1. Evaluate each expression. Give your answer in radians:
i. Without using a calculator: cos^-1(-√2/2)=
ii. Use a calculator: sin^-1(-0.512)=

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

There are a total of 30 number between 1 and 30, so the total events is 30.
Now for the favorable events (A: even and multiple of 3) there's a total of 5 numbers (6,12,18,24,30)

Using classic probability law the probability is given by the favorable events between the total events

[tex]P(A)=\frac{6}{30}=\frac{1}{5}[/tex]

Answer: X: 230

Explanation in image.

Answer:

T_n = -5 -2(n-1) = -3 - 2n

Step-by-step explanation:

This is an arithmetic sequence with a common difference of -2 (-5 -2 = -7, -7 - 2 = -9, -9 -2 = -11 ...)

so, T_n = -5 -2(n-1) = -3 -2n

we use -5 as the starting point because that's the first term. whether you simplify or not depends on you and your teacher.

Simple interest is calculated as $3000 x 2.5% = $76. Compound interest is added to the principal to determine the balance for the next period.

Simple interest is a type of interest calculation that only takes into account the principal amount of a loan or investment. It does not include any additional payments (or compounding) of the interest. It is calculated by multiplying the principal amount by the interest rate and the number of periods for which the loan is taken out.

For Suzanne's investment, the annual interest rate is [tex]$2.5 %$[/tex], and the interest is simple. Therefore, the interest she earns each year is [tex]$$ I = P \times r = 3000 \times 0.025 = 75. $$[/tex]

Her balance at the end of each year is the sum of her initial deposit and the interest earned in that year. The completed table is:

For Derek's investment, the annual interest rate is also [tex]$2.5 %$[/tex], but the interest is compounded annually. Therefore, we use the compound interest formula with [tex]P=3000[/tex], [tex]r=0.025$, and $n=1[/tex]:

[tex]$$ A = 3000 \times (1+0.025)^Y. $[/tex]

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Answer:

SAS proves that these triangles are congruent.

the value of Harry's investment after 4 years is £8,999.21 to the nearest penny.

To work out the value of Harry's investment after 4 years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

where:

A is the final amount

P is the initial principal (the amount Harry invested)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

In this case, P = £8000, r = 0.028 (2.8% expressed as a decimal), n = 1 (compounded annually), and t = 4. Plugging these values into the formula, we get:

A = £8000(1 + 0.028/1)

= £8000(1.028)

= £8,999.21

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a)0.1071

b)0.2857

c) 0.3571`.

a) The probability of observing all successes is `(5/8) × (4/7) × (3/6) × (2/5) = 0.1071`b) The probability of observing one success is `(5/8) × (3/7) × (4/6) × (4/5) = 0.2857`c) The probability of at most two successes is equal to `P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)`.The probability of observing zero successes is `(3/8) × (2/7) × (1/6) × (0/5) = 0`.The probability of observing one success is `(5/8) × (3/7) × (4/6) × (4/5) = 0.2857`The probability of observing two successes is `(5/8) × (3/7) × (4/6) × (1/5) = 0.0714`.Therefore, `P(X ≤ 2) = 0 + 0.2857 + 0.0714 = 0.3571`.

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If we are aware that Mustafa, Heloise, or Gia have penned more than [tex]22[/tex]pieces altogether. [tex]M > 8[/tex] This is the number of articles Mustafa might have written.

A numeric is a mathematical number which can be utilized to compute and describe a quantity. Numerical symbols, such as "3," are written to represent numbers. A counting system is a logical way of expressing numbers that uses digits or symbols to represent them.

The fact that we use a decimal (base 10) mathematical notation system for numbers gives the number 100 importance that it probably wouldn't otherwise have. It is a circular numeral with undertones of excellence.

[tex]M + H + A > 22[/tex]

We also know that:

[tex]H = 1/4M[/tex]

[tex]A = 3/2M[/tex]

We can substitute these expressions into the first equation:

[tex]M + 1/4M + 3/2M > 22[/tex]

Multiplying everything by the common denominator of 4:

[tex]4M + M + 6M > 88[/tex]

[tex]11M > 88[/tex]

[tex]M > 8[/tex]

So, Mufasa has written more than [tex]8[/tex] articles.

Using the equation [tex]H = 1/4M[/tex], we can find that Heloise has written:

[tex]H = 1/4(8) = 2[/tex]

Using the equation [tex]A = 3/2M[/tex], we can find that Angie has written:

[tex]A = 3/2(8) = 12[/tex]

Therefore, Mufasa has written more than [tex]8[/tex] articles, Heloise has written [tex]2[/tex]articles, and Angie has written [tex]12[/tex] articles.

To check if their combined total is more than [tex]22[/tex]:

[tex]M + H + A = 8 + 2 + 12 = 22[/tex]

So, their combined total is exactly [tex]22[/tex], which means that they have not written more than [tex]22[/tex] articles for the school newspaper.

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Answer:

7.3*10^7

Step-by-step explanation:

After 50 seconds, the person has fallen approximately 2252.5 meters below the cliff.

Assuming no air resistance, we can use the formula for distance traveled by an object under constant acceleration:

d = v_i * t + (1/2) * a * t²

where d is the distance traveled, v_i is the initial velocity, t is the time, and a is the acceleration.

In this case, the initial velocity is -9.0 m/s (negative since it is downward), and the time is 50 seconds. The acceleration due to gravity is approximately -9.81 m/s².

Substituting the given values into the formula, we get:

d = -9.0 m/s * 50 s + (1/2) * (-9.81 m/s²) * (50 s)²

≈ -2252.5 m

Therefore, the person is approximately 2252.5 meters beneath the cliff after 50 seconds.

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Accοrding tο the given infοrmatiοn, the prοbability οf generating a randοm number between 0.25 and 0.75 is 0.5 and the prοbability οf generating a number less than οr equal tο 1 is 1.

Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 represents an impοssible event and 1 represents a certain event.

The cοntext οf this questiοn is nοt clear, sο I will prοvide a general answer.

Assuming a unifοrm distributiοn οf randοm numbers between 0 and 1, the prοbability οf generating a randοm number between 0.25 and 0.75 is:

b. P(0.25 ≤ X ≤ 0.75) = 0.75 - 0.25 = 0.5

where X is the randοm variable representing the generated number.

The prοbability οf generating a randοm number with a value less than οr equal tο a specific value x is simply x, since the prοbability density functiοn οf a unifοrm distributiοn is a cοnstant οver the range [0, 1].

c. P(X ≤ x) = x fοr 0 ≤ x ≤ 1

Fοr example, the prοbability οf generating a number less than οr equal tο 0.3 is 0.3, and the prοbability οf generating a number less than οr equal tο 1 is 1.

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The impact of changing a single value in a data set on the mean, median, mode, and range can vary depending on the position and value of the changed value

The impact of changing a single value in a data set on the mean, median, mode, and range can vary depending on the value that is changed and its position in the data set.

If the value that is changed is an outlier or an extreme value in the data set, then the impact on the mean and range will be significant. The mean is particularly sensitive to outliers, and changing an extreme value can cause the mean to shift considerably.

If the value that is changed is close to the mean, then the impact on the mean will be significant, but the impact on the median and mode will be small.

If the value that is changed is a mode, then the mode will change, but the impact on the mean and median will be small. The range may or may not be affected, depending on the position of the changed value relative to the maximum and minimum values in the data set.

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Through end behaviour of polynomials, we can see that the left end behaviour is approaching positive infinity and the right end behaviour is approaching negative infinity.

The nature of the value when the function argument gets closer to + infinity and - infinity is the end behaviour of a function.

The term with the highest degree determines how a polynomial function will behave in the end.

