hello, pls help
The distance AB is divided in the specified ratio.  Calculate the coordinates of the division point T.  A=(3|2|-1), B=(-6|1|-2), 1:2 Please help me because i am not sure if i did it right: T=A+r*(B-A) T=(3,2,-1)+1/3*(-9,-1,-1) T=(0,5/3,-4/3) Is it right? Pls help me​

Answer:

To find the critical t-value for a confidence level of 80% with a sample size of 11, we need to consult a t-distribution table or use a statistical software.

Using a t-distribution table with 10 degrees of freedom (sample size - 1), we can find the critical t-value for a two-tailed test at a confidence level of 80%.

From the table, we find that the critical t-value is approximately 1.363.

Therefore, the critical t-value for a confidence level of 80% with a sample size of 11 is approximately 1.363.

Step-by-step explanation:

jew

The options that are valid conclusions about the data include:

More than half of the students are not enrolled in French or Spanish. This conclusion is valid, as 25 out of 120 students are not enrolled in either French or Spanish, and 25 is more than half of 120.

Of the students that are enrolled in French, fewer than half of them are also enrolled in Spanish. This conclusion is valid, as only 30 out of 50 students enrolled in French are also enrolled in Spanish, which is less than half.

Therefore, the valid conclusions are B and E.

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Answer:

[tex](x+4)^2+(y-4)^2=16[/tex]

Step-by-step explanation:

A tangent is a straight line that touches a circle at only one point.

Since the circle is tangent to both axes, and the center of the circle is in the second quadrant, the center of the circle lies on the line y = -x.

As the circle is tangent to the x-axis, the distance between the center of the circle and the x-axis is equal to the radius of the circle.

Similarly, as the circle is tangent to the y-axis, the distance between the center of the circle and the y-axis is also equal to the radius of the circle.

Therefore, the center of the circle will be 4 units to the left of the y-axis and 4 units up from the x-axis. Therefore, the coordinates of the center are (-4, 4).

[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute the center (-4, 4) and the radius, r = 4, into the standard equation of a circle:

[tex]\implies (x - (-4))^2+(y-4)^2=4^2[/tex]

[tex]\implies (x+4)^2+(y-4)^2=16[/tex]

Therefore, the equation of the circle that satisfies the given conditions is:

[tex]\boxed{(x+4)^2+(y-4)^2=16}[/tex]

The point estimate of the population mean is 25

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

Lower bound = 22

Upper bound = 28

The point estimate of mean is calculated as

Point estimate of mean = 1/2 * (Lower bound + Upper bound)

Substitute the known values in the above equation, so, we have the following representation

Point estimate of mean = 1/2 * (22 + 28)

Evaluate

Point estimate of mean = 25

Hence, the estimate is 25

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The standard error of the estimate has been given in  the table that was presented in the question as  3.4835.

Standard error is a term that is used in statistics to measure the accuracy with which a sample would be the representation of a given a population.

In other words, we can say that it shows  the variability or dispersion of a sample statistic, this could be the  the sample mean or sample proportion, that is gotten through the true population value.

The standard error is stated already in the question as Standard Error 3.483483

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With the numbers gotten from the abacus counting, you can compare with the complete question to see if the student is correct or not.

From the given image, we can see that we are supposed to check if the answers given by the student is correct.

However, there are no data to compare from, so I would show the total sum of each of the abacus computed.

1. For GG, the total is 19

GB = 22

2. GG= 17

GB = 15

BB= 4

From these numbers gotten from the abacus counting, you can compare with the complete question to see if the student is correct or not.

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The function that represents this situation is Total amount = 100(1 + 0.029)ᵗ + 15

The situation can be represented by a simple interest formula, where the balance increases every year by a fixed percentage of the principal amount. Let's assume that the initial amount is $100 and the interest rate is 2.90% per year, compounded annually. The formula for the balance after t years is:

B(t) = P(1 + r)ᵗ

Where P is the principal amount, r is the annual interest rate as a decimal, and t is the time in years.

In this case, the balance after t years is:

B(t) = 100(1 + 0.029)ᵗ

At the end of t years, when the money is withdrawn, the bank will give a free $15 gift, so the total amount received by the individual will be:

Total amount = B(t) + 15

So, the function that represents this situation is:

Total amount = 100(1 + 0.029)ᵗ + 15

where t is the number of years the money is saved.

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The correct measurement of the paper clip to the nearest inch is 1 inch.

Area of the triangle is 56 cm².

What is the area of triangle?

The formula for the area of a triangle is:

[tex]A = \frac{ (base \times height) }{ 2}[/tex]

where A is the area of the triangle and the base is the length of one of its sides and the height is the perpendicular distance between the base and the opposite vertex.

Alternatively for the triangle we can use Heron's formula to calculate the area of a triangle if we know the lengths of all three sides,[tex]A = \sqrt{ (s(s-a)(s-b)(s-c))}[/tex] where A is the area of the triangle, a, b and c are the lengths of the sides and s is the semi-perimeter of the triangle which is half the sum of the lengths of the sides,

[tex]s = \frac{(a + b + c)}{2}[/tex]

Here, it is clear that base of the triangle is 14 cm and height is 8 cm.

Now area of the tria is[tex] \frac{1}{2} \times 14 \times 8 = 14 \times 4 = 56 \: {cm}^{2} [/tex]

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The volume of this sphere is 10976 feet³

It is crucial that we know that the formula that used in calculating the volume of a sphere is expressed with the equation;

V = 4/3 πr3

Given that the parameters in the formula are;

From the given information,

we have that;

Radius = 14 feet

Substitute the values, we have;

Volume = 4/3 × 3.4×14³

Find the cube values, we get;

Volume = 4/3 × 3 × 2744

Multiply the values

Volume = 10976 feet³

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A. Mean: This measure of central tendency signifies the average value in a dataset, derived by summing each data point and dividing by total quantity.

B. Median: An indicator of central tendency is utilized to discern the middle value for a given set. Primarily, the tabulated elements must be listed from least to greatest before arriving at the average between two centermost figures if the number of components is even.

C. Mode: As an analysis concerning where centrality lies, this technique seeks out the most regularly occurring element in a gathered dataset.

D. Range: The range serves as an assessment of variability measured via the differences between the upper and lower bounds registered within the collection. To calculate, subtract the minimum value from the maximum quota.

E. Interquartile range: Better known as IQR, this method measuring disparity quantifies dissimilarities between the 75th percentile (Q3) and 25th percentile (Q1). To ascertain, subtract Q1 from Q3. Such information is often used to pinpoint irregularities and evaluate the discrepancies among separate datasets.

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Max and Pam will be able to spend $676.1 on their trip.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $600.00

Compounded quarterly n = 4

Time t = 3  years

Interest rate r = 4%

Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year.

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = $600( 1 + 0.04/4 )^( 4 × 3 )

A = $600( 1 + 0.01 )^( 12 )

A = $600( 1.01 )^( 12 )

A = $676.1

Therefore, the accrued amount after 3 years is $676.1.

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The angular velocity of the wheel is 11.74 radians per second and the distance travelled is 2.81 km/min.

The angular velocity is given by the formula rpm×2π/60

Angular velocity = 2 × 3.14 × 112/60

Multiply the numerator followed by division by denominator

Angular velocity = 703.36/60

Angular velocity = 11.72 radians per second

The distance travelled will be given by the formula -

Distance = circumference × revolutions per minute

Distance = 2 × 40 × 3.14 × 112

Multiply the values on Right Hand Side

Distance = 281,227 cm/min

As, 100 cm is 1 m and 1000 m is 1 km, the distance will be 2.81 km/min.

Thus, the angular velocity is 11.72 radians per second and distance is 2.81 km/min.

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The table which most accurately reflects the relationship between the distance traveled and the total cost is table D.

Given that,

A bakery charges $4.50 per delivery, plus $0.40 per mile.

The relationship is between the distance traveled and the total cost.

This is a linear relationship.

Slope = 0.4

Since delivery charge is fixed, we can write the equation as,

y = 0.4x + 4.5, where y is the total cost and x is the distance travelled.

When x = 2, y = (0.4 × 2) + 4.5 = 5.3

When x = 3, y = (0.4 × 3) + 4.5 = 5.7

When x = 7, y = (0.4 × 7) + 4.5 = 7.3

When x = 8, y = (0.4 × 8) + 4.5 = 7.7

Hence the correct option is D.

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Rounding to the nearest hundredth, the debt of Country G after 15 years would be approximately $14.89 billion dollars.

How to solve the question?

The given equation for the debt of Country G is A = 18.5(0.995), where A represents the debt after one year, and the factor of 0.995 represents the decay factor. To estimate the debt after 15 years, we can use this equation iteratively.

After the first year, the debt would be A = 18.5(0.995) = 18.4 billion dollars. To find the debt after the second year, we can use the same equation, but replace the initial debt of 18.5 billion dollars with the debt after one year, which is 18.4 billion dollars. Therefore, the debt after two years would be A = 18.4(0.995) = 18.3 billion dollars.

