Answer: O253
Step-by-step explanation:
The correct expression which represents the volume of the cone is,
V = 2x³π/3
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The height of a cone is twice the radius of its base.
Let radius of cone = x
Then, The height of cone = 2x
Hence, The volume of cone is,
V = 1/3πr²h
V = 1/3 × π × x² × 2x
V = 2x³π/3
Thus, The correct expression which represents the volume of the cone is,
V = 2x³π/3
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ5
How to find minimum and maximum of this equation.
Using it's vertex, the maximum value of the quadratic function is -3.19.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the equation is:
y + 4 = -x² + 1.8x
In standard format:
y = -x² + 1.8x - 4.
The coefficients are a = -1 < 0, b = 1.8, c = -4, hence the maximum value is:
[tex]y_v = -\frac{1.8^2 - 4(-1)(-4)}{4(-1)} = -3.19[/tex]
More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967
#SPJ1
Solve the inequality.
-1.5(4x+1) ≥ 45-25(x+1)
Answer:
x ≥ 21.5/19
Step-by-step explanation:
-1.5(4x + 1) ≥ 45 - 25(x + 1)
-6x - 1.5 ≥ 45 - 25x - 25
-6x + 25x ≥ 45 - 25 + 1.5
19x ≥ 21.5
x ≥ 21.5/19
A physics class has 40 students. of these, 15 students are physics majors and 16 students are female. of the physics majors, six are females. find the probability that a randomly selected student is female or a physics major
The probability that the randomly selected student is female or Physics major is 0.625.
Given Information
Total number of students = 40
Number of Physics major out of the total students, P = 15
Number of females in the class, F = 16
Number of females that are Physics major, (P∩F) = 6
We have to find the probability P(P∪F).
Calculating the Probability
Probability of Physics major students, P(P) = 15/40
= 0.375
Probability of female students, P(F) = 16/40
= 0.4
Probability of female students who are Physics major, P(P∩F) = 6/40
= 0.15
Since, we know that,
P(P∪F) = P(P) + P(F) - P(P∩F)
∴ P(P∪F) = 0.375 + 0.4 - 0.15
P(P∪F) = 0.625
Thus, the probability that the randomly selected student will be a Physics major or a female is 0.625
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
Apply the distributive property to factor out the greatest common factor. 16+36=16+36=
To eliminate the biggest common factor, use the distributive property: Solution: 16 + 36 = 4 (4 + 9)
To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Due to that,
To remove the most significant common factor, we must use the distributive property.
Given expression:16 + 36
1, 2, 4, 8, and 16 make up the number 16.
1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.
Then, 4 is the most prevalent component.
distributed property
The formula is ab + bc
subtracting 4 from the supplied expression.
Therefore, the distributive property is used.
Learn more about distributive property here :
https://brainly.in/question/7963814
#SPJ4
. The Pancake Restaurant served 348 pancakes. If 87 customers ate an equal number of pancakes, how many did each person eat?
Answer:
4
Step-by-step explanation:
348 / 87 = 4
There are 87 Customers. The restauraunt served 348 pancakes. You divide 348 by 87 and conclude that each customer ate 4 pancakes.
Answer:
4
Step-by-step explanation:
348 ÷ 87 = 4
each person ate 4 pancakes
In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is
The 95% confidence interval of voters not favoring the incumbent is (0.0706, 0.1294).
Sample size, n=400
Sample proportion, p = 40 / 400
= 0.1
We use normal approximation, for this, we check that both np and n(1-p) >5.
Since n*p = 40 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.1 and standard deviation = root( p * (1-p) /n )
= 0.015
For constructing Confidence interval,
Margin of Error (ME) = z x SD = 0.0294
95% confidence interval is given by Sample Mean +/- (Margin of Error)
0.1 +/- 0.0294 = (0.0706 , 0.1294)
Learn more about Margin of Error here https://brainly.com/question/15691460
#SPJ4
Find the area of the figure to the nearest square unit
Answer:
357 mi²
Step-by-step explanation:
A = LW + 0.5πr²
A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²
A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²
A = 357 mi²
Find F(5) for f(x)= 1/4(2)^x
If we have a function f(x), f(5) is f(x) but replacing x with 5. The result give us a value of y and a point of the function, (x, y).
[tex]f(5) = \frac{1}{4} ({2})^{5} = \frac{32}{4} = 8[/tex]
ANSWER A
Hello!
Substitute x = 5 to find f(5).
⇒ f(5) = 1/4(2)⁵
⇒ f(5) = 32/4
⇒ f(5) = 8
∴ The correct option is A.
Janelle makes fruit punch by mixing the ingredients listed below.
• 5 pints of orange juice
• 6 cups of grape juice
• 8 cups of apple juice
How many quarts of fruit punch does Janelle make?
Answer:
6 quarts
Step-by-step explanation:
2 pints = 1 quart
4 cups = 1 quart
• 5 pints of orange juice
5 pints = 5/2 =>2.5 quarts
• 6 cups of grape juice
6 cups = 6/4 => 1.5 quarts
• 8 cups of apple juice
8 cups = 2 quarts
2.5 + 1.5 + 2 = 6 quarts
What is the inverse of this function?
Step-by-step explanation:
f(x) = y = -1/2 × sqrt(x + 3), x >= -3
-2y = sqrt(x + 3)
4y² = x + 3
x = 4y² - 3
and now we need to rename x to y and y to x to make it a "normal" function :
y = 4x² - 3
since in the original function x >= -3, this gave us y <=0.
and therefore (remember the x of the inverse function actually stands for the y of the original function) the limit for the inverse function is x <= 0.
so, again, the full answer is
f^-1(x) = 4x² - 3, x <= 0
. A new employee at an auto detailing shop is offered one of three options for earning pay: Option 1: Receive an hourly rate of $15.25 for 8 hours plus $0.50 per bottle of wax sold to customers. Option 2: Receive $38.75 per automobile detailed in a day. Option 3: Receive $100 per day plus 2% of sales in a day. A typical day consists of 12 bottles of wax sold per detailer, 4 automobiles detailed per employee, and average daily sales are $1,500. Which option should the new employee choose in order to make the most money on an typical day, and how much will he earn in a 20-day month at this rate?
The new employee should choose the second option to make the most money on a typical day. The amount that the new employee will earn 20-day at this rate is $3,100.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
For Option 1,
Receive an hourly rate of $15.25 for 8 hours plus $0.50 per bottle of wax sold to customers. Also, A typical day consists of 12 bottles of wax sold per detailer.
Earning = ($15.25 × 8) + ($0.50×12)
= $122 + $6
= $128
For Option 2,
Receive $38.75 per automobile detailed in a day. Also, 4 automobiles are detailed per employee. Therefore, the earnings are,
Earning = $38.75 × 4
= $155
For Option 3,
Receive $100 per day plus 2% of sales in a day. Also, the average daily sales are $1,500. Therefore, the earnings are,
Earning = $100 + 0.02($1500)
= $130
Hence, The new employee should choose the second option to make the most money on a typical day.
2.)
The amount that the new employee will earn 20-day at this rate is,
Amount earned = $155 × 20 days
= $3,100
Hence, The amount that the new employee will earn 20-day at this rate is $3,100.
Learn more about Multiplication:
https://brainly.com/question/14059007
#SPJ1
Where would the line go??? Please help asap!!
Answer: Draw a line through (0,5) and (1,2)
The graph is shown below.
=====================================================
Reason:
The equation y = -3x+5 is in the form y = mx+b
m = -3 = slope
b = 5 = y intercept
The y intercept is where the graph crosses the y axis. In this case, it's at (0,5). This is one point needed.
Another point can be found by going down 3 and to the right 1 to arrive at (1,2). The motion "down 3, right 1" is from the slope of -3/1.
Therefore, this line goes through (0,5) and (1,2)
-------------
Another approach:
Plug in x = 0 to get...
y = -3x+5
y = -3(0) + 5
y = 5
The input x = 0 leads to the output y = 5
This tells us the point (x,y) = (0,5) is on the line.
Repeat for x = 1
y = -3x+5
y = -3(1)+5
y = 2
So (1,2) is another point on the line.
-------------
Check out the graph below.
Step-by-step explanation:
[tex]y=-3x+5.\\[/tex]
x | 0 | 1 |
y | 5 | 2 |
a wildlife photographer spent 5 minutes taking pictures of a bison at a park. when the bison then decided she didn't want her photograph published, the photographer spent the next 30 minutes convincing the bison that the publicity would be good for the park. by what percent was the time the photographer spent negotiating with the bison greater than the time he spent taking pictures?
The percent of time the photographer spent negotiating with the bison greater than the time he spent taking pictures is 500%
PercentageTime spent taking pictures = 5 minutesTime spent negotiating = 30 minutesPercentage of time negotiating greater than taking pictures = (difference in time) / time to take pictures × 100
= (30 - 5) / 5 × 100
= 25/5 × 100
= 5 × 100
= 500%
Learn more about percentage:
https://brainly.com/question/843074
#SPJ1
In circle N with the measure of arc \stackrel{\Large \frown}{MP}= 114^{\circ} MP ⌢ =114 ∘ , find \text{m} \angle MNPm∠MNP
According to the central angle theorem, the measure of angle MNP = 114°.
What is the Central Angle Theorem?According to the central angle theorem of a circle, the measure of central angle MNP equals the measure of intercepted arc MP.
Measure of arc MP = 114°
Measure of angle MNP = arc MP
Measure of angle MNP = 114° [central angle theorem]
Learn more about the central angle theorem on:
https://brainly.com/question/5436956
#SPJ1
2. Find the value of root4 (81)-2
Step-by-step explanation:
[tex]\sqrt[4]{81} -2\\=3-2 \\=1[/tex]
3. This is a graph of the function f(x) = -3x + 1.
-2
8
4f(x) = -3x + 1
0
y
4
2
X
a) Determine the range value when the
domain value is 1.
b) Determine the domain value when the
range value is 4.
a) [tex]-3(1)+1=\boxed{-2}[/tex]
b) [tex]4=-3x+1 \longrightarrow -3x=3 \kongrightarrow x=\boxed{-1}[/tex]
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 60% of this population prefers the color green. If 12 buyers are randomly selected, what is the probability that exactly 9 buyers would prefer green
The probability that exactly 9 buyers would prefer green is 0.1408
We will use the Binomial probability formula to find the answer
The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ-ˣ
We have
n, the number of trial = 12
x, the sample we aim to try = 9
p, the probability of success = 0.6
Substitute these values into the formula
[tex]P(9)= ^{12}C_{9} (0.6)^{9} (1-0.6)^{12-9}[/tex]
P(9) = 0.1408 (rounded to four decimal places)
Hence, The probability that exactly 9 buyers would prefer green is 0.1408
Learn more about Probability here https://brainly.com/question/23286309
#SPJ4
is y= -1/2x +25 linear???
What is the measure of the central angle of a circle with radius 18 centimeters that intercepts a12π centimeters arc?
Answer: [tex]120^{\circ}[/tex]
Step-by-step explanation:
[tex]12\pi=2(\pi)(18)\left(\frac{\theta}{360} \right)\\\\12\pi =36\pi \left(\frac{\theta}{360} \right)\\\\\frac{1}{3}=\frac{\theta}{360}\\\\\theta=120^{\circ}[/tex]
What is the vertex of the graph of the function below?
y=x²-4x+3
O A. (1,-1)
OB. (2,-1)
O C. (2,0)
O D. (1.0)
Answer:
B
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² - 4x + 3 ← is in standard form
with a = 1, b = - 4 , then
x = - [tex]\frac{-4}{2}[/tex] = 2
substitute into the equation for corresponding y- coordinate
y = 2² - 4(2) + 3 = 4 - 8 + 3 = - 1
vertex = (2, - 1 )
Please help me out. im struggling
Answer: 48
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{x}{36}=\frac{64}{x}\\\\x^{2}=36 \cdot 64\\\\x=\sqrt{36 \cdot 64}\\\\x=\sqrt{36} \sqrt{64}=48[/tex]
Describe fully the single transformation which takes shape A to shape B
Shape A was reflected over the y axis and translated 1 unit down to get shape B.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation is the movement of a point either up, down, left or right on the coordinate plane.
Shape A was reflected over the y axis and translated 1 unit down to get shape B.
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
66. Extensions
Find the equation of the line that passes through the following points: (2a, b) and (a, b + 1)
Answer:
The equation of the line that passes through the points (2a, b) and (a, b+1) is [tex]$y=-\frac{1}{a} x+2+b$[/tex].
Step-by-step explanation:
The given points are (2a, b) and (a, b+1).
It is required to find the equation of the line that passes through the points. the slope-intercept form.
Step 1 of 4
Using the given two points, to find the slope.
Given points are (2a, b) and (a, b+1).
Substitute [tex]$x_{1}[/tex]=2a,
[tex]$$\begin{aligned}&y_{1}=b \\&x_{2}=a \text { and } \\&y_{2}=b+1\end{aligned}$$[/tex]
into the formula, [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Step 2 of 4
Simplify [tex]$m=\frac{b+1-b}{a-2 a}$[/tex], further
[tex]$$\begin{aligned}m &=\frac{b+1-b}{a-2 a} \\m &=-\frac{1}{a}\end{aligned}$$[/tex]
As a result, the slope is [tex]$m=-\frac{1}{a}$[/tex].
Step 3 of 4
Use the slope [tex]$m=-\frac{1}{a}$[/tex] and the coordinates of one of the points (2a, b) into the point-slope form, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex].
Substitute [tex]$m=-\frac{1}{a}$[/tex],
[tex]x_{1}=2 a$ and$y_{1}=b$[/tex]
into the formula, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$y-b=-\frac{1}{a}(x-2 a)$[/tex]
[tex]$y-b=-\frac{1}{a} x+2$$[/tex]
Step 4 of 4
Rewrite the above equation as a slope-intercept equation. So, from the above term [tex]$y-b=-\frac{1}{a} x+2$[/tex], Add b on each side.
[tex]$$\begin{aligned}&y-b=-\frac{1}{a} x+2 \\&y=-\frac{1}{a} x+2+b\end{aligned}$$[/tex]
Therefore, the equation of the line that passes through the points is [tex]$y=-\frac{1}{a} x+2+b$[/tex].
the ratio of boys to girls in the 9th grade is 7 to 9 there are 218 girls set up the proportion to model this information
Answer:
the answer will be equal to x= 1962 over 7
Someone please help !! :(
Question 22 of 25
What is the average rate of change for this quadratic function for the interval
from x = 0 to x = 2?
Given that A varies directly as B and inversely as C and that; A=12 when B=3 and C=2. Find B when A=10 and C=1.5
1.9
Step-by-step explanation:
The above is direct and inverse variation.A = kB/C -----------(1)
A=12
B = 3
C= 2
substitute A, B and C into equation (1).
12 = K × 3/2
12 = 3k/2
12×2 = 3k
3K = 24
dividing bothsides by 3
3K/3 = 24/3
K = 8
substitute K = 8 into equation (1)
A = 8B /C --------------(2)
Equation (2) is the equation connecting
A,B and C.
Finding B when A = 10 and C = 1.5
10 = 8B / 1.5
10× 1.5 = 8B
15 = 8B
Dividing bothsides by 8 :
B = 15/8
B = 1.875
B = 1. 9 ( approximately)
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
Learn more about Trigonometric functions:
https://brainly.com/question/6904750
#SPJ1
Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
No this is not a function because the x-values repeat. In a function you can have the the output duplicate but not the input. The input at 3 has duplicates s o this is not a function.
Step-by-step explanation:
Definition
A relation is called to be a function if every domain has an unique range
f(x)=yHere
f(3)=-9,4As
f(3) has 2 corresponding values it's not a function
Find the value of X.
Answer:
151°
Step-by-step explanation:
The above shape is a quadrilateral.
sum of exterior angle of a quadrilateral is 360°.The exterior angles are :
82°, 70°, 62°, and (x -5)°
Therefore,
82 + 70 + 62 + x - 5 = 360
214 -5 + x = 360
209 + x = 360
x = 360 - 209
x = 151°
The tables represent two linear functions. The equation represented by the first table is given below.
y = 5.75x + 34.5
What linear equation is represented by the second table?
What is the solution to the system of equations?
The linear equation is represented by the second table as y= -2 .5 x-15 and the solution to the system of equations is (-6, 0).
What is the linear functions about?First, take two point from the table and as such it will be:
P (-4, -5) and Q(-2, -10)
So the two point is used to create a straight line and as such it will be:
y - y₁ = y₂ - y₁/ x₂ - x₁ (x₁-x )
y -(-5) = [tex]\frac{-10-(-5)}{-2-(-4)}[/tex] (x -(-4))
y + 5 = [tex]\frac{-5}{2}[/tex] x +4
y + 5 = [tex]\frac{-5}{2}[/tex] x - 10
y = [tex]\frac{-5}{2}[/tex] x - 15
y= -2 .5 x-15
The linear equation is represented by the second table as y= -2 .5 x-15 and the solution to the system of equations is (-6, 0)
Learn more about linear functions from
https://brainly.com/question/15602982
#SPJ1
Answer:
1st one option A to lazy to right out location
2nd one -6,0
Step-by-step explanation: