Watermelons cost $0.35 per pound. Joseph’s watermelon costs between $4.20 and $5.25. Which compound inequality correctly represents the possible weights of his watermelon?

Answer: The derivate is f'(x) = -sin(πx/2)*(π/2)

Step-by-step explanation:

We want the value of the derivate at each point marked:

As you may know, the derivate of cos(x) is equal to -sin(x)

And in our case:

f(x) = cos(πx/2)

f'(x) = -sin(πx/2)*(π/2)

Where the rule used is that the derivate of f(g(x)) is equal to f'(g(x))*g'(x)

Now, as you may see, in both the marked points the curve changes of direction, so the tangent line in that point must be zero, letsinput the values of x in the derivate and see if this is true:

f'(0) = -sin(π*0/2)*(π/2) = -sin(0)*(π/2) = 0

f'(2) = -sin(π*2/2)*(π/2) = -sin(π)*(π/2) = 0

So this makes sense.

The approximate probability of choosing one club followed by one heart from a standard deck of 52 playing cards is 5.9%.

The student's question pertains to the calculation of the probability of choosing one club and one heart from a standard deck of 52 playing cards. We start by recognizing that there are 13 clubs and 13 hearts in the deck, with each of the four suits represented equally.

Firstly, the probability of choosing a club (P(club)) is 13/52. After a club is chosen, there are 51 cards left in the deck. The number of hearts remains the same at 13 (since a club was chosen first). So, the probability of then picking a heart (P(heart)) is 13/51.

The two events, choosing a club and then a heart, are dependent events because the outcome of the second event depends on the outcome of the first. Hence, to find the combined probability, we multiply the probabilities of each event.

The probability of choosing one club followed by one heart is therefore P(club)  imes P(heart) = (13/52)  imes (13/51), which simplifies to approximately 0.059, or 5.9%.

Answer:

B. 5p³ - 2p² - 7p + 1

Step-by-step explanation:

Good luck! Hope it was found helpful to you!

Final answer:

To solve the equation log2 (x) + log2(x+7) = 3, you can combine the logarithmic terms using the property log(a) + log(b) = log(a*b). By applying this property and solving the resulting quadratic equation, we find that x = 1.

Explanation:

To solve the equation log2 (x) + log2(x+7) = 3, we need to combine the logarithmic terms using the property log(a) + log(b) = log(a*b). Applying this property, we get log2 (x*(x+7)) = 3. Next, we can rewrite this equation in exponential form as 2^3 = x * (x+7). Simplifying further, we have 8 = x^2 + 7x. Rearranging the equation, we get a quadratic equation x^2 + 7x - 8 = 0. Solving this quadratic equation, we find that x = -8 or x = 1. However, since the logarithm of a negative number is undefined, the solution is x = 1.

the answer is B hope it helps

Answer:

Complete Quick Check of...

Lesson 4: Graphing a Function Rule

Algebra 1 A: Unit 5

Step-by-step explanation:

1.C) x,0,1,2,3, y,3,-1,-5,-9

2.A) True

3.D) $698.75

4.C) cant write it out.

5.D) C = 11n; discrete

:) hope this helps!

The total impedance of the circuit is 8 + 2i.

The total impedance in a series circuit is the sum of the individual impedances. To find the total impedance of the circuit, add the real parts and imaginary parts separately. In this case, Z1 = 3 + 4i and Z2 = 5 - 2i. So, the total impedance Zt = (3 + 5) + (4 - 2)i. Simplifying this, Zt = 8 + 2i.

Final answer:

After finding the value of x by equating m<2 and m<4, we calculate m<4 and then use the property of supplementary angles in a parallelogram to find that m<3 is 163 degrees.

Explanation:

To solve for m<3 in the parallelogram with m<2 = 5x - 28 and m<4 = 3x - 10, we first find the value of x. Given that opposite angles in a parallelogram are equal (m<2 = m<4), we set the two equations equal to each other and solve for x:

5x - 28 = 3x - 10

5x - 3x = 18

2x = 18

x = 9

Now that we have the value of x, we can substitute it into the equation for either angle to find the measure of that angle. Since m<4 = 3x - 10:

m<4 = 3(9) - 10 = 27 - 10 = 17

In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, to find m<3, we subtract m<4 from 180 degrees:

m<3 = 180 - m<4

m<3 = 180 - 17 = 163

Thus, m<3 in the parallelogram is 163 degrees.

The measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 2x - 18 \).[/tex]

In a parallelogram, opposite angles are equal. Therefore, we can set up an equation based on the given angle measures:

[tex]\[ m\angle 2 + m\angle 3 = 180^\circ \][/tex]

Substitute the given expressions for[tex]\( m\angle 2 \) and \( m\angle 4 \):[/tex]

[tex]\[ (2 + 5x - 28) + (3x - 10) = 180 \][/tex]

Combine like terms:

[tex]\[ 5x + 3x - 28 - 10 + 2 = 180 \][/tex]

[tex]\[ 8x - 36 = 180 \][/tex]

Add 36 to both sides:

[tex]\[ 8x = 216 \][/tex]

Divide by 8:

[tex]\[ x = 27 \][/tex]

Now that we have the value for x, substitute it into the expression for \( [tex]m\angle 3 \):[/tex]

[tex]\[ m\angle 3 = 2(27) - 18 \][/tex]

[tex]\[ m\angle 3 = 54 - 18 \][/tex]

[tex]\[ m\angle 3 = 36 \][/tex]

Therefore, the measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 36^\circ \).[/tex]

b: neither arithmetic nor geometric

The given sequence describes the type of sequence that is neither arithmetic nor geometric. which is the correct answer would be an option (B).

An arithmetic sequence is defined as an arrangement of numbers that is a particular order.

The sequence is given in the question following as:

1, 6, 7, 13, ...

We have to identify the type of given sequence

As per the given question, we have

1, 6, 7, 13, ...

For checking as an arithmetic sequence :

Common difference between 1 and 6 is d = 6 - 1 = 5

Common difference between 6 and 7 is d = 7 - 6 = 1

Since the common difference between consecutive terms is not the same, this means it's not an arithmetic sequence.

For checking as a geometric sequence :

Common ratio between 1 and 6 is r = 6/1 = 6

Common ratio between 6 and 7 is r = 7/6

Since the common ratio between consecutive terms is not the same, this means it's not a geometric sequence

Thus, the given sequence describes the type of sequence that is neither arithmetic nor geometric.

Learn more about arithmetic sequence here:

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