Entonces, 1/8 de su salario se va en renta, y su salario mensual es de $1200.
Entiendo que deseas saber qué fracción del salario de Edna se va en renta y cuál es su salario mensual si su renta mensual es de $150. Para resolver esto, seguiré estos pasos:
1. Sabemos que Edna gasta la mitad de su salario en renta, utilidades y comida. Esto se puede expresar como 1/2 de su salario.
2. Se nos dice que 1/4 de esos gastos se va en renta. Entonces, para encontrar la fracción de su salario que se va en renta, multiplicamos 1/2 (gastos totales) por 1/4 (fracción de gastos en renta): (1/2) * (1/4) = 1/8.
3. Ahora sabemos que 1/8 de su salario se va en renta. Para hallar su salario mensual, utilizaremos la renta mensual de $150.
4. Si 1/8 de su salario equivale a $150, podemos resolver su salario (S) utilizando la siguiente ecuación: (1/8)S = 150.
5. Para encontrar S, multiplicamos ambos lados de la ecuación por 8: S = 150 * 8.
6. Finalmente, calculamos el valor: S = 1200.
Entonces, 1/8 de su salario se va en renta, y su salario mensual es de $1200.
Know more about mensual here:
https://brainly.com/question/15378983
#SPJ11
The base of a cone has a radius
of 6 centimeters. The cone is
7 centimeters tall. What is the volume
of the cone to the nearest tenth? Use 3. 14 for it.
A. 260 cm
C. 263. 8 cm3
B. 263. 7 cm
D. 264. 0 cm3
The volume of the cone to the nearest tenth is 263.8 cm^3.
What is the volume, rounded to the nearest tenth, of a cone with a radius of 6 centimeters and a height of 7 centimeters?To find the volume of the cone, we first need to use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
We are given that the radius is 6 centimeters and the height is 7 centimeters, so we can substitute these values into the formula.
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
Using the given values, we can plug them into the formula and solve:
V = (1/3)π(6 cm)^2(7 cm)
V ≈ 263.7 cm^3
Rounding this to the nearest tenth gives us the final answer of 263.8 cm^3, which is option (C).
Since 3 is less than 5, we round down, which means the answer is 263.8 cm^3, as shown in option (C).
Learn more about volume
brainly.com/question/1578538
#SPJ11
28 Laney's art teacher, Mr. Brooks, has four different colors of clay. Laney and some of her classmates will be using this clay to make different figures. The following table shows the number of pounds of each color of clay Mr. Brooks has available. Clay Amount Color (pounds) Biue 11 5 Green 8 Yellow 2 Red 15 4. Use this information to help you answer parts A through E of this problem. Part A Laney noticed that one color of clay was exactly twice the amount of clay of another color. Which color of clay weighs exactly twice the number of pounds of another color of clay? A. Blue B. Green C. Yellow D. Red. â
Blue color of clay weighs exactly twice the number of pounds of another color of clay. The correct option is a.
We need to find the color of clay that weighs exactly twice the number of pounds of another color of clay. We can start by comparing the amounts of clay for each color:
- Blue: 11 pounds
- Green: 8 pounds
- Yellow: 2 pounds
- Red: 15 pounds
To find the answer, we need to see if any of these values is exactly twice another value. We can start by dividing each amount by 2:
- Blue: 11 ÷ 2 = 5.5
- Green: 8 ÷ 2 = 4
- Yellow: 2 ÷ 2 = 1
- Red: 15 ÷ 2 = 7.5
From this, we can see that the amount of blue clay (11 pounds) is exactly twice the amount of green clay (5.5 pounds). Therefore, the answer is A. Blue.
To know more about weighs , refer here :
https://brainly.com/question/10069252#
#SPJ11
please help with question 9
The value of the function g(x) = 4x⁴ - 4x³ - 10x - 51
What are functions?Functions are defined as those expressions or equations showing the relationship between two variables.
