Answer:
T = 79e^(-kt) +60
Step-by-step explanation:
You want the particular solution to the differential equation ...
dT +k(T -60)dt = 0 . . . . T(0) = 139
SolutionThis is a separable differential equation, so we can solve it by separating the variables and integrating each side:
[tex]\dfrac{dT}{T-60}=-k\,dt\\\\\displaystyle \int{\dfrac{dT}{T-60}}=\int{-k}\,dt\\\\\ln{(T-60)}=-kt+C\\\\T-60=e^{-kt+C}=Ce^{-kt}\qquad\text{take antilogs; values of $C$ are different}[/tex]
Applying the initial condition, we have ...
139 -60 = C = 79
Then the particular solution is ...
[tex]\boxed{T=79e^{-kt}+60}[/tex]
Une enquête faite auprès des collégiens d'une ville a permis de recueillir les informations suivantes : 7
30 des élèves interrogés n'ont pas de téléphone portable;
400 élèves possèdent un téléphone portable et un ordinateur;
1 6 des élèves interrogés n'ont pas d'ordinateur;
1 15 des élèves interrogés n'ont ni téléphone portable
ni ordinateur.
Combien de collégiens ont été interrogés pour réaliser
cette enquête ?
600 élèves :
On sait que 7/30+1/6 ne font pas partie des 400 élèves qui possèdent téléphone portable et ordinateur . 7/30+1/6=12/30=2/5 mais parmi ces élèves figurent ceux qui n'ont ni l'un, ni l'autre. Ils font donc partie des 2/5 qui viennent d'être dénombrés
Il faut donc les retrancher, sinon ils seraient comptés deux fois
donc le nombre n'ayant ni l'un ni l'autre est : 2/5-1/15=5/15=1/3
Par conséquent 2/3 ont unt téléphone et un ordinateur
Comme ces 2/3 correspondent à 400 élèves, le nombre total d'élèves interrogés sera donc de 400*3/2=600 élèves.
3c + b² + (27a) - d
a = 1/3
b = 9
c = 5
d = -10
Answer:
Step-by-step explanation:
Rephrase it.
3(5) + 9² + (27 x 1/3) - (-10)
15 + 9x9 + 9 - (-10)
15 + 81 + 9 - (-10)
96 + 9 - (-10)
115
A department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. What is the percent markup? A department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. What is the percent markup?
The percent markup of a department, if they sell 300 shirts at a cost of $9 each is 50%
According to the question, we learn that a department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. This means :
The selling price of 300 shirts = 300 × $9
The selling price of 300 shirts = $2700
Selling price > cost price i.e., 2700 > 1800
when selling price is greater than cost price it means department store made a profit.
Profit = selling price - cost price
Profit = 2700 - 1800 = $900
Profit percentage = profit/ cost price × 100
Profit % =[tex]\frac{900}{1800} \times 100[/tex]
Profit % = 50%
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Barret is looking at a building on the school grounds which is shaped like a rectangle as shown. He knows the building has a height of 32x ft, width of 46x and the diagonal of the building is 200ft
The value of x is √12.73 when Barrett is aware that the structure measures 32x feet in height, 46x feet in breadth, and 200 feet diagonally.
Definition of Pythagoras Theorem:
The square of the long side of a right-angled triangle is equal to the sum of the squares of the other two sides.
It is stated in this formula:
[tex](side)^2+(side)^2=(hypotenuse)^2[/tex]
Given that,
Barrett is focusing on a rectangle-shaped structure on the school's property. He is aware that the structure measures 32x feet in height, 46x feet in breadth, and 200 feet diagonally.
We must determine what x stands for.
We know that,
The height of building is 32x.
The width is 46x
The diagonal is 200 feet
So we form a triangle
From the Pythagoras theorem,
Hyp² = Side²+ Side²
200² = (32x)² + (46x)²
40000 = 1024x² + 2116x²
3140x² = 40000
x² = 12.73
Square root on both sides
x = √12.73
Therefore, The value of x is √12.73 when Barrett is aware that the structure measures 32x feet in height, 46x feet in breadth, and 200 feet diagonally.
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A triangle has a 60 degree angle, and the two adjacent sides are 12 and 12 square root 3. Find the radius of a circle with the same vertex as a center, if the arc inside the triangle divides it into two regions of equal area.
The radius of a circle with the same vertex as a center, if the arc inside the triangle divides it into two regions of equal area is (18 × ✓π) / π
How to calculate the radiusFrom the information, the triangle has a 60 degree angle, and the two adjacent sides are 12 and 12 square root 3.
The area of a triangle will be;
A = 1/2 × a × b × sin C
= 1/2 × 12 × 12✓3 × sin 60
= 108
Area of sector = πr² / 360 × 60.
r² = (108/2) × 6 ) π
r² = 324 / π
r = 18✓π / π
The radius is 18✓π / π.
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create a frequency distribution, this time separating results for sex categories. include in your analysis the appropriate measure of central tendency. are there any differences in their measures? explain.
a) Median will be an appropriate measure for the distribution. b) Mean will be an approprate measure for the distribution.
Here we already have the data available to us. From the data, we can clearly see that
Mode < Mean < Median
Hence this is a negatively skewed distribution.
Therefore the appropriate measure of central tendency for this distribution will be the median. The median will tell us the point at which the frequency is divided by 50%.
Hence we can say that the median will a more appropriate measure.
Now if the data has another aspect of sex included, then the frequency column would be divided into separate columns with each gender identity taking up its own column.
Since now this will become multivariate data, the best measure of central tendency will be Mean.
The difference in the measure of central tendency will depend upon how skewed the data for every sex will be. For example, if in a country, men preferred to be educated over women, then the mean for men will be a lot higher than that of women. On the other hand, the EDUC for women will be a lot lower.
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6300000 in standard form
Answer:
6.3×10^6
Step-by-step explanation:
6.3×10^6
in standard form
A mathematical ________________ is a statement that contains _______________, _________________, and ___________________.
A mathematical theorem is a statement that contains hypotheses, conclusions, and proofs.
What in arithmetic is a theorem?Mathematics revolves around the theorems. A thorough proof is a specific kind of logical reasoning that has been used to demonstrate the truth of a claim, which is what a theorem is.
Which mathematical theorem is the hardest?"When n is higher than 2, there are no pretty much the entire number answers to the problem xn + yn = zn." This equation, also referred to as "Fermat's Last Theorem," was presented for the first time by French scientist Pierre de Fick in 1637 and had baffled the world's greatest minds for further than three centuries.
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Which combined inequality has the same solution set shown in the graph of x?
Number line ranging from negative four to four, with a line beginning with an open point at negative three and ending with a closed point at negative one
Responses
–3 ≤ x > –1
–3 ≤ x > –1
–3 ≤ x < –1
–3 ≤ x < –1
–3 < x ≤ –1
–3 < x ≤ –1
–3 > x ≥ –1
is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?
(a) The sample size for the above sample is 15.
(b) The sample mean for these data is 3.8.
(c) The sample median is 3.6.
(d) To compute the 20% trimmed mean for the above data set is 3.7.
(e) The sample mean is less descriptive as the location's center (median) than the trimmed mean.
The following measurements were recorded for the drying time, in hours
3.4 2.5 4.8 2.9 3.6 is:
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
(a) We have to determine the sample size for the above sample.
The number of participants or observations included in a study is referred to as the sample size. This number is commonly represented by the symbol n.
Sample Size (n) = 15
(b) We have to calculate the sample mean for these data.
Sample Mean = Total Sum of data/Total Number
Sample Mean = (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 + 5.2 + 3.0 + 4.8)/15
Sample Mean = 56.8/15
Sample Mean = 3.8
(c) We have to calculate the sample median.
To define the sample median we first represent the data in ascending order.
2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6
Sample Size(n) = 15
So Median = (n+1)/2th term
Median = (15 + 1)/2th term
Median = 16/2th term
Median = 8th term
So the 8th term in the given data is 3.6. So,
Median = 3.6
(d) We have to compute the 20% trimmed mean for the above data set.
