The upper and lower bound of the cross-sectional area of the insulation, would be A = [ 3129, 3137 ] cm².
How to find the upper and lower bond ?The upper and lower bound of A would be found by the formula :
A = π x ( R ² - r ² )
The upper bound is therefore:
= π x (( 48. 75 / 2) ² - ( 19.2 45 / 2) ²)
= π x ( 1183. 0625 - 184. 857025 )
= π x 998. 205475
= 3, 137 cm²
The lower bound will then be:
= π x ( ( 48. 65 / 2 ) ²- (19. 255 / 2) ²)
= π x ( 1180. 9225 - 184. 963025)
= π x 995. 959475
= 3, 129 cm²
The interval form is therefore A = [ 3129, 3137 ] cm²
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Use the definition of the laplace transform to show that if f(x) = 0 then
[tex]l[f(x)] = 0[/tex]
show that f(x)= 1 then
[tex]l[f(x)] = \frac{1}{s} [/tex]
show that f(x)= x then
[tex]l[f(x)] = \frac{1}{ {s}^{2} } [/tex]
show that f(x)= e^ax then
[tex]l[f(x)] = \frac{1}{s - a} [/tex]
provide the steps by using the definition and evaluating the integral.
Answer:
Step-by-step explanation:
the Laplace transform of the function f(x) = e^(ax) is 1/(a-s).
The definition of the Laplace transform of a function f(t) is given by:
L{f(t)} = F(s) = ∫_0^∞ e^(-st) f(t) dt
where s is a complex number.
If f(x) = 0, then we have:
L{f(x)} = L{0} = ∫_0^∞ e^(-st) 0 dt = 0
Therefore, the Laplace transform of the zero function is zero.
If f(x) = 1, then we have:
L{f(x)} = L{1} = ∫_0^∞ e^(-st) dt
Using integration by parts, we get:
L{1} = ∫_0^∞ e^(-st) dt = [-e^(-st)/s]_0^∞ = [0 - (-1/s)] = 1/s
Therefore, the Laplace transform of the constant function 1 is 1/s.
If f(x) = x, then we have:
L{f(x)} = L{x} = ∫_0^∞ e^(-st) x dt
Using integration by parts again, we get:
L{x} = ∫_0^∞ e^(-st) x dt = [(-e^(-st) x)/s]_0^∞ + (1/s) ∫_0^∞ e^(-st) dt
Since e^(-st) x approaches zero as t approaches infinity, the first term evaluates to zero. We can then simplify the second term using the result from part 2:
L{x} = (1/s) ∫_0^∞ e^(-st) dt = 1/s * (1/s) = 1/s^2
Therefore, the Laplace transform of the function f(x) = x is 1/s^2.
If f(x) = e^(ax), then we have:
L{f(x)} = L{e^(ax)} = ∫_0^∞ e^(-st) e^(ax) dt
Simplifying the integrand, we get:
L{e^(ax)} = ∫_0^∞ e^((a-s)t) dt
We can evaluate this integral using the formula:
∫_0^∞ e^(-bx) dx = 1/b
Setting b = a - s, we get:
L{e^(ax)} = ∫_0^∞ e^((a-s)t) dt = 1/(a-s)
Therefore, the Laplace transform of the function f(x) = e^(ax) is 1/(a-s).
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(3x^3 y^2)^3 (2x^4 y^2)^2
Answer:
108y^10x^17
Step-by-step explanation:
La probabilidad de que un vuelo se retrase es 0. 2 (=20%),¿Cuales son las probabilidades de que no haya demoras en un viaje de ida y vueta
La probabilidad de que no haya demoras en un viaje de ida y vuelta es 0.64 (64%).
How to calculate the probabilities?La probabilidad de que no haya demoras en un viaje de ida y vuelta se puede calcular utilizando la probabilidad complementaria. Si la probabilidad de que un vuelo se retrase es 0.2 (20%), entonces la probabilidad de que no haya retrasos en un vuelo individual es 1 - 0.2 = 0.8 (80%).
Para un viaje de ida y vuelta, la probabilidad de que no haya retrasos en ambos vuelos se calcula multiplicando las probabilidades de no retraso de cada vuelo.
Entonces, la probabilidad de que no haya demoras en un viaje de ida y vuelta sería 0.8 * 0.8 = 0.64 (64%), o 64 de cada 100 viajes de ida y vuelta no experimentarían retrasos.
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the college board sat college entrance exam consists of two sections: math and evidence-based reading and writing (ebrw). sample data showing the math and ebrw scores for a sample of students who took the sat follow. click on the datafile logo to reference the data. student math ebrw student math ebrw 1 540 474 7 480 430 2 432 380 8 499 459 3 528 463 9 610 615 4 574 612 10 572 541 5 448 420 11 390 335 6 502 526 12 593 613 a. use a level of significance and test for a difference between the population mean for the math scores and the population mean for the ebrw scores. what is the test statistic? enter negative values as negative numbers. round your answer to two decimal places.
A t-test with a level of significance of 0.05 results in a test statistic of -2.09, indicating a significant difference between the population mean for the math scores and the population mean for the EBRW scores.
To test for a difference between the population mean for the math scores and the population mean for the ebrw scores, we can conduct a two-sample t-test.
Using a calculator or software, we can find that the sample mean for math scores is 520.5 and the sample mean for ebrw scores is 485.5.
The sample size is n = 12 for both groups.
The sample standard deviation for math scores is s1 = 48.50 and for ebrw scores is s2 = 87.63.
Using a level of significance of 0.05, and assuming unequal variances, we can find the test statistic as:
t = (520.5 - 485.5) / sqrt(([tex]48.50^2/12[/tex]) + ([tex]87.63^2/12[/tex]))
t = 0.851
Rounding to two decimal places, the test statistic is 0.85.
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G(x)=5−2xg, left parenthesis, x, right parenthesis, equals, 5, minus, 2, x Determine for each x xx-value whether it is in the domain of g gg or not
The domain of function is the set of all possible values of x for which the function is defined. In this case, the function G(x) = 5 - 2x is defined for all real numbers of x.
The collection of all feasible input values (x-values) for which a function may be defined is known as the domain of function. In other words, it is the collection of all x values that may be passed into the function and provide a legitimate result (a y-value).
The function G(x) = 5 - 2x in this instance is a linear function, meaning it is defined for all real values of x. This is so that we may plug in any real value for x, and the function will output a real number for G(x) that corresponds. As an illustration, when we enter x = 0, we obtain G(0) = 5 - 2(0) = 5, and when we enter x = 2, we obtain G(2) = 5 - 2(2) = 1.
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Mrs. Dominguez has $9,400 to deposit into two different investment accounts. Mrs. Dominguez will deposit $3,500 into Account I, which earns 6. 5% annual simple interest She will deposit $5,900 into Account II, which earns 6% interest compounded annually. Mrs. Dominguez will not make any additional deposits or withdrawals. What is the total balance of these two accounts at the end of ten years? DE 10
Answer:
Step-by-step explanation:
The total balance of the two investment accounts at the end of ten years will be $16,564.08. To calculate the total balance of the two accounts at the end of ten years,
we need to use the formulas for simple interest and compound interest.
For Account I, the simple interest formula is:
I = Prt
where I is the interest earned, P is the principal (the amount deposited), r is the annual interest rate as a decimal, and t is the time in years.
Plugging in the values for Account I, we get:
I = (3500)(0.065)(10) = $2,275
So, after ten years, the balance in Account I will be:
B1 = P + I = 3500 + 2275 = $5,775
For Account II, the compound interest formula is:
A = P(1 + r/n)^(nt)
where A is the balance at the end of the time period, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
Plugging in the values for Account II, we get:
A = 5900(1 + 0.06/1)^(1*10) = $10,789.08
So, after ten years, the balance in Account II will be $10,789.08.
Therefore, the total balance of the two accounts at the end of ten years will be:
Total balance = Balance in Account I + Balance in Account II
= $5,775 + $10,789.08
= $16,564.08
In summary, by using the formulas for simple interest and compound interest, we can calculate that the total balance of the two investment accounts at the end of ten years will be $16,564.08.
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tim can paint a room in 6 hours . bella can paint the same room in 4 hours . how many hours would it take tim and bella to paint the room while working together y=kx+b
please help me now.
Answer: 3
Step-by-step explanation:
Answer:
2hrs 24 mins
Step-by-step explanation:
Ok so let's make this problem a bit simpler by splitting it up.
Tim paints a room in 6 hours.
So, we can also say that she paints 1/6 of that room in 1 hour
Bella paints it in 4 hours
So, we can also say that she paints 1/4 of that room in 1 hour
Now, lets see what we have:
Bella: 1/4 every hour
Tim: 1/6 every hour
The problem states that they are working together, so we need to add the values we have:
1/4 + 1/6
We cannot just add them, we must make them have the same common denominator.
LCD is 12, you can find that by just doing the times tables for 4 and 6 and seeing what number they match on first.
3/12 + 2/12 = 5/12
So, tim and bella working together paint 5/12 of a room in 1 hour.
They paint 5/12 of a room in 60 minutes
They paint 1/12 of the room in 12 minutes(divide both values by 5)
So if they paint 1/12 of the room in 12 minutes, we can multiply both values by 12 to get our answer.
They paint the full room in 144 minutes(12*12).
144 minutes is 2 hours and 24 minutes
If the Math Olympiad Club consists of 14 students, how many different teams of 6 students can be formed for competitions?
The different teams of 6 students that can be formed for competitions is 3003
How many different teams of 6 students can be formed for competitions?From the question, we have the following parameters that can be used in our computation:
Students = 14
Students in the team = 6
Using the above as a guide, we have the following:
n = 14
r = 6
The different teams of 6 students that can be formed for competitions is calculated as
Teams = nCr
substitute the known values in the above equation, so, we have the following representation
Teams = 14C6
So, we have
Teams = 14!/(6! * 8!)
Evaluate
Teams = 3003
Hence, the different teams of 6 students that can be formed for competitions is 3003
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3. What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively?
Answer:
Step-by-step explanation:
625
Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs. If no interval is specified, use the real numbers, (-00,00). f(x) = -0.002x2 + 4.2x - 50 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. at x= O A. The absolute maximum is at x= and the absolute minimum is (Use a comma to separate answers as needed.) B. The absolute minimum is at x = and there is no absolute maximum. (Use a comma to separate answers as needed.) C. The absolute maximum is at x= and there is no absolute minimum. (Use a comma to separate answers as needed.) D. There is no absolute maximum and no absolute minimum.
The correct choice is: C. The absolute maximum is at x = 1050, and there is no absolute minimum.
To find the absolute extrema of the function f(x) = -0.002x^2 + 4.2x - 50 over the interval (-∞, ∞), we need to find the critical points and then determine if there's a maximum or minimum at each point.
Step 1: Find the derivative of the function f(x) with respect to x. f'(x) = -0.004x + 4.2
Step 2: Set the derivative equal to zero and solve for x. -0.004x + 4.2 = 0 x = 1050
Step 3: Since we have only one critical point, we need to determine if it's a maximum or a minimum. To do this, we can use the second derivative test.
Step 4: Find the second derivative of the function f(x) with respect to x. f''(x) = -0.004
Step 5: Since the second derivative is negative (f''(x) = -0.004 < 0), the critical point x = 1050 corresponds to an absolute maximum. Step 6: Calculate the value of the function f(x) at x = 1050. f(1050) = -0.002(1050)^2 + 4.2(1050) - 50 = 2150
Thus, the absolute maximum is at x = 1050, and the value is 2150. Since the function is a parabola with the "mouth" facing downwards, there is no absolute minimum.
The correct choice is: C. The absolute maximum is at x = 1050, and there is no absolute minimum.
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Question content area toppart 1think about the process at a little-known vacation spot, taxi fares are a bargain. a 24-mile taxi ride takes 32 minutes and costs 9.60 $. you want to find the cost of a 47 taxi ride. what unit price do you need?question content area bottompart 1you need the unit price $
You need the unit price $0.40/mile to find the cost of a 47-mile taxi ride.
What is the unit price needed to calculate the cost of a 47-mile taxi ride in the given scenario?The cost of a 24-mile taxi ride is $9.60, so the cost per mile is 9.6/24 = $0.40/mile.Use the unit price to find the cost of a 47-mile taxi ride
The cost of a 47-mile taxi ride can be found by multiplying the unit price by the number of miles: 0.40/mile x 47 miles = $18.80.Learn more about unit
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From a Word Problem
Jack has $10 in his lunch account. He plans to
spend $2 a week on snacks. How long until
Jack's lunch account reaches zero?
Answer:
Sure, here's the solution to the word problem:
Jack has $10 in his lunch account and plans to spend $2 a week on snacks. To find out how long it will take his lunch account to reach zero, we can divide the total amount of money in his account by the amount he spends each week.
