Solve for the missing side. Round to the nearest tenth.

$9,664.47

After 15 years the account will have $9,664.47

Answer:

3/5

Step-by-step explanation:

opposite/hypotenuse

21/35

Simplify by dividing by 7 on the numerator and denominator

3/5

The correct inequality to represent the normal temperature range of a dog is |t − 101.8| ≤ 0.7. So, correct option is B.

Here, |t - 101.8| represents the absolute value of the difference between the body temperature of the dog (t) and the average temperature of dogs (101.8° F). The inequality states that this absolute value must be less than or equal to 0.7° F, which is the maximum amount that the temperature of a dog can vary from the average.

If the temperature of a dog is within this range, it is considered to have a normal body temperature. If the temperature is outside this range, it may indicate an underlying health issue or illness.

The other answer choices are incorrect because they do not accurately represent the relationship between the body temperature of a dog and the normal temperature range. For example, |t - 0.7| ≥ 101.8 makes no sense in the context of the problem, as there is no logical reason to subtract 0.7 from the body temperature.

So, correct option is B.

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(a) The lesson time in 2007 is 11.1% more than the lesson time in 2006.

(b) The lesson lasted 40 minutes in 2005.

(c) James will take 180 seconds to swim 100 meters in a year's time.

(d)  Robert will also take 180 seconds to swim 100 meters in a year's time.

(e) James and Robert will swim equally which means that their speed will be same and they will be complete at same time.

(a) The increase in lesson time from 2006 to 2007 is:

Increase = 50 - 45 = 5 minutes

The percentage increase is:

Percentage increase = (5 / 45) x 100% = 11.1%

Therefore, the lesson time in 2007 is 11.1% more than the lesson time in 2006.

(b) Let x be the lesson time in 2005. The lesson time in 2007 is 25% more than it was in 2005, so:

1.25x = 50

Solving for x, we get:

x = 40

Therefore, the lesson lasted 40 minutes in 2005.

(c) James currently takes 240 seconds to swim 100 meters. If he improves his time by 25%, his new time will be:

New time = 240 - (0.25 x 240) = 180 seconds

Therefore, he will take 180 seconds to swim 100 meters in a year's time.

(d) Robert currently takes 240 seconds to swim 100 meters. If he increases his speed by 25%, his new time will be:

New time = 240 - (0.25 x 240) = 180 seconds

Therefore, he will also take 180 seconds to swim 100 meters in a year's time.

(e) Both James and Robert will take the same time to swim 100 meters in a year's time, so they will be equally fast.

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Integration of   [tex]\int\limits^6_0 {\frac{8}{1+74e^{-0.3t} } } \, dt[/tex]   is 2.199.

We can solve this integral using the substitution method, where u = 1 + 74[tex]e^{-0.3t}[/tex] . Taking the derivative of both sides, we have du/dt = -222[tex]e^{-0.3t}[/tex] .

We can rewrite the integral in terms of u:

∫[8/(1+74[tex]e^{-0.3t}[/tex] )]dt = ∫[8/u * (-1/222) * (-222[tex]e^{-0.3t}[/tex] )]du

Simplifying this expression, we have:

= (-8/222) ∫[1/u] du

= (-4/111) ln|u| + C

where C is the constant of integration.

Substituting back for u, we have:

= (-4/111) ln|1 + 74[tex]e^{-0.3t}[/tex] | + C

To evaluate the definite integral from 0 to 6, we plug in the limits of integration:

= (-4/111) [ln | 1 + 74[tex]e^{-0.3(6)}[/tex] | - ln | 1 + 74[tex]e^{-0.3(0)}[/tex] |]

= (-4/111) [ln|1 + 74[tex]e^{-1.8}[/tex]| - ln75]

≈ 2.199

Therefore, the value of the definite integral is approximately 2.199.

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Sides AB = 3√2 and BC = 6.

The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.

In the given right triangle ABC,

Hypotenuse of the triangle = BC

Base and height = AC and AB.

Also, we see from the diagram that ∠ACB and ∠ABC are equal.

∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.

Now, by Pythagoras' theorem,

Hypotenuse² = Base² + Height²

Or, BC² = AC² + AB²

Or, BC² = (3√2)² + (3√2)²

⇒ BC² = 36

Or, BC = 6

Hence, sides AB = 3√2 and BC = 6.

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Answer:

Step-by-step explanation:

2344

What does not make the context given as such is since PPI measures the change of the price the producer receives for their product and the CPI measure the change of the price the consumer pays for the product, one should rise while the other will fall. The Option D is correct.

This is because two indexes measure different things. The PPI measures change in prices of goods and services at the producer level while CPI measures the change in prices of goods and services at the consumer level.

That tells us PPI assess prices producers receive for their goods while CPI assess prices consumers pay for those same goods. So, while we have overlap between them, they are measuring different aspects of the economy and their trends may not always move in lockstep with each other.

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Answer:

2013 - $880,000

2019 - $640,000

Step-by-step explanation:

The office building is being depreciated linearly over 25 years, which means the annual depreciation rate is:

Depreciation rate = (Cost - Scrap value) / Useful life = ($1,000,000 - $0) / 25 = $40,000 per year

To find the book value of the building in 2013, we need to determine how many years have elapsed since 2010. Since 2013 is three years after 2010, the building has been depreciated for three years. Therefore, the book value in 2013 is:

Book value in 2013 = Cost - Depreciation = $1,000,000 - ($40,000/year x 3 years) = $880,000

To find the book value of the building in 2019, we need to determine how many years have elapsed since 2010. Since 2019 is nine years after 2010, the building has been depreciated for nine years. Therefore, the book value in 2019 is:

Book value in 2019 = Cost - Depreciation = $1,000,000 - ($40,000/year x 9 years) = $640,000

Therefore, the book value of the building was $880,000 in 2013 and will be $640,000 in 2019.

If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.

The number of cans which Cole brought = 21 cans of food.

His sister brought in 7 fewer cans than he did, which means she brought in:

⇒ 21 - 7 = 14 cans of food,

Let the total number of food-cans be = "f",

So, the equation to find the number of cans is written as :

⇒ x = 21 + 14,

On adding the number of cans,

We get,

⇒x =  21 + 14 = 35,

Therefore, together they brought in 35 cans of food.

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Callie can make 5 necklaces.

So to convert from a value in inches to one in yards, we need to divide by 36. To convert a value in yards to inches, we need to multiply by 36.

Now, She has a pieces of leather cord that has a length of 4 yards.

Each necklace will have a length of 28 inches.

We have to determine the how many necklaces can Callie make?

We know that :

1 yard= 36 inches

So, Multiply by 36 into 4 yards

4 yards= 36x4= 144

Length of leather cord is 4 yards

144/4 = 5.14

Callie can make 5 necklaces.

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Answer:

Okay, let's break this down step-by-step:

   The initial point is P(-4, 5)

   The terminal point is Q(-2, 7)

To find the components of the vector V, we need to determine:

   The change in x-coordinate = -4 - (-2) = -2

   The change in y-coordinate = 5 - 7 = -2

So the vector components are:

<change in x-coordinate, change in y-coordinate>

= <-2, -2>

Therefore, the answer is choice (i): < -2,-2>

The other choices do not represent the correct changes between the given points P and Q.

Step-by-step explanation:

Answer: 358 miles

Step-by-step explanation:

Answer: 385

Step-by-step explanation: 77x5

The resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.

The problem we are trying to solve is to determine if the sample proportion of heads obtained from spinning a penny 300 times (134 heads) is significant evidence against equal probabilities of heads and tails. To do this, we will be testing the null hypothesis H0: p = 0.5, which states that the probability of getting heads is equal to 0.5.

We can calculate the z-test statistic using the formula z = (sample proportion - hypothesized proportion) / (standard error). In this case, the z-test statistic is z = (0.444 - 0.5) / (√(0.5 * 0.5 / 300)) = -0.86. This means that the sample proportion of heads is 0.86 standard errors away from the hypothesized proportion of 0.5.

Therefore, the resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.

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Answer: The correct answer is B

Step-by-step explanation:

Remember that the coordinates (4,π3) tell us the radius r=4 and the angle θ=π3. So the point should be on the circle labeled 4 and form an angle of π3 with the positive x-axis. Point B is the correct point

Answer:

[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : a₁ = 7

Step-by-step explanation:

a recursive formula allows a term in the sequence to be found from the preceding term.

the sequence here has a common ratio between consecutive terms

[tex]\frac{21}{7}[/tex] = [tex]\frac{63}{21}[/tex] = 3

thus to find a term in the sequence multiply the previous term by 3, that is

[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : first term a₁ = 7

Step-by-step explanation:

5^(x+2)  <= 3^x    

5^x  *  5^2  <= 3^x

25 <=  3^x / 5^x

25<= (3/5)^x                  LOG both sides

log 25 <= x log (3/5)

log 25 / log (3/5) <= x

- 6.3 <= x

The equation (x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2 has no solution for x

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

(x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2

Divide through the equation by x^2

so, we have the following representation

(x+7) -(x-3) = (x+35) -(x+34)

When the brackets are removed and the like terms are evaluated, we have

2x + 10 = 2x - 1

Evaluate the like terms again

So, we have

10 = -1

The above equation is false

Hence, the equation has no solution for x

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Answer:

the corresponding sides are proportional

Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.

A general exponential decay is:

f(x) = A*(b)^x

Where A is the initial value, b is the rate of decay, x is the variable.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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Answer:

Do whatever you want, but paying attention would really help you.

Step-by-step explanation:

If you find yourself bored in class, consider the following options to make the most of your time and stay engaged:

1. Actively participate: Ask questions, contribute to discussions, and try to engage with the material. Active participation can make the class more interesting and help you retain the information better.

2. Take notes: Focus on taking detailed notes, even if you think you understand the material. This will help you stay engaged and make it easier to review the content later.

3. Find connections: Try to relate the class material to your interests or real-world applications. This can make the content more engaging and relevant.

4. Set learning goals: Set specific learning objectives for each class, and try to achieve them during the session. This can help you stay focused and motivated.

5. Practice active listening: Pay attention to the teacher and try to understand the main points they are making. This can help you stay focused and better comprehend the material.

6. Break down the material: Divide the content into smaller chunks and focus on understanding each part. This can make the material more manageable and engaging.

7. Speak with your teacher: If you're consistently bored in class, consider discussing your concerns with your teacher. They may be able to offer suggestions or modify their teaching approach to better suit your learning style.

Remember, it's essential to stay engaged in class to maximize your learning experience and make the most of your education.

Answer:

watch RUN BTS EPISODE simple

Answer: The correct answer is (5, 11π/6). or C

Step-by-step explanation:

The polar coordinates of the point (x, y) = (5√3/2, -5/2) are (r, θ) = (5, 11π/6).

Explanation:

Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

Plugging in the given values:

r = √((5√3/2)^2 + (-5/2)^2)

= √(75/4 + 25/4)

= √(100/4)

= 5

θ = atan2(-5/2, 5√3/2)

≈ 11π/6 radians

So, the correct polar coordinates of the point (5√3/2, -5/2) are (r, θ) = (5, 11π/6).

It looks like there are five data points in the box plot, representing Juan's total sales during each shift. The third data point is $200, which is the median value. Since there are an odd number of data points, we know that the median is exactly in the middle of the data set. This means that two of the data points are less than $200, and two of the data points are greater than $200.

The last data point is $300, which is the maximum value. So we know that only one of the data points is between $200 and $300. Therefore, the fraction of Juan's shifts that had total sales of $225 or more is 1/5, or 20%.

Answer:

Step-by-step explanation:

To perform this and any other construction in math, you need to use the right tools which include a compass, your drawing board or paper, and a clear understanding of the instruction.

A key to getting the shape and angles of any construction includes knowing what is required of you and implementing these in your construction. In the second slide, you are told to use the segment tool to create segment AB. This tool will be a scale and the measurement will be that of a  line AB.

Next, identify the radius of the circle. This is the point from the center of the circle to any line on the circle. Understanding the instructions is key to bisecting the segment and completing the other activities.

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Adding the number 6 to the given dataset did not affect the mode, as the number 19 still appeared the most frequently in the new dataset. (option c).

Now, if we add the number 6 to this dataset, we need to determine how this will affect the mode. We can start by looking at the number 19, which was the original mode. If the number 19 still appears the most frequently in the dataset after the addition of the number 6, then the mode will remain 19. However, if another number appears more frequently than 19 after the addition of 6, then the mode will change.

In this case, the number 6 does not appear anywhere in the original dataset, so it cannot be the mode. Therefore, the mode can either remain as 19 or change to a new number, depending on whether any other number appears more frequently than 19 after the addition of 6.

To determine if the mode changes, we need to calculate the frequency of each number in the new dataset. After adding 6, the dataset becomes:

18 24 19

19 18 20

26 25 19

6

From this dataset, we can see that the number 19 still appears twice, while all other numbers appear only once. Therefore, the mode of the new dataset is still 19, and the answer to your question is (C) "The mode will change to one number."

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Complete Question:

What happens to the mode of the data set shown below if the number 6 is added?

18 24 19

19 18 20

26 25 19

A The mode will change to two numbers.

B The mode will increase by 4.

C The mode will change to one number.

D The mode will increase by 2.

The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Answer:

C. Points have no size and no dimensions.

Answer:

I think it is choice A and choice C

An example of simple random sampling is given as follows:

C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.

Samples may be classified as:

Hence the samples for this problem are classified as follows:

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Answer:A,D

Step-by-step explanation:

y = [5.3, 27]

x= [-1,3]