At the initial examination in the Framingham study, coronary heart disease was found in 5 per 1,000 men aged 30-44 years and in 5 per 1,000 women in the same age range. The inference that in this age group men and women have an equal risk of developing coronary heart disease is

Answer:

Step-by-step explanation:

There are a couple of ways you could solve this problem. B is one of them.

The correct answer is going to be Small hypotenuse / Large hypotenuse = tree / building height

Let the tree equal x

100/220 = x / 176           Multiply both sides by 176

100 * 176 / 220 = x

x = 80

Notice that 80 is almost 1/2 of 176 so the answer should be right since 100 is nearly 1/2 of 220

Answer:

it would be -34

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Since DF = EF then the triangle is isosceles with base angle being congruent, that is

∠ D = ∠ E , then

∠ D = \(\frac{180-133}{2}\) = \(\frac{47}{2}\) = 23.5°

The equations are e = 18+12t and a = 45+9t

Adrian will be father along in the book after 4 days. She will be 15 pages ahead of Ethan

Ethan's page number at the beginning of the month = 18

Adrian's page number at the beginning of the month = 45

Pages read by Ethan each day = 12 pages

Pages read by Adrian each day = 9 pages

Let e represent the page of the book that Ethan is on at the end of t days into the month. Let a represent the page of the book that Adrian is on at the end of t days into the month.

Formulating the equation we get the following:

e = 18 + 12t

a = 45 + 9t

Finding the page number of both Ethan and Adrian after 4 days by substituting the values in the equations we get:

e = 18+12(4)

e = 66

a = 45 + 9(4)

a = 81

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b. √60 is equivalent to 60^1/2

60^1/2 represents the square root of 60. The square root of a number is a value that when multiplied by itself, gives the original number. So in this case, √60 * √60 = 60. Therefore, the equivalent of 60^1/2 is √60.

Option a, 60/2 is not equivalent, because it is not the value that when multiplied by itself gives 60.

Option c, 1/60^2 is not equivalent, because it is not the value that when multiplied by itself gives 60.

Option d, 1/√60 is not equivalent, because it is not the value that when multiplied by itself gives 60.

It is important to note that 60^1/2 is not the same as (60^1)^1/2, the first one is finding the square root of 60 while the second one is finding the 1/2 power of 60 which is not the same thing.

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A quadratic equation can be solved by factoring if its coefficients are rational numbers and its discriminant, which is the expression under the square root in the quadratic formula, is a perfect square.

To determine if a quadratic equation can be solved by factoring, you must first ensure that its coefficients are rational numbers, meaning that they can be expressed as a ratio of two integers. Once you have confirmed this, you can calculate the discriminant of the quadratic equation, which is the expression b²-4ac, where a, b, and c are the coefficients of the quadratic equation in standard form.

If the discriminant is a perfect square, then the quadratic equation can be solved by factoring. If the discriminant is not a perfect square, then the quadratic equation cannot be solved by factoring using rational numbers, but may still be solvable using other methods, such as completing the square or the quadratic formula.

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It can be proved that Circles X and Y are similar.

We were told that circle Y have a  radius of s

And X have the  Radius r

Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y  by making a division on the  radii of both circles.

Then the scale factor is \(\frac{s}{r}\) which implies that circle Y will gotten by dilation of circle Y.

Therefore, both circles are similar

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1/5

2/10

3/15

5/25

6/30

7/35

8/40

9/45

10/50

Answer:

1/5

Step-by-step explanation:

4/20=1/5

Answer:

ewfwefwfewfwfwe

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The function that can be used to find the total height, h, of the building in feet, including the antenna is h = 6.8n + 13.5.

A builder is constructing an office building with n floors that will have an antenna 13.5 feet tall on its roof. Each floor of the building will be 6.8 feet high.

Therefore, the function that can be used to find the total height of the building in feet including the antenna can be calculated as follows:

Therefore,

n = numbers of floors in the building.

h = total height of the building

Hence, the function is as follows

h = 6.8n + 13.5

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The value of c that makes f(x) a valid density function over [0, 2] is c = 1/4.

The function given to us is f(x) = cx, and we are asked to find the value of c that makes this a valid density function over the interval [0, 2]. To be a valid density function, a function must satisfy two properties:

The function must be non-negative over the interval.

The integral of the function over the interval must be equal to 1.

Let's first check the first property. For f(x) to be non-negative over the interval [0, 2], c must be non-negative as well. This is because x³ is always non-negative, and multiplying it by a negative value of c would make f(x) negative for some values of x.

So, we can conclude that c ≥ 0.

Now let's check the second property. We need to find the value of c that makes the integral of f(x) over [0, 2] equal to 1:

∫₀² cx³ dx = 1

We can solve this integral using the power rule of integration:

(c/4) [x⁴]₀² = 1

(c/4) (2⁴ - 0⁴) = 1

16c/4 = 1

4c = 1

c = 1/4

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Answer:

35% of 300 is 105

Adults=105 , children=195

195 children were present.

Answer:

y'=6,-2    z'=2,-1

Step-by-step explanation:

Translations are x+4, y-4

We can apply this to the others.

y'=2+4,2-4

y'=6,-2

z'=-2+4/3-4

z'=2,-1

The expressions represent the same cost after the discount of 40%.

How to show that the two expressions 295 - 295(0.40) and 295(1 - 0.40) represent the same cost after the discount?

To show that the two expressions 295 - 295(0.40) and 295(1 - 0.40) represent the same cost after the discount, we can use the distributive property of multiplication over addition or subtraction.

The distributive property states that for any real numbers a, b, and c:

a(b + c) = ab + ac

a(b - c) = ab - ac

So, we can apply the distributive property as follows:

295 - 295(0.40)

= 295(1) - 295(0.40) [Multiplying 295 by 1]

= 295(1 - 0.40) [Using the distributive property]

Therefore, both expressions represent the same cost after the discount of 40%.

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The equation of an ellipse in standard form refers to the standard mathematical representation of an ellipse. An ellipse is a closed curve that is symmetric about its centre, characterized by two main parameters: the semi-major axis (a) and the semi-minor axis (b).

The equation of an ellipse can be written as:

x^2/a^2 + y^2/b^2 = 1

where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.

In this case, the given vertices are (4,0) and (0,3). The distance between the center and the vertex along the x-axis is the value of 'a', and the distance between the center and the vertex along the y-axis is the value of 'b'.

So, the value of 'a' is 4 and the value of 'b' is 3.

Plugging these values into the equation, we get:

x^2/4^2 + y^2/3^2 = 1

Simplifying further, we have:

x^2/16 + y^2/9 = 1

Thus, the equation of the ellipse in standard form with the given center and vertices is:

x^2/16 + y^2/9 = 1

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The equation of the ellipse in standard form with a center at the origin, vertex (4,0), and co-vertex (0,3) is:
\((x^2/16) + (y^2/9) = 1\)

To write the equation of an ellipse in standard form with a center at the origin, we need the coordinates of the vertex and the co-vertex. The standard form of the equation for an ellipse with a center at the origin is:
\((x^2/a^2) + (y^2/b^2) = 1\)
where "a" represents the semi-major axis and "b" represents the semi-minor axis.
Given the vertex (4,0) and the co-vertex (0,3), we can determine the values of "a" and "b".

The distance from the center (0,0) to the vertex (4,0) represents the semi-major axis "a". In this case, the distance is 4 units.
The distance from the center (0,0) to the co-vertex (0,3) represents the semi-minor axis "b". In this case, the distance is 3 units.
Using these values, we can substitute them into the equation:
\((x^2/4^2) + (y^2/3^2) = 1\)
Simplifying further:
\((x^2/16) + (y^2/9) = 1\)
This equation represents an ellipse that is elongated along the x-axis and compressed along the y-axis.

