the arc of radius 65 feet is 170.2 feet. And the right option is C) 170.2 feet.

An arc of a circle is the smooth curve formed from the two-chord endpoints.

To calculate the length of the arc between two cars on the ferris wheel, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the length of the arc is 170.2 feet.

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The values of the x are, x = 5,  x = 1.

What is solving an equation?

The fundamental guidelines and procedures to simplify any algebraic expression are as follows:

By multiplying factors, remove any grouping symbols like brackets and parentheses.

If the terms contain exponents, use the exponent rule to eliminate grouping.

Add or subtract like terms to combine them.

Add the constants together.

Consider, the given equation

y = x²                            ..(1)

y - 6x + 5 = 0               ..(2)

Replace y = x²  in second equation.

       x² - 6x + 5 = 0

  x² - 5x - x + 5 = 0

x(x - 5) - 1(x - 5) = 0

      (x - 5)(x - 1) = 0

⇒  (x - 5) = 0,       (x - 1) = 0

x = 5,   x = 1

Hence, the values of the x are, x = 5,  x = 1.

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At 0 degree celsius of temperature, Sales will be $-159.474 which is meaningless to interpret.

The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b. The line's slope is represented by the m. A straight line's slope is a measure of how steep it is. The gradient is another name for it. The slope equations. The ratio of a line's "change in y" to its "change in x" is known as the slope. You can get the slope of a line by dividing the distance between two points (x1,y1) and (x2,y2) by the distance between the two locations.

From the given information,

By using calculator,

A. Putting Temperature=20 in the given regression equation,

Predicted sales= 442.284

B. Slope=$ 30.0879

If temperature increases by 1 degree celsius then Sales increases by $30.0879, on average.

C. y-intercept= -159.474

At 0 degree celsius of temperature, Sales will be $-159.474 which is meaningless to interpret.

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It counts the amount of money coming in or going out over the specified time period.

The cash balance of liquid assets coming into and going out of a business is referred to as cash flow. Money spent and money received reflect inflows and outflows, respectively.

The cash flow is the difference between outflow and inflow.

Cash flow = outflow - inflow

If the value of the cash flow is negative that means the expense is more.

If the value of the cash flow is positive that means the income is more.

A reliable indicator of a company's strength, prosperity, and prospects for the future is the cash flow report. The cash flow statement is significant because it tracks any inflows or outflows of cash within the specified time period. The industry's both short- and long-term planning is influenced by this information.

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The expressions that are equivalent to 0.3(9n + 22) are:

(a)

Apply the Distributive Property: 0.3 x 9n + 0.3 x 22

Multiply the monomials: 2.7n + 0.3  x 22

Calculate the product or quotient: 2.7n + 6.6

Determine whether 0.3(9n + 22) and -2.7n - 6.6 are equivalent.

FALSE.

b.

Apply the Distributive Property: 0.3 x 9n + 0.3 x 22

Multiply the monomials: 2.7n + 0.3  x 22

Calculate the product or quotient: 2.7n + 6.6

Determine whether 0.3(9n + 22) and 2.7n + 6.6 are equivalent.

TRUE

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Answer:

4

Step-by-step explanation:

4, count the spaces as in the figure

The required percentage is 65% of the highest price city more expensive than the lowest price city for the cost of retail space.

The percentage is defined as a ratio expressed as a fraction of 100.

The highest price city for the cost of retail space is Berlin with an average cost per square foot of retail space of 469.

The lowest price city for the cost of retail space is Paris with an average cost per square foot of retail space of 284.

The difference is 469 - 284 = 185

Hence, the required percentage is :

⇒ 185/ 284 x 100%

⇒ 65%

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Answer:

First, let's find the total amount of time the children spent asleep: 10 hours - 7.5 hours = <<10-7.5=2.5>>2.5 hours

Then, let's find the amount of time the children spent dreaming by multiplying the total amount of time they spent asleep by 25%: 2.5 hours * 25% = <<2.525.01=.625>>.625 hours

We can represent this situation with the compound inequality: .625 hours <= x <= 2.5 hours

To graph this inequality, we can plot a point at 2.5 on the number line and shade in the region to the left of it. Then, we can plot a point at .625 on the number line and shade in the region to the right of it. The solution to the inequality is the region where both shaded regions overlap.

[asy]

unitsize(1 cm);

draw((-2,0)--(4,0));

draw((0,-1)--(0,1));

draw((-.2,0)--(0,.2)--(.2,0)--(0,-.2)--cycle);

draw((2.5,-1)--(2.5,1),dashed);

draw((.625,-1)--(.625,1),dashed);

label("$x$",(4,0),SE);

fill((-2,0)--(-2,1)--(2.5,1)--(2.5,0)--cycle,gray(.7));

fill((2.5,0)--(2.5,1)--(4,1)--(4,0)--cycle,gray(.7));

[/asy]

Step-by-step explanation: