If x=3t+t^2 and y=7−2t, find an equation y=mx+b of the tangent to the curve at t=2.
m=
b=

The calculated value of the area of the real room is 10.67 cm²

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

In the drawing, 3cm represents 4cm

This means that

Scale factor = 4/3

Also, we have the dimension of the scale drawing to be

Dimension = 3cm by 2 cm

So, the area of the bedroom in the scale is

Area = 3cm * 2cm

For the actual room, we have

Area = 3cm * 2cm * (4/3)²

Evaluate the exponent

Area = 3cm * 2cm * (16/9)

Evaluate the products

Area = 10.67 cm²

This means that the real area is 10.67 cm²

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a) Null: Mean = 20 days; Alt: Mean > 20 days. b) supported by t-value 6.708 > critical value at α=0.05. c) 95% confidence interval for mean patient discharge time is between 20.528 and 23.472 days, d) 99% confidence, a minimum sample size of 67 patients is required.

a) The null hypothesis is that the mean days for a patient to discharge is still 20 days, while the alternative hypothesis is that the mean days for a patient to discharge has increased and is now greater than 20 days.

Null hypothesis: 0:  = 20

Alternative hypothesis: 1:  > 20

b) We can use a one-sample t-test to test the hypothesis. We will use a significance level of 0.05.

The test statistic is given by:

t = (x - ) / (s / √n)

where x is the sample mean,  is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Here, x = 25,  = 20, s = 5, and n = 30. Plugging these values into the formula, we get:

t = (25 - 20) / (5 / √30) = 6.708

The degrees of freedom (df) for the t-distribution is n - 1 = 29. Using a t-table or calculator, the p-value for a one-tailed test with df = 29 and t = 6.708 is < 0.0001.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. There is sufficient evidence to conclude that the mean days for a patient to discharge has increased.

c) To construct a 95% confidence interval for the mean days for a patient to discharge, we use the formula:

CI = x ± tα/2 * (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the critical value for a t-distribution with df = n-1 and α = 0.05/2 = 0.025.

Here, x = 22, s = 5, and n = 40 (30 from the first sample + 10 from the second sample). The critical value for tα/2 with df = 39 is 2.022.

Plugging these values into the formula, we get:

CI = 22 ± 2.022 * (5/√40) = (20.528, 23.472)

Therefore, we can be 95% confident that the true mean days for a patient to discharge is between 20.528 and 23.472 days.

d) To find the minimum sample size required to estimate the mean days for a patient to discharge to within 2 days of error with a 99% confidence, we use the formula:

n = (zα/2 * s / E)²

where zα/2 is the critical value for a z-distribution with α = 0.01/2 = 0.005, s is the sample standard deviation (which we assume is the same as before, i.e., s = 5), and E is the desired margin of error (which is 2 days).

Plugging in the values, we get:

n = (2.576 * 5 / 2)² = 66.18

Therefore, the minimum sample size required is 67 patients.

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The constant of proportionality of the line is slope m = 2/3

Given data ,

Let the line be represented as A

Now , the value of A is

Let the point on the straight line be P ( 2 , 3 )

Now , from the proportionality , we get

y = kx

Divide by x on both sides , we get

k = y/x

So , the slope of the line is k

k = 2/3

Hence , the proportion is y = ( 2/3 )x

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Answer:

  (x -6)² +(y +2)² = 128

Step-by-step explanation:

You want the equation of the circle centered at (6, -2) through point (14, 6).

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

For center (h, k) = (6, -2), we can find the value of r² knowing that it will be the value that lets the point (14, 6) satisfy the equation.

  (14 -6)² +(6 -(-2))² = r² = 8² +8² = 128

The circle equation is ...

  (x -6)² +(y +2)² = 128

Check the picture below.

Answer:

Step-by-step explanation:

it should be shaded at the 76

The best estimate of 7,625,750,263 is 7x10⁹. So the correct option is B.

The given number is 7,625,750,263.

To express the above number in words, it is "seven billion six hundred twenty-five million seven hundred fifty thousand two hundred sixty-three". So, the given value ultimately has a billion value.

To find the correct answer let's see the given options and eliminate each one to find the correct answer. Option A is 7 x 1010 = 7070 which is not even coming to a close, so option A is eliminated.

