1. What is 3/5+3/5+3/5+3/5 equal to?

After simplification of |2-5|-(6/2+1)², the resultant answer is (A) -13.

To simplify simply means to make anything easier.

In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.

Calculations and problem-solving techniques simplify the issue.

Substitute "of" for "multiplication," and "/" for "division."

Always carry out operations in accordance with "BODMAS."

Division and multiplication are equally important (Start from left) Both addition and subtraction are equally important.

So, simplify |2-5|-(6/2+1)² as follows:

|2-5|-(6/2+1)²

|-3| - (6/2 + 1)²

We know that : |-3| = 3 and (6/2 + 1)² = 16

Then, we have:
3 - 16

- 13

Therefore, after simplification of |2-5|-(6/2+1)², the resultant answer is (A) -13.

Know more about simplification here:

https://brainly.com/question/723406

#SPJ1

Answer:

The volume would increase 8 times

Step-by-step explanation:

The volume of a cube is given by the following formula:

Volume = side^3

With a volume of 125 cm3, we have:

125 = side^3

Now, if we double the length of the side, we have that:

New volume = (2*side)^3

New volume = 8*side^3

New volume = 8 * 125 = 1000

So the ratio of the new volume over the old volume is:

New volume / Volume = 1000 / 125 = 8

So the volume increased 8 times.

Answer:

1000 miles

Step-by-step explanation:

Given the following :

Number of miles driven :

First trip = 240 miles

Second day = 205 miles

Third day = 315 miles

Fourth day; miles driven before arriving at their final destination = 220 miles

Total number of miles driven after 4 days before reaching their destination :

(240 + 205 + 315 + 220) = 980 miles

However, they still haven't reached their destination ;

Using front end estimation :

We can take the total miles recorded and make an estimation based on the first digit of the recorded miles traveled:

In other to estimate 980 using front end estimation : the actual number is replaced with a number with only one nonzero digit (which is the first digit)

Hence,

980 - - - - > we round the digit after 9 either 1 or 0, since it is greater than 4, then it is rounded to and added to the first digit, all subsequent dots are rounded to zero

Hence 980 - - - - > 1000

Hence, estimated miles driven = 1000 miles

a) The probability of the sample mean being less than 10 minutes: 0.9345

b) The probability of the sample mean being between 5 and 10 minutes: 0.9283

c) The probability of the sample mean being less than 6 minutes: 0.0465

To calculate the sample mean (xbar) for a sample of 16 queuing times, we need to use the formula:

xbar = (x₁ + x₂ + ... + x₁₆) / n

Where:

x₁, x₂, ..., x₁₆ are the individual queuing times in the sample

n is the sample size (16 in this case)

a) To calculate the probability of the sample mean being less than 10 minutes, we need to standardize the sample mean using the z-score formula and then find the corresponding probability from the standard normal distribution.

The z-score formula is given by:

z = (xbar - μ) / (σ / sqrt(n))

Where:

xbar is the sample mean

μ is the population mean (8.1 minutes)

σ is the population standard deviation (5 minutes)

n is the sample size (16)

Substituting the values into the formula, we have:

z = (10 - 8.1) / (5 / sqrt(16))

z = 1.9 / (5 / 4)

z = 1.52

Using a standard normal distribution table or calculator, we can find the probability associated with a z-score of 1.52. Let's assume it is P(Z < 1.52) = 0.9345.

b) To calculate the probability of the sample mean being between 5 and 10 minutes, we need to standardize the lower and upper bounds using the z-score formula and then find the difference between the probabilities.

For the lower bound (5 minutes):

z_lower = (5 - 8.1) / (5 / sqrt(16))

z_lower = -3.1 / (5 / 4)

z_lower = -2.48

For the upper bound (10 minutes):

z_upper = (10 - 8.1) / (5 / sqrt(16))

z_upper = 1.9 / (5 / 4)

z_upper = 1.52

Using a standard normal distribution table or calculator, we can find the probabilities associated with z_lower and z_upper. Let's assume P(Z < -2.48) = 0.0062 and P(Z < 1.52) = 0.9345.

The probability of the sample mean being between 5 and 10 minutes is:

P(-2.48 < Z < 1.52) = P(Z < 1.52) - P(Z < -2.48)

= 0.9345 - 0.0062

≈ 0.9283

c) To calculate the probability of the sample mean being less than 6 minutes, we follow the same process as in part a):

z = (6 - 8.1) / (5 / sqrt(16))

z = -2.1 / (5 / 4)

z = -1.68

Using a standard normal distribution table , we can find the probability associated with a z-score of -1.68. Let's assume it is P(Z < -1.68) = 0.0465.

Learn more about probability at https://brainly.com/question/13604758

#SPJ4

To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:

(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D

We will represent the proposition as follows:

P: (A + B)

Q: (C V -B)

R: (-D --> C)

S: A

T: D

From the given premises, we can deduce the following:

P ^ Q (Conjunction Elimination)

P (Simplification)

Now, let's apply the rules of disjunction elimination:

P (S)

A + B (Simplification)

Next, let's apply the rule of disjunction introduction:

C V -B (S ^ Q)

Using disjunction elimination again, we have:

C (S ^ Q ^ R)

Finally, let's apply the rule of modus ponens:

-D (S ^ Q ^ R)

C (S ^ Q ^ R)

Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.

To learn more about Simplification : brainly.com/question/28261894

#SPJ11

The correct answer is D) m = -√3/2. To find the slope of the given curve at the point (x, y), we need to take the derivative of the curve with respect to x and evaluate it at the given point.

The equation of the curve is x = cos(y), and we want to find the slope at the point (x, y) = (-π/3). Taking the derivative of x = cos(y) with respect to x, we get: dx/dy = -sin(y) * dy/dx. To find the slope at the point (-π/3), we substitute y = -π/3 into the derivative expression: dx/dy = -sin(-π/3) * dy/dx = -(-√3/2) * dy/dx = √3/2 * dy/dx.

Therefore, the slope of the curve at the point (-π/3) is √3/2. Hence, the correct answer is D) m = -√3/2.

To learn more about derivative   click here: brainly.com/question/25324584

#SPJ11

Answer:

8(3v+3w-2)=(8×3v+8×3w-8×2)

Step-by-step explanation:

8×3v=24v.

8×3w=24w. [24v+24w-16]=(8×3v+8×3w-2×8)

8×(-2)=-16.

Answer:

-3

Step-by-step explanation:

pick two points where the line crosses exactly and make a triangle, for example (1,1) and (0,4)

difference in y ÷ difference in x = slope/gradient

difference in y = 4 - 1 = 3

difference in x = 0 - 1 = -1

\(\frac{3}{-1}\) = -3

Using the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power, it can be seens that that the two expressions are equal to each other.

The properties of multiplication state that when multiplying two expressions with the same base, we can add their exponents together. This means that 3 to the fifth power x 3 to the third power is equal to 3 to the eighth power.

In mathematical notation, this looks like:

3^8 = 3^5 x 3^3

Using the properties of multiplication, we can add the exponents together:

3^8 = 3^(5+3)

Simplifying the exponent:

3^8 = 3^8

This shows that the two expressions are equal to each other. Therefore, we can conclude that 3 to the eighth power and 3 to the fifth power x 3 to the third power are the same value.

Note: The question is incomplete. The complete question probably is: Use the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power.

Learn more about Properties of multiplication:  

https://brainly.com/question/876455

#SPJ11

Answer:

39

Step-by-step explanation:

Are of rectangle -Area of triangle

= 45 - 6

=39

Answer:\(\color{yellow}{}\) 39 Feet squared

Area of rectangle - Area of triangle

»» 45 - 6

A=39fs

(a) The limit of tₙ exists.

(b) The limit of tₙ is 0.

(c) Using induction, we can prove that tₙ = 2ⁿ/(n+1).

(d) The main answer remains the same.

(a) In order to show that the limit of tₙ exists, we need to demonstrate that the sequence tₙ converges. We observe that as n increases, the term (n+1)/2ⁿ approaches zero. Since tₙ+₁ = [1 - (n+1)/(2ⁿ)] * tₙ, the factor (1 - (n+1)/(2ⁿ)) tends to 1 as n increases. Therefore, the product of this factor with tₙ will approach zero, indicating that the limit of tₙ exists.

(b) Considering the recursive formula tₙ+₁ = [1 - (n+1)/(2ⁿ)] * tₙ, we can observe that as n becomes large, the term (n+1)/(2ⁿ) becomes negligible. Thus, the limiting behavior of tₙ is determined by the term tₙ itself. Since tₙ is multiplied by a factor approaching 1, but never exceeding 1, the limit of tₙ is 0.

(c) We will prove tₙ = 2ⁿ/(n+1) by induction.

Base case: For n = 1, t₁ = 2/(1+1) = 1. The base case holds true.

Inductive step: Assume that tₙ = 2ⁿ/(n+1) for some positive integer k.

