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Home values are expected to decreased by 3% per year. Hadlee Recently purchased a home for $200,000. Which of the following equations can be used to represent the value of the home x years after the purchase?

A) f(x) = 200000(1.03)^x
B) f(x) = 200000(0.97)^c
C) f(x) = 3(1.03)^x
D) f(x) =3(0.97)^x

The value of angle θ in the stretched spring is determined as 45.8°.

option D.

The value of angle θ is calculated by applying the principle of trigonometry identity as shown below.

From the diagram of the stretched spring, we can notice that the shape formed is a right angle triangle.

The value of angle θ is calculated by using the trigonometry identity of cosine.

cos θ = adjacent side / hypothenuse side

cos θ = 3 ft / 4.3 ft

cos θ = 0.69767

θ = cos ⁻¹ (0.69767)

θ = 45.76⁰

θ ≈ 45.8⁰

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The complete question is below:

When the spring is stretched so that the distance from Point X to Point Z is 4.3 feet, what is the value of θ, to the nearest tenth of a degree?

Α. 24.9°

B. 27.7°

C. 62.3°

D. 45.8°

The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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Answer:

d.  2 solutions

Step-by-step explanation:

To find the number of solution present in the equation given, we will follow the steps below:

16X²= 100

Take the square root of both-side

√16X²= √100

4x = ± 10

Divide both-side of the equation by 4

4x/4 = ± 10/4

x =  ± \(\frac{5}{2}\)

x = -\(\frac{5}{2}\)   or    

It has two solutions

The given equation is 16X^2 = 100.

We can solve for X by dividing both sides by 16 and then taking the square root of both sides:

16X^2 = 100

X^2 = 100/16

X^2 = 6.25

Taking the square root of both sides:

X = ±2.5

So, there are 2 solutions to the equation: X = 2.5 and X = -2.5.

Therefore, the answer is (D) 2 solutions.

The percentage of cholesterol in young women between the age of 20 to 34 is 22.63 %

The mean of the cholesterol levels of young women = 185 mg/dl

The standard deviation = 39 mg/dl

The percentage of young women in this age group will have cholesterol levels less than 150 can be calculated using the normal distribution,

                         P(x < 150)

The standard form of this random sample can be found using the formula,

                    Z = (X - μ) / σ

where Z is the standard form

          X is the random sample

          μ is the mean

          σ is the standard deviation

For x = 155,

                Z = 155 - 185 / 39

                   = -30/39

                  = - 0.76923

Therefore, the standard form is

               P(x < 150) = P(z < -0.7609)

By using the z-table, the value of the given z can be found.

                P(z < -0.7609) = 0.2263

Therefore, the percentage of cholesterol levels is

                    = 0.2263 x 100

                    =  22.63 %

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Peter the rabbit have  51 carrots are left.

one fourth means A quarter is represented in mathematics using fractions. Mathematically, a quarter fraction is a whole divided into four equal parts. where 1 indicates the part being referenced and 4 indicates the number of parts the whole is divided into. In numeric format, it is written as ¼.

so total carrot is 84

and he ate one fourth on that day

so remaining are

84*1/4= 21

21 he eat on that the then remaining =

84 - 21  = 63

63 carrots are remain for next day and

he eat 12 carrot on next day

so remaining = 63 - 12 = 51

so 51 carrot left .

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Answer:

infinite

Step-by-step explanation:

it results in 10-10x=10-10x if you simplify

can also be simplified more into x=x

but we already know x has to equal x.

Answer:

4:6 or 2:3

Step-by-step explanation:

Let me know if this is correct!

Answer:

46.8 to 4 needs to be turned into a unit rate

46.8 divided by 4 = 11.7

4 divided by 4 = 1

11.7/1

11.7 miles in one hour

Step-by-step explanation:

Answer:

a) 820

b)450

c)  -540

d) -294

e) 1440

f) 1425

Step-by-step explanation:

a) it is an arithmetic progression with ratio=4

   a1=3,

     a2=3+r=3+4=7.....

    a20=a1+19r

so a20=3+19*4=3+76=79

S=(a1+an)*n/2 where n=20

so S=(3+79)*20/2=820

b) a15=a1+14*r=2+14*4=2+56=58

S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450

It is the same formula for all  the exercises

S=(a1+an)*n/2 ,     where n is the number of terms

c) a40=30+39*(-3)=30-87=-57

So S=(30-57)*40/2=-540

d) a14=5+13*(-4)=5-52=-47

S=(5-47)*14/2=-42*14/2=-42*7=-294

e) it is 5+7+9+......+75

nr of  terms  = (an-a1) :r+1=(75-5):2+1=36

S=(5+75)*36/2=36*40=1440

f) ratio=7-4=3

the  same formula for n= (91-4):3+1=87:3+1=29+1=30

S=(4+91)*30/2=95*30/2=2850/2=1425

Answer:

x < 2

Step-by-step explanation:

Step 1:  Subtract 7 from both sides

-3x+7-7>1-7

-3x>-6

Step 2:  Divide both sides by -3

-3x/-3>-6/-3

Since you divided by a negative, you must flip the sign.

-3x/-3>-6/-3

x<2

The M.A.S motion for two different time periods {T} = 2s and

{T} = 2/3s is calculated above.

The general equation is -

y{t} = A sin(ωt + Ф)

Given is a body describes an M.A.S according to the function -

{x} = 2 cos{(π/2)T+ π)r

Now -

For {T} = 2, we can write -

{x} = 2 cos{(π/2) x 2+ π)r

{x} = 2 cos{2π}r

{x} = 2 x 1 x r

{x} = 2r

For {T} = 2/3, we can write -

{x} = 2 cos{(π/2) x 2/3+ π)r

{x} = 2 cos{π/3}r

{x} = 2 x -0.33 x r

{x} = - 0.66r

Therefore, the M.A.S motion for two different time periods {T} = 2s and

{T} = 2/3s is calculated above.

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{Question in english -

a body describes an M.A.S according to what is specified.

x= 2 cos (π/2 T+π) r

Find its elements in:

T= 2

T= 2/3 sec

K=f/x}

Answer:

The ASAP Math program provides an opportunity for additional small group instruction for students who find the math program challenging. Students in grades 1 to 4 will come to the ASAP room two to three times a week during the math block.

Step-by-step explanation:

If a random variable X is distributed binomially with n = 8 and π = 0.70, then the standard deviation of the variable X is 1.296. The answer is option (d).

To find the standard deviation, follow these steps:

Therefore, the value of the standard deviation of X is 1.296. Hence, option (d) is correct.

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The simplified expression with positive exponents for the given expression is 16r^11.

To simplify and express the answer using positive exponents, we can use the product rule of exponents which states that when multiplying two terms with the same base, we add their exponents.

Using this rule, we can simplify 4r^7 as:

4r^7 = 4 * r * r^6

Similarly, we can simplify (4r)(r^3) as:

(4r)(r^3) = 4 * r * r^3

Now we can multiply these two simplified terms:

4r^7 * (4r)(r^3) = (4 * r * r^6) * (4 * r * r^3)

= 16 * r^(6+1) * r^(1+3)

= 16 * r^7 * r^4

= 16r^(7+4)

= 16r^11

Therefore, the simplified expression with positive exponents for the given expression is 16r^11.

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The ratio of c:d:e is 1:3:2.

To find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.

A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.

You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.

It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.

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Answer:

Option C.

Step-by-step explanation:

Slope of the line passing through (1, 1) and (0, 2)

m = \(\frac{y-y'}{x-x'}\)

m = \(\frac{2-1}{0-1}\)

m = -1

Equation of the line passing through point (1, 1) and slope = -1,

y - y' = m(x - x')

y - 1 = (-1)(x - 1)

y - 1 = -x + 1

y = -x + 2

This piece of function is true for x ≤ 1

Similarly, slope of the line passing through two points (1, -1) and (2, -3),

m' = \(\frac{-3+1}{2-1}\)

    = -2

Equation of the line passing through (1, -1) and slope = -2

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

y + 1 = -2x + 2

y = -2x + 1

This piece of function is true for x > 1

Therefore, Option C. will be the answer.

Type 1 error is the error occurs when a test indicates a significate  difference between two or more populations.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes. The significance level you select (alpha or ) determines the likelihood that you will make this mistake.

Data cleansing—also known as data cleaning, data scrubbing, or data rectification—is the process of correcting inaccurate, insufficient, duplicate, or other wrong data in a data set. It entails locating data mistakes and then correcting them by modifying, updating, or eliminating data.

Using independent samples from two independent groups, the two-sample (independent groups) t-test is used to assess whether the unknown means of two populations are different from one another.  

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Yes, there is a proportion relationship between the number of bushel and acres of land. The relationship is the number of busher is directly proportional to the number of acres of land.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

direct proportion is given as y= kx

Where y and x are the variables and k is constant.

If the bushel of orange is given by x and the acres of land by y

then x= ky

for the expression to be correct the value of k should be thesame

when x= 720 and y = 4

k= x/y

k= 720/4= 180

when x= 1260 and y= 7

k= x/y

k= 1260/7

k= 180

therefore the x is directly proportional to y

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Answer:y=-3/5+-3

Step-by-step explanation:

The parametric equations for the line are: x = at, y = 13, z = -10.

The vector equation and parametric equations for the line passing through the point (0, 13, -10) and parallel to the line x = at, where "a" is a constant, can be expressed as:

Vector Equation: r = ⟨at, 13, -10⟩

Parametric Equations: x = at, y = 13, z = -10

To find the vector equation and parametric equations for the given line, we need to consider two key components: a direction vector and a point on the line.

The given line x = at, where "a" is a constant, represents a line parallel to the x-axis with a direction vector ⟨1, 0, 0⟩. Since the desired line is parallel to this line, it will have the same direction vector.

A point on the line is given as (0, 13, -10). Using this point and the direction vector, we can construct the vector equation and parametric equations.

In the vector equation, r represents the position vector of any point on the line. Using the direction vector and the given point, the vector equation becomes: r = ⟨at, 13, -10⟩.

In the parametric equations, we express each coordinate (x, y, z) separately as functions of the parameter t. For the x-coordinate, we have x = at, indicating that it varies linearly with t. For the y and z-coordinates, we observe that they remain constant as y = 13 and z = -10.

Therefore, the parametric equations for the line are: x = at, y = 13, z = -10.

These equations describe the line passing through the given point and parallel to the line x = at, allowing us to determine the position of any point on the line by assigning appropriate values to the parameter t.

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The average change in temperature, in degrees Fahrenheit, each hour is -6.25 degrees F per hour and after 5 4/5 hours temperature will be -36.25 °F.

It is defined as the change in values of a dependent variable with respect to the independent variables.

It is given that:

The outside temperature decreases by 7.5°F in 1 1/5 hours.

Part A

1 1/5 = 6/5 = 1.2 hours

The average change in temperature, in degrees Fahrenheit, each hour:

= -7.5/1.2 = -6.25 degrees F per hour

Part B

= (6.25)x[5 4/5]

= (6.25)x[5.8]

= -36.25 °F

Thus, the average change in temperature, in degrees Fahrenheit, each hour is -6.25 degrees F per hour and after 5 4/5 hours temperature will be -36.25 °F.

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In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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The exact value of cos 180° is -1To find the exact value of cos 180° using a half-angle identity, we can use the half-angle formula for cosine .

cos^2(x/2) = (1 + cos(x))/2

Let's substitute x = 180° into the formula:

cos^2(180°/2) = (1 + cos(180°))/2

Simplifying the expression:

cos^2(90°) = (1 + cos(180°))/2

Now, we know that cos(90°) = 0, so we can substitute that value in:

0 = (1 + cos(180°))/2

Multiplying both sides by 2:

0 = 1 + cos(180°)

Rearranging the equation:

cos(180°) = -1

Therefore, the exact value of cos 180° is -1.

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Answer:

15

Step-by-step explanation:

The absolute value function graphed in this problem is given as follows:

A. y = |x - 5| - 4.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The leading coefficient a does not influence the vertex of the absolute value function.

The vertex of the graph is the turning point, hence it is given as follows:

(5, -4).

Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:

y = |x - 5| - 4.

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Answer:

cant see it

Step-by-step explanation:

Answer:

8.5×10^-5

Step-by-step explanation:

The following statements are true about the normal distribution

The normal distribution is a statistical distribution that is often used to describe real-world phenomena, such as measurements of physical characteristics, IQ scores, or test scores. It is also known as the Gaussian distribution or the bell curve.

The statements that true about the normal distribution are,

The graph of the normal distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis.

About 95% of all data values lie within 1 standard deviation of the mean.

Data values farther from the mean are less common than data values closer to the mean.

The distribution is symmetric with a single peak.

The mean, median, and mode are all equal and occur at the center of the distribution.

The  false  statement

Data values are spread evenly around the mean.

The partly true statement is

6) 50% of the data values lie at or above the mean. (This is true for a normal distribution that is perfectly symmetrical. However, if the distribution is skewed, this statement may not be true.)

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Answer: E

Step-by-step explanation: