Answer:
The recipe required 50 grams of cheese
Step-by-step explanation:
Here in the question, we are made to know that she increased all ingredients by 60%.
Now we want to know the original mass of the cheese if she used 80grams after the 60% increment.
Mathematically, the formula for percentage increase is;
% increase = increment/old value * 100%
Where increment is new value - old value
since we do not know the old value, we can say that it is x. This means that the increment is 80-x
Hence;
60= (80-x)/x * 100
60x = 100(80-x)
60x = 8000-100x
100x + 60x = 8000
160x = 8000
x = 8000/160
x = 50g
A park planner is designing a dog park. He wants to use a metal fence to enclose a kennel at the dog park. The vertices of the fence are shown below. The units on the coordinate plane are yards.
Point A (4,-4)
Point B (-4,-4)
Point C (-4,3)
Point D (1,3)
Point E (1,-1)
Point F (4,-1)
The park planner wants to add a gate between points A and F. He will not put metal fencing on that side. What is the total number of yards of metal fencing that will be needed for the kennel at the dog park?
The total number of yards of metal fencing needed for the kennel at the dog park is 27 yards.
The fence segments are determined by the vertices A, B, C, D, E, and F. The distances between consecutive vertices can be calculated using the distance formula:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's calculate the lengths of the segments:
1. Length of AB: [tex]\(\sqrt{(-4 - 4)^2 + (-4 - (-4))^2} = \sqrt{64 + 0} = 8\) yards[/tex]
2. Length of BC: [tex]\(\sqrt{(-4 - (-4))^2 + (3 - (-4))^2} = \sqrt{0 + 49} = 7\) yards[/tex]
3. Length of CD: [tex]\(\sqrt{(1 - (-4))^2 + (3 - 3)^2} = \sqrt{25 + 0} = 5\) yards[/tex]
4. Length of DE:[tex]\(\sqrt{(1 - 1)^2 + (-1 - 3)^2} = \sqrt{0 + 16} = 4\) yards[/tex]
5. Length of EF: [tex]\(\sqrt{(4 - 1)^2 + (-1 - (-1))^2} = \sqrt{9 + 0} = 3\) yards[/tex]
Now, sum up these lengths:
[tex]\[ 8 + 7 + 5 + 4 + 3 = 27 \][/tex]
So, the total number of yards of metal fencing needed for the kennel at the dog park is 27 yards.
Dionne mails a package in the shape of a right rectangular prism the package was 3 inches high 14 inches wide and 20 inches long volume is ?
Answer:
840
Step-by-step explanation:
Answer:
Step-by-step explanation:
What is the length of CD? round to the nearest tenth
Answer: it is c. 10.7 cm
Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.
To find the length of CD in a right triangle ABC where:
BA = 10 cm (the side adjacent to angle B)
angle B = 30 degrees
angle C = 90 degrees (a right angle)
angle D = 25 degrees
We can use the trigonometric ratio for tangent (tan) since we know the measure of angle B and the length of side BA. The tangent of an angle in a right triangle is the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.
In this case, we want to find CD, which is the side opposite to angle B. So, we can use the following relationship:
tan(B) = CD / BA
First, find the tangent of angle B (30 degrees):
tan(30 degrees) ≈ 0.5774 (rounded to four decimal places)
Now, we can solve for CD:
CD = tan(B) * BA
CD ≈ 0.5774 * 10 cm
CD ≈ 5.774 cm
Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.
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The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y. x=-4,y=6
Answer:
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.
Given that x varies directly with y, if we introduce a constant of proportionality, k, the expression becomes
x = ky
If x = - 4 when y = 6, then
- 4 = 6k
k = - 4/6 = - 2/3
Therefore, the equation that relates x and y is
x = -2y/3
Answer:
3/2
Step-by-step explanation:
A line has the points (3,7) and (5,19) on it. What is the slope of that line?
A) 3
B) (8,26)
C) 6
D) -6
Answer:
C) 6
Step-by-step explanation:
19 - 7 = 12
5 - 3 = 2
12/2 = 6
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A barrel contains 50 gallons of water water leaked out of the barrel at a rate of 5 gallons every 4 days at this rate how many days did it take for all 50 gallons of water to leak out of the barrel
Answer:
40 days
Step-by-step explanation:
A barrel contains 50 gallons of water leaked out of the barrel at a rate of 5 gallons every 4 days at this rate
5 gallons leaked out in 4 days
50 gallons will leak out in (50x4)/5 = 10 ×4 = 40 days
It will take 40 days for the 50 gallons(1 barrel) to leak out
A perfume company is coming out with a new perfume called "Nile" that has a bottle in the shape of a square pyramid the height of the bottle is 6 centimeters and each side is 8 centimeters long.What is the volume of the Perfume bottle in cubic cm?
Answer:
The volume of the Perfume bottle is 128 cubic cm.
Step-by-step explanation:
We are given the following in the question:
Height of bottle, h = 6 cm
Base edge of perfume bottle, a = 8 cm
The perfume bottle in the shape of square pyramid.
Volume of perfume bottle = Volume of square pyramid.
[tex]V = a^2\times \dfrac{h}{3}[/tex]
Putting values, we get,
[tex]V = (8)^2\times \dfrac{6}{3}\\\\V = 128\text{ cubic cm}[/tex]
Thus, the volume of the Perfume bottle is 128 cubic cm.
A family went to a baseball game. They parked the car in a parking lot which charged $20. The cost per ticket was $27. Write an equation for the total cost of going to the baseball game, where y is the total cost and x is the total number of people. If the family spent $236, how many people went to the game?
Answer:
[tex]y=27x+20[/tex]
8 people went to the game.
Step-by-step explanation:
Let x represent number of tickets.
We have been given that the family parked the car in a parking lot which charged $20. The cost per ticket was $27.
The cost of x tickets would be [tex]27x[/tex].
The total cost of going to baseball game would be equal to cost x tickets plus parking cost that is [tex]27x+20[/tex].
Therefore, the equation [tex]y=27x+20[/tex] represents the total cost (y) of going to the baseball game.
To find the number of people who went to game, we will equate total cost with 236 as:
[tex]236=27x+20[/tex]
[tex]236-20=27x+20-20[/tex]
[tex]216=27x[/tex]
[tex]\frac{216}{27}=\frac{27x}{27}[/tex]
[tex]8=x[/tex]
Therefore, 8 people went to the game.
List the angles of the triangle in order from smallest to largest measure.
Answer:
G, I, H
Step-by-step explanation:
6 and 4 force H to be the largest and G to be the smallest.
For any right triangle, the 90 degree angle is always the largest. The longest side of a triangle is always opposite the largest angle. Similarly, the shortest side of a triangle is always opposite the smallest angle.
Angle G is opposite side HI = 4 which is the smallest side, so angle G is the smallest angle.
Angle H is the middle angle as this is the longer leg, but it is not longer than the hypotenuse. The hypotenuse is always the longest side.
The velocity of a particle moving in a straight line is given by v(t) = t2 + 9. (a) Find an expression for the position s after a time t . S(t) = + C (b) Given that s = 3 at time t = 0, find the constant of integration C. C = Find an expression for s in terms of t without any unknown constants.
Answer:
(a)The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+c[/tex]
(b)The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+3[/tex]
Step-by-step explanation:
We know that, the first order derivative of the position of an object is the velocity of the object.
(a)
Given that, the velocity of a particle moving in straight line is
[tex]V(t)=t^2+9[/tex]
[tex]\Rightarrow \frac{dS(t)}{dt}=t^2+9[/tex]
[tex]\Rightarrow {dS(t)}=t^2dt+9\ dt[/tex]
Integrating both sides
[tex]\int {dS(t)}=\int t^2dt+\int9\ dt[/tex]
[tex]\Rightarrow S(t)=\frac{t^3}3+9t+c[/tex] [ c is an arbitrary]
The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+c[/tex]
(b)
Given that S= 3 at time t=0
[tex]\therefore 3=S(t)=\frac{0^3}3+9.0+c[/tex]
[tex]\Rightarrow c=3[/tex]
The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+3[/tex]
The position function is computed by integrating the given velocity function v(t) = t^2 + 9. The constant of integration C was found to be 3 using the given initial condition of s(0) = 3. Thus, the position function without any unknown constants is S(t) = (1/3)t^3 + 9t + 3.
Explanation:The velocity function given for the particle moving in a straight line is v(t) = t2 + 9. This function can be used to find the position function using integral calculus.
hen t=0 the position function S(t) = (1/3)*03 + 9*0 + C = C = 3.
Thus, using the constant of integration we found, we can write the position function without any unknown constants as S(t) = (1/3)t3 + 9t + 3.
(a) Finding the Position Function
To find an expression for the position, we integrate the velocity function. Here, the integral of the given velocity function v(t) = t2 + 9 is S(t) = ∫(t2 + 9)dt = (1/3)t3 + 9t + C, where C is the constant of integration.
(b) Finding the Constant of Integration
Given that s(0) = 3, w
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the table shows value for the function f, while the graph shows function g.
Which function has the greater slope?
A) f
B) g
C)They are the same.
D)Insufficient information.
Answer:
A
Step-by-step explanation:
A is the right answer
f has the greater slope, 3. The slope of g is 2.
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Two dozen unrelated students went to a party. Half of them brought their mother. Only 4 of them brought their father. How many people totally went to the party?
Answer:
34
Step-by-step explanation:
What equation is the gizmo using to find the y-coordinates?
a. y = r sin e
c. y=rtan 2
b. y = r cosa
d. none of the above
Answer:
Let play build royale together
Step-by-step explanation:
b. y = r cosa
Answer: A. y= r sin e
Step-by-step explanation: I just did it
If f(1) =7 and f(n)=-5f(n-1)-n
then find the value of
f(4)
Final answer:
Using the recursive relationship f(n) = -5f(n-1) - n, we calculated the values step by step to find that f(4) is -914.
Explanation:
The question asks us to find the value of f(4) given that f(1) = 7 and the recursive relationship f(n) = -5f(n-1) - n.
To find f(4), we need to compute it in a step-by-step manner by first finding f(2) and f(3), and using those results to finally compute f(4).
Starting with f(1) = 7, we calculate f(2):
f(2) = -5f(1) - 2 = -5*7 - 2 = -35 - 2 = -37.
Next, calculate f(3):
f(3) = -5f(2) - 3 = -5*(-37) - 3 = 185 - 3 = 182.
Finally, calculate f(4):
f(4) = -5f(3) - 4 = -5*182 - 4 = -910 - 4 = -914.
Therefore, the value of f(4) is -914.
Final answer:
Using the recursive function given, by computing step by step from f(1) up to f(4), we find that f(4) equals -914.
Explanation:
To find the value of f(4), we must use the given recursive relation f(n) = -5f(n-1) - n, starting with the base case f(1) = 7.
Find f(2):Therefore, f(4) = -914.
In a sample of people at the school dance 11 out of 15 were in favor of having the photo booth. If all 300 students were surveyed about the photo booth how many are likely to be in favor of the photo booth?
Answer:
If all the 300 students were surveyed, 220 would have been in favor of the photo booth.
Step-by-step explanation:
Sample size = 15
People out of 15 in favor of photo booth = 11
Percentage of people in favor of school dance = [tex]\frac{11}{15} \times 100\% = 73\frac{1}{3} \%[/tex]
We have to find if all 300 students are surveyed how many will be in favor of photo booth. Remember that, the sample data is the best estimator of the population data. So, the sample data of 15 students will be the best estimator for the entire population of 300 students.
Since, in the sample of 15 students, [tex]73\frac{1}{3} \%[/tex] were in favor of photo booth, we would expect that if all the 300 students were surveyed, the same percentage will be in favor of photo booth. So we need to calculate [tex]73\frac{1}{3} \%[/tex] of 300.
[tex]73\frac{1}{3} \% \text{ of 300}\\\\ = 73\frac{1}{3} \% \times 300\\\\ =\frac{220}{3} \% \times 300\\\\ =\frac{220}{300} \times 300\\\\ = 220[/tex]
This means if all the 300 students were surveyed, 220 would have been in favor of the photo booth as per the sample data.
Approximately 220 out of 300 students are likely to be in favor of the photo booth.
To determine how many of the 300 students are likely to be in favor of the photo booth, we can use the proportion given by the sample.
1. Calculate the proportion of students in favor from the sample:
Proportion = Number in favor / Total surveyed = 11 / 15
Proportion = 0.7333 (rounded to four decimal places)
2. Apply this proportion to the entire school population:
Expected number in favor = Proportion × Total school population
Expected number in favor = 0.7333 × 300
Expected number in favor ≈ 220
Therefore, out of 300 students, approximately 220 students are likely to be in favor of the photo booth.
Volume of spheres
Go to I
Find the volume of the sphere.
Either enter an exact answer in terms of pi or use 3.14 for pi and round your final answer to the nearest hundredth.
----
10-
-
-
-
-
-
-
Units 3
For a sphere of radius r the volume V is
V=(4/3)πr³
We have r=10 so
V = (4/3) π 10³ = 4000π/3
Answer: 4000π/3
The volume of a sphere can be calculated using the formula V = 4/3 * π * r³. Assuming the radius is 10 units, the calculated volume is 4186.67 cubic units.
Explanation:The volume V of a sphere can be found using the formula V = 4/3 * π * r³, where π is a constant (approximately 3.14) and r is the radius of the sphere. In your question, it appears there may be missing information as the value for the radius is not provided. Assuming that 10 is the radius of the sphere, we can substitute this value into the formula. So, V = 4/3 * 3.14 * 10³ = 4186.67 cubic units. Therefore, the volume of a sphere with a radius of 10 units is approximately 4186.67 cubic units.
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A wheel completes 2.4 revolutions in 3 seconds.
What is the angular velocity of the wheel in radians per minute?
State your answer in exact form as a simplified fraction.
Answer:
The angular velocity of the wheel in radians per minute is 96·π·rad/min
Where π = 22/7 then the angular velocity is [tex]301\frac{5}{7} \ rad/min[/tex]
Step-by-step explanation:
The number of revolutions completed per 3 seconds = 2.4 revolutions
∴ The number of revolutions completed per second = 2.4/3 = 0.8 = 4/5 revolutions
The angle per revolution = 2π radians
∴ Angular velocity per second = 0.8×2×π rad/sec
The angular velocity of the wheel in radian per second = 1.6·π·rad/sec
1 minute = 60 Seconds
∴The angular velocity of the wheel in radians per minute = 96·π·rad/minute
Where π = 22/7 then the angular velocity = [tex]301\frac{5}{7} \ rad/min[/tex].
Answer:96pi
Step-by-step explanation:
Max wants to rent a bicycle. The cost to rent a bike is a $5 insurance fee plus $3 per hour. Max has at most $20 to spend. Write an inequality to represent this scenario. Give a value that satisfies the inequality.
The inequality that represents Max's situation with renting a bicycle is 5 + 3h <= 20. Max can rent the bicycle for up to 5 hours with his $20 budget, and renting for 4 hours would satisfy the inequality.
Explanation:The inequality to represent Max's situation with renting a bicycle, considering his budget constraints, would be:
5 + 3h \<= 20
Where h represents the number of hours Max can rent the bike. To solve for h, you subtract 5 from both sides of the inequality (which represents the fixed insurance fee) and then divide by 3 (the hourly rate for renting the bike):
3h \<= 15
h \<= 5
Thus, Max can rent the bicycle for up to 5 hours to stay within his budget of $20. An example value that satisfies this inequality is 4 hours, which would cost Max $5 for insurance plus $12 for the rental time, totaling $17.
Find the volume of a cylinder with a base area of 25 pi in^2 And height equal to the radius. Give your answer both in terms of pi and rounded to the nearest tenth
Answer:
The answer to your question is Volume = 125 π in³
Step-by-step explanation:
Data
Volume = ?
Base area = 25π in²
height = radius
Process
1.- Find the radius
Area of the base = πr²
-Equal
πr² = 25π
-Solve for r
r² = 25π/π
-Simplify
r² = 25
-Result
r = 5 in
2.- Find the volume of the cylinder
Volume = πr²h
-Substitution
= (25π)(5)
-Simplification
Volume = 125 π in³
100 points!!! Simplify the bottom right so there are no radicals in the denominator.
Answer:
-
[tex] \frac{ - \sqrt{2} }{10} [/tex]
step by step:
[tex] \frac{ - 1}{5 \sqrt{2 } } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ - \sqrt{2} }{5 \times 2} = \frac{ - \sqrt{2} }{10} [/tex]
multiply by the square root of 2 to get rid of the square root of 2 on the bottom, then simplify. hope this helped :)
[tex]\\ \sf{:}\longrightarrow \dfrac{-1}{5\sqrt{2}}[/tex]
Multiply 5√2 on both numerator and denominator[tex]\\ \sf{:}\longrightarrow \dfrac{-1(5√2)}{(5√2)^2}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{25(2)}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{50}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-√2}{10}[/tex]
Help ASAP Will give Brainllest . Please explain how you got the answer
Answer:
10 yd
Step-by-step explanation:
The length of the top is
6+4 = 10 yd
The bottom must be the same length
To find the length of the bottom side, we can look around the shape to see if there are any similar sides. The sides 6ft and 4ft make up the same length as the bottom side, so, we can add.
6 + 4 = 10ft.
Best of Luck!
I need to know what is the un given side by using Soh Coa Toa
Answer:
1.68 km
Step-by-step explanation:
You want the horizontal distance (on the ground) from beneath the helicopter to the vertex of the 37 degree angle. The hypotenuse is given and is 2.1 km.
We want to find the horizontal distance when we already know the angle and the hypotenuse.
That horizontal distance could be called 'x.' Then:
x/r = adj/hyp = cos 37 degrees, which becomes adj = (2.1 km)cos 37 degrees, which is found using a calculator: adj = (2.1 km)(0.7987) = 1.68 km
what type of graph does not have scale and aces defined on it?
Answer:
C
Step-by-step explanation:
any help will be greatly received
Answer:
The shop did not meet their goal of selling 65 per month. You can tell this because if you look at the graph you see that January, May, and June are all under the 65 mark.
Hope this helps ;)
Is (2,1) a solution of the system y=3x-5
Answer:
(2,1) is a solution
Step-by-step explanation:
y = 3x-5
Substitute the point into the equation and see if it is true
1 = 3(2)-5
1 = 6-5
1=1
This is true so the point is a solution
An angle of -210 degree is in standard position. What are the coordinates of the point at which the terminal side intersects the unit circle?
Answer:
( -[tex]\sqrt{3}[/tex]/2 , -1/2)
Step-by-step explanation:
-210 degrees in standard position corresponds to an angle in the 3rd quadrant 30 degrees below the negative x-axis
The hypotenuse of the triangle here is 1, and we want the coordinates.
_______________________(0,0)
|(x = -root(3)/2)
|
| (y = -1/2)
The coordinates of the point at which the terminal side intersects the unit circle are (-√3/2, -1/2).
What is the cartesian plane?The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.
Given -210 degrees is in standard position,
-210° lies in the third quadrant,
which is 180° + 30° or π + 30°
the coordinate are x = cos(π + 30°)
and y = sin(π + 30°)
cos(π + Ф) = -cosФ and
sin(π + Ф) = -sinФ
x = cos(π + 30°) = -cos30° = -√3/2
y = sin(π + 30°) = -sin30° = -1/2
Hence the coordinates of points are (-√3/2, -1/2).
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Leora had some money in her wallet. She spent $18.62 buying groceries and had $43.55 left. How much money did she have in her wallet before she bought the groceries?
Answer:
$62.17
Step-by-step explanation:
Answer:
The answer is 62.17.Because you would add 18.62 + 43.55 to get your answer of 62.17
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Zach use the steps to solve this equation when Zack check the solution, it didn’t work. What was his mistake
Answer:C
Step-by-step explanation:
The area of the window is
Sarah is trying to figure out how many books she can purchase at the book fair. Based on the table below, how many books can she buy with $5?