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STEP-BY-STEP

Answer: We can start by figuring out how much of the pizza was covered before Mrs. Magsanoc returned by adding the portion that she covered before the phone rang to the portion that Mr. Magsanoc covered while she was away.

Mrs. Magsanoc covered 3/8 of the pizza before the phone rang.

Mr. Magsanoc covered 1/3 of the pizza while she was away.

To add the two portions, we need to find a common denominator, which is the least common multiple of 8 and 3. That is 24.

3/8 of the pizza is (3/8) * (24/8) = 3/24

1/3 of the pizza is (1/3) * (24/3) = 8/24

So, the total portion of the pizza that was covered before Mrs. Magsanoc returned is 3/24 + 8/24

Which is 11/24 or 0.458 of the pizza.

Step-by-step explanation:

The inverse function, given the function f(x) = 5(x+4) - 6, can be found to be A. 1.

First, we need to find the inverse function of f(x). To do this, we'll switch the roles of x and y (we'll use y to represent f(x)) and then solve for y.

Given the function f(x) = 5(x + 4) - 6, let's replace f(x) with y:

y = 5(x + 4) - 6

x = 5(y + 4) - 6

x = 5y + 20 - 6

x = 5y + 14

x - 14 = 5y

y = (x - 14) / 5

Now we have the inverse function, f^(-1)(x) = (x - 14) / 5. To find the value of the inverse function when x = 19, plug in 19 for x:

f^(-1)(19) = (19 - 14) / 5

f^(-1)(19) = 5 / 5

f^(-1)(19) = 1

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Another possible vertex of the square is determined as (2, 1).

option B is the correct answer.

The vertex of a figure is the point of intersection of two sides of the shape.

The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;

P = 12 units

a side length = 12 units / 4 = 3 units

To determine another possible vertex of the square, the length between the points must be equal to 3.

Let's consider point A;

A = (1, 2)

given vertex = (-1, 1)

distance between the points = √ (-1 -1)² + (1 - 2)² = √5

Let's consider point B;

B = (2, 1)

given vertex = (-1, 1)

distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3

Thus, point B is another possible vertex of the square.

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To find the perimeter and area of the fountain, which consists of two semicircles and a quarter circle, we'll need to calculate the measurements based on the given diameter of 16 feet.

First, let's calculate the perimeter:

Perimeter of a semicircle: The perimeter of a semicircle is half the circumference of a full circle. The formula is P = πr + 2r, where r is the radius.

For the two semicircles, the combined perimeter is: (πr + 2r) + (πr + 2r) = 2πr + 4r.

Perimeter of a quarter circle: The perimeter of a quarter circle is one-fourth the circumference of a full circle. The formula is P = (πd)/4, where d is the diameter.

Now, let's calculate the area:

Area of a semicircle: The area of a semicircle is half the area of a full circle. The formula is A = (πr^2)/2, where r is the radius.

For the two semicircles, the combined area is: ((πr^2)/2) + ((πr^2)/2) = πr^2.

Area of a quarter circle: The area of a quarter circle is one-fourth the area of a full circle. The formula is A = (πr^2)/4.

Given that the diameter is 16 feet, the radius (r) is half the diameter, which is 8 feet.

Calculating the perimeter:

Perimeter = 2πr + 4r = 2π(8) + 4(8) ≈ 50.27 + 32 ≈ 82.27 feet (rounded to the nearest tenth).

Calculating the area:

Area = πr^2 + πr^2/4 = π(8)^2 + π(8)^2/4 ≈ 201.06 + 50.27 ≈ 251.33 square feet (rounded to the nearest whole).

Therefore, the perimeter of the fountain is approximately 82.3 feet, and the area is approximately 251 square feet.

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Answer:

7.5 hours

Step-by-step explanation:

distance = rate * time (d=rt)

First we find her average rate, or speed:

Now we take that rate and use our second distance to find the time:

d = rt

t = d/r = 350 miles / 46.6666 miles/hour = 7.5 hours

The number that is a factor is 63 is C. 7.

In mathematics, a factor of a number is a divisor of the given number that divides it completely without leaving any remainder.

A factor is a number that divides another number by itself and leaves no remainder. In other words, if multiplying two whole numbers yields a product, then the numbers being multiplied are factors of the product because the product is divisible by them.

A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another integer to produce n. In this case, n is also said to be a multiple of m.

In this case, the factors of 63 are 1, 3, 7, 9, 21 and 63.

The factor is 7.

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Complete question

Which of the following numbers is a factor of 63

2

5

7

11

Answer:

4*\(\sqrt3\)

Step-by-step explanation:

The estimation of 0.000007328 is \(7\times10^{-6\).

Estimation is he ability to guess the amount of anything without actual measurement.

The number (n) is given as:

\(\text{n}=0.000007328\)

Multiply by 1

\(\text{n}=0.000007328\times1\)

The number is to be rounded to the nearest millionth.

So, we substitute \(\frac{1000000}{1000000}\) for 1

\(\text{n}=0.000007328\times1\)

\(\text{n}=0.000007328\times\dfrac{1000000}{1000000}\)

This becomes

\(\text{n}=7.328\times\dfrac{1}{1000000}\)

Express the fraction as a power of 10

\(\text{n}=7.328\times10^{-6\)

Approximate to a single digit

\(\rightarrow\bold{n=7\times10^{-6}}\)

Therefore, the estimation of 0.000007328 is \(7\times10^{-6}\).

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The median of 14 is the most accurate to use, since the data is skewed.

The most appropriate measure of center to represent the data depends on the nature of the data distribution. Looking at the histogram provided, it appears that the data is positively skewed, with a long tail towards the right. This means that there are a few larger values (donations in this case) that are pulling the mean towards the right, while the median is a better representative of the typical or central donation.

Therefore, in this case, the median of 14 is the most accurate measure of center to use to represent the data, since it is less affected by the extreme values and gives a better idea of the central tendency of the data. The mean of 13.2 is also close to the median and can be used as a measure of center, but it is not as representative of the typical donation due to the skewness of the data.

The median of 13.2 and the mean of 14 cannot be used to show whether the charity needs more or plenty of money, as this depends on other factors such as the expenses and goals of the charity.

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The length of arc KJG is,

⇒ arc KJG = 120.5

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

In a circle,

JH = 21 in.

Now, We get;

Angle KLJ = 90 degree

And, By definition of linear pair angle.

∠ ILH = 180 - 85

∠ ILH = 95°

Hence, WE get;

∠ KJG = 90 + 85 + 95 + 59

∠ KJG = 329 degree

So, The length of arc KJG is,

arc KJG = 329 × 2 × 3.14 × 21 / 360

arc KJG = 120.5

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The total amount money after thirteen years of savings will be $5030.63

To calculate the amount of money in the account today, we need to calculate the future value of each contribution separately and then add them together.

Let's start by calculating the future value of the initial deposit of $2400 over the first five years at an interest rate of 8% compounded annually.

Using the formula for compound interest:

Future Value = \(Principal\) * \((1 + Interest Rate)^{Time}\)

Future Value = $2400 * (1 + 0.08)⁽⁵⁾

Future Value = $2400 * (1.08)⁵

Future Value = $2400 * 1.46933

Future Value = $3526.40

So, after five years, the initial deposit will grow to $3526.40.

Now, let's calculate the future value of the additional deposit of $1000 over the last eight years at an interest rate of 5.5% compounded annually.

Future Value = $1000 * (1 + 0.055)⁸

Future Value = $1000 * (1.055)⁸

Future Value = $1000 * 1.50423

Future Value = $1504.23

So, after eight years, the additional deposit will grow to $1504.23.

Now, let's add the two amounts together to find the total amount in the account today:

Total Amount = $3526.40 + $1504.23

Total Amount = $5030.63

So, the total amount money after thirteen years of saving will be $5030.63

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Complete question:

Thirteen years ago, you deposited $2400 into a superannuation fund. Eight years ago, you added an additional $1000 to this account. You earned 8%, compounded annually, for the first five years, and 5.5%, compounded annually, for the last eight years. How much money do you have in your account today?

Answer:

Law of Cosines, all sides are known

Step-by-step explanation:

q² = p² + r² − 2pr cos(Q) or

\(\frac{-q^{2}+p^{2}+r^{2} }{2pr}\) = cos (Q)

Q = \(cos^{-1}\) \((\frac{-q^{2}+p^{2}+r^{2} }{2pr})\)

The cos law should use in the provided situation, option (A) Law of Cosines, all sides are known is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have given a triangle in which sides r, p, and q are given.

As per the cos law,

If we have three sides of a triangle known then we can find the unknown angle.

q² = r² + p² - 2rpcosQ

Q is the angle opposite to the side.

The angle can be defined as when two lines or rays converge at the same point, the measurement between them is called an "Angle."

Thus, the cos law should use in the provided situation, option (A) Law of Cosines, all sides are known is correct.

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

Convert fractions into decimal, round up if the decimal is 0.5 and/or higher, and round down if less than 0.5

Example for question 1: 5/6= 0.83 ← greater than 0.5, so round up to 2

Step-by-step explanation:

1. 2

2. 5

3. 113

4.86

5. 66

6. 19

7. 72

To find the volume of the solid obtained by rotating the region bounded by the curves about a specified axis, we can use the method of cylindrical shells.The limits of integration will be from y = 0 (the lower curve) to y = 2 (the upper curve).

In this case, the region is bounded by the curves x+y=2 and x = 3 – (y - 1), and we need to rotate it about the y-axis.

First, let's find the intersection points of the two curves:

x + y = 2

x = 3 – (y - 1)

Setting the equations equal to each other:

2 = 3 – (y - 1)

2 = 3 - y + 1

y = 2

So the curves intersect at the point (2, 2).

To find the volume, we integrate the circumference of each cylindrical shell and multiply it by the height. The height of each shell is the difference between the upper and lower curves at a given y-value.

Note: The negative sign in the volume indicates that the solid is oriented in the opposite direction, but it doesn't affect the magnitude of the volume.

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Answer: The ratio of eggs, eggs, to two cups of flour. Let me write two cups of flour. Cups of flour. In either case is, is four eggs for every three cups of flour 5/2

Step-by-step explanation: Im not sure through

Answer:

No, even though there is a strong negative correlation, not eating vegetables doesn’t necessarily cause high blood pressure

Step-by-step explanation:

Brainliest ?

Answer:

BC= 24

Step-by-step explanation:

thhe triangle is isosceles

x+8 =2x-1

x -2x = -1 -8

-x = -9

x=9

substitute x=9 into the equation of BC

BC = 3x-3= 3*9 -3 = 27 -3 = 24

Answer:

A) Amanda will pay $47.5

B) 0.5

C) $120

Step-by-step explanation:

A) From the graph given, at 45 miles, the total cost of rentage = $142.50

She now splits this cost with 2 of her friends. Thus each of them will pay;

Amount = 142.5/3 = $47.5

So,Amanda will pay $47.5

B) To find the slope, we will pick two points on the graph and use their respective coordinates to find the slope.

Coordinates we pick are;

(0, 120) and (50, 145)

Thus, slope; m = (y2 - y1)/(x2 - x1)

m = (145 - 120)/(50 - 0)

m = 25/50

m = 0.5

C) The equation for the graph will now be; y = mx + c

Where m is slope and c is y - intercept.

Thus;

y = 0.5x + 120

Coincidentally, c = 120 will be the fixed price of the truck while 0.5x will be the variable cost depending on how many miles are driven.

Thus renting for a day is simply the fixed cost of $120

the correct answer is option b.

The highest point of a normal curve

occurs at the mean, which is the central value, as shown below:

A normal curve is a bell-shaped curve with a

symmetrical distribution around the mean. The total area under the normal curve is 1. It is continuous and smooth with tails that extend indefinitely in both directions.There are certain characteristics of the normal curve:It is a unimodal and symmetrical curve.It is a bell-shaped curve

.The mean, median, and mode are all equal in a normal distribution.It is distributed in such a way that the tails are symmetrical on both sides of the mean.It is defined by its mean and standard deviation. It has an infinite domain. It is a continuous distribution and is defined by its mean and

standard deviation

.

The highest point of a normal curve occurs at the mean, which is the central value. Therefore, the correct answer is option b.

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The correct answer is b. The highest point of a normal curve occurs at the mean.

The highest point of a normal curve, also known as the peak or the mode, occurs at the mean. This means that option b is the correct answer.

A normal curve, also called a bell curve or a Gaussian curve, is a symmetric probability distribution that is commonly used in statistics. It is characterized by its mean and standard deviation. The mean represents the average or central value of the distribution, while the standard deviation measures the spread or dispersion of the data.

In a normal distribution, the highest point occurs at the mean because it is the most frequent value in the data set. As we move away from the mean in either direction, the frequency decreases. The shape of the curve is symmetrical, with equal areas on both sides of the mean.

Options a, c, and d suggest points that are a certain number of standard deviations away from the mean. While these points are important for understanding the distribution and making calculations, they do not represent the highest point of the curve.

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Answer:

15 minutes

There are 20 quarter hours in 5 hours. This is solved by first breaking down an hour into quarters. A quarter is 1/4 of an hour, or 15 minutes.

Answer:

75 minutes

Step-by-step explanation:

5 hours = 60 x 5 = 300 minutes

300 ÷ 4 = 75 minutes

Answer:

4−2x<−3

Step-by-step explanation:

check:

now --- 4°

after 1 hr --- 2°

after 2 hrs--- 0°

after 3 hrs--- -2°

after 4 hrs--- -4°

so between 3 and 4 hrs it will reach -3°

4-2x < -3

-2x < -7

x > 3 1/2

Step-by-step explanation:

Since the dilation is centered at the origin, you can multiply each of the coordinates by the scale factor. This means the image is A'(-6, -6)

Answer:

l=k/4+7/4

Step-by-step explanation:

Answer:

what language is that??

Step-by-step explanation:

Answer:

3,814,697,265,625

Step-by-step explanation:

Simplify the expression.

Answer:

y= 2/3x + 2

Step-by-step explanation:

Answer:

This is undefined because the slope is 3/0, and you can't divide by 0