Wanda sews small and large gloves. It takes her 45 minutes to sew a small pair of gloves and 120 minutes to sew a large pair of gloves. The costs of producing the gloves are $2 for a small pair and $4 for a large pair. Wanda has 16 hours available to sew gloves. The materials to make the gloves must cost at most $40. The system of linear inequalities represents this situation. {45x+120y≤9602x+4y≤40 What does the solution (16, 2) represent?

The mass and center of mass of the lamina is [tex]\frac{8}{15} k, (0, \frac{4}{7} )[/tex]

The mass of a homogenous lamina is given by [tex]$m=\iint_R \delta(x, y) d A$[/tex]

We can rewrite the equation using the limits of integration as [tex]$$m=\int_a^b \int_c^d \delta(x, y) d y d x$,[/tex] where a ≤ x ≤ b and c ≤ y ≤ d.

The objective is to find the mass and center of mass of the lamina that occupies the region D.

From the given equations, we get the limits of integration as -1 ≤ x ≤ 1 and  0 ≤ x ≤ 1-[tex]x^{2}[/tex]. Substitute the known values in the equation.

[tex]$$\begin{aligned}& m=\int_{-1}^1 \int_0^{1-x^2} k y d y d x \\& =\int_{-1}^1 \frac{1}{2} k\left(1-x^2\right)^2 d x \\& =\frac{1}{2} k \int_{-1}^1\left(1+x^4-2 x^2\right) d x \\& =\frac{k}{2}\left[x+\frac{x^5}{5}-2 \frac{x^3}{3}\right]_{-1}^1 \\\\\end{aligned}$$[/tex]

[tex]& =\frac{k}{2}\left[1+\frac{1}{5}-\frac{2}{3}+1+\frac{1}{5}-\frac{2}{3}\right] \\\\& =\frac{k}{2}\left[\frac{16}{15}\right] \\\\& =\frac{8}{15} k[/tex]

Hence, the mass of the lamina as [tex]\frac{8}{15} k[/tex].

The center of mass of the lamina is given by[tex]$(\bar{x}, \bar{y})$[/tex], where [tex]$$\begin{gathered}\bar{x}=\frac{1}{m} \iint_R x \delta(x, y) d A \text { and } \\\bar{y}=\frac{1}{m} \iint_R y \delta(x, y) d A .\end{gathered}$$[/tex]

First, find [tex]$\bar{x}$[/tex] as follows:

[tex]$$\begin{aligned}\bar{x} & =\frac{1}{\frac{8}{15} \mathrm{k}} \int_{-1}^1 \int_0^{1-x^2} k x y d y d x \\& =\frac{1}{\frac{8}{15} \mathrm{k}} \int_{-1}^1 \frac{1}{2} k x\left(1-x^2\right)^2 d x \\= & \frac{15}{8 k} \cdot \frac{k}{2} \int_{-1}^1 x\left(1+x^4-2 x^2\right) d x \\= & \frac{15}{16}\left[\frac{x^2}{2}+\frac{x^6}{6}-2 \frac{x^4}{4}\right]_{-1}^1 \\= & 0\end{aligned}$$[/tex]

Thus, the  [tex]$\bar{x}$[/tex]-coordinate of the center of gravity as 0 .

Now, evaluate [tex]$\bar{y}$[/tex].

[tex]& \bar{y}=\frac{1}{\frac{8}{15}} \int_{-1}^1 \int_0^{1-x^2} k y^2 d y d x \\\\& =\frac{1}{\frac{8}{15}} \int_{-1}^1 \frac{1}{3} k\left(1-x^2\right)^3 d x \\\\& =\frac{15}{8 k} \cdot \frac{k}{3} \int_{-1}^1\left(1-x^6-3 x^2+3 x^4\right) d x \\\\& =\frac{15}{24}\left[x-\frac{x^7}{7}-3 \frac{x^3}{3}+3 \frac{x^5}{5}\right]_{-1}^1 \\\\& =\frac{15}{24} \times \frac{32}{35} \\\\& =\frac{4}{7}[/tex]

Hence, the center of gravity of the lamina is ([tex]0, \frac{4}{7}[/tex]).

Therefore,  the mass and center of mass of the lamina that occupies the region D is [tex]\frac{8}{15} k[/tex], [tex](0, \frac{4}{7} )[/tex]

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Answer:

For the first one, shade in 1 circle at the start

Then shade in 9/4 more, so you would fully shade 2 more because every 4 equals 1.

Then shade 1 quarter of the next circle, or 1 of the 4 portions of the next circle.

