Select a random sample of 35 unmarried and 15 married subjects
A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried.
To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Select a random sample of 35 unmarried and 15 married subjects.
hence, Select a random sample of 35 unmarried and 15 married subjects.
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A company invests $32000. after 4 years of growth at the same rate each year, the investment is worth $42692. find the annual growth rate as a percentage.
Answer:
R = 33.35%
Step-by-step explanation:
that is the solution above
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 5 and width of 1 write an equation to determine the area, a, of the patio that will be painted. a = (x 20)(x 11) a = (x 15)(x 10) 5 a = (x 15)(x 10) − 5 a = (x 9)(x 10)
The equation which determines the painted area is (x+15)(x+10)-5.
Given that there is a rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a given length of 5 and width of 1.
A rectangle is a two-dimensional (2D) form in which the four angles are all right angles and the opposite sides are parallel and equal to one another. The region that the rectangle's perimeter encloses is known as its area, which is equal to the product of its length and width.
Let the length of the patio be L=x+15.
The width of the patio be W=x+10.
So, the Area of the patio will be painted is, A₁=L×W
A₁=(x+15)(x+10)
Let the Length of the bench be L₁=5
The width of the bench be W₁=1
So, the Area of the bench will be painted is, A=L₁×W₁
A₂=5×1
A₂=5
The net area of the patio that will be painted is
A=A₁-A₂
A=(x+15)(x+10)-5
Hence, the equation which is used determines the area, A, of the patio that will be painted is (x+15)(x+10)-5.
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Assume the population of human body temperatures has a mean of 98.6 degrees Fahrenheit as is commonly believed. Assume the standard deviation is .62 degrees Fahrenheit. Find the probability that the mean of a sample of 106 randomly selected humans is lower than 98.5 degrees Fahrenheit. Write your answer using a decimal. Be sure to use the appropriate rounding rules.
The probability that the mean of a sample of 106 randomly selected humans is lower than 98.5°F is 4.85%
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Z score is given as:
z = (raw score - mean) ÷ (standard deviation/√sample size)
Given mean of 98.6°F, standard deviation is 0.62°F, sample size = 106
For x < 98.5:
z = (98.5 - 98.6) ÷ (0.62÷√106) = -1.66
P(z < -1.66) = 0.0485
The probability that the mean of a sample of 106 randomly selected humans is lower than 98.5°F is 4.85%
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Find the equation of a line that passes through the points (6,4) and (8,2).
Leave your answer in the form
y
=
m
x
+
c
Answer:
y = - x + 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 4 ) and (x₂, y₂ ) = (8, 2 )
m = [tex]\frac{2-4}{8-6}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , then
y = - x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 4 ) , then
4 = - 6 + c ⇒ c = 4 + 6 = 10
y = - x + 10 ← equation of line
There are 135 people in a sport centre. 77 people use the gym. 62 people use the swimming pool. 65 people use the track. 27 people use the gym and the pool. 23 people use the pool and the track. 31 people use the gym and the track. 4 people use all three facilities. Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool
The probability that the person uses the gym and track but not the pool is; 1/5.
What is the probability that a person uses the gym and track but not the pool?According to.the task content, it follows that 31 people use the gym and track while 4 people use all three facilities.
Hence, it follows that; 31-4 = 27 people use the gym and track but not the pool. On this note, the required probability is; 27/135 = 1/5.
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Solve for x in terms of b: 2x + b = 3
A farmer has a house at the point (0, 0). He has a corn field that can be found by driving 2 units down, 3 units right, 3 units up, and 2 units right. If he instead walks diagonally to his corn field, how far has he gone? Round to 2 decimal places.
Answer:
2.45 units
5 units
5.99 units
5.10 units
Expand and simplify the following expressions....check picture i attached
The expansion of the given expressions are; 4x² - 5x - 5; 2x² - 13x + 15; -2x² - 5x + 3; 3x² + 6x - 1
How to simplify Quadratic equations?A) x(x - 5) + 3x² - 5
Expanding this gives us;
x² - 5x + 3x² - 5
⇒ 4x² - 5x - 5
B) (2x - 3)(x - 5)
Expanding the function gives;
⇒ (2x² - 3x - 10x + 15)
⇒ 2x² - 13x + 15
C) -2x(x + 3) + x + 3
⇒ -2x² - 6x + x + 3
⇒ -2x² - 5x + 3
D) 3(x + 1)² - 4
⇒ 3(x² + 2x + 1) - 4
⇒ 3x² + 6x + 3 - 4
⇒ 3x² + 6x - 1
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[tex]\huge\fbox\purple{Question}[/tex]
1)Find the H.C.F of the following set of numbers by finding all the possible factors.
a)6 and 15
b)12 and 18
c)15 and 24
d)24 and 36
e)30 and 48
f)36 and 54
g)32,40 and 56
h)28,42 and 70
I)30,75 and 90
Note=
Answer with proper explanation required and all steps to be mentioned .
