Evaluate each using the values given. x+z+y; use x = 4, y = 4, and z = 6​

Answer:

The answer is -5/8, smaller fractions are always closer to a whole number which make them more, another way to look at it is 5 is 3 numbers away from 8, and 6 is 4 numbers away from 10, which makes -5/8 greater.

Hope this helps!

There exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

In order to answer the given question, we first need to understand the definition of subspaces of a vector space.A subspace of a vector space is a subset that meets three requirements:

i) It includes the zero element of the vector space.

ii) It is closed under addition (if u and v belong to the subspace, then u + v is also in the subspace).

iii) It is closed under scalar multiplication (if u is in the subspace and k is a scalar, then ku is also in the subspace).

there exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

The reason is simple because if T∩U = Ø, then either SIT or SIU will be the trivial subspace {0}.

However, this contradicts the fact that both SIT and SIU have to contain a non-zero vector as they are subspaces that are generated by S, T, and U.

Therefore, it is proven that there exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

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By solving the equation 5[(46 - 14) / 4] we will get 40 as the answer

What is BODMAS?

The abbreviation BODMAS is used to assist pupils recall the order of mathematical operations - the right sequence in which to solve maths problems. BODMAS is an acronym that stands for B-Brackets, O-Orders (powers/exponents or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction.

Solution:

5[(46 - 14) / 4]

We will solve the round brackets first

5[ 32 / 4 ]

Now we will solve the square bracket

5 * 8 = 40

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Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

Answer:$13.15/thirteen USD and fifteen cents

Step-by-step explanation: 50.00-36.85= 13.15

A. The expression of F in terms of d is F = 200 / d²

B. The force when the distance is 10 cm is 2 N

C. The distance when the force is 8 N is 5 cm

D. When the distance, d is halved, the force F becomes four times the initial force

From the question given above,

F ∝ 1 / d²

F = K / d²

Cross multiply

K = Fd²

But

F = 50 N

d = 2 cm

Thus

K = Fd²

K = 50 × 2²

K = 200 Ncm²

Therefore, the expression is given as

F = K / d²

F = 200 / d²

F = K / d²

F = 200 / 10²

F = 2 N

F = K / d²

8 = 200 / d²

Cross multiply

8 × d² = 200

Divide both sides by 8

d² = 200 /8

d² = 25

Take the square root of both sides

d = √25

d = 5 cm

K = Fd² = constant

Thus

F₁d₁² = F₂d₂²

F × d² = F₂ × (0.5d)²

F × d² = F₂ × 0.25d²

Divide both sides by 0.25d²

F₂ = (F × d² ) / 0.25d²

F₂ = F / 0.25

F₂ = 4F

Thus, when the distance is halved, the force will increase by a factor of 4

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Answer:

Step-by-step explanation:

Given system:

This is a system of linear equations and the condition of no solution is to have the  parallel lines.

Parallel lines have same slope but different y-intercepts.

The first line

The slope is 2 and the y-intercept is -7/3

The second line

The slope is 3/m and the y-intercept is -5/m.

We need 3/m = 2 then:

With m = 1.5 the y-intercepts are different.

Answer:

m= 1.5

Step-by-step explanation:

Therefore, The journal entry for Johnny to record this transaction is Debit: New laptop for $2,500, Credit: Used laptop for $1,000, Credit: Cash for $800, Credit: Gain on exchange for $700. The journal entry for Barry to record this transaction is: Debit: Old equipment for $120,000, Debit: Loss on exchange for $10,000, Credit: New equipment for $100,000, Credit: Cash for $20,000.

