A cyclist leaves the town of Alphaville and heads toward Betaville. She travels at a constant speed of 14 km/h. At the same time, a jogger and a walker leave Betaville and head towards Alphaville. The walker travels at a constant speed of 6 km/h and the jogger travels at a constant speed of 10 km/h. If the cyclist passes that walker 4 minutes after passing the jogger, how far apart are the towns Alphaville and Betaville?

So, we would expect about 5 albino Galapagos tortoises to be born out of 500,000 Galapagos tortoises hatched, assuming that the theoretical probability holds true in practice.

Probability is a branch of mathematics that deals with the measurement and analysis of random events. It is the study of how likely an event is to occur, expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability is used in many areas of mathematics, science, and engineering, such as statistics, physics, finance, and computer science. It is a fundamental concept for understanding and predicting the behavior of random events and systems.

Here,

To find the expected number of albino Galapagos tortoises, we can use the formula:

Expected value = Probability of event * Total number of trials

In this case, the probability of an albino Galapagos tortoise being born is 0.001 or 0.001/100 = 0.00001 (as a decimal). The total number of trials is 500,000, since that is the number of Galapagos tortoises that hatched.

Therefore, the expected number of albino Galapagos tortoises is:

Expected value = 0.00001 * 500,000

= 5

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Answer:

Therefore, the answer to how much is in the checking account is $677.

Step-by-step explanation:

The amount in the checking account after all the transactions would be $677.

Here's the breakdown of the transactions:

Starting balance: $910

Bill payment: -$185

Withdrawal for lunch: -$30

Purchase of pants: -$43

Purchase of gift card: -$15

Refund for pants: +$43

Total = $910 - $185 - $30 - $43 - $15 + $43 = $677

Answer: 50%

Step-by-step explanation: each side has a 1 in 2 chance of landing on it

Answer:

three hundred five thousanths

Step-by-step explanation:

The value of solution of the expressions are,

⇒ 84.05

We have to given that;

The expression is,

⇒ (8 × 10) + (4 × 1) + (5 × 1/00)

Now, We can simplify as;

⇒ (8 × 10) + (4 × 1) + (5 × 1/100)

⇒ 80 + 4 + (5 × 0.01)

⇒ 84 + 0.05

⇒ 84.05

Thus, the value of solution of the expressions are,

⇒ 84.05

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A reduced echelon matrix in R3 is 1--1 if and only if the homogeneous system Ax = 0 has only the trivial solution if and only if there are no free variables.

The statement is true.

A reduced echelon matrix in R3 represents a linear system of equations that can be solved using Gaussian elimination.

The reduced echelon form of a matrix is obtained by performing row operations that reduce the matrix to a triangular form, with ones on the main diagonal and zeros below it.
If the homogeneous system Ax = 0 has only the trivial solution, it means that the only solution to the system is the zero vector.

In other words, there are no non-zero vectors that satisfy the system.

This is equivalent to saying that the rank of the matrix is equal to the number of columns, or in other words, there are no free variables in the system.
If the system has no free variables, it means that each variable can be expressed as a unique function of the other variables.

This implies that the system has a unique solution, or in other words, the mapping from the system of equations to the solution vector is one-to-one.
If the system is one-to-one, it means that each solution vector corresponds to a unique system of equations.

This implies that there are no redundant equations or variables, and therefore no free variables.

Hence, the homogeneous system Ax = 0 has only the trivial solution.
The statement is true.

A reduced echelon matrix in R3 is 1--1 if and only if the homogeneous system Ax = 0 has only the trivial solution if and only if there are no free variables.

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The cross section across a conic section would produce:

Triangle, Circle and Parabola

Looking at the given options, we can say that ellipse, circle and parabola are all conic sections and as such they are possible figures that can be made if we intersect a plane and a cone.

However, rectangle is not a conic section.

A cylinder which could have a rectangular cross section if the plane is perpendicular to the base or A tetrahedron could have a square cross section, which is a special case of a rectangle.

In forming a conic section , we could also form an ellipse.

Now, when we cut a cross section across a cone, we can get a circle, triangle or parabola

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The equation of the circle with a center at the origin and a diameter of 8 is x² + y² = 16

A circle is a two-dimensional shape that is defined as a set of points that are equidistant from a fixed point called the center.  The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points (locus) at a certain radius from the centre.

If the center of the circle is at the origin, then the equation of the circle can be written in the form of:

x² + y² = r²

where r denotes the circle's radius.

Since the diameter of the circle is 8, the radius is half of that, or 4. Consequently, the circle's equation is as follows:

x² + y² = 4²

x² + y² = 16

So the equation of the circle with a center at the origin and a diameter of 8 is x² + y² = 16.

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Null hypothesis: Bags are filled correctly at 441 grams. Alternative hypothesis: Bags are overfilled (mean weight > 441 grams).

The null hypothesis (H0) is that the bags are filled correctly at the 441 gram setting, meaning the mean weight of the bags is 441 grams. The alternative hypothesis (Ha) is that the bags are overfilled, meaning the mean weight of the bags is greater than 441 grams. Thus, the hypotheses can be written as:

H0: μ = 441

Ha: μ > 441

To test these hypotheses, we can use a one-sample t-test with a significance level of 0.02. We will compare the sample mean weight of a random sample of bags to the population mean of 441 grams, using the t-test statistic and the corresponding p-value. If the p-value is less than 0.02, we can reject the null hypothesis and conclude that the bags are overfilled

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The value of x in the triangle is 17.6 m.

Trigonometry deals with the relationships between the sides and angles of triangles.

The three primary trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions are often abbreviated as sin, cos, and tan.

Using the given triangle:

cos 54° = x/30   (cos = adjacent/hypotenuse)

x = 30 * cos 54°

x = 17.6 m

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Answer: 5/3

Step-by-step explanation:

y = mx +b

m is equal to the slope

b is the y intercept

therefore, m or 5/3 is the slope.

The area of the sector in terms of pi is: 75π cm²

The Length of arc = 15π cm

Area of a sector = ∅/360 * πr²

Length of arc = ∅/360 * 2πr, where r is the radius and ∅ is the reference angle.

Given the following:

Reference angle (∅) = 270°

Radius of circle (r) = 10 cm

Area of the sector = 270/360 * π * 10²

Area of the sector = 75π cm²

Length of arc = 15π cm

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The volume of the cone is1527.1 cm³

And the correct answer is an option (c)

We know that he formula for the volume of the cone is:

V = 1/3(π × r² × h)

Here, the diameter of the base of the cone is 15 cm

so, the radius of the cone would be,

r = 15/2 cm

r = 7.5 cm

And the slant heihgt of the cone is l = 27 cm

Using Pythagoras theorem the height h of the cone would be,

h = √(l² - r²)

h = √(27² - 7.5²)

h = √(672.75)

h = 25.94 cm

Using above formula, the volume of the cone would be,

V = 1/3(π × r² × h)

V = 1/3(π × (7.5)² × 25.94)

V = 1527.99 cm³

V = 1527.1 cm³

Therefore, the correct answer is an option (c)

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Find the complete question below.

Answer:

The answer for speed is 8 miles/hr

Step-by-step explanation:

speed =distance/time

s=20/2.6

s=8miles/hr

Answer:

  5.0

Step-by-step explanation:

You want the Beaufort scale number corresponding to 9.4 m/s, given the formula ...

  v = 0.83B^(3/2)

Put the given speed in the formula and solve for B.

  9.4 = 0.83B^(3/2)

  9.4/0.83 = B^(3/2)

  B = (9.4/0.83)^(2/3) ≈ 5.043

The wind speed is about 5.0 on the Beaufort scale.

Answer:

Step-by-step explanation:

Social media usage is one of the most popular online activities and in 2021, 82 percent of the population in the United States had a social networking profile, representing a two percent increase from the 80 percent usage reach in the previous year.

Social media usage is one of the most popular online activities, and in 2021, 82 percent of the population in the United States had a social networking profile, marking a two percent rise over the previous year's usage reach of 80 percent.

Brainlist?

[tex]sin^2(x)[/tex]  can be expressed as [tex](1 - cos(2x)) / 2[/tex] using the power reducing formula.

To express [tex]sin^2(x)[/tex]using the power reducing formula,

we need to recall the following trigonometric identity:
[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
Recognize that the question asks for the power reducing formula for sin^2(x).
Recall the trigonometric identity:[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
The power reducing formula for [tex]sin^2(x)[/tex] is:[tex](1 - cos(2x)) / 2.[/tex]

The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.

It is most commonly used for reducing the power of the sine and cosine functions.

The power reducing formula for cosine is:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

The power reducing formula for sine is:

[tex]sin^2(x) = (1 - cos(2x))/2[/tex]

These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]

By solving for either[tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine[tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex] we can arrive at the power reducing formulas.

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The values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing are (-∞, -3) and (1, +∞).

To find the values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing, we need to take the derivative of the function and determine where the derivative is positive.

f(x) = x³ + 3x² - 9x + 7

f'(x) = 3x² + 6x - 9

To find where f(x) is increasing, we need to find the values of x where f'(x) > 0.

3x² + 6x - 9 > 0

Simplifying this inequality, we get

x² + 2x - 3 > 0

Factoring the left side of the inequality, we get

(x + 3)(x - 1) > 0

The critical points of f(x) occur when f'(x) = 0 or when the denominator of f'(x) is undefined. The denominator of f'(x) is always defined, so we only need to find where f'(x) = 0

3x² + 6x - 9 = 0

Dividing both sides by 3, we get

x² + 2x - 3 = 0

Factoring the left side of the equation, we get

(x + 3)(x - 1) = 0

So the critical points of f(x) are x = -3 and x = 1.

Now we can use a sign chart to determine the intervals where f'(x) > 0.

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The given question is incomplete, the complete question is:

What are all values of x for which the function f is defined by f(x)= x³ +3x² -9x +7 is increasing?

Given statement "The roof area of a gable roof is made up of two rectangles"

The given statement is True.
Because, A gable roof consists of two sloping roof surfaces that meet at the top, forming a triangle shape on both ends of the building.

Each of these sloping surfaces can be represented as a rectangle, and the combined area of these two rectangles represents the total roof area.

Area is a measure of the amount of space inside a two-dimensional (2D) or three-dimensional (3D) shape.

It is typically measured in square units, such as square meters, square feet, or square inches.

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The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex.

To write the vertex form of a quadratic equation given the vertex (-4, 5) and a-value of 5, you can use the vertex form equation:

y = a(x - h)² + k

where (h, k) is the vertex and a is the a-value.

In this case, h = -4, k = 5, and a = 5. Substitute these values into the equation:

y = 5(x - (-4))² + 5

Simplify the equation:

y = 5(x + 4)² + 5

So, the vertex form of the quadratic equation is:

y = 5(x + 4)² + 5

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The vertex form of the quadratic equation is: y = 5[tex](x + 4 )^2[/tex] + 5

A quadratic equation's vertex form is provided by:

y = a[tex](x - h)^2[/tex] + k

where "a" is the coefficient of the parabola and "(h, k)" is its vertex [tex]x^2.[/tex]

Given that the vertex is (-4, 5) and a-value is 5, we can substitute the values into the vertex form equation:

h = -4

k = 5

a = 5

When we enter these numbers into the equation, we obtain:

y = 5(x -[tex](-4) ^2[/tex] + 5

Simplifying the equation, we get:

y = 5[tex](x + 4)^2[/tex] + 5

So, the vertex form of the quadratic equation is:

y = 5[tex](x + 4 )^2[/tex] + 5

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The transformed function  [tex]y =e^x + 3[/tex]  by shifting the graph of [tex]y =e^x[/tex] upwards with 3 units as per given graph.