From the information given, we have the functions;
f(x) = 4x³ + 3x² - 12x - 32
h(x) = 4x⁴ - 3x² + 2x - 19
(f + g(x) = h(x)
To determine the function, let us follow the expression
f(x) + g(x) = h(x)
Make g(x), the subject of formula
g(x) = h(x) - f(x)
Substitute the expressions
g(x) = 4x⁴ - 3x² + 2x - 19 - 4x³ + 3x² - 12x - 32
Now, collect the like terms, we get;
g(x) = 4x⁴ - 4x³ - 3x² + 3x² + 2x - 12x - 19 - 32
Add or subtract the values
g(x) = 4x⁴ - 4x³ - 10x - 51
Learn about functions at: https://brainly.com/question/25638609
#SPJ1
order: baraclude (entecavir) 0.5mg PO daily. The drug is an oral
solution with strength of 0.05 mg/mL. How many mL will you
administer?
10mL of the baraclude oral solution to the patient.
To determine the amount of the oral solution of baraclude (entecavir) to administer, we need to use the following formula:
Amount to administer (mL) = Desired dose (mg) / Strength (mg/mL)
In this case, the desired dose is 0.5mg and the strength is 0.05mg/mL. Plugging in these values, we get:
Amount to administer (mL) = 0.5mg / 0.05mg/mL = 10mL
Therefore, you will administer 10mL of the baraclude oral solution to the patient.
Hi! To calculate the number of mL to administer, you need to consider the prescribed dose and the strength of the oral solution. The order is for Baraclude (entecavir) 0.5mg PO daily, and the solution's strength is 0.05 mg/mL.
To find the required mL, divide the prescribed dose by the solution's strength:
0.5 mg (prescribed dose) ÷ 0.05 mg/mL (solution's strength) = 10 mL
You will administer 10 mL of Baraclude (entecavir) oral solution daily.
To know more about required mL click here:
brainly.com/question/14143257
#SPJ11
!!I NEEEDD HELPPP!! Please helppp :(
The customer would save $492 in the first year by switching to Intellivision.
The customer would save $207 in the second year by switching to Intellivision.
For the third year, it would be cheaper to stick with ElectroniSource.
How to find the savings ?To calculate the savings for the first year, we need to find the total cost for ElectroniSource and compare it to the flat fee from Intellivision for all three services.
The savings for the first year by switching to Intellivision would be:
$1,632 - $1,140 = $492
Therefore, the customer would save $492 in the first year by switching to Intellivision.
After the first year, Intellivision raises the rates by 25%. So the new flat fee for the second year would be:
$95 + ($95 x 25%) = $118.75
The savings for the second year by switching to Intellivision would be:
$1,632 - $1,425 = $207
Therefore, the customer would save $207 in the second year by switching to Intellivision.
For the third year, Intellivision raises the rates by 16% compared to the second year. So the new flat fee for the third year would be:
$118.75 + ($118.75 x 16%) = $137.78
Therefore, for the third year, it would be cheaper to stick with ElectroniSource, which costs $1,632 for the year, compared to Intellivision, which costs $1,653.36 for the year.
Find out more on savings at https://brainly.com/question/9153521
#SPJ1
what is the radius of a circle if 24-meter chord is 5 meters from center
Susan set up a lemonade stand to raise money for a children's hospital. She's selling cups of lemonade for $2. 50 each and brownies for $1. 50 each. She sells 280 items and raises $540.
How much money does Susan raise from selling lemonade?
If she sells 280 items and raises $540, then Susan raises $300 from selling lemonade.
To determine how much money Susan raises from selling lemonade, we'll set up a system of equations using the given information.
Let x be the number of lemonade cups and y be the number of brownies sold. We know:
1. x + y = 280 (total items sold)
2. 2.50x + 1.50y = 540 (total money raised)
First, we'll solve for x in equation 1:
x = 280 - y
Now, substitute this expression for x in equation 2:
2.50(280 - y) + 1.50y = 540
Simplify and solve for y:
700 - 2.50y + 1.50y = 540
-1.00y = -160
y = 160
Now that we have the number of brownies (y), we can find the number of lemonade cups (x):
x = 280 - 160
x = 120
Finally, calculate the money Susan raises from selling lemonade:
Money from lemonade = 120 * $2.50 = $300
So, Susan raises $300 from selling lemonade.
More on selling: https://brainly.com/question/29250593
#SPJ11
An animal reserve is home to 8 meerkats. It costs the reserve $1.50 per day to feed each meerkat. Write an equation with two variables that can be used to determine the total cost of feeding the reserve's meerkats for any number of days.
