Answer:
2.4536 years
Step-by-step explanation:
compound formula:
A=P*(1+r/n)^nt
A = 6000
P = 5000
r = rate
n = 4 times per year compounded
t = time in years
6000 = 5000(1 + .075/4)^4t
divide both sides by 5000
1.2 = (1.01875)^4t
log both sides
log(1.2) = 4t * log(1.01875)
solve for t
t = 2.4537 years
Solve the following system by graphing and identify the point of intersection -5x+2y=-4 2x-y=2
Answer: Point of intersection (0, -2)
Step-by-step explanation:
Answer:
S = (0, -2)
Step-by-step explanation:
Convert both standard form equations to slope-intercept form.
-5x+2y=-4 ⇒ y = 5/2(Decimal form: 2.5)x - 2
2x-y=2 ⇒ y = 2x - 2
Given:
⇒ L1 = y = 5/2x - 2
⇒ L2 = y = 2x - 2
The intersection is point:
⇒ S = (0, -2)
Steps:
To find intersection point we need to solve the following system of equations.
y = 5/2x - 2y = 2x-2STEP 1: Solve for x
5/2x - 2 = 2x - 2
5/2x - 2x = -2 + 2
1/2x = 0
x = 0
STEP 2: Solve for y by substituting x = 0 into first equation.
y = 5/2 * 0 - 2 = 0 - 2 = -2
Suppose that the functions p and q are defined as follows. p(x)=x+1
q(x)=2x^2-2
The value of (p*q)(5) and (q*p)(5) is 288
How to determine the composite functions?The functions are given as:
p(x)=x+1
q(x)=2x^2-2
Calculate p(5) and q(5)
p(5)=5+1 = 6
q(5)=2(5)^2-2 = 48
The functions are then calculated as:
(p*q)(5) = p(5) * q(5)
(p*q)(5) = 6 * 48
(p*q)(5) = 288
Also, we have:
(q*p)(5) = (p*q)(5)
(q*p)(5) = 288
Hence, the value of (p*q)(5) and (q*p)(5) is 288
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Complete question
Suppose that the functions p and q are defined as follows. p(x)=-x-1 q(x)=-2x^2-2 Find the following. (p*q)(5) (q*p)(5)
he cone below has a radius of 3 inches, a height of 4 inches, and a slant height of 5 inches.
What is the approximate lateral area of the cone? Use 3.14 for π and round to the nearest whole number.
38 in.2
47 in.2
75 in.2
94 in.2
The lateral area of the cone is calculated as: B. 47 in.².
How to Find the Lateral Area of a Cone?Lateral area = πrl
Given the following:
Slant height (l) = 5 inches
Radius (r) = 3 inches.
π = 3.14
Plug in the values
Lateral area = (3.14)(3)(5)
Lateral area ≈ 47 in.²
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Find the constant of variation when t varies directly as the square of s, and t = 64 when S = 4.
Answer:
The constant of variation is 4
Step-by-step explanation:
We are looking for the constant of variation when t varies directly as the square of s
t = k s^2 where k is the constant of variation
t = 64 and s = 4
64 = k 4^2
64 = k * 16
Divide each side by 16
64/16 = k * 16/16
4 = k
The constant of variation is 4
the formula for the circumference (c) of a circle is c= 2πr. calculate c if r=0.8695 mm, keeping the highest possible number of significant figures in your answer
The value of the circumference (C) of a circle, having a radius (r) = 0.8695 mm, using the formula C = 2πr, is calculated to be 5.4632296245926504416865368435231 mm.
A circle is a shape formed by all points in a plane that are at a particular distance from the center.
The linear distance around a circle is defined as its circumference. In other words, if a circle is opened to produce a straight line, the length of that line equals the circumference of the circle.
The formula for the circumference of a circle is given:
C = 2πr,
where C is the circumference of the circle, r is its radius, and π is a constant.
We are asked to find the circumference of the circle (C), given its radius (r) = 0.8695 mm.
Using the formula of the circumference C = 2πr, we can find the circumference as:
C = 2*π*(0.8695) mm,
or, C = 5.4632296245926504416865368435231 mm.
Thus, the value of the circumference (C) of a circle, having a radius (r) = 0.8695 mm, using the formula C = 2πr, is calculated to be 5.4632296245926504416865368435231 mm.
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La siguiente figura 1, ilustra el salto de una rana sobrepuesto en un plano cartesiano. La longitud del salto es de 9 ft y la altura máxima con respecto al suelo es 3 ft. Encuentra la ecuación estándar a fin de calcular la trayectoria de la rana.
3. La salinidad de los océanos se refiere a la cantidad de material disuelto que se encuentra en una muestra de agua marina. La salinidad S se puede calcular a partir de la cantidad C de cloro en agua de mar con la ecuación S = 0.03 + 1.805 C, donde S y C se miden por peso en partes por millar. Calcula la C si S es 0.35.
4. El arco de un puente es semielíptico, con eje mayor horizontal. La base del arco mide 50 ft de un lado al otro y la parte más alta del arco mide 15 ft arriba de la calzada horizontal. Encuentre la altura del arco a 12 ft del centro de la base.
Investiga la hipérbola con centro en el origen y fuera del origen. Eje focal en x y en y.
2. De las expresiones que se indican a continuación, Identifica si es una recta o ecuación lineal,
una ecuación cuadrática o de segundo grado, una ecuación de tercer grado, una
circunferencia, una hipérbola, justifica tu respuesta y elabora su respectiva gráfica.
3x – 2y + 4= 0
4x + y2 -7 = 0
x2 + y2 = 16
y = x3 - 3x +1
x2 + 4y2 = 4
3. A partir de tu investigación resuelve los siguientes ejercicios:
a) Traza la gráfica
9x2 – 4 y2 = 36
Encuentra los focos y ecuaciones de las asíntotas.
b) Traza la gráfica
4y2 – 2 x2 = 1
Encuentra los focos y ecuaciones de las asíntotas.
c) Dadas las siguientes ecuaciones, decir qué cónica representan:
9 x2 - 4 y2 - 54 x - 16 y + 29 = 0
4 x2 + 2 y2 - 7 x + y - 5 = 0
x2 - 6 x + 5 y - 11 = 0
Debido a restricciones de longitud invitamos cordialmente a leer la explicación de esta pregunta para aprender sobre las cuestiones de las ecuaciones cónicas.
¿Cómo analizar y aplicar las ecuaciones cónicas?
Según la geometría analítica, existen cinco tipos de secciones cónicas: recta, circunferencia, elipse, parábola e hipérbola. Aquí se presentan problemas que emplean este tipo de ecuaciones.
1) La trayectoria de la rana describe la forma de una parábola. Asumimos que el punto máximo de la trayectoria de la rana es de la forma (h, k) = (0, k), entonces tenemos que la ecuación de la parábola es:
y - k = C · x² (1)
Donde C es la constante del vértice.
Si sabemos que (h, k) = (0, 3) y (x, y) = (9, 0), entonces la ecuación de la parábola es:
C = (0 - 3) / 9²
C = - 1 / 27
La ecuación de la parábola es y - 3 = (- 1 / 27) · x².
2) Se determina el tipo de categoría de cada ecuación:
a) 3 · x - 2 · y + 4 = 0: Recta (a · x + b · y + c = 0)
b) 4 · x + y² - 7 = 0: Parábola ((y² - k) = 4 · p · (x - h))
c) x² + y² = 16: Circunferencia ((x - h)² + (y - k)² = r²)
d) y = x³ - 3 · x + 1: Ecuación cúbica
e) x² + 4 · y² = 4: Elipse (b² · (x - h)² + a² · (y - k)² = a² · b²)
3) Se debe hallar el valor C de la función lineal tal que S = 0.35 por medios algebraicos:
0.35 = 0.03 + 1.805 · C
0.32 = 1.805 · C
C = 0.32 / 1.805
C = 0.177
4) El arco semielíptico tiene una longitud de semieje mayor de 25 pies (paralelo al eje x) y una longitud de semieje menor de 15 pies (paralelo al eje y). Si consideramos que el centro de la elipse está en el origen, entonces tenemos que la ecuación es:
x² / 25² + y² / 15² = 1
y = 15 · √(1 - x² / 25²)
y = 15 · √(1 - 12² / 25²)
y = 13.159 pies
5) a) y b) Ahora graficamos la hipérbola y presentamos las ubicaciones de los focos y las asíntotas correspondientes. a) Las ecuaciones de las asíntotas son y = ± (3 / 2) · x, b) Las ecuaciones de las asíntotas son y = ± (√ 2 / 2) · x.
c) Se puede determinar la naturaleza de cada ecuación por métodos algebraicos:
9 · x² - 4 · y² - 54 · x - 16 · y + 29 = 0
[9 · x² - 2 · 9 · (3 · x) + 81] - [4 · y² - 2 · 8 · (2 · y) + 64] = 116
(3 · x - 9)² - (2 · y - 8)² = 116
9 · (x - 9)² - 4 · (y - 4)² = 116
(x - 9)² /12.889 - (y - 4)² / 29 = 1 - Hipérbola
4 · x² + 2 · y² - 7 · x + y - 5 = 0
[4 · x² - 2 · (7 / 4) · (2 · x) + 49 / 16] + [2 · y² + 2 · (√2 / 2) · (√2 · y) + 1 / 2] = 5
(2 · x - 7 / 4)² + (√2 · y + √2 / 2)² = 5
4 · (x - 7 / 8)² + 2 · (y + 1 / 2)² = 5
(x - 7 / 8)² / 1.25 + (y + 1 / 2)² / 2.5 = 1 - Elipse
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HELP !!show the work tooo
the probability of getting heads on a two-face coin is simply 1/2.
now, what is the probability of getting 1/2 AND 1/2 AND 1/2 AND 1/2 AND 1/2? well, AND means "times", namely
[tex]\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\implies \cfrac{1}{32}[/tex]
well, and since it's a two-face coin, the probability for each face is equal, 1/2, so Heads has a chance of 1/2 each time, or we can also say that Tails has a chance of 1/2 each time, so if Tails has the same probability over 5 times as Head does.
round 14.81 to the nearest tenth
Answer: 14.8
Step-by-step explanation: If the number in the hundredths place is less than 5, you must round down. On the contrary, if that number is 5 or greater, you must round up. This applies for rounding to any place not just the tenths place. For example, if you were to round it to the ones place, the answer would be 15.
Answer:
14.8
Step-by-step explanation:
The hundredth is smaller than 5, therefore you have to round down.
hope it helps
On average, an American hummingbird flaps its wings about 3,180 times per minute.
About how many times per second does it flap its wings?
Enter your answer in the box.
times
Answer:
53 times per second
Step-by-step explanation:
There are 60 seconds in 1 minute, so divide the 3180 flaps per minute into 60 equal parts.
3180 / 60 = 53
Which of the following lists is in order from smallest to largest? 5/8, 0.6, 6.2%, 2/3, 2/3, 5/8, 0.6, 6.2% 6.2%, 0.6, 5/8, 2/3, 0.6, 6.2%, 5/8, 2/3
Answer:
6.2%, 0.6, 5/8, 2/3
Step-by-step explanation:
For some reason, you have written the same numbers over and over. It looks like there are only really 4 numbers.
I changed each number into a decimal and then compared them.
6.2% to change a percent to a decimal, move the decimal 2 places to the left so 6.2% equals 0.062.
0.6 is already in decimal form
5/8 you divide 5 by 8. Put in your calculator 5 the division symbol and then 8 to get 0.625.
2/3 is 0.6 repeating or 0.66666 forever.
Now compare:
62% = 0.62
0.6
5/8 = 0.625
2/3 = 0.66666...
Chad used the table to show the ratios of the different types of sports game cards that he owns. For every 2 offense cards, he owns 4 defense cards. Which graph represents the proportional relationship between his defense and offense cards?
Chad’s Sports Cards
Card Type
Kicking Team
Offense
Special Teams
Defense
Quantity
1
2
3
4
The equation that shows the proportional relationship between his defense and offense cards is y = 2x
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the defense cards and x represent the offense cards.
For every 2 offense cards, he owns 4 defense cards. Hence:
4 = 2m
m = 2
y = 2x
The equation that shows the proportional relationship between his defense and offense cards is y = 2x
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Select the correct triangle. Which triangle represents a reflection of triangle Aacross line m?
The probability that a student has a Visa card (event V) is .76. The probability that a student has a Master card (event M) is .16. The probability that a student had both is .04.
Answer:
The Probability of both happening is 0.304.
Step-by-step explanation:
P(A) × P(B)
= 0.76 × 0.4
= 0.304
Find the area of the shaded region.
Please anyone help me!
Thank you
Answer:
7.26
Step-by-step explanation:
Here
Diameter=2m
Length =2.6m
Breadth=4m
Now
Area of circle=(22*2*2*4)/7
=22/7
=3.14m^2
again
Area of rectangle= lb
=2.6m*4m
=10.4m^2
So
Area of the shaded region is 10.4m^2-3.14m^2
=7.26m^2
The answer is 7.26 m².
To find the shaded area, subtract the area of the circle from the area of the rectangle.
(2.6 × 4) - (3.14 × 1²)10.4 - 3.147.26 m²Assume that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12. Compute the probability P(X < 105).
The probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.
When a random variable X is normally distributed, with the mean as μ, and standard deviation as σ, then the probability P(X < x) is calculated using the Z-score table, as the probability P(Z < z), where z is calculated using the formula, z = (x - μ)/σ.
In the question, we are asked to find the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12.
We calculate as follows:
P(X < 105)
= P(Z < (105-90)/12)
= P(Z < 1.25)
Now we check the z-score table for the value of z as 1.25.
On the left column we choose the value 1.2.
On the top row, we choose the value .05.
The intersection of these, gives us the value,
P(Z < 1.25) = 0.8944.
Thus, the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.
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A party platter contains 38 cupcakes: 13 chocolate, 11 yellow, and 14 lemon. You randomly select one cupcake, eat it, then randomly select another cupcake. Find the probability of selecting from the platter a chocolate cupcake and then a yellow cupcake.
The probability of selecting from the platter a chocolate cupcake and then a yellow cupcake is 0.10.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of selecting a chocolate cupcake and then a yellow cupcake = (number of chocolate cupcake / total number of cupcakes) x (number of yellow cupcakes / total number of cupcakes - 1)
(13 / 38) x (11 / 37) = 0.10
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Identify the vertices of the feasible region for the given linear programming constraints.
System of Linear Programming:
z=−3x+5y
x+y≥−20
x−2y≥−2
x−y≤2
Fill in the vertices of the feasible region:
(−14, )
( ,−11)
(6, )
The vertices of the feasible region are as follows,
(-14, -11), (9, -11) and (6, 4)
What is a Feasible Region?
The area of the graph where all constraints are satisfied is the feasible solution zone or feasible region. It might also be thought of as the point where each constraint line's valid regions intersect. Any decision in this region would lead to a workable resolution for our objective function.
Vertices of the Feasible Region
As it can be seen in the graph, the vertices of the feasible region surrounded by the given constraints are:
(-14, -11), (9, -11) and (6, 4)
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What are the coordinates of the point p if the coordinates of the other three vertices of the rectangle in the figure shown to the right are (3,7),(3,9) and (6,9)
Considering the given rectangle, the coordinates of p are (6,7).
What are the coordinates of p?For x, there are two vertices at x = 3 and one at x = 6, hence the x-coordinate of p is x = 6.
For y, there are two vertices at y = 9 and one at y = 7, hence the y-coordinate of p is y = 7.
Then, the coordinates of p are (6,7).
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In 1996 an outbreak of a disease affected 10 people in a large community. By 1997, the number of those infected had grown to 40. Find an exponential growth function that fits the data.
Answer: The initial population is 18 and 1 year(t=1) later it is 38
Step-by-step explanation:
38 = 18 * e^(1*k), where k is the growth rate
e^(1*k) = 38/18
Take the natural log(ln) of both sides of the = k = ln(38/18) = 0.747
P(t) = 18 * e^(0.747*t), where P(t) is the population affected at time t(years since 1996)
Circles A circular device has a diameter of 4.5 inches. What is the radius of the device? Choose one 2 points O2.25 inches O4.5 inches O 4.5 inches O 2.25 inches 10 CO D
Answer: 2.25 inches
Step-by-step explanation:
The radius of a circle is half the diameter.
What is the range of possible sizes for side xxx?
Answer:
1.6 < x < 9.6
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
5.6 - 4 < x < 5.6 + 4
1.6 < x < 9.6
the radius of the base is 4 inches and its height is 6 inches what is the surface area of the cylinder in terms of pi
0.1in has 4 threads how many threads are in 1 inch?
Answer:
40
Step-by-step explanation:
Set up a proportion
Inch/ threads = inch to threads
.1/4 = 1/x Cross multiple
.1x = 4 Divide both sides by .1
x = 40
Induced pluripotent stem cells are cells from adults that have been reprogrammed to imitate embryonic stem cells. Why might induced pluripotent stem cells be a valuable tool in science and medicine?
Induced pluripotent stem cells can be a valuable tool in science and medicine because: A. induced pluripotent stem cells can become any cell type in the body, but are from adults, avoiding the controversies associated with embryonic stem cells.
What is a cell?A cell can be defined as the fundamental functional, structural and smallest unit of life, which is typically found in all living organisms.
In Science, all living organisms are broadly grouped into two (2) main categories according to cell type and these include the following;
Unicellular organismsMulticellular organismsBasically, the reason why induced pluripotent stem cells can be a valuable tool in science and medicine is simply because they can become any cell type within the body of a living organism, but are usually derived from adults that are avoiding the controversies associated with embryonic stem cells.
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Complete Question:
Induced pluripotent stem cells are cells from adults that have been reprogrammed to imitate embryonic stem cells. Why might induced pluripotent stem cells be a valuable tool in science and medicine?
A. Induced pluripotent stem cells can become any cell type in the body, but are from adults, avoiding the controversies associated with embryonic stem cells
B. Induced pluripotent stem cells are the only type of stem cell that's truly pluripotent.
C. Induced pluripotent stem cells may become any cell type in the body, but are fraught with ethical questions over their use.
D. Induced pluripotent stem cells are derived from adult cells and therefore may have DNA abnormalities, allowing scientists to understand the effects of sun exposure or toxins on DNA
The temperature at 6am is -8f , at 9am the temperature is 6f . If the temperature rises at a constant rate , what will the temperature be at 3:00pm
Answer:
24 F
Step-by-step explanation:
Temp increases by 4F per hour.
-8F - 6F = 12F / 3hours
In a recent survey,77 % of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center. Round to the nearest three decimal places.
The probability of that exactly 8 of them favor the building of the health center is 0. 399
How to determine the probabilityFrom the information given, we have that 70% of the community favors the building of the health center
Number of citizens chosen = 14
P(8) = [tex]\frac{8}{14}[/tex] × [tex]\frac{70}{100}[/tex]
P(8) = [tex]0. 57[/tex] × [tex]0. 7[/tex]
P(8) = [tex]0. 399[/tex]
Thus, the probability of that exactly 8 of them favor the building of the health center is 0. 399
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Find the solution(s) to the system of equations represented in the graph. (5 points)
Answer:
(0, -2) and (2, 0)
Step-by-step explanation:
The solution to a systems of equations is when the x and y values are equal for two equations. This can also been seen as when the two equations intersect. So by looking at the graph you see the line and the circle intersect at the point (2, 0) and (0, -2) which are going to be the two solutions to the systems of equations.
To fight a fire breathing dragon, a knight needs a sword made of Dragon Alloy #13, which contains 7% gold, 3% silver, and 90% magic steel. The dwarves promised to forge such a sword for the knight. At the moment, they have an alloy that contains magic steel, 21% gold, and 9% silver. How much of that alloy and how much magic steel do the dwarves have to combine to get 2.7 kg of Dragon Alloy #13?
Let [tex]x[/tex] and [tex]y[/tex] be the amounts of available alloy (AA) and pure magic steel that are used, so we also have
[tex]x + y = 2.7[/tex]
DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of
[tex]0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}[/tex]
[tex]0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}[/tex]
[tex]0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}[/tex]
For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; [tex]x[/tex] kg of it will contain [tex]0.21x[/tex] kg of gold, [tex]0.09x[/tex] kg of silver, and [tex]0.70x[/tex] kg of steel. Each kg of magic steel of course contributes 1 kg of steel; [tex]y[/tex] kg of it will contribute [tex]y[/tex] kg of steel.
Then the dwarves need
• total gold: [tex]0.21x = 0.189[/tex]
• total silver: [tex]0.09x = 0.081[/tex]
• total steel: [tex]0.70x + y = 2.43[/tex]
Solve for [tex]x[/tex] and [tex]y[/tex]. The first two equations are consistent and give [tex]x = 0.90[/tex], and substituting this into the third we find [tex]y = 1.80[/tex]. So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.
Equation that represents a line which is parallel to the line y=-2/3x+1
Answer:
- 2/3
Step-by-step explanation:
Answer:
Any equation that has the same slope as the line y = -2/3x + 1 but a different y-intercept will be parallel because the lines will never intersect. For example, y = -2/3x + 2 or y = -2/3x + 3.
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What is the midpoint of the line segment graphed below?
Answer:
(4, 7/2)
Step-by-step explanation:
midpoint = x values/2, y values/2