Answer:
Like terms are numbers with or without variables that have the same variables.
Step-by-step explanation:
5x and 3x are like terms because they have the same variable.
5x and 3y are not like terms because the variables are different.
To combine them, just add or subtract them. You cannot combine non-like terms!
Answer:
Definition: Like terms - Term in math that have the same variables or powers.
Ex. 2x, -5x, and 7x.
Combine Them: 2x + 7x = 9x - 5x = 4x
Step-by-step explanation:
Students who attend Washington Middle School are either in seventh or eighth grade. At the end of the first semester 25% of the students at Washington Middle School were on the honor roll. Seventh graders represented 60% 60 % of the students on the honor roll. If 124 124 students on the honor roll were in eighth grade, how many students attend Washington Middle School? There are students who attend Washington Middle School.
Answer:
There are 1240 students who attended Washington Middle School.
Step-by-step explanation:
Given:
Students who attend Washington Middle School are either in seventh or eighth grade.
At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.
Seventh graders represented 60% of the students on the honor roll.
If 124 students on the honor roll were in eighth grade.
Now, to find the students attend Washington Middle School.
Let the total number of students be [tex]x.[/tex]
So, the students at Washington Middle School were on the honor roll:
25% of [tex]x[/tex]
[tex]=\frac{25}{100} \times x[/tex]
[tex]=\frac{25x}{100}[/tex]
[tex]=\frac{x}{4}[/tex]
As, given seventh graders represented 60% of the students.
So, the students on the honor roll represented as seventh graders:
[tex]60\%\ of\ \frac{x}{4}[/tex]
[tex]=\frac{60}{100} \times \frac{x}{4}[/tex]
[tex]=0.6\times \frac{x}{4}[/tex]
[tex]=\frac{0.6x}{4}[/tex]
As, 124 students on the honor roll were in eighth graders.
Thus,
According to question:
[tex]\frac{x}{4} -\frac{0.6x}{4} =124[/tex]
[tex]\frac{x-0.6x}{4} =124[/tex]
[tex]\frac{0.4x}{4} =124[/tex]
Multiplying both sides by 4 we get:
[tex]0.4x=496[/tex]
Dividing both sides by 0.4 we get:
[tex]x=1240.[/tex]
Therefore, there are 1240 students who attended Washington Middle School.
Ruben has his dad are building a tree house the treehouse . The tree house has an area of 384 square feet the width of the tree house is 3/8 its length.What is the length of the treehouse
Answer:
12.25 ft
Step-by-step explanation:
(3/8)x + (5/8)x = √384
0.375x + 0.625x = 19.6
x = 19.6
Since L = 5/8 * 19.6 = 12.25 ft
The length of the treehouse, we use the area (384 square feet) and the given ratio (width is 3/8 the length). After setting up the equation, we solve for the length to find that the length of the treehouse is 32 feet.
The length of the treehouse, we can set up an equation using the given area and the relationship between the width and length. Let L represent the length and W represent the width. According to the problem, W = {3}/{8}L.
The area of the treehouse is given as 384 square feet. The formula for the area of a rectangle is Area = Length imes Width, so we have:
L times W = 384 square feet
L times {3}/{8}L = 384
{3}/{8}L² = 384
L² = rac{384 times 8}{3}
L² = 128 times 8
L² = 1024
L =[tex]\sqrt{1024}[/tex]
L = 32 feet
Therefore, the length of the treehouse is 32 feet.
The average radius of Jupiter is 4.34 x 10^4 miles. The average sun radius of the sun is 4.32 x 10^5. How many times greater is the average radius of the sun?
Answer:
The average radius of sun is approximately 9.95 times the average radius of Jupiter.
