If cos A =0. 8945, find angle A to nearest tenth of a degree

The sum of the first fifteen terms of the given sequence is 220.

The given sequence can be expressed as: [tex]$2, 8, 14, \dots$[/tex], in which each term is six more than the preceding term. This is an arithmetic sequence, where the common difference between terms is 6. The formula to calculate the sum of the first n terms of an arithmetic sequence is given by [tex]$S_n = \frac{n}{2}(a_1 + a_n)$[/tex], where [tex]$a_1$[/tex] is the first term and [tex]$a_n$[/tex] is the nth term.

In the given sequence, the first term [tex]$a_1$[/tex] is 2 and the 15th term [tex]$a_n$[/tex] is 42. So, plugging these values to the formula gives us, [tex]$S_{15} = \frac{15}{2}(2+42) = \frac{15\times 44}{2} = 220$[/tex].

Therefore, the sum of the first fifteen terms of the given sequence is 220.

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Answer:

20% reduction in price

Step-by-step explanation:

Let the original price of each box be P and original quantity be Q. The unit rate is P/Q

Jack's approach

increase quantity by 25% = 0.25Q

New quantity = Q + 0.25Q = Q(1  +0.25) = 1.25Q

Unit rate = P/1.25Q

Sadia's approach

Reduce price and keep quantity same

Let price reduction be d% = d/100

Let us denote d/100 as r. This will be a decimal value. For example, a reduction of 10% means that the price is reduced by 0.10

Price reduction = P x r = Pr

New price = P - Pr = P(1-r)

Unit rate by this method =P(1-r) /Q

Both unit rates have to be the same if both values are the same

So
[tex]\dfrac{P}{1.25Q} = \dfrac{P(1-r)}{Q}\\\\\dfrac{P}{Q} \cdot \dfrac{1}{1.25} = \dfrac{P}{Q} \cdot (1-r)\\\\[/tex]

Eliminate [tex]\displaystyle {\dfrac{P}{Q}}[/tex]   common factor from both sides to get

[tex]\dfrac{1}{1.25} = 1- r[/tex]

[tex]\dfrac{1}{1.25} = 0.8\\\\[/tex]

So we get
[tex]1 - r = 0.8\\\\\implies r = 1 - 0.8 = 0.2\\\\[/tex]

0.2 works out to 0.2 x 100 = 20%

So for Sadia's idea to have the same value as Jack's idea, the price should be reduced by 20%

The value off ARU based on the information will be 35°.

We know, the incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle.

A)By property, AR is angle bisector of angle KRU.

Therefore m(<ARU) = m(<ARK) = 40°

m<ARU= 40°

B) The angle bisectors in a triangle are always concurrent and the point of intersection is known as the incenter of the triangle.

AU = AT = 20

Therefore,

AU = 20

C) AP is angle bisector of <QPR,

By definition of angle bisector

m<QPA = m<APR

3x+2 = 4x-9

4x-3x = 9+2

x =11

m<QPA = 3(11) +2 = 35°

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Answer:

The first/top option

Step-by-step explanation:

First, we can find the inequality that the line is representing. X is the number of hours she has already done, and she has five hours more to do to fulfill the 12 or more hours of required service. The inequality would be x+5≥12.

The minimum that X has to be is 7 because any value lower than 7 would make the inequality false[ ex. 6 + 5 ≠ 12 ]. The arrow would be pointing to the right, because 7 is the minimum value, not the max, so any value higher than 7 would still make the inequality true. Lastly, the circle would be filled, because 7 is included in the set of values that make the inequality true[ 7 + 5 = 12 ].

So, the answer would be the first option.

Answer:

Option B

Step-by-step explanation:

The green graph represents the percentage of calls with the Chicago service center.
For December 1993, the percentage of calls is coming out to at least 95 percent. In addition, the graph is increasing as months go by. Based on these two analysis, the estimate percentage of calls within 10 seconds in January of 1994 is:

Option B: 98

Answer:

3 liters

Step-by-step explanation:

If he took the 2 fullest containers, he took the two dots that are at 4 1/2, which is also 4.5

Now since there are two, we multiply by 2.

4.5 = 9 liters

It then says he will divide the milk evenly between 3 containers. So now we divide.

9/3 = 3

The equation that describes the graphed function is -

g(x) = - f(x) - 3.

A root function in mathematics is given as -

y = [tex]$\sqrt[n]{x}[/tex]

We can further write the function as -

y = [tex]$x^{\frac{1}{n} }[/tex]

Given is the graph of the function as shown in the image attached.

We can write the function f(x) as -

f(x) = √x

Inverting the f(x) across the {x} axis, we can write -

- f(x) = - √x

After downward translation, we can write g(x) as -

g(x) = - f(x) - 3

Therefore, the equation that describes the graphed function is -

g(x) = - f(x) - 3.

