Find the lengths of line segment
GJ.

a. The population function that shows a growth of 70 people per year is P(t) = 1650 + 70t

b. The population function that shows an annual growth rate of 3% is

P(n) = 1650 * (1 + 0.03)ⁿ

c. The population function that shows a shrinkage of 50 people per annum is P(t) = 1650 - 50t

d. The population function that shows an annual shrinkage rate of 8% per annum is P(n) = 1650 * (1 - 0.08)ⁿ

a. In this case, where the town grows by 70 people a year, we can represent the population as a linear function of time:

P(t) = 1650 + 70t

b. When the town grows at an annual rate of 3 percent, we can express the population using exponential growth:

P(n) = 1650 * (1 + 0.03)ⁿ

c. If the town shrinks by 50 people each year, we can represent the population as a linear function of time:

P(t) = 1650 - 50t

d. When the town shrinks at an annual rate of 8 percent, we can express the population using exponential decay:

P(n) = 1650 * (1 - 0.08)ⁿ

In each case, "P(t) or P(n)" represents the population of the town after "t" or "n" years, starting with an initial population of 1650 people. The formulas provide different models for how the population changes over time based on the given conditions.

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The degree measure of the largest angle is 72° in the triangle.

We have, The sum of two angles of a triangle is 6/5 of a right angle.

One of these two angles is 30° larger than the other.

Let A and B be the two angles of the triangle such that A = B + 30°.

We know that the sum of three angles in a triangle is 180°.

⇒ A + B + C = 180°

⇒ B + 30° + B + C = 180°

⇒ 2B + C = 150°

We also know that the sum of two angles of a triangle is 6/5 of a right angle.

⇒ A + B = 6/5 × 90°

⇒ B + 30° + B = 108°

⇒ 2B = 78°

⇒ B = 39°

C = 150° - 2B ⇒ 72°

A = B + 30° ⇒ 39° + 30° ⇒ 69°

Therefore, the degree measure of the largest angle in the triangle is 72°.

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With the Application of normal distribution conclusion can be All students missed at least one day of school per semester

what is normal distribution?

The normal distribution is a type of probability function that describes the distribution of a variable's values. Since most of the observations cluster around the middle peak of the curve, it is symmetric. When values of the distribution are far from the mean, the probability for those values narrow off evenly in both directions.

solution:

mean - ( standard deviation ) = 4 - 1 = 3

All students missed at least one day of school per semester

Therefore,  conclusion can be All students missed at least one day of school per semester

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Morgan will need approximately 9.82 square feet of fabric to cover the cushions.

To find the total square footage of fabric needed to cover the cushions, we first need to calculate the area of each circular cushion and then multiply it by the number of cushions.

The formula for the area of a circle is A = πr², where A is the area and r is the radius. However, we don't have the radius directly, only the circumference.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Rearranging this equation, we can find the radius in terms of the circumference: r = C / (2π).

Let's calculate the radius of each cushion using the given circumference:

C = 7.85 feet

r = C / (2π) = 7.85 / (2 × 3.14) ≈ 1.25 feet

Now we can calculate the area of each cushion:

A = πr² = 3.14× (1.25)² ≈ 4.91 square feet

Since there are two cushions, we need to double this area:

Total area needed = 2 × 4.91 square feet = 9.82 square feet

Therefore, Morgan will need approximately 9.82 square feet of fabric to cover the cushions.

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A distribution is a way of displaying data, consisting of three primary components: shape, center, and spread. The shape is the overall pattern of the distribution, while the center is the point where the distribution is balanced. The spread is the range of values of the data, often measured by the standard deviation or the interquartile range (IQR). The distribution can be visualized through graphs like histograms, box plots, or scatter plots.

A brief description of a distribution should include its shape, center, and spread. The spread is the term that should be included in the blank space.A distribution can be described as a way of displaying data. It gives us an idea about how the data are spread out.

The three primary components of any distribution are the shape, center, and spread. Shape refers to the overall pattern of the distribution. It tells us whether the data are symmetric or skewed. The symmetry means that the left half of the distribution is a mirror image of the right half, whereas a skewed distribution is not symmetrical. The tail of a distribution describes the spread of a skewed distribution. It refers to the parts of the distribution that extend out from the center of the graph.The center refers to the point where the distribution is balanced. In symmetric distributions, the center is the same as the mean and median. However, in a skewed distribution, the mean and median differ from each other.

The spread refers to the range of values of the data. It tells us how much the data are scattered or spread out. A small spread indicates that the data points are close to each other, while a large spread suggests that the data points are far from each other. It is often measured by the standard deviation or the interquartile range (IQR).The distribution of data can be visualized through different graphs like histograms, box plots, or scatter plots.

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Answer:

  1260 W

Step-by-step explanation:

You want the power supplied by a 300 V source at a current of 4.2 amperes.

The source power being supplied is the product of its voltage and current:

  P = VI

  P = (300 V)(4.2 A) = 1260 W

The circuit is consuming 1260 watts.

The price of the turkey based on the percentage given is $15.81.

It was stated that the cost is $15.50 but that there was a 2% increment in price.

Therefore, the new price will be:

= $15.50 + (2% × $15.50)

= $15.50 + $0.31

= $15.81

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Answer:

94.8

Step-by-step explanation:

sin 45 = 67/x

x = 67/sin 45

x = 94.8

Answer:

Step-by-step explanation:

85/1000 because we said that 1 meter = 1000 mililiters

Divide both sides by 5 and then you have 17/200

then divide both sides by 2 (to get it over 100) =

8.5/100

.085%

Hope that helps!!

You could also just do 85/1000 you would get the same answer!!

The common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y) is 5y + 6.

The Latin word "nomen," which also appears in words like "nominate" and "nomenclature," is the root of the English word "denominator," which means "name." And that's essentially what a fraction's denominator does: it "names" or denotes the kind of fraction that is specified by the numerator (the top part).

step1

{y + [(y - 3)/3]}/(5/9 + 2/3y)

multiply and divide with ‘9y'

9y/9y.{y + [(y - 3)/3]}/(5/9 + 2/3y)

9y.y + 9y.y - 3/3 / 9y(5/9) + 9y(2/3y)

9y.y + 3y(y - 3) / 9y(5/9) + 9y(2/3y)

9y.y + 3y(y - 3) / y.5 + 9y.2/3y

9y2 +3y2 -9y / 5y +6

12y2 - 9y / 5y + 6

The denominator will be 5y + 6

step2

The common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y) is 5y + 6.

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The area, in square inches, of the larger triangle is 12.

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Answer:

C. Supplementary Angles

One way to remember that is that C is the top half of S and Complementary Angles =90 and Supplementary angles =180. 90 is one half of 90

Answer: 36

Step-by-step explanation:

5x + 10y = 720

y=1/2x

tens = 36

Answer:

x = 11.2

Step-by-step explanation:

hypotenuse = 8.4 (radius) + 5.6 = 14  

using the Pythagorean theorem:

x² = 14² - 8.4² = 196 - 70.56 =125.44

x = √125.44 = 11.2

Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

60 percent

:) will be chocolate chip!

(My favorite!)

Answer:

60%

Step-by-step explanation:

if 6 out of the 10 cookies are chocolate chip than the fraction. would be 6/10 6/10 as a percent is 60% hope this helps

Answer:

y= 32x

Step-by-step explanation:

Use slope formula

192-128/6-4= 64/2

M=32x

Find y-intercept (if any)

128=32(4)+b

128=128+b

B=0

Answer:

-3(14+x)

Step-by-step explanation:

Notice that in the given graph in the interval (2), as x increases, y is not increasing nor it is decreasing, therefore the graph of the function is constant.

Answer: Option C. The graph of the function is constant.

Answer:

Step-by-step explanation:

Given

Initial deposit (Principal)= $250

Rate = 2%

Time = 1year (annual interest)

Required

Amount after 1 year

First we need to calculate interest

Interest = PRT/100

Interest = 250*2*1/100

Interest 2.5 * 2

Interest = $5.0

Next is to calculate amount;

Amount = Principal + Interest

Amount = $250 + $5

Amount = $255

Hence the value of a savings account at the Owl Credit Union at Dundalk High School that has an initial  deposit of $250 and pays an annual interest rate of 2% is $255.

Amount = P + I

Value of savings account is $255

Given that:

Initial deposit = $250

Annual interest rate = 2% = 0.02

Find:

Equations represents value of savings account

Computation:

Equations represents value of savings account = P + PRT

Equations represents value of savings account = 250 + (250)(0.02)(1)

Equations represents value of savings account = 250 + 5

Equations represents value of savings account = $255

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The requried translation used to create the image is 8 units to the left.

To determine the translation used to create the image, we need to compare the corresponding vertices of the two polygons.

First, we can plot the vertices of the original polygon ABCD and the new polygon A' B' C' D' on the coordinate plane,

We can see that the new polygon A' B' C' D' is a translation of the original polygon ABCD. The corresponding vertices are:

A' is 8 units to the left from A

B' is 8 units to the left from B

C' is 8 units to the left from C

D' is 8 units to the left from D

Therefore, the translation used to create the image is 8 units to the left.

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Answer:

3.19

Step-by-step explanation:

815,000 in 10 years

To find the population of a city after a certain number of years, we can use the following formula:

Population after n years = Population after 0 years × (1 + growth rate)^n

In this case, the population at year 0 (current population) is 500,000, the growth rate is 50/1000 = 0.05 (because the rate is given as 50 per 1000 people), and n is the number of years (10 in this case). Substituting these values ​​into the formula gives:

Population in 10 years = 500,000 × (1 + 0.05)^10 = 500,000 × 1.63 = 815,000

So, if the population of the city continues to grow at a rate of 50 people per 1000 people per year, it will be about 815,000 in 10 years.

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B. the proportion of the variation of the dependent variable explained by the independent variable. R^2, also known as the coefficient of determination, measures the goodness of fit of a regression model.

It represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. In other words, R^2 indicates how well the independent variable(s) account for the observed variation in the dependent variable. The correct answer, choice B, states that R^2 represents the proportion of the variation of the dependent variable explained by the independent variable.

It quantifies the strength of the relationship between the independent and dependent variables and provides an assessment of how well the regression model fits the observed data. A higher R^2 value indicates a better fit, as it indicates that a larger proportion of the variation in the dependent variable can be attributed to the independent variable(s).

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Answer:

Step-by-step explanation:

-0.92 2.49

-5.62 9.76

Rise = 9.76 - 2,49 = 7.27

Run: -5.62 - (-0.92) = -4.7

Slope (Rise/Run) = (7.27.`-0.92) = -1.55

The line has the form:

y = 1.55x + b

We need to find a value of b that forces the line through both point, Use one of the points and solve for b. I'll use (-0.92, 2.49).

y = 1.55x + b

2.49 = 1.55(-0.92) + b

b = 2.49 - 1.426 = 1.064

The equation is y = 1.55x + 1.0

Answer:

the answer is 7,21

Step-by-step explanation: