An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid has base lengths of x and 2 x, and a height of x. The distance between the 2 trapezoid bases is 20. The vertical height of the prism is 10. Which expression represents the volume of the prism? 10x3 cubic units 15x2 cubic units 20x3 cubic units 30x2 cubic units
Answers
Answer:
volume of trapezoidal prism = 15x^2 cubic units
Step-by-step explanation:
First, area of the trapezoidal bases.
Parallel sides measure x and 2x, for an average of 1.5x.
Height = x
Area of trapezoidal base = 1.5x*x = 1.5x^2
Volume of prism = area base * height
(length does not matter, height does)
= 1.5x^2 * 10 = 15x^2
The volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
An oblique prism has trapezoidal bases and a vertical height of 10 units.
As we know, the area of the trapezoidal bases:
From the figure:
Height = x
Area of trapezoidal base = (1.5x)(x) = 1.5x²
The volume of prism = area base×height
= 1.5x²×10 = 15x² cubic units
Thus, the volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
Learn more about the trapezoid here:
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Related Questions
Audrey charges a flat fee of $4 for each delivery plus a certain amount,in dollars per mile, for each mile she drives. For a distance of 30 miles, Curtis and Audrey charge the same amount
Answers
Factoriza e indica la cantidad de factores primos: P(m) = a(m+1) + b(m+1) –c(m+1)
A) 2
B) 3
C) 5
D) 1
E) 4
Answers
Answer:
Step-by-step explanation:
P (m) = a (m + 1) + b (m + 1) - c (m + 1)
P (m) = (a + b - c) (m + 1)
There are 2 prime factors
solve it using quadratic formula.
grade 9
10 points
Answers
Answer:
{-1/4, 1}{3/4, 6}Step-by-step explanation:
1. We can clear fractions and solve the resulting quadratic. We clear fractions by multiplying the equation by the product of the denominators.
[tex]\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{3}\\\\3((2x+1)^2-(2x-1)^2)=8(2x-1)(2x+1)\\\\3(8x) = 8(4x^2 -1)\\\\4x^2 -3x -1 = 0\qquad\text{factor out 8, subtract 3x}\\\\x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(4)(-1)}}{2(4)}=\dfrac{3\pm\sqrt{25}}{8}\\\\x=\dfrac{3\pm5}{8}=\left\{-\dfrac{1}{4},1\right\}[/tex]
__
2. Using the same idea here, we get ...
[tex]\dfrac{2}{x-2}+\dfrac{3}{x}=\dfrac{9}{x+3}\\\\2(x)(x+3)+3(x-2)(x+3)=9(x-2)(x)\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\4x^2-27x+18=0\\\\x=\dfrac{-(-27)\pm\sqrt{(-27)^2-4(4)(18)}}{2(4)}=\dfrac{27\pm\sqrt{441}}{8}\\\\x=\dfrac{27\pm21}{8}=\left\{\dfrac{3}{4},6\right\}[/tex]
Translate the scenario below to a linear equation, then solve.
The second angle of a triangle is double the first angle. The third angle is 40 less than the first angle. Find the three angles.
First angle=
Second angle=
Third angle=
Answers
Answer: x + 2x + x-40 = 180
First angle= 55º
Second angle= 110º
Third angle= 15º
Step-by-step explanation: The sum of the angles of a triangle is 180º
Take the values given and use x as the unknown first angle. then create terms for the other two angles based on that:
The second angle of a triangle is double the first angle becomes 2x
The third angle is 40 less than the first angle becomes x-40
x + 2x + x-40 = 180 Solve by adding like terms . x + 2x + x = 4x
4x -40 = 180 Add 40 to both sides to "cancel" the -40 on the left
4x + 40 -40 = 180 + 40 becomes
4x = 220 Divide both sides by 4 to "cancel" the 4 on the left side
4x/4 = 220/4
x = 55 This is the first angle. Substitute 55 for the "x" in the original terms
2(55) = 110 The second angle
(55) -40 = 15 the third angle
Ejenplo de numeros enteros de una cifra por extension
Answers
Answer:
Un número entero es un número entero que puede ser positivo, negativo o cero. Ejemplos de enteros son: -5, 1, 5, 8, 97 y 3,043. Ejemplos de números que no son enteros son: -1.43, 1 3/4, 3.14,. 09 y 5.643,1.
Amy gets a new kennel for her dog. A sketch of the kennel is shown here. If the roof is in the shape of a triangular prism (bottom face included), what is the surface area of the roof of the kennel, including the bottom face?
Answers
Answer:
Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2
Step-by-step explanation:
The image is attached below
For the triangular sides of the roof, area is
A = [tex]\frac{1}{2}bh[/tex]
where b is the base = 4 ft
h is the vertical height = 2.24 ft
A = [tex]\frac{1}{2}*4*2.24 =[/tex] 4.48 ft^2
for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2
For the rectangular sections of the roof, area is
A = [tex]lh[/tex]
where [tex]l[/tex] is the length of the rectangle = 5 ft
h is the height of the rectangle = 3 ft
A = 5 x 3 = 15 ft^2
For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2
For the bottom face, area is
A = [tex]lw[/tex]
where [tex]l[/tex] is the length of the house = 5 ft
w is the width of the house = 4 ft
A = 5 x 4 = 20 ft^2
Surface area of the roof of the dog kennel is
8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2
A cell phone company offers a plan that costs $35 per month plus an additional cost of $0.08 per text message.
Write an equation to represent this problem.
Answers
I think this is right
Answer:
C = 35 + 0.08t
Step-by-step explanation:
The equation is:
35 + 0.08t = C
C = Cost by month
t = cost for each additional message
2x -2=10 solve for x
Answers
Answer:
x=6
Step-by-step explanation:
Take -2 and add it to 10 and get 12. So then the equation is 2x=12. Divide 2 by 12 and get x=6.
The graph represents this system of equations. A system of equations. y equals 2 x minus 4. y equals 1 minus 3 x. A coordinate grid with 2 lines. The first line passes through (0, 1) and (1, negative 2). The second line passes through (0, 1) and (1, negative 2). What is the solution to the system of equations? (–4, 1) (–2, 1) (1, –4) (1, –2)
Answers
Answer:
(1,-2)
Step-by-step explanation
y = -3x + 1
y = 2x - 4
-3x + 1 = 2x - 4
-5x + 1 = -4
-5x = -5
x = 1
y= 2(1) - 4
y = 2 - 4
y = -2
(1,-2)
Answer:
1/2
Step-by-step explanation:
What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = StartFraction one-half EndFraction x minus StartFraction 5 Over 4 EndFraction plus 2 x equals StartFraction 5 Over 6 EndFraction plus x. + x 2 6 10 12
Answers
Answer: while solving an equation involving fractions we eliminate the fraction by multiplying the LCD of all the denominators present in the equation . LCD means Least common Denominator so for this question when we try to eliminate the denominator we first try to find the LCM (2,4,6) because that will give us the LCD.
2=2
4=2·2
6=2·3
LCM = 2·2·3
LCM = 12
It means we need to multiply the 12 to each term of equation to eliminate the fractions before solving.
12
To eliminate the fractions, multiply the equation by the 12
Equation
A equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
[tex]x-\frac{5}{4}+2x=\frac{5}{6}+x[/tex]
To eliminate the fractions, multiply by the L.C.M of the denominator of the fraction i.e. 12 to get:
12x - 15 + 24x = 10 + 12x
Find out more on Equation at: https://brainly.com/question/2972832
Dyami planted a palm tree in the back yard of his house several years ago. Initially, it was 20 centimeters high and its height increased by 30 centimeters each year. Let H be the height of the tree in centimeters t years after it was planted. Which of the following best explains the relationship between t and H?
Answers
Answer:
when t is increased , h will increased too
Answer:
Th relationship is linear because H increases by 30 each time t increases by 1.
Step-by-step explanation:
H is linear if it changes at a constant rate per unit interval. In other words, constant differences in t should correspond to constant differences in H.
Which of the following is a like radical to 3x sqrt 5
Answers
Answer:
The last option
Step-by-step explanation:
Source: Trust bro
Answer:
d) y sqrt 5
Step-by-step explanation:
radicals are like if they have the same index and radicand, here they are both square roots and have a radicand of five
HELP ASAP!
The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals?
Answers
Answer:
My conclusion about Quadrilaterals ABCD and EFCD is that both quadrilaterals are similar to each other.
THE REASON IS BECAUSE THE SIDES OF QUADRILATERAL ABCD ARE THE SAME AS THE SIDES OF QUADRILATERAL EFCD.
Step-by-step explanation:
When we are given vertices, (x1, y1) , (x2 ,y2), we use the formula:
√(x2 - x1)² + (y2 - y1)²
For quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)
Side AB: A(4, 8), B(10, 10)
√(x2 - x1)² + (y2 - y1)²
√(10 - 4)² + (10 - 8)²
= √6² + 2²
= √40
Side BC: B(10, 10), C(10, 4)
√(x2 - x1)² + (y2 - y1)²
= √(10 - 10)² + ( 4 - 10)²
= √ 0² + (-6)²
= √36
= 6
Side CD: C(10, 4), D(4, 4)
√(x2 - x1)² + (y2 - y1)²
= √ (4 - 10)² + ( 4 - 4)²
= √-6² + 0²
= √36
= 6
Side AD: A(4, 8), D(4, 4)
=√(x2 - x1)² + (y2 - y1)²
= √(4 - 4)² + (4 - 8)²
= √0² + (-4²)
= √16
= 4
Therefore, for Quadrilateral ABCD
Side AB = √40
Side BC = 6
Side CD = 6
Side AD = 4
For quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).
Side EF: E(4, 0), F(10, -2)
√(x2 - x1)² + (y2 - y1)²
= √(10 - 4)² + (-2 - 0)²
= √6² + 2²
= √40
Side FC: F(10, -2), C(10, 4)
√(x2 - x1)² + (y2 - y1)²
= √(10 - 10)² + (4 -(-2))²
= √ 0² + 6²
= √36
= 6
Side CD: C(10, 4), D(4, 4)
√(x2 - x1)² + (y2 - y1)²
= √(10 - 4)² + (4 - 4)²
= √6² + 0²
= √36
= 6
Side ED: E(4, 0), D(4, 4)
√(x2 - x1)² + (y2 - y1)²
= √(4 - 4)² + (4 - 0)²
= √0² + 4²
= √16
= 4
Therefore, for Quadrilateral EFCD
Side EF = √40
Side FC = 6
Side CD = 6
Side ED = 4
My conclusion about Quadrilaterals ABCD and EFCD is that both quadrilaterals are similar to each other.
THE REASON IS BECAUSE THE SIDES OF QUADRILATERAL ABCD ARE THE SAME AS THE SIDES OF QUADRILATERAL EFCD.
What steps do you use to solve a system of two equations using elimination? For example:
7x +2y = -32
-3x+2y = -70
Answers
Answer:
Step-by-step explanation:
eliminate either vraible, here it is easy to eleimate y, by just subtacting, then solve for x. When you get the value of x, plug in one of the equation and find y. ther you go
Answer:
x= 3.8
y= -29.3
Step-by-step explanation:
need help adding and subtracting functions
Answers
Answer:
Step-by-step explanation:
[x/2-2/1] × [2x^2 + x -3]
we can solve this very simply by multiplication
evaluate arctan(tan(2pi/3))
Answers
Answer:
For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:
[tex] arctan(tan(\frac{2\pi}{3}))[/tex]
Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:
[tex] arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]
Step-by-step explanation:
For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:
[tex] arctan(tan(\frac{2\pi}{3}))[/tex]
Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:
[tex] arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]
Find arc length. (Ignore the pencil mark, NEED ASAP)
Answers
Answer:
15.7 yd
Step-by-step explanation:
Arc length is given as 2πr(θ/360).
Where,
Radius (r) = 10 yd,
Measure of arc (θ) = 90°
π = 3.142
Arc length = 2*3.142*10(90/360)
Arc length = 62.84(¼)
Arc length = 62.84/4
Arc length = 15.71 yd
The act length is approximately 15.7 (to the nearest tenth)
I will give brainliest pls i need help
Which phrase describes the algebraic expression 3 x minus 4?
the sum of three times a number and four
four less than three times a number
the quotient of three times a number less four
the difference between four and three
Answers
Answer:
The option B, perfectly gives it to the target, because if you think about it, four less, means 4-, but backwards, and three times, means 3x, and if you put that together, that perfectly matches the one you are looking for. Hope that this would help you!
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Set of six numbers has an average of 42. When three of this numbers were removed the remaining three numbers had an average of 72. What was the sum of the removed numbers?
Answers
Answer: 36
Step-by-step explanation:
From the question, we are informed that six numbers has an average of 42. This means that the total number will be equal to:
= 42 × 6
= 252
When three of this numbers were removed the remaining three numbers had an average of 72. The total of this will be:
= 72 × 3
= 216
The sum of the removed numbers will be the difference between the two numbers above. This will be:
= 252 - 216
= 36
Solve this problem, which steps would you take? Include any theorems, definitions, or reasons that explain the steps. Make sure you include all steps needed to solve for ∠A
Answers
Answer:
∠A=123°.
Step-by-step explanation:
From the given figure it is clear the CD and CE are two tangent lines on circle with center A.
Radius is perpendicular to the tangent at the point of tangency.
[tex]\angle ADC=90^{\circ}[/tex]
[tex]\angle AEC=90^{\circ}[/tex]
Smaller arc DE = (5x-2)°
It means central angle DAE is (5x-2)°.
[tex]\angle DAE=(5x-2)^{\circ}[/tex]
Now, ADCE is a quadrilateral and sum of all angles of a quadrilateral is 360 degrees.
[tex]\angle ADC+\angle DCE+\angle AEC+\angle DAE=360^{\circ}[/tex]
[tex]90^{\circ}+(2x+7)^{\circ}+90^{\circ}+(5x-2)^{\circ}=360^{\circ}[/tex]
[tex](7x+5)^{\circ}+180^{\circ}=360^{\circ}[/tex]
[tex](7x+5)^{\circ}=360^{\circ}-180^{\circ}[/tex]
[tex](7x+5)^{\circ}=180^{\circ}[/tex]
[tex]7x+5=180[/tex]
[tex]7x=175[/tex]
[tex]x=25[/tex]
The value of x is 25.
[tex]\angle A=5x-2=5(25)-2=125-2=123^{\circ}[/tex]
Therefore, the measure of ∠A is 123°.
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answers
Answer:
fourth option
Step-by-step explanation:
Given
3x³ + 3x² - 18x ← factor out 3x from each term
= 3x(x² + x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, thus
x² + x - 6 = (x + 3)(x - 2) and
3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form
What the answer now and answer fast correct answer
Answers
Answer:
[tex] f = 12.7 [/tex]
Step-by-step explanation:
Given:
<H = 94°
FG = h = 15
<F = 58°
GH = f = ?
Use the law of sines to find f:
[tex] \frac{f}{sin(F)} = \frac{h}{sin(H)} [/tex]
[tex] \frac{f}{sin(58)} = \frac{15}{sin(94)} [/tex]
[tex] \frac{f}{0.848} = \frac{15}{0.998} [/tex]
[tex] \frac{f}{0.848} = 15.03 [/tex]
Multiply both sides by 0.848
[tex] \frac{f}{0.848}*0.848 = 15.03*0.848 [/tex]
[tex] f = 15.03*0.848 [/tex]
[tex] f = 12.74544[/tex]
[tex] f = 12.7 [/tex] (nearest tenth)
What is the value of y in the solution to the system of equations? 1/3x+1/4y=2 2x – 3y = –30 –8 –3 3 8
Answers
Answer:
8 i'm pretty sure
Step-by-step explanation:
Answer:
y = 9 1/3 or 8 if the first equation is 1/3x + 1/4y = 1.
Step-by-step explanation:
1/3x + 1/4y = 2
2x - 3y = -30
Multiply the first equation by -6:
- 2x - 3/2y = -12
Adding the last 2 equations:
-9/2 y = -42
y = -42 * -2/9
y = 9 1/3.
If the first equation is 1/3x + 1/4 y = 1
then y = -36 * -2/9
= 8.
Triangle ABC is isosceles with AB = AC.
Angle BAC = 110° and the area of the triangle is 85cm^2
Calculate AC.
Answers
Answer:
22.5 cm
Triangle area is (L x W) / 2
7.5 x 6 = 45
45 / 2 = 22.5
Step-by-step explanation:
brainlist plzzzz
plzzzz help! marking brainiest asap!
Answers
(-x^2+2x+3) + (-x^2-2x-1) = -2x^2 + 2
============================================
Explanation:
We have two large red tiles labeled with -x^2 on them. They add to -2x^2 which is found in every answer choice listed. This means that we must have a plus sign between the two parenthesis groups. If we had a subtraction sign, then -x^2 minus -x^2 would turn into 0x^2 or just 0, and the x^2 terms would go away entirely.
Because we must have a plus sign between the parenthesis, this means the answer is between C and D.
Now focus on the x terms. The slash marks mean that all of the x terms pair up and add to 0. They go away as there aren't any x terms that haven't been slashed. That explains why there are no x terms on the right hand side of any of the answer choices.
The question is: which of C or D has the x terms add to 0x? The answer would be choice D since 2x + (-2x) = 2x-2x = 0x. Choice C has 2x+2x = 4x which is what we don't want.
Lastly, choice D is further proven correct by noticing that the constants 3 and -1 add to 3+(-1) = 3-1 = 2. We have two small blue squares that add to 2 after the cancellations have happened.
please help :) Which number is less than 2.167 × 10 to the 4 power? A. 9,978 B. 1.1 x 10 to the 6 power C. 56,344,000 D. 2.468 × 10 to the 5 power
Answers
Answer: A
Step-by-step explanation
2.167x10^4 = 21,670
= 9,978
1.1x10^6 = 1100,000
= 56,344,000
2.468x10^5 = 246,800
Answer: A. 9,978
Based on the power, move the decimal point that many spaces to the right. (E.g., If it's 4.2 × 10^3, then move the decimal three spaces to the right, and you'd get 4200.)
2.167 × 10^4 = 21670
1.1 × 10^6 = 1100000
2.468 × 10^5 = 246800
Out of all the numbers mentioned in the question, 9,978 is the only one that's less than 2.167 × 10^4 = 21670.
Kellianne lined up the interior angles of the triangle along line p below. Which statements are true for line p? Check all that apply. It is a straight line with a measure of 360°. It stays the same even if the angles in the triangle change. The line will not be straight if one of the angles in the triangle is changed to an obtuse angle. The line is only straight when one of the angles is a right angle. It represents the sum of the measures of the interior angles of the triangle. The line will not be straight if all the angles in the triangle are acute. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.