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Answer: 1 [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Make it a mixed number then simplify if you can. I hope this helps.

Answer:

Rs 3520 is divided in the ratio 11:12:17 as rs 968, rs 1056, and rs 1469

Step-by-step explanation:

According to the question, we have to divide rs 3520 in the ratio 11:12:17

let the common ratio be x

so, total share= (11+12+17)x = 40 x

for the first person, share would be (11x/40x)*(Rs 3520)

=Rs 968

for the second person, share would be (12x/40x)*(Rs 3520)

=Rs 1056

for the third person, share would be (17x/40x)*(Rs 3520)

=Rs 1496

The shares are Rs 968, Rs 1056, and Rs 1469

hope this helps :)

The number of ways the letters can be permutated in the word SPEECHLESS is 100800.

What is meant by permutation?

An arrangement of items in a specific order is referred to as a permutation. A set can be permuted by arranging its components in a linear or sequential order, or by rearrangement of its components if the set is already ordered. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

The  number of letters in SPEECHLESS = 10

The letter E repeats 3 times

The letter S repeats 3 times

The letters P,C,H,L repeats one time.

When there are repeating letters in a word, the total number of distinct ways the letters in the words can be permutated is:

[tex]N= \frac{n!}{r_1!r_2!.....r_m!}[/tex]

where N = number of arrangements

 n = number of letters

r = total number of times one letter is repeated in the word

For SPEECHLESS,

Therefore the number of ways the letters can be permutated  is:

[tex]N= \frac{10!}{3!3!}[/tex] = 100800

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Answer:

Step-by-step explanation:

Difference means subtract or minus (-)

So we always switch 29 and x into x and 29

Can't really explain that much more but it's the correct answer though, trust me! :)

The number of possible outcomes in the sample space of a wireless garage door opener with 16 switches can be determined using the concept of combination is 1.

Combination is a mathematical concept that refers to the number of ways that a set of objects can be selected from a larger set without regard to their order.

To determine the number of possible outcomes in the sample space, we can use the concept of combination. In this case, the objects are the 16 switches, and the larger set is the set of all possible settings for these switches (up or down).

To calculate the number of possible combinations, we can use the formula for combination, which is:

ⁿCₓ = n! / (x! * (n - x)!)

where n is the total number of objects (16 switches), and x is the number of objects selected (in this case, also 16 switches). The exclamation mark (!) represents the factorial function, which is the product of all positive integers up to and including the given integer.

Using this formula, we can calculate the number of possible combinations as follows:

=> 16! / (16! x (16 - 16)!)

=> 16! / (16! x 0!)

=> 1

Therefore, the sample space of possible codes for a wireless garage door opener with 16 switches is 1.

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Whitney drank a total of 2.15 liters of liquid.

Liquids are those substances that can flow or be poured, are incomprehensible, and are more rigid than gases.

From the given table we can say that the drinks Whitney takes over a day, which are juice, milk, and water, all come in the liquid category.

Therefore, the total amount of liquid that Whitney drinks today will be the sum of the volume of all of the above

which is 250 ml + 400 ml + 1,500 ml

=2,150 ml

For converting ml in liters we can divide the given volume by 1000 after which we get,

2,150/1000 = 2.15 Litres.

The complete question that you might be looking for is given below -

From the given table, What is the total amount of liquid in liters that Whitney drinks today?

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The measure of x is 14, by using the definition of secants.

A straight line that intersects a circle in two points is called a secant line. A chord is the line segment that joins two distinct points of the circle. A chord is in a unique secant line and every secant line defines a unique chord. In geometry, a secant is a line that cuts any curve in at least two different points.

Given that, two secants are intersecting inside the circle making two arcs measuring 55° and 75° and an angle measuring 3x+23

We know that,

If two secants intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.

Therefore,

3x+23 = 1/2[55° + 75°]

3x+23 = 1/2 × 130

3x+23 = 65

3x = 42

x = 14

Hence, the measure of x is 14, by using the definition of secants.

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The given statement is True.

What is developing logarithms?

The emergence of logarithms was predicted by comparing arithmetic and geometric series.

True. John Napier is credited with developing logarithms and Henry Briggs is known for working with Napier to advance the concept and promote its use.

Together, they created the logarithmic tables that became a powerful tool in mathematics and science.

Therefore, The given statement is True.

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At 100 machines the unit cost will be minimum and the minimum cost is 11985.

The lowest point on the graph, that is referred to as the minimum, or min, is the vertex of a parabola. The highest point on the graph, that referred to as the maximum, or max, is the vertex of a parabola.

