Answers
So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:
[tex]\frac{(6^{\prime}+5^{\prime})}{2}\cdot2.1^{\prime}=11.55in^2[/tex]Then the total lateral surface is:
[tex]11.55in^2\cdot4=46.2in^2[/tex]Then we need to find the volume of the truncated pyramid. This is given by the following formula:
[tex]\frac{1}{3}h(a^2+ab+b^2)[/tex]Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:
[tex]\frac{1}{3}\cdot2^{\prime}\cdot(5^{\prime2}+6^{\prime}\cdot5^{\prime}+6^{\prime2})=60.7in^3[/tex]In summary, the lateral surface is 46.2in² and the volume is 60.7in³.
Related Questions
(3,-8),(-2,5) write an equation for the line in point slope form .Then rewrite the equation in slope intercept form
Answers
The equation for the line in point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x1, y1) is a point of the line. If we have two points (x1,y1) and (x2, y2), the slope is equal to:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (3, -8) and (-2, 5), we get that the slope and the equation of the line are:
[tex]m=\frac{5-(-8)}{-2-3}=\frac{5+8}{-5}=\frac{-13}{5}[/tex][tex]\begin{gathered} y-(-8)=\frac{-13}{5}(x-3) \\ y+8=-\frac{13}{5}(x-3) \end{gathered}[/tex]Therefore, the equation in slope-intercept form is calculated as:
[tex]\begin{gathered} y+8=-\frac{13}{5}x-\frac{13}{5}\cdot(-3) \\ y+8=-\frac{13}{5}x+\frac{39}{5} \\ y=-\frac{13}{5}x+\frac{39}{5}-8 \\ y=-\frac{13}{5}x-\frac{1}{5} \end{gathered}[/tex]Answer: Point-slope form:
[tex]y+8=-\frac{13}{5}(x-3)[/tex]slope-intercept form:
[tex]y=-\frac{13}{5}x-\frac{1}{5}[/tex]DEF is a right triangle. If FE= 12 and DE= 5, find DF.
Answers
Answer:
DF = 13
Explanation:
The Pythagoras theorem says that
[tex]FE^2+ED^2=DF^2[/tex]Now in our case,
FE = 12
ED =
a normal distribution with u= 40 with o=4 what is the probability of selecting a score greater than x=44?
Answers
We have the following information:'
[tex]\begin{gathered} \mu=40 \\ \sigma=4 \\ x=44 \end{gathered}[/tex]We want to calculate the following probability:
[tex]P(X>44)[/tex]then, using the information that we are given, we havE:
[tex]P(X>44)=P(X-\mu>44-40)=P(\frac{X-\mu}{\sigma}>\frac{44-40}{4})=P(\frac{X-\mu}{\sigma}>1)[/tex]since:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]we have the following:
[tex]P(X>44)=P(Z>1)=0.1587[/tex]therefore, the probability of selecting a score greater than 44 is 15.87%
why you can always solve a right triangle if you know the measures of one side and one acute angle.
Answers
In a right triangle, one angle is always 90.
If you know one acute angle, you automatically know the other (3rd) angle.
3 angles are solved.
Now, comes the sides.
If you already know 1 side, you can easily know another side by using the basic trig identities SIN, COS, or TAN.
When you know 2 sides, the 3rd side can always be find using:
• pythagorean theorem, or
,• again, trigonometric ratios (sin, cos, tan).
Graph the equation. y = 2x 20 N 18 16 14 12 10 8 6 4 N. 0 1 2 3 4 ул 6 10 2. y = 2x
Answers
Make a table, and give values to x.
Solve the equation and obtain y values.
Graph the points and join them:
x = 0
y= 2x = 2 (0) = 0
x= 2
y= 2(2) = 4
x= 4
y= 2(4) = 8
Graph:
Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (intersect at just one point), or coinciding (intersect at all points)?y = -x + 11, 2y = -2x + 22
Answers
Given
The lines,
[tex]\begin{gathered} y=-x+11\text{ \_\_\_\_\_\lparen1\rparen} \\ 2y=-2x+22\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]To find:
Whether the lines are perpendicular, coinciding, intersecting or parallel?
Explanation:
It is given that,
[tex]\begin{gathered} y=-x+11\text{ \_\_\_\_\_\lparen1\rparen} \\ 2y=-2x+22\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]That implies,
Since the slope of the two lines are,
[tex]\begin{gathered} m_1=-1 \\ m_2=\frac{-2}{2}=-1 \\ \therefore m_1=m_2 \end{gathered}[/tex]Hence, the two lines are parallel.
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Question
A triangle with area 40 square inches has a height that is four less than six times the width. Find the width and height of the
triangle
Provide your answer below:
width:
inches, height:
inches
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Answers
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the formula for the area of the triangle
[tex]Area=\frac{1}{2}\times base\times height[/tex]STEP 2: Represent the statements to get an equation
[tex]\begin{gathered} width=base \\ From\text{ the statement,} \\ six\text{ times of the width}=6w \\ four\text{ less than six times the width }=6w-4 \\ \therefore height=6w-4 \end{gathered}[/tex]STEP 3: Substitute into the formula in step 1
[tex]\begin{gathered} height=6w-4,width=base=w,Area=40in^2 \\ Area=\frac{1}{2}\times w\times(6w-4) \\ Area=\frac{w(6w-4)}{2}=\frac{6w^2-4w}{2}=40 \end{gathered}[/tex]STEP 4: Cross multiply
[tex]\begin{gathered} 6w^2-4w=40\times2 \\ 6w^2-4w=80 \\ Subtract\text{ 80 from both sides} \\ 6w^2-4w-80=80-80 \\ 6w^2-4w-80=0 \\ Divide\text{ through by 2, we have:} \\ 3w^2-2w-40=0 \\ By\text{ factorization;} \\ 3w^2-12w+10w-40=0 \\ 3w(w-4)+10(w-4)=0 \\ (w-4)(3w+10)=0 \end{gathered}[/tex]STEP 5: Find the values of w
[tex]\begin{gathered} w-4=0,w=0+4,w=4 \\ 3w+10=0,3w=0-10,3w=-10,w=\frac{-10}{3} \\ \\ Since\text{ the width cannot be negative, width=4 inches} \end{gathered}[/tex]STEP 6: Find the height
[tex]\begin{gathered} Recall\text{ from step 2:} \\ h=6w-4 \\ Substitute\text{ 4 for w} \\ h=6(4)-4=24-4=20in \end{gathered}[/tex]Hence,
width = 4 inches
height = 20 inches
Find the area of this trapezoid. Be sure to include the correct un4 cm6 cm4 cm15 cm
Answers
So,
Here we have the following trapezoid:
Remember that the area of a trapezoid can be found if we apply the following formula:
[tex]A=\frac{1}{2}(\text{base}1+\text{base}2)\cdot\text{height}[/tex]Where bases 1 and 2 are the greater and smaller bases respectively.
So, if we replace:
[tex]\begin{gathered} A=\frac{1}{2}(15+4)\cdot4 \\ A=\frac{1}{2}(19)\cdot4 \\ A=9.5\cdot4 \\ A=38 \end{gathered}[/tex]So the area is 38cm^2.
What number is 3/4 of 17
Answers
3/4 of 17 is equal to the product of 3/4 times 17, that is,
[tex]\frac{3}{4}\times17=\frac{3\times17}{4}[/tex]which gives
[tex]\frac{3\times17}{4}=\frac{51}{4}[/tex]in decimal form, the answer is 12.75.
You have two spinners each with three sections of equal size labeled with numbers 1,2,3. You spin both and observe the numbers. Let x be the sum of the two numbers. Find the probability distribution for X.