```
$10 / $2 = 5 weeks
```
Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.
Here's another way to solve the problem:
We can also set up an equation to represent the situation. Let x be the number of weeks it takes Jack's lunch account to reach zero. We know that Jack starts with $10 and spends $2 each week, so we can write the equation:
```
$10 - $2x = 0
```
Solving for x, we get:
```
x = 5
```
Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.
Answer:
in 5 weeks he will have 0$ in his account
Step-by-step explanation:
For the class party, Josue and Pho each brought 1 3/5 liters of lemonade. How many liters of lemonade did they bring altogether?
Josue and Pho brought 3 1/5 liters of lemonade altogether
Josue and Pho brought 1 3/5 liters of lemonade each, so the total amount of lemonade they brought is:
1 3/5 + 1 3/5 = 3 1/5
To add the two mixed numbers, we first need to find a common denominator. In this case, the common denominator is 5. Then we convert both mixed numbers into fractions with a denominator of 5:
1 3/5 = (5 × 1 + 3) / 5 = 8/5
1 3/5 = (5 × 1 + 3) / 5 = 8/5
Now we can add the fractions:
8/5 + 8/5 = (8 + 8) / 5 = 16/5
Finally, we can convert the fraction back to a mixed number:
16/5 = 3 1/5
Therefore, Josue and Pho brought 3 1/5 liters of lemonade altogether.
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the line whose equation is 3x-5y=4 is dilated by a scale factor of 5/3 centered at the origin. Which statement is correct?
The correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]y= (\frac{5}{3} )x[/tex] centered at the origin, and the equation of the dilated line is y= (\frac{5}{3} )x
When a line is dilated by a scale factor of k centered at the origin, the equation of the dilated line is given by y = kx, if the original line passes through the origin. If the original line does not pass through the origin, then the equation of the dilated line is obtained by finding the intersection point of the original line with the line passing through the origin and the point of intersection of the original line with the x-axis, dilating this intersection point by the scale factor k, and then finding the equation of the line passing through this dilated point and the origin.
In this case, the equation of the original line is 3x - 5y = 4. To find the intersection point of this line with the x-axis, we set y = 0 and solve for x:
3x - 5(0) = 4
3x = 4
[tex]x = \frac{4}{3}[/tex]
Therefore, the intersection point of the original line with the x-axis is (4/3, 0). Dilating this point by a scale factor of 5/3 centered at the origin, we obtain the dilated point:
[tex](\frac{5}{3} ) (\frac{4}{3},0) = (\frac{20}{9},0)[/tex]
The equation of the dilated line passing through this point and the origin is given by [tex]y= (\frac{5}{3} )x[/tex]. Therefore, the correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]\frac{5}{3}[/tex] centered at the origin, and the equation of the dilated line is [tex]y= (\frac{5}{3} )x[/tex]."
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For each problem, determine what will happen to the first factor.
10x1/2
15 x 7/2
Answer:
52.5
Step-by-step explanation:
15×7=105÷2
=52.5 ans it means fifteen times seven divided by two
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).
The theoretical probability of the spinner not landing on yellow, would be 75 %.
How to find the probability ?In order to calculate the likelihood of the spinner not landing on yellow, it is necessary to initially identify the quantity of non-yellow partitions and subsequently divide this by the full tally of sections. The spinner comprises a total of 8 individual segments.
Of these, two (i.e., sections 2 and 3) are colored in shades of yellow, hence totaling two yellow sectors. This leaves a further six compartments - numbered 1, 4, 5, 6, 7 and 8, that do not fall into the category of "yellow."
The probability is therefore :
= ( Number of not yellow sections ) / ( Total number of sections )
= 6 / 8
= 3 / 4
= 75 %
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Please help
given vectors u and v, find (a)6u (b)6u+4v (c) v-4u
u=(4,5) v=(4,0)
(a) 6u
(b) 6u+4v
(c) v-4u
For the given vectors u and v, (a) 6u = (24, 30). (b) 6u+4v = (40, 30). (c) v-4u = (-12, -20).
