You pick a card at random.
1 2 3
What is P(divisor of 54)?
Write your answer as a percentage.
%

No, the pairs of vectors 3i - 8j, 8i - 3j are not orthogonal.

The dot product will help us to determine if the pair of vectors are orthogonal or not.

If the dot product is equal to zero, then the pair of vectors are orthogonal.

The dot product of the vectors is calculated as follows;

(3i - 8j).(8i - 3j)

= (3i x 8i) - (3i x 3j) - (8j x 8i) + (8j x 3j)

= (24) - (0) - (0) + (24)

= 24 + 24

= 48

So the pairs of vectors are not orthogonal.

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There are 5 sheets of paper will she need to complete 10 problems.

We have to given that;'

Kendra is doing her math homework. For each problem, she uses 1/2 of a sheet of paper.

Hence, For complete 10 problems, number of sheets are,

⇒ 1/2 of 10

⇒ 1/2 x 10

⇒ 5

Thus, There are 5 sheets of paper will she need to complete 10 problems.

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Answer:

There are 13 diamonds in a deck of cards, including one king and one ace.

The probability of drawing a king on the first draw is 1/13, since there is one king among 13 diamonds.

Assuming that the king is not replaced, there are now 12 diamonds left, including one ace. The probability of drawing an ace on the second draw is 1/12, since there is one ace among 12 diamonds.

The probability of drawing a king on the first draw and an ace on the second draw is the product of these probabilities:

P(king first, ace second) = P(king first) * P(ace second|king first not replaced)

P(king first, ace second) = (1/13) * (1/12)

P(king first, ace second) = 1/156

Therefore, the chances of drawing a king on your first draw and an ace on your second draw, when drawing 2 cards from only the diamonds, is 1/156.

Step-by-step explanation:

Branliest please

Note that the perimeter of the trapezoid shown is 23 units. Thus, the statement is false.

To derive the perimeter we  must know the following:


a = base = 5

b = base = 8

d = side = 4
c is the hypotenuse" = (h x base of the right triangle) = (4x3)/2 = 6

Thus, Perimeter of the trapezoid = a + b + c + d =

5 + 8 + 4 + 6

= 23 units.

Thus, the statement that the perimeter of the trapezoid shown is 22 units is false.

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Full Question>

Use the trapezoid shown to mark each statement below as true or false. if false, please rewrite the statement correctly in the space below the statement!

Q: The perimeter of the trapezoid shown is 22 units.

True false?

length LD = 6 units

length DF = 9 units

length HF = 6 units

length LH = 9 units

length L'D' = 2 units

length D'F' = 3 units

length H'F' = 2 units

length L'H' = 3 units

Dilation is the scaling of an object, where it gets bigger or smaller.

Scale factor = new dimension/old dimension

length LD = 15-9 = 6units

length DF = 6-(-3) = 9units

length HF = 15-9 = 6 units

length LH = 6-(-3) = 9 units

Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.

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The area of the shaded region of a circle with a 100 degree angle and a radius of 3cm, using pi=3.14, is approximately 25.64 square centimeters.

To find the area of the shaded region of a circle, we need to subtract the area of the sector formed by the shaded region from the area of the whole circle.

The area of the whole circle is given by

A = πr²

where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14 (as given in the question).

Substituting the given values, we get

A = π(3cm)²

A = 28.26 cm² (rounded to two decimal places)

Now, let's find the area of the sector formed by the shaded region.

The angle of the sector is given as 100 degrees. To find the area of the sector, we need to use the formula:

A = (θ/360)πr²

where θ is the angle in degrees, r is the radius of the circle, and π is again approximately equal to 3.14.

Substituting the given values, we get

A = (100/360)π(3cm)²

A = 2.62 cm² (rounded to two decimal places)

Finally, we can find the area of the shaded region by subtracting the area of the sector from the area of the whole circle

Shaded area = Area of circle - Area of sector

Shaded area = 28.26 cm² - 2.62 cm²

Shaded area = 25.64 cm² (rounded to two decimal places)

Therefore, the area of the shaded region of the circle is approximately 25.64 square centimeters.

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--The given question is incomplete, the complete question is given

" Find the area of a shaded region of circle and use 3.14 for pi "--

The value of area of the figure is,

⇒ 10√10 units²

We have to given that;

To find the area of figure.

Here, We have to find length of AD and AB for area of figure.

Coordinate of A = (- 2, 2)

Coordinate of B = (- 4, -4)

Coordinate of D = (3, 2)

Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, Length of AD;

AD = √ (-2 - 3)² + (2 - 2)²

AD = √25

AD = 5

Length of AB;

AB = √ (- 2 + 4)² + (2 + 4)²

AB = √4 + 36

AB = √40

AB = 2√10

Thus, The value of area of the figure is,

⇒ AD x AB

⇒ 5 × 2√10

⇒ 10√10

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The ratio of sec θ is determined as 5/3.

option A.

The ratio is sec θ is calculated by applying the following method;

sec θ =  1/cosθ

Given that tanθ = -4/3 = oppo/adjacent

The hypotenuse side is calculated by applying Pythagoras theorem as shown below;

h = √ 4² + 3²

h = 5

The ratio of sec θ is calculated as follows;

sec θ =  1/cosθ

1/cosθ = 1/(3/5)

1/cosθ = 5/3

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The mean is 270.75 and the median is 271. While there is no single mode, then we conclude that our mode is 264 and 294 respectively.

By definition:

Mean is the sum of all the numbers in the set divided by the total number of numbers.

Median is the middle value in the set when the numbers are arranged in order.

Mode is the number that appears most frequently in the set.

If we re-arrange the data given in ascending order, we have:

264 264 267 269 273 276 294 297

To calculate Mean:

Add up all the numbers and divide by the total number of numbers:

Mean = (264 + 264 + 267 + 269 + 273 + 276 + 294 + 297) / 8

Mean = 270.75

To calculate Median:

We need to find the middle number in the set. Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers:

Median = (269 + 273) / 2

Median = 271

To calculate Mode:

We need to determine which number appears most frequently in the set. In this case, there are two numbers that appear twice (264 and 294), and the rest of the numbers appear only once. Therefore, there is no single mode for this data set.

Mode = 264 and 294

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Answer:

V = π(19.1^2)(11.8) = 13,523.8 cubic mm

V = 3.14(1.91^2)(11.8) = 13,516.9 cubic mm

The missing lengths of the following two triangles:

Case 1: x = 50 km

Case 2: x = 40 km

Case 3: Obtuse

Case 4: Acute

Case 5: Right

Case 6: m = 16, n = 8√3

Case 7: x = 3√2, y = 3

In this problem we must determine all missing lenghts in a triangle, this can be done by law of cosine:

x² = a² + b² - 2 · a · b · cos X

Where X is the angle opposite to side x.

Now we proceed to determine the missing lengths of the following two triangles:

Case 1

x = √[(14 km)² + (48 km)² - 2 · (14 km) · (48 km) · cos 90°]

x = 50 km

Case 2

x = √[(24 km)² + (32 km)² - 2 · (24 km) · (32 km) · cos 90°]

x = 40 km

In addition, we can determine if any triangle is acute, obtuse and right also by law of cosine:

cos X = - (x² - a² - b²) / (2 · a · b)

Case 3

cos X = - [(18 in)² - (12 in)² - (9 in)²] / [2 · (12 in) · (9 in)]

cos X = - 0.458 (Obtuse)

Case 4

cos X = - [(15 ft)² - (12 in)² - (14 in)²] / [2 · (12 in) · (14 in)]

cos X = 0.342 (Acute)

Case 5

cos X = - [(5 ft)² - (3 in)² - (4 in)²] / [2 · (3 in) · (4 in)]

cos X = 0 (Right)

Finaly, we determine the missing lengths of two right triangles by trigonometric functions:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Now we find the missing lengths:

Case 6

m = 8 / cos 60°

m = 16

n = 8 · tan 60°

n = 8√3

Case 7

x = 3 / sin 45°

x = 3√2

y = 3 / tan 45°

y = 3

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The  inequality given that the function f is increasing over it s domain

f(x²-2)<f (7x-8), Df =  (-∞,2) is: x ∈ (-∞,1) U (6,2).

We know the  values of x within the domain by setting the intersection points of the two functions f(x2-2) and f(7x-8).

f (x²-2) = f (7x-8)

So,

x²-2 = 7x-8

Simplify and find x

x² - 7x + 6 = 0

(x - 1)(x - 6) = 0

x = 1 or x = 6

The domain (-,2) is divided into the intervals (-,1), (1,6), and (6,2). Now let assess the interval endpoints because f is rising:

For x < 1:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) < 0

For 1 < x < 6:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) > 0

For x > 6:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) < 0

Since f is rising across its domain the inequality f(x2-2) f(7x-8) has the following solution: x ∈ (-∞,1) U (6,2).

Therefore the inequality is  x ∈ (-∞,1) U (6,2).

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Answer:

The answer should be 1,260

Answer:

75

Step-by-step explanation:

.

Answer:

  x = (1 +i√83)/6  or  x = (1 -i√83)/6

Step-by-step explanation:

You want the solutions to the quadratic equation 3x² -x +7 = 0.

The solutions to the equation ax² +bx +c = 0 are given by the formula ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The given equation has a=3, b=-1, c=7, so the solutions are ...

  [tex]x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(7)}}{2(3)}=\dfrac{1\pm\sqrt{-83}}{6}\\\\\\\boxed{x=\dfrac{1+i\sqrt{83}}{6}\quad\text{or}\quad x=\dfrac{1-i\sqrt{83}}{6}}[/tex]

<95141404393>

The equation of the line that passes through the point (4, 2) and is perpendicular to the line y = 43x is y = (-1/43)x + (90/43).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line has a slope of 43.

To find the slope of the line perpendicular to it, we use the fact that the product of the slopes of two perpendicular lines is -1.

So, the slope of the perpendicular line is -1/43.

Using the point-slope form of a line, we can write the equation of the line as:

y - y1 = m(x - x1),

where (x1, y1) = (4, 2) and m = -1/43

Plugging in the values, we get:

y - 2 = (-1/43)(x - 4)

y - 2 = (-1/43)x + (4/43)

y = (-1/43)x + (4/43) + 2

y = (-1/43)x + (90/43)

Therefore, the equation of the line is y = (-1/43)x + (90/43).

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The y-intercept of the line of best fit is: y = 20

The formula for equation of a line of best fit is:

y = mx + c

where:

m is slope

c is y-intercept

Now, the y-intercept is simply defined as the point where the line crosses the y-axis.

In this case, the line crosses the y-axis at y = 20.

Thus, we can conclude that it is the y-intercept

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A graph of triangle CAT is shown below.

A graph of triangle C'A'T, the image of ΔCAT after a reflection in the x-axis is shown below.

ΔC'A'T represents a rigid motion because the pre-image and the image are congruent.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

Next, we would apply a reflection over or across the x-axis;

(x, y)                →      (x, -y)

C (-1, 2)       →      (-1, -(2)) = C' (-1, -2)

A (-1, 4)       →      (-1, -(4)) = A' (-1, -4)

T (3, 2)       →      (3, -(2)) = T' (3, -2)

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Answer:

A stem-and-leaf plot is a graphical representation of a dataset where the numbers are separated into two parts: the stem (the leftmost digit or digits) and the leaf (the rightmost digit). The stem values are listed vertically and the corresponding leaf values are listed to the right of the stem in a row. This type of plot allows for quick and easy data analysis, as it shows the distribution of the data and provides information about the frequency and range of the values. It is particularly useful for smaller datasets and can be easily constructed by hand or with software.

The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

An approximate average rate of change of the graph from x = 3 to x =5 represents the reduction in profit from 3 to 5

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The equation of the dilated line is 9x + 15y = 10.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object or equation based on a specific scale factor of 3 is given by this mathematical expression:

(x, y)      →    (SFx, SFy)

Where:

Therefore, the transformation rule for this dilation is given by;

(x, y)      →    (3x, 3y)

3(3x + 5y) = 10

9x + 15y = 10.

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Answer:

  569 square units

Step-by-step explanation:

You want the surface area of the 8-sided shape that has a square "base" 7 units on a side, and a "height" of 20 units.

The slant height of each triangular face is the hypotenuse of a right triangle with legs 7/2 units and 20 units. That height is ...

  h = √(3.5² +20²) = √412.25 ≈ 20.304 units

The area of one triangular face is ...

  A = 1/2bh

  A = 1/2(7)(20.304) . . . one face

There area 8 congruent triangular faces, so the total area is ...

  A = 8(1/2)(7)(20.304) = 8(7)√412.25 ≈ 568.51 ≈ 569

The total surface area is about 569 square units.

<95141404393>

a) The base area of the cylinder is given as follows: 78.54 ft².

b) The height of the cylinder is given as follows: 2 ft.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The base area is given as follows:

Ab = πr².

Considering the radius of 5 ft, the base area is of:

Ab = 3.1416 x 5²

Ab = 78.54 ft².

Considering the volume of 157.08 ft³, the height of the cylinder is obtained as follows:

78.54h = 157.08

h = 157.08/78.54

h = 2 ft.

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Answer:

Step-by-step explanation:

1. The line of best fit must have an equal number of points above and below the line

2. The line of best fit could be used as a predictions showing a trend in data

Answer:

-21

Step-by-step explanation:

4×(-4)+35÷(-7)

Plus and minus together makes minus

Multiplication and division goes first

-16-5= - 21

Answer:

Step-by-step explanation:

Blue line: 0 + -4<x

Black line: 8 - 7<7

Orange: 0=0>y

Green: 1-9<y

Starting points and ending

Answer:

The correct function is y = 4(.25^x).

There were 3097 6th-grade students who went on the field trip to see the play at the theater.

We have,

If 95% of the 3260 seats in the theater were filled by the 6th-grade students,

We can find the total number of students by multiplying the total number of seats by the fill percentage as a decimal:

Number of 6th graders = 3260 x 0.95

Number of 6th graders = 3097

Therefore,

There were 3097 6th-grade students who went on the field trip to see the play at the theater.

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The circumference of the circle is 75.4 cm.

The circumference of the circle is calculated from the radius of the circle.

Considering the equilateral triangle, each of the interior angle is 60⁰, a line passing the center of any of this angle, divides it into two with each angle 30⁰.

Considering the right triangle inside the equilateral triangle, the hypothenuse is equal to the radius of the circle.

The radius of the circle is calculated as follows;

sin (30) = opp/hypo

sin (30) = 6 cm/r

r = 6 cm / sin (30)

r = 12 cm

The circumference of the circle is calculated as follows;

C = 2πr

C = 2π x (12 cm)

C = 75.4 cm

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