Rachel cycled a total distance of 59,136ft on a bicycle path surrounding a lake. She cycled 4 laps, where each lap was the same length. What was the length of each lap around the lake? Write your answer in miles.

If X and Y are two sets, then X × Y is the Cartesian product of X and Y, which is the set of all pairs (x, y) such that x ∈ X and y ∈ Y.

This means

A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}

Answer:

50 + 40

30 + 60

Step-by-step explanation:

Answer:120

Step-by-step explanation:

The actual base of the building is 1890 square feet.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

1 inch = 15 feet

Rectangular base:

Length = 4.2 in

Width = 2 in

So,

4.2 in = 4.2 x 15 feet = 63 feet

2 in = 2 x 15 = 30 feet

Now,

The actual base of the building.

= 63 x 30

= 1890 square feet

Thus,

1890 square feet.

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Answer:linear function

Step-by-step explanation:

The cost of mailing a first class letter weighing 2.5 ounces is $0.96,

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now given that,

cost of mailing a first-class letter for the first ounce = $0.46

cost of additional ounce or portion of an ounce = $0.20

Since,the weight of letter is x ounces

cost of mailing a first-class letter = $0.2x

Now,Y is the total cost for mailing a letter

Y = 0.46 + 0.2x

Therefore, the cost of mailing a first class letter weighing 2.5 ounces

Y = 0.46 + 0.2*2.5

⇒ Y = 0.46 + 0.5

Y = $0.96

Thus,The cost of mailing a first class letter weighing 2.5 ounces is $0.96

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Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Answer:

y = -4/3x + 2

Step-by-step explanation:

Slope intercept form is y = mx + b.

Rearrange the equation into slope intercept form by isolating y:

12x + 9y = 18

9y = -12x + 18

Divide each side by 9:

y = -4/3x + 2

So, the equation is y = -4/3x + 2

Answer: 12:5

Step-by-step explanation:

Total apples in the basket, add all apples: 7+5=12

Red apples:5

Total apples:red apples, 12:5

Answer:

Step by step explanation:

well this is simble you just do it

Answer:

\(14\sqrt[4]{5}+2\sqrt[3]{3}\)

Step-by-step explanation:

\(3\sqrt[4]{80}+\sqrt[3]{24}+8\sqrt[4]{5}\\=3\sqrt[4]{16*5}+\sqrt[3]{8*3}+8\sqrt[4]{5}\\=(3*2)\sqrt[4]{5}+2\sqrt[3]{3}+8\sqrt[4]{5}\\=6\sqrt[4]{5}+2\sqrt[3]{3}+8\sqrt[4]{5}\\=14\sqrt[4]{5}+2\sqrt[3]{3}\)

Answer:

464.4$

Step-by-step explanation:

Since 1 hour makes a total of 15.48$, 30 hours will make 464.4$. Simply Multiply 15.48$ by 30 hours to get your total weeks pay

Answer:

A bus driver makes $15.48 pee hour. Sheila worked 30 hrs . 30× 15.48 = 464.4 dollars

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65

Answer:

Increasing on the interval:  (-2, 0) ∪ (2, ∞)

Decreasing on the interval:  (-∞, -2) ∪ (0, 2)

Step-by-step explanation:

A function is increasing when f'(x) > 0

A function is decreasing when f'(x) < 0

Therefore, to find the intervals for which the function is increasing and decreasing, differentiate the given function.

\(\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

Given function:

\(f(x)=(x^2-4)^{\frac{2}{3}}\)

\(\begin{aligned}\textsf{Let} \; u &= (x^2-4) \quad &\implies y&=u^{\frac{2}{3}}\\\\\implies \dfrac{\text{d}u}{\text{d}x}&=2x \quad &\implies \dfrac{\text{d}y}{\text{d}u}&=\dfrac{2}{3}u^{-\frac{1}{3}}=\dfrac{2}{3} (x^2-4)^{-\frac{1}{3}}\end{aligned}\)

Therefore:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{2}{3} (x^2-4)^{-\frac{1}{3}} \times 2x\)

\(\implies f'(x)=\dfrac{4}{3}x (x^2-4)^{-\frac{1}{3}}\)

\(\implies f'(x)=\dfrac{4x}{3 \sqrt[3]{x^2-4}}}\)

Stationary points occur when f'(x) = 0:

\(\implies \dfrac{4x}{3 \sqrt[3]{x^2-4}}}=0\)

\(\implies 4x=0\)

\(\implies x=0\)

Therefore, the function has is a stationary point (turning point) when x = 0.

The derivative is undefined when the denominator equals zero.

The denominator equals zero when x² = 4, so when x = ±2.

The derivative is positive when x > 2 and negative when x < -2.

Therefore, determine the nature of the derivative in the intervals between the stationary point x = 0 and x = ±2.

\(\implies f'(-1)=\dfrac{4(-1)}{3 \sqrt[3]{(-1)^2-4}}}=\dfrac{\rm negative}{\rm negative}= \rm positive > 0\)

\(\implies f'(1)=\dfrac{4(1)}{3 \sqrt[3]{(1)^2-4}}}=\dfrac{\rm positive}{\rm negative}= \rm negative < 0\)

Therefore, the function is:

Answer:

x=3

x=-13

Step-by-step explanation:

With these type of equations, there will always be two answers because x can be positive or negative. So, there are two equations.

x+5=8

x+5=-8

Simplify both of them

x=3

x=-13

We know these are correct because if you plug them into the original equation |x+5|=8, both are good solutions

Answer:

(A)

Null hypothesis: Newspaper circulation in the city per day was = 15,000 in 2010

(B)

Alternative hypothesis: Newspaper circulation in the city today is > 15,000

(C)

Type 1 Error: This is the rejection of a true null hypothesis. It is the acceptance of the alternative hypothesis when the null hypothesis is true.

(D)

Type 2 Error: This is the non-rejection of a false null hypothesis. It is the acceptance of a null hypothesis when it is false.

Step-by-step explanation:

In statistical theory, the complete absence of any of these errors is virtually impossible.

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer: R = -5

Step-by-step explanation: 3r + 7= -8 is turned into 3(-5) + 7= 8.                                             -15 + 7=8

Answer:

1.5 pounds

Step-by-step explanation:

3/2 = 1.5

Pythagorean Theorem states that the area of the blue square + the area of the red square = the area of the purple square.

Consider the triangle

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

The side opposite to the right angle (90°)  is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Hence, Pythagorean Theorem states that the area of the blue square + the area of the red square = the area of the purple square.

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Answer:

32768x¹⁰

Step-by-step explanation:

by applying the law of indices

multiply the powers inside the parentheses with the power outside of the parentheses

then evaluating 2¹⁵ equals 32768

multiply by x¹⁰

the answer is 32768x¹⁰

Answer: There is a positive strong correlation

Step-by-step explanation: i learned that i think

You can use the definition of correlation coefficient which is just a constant value giving idea about how correlated two data sets' values are.

The correlation coefficient 0.9532 shows that the values are too much correlated(positively).

Correlation coefficient is a measure of how similar two datasets are acting.

The range of correlation coefficient is [-1, 1]

Since given correlation coefficient s 0.9532 which is too close to 1 compared with closeness to 0, we conclude that the set of data containing paired values have highly positive correlated values.

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The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.

The correct statements regarding the number line are given as follows:

Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.

These numbers are plotted marking a symbol such as a X or a circle on the number line.

The number line is increasing, so the negative numbers appear before the positive numbers.

This means that if a number a is to the left another number b, the number a is less than b, hence:

As the order in which the numbers appear is given as follows:

-3, 1 and 3.

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Answer:

x = - 2 , x = 2 are the input values

Step-by-step explanation:

g(x) = 4 , means y has the value of 4 and we want to find the values of x corresponding to this.

locate y = 4 on the y- axis , then a horizontal line through this point , intersects the graph at (- 2, 4 ) and (2, 4 )

thus when g(x) = 4 , the input values are x = - 2 and x = 2

Answer:

Thickens (Height) = 0.068 cm

Step-by-step explanation:

Given:

Diameter of disc = 14 cm

Radius of disc = 14 / 2 = 7 cm

Surface area = 3 cm²

Find:

Thickens (Height)

Computation:

Disc is a cylinder in shape

Surface area = 2πrh

3 = 2(22/7)(h)(7)

3 = 44(h)

Thickens (Height) = 0.068 cm

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

Andy basically has two stickers

Answer:

y = 2x - 5

Step-by-step explanation:

use the formula y - y1 = m (x - x1)

KM, JK, PK, and MJ are shown on the diagram.

Then the correct options are B, C, D, and F.

Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A line segment in mathematics has two different points on it that define its boundaries.

All the line segments will be

JK, JM, KM, MP, PK, and KL

The triangle KPM.

And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.

Then the correct options are B, C, D, and F.

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