A suit is being sold for 194.49, discount is 73% from the original price.

What’s the original price?

Final balance = Principal amount + Interest earned= $630 + $85.05= $715.05

The final balance earned in an account with 630 invested at 4.5% annual simple interest for 3 years is 715.05 (Option B)

Explanation: We can use the simple interest formula to calculate the final balance of an account that pays simple interest.

The simple interest formula is given as: I = P × r × t

Where;

I = Interest earned

P = Principal amount

r = rate of interest

t = time period

The principal amount (P) is 630

The rate of interest (r) is 4.5%

The time period (t) is 3 years

Substituting these values in the formula,

we have:

I = $630 × 4.5% × 3= $85.05

The final balance is the sum of the principal amount and the interest earned.

Final balance = Principal amount + Interest earned= $630 + $85.05= $715.05Therefore, the correct option is B. $715.05.

To know more about simple interest visit

https://brainly.com/question/30964674

#SPJ11

Lily's statement that she can model the data for the number of vehicles per day to a normal distribution because the distribution is symmetric is not entirely correct.

A normal distribution, also known as a Gaussian distribution, is symmetric, meaning it is evenly distributed around its mean. However, symmetry alone does not guarantee that the data follows a normal distribution. Other factors need to be considered, such as skewness and kurtosis. Skewness measures the lack of symmetry in a distribution. If the data is perfectly symmetric, the skewness will be zero. However, if the data is skewed to the right or left, indicating a long tail on one side, it deviates from a normal distribution.

Kurtosis measures the "tailedness" of a distribution. A normal distribution has a kurtosis of 3, which is referred to as mesokurtic. If the kurtosis is less than 3 (platykurtic), the distribution has lighter tails than a normal distribution. If the kurtosis is greater than 3 (leptokurtic), the distribution has heavier tails.

To determine if the data can be modeled as a normal distribution, Lily should analyze the skewness and kurtosis of the data. If the skewness and kurtosis are close to zero and 3, respectively, the data may reasonably follow a normal distribution. However, if there is significant skewness or kurtosis, alternative distribution models might be more appropriate.

Learn more about normal distribution here: brainly.in/question/1804784
#SPJ11

Answer:

x=9/2 (in fraction)

x=4.5 (in decimal)

Step-by-step explanation:

10x=12x-9

2x=9

x=9/2

10x = 12x - 9

=> 10x -12x = -9

=> -2x = -9

=> x = -9/-2

=> x = 9/2

=> x = 4.5

Answer:

12

Step-by-step explanation:

First, you will have to use trigonometry. Since the side of the triangleis the opposite of the angle 53 and the hypotenuse, you will use sin.

Sin 53 degrees = opposite side / hypotenuse side.

The opposite side is x and the hypotenuse side equals 15.

sin53= x/15

15 ( sin 53 ) =x

x= 11.97953

Round

x=12

We can observe that each term is obtained by adding 8 to the previous term. Therefore, the common difference of the sequence is 8, and we can express the nth term of the sequence as a linear function of n, given by the formula an = 8n.

To find the 60th term of the sequence, we simply plug in n = 60 into the formula and evaluate. Thus, we get a60 = 8(60) = 480. Therefore, the 60th term of the sequence is 480.

In summary, the 60th term of the sequence 8, 16, 24, ... is 480. The pattern of the sequence is obtained by adding 8 to the previous term, and the nth term of the sequence is given by the formula an = 8n. By substituting n = 60 into the formula, we can easily determine that the 60th term of the sequence is 480.

To learn more about sequence click here, brainly.com/question/30262438

#SPJ11

Answer:

X is 9

X+6x-15=4x+12

3x-15=12

3x=27

x=9

SO x is 9

Answer:

x=9

Step-by-step explanation:

x + 3(2x - 5) = 4x – 12

distrubute left side

3 times 2x; 3 times -5

x+6x-15=4x-12

add like terms

x+6x

7x-15=4x-12

get all variables on the same side

7x-15=4x-12

-4x -4x

3x-15=12

add 15 to both sides

3x-15=12

+15 +15

3x=27

divide by 3 on both sides

3x/3=27/3

x=9

As the number of flips increases from 10 to 10000, we can expect the relative frequency of the occurrence of a Head to become more stable and closer to the true probability of 0.2.

The true probability of observing a Head based on this simulation is 0.2, which means that out of 10 flips, we would expect to see 2 Heads on average. However, as the number of flips increases from 10 to 10000, we would expect the relative frequency of the occurrence of a Head to approach the true probability of 0.2.

This is because of the Law of Large Numbers, which states that as the sample size increases, the sample mean will approach the true mean. In the case of coin flipping, the more flips we make, the closer we will get to the expected proportion of Heads.

For example, if we flip the coin 100 times, we might get 30 Heads and 70 Tails, which is a relative frequency of 0.3. However, if we flip the coin 1000 times, we might get 200 Heads and 800 Tails, which is a relative frequency of 0.2. As we continue to increase the number of flips, the relative frequency will approach the true probability of 0.2.

Therefore, as the number of flips increases from 10 to 10000, we can expect the relative frequency of the occurrence of a Head to become more stable and closer to the true probability of 0.2. This is important to keep in mind when conducting any type of statistical analysis based on coin flipping or other random events.

To learn more about relative frequency, refer here:

https://brainly.com/question/29739263#

#SPJ11

Log(1), log(-1), log(i) and ii are all numbers written in the form a + bi. Log(1) = 0; log(-1) = undefined; log(i) = 0.5i; ii = -1; a = -1 and b = 0 because the number is in the form a + bi.

Given numbers are;• log(1)• log(-1)• log(i)• iiFor all numbers written in the form a + bi, we must find a and b. Here's how to do it: log(1)In this case, the log is taken in base 10. The result of this is 0. So, we have: log(1) = 0Therefore, a=0 and b=0 because the number is not in the form a + bi. log(-1)In this case, the log is taken in base 10. The result of this is undefined. This is because there is no power to which we can raise 10 to get -1. So, we have: log(-1) = undefinedTherefore, a=undefined and b=undefined because the number is not in the form a + bi. log(i)In this case, the log is taken in base 10. The result of this is 0.5iπ. So, we have: log(i) = 0.5iπTherefore, a=0 and b=0.5π because the number is in the form a + bi. iiIn this case, we are finding the square of i. i is a complex number given as i = 0 + 1i. Therefore, we have: i2 = (0 + 1i)2= (0)2 + 2(0)(1i) + (1i)2= -1This is because i2 = -1. Now, we can write ii as: ii = i × i= (0 + 1i) × (0 + 1i)= 0 + 0i + 0i + 1i2= -1So, we have: ii = -1Therefore, a=-1 and b=0 because the number is in the form a + bi.

To know more about Logrithm Visit:

https://brainly.com/question/32630067

#SPJ11

Answer:

3t - 16

Step-by-step explanation:

(18/12 t-8)*2

First simplify inside the parentheses

(3/2 t -8)*2

Then multiply

3/2t *2 -8*2

3t - 16

Step-by-step explanation:

Hey there!!!!

Given,

\(( \frac{18}{12}t - 8 )2\)

Simply wirk with it.

Take LCM.

\(( \frac{18t - 96}{12} )2\)

Now, multiply with 2.

\( \frac{18t - 96}{12} \times 2\)

cut 2 and 12.

\( \frac{18t - 96}{6} \)

Take 2 common in numerator.

\( \frac{2(9t - 48)}{6} \)

Cut 2 and 6.

\( \frac{9t - 48}{3} \)

Take 3 common.

\( \frac{3(3t - 16)}{3} \)

Cutting 3 and 3 we get,

=(3t - 16).

While simplifying you can do slowly and simply to get answer.

Hope it helps...

Neither of the segments is the perpendicular bisector of the other.

To determine which segment is the perpendicular bisector of the other, we need to find the equations of the lines containing each segment and then check if one of the lines is perpendicular to the other and passes through the midpoint of the other segment.

Let's start by finding the midpoint of segment AT. The coordinates of A and T are not given, but we don't actually need them to find the midpoint.

So, the midpoint M of segment AT is:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2)

We don't know the actual values of AT_x1, AT_x2, AT_y1, and AT_y2, but we can find their expressions in terms of x using the segment lengths and the coordinates of the endpoints. We have:

AT_x2 - AT_x1 = BT_x2 - AT_x1 = (x + 5) - (2x + 3) = -x + 2

AT_y2 - AT_y1 = BT_y2 - AT_y1 = (BT - AT) = (x + 5) - (2x + 3) = x + 2

Therefore,

AT_x1 = AT_x2 + x - 2

AT_y1 = AT_y2 - x - 2

Now, we can substitute x=2 and the expressions for AT_x1 and AT_y1 into the midpoint formula to find the coordinates of M:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2) = ((AT_x2 + 2 - AT_x2)/2, (AT_y2 - 2 - AT_y2)/2) = (1, -1)

So, the midpoint of segment AT is M(1, -1).

Next, let's find the equations of the lines containing segments AT and DT. We can use the point-slope form of the equation of a line, which states that the equation of a line passing through a point (x1, y1) with slope m is y - y1 = m(x - x1).

For segment AT, we have:

m_AT = (AT_y2 - AT_y1)/(AT_x2 - AT_x1) = (x + 2)/(x - 1)

Let's substitute x=2 to find the slope of the line containing segment AT:

m_AT = (2 + 2)/(2 - 1) = 4

So, the equation of the line containing segment AT is:

y - AT_y1 = m_AT(x - AT_x1)

y - (22 + 3) = 4(x - 22 - 1)

y - 7 = 4(x - 5)

y = 4x - 13

For segment DT, we have:

m_DT = tan(m∠ATD) = tan(41x + 8)

Let's substitute x=2 and simplify:

m_DT = tan(82 + 8) = tan(90) = undefined

This means that the line containing segment DT is vertical and its equation is x = DT_x1 = 4*2 + 1 = 9.

Now, we need to check if one of these lines is perpendicular to the other and passes through the midpoint of the other segment.

First, let's check if the line containing segment AT is perpendicular to the line containing segment DT.  We have:

m_AT * m_DT = 4 * undefined = undefined

Since undefined is not equal to -1, the lines are not perpendicular, and we can rule out the possibility that the line containing segment AT is the perpendicular bisector of segment DT.

Next, let's check if the line containing segment DT is perpendicular to the line containing segment AT. We have:

m_AT = 4

So, the slope of the line perpendicular to the line containing segment AT is -1/4. We can use the point-slope form of the equation of a line again:

y - M_y = -1/4(x - M_x)

y - (-1) = -1/4(x - 1)

y + 1 = -1/4x + 1/4

y = -1/4x + 3/4

Now, we need to check if this line passes through point D, an endpoint of segment DT. We can substitute the coordinates of D into the equation of the line and check if the equation holds true:

DT_y1 = 4*2 + 1 = 9

DT_x1 = 9

9 = -1/4*9 + 3/4

9 = -9/4 + 3/4

9 = -6/4

This is not true, so the line containing segment DT does not pass through point D. Therefore, we can conclude that the line containing segment DT is not the perpendicular bisector of segment AT.

Learn more about perpendicular bisector here: https://brainly.com/question/11006922

#SPJ1

Answer:

For a:

sin-theta=p/h

sin30= 7/h

hsin30=7

h=7/sin30

h or a=14

For b:

cos-theta=b/h

cos30= b/14

b=14cos30

b= 12.12

Answer:

ddqsc

Step-by-step explanation:

rdfgrrffferrrrrddr

Answer: $7,358

Step-by-step explanation: $26 * 283 (each student) =7,358 dollars

Answer:

Regular pentagon

Solve for perimeter

P=25cm

a Side

5

cm

Answer:It is $2 markup price.

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

-4 + (-12)

Answer:

2.4.6.8.10

Step-by-step explanation:

that's the answer

Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Step-by-step explanation:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, multiply all numbers frmo 1 to 10

So

Diagonals of Rhombus intercect at 90°.

So

Using angle sum property

\(\\ \tt\longmapsto 90+27+<RUS=180\)

\(\\ \tt\longmapsto <RUS=180-117=63°\)

Answer:

Step-by-step explanation:

The diagonals of the kite are perpendicular: RT ⊥ SU

RT is angle bisector of ∠SRU

∠RSU and ∠RUS are equal angles and are complementary with ∠SRT:

Answer:

Step-by-step explanation:

Givens

Let the width = x

Let the length = x + 5

Equation

2w + 2W = P

Solution

2x + 2(x + 5) = 192                  Remove the brackets    <=== Answer

2x + 2x + 10 = 192                  Combine like terms

4x + 10 = 192                          Subtract 10 from both sides

4x = 192 - 10                        

4x = 182                                 Divide by 4

4x/4 = 182/4

x = 45.5

The probability that it will have distinct even digits is 6/1000.

