under normal conditions, 1.5 feet of snow will melt into 2 inches of water. after a recent snowstorm, there were 4 feet if snow. how many inches of water will there be when the snow MELTS? express your answer as a fraction reduced to lowest terms or decimal rounded correctly to two decimals places. Do not include units with this answer.
Answers
If 1.5 feet of snow melts into 2 inches of water, this implies that:
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Find the value of θ from the following equation.(θ≤90°)
Answers
Answer: 10°
__________________________________________________________
We are given:
Sin(6θ) = Cos(3θ)
Solving for θ:
Simplifying Cos(3θ):
We know that:
Cos(θ) = Sin(90-θ)
So, we can say that:
Cos(3θ) = Sin(90 - 3θ)
Finding the value of θ:
Sin(6θ) = Cos(3θ)
Sin(6θ) = Sin(90 - 3θ) [Since Cos(3θ) = Sin(90 - 3θ)]
6θ = 90 - 3θ [If Sin(θ) = Sin(A) ; θ = A]
9θ = 90 [adding 3θ on both sides]
θ = 10° [dividing both sides by 9]
The intensity of the sound, I watts/m², received from a loudspeaker is
inversely proportional to the square of the distance, d metres, from the
loudspeaker.
When d = 2,1 = 30
Work out the value of I when d = 10
PLEASE HELP
Answers
Answer:
The value of I for d = 10 will be 1.2 watts/m^3
Step-by-step explanation:
Let I be the intensity of sound and d be the distance
According to given statement, "The intensity of the sound, I watts/m², received from a loudspeaker is inversely proportional to the square of the distance, d meters, from the loudspeaker. "
\(I \propto \frac{1}{d^2}\)
Removing the proportionality symbol
\(I = \frac{k}{d^2}\)
Putting d = 2 and I = 30
\(30 = \frac{k}{(2)^2}\\30 = \frac{k}{4}\\k = 30*4\\k = 120\)
Putting the value of k in the equation
\(I = \frac{120}{d^2}\)
Putting d = 10
\(I = \frac{120}{(10)^2}\\I = \frac{120}{100}\\I = 1.2\)
Hence,
The value of I for d = 10 will be 1.2 watts/m^3
What will be the result of substituting 2 for x in both expressions below?
+4
x+6-x-2
O Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
O Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
O One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
Answers
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
Equivalent Algebraic expressions:Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expressionns.
Given the algebraic expressions,
\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)
Substituting 2 for x in the first expression gives:
(1/2 × 2) + 4
1 + 4
5
Substituting 2 for x in the second expression gives:
2 + 6 - (1/2 ×2) - 2
8 - 1 - 2
8 - 3
5
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
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\(\frac{d}{dx} \int t^2+1 \ dt\)
There is a 2x on the bottom and x^2 on top of the integral symbol
Please help me my teacher did not teach us this:(
Answers
Answer:
\(\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2\)
Step-by-step explanation:
\(\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?\)
We can use Part I of the Fundamental Theorem of Calculus:
\(\displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}\)Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.
The Additivity Rule for Integrals states that:
\(\displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}\)We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.
\(\displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}\)We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.
The Order of Integration Rule states that:
\(\displaystyle\int\limits^b_a \text{f(t) dt}\ = -\int\limits^a_b \text{f(t) dt}\)We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.
\(\displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}\)Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.
When taking the derivative of an integral, we can follow this notation:
\(\displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]\)where u represents any function other than a variableFor the first term, replace \(\text{t}\) with \(2x\), and apply the chain rule to the function. Do the same for the second term; replace
\(\displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)\)Simplify the expression by distributing \(2\) and \(2x\) inside their respective parentheses.
\([-(8x^2 +2)] + (2x^5 + 2x)\) \(-8x^2 -2 + 2x^5 + 2x\)Rearrange the terms to be in order from the highest degree to the lowest degree.
\(\displaystyle2x^5-8x^2+2x-2\)This is the derivative of the given integral, and thus the solution to the problem.
I believe this is 12/29 can someone tell me if I'm right
Answers
Answer:
12/25
Step-by-step explanation:
the number of students who do not have a cat or dog is 12
What is the slope of the following equation of a line? 2x + 3y = 12
Answers
Answer:
m = -2/3
Step-by-step explanation:
2x + 3y = 12
-2x. -2x
3y = -2x + 12
÷3. ÷3. ÷3
y = -2/3x + 4
m = -2/3
if you ever see this form : ax+by=c
and it asks about the slope, then you can use this rule : slope= -a/b
and if it asks about the y-intercept, you can use this rule : y-intercept= c/b
so to get the slope of your question, all you have to do is : slope = -2/3
I hope this helped !
2
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
(2-3-2)(5-32)2
(3-2)(5-2)2
2
(33) (40)2 (32)-³(2²)
Reset
1
(37-47)(2-5) (52)
127-5-1-2-4
Next
(2-3) ¹.20
(2-3)=¹
-1
-2
12/12
Answers
Each expression should be matched to the correct location on the table as follows;
(2 · 3⁻²)³ (5·3²)²/(3⁻²)(5·2)² = 2.
(3³)(4⁰)²(3·2)⁻³(2²) = 1/2.
(3⁷· 4⁷)(2·5)⁻³(5)²/(12⁷)(5⁻¹)(2⁻⁴) = 2.
(2.3)⁻¹ (2⁰)/(2 . 3)⁻¹ = 1.
How to simplify each exponential expression?In order to match each exponential expression to the correct location on the table, we would have to simplify each exponential expression by using the properties of exponents as follows;
(2 · 3⁻²)³ (5·3²)²/(3⁻²)(5·2)² = (2³)(3⁻⁶)(5²)(3⁴)/(3⁻²) (10²)
(2³)(3⁻⁶)(5²)(3⁴)/(3⁻²) (10²) = (2.2².5²) (3⁻⁶.3⁴)/(3⁻²) (10²)
(2.2².5²) (3⁻⁶.3⁴)/(3⁻²) (10²) = (2)(10²)(3⁻²)/(3⁻²) (10²)
(2)(10²)(3⁻²)/(3⁻²) (10²) = 2
Exponential expression 2:
(3³)(4⁰)²(3·2)⁻³(2²) = (3^3)(1^2) (3^-3)(2^-3) (2^2)
(3^3)(1^2)(3^-3) (2^-3) (2^2) = (2^(-3 + 2))
(2^(-3 + 2)) = 2^-1
2^-1 = 1/2
Note: A number with an exponent of 0 is equal to 1.
Exponential expression 3:
(3⁷· 4⁷)(2·5)⁻³(5)²/(12⁷)(5⁻¹)(2⁻⁴) = (12⁷)(2⁻³)(5⁻³)(5²)/(12⁷)(5⁻¹)(2⁻⁴)
(12⁷)(2⁻³)(5⁻³)(5²)/(12⁷)(5⁻¹)(2⁻⁴) = (2⁻³)(5^(-3 + 2))/(5⁻¹)(2⁻⁴)
(2⁻³)(5^(-3 + 2))/(5⁻¹)(2⁻⁴) = (2⁻³)(5⁻¹)/(5⁻¹)(2⁻⁴)
(2⁻³)(5⁻¹)/(5⁻¹)(2⁻⁴) = 1/2⁻¹
1/2⁻¹ = 2
Exponential expression 4:
(2.3)⁻¹ (2⁰)/(2 . 3)⁻¹ = 2⁰
2⁰ = 1
Note: You should multiply numbers that have the same exponent and add exponents with the same base.
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b^2 + 8b + 16 factoring polynomials with a leading coefficient
Answers
Answer:
(b +4)²
Step-by-step explanation:
Here, you recognize the constant as the square of half the coefficient of the linear term: 16 = (8/2)². This means the trinomial is a perfect square, so can be factored accordingly.
b² +8b +16 = (b +4)²
The mug is 5/8 full, the mug contains 3/4 of water find the capacity of the mug
Answers
The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).
What is capacity?It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.
In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.
Let the capacity of the mug be x.
Given,
Mug is 5/8 full and contains 3/4 of water
So, 5/8 of the mug is filled with water
Therefore,
5/8 of x = 3/4
(5/8 )x = (3/4)
x = (3/4) × (8/5)
x = (24/20)
x = 1.2
Therefore, the capacity of the mug is 1.2.
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I need help on finding the volume, can you explain step by step please?
Answers
The formula of the volume of the cylinder is
\(V=\pi r^2h\)Where:
r is the radius of its base
h is its height
Since the radius is 1/2 the diameter
Since the diameter of the base is 8 ft, then
\(\begin{gathered} r=\frac{1}{2}\times8 \\ r=4\text{ ft} \end{gathered}\)Since the height is 12 ft, then
h = 12
Substitute r by 4 and h by 12 in the formula above to find the volume
\(\begin{gathered} V=3.14\times(4)^2\times(12) \\ V=3.14\times16\times12 \\ V=602.88ft^3 \end{gathered}\)Round it to the nearest whole number
V = 603 cubic feet to the nearest whole number
please help. on zearn find the coordinates of each shape
Answers
Answer:
◯ ( 3, \(\frac{1}{2}\) ) , ⬛( \(1\frac{1}{2}\) ,\(2\frac{1}{2}\)) , △( 0, \(4\frac{1}{2}\) )
Step-by-step explanation:
x-coordinate y-coordinate
◯ --- 3 \(\frac{1}{2}\)
⬛ --- \(1\frac{1}{2}\) \(2\frac{1}{2}\)
△ --- 0 \(4\frac{1}{2}\)
Measure the unit grids on the graph, x and y, that's the x and y coordinate.
What is 1 1/2 + 3 7/8
Answers
5 3/8
Step-by-step explanation:Hi there !
1 1/2 + 3 7/8 =
= (1×2+1)/2 + (3×8+7)/8
= ⁴⁾3/2 + 31/8
= 12/8 + 31/8
= (12 + 31)/8
= 43/8
= 5 3/8
Good luck !
Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean
(a) Find endpoints of a t-distribution with 5 % beyond them in each tail if the sample has size n = 12.
(b) Find endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20.
Answers
Answer:
a) Hence the endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n=12 is ± 1.796.
b) Hence the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ± 2.539.
Step-by-step explanation:
Here the answer is given as follows,
Veronica takes 1/3 of an hour to write 1/4 of a page of calligraphy. How long will it take veronica to write one page of calligraphy?
Answers
Answer:
4/3 or 1.3 hours
Step-by-step explanation:
just multiply both fractions by four because she writes 1/4 of a page in 1/3 of an hour I hope this helps
mark brainliest please
Oreana's 150 g bag of trail mix is x% raisins. Brandon's 250 g bag of trail mix is y% raisins. They combine the two mixes together in one bowl.
Write an expression which shows how many grams of raisins are in the bowl
Answers
The expression which shows how many grams of raisins are in the bowl will be
(0.01x) * 150 + (0.01y) * 250
What is the expression that shows the raisin?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The expression which shows how many grams of raisins are in the bowl will be:
= (x% × 150) + (y% × 250)
= (0.01x) * 150 + (0.01y) * 250
This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.
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A farmer earns $___ for each orange she sells. She had to pay $___ for fertilizer. Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money the farmer could earn selling any number of oranges, n. Make sure the values you choose make sense for this situation. (6 points) Part B: Write an algebraic expression from your written description used in Part A. Let n stand for the number of oranges. (6 points)
Answers
Part B: The algebraic expression for the amount of money the farmer could earn selling any number of oranges, n, is 0.20n - 25.
Please someone help
Answers
Answer:
E=10.353
Step-by-step explanation:
First plug in all the numbers: 1.960(31.25/\(\sqrt{35}\))
solve: E=10.353
a tip of $10 is typically suitable for which kind of service?
a mover delivering furniture
a valet who parks your car
a waiter at a fast food restaurant
Answers
Use the following functions to evaluate the composition of functions below
Answers
When we have two functions f(x) and g(x) the composition is just evaluating one function in the other one.
Here the solution is: k( l(2) ) = 5
We have the functions:
k(x) = 2*x + 3
l(x) = x - 1
We want to get the composition:
k( l(2))
Let's start with the general composition, and then evaluate it:
k( l(x) ) = 2*l(x) + 3 = 2*(x - 1) + 3
k( l(x) ) = 2*(x - 1) + 3
Now we need to evaluate it in x = 2, then we get:
k( l(2) ) = 2*(2 - 1) + 3 = 2 + 3 = 5
k( l(2) ) = 5
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if a(x) = 3x+1 and b(x) = \(square root of x-4\), what is the domain of (boa)(x)
Answers
The domain of (boa)(x) is [1, ∞].
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.
Based on the information provided above, we have the following functions:
a(x) = 3x+1
\(b(x) = \sqrt{x-4}\)
Therefore, the composite function (boa)(x) is given by;
\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)
By critically observing the graph shown in the image attached below, we can logically deduce the following domain:
Domain = [1, ∞] or {x|x ≥ 1}.
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![if a(x) = 3x+1 and b(x) = [tex]square root of x-4[/tex], what is the domain of (boa)(x)](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/gGe6IRGOQUF4aKHR4HvpxeklJAqlYD78.png)
2. The diagram above shows a wooden structure in the form of a cone mounted on hemispherical base. The vertical height of the cone is 24cm and the base 7cm. Calculate correct to 3 significant figures the surface area of the structure. (Take π= 22/7)
Answers
The surface area of the wooden structure is approximately 1012 cm².
To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.
Surface Area of the Cone:
The surface area of a cone is given by the formula:
A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.
The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:
\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)
Using the given measurements:
\(s_{cone\) = √(7² + 24²) cm
\(s_{cone\) ≈ √(49 + 576) cm
\(s_{cone\) ≈ √625 cm
\(s_{cone\) ≈ 25 cm
Now, we can calculate the surface area of the cone:
\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)
\(A_{cone\) = (22/7) × 7 cm × 32 cm
\(A_{cone\) = 704 cm²
Surface Area of the Hemispherical Base:
The surface area of a hemisphere is given by the formula:
\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.
Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:
\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²
\(A_{hemisphere\) = (22/7) × 2 × 49 cm²
\(A_{hemisphere\) = 308 cm²
Total Surface Area:
To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:
Total Surface Area = \(A_{cone} + A_{hemisphere}\)
Total Surface Area = 704 cm² + 308 cm²
Total Surface Area = 1012 cm²
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Please solve
Consider the congruence ≡8 (mod 847)
ax ≡ 8 (mod 847).
Choose a value for such that (,847)=1. Then solve the congruence
I want a to be 10, a =10
Answers
Answer:
56
Step-by-step explanation:
Joshua says that this picture represents 4.2 . Makayla says that this picture represents 42 . Use the drop-down menus to explain how either could be correct
Answers
according to the given statement both are having correct interpretation with or without decimal.
what is decimal?Both integer as well as non-integer amounts are frequently expressed using the decimal number system. The Hindu-Arabic number system has been expanded to include non-integer values. Decimal notation is the method used to represent numbers using the system of decimals. Either a whole number as well as a fractional number can be found in a decimal number. Decimal numbers that fall between integers are used to express complete and partially completed amounts numerically. A decimal point separates the whole number from the fractional portion of a decimal number. The little dot which appears among whole numbers as well as fractions is known as the decimal point.
given,
Joshua could be correct because the picture shows four full squares and two tenths of another square. This can be written as the decimal 4.2, where the 4 represents the four full squares and the 0.2 represents the two tenths of a square.
Makayla could also be correct because the picture can be interpreted as representing 42, but not as a decimal. Rather, each square could represent a value of 10, and the two smaller squares could represent a value of 1 each. This gives a total value of 42, as Makayla suggests.
So, both interpretations of the picture could be correct, depending on whether one is using a decimal or a whole-number system.
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find the value of (-7/10)(2/5)
Answers
Answer:
the answer to (-7/10)(2/5) is -7/25.
or if you need decimal form it is -0.28
Step-by-step explanation:
PLZZZZ HELP ME I WILL GIVE BRAINLEST
Answers
Answer:
request payment from a person
Step-by-step explanation:
your welcome
How many 11-card hands are possible with a 20-card deck?
Answers
There is only 1 possible 11-card hand that can be formed from a 20-card deck.
To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.
The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.
The formula for combinations is:
nCk = n! / (k!(n-k)!)
Where "!" denotes the factorial of a number.
Substituting the values into the formula:
20C11 = 20! / (11!(20-11)!)
Simplifying further:
20C11 = 20! / (11! * 9!)
Now, let's calculate the factorial values:
20! = 20 * 19 * 18 * ... * 2 * 1
11! = 11 * 10 * 9 * ... * 2 * 1
9! = 9 * 8 * 7 * ... * 2 * 1
By canceling out common terms in the numerator and denominator, we get:
20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)
Performing the multiplication:
20C11 = 39,916,800 / 39,916,800
Finally, the result simplifies to:
20C11 = 1
Consequently, with a 20-card deck, there is only one potential 11-card hand.
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Help ASAP NEED HELP
Answers
Answer:
Its C
Step-by-step explanation:
first you would do the square which would be 3x3 which is 9 next you would do the rectangle which is 9x3 which is 27
9+27=36
A number is first increased by 20 and then doubled. The result is 2 less than 5 times the number.
Answers
Answer: The number is 14
Step-by-step explanation:
A number is increased by 20: (X + 20)
Then doubled: 2(X + 20)
5 times the number: 5X
2 less than 5 times the number: 5X - 2
Setting the bold statements equal: 2(X+20) = 5X - 2
Distribute left side: 2X + 40 = 5X - 2
Move X's: 40 = 3X - 2
Move numbers: 42 = 3X
Divide both sides by 3: X = 14
PLS HELP! BRAINLIEST!!!
Which of the following tables would **NOT** be an appropriate model for the function shown?
(options are the blue tables)
Answers
Answer: Option D
Explanation:
x = input
y = f(x) = output
Table D shows the input x = 2 pair up with the output y = f(x) = 0. But this curve does not cross the x axis. So we can conclude that table D is an incorrect model to represent this curve.
Match each correlation coefficient, r, to its description.
r = −0.08
r = −0.83
r = 0.96
r = 0.06
1.) strong negative correlation
2.) weak positive correlation
3.) weak negative correlation
4.) strong positive correlation
Answers
The answers are in order
r = −0.08 --> weak negative correlation
r = −0.83 --> strong negative correlation
r = 0.96 --> strong positive correlation
r = 0.06 --> weak positive correlation
The match of each correlation is given by,
r = −0.08 implies a weak negative correlation
r = −0.83 implies a strong negative correlation
r = 0.96 implies strong positive correlation
r = 0.06 implies weak positive correlation.
We have given that,
The correlation coefficient, r, to its description.
A B
r = −0.08 strong negative correlation
r = −0.83 weak positive correlation
r = 0.96 weak negative correlation
r = 0.06 strong positive correlation
We have to match the given relation
What is the positive and negative correlation?If the correlation coefficient is greater than zero, it is a positive relationship. Conversely, if the value is less than zero, it is a negative relationship.
So the correct match is,
r = −0.08 implies a weak negative correlation
r = −0.83 implies strong negative correlation
r = 0.96 implies strong positive correlation.
r = 0.06 is implies weak positive correlation.
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