Step-by-step explanation:
We are given the following in the question:
Average radius of Jupiter =
[tex]4.34\times 10^{4}\text{ miles}[/tex]
Average radius of the sun =
[tex]4.32\times 10^{5}[/tex]
Relation between average radius of sun and average radius of Jupiter =
[tex]\displaystyle\frac{\text{Average radius of Sun}}{\text{Average radius of Jupiter}}\\\\= \frac{4.32\times 10^{5}}{4.34\times 10^{4}}\\\\\displaystyle\frac{\text{Average radius of Sun}}{\text{Average radius of Jupiter}} = 9.953917\\\\\text{Average radius of Sun} \approx 9.95\times \text{(Average radius of Jupiter)}[/tex]
Thus, the average radius of sun is approximately 9.95 times the average radius of Jupiter.
To determine how many times greater the Sun's radius is compared to Jupiter, divide the Sun's radius (695,700 km) by Jupiter's radius (71,400 km), resulting in the Sun being approximately 9.75 times greater than Jupiter in size.
Explanation:The question asks how many times greater the average radius of the Sun is compared to that of Jupiter. To find this, we will divide the Sun's radius by Jupiter's radius. The radius of Jupiter is given as 71,400 km, while the radius of the Sun is much larger at 695,700 km.
Calculating the ratio, we get:
Radius of the Sun / Radius of Jupiter = 695,700 km / 71,400 km.This simplifies to approximately 9.745.Therefore, the average radius of the Sun is roughly 9.75 times greater than that of Jupiter.
8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?
The probability of selecting the 8 tallest players randomly from a list of 27 is found by dividing the single way to choose the tallest players by the number of ways to choose any 8 players from 27, calculated using the combination formula C(n, k).
To determine the probability that the 8 tallest players will be selected from a list of 27 players, we need to consider the combinatorial aspect of the selection process. Since the selection is random, any group of 8 players can be chosen. The total number of ways to select 8 players out of 27 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of players (27), and k is the number of players to be selected (8).
Firstly, the number of ways to choose the 8 tallest players is 1, since there is only one group of the 8 tallest players. Secondly, we calculate the total number of ways to choose any 8 players from the 27, which is C(27, 8). We can then find the probability by dividing the number of ways to choose the tallest players by the total number of ways to choose any group of 8 players.
Using the combination formula, C(27, 8) is calculated as:
27! / (8! * (27-8)!)
= 27! / (8! * 19!)
Factor out the common terms from the numerator and denominator
The remaining terms give us the total number of combinations
The probability is therefore: 1 / C(27, 8).
Refer to the following breakdown of responses to a survey of room service in a hotel: Response - Frequency Not satisfied - 20 Satisfied - 40 Highly satisfied - 60 What percentage of the responses indicated that customers were satisfied?A. 40%B. 33%C. 50%D. 100%
Answer: B. 33%
Step-by-step explanation:
Given : Response - Frequency
Not satisfied - 20
Satisfied - 40
Highly satisfied - 60
Total customers = (Number of customers Not satisfied) + (Number of customers satisfied) + ( (Number of customers Highly satisfied) )
= 20+40+60=120
Now , the percentage of the responses indicated that customers were satisfied = [tex]\dfrac{\text{Number of customers are satisfied}}{\text{Total customers}}\times100[/tex]
[tex]=\dfrac{40}{120}\times100=33.33\%\approx33\%[/tex]
Hence, the percentage of the responses indicated that customers were satisfied = 33%
Thus , the correct answer is B. 33%
To find the percentage of customers who were satisfied, add up all responses, calculate the fraction of satisfied responses, then convert that to a percentage. The answer is 33%.
Explanation:To find out what percentage of the responses indicated that customers were satisfied, we first need to add up all the responses. This would include those who were Not satisfied, Satisfied, and Highly satisfied. The total number of responses will be 20 (Not satisfied) + 40 (Satisfied) + 60 (Highly satisfied) = 120 responses in total.
Next, we find the fraction of responses that were satisfied. For this, we divide the number of Satisfied responses (40) by the total number of responses (120). That gives us 40/120 = 0.333 or one-third.
To convert this fraction to a percentage, we simply multiply by 100. So, 0.333 x 100 = 33.3%, which rounds down to 33%. Thus, the answer to the question is 33%, option - B.
Learn more about Percentage Calculation here:https://brainly.com/question/329987
#SPJ3
Depending on the product, there may be a person who act as__________ a(n) in the buyer center, often by providing specifications for the product being purchased or the vendor being considered.
Answer:
Influencer
Step-by-step explanation:
An influencer is a person who has the power affect purchase decisions of others because of his ability such as knowledge, position with audience.
Final answer:
A person acting as a specifier in the buying center provides product specifications and may influence the purchase decision by setting requirements, interacting with both customer and seller but not making final purchasing decisions.
Explanation:
Depending on the product, there may be a person who acts as specifier in the buying center, often by providing specifications for the product being purchased or the vendor being considered.
A specifier plays a crucial role in the procurement process, ensuring that the product or service meets the organization's needs and standards. In a buying center, this individual might not have the authority to make final purchase decisions but is influential by setting the requirements that the potential products or suppliers must meet.
A specifier may interact closely with both the customer and seller to ensure that the right features, quality, and functionalities are captured in the procurement specifications.
This person may also assess the long-term reliability of supplier relationships, such as through exclusive dealer agreements, to safeguard the company's interests. The role of the specifier is analogous to that of a product consultant, providing insights without directly engaging in sales or price negotiations.
A street lamp casts a shadow 31.5 feet long, while an 8 foot-tall street sign casts a shadow of 14 feet long. What is the length and height of the lamp?
Answer:
The answer to your question is the height of the lamp is 18.2 ft
Step-by-step explanation:
Data
Street lamp shadow = 31.5 ft
Street sign height = 8 ft
Street sign shadow = 14 ft
Street lamp height = x
Process
1.- To find the height of the lamp use proportions. In this kind of problem, we do not look for the length, but the shadow.
Street lamp height/street lamp shadow = street sign height/street sign
shadow
Substitution
x / 31.5 = 8 / 14
Solve for x
x = (31.5)(8) / 14
Simplification
x = 254.4 / 14
Result
x = 18.2 ft
To find the length and height of the lamp, set up proportions using the shadow lengths and given values, then solve for the lamp height and length based on the information provided.
Explanation:The length of the lamp:
Set up a proportion using the shadow lengths:
I was doing my math homework and I was clueless when it came to this question, my best friend and I both came up with 30 and Get More Math Said it was incorrect. Can you help?
The high school debate team is developing a logo to represent their club. A scale drawing of the logo design is presented below, where each unit of the grid represents 3 inches in length. The team is printing out an enlargement of the new logo, where the enlargement has a height of 105 inches. The area of the enlargement will be inches2, which is times the size of the original scale drawing.
Answer:
c
Step-by-step explanation:
Answer:
The enlargement will be 2,250 which is 25 the times
Step-by-step explanation:
In the provided scale drawing, each unit represents 3 inches in length. Use this scale to add the real world measurements to the scale drawing as shown.
It can be seen from the figure that the total height of the scale drawing is 9 in + 3 in + 9 in = 21 in. It is given that the enlargement has a height of 105 inches. Find the scale factor between the scale drawing and the enlargement by dividing as shown.
The scale factor of 5 means that each dimension of the enlargement will be 5 times larger than the matching dimension of the scale drawing. So, the dimensions of the enlarged figure are shown below.
The logo is made up of three polygons: two triangles and one square. To find the total area of the logo, the area of each region must be found and added together.
To calculate the area of a triangle, use the formula below where b is the length of the base of the triangle and h is the height of the triangle.
To calculate the area of a square, use the formula below, where s is the length of the side of the square.
Now, calculate the areas of of the two logos.
Finally, determine how many times larger the area of the enlargement is than the scale drawing by dividing, as shown below.
Therefore, the area of the enlargement will be 2,250 inches2, which is 25 times the size of the original scale drawing.
to find the probability of flipping heads at least once if you flip a coin two times. The possible outcomes (we don't care about the order) are (each equally likely) TT, TH, HT, HH. Three out of four have an H in them, so the probability is 34. Is this correct? Is there a better and efficient way (especially when dealing with a higher number of flips? Please use only very basic terminology and concepts from probability because I've never taken a class.
Answer:
The probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
The probability of an event, say E, is the ratio of the favorable outcomes to the total number of outcomes, i.e.
[tex]P (E) = \frac{Favorable\ outcomes}{Total\ outcomes}[/tex]
The sample space of flipping two coins is:
S = {HH, HT, TH and TH}
Total number of outcomes = 4
Compute the probability of flipping Heads at least once as follows:
Let X = heads.
P (X ≥ 1) = P (X = 1) + P (X = 2)
[tex]=\frac{2}{4}+\frac{1}{4} \\=\frac{3}{4}[/tex]
Thus, the probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].
The experiment of flipping a coin is a binomial experiment.
Since there are only two outcomes of the experiment, either a Heads or a Tails.
So if X is defined as the number of heads in n flips of a coin then the random variable X follows a binomial distribution with probability p = 0.5 of success.
1. Determine whether the lines given by the equations 2x + 3y = and y=3/2x+4
are perpendicular.
2. Two lines having the same -intercept are perpendicular. If the equation of one of
these lines is y= −4/5x+6, what is the equation of the second line?
Answer:
1. Yes, the lines are perpendicular.
2. [tex]y=\frac{5}{4}x+6[/tex]
Step-by-step explanation:
The first equation of Exercise 1 is incomplete. Let's assume that it is:
[tex]2x + 3y =n[/tex]
Where "n" is a number.
First, it is important to remember that the equation of a line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
By definition, the slopes of perpendicular lines are negative reciprocals.
1 . If you solve for "y" from the first equation, you get:
[tex]2x + 3y =n\\\\3y=-2x+n\\\\y=-\frac{2}{3}x+\frac{n}{3}[/tex]
You can identify that the slope is:
[tex]m=-\frac{2}{3}[/tex]
The second equation of the line is:
[tex]y=\frac{3}{2}x+4[/tex]
And its slope is:
[tex]m=\frac{3}{2}[/tex]
Since the slopes are negative reciprocals, the lines are perpendicular.
2. Given the first equation of the line:
[tex]y= -\frac{4}{5}x+6[/tex]
You can identify that:
[tex]m=-\frac{4}{5}\\\\b=6[/tex]
Since the first line and the second one are perpendicular, you know that the slope of the other line is:
[tex]m=\frac{5}{4}[/tex]
According to the information given in the exercise, both lines have the same y-intercept; therefore, the equation of the second line is:
[tex]y=\frac{5}{4}x+6[/tex]
Since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year. Predict the number of cases that will be reported in 2020 and the trend continues
Answer:
20,158 cases
Step-by-step explanation:
Let [tex]t=0[/tex] represent year 2010.
We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.
Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.
We can represent this information in an exponential decay function as:
[tex]F(t)=102,390(1-0.15)^t[/tex]
[tex]F(t)=102,390(0.85)^t[/tex]
To find number of cases in 2020, we will substitute [tex]t=10[/tex] in our decay function as:
[tex]F(10)=102,390(0.85)^{10}[/tex]
[tex]F(10)=102,390(0.1968744043407227)[/tex]
[tex]F(10)=20,157.970260446597\approx 20,158[/tex]
Therefore, 20,158 cases will be reported in 2020.
a wise man once said, “ 400 reduced by 3 times my age is 163”. what is his age?
Answer:
79 years old
Step-by-step explanation:
Let his age be x
400-3x=163
400-163=3x
237=3x
Divide both side by 3
237/3 =3x/3
79=x
The man's age (x) =79 years old
Start of Questions
Write sinπ/5cosπ/8+cosπ/5sinπ/8 as a trigonometric function of one number. Keep π in your answer. Be sure to PREVIEW your answer before submitting!
Answer:
sin(13π/40)
Step-by-step explanation:
The given expression matches the pattern ...
sin(a)cos(b) +cos(a)sin(b) = sin(a+b)
Then ...
sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)
= sin(13π/40)
_____
π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)
The trigonometric expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 can be simplified to sin(13π/40) by using the sine addition formula.
Explanation:The expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 resembles the formula for the sine of a sum, sin(a+b) = sin(a)cos(b) + cos(a)sin(b). By applying this trigonometric identity, we can rewrite the expression as the sine of a single angle. Therefore, sinπ/5 cosπ/8 + cosπ/5 sinπ/8 is equivalent to sin(π/5 + π/8). To simplify it further, we must find a common denominator for the two angles, π/5 and π/8, which is 40. Thus, we get sin((8π + 5π)/40), which simplifies to sin(13π/40).
PLEASE HE LPPP!!! QUESTION AND ANSWERS IN PICTURE !!2
Answer:
Line ED
Explanation:
Opposite side is EF (because its opposite to the angle)
Hypotenuse side id FD (opposite of right angle)
Adjacent is the line leftover
Answer:
B
Step-by-step explanation:
Adjacent is the one with 90° and the angle, theta
ED in this case
Determine the point of discontinuity if it exists
v(x)=x^2-25/2x^2+13x+15
Answer:
x=-5 and x=-1.5
Step-by-step explanation:
The given function is
[tex]v(x) = \frac{{x}^{2} - 25}{2 {x}^{2} + 13x + 15} [/tex]
The points of discontinuity occurs at where the denominator is zero.
[tex]2 {x}^{2} + 13x + 15= 0[/tex]
We solve by factoring.
We first split the middle term:
[tex]2 {x}^{2} + 3x + 10x + 15= 0[/tex]
We factor by grouping:
[tex]x(2x + 3) + 5(2x + 3)= 0[/tex]
[tex](x + 5)(2x + 3) = 0[/tex]
The points of discontinuity occur at x=-5, and x=-1.5
Final answer:
The function v(x) has discontinuities at x = -3 and x = -5/2.
Explanation:
A point of discontinuity in a mathematical function refers to a location where the function fails to be continuous. In other words, it's a point at which the function exhibits a break or abrupt change in its behavior.
The point of discontinuity for the function [tex]v(x) = (x^2-25)/(2x^2+13x+15)[/tex] can be found by setting the denominator equal to zero and solving for x. In this case, the denominator factors to (x+3)(2x+5), indicating discontinuities at x = -3 and x = -5/2. These are the points where the function is not defined.
Points of discontinuity are essential to understanding the behavior and properties of functions, particularly in areas like calculus and real analysis. They are critical in identifying where a function fails to meet the criteria for continuity and in analyzing the behavior of functions in various contexts.
Since f(x, y) = 1 + y2 and "∂f/∂y" = 2y are continuous everywhere, the region r in theorem 1.2.1 can be taken to be the entire xy-plane. use the family of solutions in part (a) to find an explicit solution of the first-order initial-value problem y' = 1 + y2, y(0) = 0.
Answer:
The solution to the differential equation
y' = 1 + y²
is
y = tan x
Step-by-step explanation:
Given the differential equation
y' = 1 + y²
This can be written as
dy/dx = 1 + y²
Separate the variables
dy/(1 + y²) = dx
Integrate both sides
tan^(-1)y = x + c
y = tan(x+c)
Using the initial condition
y(0) = 0
0 = tan(0 + c)
tan c = 0
c = tan^(-1) 0 = 0
y = tan x
In this exercise we have to use our knowledge of differential equations to calculate the value of the first solution, so we have to:
[tex]y = tan x[/tex]
Then say the differential equation as:
[tex]y' = 1 + y^2[/tex]
then rewriting as:
[tex]dy/dx = 1 + y^2\\dy/(1 + y^2) = dx[/tex]
Integrate both sides, we have that:
[tex]tan^{(-1)}y = x + c\\y = tan(x+c)[/tex]
So we already have a preview of the solution, so we will have to apply the initial conditions and this results in:
[tex]y(0) = 0\\0 = tan(0 + c)\\tan c = 0\\c = tan^{(-1)} 0 = 0\\y = tan x[/tex]
See more about differential equations at brainly.com/question/2263981
Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day how long do they need to ride on the third day to make their goal of biking a total of 20 hours in the park
Answer:
Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.
Step-by-step explanation:
Given:
Goal of Total number of hours of biking in park =20 hours.
Number of hours rode on first day = [tex]5\frac34 \ hrs.[/tex]
So we will convert mixed fraction into Improper fraction.
Now we can say that;
To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.
[tex]5\frac34 \ hrs.[/tex] can be Rewritten as [tex]\frac{23}{4}\ hrs[/tex]
Number of hours rode on first day = [tex]\frac{23}{4}\ hrs[/tex]
Also Given:
Number of hours rode on second day = [tex]6\frac45 \ hrs[/tex]
[tex]6\frac45 \ hrs[/tex] can be Rewritten as [tex]\frac{34}{5}\ hrs.[/tex]
Number of hours rode on second day = [tex]\frac{34}{5}\ hrs.[/tex]
We need to find Number of hours she need to ride on third day in order to achieve the goal.
Solution:
Now we can say that;
Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.
framing in equation form we get;
Number of hours she need to ride on third day = [tex]20-\frac{23}{4}-\frac{34}{5}[/tex]
Now we will use LCM to make the denominators common we get;
Number of hours she need to ride on third day = [tex]\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}[/tex]
Now denominators are common so we will solve the numerator we get;
Number of hours she need to ride on third day =[tex]\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.[/tex]
Hence Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.
Final answer:
Rebecca and Dan need to ride for 7 9/20 hours on the third day to reach their goal of biking a total of 20 hours in the national park, having already biked 5 3/4 hours on the first day and 6 4/5 hours on the second day.
Explanation:
Rebecca and Dan are biking in a national park and want to achieve a goal of biking a total of 20 hours over three days. They biked 5 3/4 hours on the first day and 6 4/5 hours on the second day. To find the time they need to bike on the third day, we first convert the hours they biked into improper fractions:
First day: 5 3/4 hours = (5×4 + 3)/4 = 23/4 hoursSecond day: 6 4/5 hours = (6×5 + 4)/5 = 34/5 hoursNext, we add these two amounts together:
(23/4) + (34/5) = (23×5 + 34×4) / (4×5) = (115 + 136) / 20 = 251/20 hours.
Now we convert 251/20 hours to a mixed number:
251/20 = 12 11/20 hours
They have biked a total of 12 11/20 hours over the first two days. Their total goal is 20 hours, so we need to subtract the time already biked from the total goal:
20 hours - 12 11/20 hours = (20×20 - 12×20 - 11)/20 = (400 - 240 - 11)/20 = 149/20 hours.
Finally, we convert 149/20 hours back to a mixed number to find out how long they need to ride on the third day:
149/20 hours = 7 9/20 hours.
So, Rebecca and Dan need to ride for 7 9/20 hours on the third day to meet their goal of biking a total of 20 hours in the park.
A 72.5-foot rope from the top of a circus tent pole is anchored to the ground 44.4 feet from the bottom of the pole. What angle does the rope make with the pole? (Assume the pole is perpendicular to the ground.
What is the probability of rolling a die twice, and having it land on a number greater than 1 both times?
Answer: 25/36
Step-by-step explanation:
A die has six faces, therefore its sample space S is 6
Since we are rolling a die twice(at different times), the probability of one turning up the first time is 1/6(i.e expected outcome/total outcome)
Similarly, if we throw the die the second time, the probability of one turning up the second time is also 1/6
The probability of having number greater than 1 land at each time will be (1- 1/6) which is 5/6.