A transformation in a graph is a function that maps each point in the original graph to a corresponding point in a new graph.

According to the graph it shows that there is transformation to 3 unit upwards.

To transform the equation  [tex]y =e^x[/tex]  to   [tex]y =e^x + 3[/tex] , we can add 3 to both sides of the given equation:

[tex]y+3 =e^x + 3[/tex]

So the equation  [tex]y = e^x + 3[/tex]  is the transformed version of  [tex]y = e^x[/tex] Geometrically, this transformation shifts the graph of  [tex]y = e^x[/tex] upwards by 3 units, while maintaining its shape and curvature. This means that it will intersect the y-axis at the point (0, 3) and will never touch the x-axis.

In summary, the transformed function   [tex]y = e^x + 3[/tex]   by shifting the graph of  [tex]y = e^x[/tex] upwards with 3 units.

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Answer:

Bar Graph

Step-by-step explanation:

A bar graph would be the best graphical representation to display the data.

A bar graph is a good choice for displaying categorical data, where each category is represented by a separate bar. In this case, the categories are the different types of items purchased (Health & Medicine, Beauty, Household, and Grocery), and the number of purchases for each category is represented by the height of the corresponding bar.

A box plot is generally used to display numerical data, while a histogram is used to display the distribution of continuous data. A stem-and-leaf plot can also be used to display numerical data, but it is generally used for smaller datasets.

Therefore, in this case, a bar graph is the most appropriate choice to display the data.

The best graphical representation for the given dataset would be a Bar Graph. The categories of items purchased can be shown on one axis and the number of purchases on the other. Other plots such as Box plots, Histograms, and Stem-and-leaf plots are not suitable for this kind of categorical data.

To represent this data graphically, the best option would be a Bar Graph. A bar graph is a graph that uses either horizontal or vertical bars to show comparisons between categories of data. In this case, you have four categories (Item Purchased: Health & Medicine, Beauty, Household, Grocery) and the Number of Purchases associated with each category.

So, each category would be represented by a bar, and the length or height of the bar would represent the Number of Purchases.

Box plots, Histograms, and Stem-and-leaf plots are not appropriate because they are typically used for continuous data or to examine ranges of data, and the data listed here is categorical and discrete (it's countable).

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Using Pythagoras Theorem, we have the solutions as:

3) Length of AB = 32 in

4) x = 24

5) Perimeter of PRQ = 35

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

3) Using Pythagoras theorem, we can say that:

Radius = √(16² - 5²)

Radius = √231

Radius = 15.2

Thus, AB will be twice the measurement of 16 as the perpendicular distance to bth chords are the same. Thus:

AB = 16 * 2 = 32 in

4) Using Pythagoras theorem,

x = √((18 + 7)² - 7²)

x = √(625 - 49)

x = 24

5) Using Pythagoras theorem, we can say that:

PC = 8.66

RC = √((14² - 8.66²)

RC = 11

Thus:

Perimeter of PRQ = 14 + 10 + 11 = 35

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Answer:

56.55

Step-by-step explanation:

C=2πr=2·π·9≈56.54867

The equation b = 12 - (-3) would help to answer question C, "The temperature was -3 degrees and rose to 12 degrees. How much did the temperature change?"

This is because the equation b = 12 - (-3) simplifies to b = 12 + 3, which gives us the value of b (the temperature change) when the starting temperature was -3 degrees and the final temperature was 12 degrees.

The subtraction of a negative number (i.e., -3) is the same as adding its absolute value (i.e., 3), so the equation can be rewritten as b = 12 + 3. Therefore, the value of b is 15, which represents the temperature change from -3 degrees to 12 degrees.

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