The first digit can take on 5 values (0,2,4,6,8).

The second digit could take on 4 values (one less than 5 to be unique).

The third digit could take on 3 values (two less than 5 to be unique).

So that makes,

N=5.4.3

N=60

P= 60/1000

P=3/50

So there are 60 unique three digit even numbers.

There are 1000 possible outcomes.

Probability and statistics are two fundamental concepts in mathematics. Probability is about the probability of an event, whereas statistics are about how different techniques are used to process different data.

Probability and statistics allow us to process complex data in a very understandable way.

Probability is one of the most popular topics in statistics. The reason is that this one theory is often used when trying to predict something. For example, figuring out what comes out of a random series of events. For simplicity, probability is also called chance or probability. 

Learn more about probability at https://brainly.com/question/12691315.

#SPJ4

Answer:

(x + 4)^2 + (y - 1)^2 = 61.

Step-by-step explanation:

We need to find the square of the radius and the coordinates of the center.

Center = (-10 + 2)/2 , (-4 + 6)/2

= (-4, 1).

Length of the diameter

=  √((-10-2)^2 + (-4-6)^2)

= √(144 + 100)

=√244

So the radius = √244/2

and r^2 = 244/4 = 61,

So the equation of this circle is:

(x - (-4)^2 + (y - 1)^2 = 61

(x + 4)^2 + (y - 1)^2 = 61.

(x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given coordinates of the diameter of circle are  (-10,-4) and (2,6)

Diameter=√(x₂-x₁)²+(y₂-y₁)²

x₂=2,x₁=-10, y₁=-4, y₂=6

Diameter=√(2-(-10))²+(6-(-4))²

=√(12)²+(10)²

=√144+100

=√244

We know that Radius=Diameter/2

R=√244/2

Squaring both sides

R²=244/4

R²=61

So the equation of this circle is:

(x - (-4)² + (y - 1)² = 61

(x + 4)²+ (y - 1)² = 61.

Hence (x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ2

To learn more on Circles click:

https://brainly.com/question/11833983

The coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point on the directed line segment that partitions it into a ratio of 1 to 3, we can use the concept of section formula.

The section formula states that if we have two points A(x₁, y₁) and B(x₂, y₂) dividing a line segment in the ratio of m₁ : m₂, then the coordinates of the dividing point P are given by:

Px = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂)

Py = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)

In this case, the ratio is 1:3, which means m₁ = 1 and m₂ = 3. The given points are A(6, 2) and B(8, -10). Substituting these values into the formula, we can calculate the coordinates of the dividing point P:

Px = (1 * 8 + 3 * 6) / (1 + 3) = 7

Py = (1 * -10 + 3 * 2) / (1 + 3) = -2/2 = -1

Therefore, the coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point that divides the line segment between (6, 2) and (8, -10) in a 1:3 ratio, we can use the section formula. Applying the formula, where m₁ is 1 and m₂ is 3, the point P(x, y) can be determined.

By substituting the values into the formula, the x-coordinate is calculated as (1 * 8 + 3 * 6) / (1 + 3) = 7, and the y-coordinate is (1 * -10 + 3 * 2) / (1 + 3) = -1. Thus, the coordinates of the point that partitions the line segment into a ratio of 1 to 3 are (7, -1).

For more such questions segment,click on

https://brainly.com/question/28322552

#SPJ8

(a) The maximum possible value for the magnitude of R occurs when the vectors A and B are aligned in the same direction. In this case, the magnitude of R is the sum of the magnitudes of A and B: R_max = A + B = 3 m + 8 m = 11 m.

(b) The minimum possible value for the magnitude of R occurs when the vectors A and B are aligned in the opposite direction. In this case, the magnitude of R is the absolute difference between the magnitudes of A and B: R_min = |A - B| = |3 m - 8 m| = |-5 m| = 5 m.

the maximum possible value for the magnitude of R is 11 m, and the minimum possible value is 5 m.

what is direction?

In the context of various fields, the term "direction" can have different meanings:

Physics and Geometry: Direction refers to the orientation or path along which an object or phenomenon is moving or pointing. It specifies the line or vector in which an object is traveling or the position of one point relative to another. In physics, direction is often described using angles, coordinates, or vectors.

To know more about sum visit:

brainly.com/question/29645218

#SPJ11

Answer:

whats up? whatja need help with

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Pythagoras formula for the relation of the side lengths of a right-angled triangle :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90 degree angle). a and b are the "legs".

so, we have here

c² = 1² + 2² = 1 + 4 = 5

c = sqrt(5) = 2.236067977...

so, answer option c is too big (values bigger than 3).

answer options d and e are too small (values smaller than 2).

a

9/4 = 2.25

10/4 = 2.5

this is also too big .

that leaves us with b

17/8 = 2.125

18/8 = 9/4 = 2.25

that is correct

Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.

In the exponential form, the exponent indicates the number of times the base is used as a factor.

For example, in the case of 16 it can be written as 2 × 2 × 2 × 2  = \(2^{4}\), where 2 is the “base” and 4 is the “exponent.

A product in which the factors are identical is called a power of that factor.  The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.

To learn more about Exponential form please visit:

https://brainly.com/question/23275698

#SPJ4

John should use a one-sample t-test to test if the mean weekly study time from his sample differs from 21.1 hours because the population standard deviation is unknown and the sample size is less than 30.

John wants to compare the average time area high school students spend studying per week with the regional average of 21.1 hours. He selects a sample of 28 local high school students and records how much time they spend studying per week to compare it to the regional average. John does not know the standard deviation of the underlying population, but he is confident that the population is normally distributed because other studies indicate that study times are normally distributed, and graphs of his sample data indicate normality.

To test if the mean weekly study time from his sample differs from 21.1 hours, John needs to use a one-sample t-test because the population standard deviation is unknown and the sample size is less than 30. The one-sample t-test is a statistical hypothesis test used to determine if there is a significant difference between the mean of a sample and a known or hypothesized population mean when the standard deviation of the population is not known.

It tests whether the sample mean is significantly different from the hypothesized population mean, taking into account the sample size and the sample standard deviation. The null hypothesis, in this case, is that there is no significant difference between the mean weekly study time of the local high school students and the regional average of 21.1 hours.

The alternative hypothesis is that there is a significant difference between the two means. John will calculate the t-test statistic using the sample mean, sample standard deviation, and sample size, and compare it to the critical t-value for his chosen level of significance (usually 0.05). If the t-test statistic is greater than the critical t-value, he can reject the null hypothesis and conclude that there is a significant difference between the mean weekly study time of the local high school students and the regional average of 21.1 hours

For more questions on statistic

https://brainly.com/question/15525560

#SPJ8

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

rectangular ward:

perimeter = 274 ft

width = lenght - 37ft

Step 02:

lenght of the ward:

perimeter = 2*w + 2*l

274 = 2*(l - 37) + 2*l

274 = 2l - 74 + 2l

274 + 74 = 4l

348 / 4 = l

87 = l

The answer is:

The lenght of the ward:

The standard deviation must be 0.041 pounds.

To find the standard deviation, we can use the following formula:

standard deviation = (maximum allowable weight - mean weight) / z-score

where z-score is the number of standard deviations away from the mean that the maximum allowable weight is.

In this case, the mean weight is 2 pounds, the maximum allowable weight is 2.10 pounds, and we want no more than 3% of boxes to exceed this weight. The z-score corresponding to the 3rd percentile of a normal distribution is about -0.49.

Plugging these values into the formula, we get:

standard deviation = (2.10 - 2.0) / -0.49 = 0.020 / -0.49 = 0.041 pounds

So the standard deviation must be about 0.041 pounds. This means that the weights of the boxes should be normally distributed with a mean of 2 pounds and a standard deviation of 0.041 pounds, in order to meet the manager's requirement that no more than 3% of boxes contain more than 2.10 pounds of candy.

To learn more about standard deviation,

visit; brainly.com/question/16555520

#SPJ4

Answer:

its 13 or B

Step-by-step explanation: