find the distance from point (-3,7) to the line y=1/3x-2. round your answer to the nearest 10th if necessary

The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

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To meet the​ recommendation, the ramp needs to have a horizontal distance of at least 16 feet. The ramp has a horizontal distance of 17.9 feet.

If the ramp has a horizontal distance of 17.9 feet, it meets the recommended minimum distance of 16 feet for a ramp with a maximum slope of 1:12, as per the ADA Accessibility Guidelines.

It's important to note that the slope of the ramp should also be taken into consideration to ensure that it is safe and easy to use for individuals with disabilities. If the ramp's slope is too steep or too shallow, it may not meet accessibility standards and could pose a hazard to users.

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The value of y in the right triangle is 9.3 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the value of y in the right angle triangle.

Using trigonometric ratios,

sin 51 = opposite / hypotenuse

sin 51 = y / 12

cross multiply

12 sin 51  =y

y = 12 × 0.77714596145

y = 9.32575153748

y = 9.3 units

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Answer:

Sum of two rational numbers-

-10 = -5+-5

0= -5+5

15= 10+5

Step-by-step explanation:

To make the points in the scatterplot easier to find, the geom jitter() function method first builds a scatterplot and then adds a little amount of random noise to each point in the plot.

A scatterplot is produced using the ggplot2 function in R called geom jitter(). Each point in the plot receives a small bit of random noise to make them simpler to locate. The link between two variables in a dataset is visualised using this function.

The geom jitter() function can help to make data points easier to differentiate in a scatterplot by adding a small amount of random noise to each point. This is particularly useful when there is a lot of overlap between data points in the plot. The amount of jitter can be adjusted to ensure that the data points are still distinguishable, while still providing a more accurate representation of the data. Additionally, it can be used to adjust the size, color, and shape of the data points, allowing for a more customized visualization.

# Example of geom_jitter()

# Load ggplot2

library(ggplot2)

# Create data

x <- c(1,2,3,4,5,6,7,8,9,10)

y <- c(4,5,6,7,8,9,10,11,12,13)

# Plot data

ggplot(data = data.frame(x,y), aes(x, y)) +

geom_jitter()

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El número de formas en que tu amigo puede elegir dos libros de entre 15 es un problema de combinatoria. Más específicamente, es un problema de combinación sin repetición, ya que un mismo libro no puede ser elegido dos veces.

El número de formas en que se pueden elegir k elementos de un conjunto de n elementos sin repetición es n! / (n - k)!k!. En este caso, n = 15 y k = 2, por lo que el número de formas en que se pueden elegir dos libros es:

15! / (15 - 2)!2! = 15! / (13!)2! = 15 x 14 / 2 = 105

Por lo tanto, hay 105 formas en que tu amigo puede elegir dos libros de entre los 15 que le gustan.

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Answer:

40 socks

Step-by-step explanation:

There are 48 socks in total inside the drawer. 2 pairs of white socks means four white socks. The worst possible scenario (however unlikely it is) is that Laura takes all of the red, blue and green socks before picking any white sock. From that point on, Laura has to pick four more socks in order to have two white pairs. In this scenario, there are 8 socks left in the drawer, all white. Therefore, the minimum number of socks that Laura must take to be sure that she has two pairs of white socks is:

\(n=(12*4) - 8\\n=40\ socks\)

She must take at least 40 socks.

Answer:

She would have 5 cartons with 92 strawberries in each

While a common rule of thumb is to have a minimum sample size of 100 for continuous data to be statistically significant, the actual appropriate sample size may vary depending on the specific study design and research question. Option(D)

In statistics, the term "statistical significance" refers to whether an observed effect or relationship in the data is likely to be real and not just due to random chance. To determine statistical significance, we often perform hypothesis testing.

The sample size is a crucial factor in hypothesis testing. A larger sample size generally provides more reliable and precise estimates of population parameters and increases the statistical power of the test. With a larger sample size, even smaller effects or differences between groups can become statistically significant.

While there is no hard and fast rule for the minimum sample size to achieve statistical significance, a common guideline is to aim for at least 30 samples. This guideline is often used in the context of the Central Limit Theorem, which states that the sampling distribution of the sample mean becomes approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In practice, the appropriate sample size depends on various factors, including the nature of the data, the effect size being studied, the desired level of confidence, and the statistical test used. Researchers often conduct sample size calculations based on these factors before conducting their studies to ensure they have an adequate sample size to achieve meaningful results and detect significant effects if they exist.

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Answer:

c

Step-by-step explanation:

18/12 = 15/10 = 9/6 = 3/2

Answer:

12

Step-by-step explanation:

I. Find LCD value by devide all denominator,

 in this case are 3 and 4

        =   2 | 3 4

                | 3 2

        = 2 * 3 * 2

       = 12

Hope that help :)

Answer:

12.

Step-by-step explanation:

y /x = 6/8 = 3/4

y/x = 18/24 = 3/4

The relation is y = 3/4 x.

So, the missing value is 16 * 3/4

= 12.

The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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Answer:

see below

Step-by-step explanation:

y= -3x+4

Let x = -4

y= -3(-4) +4 = 12 +4 = 16

Let x = -0

y= -3(0) +4 = 0 +4 = 4

Let x = 4

y= -3(4) +4 = -12 +4 = -8

Let x = 8

y= -3(8) +4 = -24 +4 = -20

The length of diagonal KM of square is 11.31 inch.

What is square?

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

A square has four equal sides, four vertices, and is a closed, two-dimensional shape. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.

Given:

The Square JKLM, the area of JKLM is 64 sq in.

We have to find the length of diagonal KM.

Since,

Area of square = (side)^2

64 = (side)^2

Side = 8

Length of each side of square is 8 in.

By using the Pythagorean theorem,

(KL)^2 + (LM)^2 = (KM)^2

       8^2 + 8^2 = (KM)^2

          64 + 64 = (KM)^2

                 128 = (KM)^2

                 KM = 11.31

Hence, the length of diagonal KM of square is 11.31 inch.

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The equation of the model is (b) 2x = 5

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

Left = x x

Right hand side = 1 1 1 1 1

The above parameters mean that

Left = 2x

Right = 5

When represented as an equation, we have

2x = 5

Hence, the equation is (b)

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x = (qp)/w                

Simplify and get x on one side of equation

Answer:

Step-by-step explanation:

The fraction 6 3/4 is closer to 7 than it is to 6; the fraction 1 2/3 is closer to 2 than it is to 1. So the best estimation is the first choice, 7 / 2.

Answer:

7 ÷ 2

Step-by-step explanation:

4.05  -3.5  =0.55  

4.05 - 6 =-1.94  

4.05 -2.66   =1.38  

4.05  -1.5 =2.55  

Answer:

Step-by-step explanation:

first term = a=-2

second term= ar=-2*(3/2)=-3

hope this helps

hope im not so late  

The given expression is,

10639/500+22

According to

The magnitude of the electric field between the plates is 3.86 × \(10^7\)N/C. The sign indicates the direction of the electric field, which depends on the sign of the charge on the plates.

The strength of the electric field between the plates can be calculated using the formula:

E = σ/ε0

where σ is the surface charge density, ε0 is the permittivity of free space, and E is the electric field strength.

The surface charge density is given by:

σ = Q/A

where Q is the charge on each plate and A is the area of each plate.

Substituting the given values, we get:

σ = ±0.0000470 C / 0.138 \(m^2\) = ±0.000341 C/\(m^2\)

The permittivity of free space is:

ε0 = 8.85 × \(10^{-12\) F/m

Substituting the values, we get:

E = σ/ε0 = ±0.000341 C/\(m^2\) / 8.85 × \(10^{-12\) F/m = ±3.86 × \(10^7\) N/C

The magnitude of the electric field between the plates is 3.86 × \(10^7\)N/C. The sign indicates the direction of the electric field, which depends on the sign of the charge on the plates.

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Answer:

22/35

Hope that helps!

It's a thing called photo math just download it and it will give you your answer

Answer:

Step-by-step explanation:

Given that 1cm=500000cm

Then using unitary law, we get

Actual distance=2.5cm=2.5×500000=12,50,000cm

Answer: 3\(\sqrt{2}\)

The length of the longer base of the trapezoid is TP = 13 units

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be A = 100 units²

Now , the length of the longer base b = 32 units

The length of the shorter base a = 8 units

Let the height of the trapezium be = h

Area of Trapezoid = ( ( a + b ) h ) / 2

Substituting the values in the equation , we get

100 = ( 32 + 8 ) x h / 2

200 = 40h

Divide by 40 on both sides of the equation , we get

h = 5 units

Now , the height be PE , where E lies 12 units from T

Now , from the Pythagoras equation , we get

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

TP² = PE² + TE² , where PE is the height of the triangle

TP² = 5² + 12²

TP² = 169

Taking square roots on both sides of the equation , we get

TP = 13 units

Hence , the length of the trapezium is 13 units

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Answer:

12:00 am midnight

Step-by-step explanation:

Given;

I can read a 336-page book in 6 hours.

My rate r1 = 336/6 pages per hour = 56 pages per hour

Jayne can read a 144-page book in 3 hours.

Jayne rate r2 = 144/3 = 48 pages per hour

If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM

Taking 10 am as the reference time.

Let x represent the time from 10 am at which they would both be on the same page.

For me;

Since i started by noon; 2 hours after 10 am

Time t1 = x-2

For Jayne;

She started by 10 am

Time t2 = x

For them to be on the same page they must have read the same number of pages;

Number of pages read = rate × time

r1(t1) = r2(t2)

Substituting the values;

56(x-2) = 48(x)

56x - 112 = 48x

x(56-48) = 112

x = 112/(56-48)

x = 14 hours

Since 10 am is the reference, the time would be;

=10 am + x = 10 am + 14 hours

= 24:00

= 12:00 am midnight

Answer:

The time it would take the element to decay to 28 grams is approximately 22.5 minutes

Step-by-step explanation:

The give half life of element X = 6 minutes

The given initial mass of the radioactive element X = 390 grams

The mass of the element X after decay = 28 grams

The function that represent the decay of element X is given as follows here;

\(y = a \cdot (0.5)^{\dfrac{t}{h} }\)

Which is of the form;

\(N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}\)

Therefore;

h = 6 minutes = The time duration of the half life

a = N₀ = The initial mass = 390 g

N(t) = The final mass = 28 g

t = The time it takes the element to decay

Plugging in the values gives;

\(28 = 390 \times(0.5)^{\dfrac{t}{6} }\)

\((0.5)^{\dfrac{t}{6} } = \dfrac{28}{390}\)

Therefore;

\(\dfrac{t}{6} \times ln\left(0.5} \right) = ln \left(\dfrac{28}{390} \right)\)

t/6 = ln(29/390)/ln(0.5)

t = 6 ×  ln(29/390)/ln(0.5) ≈ 22.496

Given the answer to the nearest tenth of a minute, the time it would take the element to decay to 28 grams, t ≈ 22.5 minutes.