When a company exchanges an old model of a laptop for a new model, the exchange lacks commercial substance. Johnny traded a used laptop with a book value of $1,000 (historical cost of $2,500 minus accumulated depreciation of $1,500) and a fair value of $1.200 for a new laptop with a list price of $2,500. Johnny also needs to pay $800 cash to purchase the new model. The journal entry to record the transaction would be as follows:Debit: New laptop for $2,500Credit: Used laptop for $1,000Credit: Cash for $800Credit: Gain on exchange for $700 ($2,500 - $1,800)Barry trades newer used equipment for an older version of the same equipment that lacks commercial substance. The newer equipment that Barry trades away has a book value of $90,000 (historical cost of $140,000 minus accumulated depreciation of $50,000) and a fair value of $100,000. In addition to receiving the older equipment, Barry receives $20,000 in exchange. The journal entry to record the transaction would be as follows:Debit: Old equipment for $120,000Debit: Loss on exchange for $10,000 ($100,000 - $90,000)Credit: New equipment for $100,000Credit: Cash for $20,000.

Therefore, The journal entry for Johnny to record this transaction is Debit: New laptop for $2,500, Credit: Used laptop for $1,000, Credit: Cash for $800, Credit: Gain on exchange for $700. The journal entry for Barry to record this transaction is: Debit: Old equipment for $120,000, Debit: Loss on exchange for $10,000, Credit: New equipment for $100,000, Credit: Cash for $20,000.

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The correct answer is (c) No, since the sample mean of 298.3 ml is in the confidence interval.

The confidence interval provides a range of plausible values for the true population mean amount of juice dispensed per bottle based on the sample mean and standard error. Since the confidence interval includes the sample mean of 298.3 ml, it suggests that the true mean amount of juice dispensed per bottle is likely to be around this value. Therefore, there is no reason to believe that the mean amount of juice in today's bottles differs from 300 ml based on this confidence interval.

Answer (a) and (b) are incorrect because they incorrectly suggest that the sample mean or the confidence interval being below 300 ml necessarily indicates a difference from the advertised value. Answer (d) is also incorrect because the fact that the advertised value falls within the confidence interval does not by itself indicate conformity with the label promise; the confidence interval includes a range of plausible values, and some of them may be quite different from the advertised value.

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It looks like you want to evaluate the iterated integral of the function 2x(x + 2y) over a given region S. To evaluate the iterated integral, we first integrate with respect to y (dy) and then with respect to x (dx).

Let's first integrate with respect to y:

∫(2x(x + 2y)) dy = 2x(xy + y^2) + C₁

Now, we need to evaluate this expression for the limits of integration for y, which are not given in your question. I'll assume they are y = a and y = b, so we have:

[2x(xb + b^2) - 2x(xa + a^2)]

Next, we'll integrate this expression with respect to x:

∫(2x(xb + b^2) - 2x(xa + a^2)) dx = x^2(xb + b^2) - x^2(xa + a^2) + C₂

Finally, we need to evaluate this expression for the limits of integration for x, which are also not given in your question. Assuming they are x = c and x = d, we have:

[(d^2(dc + b^2) - d^2(da + a^2)) - (c^2(cc + b^2) - c^2(ca + a^2))]

This expression represents the value of the iterated integral for the function 2x(x + 2y) over the region S, given the limits of integration for x and y. Please provide the limits of integration for a more specific answer.

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Answer:

              a₁ = -5, d = 7,  a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence:    \(\boxed{\bold{a_n=7n-12}}\)

Step-by-step explanation:

a₁ + a₂ + a₃ = 6    

a₁ + a₁ + d + a₁ + 2d = 6

3a₁ + 3d = 6

a₁ + d= 2     ⇒ a₁ = 2 - d

a₄ = 16

a₁ + 3d = 16

2 - r + 3d = 16

2d = 14

d = 7

a₁ = 2-7 = -5

a₁ = -5, d = 7   ⇒  a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16

equation of arithmetic sequence:

\(a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}\)

(a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, (d) boxplot is attached, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

(a) The mean = sum of all values divided by the number of values

μ = (x1 + x2 + ..... + xn)/n

n = 20

μ = (0.0395 + 0.0443+ 0.0450 + ... + 0.0550 + 0.0571)/20

μ = 0.9878/20

μ = 0.0494

(b) Variance = sum of squared deviations from the mean divided by n-1

s² = {(x1-μ)² + (x2-μ)² + .... (xn - μ)²)/(n-1)

s² = {(0.0395-0.0494)² + (0.0443-0.0494)² + .... +(0.0571-0.0494)²}/19

s² = 0.000016

(b) The minimum is 0.0395 and the maximum is 0.0571.

since the number of data is even, the median will be the average of two middle values.

M = Q2 = (0.0496+0.0499)/2 = 0.04975

Now, the first quartile is the median of the data values below the median

so Q1 = (0.0470+0.0485)/2 = 0.04775

And third quartile will be the median of the data values above the median

Q3 = (0.0504+0.0516)/2 = 0.0510

(c) Since we know that the number of data values is even, the median will be the average of the two middle values of the data set

so M = (0.0496+0.0499)/2

or M = 0.04975

(d) The boxplot is at maximum and minimum values. It will start in Q1 and end in Q3 and has a vertical line at the median or Q2.

The boxplot is attached.

(e) The 5th percentile means 0.05(n+1)th data value

or = 0.05(20+1) = 1.05th data value

5th percentile = 0.0550 + 0.05(0.0443-0.0395) = 0.03974

similarly,

95th percentile = 0.0550 + 0.95(0.0571-0.0550) = 0.056995

Therefore, (a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

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One car travel South at 64 mi/h and the other travels west at 48 mi/h. The distance between the cars increases with rate at 80 mi/h.

To find the rate of change, we need to find the derivative of the variables with respect to time.

Let:

p = distance between 2 cars

q = distance between car 1 and the start point

r = distance between car 2 and the start point

Using the Pythagorean Theorem:

p² = q² + r²

Take the derivative with respect to time:

2p dp/dt = 2q dq/dt + 2r dr/dt

dq/dt = speed of car 1 = 64 mi/h

dr/dt = speed of car 2 = 48 mi/h

The distance of car 1 and car 2 from the start point after 4 hours:

q = 64 x 4 = 256 miles

r = 48 x 4 = 192 miles

Using the Pythagorean theorem:

p² =256² + 192²

p = 320 miles

Hence,

2p dp/dt = 2q dq/dt + 2r dr/dt

p dp/dt = q dq/dt + r dr/dt

320  x dp/dt = 256 x 64 + 192  x 48

dp/dt = 80

Hence, the distance between the cars increases with rate at 80 mi/h

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The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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Therefore, we can say: limit sin(x) as x approaches pi/2 does not exist lim sin(x) as x approaches 0 = 0.

Although the function (sin x)/x is not defined at zero, it approaches 1 arbitrarily close as x approaches zero. In other words, when x gets closer to zero, the limit of (sin x)/x = 1.

We can put g(x) equal to -1/x and h(x) equal to 1/x because sin(x) is always between -1 and 1. As x approaches either positive or negative infinity, we know that the limit of both -1/x and 1/x is zero, and as a result, the limit of sin(x)/x is also zero.

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Answer:

(0, 12 ) and (4, 0 )

Step-by-step explanation:

the y- intercept is the point on the y- axis where the line crosses.

the x- coordinate of any point on the y- axis is zero

substitute x = 0 into the equation and solve for y

y = - 3(0) + 12 = 0 + 12 = 12 ← y- intercept , then

y- intercept is (0, 12 )

the x- intercept is the point on the x- axis where the line crosses

the y- coordinate of any point on the x- axis is zero

substitute y = 0 into the equation and solve for x

0 = - 3x + 12 ( subtract 12 from both sides )

- 12 = - 3x ( divide both sides by - 3 )

4 = x ← x- intercept , then

x- intercept is (4, 0 )

Answer: =280.86 ft²

Step-by-step explanation:

A=\(\pi r^{2}\)/2             d=26.75    radius is half r=13.375

divide by 2 becuase it's a semicircle not full circle

=(3.14)(13.375)²/2

=280.86 ft²

Answer:

Median = 8

Step-by-step explanation:

Data set representing the number of bushes in the yards of the houses in the neighborhood will be,

{5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10, 11, 11, 11, 11, 11}

Total number of houses = 20

Since, 20 is an even number,

Median of the data = average of middle two term

                                = average of 20th term and 21st term of the data set

                                = \(\frac{8+8}{2}\)

                                = 8

Median of the data set = 8

Answer:

Oslo

Step-by-step explanation:

It's colder in Oslo by 7 degrees.

hope this answer helps!

There are 84 boats in the marina using algebraic equation.

We shall represent the number of boats in the marina with the letter x so that we derive an algebraic equation to solve for x as follows:

number of white boats = 3x/4

number of blue boats = 4/7 of (x - 3x/4)

number of blue boats = 4/7 × x/4

number of blue boats = x/7

number of red boats = 9

so that;

3x/4 + x/7 + 9 = x

LCM of the denominators is 28

(21x + 4x + 252)/28 = x

25x + 252 = 28x {cross multiplication}

28x - 25x = 252 {collect like terms}

3x = 252

x = 252/3 {divide through by 3}

x = 84.

Therefore, There are 84 boats in the marina using algebraic equation.

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Answer:

Step-by-step explanation:

8) D

9) B

Answer:

The cost of each pack of bottle = x = $0.91

Step-by-step explanation:

Let 'x' be the cost of one pack of a juice bottle

so the cost of 4-pack of juice bottles = 4x

The total cost of a bag of apples = $1.85

Given that the total cost of a bag of apples and 4-pack of juice bottles before tax = $5.49

Thus, the equation becomes

1.85 + 4x = 5.49

4x = 5.49 - 1.85

4x = 3.64

Divide both sides by 4

4x/4 = 3.64/4

x = 0.91

Thus,

The cost of each pack of bottle = x = $0.91

VERIFICATION

As there are 4 packs of juice bottles and each pack costs = x = $0.91

so 4-packs of bottle = 4x = 4(0.91) = $3.64

cost of a bag of apples = $1.85

Thus, total cost:

$1.85 +  $3.64 =$ 5.49

Answer:

Equation: 4x+1.85=5.49

Answer: x = 0.91

Answer:

51

Step-by-step explanation:

since 1 = 39 degrees, it'd be complementary if you were to open it up if it were a C, it would be 90. So since its this way, i believe you would take 39 and do 90 - 39 to get your answer.  Im sorry if this is wrong but i hope it helps you!!

Answer:

3,1

....................................

Answer:

960

Step-by-step explanation:

Let P, R and T denote principal amount, rate of interest and time period.

Principal amount of loan (P) = 4,000

Time period (T) = 4 years

Rate of interest (R) = 6%

Simple interest is calculated using the following formula:

Simple interest \(=\frac{4000(4)(6)}{100} =960\)

So,

Simple interest is equal to 960

Answer:

(-5)*2 - 12

Step-by-step explanation:

First multiply (-5) and 2. Then (-10) and (-12) have same signs ie. neagtive .

If two integers have same sign, add and the result will have the sign of the both integers.

(-5)*2 - 12 = -10 - 12

                = -22

The probability of choosing a fisher from Clearwater who had a license is 54/(54+36) = 0.6, and the probability of choosing a fisher from Mountain View who did not have a license is 10/(10+90) = 0.1.

Assuming that the choices are independent, the probability of both events happening together is the product of their probabilities:

P(Clearwater had a license and Mountain View did not have a license) = P(Clearwater had a license) x P(Mountain View did not have a license)

= 0.6 x 0.1

= 0.06

Therefore, the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license is 0.06.

Answer:

The probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license is 0.06

Step-by-step explanation:

To solve this problem, we can use the multiplication rule of probability, which states that the probability of two independent events both occurring is equal to the product of their individual probabilities.Let event A be the event that a fisher chosen from Clearwater Park had a license, and let event B be the event that a fisher chosen from Mountain View Park did not have a license. Then, we need to find the probability of A and B occurring together, which we can write as P(A and B).

Using the given information, we can calculate the probabilities of events A and B as follows:

P(A) = 54/(54+36) = 0.6 (the proportion of fishers at Clearwater Park with a license)

P(B) = 10/(90+10) = 0.1 (the proportion of fishers at Mountain View Park without a license)

Since the events are independent (since no one fished at both parks), we can use the multiplication rule to find the probability of A and B occurring together:

P(A and B) = P(A) * P(B) = 0.6 * 0.1 = 0.06