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Find the point of intersection using substitution. DO NOT USE ANOTHER METHOD. Show all your thinking.

Answer:B. A horizontal cross section through the center of a cone with a radius of 4 and a height of 4 in.

Step-by-step explanation:

Answer:

x = 40

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

65 + 75 + x = 180

140 + x = 180 ( subtract 140 from both sides )

x = 40

Answer: x = 40

Step-by-step explanation:

In a triangle, all the angles add up to 180 degrees.

In this case, 65 + 75 + x = 180.

Add the 65 and 75 together using column addition:

65

+75

-------

140

Now, the equation is 140 + x = 180

Subtract 140 from both sides:

x = 40

Therefore, x is 40.

a) Pea's journey takes 2.25 hours.

b) Sam spends 0.25 hours longer driving than Pea.

a. To find Pea's journey time, we use the formula:

time = distance / speed

Substituting the values given, we get:

time = 180 km / 80 km/h

time = 2.25 hours

b. To find how much longer Sam spends driving than Pea, we can subtract the journey times.

time taken by Sam = distance / speed = 200 km / 80 km/h = 2.5 hours

Time difference = Sam's journey time - Pea's journey time = 2.5 hours - 2.25 hours = 0.25 hours

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Answer:

100% because it goes to zero which means 100% is decreased

The given statement "The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line" is true because it provides the best fit line.

The simple linear regression equation estimates the relationship between two variables - a dependent variable (y) and an independent variable (x) - by fitting a straight line through the data points.

The line is chosen so that the sum of the squared deviations (also known as the sum of squared errors or SSE) between the observed values of y and the predicted values of y on the line is minimized.

In other words, the simple linear regression equation finds the line that is closest to all the data points in terms of the vertical distance between the points and the line.

This line is chosen to minimize the sum of squared deviations because it provides the best estimate of the relationship between x and y, and it allows for the prediction of y values for a given x value.

Thus, minimizing the sum of squared deviations is a crucial aspect of the simple linear regression equation because it ensures that the line of best fit provides the most accurate estimate of the relationship between the variables.

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Answer:

−18 x + 12

Step-by-step explanation:

multiply using the distributive property

Answer:

-2(9x-6)

-2 divided by 9x = - 18

-2 divided by - 6 = 12 (negative + negative =positive)

= - 18x +12

a.) The mode for the chart is 24.

b.) The probability that the winning score will be 25 = 7/50

C.)The probability that the winning score will be 23 or more = 37/50.

The number of times the game is played = 50 times

The number of games that showed the score of 25= 7

The probability of winning a score of 25 = 7/50

The scores that are 23 and above; 10+14+7+4+2= 37

The probability of winning a score of 23 and above = 37/50

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The median of 49 is the most accurate to use, since the data is skewed.

Distribution refers to the pattern of variation in a dataset. Specifically, it refers to how the values in the dataset are spread out or clustered together.

The most appropriate measure of center to represent the data depends on the shape of the distribution. In this case, we can see from the histogram that the data is skewed to the right, with a longer tail of higher values.

Therefore, the correct answer is: the median of 49 is the most accurate to use, since the data is skewed. This represents the middle value of the data when it is arranged in order, and is less sensitive to the outliers at the high end of the distribution. Using the median can give a more accurate representation of the typical donations received by the charity.

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Answer:

The time will be 1:00pm(13 hours) at which the degree Celsius will drop down to 8degrees Celsius since the temperature at 12noon was 10 degree Celsius and it is dropping at the rate of 2 degree Celsius.

a. According to the graph, Steven had saved about $100 after 2 weeks of school.

b. According to the graph, Steven probably had about $200 after 4 weeks of school because the graph shows that he saves an average of $50 per week, so after 4 weeks, he would have saved $50 x 4 = $200.

c. If Steven keeps saving at the same rate, he will have saved $350 by Week 7. This is because he saves $50 per week, so after 7 weeks, he will have saved $50 x 7 = $350.

A Zygote is/are formed immediately after the union of sperm and ovum in the fallopian tube.

A zygote is a cell formed when two gamete cells are fused by means of sexual reproduction. These cells contain a single set of chromosomes from both the father and the mother of the offspring. As a result, the zygote contains all of the genetic information required to create a completely new person. After the fertilization of the ovum by the sperm, the zygote is formed. The zygote will continue to divide into a multicellular embryo and eventually a fetus after fertilization has taken place.

The fusion of a sperm cell with an ovum in the fallopian tube leads to the formation of a zygote, which involves the combination of genetic material from both parents resulting in the creation of a single-celled zygote. This zygote then initiates the process of cell division and progresses into an embryo.

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The probability that all four cards drawn from a deck are black cards is 1/4165.

There are 26 black cards and 52 cards in a standard deck of cards. Therefore, the probability of drawing a black card from a standard deck of cards is 26/52 or 1/2. In the first draw, there are 26 black cards out of 52 cards, so the probability of drawing a black card is 26/52.

In the second draw, there are 25 black cards left out of 51 cards, so the probability of drawing a black card is 25/51. In the third draw, there are 24 black cards left out of 50 cards, so the probability of drawing a black card is 24/50. In the fourth draw, there are 23 black cards left out of 49 cards, so the probability of drawing a black card is 23/49.

Using the multiplication principle of probability, the probability that all four cards drawn from a deck are black cards is 26/52 × 25/51 × 24/50 × 23/49 = 1/4165.

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Therefore, the correct answer is:   [tex](x+10)^2=82[/tex]. ( right hand side of the equation).

An equation is a mathematical statement that indicates that two expressions are equal. It typically contains variables, which are represented by letters, and may also include constants and operators. The general format of an equation is:

expression = expression

For example, the equation x + 2 = 6 means that the expression x + 2 is equal to the expression 6. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

To solve the quadratic equation by completing the square, Jamie needs to follow the steps:

Move the constant term to the right-hand side of the equation:

[tex]x^2 + 20x = -18[/tex]

Add and subtract the square of half the coefficient of x to the left-hand side of the equation:

[tex]x^2 + 20x + (20/2)^2 - (20/2)^2 = -18[/tex]

[tex](x+10)^2 - 100 = -18[/tex]

Simplify the right-hand side of the equation:

[tex](x+10)^2 = 82[/tex]

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The two positive consecutive integers as required to be determined are; 3 and 4.

It follows from the task content that;

Let the positive consecutive Integers be; x and (x + 1).

Therefore, we have that;

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

x² + x = 4x + 2 - 2

x² - 3x = 0

x = 0 or x = 3.

Since the integers are positive, Therefore, the integers in discuss are 3 and 4.

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The additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes is 21.54 minutes (rounded to two decimal places).

Given that: Initial temperature of the liquid, T₁ = 170°F.Final temperature of the liquid, T₂ = 35°F.Constant temperature of the freezer, T = 25°F.

Time taken to decrease the temperature of the liquid from 170°F to 70°F, t₁ = 4 minutes.

The rate of change of temperature, R = (T₁ - T) / t₁ = (170°F - 25°F) / 4 minutes = 111.25°F/minute.

In the freezer, the rate of change of temperature is constant. Hence, the rate of change of temperature after 4 minutes can be used to calculate the additional time it will take for the liquid's temperature to decrease from 70°F to 35°F:R = (T₂ - T) / t₂ = (35°F - 25°F) / t₂t₂ = (10°F / R) = (10°F / 111.25°F/minute) = 0.089728 minutes ≈ 5.38 seconds.

Adding this time to the initial 4 minutes, we have the additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes: t = t₁ + t₂ = 4 minutes + 0.089728 minutes ≈ 4.089728 minutes or 4 minutes 5.38 seconds.

The additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes is 21.54 minutes (rounded to two decimal places).

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An access control list (ACL) specifies which subjects and objects users or groups can access.

An Access Control List (ACL) is a term used to describe a security mechanism that regulates who has access to an object in a computing system. An Access Control List (ACL) is a type of file that contains the names of people or groups of individuals who are allowed or denied access to a system resource.

ACLs are one of the most widely used security measures in computer networks today, and they are used to establish access control policies for network resources such as files, folders, devices, or services. This list is compiled on the basis of the requirements and policies of the security team in place.
The access control list (ACL) is a security feature that allows administrators to define and manage the permissions and rights for different users or groups to access specific resources, such as files, directories, or applications. Implementing an ACL helps to ensure proper security and privacy in a system or network.

The access control list (ACL) is correct in the blanks.

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Examining the figures of the circles, the values for x is calculated to be

11. x = 8

12. ED = 11

The value of x in the two figure is solved using the relationship between secant and angle measures

11. The formula used here is

(2x + 7) = 0.5 * (78 - 32)

(2x + 7) = 0.5 * (46)

2x + 7 = 23

solving for x

2x = 23 - 7

2x = 16

x = 8

12.

11x - 9 = 0.5 ( (15x-39) - (9x-3) )

11x - 9 = 0.5 ( 15x - 39 - 9x + 3 )

11x - 9 = 0.5 ( 6x - 36 )

11x - 9 = 3x - 18

11x + 3x = -18 + 9

14x = -9

x = 14/9 = 1.56

solving for

ED = 9x - 3 = 9 * 14/9 - 3 = 14 - 3 = 11

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The slope of the line parallel to the function: y = 50 - 0.5x include the following: C. -0.5.

In Mathematics and Geometry, parallel lines simply refers to two (2) lines that are always the same or equal distance apart and never meet.

Generally speaking, two (2) lines are considered as parallel under the following standard conditions:

Slope, m₁ = Slope, m₂.

From the function, we have:

y = 50 - 0.5x

Slope, m = -0.5

In this context, we can reasonably infer and logically deduce that the slope of the two lines would be equal and the same:

Slope of line 1 = Slope of line 2

-0.5 = -0.5

In conclusion, we can logically deduce that the slope of the given line is equal to -0.5.

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Confidence intervals provide more information than hypothesis tests as they give an estimate of the parameter value as well as a range of plausible values, whereas hypothesis tests only give a decision about the null hypothesis.

To solve problems 3 and 4 in homework 2 by constructing confidence intervals about the parameters to be tested, rather than performing hypothesis testing, we need to take the following steps:

Step 1: Calculate the sample mean and sample standard deviation from the given data.

Step 2: Calculate the standard error (SE) using the formula: SE = σ / √n`,

where `σ` is the population standard deviation (if known), or the sample standard deviation (if population standard deviation is unknown)

and `n` is the sample size.

Step 3: Calculate the margin of error (ME) using the formula: `ME = z * SE`,

where `z` is the z-score corresponding to the desired level of confidence.

Step 4: Calculate the confidence interval (CI) using the formula: `CI = sample mean ± ME.

Step 5: Interpret the confidence interval in the context of the problem.

Statement: Do you get the same results as before.

No, we do not get the same results as before.

When we construct a confidence interval, we obtain a range of plausible values for the parameter with a certain level of confidence, whereas in hypothesis testing, we either reject or fail to reject the null hypothesis based on the sample data at a certain level of significance.

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The area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence. So the correct answer is d. 7 3/4.

When measuring the area of a shape, we are determining the amount of surface the shape takes up.

To calculate the area enclosed by each fence, we must multiply the length and width of each.

The area enclosed by the wood fence is

6 1/2 x 2 1/4 = 14 7/8 square yards,

and the area enclosed by the metal fence is

2 3/4 x 2 1/2 = 6 7/8 square yards.

To determine how many times greater the area enclosed by the wood fence is than the area enclosed by the metal fence, we must divide the area of the wood fence by the area of the metal fence:

14 7/8 / 6 7/8 = 7 3/4.

This means the area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence.

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The key features of the function are Base = 0.72, Rate = decrement and it decays

Given that

y = 3000 * (0.72)ˣ

The given equation is in the form of exponential decay:

Base: The base of the exponential function is the constant term that is being raised to a power. In this case, the base is 0.72.

Rate of change: The rate of change is the factor by which the function is being multiplied or divided as the input variable increases.

Since the base is less than 1, the function is decreasing as x increases. The rate of decrease is given by the base, which is 0.72.

Growth or decay: As the base is less than 1, the function is decreasing, which means it is a decay function.

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The property of the average of any two odd integers being odd is true for all integers.

This is because the sum of any two odd integers is always an even integer. For example, if we take any two odd integers, say 3 and 7, then the sum of these two is 10, an even integer. Therefore, the average of 3 and 7, which is (3 + 7)/2, is also an even integer, in this case, 5.

Since all even integers are divisible by 2, the average of any two odd integers must be an odd integer.

Therefore, the property is true for all integers.


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Answer: Inequality 1

Step-by-step explanation: Let's solve each inequality first.

4(2.8z+175 )>-26.6

let's distribute the 4.

4(2.8z)+4(175)

11.2z+700>-26.6

Now let's isolate the variable by subtracting 700 on each side.

11.2z>-726.6

Now let's divide both sides by 11.2

z>-64.875

Oh? This one already has 5 as a solution as 5 is more than -64.875!

Probability of the null hypothesis being true is greater than the significance level.

The probability that the null hypothesis is true depends on the significance level set before the hypothesis test. In this case, the significance level was set at 0.05 and the p-value obtained was 0.10. This means that the probability of the null hypothesis being true is greater than the significance level (0.10 > 0.05), so the null hypothesis cannot be rejected.

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The cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).

Thus, οptiοn D is cοrrect.

Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetry using the principles οf algebra.

The rectangle IJKL is fοrmed by cοnnecting the pοints I, J, K, and L in a clοckwise οr cοunterclοckwise manner. Since I and J have the same x-cοοrdinate and are οn οppοsite sides οf the x-axis, and L and K have the same y-cοοrdinate and are οn οppοsite sides οf the y-axis, it fοllοws that the diagοnals οf the rectangle IJKL intersect at the οrigin (0,0).

Therefοre, the cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).

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The annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches. 0.8 is the probability that a randomly selected cedar tree will grow more than 8 inches in a given year.

The annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches.

To find the probability that a randomly selected cedar tree will grow more than 8 inches in a given year, the following steps should be followed:

Calculate the range of increase in height of cedar trees:

The range of increase in height is

(12 - 7) = 5 inches.

Calculate the probability that a cedar tree will grow more than 8 inches:

P(X > 8) = (12 - 8) / 5 = 0.8

where X is the annual increase in height of a cedar tree.

Round the answer to four decimal places:

Therefore, the probability that a randomly selected cedar tree will grow more than 8 inches in a given year is 0.8000 or 0.8 (rounded to four decimal places).

Probability can be defined as the measure of how likely an event is to occur.

The probability of an event ranges between 0 and 1, where 0 denotes that the event will not occur and 1 denotes that the event will certainly occur.

If a random variable X has a uniform distribution over an interval (a, b), then the probability of X falling between two values c and d is given by:

P(c < X < d) = (d - c) / (b - a)

In this problem, the annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches.

Therefore, the probability that a randomly selected cedar tree will grow more than 8 inches in a given year is: P(X > 8) = (12 - 8) / (12 - 7) = 4 / 5 = 0.8 (rounded to four decimal places).

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Answer: Stocks

Step-by-step explanation: People mainly live on wim's so stocks at times can be unpredictable.

The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.

The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven. This is because the restaurant only sells nuggets in packs of five and seven. This means that if you wanted to order eleven nuggets, it would not be possible.

To explain this mathematically, eleven can be written as 5+5+1, 7+4, or 3+3+3+2. As none of these can be made with just five and seven packs of chicken nuggets, it is impossible to order eleven.

If the restaurant sold chicken nuggets in packs of three and seven, then it would be possible to order eleven nuggets (3+3+3+2).

In conclusion, the largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.

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1. The accumulated amount for the investment at CAPITEC is R36,750.

2. The accumulated amount for the investment at FNB is R33,480.

3. Lebo will earn more interest if she invests her money at Capitec than at FNB.

The accumulated amount for the investment at Capitec with a principal amount of R30,000 invested at a simple interest rate of 7.5% for 3 years can be calculated as follows:

[tex]= Principal + (Principal * Rate * Time)\\= R30,000 + (R30,000 * 0.075 * 3)\\= R30,000 + R6,750\\= R36,750[/tex]

The accumulated amount for the investment at FNB with a principal amount of R30,000 invested at a compound interest rate of 3.5% per annum for 3 years can be calculated using the compound interest formula:

[tex]= Principal * (1 + Rate)^Time\\= R30,000 * (1 + 0.035)^3\\= R30,000 * 1.116\\= R33,480[/tex]

Now, based on the calculations, the investment at Capitec will yield R36,750 after 3 years while the investment at FNB will yield R33,480 after 3 years. Therefore, Lebo will earn more interest if she invests her money at Capitec than at FNB.

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The given probability is 0.37 which is the probability of a supply container dropped from an aircraft by a parachute hitting a target. So the expected number of container drops needed to hit a target is approximately 2.7027.

       To find out the expected number of container drops needed to hit a target, we can use the formula given below;            

                      E(X) = (1/p) E(X)

                             = (1/0.37)E(X)

                             = 2.7027

          Thus, the expected number of container drops needed to hit a target is approximately 2.7027.

An expected value is a statistical concept that represents the theoretical average value of a random variable. It is represented as E(X).

            The expected value is calculated by multiplying each possible value of the random variable by its probability and then adding all of the products.

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