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Related Questions
Attached as an image. Please help.
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The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.
How to find the solution of an ordinary differential equation with separable variablesHerein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:
dy / dt = 3 · y · (1 - y / 14)
dy / [3 · y · (1 - y / 14)] = dt
dy / [- (3 / 14) · y · (y - 14)] = dt
By partial fractions we find the following expression:
- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt
- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.
y = 14 / [1 - C · tⁿ], where n = - 14² / 3.
If y(0) = 10, then the particular solution is:
y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.
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En la final de un concurso escolar de
matemática participan 6 alumnos de los
cuales 3 son alumnos del colegio A. Si se
premia a los dos primeros con regalos
diferentes, entonces la probabilidad de que
los alumnos del colegio A obtengan los dos
premios (no hay empates), es:
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Usando la distribución hipergeométrica, la probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es: 0.2 = 20%.
¿Qué es la fórmula de distribución hipergeométrica?La fórmula es:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
x es el número de éxitos.N es el tamaño de la población.n es el tamaño de la muestra.k es el número total de resultados deseados.Los valores de los parámetros son:
N = 6, k = 3, n = 2.
La probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es P(X = 2), por eso:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,6,2,3) = \frac{C_{3,2}C_{3,0}}{C_{6,2}} = 0.2[/tex]
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Calcular el valor del ángulo que falta de dun triangulo rectangulo si uno de sus lados mide 25 grados.
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Considerando la definición de triángulo rectángulo y sus propiedades, el valor del ángulo que falta de un triángulo rectángulo es 65°.
Definición de triánguloUn triángulo es un polígono que está determinado por tres segmentos de recta que se denominan lados, o por tres puntos no alineados llamados vértices.
En otras palabras, un triángulo es un polígono conformado por tres lados, así como por tres vértices y tres ángulos interiores.
Una de las propiedades de cualquier triángulo indica que la suma de los ángulos interiores es igual a 180°.
Definición de triángulo rectánguloEl triángulo rectángulo es una figura geométrica que se considera como un polígono formado por tres lados que forman un ángulo recto y dos ángulos agudos.
En otras palabras, el triángulo rectángulo es aquel que tiene un ángulo interior que es recto, es decir, mide 90º.
Valor del ángulo faltante en este casoEn este caso, sabes que:
Al ser un triángulo rectángulo, un ángulo interior mide 90°.Otro ángulo interior mide 25°. La suma de los ángulos interiores es igual a 180°.Entonces, el valor del ángulo faltante se puede calcular mediante:
90° + 25° + ángulo faltante= 180°
Resolviendo:
115° + ángulo faltante= 180°
ángulo faltante= 180° - 115°
ángulo faltante= 65°
Finalmente, el valor del ángulo que falta de un triángulo rectángulo es 65°.
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David rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 84 cents for each mile driven. David had to pay $250.67 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
277 miles
Step-by-step explanation:
$2,870 per month. He pays $574 a month for rent. What percent of his monthly pay goes to rent?
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we know that 2870 is the 100%, what is 574 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 2870 & 100\\ 574& x \end{array} \implies \cfrac{2870}{574}~~=~~\cfrac{100}{x} \\\\\\ 5=\cfrac{100}{x}\implies 5x=100\implies x=\cfrac{100}{5}\implies x=20[/tex]
The percent of his monthly pay which goes to rent if he earns a total of $2,870 per month is 20%.
What percent of his monthly pay goes to rent?Amount earned per month = $2,870
Amount paid for rent = $574
Let
The unknown percent = x
x% of $2,870 = $574
x/100 × 2,870 = 574
2,870x/100 = 574
cross product
2,870x = 57,400
divide both sides by 2,870
x = 57,400/2,870
x = 20%
Ultimately, 20% of the monthly pay goes to rent.
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This graph represents a quadratic function. An upward parabola on a coordinate plane vertex at (minus 2, 2) and passes through (minus 3, 5) and (minus 1, 5). What is the value of a in the function’s equation? A. -2 B. -3 C. 2 D. 3
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Answer: 3
Step-by-step explanation:
Substituting into vertex form, the equation is
[tex]y=a(x+2)^2 +2[/tex]
Substituting in the coordinates (-3, 5),
[tex]5=a(-3+2)^2 +2\\\\5=a+2\\\\a=3[/tex]
The diagonals of a rectangle enclose an angle of measure 78 degree
. If the perimeter of the rectangle is 36cm, what is its area?
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The area of the rectangle with a perimeter of 36 cm is determined as: 80.1 cm².
What is the Area of a Rectangle?Area of a rectangle = (length)(width).
Given the following:Angle of measure 78 degree enclosed by the diagonals of the rectangle
Perimeter = 36 cm
To find the area, we need to find the length and width of the rectangle using the trigonometric ratios.
