Answer:
[tex]\frac{7}{12}[/tex] of the cake
Step-by-step explanation:
add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.
a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24
b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]
c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]
subtract found value from total to find left over cake.
a. 24 - 7 = 14
simplify.
a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]
You are left with [tex]\frac{7}{12}[/tex] of the cake.
find the angle vector (9,7) makes with the x axis
Answer:
≈ 37.9°
Step-by-step explanation:
Using the tangent ratio
tanΘ = [tex]\frac{y}{x}[/tex] where (x, y ) = (9, 7 )
tanΘ = [tex]\frac{7}{9}[/tex] , thus
Θ = [tex]tan^{-1}[/tex] ([tex]\frac{7}{9}[/tex] ) ≈ 37.9° ( to the nearest tenth )
The system of equations y = negative one-half x + 4 and y = 2x – 1 is shown on the graph below. According to the graph, what is the solution to this system of equations? (2, 3) (3, 2) (–1, 4) (4, –1)
Answer:
(2, 3 )
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
point of intersection = (2, 3 ) ← is the solution
pls help me I will give BRANLIEST!!!and follow you back (ー_ー゛)its due in 5minutes
Answer:
$186.89
Step-by-step explanation:
Let's start by finding the area of the floor.
Area of a trapezium can be found with the formula:
A=(a+b)/2*h
Let's plug our values in.
A=(10+16)/2*7.6
Simplify.
A=26/2*7.6
A=13*7.6
A=98.8
The area of the floor is 98.8 square meters.
Find how many litres of paint are needed.
98.8/1.9=52
He needs 52 liters of paint.
52/5=10.4
He needs 11 5 liter cans of paint.
Each one costs %16.99.
16.99*11=186.89
It would cost $186.89 to buy all the paint he needs.
Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B. What is the ratio of the volume of sphere A to sphere B?
Answer:
8 : 1
Step-by-step explanation:
From the above question, we are given the following parameters
Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B.
Volume of a sphere = 4/3πr³
For Sphere A , diameter = 6
Radius = Diameter ÷ 2 = 6÷ 2 = 3
Volume of Sphere A = 4/3 × π × 3³
= 113.09733553 cubic units
Approximately = 113.1 cubic units
We were given a scale factor (k) of 2
Because we are dealing with volume, the scale factor will be cubed
In order to find the Volume of the sphere B
k³ = Volume of Sphere A/ Volume of Sphere B
2³ = 113.1 / Volume of Sphere B
Volume of Sphere B = 113.1/ 2³
= 14.1375 cubic units.
The ration of the Volume of Sphere A to Sphere B
Sphere A: Sphere B
113.1 : 14.14
= 8: 1
Answer:
1:8
Step-by-step explanation:
Took the test and got it right trust
compare two spheres. first has a diameter of 8 yards. The second sphere has a diameter of 1064 yards. Determine the ratio of the volume of the larger sphere to the volume of the smaller sphere
Answer:
The ratio of the volume of the larger sphere to the volume of the smaller sphere is
2352637 : 1Step-by-step explanation:
Volume of a sphere is
[tex] \frac{4}{3} \pi {r}^{3} [/tex]
Where r is the radius
radius = diameter / 2
For First sphere
diameter = 8yards
radius = 8 / 2 = 4 yards
Volume of first sphere is
[tex] \frac{4}{3} \pi( {4})^{3} \\ \\ = \frac{256}{3} \pi \: {yd}^{3} [/tex]
For second sphere
diameter = 1064 yards
radius = 1064 / 2 = 532 yards
Volume of second sphere is
[tex] \frac{4}{3} \pi( {532})^{3} \\ \\ = \frac{602275072}{3} \pi \: {yd}^{3} [/tex]
Since the volume of the second sphere is the largest
Ratio of the second sphere to the first one is
[tex] \frac{602275072}{3} \pi \div \frac{256}{3} \pi \\ \\ = \frac{602275072}{3} \pi \times \frac{3}{256} \pi \\ \\ = \frac{602275072}{256} \\ \\ = \frac{ 2352637}{1} \\ \\ = 2352637: 1[/tex]
Hope this helps you
Evaluate ƒ(x) = –x2 + 1 for x = –3. a) 4 b) –4 C) –9 D) –8
[tex]f(x)=-x^2+1[/tex]
Plug in the value [tex]x=-3[/tex] into this function
[tex]f(-3)=-(-3)^2+1[/tex]
[tex]=-(9)+1[/tex]
[tex]=-8[/tex]
Thus, your answer will be D) -8. Let me know if you need any clarifications, thanks!
