The graph of a linear function is shown on the coordinate grid.


What is the y-intercept of the graph of this function?



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The Graph Of A Linear Function Is Shown On The Coordinate Grid.What Is The Y-intercept Of The Graph Of

Answers

Answer 1

Answer:

[tex]\dfrac{4}{3}[/tex]

Step-by-step explanation:

We can find the y-intercept of this line by:

1) finding the slope using the given points

[tex]m = \dfrac{8-(-7)}{4-(5)}[/tex]

[tex]m = \dfrac{8+7}{4+5}[/tex]

[tex]m = \dfrac{15}{9}[/tex]

[tex]m=\dfrac{5}{3}[/tex]

2) forming an equation for the line using point slope form

[tex]y - b = m(x - a)[/tex]     where [tex](a,b)[/tex] is a point on the line

... using the point (4,8)

[tex]y - 8 = \frac{5}{3}(x - 4)[/tex]

3) plugging 0 in for x to get the y-intercept

[tex]y - 8 = \frac{5}{3}(0 - 4)[/tex]

[tex]y - 8 = \frac{5}{3}(-4)[/tex]

[tex]y = 8 -\frac{20}{3}[/tex]

[tex]y = \frac{24}{3} -\frac{20}{3}[/tex]

[tex]\boxed{y=\dfrac{4}{3}}[/tex]


Related Questions

Find the value of x in the following equation
3.6(2x+5)=7.2x+18

Answers

Answer
X = 1
Hope it helps

i need help with this question

Answers

The solution of the equation log(t - 3) = log(17 - 4t), is 4.

option A.

What is the solution of the equation?

To find the solution for the equation log(t - 3) = log(17 - 4t), we can use the properties of logarithms.

Step 1: Remove the logarithms on both sides.

Applying the property of logarithms that states log(a) = log(b) if and only if a = b, we can remove the logarithms from both sides of the equation:

t - 3 = 17 - 4t

Step 2: Add 4t to both sides.

Adding 4t to both sides of the equation to isolate the t term on one side:

t + 4t - 3 = 17

Step 3: Combine like terms.

Combining like terms on the left-hand side:

5t - 3 = 17

Step 4: Add 3 to both sides.

Adding 3 to both sides of the equation to isolate the t term:

5t - 3 + 3 = 17 + 3

5t = 20

Step 5: Divide by 5.

Dividing both sides of the equation by 5 to solve for t:

5t/5 = 20/5

t = 4

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Scientists measure a bacteria population and find that it is 10,000. Five days later, they
find that the population has doubled. Which function f could describe the bacteria
population d days after the scientists first measured it, assuming it grows exponentially?
A. f(d) 10,000. 2ª
B. f(d) = 10,000. (√2)ª
C. ƒ(d) = 10,000 • (-)ª
D. f(d) = 10,000.25d

Answers

The function that describes the bacteria population is f(d) = 10,000 * 2^(d/5). option A.

How to find that the population has doubled. Which function f could describe the bacteria

The function that could describe the bacteria population d days after the scientists first measured it, assuming it grows exponentially, is:

f(d) = 10,000 * 2^(d/5)

Here, the population is doubling every 5 days, which means that the growth rate is 100% in 5 days, or 20% per day. Using the formula for exponential growth, where N(t) is the population after t time units, N0 is the initial population, and r is the growth rate:

N(t) = N0 * (1 + r)^t

We can substitute N0 = 10,000, r = 0.2 (20% per day), and t = d/5 (since the population is doubling every 5 days) to get:

N(d) = 10,000 * (1 + 0.2)^(d/5)

Simplifying:

N(d) = 10,000 * 2^(d/5)

Therefore, the function that describes the bacteria population is f(d) = 10,000 * 2^(d/5), which is option A.

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If 55% of a number is 110 and 40% of the same number is 80, find 95% of that number.

Answers

Answer:

.40n = 80, so n = 200

.95 × 200 = 190

Answer:

190

Step-by-step explanation:

reply the foto I applied in the files place??

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The length of Route 4 is:

12 km + 11 km + 7 km + 12 km = 42 km.

What is the distance?

Distance refers to the amount of space between two objects or points. It is a measure of the length of the path traveled by an object or a person from one point to another. The most common units of distance are meters, kilometers, feet, miles, and yards.

To find the length of Route 4, we can add up the distances between each consecutive pair of bus stops:

Route 4: C-F-G-H-C

Distance(C-F) + Distance(F-G) + Distance(G-H) + Distance(H-C)

= 12 km + Distance(F-G) + Distance(G-H) + 12 km

We can see that Route 2 follows the same path from C to H, so the distance between G and H is the same on both routes.

Thus, Distance(G-H) = Distance(C-H) - Distance(C-G) = 12 km - 5 km = 7 km.

Similarly, we can see that Route 1 follows the same path from F to H, so the distance between F and G is the same on both routes.

Thus, Distance(F-G) = Distance(C-F) + Distance(C-D) + Distance(D-E) + Distance(E-F) - Distance(C-E) = 17 km - 6 km = 11 km.

Therefore, the length of Route 4 is:

12 km + 11 km + 7 km + 12 km = 42 km.

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you roll a 6-sided dice. what is the probability that you rolled a 5, given that the number rolled was greater than 3?

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The probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.

We need to find the probability that you rolled a 5, given that the number rolled was greater than 3. Let's break this down step by step:

1. Identify the total number of outcomes: Since it is a 6-sided dice, there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).

2. Determine the number of outcomes greater than 3: The outcomes greater than 3 are 4, 5, and 6. There are 3 possible outcomes that satisfy this condition.

3. Identify the number of outcomes that result in rolling a 5: There is only 1 outcome that results in rolling a 5.

4. Calculate the probability: To find the probability, divide the number of outcomes that result in rolling a 5 (1) by the total number of outcomes greater than 3 (3).

Probability = (Number of outcomes with a 5) / (Number of outcomes greater than 3) = 1/3

So, the probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.

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The probability that the number rolled was a 5, given that it was greater than 3, is [tex]$\frac{1}{3}$[/tex].

The number rolled was greater than 3, it must be either a 4, 5, or 6.

The probability that the number rolled was a 5, given that it was greater than 3.

Let [tex]$A$[/tex] be the event that the number rolled is a 5 and let [tex]$B$[/tex] be the event that the number rolled is greater than 3.

Then, we want to find. [tex]$P(A|B)$[/tex], the probability of [tex]$A$[/tex] given [tex]$B$[/tex].

By Bayes' theorem, we have:

Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

The risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately by conditioning it relative to their age, rather than simply assuming that the individual is typical of the population as a whole.

One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference.

The probabilities involved in the theorem may have different probability interpretations.

Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence.

Bayesian inference is fundamental to Bayesian statistics, being considered by one authority as; "to the theory of probability what Pythagoras's theorem is to geometry."

[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$[/tex]

[tex]$P(A) = \frac{1}{6}$[/tex], since there is only one way to roll a 5 on a 6-sided die.

[tex]$P(B) = \frac{3}{6} = \frac{1}{2}$[/tex], since there are three outcomes (4, 5, or 6) that satisfy. [tex]$B$[/tex], out of a total of six possible outcomes.

[tex]$P(B|A)$[/tex], the probability of rolling a number greater than 3, given that the number rolled is a 5, note that. [tex]$B$[/tex] is true only if the number rolled is a 4, 5, or 6.

Since there is only one way to roll a 5, and only one of these three outcomes satisfies. [tex]$A$[/tex], we have:

[tex]$P(B|A) = \frac{1}{1} = 1$[/tex]

Substituting these values into Bayes' theorem, we get:

[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{1 \cdot \frac{1}{6}}{\frac{1}{2}} = \frac{1}{3}$[/tex]

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There are only Ured counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3
7
The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6
13
Find the number of red counters and the number of green counters that were in the bag originally

Answers

Number of red counters in the original bag is 3, and the number of green counters is 7.

Let's use algebra to solve the problem. Let U be the number of red counters and G be the number of green counters originally in the bag.

From the first part of the problem, we know that

Probability (selecting a green counter) = G / (U + G) = 3/7

Solving for U in terms of G, we get

U = (7G - 3G) / 3 = 4G/3

So we know that there were 4G/3 red counters and G green counters in the bag originally. But since the number of counters must be a whole number, we can assume that there were 4R red counters and 3G green counters originally, where R and G are both integers and R + G is the total number of counters.

After adding 2 red and 3 green counters, the number of counters in the bag is now R + 2 + G + 3 = R + G + 5.

From the second part of the problem, we know that

P(selecting a green counter) = (G + 3) / (R + G + 5) = 6/13

Solving for R in terms of G, we get

R = (13G - 9G - 15) / 7 = 4G/7 - 15/7

Since R must be an integer, we can try different values of G to see if R is an integer. For example, if G = 7, then R = 3 and the total number of counters is 10.

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The given question is incomplete, the complete question is:

There are only U red counters and G green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7. The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13. Find the number of red counters and the number of green counters that were in the bag originally

Mariella works for $10 an hour. She works 8 hours a day and works a 5 day work week. How much does Mariella make in a month? How much does Mariella make a year?

Answers

She makes 400 in a month
She makes 4,800 a year
Ok so if she makes 10 an hour and she she works 8 hours on a 5 day schedule (that’s 80$ + 80+80+80+80 =480and multiple that by 30 (it 30 days in a month) it equals 2800 as the monthly salary. And you take 2800 and multiple by how many months we have (12) and you make 42000k a year

what is the 4th term/number of (a+b)^9, pascal’s triangle?

Answers

Step-by-step explanation:

hope this will help you Thanks

Use the medians to compare the lengths of the alligators from the two swamps

Answers

Comparing the medians, we can see that the median length of alligators in Swamp A and Swamp B is the same, which suggests that the two swamps may have similar populations of alligators in terms of length.

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.

To compare the lengths of the alligators from two different swamps using medians, we need to collect data on the lengths of alligators from each swamp. Then we can calculate the median length of alligators in each swamp and compare them.

Let's say we have collected the following data on the lengths of alligators from Swamp A and Swamp B:

Swamp A: 4 feet, 5 feet, 6 feet, 7 feet, 8 feet

Swamp B: 3 feet, 5 feet, 6 feet, 7 feet, 9 feet

To find the median length of alligators in Swamp A, we need to arrange the lengths in order from smallest to largest: 4, 5, 6, 7, 8. The middle value is 6, so the median length of alligators in Swamp A is 6 feet.

To find the median length of alligators in Swamp B, we also need to arrange the lengths in order from smallest to largest: 3, 5, 6, 7, 9. The middle value is also 6, so the median length of alligators in Swamp B is also 6 feet.

Comparing the medians, we can see that the median length of alligators in Swamp A and Swamp B is the same, which suggests that the two swamps may have similar populations of alligators in terms of length. However, it is important to note that this comparison is based only on the median length and not on the full distribution of alligator lengths, so it is possible that there are other differences between the two populations of alligators that are not captured by this comparison.

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HLEP me please with math

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For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

Explain about the scale factor:

On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.

Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.

From the diagram:

coordinate of A = (1,1)

coordinate of A' = (5,5)

Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'

Same applies with the coordinates of B, C and D.

Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

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Write the perimeter of each figure as a polynomial in standard form.

Answers

The perimeter of the rectangle is 16x + 2

What is the perimeter of a rectangle?

The perimeter of a rectangle is given by P = 2(L + B) where

L = length of rectangle and W = width of rectangle

Given the rectangle in the figure, we desire to find its perimeter. We proceed as follows.

We notice that its length and breadth are

L = 5x + 2 and W = 3x - 1

So, since the perimeter of the rectangle is P = 2(L + B), we substitute the values of the variables into the equation.

So, with

L = 5x + 2 and W = 3x - 1

We have that

P = 2(L + B)

= 2(5x + 2 + 3x - 1)

= 2(5x + 3x + 2 - 1)

= 2(8x + 1)

= 16x + 2

So, the perimeter is 16x + 2

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a client is receiving an iv solution of 2 grams of medication diluted in 100 ml of normal saline over a one hour time period. how many mg of medication is the client receiving per minute? (enter numeric value only. if rounding is required, round to the nearest whole number.)

Answers

The client will be receiving 1.67 ml of medication in one minute and it will have 0.334 g of medication per minute.

Here 2g  of medication is diluted with 100 ml of normal saline. So concentration of 1ml of normal saline would be,

Concentration of 1 ml = 2/100 = 0.02 g/ml

It is delivered over a period of 1 hour. So, the amount delivered per minute will be,

Amount per minute = Volume/ time = 100/60 = 1.67 ml

Amount of medication in 1.67 ml = Volume × Amount per ml

                                                     = 1.67 × 0.02 = 0.334 g

So 0.334 g of medication will be received per minute. So the rate will be 1.67 ml per minute.

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8.G.B.6
The better definition of squares is

Answers

A number multiplied by itself.

What is square?

In mathematics, a square is a number that is obtained by multiplying a number by itself. It is also a geometric shape with four equal sides and four right angles. The area of a square is calculated by multiplying the length of one of its sides by itself. The formula for calculating the area of a square is A = s^2, where A is the area and s is the length of one side.

Squares have many important applications in mathematics, including in algebra, geometry, trigonometry, and calculus. They are used in the Pythagorean theorem, which relates to the sides of a right triangle, and they are used to represent variables in algebraic equations. Squares are also important in geometry, where they are used to construct geometric shapes and to calculate their areas and perimeters.

The better definition of squares is:

A number multiplied by itself.

In mathematics, a square refers to the product of a number multiplied by itself. For example, the square of 4 is 16, because 4 multiplied by 4 equals 16. Squares have a variety of important applications in mathematics, including in geometry, algebra, and calculus.

While a result that has been proved to be true is sometimes referred to as a "square" in certain contexts, it is not the primary definition of the term. Similarly, a triangle with a right angle is referred to as a "right triangle" or a "right-angled triangle," but not a square.

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4. The radius of a cylinder is 3x-2 cm. The height of the cylinder is x +3 cm. What is the
surface area of the cylinder? Use the formula A=2x²+2xrh.
02x (3x2+10x-8)
O 27(12x+7x-2)
O 27(12x²-2x+13)
O 27(12x²-5x-2)

Answers

Answer:

D: 27(12x² - 5x - 2).

Step-by-step explanation:

The formula for the surface area of a cylinder is: A = 2πr² + 2πrh

Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:

A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)

A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)

A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π

A = 24πx² - 10πx - 4π

A = 2π(12x² - 5x - 2)

Therefore, the answer is option D: 27(12x² - 5x - 2).

Answer:

D

Step-by-step explanation:

What is the value of x? Only enter numerical values. ​​

Answers

Answer:

x=15

Step-by-step explanation:

. imagine you had a research question in which you wanted to compare a sample mean to the mean of a population. under these circumstances you would either do a z-test or a one-sample t-test. what key piece of information would be missing if you needed to do a one-sample t-test?

Answers

Sample size and sample standard deviation are the key information needed for a single-sample t-test.

 

In the event that you need to compare the test cruel with the populace cruel, and you perform a single-sample t-test rather than a z-test, the vital piece of data that will be lost is the populace standard deviation.

Within the z-test, the populace standard deviation is known and the standard mistake of the cruel is calculated utilizing the populace standard deviation.

In a single-sample t-test, the populace standard deviation is obscure, and the standard mistake of the cruel is evaluated from the test standard deviation. 

Therefore, sample size and sample standard deviation are the key information needed for a single-sample t-test. 

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X-y=-3 ordered pairs

Answers

The ordered pairs of the relation x - y = -3 is shown below

Listing the ordered pairs of the relation

To list some ordered pairs that satisfy the equation x - y = -3, we can choose any value of x and solve for y.

For example:

If x = 0, then y = 3. So one ordered pair is (0, 3).If x = 1, then y = 4. So another ordered pair is (1, 4).If x = -1, then y = 2. So another ordered pair is (-1, 2).If x = 2, then y = 5. So another ordered pair is (2, 5).If x = -2, then y = -1. So another ordered pair is (-2, -1).

We can continue to choose any value of x and find the corresponding value of y that satisfies the equation x - y = -3 to generate more ordered pairs.

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students in a statistics class are conducting a survey to estimate the mean number of hours each week that students at their college study. the students collect a random sample of 49 students. the mean of the sample is 12.2 hours. the standard deviation is 1.6 hours. what is the 95% confidence interval for the number of hours students in their college study?

Answers

We can say with 95% confidence that the true mean number of hours that students at the college study is between 11.76 and 12.64 hours per week.

What is confidence interval?

Based on a sampling from the population, a confidence interval is a range of values that is likely to include the real population parameter (such as the population mean). The confidence level, which is often stated as a percentage (e.g., 95%), expresses how confident we are in the interval.

The likelihood that a finding arose by accident or as a result of random variation in the data is referred to as statistical significance, on the other hand. In general, if a result is unlikely to have happened by chance, it is deemed statistically significant.

The 95% confidence interval is given as:

CI = X ± Zα/2 (σ/√n)

The critical value for 95% is 1.96.

Substituting the value:

CI = 12.2 ± 1.96 (1.6/√49)

CI = 12.2 ± 0.44

CI = (11.76, 12.64)

Hence, we can say with 95% confidence that the true mean number of hours that students at the college study is between 11.76 and 12.64 hours per week.

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help me please with this question what is 11/12 divided by 4

Answers

Answer:

[tex]\frac{11}{8}[/tex]

Step-by-step explanation:

[tex]\frac{11}{2}[/tex] ÷ 4 = [tex]\frac{11}{2}[/tex]  x [tex]\frac{1}{4}[/tex] = [tex]\frac{11}{8}[/tex]

So, the answer is [tex]\frac{11}{8}[/tex]

A clinical trial is performed to test a new drug designed to lower blood sugar levels. One hundred fifty participants are randomly assigned to take the new drug, and 150 participants are randomly assigned to take a placebo. After 6 months of treatment, blood sugar levels are measured and compared to the starting levels. For those who took the new drug, the blood sugar levels had a mean reduction of 25 points with a standard deviation of 3.1, while for those who took the placebo, the blood sugar levels showed a mean reduction of 18 points with a standard deviation of 2.8. Assuming the standard deviations are true for the entire population, calculate 90% confidence intervals and evaluate whether there is evidence the new drug is working.
The interval for the new drug is from 24.584 to 25.416 points.

The interval for the placebo is from 17.624 to 18.376 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is working.


The interval for the new drug is from 24.504 to 25.496 points. The interval for the placebo is from 17.552 to 18.448 points.

Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is working. The interval for the new drug is from 24.584 to 25.416 points. The interval for the placebo is from 17.624 to 18.376 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is not working.

The interval for the new drug is from 24.504 to 25.496 points. The interval for the placebo is from 17.552 to 18.448 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is not working.

Answers

Okay, here are the steps:

1) For the new drug group, the mean reduction is 25 points and standard deviation is 3.1.

To get the 90% CI, we calculate:

Mean ± (1.645 * SD)

= 25 ± (1.645 * 3.1)

= 24.584 to 25.416

2) For the placebo group, the mean reduction is 18 points and standard deviation is 2.8.

To get the 90% CI, we calculate:

Mean ± (1.645 * SD)

= 18 ± (1.645 * 2.8)

= 17.624 to 18.376

3) Since the CI for the new drug (24.584 to 25.416) lies above the CI for the placebo (17.624 to 18.376), there is evidence that the drug is working.

The other options are incorrect. The CI for the new drug does not lie below the placebo CI, so there is evidence the drug is working, not not working.

Thekey is to compare the CI ranges for the two groups. If the CI range for the new drug group lies above the CI range for the placebo group, that indicates the new drug is likely more effective in reducing blood sugar levels, providing evidence that the drug is working.

Does this help explain the steps? Let me know if you have any other questions!

angles of triangles- does anyone know how to do this?

Answers

(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)

(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)

(3) m∠1= 152°-115°=37°

(4) m∠1=88°m∠2=42° m∠3=113°

What is an angle?

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.

Define triangle?

A triangle is a closed two-dimensional shape with three straight sides and three angles.

(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)

(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)

(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)

(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)

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A seed company planted a floral mosaic of a national flag the perimeter of the flag is 2220 feet determine the flags width and length if the length is 450 feet greater than the width

Answers

A seed company planted a floral mosaic of a national flag the perimeter of the flag is 2220 feet determine the flags width and length if the length is 450 feet greater than the width

The width of the flag is 330 feet and the length is 780 feet.

What is width?.

Width refers to the measurement or extent of something from side to side, typically in reference to its distance between its two opposite edges or boundaries. It is one of the two dimensions of a two-dimensional object or the distance between opposite sides of a three-dimensional object. In other words, width is the measurement of the distance between the left and right edges of an object or shap

Let's assume that the width of the flag is x feet.

As per the given information, the length of the flag is 450 feet greater than the width. Therefore, the length of the flag will be:

length = x + 450 feet

The perimeter of the flag is given as 2220 feet.

Perimeter of the flag = 2(length + width)

Substituting the values of length and width in the above equation, we get:

2220 = 2[(x + 450) + x]

Simplifying the above equation, we get:

2220 = 4x + 900

Subtracting 900 from both sides of the equation, we get:

1320 = 4x

Dividing both sides of the equation by 4, we get:

x = 330

Therefore, the width of the flag is 330 feet.

Using the length equation we derived earlier, we can find the length of the flag:

length = x + 450 = 330 + 450 = 780 feet

So the width of the flag is 330 feet and the length is 780 feet.

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your friend is bringing half of a crate of popsicles to the picnic. of you put what is left in the crate evenly into 6 ice buckets, what fraction of the crate will go into each of ice bucket​

Answers

The fraction of crate that will fit in each ice bucket is therefore determined to be - 1/12.

Describe the fraction in detail:

A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, at which numerator and the denominator are divided.

In a simple fraction, both are integers. In a complex fraction, a fraction can be found in either the numerator or the denominator.Proper fractions are those whose numerator is less than their denominator. The fraction is deemed improper when the numerator above the denominator.

data provided

proportion of the friend's crate is equal to half.There are six ice buckets in total.

The number of ice buckets / proportion of crate in each bucket equals fraction of crate provided by friend.

crate fraction in each bucket equals (1/2) / 6

Each bucket's fraction of the crate is 1 / (2*6).

Each bucket's percentage of the crate is 1/12.

The amount of crate that will fit in each ice bucket is therefore determined to be - 1/12.

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c. what is the probability that the duration of a rainfall event at this location is between 2 and 3 hours? d. what is the probability that a rainfall duration exceeds the mean value by more than 2 standard deviations?

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The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.

a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:

P(X ≥ 2) = [tex]e^{(-λ2) }= e^{(-1/2.7252)[/tex] ≈ 0.4800

P(X ≤ 3) = 1 - [tex]e^{(-λ3)} = 1 - e^{(-1/2.7253)[/tex] ≈ 0.6674

P(2 ≤ X ≤ 3) = [tex]e^{(-λ2)} - e^{(-λ3)} = e^{(-1/2.7252)} - e^{(-1/2.7253)}[/tex] ≈ 0.1474

b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:

P(X > 5.45) =[tex]e^{(-λ5.45)} = e^{(-1/2.7255.45)}[/tex] ≈ 0.0498

Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.

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Complete Question:

Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.

a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)

b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)

g fit the logistic regression model to predict diabetic status based on age and glucose levels. what is the odds of ratio of being diabetic for older adults compared to adults while controlling for glucose levels? round your answer to 0.01.

Answers

To calculate the odds ratio of being diabetic for older adults compared to adults while controlling for glucose levels in a logistic regression model, we exponentiate the coefficient estimate for Age. For example, if the estimate is 0.05, the odds ratio is 1.65.

To obtain the odds ratio for older adults compared to adults while controlling for glucose levels in a logistic regression model predicting diabetic status based on age and glucose levels, we would need to look at the coefficient estimate for the age variable. Let's say the logistic regression model is

logit(P(Diabetic)) = β_0 + β_1Age + β_2Glucose

where P(Diabetic) is the probability of being diabetic, Age is the age in years, and Glucose is the glucose level in mg/dL. β_1 represents the coefficient estimate for Age.

To calculate the odds ratio for older adults (e.g., those who are 10 years older than the average age in the sample) compared to adults while controlling for glucose levels, we can exponentiate the coefficient estimate for Age and round to 0.01. That is

OR = exp(β_1*10)

For example, if the coefficient estimate for Age is 0.05, then:

OR = exp(0.05*10) = 1.65

This means that for every 10-year increase in age, the odds of being diabetic compared to non-diabetic increase by a factor of 1.65 while holding glucose levels constant.

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To celebrate the first day of school, Grace brought in a tray of caramel brownies and walnut brownies. She brought 80 brownies in all. 56 of the brownies were caramel. What percentage of the brownies were caramel?

Answers

Answer: 70% of the brownies are caramel.

Step-by-step explanation: First take 56/80 because 56 of the brownies were caramel out of the 80. Which divided that give you 0.7. Multiply then by 100 which will give you 70. So the answer is there are 70% caramel brownies.

The Olympic record for the men's 50-meter freestyle is 21.91 seconds. Express this speed in meters per second

Answers

Answer:

50 meters/21.91 seconds = 2.282 m/sec

Which one is bigger three years or 30 months??

Answers

3 years is 36 months, so 3 years is bigger

The value of a ratio is ______

A. The sum of the two quantities in the ratio.

B. The quotient of the two quantities in the ratio.

C. The difference of the two quantities in the ratio.

D. The product of the two quantities in the ratio.​

Answers

Answer:

B. The quotient of the two quantities in the ratio.

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