You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107 subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:
One group took a four-month stress management program, another underwent a four-month exercise program and the thirst received usual heart care from their personal physicians. In the next three years, only three of the 33 people in the stress management group suffered "cardiac events", defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, seven of the 34 people in the exercise group and 12 out of the 40 patients in usual care suffered such events.
a. Use the information in the news article to make a two-way table that describes the study results.
b. What are the success rates of the three treatments in preventing cardiac events?

the given P=15250

r=7.5/100=0.075

t=x

y = 15250*(1 - 0.075)^x

after 8 years we would have

x = 8

y = 15250*(1 - 0.075)^8

y = $8,173.42

Answer: after 8 years the value of the car would be $8,173.42

Answer:

A. (-2, 0)

I hope this helps you.

since r is so widely used, it is appropriate to calculate r for nonlinear data: False.

The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.

In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.


n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.

When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.

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The area of the polygon is 37.81 units and the perimeter is 33.02 units.

The given points are in order, we have:

a(-3, 2)

f(2, -3)

b(0, 5)

c(3, 2)

d(5, 4)

e(7, 2)

g(0, -1)

Using the distance formula, we can find the lengths of the sides of the polygon. Then, we can add up the lengths of all the sides to find the perimeter of the polygon.

As per the shown figure,

Length of side fa = 7.07 units

Length of side ef = 7.07 units

Length of side de = 7.6 units

Length of side cd = 2.8 units

Length of side bc = 4.24 units

Length of side ab = 4.24 units

The perimeter of the polygon is:

= fa + ef + de + cd + bc + ab

= 7.07 + 7.07 + 7.6 + 2.8 + 4.24 + 4.24

= 33.02 units

The area of the polygon is:

= area of rectangle (1) + area of sqare (2)

= 7.07 × 4.24 + 2.8 × 2.8

= 37.81 units

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In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.

In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Here we have to find the 3 shortcuts to prove the triangles are similar.

According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).

Here we must know that the term similarity and congruent are similar terms.

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The pair of the line together that could be perpendicular to RS and should be considered will be EA and FG.

It should be noted that in terms of elementary geometry, two geometric objects should be considered as perpendicular when they intersect at a right angle.

In such a case, a line is treated to be perpendicular to another line in the case when the two lines intersect at a right angle.

Therefore, based on the information, the pair of the line together that could be perpendicular to RS and should be EA and FG.

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Based on the given information, the question is asking about the apparent relationship between two variables: study hours and test score. The correct answer is c.

Test score tends to increase as the number of study hours increases. This suggests a positive correlation between the two variables, meaning that as one variable (study hours) increases, the other variable (test score) also tends to increase.
The apparent relationship between the two variables under consideration, which are study hours and test score, can be described as follows:
Your answer: c. Test score tends to increase as the number of study hours increases.
This is because, generally, the more time a person spends studying, the better their understanding of the material, which often leads to a higher test score.

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The length of an arc is given by the formula >>>>

Where

"l" is the length of the arc

θ is the measure of the arc

r is the radius of the circle

Given,

θ = 150°

r = 12

Substituting into the formula, we get >>>

The length of A

is good answer the x value and y value

Answer:

No, the inverse function does not pass the horizontal line test.

Step-by-step explanation:

The formula for the function's inverse is

(a) f⁻¹(y) = Iny/In(0.7)

(b) f⁻¹(y) = [Iny - In(4.5)]/In(2.7)

(a) The function is;

f(x) = 0.7ˣ where y = f(x).

So y = 0.7ˣ

Taking In on both side,

Iny = x In(0.7)

Divide by In(0.7) on both side, we get

x = Iny/In(0.7)

f⁻¹(y) = Iny/In(0.7)

(b) The function is;

f(x) = 4.5(2.7)ˣ where y = f(x).

So y = 4.5(2.7)ˣ

Divide by 4.5 on both side, we get

y/4.5 = (2.7)ˣ

Taking In on both side,

In(y/4.5) = In(2.7)ˣ

Iny - In(4.5) = xIn(2.7)

Divide by In(2.7) on both side, we get

x = [Iny - In(4.5)]/In(2.7)

f⁻¹(y) = [Iny - In(4.5)]/In(2.7)

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The complete question is:

For each of the following functions, write the formula for the function's inverse.

a. f(x) = 0.7ˣ where y = f(x).

f⁻¹(y) =

b. f(x) = 4.5(2.7)ˣ where y = f(x).

f⁻¹(y) =

Answer:75

Step-by-step explanation:

since there are 15 students and they each need 5 plates you just do 15x5 and get 75

The probability formula is given by:

The person selects one of six envelopes.

There is a probability that the person selects an envelope that contains a $491 of 3 envelopes OR an envelope that contains a $1003 check of 3 envelopes

Then, the expected value is given by

Answer:

D

Step-by-step explanation:

because youe last number is 90

Midpoint formula:

(X1+x2)/2, (y1+y2)/2

Midpoint: (-12+7)/2 , (5+9)/2

=( -5/2,7)

The answer is a.

The approximate number of students with Scores between 68 and 83 is 98.Answer: a. 98

The five-number summary for scores on a statistics exam is: 35, 68, 77, 83 and 97. In all, 196 students took this exam About how many students had scores between 68 and 83?

The five-number summary consists of the minimum value, the first quartile, the median, the third quartile, and the maximum value.

The interquartile range is the difference between the third and first quartiles. Interquartile range (IQR) = Q3 – Q1, where Q3 is the third quartile and Q1 is the first quartile. The 5-number summary for scores on a statistics exam is given below:

Minimum value = 35

First quartile Q1 = 68

Median = 77

Third quartile Q3 = 83

Maximum value = 97

The interval 68–83 is the range between Q1 and Q3.

Thus, it is the interquartile range.

The interquartile range is calculated as follows:IQR = Q3 – Q1 = 83 – 68 = 15

The interquartile range of the scores between 68 and 83 is 15. Therefore, the number of students with scores between 68 and 83 is roughly half of the total number of students. 196/2 = 98.

Thus, the approximate number of students with scores between 68 and 83 is 98.Answer: a. 98

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The greatest factor they have in common is 15. LCM of 18 and 20:

We can find the LCM (Least Common Multiple) of 18 and 20 by listing their multiples until we find the first one that they have in common:

Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, ...

Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, ...

So the LCM of 18 and 20 is 180.

GCF of 105 and 135:

We can find the GCF (Greatest Common Factor) of 105 and 135 by listing their factors and finding the greatest one they have in common:

Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135

The greatest factor they have in common is 15. Therefore, the GCF of 105 and 135 is 15.

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The distance between the points (-4, 2, -3); (0,5, 1) is approximately 6.4031 units. Therefore, the option (a) (5.5, 9, 5.5) is correct.

Using the distance formula, we can calculate the distance between two points\((x1, y1, z1)\) and \((x2, y2, z2)\). The distance between two points is given by: \(d = sqrt( (x2 - x1)² + (y2 - y1)² + (z2 - z1)² )\). Substituting the values of the given points, we get: \(d = sqrt( (0 - (-4))² + (5 - 2)² + (1 - (-3))²)\)

\(= sqrt( 4² + 3² + 4² )\)

\(= sqrt( 16 + 9 + 16 )\)

\(= sqrt( 41 )\)

= 6.4031 units (approx). Therefore, the option (a) 6.4031 is correct.11.

The coordinates of the midpoint of the line segment joining the points (4,8, 4) and (7, 10, 7) is (5.5, 9, 5.5).The midpoint of a line segment between two points (x1, y1, z1) and (x2, y2, z2) is given by the formula:( (x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2 ) Substituting the given values, we get: ( (4 + 7)/2, (8 + 10)/2, (4 + 7)/2 )= (11/2, 18/2, 11/2)

= (5.5, 9, 5.5)

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Answer:

180

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

3x3(2+3) =

3x3(2+3) =3x 3(5) = 3x15 =

45

45x4 = 180

Answer:

Matthew drank 4 more glasses of water than Nicole: equation

Four more glasses of water than Nicole: expression

Step-by-step explanation:

We can model "Matthew drank 4 more glasses of water than Nicole" as an equation as follows:

\(m=n+4\)

However, "Four more glasses of water than Nicole" is only an expression. It doesn't include an equality.

supersciencestudy is correct, an equation must include an equality.

Girl have to pay total R159014 to bank  and compound interest is R31014.

A  girl borrow R128000 from a bank to buy a piece of land.

Land charge is 15% Per Annum and time is 1 \(\frac{1}{2}\)  year.

Compounding  with half yearly.

So land charge will be (15/2)  %  per half yearly and time will be 2 x 1 \(\frac{1}{2}\)  = 3 half  years.

Total amount ( A ) =P (1+R/100)^T

P = initial principal = 128000

R = (15/2) %

T = 3 half yearly

A =P\((1+\frac{R}{100} )^{T}\)

A=128000\((1+\frac{15}{2*100} )^{3}\)

A=128000\((\frac{43}{40} )^{3}\)

A=159014

Total interest amount = 159014 – 128000 = 31014

Therefore , total payable amount is R159014 and interest amount is R31014.

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Answer: 71  1/2$

Step-by-step explanation:

Answer: Same Side Interior Angles

Step-by-step explanation:

Imma help you eliminate the options.

-These angles are inside the parallel lines, meaning that they have to be interior angles. That eliminates any answers involving exterior angles. Next, simply by definition, it wouldn't be corresponding. Finally, alternate interior angles is eliminated because the angles are on the SAME SIDE of the transversal, meaning that Same-Side interior angles is the answer.

Answer:

The equation that represents the Pythagorean Theorem would be \(a^2 + b^2 = c^2\)

Step-by-step explanation:

The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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Answer:

$6.30

Step-by-step explanation:

25.20 divided by 4.

Answer:

D

Step-by-step explanation:

Let's solve your equation step-by-step.

x2+4=3x+8

Step 1: Subtract 3x+8 from both sides.

x2+4−(3x+8)=3x+8−(3x+8)

x2−3x−4=0

Step 2: Factor left side of equation.

(x+1)(x−4)=0

Step 3: Set factors equal to 0.

x+1=0 or x−4=0

x=−1 or x=4

Answer:

x=−1 or x=4

Every subgroup of the integers has finite index. It is True.

True. Proof: Let H be a subgroup of the integers. By the division algorithm, for any integer n and any positive integer d, there exist unique integers q and r such that n = dq + r and 0 ≤ r < d. In particular, if we take d = |H|, then for any integer n, we have n = dq + r for some integer q and some 0 ≤ r < |H|. This means that any integer n can be written in the form n = h + r for some integer h in H and some 0 ≤ r < |H|. Therefore, the residue classes {h + r : r = 0, 1, ..., |H| - 1} form a complete set of coset representatives for H in Z. Since there are |H| such cosets, it follows that [Z : H] = |H|. Therefore, every subgroup of the integers has finite index.

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Answer:

63

Step-by-step explanation:

60% of $100 is just %60 and 5% of 60 is 3 so, 60 + 3 = $63

Answer:

$45

Step-by-step explanation:

So, first we would find 60% of the $100

100 x .60 = 60

(When finding the amount of a percentage we move the decimal over twice)

then subtract what we got from the original price to find what he paid before tax:

100 - 60 = 40

Now we find 5% of $100:

100 x .05 = 5

Finally, we add this to what he was paying before taxes:

40 + 5 = 45, so $45

Hope this helps!! :)

The new laboratory rectangular box to ship glass pipes has the dimensions as deigned by the company as

information from the question

The company's design team has created a box with:

volume of a rectangular box is given by

= length * width * height

length = L

width = L - 2

height = 2L + 9

Multiplying gives

45 = L * (L - 2) * (2L + 9)

45 = L * ( 2L² +5L - 18)

45 = 2L³ + 5L²- 18L

2L³ + 5L² - 18L - 45 = 0

Using calculator to the equation gives

L = -3   OR   3   OR    -5/2

taking the positive value

L = 3

width = L - 2 = 3 - 2 = 1

height = 2L + 9 = 2 * 3 + 9 = 15

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