To compute the 20% termed mean, remove 20% of the largest and 20% of the smallest elements from the sample and compute the mean of the new sample.
New sample: 2.9 3.0 3.3 3.4 3.6 3.7 4.0 4.4 4.8
New Mean = 33.3/9
New Mean = 3.7
(e) We have to check is the sample mean for these data more or less descriptive as a center of location than the trimmed mean.
The mean value is 3.8, the median value is 3.6, and the trimmed mean value is 3.7. As a result, the sample mean is less descriptive as the location's center (median) than the trimmed mean.
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The complete question is:
The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.
3.4 2.5 4.8 2.9 3.6
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
Assume that the measurements are a simple random
sample.
(a) What is the sample size for the above sample?
(b) Calculate the sample mean for these data.
(c) Calculate the sample median.
(d) Compute the 20% trimmed mean for the above data set.
(e) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?
Which of the following statements are true about the right triangle? Select all that apply.
Answer:
the answer is B) and E)
Step-by-step explanation:
it's not that complicated, just have to subtract 12 from 37
Answer:This is a right triangle.One of the legs has a length of 20.
Step-by-step explanation:
A composite figure is shown.
Which of the following represents the total area of the figure?
The total area of the composite figure is 484 square feet.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
Given:
A composite figure is shown.
To find the complete area:
Here, we have dissected three figures separately.
So, the complete area,
= The area of the triangle with a height 22 feet and base 8 feet +
the area of the rectangle with a length 16 feet and width 22 feet +
the area of the triangle with a height 4 feet and base 22 feet
= (1/2 x 22 x 8) + (16 x 22) + (1/2 x 4 x 22)
= 88 + 44 + 352
= 484 square feet.
Hence, the area is 484 square feet.
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(Theoretical Probability MC)
Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles. Determine P(not green) when choosing one marble from the bag.
92%
88%
24%
12%
The probability of not selecting a green marble is equal to the total number of non-green marbles in the bag divided by the total number of marbles in the bag.
What is the meaning of probability and it will be calculated?To calculate the probability: there are three green marbles out of a total of twenty-five marbles, so the probability of selecting a green marble is 3/25.
The likelihood of not selecting a green marble is then 1 - 3/25 = 22/25.
This is equal to 22/25 * 100 = 88% as a percentage.
As a result, P(not green) = 88%
Probability denotes the possibility of something happening. It is a mathematical branch that deals with the onset of a random event. The value ranges from zero to one. Probability has been tried to introduce in mathematics to predict the probability of events occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in probability distribution, in which you will learn about the possible outcomes of a random experiment.
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A man keeps birds in a big cage in his garden
2/5 of the birds are brown
4 of the birds of black
the rest of the birds are white
the man takes a bird out the cage at random
the probability that this bird is black is 0.2
how many of the birds in the cage are white
If C.P. of 100 pencils is Rs.250 and S.P. of 1 dozen pencils is Rs.33, find the gain or loss per cent.
CP of 100 pencils = Rs.250
CP of 1 pencil = 250/100 = 2.5
SP of 1 dozen pencils = Rs.33
SP of 12 pencils = Rs.33
SP of 1 pencil = \frac{33}{12}=2.75
SP>CP
So, Profit% = SP - CP/ CP × 100 = 2.75 - 2.5/2.5 × 100 = 10 %
Hence The profit % is 10%
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Marta’s jump rope is 10 inches shorter than three times the length of David’s rope.
If both of their ropes lay together end to end, they measure 120 inches long. How long is each person’s jump rope?
Marta's rope is 10 inches shorter than three times the length of David's rope and they measure 120 inches long together , then Marta's rope is 77.5 inches long and David's rope is 32.5 inches long.
Let's call the length of David's rope x.
According to the problem, Marta's rope is 10 inches shorter than three times the length of David's rope, so we can write an equation for Marta's rope:
length of Marta's rope = 3 * x - 10
And the combined length of both of their ropes is 120 inches, so we can write another equation:
x + (3 * x - 10) = 120
Expanding the second equation and solving for x, we get:
4x - 10 = 120
Adding 10 to both sides:
4x = 130
Dividing both sides by 4:
x = 32.5
So, David's rope is 32.5 inches long.