We can repeat this process for each subsequent year, using the previous year's debt to calculate the next year's debt. After 15 years, the debt would be:

A = 18.5(0.995)¹⁵

A = 18.5(0.80424)

A = 14.8866 billion dollars

Rounding to the nearest hundredth, the debt of Country G after 15 years would be approximately $14.89 billion dollars.

It's important to note that this estimate assumes that the decay factor remains constant over the 15-year period. In reality, economic and political factors could impact the decay rate and the actual debt of Country G.

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128

With the help of Apollonius theorem, we know that

3(sum of square of sides)=4(sum of square of medians)

3(sum of square of sides)=4×96

sum of square of sides= 4×96/3= 128

The length of the rectangular prism will be 13.5 cm.

Given that:

Volume, V = 324 cubic cm

Height, H = 4 cm

Width, W = 6 cm

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

Then the length of the rectangular prism is calculated as,

324 = L x 6 x 4

324 = 24L

L = 13.5 cm

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For simplicity, let's use common denominators.

1/2 = 3/6

So, let's first figure out the fractional value of the water added. We can accomplish this by taking the resulting amount and subtracting the initial amount of water.

3/6 - 1/6 = 2/6

2 gallons = 2/6 of the tank

Next, let's figure out how many gallons will fill 1/6 of the tank.

2 gallons = 2/6 of the tank

1 gallon = 1/6 of the tank

Now that we know how many gallons 1/6 of the tank is, we can figure out how many gallons 6/6 of the tank is.

1 gallon = 1/6 of the tank

6 gallons = 6/6 of the tank

Answer: The total capacity of the aquarium tank is 6 gallons.

Hope this helps!

Answer: To place √31 on the number line, we first need to find its approximate value.

√31 is between 5 and 6 since 5²=25 and 6²=36. To find a more precise value, we can use a calculator or estimate using long division.

Using a calculator, we get:

√31 ≈ 5.56776436

Rounding to tenths, we get:

√31 ≈ 5.6

To place 5.6 on the number line, we can mark the point between 5.5 and 5.7.

Here's a rough sketch of what it might look like:

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         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

Step-by-step explanation:

71*8=568

568+379=947

Step-by-step explanation:

Answer: $840 left

Step-by-step explanation:

2,100 * 0.20 = 420

So, 20% of 2,100 is 420

420 * 3 = 1,260

2,100 - 1,260 = 840

Answer:

Step-by-step explanation:

The requried solution of the given trigonometric function is sin7π/12 is  (√3 + 1)/(2√2).

We know that 7π/12 = 9π/12 - 2π/12.

So, we can rewrite sin(7π/12) as sin(9π/12 - 2π/12).

Using the trigonmetric identity,
sin(A - B) = sinAcosB - cosAsinB, we can rewrite sin(9π/12 - 2π/12) as sin(9π/12)*cos(2π/12) - cos(9π/12)*sin(2π/12).

We know that,
sin(2π/12) = sin(π/6) = 1/2 and cos(2π/12) = cos(π/6) = √3/2.

Also, sin(9π/12) = sin(3π/4) = 1/√2 and cos(9π/12) = cos(3π/4) = -1/√2.

Substituting these values, we get:

= sin(7π/12) = sin(9π/12 - 2π/12)

= sin(9π/12)cos(2π/12) - cos(9π/12)sin(2π/12)

= (1/√2)(√3/2) - (-1/√2)(1/2)

= (√3/2√2) + (1/2√2)

= (√3 + 1)/(2√2)

Therefore, sin(7π/12) = (√3 + 1)/(2√2).

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Answer:

c = 47

Step-by-step explanation:

The solution of the equation is the value of x.

Given "a" is a solution of the equation, and a = -6, to find the value of c, substitute x = -6 into the given equation and solve for c.

⇒ 4x + 1 + 7c = 6c - 3x + 6

⇒ 4(-6) + 1 + 7c = 6c - 3(-6) + 6

⇒ -24 + 1 + 7c = 6c + 18 + 6

⇒ -23 + 7c = 6c + 24

⇒ -23 + 7c - 6c = 6c + 24 - 6c

⇒ -23 + c = 24

⇒ -23 + c + 23 = 24 + 23

⇒ c = 47

Therefore, the value of c that makes a = -6 a solution of the equation is 47.

The value of 'c' for which 'a' is a solution of the given equation can be found by substituting 'a' into the equation and simplifying. In this case, 'a' is -6, and by substituting this value into the equation and simplifying, we find that when 'c' is 47, 'a' becomes a solution.

To find the value of c for which a is a solution of the equation, we have to substitute the value of a into the equation and solve for c. Here, a = -6, which means x can be considered as -6 in the equation.

Step 1: Substitute the value of a (x) into the equation. So the equation 4x + 1 + 7c = 6c - 3x + 6 becomes 4(-6) + 1 + 7c = 6c - 3(-6) + 6.