The formula for the minimum value is given by -b/2a

Here we have

The medical equipment industry manufactures X-ray machines. If x machines are made, the unit cost is given by the function
C(x) = 0.9x²-180x+20,985.  

Compare given C(x) with the standard equation ax² + bx + c  

=> a = 0.9, b = -180 and c = 20,985  

We can find the x - coordinate where the minimum value occurs using the formula -b/2a    

The x-coordinate where the minimum value occurs = - (- 180)/2(0.9)

= (180)/1.8 = 100

Hence at x = 100, the unit cost will be minimum

The unit cost can be calculated as follows

C(100) = 0.9(100)²-180(100)+20,985

= 0.9(10000) -18000 + 20,985    

= 9000 - 18000 + 20985

= 11985

Therefore,

At 100 machines the unit cost will be minimum and the minimum cost is 11985.

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Answer:

56 is 40% of the original number

Step-by-step explanation:

Let [tex]n[/tex] represent the original number

We are given that  

30% of number is 42

70% of the same number is 98

Lets convert the precents to decimals

30% as a decimal is [tex]0.3[/tex]

70% as a decimal is [tex]0.7[/tex]

We can create an equation for each scenario

[tex]0.3n=42\\0.7n=98[/tex]

We can choose either one to evaluate [tex]n[/tex].

[tex]0.3n=42[/tex]

Lets solve for [tex]n[/tex].

Divide both sides by [tex]0.3[/tex].

[tex]n=\frac{42}{0.3}[/tex]

Evaluate [tex]\frac{42}{0.3}[/tex].

[tex]n=140[/tex]

Now that we know what the original number is we can calculate what 40% of the number is.

40% as a decimal is [tex]0.4[/tex].

[tex]140*0.4=56[/tex]

1) Given that the perimeter of the rectangle is at least 40 cm, the  inequality and show that it reduces to x ≥ 3 2/3 is:  12x - 4 >= 40

2) The smallest possible value of x is 4

3) The area of the rectangle is  57 cm²

(i) The perimeter of a rectangle is given by the formula P = 2(l + b), where l is the length and b is the breadth. Substituting the given values, we get:

P = 2(4x + 3 + 2x - 5) cm

P = 2(6x - 2) cm

P = 12x - 4 cm

We are given that the perimeter is at least 40 cm, so we can write the inequality:

12x - 4 ≥ 40

Simplifying this inequality, we get:

12x ≥ 44

Dividing both sides by 12, we get:

x ≥ 11/3

x ≥ 3 2/3

So the inequality reduces to x ≥ 3 2/3

II) Note that if x is a perfect square, the smallest possible value of x is 4, because 4 is the smallest perfect square.

III) Substituting x = 4 in the length and breadth of the rectangle, we get:

Length = 4x + 3 = 19 cm

Breadth = 2x - 5 = 3 cm

Therefore, the area of the rectangle is:

Area = Length x Breadth = 19 cm x 3 cm = 57 cm²

Thus, it is correct to state that the area of the rectangle is 57cm².

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As per unitary method, it will take 9 years for the man to be three times as old as his son.

The unitary method is a mathematical technique that involves finding the value of a single unit, and then using that unit to find the value of a larger quantity.

First, let's define our variables:

Let the man's age be M

Let the son's age be S

According to the problem, we know that:

M = 42

S = 12

We want to find out how many years it will take for the man's age (M) to be three times his son's age (S). Let's call this number of years "y".

Using the unitary method, we can set up the following equation:

M + y = 3(S + y)

Here's what this equation means:

M + y represents the man's age after y years

S + y represents the son's age after y years

3(S + y) represents three times the son's age after y years

We can simplify this equation by distributing the 3:

M + y = 3S + 3y

Next, we can isolate the variable y (which represents the number of years we're trying to find) by moving all the other terms to the opposite side of the equation:

y - 3y = 3S - M

Simplifying this, we get:

-2y = 3S - M

Finally, we can solve for y by dividing both sides by -2:

y = (M - 3S) / -2

Plugging in the values we know, we get:

y = (42 - 3(12)) / -2

y = 9

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Complete Question:

A man's age is 42 years and his son's age is 12 years. After how many years will the man be thrice as old as his son?

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

The formula for Percent Decrease is: Decreased Value = (Original Value – New Value)/Original Value.

The computation of our Percent Decrease:

= (64 - 21)/61 * 100

= 70.49%

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Answer:

Two geometric objects are perpendicular if they intersect at a right angle.

Step-by-step explanation:

How you know:

The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.

Answer:

Find the indicated side of the

triangle.

b

30°

12

a = -

Step-by-step explanation:

The cost per minute is $0.04.

Unit rates are defined as rates that are expressed as multiples of 1, such as 2 feet per second or 5 miles per hour.

Given:

Sahalin cellphone plan costs $30 a month.

In a month of may she used cellphone 12.5 hours.

First convert 12.5 hours in minute.

As we know 1 hour = 60 minutes

So, 12.5 hours = 12.5 x 60

                       = 750 minutes

and, the cost per minute

= 30/750

= 0.04

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The solution of the quadratic equation for y is given as follows:

y = 0.17 and y = 1.69.

The quadratic equation for this problem is defined as follows:

7y² - 13y + 2 = 0.

The coefficients are given as follows:

a = 7, b = -13 and c = 2.

Hence the discriminant is of:

D = (-13)² - 4 x 7 x 2

D = 113.

The first root is of:

y = (13 + sqrt(113))/14

y = 1.69.

The second root is of:

y = (13 - sqrt(113))/14

y = 0.17.

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The rectangular prism's volume can be represented by a cube whose dimensions are 6 inches.

A right rectangular prism is what?

The right rectangular prism has two simultaneous end panels that are orthogonal to each of the bases, two adjacent lateral faces, and four rectangle-shaped lateral faces. The faces of an oblique prism, a non-right oblong prism, are parallelograms. Alternative name for a right rectangular prism is a cuboid.

To begin, determine the rectangular prism's volume. To calculate this, multiply the length by the breadth by the height, which equals 9 ×4 ×6. 216 cubic inches make up this.

The side length of a cube with a 216 cubic inch capacity must now be determined. The recipe for A cube's volume is equal to its side length raised to the third power (cubed). You are now attempting to determine where s³= 216 This can also be expressed as s = ∛216.

The only thing left to do is to discover the number that, when multiplied by itself three times, equals 216, or its cubic root. It is quite easy to determine that 6× 6× 6, sometimes known as 6 cubed, equals 216. This indicates that the cube's side length is 6 inches.

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An elevation of negative 25 feet is less than an elevation of 0 feet: True.

An elevation of negative 25 feet is greater than an elevation of 5 feet: False.

An elevation of negative 25 feet is less than an elevation of negative 5 feet: True.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In this context, we can reasonably infer and logically deduce that all numerical values (numbers) to the left are always less than numerical values (numbers) located to the right of a number line such as the following:

-25 < 0.

-25 < 5.

-25 < -5.

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Answer:

The graph of the function will shift vertically up by $5.

Step-by-step explanation:

The original function is m(x) = 2x + 15, where x is the number of people in the car. If the per car charge is changed to $20 per car, the new function becomes m(x) = 2x + 20, because the charge per car has increased by $5.

This means that the y-intercept of the new function is 20 instead of 15, which represents the minimum cost for a car, regardless of the number of people inside. So the graph of the new function will be shifted vertically up by $5 from the graph of the original function.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The mean, median, range, and standard deviation are all measures that can be used to calculate information about a set of numbers, such as the ages of ten randomly selected students.

The mean is the result of totaling the ages of ten randomly selected students and then dividing by ten. This calculation is also known as the average. To calculate the mean, first add up all of the ages, which gives us the sum. Then divide the sum by the number of students, which in this case is 10. The result is the mean, or the average age of the group.

The median is the middle value of a group of numbers. To calculate the median, first put the ages in order from least to greatest. Then find the middle value. If there is an even number of values, then the median is the average of the two middle values.

The range is the difference between the highest and lowest values. To calculate the range, just subtract the smallest number from the largest.

The standard deviation is a measure of variation in a set of numbers. To calculate standard deviation, first subtract the mean from each value, then square each of those differences. Add up these squared differences and divide by the number of values. Then take the square root of that number. The result is the standard deviation.

The mean, median, range, and standard deviation are all measures that can be used to calculate information about a set of numbers, such as the ages of ten randomly selected students.

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Smaller sample size results in smaller sampling variation of the OLS estimator for the slope coefficient in the sample regression model due to the fact that it reduces the amount of variability in the data. Smaller error variance also reduces sampling variation as it reduces the amount of overall variation in the data.

The sampling variation of the OLS estimator for the slope coefficient in the sample regression model is affected by a variety of factors. A smaller sample size will result in smaller sampling variation because it reduces the amount of variability in the data. This is due to the fact that a smaller sample size will contain less variation in the independent variable, and therefore the estimated slope coefficient will have less variation. Additionally, a smaller error variance will also reduce the sampling variation as it reduces the amount of overall variation in the data. Finally, smaller variation in the independent variable in the sample will also lead to smaller sampling variation of the OLS estimator. This is because the slope coefficient is estimated by minimizing the sum of squared residuals, which is a function of the variation in the independent variable. Thus, if the variation in the independent variable is reduced, the slope coefficient will have less variation. In conclusion, all three factors can lead to reduction in the sampling variation of the OLS estimator for the slope coefficient in the sample regression model.

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