Question 1
A 16-ounce bag of sugar is supposed to weigh 16 ounces, but it is acceptable for the weight of the bag to vary as much as 0.4 ounce. Which absolute value inequality can be used to find X, the acceptable
weight of a bag of sugar?

Answer:

Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.

Step-by-step explanation:

Answer:

4, 5 and 6

Step-by-step explanation:

Consecutive means right next to each other.

4 x 5 x 6 = 120 cubic inches.

4 X 5 = 20

20 X 6 = 120

The values of the consecutive numbers will be 4, 5, and 6.

Let the numbers be represented by a, a+1, and a+2.

Therefore, a(a+1)(a+2) = 120

a³ + 3a² + 2a = 120

a = 4

Therefore, a + 1 = 4+1 = 5

a + 2 = 4 + 2 = 6

Therefore, the values will be 4, 5, and 6.

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Answer:

The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.

Step-by-step explanation:

The Newton's method is a numerical method by approximation that help find roots of a equation of the form [tex]f(x) = 0[/tex] with the help of the equation itself and its first derivative. The Newton's formula is:

[tex]x_{i+1} = x_{i} - \frac{f(x_{i})}{f'(x_{i})}[/tex]

Where:

[tex]x_{i}[/tex] - i-th approximation, dimensionless.

[tex]x_{i+1}[/tex] - (i+1)-th approximation, dimensionless.

[tex]f(x_{i})[/tex] - Function evaluated at the i-th approximation, dimensionless.

[tex]f'(x_{i})[/tex] - First derivative of the function evaluated at the i-th approximation, dimensionless.

The function and its first derivative are [tex]f(x) = x^{3}+x+8[/tex] and [tex]f'(x) = 3\cdot x^{2}+1[/tex], respectively. Now, the Newton's formula is expanded:

[tex]x_{i+1} = x_{i}-\frac{x_{i}^{3}+x_{i}+8}{3\cdot x_{i}^{2}+1}[/tex]

If [tex]x_{1} = -1[/tex], the value of [tex]x_{2}[/tex] is:

[tex]x_{2} = -1 - \frac{(-1)^{3}+(-1)+8}{3\cdot (-1)^{2}+1}[/tex]

[tex]x_{2} = -1.5000[/tex]

The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.

Answer:

-2.5000

Step-by-step explanation:

Answer:

z(max) = 650 $

x₁ = 10 units

x₂ = 15 units

Step-by-step explanation:

That is a linear programming problem, we will use a simplex method to solve it

Formulation:

Let´s call  x₁  number of chairs   and x₂ number of tables then :

Item              (in hours)     cutting       assembly      finishing        Profit ($)

Chairs (x₁)                              1                   2                     1                      20

Tables (x₂)                              2                   1                      1                      30

Availability                           40                 42                   25

Objective Function

z  =  20*x₁   +  30x₂   ( to maximize) subject to:

x₁  +  2x₂   ≤  40

2x₁  + x₂    ≤  42

x₁ + x₂     ≤    25

x₁  ,   x₂  >= 0

Using excel or any other software we find:

z(max) = 650

x₁ = 10

x₂ = 15

The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674

Let x represent chairs, and y represent tables

So, the given parameters are:

Cutting:

So, the constraint is:

[tex]\mathbf{x + 2y \le 40}[/tex]

Assembly:

So, the constraint is:

[tex]\mathbf{2x + y \le 42}[/tex]

Finishing:

So, the constraint is:

[tex]\mathbf{x + y \le 25}[/tex]

The unit profit on the items are:

So, the objective function to maximize is:

[tex]\mathbf{Max\ z = 20x + 30y}[/tex]

And the constraints are:

[tex]\mathbf{x + 2y \le 40}[/tex]

[tex]\mathbf{2x + y \le 42}[/tex]

[tex]\mathbf{x + y \le 25}[/tex]

[tex]\mathbf{x,y \ge 0}[/tex]

Using graphical method (see attachment for graph), we have the following feasible points:

[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]

Calculate the objective function using the feasible points.

[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]

[tex]\mathbf{z = 650}[/tex]

[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]

[tex]\mathbf{z = 580}[/tex]

[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]

[tex]\mathbf{z = 673.5}[/tex]

Approximate

[tex]\mathbf{z = 674}[/tex]

Hence, the maximum revenue is 674

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Answer:

8w : 3.8974342 ≈ 3.9 or 4 (hope it help)

Step-by-step explanation:

1w : 2

2w : 2 + 10% = 2.2

3w : 2.2 + 10% = 2.42

4w : 2.42 + 10% = 2.662

5w : 2.662 + 10% = 2.9282

6w : 2.9282 + 10% = 3.22102

7w : 3.22102 + 10% = 3.543122

8w : 3.543122 + 10% = 3.8974342

3.8974342 ≈ 3.9 or 4

Answer:

123 domestic stamps

89 foreign stamps

Step-by-step explanation:

Answer:

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

Which equation represents the total number of stamps Malik collected?  

✔ x + y = 212

Which equation represents the difference in the number of foreign and domestic stamps Malik collected?  

✔ x – y = 34

Which system of linear equations represents the situation?  

✔ x – y = 34 and x + y = 212

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

This system of equations models the given information for both stamp types.

x – y = 34

x + y = 212

Solve the system of equations.  

How many foreign stamps does Malik have?

✔ 89  foreign stamps

How many domestic stamps does Malik have?

✔ 123 domestic stamps

Step-by-step explanation:

its right on 2021 edge! :) hope this helps

Answer:

A

Step-by-step explanation:

the graph of x'3 is B

the graph of x'(-1/3) is C

Answer:

the probability that the sample mean will be larger than 1224 is  0.0082

Step-by-step explanation:

Given that:

The SAT scores have an average of 1200

with a  standard deviation of 60

also; a sample of 36 scores is selected

The objective is to determine  the probability that the sample mean will be larger than 1224

Assuming X to be the random variable that represents the SAT score of each student.

This implies that  ;

[tex]S \sim N ( 1200,60)[/tex]

the probability that the sample mean will be larger than 1224 will now be:

[tex]P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })[/tex]

[tex]P(\overline X > 1224) = P(Z > 2.4 })[/tex]

[tex]P(\overline X > 1224) =1 - P(Z \leq 2.4 })[/tex]

From Excel Table ; Using the formula (=NORMDIST(2.4))

P(\overline X > 1224) = 1 -  0.9918

P(\overline X > 1224) = 0.0082

Hence;  the probability that the sample mean will be larger than 1224 is  0.0082

Step to step explanation:

Confidence interval for mean, when population standard deviation is unknown:

[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = sample mean

n= sample size

s= sample standard deviation

[tex]t_{\alpha/2}[/tex] = Critical t-value for n-1 degrees of freedom

We assume the family size is normal distributed.

Given, n= 31 , [tex]\overline{x}=3.1[/tex], s= 1.42 ,

[tex]\alpha=1-0.9=0.10[/tex]

Critical t value for [tex]\alpha/2=0.05[/tex] and degree of 30 freedom

[tex]t_{\alpha/2}[/tex] = 1.697  [By t-table]

The required confidence interval:

[tex]3.1\pm ( 1.697)\dfrac{1.42}{\sqrt{31}}\\\\=3.1\pm0.4328\\\\=(3.1-0.4328,\ 3.1+0.4328)=(2.6672,\ 3.5328)\approx(2.67,\ 3.53)[/tex]

Hence,  the 90% confidence interval for the estimate = (2.67, 3.53)

Answer:

810.66 ft²

Step-by-step explanation:

Short answer:

Shaded region:

Answer: 810.66 ft²

I agree.

Answer:

40

Step-by-step explanation:

20 * 1

= 20

20 * 2

= 40

Answer:

40

Step-by-step explanation:

The first step is to multiply 20 by 1. Whenever you multiply something by 1, it will always stay the same no matter what.

20*1=20

The next step is to multiply by 2. When multiplying anything by two, it is the same as adding the same number to itself. so

20*2=40 or 20+20=40

Hope this helps. Feel free to ask any follow-up questions if you are still confused

Have a great day! :)

Answer:

25

Step-by-step explanation:

150/6

The Unit rate of calories per ounce will be 25 calories per ounce.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Weight of the Greek yogurt container = 6 ounce

Calories per container = 150 calories

The Unit rate of calories per ounce = 150 / 6 = 25

Therefore, the unit rate of calories per ounce will be 25 calories per ounce.

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Answer: In so many ways ;

And so on .

720

you would be using permutation i believe

because carpet has 6 letters you have six placement options

_x_x_x_x_x_

if you can only use the letters once

you can put all letters in p1

so 6x_x_x_x_x_

but because of that you would only be able to put all but one in p2 and one less than p2 in p3 going all the way to 1 in the last

so 6x5x4x3x2x1

i might be wrong but this has worked for me

Answer:

$0.80

Step-by-step explanation:

If price level rises to 1.25 from 1 then:

Value of dollar = 1/1.25 = $0.80

Answer:

The expected value of the game is $0.33.

Step-by-step explanation:

There are N = 36 outcomes of rolling two 6-sided fair dice.

The sample for the sum of two numbers to be 7 is:

S = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)}

n (S) = 6

It is provided that there is a 7 to 1 odds against rolling a sum of 6 with the roll of two fair dice.

That is, you win $7 if you succeed and you lose $1 if you fail.

Compute the expected value of the game as follows:

[tex]E(X)=\sum x\cdot P (X=x)[/tex]

         [tex]=[\$(7)\times \frac{6}{36}]+[\$(-1)\times \frac{30}{36}]\\\\=\frac{7}{6}-\frac{5}{6}\\\\=\frac{7-5}{6}\\\\=\frac{1}{3}\\\\=\$0.33[/tex]

Thus, the expected value of the game is $0.33.

Answer:

-4

Step-by-step explanation:

give me brainliest please

Answer: x= 4.25 y= 12.75

Step-by-step explanation:

Answer:

The estimate is  [tex]P__{hat}} \pm E = 0.37 \pm 0.0348[/tex]

Step-by-step explanation:

From the question we are told that  

    The sample size is  n =  522

    The sample proportion of students  would like to talk about school is  [tex]\r p__{hat}} = 0.37[/tex]

  Given that the confidence level is  90 % then the level of significance can be mathematically evaluated as

                  [tex]\alpha = 100 - 90[/tex]

                  [tex]\alpha = 10\%[/tex]

                  [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is  

               [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10}{2} } = 1.645[/tex]

Generally the margin of error can be mathematically represented as

               [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r P_{hat}(1- \r P_{hat} )}{n } }[/tex]

=>            [tex]E = 1.645 * \sqrt{\frac{0.37 (1- 0.37 )}{522 } }[/tex]

=>             [tex]E = 0.0348[/tex]

Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is  

                       [tex]P__{hat}} \pm E[/tex]

substituting values

                     [tex]0.37 \pm 0.0348[/tex]

Answer:

see explanation

Step-by-step explanation:

(1)

2x - 3 ≤ 3 ( add 3 to both sides )

2x ≤ 6 ( divide both sides by 2 )

x ≤ 3

(2)

2 - 3y > 16 ( subtract 2 from both sides )

- 3y > 16

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

y < - [tex]\frac{14}{3}[/tex]

Answer:

a. B1 is better than B2.

Step-by-step explanation:

Hyperplane is a geometric shape which has subspace whose dimension is one less than ambient space. Hyperplane that maximizes the margin it will have better generalization. Margin is calculated by [tex]\frac{2}{||W||}[/tex]. The correct option is a.

Answer:

A

Step-by-step explanation:

Answer:

80 trees have a diameter smaller than 120cm

Step-by-step explanation:

Step 1

To solve this question, we would make use of the Z score formula.

z = x - μ/σ

Where

z = z score

x = Raw score = 120cm

μ = Population mean = 150cm

σ = Population standard deviation = 30cm

Hence,

z =120 - 150/30

z = -1

The z score = -1

Step 2

We find the Probability of the calculated z score using the z score table.

P(z) = P(z = -1) = P(x<120) = 0.15866

Approximately to the nearest hundredth = 0.16

Converting to percentage = 0.16 × 100 = 16%

The percentage of trees with a diameter smaller than 120cm = 16%

Therefore, the number of trees with a diameter smaller than 120cm

= 16% × 500 trees = 80trees

Answer:

(16x + 21) and (16x - 6)

Step-by-step explanation:

f(g(x)) = f(6 + 4x)

Applying the f(x) function on (6 + 4x) gives

4(6 + 4x) - 3

Which equals 16x + 24 - 3

= 16x + 21

g(f(x)) = g(4x - 3)

Applying the g(x) function on (4x - 3) gives

6 + 4(4x - 3)

Which equals 6 + 16x - 12

= 16x - 6

Answer:

(g∘f)(x)=48x2+48x+10

(g∘f)(x)=12x^2-6

Step-by-step explanation:

To find (f∘g)(x), use the definition of (f∘g)(x),

(f∘g)(x)=f(g(x))

Substituting 3x2−2 for g(x) gives

(f∘g)(x)=f(3x2−2)

Find f(3x2−2), where f(x)=4x+2, and simplify to get

(f∘g)(x)(f∘g)(x)(f∘g)(x)=4(3x2−2)+2=12x2−8+2=12x2−6

To find (g∘f)(x), use the definition of (g∘f)(x),

(g∘f)(x)=g(f(x))

Substituting 4x+2 for f(x) gives

(g∘f)(x)=g(4x+2)

Find g(4x+2), where g(x)=3x2−2, and simplify to get

(g∘f)(x)=3(4x+2)^2−2

(g∘f)(x)=48x2+48x+12−2

(g∘f)(x)=48x2+48x+10

Answer:

14 and 9

Step-by-step explanation:

Y values are always the second number in the parenthesis. The X value is the first one. I like to think of Y being dependent on X, so X goes first, then Y.

Answer:

THE M ONE

Step-by-step explanation:

IT HAS A DIFFERENT VARIABLE

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

                    ✌ -ZYLYNN JADE ARDENNE

Answer:

l = 44 ft

w = 20 ft

Step-by-step explanation:

Perimeter is

P = 2 ( l+w)

The width is

w = l -24

We know the perimeter is 128 and substituting into the equation for perimeter

128 = 2 ( l + l-24)

128 = 2 ( 2l -24)

Divide by 2

128/2 = 2/2 ( 2l-24)

64 = 2l - 24

Add 24 t o each sdie

64+24 = 2l

88 = 2l

Divide by 2

44 =l

The length is 44

Now find w

w = l - 24

w = 44-24

w = 20

Answer:

[tex]\boxed{l=44 \: \mathrm{feet}, \: \: w=20 \: \mathrm{feet}}[/tex]

Step-by-step explanation:

The width (w) = l - 24

The length (l) = l

The perimeter (P) = 128

The shape is a rectangle. Use the formula for the perimeter of a rectangle.

P = 2w + 2l

Plug in the values.

128 = 2(l - 24) + 2l

Solve for l.

Expand brackets.

128 = 2l - 48 + 2l

Combine like terms

128 = 4l - 48

Add 48 on both sides.

176 = 4l

Divide both sides by 4.

44 = l

Apply formula again.

P = 2l + 2w

Solve for w.

Subtract 2w and P on both sides.

-2w = 2l - P

Divide both sides by -2.

w = -l + P/2

Plug in the values for l and P, solve for w.

w = -(44) + 128/2

w = -44 + 64

w = 20

The length is 44 feet.

The width is 20 feet.

Answer:

I got x=3,-3

Step-by-step explanation:

Squares are the results of multiplying a value by itself. The value of x in the given equation 2x² - 5 = 13 is -3 and 3.

Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.

The value of x for the given equation 2x²-5=13, can be solved as shown below.

2x² - 5 = 13

Add 5 on both the sides of the equation,

2x² - 5 + 5 = 13 + 5

2x² = 18

Divide both the sides of the equation by 2,

2x² / 2 = 18 / 2

x² = 9

Taking the square root on both the sides of the equation,

√x² = √9

x = ±3

x = -3, 3

Hence, the value of x in the given equation 2x² - 5 = 13 is -3 and 3.

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Answer: 0.06x

Step-by-step explanation:

The given statement:  A number is 30% of 20% of the number x.

The required algebraic expression would be:

30% of 20% of x

[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex]  [we divide a percentage by 100 to convert it into decimal]

[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]

Hence, the required algebraic expression would be :

0.06x

Answer:

Step-by-step explanation:

The vertices of the already rotated triangle are:

D '(4, 4)

E '(1, 3)

F '(2, 1)

Answer:

D '(4, 4)

E '(1, 3)

F '(2, 1)

Step-by-step explanation:

Answer:

[tex]C.\ 200[/tex]

Step-by-step explanation:

Given

Let R represents rows and C represents Columns

When R = 8, C = 25

When R = 10, C = 20

Required

Given that there exist an inverse variation, determine the constant of proportionality;

We start by representing the variation;

[tex]R\ \alpha \ \frac{1}{C}[/tex]

Convert proportion to an equation

[tex]R\ = \ \frac{k}{C}[/tex]

Where k is the constant of proportion;

[tex]R * C\ = \ \frac{k}{C} * C[/tex]

Multiply both sides by C

[tex]R * C\ = k[/tex]

Reorder

[tex]k = R * C[/tex]

When R = 8, C = 25;

The equation  [tex]k = R * C[/tex] becomes

[tex]k = 8 * 25[/tex]

[tex]k = 200[/tex]

When R = 10, C = 20;

The equation  [tex]k = R * C[/tex] becomes

[tex]k = 10 * 20[/tex]

[tex]k = 200[/tex]

Hence, the concept of proportionality is 200

Answer:

5 triangles from the vertex

Answer:

5 triangles from the vertex

Step-by-step explanation:

When you solve this equation using the quadratic formula, you will get [tex]x = \frac{-20\pm \sqrt{400-4k^2}}{2k}[/tex]. The only way for this number to be irrational is for [tex]\sqrt{400-4k^2}[/tex] to be irrational. The square root of any number that is not a perfect square is irrational*, so the solutions of the quadratic are rational if and only if [tex]400-4k^2[/tex] is a perfect square. We can factor out the 4 (which is already a perfect square), which means that [tex]100-k^2[/tex] must be a perfect square. This occurs exactly when k is equal to one of the following:[tex]\sqrt{100},\sqrt{99},\sqrt{96},\sqrt{91},\sqrt{84},\sqrt{75},\sqrt{64},\sqrt{51},\sqrt{36},\sqrt{19}, \sqrt{0}[/tex].

Of these, the only positive integer values of k are: [tex]\sqrt{100}, \sqrt{64}, \sqrt{36}[/tex], or simply 6, 8, and 10.

* This is quite simple to show: Take any rational number, a/b. Without loss of generality, we can assume that a/b is in reduced form, that is, a and b have no common factors. (a/b)^2 is a^2/b^2, and since a and b have no common factors, neither do a^2 and b^2. Therefore, a^2/b^2 cannot be an integer. In the event that a/b is an integer, b would equal 1, and this proof would not hold.