The slope-intercept form of the inequality is given as follows:
y-4≥-2x-6y ≥ -2x -6 + 4y ≥ -2x-2.What is the slope-intercept format of a function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.Hence the inequality for this problem is simplified as follows:
y-4≥-2x-6y ≥ -2x -6 + 4y ≥ -2x-2.More can be learned about slope-intercept at https://brainly.com/question/24808124
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HELPPPP
i need to have this doen by 9:17 am today pls help
im begging you
Answer:
[tex]26a - 10 = 2(13a - 5)[/tex]
Which of the following sets would have a graph with an open circle on 5 and a ray pointing left on the number line?
A. {x | x R, x < 5}
B.{x | x R, x > 5}
C.{x | x R, x ≤ 5}
{x | x ∈ R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.
What is an interval notation?In interval notation, the set {x | x R, x < 5} can be written as (-∞, 5). The symbol (-∞) represents negative infinity, which means all numbers less than any finite number.
So, the interval (-∞, 5) includes all real numbers less than 5, but does not include 5 itself.
To graph this set on a number line, we would draw an open circle at the point 5, because 5 is not included in the set. Then, we would draw a ray pointing to the left, because the set includes all numbers less than 5.
The ray extends indefinitely to the left, because there is no greatest number that is less than 5.
Therefore, the graph of the set {x | x R, x < 5} on a number line would have an open circle at 5 and a ray pointing to the left.
What does an open circle on a number line indicate?
An open circle on a number line indicates that the number is not included in the set.
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From the top of an 18-meter lighthouse, the angle of depression to sight a boat is 4°. What is the distance between the boat and the base of the lighthouse, to the nearest tenth?
ASAP TIMED
Step-by-step explanation:
The side opposite to the 4 degree angle is 18 m
The side adjacent the 4 degree angle is x
tan(4) = opposite / adjacent
adjacent = opposite / (tan(4))
adjacent = 18 / tan(4)
adjacent = 257.41
Help pls!
A scale drawing of a famous statue uses a scale factor of 250:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
O248.8 feet
O 250 feet
O251.2 feet
300 feet
In linear equation, The actual height of the statue is 300 feet.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
A scale factor of a famous statue uses a scale factor of 250:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
= 1.2 x 250
The actual height of the statue is 300 feet.
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Answer:(D) 300
Step-by-step explanation: the scale factor is 250:1 and the Hight of the drawing is 1.2 feet you need to multiply 1.2 by 250
1.2 x 250 = 300
what is the solution to 4x-5>_7
The provided assertion states that is the answer to a inequality 4x - 5 ≥ 7 is x ≥ 3.
What justifies an inequality?In mathematics, "inequality" refers to a connection between two formulas or numbers that is not identical to each other. As a result, disparity results from a lack of balance.
To solve 4x - 5 ≥ 7, we can isolate the variable x by adding 5 to both sides of the inequality:
4x - 5 + 5 ≥ 7 + 5
Simplifying:
4x ≥ 12
Next, we can isolate x by dividing both sides by 4:
4x/4 ≥ 12/4
Simplifying:
x ≥ 3
Therefore, the solution to the inequality 4x - 5 ≥ 7 is x ≥ 3.
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on a control chart, what separates common from assignable causes of variation? a. specification limits b. mean divided by standard deviation c. control limits d. production limits e. x-bar lines
On a control chart, Control limits separates common from assignable causes of variation option C.
Shewhart charts, after Walter A. Shewhart, are another name for control charts. It is a statistical process control tool that aids in tracking process advancements over time. For instance, hospital management decides to utilise a solution technique in order to shorten the time required to admit a patient.
The process flow diagram for how patients are admitted to the hospital is first created. The average amount of time it takes to admit a patient each day is then measured. Lastly, plot the process variables across time on a control chart.
This control chart's goals are to identify any "special" reasons of variation as well as to document any process improvements.
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A circle with radius of 2 cm sits inside a circle with of 4 cm
Answer:
Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.
Step-by-step explanation:
please
give brianliest
Answer: Area = 0
Step-by-step explanation:
((2*2)*3.14)-(4*3.14) = 0
PLEASE HELP ASAP!!!!!!!!!!!!!!
Rewrite each of the following expressions without using absolute value
1.|x-1| if x>1
2. |x-y| if x>y
3. |3-[tex]\sqrt{4}[/tex]
4. |4r -12| if r<3
5. |[tex]\sqrt{15} -5+1[/tex]
6. |4-[tex]\sqrt{7}[/tex]
7. |7m-56| if m<8
8. |z-7|-|z-9| if z<7
Answer:
1 4(3-r) or 12-4r
2. 7( 8-m) or 56-7m
3. -2
Step-by-step explanation:
1) |4r−12| , if r<3
|4r-12|
Factor out a 4
4|r-3|
|r-3| will be less than 0 since r is less than 3
So we can rewrite it as 3-r to remove the absolute value signs and make it positive
4 (3-r)
12 -4r
2. |7m–56| , if m<8
Factor out a 7
7| m-8|
|m-8| will be less than 0 since m is less than 8
So we can rewrite it as 8-m to remove the absolute value signs and make it positive
7( 8-m)
56-8m
3) |z−7|−|z−9| , if z<7
|z-7| will be less than 0 since z is less than 7 and |z-9| will be less than 0 since z is less than 7
So we can rewrite it as 7-z and 9-z to remove the absolute value signs and make it positive
7-z - (9-z)
Distribute the minus sign
7-z-9+z
-2
combined with a high tide on september 16, 2020 by how many feet did that storm surge submerge the lowest parts of pensacola beach? enter a number (no words) in the blank.
The steps to find the depth through which the storm submerges the lowest parts of the Pensacola Beach is given below.
How to solve for the feet that the storm submerges?As it has been given in the question, Pensacola beach is located 5-10 feet above sea level.
The ocean water rises upto 5.5 feet during a storm
Hence you need to add up the height of the highest tide on 16 September to 5.5 feet.
If the combined height of the highest tide and the storm tide is greater than 10 feet, then the whole Pensacola beach submerges.
You just subtract the combined height of the storm and the highest tide from the height of the beach.
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Portions of Pensacola Beach, a coastal community built on a barrier island, are located at 3 - 10 feet above sea level.
Hurricane Sally, which struck Pensacola on September 16, 2020 and brought a 5.5 foot storm.
Combined with a high tide on September 16,202, by how many feet did that storm surge submerge the lowest parts of Pensacola Beach? (Hint: use the information in question and change the date on the tidal chart to September 16, 2020) Now, compare your answers above, and think about how the type (pattern) and size of the tides differ for these two locations
The Sport Bat Corporation manufactures baseball bats for professional baseball teams. The company needs
capital to upgrade their equipment now that they are experiencing a good level of success. They look to borrow
$2 million to perform the upgrade. Explain how this need for capital will spread through the financial system.
The need for capital by the Sport Bat Corporation will spread through the financial system as it interacts with banks, investors, and the broader financial markets.
How the need for capital will spread throughout the system?When the Sport Bat Corporation needs to borrow $2 million to upgrade their equipment, they will likely seek a loan from a financial institution, such as a bank. The bank will evaluate the creditworthiness of the company and may require collateral or a personal guarantee before approving the loan.
Once the loan is approved, the bank will add the Sport Bat Corporation's loan to their portfolio of assets. The bank may choose to sell the loan to other investors, such as insurance companies or pension funds, to diversify their portfolio and manage risk.
These investors will then receive the interest payments on the loan as a source of income. The loan may be bundled together with other loans and sold as a package, called a securitization, to other investors in the financial markets, thus representing the spread of the loan throughout the financial system.
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Will ran around a track that was 1/4 of a mile long. He ran around the track 12 times. How many miles did Will run?
When Will ran around the track 12 times, he ran a total distance of 12 x 0.25 = 3 miles. The answer is 3 miles.
What is a lap?The lap is the total distance a runner has to cover to complete one full circuit of the track. Depending on the size of the track, the lap distance can vary.
In the case of Will, he ran a total of 12 laps of a track that was 1/4 of a mile long.
This means that he ran a total distance of 12 x 0.25 = 3 miles.
This is because 1/4 of a mile is equal to 0.25 miles.
The equation used to calculate the total distance run by Will is: Distance = Number of laps x Length of each lap.
This equation can be used to calculate the total distance run by any runner on any track of any length.
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a researcher wishes to test the hypothesis that the difference between two population means is zero. if the sample means are 106.4 and 99.2, the standard error of the difference is 6.1, and the critical value needed to reject the null hypothesis is 2.09, what should the researcher decide about the difference between the two populations means?
There is not enough evidence to suggest that the difference between the two population means is statistically significant at the 5% significance level.
To test the hypothesis that the difference between two population means is zero, the researcher can use a two-sample t-test. The test statistic is calculated as the difference between the sample means divided by the standard error of the difference.
In this case, the sample means are 106.4 and 99.2, and the standard error of the difference is 6.1. Therefore, the test statistic is (106.4 - 99.2) / 6.1 = 1.18.
To decide whether to reject the null hypothesis that the difference between the two population means is zero, the researcher needs to compare the test statistic to the critical value. The critical value needed to reject the null hypothesis at a 5% significance level with 2 degrees of freedom (n1 + n2 - 2 = 2) is 2.09.
Since the test statistic of 1.18 is less than the critical value of 2.09, the researcher fails to reject the null hypothesis.
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can anybody help me with this im kinda stumped
Answer:
C is the correct function.
outdoor equipment purchased 215 hydra insulated water bottles. the demand for the hydra water bottle is normally distributed with a mean of 150 and a standard deviation of 77. what is the probability that outdoor equipment will meet all of their demand?
The probability that outdoor equipment will meet all of their demand is 0.0478.
We are given that Outdoor equipment purchased 215 hydra insulated water bottles. The demand for the hydra water bottle is normally distributed with a mean of 150 and a standard deviation of 77.The formula for calculating the probability of demand can be given by: P(X ≤ 215)P(X ≤ 215) is the probability of selling all 215 water bottles.
It means that they will sell a maximum of 215 bottles. The probability of selling less than or equal to 215 bottles is calculated as: P(X ≤ 215)=P(Z ≤ (215 - 150)/77)=P(Z ≤ 0.844).
Therefore, P(X ≤ 215) = 0.8023P(X ≤ 215) = 0.8023P(X = 215) is calculated as: P(X = 215) = P(X ≤ 215) - P(X ≤ 214). Therefore, P(X = 215) = 0.8023 - P(Z ≤ (214.5 - 150)/77)= 0.8023 - 0.7545 = 0.0478.
Therefore, the probability that outdoor equipment will meet all of their demand is 0.0478.
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on the math portion of the sat the scores are roughly normal with a mean of 500 and a standard deviation of 100. between what two values do approximately 95% of scores lie?
The scores on the math portion of the SAT are roughly normally distributed, with a mean of 500 and a standard deviation of 100. Approximately 95% of scores lie within two standard deviations of the mean, which is between 300 and 700.
To calculate this, we need to know that 68% of scores lie within one standard deviation of the mean, and 95% of scores lie within two standard deviations of the mean. To calculate the two standard deviations from the mean, we must use the equation (x + 2σ) and (x - 2σ). The 'x' in this equation is the mean, and the 'σ' is the standard deviation. Plugging in the values, we get: (500 + 2(100)) = 700 and (500 - 2(100)) = 300. Therefore, approximately 95% of scores on the math portion of the SAT lie between 300 and 700.
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5. Janice is creating a design that is part of a logo consisting of a small and a large circle.
The diameter of the small circle is of the diameter of the large circle. The diameter of
the large circle is 27 centimeters. To the nearest tenth of a centimeter, what is the area
of the smaller circle?
27 cm
Answer: The area of the smaller circle is [tex]65.6cm^{2}[/tex].
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex], r is the radius.
1. Find out the diameter of the small circle.
[tex]\frac{1}{3}(27)= 9[/tex]
2) Find out the radius, r.
[tex]radius = \frac{diameter}{2} =\frac{9}{2} =4.5[/tex]
3) We plugin r = 4.5 into the formula to solve the area of the smaller circle.
[tex]A=\pi r^{2}=\pi (4.5)^{2} =65.6cm^{2}[/tex]
inspect the furnsale7 data set. what structure do these data appear to take? panel data time series cross sectional
The furnsale7 data set appears to take the form of a panel data structure.
Panel data is a type of longitudinal data that combines observations over multiple time periods for the same individual or group.
This type of data contains multiple observations for the same unit over time and provides valuable insight into changes that occur over time.
Panel data can provide valuable insights into long-term trends and changes in behavior or trends in a population. Panel data can also be used to study economic growth and development, market trends, and consumer behavior.
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what is the number of degrees of freedom associated with the appropriate t-test for testing to see if there is a difference between the mean number of lesions per leaf produced by the two strains?
The degrees of freedom associated with the t-test is [tex]n_1 + n_2[/tex] - 2. The t-distribution is used to calculate the p-value of the t-test. There is no significant difference between the mean number of lesions per leaf produced by the two strains.
The appropriate t-test for testing to see if there is a difference between the mean number of lesions per leaf produced by the two strains has [tex]n_1 + n_2[/tex] - 2 degrees of freedom.
Here, [tex]n_1[/tex] is the sample size of the first group and [tex]n_2[/tex] is the sample size of the second group. This t-test is a two-sample t-test where the samples are independent and normally distributed with equal variances.
The formula for the t-test is:
[tex]t = (x_1 - x_2) / (s \times \sqrt{(1/n_1 + 1/n_2))}[/tex]
Where [tex]x_1[/tex] and [tex]x_2[/tex] are the sample means of the two groups, s is the pooled standard deviation, and [tex]n_1[/tex] and [tex]n_2[/tex] are the sample sizes of the two groups.
The pooled standard deviation is calculated as:
s = [tex]\sqrt{((n_1 - 1) \times s_1^2 + (n_2 - 1) \times s_2^2)} / (n_1 + n_2 - 2)[/tex]
Where [tex]s_1[/tex] and [tex]s_2[/tex] are the sample standard deviations of the two groups.
The p-value is the probability of getting a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true. If the p-value is less than the significance level (usually 0.05), then the null hypothesis is rejected and it is concluded that there is a significant difference between the mean number of lesions per leaf produced by the two strains. Otherwise, the null hypothesis is not rejected.
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.96*.96a town has two fire engines operating indepen- dently. the probability that a specific engine is avail- able when needed is 0.96. (a) what is the probability that neither is available when needed? (b) what is the probability that a fire engine is avail- able when needed?
The probability that a specific fire engine is not available when needed is 0.04 (since the probability of it being available is 0.96).
The question asks for two probabilities related to the availability of fire engines in a town. The first part asks for the probability that neither engine is available when needed, and the second part asks for the probability that a fire engine is available when needed.
To calculate the probability that neither engine is available when needed, we need to use the multiplication rule for independent events. We know that the probability that one specific engine is not available when needed is 0.04 (1 - 0.96). Since the two engines operate independently, the probability that both are not available when needed is the product of their individual probabilities:
P(neither available) = P(engine 1 not available) * P(engine 2 not available)
P(neither available) = 0.04 * 0.04
P(neither available) = 0.0016
Therefore, the probability that neither fire engine is available when needed is 0.0016.
To calculate the probability that a fire engine is available when needed, we can simply use the given probability of 0.96:
P(available) = 0.96
Therefore, the probability that a fire engine is available when needed is 0.96.
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The speed of the ISS is 27,576 kilometres per hour.
The station travels 42,600 in 1 orbit
Work out the number of full orbits the station does in 1 day.
Answer:
15 Full orbits per day
Step-by-step explanation:
To work out the number of full orbits the ISS does in 1 day, we need to know how long it takes for the ISS to complete one orbit around the Earth.
We can use the information given to us to calculate the time it takes for the ISS to complete one orbit:
Distance traveled in one orbit = 42,600 kilometers
Speed of the ISS = 27,576 kilometers per hour
To calculate the time taken for one orbit:
Time taken = Distance traveled / Speed
Time taken = 42,600 kilometers / 27,576 kilometers per hour
Time taken = 1.54 hours (rounded to 2 decimal places)
So, the ISS takes approximately 1.54 hours to complete one orbit around the Earth.
Now, we can calculate the number of orbits the ISS does in one day:
Number of orbits per day = 24 hours / Time taken for one orbit
Number of orbits per day = 24 hours / 1.54 hours
Number of orbits per day = 15.58 (rounded to 2 decimal places)
Therefore, the ISS completes approximately 15 full orbits around the Earth in one day.
A self-serve car wash charges $5.96 to use its facilities, plus an additional $0.50 for each minute the customer is at the self-serve car wash. If Tiffany was at the car wash for 9 minutes, how much was she charged?
A.
$6.46
B.
$10.46
C.
$4.50
D.
$14.96
Lucas is making one dozen snacks for his team. He uses 1/4 cup of dried cherries and 2/4 of dried apricots for each snack. How many cups of dried fruit does Lucas need for his one dozen snacks
The total number of cups of dried fruit Lucas need for his one dozen snacks are 3 cups of dried cherries and 6 cups of dried apricots
Cups used of dried cherries = 1/4
Cups used of dried apricots = 2/4
An element of a number or any number of equal pieces is represented by a fraction. A fraction with a numerator and denominator exists.
Lucas is making one dozen snacks, which means the total number of snacks made is = 12.
Calculating the total amount of dried cherries -
= 1/4 cup/serving x 12 servings
= 3 cups of dried cherries
Similarly,
Calculating the total amount of dried apricots -
1/2 cup/serving x 12 servings
= 6 cups of dried apricots
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you need to have a password with 4 letters followed by 2 even digits between 0 and 9 , inclusive. if the characters and digits cannot be used more than once, how many choices do you have for your password?
There are 6,354,000 choices for the password.
To generate a password, you need to have 4 letters followed by 2 even digits between 0 and 9, inclusive.
If the characters and digits cannot be used more than once,
Solution: We have to find the number of choices of the password with given conditions.
To find the number of choices, let us follow the following steps:
Step 1: Choose the first letter in 26 ways
Step 2: Choose the second letter in 25 ways (excluding the letter that we have already chosen)
Step 3: Choose the third letter in 24 ways (excluding the 2 letters that we have already chosen)
Step 4: Choose the fourth letter in 23 ways (excluding the 3 letters that we have already chosen)
Step 5: Choose the first even digit in 5 ways (from 0, 2, 4, 6, and 8)
Step 6: Choose the second even digit in 4 ways (excluding the even digit that we have already chosen)
Therefore, the total number of choices for the password with the given conditions is given by:
Total number of choices = 26 × 25 × 24 × 23 × 5 × 4= 6,354,000.
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As shown below, Ghana makes a triangular decoration out of clay.
When she fires it in the kiln, it shrinks proportionally. If the base of the
finished decoration is only 9 inches after firing, what is the height, in inches,
of the finished decoration?
A
B
с
D
4
5
6
10 in.
8
15 in.
TIPS AND F
Check your answe
makes sense. Since
half of 15, the answ
more than half of 10
Answer:
Since the decoration is in the shape of a triangle, we can use the formula for the area of a triangle to solve for its height. The area of a triangle is given by:
Area = (1/2) x base x height
Let's call the height of the decoration h. We know that the base after firing is 9 inches, so we can plug in the given values and solve for h:
Area = (1/2) x 9 x h
Area = 4.5h
We don't know the exact area of the decoration, but we do know that the decoration maintains its shape after firing. This means that the ratio of the areas before and after firing is the same, and so is the ratio of the heights and bases. Since the height and base are proportional, we can write:
h / 15 = 9 / 10
Simplifying the equation, we get:
h = (9/10) x 15
h = 13.5
Therefore, the height of the finished decoration is 13.5 inches.
Tom
Sean
Darryl
Anne
0825
$300
$750
$1,300
$145
Return
7%
10%
EF
After One Year
A
C
156
10.5
The number that goes to column D is the total equity of $825.
Explain about the total equity?The sum that investors put in a firm in return for stock, plus all future profits realized by the company, less all future dividends paid out, is referred to as total equity.Any investment made by the business's owner counts as equity, as do the total assets less the total liabilities. To give just a few examples, consider common stock, extra special capital, preferred stock, interest income, and total other comprehensive income.Using annual rate of return APR:
A = P *[tex](1 + r/n)^{nt}[/tex]
P = $750.
r = 10%
t = 1 year
n = 1
A = 750 * [tex](1 + 0.1/1)^{1*1}[/tex]
A = 750 * 1.1
A = 825
Thus, the number that goes to column D is the total equity of $825.
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construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place. n=5, s=4.4, c=0.95
Therefore, the 95% confidence interval for the population standard deviation is approximately (2.6, 12.3).
To construct a 95% confidence interval for the population standard deviation, we will use the chi-square distribution. Here are the steps:
Step 1: Identify the given values.
n = 5 (sample size)
s = 4.4 (sample standard deviation)
c = 0.95 (confidence level)
Step 2: Find the degrees of freedom.
df = n - 1 = 5 - 1 = 4
Step 3: Find the chi-square values.
For a 95% confidence interval, we will use the values corresponding to 2.5% and 97.5% in the chi-square distribution table. For df = 4:
Chi-square (0.025) = 11.143
Chi-square (0.975) = 0.485
Step 4: Calculate the confidence interval for the population variance.
Lower limit:[tex] (n - 1) * s^2 / Chi-square (0.025) = 4 * (4.4)^2 / 11.143 = 6.960[/tex]
Upper limit:[tex] (n - 1) * s^2 / Chi-square (0.975) = 4 * (4.4)^2 / 0.485 = 151.977[/tex]
Step 5: Calculate the confidence interval for the population standard deviation by taking the square root of the variance limits.
Lower limit: [tex]√6.960 = 2.6[/tex]
Upper limit:[tex] √151.977 = 12.3[/tex]
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PLEASE HELP ME if you you thank you so much! I need all calculations to receive full credit
Answer:
The television tower is 132 feet high.
Step-by-step explanation:
Let h be the height of the television tower. Set up and solve this proportion.
[tex] \frac{3}{5} = \frac{h}{220} [/tex]
[tex]5h = 660[/tex]
[tex]h = 132[/tex]
A regular sized box of a certain cereal brand has dimensions of 2 inches by 6 inches by 11 inches and cost $3.99.
The family sized version has dimensions of 3 inches by 8 inches by 15 inches and cost $5.69.
A. How many more square inches of cardboard is needed for the family sized box than the regular sized box? Show your work.
B. How many more cubic inches of cereal fit in the family sized box than the regular sized box? Show your work.
C. Which cereal costs less per cubic inch of cereal? Show your work.
The family-sized box requires 130 more square inches of cardboard than the regular-sized box, has an additional 228 cubic inches of cereal capacity, and costs less per cubic inch of cereal.
According to the given data:To calculate the additional square inches of cardboard needed for the family-sized box, we need to find the difference in surface area between the regular-sized box and the family-sized box.
The regular-sized box has a surface area of 2 x 6 + 2 x 11 + 6 x 11 = 104 square inches.
The family-sized box has a surface area of 2 x 8 + 2 x 15 + 3 x 15 + 3 x 8 + 3 x 15 = 234 square inches.
Therefore, the additional square inches of cardboard needed for the family-sized box is 234 - 104 = 130 square inches.
B. To find how many more cubic inches of cereal fit in the family-sized box than the regular-sized box, we need to calculate the difference in volume between the two boxes.
The regular-sized box has a volume of 2 x 6 x 11 = 132 cubic inches.
The family-sized box has a volume of 3 x 8 x 15 = 360 cubic inches.
Therefore, the additional cubic inches of cereal that fit in the family-sized box is 360 - 132 = 228 cubic inches.
C. To determine which cereal costs less per cubic inch of cereal, we need to divide the cost of each box by its respective volume.
The regular-sized box costs $3.99 for 132 cubic inches of cereal, which gives us a cost of $0.03 per cubic inch.
The family-sized box costs $5.69 for 360 cubic inches of cereal, which gives us a cost of $0.02 per cubic inch.
Therefore, the family-sized box costs less per cubic inch of cereal.
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Please answer with explanation!
The extreme values of the function f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27 are minimum = 0 and maximum = 18
Calculating the extreme values of the functionGiven that
f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27
To find the extreme values of the function f(x, y, z) subject to the given constraint, we can use the method of Lagrange multipliers.
Defining the Lagrangian function L as follows:
L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z))
where g(x, y, z) is the constraint function and λ is the Lagrange multiplier.
In our case, we have:
f(x, y, z) = x^2 + y^2 + z^2
g(x, y, z) = x^2 + y^2 + z^2 + xy - 27
So, our Lagrangian function becomes:
L(x, y, z, λ) = x^2 + y^2 + z^2 - λ(x^2 + y^2 + z^2 + xy - 27)
To find the extreme values of f(x, y, z) subject to the constraint g(x, y, z) = 0, we need to solve the following system of equations:
∂L/∂x = 0
∂L/∂y = 0
∂L/∂z = 0
∂L/∂λ = 0
g(x, y, z) = 0
Taking the partial derivatives of L with respect to x, y, z, and λ, we get:
∂L/∂x = 2x - λ(2x + y) = 0
∂L/∂y = 2y - λ(2y + x) = 0
∂L/∂z = 2z - λz = 0
∂L/∂λ = x^2 + y^2 + z^2 + xy - 27 = 0
From the third equation, we get:
2z - λz = 0
z(2 - λ) = 0
So, either z = 0 or λ = 2.
If z = 0, then from the first two equations, we get:
2x - λy = 0
2y - λx = 0
Multiplying the first equation by y and the second equation by x, we get:
2xy - λy^2 = 0
2xy - λx^2 = 0
Subtracting the second equation from the first, we get:
λ(x^2 - y^2) = 0
Since λ cannot be zero, we have x^2 = y^2 and x = y
Similarly, if λ = 2, then from the first two equations, we get:
2x - 2y = 0
x = y
Substituting x = y into the constraint equation, we get:
2x^2 + x^2 = 27
x^2 = 9
x = ±3
So, the possible critical points are:
(3, 3, 0)
(-3, -3, 0)
(0, 0, 0)
Recall that
f(x, y, z) = x^2 + y^2 + z^2
So, we have
f(3, 3, 0) = 3^2 + 3^2 + 0^2 = 18
f(-3, -3, 0) = -3^2 + -3^2 + 0^2 = 18
f(0, 0, 0) = 0^2 + 0^2 + 0^2 = 0
Hence, the minimum is 0 and the maximum is 18
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DUE IN 5 HOURS HELP!
The graph below shows a company's profit f(x), in dollars, depending on the price of goods x, in dollars, being sold by the company:
Part A: What do the x-intercepts and maximum value of the graph represent in context of the described situation?
Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit for the company in the situation described?
Part C: What is an approximate average rate of change of the graph from x = 1 to x = 3, and what does this rate represent in context of the described situation?
Answer:
Step-by-step explanation:
Credits : sqdancefan (Brainly.com)
I changed some of it myself :)
Answer:
A) intercept: 0 profit : Maximum(max) : max profit. increasing x <4 ; decreasing x > 4
B) average slope: ≈50, about $50 increasing profit for each $1 increasing in price.
Step-by-step explanation:
A) The vertical axis of the graph represents profit, so the x-intercepts represent prices in the produce 0 profit. The maximum value of the graph is the maximum profit that can be obtained for anyprice
The higher or largest number of the chart is the maximum reach
B) We read the value of f(1) from the graph to be about 120, so the average rate of change is about ...
(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50
The average rate of the change from x = 1 to x = 4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in what interval.
______
* if we take the peak profit to be $270 we can write f(x) as ...
f(x) 16.875x(x-8)
Then f(1) = 118.15 ad average rate if changed is 50.625. For the purpose here, we judge the extra precision to be pointless