Juanita wants to buy 12.5 pounds of stones to decorate her garden. The stone normally sells for $1.80 a pound. The salesman offers her a total price of $21.25. How much is she saving per pound with the salesman’s offer? Round to the nearest hundredth.
Juanita is saving $0.10 a pound.
Juanita is saving $0.17 a pound.
Juanita is saving $1.00 a pound.
Juanita is saving $1.17 a pound.

Answer:

n < 4

Step-by-step explanation:

\(\frac{1}{2} n+3<5\)

     -3     -3

\(\frac{1}{2} n\) < 2

divide  both sides by \(\frac{1}{2}\)

n < 4

Hope this helps!!!

The " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

The equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.    

" Eight  further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've =  " 3" is the value to which the expression on the left side is equal, so we've 3  Putting it all together the  judgment " Eight  further than the quotient of a number and 7 is equal to 3" can be  restated into the equation ( x/ 7) =  3  

In this equation, x represents the number we're trying to find. To  break for x, we can manipulate the equation using algebraic operations to  insulate x on one side of the equation.  By abating 8 from both sides of the equation, we get ( x/ 7)- 8 =  3- 8  Simplifying, we have  x/ 7 = -5

To  insulate x, we can multiply both sides of the equation by 7  *( x/ 7) = -5 * 7  This gives us  x = -35  thus, the equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

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Answer:

False

Step-by-step explanation:

9 cannot be equal to 31

1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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a) Let X represent the random variable of the number of Californians in the sample of 6 people who have been to Disneyland.

b) X is a binomial random variable because it records the number of successes (people who have been to Disneyland) in a fixed number of trials (6 people).

c) The probability =3.05.

d) The mean of X is 2.46.

e) The standard deviation of X is 1.2.

f) The probability 68.27%.

It is used to measure the spread of data around the mean or expected value.

a) Let X represent the random variable of the number of Californians in the sample of 6 people who have been to Disneyland.

b) X is a binomial random variable because it records the number of successes (people who have been to Disneyland) in a fixed number of trials (6 people).

c) The probability of exactly 3 people having been to Disneyland is 3.05.

This is calculated using the binomial probability formula:

P(x=3) = (6³) * (0.41³) * (0.59³)

= 3.05

d) The mean of X is 2.46. This is calculated using the binomial mean formula:

μ = n * p

= 6 * 0.41

= 2.46

e) The standard deviation of X is 1.2. This is calculated using the binomial standard deviation formula:

σ = √[n * p * (1 - p)]

= √[6 * 0.41 * (1 - 0.41)]

= 1.2

f) The probability that the number of Californians in the sample that have been to Disneyland is within one standard deviation of the mean is 68.27%.

This is calculated using the standard normal distribution z-score formula:

P(1.19<z<2.73) = 0.6827

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Answer:

D

Step-by-step explanation:

0.6x17.5 which is 10.5

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer:

Correct option: D. 0.6

Step-by-step explanation:

The Venn diagram shows that there is no intersection between events A and B, so we have that:

P(A and B) = 0

Therefore the probability of A or B is:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = P(A) + P(B)

So, If the sum of the probabilities needs to be 1, we have that:

Total = P(A or B) + P(neither)

Total = P(A) + P(B) + P(neither)

1 = 0.2 + P(B) + 0.2

P(B) = 1 - 0.2 - 0.2 = 0.6

So the correct option is D.

Answer:0.6

Step-by-step explanation:

Answer:  16.97

Step-by-step explanation:

To find the distance from W to X, you can use the distance formula ...or... draw a right triangle using W and X as the vertices and use Pythagorean Theorem to find the hypotenuse. I will solve using the latter.

The y-distance from W to X is 12.

The x-distance from W to X is 12.

hypotenuse² = 12² + 12²

                      = 144 + 144

                      = 288

hypotenuse = \(\sqrt{288}\)

                     = 16.97

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

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Answer:

b .3

Step-by-step explanation:

every thing else is even and if u add them up u will get to 32 eventually

Answer:

B.) 3

Step-by-step explanation:

To do this problem, we should find out what factors can equal 32. So let's start with finding out. This problem is going to require multiplication and division.

Letter A is a multiple of 32, because:

32 ÷ 2 = 16, which means that 16 x 2 = 32.

Because 2 can be divided equally into 32, this answer is wrong.

_________________

Letter C is a multiple of 32, because:

32 ÷ 4 = 8, which means that 8 x 4 = 32.

Because 4 can be divided equally into 32, this answer is also wrong.

_________________

And, because the last answer equaled 8, that means that:

32 ÷ 8 = 4, which means that 4 x 8 = 32.

Which is also wrong.

_________________

This leaves us with 32 ÷ 3 = 10.6666666667. This answer cannot be multiplied evenly into 32, so it is correct.

I hope that this helps.

Answer:

Step-by-step explanation:

0.14x + 0.06(20,500 - x) = 2,670.00

0.14x + 1,230 - 0.06x = 2,670.00

0.08x + 1,230 = 2,670.00

0.08x = 2,670.00 - 1,230

0.08x = 1,440.00

x = 1,440.00 / 0.08

x = 18,000.00

invested $18,000.00 in the bond account and $2,500.00 (20,500 - 18,000) in the certificate of deposit account.

Answer:

D

Step-by-step explanation:

10.50÷3=3.50

Answer:

D. $3.50

Step-by-step explanation:

The phone company charges a total of $10.50 for 3 hours so for one hour you would have to divide 10.50 by 3 to get the answer for ONE hour.

The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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Answer:

S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:

(3,p): The first element is 3 and the second element is p.

(3,0): The first element is 3 and the second element is 0.

(4,q): The first element is 4 and the second element is q.

(1,4): The first element is 1 and the second element is 4.

Answer:

4

Step-by-step explanation:

1) True

2) False

3) True

4) False

The first is true.

The second is false.

The third is true because an integer is only whole numbers, but rational numbers include fractions.

The fourth is false. All whole numbers are integers.

Step-by-step explanation:

The given equations are :

2x+ y =5 ....(1)

5x+3y = 12

We need to find the matrix equation that represents the system of equations.

\([A]=\left[\begin{array}{cc}2&1&\\5&3\end{array}\right]\)

\([B]=\left[\begin{array}{cc}5\\12\end{array}\right]\)

And

\([X]=\left[\begin{array}{cc}x\\y\end{array}\right]\)

Hence, the matrix equation is :

\(\left[\begin{array}{cc}2&1&\\5&3\end{array}\right] \left[\begin{array}{cc}x\\y\end{array}\right]=\left[\begin{array}{cc}5\\12\end{array}\right]\)

Hence, the correct option is (b).

Answer:

0

Step-by-step explanation:

\(\displaystyle \frac{F(b)-F(a)}{b-a}\\\\=\frac{F(\pi)-F(-\pi)}{\pi-(-\pi)}\\\\=\frac{\sin(4\pi)-\sin(-4\pi)}{2\pi}\\\\=\frac{0-0}{2\pi}\\\\=0\)

Not sure how the correct answer is stated as 45/28, but the answer is definitely 0.

Answer: It would be C

Step-by-step explanation:

80/16= 5oz

Answer:

Step-by-step explanation:

Answer:

4.6 x 10^7

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The left-hand side of the equation represents the logarithm of 64 with base x, and it is not possible to find a real value of x that satisfies the equation.

solve the equation logₓ(64) + 5 = 2, we can follow these steps:

Step 1: Move the constant term to the other side of the equation:

logₓ(64) = 2 - 5

logₓ(64) = -3

Step 2: Rewrite the equation in exponential form:

x^(-3) = 64

Step 3: Rewrite 64 as a power of x:

x^(-3) = x^6

Step 4: Set the exponents equal to each other:

-3 = 6

The equation -3 = 6 is not true, which means there is no real solution to the given equation.

Therefore, the equation logₓ(64) + 5 = 2 has no solution in the real number system.

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\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer:

c) The population is the parents of the pediatrician's patients; the sample is the

10

1010 parents of patients selected.

Step-by-step explanation:

Answer:

c) The population is the parents of the pediatrician's patients; the sample is the

10

1010 parents of patients selected.

Step-by-step explanation:

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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Answer:

\(-x^4-5x^3+8x^2\)

Step-by-step explanation:

\(\left(-x^2\right)x^2+\left(-x^2\right)\cdot \:5x+\left(-x^2\right)\left(-8\right)\\-x^2x^2-5x^2x+8x^2\\-x^4-5x^3+8x^2\)

Answer: −x4−5x3+8x2

Step-by-step explanation:

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3500\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}\)

\(A=3500\left(1+\frac{0.02}{1}\right)^{1\cdot 5}\implies A\approx 3864.28~\hfill \underset{earned~interest}{\stackrel{3864.28~~ - ~~3500}{\approx 364.28}}\)

Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

<95141404393>

The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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