A rectangular pyramid is sliced. The slice passes through line segment AB and is parallel to the base.
Which two-dimensional figure represents the cross section?
A. A rectangle the same size as the base
B. A rectangle that is smaller than the base
C. A quadrilateral that is not a rectangle
D. A triangle with a height the same as the pyramid

Answer: 140

Step-by-step explanation: 120-(-20) to 120 + 20 goes to 140.

The value of cos E in the triangle is √2/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Trigonometric ratio is only applied in right triangles.

Some of the trigonometric functions are ;

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

In the triangle taking reference from angle E, 5 is the opposite and 5 is the adjascent and 5√2 is the hypotenuse.

Therefore;

cos E = 5/5√2

cos E = 1/√2

rationalizing the value;

cos E = √2/2

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The probability of Lashonda winning a prize is 9/11.

To find the probability of Lashonda winning a prize, we can use the odds given. The odds in favor of Lashonda winning a prize are expressed as 9/2.

Odds are typically represented as a ratio of favorable outcomes to unfavorable outcomes.

In this case, the favorable outcomes are Lashonda winning a prize, and the unfavorable outcomes are Lashonda not winning a prize.

The odds in favor of Lashonda winning a prize can be written as 9:2, where 9 represents the favorable outcomes and 2 represents the unfavorable outcomes.

To calculate the probability, we add the favorable and unfavorable outcomes to get the total number of possible outcomes.

In this case, the total number of outcomes is 9 + 2 = 11.

The probability of Lashonda winning a prize can be calculated as the ratio of the favorable outcomes to the total number of outcomes:

Probability = Favorable outcomes / Total outcomes

Probability = 9 / 11.

Therefore, the probability of Lashonda winning a prize is 9/11.

In conclusion, based on the given odds in favor of Lashonda winning a prize being 9/2, the probability of Lashonda winning a prize is 9/11.

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The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.

The integral of f(x) = ex - e with respect to x can be computed as follows:

∫[0, 2] (ex - e) dx

Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:

∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx

Integrating each term separately:

= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2

= (e2 - e0) - (e0 - e0)

= e2 - 1

The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

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Step-by-step explanation:

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon

Given the function `f(x)=1/x-1 -2` the task is to write the equation of the asymptote(s) of f and determine the x-intercept of f. Asymptotes are lines that the curve of a function approaches but never touches. There are two types of asymptotes: vertical and horizontal.

Vertical Asymptote Vertical asymptotes occur when a function approaches infinity or negative infinity at a specific value of x. This can occur in a rational function where there is a division by zero.

A vertical asymptote is found when the denominator of the rational function becomes zero. Since division by zero is undefined, it means that the rational function approaches infinity or negative infinity.

The equation of the vertical asymptote is x = a where a is the value that makes the denominator zero.

Horizontal AsymptoteA horizontal asymptote occurs when a function approaches a constant value (y) as x approaches infinity or negative infinity. A horizontal asymptote occurs when the degree of the numerator and denominator is the same.

The horizontal asymptote is found by comparing the degrees of the numerator and denominator and dividing the leading coefficient of the numerator by the leading coefficient of the denominator.3.1 Equation of the asymptotes of the equation of the vertical asymptote is x=1.

The degree of the numerator is less than the degree of the denominator. Therefore, the horizontal asymptote is y=0The equation of the horizontal asymptote is y=0.3.2 X-intercept of fTo find the x-intercept of f, set y=0.f(x) = 0= 1/(x-1) -2Add 2 to both sides2 = 1/(x-1)Take the reciprocal of both sides of the equation.1/2 = (x-1)x-1 = 2x = 3Hence, the x-intercept of the function is (3,0)

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Based on the given transformations, the correct graph that represents function g(x) = tan(x-4) + 2 is option c.

To determine the graph that represents function g(x) = tan(x-4) + 2, we can analyze the transformations applied to the parent tangent function.

The parent tangent function has the form f(x) = tan(x). The given function g(x) = tan(x-4) + 2 introduces two transformations:

1. Horizontal shift: The function is shifted 4 units to the right compared to the parent function f(x) = tan(x). This means the graph of g(x) will be shifted to the right by 4 units.

2. Vertical shift: The function is shifted 2 units up compared to the parent function f(x) = tan(x). This means the graph of g(x) will be shifted upward by 2 units.

Based on the given transformations, the correct graph that represents function g(x) = tan(x-4) + 2 is option c. The graph in option c shows a rightward shift of 4 units (horizontal shift) and an upward shift of 2 units (vertical shift), matching the transformations described for g(x).

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Triangle PQR is similar to triangle P”Q”R” because the rotation and dilation transformations preserve the shape and angles of the original triangle.

The rotation simply changes the orientation of the triangle, but the angles and side lengths remain the same. The dilation scales all the side lengths by a factor of 9, which preserves the ratios of the side lengths and the angles of the original triangle.

Since similarity of two triangles is defined as the correspondence between the angles of one triangle to the angles of another triangle, and the ratio of the lengths of the corresponding sides is constant, PQR is similar to P”Q”R” because the angles of PQR and P”Q”R” are congruent, and the ratio of the lengths of the corresponding sides is the same. This means that PQR and P”Q”R” have the same shape and are therefore similar.

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-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.

First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.

Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:

lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.

For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:

a - 1 = a.

To solve this equation for "a," we subtract "a" from both sides:

-1 = 0.

Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

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Answer:

the radius of the cylinder is approximately 2.26 feet.

Step-by-step explanation:

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

Given that the volume is 400 feet, the height is 25 feet, and using π ≈ 3.14, we can rearrange the formula to solve for the radius:

400 = 3.14 * radius^2 * 25

Divide both sides of the equation by (3.14 * 25):

400 / (3.14 * 25) = radius^2

Simplifying:

400 / 78.5 ≈ radius^2

5.09 ≈ radius^2

To find the radius, we take the square root of both sides:

√5.09 ≈ √(radius^2)

2.26 ≈ radius

Rounding to the nearest hundredth, the radius of the cylinder is approximately 2.26 feet.

Answer:

Step-by-step explanation:

Volume Formula for a cylinder is  V=πr²h

Substitute the following:    400 = 3.14(r²)(25)

r=[tex]\sqrt{\frac{V}{\pi h} }[/tex]

r=[tex]\sqrt{\frac{400}{\pi 25} }[/tex]

r≈2.25676ft

Step-by-step explanation:

a number consists of digits in the place of certain values of the powers of 10.

2013 consists of a digit 2 in the thousands units position.

of a digit 0 in the hundreds units position.

of a digit 1 in the tens units position.

and of a digit 3 in the (single) units position.

so, to which power do we need to have this 3 ?

I think you made a mistake there. you say we need it to the power of 2013 ?

3²⁰¹³ = 2.786671338...e960 =

= 2.786671338... × 10⁹⁶⁰

Answer:

That Platonic solid is a dodecahedron.

B is the correct answer.

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

Answer:  Choice C.   [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]

===================================================

Work Shown:

Part 1

[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]

Part 2

[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]

The ray or segment that is a chord is (d) segment FC

From the question, we have the following parameters that can be used in our computation:

The circle

By definition, a chord is a straight line that joins points of the circle without passing through the center

The ray that has the above properties is ray FC

Hence, the segments that is a chord is (d) FC

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Starting with an initial population of 3.3 million yeast cells and a constant relative growth rate of 0.4465 per hour, the population size reaches approximately 5.892 million cells after 4 hours.

To calculate the population size after 4 hours, we can use the formula for exponential growth:

Population size = Initial population * [tex](1 + growth rate)^t^i^m^e[/tex]

Given that the initial population is 3.3 million cells and the relative growth rate is 0.4465 per hour, we can plug in these values into the formula:

Population size = 3.3 million *[tex](1 + 0.4465)^4[/tex]

Calculating the exponent first:

[tex](1 + 0.4465)^4 = 1.4465^4[/tex] ≈ 1.7879

Now, we can substitute this value back into the formula:

Population size = 3.3 million * 1.7879

Calculating the population size:

Population size = 5.892 million

Therefore, the population size after 4 hours is approximately 5.892 million cells.

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Answer:

113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06

314.16-201.06=113.1

Step-by-step explanation:

a probability is always the ratio of

desired cases / totally possible cases.

so, in this case it is the

area of the triangle / area of the circle.

as everything of the triangle is also a part of the circle.

and so, that fraction of the area of the whole circle that is the area of the triangle in refutation to the area of the whole circle is the probability that a random point inside the circle would be also inside the triangle.

the area of a right-angled triangle is

leg1 × leg2 / 2

in our case

12 × 12 / 2 = 72 units²

the area of a circle is

pi × r²

in our case that is

pi × 12² = 144pi units²

the requested probability is

P = 72 / 144pi = 1/2pi = 0.159154943... ≈ 0.16

Answer:

Step-by-step explanation:

39 !!!!!

Answer:

In the given equation, V(r) represents the volume of the air inside a basketball when the radius of the basketball is r.

Step-by-step explanation:

The function V(r) represents the volume of the basketball when the radius is r. So, the correct interpretation is that V(r) represents "the volume of the basketball when the radius is r."

Answer:

There are 12 blocks in the bottom layer

Step-by-step explanation:

We see from the diagram that in the bottom layer,

length = 3 cm

width = 4 cm

And that there are 3 blocks for the 3 cm length,

Hence each block has a length of 1 cm (the 3 then make up 3 cm)

And there are 4 blocks for the 4 cm width

Hence the width is also 1 cm (4 of these make up 4 cm width)

Now, to find the total number of blocks,

we just multiply the length and width,

so, (3)(4) = 12

so there are 12 blocks in the bottom layer

The length of this line segment is: B. 2√13 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(4 + 2)² + (1 + 3)²]

Distance = √[(6)² + (4)²]

Distance = √[36 + 16]

Distance = √52

Distance = 2√13 units.

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We can solve for the missing elements as follows:

1. Radius - 10 inches

Diameter - 20

Circumference -  62.8

Area - 314

2.  Radius  - 6ft

Diameter - 12

Circumference - 37.68

Area - 113.04

3.  Radius - 18

Diameter - 36 yards

Circumference - 113.04

Area - 1017.36

4.  Radius 15

Diameter - 30 cm

Circumference 94.2

Area - 706.5

5.  Radius - 5 mm

Diameter 10

Circumference 31.4

Area -78.5

6. Radius 20

Diameter - 40 inches

Circumference  125.6

Area -1256

To solve for the given values, we will use the formulas for area, circumference. Also, we can obtain the radius by dividing the diameter by 2 and the diameter is 2r. So we will solve for the values this way:

1. radius = 10 inches

diameter = 20

circumference = 2pie*r 2 *3.14*10 = 62.8

Area = 314

2. radius = 6ft

diameter = 12

circumference = 37.68

Area = 113.04

3. radius = 18

diameter = 36 yards

circumference = 113.04

Area = 1017.36

4. radius = 15

diameter = 30 cm

circumference = 94.2

Area = 706.5

5. radius = 5 mm

diameter = 10

circumference = 31.4

Area = 78.5

6. radius = 20 inches

diameter = 40 inches

circumference = 125.6

area = 1256

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Answer: -15/17

Step-by-step explanation:

sin ∅ = 8/17

If you drew a a line in the 2rd quadrant because tan ∅ <0, which means tan∅ is negative.

Tan∅= sin∅/cos∅            

they told you sin∅ is positive which is related to your y.

but cos∅ needs to be negative which is related to x

This happens in the second quadrant x is negative and y is positive.

Now we know which way to draw our line.  Label the opposite of the angle 8 and the hypotenuse 17 because sin∅ = 8/17

Use pythagorean to find adjacent.

17² = 8² + a²

225 = a²

a = 15

The adjacent is negative because the adjacent is on the x-axis in the negative direction.

cos ∅ = adj/hyp

cos∅ =  -15/17

Answer: -15/17

Step-by-step explanation:

In the first quadrant, all sine, cosine and tan are all positive. In the second quadrant, only sine is positive. Third quadrant, only tangent is positive and fourth quadrant, only cosine is positive.

Therefore, when sine is positive and tan is negative, the angle can only be in quadrant 2. Then draw the triangle. Draw a triangle with the angle from the origin, with the opposite leg from the angle with value of 8 and the hypotenuse of value 17. Since cosine is what the question is asking for, and we know the data given forms an right triangle, the value of the other leg is 15. It is an 8-15-17 special triangle or use the Pythagorean Theorem.

Finally, taking the cosine of the angle from the origin gives -15/17 since it is in quadrant 2.

Answer:

True

EXPLANATIONDETAIL STEPS:

(A)Determine whether y = 5 is a function: Click for video explanations: True

(B)Determine whether x = -2 is a function: Click for video explanations: False

(7)Determine whether y = 2x-5 is a function: Click for video explanations: True

(D)Determine whether 2y = x-4 is a function: Click for video explanations: True

(A)Determine whether

=

is a function: Click for video explanations: True

(B)Determine whether

=

is a function: Click for video explanations: False

(7)Determine whether

=

is a function: Click for video explanations: True

(D)Determine whether

=

is a function: Click for video explanations: True

For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.

B: They have a law of formation:

A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.

This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.

C: They are ordered:

In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.

Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.

A: They may or may not be infinite:

Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.

On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.

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Note: the translated question is:

To have a sequence it is essential that the numbers that form it:

A: be infinite

B: they have a law of formation C: they are ordered

Answer:

Step-by-step explanation:

Converting between Fraction, Decimal, and Percent:

Fraction to Decimal: Divide the numerator by the denominator. The result is the decimal form.

Example: 1/4 = 1 ÷ 4 = 0.25

Decimal to Fraction: Write the decimal as a fraction by placing the decimal value over the appropriate power of 10.

Example: 0.75 = 75/100 = 3/4

Fraction to Percent: Divide the numerator by the denominator and multiply by 100.

Example: 1/3 = (1 ÷ 3) × 100 = 33.33...%

Percent to Fraction: Write the percent as a fraction with a denominator of 100 and simplify if necessary.

Example: 40% = 40/100 = 2/5

Decimal to Percent: Multiply the decimal by 100 and add the percent symbol (%).

Example: 0.75 = 0.75 × 100 = 75%

Percent to Decimal: Divide the percent by 100.

Example: 40% = 40 ÷ 100 = 0.4

The speed of the boat in water without a current is 15 miles per hour

From the question, we have the following parameters that can be used in our computation:

Current of river = 4 miles per hour

Distance travelled = 209 miles

Time = 30 hours.

Represent the speed with x

So, we have

Next, we have

Time = Speed/Distance

So, we have

209/(x - 4) + 209/(x + 4) = 30

When evaluated, we have

x = 15

Hence, the speed is 15 miles per hour

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Answer:

y=2

Step-by-step explanation:

The equation of a parabola in the form [tex](y-k)^2=4p(x-h)[/tex] has an axis of symmetry of [tex]y=k[/tex]. Therefore, the axis of symmetry is [tex]y=2[/tex].

Answer:

y = 2

Step-by-step explanation:

The axis of symmetry of a parabola is a line that divides the parabolic curve into two symmetric halves. It is a line of symmetry that passes through the vertex of the parabola.

Given equation of the parabola:

[tex](y-2)^2=20(x+1)[/tex]

As the y-variable is squared, the given parabola is horizontal (sideways).

The standard form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

Comparing the given equation with the standard equation, we can see that:

As the axis of symmetry is given by the formula y = k, the axis of symmetry of the given parabola is y = 2.