1. The population of a town was 500 in 2010. The population grows at a rate of 9.6% annually.
(a) Use the exponential growth model to write an equation that estimates the population t years after 2010.
(a) Estimate the population of the town in 2020. Show your work.

Answer:

1.) not safe

2.)

[tex]18 \sqrt{3} [/tex]

Step-by-step explanation:

1.) given the length of the ladder = 15ft.

and the height to the top of ladder when leaned against a wall is 14.8ft. This all forms a right triangle.

with what we are given we can solve for the angle it creates from the ground to the leaned ladder by using the SOHCAGTOA. Whike we do this keep in mind its not safe for a ladder to create an angle more than 70 degrees.

in this case if we are solving for the angle where the height is opposite we will use SOH. because we know the oposite and the hyp. Sin(theta) = opp/hyp

[tex] \sin(theta) = \frac{14.8}{15} [/tex]

[tex]sin^{ - 1} ( \frac{14.8}{15} ) = 81 \: degrees[/tex]

therefore not safe.

2.)

your givin 90 and 60. remember all interior angles add up to 180.

therefore 30 would be the unknown angle.

knowing that we use the chart at the top.

across from 30 is 6. so we put that by x. (remember we are doing this to find the height for our area of a triangle formula = base time height devide by 2.)

we need to find the height so since we kmow what x is we know what is across from 60 which is

[tex]6 \sqrt{3} [/tex]

so we plug that into our formula for area of triangle and u should get 18

[tex] \sqrt{3} [/tex]

Answer:

Step-by-step explanation:

(-3,1) (5,3)

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{3-1}{5-(-3)}\\\\=\frac{2}{5+3}\\\\=\frac{2}{8}\\\\=\frac{1}{4}[/tex]

= 0.25

Answer:  (3,4)

This is what I had wrote, sorry if I'm wrong.

Answer:

b

Step-by-step explanation:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

The correct value of the h function is; h= -9.8t² + 45t + 1

Answer:

Using the discriminant, no real solution exists and the baseball will not hit the roof.

Step-by-step explanation:

We are told the height is expressed as;h= -9.8t² + 45t + 1

Also that the Astrodome has a maximum height of 63.4 m

Thus, to find out if the baseball hit at a velocity of 45 m/s will hit the roof, we'll replace h with 63.4m.

Thus;

63.4 = -9.8t² + 45t + 1

Subtract 63.4 from both sides to give;

-9.8t² + 45t + 1 - 63.4 = 0

-9.8t² + 45t - 62.4 = 0

Using quadratic formula, we have;

t = -45 ± √{(45² - (4 * (-9.8) * (-62.4)}

t = -45 ± √(2025 - 2446.08)

t = -45 ± √(-421.08)

The discriminant is -421.08

This value is less than 0.

Thus, no real solution exists and the baseball will not hit the roof.

Answer:

1/4

Step-by-step explanation:

(0,1) (4,2)

m=(y2-y1)/(x2-x1)

m=(2-1)/(4-0)

m=1/4

Answer:

9

Step-by-step explanation:

Composite Numbers before 10: 4, 6, 8, and 9

The only one of those 4 that is NOT a multiple of 2: 9

The number being referred to in the question is 9. It is less than 10, not a multiple of 2, and is a composite number, as it has factors other than 1 and itself.

The question is asking for a number which is less than 10 and is not a multiple of 2, but is a composite number. In mathematics, a composite number is a positive integer that has at least one positive integer divisor other than one or itself. If we look at the numbers less than 10 which are not multiples of 2, we are left with the numbers 1, 3, 5, 7, and 9. Out of these, the only composite number is 9, because it could be divided evenly by 3 and 1 apart from itself. Therefore, the number you are referring to is 9.

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The height of the cone (h) is approximately 12.8 centimeters to the nearest tenth of a centimeter.

To find the height of the cone (h) to the nearest tenth of a centimeter, we can follow these steps:

Calculate the radius (r) of the base:

The formula for the circumference of a circle is C = 2πr.

We are given the base circumference C = 44 cm.

Solving for r, we get: r = C / (2π) ≈ 7.07 cm (round to two decimal places).

Use the Pythagorean theorem to find the height (h):

The Pythagorean theorem states that a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.

In this case, the slant height (16.2 cm) is the hypotenuse, and the radius (7.07 cm) and the height (h) are the legs.

Therefore, we can write the equation: 16.2² = 7.07² + h².

Solve for the height (h):

Rearranging the equation to isolate h, we get: h² = 16.2² - 7.07² ≈ 163.97 cm².

Taking the square root of both sides, we get: h ≈ 12.8 cm.

Round the height to the nearest tenth of a centimeter:

Rounding 12.8 cm to the nearest tenth gives us: h ≈ 12.8 cm (to the nearest tenth).

Therefore, the height of the cone (h) is approximately 12.8 centimeters to the nearest tenth of a centimeter.

Final answer:

The height of the cone is calculated using the base radius, found from the given base circumference, and applying the Pythagorean theorem with the slant height as the hypotenuse. The height comes out to be approximately 14.6 cm.

Explanation:

To calculate the height of the cone (h) given its slant height and base circumference, we first need to find the base radius (r) using the formula for the circumference of a circle: C = 2πr. Given that the base circumference is 44 cm, solving for r we get:

r = C / (2π)
 = 44 cm / (2 * 3.1416)
 ≈ 7 cm

Next, we use the Pythagorean theorem in the right-angled triangle formed by the radius, slant height, and the height of the cone. The slant height is the hypotenuse of the triangle, 16.2 cm in this case, and the opposite side to the angle at the cone's base is the height we need to find.

Using the formula h = √(slant height)^2 - (radius)^2, we substitute the values into the equation:

h = √(16.2 cm)^2 - (7 cm)^2
 = √262.44 cm^2 - 49 cm^2
 = √213.44 cm^2
 ≈ 14.6 cm

Therefore, the height of the cone, rounded to the nearest tenth, is 14.6 cm.

Final answer:

To rearrange the equation so x is the independent variable, add 4y to both sides and then divide by -5 to solve for x.

Explanation:

To rearrange the equation so x is the independent variable, we need to isolate x on one side of the equation. Let's start by adding 4y to both sides of the equation:

-5x - 4y + 4y = -8 + 4y

-5x = 4y - 8

Next, divide both sides of the equation by -5 to solve for x:

x = (4y - 8) / -5

So, the rearranged equation with x as the independent variable is:

x = (-4y + 8) / 5

Therefore, as per the explaination above,  the answer to the required question is x = (-4y + 8) / 5

Answer:

3.8 meters

Step-by-step explanation:

Answer:

D. more than 102

E. between 90 and 102 messages

F. less than 78

Step-by-step explanation:

The median number of texts is 90, with approximately 25 students sending fewer than 78 texts (Q1) and 25 sending more than 102 texts (Q3) per day.

For a sample of 100 students, the median number of text messages sent per day is 90, the first quartile (Q1) is 78, and the third quartile (Q3) is 102. This implies that approximately 25 students in the sample send fewer than 78 text messages per day (since Q1 marks the 25th percentile) and approximately another 25 students send more than 102 text messages per day (since Q3 marks the 75th percentile). Hence, the interquartile range (IQR), which measures the middle 50% of the data, is the difference between the third and first quartiles, which is 102 - 78 = 24 messages.

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Answer:

35x+5=10

Step-by-step explanation:

Answer:

2s = 16

Step-by-step explanation:

In the choir, there are 16 altos and s sopranos.

Let the number of altos be a.

=> a = 16

There are twice as many sopranos as altos.This means that:

a = 2s

Since the number of altos, a, is 16, the equation that represents this situation is:

2s = 16

An equation representing the number of sopranos in a choir, given the number of altos is s = 2 x 16, which simplifies to s = 32.

The question asks us to write an equation to represent the number of sopranos in a choir based on the number of altos. Given that there are 16 altos and the number of sopranos is twice as many, we can represent the number of sopranos as s. The relationship between the altos and sopranos can be expressed mathematically as s = 2 × 16. Therefore, the equation that represents this situation is s = 32, where s stands for the number of sopranos in the choir.

Answer:

x = -1

y = -9

Step-by-step explanation:

7x - 3y = 20

7x - 3(5х – 4) = 20

7x - 15x + 12 = 20

-8x = 20 - 12

x = 8/-8

x = -1

7x - 3y = 20

7(-1) - 3y = 20

-7 - 3y = 20

-3y = 20 + 7

-3y = 27

y = 27/-3

y = -9

Answer:

The two numbers are 5 and 12, the lesser is 5.

5 is the lesser number, therefore the answer. Hope this helped! :D

Answer:

y = f(x + 90)

Step-by-step explanation:

f(x)=Acos(Bx+C)+D,

A is the amplitude: A = 1

B is the 360/period: 360/360 = 1

D is the mean line: y = 0

f(-270) = 0

sin(x + C) = 0

-270 + C = -180

C = 90

y = f(x + 90)

Answer:

B and C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A= very light

B= heavy

C= REALLY HEAVY

Answer:

Event

Step-by-step explanation:

I got the question right ._.

An outcome is a possible result of some event occurring.

The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.

An outcome is a possible result of some event occurring.

For example, when you flip a coin, “heads” is one outcome; tails is a second outcome.

Total outcomes are computed simply by counting all possible outcomes.

Learn more about probability here:

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Answer:

[tex]0\leq x\leq 15[/tex]

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one

For the graph below, what should the domain be so that the function is at least 200?   graph of y equals minus 2 times the square of x plus 30 times x plus 200

My answer:

Given the above information, we have:

[tex]y=-2x^2+30x+200[/tex]

To make  the function is at least 200, it means that:

[tex]y=-2x^2+30x+200[/tex] ≥ 200

<=> [tex]-2x^2+30x[/tex] ≥ 0

<=> x(-2x+30) ≥ 0

This is the product of two numbers hence would be positive only if either both are positive or both are negative

x ≥ 0 and  (-2x+30) ≥ 0

<=> 0 ≤ x ≤ 15

Then we get

[tex]x\leq 0 and -2x+30\leq 0\\\\x\leq 0 and x\geq 15[/tex]

This is inconsistent as a value cannot be less than 0 and greater than 15

=> our correct answer is[tex]0\leq x\leq 15[/tex]

Hope it will find you well.

Answer:

A) 39.6 divided by 8.25 is true.

Answer:

D

Step-by-step explanation:

Got it right on test

Answer:

The radius of a cone is the radius of its circular base. You can find a radius through its volume and height. Multiply the volume by 3.

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

AB is 4 of 5 parts BC is i of 5 parts

75 divided by 5 = 15

75 minus 15=60

Answer:

6

Step-by-step explanation:

We can use the geometric mean theorem:

The altitude on the hypotenuse is the geometric mean of the two segments it creates.

In your triangle, the altitude is the radius CM and the segments are AC and BC.

[tex]CM = \sqrt{AC \times BC} = \sqrt{ 9 \times 4} = \sqrt{36} = \mathbf{6}\\\text{The radius of the circle M is $\large \boxed{\mathbf{6}}$}[/tex]

The length of the radius of the circle is 6 units

The given parameters are:

AC = 9

BC = 4

To calculate the radius (r), we make use of the following equation:

[tex]r = \sqrt{AC * BC}[/tex]

Substitute known values

[tex]r = \sqrt{9 * 4}[/tex]

Evaluate the product

[tex]r = \sqrt{36}[/tex]

Evaluate the square root

[tex]r = 6[/tex]

Hence, the length of the radius of the circle is 6 units

Read more about radius at:

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Answer:

Step 4

Step-by-step explanation:

Tasha was correct in all the steps leading up to the fourth one. However, in the fourth step was where she messed up.

She said that: [tex]\frac{1}{256} =-\frac{1}{4^{-4}}=4^{-4}[/tex]

However, when we have a negative exponent, in order to get rid of the negative, we simply take the reciprocal of the number and then make the exponent positive. Here, the answer should be:

[tex]\frac{1}{256} =\frac{1}{4^{4}}=4^{-4}[/tex]

Answer:

Step 4

Step-by-step explanation:

1/256 = 4^-4 or 1/4⁴

Answer:

d

Step-by-step explanation:

Answer:

The probability that [tex] \\ P(x<85)[/tex] is, approximately, 0.3594 or about 35.94% (or simply 36%).

Step-by-step explanation:

Firstly, we have to know that the random variable, in this case, is normally distributed. A normal distribution is completely determined by its two parameters,  namely, the population mean and the population standard deviation. For the case in question, we have a mean of [tex] \\ \mu = 89[/tex], and a standard deviation of [tex] \\ \sigma = 11[/tex].

To find the probability in question, we can use the standard normal distribution, a special case of a normal distribution with mean equals 0 and a standard deviation that equals 1.

All we have to do is "transform" the value of the raw score (x in this case) into its equivalent z-score. In other words, we first standardize the value x, and then we can find the corresponding probability.

With this value, we can consult the cumulative standard normal table, available in most Statistics textbooks or on the Internet. We can also make use of technology and find this probability using statistical packages, spreadsheets, and even calculators.

The corresponding z-score for a raw score is given by the formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

And it tells us the distance of the raw score from the mean in standard deviations units. A positive value of the z-score indicates that the raw value is above the mean. Conversely, a negative value tells us that the raw score is below the mean.

With all this information, we are prepared to answer the question.

The corresponding z-score

According to formula [1], the z-score, or standardized value, is as follows:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

From the question, we already know that

x = 85

[tex] \\ \mu = 89[/tex]

[tex] \\ \sigma = 11[/tex]

Thus

[tex] \\ z = \frac{85 - 89}{11}[/tex]

[tex] \\ z = \frac{-4}{11}[/tex]

[tex] \\ z = -0.3636 \approx -0.36[/tex]

Consult the probability using the cumulative standard normal table

With this value for z = -0.36, we can consult the cumulative standard normal table. The entry for use it is this z-score with two decimals. This z-score tells us that the raw value of 85 is 0.36 standard deviations below from the population mean.

For z = -0.36, we can see, in the table, an initial entry of -0.3 at the first column of it. We then need to find, in the first line (or row) of the table, the corresponding 0.06 decimal value remaining. With this two values, we can determine that the cumulative probability is, approximately:

[tex] \\ P(x<85) = P(z<-0.36) = 0.3594[/tex]

Then, [tex] \\ P(x<85) = 0.3594[/tex] or, in words, the probability that [tex] \\ P(x<85)[/tex] is, approximately, 0.3594 or about 35.94% (or simply 36%).

Remember that this probability is approximated since we have to round the value of z to two decimal places (z = -0.36), and not (z = -0.3636), because of the restrictions to two decimals places for z of the standard normal table. A more precise result is [tex] \\ P(x<85) = 0.3581[/tex] using technology, shown in the graph below.

Notice that, in the case that the cumulative standard normal table does not present negative values for z, we can use the next property of the normal distributions, mainly because of the symmetry of this family of distributions.

[tex] \\ P(z<-a) = 1 - P(z<a) = P(z>a)[/tex]

For the case presented here, we have

[tex] \\ P(z<-0.36) = 1 - P(z<0.36) = P(z>0.36)[/tex]

[tex] \\ P(z<-0.36) = 1 - 0.6406 = P(z>0.36)[/tex]

[tex] \\ P(z<-0.36) = 0.3594 = P(z>0.36)[/tex]

Which is the same probability obtained in the previous step.

The graph below shows the shaded area for the probability of  [tex] \\ P(x<85)[/tex] finally obtained.  

Final answer:

To find P(x<85), calculate the z-score and use the standard normal distribution to find the cumulative probability. Susan's z-score for her final exam is 2, meaning her performance was significantly above the average. The central limit theorem helps to analyze the mean of large sample sizes, while binomial distributions apply to scenarios such as analyzing a basketball player's field goal completion rate.

Explanation:

Finding Probability in a Normal Distribution

To find the probability P(x<85) when the number of points scored by each team in the NHL at the end of the season is normally distributed with a mean (μ) of 89 and a standard deviation (σ) of 11, we use the standard normal distribution. First, we calculate the z-score for x=85, which is the value for which we want to find the cumulative probability. The z-score is calculated using the formula z = (x - μ) / σ. Substituting the given values, we get z = (85 - 89) / 11 = -0.3636. Then we look up this z-score in the standard normal distribution table or use a calculator or software to find the cumulative probability associated with this z-score.

To express the number 13.7 in terms of the mean and standard deviation of the given data, you would use the formula for the z-score again.

If Susan's biology class has a mean final exam score of 85 and a standard deviation of 5, and Susan scored a 95 on her final exam, her z-score would be z = (95 - 85) / 5 = 2. This means Susan's score is 2 standard deviations above the mean, indicating she performed significantly better than the average student.

When dealing with sample sizes larger than one, the central limit theorem tells us that the sampling distribution of the sample mean will tend to be normal regardless of the shape of the population distribution, especially as the sample size increases (typically n > 30 is considered large enough). This is reflected in the examples involving the estimation of mean final exam scores and calculating probabilities with a sample size of 55.

The probability distribution question for the basketball player's shots would involve the binomial distribution, where the probability of success is given by the player's field goal completion rate. The mean and standard deviation for this binomial distribution can be calculated using the formulas for a binomial distribution.

Answer: Tanyia lives 18 miles away from the airport.

Step-by-step explanation: First, I took $3.25(initial fee) away from $25.40(starting amount) which equals $22.15. Then, I subtracted -$9.35(How much money Tanyia had after the taxi ride)from $22.15 which came out to $31.50. Lastly, I divided $31.50 by $1.75(cost per mile) which came out to 18.

Hope this helps!

Answer:

R = $ 40

Step-by-step explanation:

Answer:

$40 dollars

i ready