For example:

If f(x) = x³ + 2x² – 4x + 5 is given,

The end behaviour is determined by x³.

As a result, f(x) + as x + and f(x) - as x -

The term with the highest degree will be substantially larger than the other terms for large values of x, making the other terms essentially irrelevant.

The degree of the x³ coefficient is odd and it is positive.

Hence, the final behaviour is f(x) + as x + and f(x) - as x -.

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Answer:  1 1/4

Step-by-step explanation:

the heaviest bunch of grapes weights 1 7/8 pounds

A line plot labeled 0 to 2 with tick marks every one-eighth unit. Above the tick mark at five-eighths is one dark blue dot. Above the tick mark for six-eighths is a column of two light blue dots. Above the tick mark at 1 there is a column of three light blue dots. Above the tick mark at one and four-eighths is a column of two light blue dots. Above the tick mark for one and five-eighths is a column of four light blue dots. Above the tick mark for one and seven-eighths is one light blue dot.

Therefore , the solution of the given problem of area comes out to be  region is 24.5 square units in size.

How much room is needed to fully cover the outside can be used to estimate its overall size. When calculating a trapezoidal shape's surface, the immediate environs are taken into account. The surface area of something determines its overall dimensions. The internal water volume of a cuboid is given by the total of the borders for each of its six rectangular edges.

Here,

We must first calculate the areas of the three shapes in order to add them up to get the area of the territory.

Triangle 1: The height is equal to the distance of the y-coordinates of the x-axis (which is 0) and the y-coordinates of (3,6), which is 6. Consequently, the triangle's size is:

=> 1/2 * base * height

= >1/2 * 3 * 6 = 9

The segment between the x-axis and the location where the line y=10-x meets the x-axis, which is the base in triangle 2 (10,0).

Triangle 2:

=> 1/2 * base * height = 1/2 * 4 * 1 = 2

Trapezoid:

The three shapes' combined regions result in:

=> 9 + 2 + 13.5 = 24.5

The region is 24.5 square units in size and is circumscribed by the x-axis, lines x=2, x=6, lines y=x+3, and y=10-x.

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Answer:

[tex]5 < x < 23[/tex]

Step-by-step explanation:

Accoriding to the Triangle Inequality Theorem:

9 + x > 14 ------> x > 5

14 + 9 > x ------> x < 23

So we have 5 < x < 23.

Answer:

100

Step-by-step explanation:

25% can also be converted to 0.25

if you want to INCREASE it by 25%, you're adding 25% to your current 100% to get 125% of 80

125% is the same as 1.25, so you multiply 80 by 1.25

80 * 1.25 = 100

Answer:

100

Step-by-step explanation:

To increase 80 by 25%, you need to add 25% of 80 to 80.

First, we find what 25% of 80 is.

To find a percent of a number, multiply the percent by the number.

Change the percent to a decimal by dividing the percent by 100.

25% of 80 = 25% × 80 = 25/100 × 80 = 0.25 × 80 = 20

25% of 80 is 20.

Now we add 20 to 80.

80 + 20 = 100

Answer: 100

Using distance formula, the triangle ABC is a scalene triangle

To classify the triangle, we need to determine whether its sides are equal in length (in which case it's equilateral or isosceles), or whether they are all different lengths (in which case it's scalene). We can use the distance formula to calculate the length of each side of the triangle, as follows:

The distance formula gives us the distance between two points (x1, y1) and (x2, y2) in the coordinate plane:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

Using this formula, we can find the length of each side of triangle ABC:

AB = √[(4-1)^2 + (4-0)^2] = √(9 + 16) = √25 = 5

BC = √[(6-4)^2 + (2-4)^2] = √(4 + 4) = 2√2

AC = √[(6-1)^2 + (2-0)^2] = √(25 + 4) = √29

We can see that AB = 5, BC = 2√2, and AC = √29. Since all three sides have different lengths, the triangle is scalene.

Note that the midpoints of the sides AB and BC are not relevant for determining the type of triangle. Also, it's not accurate to say that the midpoint of AB is (4/3, 2), as the coordinates of the midpoint are actually ((1+4)/2, (0+4)/2) = (2.5, 2), and similarly for the midpoint of BC.

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The required circumference of the given circle is 45.27 cm approx.

In geometry, the perimeter of a circle or ellipse is its circumference. In other words, the circumference would equal the length of the arc if the circle were expanded up and straightened out to a line segment.

The term "perimeter" is most frequently used to describe the radius of any closed shape.

The circumference of a circle is the length around its periphery.

It is similar to the edges of other shapes, including squares.

It can be viewed as the line that defines the shape.

So, calculate the diameter using the Pythagorean theorem as follows:

h² = a² + b²

h² = 8² + 12²

h² = 64 + 144

h² = 208

h = √208

h = 14.42

Now, calculate the circumference as follows:

Radius = 14.42/2 = 7.21

Now,

= 2πr

= 2*3.14*7.21

= 45.2788

Therefore, the required circumference of the given circle is 45.27 cm approx.

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Andrew needs to save money for 3.8 months, or about 4 months (rounded up) to buy that refrigerator.

Based on the given information, Andrew's budget can be broken down as follows:

Housing: $46,200 (30% of $154,000)

Gas: $12,320 (8% of $154,000)

Internet: $3,080 (2% of $154,000)

Personal care: $7,700 (5% of $154,000)

Food: $38,500 (25% of $154,000)

Saving: $23,100 (15% of $154,000)

Child: $23,100 (15% of $154,000)

Small business income: $25,000

To calculate how long it will take for Andrew to save enough money to buy the $95,000 refrigerator, we need to calculate his monthly savings based on his budget.

Andrew's total monthly income (before expenses) is

His total monthly expenses (including savings) are

Therefore, his monthly savings are $179,000 - $154,000 = $25,000. To save up $95,000, he will need $95,000 / $25,000 = 3.8 months, or about 4 months (rounded up).

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Answer: D) square root 49

Step-by-step explanation: a rational number is a number that eventually ends. Square root 49 is the answer, because it terminates.

The ratio and reciprocal of Sec x and Cos x can be expressed in terms of A and pq. When A is equal to 3/2, Sec A will be equal to 3/2 and Cos A will be equal to 2/3.

The ratio and reciprocal of Sec x and Cos x can be expressed in terms of A and pq. Sec x = A/pq and Cos x = pq/A. The reciprocal of Sec x is Cos x = pq/A and the reciprocal of Cos x is Sec x = A/pq.

When A = 3/2, Cos A = 2/3. Therefore, Sec A = 3/2 and Cos A = 2/3.

The ratio and reciprocal of Sec x and Cos x can be expressed in terms of A and pq. When A is equal to 3/2, Sec A will be equal to 3/2 and Cos A will be equal to 2/3.

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There are 184,756 possible 9 player batting orders for a softball team with 20 players.

The formula to calculate the combination number of possible batting orders for a team with n players is n!/(n-r)! where n = the total number of players, and r = the number of players in the batting order. Therefore, for a softball team with 20 players, the number of possible 9 player batting orders is 20!/(20-9)! = 184,756.

20! = 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

(20-9)! = (20 - 9) × (19 - 9) × (18 - 9) × (17 - 9) × (16 - 9) × (15 - 9) × (14 - 9) × (13 - 9) × (12 - 9) × (11 - 9) × (10 - 9) × (9 - 9)

20!/(20-9)! = 184,756

Therefore, there are 184,756 possible 9 player batting orders for a softball team with 20 players.

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the common ratio of the geometeric sequence -7, -42, -252 is 6.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed non-zero constant, called the common ratio. We can find the common ratio (r) of the sequence -7, -42, -252 by dividing any term by its previous term. For example:

-42 / (-7) = 6

-252 / (-42) = 6

Since the ratio is the same for both, we can conclude that the common ratio is 6. Therefore, each term is obtained by multiplying the previous term by 6.

To check, we can multiply any term by 6 to obtain the next term in the sequence. For example:

-7 * 6 = -42

-42 * 6 = -252

So, the common ratio of the sequence -7, -42, -252 is 6.

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Answer:

Step-by-step explanation:

To determine which size of shampoo is the better buy, we need to calculate the unit price, which is the price per ounce for each size.

For the regular size, the unit price is:

$8.00 / 20 oz = $0.40/oz

For the economy size, the unit price is:

$10.00 / 40 oz = $0.25/oz

Since the unit price for the economy size is lower than the unit price for the regular size, the economy size is the better buy.

Therefore, the economy size of shampoo is the better buy.

Answer:

Step-by-step explanation:

To solve this problem, we need to find the number of cells in each colony after 1 minute (60 seconds) and compare them.

For the colony growing at 20°C, the expression for the number of cells is:

N(20°C) = t^2 - 7t - 7

Substituting t = 60 seconds:

N(20°C) = (60)^2 - 7(60) - 7 = 3533

Therefore, the number of cells in the colony growing at 20°C after 1 minute is 3533.

For the colony growing at 30°C, the expression for the number of cells is:

N(30°C) = t^2 - 6t - 7

Substituting t = 60 seconds:

N(30°C) = (60)^2 - 6(60) - 7 = 3563

Therefore, the number of cells in the colony growing at 30°C after 1 minute is 3563.

Comparing these results, we see that the colony growing at 30°C has a greater number of cells after 1 minute than the colony growing at 20°C. Therefore, the colony growing at 30°C will have a greater number of cells than the colony growing at 20°C after 1 minute.

Answer:

78.25

Step-by-step explanation:

First find the tip.

62.60 * 20%

62.60*.2 = 12.52

Then find the tax

62.60 * 5%

62.60 * .05

3.13

Now add the cost of the food, tip, and tax.

62.60+12.52+3.13

78.25

The area of the shaded portion of the circle is 942 units².

The diagram is a circle inscribed in another circle.  The area of the shaded portion of the circle can be found as follows:

area of the shaded portion = area of the bigger circle - area of the smaller circle

Therefore,

area of the bigger circle = πr²

area of the bigger circle = 20²π

area of the bigger circle = 400π units²

area of the smaller circle = πr²

area of the smaller circle = 10²π

area of the smaller circle = 100π units²

Therefore,

area of the shaded portion = 400π - 100π

area of the shaded portion = 300π

area of the shaded portion = 300 × 3.14

area of the shaded portion = 942 units²

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There are 18.75 quarts of apple juice in a case of 24 bottles.

To calculate the number of quarts of apple juice in a case of 24 bottles, we must first calculate the number of ounces in the case. To do this, we can use the formula:

Total Ounces = Number of Bottles x Ounces per Bottle

Total Ounces = 24 x 25

Total Ounces = 600

Now that we have the total ounces of apple juice in the case, we can convert this to quarts using the formula:

Quarts = Ounces ÷ 32

Quarts = 600 ÷ 32

Quarts = 18.75

Therefore, there are 18.75 quarts of apple juice in a case of 24 bottles.

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The sets of side lengths that are similar to the triangle that Kendall drew are; A. 16, 30, 35, and D. 8, 15, 17​.

The tangent of a right triangle is given as the opposite side divided by the adjacent side. Now, we are given the value of the tangent to be 1.8750.

To obtain the tangents, we are going to divide the opposite by the adjacent as follows:

30/16 = 1.875

8/6 = 1.333

8/1.875 = 4.266

15/8 = 1.875.

So, the set of side lengths that are similar to the triangle that Kendall drew are 16, 30, 35, and 8, 15, 17​.

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