The HCF are
3631261881415What is HCF?This is the common factor that is the highest that a group of numbers can have in common.
1. 6 and 15
factors of 6 = 1, 2, 3, 6
factors of 15: 1, 3, 5, 15
The HCF is the number they have in common = 3
2. 12 and 18
The factors of 12: 1, 2, 3, 4, 6, 12
The factors of 18: 1, 2, 3, 6, 9, 18
The HCF = 6
3. 15 and 24
Factors of 15: 1, 3, 5, 15
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The HCF = 3
4. 24 and 36
The factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The HCF : 12
5. 30 and 48
The factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The HCF = 6
6. 36 and 54
The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The hcf = 18
7. 32,40 and 56
The factors of 32: 1, 2, 4, 8, 16, 32
The factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
The HCF is 8
8. 28,42 and 70
The factors of 28: 1, 2, 4, 7, 14, 28
The factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
The HCF = 14
9. 30,75 and 90
The factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 75: 1, 3, 5, 15, 25, 75
The factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The HCF is 15
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A single card is drawn from each of two decks of 52 cards. What is the probability of getting a heart from the first deck and then a diamond on the second deck?
A. 0.09%
B. 6.25%
C. 13%
D. 52%
Probability helps us to know the chances of an event occurring. The correct option is A.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of getting a heart from the first deck is 13/52. And the probability of getting a diamond from the second deck is 13/52. The probability of getting a heart from the first deck and then a diamond on the second deck is,
Probability = (13/52) × (13/52) = 0.0625 = 6.25%
Hence, the correct option is A.
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I need some help please
What is the equation of the function shown in the graph?
Answer:
y = -2x+2
Step-by-step explanation:
See attached image
The given diagram shows the steps for constructing a line parallel to line AB and passing through point P, but an error has occurred in the construction. What needs to be corrected in the diagram to fix the error? A. The third arc should be drawn centered at point F. B. A fourth arc needs drawn so that it passes through point P. C. The second arc should be drawn centered at point D. D. The first arc should pass through point B.
Construction is a process in which required steps are considered to draw a given shape by the use of construction instruments and materials. Thus to correct the error in the given question, the third arc should be drawn centered at point F. Answer is option A.
Majorly, the use of a straight edge and a pair of compasses to draw the image of a given object is referred to as construction. Which required adhering to some steps.
The construction of a parallel line through a given point to a given line involves following the appropriate procedure. If not, an error would be committed which would result in an inappropriate shape or figure.
Therefore, to fix the error in the given question, it is important that the third arc should be drawn centered at point F. Thus, the correct answer is option A.
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Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a not-equals 1 and b not-equals 1?
The following logarithmic expression can be used to approximate the given expression,
[tex]\frac{log_{b} x}{log_{b} a}[/tex]
Finding the Logarithmic Expression
It is given that for all positive numbers a, b, and x on the condition that a≠1 and b≠1.
Now, for positive values of m and n, we have the following logarithmic expression,
[tex]\frac{log_{m} x}{log_{n} a}[/tex]
Here, m, n and x are all positive numbers.
The logarithmic property imposes that m and n are not equal to 1.
So, by substituting the values m and n by a and b respectively, we get the following logarithmic expression,
[tex]\frac{log_{b} x}{log_{b} a}[/tex]
Therefore, [tex]\frac{log_{b} x}{log_{b} a}[/tex] is the required expression.
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Describe a new situation that can be modeled by the part-to-part ratio 2:3 and interpret what the ratio means in the situation. Use complete sentences in your answer.
20 girls and 30 boys
What is arithmetic ?
A branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them
To make the new situation:
Suppose A classroom has 50 people.
The ratio of girls to boys is 2:3, so in other words, we need to find out how many boys and girls there are, and there are 2 girls for every three boys, So ,how many boys and girls are there?
