In Exercises 23-26, evaluate the trigonometric function by
memory or by constructing an appropriate triangle for the
given special angle.
23. (a) cos 60°
24. (a) cot 45°
25. (a) sin 45°
26. (a) sin 60°
(b) csc 30°
(b) cos 45°
(b) cos 30°
(b) tan 45°
27. (a) sin 10°
28. (a) tan 23.5°
29. (a) sin 16.35°
(c) tan 60°
(c) csc 45°
(c) tan 30°
(c) sec 30°
In Exercises 27-36, use a calculator to evaluate each
function. Round your answers to four decimal places. (Be
sure the calculator is in the correct angle mode.)
(b) cos 80°
(b) cot 66.5°
(b) csc 16.35°

23~29 Pls

The value of [tex]${ }^5 \mathrm{C}_2$[/tex] is 10.

The Combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.

A combination is the choice of r things from a set of n things without replacement and where order does not matter.

Here We have to find. [tex]${ }^5 \mathrm{C}_2$[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]=\frac{5 !}{2 ! \times(5-2) !}[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =\frac{5 !}{3 ! \times 2 !}[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =\frac{5 \times 4 \times 3 !}{2 \times 1 \times 3 !}[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =5 \times 2[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]=10\end{aligned}[/tex]

Therefore, the exact number of [tex]${ }^5 \mathrm{C}_2$[/tex] is 10.

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The total cost of boarding their dog including the registration fee is $237.50.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

We have to find the cost of boarding dog for 1 day.

Cost for three days = $97.50

Cost for 1 day = $97.50 / 3 = $32.50

Given that, the Kittle family boarded their dog at the kennel for 7 days.

Cost for 7 days = $32.50 × 7 = $227.50

Also given, owners are also charged a $10 registration fee.

Total cost = $227.50 + $10

                 = $237.50

Hence the total cost is $237.50.

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The complete question is as follows :

The table show the cost of boarding a dog at a dog kennel. Owners are also charged a $10 registration fee. The Kittle family boarded their dog at the dog kennel for 7 days what was the total, with registration fee, of boarding their dog?

Days    Cost($)

3          97.50

4          130.00

5          162.50

6          195.00

The value of k could be 2 by using the given expression  B  = kG.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables, constants.

Given ,

the number of boys in each class varies directly with the number of girls. in one class there are 14 boys and 7 girls.

using b=kG

So here we have to find the value of k.

From the given expression

that is ,

B = kG

where by substituting the given values ,

we get,

14 = k * 7

k = 14/7

k = 2

Hence, The value of k could be 2 by using the given expression B  = kG.

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Examining the figure properly shows that chord AB in the circle has its length to be equal to 16

Information given from the question is interpreted as

let the center of the circle be O

BE = opposite = ?

OE = adjacent = 6

OB = OA = hypotenuse = radius = 10

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

10² = BE² + 6²

100 = BE² + 36

BE² =  100 - 36

BE = √64

BE = 8

Since line OE is the perpendicular bisector, BE = AE

and from the figure AB = BE + AE

= 8 + 8

= 16

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Using percentage profit formula, the selling price must be $24.8

Profit percentage is calculated by dividing the net profit by the total revenue and multiplying it by 100. For example, if a business has a net profit of $50,000 and total revenue of $500,000, its profit percentage is 10%.

The initial cost of the desert can be calculated using the formula of percentage profit.

percentage profit = [(selling price - cost price) / cost price] * 100

87.5 / 100 = 24 - x / x

0.875 = 24 - x / x

0.875x = 24 - x

24 = 1.875x

x = 12.8

The cost price is 12.8

The profit will be = 24 - 12.8 = 11.2

In order to keep making same percentage profit with the new cost of production.

Selling price = 11.2 + 13.60

Selling price = 24.8

The selling price is $24.8

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If Eugene calculates how long it will take to earn his first million dollars if he earns an average gross pay of $975.00 per week.: D. Yes, Eugene needs to round the years up to the nearest whole number to show the time required to earn the full million dollars.

To determine if Eugene's answer is viable, we need to find how long it will take him to earn his first million dollars at an average gross pay of $975.00 per week.

$1,000,000 / $975.00 per week

= 1025.64 weeks

So, it will take Eugene approximately 1025.64 weeks or approximately 19.71 years (rounded to the nearest year) to earn his first million dollars.

Therefore the correct option is D.

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Answer:

∠HKJ = 180 (STRAIGHT ANGLE)

∠HKI = 180-106 = 74

Answer:

many, many answers

Step-by-step explanation:

as we know an avarage is the number in between all given values. so it can be 6.5 and 7.5, 6 and 8 5 and 9, 4 and 10 and so on

The number of 3s that will be rolled when dice is rolled 360 times will have a standard deviation of 7.1.

The standard deviation (or ) is a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean.

Let X = the total number of 3s produced by rolling the die 360 times. As a result, the number of 3s that will be rolled will have a standard deviation of 7.1.

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If $3,000 is loaned for 4 months at 4.5% AR , He earned $45 interest .

What is interest ?

Interests are subjects that fascinate you and want to learn more about. Interests are usually more about learning and discovering ideas, concepts, and knowledge like history, animal behavior, or even pop culture. For example, if your interest is history, going to museums would be your hobby.

Have given ,

$3,000 is loaned for 4 months at a 4.5% annual rate ,

To find how much interest is earned ,

annual rate is 4.5% then 4 months rate will be [tex]\frac{4.5}{3}[/tex] = 1.5%

So, he earned 1.5% interest for $3,000 ,

Let's calculate , [tex]\frac{3000*1.5}{100}[/tex]

[tex]\frac{4500}{100}[/tex] = $45

If $3,000 is loaned for 4 months at 4.5% AR , He earned $45 interest .

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A result is called "statistically significant" when the p-value is less than the significant level, typically 0.05.

This means that there is less than a 5% chance that the results are due to chance alone, and suggests that there is a real effect present in the data.

The Null Hypothesis is the assumption that there is no significant difference between the measured phenomenon and a certain value or set of values. A statistically significant result means that the observed data are inconsistent with the assumption of no difference, or no effect.

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Answer:

is 9

Step-by-step explanation:

There are 256 expected value  for both a and b, so there are 256 x 256 = 65536 possible pairs of (a,b). Of these, there are 2112 pairs for which the sum of a and b is divisible by 12.

1. There are 256 possible values for both a and b. That means there are 256 x 256

= 65536 possible pairs of (a,b)

2. To find the number of pairs for which the sum of a and b is divisible by 12, we can look at the numbers 0 to 255 and see how many multiples of 12 there are. There are 21 multiples of 12 from 0 to 255, so

21 x 21

= 441.

3. Each multiple of 12 can be paired with any other number from 0 to 255, so there are 21 x 256 = 2112 pairs of (a,b) for which the sum is divisible by 12.

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Answer:

138

Step-by-step explanation:

Divide the shaded area to a rectangle and a triangle

Shaded rectangle area = 10 * 12 = 120

Shaded triangle area = (6 * 12)/2 = 72/2 = 36

Area of unshaded rectangle

Shaded area= 120 + 36 - 18 = 156 - 18 = 138

Hope this helps :)

Have a great day!

The easiest way to learn about angles depends on the individual learner, methods like Visualization, Practice Problems, and Hands-on activities can be utilized.

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A frequency table is a form of data presentation that shows the number of occurrences of each value of the variable being studied. It can be used to show the average value of the variable, the intensity of the variable, and the number of times a certain value appears.

A frequency table is a data presentation tool that is used to show the number of occurrences of each value of a variable being studied. It is often used to show the average value of a variable, the intensity of a variable, and the number of times a certain value appears. To construct a frequency table, you first need to list all the possible values of the variable that you are studying. Next, count the number of occurrences of each value, and then list this count for each value. You can then use this data to calculate the average value of the variable, the intensity of the variable, and the number of times a certain value appears. Additionally, frequency tables can be used to show the times per second variations occur in various wave bands.

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The outer perimeter of the figure is calculated as 62.84m

Perimeter is the distance around the edge of a shape. It is the sum of all the sides of a shape.

Perimeter is the total length of the outside boundary of a shape. It is calculated by adding up all of the sides of the shape.

In this problem, we already have the values given to us and we simply need to compute them.

a) P = 18.84m

b) 12m + 12m = 24m

c) 10m + 10m = 20m

The total outer perimeter of the figure is calculated as

P = 18.84 + 24 + 20 = 62.84m

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The prime factor trees of the numbers 90 and 135 will be 2 × 3² × 5 and 3³ × 5.

The corresponding value integer that can be divided by both is known as the lowest relevant multiple, commonly referred to as the lowest common multiple of pair (or more) numerals a and b.

The numbers are given below.

90 and 135

The prime factors of the number 90 will be given as,

90 = 2 × 3 × 3 × 5

90 = 2 × 3² × 5

The prime factors of the number 135 will be given as,

135 = 3 × 3 × 3 × 5

135 = 3³ × 5

The prime factor trees of the numbers 90 and 135 will be 2 × 3² × 5 and 3³ × 5.

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Answer:

Square root of 85

Step-by-step explanation:

Answer:

Step-by-step explanation: (Don't read this if you are taking a test, please! I don't want you to get in trouble!)

