The barista at The Sweet Slice Cafe kept track of how many customers ordered each type of drink yesterday.
hot chocolates 50
iced teas
12
espressos
13
Americanos
3
What is the probability that a randomly selected customer ordered an iced tea?
Write your answer as a fraction or whole number.
P(iced tea) =

The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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The measures of the non-right angles of each triangle are 40 degrees and 50 degrees.

The sum of the interior angles of a regular 18-gon can be found using the formula:

S = (n - 2) × 180 degrees

n is the number of sides of the polygon.

Substituting n = 18 we get:

S = (18 - 2) × 180 degrees

= 2880 degrees

The 18-gon into 36 right triangles need to draw 18 lines from the center of the polygon to its vertices dividing the polygon into 36 congruent sectors each with a central angle of 360 degrees / 18 = 20 degrees.

Each sector is an isosceles triangle with two sides of equal length radiating from the center of the polygon.

The vertex angle of each isosceles triangle is equal to twice the central angle or 40 degrees.

Since the vertex angle of a right triangle is 90 degrees the two non-right angles of each right triangle are 40 degrees and 50 degrees.

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Answer:

a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation (1

point)

b) What is the vertex of the parabola? (1 point)

Step-by-step explanation:

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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The lines intercept at the point (3, 9), and:

A system of linear equations can have one solution, no solutions, and infinite solutions, these are the only options.

If we have a system of equations, the solutions of the system are the points where the graphs of the equations intercept.

Here we know that the solution of the system of linaer equations is (3, 9), this means that the interception of the linear equations is at that point.

Can you have more than one solution to a Linear system of equations?

Yes, you can have:

no solution.

one solution

infinite solutions.

These are the 3 options.

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Answer:

C

Step-by-step explanation:

Trapezoid ABCD was transformed to produce trapezoid A'B'C'D'.

"the two figures are congruent" = the 2 figures have ≅ sides and ≅angles

❌A. Trapezoid ABCD was dilated to produce trapezoid A'B'C'D'.

Dilation will change the measure of the sides

❌B. By definition, transformations always produce congruent figures.

Not all transformations produce ≅ figures, for example dilation

✅C. The transformations applied to trapezoid ABCD were rigid transformations.

A rigid transformation does not change the shape and the size of a figure therfore the 2 figures have ≅ sides and ≅angles

❌D. The transformations applied to trapezoid ABCD were not rigid transformations.

Answer: The transformations applied to trapezoid ABCD were rigid transformations.

(C)

Step-by-step explanation:

9514 1404 393

Answer:

  1.1h

Step-by-step explanation:

The property tax is 10% of h, or 0.1h. Then the total of the price and the tax is ...

  h + 0.1h = 1.1h

Answer:

Step-by-step explanation:

There are 2 ways to make 11. Pretend that one die is red and the other green.

red        green

5              6

6              5

And there is just one way to make 12

red          green

6               6

So you have 3 ways to succeed.

The total number of ways to throw to dice = 6 * 6

P(11 or 12) = 3/36 = 1/12

So one in 12 times you should get a result of 11 or 12.

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

a segment joining the midpoints of two sides of a triangle ( midsegment ) is half the length of the third side.

PQ is a midsegment of the triangle , then

PQ = \(\frac{1}{2}\) RT , that is

15x - 17 = \(\frac{1}{2}\) (23x - 6) ← multiply both sides by 2 to clear the fraction

30x - 34 = 23x - 6 ( subtract 23x from both sides )

7x - 34 = - 6 ( add 34 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

Then

RT = 23x - 6 = 23(4) - 6 = 92 - 6 = 86

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

\(173 \div 2 = 86.5 \\ \)

Step-by-step explanation:

Each of the two employees earn $86.50

Answer:

F and H are both 121 degrees

Step-by-step explanation:

"A kite has 4 interior angles and the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equal." - Cue math

Ok, so the two acute angles add up to 118 degrees, and in order to find the remaining angles we need, subtract 118 from 360 to get 242. Because the two obtuse angles are equivalent, divide 242 by 2 to get the measure of each.

The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

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Using the fact that ∠A is congruent to ∠B and ∠C is a complement of ∠A, we determined that the measure of ∠B is 65° based on the given measure of ∠C as 25°.

If ∠A is congruent (≅) to ∠B and ∠C is a complement of ∠A, we can use the properties of complementary angles to find the measure of ∠B.

Given that m∠C = 25° and ∠C is a complement of ∠A, we know that ∠A + ∠C = 90°.

Since ∠A is congruent to ∠B, we can replace ∠A with ∠B in the equation:

∠B + ∠C = 90°.

Substituting the given value, we have:

∠B + 25° = 90°.

To isolate ∠B, we subtract 25° from both sides of the equation:

∠B = 90° - 25°.

Simplifying, we get:

∠B = 65°.

Therefore, the measure of ∠B is 65°.

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Answer:

C

Step-by-step explanation:

(4x + 1) and 57 are vertically opposite angles and are congruent, so

4x + 1 = 57 ( subtract 1 from both sides )

4x = 56 ( divide both sides by 4 )

x = 14

The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

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Answer:

What is the question You are just stateing facts?

Step-by-step explanation:

Answer:

I) 36 ÷ 4 - 36 ÷9=5

ii). 8×3-12=12

Answer:

Step-by-step explanation:

The question is misleading. It was not specified that his salary is Rs 9,600 per month. That is 115,200 yearly. Of that, 115,200- 85,000 = 30,200 is taxable.

tax = Rs 377.50/month = Rs 4,530/year

4,530/30,200 = 0.15 = 15%

The statement that is not true is (a) A = 74 degrees

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

The dilation of ABC by a scale factor of 2

This means that

Scale factor = 2

The general rule of dilation is that

using the above as a guide, we have the following:

AC = 2 * 5 = 10

C = 53 degrees

BC = 2 * 3 = 6

A = 37 degrees

Hence, the statement that is not true is (a) A = 74 degrees

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Answer:

x" means that the value of y depends upon the value of x, so: y can be written in terms of x (e.g. y = 3x ). If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s . this should help I asked my brother for the answer and he told me to put this happy to help :0

Answer:

120 square inches.

Step-by-step explanation:

The area of the square pyramid building is the amount of space on it

The maximum base length of the building is 67.42 cm

The given parameters are:

Base = b

Slant height (l) = 5b

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * b * 5b

Evaluate the product

L = 10b^2

The total surface area is calculated using:

T = L + b^2

So, we have:

T = 10b^2 + b^2

Evaluate the sum

T = 11b^2

The maximum surface area is 50,000 square feet

So, we have:

11b^2 = 50000

Divide both sides by 11

b^2 = 50000/11

Take the square root of both sides

b = 67.42

Hence, the maximum base length of the building is 67.42 cm

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Answer: 71 feet

Step-by-step explanation:

Let's assume that the side length of the base of the square pyramid is x. Then, the slant height of the pyramid would be 5x, as given in the problem.

The lateral surface area of a square pyramid can be calculated using the formula:

Lateral surface area = (perimeter of base) × (slant height) / 2

The perimeter of the square base is 4x. So, the lateral surface area of the square pyramid can be written as:

Lateral surface area = 4x × (5x) / 2 = 10x^2

We are told that the construction material used for the outside of the building is between 20,000 square feet and 50,000 square feet. So, we can set up the following inequality:

20,000 ≤ 10x^2 ≤ 50,000

Dividing both sides by 10, we get:

2000 ≤ x^2 ≤ 5000

Taking the square root of both sides, we get:

44.7 ≤ x ≤ 70.7

Since we are looking for the maximum possible value of x, we can round 70.7 up to the nearest foot, which is 71 feet.

Therefore, the maximum possible side length of the base of the building is 71 feet.

It's a function because there's only one y-value for any x-value used by the graph.  That's the definition of a function: exactly one y-value (output) for each x-value (input).

Pick and x-value and ask, "What's the y-value for this x-value on the graph?"  You only get one answer.

Answer:

11/8

Step-by-step explanation:

1 3/8 = 1 + 3/8 = 1/1 + 3/8 = 8/8 + 3/8 = 11/8

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

E. None of the above.

Step-by-step explanation:

The n-th root of a complex number can be calculated by the De Moivre's Theorem:

\(z^{1/n} = r^{1/n}\cdot \left[\cos \left(\frac{\theta + 2\cdot k\cdot \pi}{n} \right)+i\,\sin \left(\frac{\theta + 2\cdot k\cdot \pi}{n}\right)\right]\), for \(k \in \mathbb{N}_{O}\) (1)

Where:

\(n\) - Grade of the root.

\(r\) - Norm of the complex number.

\(\theta\) - Direction of the complex number, measured in radians.

\(k\) - Index of the solution.

If we know that \(z^{1/3} = (-1+i)^{1/3}\), then the root of the number is:

Norm

\(r = \sqrt{(-1)^{2}+1^{2}}\)

\(r = \sqrt{2}\)

Direction

\(\theta = \tan^{-1} \left(\frac{1}{-1}\right)\)

\(\theta = \frac{3\pi}{4}\)

If \(k = 0\), then the root of this number is:

\(z^{1/3} = 2^{1/6}\cdot \left[\cos \left(\frac{\frac{3\pi}{4} }{3} \right)+i\,\sin \left(\frac{\frac{3\pi}{4} }{3} \right)\right]\)

\(z^{1/3} = 2^{1/6}\cdot \left[\cos \frac{\pi}{4}+i\,\sin \frac{\pi}{4} \right]\)

\(z^{1/3} = 2^{1/6}\cdot \left[\cos 45^{\circ}+i\,\sin 45^{\circ}\right]\)

Hence, the right answer is E.