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Answer:

-66+3x ..... Hope it helps

Hey there!

3(–22 + x)

3(–22) + 3(x)

3(–22) = –66

3(x) = 3x

Answer: 3x – 66 ☑️

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

1

Step-by-step explanation:

assuming you want when h(x) equals 0 then x would be 1  because 3(1) - 3 is 0

The x-intercept or root of the function g(x) = 3x - 3 will be 1.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

h(x) = 3x - 3

If the value of the function f(x) is zero. Then the x-intercept of the function  is given as,

h(x) = 0

3x - 3 = 0

Simplify the equation, then the value of x is given as,

3x = 3

x = 3/3

x = 1

The x-intercept or root of the function g(x) = 3x - 3 will be 1.

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Answer:

y - 13 = 3(x - 5)

Step-by-step explanation:

x represents week and y represents inches. Week 2 and week 5 = 2 to 5 = three number difference. The inches which is 4 and 13 have a 9 inched difference. So like I said week represents x and y represent inches so now u have to find the slope, which would be y/x so replace it with the numbers we got so it would now be 9/3. The simplified version would be 3. So the slope is 3.

Point-slope equation: y-y^1=m(x-x^1), y^1 and x^1 are just some random points on the graph, but since we don't have a graph we can use either week 2 and 4 inches or week 5 and 13 inches because if this were a graph, those would be existing points on the graph. And m is the slope so just replace m with 3. We'll use 5 and 13 so: y - 13 = 3(x - 5)

side note: kinda took a long time sorry haha, I had to refresh my knowledge on point-slope equations since it's been a long time since i learned it.

If you obtained a 60-day note from a bank for $8000.00, with $216.99 in interest and $67.20 in other charges, the total amount owed at the end of the 60 days would be $8284.19.

To calculate the total amount owed at the end of the 60 days, we need to add the principal amount, interest, and other charges.

The principal amount of the loan is $8000.00.

The interest charged on the loan is $216.99.

The other charges on the loan amount to $67.20.

To find the total amount owed, we add the principal, interest, and other charges:

Total amount owed = Principal + Interest + Other charges

Total amount owed = $8000.00 + $216.99 + $67.20

Total amount owed = $8284.19

Therefore, at the end of the 60 days, you would owe a total of $8284.19.

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Answer:

y<3

Step-by-step explanation:

It is  y<3 because all areas below y=3 are shaded.

In addition, the line y=3 is dotted, which means it is not part of the inequality (i.e. strict inequality).

If it had been a full line, then it would be y<=3.

a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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Answer:

m = ½; b = 0

Please mark my answer as brainliest

the equation can be written y=mx+d.so

m=1/2 and d=3

Answer:

25% off coupon

The solution to the systems of equations graphically is (2, 4)

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

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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By working with fractions, we will see that Tom originally had 144 marbles.

Let's say that the original number of marbles is M.

Then, he gives 1/4 of them to Bob, so Bob has M/4 marbles.

Bob gives 1/3 of what he had to John, so John has:

Then, John gives 1/2 of what he has to Kevin, so Kevin has:

Then Kevin gives 1/6 (Then he keeps 5/6 of the marbles) of what he has to Michael, and after that he has 5 marbles, this means that:

(5/6)*(M/24) = 5

Solving for M, we get:

M = (6/5)*24*5 = 144

This means that Tom originally had 144 marbles.

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Answer:

1 1/2

Step-by-step explanation:

1 YARD = 3 FEET

3/4 X 3 = 9/4 = 2 1/4

\(3\frac{3}{4} - 2\frac{1}{4}\)

\(1\frac{3-1}{4}\) = \(1\frac{2}{4}\)

To transform to the simplest form. divide both the numerator and the denominator by 2

1 1/2

Answer:

36.8%

Step-by-step explanation:

First, we have the find the amount of change, by taking

$19 - $12 = $7

Then

7 divided by 19, times 100 = 36.8%

So, the percentage decrease is 36.8%