Given vectors u and v.
a) To find 6u, we simply multiply each component of u by 6:
6u = 6(4, 5) = (6(4), 6(5)) = (24, 30)
Therefore, 6u = (24, 30).
b) To find 6u + 4v, we first need to find 4v by multiplying each component of v by 4:
4v = 4(4, 0) = (4(4), 4(0)) = (16, 0)
Next, we add 6u and 4v by adding the corresponding components:
6u + 4v = (24, 30) + (16, 0) = (24+16, 30+0) = (40, 30)
Therefore, 6u + 4v = (40, 30).
c) To find v - 4u, we first need to find 4u by multiplying each component of u by 4:
4u = 4(4, 5) = (4(4), 4(5)) = (16, 20)
Next, we subtract 4u from v by subtracting the corresponding components:
v - 4u = (4, 0) - (16, 20) = (4-16, 0-20) = (-12, -20)
Therefore, v - 4u = (-12, -20).
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Lana offered to buy groceries for her roommates, Pam and Cheryl. The total bill was $74. She forgot to save the individual receipts but remembered that Pam's groceries were $0. 05 cheaper than half of her groceries, and that Cheryl's groceries were $2. 10 more than Pam's groceries. How much was each share of the groceries?
Lana paid $36, Pam paid $17.95, and Cheryl paid $20.05, by using substitution or elimination, for the groceries.
Let's start by assigning variables to the unknown quantities in the problem. Let's call the cost of Lana's groceries "L", the cost of Pam's groceries "P", and the cost of Cheryl's groceries "C". We can set up a system of equations based on the information given:
1) P = 0.5L - 0.05 (Pam's groceries were $0.05 cheaper than half of Lana's groceries)
2) C = P + 2.10 (Cheryl's groceries were $2.10 more than Pam's groceries)
3) L + P + C = 74 (the total bill was $74)
We now have three equations with three unknowns, which we can solve using substitution or elimination. Let's use substitution:
Substitute equation 1 into equation 2 for P:
C = (0.5L - 0.05) + 2.10
Simplify:
C = 0.5L + 2.05
Substitute equations 1 and 3 into the equation above:
L + P + C = 74
L + (0.5L - 0.05) + (0.5L + 2.05) = 74
Simplify:
2L + 2 = 74
2L = 72
L = 36
Now that we know the cost of Lana's groceries, we can use equation 1 to find the cost of Pam's groceries:
P = 0.5L - 0.05
P = 0.5(36) - 0.05
P = 17.95
Finally, we can use equation 2 to find the cost of Cheryl's groceries:
C = P + 2.10
C = 17.95 + 2.10
C = 20.05
Therefore, Lana paid $36, Pam paid $17.95, and Cheryl paid $20.05 for the groceries.
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Given the center, a vertex, and one focus, find an equation for the hyperbola:
center: (-5, 2); vertex (-10, 2); one focus (-5-√29,2).
The equation of the hyperbola is -(x + 5)²/71 + (y - 2)² = -71
How to calculate the valueWe can also find the distance between the center and the given focus, which is the distance between (-5, 2) and (-5 - √29, 2):
d = |-5 - (-5 - √29)| = √29
Substituting in the known values, we get:
c² = a² + b²
(√29)² = (10)² + b²
29 = 100 + b²
b² = -71
(x - h)²/a² - (y - k)²/b² = 1
where (h, k) is the center of the hyperbola.
Substituting in the known values, we get:
(x + 5)²/100 - (y - 2)²/-71 = 1
Multiplying both sides by -71, we get:
-(x + 5)²/71 + (y - 2)²/1 = -71/1
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Use the scatter plot to fill in the missing coordinate of the ordered pair.(,12)
Answer: Pairs (0, 14) and (10, 0
Step-by-step explanation:
For each of the following equations, • find general solutions; solve the initial value problem with initial condition y(0)=-1, y'0) = 2; sketch the phase portrait, identify the type of each equilibrium, and determine the stability of each equilibrium. (a) 2y" +9y + 4y = 0 (b) y" +2y - 8y=0 (c) 44" - 12y + 5y = 0 (d) 2y" – 3y = 0 (e) y" – 2y + 5y = 0 (f) 4y" +9y=0 (g) 9y' +6y + y = 0
(a) y(x) = c1 e^(-4x/3) cos(2x) + c2 e^(-4x/3) sin(2x), stable node at the origin;
(b) y(x) = c1 e^(2x) + c2 e^(-4x), unstable node at the origin;
(c) y(x) = c1 e^(-x/22) cos(sqrt(119)x/22) + c2 e^(-x/22) sin(sqrt(119)x/22), stable node at the origin;
(d) y(x) = c1 e^(sqrt(3)x/2) + c2 e^(-sqrt(3)x/2), unstable saddle at the origin;
(e) y(x) = c1 e^x cos(2x) + c2 e^x sin(2x), stable spiral at the origin;
(f) y(x) = c1 cos(3x/2) + c2 sin(3x/2), stable limit cycle around the origin;
(g) y(x) = c1 e^(-x/3) + c2 e^(-x), stable node at the origin.
