Answer:
[tex]r=\frac{1}{3+2cos\theta}[/tex]
Step-by-step explanation:
Let us write the equations in standard form:
[tex]r=\frac{1}{3+2cos\theta} \implies r=\frac{\frac{1}{3} }{1+\frac{2}{3}\cos \theta }[/tex]
We have
[tex]e=\frac{2}{3}\:<\:1[/tex] and
[tex]ep=\frac{1}{3}[/tex]
Since the eccentricity of this conic is less than 1, the conic represents an ellipse.
The second equation is [tex]r=\frac{3}{2+3\sin \theta}[/tex].
This is a hyperbola, because eccentricity is more than 1.
The third equation is [tex]r=\frac{5}{2+2\sin \theta}[/tex].
This is a parabola, because eccentricity is 1.
The fourth equation is [tex]r=\frac{2}{2-3\sin \theta}[/tex].
This is also a hyperbola, because eccentricity is more than 1.
which expression shows 9 sqrt 16^3 in simplified radical form with the smallest possible index?
Answer:
16^3 is 16^(3/9) = 16^(1/3) = 2 ³√2
Step-by-step explanation:
is it 9 times square root of 16 cubed, or is it really 9th root? I think it's
9th root of 16^3 is 16^(3/9) = 16^(1/3) = 2 ³√2
what are the solution of the equation 6x^2-x-1=0
Answer:
Two solutions were found :
6x^2-x1=0
x = -1/3 = -0.333
x = 1/2 = 0.500
The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.
What is a quadratic equation ?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
6x² - x - 1 = 0
Here a = 6, b = -1, c = -1
[tex]\rm x = \dfrac{-(-1) \pm\sqrt{(-1)^2-4(6)(-1)}}{2(6)}[/tex]
[tex]\rm x = \dfrac{1 \pm\sqrt{25}}{12}[/tex]
[tex]\rm x = \dfrac{1 \pm 5}{12}[/tex]
x = 6/12 = 1/2 or
x = -4/12 = -1/3
Thus, the solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.
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Find the values of x and y when the smaller triangle shown here has the given area.
The values of x and y, when the smaller triangle has an area of 10 cm² are x = 4cm and y = 5cm.
Explanation:In the given triangle, the area can be expressed as [tex]\( \frac{1}{2} \times x \times y \)[/tex], where x and y represent the base and height of the triangle, respectively. Since the area is given as 10 cm², the equation becomes [tex]\( \frac{1}{2} \times x \times y = 10 \)[/tex].
To find x and y, we can rearrange the equation:
[tex]\[ x \times y = \frac{10 \times 2}{1} \][/tex]
[tex]\[ x \times y = 20 \][/tex]
Now, we need to find two numbers whose product is 20. The pair x = 4 and y = 5 satisfies this condition, as 4 × 5 = 20. Therefore, the values of x and y that satisfy the given area are x = 4cm and y = 5cm.
In conclusion, the solution x = 4cm and y = 5cm satisfies the given area condition. This is determined by substituting these values into the area formula, resulting in an area of 10 cm².
(PLEASEEE dont ignore, need help) ❗️⚠️ State whether the two triangles are similar. If so, write a similarity statement and tell if they are similar by AA, SSS, or SAS
Answer:
Step-by-step explanation:
For 2 triangles to be similar, they have to have congruent angle measures with corresponding sides that exist in proportion to one another. #14 shows a triangle with 2 angle measures given. We can find the third angle in that triangle to be 65. The one on the right in #14 shows a triangle with 66 degrees in the position corresponding to 65 on the left. Those are not similar (we know nothing about the side lengths so we have no choice but to work with the angles).
#15 shows 2 triangles that are "attached" by angle M in the center. Those 2 angles meet to create vertical angles, and vertical angles are congruent, so angle HMG and angle KMJ are congruent. If both triangles have 2 angles that are corresponding and congruent, then the third angles in both will also be guaranteed to be congruent. So those 2 triangles are similar by AA
TIMED PLEASE HURRY
Two hundred students were surveyed about their favorite fruit. How many more students preferred apples than cherries?
2
4
35
70
Answer:
The answer is 4.
Step-by-step explanation:
I believe that, if I'm correct, 2 students are equal to 1%. 2 x 35 = 70. 2 x 33 = 66. 70 - 66 = 4 more students. I hope this is correct.
The total number of students who preferred apples than cherries are 70 if the two hundred students were surveyed about their favorite fruit option, fourth is correct.
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
From the diagram, we can see the total 35% students preferred apples.
Total number of students = 200
The number of students who preferred apples than cherries = 200×35%
= 200(35/100)
= 2(35)
= 70
Thus, the total number of students who preferred apples than cherries are 70 if the two hundred students were surveyed about their favorite fruit option fourth is correct.
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Sam can wash 8 cars is in 1 hour. Shelley can wash 6 cars in 1 hour. How much time does it take them to wash 70 cars if they work together?
the answer for this question is twelve
Ahmed and Gavin are playing both chess and checkers. The probability of Ahmed winning the chess games is 45%. The probability of Ahmen winning the checkers games is 0.36
Which of these events is more likely
A: Ahmed wins the chess game
B: Ahmed wins the checkers game
C: Neither. Both events are equally likely
Answer:
Option A. Ahmed wins the chess game
Step-by-step explanation:
we know that
The probability of Ahmed winning the chess games is 45%
45%=045/100=0.45
The probability of Ahmen winning the checkers games is 0.36
Compare the probability
0.45> 0.36
so
Is more likely that Ahmed wins the chess game
Answer:
A
Step-by-step explanation:
You are riding your bike and notice the square sign above. You mentally draw a straight line from point A to C. Describe the angle relationship between ∠DCA and ∠BCA. (2 points)
Answer:
those angles are congruent
Step-by-step explanation:
ABCD is a rhombus. The diagonals of a rhombus are angle bisectors. The two angles that result from bisecting angle C are congruent.
Answer:
They are the same.
Step-by-step explanation:
If you draw a straight line from point A to C you'd get two triangles, the ADC and the ABC.These triangles are congruent because they have the criterion LAL ( AD = AB, DC = BC, ∠ADC = ∠ABC.Now that these triangles are congruent we can conclude that the ∠DCA = ∠BCAMadame Pickney has a rather extensive art collection and the overall value of her collection has been increasing each year. Three years ago, her collection was worth $600,000. Two years ago, the value of the collection was $690,000 and last year, the collection was valued at $793,500.
Assume that the rate at which Madame Pickney’s art collection’s value increase remains the same as it has been for the last three years. The value of the art collection can be represented by a geometric sequence. The value of the collection three years ago is considered the first term in the sequence.
What explicit rule can be used to determine the value of her art collection n years after that?
Answer:
an = 600,000 (1.15)^(n-1)
Step-by-step explanation:
So the first year, a₁ = 600,000. The next year, a₂ = 690,000. So:
r = a₂ / a₁
r = 690,000 / 600,000
r = 1.15
So an = 600,000 (1.15)^(n-1).
Your answer is correct!
HELP!!
Polygon ABCDE has the vertices A(2, 8), B(4, 12), C(10, 12), D(8, 8), and E(6, 6). Polygon MNOPQ has the vertices M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8), and Q(-6, 6).
A transformation or sequence of transformations that can be performed on polygon ABCDE to show that it is congruent to polygon MNOPQ is a
If polygon MNOPQ is translated 3 units right and 5 units down, it will coincide with a congruent polygon, VWXYZ, with its vertices at
Answer:
1). Option C
2). Option A
Step-by-step explanation:
The given vertices of polygon ABCDE are A(2, 8), B(4, 12), C(10, 12), D(8, 8) and E(6, 6)
After reflection new polygon formed MNOPQ has the vertices M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8) and Q(-6, 6).
By comparing the vertices we find the x-coordinates of polygon ABCDE have been changed to MNOPQ by negative notation only.Y- coordinates are same.
Therefore, polygon ABCDE has been reflected across the y-axis.
Option C. is the answer.
If polygon MNOPQ is translated 3 units right and 5 units down then the new vertices of congruent polygon VWXYZ will be
M(-2, 8) = [(-2 - 3), (8 + 5)] = (-5, 13)
N(-4, 12) = [(-4 - 3), (12 + 5)] = (-7, 17)
O(-10, 12) = [(-10 - 3),(12 + 5)] = (-13, 17)
P(-8, 8) = [(-8 - 3), (8 + 5)] = (-11, 13)
Q(-6, 6) = [(-6 -3),(6 + 5)] = (-9, 11)
Therefore, Option A. is the correct option.
Simplify the complex fraction
((3x-7)/x^2)/(x^2/2)+(2/x)
I really need steps on how to do this properly cause I really can't figure it out[tex]\frac{\frac{3x-7}{x^2} }{\frac{x^2}{2}+ \frac{2}{x} }[/tex]
Answer:
The simplest form is 2(3x - 7)/x(x³ + 4)
Step-by-step explanation:
* Lets revise how can divide fraction by fraction
- To simplify (a/b)/(c/d), change it to (a/b) ÷ (c/d)
∵ a/b ÷ c/d
- To solve it change the division sign to multiplication sign and
reciprocal the fraction after the sign
∴ a/b × d/c = ad/bc
* Now lets solve the problem
∵ [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{2}}{2}+\frac{2}{x}}[/tex]
- Lets take the denominator and simplify by make it a single
fraction, let the denominator of it 2x and change
the numerator
∴ [tex]\frac{x^{2}}{2}+\frac{2}{x}=\frac{x(x^{2})+2(2)}{(2)(x)}=\frac{x^{3}+4}{2x}[/tex]
∴ The fraction = [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+4}{2x}}[/tex]
* Now lets change it by (up ÷ down)
∴ [tex]\frac{3x-7}{x^{2}}[/tex] ÷ [tex]\frac{x^{3}+4}{2x}[/tex]
- Change the division sign to multiplication sign and reciprocal
the fraction after the sign
∴ [tex]\frac{3x-7}{x^{2}}[/tex] × [tex]\frac{2x}{x^{3}+4}[/tex]
∴ [tex]\frac{(2x)(3x-7)}{(x^{2})(x^{3}+4)}[/tex]
- We can simplify x up with x down
∴ [tex]\frac{2(3x-7)}{x(x^{3}+4)}[/tex]
* The simplest form is 2(3x - 7)/x(x³ + 4)
You place the letters for the word smart in a bag. What is the probability of getting an even number when rolling a six-sided number cube?
A)0.5
B)5%
C)2/6
D)30%
You place the letters for the word smart in a bag.what is the probability of choosing a letter that is not a vowel?
A)0.2
B)1/5
C)80%
D)0.75
Answer:
1) The probability of getting an even number when rolling a six-sided number cube is 0.5. Choice A
2) 80%. Choice C
Step-by-step explanation:
1)
We are required to determine the probability of getting an even number when rolling a six-sided number cube. The six-sided number cube has the following numbers written on its faces;
1, 2, 3, 4, 5, 6
The numbers; 2, 4, and 6 are even
The probability of getting an even number;
= ( number of faces with even numbers)/ (total number of faces)
= 3/6
0.5
2)
We are required to determine the probability of choosing a letter that is not a vowel after placing the letters for the word smart in a bag.
The non-vowels in the word smart are; s, m, r, and t. There are 4 non-vowels out of a total of 5 letters. The required probability is thus;
(4/5)*100 = 80%
Help asap!!!
What is the measure in degrees for the central angle of a circle whose radius is 6.5 cm and intercepted arc length is 5.7 cm? Round to the nearest hundredth if necessary
61.89
50.27
31.45
55.81
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=6.5\\ s=5.7 \end{cases}\implies 5.7=\cfrac{\theta \pi (6.5)}{180}\implies 1026=6.5\pi \theta \\\\\\ \cfrac{1026}{6.5\pi }=\theta \implies \stackrel{\textit{rounded up, using }\pi =3.14}{50.27=\theta }[/tex]
The measure of the angle at the centre of the circle made by the arc of length 5.7 cm that has a radius of 6.5 cm is 50.27°.
What is the Length of an Arc?Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,
[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]
where
θ is the angle, that arc creates at the centre of the circle in degree.
As we know that the length of an arc is given by the formula,
[tex]\rm{ Length\ of\ an\ Arc = 2\pi r \times \dfrac{\theta}{360^o}[/tex]
Given the length of the arc is 5.7 cm, while the radius of the circle is 6.5cm, therefore, the angle made by the arc at the centre of the circle is,
[tex]5.7 = 2\pi (6.5) \times \dfrac{\theta}{360^o}\\\\[/tex]
θ = 50.27°
Hence, the measure of the angle at the centre of the circle made by the arc of length 5.7 cm that has a radius of 6.5 cm is 50.27°.
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An iguana at a pet store is 5 feet long Measurement for iguana cages are given in inches How many inches long is the iguana?
Answer: if the iguana is five feet it would be 60 inches
What is the product of (4x + 3)(-2x - 5)?
Answer:
Expand the polynomial using the FOIL method.
− 8 x^ 2- 26 x − 15
In a train yard, there are 6 flat cars, 7 boxcars, and 3 livestock cars. A train is made up of 9 cars. Which would you use to find the number of ways the train could be made up?
A. 16P9
B. 16P7
C. 9P16
D. 9P7
Answer:
Option A
Step-by-step explanation:
In a train yard there are 6 flat cars, 7 box-cars and 3 livestock cars.
So total number of cars = 6 + 7 + 3
= 16
Now a train is to be made by 9 cars, out of 16 cars.
So number of ways the train can be made up will be =[tex]^{n}P_{r}[/tex]
where n = 16 and r = 9
so number of ways =[tex]^{16}P_{9}[/tex]
Option A is the answer.
Considering the definition of permutation, you use 16P9 to find the number of ways the train could be made up. (Option A).
What is PermutationPermutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.
In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:
take all the elements of a set.the elements of the set are not repeated.order matters.To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
[tex]mPn=\frac{m!}{(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
This caseIn a train yard there are 6 flat cars, 7 box-cars and 3 livestock cars. So total number of cars is 6 + 7 + 3= 16.
A train is made up of 9 cars, out of 16 cars.
To obtain the total of ways in which 16 elements can be placed in 9 positions, you use the permutation 16P9.
Finally, you use 16P9 to find the number of ways the train could be made up. (Option A).
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The equation for the number of pizzas a store has on hand is modeled by the linear equation y = 148 – 24d, where d is the number of days. How many pizzas will the store have on hand after five days?
A. 120
B. 76
C. 124
D. 28
The store will have 29 pizzas.
This is because:
Y = pizzasD = daysY = 148 -24DY=148-24(5)Y=148-120Y=28D is the correct answer
graph the equation by plotting three points. if all three are correct, the line will appear.
-3y=5x-7
Answer:
(x, y) = (-1, 4), (2, -1), (5, -6)
Step-by-step explanation:
You can choose any value you like for either x or y, then solve for the other value. I like to plot points with integer coefficients, so I would look for sets of those.
The nature of this equation is that it will have integer solutions with x-values spaced 3 apart and y-values spaced 5 apart. (The spacing of each corresponds to the coefficient of the other.) So, the trick is to find an x-value that gives an integer solution for y. (You will need to try at most 3 consecutive integers.)
Solving the equation for y, we get ...
y = -5/3x +7/3
Right away, we know that x=0 will not give an integer solution for y. Nor does x=1. The third consecutive integer that is easy to try is x = -1, so ...
y = (-5/3)(-1) +7/3 = (5+7)/3 = 4 . . . . an integer value for y
Our first point is then (x, y) = (-1, 4).
Since the slope is negative, we know that increasing x will decrease y. Thus we can simply add (3, -5) to any point to get another point on the line.
Two more points on the line are ...
(-1, 4) +(3, -5) = (2, -1)
(2, -1) +(3, -5) = (5, -6)
Three integer-valued points on this line are (-1, 4), (2, -1), (5, -6).
The scatter plot shows the results of a survey in which 10 students were asked how many hours they spent studying for a test and the score they earned. How many students scored a 90 or above? Enter your answer in the box.
it want let me upload photo but the the answer is 5
Answer: the scatter plot you just sent me the answer would be 5
Identify the area of segment MNO to the nearest hundredth. HELP PLEASE!!
The area of a right triangle with side lengths 7 and 7 is [tex]\frac{bh}{2} = \frac{7*7}{2} = \frac{49}{2} = 24.5[/tex]
Answer: ≈ 13.98 in2
Step-by-step explanation:
A segment of a circle is a region bounded by an arc and its chord.
To determine the area of the segment, begin by finding the area of the sector defined by the central angle.
A sector of a circle is a region bounded by two radii of the circle and their intercepted arc.
The formula for the sector area is A = πr2 (m∘/360∘).
It is given in the figure that central angle MNO is a right angle. So, m∠MNO = 90∘. It is also given that r = 7 in.
Substitute the given values into the formula and simplify.
A = π(7)2 (90∘/360∘) = 49/4π in2
Find the area of △MNO.
Since the radii in a circle are congruent, NO = NM = 7. To find the area of △MNO, use the formula for the area of a triangle, A = 1/2bh.
Substitute 7 for b and 7 for h, then simplify.
A = 1/2 (7) (7) = 24.5 in2
The area of the segment is the difference between the two areas, the area of the sector and the area of the triangle.
A = 49/4π − 24.5 ≈ 13.98 in2
Therefore, the area of segment MNO is ≈ 13.98 in2.
Please help me please
Answer:
BF = 30
Step-by-step explanation:
Since B and F are midpoints then BF is parallel to CE and half it's size
BF = 0.5 × CE = 0.5 × 60 = 30
How much does a person owes me at the end off 55 months if was supposed to pay me 1000.00 per months at 12 % per month?
Answer:
b
Step-by-step explanation:
Please help me with this..
Answer:
w = 93°
Step-by-step explanation:
The angle with measure 142° forms a straight angle with the third angle in the triangle and are supplementary, thus
third angle = 180° - 142° = 38°
The sum of the 3 angles in the triangle = 180°
w = 180° - (38 + 49)° = 180° - 87° = 93°
Help with this question, please!
Answer:
52 ft
Step-by-step explanation:
For each chord, the product of segment lengths is a constant. We can find that constant as the product of the segment lengths of the bisected chord:
(24 ft)·(24 ft) = 576 ft^2
Then the missing segment length (DX) of the diameter chord is ...
DX·(36 ft) = 576 ft^2
DX = (576 ft^2)/(36 ft) = 16 ft
So, the total length of the diameter chord is ...
DX +XL = 16 ft + 36 ft
DL = 52 ft
_____
We know DL is a diameter because the perpendicular bisector of any chord intersects the center of the circle.
Jackson made $300 in interest by placing $1,000 in a savings account with simple interest for 2 years. What was the interest rate?
Answer:
The interest rate was 15%
Step-by-step explanation:
The simple interest formula is the easiest and most straightforward to use since it doesn't involve using logs or natual logs or Euler's number. It is
I = Prt
Filling in using our info gives us 300 = 1000(r)(2)
and 300 = 2000r
Divide both sides by 2000 and you get r = .15. Multiply by 100 to get the percentage.
A box plot is also known as a(n) box-and-whisker plot. Use the box plot below to find each of the following.
Minimum: _____
First quartile: _____
Median: _____
Third quartile: _____
Maximum: _____
Answer:
the min is 53 the max is 90 median is 65 first quartile is 60 and the third quartile is 82
Step-by-step explanation:
The correct answers are: Minimum: 53, First quartile: 60, Median: 65, Third quartile: 82, Maximum: 90.