Answers
From the given problem with two spinners with three sections of equal size labeled as 1, 2, and 3.
Spinner 1 : 1 2 3
Spinner 2 : 1 2 3
The sum is as follows :
1+1 = 2
1+2 = 3
1+3 = 4
2+1 = 3
2+2 = 4
2+3 = 5
3+1 = 4
3+2 = 5
3+3 = 6
There are 9 total outcomes
There are (1) 2,
(2) 3's
(3) 4's
(2) 5's
and
(1) 6
and their corresponding probability can be calculated by :
[tex]\text{probability}=\frac{\text{ quantity}}{\text{ total quantity}}[/tex]Probability of 2 = 1/9
Probability of 3 = 2/9
Probability of 4 = 3/9 or 1/3
Probability of 5 = 2/9
Probability of 6 = 1/9
Construct the probability distribution :
To check if your probability distribution is correct.
The sum of P(X) must be equal to 1
1/9 + 2/9 + 1/3 + 2/9 + 1/9 = 1
Therefore the distribution is correct.
What makes a function a function?
Answers
In a relationship between two variables x and y, the data set is a function, if every element of the domain corresponds to exactly one element of the range
that means
one element of x corresponds to exactly one element of y
In any function, there is an input value (independent variable or x variable) and there is an output value (dependent variable or y variable)
What makes a function a function? ------> one element of the input (variable x) corresponds to exactly one element of the output (variable y)
if the author sells x Books per day his profit will be : J(X)= (-0.001x^2)+3x-1800Find the max profit per dayFind the amount of books the author must sell for the most profit
Answers
The given function in a quadratic function in standard form where
a = -0.001, b = 3, and c = -1800
It is a parabola that is facing downwards, therefore, the vertex of this parabola, (x,y) is the maximum of the function where
x is the amount of books that the author must sell for the most profit, and
y is the max profit per day.
We can find the vertex using
[tex]x=\frac{-b}{2a}[/tex]Substitute the following values, and we get
[tex]\begin{gathered} x=\frac{-b}{2a} \\ x=\frac{-3}{2(-0.001)} \\ x=\frac{-3}{-0.002} \\ x=1500 \end{gathered}[/tex]Now that we have x, plug it in the original function to solve for y
[tex]\begin{gathered} J(x)=\mleft(-0.001x^2\mright)+3x-1800 \\ J(1500)=-0.001(1500)^2_{}+3(1500)-1800 \\ J(1500)=-2250+4500-1800 \\ J(1500)=450 \end{gathered}[/tex]We have determine that the vertex of the function is at (1500,450). We can now conclude that
The max profit per day is $450.
The amount of of books the author must sell for the most profit is 1500 books.
The mass of a typical comet is about 1 x 10¹3 kg, while the mass of a typical asteroid is about 3 x 10¹⁹ kg.
Approximately how many times the mass of a typical comet is the mass of a typical asteroid?
100,000 times
300,000 times
1,000,000 times
O 3,000,000 times
Answers
The mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
It is given in the question that:-
Mass of a typical comet = [tex]1*10^{13}kg[/tex]
Mass of a typical asteroid = [tex]3*10^{19}kg[/tex]
We have to find the how many times the mass of a typical comet is the mass of a typical asteroid.
Mass of a typical asteroid/ Mass of a typical comet is given by:-
[tex]\frac{3*10^{19}}{1*10^{13}}=3*10^6[/tex]
We can write [tex]3*10^6[/tex] as 3,000,000.
Hence, the mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
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Solve the following system of linear equations by graphing.{5x - 2y = 10 {x - y = -1 Graph the equations on the same set of axes.Note: Use different points on each line when plotting the graphs.The solution point is: (_, _)
Answers
Kindly Check below
1) The first thing we need to do in this question, is to pick the method we are going to use to solve this system. Let's use the Elimination Method.
2) So, let's solve this system analytically (algebraically):
[tex]\begin{gathered} 5x-2y=10 \\ x-y=-1\:\:(\times-2) \\ \\ 5x-2y=10 \\ -2x+2y=2 \\ ------- \\ 3x=12 \\ \\ \frac{3x}{3}=\frac{12}{3} \\ \\ x=4 \end{gathered}[/tex]Now, let's plug into the 2nd original equation x=4 and solve it for y:
[tex]\begin{gathered} x-y=-1 \\ \\ 4-y=-1 \\ \\ -y=-1-4 \\ \\ y=5 \end{gathered}[/tex]So we know the solution is (4,5).
3) Now, let's graph these equations by setting two t-tables. Let's rewrite those equations from the Standard form to the Slope-intercept form.
5x-2y=10 -2y=10-5x, y=-5+5/2x
x-y=-1,-y=-1-x, y=x+1
4) Now, let's plot those points and trace the lines through them
(-2,-10), (-1,-7.5), (0,-5), (1,-2.5), (2,0)
(-2,-1), (-1,0), (0,1), (1,2), (2,3)
What is the slope of a line parallel to the line whose equation is 5x-3y=18
Answers
Slope and slant both refer to an incline away from a reference surface or line that is generally straight.The definition of slope is "a vertical inclination in an oblique direction"Here, the land abruptly slopes either upward or downhill.
How to Determine a Line's Slope?
slope,The inclination of a line with respect to the horizontal is measured numerically.The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). To determine how much the y coordinates have changed, find the difference.To determine how much the x coordinates have changed, find the difference.Find the slope by dividing y by x.
Y=mx+b, where m is the slope and b is the y-intercept, is the slope-intercept form.
y=mx+b
Change the formula to 3y+18=5x.
−3y+18=5x
From both sides of the equation, deduct 18.
−3y=5x−18
Simplify by multiplying each term in 3y=5x18 by 3.
Subtract 3 from each term in 3y=5x18.
−3y/−3=5x/−3+−18/−3
Make the left side simpler.
Tap to take additional steps:Y= -5X/3+-18/-3
Make the right side simpler.
Tap to take additional steps: y=5x/3+6
Write in the form y=mx+b.
Tap to take additional steps: y=5/3x+6
The slope is- 5/3 using the slope-intercept form.
.
m=−5/3
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hi I'm 9 years old my name is Emma can
Answers
Given:
Perimeter = 40 feet,
The measure of the four sides is 11 feet, g, 11 feet, and g.
We know that the perimeter = the sum of the four sides.
[tex]\text{perimeter =11+g+11+g}[/tex]Replace perimeter =40, we get
[tex]\text{40=11+g+11+g}[/tex]Adding 11 and 11, we get
[tex]\text{40=11+11+g+g}[/tex][tex]\text{40=22+g+g}[/tex]What is the diameter of a circle with radius 15
Answers
Given Data:
The radius of the circle is r=15.
The diameter of the circle can be determined as,
[tex]\begin{gathered} d=2r \\ =2\times15 \\ =30 \end{gathered}[/tex]Thus, the required diameter of a circle is 30.
Students were divided into 10 teams with 12 on each team. later, the same day students were divided into teams with 3 on each team. how many teams were there then?
Answers
At first, the students were divided into 10 teams with 12 on each of them; we can write this as:
team 1 = 12 students
team 2 = 12 students
team 3 = 12 students
team 4 = 12 students
team 5 = 12 students
team 6 = 12 students
team 7 = 12 students
team 8 = 12 students
team 9 = 12 students
team 10 = 12 students
Sum up the number all the students and this adds up to: 120 students.
Then, the question says these 120 students were divided into teams with 3 students on each team.
This time the number of teams created will be more.
team 1 = 3 students
team 2 = 3 students
teams 3 = 3 students
...
And so on.
In order to get the number of teams, we simply divide the number of students by the number of students in a team.
[tex]\frac{120}{3}=40\text{ teams}[/tex]Therefore, the number of 3 person teams are 40 teams
Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The circle's radius is 2 units long and the terminal point is (−1.79,−0.89).The terminal point is how many radius lenghts to the right of the circle's center?h= radii Then, cos−1(h)=Does the number we get in part (b) give us the correct value of θ? Therefore, θ=
Answers
Given the terminal point ( -1.79 , -0.89 )
So, the x- coordintes = -1.79
[tex]\begin{gathered} \theta=\cos ^{-1}h \\ \\ h=-\frac{1.79}{2} \\ \\ \theta=\cos ^{-1}(-\frac{1.79}{2})=206.5^o \end{gathered}[/tex]
help meeeeeeeeee pleaseee !!!!!
Answers
If the average daily sales price of the toy is $6.50, then 2750 toys will have been sold overall.
Variables and functionsIn the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
While the dependent values are the codomain, the independent values are known as the domain.
Given that y = 6000 - 500x is the function that depicts the price-sales relationship for the quantity of toys
The total number of toys sold if the toy sells for $6.50 per day is: y = 6000 - 500 (6.50) y = 6000 - 3250 y = 2750 toys
The total quantity of toys sold is provided above.
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find a b c d e f from the picture
Answers
Given data:
The value of a is (3+4+2)=9
The value of b is (5+1+2)=8
The value of c is (1+8+1)=10
The value of d is (
9(11 - x) = 3(3x -9) what is x
Answers
x = 7
Explanation:9(11 - x) = 3(3x -9)
Expanding the expression:
9(11) - (9x) = 3(3x) -3(9)
99 - 9x = 9x - 27
collect like terms:
99 + 27 = 9x + 9x
126 = 18x
Divide both sides by 18:
126/18 = 18x/18
x = 7
Brainliest and 20 points please solve
Answers
Answer:
part a: x = 5
part b: no
Step-by-step explanation:
part a : 8x + 3 = 9x - 2, subtract 8x from both sides which leaves you with 1x or just x. add 2 to both sides which gives you 5. 5 is equal to 1x.
part b: a complementary angle is 2 angles whos sum equals 90 degrees. m<ABC = 43 & m<DBE = 43 & they both equal 86 not 90.
Answer/Step-by-step explanation:
A C
\ (8x + 3) /
\ /
\ /
\ /
B
/ \
/ \
/ \
/ (9x - 2) \
D E
A. Solve for x.
m∠ABC = m∠DBE
(8x + 3) = (9x - 2)
8x + 3 = 9x - 2
-9x -9x
------------------------
-x + 3 = -2
-3 -3
--------------------
-x = -5
÷-1 ÷-1
----------------
x = 5
B. Are vertical angles also complementary angles?
No, vertical angles are angles that are congruent to each other or in other words, equal. In the equation above (8x + 3) = (9x - 2). If I were to plug 5 into the equation I would get
(8(5) + 3) = (9(5) - 2)
(40 + 3) = (45 - 2)
43 = 43
Complementary angles equal to 90°. It wouldn't make sense to add these numbers together because I would end up with a fraction if I set the equation equal to 90°
I hope this helps!
What it 3 1/8 + 3/4?
Answers
The given expression is:
[tex]\begin{gathered} 3\frac{1}{8}+\frac{3}{4}=3\frac{1+6}{8} \\ =3\frac{7}{8} \end{gathered}[/tex]Therefore, the value of the expression is:
3 7/8
.
A traffic light weighing 16 pounds is suspended by two cables (see figure). Find the tension in each cable. (Round your answers to one decimal place.) lb (smaller value) lb (larger value)
Answers
Step 1: Draw an image to illustrate the problem
Consider the forces along the horizontal axis.
[tex]\begin{gathered} -T_1\cos \theta_1+T_2\cos \theta_2=0 \\ \text{ therefore} \\ T_2\cos 20^0=T_1\cos 20^0 \end{gathered}[/tex][tex]\text{ Dividing both sides by }\cos 20^0[/tex][tex]\begin{gathered} \frac{T_2\cos20^0}{\cos20^0}=\frac{T_1\cos 20^0}{\cos 20^0} \\ \text{thus} \\ T_2=T_1 \end{gathered}[/tex]Consider the forces along the vertical axis.
[tex]\begin{gathered} T_1\sin 20^0+T_2\sin 20^0-16=0 \\ T_1\sin 20^0+T_1\sin 20^0-16=0\text{ (}T_1=T_2) \\ \text{ Thus} \\ 2T_1\sin 20^0=16 \\ T_1=\frac{16}{2\sin 20^0}\approx23.39\text{ pounds} \end{gathered}[/tex]then T₁ = 23.39 pounds
Since T₁=T₂, then T₂ = 23.39 pounds
Hence, smaller value = 23.4 pounds to one decimal place and
larger value = 23.4 pounds to one decimal place
if RS=2x+6 ST=x+4 and RT= 40 Find RS
Answers
RS + ST = RT
Substituting with data,
2x + 6 + x + 4 = 40
(2x + x) + (6 + 4) = 40
Identify the value for C in the following equation that would make theconic section a hyperbola: 2x2 + y2 + 3x + 5y + 1 = 0
Answers
ANSWER:
C = -1
STEP-BY-STEP EXPLANATION:
We know that the general formula of hyperbola is the following
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Which means that the sign must have y must be negative for it to be a hyperbola.
Therefore y must be equal to -1.
[tex]2x^2-1y^2+3x+5y+1=0[/tex]The length of the longest slide is what inches the other two sides will each be what inches in length?
Answers
We know that the rod from which we made the triangle is 13 in long, this means that the perimeter of the triangle. from the diagram given we notice that the perimeter is:
[tex]x+(x-1)+(x-1)[/tex]equating this to 13 and solving for x we have:
[tex]\begin{gathered} x+(x-1)+(x-1)=13 \\ 3x-2=13 \\ 3x=13+2 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]Hence, the value of x=5 which means that the longest side measure 5 inches. To determine the length of the other sides we notice that they are given by x-1, which means that their length is 5-1=4 inches,
Therefore, the length of the longest side is 5 inches. The other two sides will each be 4 inches in length.
Rectangle WXYZ has vertices located at W(−6, 4), X(−6,−1), Y(2,−1), and Z(2, 4) on a coordinate plane. It is translated 4 units right and 2 units down to produce rectangle W'X'Y'Z'. What is the location of the vertices of the transformed rectangle?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Rectangle WXYZ
W(−6, 4)
X(−6,−1)
Y(2,−1)
Z(2, 4)
Step 02:
Translated
4 units right ===> x + 4
2 units down ===> y - 2
W' (−6+4, 4 -2) = W' (-2, 2)
X' (−6+4,−1 - 2) = X' (-2,-3)
Y' (2+4,−1-2) = Y' (6,-3)
Z' (2+4, 4-2) = Z' (6, 2)
The answer is:
W' (-2, 2)
X' (-2,-3)
Y' (6,-3)
Z' (6, 2)
In college, we study large volumes of information- information that, unfortunately, we go not often retain for very long. The function f(x) = 80e +20 describes the percentage of information, fx), that a particular person remembers x weeks after learning the information. a. Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b. Substitute 1 for x and find the percentage of information remembered after 1 week C. Find the percentage of information that is remembered after 4 weeks. d. Find the percentage of information that is remembered after 1 year.
Answers
a)
[tex]f(0)=80\cdot e^{-0.5\cdot0}+20=100[/tex]b)
[tex]f(1)=80\cdot e^{-0.5}+20=68.52[/tex]c)
[tex]f(4)=80\cdot e^{-0.5\cdot4}+20=30.82[/tex]d)
[tex]f(48)=80\cdot e^{-0.5\cdot48}+20=20[/tex]