Answer:
$10
Step-by-step explanation:
We Know
Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.
Let C be the total cost, and x be the number of minutes she talks; we have the equation.
C = 0.05x + 10
If Terri does not make any calls, what would her bill be?
C = 0.05(0) + 10
C = $10
So, her bill will be $10
(8,-4) and (-1-2) to the nearest tenth
for class three girls taking classes at a martial art school, there are 4 boys who are taking classes, if there are 236 boys taking classes, predict the number of girls taking classes at the school. what's the answer
There are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.
What is ratio?A ratio is a means to indicate the relative sizes of two or more items for the purpose of comparison. It can be shown with a colon or as a fraction. Mathematicians employ ratios for a variety of purposes, including comparing numbers, scaling up or down, and resolving proportions. Moreover, ratios can be employed in other mathematical processes, simplified, and transformed to percentages or decimals.
Given that for every three girls there are 4 boys in class.
Thus, the proportion can be given as:
4x = 236
x = 59
Now, the proportion of girls are 3x.
3(59) = 177 girls.
Hence, there are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.
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the relation r is defined on z as follows: [ is an even number] prove that the relation is an equivalence relation. for full credit you must prove that the relation is reflexive, symmetric, and transitive using the formal definitions of those properties as shown in lectures. you must give your proof line-by-line, with each line a statement with its justification. you must show explicit, formal start and end statements for the overall proof and for the proof case for each property. you can use the canvas math editor or write your math statements in english. for example, the universal statement that is to be proved was written in the canvas math editor. in english it would be: for all integers m and n, m is related to n by the relation r if, and only if, the difference m minus n is an even number.
Let m and n be two arbitrary integers. We want to prove that the relation R is an equivalence relation, i.e. it is reflexive, symmetric, and transitive.
Reflexive: We must show that mRm for all m ∈ Z.
Since the difference of m and m is 0, which is an even number, we have mRm.
Therefore, the relation R is reflexive.
Symmetric: We must show that if mRn, then nRm.
Let mRn, i.e., the difference of m and n is an even number.
Then the difference of n and m is also an even number.
Therefore, nRm, and the relation R is symmetric.
Transitive: We must show that if mRn and nRp, then mRp.
Let mRn and nRp, i.e., the difference of m and n is an even number and the difference of n and p is also an even number.
The sum of the difference of m and n and the difference of n and p is the difference of m and p, which is an even number.
Therefore, mRp, and the relation R is transitive.
Since the relation R is reflexive, symmetric, and transitive, it is an equivalence relation.
Conclusion: The relation R is an equivalence relation.
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The Tire Rack, America’s leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 the highest rating) for 18 maximum performance summer tires (Tire Rack website, February 3, 2009). The variable Steering rates the tire’s steering responsiveness, Tread Wear rates quickness of wear based on the driver’s expectations, and Buy Again rates the driver’s overall tire satisfaction and desire to purchase the same tire again. (Data is in TireRack file)
1. Develop an estimated regression equation that can be used to predict the Buy Again rating given based on the Steering rating. At the .05 level of significance, test for a significant relationship. Interpret the coefficients (Say what they mean in terms of change in you corresponding to a change in x)
2. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain.
3. Develop an estimated regression equation that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating.
4. Is the addition of the Tread Wear independent variable significant? Use 0.05 level of significance.
1 Tire Steering read WeaBuy Again 2 Goodyear 8.9 8.5 8.1 3 Michelin F89 9 8.3 4 Michelin H 8.3 8.8 8.2 5 Dunlop SI 8.2 8.5 7.9 6 Goodyear 7.9 7.7 7.1 7 Yokoham 84 8.2 8.9 8 Yokoham 7.9 7 7.1 9 Kumho P 7.9 7.9 8.3 10 Goodyear 7.6 5.8 4.5 11 Hankook 7.8 6.8 6.2 12 Michelin E 7.4 4.8 13 IMichelin N7 14 Michelin S 6.9 15 Kumho 776.6 16 Dunlop SI 6.2 4.2 17 Bridgestof 5.7 5.5 18 Goodyear 5.7 5.4 19 Dunlop SI57 5 5 34 3.6 2.9 3.3
Tire Steering Tread Wear Buy Again
Goodyear Assurance TripleTred 8.9 8.5 8.1
Michelin HydroEdge8.9 9 8.3
Michelin Harmony 8.3 8.8 8.2
Dunlop SP 60 8.2 8.5 7.9
Goodyear Assurance ComforTred 7.9 7.7 7.1
Yokohama Y372 8.4 8.2 8.9
Yokohama Aegis LS4 7.9 7 7.1
Kumho Power Star 758 7.9 7.9 8.3
Goodyear Assurance 7.6 5.8 4.5
Hankook H406 7.8 6.8 6.2
Michelin Energy LX4 7.4 5.7 4.8
Michelin MX4 7 6.5 5.3
Michelin Symmetry 6.9 5.7 4.2
Kumho 722 7.2 6.6 5
Dunlop SP 40 A/S 6.2 4.2 3.4
Bridgestone Insignia SE200 5.7 5.5 3.6
Goodyear Integrity 5.7 5.4 2.9
Dunlop SP20 FE 5.7 5 3.3
Show transcribed image text
The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.
The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.
The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.
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Two lines are plotted on the same coordinate plane. The first line passes through the points (-5, -5) and (-3, -3). The second line passes through the points (3, 1) and (4, 2). The two lines are best described as:
A. intersecting, not perpendicular
B. intersecting and perpendicular
C. parallel
D. no relationship
The slopes of the two line are equal. Hence, the two lines are parallel.
What is slope of a line?A line's slope is a gauge of the line's steepness. The ratio of the vertical change (change in y) to the horizontal change (change in x) between any two locations on the line is what is meant by this term. When a line moves from left to right, the slope might be positive, negative, zero, or undefined. When a line moves from left to right, the slope can be negative (when the line is vertical). The slope is determined using the following formula and is represented by the letter m:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
Given that, the first line passes through the points (-5, -5) and (-3, -3).
The slope is given by:
slope = (change in y) / (change in x)
slope = (-3 - (-5)) / (-3 - (-5)) = 1
The second line passes through the points (3, 1) and (4, 2).
slope = (2 - 1) / (4 - 3) = 1
The slopes of the two line are equal. Hence, the two lines are parallel.
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Lara opened a savings account 1 year ago. The account earns 11% interest, compounded
continuously. If the current balance is $7,000.00, how much did she deposit initially?
Round your answer to the nearest cent.
As a result, Lara made a $6,262.71 initial deposit into her savings account.
How long will it take for your money to double if the interest rate is 12% annually compounded?A credit card user who pays 12% interest (or any other loan type that charges compound interest) will double their debt in six years. The rule can also be applied to determine how long it takes for inflation to cause money's value to decrease by half.
To calculate the initial investment, we can apply the continuous compounding formula:
A = Pe(rt)
Where:
A = the current balance ($7,000.00)
P = the initial deposit (unknown)
r = the annual interest rate (11% or 0.11 as a decimal)
t = the time in years (1 year)
Plugging in these values, we get:
$7,000.00 = Pe(0.11 * 1)
A shorter version of the exponential expression:
$7,000.00 = Pe0.11
$7,000.00 = P * 1.1166 (rounded to 4 decimal places)
Dividing both sides by 1.1166:
P = $6,262.71 (rounded to the nearest cent)
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2(2x-5)=-18 solve the equation algebraically. show all work
Answer:
Step-by-step explanation:
2(2x-5) = 18 (FOIL)
4x-10=18
4x = 28
x= 7
Answer:
x = -2
Step-by-step explanation:
2(2x - 5) = -18
Divide both sides by 2.
2x - 5 = -9
Add 5 to both sides.
2x = -4
Divide both sides by 2.
x = -2
a fraction nonconforming control chart is to be established with a center line of 0.01 and two-sigma control limits. (a) how large should the sample size be if the lower control limit is to be nonzero? (b) how large should the sample size be if we wish the probability of detecting a shift to 0.04 to be 0.50?
a) Sample size if the lower control limit is to be nonzero: 50
b) Sample size if the probability of detecting a shift to 0.04 is to be 0.50: 100
a) How large should the sample size be if the lower control limit is to be nonzero?
n = (2σ / d)²We know that:
Center line (CL) = 0.01
Sigma (σ) = LCL = 0.005
d = Centerline - LCL = 0.01 - 0.005 = 0.005
Substituting the values in the formula, we get
n = (2 * 0.005 / 0.01)²= 50 Hence, if the lower control limit is to be nonzero, the sample size should be 50.
b) How large should the sample size be if we wish the probability of detecting a shift to 0.04 to be 0.50?
The probability of detecting a shift to 0.04 is denoted by β and is calculated using the following formula:
β = Φ [(-Zα/2 + Zβ) / √ (p₀q₀/n)], Where, Φ is the standard normal distribution function, Zα/2 is the critical value for the normal distribution at the (α/2)th percentile, Zβ is the critical value for the normal distribution at the βth percentile, p₀ is the assumed proportion of nonconforming items, q₀ is 1 – p₀, and n is the sample size.
In order to determine the sample size, we must first select a value for β. If we select a value for β of 0.50, then β = 0.50. This implies that we have a 50% chance of detecting a shift if one occurs. Since the exact value for p₀ is unknown, we assume that p₀ = 0.01, which is equal to the center line.
n = (Zα/2 + Zβ)² p₀q₀ / β², Substituting the values in the formula, we get,
n = (Zα/2 + Zβ)² p₀q₀ / β²= (1.96 + 0.674)² (0.01) (0.99) / 0.50²= 99.7 ≈ 100
Hence, if we wish the probability of detecting a shift to 0.04 to be 0.50, the sample size should be 100.
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three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. kaitlyn got a score of 74.5 ; this version has a mean of 68.5 and a standard deviation of 12 . kiersten got a score of 244.8 ; this version has a mean of 210 and a standard deviation of 29 . rebecca got a score of 7.24 ; this version has a mean of 6.7 and a standard deviation of 0.3 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Step-by-step explanation:
kaitlyn score is 6 points above the mean
z-score = 6 / 12 = .5
kiersten score is 34.8 above the mean z-score = 34.8/29 = 1.2
rebecca score is .54 above the mean z -score = .54/ .3 = 1.8
rebecca scored the highest percentile (highes z-score) of the three....the best
The number of bacteria in a culture is growing at a rate of 3,000e^(2t/5) per unit of time t. At t=0, the number of bacteria present was 7,500. Find the number present at t=5.a. 1.200 e^2b. 3,000 e^2c. 7,500 e^2d. 7,500 e^5e. 15.000/7 e^7
The number of bacteria present with the given growth rate at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.
What is exponential growth?An exponential growth pattern is one in which the rate of increase is proportionate to the value of the quantity being measured at any given time. This indicates that the amount by which the quantity increases in each period is a constant proportion of the quantity's present value. Many branches of mathematics and science, such as physics, biology, and finance, utilise exponential growth. Modeling population expansion, the spread of infectious illnesses, the decay of radioactive materials, and the behavior of financial assets are all popular applications.
Given that, the number of bacteria present was 7,500.
The exponential growth is given by the formula:
[tex]N(t) = N(0) * e^{(kt)}[/tex]
Substituting the values N(0) = 7,500 and the growth rate is k = 2/5 we have:
[tex]N(5) = 7,500 * e^{(2/5 * 5)}\\N(5) = 7,500 * e^2[/tex]
Hence, the number of bacteria present at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.
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please help me
9-9÷9÷9-9÷9
Answer:
0
Step-by-step explanation:
0
Thank me...........
use the unique factorization theorem to write the following integers in standard factored form. (a) 504 (b) 819 (c) 5,445
Using the Unique factorization theorem for the following integers the standard factored form of 504 is 2³ x 3²x 7 , for 819 is 3² ×7×13 and for 5,445 is 3²×5×7².
The Unique Factorization Theorem states that any positive integer can be written as a product of prime numbers in a unique way. To write each of the integers in standard factored form.
Using this theorem, we can factorize any positive integer into its prime factors. Here are the steps to factorize a number:
Find the smallest prime factor of the number. Divide the number by this prime factor, and repeat step 1 with the result. Continue this process until the result is 1.The prime factors obtained in this process can then be multiplied together to obtain the standard factored form of the original number . Therefore,
)504 = 2³ x 3² x 7)819 = 3² ×7×13)5,445 =3²×5×7²To learn more about 'Unique Factorization Theorem':
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What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
WILL GIVE BRAINLIEST 15 POINTS PLEASEE Fill in the blanks pleaseee
Therefore, we have the values of:
a = -g(x) for -10 < x < -8
b = lower limit of the range where g(x) = -6
c = -C for -1 < x < 1
d = upper limit of the range where g(x) = 4
e = we cannot determine the value of e based on the given information.
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.
Here,
We can find the values of a, b, c, d, and e by examining the given information:
For -15 < x < -10: g(x) = -(-10) = 10
For -10 < x < -8: g(x) = -a
For -1 < x < 1: g(x) = -C
For b < x < l: g(x) = -(-6) = 6
For 10 < x < 15: g(x) = -8
For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.
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Y=5x+17 Y=-2x+4 solve with elimination
Answer:
x = -13/7
y = 54/7
Step-by-step explanation:
Y = 5x + 17 Y = -2x + 4
5x + 17 = -2x + 4
7x + 17 = 4
7x = -13
x = -13/7
Not put -13/7 in for x and solve for y
y = 5(-13/7) + 17
y = 54/7
So, the answer is x = -13/7 and y = 54/7
Answer: x = -13 / 7, y = 54/7
Step-by-step explanation:
To eliminate a variable, we can substitute y for 5x + 17
We get 5x + 17 = -2x + 4
7x = -13
x = -13 / 7
Substituting x into the 2nd equation y = 5 * -13 / 7 + 17
y = 119/7 - 65/7
y = 54/7
243➗ _ =81
Multiplying and dividing integers
Given:
81x = 243x
= 243 / 81x
= 3
Answer:x = 3
h(x)= -x + 5, solve for x when h(x) = 3
According to the given information, the solution to H(x) = 3 is x = 2.
What is equation?
In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS and RHS are separated by an equals sign (=), indicating that they have the same value. The general form of an equation is: LHS = RHS
To solve for x when H(x) = 3, we substitute 3 for H(x) in the equation and solve for x:
H(x) = -x + 5
3 = -x + 5
Subtracting 5 from both sides, we get:
-2 = -x
Multiplying both sides by -1, we get:
2 = x
Therefore, the solution to H(x) = 3 is x = 2.
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[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{h(x) = -x + 5}\\\\\mathtt{3 = -x + 5}\\\\\mathtt{-x + 5 = 3}\\\\\textsf{SUBTRACT 5 to BOTH SIDES}\\\\\mathtt{-x + 5 - 5 = 3 - 5}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{-x = 3 - 5}\\\\\mathtt{-x = -2}\\\\\mathtt{-1x = -2}\\\\\textsf{DIVIDE }\mathsf{-1}\textsf{ to BOTH SIDES}\\\\\mathtt{\dfrac{-1x}{-1} = \dfrac{-2}{-1}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{x = \dfrac{-2}{-1}}\\\\\mathtt{x = 2}[/tex]
[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
An object moves in the xy-plane so that its position at any time tis given by the parametric equations X(0 = ? _ 3/2+2andy (t) = Vt? + 16.What is the rate of change of ywith respect t0 when t = 3 1/90 1/15 3/5 5/2'
The given parametric equations are X(t) = -3/2 + 2t and y(t) = vt² + 16, the rate of change of y with respect to "t" when t = 3 is 6v
We have the parametric equations that are X(t) = -3/2 + 2t and y(t) = vt² + 16.
At time t, the rate of change of y with respect to t is given by the derivative of y with respect to t, that is dy/dt.
So, y(t) = vt² + 16
Differentiating with respect to t, we get
⇒ dy/dt = 2vt.
Now, t = 3 gives us,
y(3) = v(3)² + 16 ⇒ 9v + 16.
Therefore, the rate of change of y with respect to t at t = 3 is
dy/dt ⇒ 2vt ⇒ 2v(3) ⇒ 6v.
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A box with a square base and open top must have a volume of 62500 cm3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A'(x). A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x² .] A'(x) = 0 when x =
The area of the square base = x².
we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...
The dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.
To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.
Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x
Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x² A'(x) = 0 when x = (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
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Head Stevedore loads extra large boxes, also in the shape of perfect cubes. The volume of each box is 512 cubic feet
As per the volume, the dimension of an Extra Large Box is 3.78 feet.
Let's call the length of one side of the cube "s". Since the volume of the cube is given as 512 cubic feet, we can set up an equation to relate the volume to the length of one side:
Volume of cube = s³ = 512 cubic feet
To solve for "s", we can take the cube root of both sides of the equation:
s = ∛512
We can simplify this expression by finding the prime factorization of 512:
512 = 2⁹
Therefore, we can rewrite the expression for "s" as:
s = ∛2⁹
Using the properties of exponents, we know that the cube root of 2^9 is the same as 2 raised to the power of (1/3) times 9:
s = [tex]2^{1/3} \times 9^{1/3}[/tex]
We can simplify this expression further by recognizing that 9 is a perfect cube, and its cube root is 3:
s = [tex]2^{1/3} \times 3[/tex]
Therefore, the length of one side of the cube-shaped box is:
s = [tex]2^{1/3} \times 3[/tex] feet
Since all sides of the cube are equal in length, the dimensions of the box are:
Length = Width = Height = [tex]2^{1/3} \times 3[/tex] feet = 3.78 feet.
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Complete Question:
Head Stevedore loads Extra Large Boxes, also in the shape of perfect cubes. The volume of each box is 512 cubic feet. What are the dimension of an Extra Large Box?
suppose that 27.5% of car engines will fail if they have not had routine maintenance in the past five years. if routine maintenance is given to 23 cars, what is the probability that exactly 10 will not have engine failure? round your answer to six decimal places.
The probability that exactly 10 out of 23 cars will not have engine failure is 0.007638.
Step-by-step explanation: First, calculate the probability of an engine failing in five years with no routine maintenance, which is 27.5%. This can be written as a decimal, 0.275.Next, calculate the probability of an engine not failing in five years with routine maintenance. This probability is 100%-27.5% = 72.5%, written as a decimal 0.725.
Now, using the Binomial Distribution formula (nCr), calculate the probability of exactly 10 engines not failing out of 23 cars, where n = 23, r = 10 and p = 0.725. The equation would be [tex](23C10)*(0.725^{10})*(0.275^{13}) = 0.0076379904[/tex]
Finally, round the result to 6 decimal places, giving an answer of 0.007638.
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The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value proble,dN/dt=N(1-0.0005N), N(0)=1(a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedure over a long period of time.dN/dt = N(1 − 0.0005N), N(0) = 1.(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a).How many supermarkets are expected to adopt the new technology whent = 15?(Round your answer to the nearest integer.)
(a) To predict how many supermarkets are expected to adopt the new procedure over a long period of time, we can analyze the behavior of the differential equation using a phase portrait.
The equation can be rewritten as dN/N = (1-0.0005N)dt. Integrating both sides, we get ln|N| = t - 0.0005N^2/2 + C, where C is the constant of integration. Solving for N, we have:
N(t) = +/- sqrt((2ln|N| - 2C)/0.001)
We can see that the solutions are of the form of a hyperbola, with N approaching the asymptotes y=0 and y=2000. The equilibrium point is N=0, which is unstable, and the critical point is N=2000, which is stable.
Therefore, over a long period of time, we expect the number of supermarkets using the computerized checkout system to approach 2000.
(b) To solve the initial-value problem, we can use the separation of variables:
dN/N = (1-0.0005N)dt
ln|N| = t - 0.00025N^2 + C
N(0) = 1
Substituting N=1 and t=0, we get C=0. Therefore, the solution is:
ln|N| = t - 0.00025N^2
N = e^(t-0.00025N^2)
Using a graphing utility, we can plot the solution curve for N(t):
The graph confirms that the solution curve approaches 2000 as t increases.
When t=15, we can evaluate N(15) using the solution:
N(15) = e^(15-0.00025N^2)
Rounding to the nearest integer, we get N(15) = 1719.
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Unit 7 polygons and quadrilaterals
Homework 7 trapezoids
** this is a 2-page document **
Directions: if each quadrilateral below is a trapezoid, find the missing measures
Angle L can be calculated as follows:
angle L = angle - 180 LMO stands for angle. MNO \sangle L = 180 - 150 - 30 degree angle L = 0
As a result, angle L is 0 degrees.
1. We know that sides AB and CD of trapezoid ABCD are parallel. We can use the tangent function to find the length of side AD because angle B is a right angle and angle ABD is 45 degrees:
AD/AB = tan(45)
AD=AB * tan(45) AD=AB
As a result, AD = 10.
2. We know that the sides PQ and RS of the trapezoid PQRS are parallel. We can use the sine function to find the length of side PS because angle Q is a right angle and angle PSQ is 60 degrees:
PS/QS sin(60) =
PS = sin * QS (60)
5 * sqrt = PS (3)
As a result, PS = 5*sqrt (3).
3. We know that the sides UV and WX of a trapezoid UVWX are parallel. We can use the cosine function to find the length of side WU because angle V is a right angle and angle WVU is 30 degrees:
WU/UV cos(30) =
UV * cos WU (30)
5 * sqrt(3) / 2 = WU
As a result, WU = (5/2)*sqrt (3).
4. We know that the sides LM and NO of the trapezoid LMNO are parallel. We can use the sine function to find the length of side MO because angle L is a right angle and angle MNO is 30 degrees:
MO/NO sin(30) =
MO = 4 / 2 MO = NO * sin(30)
As a result, MO = 2.
Because angles MNO and LMO add up to 180 degrees, we can calculate angle LMO as follows:
LMO angle = 180 - angle LMO MNO angle = 150 degrees
Finally, because angle N is a right angle, we can calculate angle L as follows:
angle L = angle - 180 LMO stands for angle. MNO\sangle L = 180 - 150 - 30 degree angle L = 0
As a result, angle L is 0 degrees.
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assistants please --------> The members of a weight loss support group just collectively weighed in at 1,519 pounds, which is 2% lighter than their previous weight. How much did the group weigh last time?
Work Shown:
x = previous total weight
2% of x = 0.02x = amount of weight lost
x - 0.02x = 0.98x = current total weight
0.98x = 1519
x = 1519/0.98
x = 1550 pounds
Check:
2% of 1550 = 0.02*1550 = 31
The group collectively lost 31 pounds.
1550-31 = 1519
The answer is confirmed.
Note that 98% of 1550 = 0.98*1550 = 1519
what type of data is a questionnaire
Answer:
A questionnaire can collect quantitative, qualitive or both types of data.
Step-by-step explanation:
Answer:
Categorical data
Step-by-step explanation:
Data that relates to certain categories e.g males, females or any types of car
In 915. 23, the digit 3 is in the
place.
Answer:
hundreth
Step-by-step explanation:
the 2 is in the tenth and the 3 is in the hundreth
The Jones family has two dogs whose ages add up to 15 and multiply to 44. How old is each dog?
As per the equations, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.
What is factoring?Factoring is the process of breaking down a mathematical expression or number into its component parts, which can then be multiplied together to give the original expression or number. In algebra, factoring is often used to simplify or solve equations.
What is an equation?An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). The expressions on both sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation.
In the given question,
Let's call the age of the first dog "x" and the age of the second dog "y". We know that their ages add up to 15, so we can write:
x + y = 15
We also know that their ages multiply to 44, so we can write:
x * y = 44
Now we have two equations with two unknowns, which we can solve simultaneously to find the values of x and y.
One way to do this is to use substitution. From the first equation, we can solve for one variable in terms of the other:
y = 15 - x
We can substitute this expression for y into the second equation:
x × (15 - x) = 44
Expanding the left side, we get:
15x - x^2 = 44
Rearranging and simplifying, we get a quadratic equation:
x^2 - 15x + 44 = 0
We can factor this equation as:
(x - 11)(x - 4) = 0
Using the zero product property, we know that this equation is true when either (x - 11) = 0 or (x - 4) = 0.
Therefore, the possible values of x are x = 11 and x = 4.If x = 11, then y = 15 - x = 4, which means that the ages of the two dogs are 11 and 4.
If x = 4, then y = 15 - x = 11, which means that the ages of the two dogs are 4 and 11.
Therefore, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.
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Find the probability of
drawing a spade, then
drawing a face card out of a
deck
The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).
What is the probability?The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.
Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.
To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:
P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)
= (1/4) x (12/51)
= 3/52
Therefore, the probability of drawing a spade, then drawing a face card out of a deck is [tex]3/52[/tex] , or approximately [tex]0.0588[/tex] (rounded to four decimal places).
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Rosa wants to Invest $1400 a savings account that pays 4.4% simple Interest. How long will take for this investment to double In value? Round your answer to the nearest tenth.
Answer: 31.8 years
Step-by-step explanation:
The formula to calculate the simple interest is:
I = Prt
where:
I = Interest
P = Principal amount
r = Rate of interest
t = Time (in years)
We want to know how long it will take for the investment to double in value. That means the interest earned should be equal to the principal amount. So, we can write:
2P = P + I
Simplifying:
P = I
Now, we can substitute the values given in the problem:
1400 = 14000.044t
Simplifying:
t = 1400/(1400*0.044) = 31.82 years
Therefore, it will take approximately 31.8 years for the investment to double in value.
statistical literacy (a) if we have a distribution of x values that is more or less mound-shaped and somewhat symmetric, what is the sample size needed to claim that the distribution of sample means x from random samples of that size is approximately normal? (b) if the original distribution of x values is known to be normal, do we need to make any restriction about sample size in order to claim that the distribution of sample means x taken from random samples of a given size is normal
It is important to be aware that the distribution of sample means x may not match the distribution of the original x values exactly, due to sampling variability.
then the sample size needs to be larger, possibly 50 or 30the sample size needed to claim that the distribution of sample means x from random samples of that size is approximately normal depends on the shape of the original distribution of x values. If the distribution is mound-shaped and somewhat symmetric, then the sample size needs to be fairly large, around 30 or more. However, if the original distribution of x values is strongly skewed or has outliers statisticl literacyif the original distribution of x values is known to be normalize size needs to be large, then the sample size does not need to be restricted in order to claim that the distribution of sample means x taken from random samples of a given size is normal. The sample size should still be at least 30, as this is necessary to produce a reliable result.
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