To read a box plot, we look at the five-number summary: the minimum, first quartile, median, third quartile, and maximum.
The box plot shows the middle 50% of the data, which is the interquartile range (IQR). The IQR is represented by the box, with the median represented by the line inside the box.
The whiskers extend from the box to the minimum and maximum values, respectively.
In this box plot, the minimum value is 53 and the maximum value is 90. The IQR is 65 - 60 = 5, which means that the middle 50% of the data is within 5 points of the median. The median is 65, so the first quartile is 60 and the third quartile is 82.
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Antoine has $18.20 to spend on some oranges and a pumpkin. Oranges cost
$1.30 per pound, and a pumpkin costs $5.20
The inequality 1.30x + 5.20 18.20 models this situation, where x is the
number of pounds of oranges.
Solve the inequality. How many pounds of oranges can Antoine buy?
Answer:
10 pounds
Step-by-step explanation:
You forgot the inequality sing, but since Antoine can't spend more than $18.20, I am positive that the sign is [tex]\leq[/tex] (Antony can spend $18.20 or less than $18.20).
Therefore, our inequality is: [tex]1.30x+5.20\leq 18.20[/tex]
where [tex]x[/tex] is the pounds of oranges
Let's solve step-by-step to find how many pounds of oranges he can buy
Step 1. Subtract 5.20 fro both sides of the inequality
[tex]1.30x+5.20-5.20\leq 18.20-5.20[/tex]
[tex]1.30x\leq 13[/tex]
Step 2. Divide both sides of the inequality by 1.30
[tex]\frac{1.30x}{1.30} \leq \frac{13}{1.30}[/tex]
[tex]x\leq 10[/tex]
We can conclude that Antony can buy 10 pounds of oranges.
Which function transforms the graph of y=x^2 so that it is first shifted down 2 units and is then reflected across the x-axis?
A. [tex]y=(-x)^2+2[/tex]
B. [tex]y=-x^2+2[/tex]
C. [tex]y=-x^2-2[/tex]
D. [tex]y=-(x+2)^2[/tex]
the awnser should be -x^2 +2
Answer:
y = -x^2+2
Step-by-step explanation:
shift down y=x^2 for 2 units then it becomes y = x^2-2
reflect across x-axis then it becomes y = -(x^2-2) which is y = -x^2+2
One number is 4 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 538, find the numbers
Answer:
73
292
173
Step-by-step explanation:
x = first number
4x = second number
100 + x = third number
x + 4x + 100 + x = 538
6x + 100 = 538
6x + 100 - 100 = 538 - 100
6x = 438
6x/6 = 438/6
x = 73
Check:
73 + 4(73) + 100 + 73 = 538
73 + 292 + 173 = 538
538 = 538
Answer:
The numbers are 73, 173 and 292.
Step-by-step explanation:
If the numbers are x, y and z we have:
y = 4x
z = x + 100
x + y + z = 538
Substituting for y in the last equation:
x + 4x + z = 538
5x + z = 538.............(1)
From the second equation:
z - x = 100................(2)
Equation (1) - (2) gives:
6x = 438
x = 73
Therefore y = 4x) = 4(73) = 292
and z = x + 100 = 73 + 100 = 173.
Suppose medical records indicate that the length of newborn babies (in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6 find the probability that a given infant is longer than 20 inches.
Step-by-step answer:
The normal probability curve is symmetrical about the mean.
This means that for an event that is normally distributed, there is a 50% probability that it falls below the mean, and a 50% probability that it falls above.
From the given information, the mean is 20" and we need the probability that a given infant is longer than 20", namely the mean.
Therefore by the definition of the normal probability curve, there is a 50% probability that the length falls above 20".
This can be verified by referencing a normal probability table with Z=0, meaning at the mean, the probability is equal to 0.5 for Z<0, and therefore 0.5 for Z>0.
Z=(X-mean) / Standard deviation
When Z>0, X (measurement) is greater than the mean
When Z<0, X is less than the mean.
Answer:
0.5, half therefore 50%