____________________________________

For the second one, shade in 2 circles at the start

Then shade 8/5 more, so fully shade one more because every 5 numbers equals one shaded circle.

Then shade 3/5 of the next circle. So you would shade 3 of the 5 portions of the circle

The sequence is a geometric sequence with a common ratio of 7. Since, the common ratio is greater than 1, the sequence diverges.

A convergent series is a series whose partial sums tend to a specific number, also called a limit. A divergent series is a series whose partial sums, by contrast, don't approach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

The given sequence is 1/117659, 1/16807, 1/2401...

Here, common ratio is

1/16807 ÷ 1/117659

= 1/16807 × 117659/1

= 117659/16807

= 7

Now, 1/2401 ÷ 1/16807

= 1/2401 × 16807/1

= 16807/2401

= 7

Hence, the sequence is a geometric sequence with a common ratio of 7. Since, the common ratio is greater than 1, the sequence diverges.

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Answer:

b). parameter

Step-by-step explanation:

A parameter is a fixed value in the model that is not a decision variable and is not changed during the optimization process. It is used to represent known quantities that are used in the model but are not being optimized. For example, in a linear programming model, the cost of a product may be represented by a parameter, as the cost is not a decision variable and is fixed.

The triangle after translation will have coordinates A'(-9, 7), B'(-6, 10) and C'(-3, 5)

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a triangle A(-5,1) B(-2,4) C(1,-1) is being translated 4 units left and 6 units up

To translate the point P(x, y), a units left and b units up, use P'(x-a, y+b).

Therefore, coordinates for A'B'C' are =

A(-5, 1) = A'(-5-4, 1+6) = (-9, 7)

B(-2, 4) = B'(-2-4, 4+6) = (-6, 10)

C(1, -1) = C'(1-4, -1+6) = (-3, 5)

Hence, The triangle after translation will have coordinates A'(-9, 7), B'(-6, 10) and C'(-3, 5)

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The entire surds are √128, √225,√180, √117 respectively

An entire surd is a surd in which the entire number is under the root sign.

Given here are 8√2,5√9,6√5,3√13

thus their entire roots are  8√2 =√2×64

                                                   = √128

again, 5√9 = √9×25

                   = √225

          6√5=√5×36

                 = √180

Similarly 3√13= √117

Hence, the respective entire surds are √128, √225,√180, √117

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The number of cups sold at the first game is 55.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of each souvenir = $2.25

The total amount collected from the souvenir cups sales = $123.75

The number of cups sold at the first game.

= 123.75/2.25

= 55

Thus,

The number of cups sold is 55.

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Answer: 1. Given two sides

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.

Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point

[tex]r(x) = f(g(x))[/tex]therefore the derivative of r is given by [tex]r'(x) = f'g(x)\times g'(x)[/tex]

[tex]r'(1) = f'(g(1))\times g'(1)[/tex] from the graphs

r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0

Similarly s'(1) = g'(f(1))\times f'(1) from the graphs

 f(1)=1.5, f'(1)

=\dfrac{ (3-0)}{(0-2)}

= -3/2 , g'(3/2) = 0

s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0

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Complete question:

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

Noel can expect to earn a total profit of $572 if he sells all 22 blocks at the fair. Profit is an important measure of the financial performance of a business.

Profit is the amount of money that is gained from a business activity after all expenses have been paid. It is calculated by subtracting the costs of producing or acquiring a product or service from the revenue generated by selling that product or service.

To find the total profit that Noel can expect to earn from selling all 22 blocks, we need to multiply the profit from each block by the number of blocks he plans to sell.

We can use the following equation to calculate the total profit:

Total profit = Profit per block x Number of blocks

Plugging in the values we know, we get:

Total profit = $26 x 22 = $<<26*22=572>>572

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a) The velocity of particle at t=2s is 5m/s

b) The velocity of particle at t=4s is 20m/s

To obtain the function of velocity from the graph we need to find the equation of accleration- time graph

so the equation of accleration is :

a= [tex]\frac{10-0}{4-0}[/tex]t

a= 5/2t

and we know that :

a= [tex]\frac{dv}{dt}[/tex]

=> dv= adt

=> dv= [tex]\frac{5}{2}[/tex] t dt

integrating both side we get:

v= [tex]\frac{5}{4}[/tex][tex]t^2[/tex]  +c

where c is constant

it is given that at t=0s it starts from rest so

v=0 at t=0

=> 0 = 0+c

=>c=0

so v=[tex]\frac{5}{4}t^2[/tex] ---- (i)

a) as we have got the equation of velocity with respect to time

 we have to find velocity at t=2s

putting t=2s we get

 v = 5/4 *4

 so velocity of particle at t=2s is 5m/s

b) as we have got the equation of velocity with respect to time

 we have to find velocity at t=4s

putting t=4s we get

 v = 5/4 *16

 so velocity of particle at t=2s is 20m/s

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equation of simple straight line

Complete question:

the figure shows the acceleration graph for a particle given that particle starts from rest at t=0.

determine the velocity of partice at

a)2s

b)4s

The sample of toys below are likely to have come from a population with mean price greater than $10 then the p-value of the test is 0.139.

R code

⇒ x = c(10,12,15,8,9,10,13,7,20,10)

⇒ t.test(x,mu = 10, alternative = "greater")

on sample t test

data: x

t = 1.1543, df = 9, p value = 0.1391

alternative hypothesis: true mean is greater than 10

95 percent confidence interval:

9.176629 Inf

sample estimates:

mean of x

11.4

Hence we get the required answer.

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The option that gives the number of solutions to the system of equations is given as follows:

A. One solution.

For a system of linear equations, the system is composed by multiple lines, and the number of solutions is defined according to the features of the lines.

The possible numbers of solutions are given as follows:

From the graph given in this problem, we have that the two lines intersect at one point, hence the system of equations has one solution and the correct option is given by option A.

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Answer:

Account A = $20.8

Account B = $

Step-by-step explanation:

how much is the principal in each​ account?

Formula  = (P x R x T)/100

Account A: -

2.00 = P(3.2)(3) / 100

(2 x 100) / (3.2 x 3) = P

P = $ 20.8

Account B: -

20.7 = P(3.2)(18) / 100

(20.7 x 100) / (3.2 x 18) = P

P = $35.9

Which account earned you the most interest the first​ month?

Account A: -

3 months ----> $2

1 month ----> $x

x = 2 / 3

x = $0.67

Account B: -

18 months ----> 20.7

1 month ----> $y

y = 20.7 / 18

y = $1.15

Account B has earned more as 1.15 > 0.67 ( 1.15 IS greater than 0.67)

I hope my answer helps you.

Answer:

36 = 2h

Step-by-step explanation:

Here h represents the heigh

We know that the height of the door was twice the height of the window so that the equation will be

36 = 2h

Answer:

Step-by-step explanation:

758 +630+7+105=1400 ^

Answer: A

the total employees in the company is

                  758 + 530 + 7 + 105 = 1400 (employee)

the percent of the employees walk to work is

                  7/1400.100% = 0,005 . 100% = 0,5%

Step-by-step explanation:

we can add 2 to both sides to get 3y = -y2 + 2, which simplifies to 3y = -(y2 - 2).

5y + 2(3y − 1) = 8y - (y2)

5y + 2(3y - 1) can be rewritten as 5y + 6y - 2.

Then, we can combine like terms on the left side to get

11y - 2.

On the right side, we can combine like terms to get 8y - y2.

Now, we have 11y - 2 = 8y - y2. We can subtract 8y from both sides to get 3y - 2 = -y2.

Finally, we can add 2 to both sides to get 3y = -y2 + 2, which simplifies to 3y = -(y2 - 2).

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Answer: b) The set of all x-coordinates

Step-by-step explanation:

There is no association between the two variables if the correlation is 0.hintlinks to an external site. textbook pageslinks to an external site is False statement.

A correlation of zero means that there is no linear relationship between two variables, however, this does not necessarily mean that there is no relationship at all. It's crucial to keep in mind that correlation does not equal causation.For example, two variables may have no linear relationship, but still be related in some way, such as through a third variable or a non-linear relationship. Therefore, correlation does not necessarily mean that there is no relationship between two variables.

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The perimeter of the given composite figure is; 5¹/₂ cm

To get the perimeter of the given composite figure, what we will do is to dd up the given segment side lengths and we are given the following;

AE + DC = 1¹/₅ cm

AB = 1 ³/₄ cm

DE = 1 ¹/₄ cm

BC = 1 ³/₁₀ cm.

Thus, we can say that the Perimeter is;

Perimeter = AE + DE + DC + BC + AB

Perimeter  = (AE + DC) + DE + BC + AB

= 1¹/₅ + 1 ¹/₄ + 1 ³/₁₀ + 1 ³/₄

= (1²/₁₀ + 1³/₁₀) +(1¹/₄ + 1³/₄)

= 2⁵/₁₀ + 3

= 5¹/₂ cm

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Answer:

lines a and b must be parallel

Answer:(A)

Step-by-step explanation:edge

Answer:

23 purple marbles

115 yellow marbles

Step-by-step explanation:

Let y represent the yellow marble

Let p represent the purple marbles

So, we have the equations

y = 5p

Therefore, y + p = 138

5p + p = 138

6p = 138

p = 23 marbles

Now let's put 23 in for the p in the equation to find the number of yellow marbles

y = 5(23)

y = 115 marbles

Chris can only buy a maximum of 5 DVDs.

What is a division?

The division is a mathematical operation that involves dividing one number (the dividend) by another number (the divisor) to find the quotient. It is represented by the symbol "/" or "÷".

To determine how many DVDs Chris can buy, we need to subtract the cost of shipping from the total amount of money Chris has available and then divide the remaining amount by the cost of each DVD.

First, we subtract the cost of shipping from the total amount of money Chris has available:

$100 - $9.99 = $90.01

Then, we divide the remaining amount by the cost of each DVD:

$90.01 / $15.99 = 5.63

Chris can buy 5 DVDs.

Hence, Chris can only buy a maximum of 5 DVDs.

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Answer:

[tex]\frac{141}{a^{2} }[/tex]

Step-by-step explanation:

[tex]\frac{6}{a^{2} } + \frac{5a^{-2} }{3^{-3} }[/tex]

[tex]\frac{141}{a^{2} }[/tex]

Babies will not fall asleep more quickly when they hear the sound of a recorded heartbeat by opposite of null hypothesis.

The researcher has proposed a hypothesis that babies will fall asleep more quickly when they can hear the sound of a recorded heartbeat. To test this hypothesis, the researcher must develop a null hypothesis. The null hypothesis is the opposite of the researcher's hypothesis and states the expected outcome if the researcher's hypothesis is false. In this case, the null hypothesis is that babies will not fall asleep more quickly when they hear the sound of a recorded heartbeat. To test these hypotheses, the researcher must design a study and collect data to determine if the hypothesis is true or false. The researcher must also consider variables that could affect the outcome of the study, such as the age of the babies, the type of recorded heartbeat, and any other factors that could impact the outcome. The results of the study will then be used to either reject or accept the null hypothesis and determine if the researcher's hypothesis is true or false.

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Answer:

(-1,1)

Step-by-step explanation:

1/4 (-4) = -1

1/4(4) = 1

(-1,1)

Answer: D. 550

Step-by-step explanation: Among the choices, 550 is the right answer, because simply it is divisible by 2, 5, and 10, unlike the other choices that are not divisible by 2, 5, or 10.

550 ÷ 10 = 55

550 ÷ 5 = 110

550 ÷ 2 = 275

False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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Answer:

4

Step-by-step explanation:

[tex]\sqrt{16}[/tex] = 4

The side lengths of the square is 4.

Area = Length times width

Area = 4 x 4

Are = 16

Both automobiles' lines have the equation "y = 3x," and their respective gas mileage is 3 miles per gallon. Wyatt's automobile gets more miles per gallon of gas than Camden's vehicle does.

We must compute the mileage (the distance driven per gallon of fuel) for each automobile using the provided information to determine the difference between the ranges of travel for Camden's and Wyatt's vehicles.

We can determine the miles for Wyatt's automobile using the data points (5, 15) and (7, 21). The equation for the slope of the line connecting these two locations is

(y2 - y1) / (x2 - x1) = (21 - 15) / (7 - 5) = 6/2 = 3

"Y = mx + b" is the equation for the line connecting these two points, where m denotes the line's slope and b its y-intercept. We may determine the equation of the line by adding the values of m as well as the dimensions of one of the endpoints into this equation:

y = 3x + b

15 = 3(5) + b

15 = 15 + b

0 = b

"Y = 3x" is the equation for the line passing thru the points (5, 15) and (7, 21).

We can determine the miles for Camden's automobile using the data points (10, 30) and (14, 42). The equation for the slope of the line connecting these two locations is

(y2 - y1) / (x2 - x1) = (42 - 30) / (14 - 10) = 12/4 = 3

"Y = mx + b" is the equation for the line connecting these two points, where m denotes the line's slope and b its y-intercept. We may determine the equation of the line by incorporating the values of m as well as the dimensions of one of the endpoints into this equation:

y = 3x + b

30 = 3(10) + b

30 = 30 + b

0 = b

"Y = 3x" is the equation for the line passing through the points (10, 30) & (14, 42).

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The question is -

Computes the miles per gallon of your car via the miles traveled and the number of gallons used. Also, if you enter the cost per gallon and how many miles you drive a day, it will estimate your monthly and yearly gas expenses with data points (5, 15) and (7, 21).