We can use the first equation to find the length of Marta's rope:
length of Marta's rope = 3 * x - 10 = 3 * 32.5 - 10 = 87.5 - 10 = 77.5 inches
So, Marta's rope is 77.5 inches long.
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How do I solve this equation?
3(5)-3(4)•y
when y is 2
Answer:
-9
Step-by-step explanation:
3(5)-3(4)•y
3(5)-3(4)•2
15 - 12 · 2
15 - 24
-9
Answer:
To solve the equation 3(5) - 3(4)•2, we need to simplify each term and then substitute the value of 2 for y.
Starting with the first term:
3(5) = 15
Next, the second term:
-3(4)•2 = -24
So, putting it all together:
15 - 24 = -9
So when y is 2, the equation simplifies to -9.
Step-by-step explanation:
You are a bookstore owner and want to calculate the usual amount of money
made each day, but you know that you make four times more on Mondays
than any other day. Which measure of central tendency should you use?
A. All measures of center work equally well.
B. Mode
C. Median
D. Mean
Answer:
Median
Step-by-step explanation:
I took the test myself.
The square rootof 144xsquareduvuded by 4
which equation is standard form has a slope of -2/5 and passes through the point (5,-8)
The equation of the line with a slope of -2/5 and passing through the point (5, -8) in standard, slope-intercept, form is; y = -0.4·x - 6
What is an equation?An equation consists of expressions and or numbers, expressed to be equivalent, by joining them with an '=' sign.
A standard form of the equation of a straight line is the slope-intercept form, which can be presented as follows; y = m·x + c
Where;
m = The slope of the graph of the equation
c = The y-intercept
The equation in the slope-intercept form can be obtained from the point-slope form, using the details of the slope of the graph of the equation (-2/5), and the point through which the graph of the equation passes (5, -8)
The point-slope of the equation is therefore;
y - (-8) = (-2/5)×(x - 5)
y + 8 = -2·x/5 + 2
y = -2·x/5 + 2 - 8 = -2·x/5 - 6 = -0.4·x - 6
The equation with a slope of -2/5 and passing through the point (5, -8), therefore is; y = -0.4·x - 6
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PLSSSS HELP
Brian's mathematics test had 85 problems: 20 arithmetic, 30 algebra, and 35 geometry problems. Although he answered 70% of the arithmetic problems, 40% of the algebra problems, and 60% of the geometry problems correctly, he didn't pass the test because he got less than 60% of the problems right. How many more questions would he have needed to answer correctly to earn a 60% passing grade?
Answer:
4
Step-by-step explanation:
You want to know how many more questions Brian needed to answer correctly to get a passing grade of 60% on his 85-question test, given that he answered correctly 70% of the 20 arithmetic problems, 40% of the 30 algebra problems, and 60% of the 35 geometry problems.
Correct answersThe number of correct answers Brian supplied was ...
0.70·20 +0.40·30 +0.60·35 = 14 +12 +21 = 47
The number of correct answers Brian needed for a passing grace was ...
0.60·85 = 51
Brian needed to answer 51 -47 = 4 more questions correctly to earn a passing grade.
What is the longest line segment that can be drawn in a right rectangular prism that is 14 cm long, 13 cm wide, and 9 cm tall?
The longest line segment that can be drawn in a right rectangular prism with dimensions of 14 cm long, 13 cm wide, and 9 cm high is about 21.2 cm.
The right triangular face's hypotenuse is another name for this diagonal, which is also referred to as the space diagonal.
In this instance, the right triangle face with sides of 14, 13, and 9 cm can be taken into consideration. With the Pythagorean theorem in use,
we have:
14² + 13² + 9² = c²
196 + 169 + 81 = c²
446 = c²
c = [tex]\sqrt(446)[/tex]
c = 21.2 cm (rounded to the nearest tenth)
So the longest line segment that can be drawn in a right rectangular prism with dimensions of 14 cm long, 13 cm wide, and 9 cm high is about 21.2 cm.
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Calculate
-73 - 110
Answer:
Step-by-step explanation:
-183
Answer:
Any negative minus a positive is a negative:
-183
Step-by-step explanation:
Hope it helps! =D
or A line passes through the points (1,1) and (2,7). Write its equation in slope-intercept form.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 1 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 6}(x-\stackrel{x_1}{1}) \\\\\\ y-1=6x-6\implies {\Large \begin{array}{llll} y=6x-5 \end{array}}[/tex]
Pls help me with this! I keep getting this one wrong
Tysm!
Answer:
31.4 in^2
Step-by-step explanation:
Circumference formula: pi times 2 times radius
so equation would be 3.14 (pi value) times 2 times 5 and you get your answer
the rocket coaster has 15 cars, some that hold 3 people and some that hold 5 people. there is room for 63 people altogether. how many 3-passenger cars are there? how many 5-passenger cars are there?
There are 6 cars that hold 3 people and 9 cars that hold 5 people.
How to determine the number of passengersLet's call the number of 3-passenger cars "x" and the number of 5-passenger cars "y".
We know the total number of cars is 15, so:
x + y = 15
We also know that the total number of passengers is 63, so:
3x + 5y = 63
Now we can use the first equation to solve for one of the variables in terms of the other:
y = 15 - x
Substitute this expression for y into the second equation:
3x + 5(15 - x) = 63
Expand
3x + 75 - 5x = 63
Evaluate like terms:
2x = 12
Divide both sides by 2:
x = 6
Recall that
y = 15 - x
So, we have
y = 15 - 9
y = 6
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The graph of a pair of linear equations is shown in the coordinate plane below.
Which value is the x-coordinate of the solution?
-5
-3
-2
0
The value of the x-coordinate of the solution will be -2. Then the correct option is C.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equations are given below.
y = (5/2)x + 2 ...1
y = - x - 5 ...2
From equations 1 and 2, then we have
(5/2)x + 2 = - x - 5
(7/2)x = -7
x = -2
The value of the x-coordinate of the solution will be -2. Then the correct option is C.
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Chef Ramsy used 1/4 of a bag of flour to make some muffins and twice as many cupcakes.The amount of flour he used for each muffins was 3 times as much as each cupcake.Chef Ramsy used 5/6 of the remaining bag of flour on a cake.He used 256.5g more flour on the cake than the muffins.
What friction of the bag of flour was used on the muffins?
How much flour was there in the bag at first?
Answer:
I'd say about a couple
you're welcome
me pueden decir los múltiplos de 5? porfas:(
Los múltiplos de 5 son 5,10,15,20,25,30,35,40,45,50,..........
Definición de múltiplosLos múltiplos son números que se multiplican por un número con un entero positivo (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, etc.). En términos simples, un múltiplo es el producto de un número con otro número (enteros enteros, no fracciones ni decimales).
Los números múltiples son mayores o iguales que el número en sí. Esto se debe a que el primer múltiplo se multiplica por 1. Entonces, el primer múltiplo es el número mismo. Un número o números pueden tener múltiplos de una lista ilimitada de múltiplos. Porque los números se pueden multiplicar continuamente por otros enteros más grandes.
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which measurement is equivalent to 2.34 meters? responses 0.0234 cm 0.0234 cm 23.4 cm 23.4 cm 234 cm 234 cm 2340 cm
Option 234 cm is the correct option.
The measurement equivalent to 2.34 meters is: 234 cm
To convert meters to centimeters,
you multiply the number of meters by
100.
So, 2.34 meters multiplied by 100 is equal to 234 centimeters.
An object is only identified or classified using numbers on a nominal scale, which is a measuring scale. Only non-numeric (quantitative) factors or situations where numbers have no meaning are often addressed by this assessment.
By increasing the number of metres by 100, one may convert measurements from metres to centimetres. One metre equals one hundred centimetres, or 1 m = 100 cm, as is common knowledge.
Cm is used to represent it in writing. It may also be described as the unit of length in the current metric system, the International System of Units (SI). It is equal to one hundredth of a metre.
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