cc[tex]\frac{p-8}{p^2-12p+32} ÷\frac{1}{10}[/tex]

For the given triangle find the exact value for cos(A) will be 5/13.

The sine is the side that faces away from the angle being examined.

The sine of the angle under consideration is called the cosine.

or the hypotenuse divides the opposite side to get the sine.

or the hypotenuse divides the adjacent side by the cosine.

Cosine is adjacent/hypotenuse, so keep that in mind. The values provided for this triangle can be plugged in.

Cos(A) = 5/13.

Avoid using a decimal response because rounding would be required and you wouldn't be providing an accurate figure. 5/13 as your response.

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The complete question

For the given triangle find the exact value for cos(A) assume angle C is a right angle

The central angle intercepting the arc for each sector of the garden is 1.3325 radian.

If a sector of any circle of radius r measures θ,

area of the sector can be given by: Area of sector = θ 360 × π r 2.

Given:

The area of the circular garden is 56.25 square meters.

So, area of Circle = πr²

53.25 = πr²

r² = 16.9585

r= 4.11 m

Area of each sector = 56.25/5= 11.25 square meters.

[tex]\theta[/tex]/360 x πr² = 11.25

[tex]\theta[/tex]/360 x 53.04 = 11.25

[tex]\theta[/tex]= 76.35 degree.

Hence, the central angle is 76.35 degree or 1.3325 radian.

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Since Martha can swim 12 yards in six seconds, an equation representing the number of yards, y, she can swim in x seconds is y = 2x.

An equation is an algebraic statement claiming that two mathematical expressions are equivalent or equal.

An equation is depicted using the equation symbol (=).

The number of yards Martha can swim in six seconds = 12 yards

The number of yards Martha can swim in 1 second = 2 yards (12/6)

Let the number of seconds Martha can swim = x

Let the number of yards she can swim = y

Therefore, y = 2x

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Answer: 5π ft

Step-by-step explanation:

Numeric Variables, as they are referred to by the creators of SPSS Statistics, are a combination of ratio and interval variables.

Numeric Variables are a type of data used in statistical analysis, and are a combination of both ratio and interval variables. Ratio variables are those that can be measured, counted, and compared, and include ratios and differences between values. Interval variables are those that measure an amount, such as temperature, but are not able to be compared in terms of ratios or differences. The creators of SPSS Statistics refer to these combined variables as Numeric Variables. Numeric Variables can be used to measure and compare data, as well as to create graphs and charts. They are particularly useful in understanding the relationships between different sets of data.

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Answer:

-4d= 2

a+b= -1

c divided by b= -2

Step-by-step explanation:

-4d -> -4(-1/2)=2

a+b -> -4+3=-1

c divided by b -> -6 divided by 3=-2

The v-t and s- t graphs that describe the motion of the second stage for 0≤t≤60 are v(60)=1170, s(60)=29800.

The graph defines the acceleration and velocity of the rocket.

In graphs, 0-30 is the linear equation and 0-60 is constant acceleration.

First, we have to find the velocity, for velocity, there is the relationship of acceleration is the derivative of velocity with respect to time.

a=dv/dt  ---> ∫dv=∫a dt

v=ds/dt-----> ∫ds=∫v dt

We have to find the first stage of the question which is 0≤t≤30.

a(t)=12t

By this we can find velocity:

∫dv=∫a dt

[tex]\int\limits^v_0 {dv} \, =\int\limits^t_0 {12t} \, dt\\ \\V(t)=\frac{12t^2}{2}\\\\V(t)=6t^2[/tex]

[tex]\int\limits{ds} \,= \int\limits {v} \, dt\\\\\int\limits^s_0 {ds} \, =\int\limits^t_0 6t^2 } \, dt\\\\s=\frac{12t^3}{6}[/tex]

S=2t³

Next to find the second stage:

for this, we have to find the limits and just plug the values

v(t)=6t²=450

s(t)=2t³=4500

30≤t≤60 second stage

a=24

∫dv=∫a dt

∫dv=∫24dt

[tex]v]^v_4_5_0=24]^t_3_0\\[/tex]

v-450=24t-720

v=24t-270

∫ds=∫v dt

∫ds=∫24t-270 dt

[tex]s]^s_4_5_0_0=12t^2-270t]^t_3_0[/tex]

s-4500=(12t²-270t)-(12(900)-270(30))

s-4500=(12t²-270t)-(10800-8100)

s-4500=(12t²-270t)-(2700)

s=(12t²-270t)-(2700)+4500

s=12t²-270t+2800

for the time 60s just plug the values in the v and s.

v(60)=24(60)-270

v(60)=1170

s(60)=12(3600)-270(60)+2800

43200-16200

s(t)=29800.

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The water that should be added to 14mL of 9% alcohol solution to reduce the concentration to 7% is 4ml.

Here; In this problem we have a concentration problem, represented by the volume of the solvent divided by the volume of the entire solution. The initial and final concentrations of the solutions are presented in the following formulas;

Given;

14mL of 9% alcohol solution.

Initial concentration;

9/ 100 = x / 14

x = 63/50

Final concentration;

7 / 100 = x / (14 + y)

(14 + y)=x*100/7

y=18-14

y=4

Therefore, water must be added to reduce the concentration will be 4ml.

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The translation of the verbal expression "4 less than twice a number" in to an algebraic expression is 2n - 4.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression.

Let the number is n.

The phrase can be expressed as,

2n - 4.

Therefore, the expression is 2n - 4.

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With equal probability and flip it, given that the flip was heads, the probability that I flipped the two-headed coin is: 0.6667

Let's call the event of flipping the fair coin "F" and the event of flipping the two-headed coin "T".

The probability of flipping heads given that we flipped the fair coin is 1/2, so P(heads | F) = 1/2.

The probability of flipping heads given that we flipped the two-headed coin is 1, so P(heads | T) = 1.

The probability of flipping the fair coin is 1/2 and the probability of flipping the two-headed coin is 1/2, so P(F) = P(T) = 1/2.

Using Bayes' Theorem, we can find the probability that we flipped the two-headed coin given that the flip was heads:

Plugging in the values, we get:

So the probability that we flipped the two-headed coin given that the flip was heads is 2/3, or approximately 0.6667.

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The following expression can be used to calculate the monthly payment for a 30-year loan for $190,000 at 11.4% interest, compounded monthly is, $190,000 x 0.0095 x (1 + 0.0095)³⁶⁰ / ((1 + 0.0095)³⁶⁰ - 1). So Option A is correct

A loan or deposit amount is subject to compound interest as interest. In everyday life, it is the most prevalent idea. Both the principal and the interest accrued over time affect the compound interest for a given amount. Between compound and simple interest, this is the primary distinction.

Where,

A = compound interest

P = Principle Amount

r = Interest rate

n = number of period for which interest is calculated

t = time

The expression to calculate the monthly payment for a 30-year loan for $190,000 at 11.4% interest, compounded monthly is:

$190,000 x 0.0095 x (1 + 0.0095)³⁶⁰ / ((1 + 0.0095)³⁶⁰ - 1)

This expression uses the formula for calculating the monthly payment for an annuity with a fixed interest rate.

The interest rate (0.0095) is the monthly rate, obtained by dividing the annual interest rate (11.4%) by 12.

The 360 represents the total number of payments over the 30-year loan term.

Hence, The expression in Option A can be used.

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I don't really know I just gotta do the give an answer challenge, sorry bro

Answer:

Step-by-step explanation:

Mean = add up all numbers and divide on how many  

26+31+19+23+16= 115

115/5= 23

Median = find the middle number

16, 19, 23, 26, 31

23

Mode = the most repeating number

there is none

The quantity of pollution that has been reduced as a result of the cleaning device U = Y1 − Y2.

Exercise 5.10 provided the combined distribution of the amount of pollution emitted from a smokestack without a cleaning device (Y1) and a smokestack that has a cleaning device (Y2).

the joint distribution of the amount of pollutant emitted from a smokestack without a cleaning device (y1) and a similar smokestack with a cleaning device (y2)

U = Y1 Y2 calculates the quantity of pollution that has been reduced as a result of the cleaning device.

U = Y1 − Y2.

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The test statistic you have chosen is an appropriate measure to compare the difference in average birth weights between two groups of babies (babies of non-smokers and those of mothers who smoke).

The test statistic chosen is the absolute difference between the average birth weights of the two groups, which can be used to test the hypothesis that there is a difference in the average birth weight between the babies of non-smokers and the babies of mothers who smoke. This test statistic is commonly used in hypothesis testing to compare means between two groups.

The absolute difference between the average birth weights accounts for any direction of the difference (i.e. whether the non-smokers group has higher average birth weight or the smokers group has higher average birth weight), making it a suitable test statistic for hypothesis testing.

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The mean number of siblings for the sample of 100 students is likely to be close to 1.8 siblings, with a standard deviation of 0.7/√100 = 0.07 siblings.

A skewed distribution is one in which the data deviates from the normal distribution and has a longer tail on one side. In the case of the number of siblings, the distribution is skewed to the right, meaning that there are more students with higher numbers of siblings. The mean of 1.8 siblings and standard deviation of 0.7 sibling indicate the average and spread of the number of siblings in the entire student population of the high school. When a random sample of 100 students is selected, the mean number of siblings in the sample will be calculated. This mean will provide an estimate of the mean of the population, but there is still a chance of sampling error.

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The length of the sides of the original square is -2.1 unit²

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

Let l represent the original side and A represent the original area. Hence:

Area = length * length

A = l * l

A = l²

The side of a square is increased by 5 units, the area is increased by 4 square units. Hence:

A + 4 = (l + 5) * (l + 5)

A + 4 = l² + 10l + 25

but A = l², hence:

l² + 4 = l² + 10l + 25

l = -2.1 units

The length is -2.1 unit²

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The expression with the least value is -2/3 - 1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1)

−2/3 − (−1/2)

= -2/3 + 1/2

= (-4 + 3) / 6

= -1/6

2)

−2/3 − 1/2

= -2/3 - 1/2

= (-4 - 3)/6

= -7/6

3)

−2/3 − (−1)

= -2/3 + 1

= (-2 + 3)/3

= 1/3

4)

−2/3 − 1

= (-2 - 3) / 3

= -5/3

From (1), (2), (3), (4) we get,

-5/3 < -7/6 < -1/6 < 1/3

Thus,

-5/3 is the least value.

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taking a looksie at the picture above, we can see the parabola has zeros/solutions at x = -2 and x = 1, we can also see that it passes through (0 , 2) as well, so

[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a( x +2 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ a ( 0 +2 )( 0 -1 ) = 2\implies -2a=2\implies a=\cfrac{2}{-2}\implies \boxed{a=-1} \\\\[-0.35em] ~\dotfill\\\\ -(x+2)(x-1)=y\implies -(x^2+x-2)=y\implies {\Large \begin{array}{llll} -x^2-x+2=y \end{array}}[/tex]

Check the picture below.

It can be concluded that S is an open subset of (Y,d) if and only if there exists an open subset U of (X,d) such that S = f(U).

Let (X,d) and (Y,d) be two metric spaces and let S be a subset of Y. Then S is an open subset of (Y,d) if and only if there exists an open subset U of (X,d) such that S = f(U). To prove this statement, we must show that if S is open then there exists an open subset U of (X,d) such that S = f(U). Conversely, if there exists an open subset U of (X,d) such that S = f(U), then S must be open.

To prove the first part of the statement, assume that S is open. By definition, this means that for every point p in S, there exists a radius r>0 such that the ball B(p,r) is contained in S. Since S = f(U) for some U subset of X, this implies that for every point p in U, there exists a radius r>0 such that the ball B(p,r) is contained in U. Therefore, U is open.

To prove the second part of the statement, assume that there exists an open subset U of (X,d) such that S = f(U). To show that S is open, we must show that for every point p in S, there exists a radius r>0 such that the ball B(p,r) is contained in S. Since S = f(U), this implies that for every point p in U, there exists a radius r>0 such that the ball B(p,r) is contained in U. Since U is open, this implies that for every point p in S, there exists a radius r>0 such that the ball B(p,r) is contained in S. Therefore, S is open.

Therefore, it can be concluded that S is an open subset of (Y,d) if and only if there exists an open subset U of (X,d) such that S = f(U).

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Complete question :

Let (X,d) and (Y,d) be two metric spaces and let S be a subset of Y. Is it true that S is an open subset of (Y,d) if and only if there exists an open subset U of (X,d) such that S = f(U)?

The number '25' can be described as a probable outlier. The correct answer would be option (A).

A box and whisker plot (also known as a box plot) depicts a five-number summary of a set of data: lowest, lower quartile, median, upper quartile, and maximum.

It shows the median (middle value), first and third quartiles (25th and 75th percentiles), and any potential outliers.

Outliers are defined as observations that fall more than 1.5 times the interquartile range (IQR) away from the nearest quartile. In the box plot, the number '25' is shown outside of the whiskers, indicating that it is far away from the majority of the data and is therefore considered a probable outlier.

Hence, the correct answer would be an option (A).

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Isosceles triangles have two equal angles.  The two equal angles are the bottom left and bottom right.

X = 28

Y = 152

See picture for explanation

- Jeron

Is 9 kg bigger than 4 pounds? Nine kilograms is definitely heavier, as one kilogram is equivalent to 2.2 pounds.

The correct answer is  (f + g)(x)= -5x²-9x+11.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

you have two functions f(x) and g(x) the sum of them f(x) + g(x) is represented as (f + g)(x)

then if our functions are f(x) =2-9x,

and g(x) = -5x² + 9

then (f + g)(x)

= f(x) + g(x)

= -5x²-9x+11

Hence, The correct answer is -5x²-9x+11.

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The solution of the polynomial is as follows:

(3n⁴ - 2n² + 6n³) + (8n² + 3n³ - 1) - (6n⁴ - n³) = -3n⁴ + 10n + 6n² - 1

(2v - 4 - 4v³) - (5v³ - 6v - 7) + (7v³ + 8v) = -2v³ + 16v + 3

Polynomials are algebraic expressions that consist of variables and coefficients. Let's add and subtract the polynomials.

The like terms of the polynomials are usually added or subtracted.

Hence,

(3n⁴ - 2n² + 6n³) + (8n² + 3n³ - 1) - (6n⁴ - n³)

let's open the brackets

3n⁴ - 2n² + 6n³ + 8n² + 3n³ - 1 - 6n⁴ + n³

3n⁴ - 6n⁴ + 6n³  + 3n³ + n³  - 2n² + 8n² - 1

-3n⁴ + 10n + 6n² - 1

Therefore, let's solve the second polynomial.

(2v - 4 - 4v³) - (5v³ - 6v - 7) + (7v³ + 8v)

Open the brackets

2v - 4 - 4v³ - 5v³ + 6v + 7 + 7v³ + 8v

collect like terms

- 4v³ + 7v³ - 5v³ + 2v + 6v + 8v - 4 + 7

Hence,

-2v³ + 16v + 3

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In a population of 600 elements, if a sample of 256 elements is selected and the variance of the population is 1,024, the he standard error of the mean is:

approximately 4.

The standard error of the mean is approximately equal to the standard deviation of the population divided by the square root of the sample size.

In this case, the standard deviation of the population is equal to the square root of the variance, which is equal to:

Therefore, the standard error of the mean would be equal to 32 / sqrt(256) = approximately 4.

The standard error of the mean is a measure of the variability of the mean of a sample. It gives us an estimate of how much the mean of a sample would vary from the true population mean if we were to take many samples from the same population.

The standard error of the mean is equal to the standard deviation of the population divided by the square root of the sample size.

The smaller the sample size, the larger the standard error of the mean. This makes sense because the mean of a smaller sample is less likely to be representative of the true population mean.

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The domain and range of this relation should be stated as follows;

Domain = {3, 3}.

Range = {1, ∞}.

Function: No.

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

In this scenario, the points on this graph are given by the following ordered pairs:

(3, 1) and (3, ∞).

Therefore, the domain and range are as follows;

Domain = {3, 3}.

Range = {1, ∞}.

In conclusion, the relation is not a function because its input value (domain) is not uniquely mapped to an output value (range).

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The value of x on the line is (d) 55

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

The parallel lines and the transversal

Given that the line a and b are parallel line, we have the following equation:

x + 45 = 100

Subtract 45 from both sides of the equation

So. we have

x = 100 - 45

Evaluate

x = 55

Hence, the value of x is 55

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The area of the compound shape is given as follows:

154.2 cm².

The shape is composed as follows:

For the rectangle, the area is given by the multiplication of the dimensions, hence:

Ar = 8 x 13

Ar = 104 cm².

For the circle, the area is given by the multiplication of pi = 3.14 by the radius squared, hence:

Ac = 3.14 x 4²

Ac = 50.2 cm².

Hence the total area is given as follows:

A = Ar + Ac

A = 104 + 50.2

A = 154.2 cm².

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The piecewise function on the graph is the one in option C.

y = x² + 2  if x < 1

y = -x + 2  if x ≥ 1

Here we have the graph of a piecewise function, and we can see that the jump is at x = 1.

The first part ends with a open circle, so its domain is x < 1

The second part starts with a closed circle, so its domain is x ≥ 1

Also, notice that the first part is quadratic and the second is linear, then the only option that meets all of these requiriments is the one in option C.

y = x² + 2  if x < 1

y = -x + 2  if x ≥ 1

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