The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters. The number of times one needs to use the completely filled cone to completely fill the cylinder with water is ?
Solution:
Let volume of cylinder be K times more than volume of Cone.
⇒K × Volume of Cone = Volume of Cylinder
[tex]K \times \frac{\pi\times r^2 \times h }{3}=\pi \times R^2 \times H\\\\K \times 5^2 \times 10= 3 \times 10^2 \times 20\\\\250 K=3 \times 100 \times 20\\\\K=\frac{6000}{250}\\\\K=24[/tex]
⇒Number of times one needs to use the completely fill cone to completely fill the cylinder with water is=24
What is the scale factor when △RST is dilated to △R'S'T'? What is the value of x?
A. Scale factor 0.75, x = 8
B. Scale factor 0.75, x = 4.5
C. Scale factor 1.3, x = 8
D. Scale factor 1.3, x = 4.5
If h(x) = 6 - x, what is the value of ( h o h)(10)?
The networking organization you joined is throwing a party. You are in charge of buying the chips, which cost two dollars and fifty cents per bag and salsa, which costs four dollars per jar. The chips & salsa budget you are given totals $60. The inequality 2.5x + 4y 60 represents the possible combinations of chips (x) and salsa (y) you can buy. graph of the inequality 2.5 x plus 4 y is less than or equal to 60 Which of the following does not represent a solution to the inequality?
The population of a local species of dragon fly can be found using an infinite geometric series where a1=36 and the common ratio is 1/2 write the sum in sigma notation and calculate the sum that will be the upper limit of this population
Please helpppp now 99 points
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −15
0 −10
1 −5
g(x)
g(x) = 2x + 8
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
What is the Value of X? Sin(x+22 degree) = Cos( 2x-7 degree) I might have a idea of what it is but I’m not sure
The value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees) can be found by using the identity sin(90° - x) = cos(x), leading to x = 22.67° (or in radians by converting degrees to radians).
To find the value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees), we can utilize the trigonometric identity sin(90° - x) = cos(x). By setting the angle inside the cosine to equal 90° - (x + 22°), we can equate this to (2x - 7°) as both represent the same cosine value.
So we have the equation 90° - (x + 22°) = 2x - 7°. Solving for x, we combine like terms: 68° = 3x, which then gives us x = 68°/3. Therefore, x = 22.67°, which is the angle in degrees.
If we needed to find x in radians, we would have to convert degrees to radians by using the conversion factor: π radians = 180°. This would yield x as x = (22.67°/180°) * π.
You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?
answers :
a.using a paid membership card to buy it at a 10 percent discount
b.buying it online at a 10 percent discount with a $5 shipping charge
c.buying it at a 10 percent discount without sales tax
how do I get from step 3 to step four? please explain.
sin x = opposite over hypotenuse
sin 45° = 50 over x
0.707106781 ≈ 50 over x
(0.707106781)x ≈ 50
x ≈ 70.71
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box.
central angle theta (in radians) = arc length / radius
So theta = 5.6/8 = 0.7 radians
The central angle measure for a circle with an 8 cm radius and a 5.6 cm intercepted arc length is 0.7 radians.
The question asks to find the measure in radians for the central angle of a circle with a radius of 8 cm and an intercepted arc length of 5.6 cm. To calculate the central angle in radians, we use the formula θ = [tex]\frac{l}{r}[/tex], where θ is the central angle in radians, l is the arc length, and r is the radius of the circle. Substituting the given values, we get θ = [tex]\frac{5.6}{8}[/tex]
Through calculation, θ = 0.7 radians. So, the measure of the central angle that intercepts an arc length of 5.6 cm in a circle with a radius of 8 cm is 0.7 radians.
Need help ASAP
Which statements are true? Select each correct answer.
40m^6−4=4(10m^6−1)
6m^2+18m=6m^2(1+3m)
32m^4+12m^3=4m^3(8m+3)
15m^3−6m=3m(5m^2−6m)
Given the geometric sequence where a1 = 2 and r = √2 find a9
32
32√2
256
256√2
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
There is a geometric sequence:
where a₁ = 2
r = √2
We need to find a₉:
As we know the formula for "nth term ":
[tex]a_n=ar^{n-1}\\\\a_9=ar^{9-1}\\\\a_9=ar^8\\\\a_9=2\times (\sqrt{2})^8\\\\a_9=32[/tex]
Hence, First option is correct.
The next number in the arithmetic sequence 15, 22, 29, ___ is:
A. 34
B. 35
C. 36
D. 37
According to these three facts, which statements are true? - Circle D has center (2, 3) and radius 7. - Circle F is a translation of circle D, 2 units right. - Circle F is a dilation of circle D with a scale factor of 2.
A) Circle F and circle D are similar.
B) The center of circle F is (0, 3).
C) The radius of circle F is 28.
D) Circle F and circle D are congruent.
(Again, you can choose more than one option.)
Find the equation, (f(x) = a(x-h)2+ k), for a parabola containing point (-1,0) and having (-3, 4) as a vertex. What is the standard form of the equation?
PLEASE!!!!!!!!!!!!!HURRY!!!!!!!!!!!!!!!!!!!!!!!20 points!!!!!!!!!!!!!!!!!!!!!!1
A group of children are asked whether they prefer vanilla or chocolate ice cream. The data are collected in the table.
Jordan needs 6 3/10 gallons of milk to make 4 1/2 gallons of ice cream. How many gallons of milk will jordan need to make one gallon of ice cream
Answer:
[tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream
Step-by-step explanation:
Using unitary method,
Unitary method is a method use to find the value of a unit quantity.
[tex]6\frac{3} {10}[/tex] gallon of milk needed to make [tex]4\frac{1}{2}[/tex] gallon of milk
[tex]\frac{63}{10}[/tex] gallon of milk needed to make [tex]\frac{9}{2}[/tex] gallon of ice cream
One gallon of ice cream needed = [tex]\frac{63}{10} \times \frac{2}{9}[/tex] gallon of milk
= [tex]\frac{7}{5}[/tex] gallon of milk
= [tex]1\frac{2}{5}[/tex] gallon of milk
Thus, [tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream.
In this parallelogram m angle bad =75 so m angle bcd
How many ways can 6 students desks be arranged in a row permutation or combination?
Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded 2 times per year. What will the account balance be after 6 years?
She invests some amount in a saving account of fixed interest compounded half-yearly. It says to find its Future Value after six years.
The principal amount is P = $4,848.
Annual interest rate is 5% i.e. r = 0.05
Compounding period is two times per year i.e. n = 2.
Time of investment is t = 6 years.
We know the formula of Future Value is given by :-
[tex] FV=P*(1+\frac{r}{n})^{nt} [/tex]
We can plug the given values in the formula to calculate the answer.
[tex] FV = 4848*(1+\frac{0.05}{2})^{(2*6)} \\\\
FV = 4848*(1+0.025)^{(12)} \\\\
FV = 4848*(1.025)^{(12)} \\\\
FV = 4848*(1.344888) \\\\
FV = 6520.02102 [/tex]
Hence, future value of investment after six years is 6,520.02 dollars.
The question involves calculation of compound interest. The formula to use is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.
Explanation:This question involves the concept of compound interest. Compound interest is calculated each period on the original deposit, or principal, along with any interest previously earned. Unlike simple interest which only takes into account the principal amount, compound interest accounts for the interest that accumulates on the initial amount as well as the interest that has previously been added.
In Brenda's case, as she's benefiting from compounded interest, the formula to use here is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.
So, plug in the given values: P=$4848, r=0.05 (as 5% = 5/100), t=6, and n=2 (since it's compounded semi-annually). This will allow us to find the final account balance after 6 years.
Learn more about Compound Interest here:https://brainly.com/question/14295570
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The area of a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than twice x. solve for x. Round to the nearest whole number.
Answer: The answer is actually 6.
Step-by-step explanation:
The value of x is 6, rounded to the nearest whole number.
To solve for x given the conditions:
1. Define the variables based on the problem:
- Length of the rectangle [tex](\( L \)) = \( x + 2 \)[/tex]
- Width of the rectangle [tex](\( W \)) = \( 2x - 5 \)[/tex]
2. Write the equation for the area of the rectangle:
- Area [tex](\( A \)) = \( L \times W \)[/tex]
- Given that the area is 56 cm², we have:
[tex]\[ (x + 2)(2x - 5) = 56 \][/tex]
3. Expand the equation:
[tex]\[ (x + 2)(2x - 5) = 2x^2 - 5x + 4x - 10 = 2x^2 - x - 10 \][/tex]
4. Set up the equation:
[tex]\[ 2x^2 - x - 10 = 56 \][/tex]
5. Move all terms to one side of the equation to set it to zero:
[tex]\[ 2x^2 - x - 10 - 56 = 0 \] \[ 2x^2 - x - 66 = 0 \][/tex]
6. Solve the quadratic equation using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\ where \( a = 2 \), \( b = -1 \), and \( c = -66 \).[/tex]
7. Calculate the discriminant:
[tex]\[ \Delta = b^2 - 4ac = (-1)^2 - 4(2)(-66) = 1 + 528 = 529 \][/tex]
8. Calculate the roots:
[tex]\[ x = \frac{-(-1) \pm \sqrt{529}}{2(2)} = \frac{1 \pm 23}{4} \][/tex]
So, the solutions are:
[tex]\[ x = \frac{1 + 23}{4} = \frac{24}{4} = 6 \][/tex]
and
[tex]\[ x = \frac{1 - 23}{4} = \frac{-22}{4} = -5.5 \][/tex]
Since x must be a positive value in the context of this problem, we have: x = 6
9. Verify the solution:
Length L = x + 2 = 6 + 2 = 8 cm
Width W = 2x - 5 = 2(6) - 5 = 12 - 5 = 7 cm
Area = [tex]\( 8 \times 7 = 56 \)[/tex] cm², which matches the given area.
Therefore, ( x = 6).
Jerry's beginning balance in his checkbook was $457.56. He made deposits of $20, $80, and $165 and wrote checks for $216.58. His bank charge was $3.50. What was his ending balance for the month? a. $552.10 b. $505.98 c. $722.56 d. $502.48
PLEASE FULL ANSWERS! need all the help I can get
Which of the binomials below is a factor of this trinomial? 5x2 + 20x + 15
factor X + 1 is the answer
PLEASE HELP!! FIRST CORRECT ANSWER GETS BRAINLIEST!!
In a rectangle, a diagonal forms a 36° angle with a side. Find the measure of the angle between the diagonals, which lies opposite to a shorter side.
Answer:
The answer is 72 degrees
Step-by-step explanation:
The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.
1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees
2. ∠ABD= ∠BDC = 36 - alternate interior angles
3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54
4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.
5. 180 - 54*2 = 72 degrees
I hope this helps!
Can someone graph these 2 equations for me??
y=5(1/2)^x +4
y=4(1/6)^(x+2)
Simplify the expression. 3–9 • 36 • 36
To simplify expressions, one needs to apply rules correctly, such as combining like terms and using exponentiation rules. The process includes correctly applying the rule that simplifies multiplications of the same base by adding their exponents. Cubing exponentials involves multiplying the original exponent by 3.
Explanation:To simplify mathematical expressions, it's crucial to follow the correct rules and operations. In this case, the example provided shows the exponentiation and multiplication rules. Specifically, when dealing with expressions like 3².3⁵, this is equivalent to multiplying 3 x 3 and then taking that result and multiplying it by 3 five more times. According to the rule xPx9 = x(p+q), where x is the base and p and q are the exponents, it simplifies to adding the exponents when the base number is the same and multiplied together.
The process of simplifying expressions involves several steps:
Identifying like terms and combining them.Applying the rules of exponents correctly.Dividing or multiplying to simplify equations as demonstrated with loop equations, dividing by a constant to simplify the equation.Additionally, when cubing exponentials, one should cube the digit normally and multiply the existing exponent by 3, a rule demonstrated in squaring operations as well.
helppppppppppppppppppppppppppppppppppp
Elizabeth rode her bike 6 1/2 miles from her house to the library and then another 2 2/5 miles to her friend Milo's house. If Carson's house is 2 1/2 miles beyond Milo's house, how far would she travel from her house to Carson's house?
Answer:
Step-by-step explanation:
11.4