Let's see the second option which is 7x10⁹ which is 7000000000, which is 7 billion. So, option B is very near to the answer.

Let's see the third option which is 8x10¹⁰ which is 80 billion, it is not an estimated value. So, it is also eliminated and the final option is 8x10⁹ which is 8 billion which is also high value So, it is also eliminated.

From the above analysis, we can conclude that the best estimated value for 7,625,750,263 is 7x10⁹ which is option B.

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Using an exponential function and integration, it is found that over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.

Exponential function:

A decaying exponential function is modeled by:

⇒ A (t) = A (0) (1 - r)ⁿ

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

In this problem:

In the first year, the country emits 80,000 kilotons, hence . A (0) = 8000

Emissions will decrease 2.5% in each successive year, hence r = 0.026

Then, the equation for the amount emitted each year is:

⇒ A (t) = A (0) (1 - r)ⁿ

⇒ A (t) = 80000 (1 - 0.025)ⁿ

⇒ A (t) = 80,000 (0.975)ⁿ

The total amount emitted over the course of the 11 year period is:

T = ∫ 0 to 11 ( A (t) ) dt

Hence:

T = ∫ 0 to 11 ( 80000 (0.974)ⁿ ) dt

Applying the Fundamental Theorem of Calculus:

T = 763,968 kilotons

Hence, Over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.

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The expanded form of log y^10 is either 10 log y or 10 ln y

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.

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Answer: To factorize 3h² + 12h, we can first find the greatest common factor (GCF) of the two terms, which is 3h:

3h(h + 4)

This is the fully factorized form of 3h² + 12h.

a) The average slope or rate of change between (0, 1) and (2, 4) is 3/2.

b) The average slope or rate of change between (-2, 1/4) and (-1, 1/2) is 1/4.

c) The slope or rate of change is not constant between these two pairs of points, since the average slopes are different.

d) The function connecting these pairs of points is not a linear function.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The average slope or rate of change between two points (x1, y1) and (x2, y2) on a line is given by:

average slope = (y2 - y1) / (x2 - x1)

For the points (0, 1) and (2, 4), the average slope is:

average slope = (4 - 1) / (2 - 0) = 3/2

For the points (-2, 1/4) and (-1, 1/2), the average slope is:

average slope = (1/2 - 1/4) / (-1 - (-2)) = 1/4

When the average slopes of these two pairs of points differ, the slope or rate of change is not constant. As a result, the function connecting these point pairs is not linear.

Because a linear function has a constant slope, a function with a variable slope cannot be linear.

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Answer:

angle 5 is 120 since there is Z shape with angle 3

Answer:

245 inches

Step-by-step explanation:

Yards->Inches

1 yard = 36 inches

Therefore, 6 yards = 36 x 6 = 216 inches

Feet->Inches

1 feet = 12 inches

Therefore, 2 feet = 2 x 12 = 24 inches

Adding all inches,

=> 216 + 24 + 5

=> 245 inches

Answer:

We can use Bayes' theorem to calculate P(R), which states that the probability of an event A given event B is equal to the probability of B given A multiplied by the probability of A, divided by the probability of B:

P(R|T) = P(T|R) * P(R) / P(T)

We can rearrange this equation to solve for P(R):

P(R) = P(R|T) * P(T) / P(T|R)

We are given that P(RI-T) = 0.25, which can be written as:

P(R∩T) = P(R|T) * P(T) = 0.25

We are also given that P(-R|T) = 0.2, which can be written as:

P(-R∩T) = P(-R|T) * P(T) = 0.2 * 0.1 = 0.02

We can use the law of total probability to find P(T|R):

P(T|R) = P(RI-T) / P(R) = 0.25 / P(R)

We can substitute these values into the equation for P(R) to get:

P(R) = P(R|T) * P(T) / P(T|R)

= 0.25 / [P(T|R) * P(T) + P(-R|T) * P(T)]

= 0.25 / [0.25 + 0.02]

= 0.1060

Therefore, the answer is option C: 0.1060.

The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.

Option D is correct.

if angle A is obtuse and if a > b then the triangle has one solution

We are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.

Finding remaining sides c and ∠B and ∠C

Using the Law of sines to find ∠B

a/sin A = b/sin B

7/sin 119° = 4/sin B

7 * sin B = 4 * sin 119

7*sin B = 4(0.874)

sin B = 3.496/7

B = sin^-1(0.4994)

B = 29.96 = 30°

We know that sum of angles of triangle = 180°

So, 180° = 119° + 30° +∠C

180° = 149° + ∠C

=> ∠C = 180° - 149°

∠C = 31°

Now finding c

b/sin B = c /sin C

4/Sin 30 = c/sin 31

4* sin 31 = c*sin 30

4*0.515 = c* 0.5

=> c =  4*0.515/0.5

c = 4.12 ≈ 4

So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.

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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree

A = 119°, a=7, b=4

Question 7 options:

one solution; c ≈ 7; B = 30°; C = 119°

no solution

one solution; c ≈ 4; B = 31°; C = 30°

one solution; c ≈ 4; B = 30°; C = 31°

The result of the division of the two complex numbers is equal to z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)].

In this problem we find two complex numbers in rectangular form, whose division must be found. This can done by easily by means of complex numbers in polar form and definition of division:

Complex number (rectangular form)

z = r · (cos θ + i sin θ)

Complex number (polar form)

[tex]z = r\cdot e^{i\cdot \theta}[/tex]

Where:

Division between two complex numbers in polar form:

[tex]\frac {z_{1}}{z_{2}} = \left(\frac{r_{1}}{r_{2}}\right)\cdot e^{i\cdot (\theta_{1}-\theta_{2})}[/tex]

This number is equivalent to the following expression in rectangular form:

z₁ / z₂ = (r₁ / r₂) · [cos (θ₁ - θ₂) + i sin (θ₁ - θ₂)]

If we know that r₁ = 8, r₂ = 9, θ₁ = π / 10 and θ₂ = π / 12, then the division of the two complex numbers is:

z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)]

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Answer:

B

D

E

( all of the answers (E, D, B) have no real solutions)

The length of the other legs of the isosceles right triangle is 13 + 13√2 centimetres.

The hypotenuse of an isosceles right triangle is 13 centimetres longer than either of its legs.

An isosceles right triangle is a right triangle whose legs are the same length. The sides of a right triangle can be found using Pythagoras's theorem.

Therefore,

let

y = other legs

Therefore,

(x + 13)² = x² + x²

(x + 13)(x + 13) = 2x²

x² + 13x + 13x + 169 = 2x²

x² - 26x - 169 = 0

Therefore, using the quadratic formula,

[tex]\frac{-b+\sqrt{b^{2} - 4ac } }{2a}[/tex]

where

x = 13 ± 13√2

Therefore, we can only use positive values

x = 13 + 13√2

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The finance charge for Sandra Lazzaro, using the average daily balance method, is $13.63.

The average daily balance is one of the methods for computing the finance charges (interest and other fees).

The average daily balance method uses the balance owed at the end of each day of the billing period, and not the balance owed at the end of the week, month, or year.

Billing period for the credit card = 31 days

Unpaid credit card balance = $750

Payment made three days before month-end = $600

Finance charge rate per month = 2.2%

Method = Average daily balance

Day        Description    Amount    Average Balance

1 - 28     Balance           $750       $21,000 ($750 x 28 days)

29 - 31   Payment        -$600       $-1,800 ($600 x 3 days)

31           Total                              $19,200

Average daily balance = $619.35 ($19,200 ÷ 31)

Finance charge = $13.63 ($619.35 x 2.2%)

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The accrued value of the account in 10 years is $641.75

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

Using the above as a guide, we have the following:

Amount = P * (1 + 0.25r)ᵗ

Where

P = Principal = 600

r = Rate = 2.7% = 0.27

t = time = 10

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

Amount = 600 * (1 + 0.25 * 0.27)¹⁰

Evaluate

Amount = 641.75

Hence, the amount is 641.75

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Hi Annie. I was interested in engaging you about your post because of my differing view. However, I think I am open to changing my views because I am not dogmatic. Do you think I am too pliable?

Throughout the Civil War, African Americans assumed crucial roles in the Union war effort. From enlisting as soldiers to acting as laborers and even spies, their contributions left an indelible impact on history.

Despite being subjected to rampant discrimination and racism from both Confederacy and Union forces, these individuals exhibited incredible heroism and bravery.

Excelling in dangerous missions that often led them to become prisoners of war, they persevered as they fought for the freedoms of themselves and others.

Hari Jones' TED talk shines a much-needed light on this overlooked aspect of history, revealing not only the extensive involvement of African American soldiers but also the pivotal role played by women in areas such as nursing, cooking, and espionage.

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Answer:

X       H(x)=2x+3

-4       -5

0        3

1         5

2        7

3        9

Answer:

( -6, 6)

Step-by-step explanation:

The expression that represents the total amount that Ignatio and his friends spent is 15t

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

After spending on t games, we have

f(t) = Rate * t

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

f(t) = 15 * t

Evaluate

f(t) = 15t

Hence, the expression that represents the total amount that Ignatio and his friends spent is 15t

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If the Amethyst Woodstar species of hummingbird beats its wings about 80 times per second and there are 60 seconds in a minute, it beats its wings D. 43,200 times in 9 minutes.

The number of times that the Amethyst Woodstar species of hummingbird beats its wings in 9 minutes can be determined using the mathematical operation of multiplication.

The number of times it beats its wings = 80 seconds per second

The total number of minutes involved = 9 minutes

1 minute = 60 seconds

The total number of times it beats in 9 minutes = 43,200 (80 x 60 x 9)

Thus, using multiplication operation, the number of times the bird beats its wings is Option D.

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Let's start by setting up a proportion to represent the ratio of Illinois students to Michigan students:

Illinois students / Michigan students = 6/5

We can simplify this proportion by multiplying both sides by 5:

Illinois students = 6/5 * Michigan students

Next, we can use the information in the table to set up an equation that relates the number of Illinois students, Michigan students, and Indiana students:

Illinois students + Michigan students + Indiana students = 175

We can substitute the expression we obtained for the number of Illinois students into this equation:

6/5 * Michigan students + Michigan students + Indiana students = 175

Multiplying both sides by 5 to eliminate the fraction, we get:

6 * Michigan students + 5 * Michigan students + 5 * Indiana students = 875

Combining like terms, we get:

11 * Michigan students + 5 * Indiana students = 875

Now we can use the fact that the ratio of Illinois students to Michigan students is 6:5 to set up another equation:

Illinois students / Michigan students = 6/5

Substituting the values from the table, we get:

Illinois students / Michigan students = 24/20

Cross-multiplying, we get:

Illinois students * 20 = Michigan students * 24

Simplifying, we get:

Illinois students = 6/5 * Michigan students = 24/20 * Michigan students = 6/5 * 24 Michigan students = 28.8 Michigan students

Since the number of students must be a whole number, we can round 28.8 up to 29. This means that there were 29 Michigan students.

Substituting this into the equation we obtained earlier, we get:

11 * 29 + 5 * Indiana students = 875

Solving for Indiana students, we get:

5 * Indiana students = 875 - 11 * 29 = 546

Dividing both sides by 5, we get:

Indiana students = 546/5 = 109.2

Since the number of students must be a whole number, we can round 109.2 up to 110. This means that there were 110 Indiana students.

Therefore, the answer is 110 students from Indiana.

When a student is chosen at random, the student is more likely to be from Mrs Johnson's class.

The probability that the student got A in the first semester will be 0.15.

When a student is chosen at random, the student is more likely to be from Mrs Johnson's class. It should be noted that this is because 152 students out of 300 are from her class compared to Dixon who has 148 students.

The probability that the student got A in the first semester will be:

= 46 / 300

= 0.15

The probability for the last question will be:

= 14 / 148

= 0.095.

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The percentage of females that do not satisfy the requirement is given as follows:

55.17%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 998, \sigma = 202[/tex]

The proportion that does not satisfy the requirement is the p-value of Z when X = 1025, hence:

Z = (1025 - 998)/202

Z = 0.13

Z = 0.13 has a p-value of 0.5517.

Hence the percentage is given as follows:

0.5517 x 100% = 55.17%.

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In 12 days, both Eve and Jenna will work out on the same day again.

To find the number of days until Eve and Jenna work out on the same day again, we need to find the least common multiple (LCM) of 6 and 4.

One way to find the LCM is to list the multiples of each number until we find a multiple that they have in common:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ...

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...

From this list, we see that the least common multiple of 6 and 4 is 12.

This means that in 12 days, both Eve and Jenna will work out on the same day again.

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