We need to show that tₖ₊₁ = 2^(k+1)/(k+2). Using the recursive formula tₙ₊₁ = [1 - (n+1)/(2ⁿ)] * tₙ,

we have:

tₖ₊₁ = [1 - (k+1)/(2ᵏ)] * tₖ

      = [2ᵏ - (k+1)]/(2ᵏ * (k+1)) * 2ᵏ/(k+1)  (by substituting tₖ = 2ⁿ/(n+1))

      = 2^(k+1)/(k+2)

Therefore, the formula tₙ = 2ⁿ/(n+1) holds true for all positive integers n by induction.

(d) The answer for part (b) remains the same: The limit of tₙ is 0.

Learn more about limit

brainly.com/question/31412911

#SPJ11

Answer: 11/7 tons

Step-by-step explanation:

To determine how much sugar one container can hold, you need to divide the total amount of sugar (6 2/7 tons) by the number of containers (4).

First, convert the mixed number 6 2/7 to an improper fraction:

(7 * 6) + 2 = 44/7

Now, divide 44/7 tons by 4 containers:

(44/7) / 4 = (44/7) * (1/4) = 44/28

Simplify the fraction:

44/28 = 11/7

So, each container can hold 11/7 tons of sugar.

Answer:

105.8

Step-by-step explanation:

All you have to do is add them up :)

Answer:

95.80

Step-by-step explanation:

Btw this is very easy Hope this Helps tho (✿◡‿◡)

The domain of the function f(x) = x² - 2x + 1 is all real numbers, which is denoted as (-∞, +∞).

To find the domain of the function f(x) = x² - 2x + 1, we determine the set of all possible values for x that make the function well-defined.

The given function is a polynomial-function, and polynomial functions are defined for all real numbers. So, the domain of f(x) = x² - 2x + 1 is the set of all real numbers, which can be represented as (-∞, +∞).

It means that any real-number can be substituted into the function, and it will give a valid output. There are no limitations on the possible values of x in this case.

Therefore, the domain is all real numbers.

Learn more about Domain here

https://brainly.com/question/25727478

#SPJ4

The given question is incomplete, the complete question is

Find the domain of the function f(x) = x² - 2x + 1.

The system has nontrivial solutions for all values of "a".

To determine the values of "a" for which the system has nontrivial solutions, we need to examine the coefficient matrix and its determinant.

The given system of equations can be represented in matrix form as:

[ 3 3 -2 ] [ x ] [ 0 ]

[ -6 a 4 ] * [ y ] = [ 0 ]

[ 2 4 4 ] [ z ] [ 0 ]

Let's calculate the determinant of the coefficient matrix:

| 3 3 -2 |

| -6 a 4 |

| 2 4 4 |

Expanding the determinant along the first row:

3(a4 - 44) - 3(-64 - 24) + (-2)(-64 - 2a)

Simplifying further:

12a - 48 - (-72) - 12a = 12

The determinant is 12 for all values of "a".

To have nontrivial solutions, the coefficient matrix must be singular, i.e., the determinant must be zero. However, in this case, the determinant is non-zero (12) for all values of "a". Therefore, the system has nontrivial solutions for all values of "a".

To learn more about nontrivial solutions here:

https://brainly.com/question/30452276

#SPJ4

Answer:

Average cost per ounce is $0.65

Step-by-step explanation:

My Notes:

Monday - 12 Oz. = $7.80

Wednesday - 9 Oz. = $5.85

Find the average cost per 1 Oz. per candy.

\(\frac{12}{7.8} = 0.65\)

The AVERAGE cost per ounce is $0.65.

Answer + Step-by-step explanation:

let R be the set of farmers cultivating rice.

let W be the set of farmers cultivating wheat.

let n be the total number of farmers.

i) Check the attachment.

ii) Card R∪W = Card R + Card W - Card R∩W

Note : Card R denotes the number of farmers cultivating rice.

\(CardR\cup W=n-\frac{20}{100} n = \frac{80}{100} n\)

\(CardR=\frac{70}{100} n\)

\(CardW=\frac{60}{100}n\)

\(CardR \cap W=450\)

Card R∪W = Card R + Card W - Card R∩W

\(\Longleftrightarrow \frac{80}{100} n=\frac{70}{100} n + \frac{60}{100} n-450\)

\(\Longleftrightarrow \frac{50}{100} n=450\)

\(\Longleftrightarrow n= 2 \times 450 = 900\)

iiI) the number of farmers who are cultivating rice only :

\(900\times \frac{70}{100} -450=180\)

Using the probability, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

In the given question,

If you choose two cards out of a deck of cards, then we have to find the chances one is a red face card and the other is a black non-face card.

As we know that in a deck having 52 cards. In which 26 are red and 26 are black.

We have to choose a red face card.

As we know that in a deck have 12 face cards. In which 6 red face cards and 6 black face cards.

So the chance of getting red face card is

P(R)=Total number of red face cards/Total number of cards

P(R)=6/52

We have to choose a black non-face card.

We know that in a deck have 6 black face cards and total black cards are 26. So the non face cards are 20.

So the chance of getting black non-face card is

P(B)=Total number of black non-face cards/Total number of cards

P(B)=20/52

Now the chances of getting one is a red face card and the other is a black non-face card is

P(R or B)=P(R)+P(B)

P(R or B)=6/52+20/52

P(R or B)=(6+20)/52

P(R or B)=26/52

P(R or B)=1/2

Hence, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

To learn more about probability link is here

brainly.com/question/11034287

#SPJ4

The horizontal distance to the control tower is approximately 18506.83m

Data;

To solve this problem, we need to use trigonometric ratio SOHCAHTOA.

In this case, we have the value of opposite and angle and we need to find the adjacent to the angle. The tangent of the angle would be perfect for this.

\(tan\theta = \frac{opposite}{adjacent} \\tan11.4 = \frac{3900}{x}\\x = \frac{3900}{tan11.4}\\ x = 18506.83m\)

The horizontal distance to the control tower is approximately 18506.83m

Learn more on trigonometric ratio here;

https://brainly.com/question/4326804

Since the researcher is merely observing and comparing existing groups without any manipulation or intervention, this study is classified as an observational study.

In an observational study, the researcher observes and collects data on existing groups or individuals without intervening or manipulating any variables. In this case, the researcher selected two groups of grocery shoppers (one group shopping at a health food supermarket and the other at a neighborhood grocery store) and observed their food costs over a month. The researcher did not control or manipulate any factors or assign participants to specific groups.

To know more about observational study,

https://brainly.com/question/30692280

#SPJ11

Step-by-step explanation:

perimeter = 7 + 6 + 9.5 + 6.5

= 29

area of rectangle = 6 X 7 = 42

area of triangle = ½ X 2.5. X 6 = 7.5

total area = 42 + 7.5 = 49.5

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

the given figure is a composition of a rectangle as well as a right angled triangle !

we've been given the two sides of the rectangle and we're required to find out the height of the triangle , so as to find it's area ~

we know the the opposite sides of a rectangle are equal , therefore we can break the longest side ( length = 9.5 cm ) into two parts ! the first part of length = 7 cm which is the length of the rectangle and the rest 2.5 cm ( 9.5 - 7 = 2.5 ) will become the height of the triangle !

\(perimeter \: of \: figure = perimeter \: of \: rectangle + perimeter \: of \: triangle \\ \\ \)

now ,

perimeter of rectangle = 2 ( l + b )

where ,

l = length

b = breadth

\(\longrightarrow \: perimeter = 2(7 + 6) \\ \longrightarrow \: 2(13) \\ \longrightarrow \: 26 \: cm\)

and ,

\(perimeter \: of \: \triangle = 6.5 + 2.5 + 6 \\ \longrightarrow \: 15 \: cm\)

Perimeter of figure in total = 26 cm + 15 cm

thus ,

\(\qquad\quad\bold\red{perimeter \: = \: 41 \: cm}\)

\(area \: of \: figure = area \: of \: rectangle + area \: of \: rectangle \\ \)

now ,

area of rectangle = l × b

where ,

l = length

b = breadth

\(area \: of \: rectangle = 7 \times 6 \\ \longrightarrow \: 42 \: cm {}^{2} \)

and ,

\(area \: of\triangle = \frac{1}{2} \times base \times height \\ \\ \longrightarrow \: \frac{1}{\cancel2} \times \cancel6 \times 2.5 \\ \\ \longrightarrow \: 3 \times 2.5 \\ \\ \longrightarrow \: 7.5 \: cm {}^{2} \)

Area of figure in total = 42 cm² + 7.5 cm²

thus ,

\(\qquad\quad\bold\red{Area \: = \: 49.5 \: cm^{2}}\)

hope helpful :)

The trefoil knot crosses the yz-plane twice, with the only intersection point in the (+,+,-) octant being (0, -1, 0). The arc length between P (1,0) and Q is exactly 2.625 units.

Given the parametrization of the trefoil knot as 7(4) = (sin(t) + 2 sin(2t), cos(t) - 2 cos(2t), 2 sin(3t)), we can analyze the properties of the curve.

The trefoil knot crosses the yz-plane X times:

To determine the number of crossings with the yz-plane, we need to find the values of t when the x-coordinate of the parametrization becomes zero. In this case, sin(t) + 2 sin(2t) = 0. By analyzing the behavior of the sine function, we can see that it crosses zero twice within a single period, resulting in two crossings.

The only intersection point in the (+,+,-) octant is Y:

To find the intersection point in the (+,+,-) octant, we look for values of t where the x, y, and z coordinates are positive. From the parametrization, we can determine that when t = 0, the point lies in the (+,+,-) octant. Thus, the intersection point in the (+,+,-) octant is (0, -1, 0).

The arc length between P (1,0) and Q=Z is exactly 2.625 units:

To calculate the arc length between P (1,0) and Q, we can integrate the arc length formula using the given parametrization and the limits of integration. The resulting arc length is precisely 2.625 units.

Learn more about Integration here: brainly.com/question/31744185

#SPJ11

Answer:

x=60

Step-by-step explanation:

these shapes seem to be flipped

side WZ seems to be similar to PS

and Side ZY seems to be similar to RS

ewe can make ratios on the side lengths

40/75=32/x

cross multiply

40x=75(32)

40x=2400

/40.  /40

x= 60

hopes this helps please mark brainliest

Given the volume of the sphere as 26667 cm³, we calculated the radius to be approximately 17.7 cm using the formula for the volume of a sphere. By multiplying the radius by 2, we found that the diameter of the sphere is approximately 35.4 cm.

To calculate the diameter of a sphere when given its volume, we can use the formula for the volume of a sphere:

V = (4/3) * π * r³

Where V is the volume and r is the radius of the sphere. Since we are given the volume, we can rearrange the formula to solve for the radius:

r = (\(\sqrt[3]{(3V / (4\pi )}\)))

Substituting the given volume V = 26667 cm³ into the formula, we have:

r = (\(\sqrt[3]{(3 * 26667 / (4\pi )))}\)

Calculating this expression, we find:

r ≈ (\(\sqrt[3]{80001 / \pi ))}\) ≈ 17.7 cm

Now that we have the radius, we can calculate the diameter by multiplying the radius by 2:

d = 2 * r ≈ 2 * 17.7 ≈ 35.4 cm

For more such information on: volume

https://brainly.com/question/463363

#SPJ8

Answer:

The value of p(-a) must be 0

There is an x intercept of the function at (-a,0)

Step-by-step explanation:

(x + a) is a factor of a function p(x)

that means, that p(x) must have an x-intercept at the point x = -a

This can be written in two different ways,

If (x + a) is a factor of a polynomial function, p(x), then the two statements that are true are:

A factor of a polynomial function is a binomial that, when multiplied by another polynomial, gives the original polynomial function. If (x + a) is a factor of p(x), then p(x) can be written as (x + a)q(x), where q(x) is another polynomial function.

According to the Factor Theorem, if (x + a) is a factor of p(x), then p(a) = 0. This means that the value of the polynomial function at x = a is 0.

Additionally, if p(a) = 0, then there is an z-intercept of the function at (a,0). This is because the z-intercept is the point where the function crosses the z-axis, and this occurs when the value of the function is 0.

Therefore, the two statements that are true are "The value of p(a) must be 0" and "There is an z-intercept of the function at (a,0)".

Learn more about Polynomial Function here: brainly.com/question/12976257

#SPJ11

Answer:

6

Step-by-step explanation:

The combined perimeter of

2b (14y - 12)

2c (18y + 4)

2d (14y - 16), is

Add the like terms

The combined perimeter is (46y - 24)

The combined area of

1b (10y^2 - 27y +5)

1c (20y^2 + 11y - 3)

1d (12y^2 -24y), is

Add the like terms

The combined area is (42y^2 - 40y + 2)

Answer:

Step-by-step explanation:

Distribute:

=(62)(9.22)+(36(2d+8)(2d−8))(9.22)+(−6p)(9.22)+(92)(9.22)+(36)(9.22)+−36

=571.64+1327.68d2+−21242.88+−55.32p+848.24+331.92+−36

Combine Like Terms:

=571.64+1327.68d2+−21242.88+−55.32p+848.24+331.92+−36

=(1327.68d2)+(−55.32p)+(571.64+−21242.88+848.24+331.92+−36)

=1327.68d2+−55.32p+−19527.08

this is what I got I'm sorry

Answer:

Volume = l x w x h

Volume = 19 x 1.7 x 6

= 193.8