Therefore the probability of having number greater than 1 land at "both times" will be 5/6×5/6 = 25/36
Newton’s law of cooling states that for a cooling substance with initial temperature T0 , the temperature T(t) after t minutes can be modeled by the equation T(t)=Ts+(T0−Ts)e−kt , where Ts is the surrounding temperature and k is the substance’s cooling rate.A liquid substance is heated to 80°C . Upon being removed from the heat, it cools to 60°C in 12 min.What is the substance’s cooling rate when the surrounding air temperature is 50°C ?The substances cooling rate when the surrounding air temperature is 50C is 0.0916.0.06870.07320.08130.0916
Answer:
k = 0.0916
Step-by-step explanation:
T(t) = [tex]T_{s} + ( T_{o} - T_{s} )e^{-kt}[/tex]
from question; t = 12 mins , [tex]T_{s}[/tex] = 50 C , [tex]T_{o}[/tex] = 80 C , T = 60 C
60 = 50 + (80 - 50) [tex]e^{-12k}[/tex]
60-50 = 30 [tex]e^{-12k}[/tex]
10/30 = [tex]e^{-12k}[/tex] (Taking natural Log of both sides)
In(0.3333) = In [tex]e^{-12k}[/tex]
-1.0986 = -12k
k = 0.0916
Which of the following variables are qualitative and which are quantitative? If the variable is quantitative, then specify whether the variable is discrete or continuous.a. Points scored in a football game.b. Racial composition of a high school classroom.c. Heights of 15-year-olds.
Quantitative in general involves number while qualitative does not involves number. For example, you can count the point scored in a football game which is considered as quantitative. While you cannot count racial composition because it involves different quality or type.
Quantitative is further divided into two type; discrete and continuous. Discrete variable involves integers while in between two values of a continuous variable, there are an infinite number which is valid and this is not the case for discrete variables.
Qualitative is variable something that you cannot count.
Answer:
A. Points scored in a football game - Quantitative; discrete
B. Racial composition of a high school classroom - Qualitative
C. Heights of 15-year-olds - Quantitative; continuous
Points scored in a football game is a discrete quantitative variable, racial composition of a high school classroom is a qualitative variable, and heights of 15-year-olds is a continuous quantitative variable.
Explanation:The variables given in this question can be classified as either qualitative or quantitative.
Points scored in a football game: This is a quantitative variable as it involves numerical measurements. Moreover, since points scored in a game can only take on whole number values (for example, you cannot score 2.5 points in a football game), it is specifically a discrete variable.Racial composition of a high school classroom: This is a qualitative variable as it involves non-numerical categories or types, namely, different races.Heights of 15-year-olds: This variable is quantitative, as it involves measurement of a physical characteristic (height). Furthermore, since height can take on any value within a certain range (for example, a 15-year-old could be 1.52 meters tall or 1.523 meters tall), this is a continuous variable.Learn more about Qualitative vs Quantitative Variables here:https://brainly.com/question/31565073
#SPJ3
Red apples cost $1.20 per pound green apple cost 1.50$ per pound what is the total cost if you buy 3 pounds of red apples and 2 pounds of green apples
6.60 would be the total cost for both 3 pounds and two pounds :D
Answer:
$6.60
Step-by-step explanation:
multiply 1.20 (red apples) by 3 (lbs) = 3.6
and 1.50 (green apples) times 2 (lbs) = 3
then add the two totals = $6.60
find the equation of the line that is perpendicular to y=3x and passes through the point (4,-2)
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
y = 3x
Comparing with the slope intercept form, slope = 3
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.
Therefore, the slope of the line passing through (4,-2) is - 1/3
To determine the intercept, we would substitute m = - 1/3, x = 4 and
y = -2 into y = mx + c. It becomes
- 2 = - 1/3 × 4 + c = 4/3 + c
c = - 2 + 4/3 = - 2/3
The equation becomes
y = - x/3 - 2/3
The function f(x) = Negative Startroot x EndRoot is shown on the graph.
On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the left through (4, negative 2).
Which statement is correct?
The domain of the function is all real numbers less than or equal to −1.
The range of the function is all real numbers greater than or equal to 0.
The range of the function is all real numbers less than or equal to 0.
The domain of the function is all real numbers less than or equal to 0.
Answer:
the answer is c
Step-by-step explanation:
i took the test and got a 100
The range of the function is all real numbers less than or equal to 0.
A function is an expression that shows the relationship between two or more variables or numbers.
The domain of a function is the set of input values while the range is the set of output values.
From the graph, The range of the function is all real numbers less than or equal to 0.
Find out more on function at: https://brainly.com/question/10439235
INPUT SU,0 IF OFF OUTPUT M,0 OUTPUT T,0 OUTPUT W,0 OUTPUT TH,0 OUTPUT F,0 ELSE ON OUTPUT M,0 OUTPUT T,0 OUTPUT W,0 OUTPUT TH,0 OUTPUT F,0 ENDIF INPUT M,0 INPUT T,0 INPUT W,0 INPUT TH,0 INPUT F,0 OR OR OR OR INPUT SA,0 INPUT SU,0 AND NOT OR ON OUTPUT SU,0 OFF OUTPUT SU,0 END
It takes painter A 3 hours to paint a certain area of a house. It takes painter B 5 hours to do the same job. How long would it take them, working together, to do the painting job?
Answer:
Step-by-step explanation:
First step is to read the question thoroughly and make sure you understand it alright. Second step is to get paper and a pencil and write down the question. Third step is to grab a calculator if you don't have one then try to use addition. Fourth step is to write down the problem which is 3 + 5 = 8 so that equals 8 as u can see. Fifth step is to write the answer and there is your answer hopefully i helped out thank you for having patients Have a Great EveningIt would take them 8 hours to complete the painting task if they worked together.
What is the addition operation?The addition operation in mathematics adds values on each side of the operator.
For example 4 + 2 = 6
If painter A can paint the area in 3 hours, and painter B can paint the same area in 5 hours, then it would take them a total of 3+5=8 hours to paint the area together.
It's worth noting that this assumes that both painters are able to work at their full capacity while working together and that they are able to divide the work between them in an efficient manner. If either of these conditions is not met, it could take them longer than 8 hours to complete the job.
Hence, working together, it would take them 8 hours to complete the painting job.
Learn more about Addition operations here:
brainly.com/question/25834626
#SPJ2
An isosceles triangle has exactly two sides that are equal in length (congruent). If the base (the third side) measures 46 inches and the perimeter is 119 inches, find the length of the two congruent sides, called legs.
Answer:
36.5 Inches
Step-by-step explanation:
The perimeter of the triangle is the sum of all three(3) sides.
let the length of one congruent side be 'a', Therefore;
a + a + 46 = 119
2a = 119 - 46
a = 73/2
a = 36.5 inches.
Describe and sketch the surface in R^3 represented by the equation x + y = 2
Answer:
The Surface in R^3
Step-by-step explanation:
Represented by the equation x+y=2
when y=0
then 0=2-x
x=2
similarly
when x=0
then 0=2-y
y=2
the sketch and description is in attached file
Answer: The equation is a plane.
Graph is attached.
The equation [tex]x + y = 2[/tex] is an equation of a plane in [tex]R^3[/tex].
z can take any value and x and y must satisfy the equation [tex]x + y = 2[/tex].
3 such points are: [tex]A = (0, 2, 0), B = (2, 0, 0), C = (1, 1, 3)[/tex].
Then we plot the points and draw a plane through them.
Learn more: https://brainly.com/question/1655368
30 POINTS AND RAINLIEST! URGENT DUE IN 30 MINS!
Koji is installing a rectangular window in an office building. The window is 823 feet wide and 534 feet high.
The formula for the area of a rectangle is A=bh.
I NEED A FRACTION!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the area of the window?
Enter your answer as a mixed number in simplest form in the box.
$$
Answer:
We have: b = 823 foot
h = 534 Ft ,
Substitute their values,
A = 823 * 534
A = 439482 Ft² briefly, Your Answer would be: 439482 Ft²
~
For a fraction;
49 and 10/12
multiply 8 and 2/3 by 5 and 3/4!