If tan⁡θ=-5/2 and sin⁡θ>0, find the exact values of sin⁡θ,cos⁡θ,sec⁡θ,csc⁡θ,cot⁡θ.

The cost of ending inventory using the weighted-average method is $198.24.

An ending inventory is often derived by adding new purchases to beginning inventory and then subtracting the cost of goods sold.

To calculate it using the weighted-average, we must compute the weighted average cost per unit and then multiply the weighted average cost per unit by the number of units in ending inventory to get the cost of ending inventory.

The total cost of goods available for sale is:

= (4 x 1.50) + (11 x 2.00) + (11 x 2.50) + (16 x 2.75) + (17 x 3.50) + (21 x 3.70) + (31 x 3.90) + (17 x 4.30)

= $430.7

The total units available for sale is:

= 4 + 11 + 11 + 16 + 17 + 21 + 31 + 17

= 128

The weighted average cost per unit is:

= $430.70 / 128 units

= $3.36484375

= $3.36

The cost of ending inventory will be:

= 59 units x $3.36

= $198.24

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For circle O, For circle O, m CD=125° and m∠ABC = 55°. In the figure, ∠ ABO and ∠ BCO have measures equal to 35°.

For circle O, m(arc CD) = 125° and m∠ABC = 55°.

First, we use central angle to find that ∠COB is 125°,

give that ∠COB = arc CD

Next, we use complementary angles to find that ∠BCA is 35°,

given that ∠ABC +  ∠BCA = 90°.

Then, we use the sum of interior angles in a triangle to find that ∠CBO is 20°; given that:

∠CBO + ∠COB + ∠BCO = 180°.

∠BCO = ∠BCA = 35°

∠COB = 125°

125° + 35° = 160°

180° +  160° =  20°

Finally, we use angle addition postulate to find that ∠ABO is also 35°.

Therefore, <ABO and <BCO both have measures of 35° in the figure.

The above answer is in response to the question below;

For circle O, and m∠ABC = 55°. In the figure, ∠_____ and ∠____ have measures equal to 35°.

a. the first could be AOB, ABO, or BOA

b. the second could be BCO, OBC, or BOC

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Answer:

1.4:1

= 14:10

= 7:5

Hence, ans is 7:5

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Answer:

83

Step-by-step explanation:

Add them all together and then divide by 10 (which is the number of digits there are)

Answer:9.125

Step-by-step explanation:

Answer:

54.6 square yards

Step-by-step explanation:

For any regular polygon, the area of the polygon is given by:

[tex]A_{regular~polygon}=\frac{1}{2}nsa[/tex], where

Heptagons are 7-sided polygons, so n=7.

The length of a side and the apothem are given, so substitute and calculate:

[tex]A_{heptagon}=\frac{1}{2}(7)sa[/tex]

[tex]A_{heptagon}=\frac{1}{2}(7)(3.9~yd)(4.0~yd)[/tex]

[tex]A_{heptagon}=54.6 ~yd^2[/tex]

The correct interpretation of the p-value is 3.34.

We are given that;

t-value=3.34

Number of customers= 200

Now,

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming that the null hypothesis is true. In this case, the p-value of 0.001 means that there is a 0.1% chance of getting a t-value of 3.34 or higher (or -3.34 or lower) if the true slope of the linear relationship between the two ratings is zero. The p-value is very small, which indicates that the data provide strong evidence against the null hypothesis and in favor of the alternative hypothesis.

The p-value of 0.001 means that there is a 0.1% chance of getting a t-value of 3.34 or higher (or -3.34 or lower) if there is no linear relationship between the two ratings.

Therefore, by probability the answer will be 3.34

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The statement which correct describe "confidence-interval" is (d) confidence level is considered as probability that something will fall within "confidence-interval".

A "Confidence-Interval" is a statistical term used to describe the amount of uncertainty associated with a sample estimate. It refers to the percentage of all possible samples that can be expected to include the true population parameter being estimated.

For example, if a study reports a 95% confidence level, it means that 95% of all possible samples would contain the true population parameter. This can be considered as the probability that the estimate falls within a certain range or interval, called the confidence interval.

Therefore, option (d) is the correct statement.

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The given question is incomplete, the complete question is

Which statement correctly describes confidence level?

(a) A confidence level is the probability that a simple event will occur.

(b) A confidence level is a value that is added and subtracted from a given value to give an interval where something will likely happen.

(c) A confidence level is the probability that something will fall outside of a confidence interval.

(d) A confidence level is the probability that something will fall within a confidence interval.

Answer:

A confidence level is the probability that something will fall within a confidence interval.

Step-by-step explanation:

Plato/Edmentum

Let the number of twin births in 2000 be x.

According to the problem, the number of twin births in 2015 increased by 14%, which means the number of twin births in 2015 is:

x + 0.14x = 1.14x

We also know that the number of twin births in 2015 is approximately 133,950, so we can set up the following equation:

1.14x = 133,950

Solving for x, we get:

x = 117,500

Therefore, there were approximately 117,500 twin births in 2000.

Answer:

Step-by-step explanation:

To find the margin of error for a 98% confidence level, we need to use the z-score that corresponds to this confidence level, which is 2.33 (found in a z-table or using a calculator).

The formula for the margin of error (E) is:

E = z*(sqrt(p*q/n))

Where:

z is the z-score for the desired confidence level (2.33 for 98% confidence)

p is the sample proportion (0.4, or 40%)

q is the complement of the sample proportion (1 - 0.4 = 0.6)

n is the sample size (800)

Substituting these values into the formula, we get:

E = 2.33*(sqrt(0.4*0.6/800)) = 0.045

So the margin of error for a 98% confidence level, with a sample size of 800 and a sample proportion of 40%, is 0.045 or approximately 4.5%. This means that we can be 98% confident that the true population proportion is within 4.5% of the sample proportion.

Answer:

--------------------------

As per given, the distance from the center to both of the chords is same, therefore both chords have same length:

The length of each chord is:

Use Pythagorean theorem to find the radius, the distance from the center to one end of the chord:

(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.

(a) For loan 1, $3200 at 6.7% for 4 years and 7 months (4 years in college + 3 months deferment), the simple interest = 3200 * 0.067 * (55/12) ≈ $1023.33.

(b) For loan 2, $12,000 at 7.3% for 2 years and 7 months (2 years in college + 3 months deferment), simple interest = 12000 * 0.073 * (31/12) ≈ $2362.33.

(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.

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The expression to find the angle BGC is 11x + 34.

The equation that would help us find the angles of AGB and BGC is 90 = 11x + 46.

The correct equation that would help us find the angles of ABG, AGF, and AGE is 15x + 120 = 180.

In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).

By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;

∠AGB + ∠BGC = 90.

12 + 11x + 34 = 90

11x + 46 = 90

90 = 11x + 46.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of angles ABG, AGF, and AGE are supplementary angles:

12 + 90 + 15x + 18 = 180°

120 + 15x = 180°

15x + 120 = 180

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The row operation performed to obtain  [0    0     -3     9] is R₃ - R₂.

A row operation in a matrix involves making a change to one or more rows of the matrix. The three elementary row operations are, interchanging rows, rows addition, and rows multiplication.

The given matrix;

[9  -2  -9  9]            [9  -2  -9  9]

[1   2  -6   -1]  into   [1   2  -6   -1]

[1  2  -9    8]            [0  0  -3    9]

If we perform R₃ - R₂, that is row 3 minus row 2, we will have the following;

[1  2  -9    8] - [1   2  -6   -1]

= [(1-1)  (2-2)   (-9 + 6)   (8 + 1)]

= [0    0     -3     9]

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Answer: 34.9

Step-by-step explanation: 100 - 65.1

The value of the variable w is 56

Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.

Also, algebraic expressions are made up of mathematical or arithmetic operations, such as;

From the information given, we have the algebraic equation as;

w - 54 = 2

To determine the value of the variable, we take the steps;

collect the like terms

w = 2 + 54

Now, add the values

w = 56

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Answer: 5 and 2

Step-by-step explanation:

In an arithmetic sequence, the difference between consecutive terms is constant. Since the third and fourth terms are -1 and -4, the common difference is -4 - (-1) = -3. Therefore, the second term is -1 - (-3) = 2 and the first term is 2 - (-3) = 5. So the first and second terms of the sequence are 5 and 2 respectively.

He will need to use the wheelbarrow at least 41 times to fill the delivery truck to 70% of its capacity.

Volume is a measure of the amount of space that a substance or object occupies in three dimensions. It is typically measured in units such as cubic meters (m³), cubic centimeters (cm³), liters (L), or gallons (gal), depending on the system of measurement being used.

First, let's calculate the total volume of the delivery truck:

Volume of delivery truck = length x width x height

Volume of delivery truck = 11 ft x 8 ft x 6 ft

Volume of delivery truck = 528 cubic feet

To fill the delivery truck to 70% of its capacity, Johnny needs to put 0.7 x 528 = 369.6 cubic feet of planting soil in the truck.

Now, let's calculate the volume of planting soil that fits in the wheelbarrow:

Volume of wheelbarrow = length x width x height

Volume of wheelbarrow = 2 ft x 3 ft x 1.5 ft

Volume of wheelbarrow = 9 cubic feet

Number of loads = Total volume of planting soil needed / Volume of each load

Number of loads = 369.6 cubic feet / 9 cubic feet

Number of loads = 41.0666667

Since Johnny cannot use a fraction of a load, he will need to use the wheelbarrow at least 41 times to fill the delivery truck to 70% of its capacity.

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Answer: 89.64 kilometers per hour

Step-by-step explanation: Convert 24.9 meters per second into Kilometers per minute by multiplying by 1000 to get 0.0249 kilometers per minute, which gives you 1.494 kilometers per minute. Then, you must convert this to kilometers per hour by multiplying by 60 to get 89.64 kilometers per hour

The statement that "if you took a true "if-then' statement and reversed the clauses, the new statement would also be true" is False.

By reversing the clauses within an accurate "if-then", one will manifest a new statement known as the "converse" of the initial formula. Though, it is not inevidably true.

For instance, if the original expression was "If it rains, then the ground gets wet", its converse is "If the ground gets wet, then it rains". Unfortunately, that specific converse has the potential to be incorrect since there are several other methodologies from which the land can gain moisture beside rain (e.g. sprinkler system, someone unintentionally pouring water, etc.).

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The type of statistical technique used here is inferential

We are given that;

Annual-sales distribution of cottage industries of the same standard=500

Number of industries=500

Now,

a) The type of statistical technique used here is descriptive statistics, which involves summarizing, organizing, and presenting data in a meaningful way. Descriptive statistics can use tables, graphs, and numerical measures such as mean, median, mode, range, standard deviation, etc. to describe the main features and patterns of a data set.

b) The type of statistical technique used here is inferential statistics, which involves drawing conclusions or making predictions about a population based on a sample. Inferential statistics can use methods such as estimation, hypothesis testing, confidence intervals, regression analysis, etc. to make inferences about the population parameters from the sample statistics.

Therefore, by statistics the answer will be inferential.

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Answer:

8 = 2m + 4

2m = 4, so m = 2

So the equation of this line is y = 2x + 4.

D is the correct answer.

Proportionately, if $170,500 profits in the second year of operation represent 576% of the company's first-year profits, the first-year profits will be $29,600.

A proportion describes two ratios equated to each other.

Proportion is a fractional value that compares one value or quantity to another.

The profits for the second year of operation = $170,500

Let the profits for the first year of operation = x

Proportionately, if $170,500 is 576% of x, x = $29,600 ($170,500 ÷ 576%)

Using equations, 5.76x = $170,500

x = $29,600 ($170,500  ÷ 5.76)

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Answer:

The market trader should sell each of the remaining 20 packs of muffins for £1.30 to meet his target.

Step-by-step explanation:

To find out how much the market trader needs to sell the remaining 20 packs of muffins, we first need to calculate his total cost and his target revenue.

The cost of the loaves of bread is:

100 loaves x 84p/loaf = £84

The cost of the packs of muffins is:

60 packs x £1.10/pack = £66

Therefore, the total cost for the trader is:

£84 + £66 = £150

To make a 40% profit, the trader needs to make £150 x 40/100 = £60 in profit.

His target revenue is, therefore:

£150 + £60 = £210

The revenue from the loaves of bread is:

100 loaves x £1.20/loaf = £120

The revenue from the 40 packs of muffins sold at £1.60 per pack is:

40 packs x £1.60/pack = £64

So the total revenue from the loaves of bread and the 40 packs of muffins is:

£120 + £64 = £184

This means that the trader needs to make:

£210 - £184 = £26

from the sale of the remaining 20 packs of muffins.

To sell 20 packs of muffins to make £26, he needs to sell each pack for:

£26/20 = £1.30 per pack

Therefore, the market trader should sell each of the remaining 20 packs of muffins for £1.30 to meet his target.

The height of the person that cast a shadow of 1.5 foot is 6 foot.

When the sun is at a certain angle in the sky, a 100 foot building will cast a 25 foot shadow. A person cast a shadow of 1.5 foot at the same time.

Therefore, the height of the person can be found by setting up a proportional relationship between the length of shadow and the actual height of the building and person.

Hence,

let

x = height of the person

Therefore,

100 / 25 = x / 1.5

cross multiply

25x = 100 × 1.5

25x = 150

divide both sides of the equation by 25

x = 150 / 25

x = 6

Therefore,

height of the person  = 6 foot.

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When -3 (row 1) is added to row 2, the result would be [ 1 - 4 | 8 ]

[ 0 10 | 10 ].

The first thing to do is to multiply each element in row 1 by - 3 :

- 3 x 1 = - 3

- 3 x - 4 = 12

- 3 x 8 = - 24

Then, we need to add the result to the elements in row 2:

3 + ( - 3 ) = 0

- 2 + 12 = 10

10 + ( - 24 ) = - 14

The resulting matrix would therefore be:

[ 1 - 4 | 8 ]

[ 0 10 | - 14 ]

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