Step 2: Simplify both sides of the equation. We get -24 + 1 + 7c = 6c + 18 + 6.

Step 3: Continue simplifying to -23 + 7c = 6c + 24.

Step 4: By rearranging terms, we find c = 47.

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Answer:

[tex]P= 49.2m[/tex], [tex]A=140.4m^2[/tex]

Step-by-step explanation:

The diagonal splits the rectangle into two right triangles so we can use Pythagorean theorem to find the length of the missing side.

Pythagorean theorem states that a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides

So we can label our unknown side as x

x^2 + 9^2 = 18^2

x^2 + 81 = 324

Subtract 81 from both sides to isolate the x

x^2 = 243

Find the square root of both sides

√x^2 = √243

x ≈ 15.6

(The instruction said round to the nearest 10th).

So now we know

l = 15.6m and w = 9m

P= 2l + 2w

A= lw

P= 2(15.6) + 2(9)

P= 31.2 + 18

P= 49.2m

A=15.6(9)

A=140.4m^2

Answer:

Please help me by marking me brainliest

Step-by-step explanation:

To determine which bus is the most consistent, we need to compare the measures of variability for each data set.

The range is the simplest measure of variability, and it is calculated by subtracting the minimum value from the maximum value in the data set. From the given line plots, we can see that Bus 18 has a range of 16 (from 6 to 22), while Bus 47 has a range of 24 (from 4 to 28). Therefore, Bus 18 has a smaller range, which might suggest that it is more consistent.

However, the interquartile range (IQR) is a better measure of variability, as it is less sensitive to extreme values. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) of the data set.

From the given line plots, we can see that Bus 18 has an IQR of 16 (from Q1=10 to Q3=26), while Bus 47 has an IQR of 24 (from Q1=6 to Q3=30). Therefore, Bus 18 has a smaller IQR, which indicates that it is more consistent than Bus 47.

In conclusion, we can determine that Bus 18 is the most consistent based on its smaller IQR. This means that the travel times for Bus 18 students are more tightly clustered around the median than the travel times for Bus 47 students.

Using the measures of variability, it can be concluded that Bus 18 is the most consistent because it has a lower Interquartile Range (IQR) and a lower range in its times.

The most consistent bus can be found by using measures of variability, specifically the range and the interquartile range (IQR). The range is the difference between the highest and lowest values, while the IQR represents the middle 50% of data. In this case, the range of Bus 47 is 24 (28-4) and that of Bus 18 is 16 (22-6). Similarly, the IQR of Bus 47 is 12 (22-10) and 8 for Bus 18 (16-8).

A lower IQR and range indicate more consistency, as the data points are closer together. Therefore, Bus 18 is the most consistent in terms of travel times as it has both a lower range and a lower IQR.

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If the average wingspan of monarch butterflies at a butterfly preserve is 8.5. the probability, to t nearest hundredth, that monarch butterflies have a wingspan longer than 8.8 centimeters is : 0.23.

First step is to standardize the value of 8.8 centimeters using the z- score  formula:

z = (x - mu) / sigma

where:

x  = wingspan

mu = mean wingspan

sigma= standard deviation

z  standardized score

Substituting the given values

z = (8.8 - 8.5) / 0.4

z = 0.75

So,

P(z > 0.75) = 1 - P(z <= 0.75)

Using a standard normal distribution table  P(z <= 0.75) = 0.7734

P(z > 0.75) = 1 - P(z <= 0.75)

= 1 - 0.7734

= 0.2266

= 0.23 (  Approximately)

Therefore the probability is 0.23.

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The value of standard deviation 's' is 2.08700, as indicated in the display.

Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the average of the squared deviations from the mean, it is the square root of the variance.

The value of s is 2.08700, as indicated in the display.

The symbol "Sx" represents the sample standard deviation, which is commonly denoted as "s". The other values in the display are:

So, the correct answer is 2.08700.

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The amount that Floyd will be paid each month from this annuity is $6,374.83 each month.

To calculate the monthly payments from a 20-year annuity with an initial investment of $1,000,000 at an APR of 4.6% compounded monthly, we can use the formula for calculating the monthly payment of an ordinary annuity: Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Data

P = $1,000,000)

r = 4.6% / 12 / 100 = 0.00383

n = = 20 * 12 = 240

Plugging in the values. The monthly payment will be:

= $1,000,000 * 0.00383 * (1 + 0.00383)^240 / ((1 + 0.00383)^240 - 1)

= $1,000,000 * 0.00383 * 1.66538674279

= $6,378.43122

= $6,378.43

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