The answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7
What is the linear function?A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
According to the given information:The given plot displays the distribution of the number of roses purchased per day at a grocery store. The best measure of variability for this data would be the interquartile range (IQR) since it is robust to outliers and provides a measure of the spread of the middle 50% of the data.
To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
From the plot, we can see that there are a total of 11 data points: one at 1, two at 2, three at 6, three at 7, two at 8, and three at 9. The median (Q2) is 7 since it is the middle value when the data are arranged in order.
To find Q1, we need to find the median of the lower half of the data. Since there is one data point below 6 and three data points at 6, the lower half of the data consists of four points: 1, 2, 6, and 6. The median of this set is (1+2)/2 = 1.5.
To find Q3, we need to find the median of the upper half of the data. Since there are two data points at 8 and three data points at 9, the upper half of the data consists of five points: 8, 8, 9, 9, and 9. The median of this set is (8+9)/2 = 8.5.
Therefore, the IQR is Q3-Q1 = 8.5-1.5 = 7.
Therefore, the answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7
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We might choose to display data with a stemplot rather than a boxplot because a stem plot I. reveals the shape of the distribution.
II. is better for large datasets.
III. displays the actual data.
Statements I, II, and III are partially correct, but statement II needs to be corrected to indicate that stem plots are better for small to moderate-sized datasets.
We might choose to display data with a stem plot rather than a boxplot because:
Reveals the shape of the distribution.
Is better for small to moderate-sized datasets.
Displays the actual data.
A stem plot is a type of graph that shows the distribution of data by grouping the observations into stems and leaves.
It allows for the display of the actual data values, which is not possible in a boxplot.
Additionally, stem plots are particularly useful for small to moderate-sized datasets as they provide a detailed view of the distribution, allowing for the identification of patterns such as skewness, multimodality, and outliers.
On the other hand, boxplots are better for large datasets as they provide a more concise summary of the distribution, including information about the median, quartiles, and outliers, while still conveying information about the spread and shape of the distribution.
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yo can i get some help
Answer:
on what
Step-by-step explanation:
does the math term "mean," mean avarage of most common?
Answer: The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.
Step-by-step explanation: You can find the mean, or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.
Given that f(x)=x-9,g(x) = 3x^2- 2x + 5, and h(x)=-6x, find each function.
(f+h)(x)=
engineers designing the next generation of space shuttles plan to include two fuel pumps - one active, the other in reserve. if the primary pump malfunctions, the second is automatically brought on line. suppose a typical mission is expected to require that fuel be pumped for at most 50 hours. according to the manufacturer?s specifications, pumps are expected to fail once every 100 hours. what are the chances that such a fuel pump system would not remain functioning for the full 50 hours?
The probability that this particular fuel pump system when put into the required condition would not remain functional for the full 50 hours is 0.0199.
Therefore, the probability of a fuel pump failing in a mission can be evaluated using the formula designed for probability of failure in a system with two pumps in series connection
P(failure) = P(pump 1 fails) + P(pump 2 fails) - P(both pumps fail)
Here
P(pump 1 fails) = P(pump 2 fails) = 0.01
P(both pumps fail) = (0.01)² = 0.0001.
Now,
P(failure) = 0.01 + 0.01 - 0.0001 = 0.0199
The probability that this particular fuel pump system when put into the required condition would not remain functional for the full 50 hours is 0.0199.
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6PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
b. 8/17
Step-by-step explanation:
hope this helps ;)
Ashley and Nicole are at softball practice. Ashley hits a softball 65 meters. Nicole hits a soft ball 6,700 centimeters. who hit the softball farther, Ashley or Nicole
Answer: Ashley hit the softball farther.
Step-by-step explanation: Ashley hit the softball farther, since her distance of 65 meters is greater than Nicole's distance of 6,700 centimeters.To compare these distances, we need to convert Nicole's distance from centimeters to meters, since Ashley's distance is given in meters.To do this, we can divide Nicole's distance by 100, since there are 100 centimeters in a meter:6700 cm / 100 cm/m = 67 mTherefore, Ashley hit the softball 65 meters, which is less than the 67 meters that Nicole hit it. This means that Ashley hit the softball farther.
cupcake delight shop made 4 1/2 as much revenue on doughnuts as muffins. if total sales were 44,000 what dollar amount of each was sold?
The revenue from muffins was $8,000. To find the revenue from doughnuts: 4.5x = 4.5 * 8,000 = $36,000 Therefore, the cupcake delight shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.
Let's use the given terms and set up a system of equations to solve this problem:
Let x be the revenue from muffins, and y be the revenue from doughnuts. We know the following:
1. y = 4.5x (Cupcake Delight Shop made 4 1/2 times as much revenue on doughnuts as muffins)
2. x + y = 44,000 (Total sales were $44,000)
Now we'll solve the system of equations step-by-step:
Step 1: Replace y with 4.5x in the second equation (using equation 1):
x + 4.5x = 44,000
Step 2: Combine the x terms:
5.5x = 44,000
Step 3: Divide both sides by 5.5 to solve for x:
x = 8,000
Step 4: Plug x back into equation 1 to find y:
y = 4.5 * 8,000
y = 36,000
So, Cupcake Delight Shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.
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The dollar amount of muffins sold is $8,000, and the dollar amount of doughnuts sold is $36,000.
To solve this problem, let's assign variables to the revenue for doughnuts and muffins:
Let D = revenue from doughnuts
Let M = revenue from muffins
We are given that the shop made 4 1/2 times as much revenue on doughnuts as muffins:
D = 4.5M
We are also given that the total sales were $44,000:
D + M = 44,000
Now, we can solve for the dollar amount of each item sold:
Replace D with 4.5M in the second equation:
4.5M + M = 44,000
Combine like terms:
5.5M = 44,000
Divide by 5.5 to isolate M:
M = 44,000 / 5.5
M = 8,000
Plug the value of M back into the first equation to find the value of D:
D = 4.5M
D = 4.5 × 8,000
D = 36,000.
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Once chosen, a score, event, or participant CANNOT be returned to the population to be selected again. This technique is referred to as
a. random sampling without replacement.
b. random sampling with replacement.
c. stratified random sampling.
d. convenience sampling.
The technique being described is random sampling without replacement, which is option a.
This technique is called "sampling without replacement."
However, you've also mentioned convenience sampling, which is a different method.
Let me briefly explain both concepts.
Sampling without replacement is a method in which each item, score, event, or participant is chosen from the population and is not returned to the pool for further selections.
This ensures that each element can only be selected once, eliminating the chance of duplication in the sample.
This method is often used in surveys, experiments, and research to maintain the independence of observations and provide a more accurate representation of the population.
Select an item, score, event, or participant from the population.
Record the selected item and remove it from the population.
Repeat steps 1-2 until the desired sample size is obtained.
Convenience sampling, on the other hand, is a non-probability sampling method where researchers select participants based on their accessibility and ease of recruitment.
This approach may introduce bias and limit the generalizability of the study results, as it does not ensure that the sample is representative of the population.
Identify the target population.
Recruit participants who are easily accessible and willing to participate.
Collect data from the selected participants.
In summary, sampling without replacement is a technique that prevents the same item from being selected more than once, while convenience sampling is an approach that focuses on selecting participants based on their accessibility. Both methods serve different purposes in research and should be chosen based on the study's objectives and available resources.
Option a is correct.
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What is this? There should be a screenshot below.
Answer:
156
Step-by-step explanation:
Use the system of PEMDAS.
6*3 = 18
6*4 = 24
6*5 = 30
6*8 = 48
2[3*4+1/2(3*4)] = 36
Add all.
18+24+30+48+36 = 156
Eric puts several CDS in a case . four CDS are country, six are rap and ten are pop. if Eric picks one CD from the case without looking, what is the probability that he will pick a pop CD.
A 3/10
B 1/4
C 1/3
D 1/2
Answer:
There are a total of 4 + 6 + 10 = 20 CDs in the case. Eric has a 10/20 = 1/2 chance of picking a pop CD since there are 10 pop CDs in the case.
Therefore, the answer is D) 1/2.
Answer:
Step-by-step explanation:
Eric has a total of 4 + 6 + 10 = 20 CDs in the case.
The probability of picking a pop CD is the number of pop CDs divided by the total number of CDs:
P(pick a pop CD) = 10/20 = 1/2 = 0.5
Therefore, the probability of Eric picking a pop CD is 0.5 or 50%.
Question 2(Multiple Choice Worth 4 points)
(01.04 LC)
Given the linear functions f(x) = x -2 and g(x)=-3x + 4, determine (f- g)(x).
(f-g)(x) = -3x - 8
(f-g)(x)=-3x²-8
(f-g)(x) = -3x² + 10x - 8
(f-g)(x) = -3x² - 2x - 8
The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.
What is linear function?A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.
According to given information:To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).
The expression for (f - g)(x) can be found by subtracting g(x) from f(x):
(f - g)(x) = f(x) - g(x)
Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:
(f - g)(x) = f(x) - g(x)
= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]
= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]
= 4x - 6 [Combine like terms]
Therefore, (f - g)(x) = 4x - 6.
Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.
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Convert 2.340 x 10-4 to decimal format.A) 23,400 B) 2,340 C) 0.000234 D) 0.0002340 E) 0.002340
After converting 2.340 x 10⁴ to decimal format we will be getting 0.000234. So, the correct answer choice is options (C) which is 0.000234.
In order to convert the given epression i.e. 2.340 x 10⁴ to decimal format, we are required to move the decimal point four places to the left since the exponent is negative.
In order to find the correct decimal format, starting with 2.340, we move the decimal point four places to the left, then the value we will be getting is equal to 0.000234
Therefore, from the above calculation we can draw the inference that the correct answer is option C) i.e 0.000234.
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3. Find the area of the shape below. Break
the larger shape into smaller pieces if needed.
8.4m
4m
11.4m
8m
ak direst
boyut ved FI
The total area of the given figure is 85.2m² respectively.
What is the area?The quantity of unit squares that cover a closed figure's surface is its area.
Square units like cm² and m² are used to measure area.
A shape's area is a two-dimensional measurement.
The space inside the perimeter or limit of a closed shape is referred to as the "area".
Area of rectangle one:
= l*b
= 4*11.4
= 45.6m²
Area of rectangle second:
= l*b
= 4*8.4
= 33.6m²
Area of the triangle:
= 1/2*b*h
= 1/2*4*(11.4-8.4)
= 1/2*4*3
= 2*3
= 6m²
Total area of the figure: 45.6 + 33.6 + 6 = 85.2m²
Therefore, the total area of the given figure is 85.2m² respectively.
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Yesterday, the track coach at Milton Middle School had the runners jog 3 times around the track for every 1 time they sprinted around it.
If the runners jogged 6 more laps than they sprinted, how many laps did they run altogether?
Therefore , the solution of the given problem of unitary method comes out to be the athletes completed a total of 12 laps.
What is an unitary method ?Finish the project using the tried-and-true basic methodology, the actual variables, and any pertinent knowledge you gain from the broad and specific questions. In response, customers might be given another opportunity to sample expression the products. We'll miss out on important breakthroughs in programming comprehension if these changes don't take place.
Here,
In accordance with the information provided, for each sprint around the track, the runners jogged three times. So, three times as many laps are jogged around the track.
Furthermore, it is known that the runners jogged six more laps than they ran. Therefore, we can construct the following equation:
Jogging laps equals sprinting laps plus six.
=> 3x = x + 6
=> 3x - x = 6
=> 2x = 6
=> x = 6/2
=> x = 3
Total laps equal 3x + x = 4x times the amount of jogged and sprinting laps.
By changing the value of x, we obtain:
Laps completed = 4 (3) = 12
As a result, the athletes completed a total of 12 laps.
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write a function that models the total amount of money Julia has after x weeks use x
The function that models the total amount of money Julia has after x weeks is f(x) = 27x + 254
How to solve an equation?An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.
Let f(x) represent the total amount of money Julia has after x weeks.
Julia has $254 and saves $27 each week, hence:
f(x) = 27x + 254
The function is f(x) = 27x + 254
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Find the domain and range of the exponential function h(x) = 125x. Explain your findings. As x decreases, does h increase or decrease? Explain. As x increases, does h increase or decrease? Explain. need anwsred ASAP
The domain is all real numbers, range is all positive real numbers. As x decreases, h(x) will decrease. As x increases, h(x) will increase.
The domain of the exponential function h(x) = 125x is all real numbers, as x can take on any value.
The range of the function is all positive real numbers, as the base (125) raised to any power (x) will always be positive.
As x decreases, h(x) will decrease. This is because when the base of an exponential function is greater than 1, as is the case here with 125, the function increases as the exponent increases, and decreases as the exponent decreases. So, as x becomes more negative, h(x) becomes smaller.
As x increases, h(x) will increase. This is because, as mentioned above, when the base of an exponential function is greater than 1, the function increases as the exponent increases. So, as x becomes more positive, h(x) becomes larger.
Overall, the function h(x) = 125x is an increasing function with a domain of all real numbers and a range of all positive real numbers.
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a cylindrical can with radius 1 inch is being filled with pineapple juice at a rate of 2 in^3/s. how fast is the height of the pineapple juice increasing
To determine how fast the height of the pineapple juice is increasing in a cylindrical can with radius 1 inch and filling rate of [tex](2)^{\frac{3}{s} }[/tex], we can use the formula for the volume of a cylinder and then differentiate it with respect to time.
The formula for the volume of a cylinder is [tex]V = πr^2h[/tex], where V is the volume, r is the radius, and h is the height. In this case, r = 1 inch.
Now, we are given [tex]\frac{dV}{dt}= (2)^{\frac{3}{s} }[/tex], which is the rate at which the volume of pineapple juice is increasing.
1. Plug in the radius value into the volume formula: [tex]V=π(1)^{2h}=πh[/tex].
2. Differentiate both sides of the equation with respect to time: [tex]\frac{dV}{dt} = π(\frac{dh}{dt})[/tex].
3. Plug in the given value of [tex]\frac{dV}{dt} :2 = π \frac{dh}{dt}[/tex].
4. Solve for [tex]\frac{dh}{dt} : \frac{dh}{dt} = \frac{2}{π}[/tex].
So, the height of the pineapple juice is increasing at a rate of [tex]\frac{2}{π}[/tex] inches per second.
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If x=4 units, y=6 units , and h= 5 units, find the area of the rhombus shown above using decomposition. Please help
the area of the rhombus is approximately 74.60 square units.
How to solve the question?
To find the area of a rhombus using decomposition, we first need to draw its diagonal lines. Let's label the points where the diagonals intersect as points A and B.
Now we can decompose the rhombus into two congruent triangles, ABC and ABD, where AB is the diagonal and AD and BD are half of the diagonals.
We can find the length of AD and BD using the Pythagorean theorem. Since x=4 units and y=6 units, we have:
AD²= (x/2)² + h²
AD² = (4/2)²+ 5²
AD²= 4² + 5²
AD² = 41
AD = sqrt(41)
Similarly, we can find the length of BD:
BD²= (y/2)² + h²
BD²= (6/2)² + 5²
BD²= 3²+ 5²
BD²= 34
BD = √(34)
Now we can find the area of each triangle:
Area of ABC = (AB * BD) / 2
Area of ABC = (2 * √(41) * √(34)) / 2
Area of ABC = √(1394)
Since the rhombus is made up of two congruent triangles, its total area is twice the area of one triangle:
Area of rhombus = 2 * Area of ABC
Area of rhombus = 2 * √(1394)
Area of rhombus ≈ 74.60 square units
Therefore, the area of the rhombus is approximately 74.60 square units.
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16. Find the perimeter and area of the following shape.
3n + 14
4n-8
3n+12
Question 11(Multiple Choice Worth 2 points)
(Circle Graphs LC)
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 54°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
If a circle graph were created using the findings, A. Kayaking would be the lake activity with a central angle of 54°.
Explain about the central angle:A central angle is one having endpoints on the perimeter and a vertex in the centre of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle.
The proportion of the entire number of campers in degrees is used to calculate the central angle from each lake activity.There are 360 degrees in a circle. This sum is proportionately split amongst the lake programs according to the amount of campers having participated.Lake Activity Number Degrees
of Campers
Kayaking 15 (15/100 x 360°) = 54°
Wakeboarding 11 (11/100 x 360°) = 40°
Windsurfing 7 (7/100 x 360°) = 25°
Waterskiing 13 (13/100 x 360°) = 47°
Paddleboarding 54 (54/100 x 360°) = 194°
Total number 100
Thus, Kayaking hence has a 54° central degree when viewed proportionately.
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If a certian company makes a mistake on 3% of the coins and they make 20000000 coins a day, how many coins are mistakes in 20 days?
BRAINLIEST FOR BEST ANSWER!!!!
The number of coins that are mistakes in 20 days are 12000000
How many coins are mistakes in 20 days?From the question, we have the following parameters that can be used in our computation:
Mistake on 3% of the coins
Rate = 20000000 coins a day,
This means that
Mistakes = 3% * 20000000 * days
For the coins that are mistakes in 20 days, we have
Mistakes = 3% * 20000000 * 20
Evaluate
Mistakes = 12000000
Hence, the coins are mistakes in 20 days are 12000000
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uppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. when carrying gallons of fuel, the airplane weighs pounds. when carrying gallons of fuel, it weighs pounds. how much does the airplane weigh if it is carrying gallons of fuel?
The weight of the plane if it is carrying gallons of fuel is 2336 pounds, under the condition of when carrying 10 gallons, and 45 gallons he airplane weighs 2056 and 2252 pounds.
We can utilize the two given points to create two linear equations
y = mx + b
2056 = 10m + b
2252 = 45m + b
We can find m and b by subtracting the first equation from the second equation:
(45m + b) - (10m + b) = 2252 - 2056
35m = 196
m = 5.6
For finding b by substituting m into one of the original equations:
2056 = 10(5.6) + b
b = 2000
The equation is
y = 5.6x + 2000
To evaluate how much the airplane weighs when carrying 60 gallons of fuel, now lets substitute x into the equation
y = 5.6(60) + 2000
y = 336 + 2000
y = 2336
The weight of the plane if it is carrying gallons of fuel is 2336 pounds, under the condition of when carrying 10 gallons, and 45 gallons he airplane weighs 2056 and 2252 pounds.
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The complete question is
Suppose that the weight (in pounds) of an airplane is a linear... Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 10 gallons of fuel, the airplane weighs 2056 pounds. When carrying 45 gallons of fuel, it weighs 2252 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?
Kat is a senior in high school, and wants to throw a graduation party for here and her friends. She will pay $225 for the venue and $80 per hour for the DJ. She has saved $410 and will earn another $560 by the party.
a) write an inequality to represent the possible number of hours Kat can afford to book the DJ
b) using your inequality in part a, what is one possible length cat can affairs to book the DJ?
The inequality to represent the possible number of hours Kat can afford to book the DJ is 80x + 225 ≤ 970 and one possible length Kat can afford to book the DJ is 9 hours.
Understanding Inequality with respect to Kat(a) Let x be the number of hours that Kat can book the DJ. Then, the total cost of the DJ is 80x, and the total cost of the party is 80x + 225.
Since Kat has $410 saved and will earn another $560, the total amount she can spend on the party is $410 + $560 = $970.
Therefore, we can write the following inequality to represent the possible number of hours Kat can afford to book the DJ:
80x + 225 ≤ 970
b) To solve for x, we can start by subtracting 225 from both sides of the inequality:
80x ≤ 745
Then, we can divide both sides by 80:
x ≤ 9.3125
Since Kat can only book the DJ in whole hours, the largest integer less than or equal to 9.3125 is 9. Therefore, one possible length Kat can afford to book the DJ is 9 hours.
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An experiment consists of rolling two fair number cubes. The diagram shows the sample space of all equally likely outcomes. What is the probability of rolling two 3's? Express your answer as a fraction in simplest form.
the probability of rolling two 3's is 1/36.Since we are rolling two number cubes, the sample space contains 6x6 = 36 equally likely outcomes, one for each possible pair of numbers that can be rolled.
what is probability ?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated as the number of ways the event can occur, divided by the total number of possible outcomes.
In the given question,
Since we are rolling two number cubes, the sample space contains 6x6 = 36 equally likely outcomes, one for each possible pair of numbers that can be rolled.
To find the probability of rolling two 3's, we need to count the number of outcomes that result in two 3's, and divide by the total number of possible outcomes.
From the diagram, we can see that there is only one outcome that results in two 3's, namely the outcome where the first cube shows a 3 and the second cube shows a 3. Therefore, the number of favorable outcomes is 1.
The probability of rolling two 3's is therefore:
P(rolling two 3's) = favorable outcomes / total outcomes = 1/36
So the probability of rolling two 3's is 1/36.
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There are 3 red pens and 12 black pens in a package, which ratio is equivalent to 3/12
Therefore , the solution of the given problem of ratio comes out to be this indicates that there are 4 black pens in the package for every red pen.
What is a ratio?A group comprising values both variable "a" and "" that seem to be equal is found using the straightforward formula "a / b," whenever "b" might be a greater number than zero. A ratio is created by combining two ratios. The ratio , fraction could have been 1:1 if there were just one guy and three women. There are 1/4 men and 3/4 women in the group.
Here,
By dividing the numerator and denominator by their greatest common divisor (GCD), the ratio 3/12 can be made simpler.
Due to the fact that both 3 and 12 can be divided by 3, their GCD equals 3.
The result of dividing the numerator and denominator by 3 is:
=> 3 ÷3 = 1.
=> 12 ÷ 3 = 4
Thus, 1/4 is the simple ratio that corresponds to 3/12.
Let's now use a simplified equivalent ratio to represent the ratio of red to black pens in the package:
Black pens 3: 12 Red pens:
=> 3 ÷ 3 = 1
=> 12 ÷ 3 = 4
Consequently, the rounded equivalent ratio of red to black pens is 1 to 4.
This indicates that there are 4 black pens in the package for every red pen.
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Find the surface area the regular pyramid 10m 8m 6.9m
The requried surface area of the regular pyramid is 147.6 cubic meters.
The surface area of the regular pyramid is given as:
Surface area = base area + 1/2 [perimeter×slant height]
Surface area = 1/2 × base × height + 1/2 [perimeter×slant height]
Surface area =1/2 × 8 × 6.9 + 1/2 [3×8 × 10]
Surface area =147.6 cubic meters
Thus, the requried surface area of the regular pyramid is 147.6 cubic meters.
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85 POINTS ASAP 85 POINTS ASAP Polygon ABCD with vertices at A(1, −1), B(3, −1), C(3, −2), and D(1, −2) is dilated to create polygon A′B′C′D′ with vertices at A′(2, −2), B′(6, −2), C′(6, −4), and D′(2, −4). Determine the scale factor used to create the image.
one fourth
one half
2
4
The scale factor used to create the image include the following: C. 2.
What is a scale factor?In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).
Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:
Scale factor = side length of image/side length of pre-image
By substituting the given side lengths or dimensions into the formula for scale factor, we have the following;
Scale factor = 2/1
Scale factor = 2.
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An equation to the line tangent to y= x^3 + 3x^2 +2 at its point of inflection isa) y= -6x-6b) y= -3x +1c) y= 2x +10d) y= 3x-1e) y= 4x+1
The equation of the tangent line at the point of inflection is y = -3x + 1, which corresponds to option (b).
To find the equation of the tangent line at the point of inflection for the given function [tex]y = x^3 + 3x^2 + 2,[/tex] we first need to determine the point of inflection. A point of inflection occurs where the second derivative changes sign.
First, let's find the first and second derivatives of the given function:
[tex]y' = 3x^2 + 6x[/tex] (first derivative)
[tex]y'' = 6x + 6[/tex] (second derivative)
To find the point of inflection, set the second derivative equal to zero and solve for x:
[tex]6x + 6 = 0 x = -1[/tex]
Now, plug x = -1 back into the original function to find the corresponding y-coordinate:
[tex]y = (-1)^3 + 3(-1)^2 + 2\\y = -1 + 3 + 2\\y = 4[/tex]
The point of inflection is (-1, 4). Next, find the slope of the tangent line at this point using the first derivative:
[tex]y'(-1) = 3(-1)^2 + 6(-1)\\y'(-1) = 3 - 6\\y'(-1) = -3[/tex]
Now, use the point-slope form of the equation of a line to find the tangent line:
y - y1 = m(x - x1)
y - 4 = -3(x - (-1))
y - 4 = -3(x + 1)
Simplify the equation to get the answer:
y = -3x - 3 + 4
y = -3x + 1
The equation of the tangent line at the point of inflection is y = -3x + 1, which corresponds to option (b).
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Determine the value of y-intercept of a line with the given slope -3 that is a tangent
line to the curve y = -x² - 5x -5.
a. 0
b. -1
c. -3
d. -4
The y-intercept of the tangent line is b. -1
What is the y intercept of a line?The y-intercept of a line is the value of y at which the line crosses the y axis
To determine the value of y-intercept of a line with the given slope -3 that is a tangent line to the curve y = -x² - 5x -5.
We proceed as follows
First we differentiate the equation of the curve.
So, y = -x² - 5x -5.
dy/dx = d(-x² - 5x -5)/dx
= d-x²/dx - d5x/dx - d5/dx
= -2x - 5 - 0
= -2x - 5
Since the derivative of the curve equals the value of the tangent at the point, we have that
dy/dx = -3
-3 = -2x - 5
-3 + 5 = -2x
2 = -2x
x = 2/-2
x = -1
So, substituting x = -1 into the equation for y to find the y intercept, we have that
y = -x² - 5x -5.
y = -(-1)² - 5(-1) -5
= -1 + 5 - 5
= -1 + 0
= -1
So, the y-intercept is b. -1
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