In 1990, a large measles outbreak occurred in Philadelphia in predominantly unvaccinated preschool children. There were 892 unvaccinated children identified with 486 cases of measles of which 6 died. 1. Calculate the attack rate (show the formula, decimal point calculation, and response in %). 2. Calculate the case fatality rate (show the formula, decimal point calculation, and response in %).

Answer:

28 pillows

Step-by-step explanation:

\( = 10 \frac{1}{2} \div \frac{3}{8} \\ = \frac{21}{2} \div \frac{3}{8} \\ = \frac{21}{2} \times \frac{8}{3} \\ = 28\)

Using PEDMAS, the expression is 188.75

BODMAS is an acronym and it stands for parentheses, exponents, division, multiplication, addition, subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS.

To solve this problem, we just need to apply PEDMAS rule here and evaluate the expression.

210 ÷ 5.2 * 9 3/4 - 205 = 755 / 4 = 188.75

The expression has a value of 188.75

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Answ  Find the distance between the following pairs of points:

           (i) (2, 3), (4, 1) (ii) (–5, 7), (–1, 3) (iii) (a, b), (–a, –b)Sol. (i) Here x1 = 2, y1 = 3, x2 = 4 and y2 = 1         ∴ The required distance         er:

Step-by-step explanation:

Answer:

y = 15x+32

Step-by-step explanation:

Given

y to be the total minutes Andrew will play video games today

x is the total number of games played after school

If he wants to play an additional 15 minutes each of x games after school today, the total minutes he will use for the x games will be 15* x = (15x)minutes

We are told that he has initially spent 32minutes on video games. hence;

Total minutes Andrew used on games y = (15*x)+32

The required equation will be y = 15x+32

Answer:

n/a nuyt

Step-by-step explanation:

Using trigonometric ratios, we have been able to deduce that;

BE = 10 cm; sin B = 3/5 and cos B = 4/5

The basic trigonometric ratios for an angle θ are expressed as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Now, looking at the given triangle NEB, we are given that;

NE = 7.5 cm

tan B = 3/4

angle E = 90°

If tan B = 3/4, then it means that;

3/4 = NE/BE

since NE = 7.5, then we can say that;

3/4 = 7.5/BE

BE = (7.5 * 4)/3

BE = 10 cm

By Pythagoras theorem, we can say that BN = 12.5 cm.

Thus;

sin B = opposite/hypotenuse = 7.5/12.5 = 3/5

cos B = adjacent /hypotenuse = 10/12.5 = 4/5

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Using trigonometric ratio, the side BN is 12.5 units, sin and cos angle of B are 36.9 degrees respectively

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In this problem;

A)

Tan B = 3/4

BN = ?

Tan B = NE / BE

3/4 = NE / BE

BE = NE / 3/4

BE = 7.5 / 0.75

BE = 10

The side BN can found using Pythagoras theorem

BN² = BE² + NE²

BN² = 10² + 7.5²

BN = 12.5

B)

Sin B = NE / NB

sin B = 7.5 / 12.5

sin B = 0.6

B = sin⁻¹(0.6)

B = 36.9°

C)

Cos B = BE / NB

cos B = 10 / 12.5

B = cos⁻¹(10/12.5)

B = 36.9°

The length of Bn is 12.5cm, and sin and cos angle of B is 36.9 degrees respectivelt

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The formula to determine xx is

Total Cost = (Parking Cost + Ticket Cost) × Number of People

3 or 4 people can go to the amusement park with available budget.

The equation which can be used to determine the number of people who can go to the amusement park is:

Total Cost = (Parking Cost + Ticket Cost) × Number of People

Therefore;

The total cost is limited to the available budget of $137.75

The parking cost is $15.25

The ticket cost is $24.50

Number of people is X

So, $137.75 = ( $15.25 + $24.50) × X

$137.75 = $39.75 × X

$137.77 = X

$39.75

X = 3.47

Based on the answer gotten, 3 or 4 people can go to the amusement park with available budget.

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(C) Regression analysis is the statistical method commonly used to estimate the level and trend in a time series by modeling the relationship between the data and independent variables.

Regression analysis is the statistical method used to estimate the level and trend in a time series. Time series data represents observations taken at different points in time and is commonly used to analyze trends and patterns over time.

Regression analysis allows us to model the relationship between a dependent variable (in this case, the time series data) and one or more independent variables (such as time or other relevant factors). By using regression analysis, we can identify the underlying trend in the time series and estimate its level.

The regression model captures the relationship between the dependent variable (the time series) and the independent variable(s) by fitting a line or curve that best represents the data. This line or curve helps to identify the overall trend and level of the time series.

While moving average, simulation method, covariance analysis, and correlation analysis are useful techniques in analyzing time series data, they are not specifically designed to estimate the level and trend in a time series. Therefore, (C) regression analysis is the most appropriate method for estimating the level and trend in a time series.

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Dilations are transformations that change the size of an object while maintaining its shape. They are performed by multiplying the coordinates of each point by a scale factor.

Here's a step-by-step explanation of how dilations work:

Scale Factor: The scale factor determines how much the object will be enlarged or reduced. A scale factor greater than 1 enlarges the object, while a scale factor between 0 and 1 reduces it.Center of Dilation: A center of dilation is a fixed point that serves as the origin for scaling. All points of the object will be dilated with respect to this center.

Calculation: To dilate a point (x, y) with a scale factor of "k" and a center of dilation at (h, k), you can use the following formulas:

New x-coordinate: x' = h + (x - h) * k

New y-coordinate: y' = k * (y - k) + k

Transformation: Apply the dilation formulas to each point of the object, calculating their new coordinates.

By multiplying the original coordinates by the scale factor, the object expands or contracts from the center of dilation. It's important to note that the shape of the object remains the same during dilation, only its size changes.

Practice with different scale factors and centers of dilation to gain a better understanding of dilations.

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The 100 feet per second rate at which rocket is rising vertically upwards and the 50 feet distance of the observation position from the launch, indicates;

A) The height of the rocket after exactly 2 seconds is 200 feet

B) The rate of the angular motion at which to scan upwards to keep track of the rocket is 2/17 radians per second

Angular motion is a circular motion of an object about a fixed axis, described in radians per second.

The rate at which the rocket is rising up in the air = 100 feet per second

The horizontal distance from the point of launch to the observer = 50 feet

The time at which the height of the rocket is required = 2 seconds

A) The height of the rocket after 2 seconds, h = 2 s × 100 ft/s = 200 ft

B) The angle of elevation of the line of sight to the rocket = θ

tan(θ) = h/50

sec²(θ)·(dθ/dt) = (1/50)·(dh/dt)

(dθ/dt) = (1/50) × (dh/dt)/sec²(θ)  = (1/50)×(dh/dt)×(cos²(θ))

At time, t = 2 seconds, the height of the rocket = 200 feet

Therefore;

tan(θ) = 200/50 = 4

θ = arctan(4)

dh/dt = The vertical velocity of the rocket = 100 ft/s

(dθ/dt) = (1/50)× 100 ×(cos²(arctan(4))) = 2/17

The rate at which the eyes is scanning upwards is 2/17 radians per second

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Answer:

The system of linear equations consist of parallel lines

Step-by-step explanation:

Here, we want to classify the system of linear equations

Firstly, let us write both in the standard forms

For the first;

y = 3x + 2

For the second;

y = 3x-1

The general form of a linear equation is;

y = mx + b

where m is the slope and b is the y-intercept

In both cases, m = 3 and that means the slope is the same

When two lines have same slope values, they are said to be parallel to each other

Answer:

He only added Sundays run

Step-by-step explanation:

Answer:

Step-by-step explanation:

(6^2)^p = 6^(2p) = 6^10

2p = 10

p = 5

Answer:

The probability he rolls a 2 or lower and the coin lands on heads is 16.66%.

Step-by-step explanation:

Since Kane rolls a dice and flips a coin at the same time, to determine what is the probability he rolls a 2 or lower and the coin lands on heads the following calculation must be performed:

Given = 6 sides = 2/6

Coin = 2 sides = 1/2

2/6 x 1/2 = X

0.333 x 0.5 = X

0.1666 = X

0.1666 x 100 = 16.66

Therefore, the probability he rolls a 2 or lower and the coin lands on heads is 16.66%.

Answer: C

Step-by-step explanation:

IT is dividing by 6

The value of x in the given diagram of two similar triangle is  9 units.

Let us consider the name of two triangles be ABC and PQR.

Such that,

In triangle ABC,

AB = 12 , BC = 54 , m∠BAC = 90° and marked angle  is ∠ABC .

In triangle PQR,

PQ = 2 , QR = x, m∠QPR = 90° and marked angle  is ∠PQR .

In triangle ABC and PQR we have,

m∠BAC = 90° = m∠QPR

m∠ABC = m∠PQR  (given )

By AA corollary,

Triangle ABC is similar to triangle PQR with correspondence ABC ↔ PQR.

Corresponding sides of the similar triangle are in proportion.

AB / PQ = BC / QR

⇒ 12 / 2 = 54 / x

⇒ 12x  = 54 × 2

⇒ x = ( 54 × 2 ) / 12

⇒ x = 9

Therefore, the value of x in the given triangle is equal to 9 units.

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Step-by-step explanation:

she sell 5piece out of 6 per hour

for 36 hour, she sell:

5 × 36 = 180piece of pie

one pie is cut to 6 piece

180/6 = 30pie

If we consider a system where block A has a length of 0.75 times block B's length, block B has a length of 10, and block C has a length of 0.5 times block A's length, we can determine which block is harder to tip over.

To analyze the stability of the system, we can compare the center of mass of each block relative to its base of support. The block with a higher center of mass is more likely to tip over.

For block A, its center of mass is located at a distance of 0.375 times its length from its base.

For block B, its center of mass is located at a distance of 5 units from its base.

For block C, its center of mass is located at a distance of 0.375 times block A's length from its base.

Comparing the distances, we see that block B has the highest center of mass at 5 units, making it easier to tip over compared to blocks A and C. Thus, in this system, block B is harder to keep stable and more prone to tipping over.

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Answer:

mean = 3

Step-by-step explanation:

The mean of a data set is the average of all the elements in the set. This can be calculated using the formula:

\(\text{mean} = \dfrac{\text{sum of elements}}{\text{number of elements}}\)

From the bar graph, we can determine the total number of elements in the data set by counting the number of Xs.

We can see that there are 11 elements in the data set.

We can also determine the number of Xs for each number of times that a person played mini-golf last summer:

0, 1, 2, (5 × 3), 4, 5, 6

Now, we can plug these values into the above formula to calculate the mean.

\(\text{mean} = \dfrac{0+1+2+5(3) + 4 + 5 + 6}{11}\)

\(\text{mean} = \dfrac{33}{11}\)

\(\boxed{\text{mean} = 3}\)

Using translation concepts, it is found that the change from f(x) to g(x) can be described in two ways:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is:

f(x) = -x - 5.

The function g(x) is:

g(x) = -x - 2.

The change from f(x) to g(x) can be described in two ways:

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Answer:

  102.8 cm

Step-by-step explanation:

The perimeter of a semicircle is the sum of the length of the diameter and the length of the curved edge. The curved edge is half the circumference of a circle with the same radius.

  perimeter = diameter + curved edge

  = 2r +1/2(2πr) = r(2 +π)

  = (20 cm)(2 +π) ≈ 102.8 cm

The perimeter of the window is about 102.8 cm.

Answer:

37 degrees

Step-by-step explanation:

The angles within a triangle always add up to 180 degrees. Right angles are always 90 degrees. 53 + 90 = 143 degrees. 180 - 143 = 37 degrees

Step-by-step explanation:

x + y = 24

2x - y=21

I'm guessing the question was find both numbers.

3x = 35

x=15

3y = 27

y=9

Answer:

6/16 and 4/16

Step-by-step explanation:

Hope this helps :D

Answer:

2:00 PM

Step-by-step explanation:

20 = 2² × 5

Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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The correct answer is c. Line graphs show the change in one or more variables progressively across time.

Histograms show the distribution of data, pie charts show the proportions of a whole, bar charts compare categories or groups, and diagrams show the relationships between different elements.

The correct answer is c. Line graphs show the change in one or more variables progressively across time

A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighbouring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics. Frequency, which can be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data.

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Line graphs show the change in one or more variables progressively across time. C

A line graph is a type of chart that displays data as a series of data points connected by straight lines.

The horizontal axis of the graph typically represents time, while the vertical axis represents the value of the variable being measured.

By connecting the data points with lines, a line graph can show the trend or pattern of change in the variable over time.

Line graphs are commonly used in fields such as economics, finance, and science to visualize trends in data over time.

They can be used to identify patterns, compare different variables, or forecast future trends.

In contrast, histograms, pie charts, bar charts, and diagrams are different types of charts that are used to display data in different ways.

Histograms are used to show the distribution of data within a single variable, while pie charts and bar charts are used to compare different categories or groups of data.

Diagrams are used to represent complex systems or relationships, often using visual symbols or icons to represent different components.

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