Answer:
y = 12x
Step-by-step explanation:
First let's find the total cost of feeding all the meerkats per day:
8*1.5 = 12
That means it costs $12 to feed all the meerkats each day. Now we can construct our equation
Let y = cost
Let x = days
y = 12x
This equation tells us the cost for feeding the meerkats an x number of days
Find g(x), where g(x) is the translation 1 unit left of f(x)=x2.
write your answer in the form a(x–h)2+k, where a, h, and k are integers.
To find g(x), the translation 1 unit left of f(x) = x², we need to replace x with (x+1) because moving left means we need to subtract 1 from x. Therefore, g(x) = f(x+1) = (x+1)².
To write g(x) in the form a(x-h)² + k, we need to expand (x+1)² first. Using the formula (a+b)² = a² + 2ab + b², we get:
g(x) = (x+1)² = x² + 2x + 1
Now we can write g(x) in the vertex form by completing the square. We add and subtract (2/2)² = 1 to the expression to get:
g(x) = x² + 2x + 1 - 1 + 1
= (x+1)² + 0
Therefore, g(x) = (x+1)² + 0 is the vertex form of g(x), where a=1, h=-1, and k=0. This means that the vertex of the parabola g(x) is (-1,0), and it opens upwards. The translation 1 unit left of f(x)=x² results in a horizontal shift of the parabola to the left by 1 unit without changing its shape or orientation.
To know more about find g(x) refer here
https://brainly.com/question/28440771#
#SPJ11
rewrite the expression 4^-2 x 8^0 x 5^6
The figure shown is composed of two congruent triangles and a square Measurements are given in inches 6 in 5 in 4 in A 5 in What is the total area of the figure in square inches 5 in 4 in 5 in
Answer:
60 square inches
Step-by-step explanation:
Pt refers to Pythagoras Theorem. You know two sides of a right angled triangle, how do you find the 3rd side? Pythagoras Theorem. Then the rest is easy. Just do the area of all of the 4 triangles and the area of the square and add them up
Help me find the Equation
The required quadratic function is y = -17/324 (x-12)(x-48)
What is the Graph of a function?The graph of a function is a visual representation of the relationship between the input values (often referred to as the "domain") and the output values (often referred to as the "range") of the function. The graph is typically drawn on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.
The graph of the function is in the image below:
The domain is (12,48)
Range: (0, 17)
The maximum value is 17
Axis of symmetry: x = 30
Read more about equations here:
https://brainly.com/question/22688504
#SPJ1
Stewart, Oswaldo, Kevin, and Flynn go to a soccer day at the FC Dallas' arena, Toyota Stadium, in Frisco, Texas. The coach has a computer and video system that can track the height and distance of their kicks. All four soccer players are practicing up-field kicks, away from the goal. Stewart goes first and takes a kick starting 12 yards out from the goal. His kick reaches a maximum height of 17 yards and lands 48 yards from the goal. Oswaldo goes next and the computer gives the equation of the path of his kick as y=-= +148 - 24, where y is the height of the ball in yards and x is the horizontal distance of the ball from the goal line in yards. After Kevin takes his kick, the coach gives him a printout of the path of the ball Hegy Kevin's Kick Finally, Flynn takes his kick but the computer has a problem and can only give him a partial table of data points of the ball's trajectory. Flynn's Table: Distance from the 10 11 12 13 14 15 16 17 18 19 20 goal line in yards Height in yards 0 4.7 8.75 12.2 15 17.2 18.75 19.7 20 19.7 18.75 The computer is still not working but Stewart, Oswaldo, Kevin, and Flynn want to know who made the best kick. For each soccer player, • Write an equation to represent the quadratic function. • Create a graph to represent the quadratic functions • Identify the following: Domain o Range Maximum value (height) Axis of Symmetry x-intercepts Which soccer player made the best kick? Whose kick went the highest? Whose kick went the longest? Explain your answer and support with reasoning.
Evaluate the iterated integral by converting to polar coordinates.∫8−8∫√64−x20(x2+y2) dy dx
To convert to polar coordinates, we need to express x and y in terms of r and θ. We have:
x = r cos θ
y = r sin θ
Also, we need to change the limits of integration. The region of integration is the circle centered at the origin with radius 8, so we have:
-π/2 ≤ θ ≤ π/2 (for the upper half of the circle)
0 ≤ r ≤ 8
Now we can express the integrand in terms of r and θ:
[tex]x^2 + y^2 = r^2[/tex] (by Pythagoras)
[tex]20(x^2 + y^2) = 20r^2[/tex]
So the integral becomes:
∫-π/2π/2∫[tex]08r^3 cos^2 θ sin θ dr dθ[/tex]
We can simplify cos^2 θ sin θ using the identity cos^2 θ sin θ = (1/3)sin^3 θ, so we get:
∫-π/2π/2∫[tex]08r^3 (1/3)sin^3 θ dr dθ[/tex]
The integral with respect to r is easy to evaluate:
∫0^8r^3 dr = (1/4)8^4 = 2048
The integral with respect to θ is also easy to evaluate using the fact that sin^3 θ is an odd function:
∫-π/2π/2(1/3)[tex]sin^3[/tex] θ dθ = 0
Therefore, the value of the iterated integral is:
2048(0) = 0
The volume of the solid is zero. This makes sense because the integrand is an odd function of y (or sin θ) and the region of integration is symmetric with respect to the x-axis.
Learn more about polar coordinates
https://brainly.com/question/11657509
#SPJ4
find the missing side. round your answer to the nearest tenth
The value of the missing side is 58. 75
How to determine the valueTo determine the value of the missing side, we need to know the different identities and their ratios.
These trigonometric identities are;
secantcosecanttangentcotangentsinecosineWe have their ratios as;
sin θ = opposite/hypotenuse
tan θ = opposite/adjacent
cos θ = adjacent/hypotenuse
We have that the;
Angle = 57 degrees
Adjacent = 32
Hypotenuse side = x
Then, we have;
Substitute the values for the cosine identity, we get
cos 57 = 32/x
cross multiply
x = 58. 78
Learn about trigonometric identities at: https://brainly.com/question/7331447
#SPJ1
The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
number of meals dispensed. n. 1. 3. 6. 7. amount of pet food remaining . f of n. cups. 21. 15. 6. 3.
based on the table, which function models this situation?
The function that models this situation is f(n) = -3n + 24.
To find the function, we need to analyze the relationship between the number of meals dispensed (n) and the amount of pet food remaining (f(n)).
1. Observe the change in f(n) when n increases by 1 meal. From n=1 to n=3, f(n) decreases from 21 to 15, a change of -6. From n=6 to n=7, f(n) decreases from 6 to 3, a change of -3.
2. The decrease in f(n) is not constant, so the function is not linear. However, the decrease becomes smaller as n increases.
3. Consider the average rate of change in f(n) per meal: (-6/2) = -3, (-3/1) = -3.
4. Since the average rate of change is constant, the function is linear.
5. The function has the form f(n) = -3n + b. To find b, plug in the value of n and f(n) from the table: 21 = -3(1) + b, which gives b = 24.
6. Therefore, the function that models this situation is f(n) = -3n + 24.
To know more about rate of change click on below link:
https://brainly.com/question/31226174#
#SPJ11
I forgot please help me out here. Is 25 fl oz greater than 1 pint, or 1 pint greater than 25 fl oz. Please help me out thank you so much
The 25 fluid ounces is greater than one pint is correct statement .
Relation between fluid ounces and pint ,
There are 16 fluid ounces in one pint.
Conversion of fluid ounces to pint
This implies that,
1 fluid ounces is equal to one by sixteen pint.
To be precise,
25 fluid ounces is equal to 25 / 16pints
⇒ 25 fluid ounces is equal to 1.5625.
However, since 1.5625 is greater than 1,
This implies that 25 fluid ounces is greater than 1 pint.
So, 25 fluid ounces is greater than 1 pint.
Because 25 is greater than 16.
And 1 pint is not greater than 25 fluid ounces.
Therefore, the 25 fluid ounces is greater than one pint.
learn more about pint here
brainly.com/question/31293288
#SPJ4
Please help me!!!
b) use your answer from part (a)to determine the value of y when x = –6.
the value of y is -5/8. So, In part (a), we found that the rational function f(x) = (5x + 20)/(x^2 - 20) had a vertical asymptote at x = -2√5 and x = 2√5, a horizontal asymptote at y = 0, an x-intercept at (-4, 0), a y-intercept at (0, -1), and a hole at (-4, 5/18).
To find the value of y when x = -6, we simply substitute -6 for x in the function:
f(-6) = (5(-6) + 20)/((-6)^2 - 20)
We simplify this expression by first multiplying 5 and -6 to get -30, and then adding 20 to get -10 in the numerator. In the denominator, we evaluate (-6)^2 to get 36, and then subtract 20 to get 16. So, we have:
f(-6) = -10/16
This fraction can be simplified by dividing both the numerator and denominator by 2:
f(-6) = (-10/2)/(16/2) = -5/8
Therefore, when x = -6, the value of y is -5/8.
To know more about rational function refer here:
https://brainly.com/question/20850120#
#SPJ11
9.
What is the solution set for this inequality?
negative five D plus five and one over two symbol seventeen.
Answer:
Step-by-step explanation:
7) Compute the derivative of the function m(x) = -5xğ · V(x2 – 9)3. =
The answer for the derivative of m(x) is:
m'(x) = -10x(x^2 – 9)^(3/2) - 15x^3(x^2 – 9)^(1/2)
This is the final result after applying the product rule and the chain rule.
By use the product rule and the chain rule how we find the derivative?We can use the product rule and the chain rule to find the derivative of the function
First, let's break down the function as follows:
[tex]m(x) = -5x^2 · V(x^2 – 9)^3[/tex][tex]= -5x^2 · (x^2 – 9)^3/2[/tex]
Using the product rule, we have:
[tex]m'(x) = [-5x^2]' · (x^2 – 9)^3/2 + (-5x^2) · [(x^2 – 9)^3/2]'[/tex]Taking the derivative of the first term:
[tex][-5x^2]' = -10x[/tex]Taking the derivative of the second term using the chain rule:
[tex][(x^2 – 9)^3/2]' = (3/2)(x^2 – 9)^(3/2-1) · 2x[/tex][tex]= 3x(x^2 – 9)^(1/2)[/tex]
Putting it all together:
[tex]m'(x) = -10x · (x^2 – 9)^(3/2) + (-5x^2) · 3x(x^2 – 9)^(1/2)[/tex][tex]= -10x(x^2 – 9)^(3/2) - 15x^3(x^2 – 9)^(1/2)[/tex]
To compute the derivative of a function, we need to apply the rules of differentiation, which include the product rule and the chain rule. In this case, we have a product of two functions, [tex]-5x^2[/tex] and [tex]V(x^2 – 9)^3[/tex], where V represents the square root. We apply the product rule to differentiate the two functions.
The product rule states that if we have two functions, u(x) and v(x), then the derivative of their product, u(x) · v(x), is given by u'(x) · v(x) + u(x) · v'(x). We use this rule to differentiate the two terms in the product.For the first term, [tex]-5x^2[/tex], the derivative is straightforward and is simply -10x.
For the second term, [tex]V(x^2 – 9)^3[/tex], we need to use the chain rule because the function inside the square root is not a simple polynomial. The chain rule states that if we have a function g(u(x)), where u(x) is a function of x, then the derivative of g(u(x)) is given by g'(u(x)) · u'(x). In this case, we have [tex]g(u(x)) = V(u(x))^3[/tex], where [tex]u(x) = x^2 – 9[/tex]. We need to apply the chain rule with [tex]g(u) = V(u)^3[/tex] and [tex]u(x) = x^2 – 9[/tex].
To apply the chain rule, we first take the derivative of the function [tex]g(u) = V(u)^3[/tex] with respect to u. The derivative of [tex]V(u) = u^(1/2[/tex]) is [tex]1/(2u^(1/2))[/tex].
Learn more about Derivative
brainly.com/question/30365299
#SPJ11
Find u × v, v x u, and v x v.
u = 2i + 6k
v = 4i + 7j - 5k.
To find u × v, we use the cross product formula:
u × v = | i j k |
| 2 0 6 |
| 4 7 -5 |
Expanding the determinant, we get:
u × v = (0*-5 - 6*7) i - (2*-5 - 6*4) j + (2*7 - 0*4) k
u × v = -42i - 22j + 14k
To find v × u, we use the same formula but switch the order of u and v:
v × u = | i j k |
| 4 7 -5 |
| 2 0 6 |
Expanding the determinant, we get:
v × u = (7*6 - (-5)*0) i - (4*6 - (-5)*2) j + (4*0 - 7*2) k
v × u = 42i + 18j - 14k
Finally, to find v × v, we again use the cross product formula with v as both inputs:
v × v = | i j k |
| 4 7 -5 |
| 4 7 -5 |
Expanding the determinant, we get:
v × v = (7*(-5) - (-5)*7) i - (4*(-5) - (-5)*4) j + (4*7 - 7*4) k
v × v = 0i - 0j + 0k
v × v = 0
So the cross product of v with itself is the zero vector.
To find u × v, v × u, and v × v, we'll use the cross product formula:
u × v = (u_yv_z - u_zv_y)i + (u_zv_x - u_xv_z)j + (u_xv_y - u_yv_x)k
Given u = 2i + 6k and v = 4i + 7j - 5k, we have:
u_x = 2, u_y = 0, u_z = 6
v_x = 4, v_y = 7, v_z = -5
Now, calculate u × v:
(0 * (-5) - 6 * 7)i + (6 * 4 - 2 * (-5))j + (2 * 7 - 0 * 4)k
= (-42)i + (34)j + (14)k
u × v = -42i + 34j + 14k
Next, calculate v × u:
(7 * 6 - (-5) * 0)i + ((-5) * 2 - 4 * 6)j + (4 * 0 - 7 * 2)k
= (42)i + (-34)j + (-14)k
v × u = 42i - 34j - 14k
Finally, calculate v × v:
(7 * (-5) - (-5) * 7)i + ((-5) * 4 - 4 * (-5))j + (4 * 7 - 7 * 4)k
= (0)i + (0)j + (0)k
v × v = 0i + 0j + 0k
In summary:
u × v = -42i + 34j + 14k
v × u = 42i - 34j - 14k
v × v = 0i + 0j + 0k
Learn more about cross product formula here: brainly.com/question/30404174
#SPJ11
A triangle has side lengths 6 cm, 7 cm, and √13 cm. Is this triangle a right triangle? Do these side lengths form a Pythagorean triple? Explain.
A triangle with side lengths 6 cm, 7 cm, and √13 cm is right triangle and the side lengths form a Pythagorean triple.
To determine if the triangle with side lengths 6 cm, 7 cm, and √13 cm is a right triangle and if these side lengths form a Pythagorean triple, we'll use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Identify the longest side. In this case, it's the side with length 7 cm.
Check if the Pythagorean theorem holds true for these side lengths:
(6 cm)² + (√13 cm)² = (7 cm)²
Calculate the squares of the side lengths:
(6 cm)² = 36 cm²
(√13 cm)² = 13 cm²
(7 cm)² = 49 cm²
Check if the sum of the squares of the two shorter sides equals the square of the longest side:
36 cm² + 13 cm² = 49 cm²
Compare the results:
49 cm² = 49 cm²
Since the equation holds true, the triangle is indeed a right triangle, and the side lengths 6 cm, 7 cm, and √13 cm form a Pythagorean triple.
To learn more about Pythagorean triple refer here
https://brainly.com/question/15190643#
#SPJ11
How do you use the definition of a derivative to find f' given f(x)=√4x+3 at x>-3/4?
The derivative of f(x) is -3/4.
How to find derivative?To find the derivative, use the definition of a derivative:
f'(x) = lim h→0 [f(x + h) - f(x)] / h
Substitute f(x) = √(4x + 3) into this definition:
f'(x) = lim h→0 [√(4(x + h) + 3) - √(4x + 3)] / h
Multiplying by the conjugate of the numerator:
f'(x) = lim h→0 [(√(4(x + h) + 3) - √(4x + 3)) * (√(4(x + h) + 3) + √(4x + 3))] / [h * (√(4(x + h) + 3) + √(4x + 3))]
Expanding the numerator, we get:
f'(x) = lim h→0 [(4(x + h) + 3) - (4x + 3)] / [h * (√(4(x + h) + 3) + √(4x + 3)) * (√(4(x + h) + 3) + √(4x + 3)))]
f'(x) = lim h→0 [4h] / [h * (√(4(x + h) + 3) + √(4x + 3)))]
Canceling out the h terms, we get:
f'(x) = lim h→0 4 / (√(4(x + h) + 3) + √(4x + 3)))
Now, we can evaluate the limit as h approaches 0:
f'(x) = 4 / (√(4x + 3) + √(4x + 3))
f'(x) = 4 / (2√(4x + 3))
f'(x) = 2 / √(4x + 3)
Therefore, the derivative of f(x) is -3/4.
Learn more about derivative
brainly.com/question/25324584
#SPJ11
Ellen mixed 1over 4 kg of flour with 2 over 9 kg of sugar. Determine a reasonable estimate for the amount of flour and sugar combined
A reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.
To determine a reasonable estimate for the amount of flour and sugar combined, we first need to add the fractions 1/4 and 2/9. To do this, we need to find a common denominator. The least common multiple of 4 and 9 is 36. We can convert 1/4 to 9/36 by multiplying both the numerator and denominator by 9. We can also convert 2/9 to 4/36 by multiplying both the numerator and denominator by 4. Now we can add the fractions:
9/36 + 4/36 = 13/36
So Ellen mixed 13/36 kg of flour and sugar combined. To convert this to a decimal, we can divide the numerator by the denominator:
13 ÷ 36 ≈ 0.36
Therefore, a reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.
To know more about reasonable estimate, refer to the link below:
https://brainly.com/question/23707423#
#SPJ11
Bonnie bought 12 bottles of pineapple juice and apple juice. The bottles of pineapple juice, p, were on sale for $1 per bottle, and the bottles of apple juice, a, were on sale for $1.75 per bottle. Bonnie spent a total of $15. How many bottles of pineapple juice and apple juice did Bonnie buy?
Answer:
Step-by-step explanation:
Let's use a system of equations to solve the problem.
We know that Bonnie bought a total of 12 bottles, so:
p + a = 12
We also know that Bonnie spent a total of $15, so:
1p + 1.75a = 15
We can solve this system of equations by substitution or elimination. Here, we'll use substitution:
p = 12 - a (from the first equation)
1(12 - a) + 1.75a = 15 (substituting p in the second equation)
12 - a + 1.75a = 15
0.75a = 3
a = 4
So Bonnie bought 4 bottles of apple juice. We can find the number of bottles of pineapple juice by substituting a=4 into the first equation:
p + 4 = 12
p = 8
Therefore, Bonnie bought 8 bottles of pineapple juice and 4 bottles of apple juice.
Problem List Previous Problem Next Problem = (1 point) An alternating current E(t)=120sin(12t) has been running through a simple circuit for a long time. The circuit has an inductance of L=0.31 henrys, a resistor of R=7ohms and a capacitor of capcitance C=0.029 farads. What is the amplitude of the current I?
The amplitude of the current I is 16.9 Amperes
How to determine the amplitude of the current ITo find the amplitude of the current I in the given circuit with an alternating current E(t) = 120sin(12t), inductance L = 0.31 H, resistance R = 7 ohms, and capacitance C = 0.029 F, we need to determine the impedance (Z) of the circuit first.
The impedance Z can be calculated using the formula:
Z = √((R²) + (XL - XC)²)
Where XL is the inductive reactance, and XC is the capacitive reactance. XL can be calculated as:
XL = 2πfL
And XC can be calculated as:
XC = 1/(2πfC)
Here, f is the frequency of the alternating current, which can be determined from the given function E(t) = 120sin(12t) as:
f = 12/(2π) = 1.91 Hz
Now, we can calculate XL and XC:
XL = 2π(1.91)(0.31) = 3.74 ohms
XC = 1/(2π(1.91)(0.029)) = 2.89 ohms
Next, we can find the impedance Z:
Z = √((7²) + (3.74 - 2.89)²) = √(49 + 0.72) = 7.1 ohms
Finally, we can find the amplitude of the current I using Ohm's law:
I = E(t)/Z
Since we're looking for the amplitude, we only need the maximum value of E(t), which is 120 V:
I = 120/7.1 = 16.9 A
Learn more about current at
https://brainly.com/question/2333610
#SPJ11
Can someone please help me ASAP? It’s due tomorrow
Applying the concept of combination, the number of different sandwiches that can be created is determined as: D. 6.
How to Apply the Concept of Combination to Determine How May Sandwiches to be Created?To determine the number of different sandwiches that can be created with two different meats, we can use the concept of combinations.
In this case, we need to choose 2 meats out of 4 options. The number of combinations of 2 items that can be chosen from a set of 4 items is given by the formula:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items to be chosen, and the exclamation mark (!) denotes the factorial function.
In this case, we have:
n = 4 (since there are 4 meat options)
r = 2 (since Regan wants to choose 2 meats)
Therefore, the number of different sandwiches that can be created is:
4C2 = 4! / 2!(4-2)! = 6
This means there are 6 different ways to choose 2 meats out of 4, and hence 6 different sandwich options.
Learn more about combination on:
https://brainly.com/question/11732255
#SPJ1
the area of a rectangle is 65 sqare meters. the lenght of the rectrangle is 3 m less thans twice the width. find the dimensions of the rectangle
The dimensions are;
Length = 7 meters
Width = 5 meters
How to determine the valueThe area of a rectangle is expressed as;
Area = length × width
From the information given, we have that;
Length = 2w - 3
Area = 65
Substitute the values
65 = (2w - 3)w
expand the bracket
65 = 2w² - 3w
solve the quadratic equation;
2w² + 13w - 10w - 65
Factorize the terms
w(2w + 13) - 5(2w + 13)
w = 5
Substitute the value
Length = 2w - 3 = 2(5) - 3 = 7
Learn about area at: https://brainly.com/question/25292087
#SPJ1
In the following equation, what is the value of c?
8^c = (8^-4)^5
Kellen runs for at least 1 hour but for no more than 2 hours. He runs at at an
average rate of 6. 6 kilometers per hour. The equation that models the distance he
runs for t hours is = 6. 6t
Find the theoretical and practical domains of the equation.
Select ALL correct answers.
The correct answers are:
The theoretical domain is 1 ≤ t ≤ 2.
The practical domain is 1 ≤ t ≤ 2.
Find out the theoretical and practical domain?The equation that models the distance Kellen runs for t hours is given as 6.6t, where t is the time in hours.
The theoretical domain of the equation refers to all the possible values that t can take in the equation without any restrictions. In this case, the only restriction is that Kellen runs for at least 1 hour but for no more than 2 hours. Therefore, the theoretical domain of the equation is:
1 ≤ t ≤ 2
The practical domain of the equation refers to the values of t that make sense in the context of the problem. Since Kellen runs for at least 1 hour, the practical domain should start at 1 hour. Also, since he cannot run for more than 2 hours, the practical domain should end at 2 hours. Therefore, the practical domain of the equation is:
1 ≤ t ≤ 2
Learn more about Equation
brainly.com/question/13763238
#SPJ11
In a recent Game Show Network survey, 30% of 5000 viewers are under 30. What is the margin of error at the 99% confidence interval? Using statistical terminology and a complete sentence, what does this mean? (Use z*=2. 576)
Margin of error:
Interpretation:
The margin of error at the 99% confidence interval is 1.39%. Interpretation: we can be 99% confident that the true proportion of viewers under 30 in the population falls within the range of 30% ± 1.39%.
To calculate the margin of error at the 99% confidence interval, we can use the formula:
Margin of error = z* × √(p × (1 - p) / n)
where z* is the critical value (2.576 for a 99% confidence interval), p is the sample proportion (0.30), and n is the sample size (5000).
Margin of error = 2.576 × √(0.30 × (1 - 0.30) / 5000) ≈ 0.0139 or 1.39%
The interpretation of this result is that we can be 99% confident that the true proportion of viewers under 30 in the population falls within the range of 30% ± 1.39%. In other words, if we were to conduct the survey multiple times, we would expect the proportion of viewers under 30 to fall within this interval 99 out of 100 times. This information is useful for understanding the level of uncertainty in the survey results and can help guide decision-making based on the findings.
Learn more about margin of error here: https://brainly.com/question/29328438
#SPJ11