A store sells a 10-pound bag of flour for $5.20. If Larry can buy a 2-pound bag of flour at the same rate, what would be the price of the 2-pound bag?

Answer:

16

Step-by-step explanation:

36 miles is the fewest number of miles she can walk in February

There are 28 days in February.

Every third day is 28/3 = 9.333 = 9 days of walking.

since she walks four miles,

9*4 = 36

Hence, 36 miles is the fewest number of miles she can walk in February

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The probability that the time until the first critical-part failure is less than 1 year is 0.2548. So the correct answer is (D) 0.254811.

Given that the time until the first critical part failure for a certain car is exponentially distributed with a mean of 3.4 years.

f(t) = λe^(-λt)

where λ is the rate parameter and is equal to 1/mean = 1/3.4 = 0.2941.

To find the probability that the time until the first critical-part failure is less than 1 year, we need to calculate the cumulative distribution function (CDF) of the exponential distribution up to 1 year:

F(1) = ∫[0,1] λe^(-λt)dt

Using integration by substitution, let u = λt, then du/dt = λ and dt = du/λ.

F(1) = ∫[0,λ] e^(-u)du

= [-e^(-u)]_[0,λ]

= -e^(-λ) + e^(-0)

= 1 - e^(-0.2941 * 1)

= 0.2548 (rounded to four decimal places)

Therefore, the likelihood that the period until the first critical-part failure is less than 1 year is 0.2548. So the correct answer is (D) 0.254811.

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By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

a. To find the given series i.e.,  5∑n=0(9(2)n)−7(−3)nTo find 5∑n=0(9(2)n)−7(−3)n,

we need to find the first five terms of the series. The given series is,

5∑n=0(9(2)n)−7(−3)n5[(9(2)0)−7(−3)0] + [(9(2)1)−7(−3)1] + [(9(2)2)−7(−3)2] + [(9(2)3)−7(−3)3] + [(9(2)4)−7(−3)4]

After evaluating, we get:

5[(9*1) - 7*1] + [(9*2) - 7*(-3)] + [(9*4) - 7*9] + [(9*8) - 7*(-27)] + [(9*16) - 7*81]15 + 57 + 263 + 1089 + 4131= 5555b.

Given premises: p → q, ¬p → r, r → s.

We are to prove that ¬q → s. i.e.,

Premises: (p → q), (¬p → r), (r → s)

Conclusion: ¬q → s

To prove ¬q → s,

we need to assume ¬q and show that s follows.

Then we use the premises to derive s.

Proof:

1. ¬q        Assumption

2. ¬(¬q)    Double negation

3. p         Modus tollens 2,1 & p → q

4. ¬¬p      Double negation

5. ¬p        Modus ponens 4,3 (Conditional elimination)

6. r         Modus ponens 5,2 (Conditional elimination)

7. s         Modus ponens 6,3 (Conditional elimination)

8. ¬q → s     Conditional introduction (Implication)

Thus, ¬q → s is proven.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent, we need to show that their negation is equivalent. i.e.,

we show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p)Negation of (p ∨ ¬q) = ¬p ∧ q Negation of (q ∧ ¬p) = ¬q ∨ p

Thus, we are to show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p) is equivalent to ¬p ∧ q ↔ ¬q ∨ p

Proof:

¬(q ∧ ¬p)  ≡  ¬q ∨ p       Negation of (q ∧ ¬p)(p ∨ ¬q)   ≡  ¬(q ∧ ¬p)  

De Morgan's laws ∴ (p ∨ ¬q) ≡ ¬q ∨ p

By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

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a. The formula given is, ∑n=0(9(2)n)−7(−3)n. Let’s find out the first five terms of the given formula as follows:

First term at n = \(0:9(2)^0-7(-3)^0= 9 + 7= 16\)

Second term at n = \(1:9(2)^1-7(-3)^1= 18 + 21= 39\)

Third term at n = \(2:9(2)^2-7(-3)^2= 36 + 63= 99\)

Fourth term at n = \(3:9(2)^3-7(-3)^3= 72 + 189= 261\)

Fifth term at n = \(4:9(2)^4-7(-3)^4= 144 + 567= 711\)

Therefore, the first five terms of the given formula are: 16, 39, 99, 261, 711.

b. To prove that ¬q→s from p→q, ¬p→r, and r→s,

we need to use the law of contrapositive for p→q as follows:

¬q→¬p       (Contrapositive of p→q)¬p→r         (Given)

∴ ¬q→r        (Using transitivity of implication) r→s           (Given)

∴ ¬q→s        (Using transitivity of implication)

Therefore, ¬q→s is proved.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent,

we need to use the De Morgan’s laws as follows:

¬(p∨¬q) ≡ ¬p∧q     (Using De Morgan’s law)      

≡ q∧¬p     (Commutative property of ∧)

Therefore, ¬(p∨¬q) and q∧¬p are equivalent.

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\(\displaystyle \lim_{x\to \infty} 1+\cfrac{ln(x)}{x}\implies \lim_{x\to \infty} \cfrac{x+ln(x)}{x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{using L'Hopital once} }{\cfrac{\frac{d}{dx}[x+ln(x)]}{\frac{d}{dx}(x)}}\implies \cfrac{ ~~ 1+ \frac{ 1 }{ x } ~~ }{1}\implies 1+\cfrac{1}{x}\implies \cfrac{x+1}{x}\)

\(\stackrel{ \textit{using L'Hopital twice} }{\cfrac{\frac{d}{dx}[x+1]}{\frac{d}{dx}(x)}}\implies \cfrac{1}{1}\implies 1 \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to \infty} \cfrac{x+ln(x)}{x}\implies \lim_{x\to \infty} 1\implies \text{\LARGE 1}\)

Hope you could get an idea from here.

Doubt clarification - use comment section.

The equation \(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2\) has been proved to be true

The equation is given as:

\(\frac pq = \frac qr\)

Cross multiply

\(pr = q^2\)

Rewrite as:

\(q^2 = pr\)

Also, we have:

\(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2\)

Substitute \(q^2 = pr\)

\(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^3r^3\)

Expand

\(p^3+q^3+r^3=\frac{1}{p^3} \times p^3r^3 +\frac{1}{q^3} \times p^3r^3 +\frac{1}{r^3} \times p^3r^3\)

Simplify

\(p3+q3+r3=r^3 +\frac{1}{q^3} \times p^3r^3 + p^3\)

Rewrite as:

\(p3+q3+r3=r^3 +\frac{1}{q^3} \times (pr)^3 + p^3\)

Substitute \(pr = q^2\)

\(p3+q3+r3=r^3 +\frac{1}{q^3} \times (q^2)^3 + p^3\)

\(p3+q3+r3=r^3 +\frac{1}{q^3} \times q^6 + p^3\)

Divide q^6 by q^3

\(p3+q3+r3=r^3 +q^3 + p^3\)

Rewrite the equation as:

\(p3+q3+r3=p^3 +q^3 + r^3\)

Hence, the equation has been proved

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The first partial derivatives of z with respect to x and y in the equation x + sin(y + z) = 0 are ∂z/∂x = -1 and ∂z/∂y = -cos(y + z).

To find the first partial derivatives of z with respect to x and y, we need to differentiate the given implicit equation with respect to x and y while treating z as a function of x and y.

Differentiating the equation with respect to x:

∂/∂x (x + sin(y + z)) = 1 + ∂z/∂x

Differentiating the equation with respect to y:

∂/∂y (x + sin(y + z)) = cos(y + z) (1 + ∂z/∂y)

The term ∂z/∂x represents the partial derivative of z with respect to x, and ∂z/∂y represents the partial derivative of z with respect to y.

So, the first partial derivatives of z are:

∂z/∂x = -1

∂z/∂y = -cos(y + z)

These derivatives indicate how the variable z changes with respect to changes in x and y in the given equation x + sin(y + z) = 0. The value of -1 for ∂z/∂x means that for every unit increase in x, z decreases by 1. The value of -cos(y + z) for ∂z/∂y indicates how z changes with respect to changes in y, with the specific relationship determined by the trigonometric function cos(y + z).

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By using properties of parallel lines, the results obtained are

x = 80°, y = 130°

What are parallel lines?

Parallel lines

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Transversal is a line that intersects two or more parallel lines

Here, by using properties of parallel lines,

x + 50 + x - 30 = 180 [Co interior angles are supplementary]

2x + 20 = 180

2x = 180 - 20

2x = 160

x = \(\frac{160}{2}\\\)

x = 80°

x - 30 + y = 180 [Co interior angles are supplementary]

80 - 30 + y = 180

50 + y = 180

y = 180 - 50

y = 130°

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Complete Question

The diagram has been attached

Find the values of x and y that make k || j and

m || n.

x =

y =

Answer:

130 grams

Step-by-step explanation:

Add the second amount which equals 150, and then subtract by 20.

The average of the sample ranges for the weight of packages of Skittles is 0.11. So, the correct answer is (e) 0.11.

To find the average of the sample ranges for the weight of packages of Skittles, we first calculate the range for each sample. The range is the difference between the maximum and minimum values in each sample.

Sample 1: Range\(= 3.62 - 3.58 = 0.04\)

Sample 2: Range\(= 3.65 - 3.49 = 0.16\)

Sample 3: Range \(= 3.65 - 3.45 = 0.20\)

Sample 4: Range \(= 3.64 - 3.54 = 0.10\)

Sample 5: Range\(= 3.62 - 3.49 = 0.13\)

Next, we calculate the average of these sample ranges:

A\(verage = (0.04 + 0.16 + 0.20 + 0.10 + 0.13) / 5 = 0.11\)

Therefore, the average of the sample ranges for the weight of packages of Skittles is \(0.11\). So, the correct answer is (e) \(0.11.\)

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Displacement from the origin will be 16.76 block

Pythagoras Theorem:

                                   Pythagoras theorem can be used to find the unknown side of a right-angled triangle.Theorem stats that,

                c² = a² + b²

                         where 'c' is the hypotenuse and 'a' and 'b' are the two legs.

In figure,

              O is origin,

             First travel 21 block north that means OA = 21 block.

             then,

                         travel 16 block East that means AB = 16 block.

             again finally,

                        travel 26 block South that means BC = 26 block.

Join OC,

            OC = 16 block

            CD = 5 block

we have to find the value of OD

Apply Pythagoras theorem,

                                                OD² = OC² + CD²

                                                OD = √(OC² + CD²)

                                                OD =√(16² + 5²)

                                                OD =√(256 + 25)

                                                 OD = √(256 + 25)

                                                 OD = √281 block

                                                 OD = 16.76 block

Thus,

              Displacement from the origin will be 16.76 block

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The derivative of a function represents the rate of change of the function with respect to its variable. This rate of change is described as the slope of the tangent line to the curve of the function at a specific point. The derivative of the cosine function can be found by applying the limit definition of the derivative to the cosine function.

\(f(x) = cos(x) then f'(x) = -sin(x)\).

Let's proceed with the proof.  Definition of the Derivative: The derivative of a function f(x) at x is defined as the limit as h approaches zero of the difference quotient \(f(x + h) - f(x) / h\) if this limit exists. Using this definition, we can find the derivative of the cosine function as follows:

\(f(x) = cos(x) f(x + h) = cos(x + h)\)

Now, we can substitute these expressions into the difference quotient: \(f'(x) = lim h→0 [cos(x + h) - cos(x)] / h\)

We can then simplify the expression by using the trigonometric identity for the difference of two angles:

\(cos(a - b) = cos(a)cos(b) + sin(a)sin(b)\)

Applying this identity to the numerator of the difference quotient, we obtain:

\(f'(x) = lim h→0 [cos(x)cos(h) - sin(x)sin(h) - cos(x)] / h\)

We can then factor out a cos(x) term from the numerator:

\(f'(x) = lim h→0 [cos(x)(cos(h) - 1) - sin(x)sin(h)] / h\)

We can then apply the limit laws to separate the limit into two limits:

\(f'(x) = lim h→0 cos(x) [lim h→0 (cos(h) - 1) / h] - lim h→0 sin(x) [lim h→0 sin(h) / h]\)

The first limit can be evaluated using L'Hopital's rule:

\(lim h→0 (cos(h) - 1) / h = lim h→0 -sin(h) / 1 = 0\)

Therefore, the first limit becomes zero:

\(f'(x) = lim h→0 - sin(x) [lim h→0 sin(h) / h]\)

Applying L'Hopital's rule to the second limit, we obtain:

\(lim h→0 sin(h) / h = lim h→0 cos(h) / 1 = 1\)

Therefore, the second limit becomes 1:

\(f'(x) = -sin(x)\)

Thus, we have proved that if \(f(x) = cos(x), then f'(x) = -sin(x)\).

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Step-by-step explanation:

Answer:

1/14 of 400 batteries = 56 batteries

Step-by-step explanation:

\(400 \times 0.14\)

Answer:

Actual: 28.57

Rounded: 29

Step-by-step explanation:

400/14 = 28.57

Round to nearest whole number: 29

Correct on A P E X

Answer: 4,700

Step-by-step explanation: 678 is above 650, meaning it is closer to 700 than it is 600

so rounding this makes it 4,700

unless you meant it as a decimal which 4.678 would result in 4.68 since the 8 before 7 would round up the 7 to an 8 making it 4.68

Hope this helps ^_^

Answer:

It's 4,700.

Step-by-step explanation:

When rounding to the nearest hundred, we use the following rules:

1) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

2) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

3) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

Answer:

(1, -11)

The correct answer is B

There are a total of 56 different ways that 5 cellular telephones can be selected from 8 cellular phones.

This can be calculated using the combination formula:

C(n,k) = n! / (k! * (n-k)!)

where n is the total number of items, and k is the number of items being selected.

Plugging in the values for this problem:

C(8,5) = 8! / (5! * (8-5)!)

= 8! / (5! * 3!)

= (8 * 7 * 6 * 5!)/ (5! * 3!)

= (8 * 7 * 6)/ (3 * 2 * 1)

= 56

Therefore, there are 56 different ways that 5 cellular telephones can be selected from 8 cellular phones.

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Answer:

to me it look like a reflection

Step-by-step explanation:

note in photo

Complete question :

i put $100 in a savings account at v% yearly interest. How much money will i have in my account at the end of the year

Answer:

100 + v

Step-by-step explanation:

Given that:

Interest yearly = v%

Amount deposited = principal = $100

Amount earned at the end of the year:

A = P(1 + rt)

A = 100(1 + 0.01v)

A = 100 + v

Where A = final amount

Final amount at the end of the year = 100 + v

Answer:

B.

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{2}{3} * 5 = \frac{2}{3}\frac{3}{2} x \\\)

x = 10/3

Answer:

3/8 in.

Step-by-step explanation:

If the giant bee is four times longer than a worker bee, you'd divide the giant bee's length by 4 to get the worker bee's length. 1.5 ÷4=0.375. 0.375 is equivalent to 3/8. So 3/8 in.

The slope of a beer's law plot represents that one can quantitatively determine the molar absorptivity of a substance, which is essential for accurately determining concentrations of unknown samples using spectrophotometric methods.

In Beer's law, the relationship between the concentration of a substance and its absorbance is described by the equation A = εbc, where A is the absorbance, ε is the molar absorptivity (also known as the molar absorptivity coefficient), b is the path length of the sample, and c is the concentration of the substance.

When plotting a graph of absorbance versus concentration, the slope of the line represents the molar absorptivity (ε). The molar absorptivity is a constant that reflects the substance's ability to absorb light at a specific wavelength. A higher molar absorptivity indicates that the substance has a greater tendency to absorb light and is more sensitive to changes in concentration.

Conversely, a lower molar absorptivity indicates weaker absorption characteristics.

In summary, by measuring the slope of the Beer's law plot, one can quantitatively determine the molar absorptivity of a substance.

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Answer:

SAS, ASA, SSS, ASA, Yes

Step-by-step explanation:

9514 1404 393

Answer:

  "complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

  (x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

  2a = 1

  a = 1/2

That means we can write ...

  (x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

  \(x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}\)

_____

Another way to consider this is ...

  x² +bx +c

  = x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

  = (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

  x² +x +1 = (x +1/2)² +(1 -(1/2)²)

  = (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

Answer:

66 to 70 and 85 to 90

Step-by-step explanation:

Answer:

In the graph we have y = other nuts and x = peanuts:

Now, looking at the table we can see that.

A = 9 peanuts and 7 other nuts, so this point is: A = (9,7)

we do the same to locate the other 4 points.

B = (6, 5)

C = (8, 9)

D = ( 5, 7)

E = (7, 4)

Now you need to see the graph and find those coordinates and select them.

where for example:

A = (9, 7) you need to find the point where the line number 9 in the horizontal axis crosses with the line 7 in the vertical axis (this is the bottom point on the far right)

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

Answer:

19) c  20) A 21) B  

Step-by-step explanation:

22)  D

23)  A

24)  D

Answer:

-2/5

Step-by-step explanation:

Answer:

x = -2/5 or -0.4

Step-by-step explanation:

The non-permissible replacement of the variable in a certain expression is the value of x that will make the denominator of the expression zero.

=============================================================

Then,

⇒ 5x + 2 = 0

⇒ 5x = -2

⇒ x = -2/5 or -0.4