The formula to find a hypotenuse is a^2 + b^2 = c^2 (a squared plus b squared = c squared).

The hypotenuse is the diagonal leg (line WH).

The line WJ = 7, and the line JH = 6.  Let's make line WJ a, and line JH b.

7^2 + 6^2 = c^2.  When you square a number, you multiply that number by itself.  7x7 + 6x6 = c^2.  7x7 = 49 and 6x6 = 36.  Now you have 49 + 36 = c^2

49 + 36 = 85.  85 = c^2.  Square root both sides.  The square root of 85 = the square root of c^2 (c). c = 9.21954446.  If you have to round the hypotenuse to the nearest hundredth, then your answer is 9.22.  The answer for the length of the hypotenuse is 9.22

I hope this helps, but please don't use this on a test!

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x-9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{1} \implies -5}}[/tex]

so we're really looking for the equation of a line whose slope is -5 and it passes through (7 , -3)

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- 5}(x-\stackrel{x_1}{7}) \implies y +3= -5 (x -7) \\\\\\ y+3=-5x+35\implies {\Large \begin{array}{llll} y=-5x+32 \end{array}}[/tex]

The amount of water and sugar he needs respectively to make 5% syrup are; 4.75 lbs and 0.25 lbs

Algebraic word problems are defined as questions that require translating sentences to equations, and then solving those equations. and a single variable.

Now, we are told that Anton wants to make 5 lb of sugar syrup. To get the amount of sugar that he needs to make 5% syrup. Thus;

Let x represent the number of pounds of sugar he needs to make 5% syrup

Thus;

x/5 = 5%

x/5 = 0.05

Multiply both sides by 5 to get;

x = 0.25

Thus, he needs 0.25 lbs of sugar and amount of water required = 5 - 0.25 = 4.75 lbs of water

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If a research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The minimum sample size required for the estimate is: 374.54.

n=((z⍺/2×sigma)/E)^2

Confidence interval ,c =90%

Maximum error, E =0.17

Variance, sigma^2=4

Z-score for 90% confidence interval=1.645

sigma=√4

sigma =2

Sample size = ((1.645×2)/0.17)^2

Sample size = 374.54

Therefore the sample size is 374.54.

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Answer:

3 out of 4

Step-by-step explanation:

the denominator represent the whole number and numerator represent the amount

A line segment is a straight line of points that start at one point and end at another point. A Line segment AB is written down as AB'.

In geometry, the line segment is edged by two definite points on a line. In another word, we can a segment of a line is part of the line that joins two points.

A line has no terminal points and expands limitlessly in both directions but a line segment has two definite endpoints. The dissimilarity between a line segment and a ray is that a ray has only one endpoint and its other end extends infinitely.

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The  two squares of the the product of two consectuitve natural numbers os 1.5 times the square of the lesser number are 2 and 3.

The expression that of the statement that the two squares where the product of two consecutive natural integers is 1.5 times the square of the smaller number can be written  as

x(x+1)=(1.5)(x^2)

we can open the bracket

x^2 +x = 1.5x^2

then we can re arrange

0.5x^2 -x=0

then we can factorize

x(0.5x-1)=0

x=0 or 0.5x=1

x=0 or x=2

Therefore, The number can be 0 and 1 or 2 and 3

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The last option is equivalent to the slope of the linear function and this is given by

2/5

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m is calculated using the formula

m = (y₀ - y₁) / (x₀ - x₁)

The value of the slope is constant for a linear function

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Answer:

168

Step-by-step explanation:

Gift Cards sold by  Ernie = 66

Gift cards sold by  Hessie = 24

Gift Cards sold by Makayala = 78

Common Factor = 6

66 = 6 x 11

24 = 6 x 4

78 = 6 x 13

The total number of gift cards sold is the sum of each person, that being  66 + 24 + 78 which equals 168

Total number of gift cards that all three sold = 168

Answer:

7.3 m²

Step-by-step explanation:

Area of a rectangle = length x width

A = 2.9m x 2.5m = 7.25 m²≅7.3 m²

The product of 1.3 and 0.7 based on the grid is option D 0.91.

Decimals are a form of number in algebra that have an integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number.

According to the grid 1.3 is represented using 13 squares in a row, while 0.7 is represented using 7 squares in column.

The product of 1.3 and 0.7 can thus be calculated by counting all the number of squares in the 13 rows and 7 columns.

The total number of squares in the grid id 91. Since, there are two decimal places we divide 91 by 100.

Thus, the product is 0.91.

The product can be calculated as follows:

(1.3) (0.7) = 0.91

Hence, the product of 1.3 and 0.7 is 0.91.

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