The large cone can hold more ice cream than the four smaller cones combined.
The large cone is a better deal.
What is a cone?A cone is a three-dimensional structure with a round base and a point at the top, known as the vertex.
A cone is a three-dimensional solid geometric object with a point at the top and a circular base. A cone has a vertex and one face. For a cone, there are no edges.
The radius, height, and slant height of the cone are its three constituent parts.
For the supersized cone,
Volume = π(5)(5)(12)/3 = 314.29 cubic inches
For a small cone,
Volume= π(2.5)(2.5)(6)/3 = 39.29 cubic inches
Combined volume of 4 such cones = 4*39.29 = 157.16 cubic inches
As the volume of the larger cone is more, thus it holds more ice cream. Also it is a better deal, as it costs less than 4 small cones.
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If 70 mL of solution contains 280 mg of drug, how many milligrams of drug are in 50 mL of solution?
BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B.) (1, -5)
Given, equation:
[tex]\sf \dfrac{(x-1)^2}{25} -\dfrac{(y+5)^2}{49} =1[/tex]
Comparing it with standard formula of hyperbola:
[tex]\sf \dfrac{(x-h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1[/tex]
where (h, k) is center
The given equation in standard form:
[tex]\sf \dfrac{(x-1)^2}{5^2} -\dfrac{(y-(-5))^2}{7^2} =1[/tex]
Determined:
(h, k) = (1, -5)
a = 5, b = 7
So, here (1, -5) is the center of the given hyperbola.
A random variable X has a gamma density function with parameters α= 8 and β = 2.
Without making any assumptions, derive the moment generating function of X and use to
determine the mean and variance of X.
I know you said "without making any assumptions," but this one is pretty important. Assuming you mean [tex]\alpha,\beta[/tex] are shape/rate parameters (as opposed to shape/scale), the PDF of [tex]X[/tex] is
[tex]f_X(x) = \dfrac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} = \dfrac{2^8}{\Gamma(8)} x^7 e^{-2x}[/tex]
if [tex]x>0[/tex], and 0 otherwise.
The MGF of [tex]X[/tex] is given by
[tex]\displaystyle M_X(t) = \Bbb E\left[e^{tX}\right] = \int_{-\infty}^\infty e^{tx} f_X(x) \, dx = \frac{2^8}{\Gamma(8)} \int_0^\infty x^7 e^{(t-2) x} \, dx[/tex]
Note that the integral converges only when [tex]t<2[/tex].
Define
[tex]I_n = \displaystyle \int_0^\infty x^n e^{(t-2)x} \, dx[/tex]
Integrate by parts, with
[tex]u = x^n \implies du = nx^{n-1} \, dx[/tex]
[tex]dv = e^{(t-2)x} \, dx \implies v = \dfrac1{t-2} e^{(t-2)x}[/tex]
so that
[tex]\displaystyle I_n = uv\bigg|_{x=0}^{x\to\infty} - \int_0^\infty v\,du = -\frac n{t-2} \int_0^\infty x^{n-1} e^{(t-2)x} \, dx = -\frac n{t-2} I_{n-1}[/tex]
Note that
[tex]I_0 = \displaystyle \int_0^\infty e^{(t-2)}x \, dx = \frac1{t-2} e^{(t-2)x} \bigg|_{x=0}^{x\to\infty} = -\frac1{t-2}[/tex]
By substitution, we have
[tex]I_n = -\dfrac n{t-2} I_{n-1} = (-1)^2 \dfrac{n(n-1)}{(t-2)^2} I_{n-2} = (-1)^3 \dfrac{n(n-1)(n-2)}{(t-2)^3} I_{n-3}[/tex]
and so on, down to
[tex]I_n = (-1)^n \dfrac{n!}{(t-2)^n} I_0 = (-1)^{n+1} \dfrac{n!}{(t-2)^{n+1}}[/tex]
The integral of interest then evaluates to
[tex]\displaystyle I_7 = \int_0^\infty x^7 e^{(t-2) x} \, dx = (-1)^8 \frac{7!}{(t-2)^8} = \dfrac{\Gamma(8)}{(t-2)^8}[/tex]
so the MGF is
[tex]\displaystyle M_X(t) = \frac{2^8}{\Gamma(8)} I_7 = \dfrac{2^8}{(t-2)^8} = \left(\dfrac2{t-2}\right)^8 = \boxed{\dfrac1{\left(1-\frac t2\right)^8}}[/tex]
The first moment/expectation is given by the first derivative of [tex]M_X(t)[/tex] at [tex]t=0[/tex].
[tex]\Bbb E[X] = M_x'(0) = \dfrac{8\times\frac12}{\left(1-\frac t2\right)^9}\bigg|_{t=0} = \boxed{4}[/tex]
Variance is defined by
[tex]\Bbb V[X] = \Bbb E\left[(X - \Bbb E[X])^2\right] = \Bbb E[X^2] - \Bbb E[X]^2[/tex]
The second moment is given by the second derivative of the MGF at [tex]t=0[/tex].
[tex]\Bbb E[X^2] = M_x''(0) = \dfrac{8\times9\times\frac1{2^2}}{\left(1-\frac t2\right)^{10}} = 18[/tex]
Then the variance is
[tex]\Bbb V[X] = 18 - 4^2 = \boxed{2}[/tex]
Note that the power series expansion of the MGF is rather easy to find. Its Maclaurin series is
[tex]M_X(t) = \displaystyle \sum_{k=0}^\infty \dfrac{M_X^{(k)}(0)}{k!} t^k[/tex]
where [tex]M_X^{(k)}(0)[/tex] is the [tex]k[/tex]-derivative of the MGF evaluated at [tex]t=0[/tex]. This is also the [tex]k[/tex]-th moment of [tex]X[/tex].
Recall that for [tex]|t|<1[/tex],
[tex]\displaystyle \frac1{1-t} = \sum_{k=0}^\infty t^k[/tex]
By differentiating both sides 7 times, we get
[tex]\displaystyle \frac{7!}{(1-t)^8} = \sum_{k=0}^\infty (k+1)(k+2)\cdots(k+7) t^k \implies \displaystyle \frac1{\left(1-\frac t2\right)^8} = \sum_{k=0}^\infty \frac{(k+7)!}{k!\,7!\,2^k} t^k[/tex]
Then the [tex]k[/tex]-th moment of [tex]X[/tex] is
[tex]M_X^{(k)}(0) = \dfrac{(k+7)!}{7!\,2^k}[/tex]
and we obtain the same results as before,
[tex]\Bbb E[X] = \dfrac{(k+7)!}{7!\,2^k}\bigg|_{k=1} = 4[/tex]
[tex]\Bbb E[X^2] = \dfrac{(k+7)!}{7!\,2^k}\bigg|_{k=2} = 18[/tex]
and the same variance follows.
Assume a = b and c ≠ 0
Which of the following sentences is not true?
1) a+c=b+c
2) a-c=b-c
3) ac = bc
4) a/c = b/c
5) none of these
Answer:
None of these is not true
Solve the logarithmic equation by writing in exponential form or by
graphing.
log (5-2x) = 0
Answer:
Hello,
Step-by-step explanation:
[tex]log(5-2x)=0\\\\\ \Longleftrightarrow\ 10^{log(5-2x)}=10^0\\\\\\\Longleftrightarrow\ 5-2x=1\\\\\Longleftrightarrow\ 2x=5-1\\\\\\\Longleftrightarrow\ x=\dfrac{4}{2}\\\\\\\Longleftrightarrow\ \boxed{x=2}\\[/tex]
Solve the system of equations.
y = 2x+ 3
y=x^2+3x+3
Answer:
(0,3)
(-1,1)
Step-by-step explanation:
Hello!
Since both equations are equal to y, we can set the right-hand side of the equations equal to each other.
[tex]y = 2x + 3\\y = x^2 + 3x + 3[/tex][tex]y = y[/tex][tex]2x + 3 = x^2 + 3x + 3[/tex]Solve for x[tex]2x + 3 = x^2 + 3x + 3[/tex][tex]0 = x^2 + x[/tex][tex]0 = x(x + 1)[/tex][tex]x = 0, x =-1[/tex]X can either be 0 or -1. Remember, a solution to a system is not complete without a y-value. Plug in 0 and -1 for x in the first equation, and find the corresponding y-values.
[tex]y = 2(0) + 3\\y = 3[/tex]
And
[tex]y = 2(-1) + 3\\y = -2 + 3\\y = 1[/tex]
So the solutions to the system are (0,3) and (-1,1)
Hector wants to laminate the tabletop in his study room. The tabletop is the shape of an isosceles trapezoid shown here. If laminating costs $4 per square foot, what is the total cost to laminate the tabletop?
A trapezoid with a height of 4 feet and bases of 6 feet and 10 feet is shown.
$136
$128
$112
$32
The total cost to laminate the table top is $128.
What is the total cost to laminate the table top?A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides.
The first step is to determine the area of the table top.
Area of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
0.5 x (6 + 10) x 4 = 32 square foot
Now, multiply the area by the cost per square foot
32 x 4 = $128
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You have a $10,000, you must choose between Gamble A and Gamble B. Gamble A will cost $5,000. If you win, you will get $15,000, but if you lose, you will get nothing. On the other hand, Gamble B will cost $10,000 that will give $30,000 if you win, otherwise get nothing if lost. You are risk averse, and your preference for wealth (W) is specified by the relationship U(W)= √W. Probability of wining is 0.4 and losing is 0.7. Which gamble will you choose and why?
Seven more than 4 times a number is 43 solve in algebraic equation?
Answer:
x = 9
Step-by-step explanation:
4x + 7 = 43
4x = 36
x = 9
Use the equation and type the ordered-pairs. y=3^x
The ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)
How to type the ordered pairs?The equation is given as:
y = 3^x
Let x = 0, 1 and 2
y = 3^0 = 1
y = 3^1 = 3
y = 3^2 = 9
So, we have the following ordered pairs (0,1), (1,3) and (2,9)
Hence, the ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)
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You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in your salary?
Answer: 6 %
Step-by-step explanation: 6 % of 12.5 = 0.75. 12.5 plus 0.75 = 13.25
What do l do??? Need help
Answer:
you have to put the formula of perimeter
Answer:
12a. L+8m + 14m
12b. 10m+8m +14m
12c. 66
12d.420m
12e.252m
quick questions
volume= 288cm cubed
at the movie theatre, child admission is $6.10 and adult admission is $9.70. On Monday , 146 tickets were sold for a total sales of $1074.20.HOw many adult tickets were sold that day ?
Answer:
51
Step-by-step explanation:
Let c be the number of child tickets sold.
Let a be the number of adult tickets sold.
From the information given from the question, we can deduce:
6.10c + 9.70a = 1074.20 - Equation 1
c + a = 146 - Equation 2
From here, we can use the substitution method in solving simultaneous equations to find a and c. We will use Equation 2 as the base.
c = 146 - a - Equation 2A
We will then substitute equation 2A into Equation 1 to find a.
6.10(146-a) + 9.70a = 1074.20
890.6 - 6.10a + 9.70a = 1074.20
890.6 + 3.6a = 1074.20
3.6a = 1074.20 - 890.6
3.6a = 183.6
a = [tex]\frac{183.6}{3.6}[/tex]
a = 51
Therefore we know that 51 adult tickets were sold that day.
After that you can substitute a into equation 2 to find c.
the function f(t) = 5 cos(pi/4*t) + 11 represents the tide in dark sea. it has a maximum of 16 feet when time (t) is 0 and a minimum of 6 feet. the sea repeats this cycle every 8 hours. after six hours, how high is the tide?
The height of the tide after eight hours is 16 feet.
How to illustrate the function?From the information given, the function is given as 5cos (π/4)t + 11.
In this case, the time is given as eight hours. This will be:
f(8) = 5 × cos (π/4) × 8 + 11
f(8) = 5 × cos(2π) + 11
= (5 × 0.999) + 11
= 16 feet
The height is 16 feet.
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SOLVE AND EXPLAIN HOW TO SOLVE
Answer:
4.13
Step-by-step explanation:
Using sine ratio where it states that sine of a measurement is equal to ratio of opposite of measurement to hypotenuse (slant side/side with slope)
From the question, our opposite is x, hypotenuse is given as 15 units and the measurement is 16°. Apply the formula:
[tex]\displaystyle{\sin 16^{\circ} = \dfrac{x}{15}}[/tex]
Move 15 to multiply sin(16°):
[tex]\displaystyle{15\sin 16^{\circ} = x}[/tex]
Go ahead and input the value in a calculator since it's not a special triangle - a measurement that can be found using hand method - after you find the value, round it to 2 decimal places:
[tex]\displaystyle{x = 4.13456033...}[/tex]
Therefore, after rounding to 2 decimal places, the answer is:
[tex]\displaystyle{x=4.13}[/tex]
Therefore, the value of x is 4.13 units.
Please tell me fast I am on a time crunch
Please tell me fast on a time crunch
Answer:
x ≥ -6
Step-by-step explanation:
x - 4 ≤ 3x + 8
Add 4 to both sides.
x ≤ 3x + 12
Subtract 3x from both sides.
-2x ≤ 12
Divide both sides by -2. Remember to change the direction of the inequality sign since you are dividing by a negative number.
x ≥ -6
Answer:
[tex]x \geqslant - 6[/tex]
Step-by-step explanation:
[tex]x - 4 \leqslant 3x + 8 = = > \\ - 12 \leqslant 2x = = = > \\ x \geqslant - 6[/tex]
Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
The function is illustrated below based on the information.
How to describe the function?When x <= 8000
The cost remains constant at 0.35 when x increases from 0 to 8000. The slope of the cost function over this part is 0
When 8000 < x <= 20000
The cost remains constant at 0.75 when x increases from 8000 to 20000 and the slope of the cost function over this part is 0.
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Carol and Janis decide to sew fancy masks to sell on Etsy. Carol can cut, pin, sew and pack a mask in 30 minutes. Working together they can complete a package in 16 minutes. How long does it take Janis to complete a package alone?
it would take Janis 14 minutes to complete a package alone
How to determine the valueFrom the information given,
Let's say that
Carol working time = x = 30 minutes
Janis working time = y
x + y = 16 minutes
Let's make 'y' the subject
30 - 16 = y
y= 14 minutes
Thus, it would take Janis 14 minutes to complete a package alone
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Remove all perfect squares from inside the square roo
√28
Answer:
√2² cannot be answer yesah
I need help with this geometry question asap!
Answer:
(a) Theorem 9
Step-by-step explanation:
Any of the given theorems can be used to prove lines are parallel. We need to find the one that is applicable to the given geometry.
AnalysisThe marked angles are between the parallel lines (interior) and on opposite sides of the transversal (alternate).
Theorem 9 applies to congruent alternate interior angles.
I have no clue what this question is asking nor how to answer it
Which of the following numbers are solutions of the sentence x-3< 2?
| -3
|| 0
||| 2
IV 5
II only
III only
I and III only
I, II, and III only
Or
I, II, III, and IV
Answer:
IV 5
Step-by-step explanation:
you have to solve for x:
x-3<2
x-3+3<2+3
x=5
could you put the brainlyest Icon for me? I have 1500 points, but no brainlyest, so I can't move up the ranks.
Let f(x) = 3x²+2, g(x) = 3x - 5. Find the following value or expression.
(fog)(x)
Answer:
(f∘g)(x) = 27x² -90x +77
Step-by-step explanation:
The composition of functions (f∘g)(x) is interpreted to mean f(g(x)). The value is found the way any function value is found. The argument is substituted for the variable in the function definition.
SubstitutionAfter substituting g(x) for the argument of f(x), the resulting expression can be simplified.
[tex](f\circ g)(x) =f(g(x))=f(3x-5)\\\\=3(3x-5)^2+2=3(9x^2-30x+25)+2\\\\\boxed{(f\circ g)(x)=27x^2-90x+77}[/tex]
Find the zeros of the function. Enter the solutions from least to greatest. f(x) = (x - 2)(3x + 3)
The zeros of the given function are x = 2 and x = -1
Zeros of a functionFrom the question, we are to determine the zeros of the given function
The given function is
f(x) = (x - 2)(3x + 3)
To determine the zeros of a function, we will set the function equal to zero
That is,
(x - 2)(3x + 3) = 0
Then,
x - 2 = 0 OR 3x + 3 = 0
x = 2 OR 3x = -3
x = 2 OR x = -3/3
x = 2 OR x = -1
Hence, the zeros of the given function are x = 2 and x = -1
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Suppose we want to choose 5 letters, without replacement, from 15 distinct letters.
[tex]order \: does \: not \:matter \\ sample \: space = 15 \: letters \\ no \: repetition\\ P(A) = 15C5 = 3003 \: ways[/tex]
Write an equivalent expression in simplest form for each given expression. Then, choose the answer that explains why the expressions are equivalent.
(A) 2y + 4(y + 1) = y +
First use the Property to simplify the expression in parentheses, then
combine like terms.
(B) 9y + 6 + 2(5 + y) = y +
After applying the Distributive Property, use the Properties to
combine like terms.
The equivalent expressions are 6y + 4 and 11y + 16
How to determine the equivalent expressions?Expression (A)
We have:
2y + 4(y + 1)
Open the bracket
2y + 4y + 4
Evaluate the like terms
6y + 4
Expression (B)
We have:
9y + 6 + 2(5 + y)
Open the bracket
9y + 6 + 10 + 2y
Evaluate the like terms
11y + 16
Hence, the equivalent expressions are 6y + 4 and 11y + 16
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The length of two sides of the right triangle ABC shown in the illustration are given. Find the length of the third side in centimeters. a=12cm and c=37cm
By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.
How to find the missing side of a right triangle
In this question we know the lengths of two sides of the right triangle. By Pythagorean theorem we get the length of the missing side:
a² + b² = c²
b² = c² - a²
b = √(c² - a²)
b = √(37² - 12²)
b = 35
By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.
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Ned and Sam are playing a game. Ned has -3 points. Sam has -8 points. How many more points does Ned have than Sam? Please provide an equation and an answer.
Answer:
5 points
Step-by-step explanation:
Subtracting their scores, we get (-3)-(-8)=5
which integer is closest to the third root of -23
Answer:
The number 23 is prime. Therefore, the cube root of 23 = ∛23 = 2.8439.
Step-by-step explanation:
Which of the following functions are discontinuous?
Answer:
D. I, II, and III
Step-by-step explanation:
A discontinuous function is a function which is not continuous.
If f(x) is not continuous at x = a, then f(x) is said to be discontinuous at this point.
To prove whether a function is discontinuous, find where it is undefined.
A rational function is undefined when the denominator is equal to zero.
Therefore, to find the values that make a rational function undefined, set the denominator to zero and solve.
Function I
Denominator: x - 2
Set to zero: x - 2 = 0
Solve: x = 2
Therefore, this function is undefined when x = 2 and so the function is discontinuous.
Function II
Denominator: 4x²
Set to zero: 4x² = 0
Solve: x = 0
Therefore, this function is undefined when x = 0 and so the function is discontinuous.
Function III
Denominator: x² + 3x + 2
Set to zero: x² + 3x + 2 = 0
Solve:
⇒ x² + 3x + 2 = 0
⇒ x² + x + 2x + 2 = 0
⇒ x(x + 1) + 2(x + 1) = 0
⇒ (x + 2)(x + 1) = 0
⇒ x = -2, x = -1
Therefore, this function is undefined when x = -2 and x = -1, and so the function is discontinuous.
Therefore, all three given functions are discontinuous.