The answer would be :
Let the two parts in which we divide 50 be 2x and 3x respectively
2x+3x=50
5x=50
x= [tex]\frac{50}{5}[/tex]
x=10
Here,
2x= 2×10=20
3x =3*10=30
20 girls and 30 boys.
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Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,100 per hour and a standard deviation of $250. What is the operating cost for the lowest 3% of the airplanes
Using the normal distribution, it is found that the operating cost for the lowest 3% of the airplanes is of at most $1,630.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 2100, \sigma = 250[/tex].
The operating cost for the lowest 3% of the airplanes is of at most the 3rd percentile, hence at most X when Z = -1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.88 = \frac{X - 2100}{250}[/tex]
X - 2100 = -1.88(250)
X = 1630.
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Myles is tracking the growth of his palm tree. it was 62 inches when he bought it, and it has grown 6 inches per year. what does the initial value represent? what is the input for the initial value? what is the output for the initial value?
What is initial value?
It is given that,
The height of the palm tree at the time Myles bought it was 62 inches.
He is tracking the growth of the tree and he has observed that it has grown 6 inches per year.
So, the initial value of the tree, here, is representing the height of the palm tree when it was bought.
As can be seen clearly, there is no input for the initial value. And, the output for the initial value is given to be 62 inches.
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Choose the most convenient method to graph the line 3x−2y=−12.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at −12.
Recognize the equation as that of a horizontal line passing through the y-axis at −12.
Identify the slope and y-intercept, and then graph.
Find the x- and y-intercepts and then graph.
There are 11 kids at a birthday party. If there are 6 girls and 5 boys at the party, whta fractof the kids are boys?
Answer:
Step-by-step explanation: The answer is 5/11.
Hello!
Fraction of boys = Number of boys / Total kids
Fraction of boys = [tex]\boxed {\frac{5}{11}}[/tex]
There is a reflection at the boundary between two materials if there is a change of __________ at the boundary.
There is a reflection at the boundary between two materials if there is a change of the speed of light in the material at the boundary.
This bending is referred to as refraction. whilst a wave traveling at an angle adjusts its velocity upon crossing a boundary among materials,. This bending is known as refraction. As a wave crosses a boundary into a new medium, its pace, and wavelength exchange simultaneously as its frequency stays equal.
While light from air hits a smooth piece of glass (n = 1. five) with the ray perpendicular to the glass floor, of the subsequent will occur while light from air hits a clean piece of glass with the ray perpendicular to the glass surface, the part of the light passing into the glass: will now not exchange its frequency.
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example : 4(m+4) = 4m + 16
1 6(m+3)=?
Consider the following system of linear inequalities and corresponding graph:
The solution to the graph is the yellow area highlighted in the graph. The point (2, 0) is a solution since it lies on the yellow area.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The compound inequality represented by the graph is y ≥ 2x - 4, x > -3 and y < 5.
The solution to the graph is the yellow area highlighted in the graph. The point (2, 0) is a solution since it lies on the yellow area.
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What are the rigid transformations that will map
△ABC to △DEF?
Translate vertex A to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex B to vertex D, and then rotate
△ABC around point B to align the sides and angles.
Translate vertex B to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex A to vertex D, and then rotate
△ABC around point A to align the sides and angles.
The rigid transformations which will map the triangle ABC to triangle DEF is; Translate vertex A to vertex D, and then rotate△ABC around point A to align the sides and angles.
Which transformation best maps △ABC to △DEF?It follows from the task content that the two triangles given are △ABC to △DEF.
Hence, in a bid to map the triangle ABC to DEF, Vertex A is translated to point D which represents vertex D in△DEF. Afterwards, the triangle ABC is simply rotated about the translated vertex A until all sides and angles of both triangles align.
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In the week that ended June 19, the U.S. commercial crude oil inventory decreased by3.8million barrels. Now if the inventory was 353.9million barrels in the week that followed, what was the U.S. crude oil inventory before the decline?
Answer:
353.9 + 3.8 = 357.7 million barrels of oil
B = 54°, b=15, c=
c = ? (Round answers to
the nearest hundredth.)
Answer:
18.54
Step-by-step explanation:
sine is opposite/hypotenuse, and you have opposite (b=15), so use that
sin(54) = 15/c
c = 15/sin54
then use calculator
c = 18.54
B is the midpoint of AC. AB= 3(3x-1) and AC=5(2x+2) find X, AB, BC, and AC
Answer:
x = 2
Step-by-step explanation:
AB is given as 3(3x-1) multiply inside the parenthesis with 3
AB = 9x - 3
AC is given as 5(2x+2) multiply inside the parenthesis with 5
AC = 10x + 10
if B is midpoint of AC then AB = BC and AC = AB + BC if we write this equation using the given values
9x - 3 + 9x - 3 = 10x + 10 add like terms
18x - 6 = 10x + 10 transfer like terms to the same side of the equation
18x - 10x = 10 + 6
8x = 16 divide both sides by 8
x = 2 replace x with 2 in given expressions to find the value of each component
Answer: x = 2; AB = 15; BC = 15; AC = 30
Step-by-step explanation:
AB = BC = 3(3x - 1) = 9x - 3
AC = 5(2x + 2) = 10x + 10
AB + BC = AC
(9x - 3) + (9x - 3) = 10x + 10
9x - 3 + 9x - 3 = 10x + 10
18x - 6 = 10x + 10
8x - 6 = 10
8x = 16
x = 2
Plug x = 2 to find AB, BC, and AC.
AC = BC = 3(3x - 1) = 9x - 3 = 9(2) - 3 = 18 - 3 = 15
AC = 5(2x + 2) = 10x + 10 = 10(2) + 10 = 20 + 10 = 30
use the geometric model to factor 3x^2+4x+1
The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.
\What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.
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4 12-sided dice are rolled. What is the probability that the number of dice showing a two digit number is equal to the number of dice showing a one digit number
Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
I'll take a stab at this one. if the number of dice showing a two-digit number = the number of dice showing a one-digit number, then 2 must show a two-digit number and 2 must show a one-digit number
There are 3 two-digit numbers and 9 one-digit numbers on each die
So....the probability is
C(4,2) (3/12)^2 (9/12)^2 =
C(4,2) (1/4)^2 (3/4)^2 =
27/128.
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Can someone help with this section? Please ASAP
The values of the trigonometric functions are
7. [tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{5}{12}[/tex]
8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{16}{12}[/tex]
[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
Trigonometric functionsFrom the question, we are to determine the values of the given trigonometric functions
7.
In the given triangle,
Opposite = 12
Adjacent = 5
Hypotenuse = ?
Hyp² = Opp² + Adj² (Pythagorean theorem)
∴ Hyp² = 12² + 5²
Hyp² = 144 + 25
Hyp² = 169
Hyp =√169
Hyp = 13
Using SOH CAH TOA
[tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{1}{sin\theta} =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{1}{cos\theta} =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{1}{tan\theta} =\frac{5}{12}[/tex]
8.
Hypotenuse = 16
Adjacent = 12
Opposite = ?
Hyp² = Opp² + Adj² (Pythagorean theorem)
Opp² = Hyp² - Adj²
∴ Opp² = 16² - 12²
Opp² = 256 - 144
Opp² = 112
Opp =√112
Opp = 4√7
Using SOH CAH TOA
[tex]sin\theta = \frac{4\sqrt{7} }{16} = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta = \frac{4\sqrt{7} }{12}= \frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta =\frac{1}{sin\theta} =\frac{16}{4\sqrt{7} } = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{1}{cos\theta} =\frac{16}{12}[/tex]
[tex]cot\theta =\frac{1}{tan\theta} =\frac{12}{4\sqrt{7}} = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
Hence, the values of the trigonometric functions are
7. [tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{5}{12}[/tex]
8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{16}{12}[/tex]
[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
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Can someone solve this?
Answer:
n(AnB)= {4, 29}
n(BnC)= {9,29}
n(AnC)= {29}
Given the equation startfraction 2 x 2 over y endfraction = 4 w 2 what is the value of x?
The value of x is 2wy + y - 1.
Given: (2x + 2)/y = 4w + 2
To find: the value of x
the following steps will be used.
First, Multiply both sides by y
y * (2x + 2)/y = (4w + 2) * y
2x + 2 = 4wy + 2y
Subtract 2 from both sides
2x + 2 - 2 = 4wy + 2y - 2
2x = 4wy + 2y - 2
Multiply both sides by ½
½ * 2x = ½(4wy + 2y - 2)
x = ½(4wy + 2y - 2)
Open bracket
x = ½ * 4wy + ½ * 2y - ½ * 2
x = 2wy + y - 1
Hence, the value of x is 2wy + y - 1.
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