Answer:
D. -8
Step-by-step explanation:
We are given
f(x)= -x^2+1
and asked to evaluate f(x) for x= -3. Therefore, we must substitute -3 for x in the function.
f(x)= -x^2+1 for x= -3
f(-3)= -(-3^2)+1
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
First, evaluate the exponent: -3^2
-3^2= -3*-3= 9
f(-3)= -(9)+1
f(-3)=-9+1
Next, add -9 and 1
f(-3)= -8
When f(x)= -x^2+1 is evaluated for x= -3, the result is -8. Therefore, the correct answer is D. -8
Find an exact value. tangent of seven pi divided by twelve
Answer: negative 2 minus radical 3
Step-by-step explanation:
We can use the tangent half-angle formula to find the exact value of tangent of 7π/12:
tan(θ/2) = ±√[(1-cosθ)/1+cosθ)]
Here, θ = 7π/6, and cos(7π/6) = -sqrt(3)/2.
Substituting these values, we get:
tan(7π/12) = ±√[(1-(-sqrt(3)/2))/(1+(-sqrt(3)/2))]
= ±√[(2+sqrt(3))/(2-sqrt(3))]
Multiplying the numerator and denominator by (2+sqrt(3)), we get:
= ±√[(2+sqrt(3))^2/(4-3)]
= ±√[(2+sqrt(3))^2]
= ±(2+sqrt(3))
Since 7π/12 lies in the second quadrant, and tangent is negative in the second quadrant, the exact value of tangent of 7π/12 is - (2+√3)
What is the coefficient of b in the expression b² - 5b +18
Answer: -5
Step-by-step explanation:
A coefficient is a number that a variable is multiplied by.
Hope it helps <3
Answer:
well technically, there are two coefficients
the coefficient of (b^2) is 1 and the coefficient of b (itself) is -5.
But if you sre just looking for the coefficient ot just plain b, it is -5
Step-by-step explanation:
the reason I say the coefficient to (b^2) is 1 because if there is no number in front of the variable, it is automatcally assumed to be 1.
now, as for just plain b, it is -5 because the sign, positive or negative, before a number coefficient gets attached to that number. so, the entire term is -5b, which makes the coefficient to just plain b to be -5
Frank the lumberjack has a log that is 291 centimetres long. He cuts it into three pieces. Work out the length of the third piece if the first two pieces are 67cm and 181cm long.
Answer:
43cm
Step-by-step explanation:
Given
Length of Log = 291cm
First Piece = 67cm
Second Piece = 181cm
Required
Determine the length of the third piece
Given that the log was cut into three;
this implies that;
Length of Log = First Piece + Second Piece + Third Piece
Substitute values for first piece, second piece and length of log;
[tex]291 = 67 + 181 + Third\ Piece[/tex]
[tex]291 = 248 + Third\ Piece[/tex]
Subtract both sides by 248
[tex]291 - 248 = 248 - 248 + Third\ Piece[/tex]
[tex]43 = Third\ Piece[/tex]
[tex]Third\ Piece = 43[/tex]
Hence, the length of the third piece is 43cm
Determine whether the function shown in the graph is even or odd. The graph starts at the top left, continues down through the x axis at negative two to a minimum around y equals negative five, goes up to a maximum on the x axis at y equals negative one, goes back down to a minimum around y equals negative five, and goes back up through the x axis at two.
Answer:
Might be D
Step-by-step explanation:
took the test and that was the other one i was thinking
Answer: D: The function is odd because it is symmetric with respect to the origin.
Step-by-step explanation:
Lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. The table shows her data. A 2-row table with 10 columns. The first row is labeled number of coin flips with entries 0, 10, 20, 30 ,40, 50, 60, 70, 80, 90. The second row is labeled number of heads up with entries 0, 7, 12, 18, 23, 30, 35, 38, 42, 45. According to the line of best fit, about how many times would the coin land heads up in 100 flips? 48 50 51 53
Answer:
b is the right option
Step-by-step explanation:
According to the line of best fit, the coin would land heads up about 52.73 times in 100 flips, which we can round to 53.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
We can use linear regression to find the line of best fit for the given data, which will give us a linear equation that models the relationship between the number of coin flips and the number of times the coin lands heads up.
Using a calculator or statistical software, we can find that the line of best fit for the given data is:
y = 0.4975x + 2.9825
where y is the number of times the coin lands heads up, and x is the number of coin flips.
To find how many times the coin would land heads up in 100 flips, we can substitute x = 100 into the equation and solve for y:
y = 0.4975(100) + 2.9825
y = 49.75 + 2.9825
y ≈ 52.73
Therefore,
According to the line of best fit, the coin would land heads up about 52.73 times in 100 flips, which we can round to 53.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ7
NEED HELP ASAP WILL AWARD BRAINLIEST!!!!!
Answer: 69
Step-by-step explanation:
Please help. First person to answer correctly with explanation will get brainiest!!!
Answer:
64° aka D
Step-by-step explanation:
∠J + ∠L + ∠LKJ = 180°
58° + 58° + ∠LKJ = 180°
116° + ∠LKJ = 180°
∠LKJ = 180° - 116°
= 64°
hope i helped
-lvr
A cylinder has a volume of 390cm^3 If a cone has the same dimensions as the cylinder, what is it's volume?
Answer:
Volume of cone = 130 cm³
Step-by-step explanation:
Given:
Volume of cylinder = 390 cm³
dimensions of cylinder = dimensions of cone
Find:
Volume of cone
Computation:
Volume of cylinder = πr²h
390 = πr²h
124.090909 = r²h
So,
Volume of cone = (1/3)πr²h
Volume of cone = (1/3)(22/7)r²h...........[124.090909 = r²h]
Volume of cone = (1/3)(22/7)(124.090909)
Volume of cone = 130 cm³
Write the equation of a function whose parent function, f(x) = x + 8, is shifted 2 units to the right.
Answer:
[tex]\huge\boxed{f(x - 2) = x + 6}[/tex]
Step-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units to the left
f(x - n) - shift the graph n units to the right
===========================================
f(x) = x + 8
shift the graph 2 units to the right
f(x - 2) = (x - 2) + 8 = x - 2 + 8 = x + 6
the full screen guys
Answer:
(-2 2/3,0)
(0,2)
Step-by-step explanation:
Just did it
Answer:
Step-by-step explanation:
the two points are(0,2), (-8/3,0)
the figure is cut into 8 equal pieces shade 3/4 of the figure
Answer:
You have to shade 6 pieces.
Step-by-step explanation:
Hope it helps!
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of randomly selected 583 adults showed that 58 % of them would erase all of their personal information online if they could. Find the value of the test statistic.
Answer:
Test statistic = 3.863
Step-by-step explanation:
We are told that most adults would erase all of their personal information online if they could. Since the word "most" is used, it means more than 50% or 50 percent.
So, p_o = 0.5
Also, we are told that 58 % of them would erase all of their personal information online if they could.
Thus, p^ = 0.58
Number of randomly selected adults; n = 583
The test statistic formula for hypothesis test for proportion is given by:
z = (p^ - p_o)/[√[p_o(1 - p_o)/n]
Plugging in the relevant values, we have;
z = (0.58 - 0.5)/[√[0.5(1 - 0.5)/583]
z = 0.08/0.02070788416
z = 3.863
what percentage of the population has a heart rate between 68 and 77
Answer:
49.87% of the population has a heart rate between 68 and 77.
Step-by-step explanation:
We are given that the mean of the data for the resting heart of adults is 68 beats per minute and the standard deviation is 3 beats per minute.
Let X = the data for the resting heart of adults
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 68 beats per minute
[tex]\sigma[/tex] = standard deviation = 3 beats per minute
Now, the percentage of the population that has a heart rate between 68 and 77 is given by = P(68 < X < 77)
P(68 < X < 77) = P(X < 77) - P(X [tex]\leq[/tex] 68)
P(X < 77) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{77-68}{3}[/tex] ) = P(Z < 3) = 0.9987
P(X [tex]\leq[/tex] 68) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{68-68}{3}[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50
The above probability is calculated by looking at the value of x = 3 and x = 0 in the z table which has an area of 0.9987 and 0.50 respectively.
Therefore, P(68 < X < 77) = 0.9987 - 0.50 = 0.4987 or 49.87%
What is the following product?
Answer:
[tex]\boxed{6\sqrt{6} }[/tex]
Step-by-step explanation:
[tex]\sqrt{12} \sqrt{18}[/tex]
Multiply square roots.
[tex]\sqrt{12 \times 18}[/tex]
[tex]\sqrt{216}[/tex]
Simplify square root.
[tex]\sqrt{36} \sqrt{6}[/tex]
[tex]6\sqrt{6}[/tex]
will mark brainliest!!!plz helppp
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].
Let's simplify that.
Distribute with [tex]-6(x-2)[/tex]:
[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]
Combine the end like terms [tex]12+3[/tex]:
[tex]f(x-2)=(x-2)^2-6x+15[/tex]
Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:
[tex]f(x-2)=x^2-4x+4-6x+15[/tex]
Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:
[tex]f(x-2)=x^2-10x+19[/tex]
We are given [tex]g(x)=f(x-2)[/tex].
So we have that [tex]g(x)=x^2-10x+19[/tex].
The vertex happens at [tex]x=\frac{-b}{2a}[/tex].
Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].
[tex]a=1[/tex]
[tex]b=-10[/tex]
[tex]c=19[/tex]
Let's plug it in.
[tex]\frac{-b}{2a}[/tex]
[tex]\frac{-(-10)}{2(1)}[/tex]
[tex]\frac{10}{2}[/tex]
[tex]5[/tex]
So the [tex]x-[/tex] coordinate is 5.
Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:
[tex]5^2-10(5)+19[/tex]
[tex]25-50+19[/tex]
[tex]-25+19[/tex]
[tex]-6[/tex]
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].
Let's put [tex]f[/tex] into this form.
We are given [tex]f(x)=x^2-6x+3[/tex].
We will need to complete the square.
I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].
So If you add something in, you will have to take it out (and vice versa).
[tex]x^2-6x+3[/tex]
[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]
[tex](x+\frac{-6}{2})^2+3-3^2[/tex]
[tex](x+-3)^2+3-9[/tex]
[tex](x-3)^2+-6[/tex]
So we have in vertex form [tex]f[/tex] is:
[tex]f(x)=(x-3)^2+-6[/tex].
The vertex is (3,-6).
So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].
This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).
The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate how much water was in the pool initially
Answer:
900L per minute
Step-by-step explanation:
1- 70 - 20 = 50
2- in this 50 min the 45000L was drowned
3- 45000L / 50 = 900L
.. ..
A tissue sample is three cells thick. Each cell has a thickness of 0.000004m. What is the thickness of the tissue sample in mm. Give your answer in standard form. PLZ SHOW WORKING
Answer:
4000 nm
Step-by-step explanation:
Conversion from meters to nanometers: 1 meter is 1(10⁹) nm
Step 1: Convert 0.000004 to scientific notation
0.000004 = 4(10⁻⁶)
Step 2: Convert by multiplication
4(10⁻⁶) x 1(10⁹) = 4000 nm
A function f(x) has x-intercepts of -3 and -5 what is the constant term in the function f(x)=x^2+8x+
Answer:
[tex]x^{2}[/tex]
Step-by-step explanation:
because x^{2} represents the quadratic equation, so I don't think it will affect it
What is the solution to the equation ? 5{n-1 over 10}= 1 over 2
Answer:
n = 2
Step-by-step explanation:
Given
5( [tex]\frac{n-1}{10}[/tex] ) = [tex]\frac{1}{2}[/tex] ← distribute parenthesis on left side
[tex]\frac{n-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
Since denominators are both 2 then equate numerators
n - 1 = 1 ( add 1 to both sides )
n = 2
. What is the solution set for
|k - 6|+17 = 30
A. (-19, 7}
B. (-7, 19)
C. (-19, 19)
D. {-41, 19)
Answer:
Hope this is correct and helpful
HAVE A GOOD DAY!
please i need this answer in two minutes
1. Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20 an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah’s annual gross income and annual net income.
Answer: $55,489.20
Step-by-step explanation:
Given the following information :
Base salary = $10.20 per hour
Overtime pay = $10.20 * 1.5 = $15.3
Average sale per hour = $60
Tips = 20% of sale
Regular shift hour = 8hours
Work week:
3 10-hour shift = 24hrs regular (6 hrs overtime)
1 11 - hour shift = 8hrs regular (3 hrs overtime)
1 5 - hour shift = 5 hours
Total hours per week = 37hrs regular, 9hrs overtime
WEEKLY :
Income from tips = $60 * 46 * 0.2 = $552
Regular pay: 37 * 10.20 = $377.40
Overtime: 9 * $15.30 = $137.70
Total = $(137.70 + 377.40 + 552) = $1067.10
Number of weeks in a year = 52
Annual gross = $1067.10 * 52 = $55,489.20
Rectangle divided into four rectangles. The perimeters of rectangle #1, #2, #3 #4 are 10 cm, 20 cm, 28 cm and 18 cm respectively. Find the perimeter of big rectangle.
Answer:
The perimeter of the big rectangle is 38 cm
Step-by-step explanation:
Rectangle 1 and rectangle 2 share the same width, let their width be a cm while Rectangle 3 and rectangle 4 share the same width, let their width be b cm
Rectangle 1 and rectangle 3 share the same length, let their length be x cm while Rectangle 2 and rectangle 4 share the same length, let their length be y cm
The perimeter of a rectangle = 2(length + breadth).
For rectangle 1:
Perimeter = 2(a + x) = 10
a + x = 5 1)
For rectangle 2:
Perimeter = 2(a + y) = 20
a + y = 10 2)
For rectangle 3:
Perimeter = 2(b + x) = 28
b + x = 14 3)
For rectangle 4:
Perimeter = 2(b + y) = 18
b + y = 9 4)
Adding equations 1, 2, 3 and 4 gives:
a + x + a + y + b + x + b + y = 5 + 10 + 14 + 9
a + a + b + b + x + x + y + y =38
2a + 2b + 2x + 2y = 38
2((a + b) + (x + y)) = 38
For the big rectangle, let its width = c = a + b and its length be d = x + y
The perimeter of the big rectangle = 2 (c + d)
Therefore:
2((a + b) + (x + y)) = 38
2(c + d) = 38 cm = The perimeter of the big rectangle
The perimeter of the big rectangle is 38 cm
Help plz down below with the question
Answer:
The SAS Postulate
Step-by-step explanation:
SAS means Side-Angle-Side; that is, two sides are equal and an angle between those sides are equal. We're given two sides: TK and TL, and we're given that 1 is congruent to 2. Knowing the latter, we can conclude that the angle between them (let's call it 1.5 for our purposes) will be congruent to itself. Since 1.5 is the angle right in the middle of two congruent sides, our answer is SAS.
please help :) Which of these numbers is the greatest? A. 1.9 x 10 to the 5 power B. 9.1 x 10 to the 2 power C. 7.9 x 10 to the 4 power D. 89,900
Answer: The answer is A.
Step-by-step explanation:
1.9x10^5= 190000
9.1x10^2= 910
7.9x10^4 =79000