Please help and show work

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

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The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

Amounts of weight that male college students gain during their freshman year are normally distributed

mean of μ = 1.1 kg and

Standard deviation of o= 4.6 kg.

Z score=x-μ/o

=25-1.1/4.6

=23.9/4.6

=5.196

Z score=x-μ/o

=25-1.1/0

=0

Z score=25-1.1/3

=23.9/3

=7.966

By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

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Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

We can see that Natalie is reducing the amount she owes by $18 every two weeks.

Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.

This means that after n weeks, the amount she still owes is:

$180 - $18n

Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:

$180 - P

After two weeks, she will owe:

($180 - P) - P = $180 - 2P

After four weeks, she will owe:

($180 - 2P) - P - P = $180 - 4P

After six weeks, she will owe:

($180 - 4P) - P - P = $180 - 6P

And after eight weeks, she will owe:

($180 - 6P) - P - P = $180 - 8P

We can set up an equation using the information we have:

$180 - 8P = $108

Solving for P, we get:

P = $9

Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

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The complete question:

Natalie borrowed money from her parents to pay for a trip. ​Natalie will ​pay her parents in equal amounts every week until she pays back the ​entire amount she borrowed. ​ ​The table below shows the amount of ​money Natalie still owes her parents at the end of every two weeks for ​the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?

Week 0 = $180

Week 2 = $162

Weeks 4 = $144

Week 6 = $126

Week 8 = $108

Answer:

3) -11

Step-by-step explanation:

f(-3)=5*(-3)+4

f(-3)=(-15)+4

f(-3)=-11

Given:

f(x) = 5x + 4

To Find:

f(-3)

Answer:

(3) -11

Step-by-step explanation:

Evaluate 5x + 4 where x = -3:

\( \longrightarrow \) 5(-3) + 4

5(-3) = -15:

\( \longrightarrow \) -15 + 4

4 - 15 = -11:

\( \longrightarrow \) -11

Lilliana runs 2 laps on Saturday.

In mathematics and physics, distance refers to the numerical value that measures the space between two points, objects, or locations. It is a scalar quantity that represents the length of the shortest path between two points.

Distance can be measured in various units, such as meters, kilometers, miles, or light-years, depending on the scale of the space being measured. In one-dimensional space, such as a straight line, distance is simply the absolute value of the difference between the two points. In two-dimensional space, such as a plane, distance is calculated using the Pythagorean theorem, which relates the sides of a right triangle. In three-dimensional space, such as physical space, distance is calculated using the distance formula, which extends the Pythagorean theorem to three dimensions.

Distance is an important concept in many areas of mathematics and science, including geometry, physics, and statistics. It is often used in real-world applications, such as navigation, transportation, and astronomy.

We know that Lilliana runs the same distance every day for a week. On Monday, Wednesday, and Friday, she runs 2 laps on the running trail which we can assume is a distance of x and then runs 6 more miles. This gives us a total of x + 6 miles. Therefore, she runs a total distance of 2(x) + 6 miles on those days.

On Tuesday and Sunday, she runs 4 laps on the trail which is a distance of 2x, and then runs 2 more miles which gives us a total of 2x + 2 miles. Therefore, she runs a total distance of 2(2x) + 2 miles on those days.

On Saturday, she runs the same distance as every other day. Therefore, she runs a total distance of 2(x) + 6 miles on Saturday as well.

We can now set up an equation to find x:

2(2x) + 2 + 2(x) + 6 + 2(x) + 6 = 7(2x) + 6

6x + 16 = 14x + 6

10x = 10

x = 1

Now that we know x is 1 mile, we can find out how many laps Lilliana runs on Saturday. We know that 2 laps is 1 mile, so she must run 2 laps on Saturday.

Therefore, Lilliana runs 2 laps on Saturday.

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Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

The values of a and b are a = -3 and b = 42. The solutions for x can be written as:

x = -3 - √42

x = -3 + √42

To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:

Step 1: Move the constant term to the right side:

2x² + 12x - 66 = 0

Step 2: Divide the equation by the leading coefficient (2):

x² + 6x - 33 = 0

Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:

x² + 6x + (6/2)² = 33 + (6/2)²

x² + 6x + 9 = 33 + 9

x² + 6x + 9 = 42

Step 4: Rewrite the left side as a perfect square:

(x + 3)² = 42

Step 5: Take the square root of both sides:

√(x + 3)² = ±√42

x + 3 = ±√42

Step 6: Solve for x:

x = -3 ± √42.

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The length of the diagonal of the rectangle is AC = 17.69 units

The diagonal of a rectangle is calculated by the formula

From the Pythagoras Theorem , The hypotenuse² = base² + height² , and

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

Given data ,

Let the rectangle be represented as ABCD

Now , the measure of side AB = 12 units

The measure of side BC = 13 units

Let the length be BC and the width be AB

where the diagonal of the rectangle is AC

Now , Diagonal of a Rectangle = √ ( Length )² + ( Width )²

On simplifying , we get

The diagonal of the rectangle AC = √ ( 12 )² + ( 13 )²

The diagonal of the rectangle AC = √ ( 144 + 169 )

The diagonal of the rectangle AC = √313

The diagonal of the rectangle AC = 17.69 units

Hence , the diagonal of the rectangle is 17.69 units

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Answer:

2062 4/11

Step-by-step explanation:

Okay so assuming 2003 4/11 is a mixed number, we just add:

2003 4/11 + 59 = 2062 4/11

Hope this helps:)

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

-------------------------

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

Answer:

Remaining balance = AED 13.75

Step-by-step explanation:

Given that:

Amount of gift card = AED 20

Amount left after buying 3 songs = AED 16.25

Cost of 3 songs = 20 - 16.25 = AED 3.75

Cost per song = \(\frac{3.75}{3}\)

Cost per song = AED 1.25

Cost of 5 songs = 5(1.25) = AED 6.25

Remaining balance = 20 - 6.25 = AED 13.75

Hence,

Remaining balance = AED 13.75

Answer:

12.56637061 ?????

Step-by-step explanation:

Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

Answer:

3-5(-3)

3 minus -15

-12

Step-by-step explanation:

There are 13 $20 bills and 16 $5 bills 6 in the collection.

A system of linear equations is a set of two or more linear equations involving the same variables. The solution to a system of linear equations is the values of the variables that satisfy all the equations in the system.

To solve the following problem use variables and form linear equations according to the given conditions in the problem. Solve the equation for the values of variables.

Here we have

Part of the proceeds from a garage sale was ​$340 worth of ​$5 and ​$20 bills. There were 3 more ​$5 bills than ​$20 ​bills

Let's use variables to represent the number of $5 and $20 bills.

Let x be the number of $20 bills, then the number of $5 bills is x + 3.

The total value of the $20 bills is 20x,

The total value of the $5 bills is 5(x + 3) = 5x + 15.

According to the problem,

The total value of the bills is $340, so we can set up the equation:

20x + 5x + 15 = 340

Simplifying and solving for x, we get:

25x = 325

x = 13

Therefore,

There are 13 $20 bills and 16 $5 bills 6 in the collection.

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Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

Answer:

DAB = BCD

Step-by-step explanation:

DAC = BAC = 90 degrees and DAB = ABC = 90 degrees don't work because they're both equilateral triangles and don't have a right angle that would equal 90. DAB = ABC are clearly not congruent so the answer is DAB = BCD. Also DAB = BCD share the same midsection line.

Answer:

\(x=5\)

Step-by-step explanation:

The perimeter of a figure is the sum of all its sides.

The sides are x, (x+3), and (2x). The perimeter is 23, so the sum of the expression equates to 23. Thus:

\(x+(x+3)+(2x)=23\)

Combine like terms:

\(4x+3=23\)

Subtract 3 from both sides:

\(4x=20\)

Divide both sides by 4:"

\(x=5\)

And we're done!

It is just a way of describing a set.

You put the set in braces (sometimes called curly brackets), {}, which is a typical way to show that you are talking about sets.

Here are a few examples:

{x| x > 0} This is read: The set of all x such that x is greater than 0.

Reading it character by character:

{ — shows you that we are talking about a set, and it sort of opens up, or starts the set

x — tells you that we are talking about a set of elements x

| (and a : is also used sometimes) — such that (this is just notation). This says that you are about to be given to rule to see what “rule” or characteristic the x’s will have.

x > 0 — This just says what characteristics x must have to be in this set. So 7, 1/2, .3 and pi are all in this set, while -1, 0, -radical(2) are not.

So this example is just how you would use set builder notation to talk about the set “the positive real numbers”

So why use it? Because it can describe more complicated sets much more succinctly.

2. {3n + 1 | n is an element of the natural numbers} (and this could be written more succinctly if I used certain symbols) would be the set {4, 7, 10, 13, …}

3. {n^2 + n + 1 | n is an element of the natural numbers} would be the set {3, 7, 13, 21, …} and notice here, if you didn’t see the set builder notation, you might have trouble knowing what the next term in the set was.

Answer:

.3

Step-by-step explanation:

7+7+6=20

6 green out of 20 total

.30 chance

The Relative Maximum will be (7, 50) and minimum is (12, 0).

We have the graph showing average low temperatures in international falls minnesota.

From the graph the maximum y coordinate is 50.

So, the Relative Maximum will be (7, 50).

and, the minimum y coordinate is 0.

So, the Relative minimum is (12, 0)

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Answer: 9

Step-by-step explanation: Since the distance between these is only horizontal, it is easy to find. 4 + 5 = 9

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

The coordinate of the other stop sign located will be (21, 3).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Kelsey’s neighborhood has a straight road with stop signs at both ends and a fire hydrant at its midpoint. On a map, the fire hydrant is located at (12,7) and one of the stop signs is located at (3,11).

Then the coordinate of the other stop sign located is given as,

(12, 7) = [(x₁ + 3) / 2, (y₁ + 11) / 2]

(24, 14) = [x₁ + 3, y₁ + 11)

(21, 3) = (x₁, y₁)

(x₁, y₁) = (21, 3)

The coordinate of the other stop sign located will be (21, 3).

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Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)