factorize:(sin alpha + cos alpha) ^ 2 - (sin alpha - cos alpha) ^ 2 ​

The coterminal angle is 299°, lies in the IV quadrant and the reference angle is 61°.

Coterminal angles: are angles in standard position (angles with the initial side on the

positive x-axis) that have a common terminal side. For example, the angles 30°, –330°

and 390° are all coterminal.

For angle 659°,

coterminal angle = 659 - 360

                            = 299°

For quadrant,

299/90 = 3.32

After truncating it's equal to 3.

Therefore, it lies in the IV quadrant.

A reference angle is the size of the smallest acute angle, t, formed by the terminal side of the angle t and the horizontal axis.

659 = 2*360-61

Therefore, the reference angle is 61°.

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The expression [tex]s(n) = 2 + \sum\limits_{i = 2}^{n} [5 + 2 \cdot (i - 2)][/tex] represents the n-th element of the series.

In this question we find a sequence with a progressive difference between any two consecutive terms, whose definition is shown below:

s(1) = a

[tex]s(n) = a + \sum\limits_{i = 2}^{n} [b + r \cdot (i - 2)][/tex]

Where:

First, determine value of the first element of the sequence:

a = 2

Second, find the difference between the first and second elements of the sequence:

b = 7 - 2

b = 5

Third, determine the increase for the difference between two consecutive elements of the sequence:

r = 2

The formula for the n-th term is [tex]s(n) = 2 + \sum\limits_{i = 2}^{n} [5 + 2 \cdot (i - 2)][/tex].

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The expression when the brackets are removed is 15x - 4

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

6 + 5(3x - 2)

The above expression has brackets

So, we start by expanding the brackets

Solving further, we have

6 + 5(3x - 2) = 6 + 15x - 10

Collect the like terms

This gives

6 + 5(3x - 2) = 15x - 10 + 6

Evaluate the like terms

So, we have

6 + 5(3x - 2) = 15x - 4

Hence, the expression is 15x - 4

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For the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by        ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.

As given in the question,

Confidence interval for population mean is given by:

[tex]\bar{x}[/tex] ± z × ( σ / √n)

Where,

σ = population standard deviation.

n= sample size

[tex]\bar{x}[/tex] = Sample mean

Given values from the random sample size are :

σ = 0.01 inches

n= 10

[tex]\bar{x}[/tex] = 1.5045

Critical value confidence interval (using x-value table)

z  for 99% = 2.576 and Significance level = 0.01

z for 95% = 1.960 and Significance level = 0.05

99% two-sided confidence interval on the mean hole diameter is equal to :

[tex]\bar{x}[/tex] ± z × ( σ / √n)

= 1.5045 ± 2.576 × ( 0.01 / √10)

= 1.5045 ± 0.00815 (approximately)

= 1.5045 - 0.00815 , 1.5045 + 0.00815

= ( 1.49635 , 1.51265 )

95% two-sided confidence interval on the mean hole diameter is equal to :

[tex]\bar{x}[/tex] ± z × ( σ / √n)

= 1.5045 ± 1.960 × ( 0.01 / √10)

= 1.5045 ± 0.00620 (approximately)

= 1.5045 - 0.00620 , 1.5045 + 0.00620

= ( 1.4983 , 1.5107 )

Therefore, for the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and  ( 1.49635 , 1.51265 ) respectively.

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The length of the equal sides is 11.1cm

From the question, we have

perimeter = 30 cm

base = 7.8 cm

perimeter =  sum of all sides

30=7.8+x+x

30-7.8=2x

x = 22.2/2 =11.1cm

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

Complete question: An isosceles triangle has a perimeter of 30 cm. If the base is 7.8 cm long, find the length of the equal sides. ​

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Using the corresponding angle theorem, the value of m∠E is 155.

In the given question we have to find the value of m∠E.

As we know that,

According to the corresponding angle theorem, if a transversal meets two parallel lines, the corresponding angles must be congruent.

So from the figure

4x−35=x+10

Add 35 on both side we get

4x=x+10+35

4x=x+45

Subtract  on both side

4x−x=x+45−x

3x=45

Divide by 3 on both side we get

x=15

So the value of x+10

=15+10

=25

As we know that value the angle of straight line is 180.

So m∠E+25=180

Subtract 25 on both side we get

m∠E=180−25

m∠E=155

Hence, the value of m∠E is 155.

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Answer:

Step-by-step explanation:

We can tell that an equation has multiple/ infinitely many solutions if we try to solve it and get a variable or a number equal to itself.

Let's solve the given equation and see what we'll get :-

[tex]\sf 15-10b-6=-10b+9[/tex]

Add 10b to both sides:-

[tex]\sf 15-10b-6+10b=-10b+9+10b[/tex]

Simplify:-

[tex]\sf 15-6=9[/tex]

Subtract:-

[tex]\sf 15-6=9[/tex]

[tex]\sf 9=9[/tex]

As we can see, both sides ended up equal, therefore, this equation has infinitely many solutions!

Hope this helps!

Have a great day!

The changes in his account is that (d) The balance of the account increases by 6% each year.

The function of the account balance is given as

f(x) = 4,000 (1.06)*

The above function is an exponential growth function

Such that the growth factor (b) is the number in bracket

This is represented as

b = 1.06

The percentage growth rate (r) is calculated as:

r = b - 1

Substitute known values

r = 1.06 - 1

Evaluate the difference

r = 0.06

Express as percentage

r = 6%

This implies that the balance increases by 6% each year.

So, the true statement is (d)

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Answer:

Step-by-step explanation:

An equation of the line that passes through the point (-3, -1) and is perpendicular to the line x - 2y = 6 is y = -2x - 7.

Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Next, we would rewrite the given equation representing a line in standard form:

x - 2y = 6

2y = x - 6

y = x/2 - 6

Therefore, slope (m) = 1/2

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

At point (-3, -1), an equation of this line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - (-1) = -2(x - (-3))

y + 1 = -2(x + 3)

y + 1 = -2x - 6

y = -2x - 6 - 1

y = -2x - 7

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Irrational Number

Step-by-step explanation:

Alternatively, 3 is a prime number or rational number, but √3 is not rational number.

Here, the given number √3 is equal to

1.73205080756 which gives the result of non

terminating and non recurring decimal and keep on extending , and cannot be expressed as fraction ..,

Therefore √3 is Irrational Number.

The interest rate on loan is 5.25%.

What is principal amount?

The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.

What is simple interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is  I=P.r.t

Given, Principal amount=$125,000, time=10years, Interest=$65,625.

Let r be the rate of interest, on applying simplest interest formula

                                               I=P.r.t

Where P=principal amount, r=rate, t=time.

I=125,000 x r x10

65,625=125,000 x r x10

r=[tex]\frac{65,625}{125,000(10)}[/tex]

r=0.0525

r=5.25%

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Answer:

25%

Step-by-step explanation:

Lets find how many people were at the pool at the 4th week.

1060 - 110 + 145 - 247 =

848

Use percent error formula,

[tex]\frac{v_a-v_e }{v_e}[/tex]

Actual - Estimate over Estimate

Actual (1st week): 1060

Estimate (4th week): 848

Plug into formula.

[tex]\frac{1060-848}{848}[/tex]

Simplify.

[tex]\frac{212}{848}[/tex]

Divide.

0.25

Multiply by 100 and write with a percentage sign.

0.25*100 = 25

25%

Answer:

The percent decrease is 20%

Step-by-step explanation:

First week : 1060 people

Second week: 1060 - 110 = 950 people

Third week : 950 + 145 = 1095 people

Fourth week: 1095 - 247 = 848 people

Make 1060 the whole (100%), we need to figure out 848 percent

848      x

1060   100

848 x 100 = 84800

84800  divided by 1060 = 20

From 1060 people to 848 people is a 20% decrease

The sequence of transformations applied to function f(x) to produce function r(x) is a reflection across the y-axis and dilation by a scale factor of 1/4.

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function f(x) = -x would be transformed to function r as follows:

f(x) = -(-x)

r(x) = x

By applying a dilation with a scale factor of 1/4 to function r, we have:

r(x) = (1/4 × x)    → r(x) = f(1/4x)

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Answer:

The answer is false.

Step-by-step explanation:

If you do not already know this, a negative and a negative equals a positive. Therefore, instead of –8 • –4 = –32, the correct answer would be –8 • –4 = 32.

Hope that helps! Have an amazing rest of your day! Brainliest welcome! :)

Answer: is false.

hope this helps

have a good day

Step-by-step explanation:

Answer:

The unit price per pretzel is 57 cents (fifty-seven cents) each!

Step-by-step explanation:

Step One: Divide

Since the price is 171 dollars for 300 large pretzels, and you want to find the price of each pretzel, divide the price by the amount of pretzels.

171 / 300 = 0.57

Step Two: Convert

The answer is 0.57, but since you want to know the unit price, you need to convert it to dollars, and that's simple.

0.57 of a dollar is 57 cents.

Step Three: Get your Answer

Your answer is 57 cents per pretzel! You can double-check this by multiplying 0.57 by 300, getting 171.

Hope my answer helped you!

The percentage in 2009, calculated from the logarithmic function is given as follows:

16.5%.

Which underestimates the graphed amount by 0.4%.

According to the model, the year in which 18.4% of the domestic gross product will go towards healthcare is:

2020.

The logarithmic function in the context of this problem is given as follows:

f(x) = 1.2ln(x) + 15.2.

In which x is the number of years since 2006.

2009 is three years after 2006, hence the percentage is obtained as follows:

f(3) = 1.2ln(3) + 15.2 = 16.5%.

The percentage on the graph is given by:

16.9%.

Hence the function underestimates the graphed amount by 0.4%.

The year in which 18.4% of the domestic gross product will go towards healthcare is x for which f(x) = 18.4, hence:

18.4 = 1.2ln(x) + 15.2.

1.2ln(x) = 3.2

ln(x) = 3.2/1.2

ln(x) = 2.67.

ln and the exponential are inverse functions, hence:

x = e^2.67 = 14.4.

2006 + 14 = 2020.

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25 is 2.87 percent of 872.

First, let us understand the percentage:

A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.

To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.

We need to find 25 is what percent of 872.

Let 25 be x percent of 872.

So,

872 * x % = 25

872 * x / 100 = 25

872x = 25 * 100

x = 25 * 100 / 872

x = 2.87 %

So, 2.87 % of 872 is 25.

Thus, 25 is 2.87 percent of 872.

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Answer:

larger number = 3

smaller number = -1

Step-by-step explanation:

x = larger number

y = smaller number

x+y=2

8-2y=4x-2 ---> 10 = 4x+2y

10 = 4x+2y

5=2x+y

y = 5-2x

2x=5-y

x+5-2x = 2

-x+5=2

-x=-3

x=3

3+y=2

y=-1

In the game where average score was 40 , then Jim's score was 100 .

In the question ,

it is given that ,

the average score in the game was 40  .

and also given that the Jim's score was 5/2 of the average .

So ,  the Jim's score can be calculated using the equation .

Jim's score = (5/2) × (Average score of the game)

Substituting the value of average in the equation ,

we get,

Jim's Score = (5/2) × 40

= 5 × 20

= 100

Jim's score is 100 .

Therefore , The Jim's score in the game where average score was 40 is 100   .

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The equation of the line is y = (-3/5)x - 3

The equation of the line given

y = (5/3)x + 1

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Comparing the given equation

slope of the line m = 5/3

The slope of the perpendicular line = -1/m

= -1 ÷ 5/3

= -3/5

The line is passing through the point (-10, 3)

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the values in the equation

y - 3 = (-3/5)(x - (-10))

y - 3 = (-3/5)x - 6

y = (-3/5)x - 6 + 3

y = (-3/5)x - 3

Hence, the equation of the line is y = (-3/5)x - 3

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Frank equation is : 0.25x + 1.95 = y

Alice equation is : 0.4x + 1.5 = y

This question is incomplete and actual question is

Frank and Alice are penguins. At birth, Frank’s beak was 1.95 inches long, while Alice’s was 1.50 inches long. Frank’s beak grows by 0.25 inches per year and Alice’s grows by 0.40 inches per year. Write an equation to represent the length of each penguin’s beak in x years.