Answers
Answer:
It stays the same even if the angles in the triangle change. It represents the sum of the measures of the interior angles of the triangle. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.Step-by-step explanation:
The sum of angles in a triangle is always 180°, even if all are acute or one is obtuse or a right angle. That means their sum will always produce a straight line. Thus, the following statements are true
It stays the same even if the angles in the triangle change. It represents the sum of the measures of the interior angles of the triangle. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.Answer:
B,E,G,H
Step-by-step explanation:
i got 100% on edge!
Ans with steps.. Tysm Plzz asap!!
Answers
Answer:
10x^2 + 8x
Step-by-step explanation:
Area of the outer rectangle = 5x(3x + 2) = 15x^2 + 10x
Area of the inner rectangle = x(5x - 2) = 5x^2 - 2x
Area of the shaded region = (15x^2 + 10x) - (5x^2 - 2x)
= 10x^2 + 8x
5x(3x + 2) - x(5x - 2) required expression.
Step-by-step explanation:
I get there are 2 rectangles in figure.
How can I get the area of shaded region? What if, I subtract the area of inner rectangle from outer rectangle. Ya It will surely work (⌒o⌒).
Now,
Area of outer rectangle = [tex]\sf length \times breadth[/tex]
[tex]5x \times (3x + 2)[/tex]
[tex]5x(3x + 2)[/tex]
Again,
Area of inner rectangle = [tex]\sf length \times breadth[/tex]
[tex]=x \times (5x - 2)[/tex]
[tex]=x(5x - 2)[/tex]
[tex] \sf Area \:of \:Shaded\: region = \: Area_{\:outer}-Area_{\:inner}[/tex]
[tex] \sf \: 5x(3x + 2) - x(5x - 2)[/tex]
If We simplify further then,
= 15x² + 10x - 5x² + 2x
= 10x² + 12x
Area of shaded region is 10x² + 12x in a simple way.
Now use technology and use the cumulative probability 0.95, the mean muequals10.5, and the standard deviation sigmaequals4.10 to determine the value for x0, rounding to one decimal place.
Answers
Answer:
18.5
Step-by-step explanation:
In the above question, we are given the following values
Cumulative probability ( confidence interval) = 0.95 = 95%
Mean = 10.5
Standard deviation = 4.10
We are asked to find the value of x.
To solve for x , we would be using the z score formula.
z score = (x-μ)/σ,
where x is the raw score,
μ is the population mean
σ is the population standard deviation
z score was not given in the question, but we have our cumulative probability as 95%(0.95).
Using the appropriate table,
the z score for 95% confidence is z = 1.96.
Therefore,
z score = (x-μ)/σ,
1.96 = x - 10.5/4.10
Cross multiply
1.96×4.10 = x - 10.5
x = (1.96 × 4.10) + 10.5
x = 8.036 + 10.5
x = 18.536
Approximately to 1 decimal place
x = 18.5
The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of days. About what percentage of births would be expected to occur within days of the mean pregnancy length?
About what% of births would be expected to occur within days of the mean pregnancy length.
Answers
Answer: About 99.74% of births would be expected to occur within 24 days of the mean pregnancy length.
Step-by-step explanation:
Complete question is attached below.
Given: The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 8 days.
i.e. [tex]\sigma= 8[/tex]
let X denotes the random variable that represents the lengths of pregnancy.
The probability of births would be expected to occur within 24 days of the mean pregnancy length:
[tex]P(\mu-24<X<\mu+24)=P(\dfrac{\mu-24-\mu}{8}<\dfrac{X-\mu}{\sigma}<\dfrac{\mu+24-\mu}{8})\\\\=P(\dfrac{-24}{8}<Z<\dfrac{24}{8})\ \ \ [\because Z=\dfrac{X-\mu}{\sigma}]\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=P(Z<3)-(1-P(Z<3))\\\\=2P(Z<3)-1[/tex]
[tex]= 2(0.9987)-1\ \ \ [\text{ By z-table}]\\\\=0.9974[/tex]
=99.74%
Hence, about 99.74% of births would be expected to occur within 24 days of the mean pregnancy length.