A side of the rectangle = x cm
The other side = (36 - 2x)/2 = (18 - x) cm
Angle of the diagonal base = (180 - 78)/2 = 51°
Apply the tangent ratio to find x:
Tangent ratio is tan ∅ = opposite/adjacent side of a right triangle. We have the following,
∅ = 51°
Opposite side = x cm
Adjacent side = (18 - x) cm
Tan 51° = x/(18 - x)
1.235 = x/(18 - x)
1.235(18 - x) = x
22.23 - 1.235x = x
22.23 = x + 1.235x
22.23 = 2.235x
22.23/2.235 = 2.235x/2.235
x = 9.946 cm (one side length)
The other side length = 18 - x = 18 - 9.946 = 8.054 cm
Area of the rectangle = (9.946)(8.054)
Area of the rectangle = 80.1 cm²
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Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B? (5 points)
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Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. Now, in order to show that circle A is similar to circle B, we will have to dilate circle A by a scale factor of 4. We can use transformations like dilation and translation to make two circles similar.
Given Information:
For circle A,
Center, C1(x, y) = (6, 7)
Radius, r1 = 4
For circle B,
Center, C2(x, y) = (2, 4)
Radius, r2 = 16
Showing the Two Circles Similar
Now, to make circles A and B similar, we will have to make their centers coincide. It can be done by following the steps listed below:
First, translate circle A using the rule (x + 4, y + 3).Then, rotate circle A by 45° about the center.In the third step, dilate circle A by a scale factor of 4 (r2/r1).Finally, Reflect circle A about the origin to make it similar to circle BHence, we can now see that circle A is similar to circle B.
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Factor the common factor out of 8^3 + 12x
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The factorized expression of 8^3 + 12x is 4(128+ 3x)
How to factor the common factor out?The expression is given as:
8^3 + 12x
Evaluate 8^3
8^3 + 12x = 512 + 12x
Factor out 2 from the expression
8^3 + 12x = 2(256+ 6x)
Factor out 2 from the expression
8^3 + 12x = 2 * 2(128+ 3x)
Evaluate the product
8^3 + 12x = 4(128+ 3x)
Hence, the factorized expression of 8^3 + 12x is 4(128+ 3x)
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AN ARTICLE STATED THAT “INTERNAL SURVEYS PAID FOR BY DIRECTORY ASSISTANCE PROVIDERS SHOW THAT EVEN THE MOST ACCURATE COMPANIES GIVE OUT WRONG NUMBERS 15% OF THE TIME.” ASSUME THAT YOU ARE TESTING SUCH A PROVIDER BY MAKING 10 REQUESTS AND ALSO ASSUME THAT THE PROVIDER GIVES THE WRONG TELEPHONE NUMBER 15% OF THE TIME. FIND THE PROBABILITY OF GETTING ONE WRONG NUMBER.
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Using the binomial distribution, there is a 0.3474 = 34.74% probability of getting one wrong number.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are given by:
p = 0.15, n = 10.
The probability of getting one wrong number is P(X = 1), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
P(X = 1) = C(10,1) x (0.15)¹ x (0.85)^9 = 0.3474
0.3474 = 34.74% probability of getting one wrong number.
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Can anyone please help me with this assignment
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1. The sentences translated to equations looks like:
a) 4x = 32.
b) x + 6y = 43.
c) 3x + 7 = 9x - 4.
d) 76 - 2x = 8x.
2. The equations translated to sentences looks like:
a) The sum of 16 and 9 times x is 50.
b) The sum of the square of x and 6 times y is 4 times w.
c) Three times x is 52.
d) Five-sixth is equal to the product of -10 and x.
Practice Part 1: Translate sentence to equation
a)Four times a number is thirty-two.
Assuming the number to be x, we get the equation, 4x = 32.
b)The sum of and six times is equal to forty-three.
The sentence, when translated to an equation looks like, x + 6y = 43.
c)The sum of 7 and three times equals the difference of 9 times and 4.
The sentence, when translated to an equation looks like, 3x + 7 = 9x - 4.
d)Two times less than 76 is equal to the product of 8 and
The sentence, when translated to an equation looks like, 76 - 2x = 8x.
Practice Part 2: Translate equation into sentence
a) 9x + 16 = 50.
- The sentence for the given equation is, the sum of 16 and 9 times x is 50.
b) x² + 6y = 4w.
- The sentence for the given equation is, the sum of the square of x and 6 times y is 4 times w.
c) 3x = 52.
- The sentence for the given equation is, three times x is 52.
d) 5/6 = -10x.
- The sentence for the given equation is, five-sixth is equal to the product of -10 and x.
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Suppose that 5 workers can complete a certain task in 12 days. If there are 4 workers, how many days would it take for them to finish the same task
Answers
Answer:
15 days
Step-by-step explanation:
5 workers times 12 days is 60 days per worker which gets reduced based on how many workers there are. 60 divide by 4 workers now brings down to 15 days. 5 workers, 12 days. 10 workers 6 days etc.
8x+4y=7
6x-8y=41
using ELIMINATION METHOD
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Answer:
([tex]\frac{5}{2}[/tex] , - [tex]\frac{13}{4}[/tex] )
Step-by-step explanation:
8x + 4y = 7 → (1)
6x - 8y = 41 → (2)
multiplying (1) by 2 and adding to (2) will eliminate y
16x + 8y = 14 → (3)
add (2) and (3) term by term to eliminate y
22x + 0 = 55
22x = 55 ( divide both sides by 22 )
x = [tex]\frac{55}{22}[/tex] = [tex]\frac{5}{2}[/tex]
substitute this value into either of the 2 equations and solve for y
substituting into (1)
8([tex]\frac{5}{2}[/tex] ) + 4y = 7
20 + 4y = 7 ( subtract 20 from both sides )
4y = - 13 ( divide both sides by 4 )
y = - [tex]\frac{13}{4}[/tex]
solution is ( [tex]\frac{5}{2}[/tex] , - [tex]\frac{13}{4}[/tex] )
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10).
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The graph is shown in the attached image.
Consider the line 3x - 4 y = 7.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
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Answer:
The slope of a line perpendicular to this line is -1/3. The slope of a line parallel to this line would be 3.
Step-by-step explanation:
Perpendicular lines have opposite(sign) and reciprocal slopes.
Parallel lines have the same slope.
what is the range of the function f (x) = lxl +5?
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The range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.
Given that the function is f(x)=IxI+5.
We are required to find the range of the function.
Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y. The value of x is known as domain of the function and the value of y is known as codomain of the function. Range of a function is a limit of values in which the values of function lies.
Function is f(x)= IxI+5
We know that IxI=x for x>=0 and -x<0.
We have to just put the value of IxI in f(x) to get the range of function.
f(x)=x+5 for x>=0 and -x+5 for x<0.
Hence the range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.
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A company has two large computers. The slower computer can send all the company's email in 60 minutes. The faster computer can complete the same job in 15 minutes. If both computers are working together, how long will it take them to do the job?
Do not do any rounding
Minutes =
Answers
Answer:
15.25 given using both
Step-by-step explanation:
Slow com= 60 all mail
Fast clm= 15 all mail
Given both bejng used
60 min ÷ 15 min = intervall of 4 unbroken min
and
15min÷60min= 0.25
0.25mjn×60sec= 15sec
Sret =15min anfd 15 seconds/ 15.25min
Divide. write your answer in simplest form. 7/9 divided by 8/15
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Explanation:
7/9 divided by 8/15 can also be written as 7/9 x 15/8. We multiply the top and the bottom. It would look like 7x15/9x8. That equals 105/72. Simplified it is 35/24
Answer:
Step-by-step explanation:
7/9 * 15/8 = 105/72 = 35/24
The points
(−1.2,2.9) and (2.9,9.46) are on the graph of a linear relationship between two variables, x and y
Write a formula that expresses
y in terms of x
What is the value of y when x=115
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[tex](\stackrel{x_1}{-1.2}~,~\stackrel{y_1}{2.9})\qquad (\stackrel{x_2}{2.9}~,~\stackrel{y_2}{9.46}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9.46}-\stackrel{y1}{2.9}}}{\underset{run} {\underset{x_2}{2.9}-\underset{x_1}{(-1.2)}}}\implies \cfrac{6.56}{2.9+1.2}\implies \cfrac{6.56}{4.1}\implies 1.6[/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}{2.9}=\stackrel{m}{1.6}(x-\stackrel{x_1}{(-1.2)}) \\\\\\ y-2.9=1.6(x+1.2)\implies y-2.9=1.6x+1.92\implies \boxed{y=1.6x+4.82} \\\\\\ \textit{when x = 115, what is "y"?}\qquad y=1.6(115)+4.82\implies y=188.82[/tex]
The following diagrams show six lines with equations of the form y =mx +c
I have the answers but I do not know how to FIND the right one. Please help!
Answers
Answer:
understand the meaning of m > 0 and c > 0.
Step-by-step explanation:
The slope-intercept form of the equation of a line tells you its slope and its y-intercept.
y = mx +c . . . . line with slope m and y-intercept c
Slope (m)The slope is the rate of increase moving from left to right. It is positive (m>0) when the line slants upward to the right. It is negative (m<0) when the line slants down to the right.
m > 0: lines 3, 5, 6m < 0: lines 1, 2, 4Y-intercept (c)The y-intercept is where the line crosses the (vertical) y-axis. It is positive (c>0) when the line crosses above the x-axis, where y-values are positive. It is negative (c<0) when the line crosses below the x-axis. If the line passes through the origin, then c=0.
c > 0: lines 4, 5c < 0: lines 1, 3c = 0: lines 2, 650 POINTS PLEASE HELP I NEED ANWSER NOW what would the reflection look like
Answers
Answer:
Point C will be at (3,1), Point B will be at (7,1) and Point A will be at (7,5)
Step-by-step explanation:
What is the multiplicative rate of change of the function? which answer is it? These are the options 1/5, 2/5, 2, or 5
Answers
Reason is multiply 2 x 1/5 = 2/5.
multiply 2/5 x 1/5 = 2/25.
Multiply 2/25 x 1/5 = 2/125.
So you see from the chart, the rate of change is 1/5.
Multiply each of the following(2a-3b)and(a^2+2b^2)
Answers
Answer: [tex]\Large\boxed{2a^3+4ab^2-3a^2b-6b^3}[/tex]
Step-by-step explanation:
Given expression
(2a - 3b) (a² + 2b²)
Apply the FOIL method (First Outer Inner Last)
Please refer to the attachment below for a graphical understanding
= 2a · a² + 2a · 2b² - 3b · a² - 3b · 2b²
Simplify by multiplication
=2 (a · a²) + 4 (a · b²) - 3 (b · a²) - 6 (b · b²)
[tex]\Large\boxed{=2a^3+4ab^2-3a^2b-6b^3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Your answer is 2a³ + 4ab² - 3a²b - 6b³.
Step-by-step explanation:
(2a - 3b) (a² + 2b²)
=2a (a² + 2b²) -3b (a² + 2b²)
=2a.a² + 2a.2b² - 3b.a² - 3b.2b²
=2a³ + 4ab² - 3a²b - 6b³ ans.
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Find (g*f)(3)
f(x)= 7x + 8
g(x)= -1/x
Answers
Answer:
-21-24/x
Step-by-step explanation:
f(x) is a function on his own which is f(x)=7x+8
we multiple it with another function which is g(x)=-1/x
that gives us (g*f)=-7-8/x
then multiple it by 3 we have -21-24x
Simplify each expression. Select the correct answer from the drop-down menu.
−6(3i)(−2i) =
2(3 − i)(−2 + 4i) =
Answers
Answer:
Step-by-step explanation
-6(3i)(-2i)=-6(3i*-2i)=-6*-6i²=36i²
2(3-i)(-2+4i)=(6-2i)(-2+4i)=-12+24i+4i-8i²=-8i²+28i-12
Answer:
1. -36
2. -4+28i
3. 10+8i
Step-by-step explanation:
EDGE2022
How many three-digit positive integers have three different digits and at least one prime digit?
Answers
Answer:
252
Step-by-step explanation:
using a brute force method in c++
#include <stdio.h>
int main(){
int a, b, c, n = 0;
for(a = 1; a <= 9; a++)
for(b = 0; b <= 9; b++)
for(c = 0; c <= 9; c++)
if((a==3 || b==3 || c==3)) n++;
printf("%d\n", n);
}
thank you for helping
Answers
Explanation:
Step 1:
A triangle equals 180 and we already know two angles so we add 40 plus 45 which equals 85 then subtract 85 from 180 to find the missing angle which equals 95
Step 2: Now since we know the missing angle we use the straight line rule which states:Any straight line equals 180.and under close examination we see the 95 degree angle forms a straight line with the exterior angle so we subtract 95 from 180 and we get 85
what the difference between graphing lines and graphing inequalities?
what the difference between arithmetic and geometric ?
how do you explain using sigma notation ?
how to simplify into logarithmic?
Answers
Answer:
Step-by-step explanation:
graphing lines is just what it sounds like, you are taking the equation of the line and putting it on the graph. graphing inequalities shows the area of the coordinate plane that satisfies the inequality, it almost always splits the graph.
arithmetic: -6 , 1 , 8 , 15 , 22
geometric: 2 , 4 , 8 , 16, 32
please help this is affecting my grade pls help i beg of you <3
Answers
Answer:
C - On the number line, move 3 units to the left. End at -7. The dolphin was 7 feet below sea level.
Step-by-step explanation:
The dolphin's starting point was -4 (4 feet below sea level). If the dolphin if diving down by 3 feet, you add -3 to its starting point.
-4 + -3 = -7.
Please help me with this question!!!!,
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
The contrapositive of the statement is False.
Because we already know, Cube is a 3 - dimensional shape with 6 faces, all its sides are equal and all faces are congruent.
But the contrapositive of the statement is not true, because not only cube has six faces.
There are other 3 - D shapes that have 6 faces.
[tex] \qquad \large \sf {Conclusion} : [/tex]
The contrapositive of the statement is false.