Given that

Frank’s beak was 1.95 inches long and Frank’s beak grows by 0.25 inches per year

let y be the total long

equation is 0.25x + 1.95 = y

while Alice’s was 1.50 inches long and Alice’s grows by 0.40 inches per year

equation is 0.4x + 1.5 = y

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The simple interest would be $84.

What is simple interest?

Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principle by the daily interest rate and the number of days between installments.

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest.

Interest = (Principle x Rate x Time in years)/100

            = (1200 x 3.5 x 2)/100

            = 84

The simple interest would be $84.

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The amount of money spend on music from the fractional value is $1.30;

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

spends 3/4 of her money on game apps

spends $0.98 on music apps.

So, we can assume the total amount to be K;

So, The fraction of money spend on music is K/4;

According to the question, we have:

[tex]\frac{1}{4} \times k[/tex] = $0.98;

⇒K = $3.92;

So, The total amount with Kim is $1.30;

Hence,

The amount of money spend on music is $1.30;

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The positive value of Z is 2.17.

What do you mean by normal distribution?

A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction. Because of its flared appearance, a normal distribution's graphic representation is occasionally referred to as a bell curve. The specific shape may change depending on how the population is distributed, but the peak and curve are always symmetrical and in the centre.

The information can be represented in the standard normal curve below:

It is given that 97% of the standard normal curve lies between −z and z.

The area in between is 0.97 meaning that one side is (0.97)/2 = 0.485

In addition, the region not shaded is the level of significance represented by (1-0.97)/2 = 0.03/2 = 0.015

From the Z-Score table (0 to Z table), this probability corresponds to the Z value of Z= 2.17 and -2.17

Thus the positive value of Z is 2.17.

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Answer: 7(x^3-5)

Step-by-step explanation:

the common number between 7 and 35 is seven( 7*1=7, 7*5=35)

so with the 7 outside the parenthesis we end up having inside the parenthesis x^3 and 5 because x=1 and 7*1=7 and the 5 because 7*5=35 so if we distribute the seven we would get the original answer

Answer:

[tex]7(x^3-5)[/tex]

Step-by-step explanation:

Given expression:

[tex]7x^3-35[/tex]

To factor the given expression, begin by rewriting 35 as 7 · 5:

[tex]\implies 7x^3-7 \cdot 5[/tex]

Now factor out the common term 7:

[tex]\implies 7(x^3-5)[/tex]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \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}[/tex]

so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \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}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}[/tex]

now, keeping in mind that perpendicular lines have negative reciprocal slopes

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}[/tex]

so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{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}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}[/tex]

The average age of all the animals at the animal rescue center is 5.4 months .

In the question ,

it is given that ,

at an animal rescue center .

percent of dogs that are present in the animal rescue = 80%

percent of cats that are present in the animal rescue = 20%

let suppose that there are total of 100 animals in the animal rescue .

So , the number of dogs = 80

and the number of cats = 20

also given that ,

the average age of dogs = 6 months

the average age of cats = 3 months .

So , the average age of all the animals can be calculated by

Average age = (80×6 + 20×3)/100

= (480 + 60)/100

= 540/100

= 5.4 months

Therefore , The average age of all the animals at the animal rescue center is 5.4 months .

At an animal rescue 80% of the animals are dogs and 20% of the animals are cats. If the average age of the dogs is six months and the average age of the cat is three months what is the average age of all the animals ?

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Answer:

  G.  12

Step-by-step explanation:

You want the number of ways 1 male and 2 females can be chosen from a group of 2 males and 4 females.

From a group of 2 males, there are 2 ways that 1 male can be chosen. (He can be one, or the other.

From a group of 4 females, there can be 4C2 = 4!/(2!(2!)) = 4·3/2 = 6 ways that 2 females can be chosen.

The total number of possible groups is the product of the numbers of groups of males and of females:

  possible groups = 2 · 6 = 12

G. There are 12 possible groups of 3 people.

__

Additional comment

If the males are {a, b} and the females are {A, B, C, D}, the 12 possible groups are ...

  aAB aAC aAD aBC aBD aCD bAB bAC bAD bBC bBD bCD

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