(a) The characteristic equation is 2r^2 + 9r + 4 = 0, with roots r1 = -4/3 and r2 = -1/2. The general solution is y(x) = c1 e^(-4x/3) cos(2x) + c2 e^(-4x/3) sin(2x). The equilibrium at the origin is a stable node since both eigenvalues have negative real parts.
(b) The characteristic equation is r^2 + 2r - 8 = 0, with roots r1 = 2 and r2 = -4. The general solution is y(x) = c1 e^(2x) + c2 e^(-4x). The equilibrium at the origin is an unstable node since both eigenvalues have positive real parts.
(c) The characteristic equation is 44r^2 - 12r + 5 = 0, with roots r1 = (3 + sqrt(119))/22 and r2 = (3 - sqrt(119))/22. The general solution is y(x) = c1 e^(-x/22) cos(sqrt(119)x/22) + c2 e^(-x/22) sin(sqrt(119)x/22). The equilibrium at the origin is a stable node since both eigenvalues have negative real parts.
(d) The characteristic equation is 2r^2 - 3 = 0, with roots r1 = sqrt(3)/2 and r2 = -sqrt(3)/2. The general solution is y(x) = c1 e^(sqrt(3)x/2) + c2 e^(-sqrt(3)x/2). The equilibrium at the origin is an unstable saddle since the eigenvalues have opposite signs.
(e) The characteristic equation is r^2 - 2r + 5 = 0, with roots r1 = 1 + 2i and r2 = 1 - 2i. The general solution is y(x) = c1 e^x cos(2x) + c2 e^x sin(2x). The equilibrium at the origin is a stable spiral since both eigenvalues have negative real parts and non-zero imaginary parts.
(f) The characteristic equation is 4r^2 + 9 = 0, with roots r1 = 3i/2 and r2 = -3i/2. The general solution y(x) = c1 cos(3x/2) + c2 sin(3x/2), stable limit cycle around the origin.
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Language arts
Common Core
Sixth grade
P. 6 Compare and order rational numbers: word problems ETK
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Manuel and his friends built model cars using pieces of wood and plastic wheels. They rolled
the cars down a ramp and measured to see whose car would coast the farthest. Manuel's car
coasted 10 feet, Richard's car coasted 10. 5 feet, and Diego's car coasted 10
2
feet.
6
How many of the cars coasted more than 10. 75 feet?
Submit
Number of cars that coasted more than 10.75 feet = 1
How many of the cars coasted more than 10.75 feet?To solve this problem, you need to compare the distance each car coasted to 10.75 feet, which is the threshold for determining whether a car coasted more or less than 10.75 feet.
Manuel's car coasted 10 feet, which is less than 10.75 feet, so it did not coast more than 10.75 feet.
Richard's car coasted 10.5 feet, which is also less than 10.75 feet, so it did not coast more than 10.75 feet either.
Diego's car coasted 102 feet, which is more than 10.75 feet. Therefore, only one car coasted more than 10.75 feet, and the answer is 1.
So the answer is:
Number of cars that coasted more than 10.75 feet = 1
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How many of the shapes below are trapeziums?
Answer:
2
Step-by-step explanation:
The K and N are the trapeziums and the two lines opposite to them go in a parallel line
Farmer John is building a new pig sty for his wife on the side of his barn. The area that can be enclosed is modeled by the function A(x) = - 4x^2 + 120x, where x is the width of the sty in meters and A(x) is the area in square meters.
What is the MAXIMUM area that can be enclosed?
the MAXIMUM area that can be enclosed is 900 m²
To find the maximum area that can be enclosed, we need to find the vertex of the parabolic function A(x) = -4x^2 + 120x. The vertex represents the maximum point on the parabola.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a is the coefficient of the x^2 term and b is the coefficient of the x term. In this case, a = -4 and b = 120, so x = -120/(2*(-4)) = 15.
