tom has a rectangular prism - shaped suitcase that measures 9 inches by 9 inches by 24 inches. he needs a second suitcase that has the same volume but smaller surface than his current suitcase. which suitcase size would fit Toms needs
Answers
ANSWER:
18 inches by 9 inches by 12 inches
EXPLANATION:
The volume of Tom's rectangular prism-shaped suitcase which measures 9 inches by 9 inches by 24 inches is;
[tex]\begin{gathered} Volume=l*w*h \\ \\ =9*9*24 \\ \\ =1944\text{ }square\text{ }inches \end{gathered}[/tex]So the volume of Tom's suitcase is 1944 cubic inches
The surface area will be;
[tex]\begin{gathered} SA=2(lw+wh+hl) \\ \\ =2(9*9+9*24+24*9) \\ \\ =2(81+216+216) \\ \\ =2(513) \\ \\ =1026\text{ }square\text{ }inches \end{gathered}[/tex]So the volume of the suitcase is 1026 square inches
*Let's go ahead and determine the volume and surface area of a suitcase that measures 18 inches by 18 inches by 6 inches;
[tex]\begin{gathered} Volume=l*w*h \\ \\ =18*18*6 \\ \\ =1944\text{ cubic inches} \end{gathered}[/tex][tex]\begin{gathered} Surface\text{ }Area=2(18*18+18*6+6*18) \\ \\ =2(324+108+108) \\ \\ =2(540) \\ \\ =1080\text{ square inches} \end{gathered}[/tex]We can see that the suitcase that measures 18 inches by 18 inches by 6 inches has the same volume as the first one but a higher surface area which doesn't fit Tom's needs
*Let's go ahead and determine the volume of a suitcase that measures 12 inches by 10 inches by 9 inches;
[tex]\begin{gathered} Volume=12*10*9 \\ \\ =1080\text{ cubic inches} \end{gathered}[/tex]We can see that the suitcase that measures 12 inches by 10 inches by 9 inches has a different volume from the first one which doesn't fit Tom's needs.
Let's go ahead and determine the volume of a suitcase that measures 16 inches by 5 inches by 9 inches;
[tex]\begin{gathered} Volume=16*5*9 \\ \\ =720\text{ cubic inches} \end{gathered}[/tex]We can see that the suitcase that measures 16 inches by 5 inches by 9 inches has a different volume from the first one which doesn't fit Tom's needs.
*Let's go ahead and determine the volume and surface area of a suitcase that measures 18 inches by 9 inches by 12 inches;
[tex]\begin{gathered} Volume=l*w*h \\ \\ =18*9*12 \\ \\ =1944\text{ cubic inches} \end{gathered}[/tex][tex]\begin{gathered} Surface\text{ }Area=2(18*9+9*12+12*18) \\ \\ =2(162+108+216) \\ \\ =2(486) \\ \\ =972\text{ square inches} \end{gathered}[/tex]We can see that the suitcase that measures 18 inches by 9 inches by 12 inches has the same volume as the first one and s smaller surface area which fits Tom's needs
Related Questions
If the formula x=1/n, is used to find the mean of the following sample, what is the value of n? 2, 63, 88, 10, 72, 99, 38, 19
Answers
Given:
The formula is:
[tex]x=\frac{1}{n}\sum_{i=1}^nx_i[/tex]Series is:
[tex]2,63,88,10,72,99,38,19[/tex]Find-:
The value of "n"
Explanation-:
In the given formula "n" represent the number of member in a series.
Given series is:
[tex]2,63,88,10,72,99,38,19[/tex]The number of members is:
The members are 8.
So the value of "n" is:
[tex]n=8[/tex]The value of "n" is 8.
Answer: The answer to this problem is 6
Step-by-step explanation: i took the quiz, this is the correct answer.
how do I do domin and range on a graph
Answers
Consider that the domain are the set of x values with a point on the curve.
In this case, based on the grap, you can notice that the domain is:
domain = (-8,2)
domain = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2}
In this case you can observe that the circle has a left limit given by x = -8 (this can be notices by the subdivisions of the coordinate system) and a right limit given by x = 2. That's the reason why it is the interval of the domain.
The range are the set of y values with a point on the curve.
range = (-3,7)
range = {-3,-2,-1,0,1,2,3,4,5,6,7}
In this case, you observe the down and up limits of the circle.
The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Equation 1
Equation 2
Equation 1 is modeled for the percentage of never-married American adults, y, x years after 1970 and Equation 2 is modeled for the percentage of married
American adults, y, x years after 1970. Use these models to complete parts a and b.
a. Determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For
that year, approximately what percentage of Americans, rounded to the nearest percent, will belong to each group?
In year
the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately % percentage of
Americans will belong to each group.
Answers
After 4 years the percentage of never-married adults will be the same as the percentage of married adults.
The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Multiply the second equation with 3
-3x + 10y = 160 .....equation 1
3x + 6y = 492........equation 2
adding equation 1 and 2
16y = 652
y = 40.75
x + 2y = 164
x = 164 - 2 (40.75)
x = 82.5
Let the number of years be t
-3x+10y x t = x+2y
t = 4x - 8y
t = 330 - 326
t = 4 years
Therefore, after 4 years the percentage of never-married adults will be the same as the percentage of married adults.
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Omaha Beef Company purchased a delivery truck for $66,000. The residual value at the end of an estimated eight-year service life is expected to be $12,000. The company uses straight-line depreciation for the first six years. In the seventh year, the company now believes the truck will be useful for a total of 10 years (four more years), and the residual value will remain at $12,000. Calculate depreciation expense for the seventh year.
Answers
Given:
Company purchased = $66000
Find-:
Depreciation expense for the seventh year
Sol:
First, depreciate for 6 years using the regular method:
[tex]\begin{gathered} =\frac{\text{ Cost - salvage value}}{\text{ initial useful life}} \\ \\ =\frac{66000-12000}{8} \\ \\ =6750 \end{gathered}[/tex]The annual depreciation is 6750.
For 6 years
[tex]\begin{gathered} =6750\times6 \\ \\ =40500 \end{gathered}[/tex]So
[tex]\begin{gathered} \text{ Remaining useful life = 10-6} \\ =4 \\ \\ =\frac{66000-40500-12000}{4} \\ \\ =\frac{13500}{4} \\ \\ =3375 \end{gathered}[/tex]For seventh-year depreciation expense is $3375
Segment AC has a midpoint B. If AB = 2x - x - 42 andBCI_x+11x +21, find the length of Ac.
Answers
The equation for the segment AB is;
[tex]2x^2-x-42[/tex]The equation for the segment BC is ;
[tex]x^2+11x+21[/tex]If segment AC has midpoint at B , this means ;
AC = AB + BC
To get AC we add the equation for AB and BC
Performing addition as;
[tex]2x^2-x-42+x^2+11x+21[/tex]Collect like terms as;
[tex]2x^2+x^2+11x-x-42+21=AC[/tex][tex]3x^2+10x-21=AC[/tex]Answer
[tex]AC=3x^2+10x-21[/tex]
Julia found the equation of the line perpendicular toy = -2x + 2 that passes through (5.-1).Analyze Julia's work. Is she correct? If not, what washer mistake?1 y25= 1/2 (-2) + 6Yes, she is correct,No, she did not use the opposite reciprocal for theslope of the perpendicular line.No, she did not substitute the correct x and yvaluesNo she did not apply inverse operations to solve forthe y-intercept.3+5b=555y=x5.5
Answers
The given line is
[tex]y=-2x+2[/tex]The line passes through (5, -1),
Perpendicular lines have opposite slopes, so we use the following equation to find the new slope knowing that the slope of the given line is -2.
[tex]\begin{gathered} m\cdot m_1=-1 \\ m\cdot(-2)=-1 \\ m=\frac{-1}{-2} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, we use the slope, the point, and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=\frac{1}{2}(x-5) \\ y+1=\frac{1}{2}x-\frac{5}{2} \\ y=\frac{1}{2}x-\frac{5}{2}-1 \\ y=\frac{1}{2}x+\frac{-5-2}{2} \\ y=\frac{1}{2}x-\frac{7}{2} \end{gathered}[/tex]Therefore, the equation of the new perpendicular line is[tex]y=\frac{1}{2}x-\frac{7}{2}[/tex]So, she's not correct, she didn't substitute the correct x and y values.
The right answer is C.Translate this phrase into an algebraic expression.72 decreased by twice a numberUse the variable n to represent the unknown number.
Answers
When the questions uses the word "decreased" this means that a value was subtracted by another value. The word "twice" symbolizes that a number was doubled or multiplied by 2. With this understanding, we can create the expression:
[tex]72-2n[/tex]The previous tutor helped me with solution but we got cut off before we could graph I need help with graphing please
Answers
We want to graph the following inequality system
[tex]\begin{gathered} x+8\ge9 \\ \text{and} \\ \frac{x}{7}\le1 \end{gathered}[/tex]First, we need to solve both inequalities. To solve the first one, we subtract 8 from both sides
[tex]\begin{gathered} x+8-8\ge9-8 \\ x\ge1 \end{gathered}[/tex]To solve the second one, we multiply both sides by 7.
[tex]\begin{gathered} 7\cdot\frac{x}{7}\le1\cdot7 \\ x\le7 \end{gathered}[/tex]Now, our system is
[tex]\begin{gathered} x\ge1 \\ \text{and} \\ x\le7 \end{gathered}[/tex]We can combine those inequalities into one.
[tex]1\le x\le7[/tex]The number x is inside the interval between 1 and 7. Graphically, this is the region between those numbers(including them).
Find the area of the shaded circles. Leave your answer in terms of pi or round to the nearest 10th
Answers
step 1
Find out the area of the complete circle
[tex]A=\pi\cdot r^2[/tex]we have
r=10 units
substitute
[tex]\begin{gathered} A=\pi\cdot10^2 \\ A=100\pi\text{ unit2} \end{gathered}[/tex]Remember that the area of the complete circle subtends a central angle of 360 degrees
so
Applying proportion
Find out the area of the circle with a central angle of 330 degrees
100pi/360=x/330
solve for x
x=(100pi/360)*330
x=91.67pi unit2the perimeter of a geometric figure is the sum of the lengths of the sides the perimeter of the pentagon five-sided figure on the right is 54 centimeters A.write an equation for perimeter B.solve the equation in part a C.find the length of each side i need help solve this word problem
Answers
A.
The perimeter of the pentagon is the sum of the 5 sides of the figure
the sum of the five sides = x + x + x+ 3x +3x (centimeter)
=> 9x
we are also told that the perimeter is 54 centimeter
=> 9x = 54
B.
to solve the equation 9x = 54
divide both sides by the coefficient of x
[tex]\begin{gathered} \frac{9x}{9}=\frac{54}{9}\text{ } \\ x\text{ = 6} \end{gathered}[/tex]C. to get the length of each sides, substitue the value for x=6 into the sides so that we will have
6, 6, 6, 3(6), 3(6)
=> 6, 6, 6, 18,18 centimeters
True or false? Based only on the given information, it is guaranteed thatAD EBDADGiven: ADI ACDBICBAC = BCBCDO A. TrueB. FalseSUBMIT
Answers
According to the information given, we can assure:
For both triangles, two interior angles and the side between them have the same measure and length, respectively. This is consistent with the ALA triangle congruence criterion.
ANSWER:
True.
Amelia used 6 liters of gasoline to drive 48 kilometers.How many kilometers did Amelia drive per liter?kilometers =At that rate, how many liters does it take to drive 1 kilometer?liters =
Answers
Answer:
8km /hr
1/ 8 of a litre.
Explanation:
We are told that Amelia drives 48 kilometres in 6 hours, this means the number of kilometres she drives per litre is
[tex]48\operatorname{km}\div6\text{litres}[/tex][tex]\frac{8\operatorname{km}}{\text{litre}}[/tex]Hence, Amelia drives 8 kilometres per litre.
The next question can be rephrased as, given that Amelia drives 8 km per litre, how many litres will it take to drive one kilometre?
To answer this question, we make use of the equation
[tex]\operatorname{km}\text{ travelled = 8km/litre }\cdot\text{ litres}[/tex]Now, we want
km travelled = 1 km
and the above equation gives
[tex]\begin{gathered} 1=\frac{8\operatorname{km}}{\text{litre}}\cdot\text{litres} \\ 1=8\cdot\text{litres} \end{gathered}[/tex]Dividing both sides by 8 gives
[tex]\text{litres}=\frac{1}{8}[/tex]Hence, it takes 1/8 of a litre to drive 1 kilometre.
Trying to solve this problem kind of having a hard time
Answers
Future Value of an Investment
The formula to calculate the future value (FV) of an investment P for t years at a rate r is:
[tex]FV=P\mleft(1+\frac{r}{m}\mright)^{m\cdot t}[/tex]Where m is the number of compounding periods per year.
Leyla needs FV = $7000 for a future project. She can invest P = $5000 now at an annual rate of r = 10.5% = 0.105 compunded monthly. This means m = 12.
It's required to find the time required for her to have enough money for her project.
Substituting:
[tex]\begin{gathered} 7000=5000(1+\frac{0.105}{12})^{12t} \\ \text{Calculating:} \\ 7000=5000(1.00875)^{12t} \end{gathered}[/tex]Dividing by 5000:
[tex]\frac{7000}{5000}=(1.00875)^{12t}=1.4[/tex]Taking natural logarithms:
[tex]\begin{gathered} \ln (1.00875)^{12t}=\ln 1.4 \\ \text{Operating:} \\ 12t\ln (1.00875)^{}=\ln 1.4 \\ \text{Solving for t:} \\ t=\frac{\ln 1.4}{12\ln (1.00875)^{}} \\ t=3.22 \end{gathered}[/tex]It will take 3.22 years for Leila to have $7000
If 1 centimeter equals 3 ft what is the actual length of the 5cm side of the yard?
Answers
this is
[tex]\begin{gathered} \frac{1}{3}=\frac{5}{x} \\ 1\times x=3\times5 \\ x=15 \end{gathered}[/tex]answer: 15 ft
(a)If Diane makes 75 minutes of long distance calls for the month, which plan costs more?
Answers
Answer:
Step-by-step explanation:
huh the proper question
Find the midpoint of the coordinates (3. -18) and (-5, -10) WHAT IS THE XVALUE?
Answers
Given the points (3, -18) and (-5, -10)
Let the midpoint of the given coordinates is (x , y)
[tex]x=\frac{3+(-5)}{2}=\frac{-2}{2}=-1[/tex][tex]y=\frac{(-18)+(-10)}{2}=\frac{-28}{2}=-14[/tex]So, the coordinates of the midpoint is (-1 , -14)
Let h(t)=tan(4x + 8). Then h'(3) is
and h''(3) is
Answers
The most appropriate choice for differentiation will be given by
h'(3) = 24.02
h''(3) = [tex]210.48[/tex]
What is differentiation?
Differentiation is the process in which instantaneous rate of change of function can be calculated based on one of its variables.
Here,
h(x) = tan(4x + 8)
h'(x) = [tex]\frac{d}{dx} (tan(4x + 8))[/tex]
= [tex]sec^2(4x + 8)\frac{d}{dx}(4x + 8)[/tex]
= [tex]4sec^2(4x + 8)[/tex]
h'(3) =
[tex]4sec^2(4\times 3 + 8 )\\4sec^220\\24.02[/tex]
h''(x) =
[tex]\frac{d}{dx}(4sec^2(4x + 8))\\4\times 2sec(4x + 8)\times \frac{d}{dx}(sec(4x + 8))\\8sec(4x + 8)sec(4x+8)cosec(4x+8)\times\frac{d}{dx}(4x + 8)\\32sec^2(4x + 8)cosec(4x +8)[/tex]
h''(3) =
[tex]32sec^2(4\times 3+8)cosec(4\times 3+8)\\32sec^220cosec20[/tex]
[tex]210.48[/tex]
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Can you please help me solve this and the test statistics and p value
Answers
The claim is that the population mean for the smartphone carrier's data speed at airports is less than 4.00 Mbps
The parameter of the study is the population mean, symbolized by the Greek letter mu "μ"
The researchers believe is that his value is less than 4, you can symbolize this as:
[tex]\mu<4[/tex]This expression does not include the "=" symbol, which indicates that it represents the alternative hypothesis. The null and alternative hypotheses are complementary, so if the alternative hypothesis represents the values of μ less than 4, then the null hypothesis, as its complement, should represent all other possible values, which are those greater than and equal to 4. You can represent this as:
[tex]\mu\ge4\text{ or simply }\mu=4[/tex]The statistical hypotheses for this test are:
[tex]\begin{gathered} H_0\colon\mu=4 \\ H_1\colon\mu<4 \end{gathered}[/tex]Option A.
In the display of technology, you can see the data calculated for the test.
The second value shown in the display corresponds to the value of the test statistic under the null hypothesis, you have to round it to two decimal places:
[tex]t_{H0}=-2.432925\approx-2.43[/tex]The value of the test statistic is -2.43
The p-value corresponds to the third value shown in the display.
The p-value is 0.009337
To make a decision over the hypothesis test using the p-value you have to follow the decision rule:
- If p-value ≥ α, do not reject the null hypotheses.
- If p-value < α, reject the null hypotheses.
The significance level is α= 0.05
Since the p-value (0.009337) is less than the significance level of 0.05, the decision is to reject the null hypothesis.
Conclusion
So, at a 5% significance level, you can conclude that there is significant evidence to reject the null hypothesis (H₀: μ=4), which means that the population mean of the smartphone carrier's data speed at the airport is less than 4.00 Mbps.
Rewrite the following equation in slope-intercept form.
y + 8 = –3(x + 7)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer: y = -3x - 21
Step-by-step explanation:
Slope intercept form: y = mx + b
m is the slope, and b is the y-intercept.
y + 8 = -3(x + 7)
Start by distributing -3 into the parenthesis.
y + 8 = -3x - 21
subtract 8 from both sides to get the final answer.
y = -3x - 29
Answer:
Slope-intercept form,
y = -3x - 29Step-by-step explanation:
Now we have to,
→ Rewrite the given equation in the slope-intercept form.
The slope-intercept form is,
→ y = mx + b
The equation is,
→ y + 8 = -3(x + 7)
Then the value of y will be,
→ y + 8 = -3(x + 7)
→ y + 8 = -3x - 21
→ y = -3x - 21 - 8
→ [ y = -3x - 29 ]
Hence, answer is y = -3x - 29.
help pleaseeeeeeeeeeeeeeeee
Answers
Answer:
b) 28
c) 52
Step-by-step explanation:
f(2) = -2³ + 7(2)² - 2(2) + 12
= -8 + 28 - 4 + 12
= 28
f(-2) = -(-2)³ + 7(-2)² - 2(-2) + 12
= 8 + 28 + 4 + 12
= 52
Reginald wants to buy a new collar for each of his 3 cats. The collars come in a choice of 6 different colors. How many selections of collarsfor each of the 3 cats are possible if color repetitions are allowed
Answers
We will have the following:
Assuming that color repetitions can be made, then total number of selections for collars for the 3 cats will be:
[tex]6\ast6\ast6=216[/tex]So, there will be a total of 216 possible permutations of choices.
help meeeeeeeeee pleaseee !!!!!
Answers
The composition of the two functions evaluated in x = 2 is:
(f o g)(2) = 33
How to find the composition?Here we have the next two functions:
f(x) = x² - 3x + 5
g(x) = -2x
And we want to find the composition:
(f o g)(2) = f( g(2))
So we need to evaluate f(x) in g(2).
First, we need to evaluate g(x) in x = 2.
g(2) = -2*2 = -4
Then we have:
(f o g)(2) = f( g(2)) = f(-4)
f(-4) = (-4)² - 3*(-4) + 5 = 16 + 12 + 5 = 28 + 5 = 33
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El contratista encargado de construir el
cerco perimetral desea saber la expresión
algebraica correspondiente al perímetro de
todo el lote
Medidas:
25p-8
40p+2
Answers
El perímetro del lote tiene una medida de 130 · p - 12 unidades.
¿Cuál es la longitud del cerco perimetral para un lote?
El perímetro es la suma de las longitudes de los lados de una figura, un rectángulo tiene cuatro lados, dos pares de lados iguales. En consecuencia, el perímetro del lote es el siguiente:
s = 2 · w + 2 · l
Donde:
w - Ancho del lote.l - Largo del lote.s - Perímetro del lote.Si sabemos que w = 25 · p - 8 y l = 40 · p + 2, entonces el perímetro del lote es:
s = 2 · (25 · p - 8) + 2 · (40 · p + 2)
s = 50 · p - 16 + 80 · p + 4
s = 130 · p - 12
El perímetro tiene una medida de 130 · p - 12 unidades.
ObservaciónNo se ha podido encontrar una figura o imagen asociada al enunciado del problema. Sin embargo, se puede inferir que el lote tiene una forma rectangular debido a las medidas utilizadas. En consecuencia, asumimos que la medida del ancho es igual a 25 · p - 8 unidades y del largo es igual a 40 · p + 2 unidades.
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The statement listed below is false. Let p represent the statement.
Answers
We will have that the negation of the statement would be:
*That product did not emerge as a toy in 1949. [Option B]
Need help Instructions: Find the measure of each angle Calculate the length of each side Round to the nearest tenth
Answers
Given,
The length of the perpendicular is 4.
The measure of the hypotenuse is 14.
Required:
The measure of each angle of the triangle.
As it is a right angle triangle,
The measure of angle C is 90 degree.
By using the trigonometric ratios,
[tex]\begin{gathered} cosA=\frac{AC}{AB} \\ cosA=\frac{4}{14} \\ A=cos^{-1}(\frac{4}{14}) \\ A=73.4^{\circ} \end{gathered}[/tex]By using the trigonometric ratios,
[tex]\begin{gathered} sinB=\frac{AC}{AB} \\ sinB=\frac{4}{14} \\ B=sin^{-1}(\frac{4}{14}) \\ B=16.6^{\circ} \end{gathered}[/tex]Hence, the measure of angle A is 73.4 degree, angle B is 16.6 degree and angle C is 90 degree.
Graph the parabola. I have a picture of the problem
Answers
Let's begin by listing out the given information
[tex]\begin{gathered} y=(x-3)^2+4 \\ y=(x-3)(x-3)+4 \\ y=x(x-3)-3(x-3)+4 \\ y=x^2-3x-3x+9+4 \\ y=x^2-6x+13 \\ \\ a=1,b=-6,c=13 \end{gathered}[/tex]The vertex of the function is calculated using the formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{-6}{2(1)}=\frac{6}{2}=3 \\ x=3 \\ \\ y=(x-3)^2+4 \\ y=(3-3)^2+4=0^2+4=0+4 \\ y=4 \\ \\ (x,y)=(h,k)=(3,4) \end{gathered}[/tex]For the function, we assume values for x to solve. We have:
[tex]\begin{gathered} y=(x-3)^2+4 \\ x=1 \\ y=(1-3)^2+4=-2^2+4=4+4 \\ y=8 \\ x=2 \\ y=(2-3)^2+4=-1^2+4=1+4 \\ y=5 \\ x=3 \\ y=(3-3)^2+4=0^2+4=0+4 \\ y=4 \\ x=4 \\ y=(4-3)^2+4=1^2+4=1+4 \\ y=5 \\ x=5 \\ y=(5-3)^2+4=2^2+4=4+4 \\ y=8 \\ \\ (x,y)=(1,8),(2,5),(3,4),(4,5),(5,8) \end{gathered}[/tex]We then plot the graph of the function:
80.39 rounded to nearest whole number
Answers
Answer:
80
Step-by-step explanation:
It is 80 because .39 is not quite 4.
so in a instance like this you would round .39 to .4 and .4 cant be rounded up to .5 so it would go down because it is to the nearest whole number to instead of it being 81 ( if it could be rounded to 80.5 ), it goes to just 80.
One way to help with rounding is:
" 4 and below let it go
if its 5 and above give it a shove. " rugrat k aka rgr k
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Write an equation of variation to represent the situation and solve for the indicated information Wei received $55.35 in interest on the $1230 in her credit union account. If the interestvaries directly with the amount deposited, how much would Wei receive for the sameamount of time if she had $2000 in the account?
Answers
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, thenthe unit cost is given by the function C(x) = 0.5x? - 260x +53,298. How many cars must be made to minimize the unit cost?Do not round your answer.
Answers
Okey, here we have the following function:
[tex]C(x)=0.5x^2-260x+53298[/tex]Considering that "a" is a positive coefficient, then it achieves the minimum at:
[tex]x=-\frac{b}{2a}[/tex][tex]\begin{gathered} x=-\frac{(-260)}{2(0.5)} \\ =\frac{260}{1} \\ =260 \end{gathered}[/tex]Now, let's find the minimal value of the quadratic function, so we are going to replace x=260, in the function C(x):
[tex]\begin{gathered} C(260)=0.5(260)^2-260(260)+53298 \\ C(260)=0.5(67600)-67600+53298 \\ =33800-67600+53298 \\ =19498 \end{gathered}[/tex]Finally we obtain that the number of cars is 19498.
A coin is tossed nine times what is the probability of getting all tails express your answer as a simplified fraction or decimal rounded to four decimal places
Answers
The probability of getting a tail on each toss is:
[tex]\frac{1}{2}[/tex]Since there is only one way of getting all tails, it follows that the required probability is given by:
[tex](\frac{1}{2})^9\approx0.0020[/tex]Hence, the required probability is approximately 0.0020