Use the following to answer questions 19-21 Breast cancer is one of the leading causes of death in women prior to age 50. A study of the effectiveness of regular breast self-examination (BSE) reported in the American Journal of Public Health found that 23 of 53 women who discovered a tumor through BSE had a tumor in an early stage. Of 178 women who discovered a tumor by accident, 48 had a tumor in an early stage. Let p1 and p2 denote the proportion of women who detected early stage tumor through BSE and by accident, and let p1 and p2 denote the corresponding estimates.

The SE of p1-p2 is:________

Answer:

h(-2) = -1

Step-by-step explanation:

h(x)=-2x-5

Let x= -2

h(-2)=-2*-2-5

      = 4 -5

h(-2) = -1

Answer:

(2x+1)(1x+2) = 2x^2 + 4x + x + 2 = 2x^2 + 5x + 2

i think

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

cos(θ)= 18/30 = 3/5

sin(θ)= 24/30 = 4/5

tan(θ)= 24/18 = 4/3

cos(ϕ)= 24/30 = 4/5

sin(ϕ)= 18/30 = 3/5

tan(ϕ)= 18/24 = 3/4

The value of the trigonometric ratios have been determined.

In a Right angled triangle , the trigonometric ratios are used to determine the value of angles and sides.

The side length of the triangle as given in the figure is 18 , 24 , 30

The value of the trigonometric ratios are

cos θ = Base / Hypotenuse

sin θ =  Perpendicular / hypotenuse

tan θ =  Perpendicular / Base

cos(θ)= 18/30 = 3/5

sin(θ)= 24/30 = 4/5

tan(θ)= 24/18 = 4/3

cos(ϕ)= 24/30 = 4/5

sin(ϕ)= 18/30 = 3/5

tan(ϕ)= 18/24 = 3/4

Therefore the value of the trigonometric ratios have been determined.

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Answer:

Step-by-step explanation:

the consecutive are 39,40,41 and the smallest here is 39

Hope this helped

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Total soccer players: 300

Total netball players = 200

Ratio of soccer to netball = soccer / netball = 300/200 = 3/2

Answer: 3/2

Answer:

28.52

Step-by-step explanation:

105.87 - 77.35 = 28.52

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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Answer:

120

Step-by-step explanation:

If 6 = 5%, then 6 = 1/20 of the total grade. 6×20= 120

Answer:

129792

Step-by-step explanation:

         156

     ×  832

    ----------

         312

      468

+  1248

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

  129792

Domain of f is ( -4 ,1 ) and Range of f is (4 , -5)

The domain refers to the set of possible input values.

The domain of a graph consists of all the input values shown on the x-axis.

The range is the set of possible output values, which are shown on the y-axis.

According to the graph ,

The horizontal extent of the graph is starting from -4 and ending on 1

Therefore , the domain of graph is (-4 , 1)

These points are not included in the domain , you can observe the end points of curves is not filled

The vertical extent of graph is starting from 4 and going downwards till -5

so, Range of graph is (4 , -5)

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Answer:

Equation has no solutions.

Step-by-step explanation:

7x + 28 - 6x - 18 = x + 5

7x + 10 - 6x = x + 5

x + 10 = x + 5

x + 10 - 10 = x + 5 - 10

x = x - 5

x - x = x - x - 5

0 ≠ - 5

a. The missing value in the table 0.03

b. The mean is 4.18

c. The variance is 3.23 and standard deviation is 1.80

d.  The larger the standard deviation, the greater the spread of the probability distribution.

A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.

a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.

b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:

E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)

E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18

So, the mean number of calls per hour to the call center in the last month is 4.18.

c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:

Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)

Var(X) = 3.23

The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:

=> SD(X) = √(Var(X)) = √(3.23) = 1.80

d. Interpretation:

The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.

The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.

This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).

Complete Question:

The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.

x 1 2 4 5 6 7

P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03

a. What is the missing value in the table?

b. Find the mean.

c. Find the variance and standard deviation.

d. Interpret your results.

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You have to find the equation of the linear function h(x), given that you know two points of the said function.

h(3)=-2 → this notation indicates the ordered pair (3,-2)

h(-3)=16 → this notation indicates the ordered pair (-3,16)

The first step to determine the equation of any line or linear function is to calculate its slope. To do so you have to use the following formula:

Where

(x₁,y₁) are the coordinates of one point of the line

(x,₂,y₂) are the coordinates of a second point of the line

Using the ordered pairs:

(3,-2) as (x₁,y₁)

(-3,16) as (x,₂,y₂)

Calculate the slope as follows:

So the slope of the linear function is m=-3

To determine the equation you can use the point-slope form:

Where

m represents the slope

(x₁,y₁) are the coordinates of one point of the line

I will use the point (3,-2) and the slope m=-3 to determine the equation but you can use either ordered pair to do so.

Now, what's left is to write the equation in slope-intercept form:

-Distribute the multiplication on the parentheses term:

-Pass "+2" to the right side of the equal sign by applying the opposite operation to both sides of the equal sign "-2"

The equation of the linear function is:

To find the value of h(5), you have to replace the equation of the function with x=5 and calculate the corresponding h(x) value

So:

The number of observations in the data table indicates the number of types of dogs in the shelter.

A data table is a table where the data are arranged in one or more rows and columns. It includes a header in the top, which makes it more understandable.

Given is a data table.

2, 3, 1, 4, 3.5, 2.5, 2, 2.5, 1.5, 3, 2, 2.5

Each value in the data table indicates the number of cups of dog foods each dog has to be fed.

Number of observations in the data table = 12

So one dog has to be fed 2 cups

Second dog has to be fed 3 cups.

........................

12th dog has to be fed 2.5 cups.

So the number of observations indicate the number of dogs or number of each type of dogs in the shelter.

Hence the number of dogs in the shelter is signified by the number of observations.

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The incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

\(\rm a^b = c\\log_ac =b\)

The question is incomplete.

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

We have:

2ln(x) = In(3x) - [In(9) - 2ln(3)]

In(x²) = In(3x) - [In(9) - In(9)]

ln(x²) = ln(3x) - 0

ln(x²) = ln(3x/0)   (incorrect step)

ln(x²) = ln(3x)

x² = 3x  (correct step)

x² - 3x =0

x(x - 3) = 0

x = 0, 3

Thus, the incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

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Answer:

Scalene

Step-by-step explanation:

It is not isosceles because an isosceles triangle needs to have at least 2 congruent sides

It is not equilateral because not all of the sides are the same length

It appears to be a right triangle, not an acute triangle

The answer is scalene because all sides are a different length

Hope this helps :-)

Hi The answer is scalene

Answer:

23 is the possible minimal number of breaks required to separate all the squares.

Step-by-step explanation:

The crunchy granola bar is six by 4 squares.

Gives m=6 and n=4

It means there is m x n= 6 x 4=24 pieces in the crunchy granola bar.

Break the bar several times in such a way that all squares become separate. It means breaking the bar into single pieces. Which says single piece =k

To get 24 separate pieces of a crunchy granola bar. We use the formula:

                                                            = (m x n) – k

                                                            = (6 x 4) – 1

                                                            = 24 – 1

                                                             = 23 is the possible minimal number of breaks required to separate all the squares.

The age of Ngozi if ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 is 3.68 years.

Let

Ada age = x

Agnes age = 13 1/3x

Ngozi age = 2x

30 = x + 13 1/3x + 2x

30 = 3x + 40/3x

30 = 49/3x

divide both sides by 49/3

x = 30 ÷ 49/3

multiply by the reciprocal of 49/3

x = 30 × 3/49

x = 1.84 years

Ngozi age = 2x

= 2(1.84)

= 3.68 years

Therefore, Ngozi is 3.68 years old

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\(f(x) = x + 2\\g(x) = x\\(g \circ f) = g(f(x)) = x + 2\\g \circ f)(3) = 3 + 2 = 5\)

Step-by-step explanation:

Find the factors of x that makes it zero.. Equate the equation to y and use it to find the value of y. Then get your values for x and y and plot the graph

Answer:

the answer is y < 5/3

Step-by-step explanation:

3y < 5

y < 5/3

Answer:

Second option is the correct answer.

Step-by-step explanation:

\( \frac{2}{3} x - 5 > 3 \\ \\ \frac{2}{3} x > 5 + 3\\ \\ \frac{2}{3} x > 8 \\ \\ x > 8 \times \frac{3}{2} \\ \\ x > 12\)

Answer:

The standard form of equation of the line through the given points. through (0.-4) and (-3,-2) is \(\frac{2}{3}x+y=-4\)

Step-by-step explanation:

The standard form of equation is \(Ax+By=C\)

Finding slope

Using the given points (0,-4) and (-3,-2) we can find slope using formula:\(Slope=\frac{y_2-y_1}{x_2-x_1}\)

\(Slope=\frac{-2-(-4)}{-3-(0)}\\Slope=\frac{-2+4}{-3} \\Slope=-\frac{2}{3}\)

Finding y-intercept

Using point (0,4) and Slope=-2/3 we can find y-intercept

\(y=mx+b\\-4=-\frac{2}{3}(0)+b\\-4=0+b\\b=-4\)

The slope intercept form of the line through the given points. through (0.-4) and (-3,-2) having slope =-2/3 and b=-4 will be:

\(y=mx+b\\y=-\frac{2}{3}x-4\)

Now, standard form of equation will be: \(\frac{2}{3}x+y=-4\)

So, The standard form of equation of the line through the given points. through (0.-4) and (-3,-2) is \(\frac{2}{3}x+y=-4\)

Answer:

84

34

27

Step-by-step explanation:

Given :

Mean = 16

To find :

Age of the fifth boy

So,

\(x + 15 + 14 + 18 + 19 = 5 \times 16\)

\( = >x + 66= 80\)

\( = > x = 80 - 66\)

\( = > x = 14\)

Hence, the age of the fifth boy is 14 years

Answer:

Correct answer is B, 69.3 feet

Step-by-step explanation:

Since we have a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg, so the length of the shorter leg is 1/√3, or √3/3 times the length of the longer leg.

\(120( \frac{ \sqrt{3} }{3}) = 40 \sqrt{3} = 69.3\)

Film cameras allow a limited number of shots per role. 36 images can a photographer typically shoot on a roll. Thus, option A is the correct option.

The most cost-effective per shot is the roll, which typically yields 36 exposures. The 35mm format comes in a few different forms. On a roll of 35mm film, half-frame cameras may capture twice as many images at a smaller size.

Rolls of film typically have 24 or 36 exposures. The number of pictures you may take before loading a new roll may be limited as a result. However, some photographers view this as a benefit since it forces them to be more deliberate and exact when creating their images.

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Answer:

RT = 20

Step-by-step explanation:

Given that,

Point S lies on the line segment RT.

We have, ST = 3x-8, RT = 4x and RS = 4x-7

It is clear that, RT = RS+ST

Putting the values, we get :

4x = 4x-7 + 3x-8

Taking like terms together,

4x-4x-3x = -7-8

-3x = -15

x = 5

Put the value of x in RT = 4x.

So,

RT = 4(5)

RT = 20

Hence, length of RT = 20.