To find the y-coordinate of the vertex, we can substitute x = 15 into the function: A(15) = -4(15)^2 + 120(15) = 900. Therefore, the maximum area that can be enclosed is 900 square meters.
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If Sarah uses 3/4 yard of ribbon to make a hair bow. How many yards of ribbon will Sarah use to make 9 hair bows?
If Sarah uses 3/4 yard of ribbon to make a hair bow, she will need 6 and 3/4 yards of ribbon to make 9 hair bows.
To find out how many yards of ribbon Sarah will use to make 9 hair bows, we need to multiply the amount of ribbon used for one hair bow (3/4 yard) by the number of hair bows she wants to make (9).
So, the equation we need to use is:
3/4 yard of ribbon per hair bow x 9 hair bows = ? yards of ribbon
To solve for the answer, we can simplify the equation:
3/4 x 9 = 27/4
So Sarah will need 27/4 yards of ribbon to make 9 hair bows.
To convert this fraction to a mixed number, we can divide the numerator (27) by the denominator (4) and write the remainder as a fraction:
27 ÷ 4 = 6 with a remainder of 3
In summary, Sarah will need 6 and 3/4 yards of ribbon to make 9 hair bows, if she uses 3/4 yard of ribbon to make one hair bow.
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Matthew is saving money for a pet turtle. The data in the table represent the total amount of money in dollars that he saved by the end of each week.
A graph of the points that represent this data are shown on the coordinate plane attached below.
How to construct and plot the data in a scatter plot?In this scenario, the week number would be plotted on the x-axis (x-coordinate) of the scatter plot while the amount of money (in dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the week number and the amount of money (in dollars), a linear equation for the line of best fit is as follows:
y = 1.19x + 1.05
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What is the value of 45 nickels as a decimal number ?
Answer:
2.25
Step-by-step explanation:
45 nickels
45*5=225
225 cents
2.25
The value of 45 nickels in decimal number can be 2.25.
In the decimal system, each digit's value depends on its position or place value within the number.
A nickel is worth 0.05 dollars.
To find the value of 45 nickels, multiply the number of nickels by the value of each nickel:
So, Value = Number of nickels × Value of each nickel
= 45 × 0.05
= 2.25
Therefore, the value of 45 nickels is $2.25 as a decimal number.
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WILL GIVE BRAINLIEST
Tamara has decided to start saving for spending money for her first year of college. Her money is currently in a large suitcase under her bed, modeled by the function s(x) = 325. She is able to babysit to earn extra money and that function would be a(x) = 5(x − 2), where x is measured in hours. Explain to Tamara how she can create a function that combines the two and describe any simplification that can be done
To create a function that combines the two scenarios, we need to add the amount of money you earn from babysitting to the amount of money you have in your suitcase. We can represent this with the following function:
f(x) = s(x) + a(x)
Where f(x) represents the total amount of money you have after x hours of babysitting. We substitute s(x) with the given function, s(x) = 325, and a(x) with the given function, a(x) = 5(x-2):
f(x) = 325 + 5(x-2)
Simplifying this expression, we can distribute the 5 to get:
f(x) = 325 + 5x - 10
And then combine the constant terms:
f(x) = 315 + 5x
So the function that combines the two scenarios is f(x) = 315 + 5x. This function gives you the total amount of money you will have after x hours of babysitting and taking into account the initial amount of money you have in your suitcase.
In summary, to create a function that combines the two scenarios, we simply add the amount of money earned from babysitting to the initial amount of money in the suitcase. The function f(x) = 315 + 5x represents this total amount of money.
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Complete the sentences about the expressions 3x+4 –2x
, and 5x+2x+x
.
CLEAR CHECK
In the expression 3x+4 –2x
, you can combine
like terms, and the simplified expression is
.
In the expression 5x+2x+x
, you can combine
like terms, and the simplified expression is
For the expressions 3x+4 –2x, and 5x+2x+x the simplified expression after combining like terms is x+4 and 8x.
The given expressions are 3x+4 –2x, and 5x+2x+x
We have to simplify these expressions by combining the like terms
For the expression 3x+4 –2x
We have to combine like terms
x+4
Now for expression 5x+2x+x
Combine the like terms to get
8x
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!!PLEASE HELPP!! (check if I’m right pls)
Answer: It's correct
Step-by-step explanation: