Answer:
6902.97m³
Step-by-step explanation:
volume of a sphere =4/3πr³
=4/3×3.142×13×13×13=9203.965m³
1/4×9203.965=2300.99125m³
9203.965-2300.99125=6902.974
=6902.97m³
What is the Area and Perimeter? WILL MARK AS BRAINLIEST.
Answer:
24
Step-by-step explanation:
4x6=24
Given right triangle A B C ABC with altitude B D ‾ BD drawn to hypotenuse A C ‾ AC . If A D = 11 AD=11 and A C = 21 , AC=21, what is the length of A B ‾ AB in simplest radical form?
The length of AB is [tex]2\sqrt{105}[/tex].
What is an altitude?An altitude is a line which passes through the vertex of the triangle and meets the opposite side at the right angle. A triangle has three altitudes.
Consider the triangle ABC, with right angle at B,
Let AB = x, BC = y, BD = z.
By pythagoras theorem,
[tex]AC^{2} =AB^{2} +BC^{2}[/tex]⇒[tex]x^{2} +y^{2} = 21^{2}[/tex]----------(1)
From triangle ADB,
[tex]z^{2} +11^{2} =x^{2}[/tex]-------(2)
[tex]z^{2} +10^{2} =y^{2}[/tex]--------(3)
(2)-(3), we get, [tex]x^{2} -y^{2} =21[/tex]-----(4)
subtract (1) and (4) we get,
[tex]x^{2} =420[/tex]
⇒[tex]x=2\sqrt{105}[/tex]
Hence, the length of AB is [tex]2\sqrt{105}[/tex] in simplest radical forms.
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write each equation in slope-intercept form. Identify the slope and y-intercept. Then graph the line described by the equation.
-4x+2y=10
Answer:
y = 2x + 5
The slope: 2
Y-intercept: 5
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = the slope
b = y-intercept
Our equation
-4x+2y=10
2y = 4x + 10
y = 2x + 5
The slope: 2
Y-intercept: 5
9.
Hanif makes green paint by mixing blue paint and
yellow paint in the ratio
blue: yellow = 7:3
He buys blue paint in 50 litre containers, each costing £225
He buys yellow paint in 20 litre containers, each costing £80
He wants to sell the green paint in 5 litre tins.
Make 40% profit on each tin.
How much should he sell each tin for?
Answer:
your profit is 400
Step-by-step explanation:
50×225
Anya fed her dog 3/4 cup of dog food in the morning and another 5/6 cup in the evening. How much did her dog eat over the course of the day?
Answer: 1 7/24
Step-by-step explanation:
For positive acute angles A and B, it is known that sun A=40/41 and tan B= 20/21. Find the value of sin(A+B) in simplest form
The exact value of the trigonometric function sin (A + B) is equal to 1020 / 1189.
How to find the exact value of a trigonometric function of a sum of angles
In this problem we must determine the exact value of the sine of the sum of two acute angles. There are acute angles in the first quadrant, thus:
sin θ > 0
cos θ > 0
tan θ = sin θ / cos θ
In addition, by trigonometric formulas:
cos θ = √(1 - sin² θ)
cos θ = 1 / √(tan² θ + 1)
Where θ is the angle, in degrees.
sin (α + β) = sin α · cos β + cos α · sin β
If we know that sin A = 40 / 41 and tan B = 20 / 21, then the exact value of sin (A + B) is:
cos A = √[1 - (40 / 41)²]
cos A = 9 / 41
cos B = 1 / √[1 + (20 / 21)²]
cos B = 21 / 29
sin B = √[1 - (21 / 29)²]
sin B = 20 / 29
sin (A + B) = (40 / 41) · (21 / 29) + (9 / 41) · (20 / 29)
sin (A + B) = 1020 / 1189
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Line M goes through the points (-2,-8) and (1,1). Which pair of points
lies on a straight line that intersects Line M?
(-3,-2), (2,6)
(-2,-1), (3,14)
(0,2), (1,5)
(2,1), (-5,-20)
The equation of line m passing through the points (-2,-8) and (1,1) is y = 3x - 2
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept.
Line M goes through the points (-2,-8) and (1,1). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-8)=\frac{1-(-8)}{1-(-2)} (x-(-2))\\\\y=3x-2[/tex]
The equation of line m is y = 3x - 2
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what are the relative minimum and relative maximum values over the interval [1, 5] for the function shown in the graph?
The relative minimum and the relative maximum for the attached graph over the interval [ 1, 5 ] of the function given in graph is equal to -14 and -3 respectively.
Graph is attached.
Function shown in the attached graph over the interval [ 1, 5 ] is :
Representing the parabola function.
Vertex representing lowest point of the graph in the interval [ 1, 5 ] is given by :
( 4.5 , -14 )
Vertex representing highest point of the graph in the interval [ 1, 5 ] is given by :
( 1.5 , -3)
Relative minimum and maximum is represented by the y -coordinate of the graph.
Lowest point gives relative minimum = -14
Highest point gives relative maximum = -3
Therefore, for the function in the graph the relative minimum = -14 and relative maximum= -3.
The above question is incomplete , the complete question is:
what are the relative minimum and relative maximum values over the interval [1, 5] for the function shown in the graph?
Graph is attached.
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The town of Valley View conducted a census this year, which showed that it has a population
of 1,800 people. Based on the census data, it is estimated that the population of Valley View
will grow by 12% each decade.
Write an exponential equation in the form y = a(b) that can model the town population, y, x
decades after this census was taken.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential function to model the population of Valley View is [tex]y = 1800(1.012)^t[/tex].
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
An exponential function is written in the form -
[tex]y=ab^t[/tex]
Here, y is the function, a is the base value b is the rate and t is time period.
The number of people in Valley view is 1800. So, the base is a = 1800.
The function y depicts the towns population.
Each decade the population grows by 12%.
The growth rate per year is = 12 / 10
The growth rate is 1.2%
The value for b will be = 1 + r
b = 1 + 1.2/100
b = 1 + 0.012
b = 1.012
So, the exponential equation will be -
[tex]y = 1800(1.012)^t[/tex]
Therefore, the exponential equation is [tex]y = 1800(1.012)^t[/tex].
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(-2/3) (4/5) + (-2/3) (-2/5)
Answer: -0.26666666666
Step-by-step explanation:
£200 is invested for 10 years at 9 compound interest per annum
After 10 years at 9% compound interest per annum, The amount will be £393.57.
The amount of money you will have after 10 years can be calculated using the formula for compound interest:
[tex]A = P * (1 + r/n)^{nt}[/tex]
where:
A is the final amount,
P is the initial amount (principal),
r is the interest rate as a decimal,
n is the number of times the interest is compounded per year,
t is the number of years the money is invested.
In this case:
P = £200
r = 9% = 0.09
n = 1 (because interest is compounded annually)
t = 10
So, plugging in the values, we get:
[tex]A = 200 * (1 + 0.09/1)^{1 * 10)} = 200 * (1.09)^{10}[/tex]
[tex]A = 200 * 1.96787 = 393.57[/tex]
So, after 10 years at 9% compound interest per annum, you will have £393.57.
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The ordered pair (a,b) satisfies the inequality y < x+5
(-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is y < x+5
First, we have to find the x-intercept which occurs at y = 0
0 < x + 5
x<-5
For y-intercept,
y < 0+ 5
y <5
As a result, the obtained ordered pair is (-5, 0 ) and (0, 5).
Hence, (-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5
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Simplify. Express your answer as a single term, without a denominator.
j^-5k^-5 x jk^-7
The simplified expression is j^-4k^-12
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
j^-5k^-5 x jk^-7
Rewrite as
j^-5k^-5 x jk^-7 = j^-5 * j * k^-5k^-7
Apply the law of indices in the products
j^-5k^-5 x jk^-7 = j^-4 * k^-12
So, we have
j^-5k^-5 x jk^-7 = j^-4k^-12
Hence, the expression is j^-4k^-12
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100 Points!!
Will mark brainliest
A cake recipe says to bake the cake until the center is 180 degrees F, then let the cake cool to 100 degrees F. The table shows temperature readings for the cake.
a. Given a room temperature of 69 degrees F, what is an exponential model for this data set?
b. How long does it take the cake to cool to the desired temperature?
Please don't answer just for the points
The exponential model is [tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex] and It takes the cake 9.32 minutes to cool to the desired temperature
We can solve this by using Newton's Law of cooling,
[tex]T(t)=C+(T_o-C)e^k^t[/tex]
where
T(t) is the temperature at any given time
C is the surrounding temperature
T₀ is the initial temperature
k is a negative constant
t is the time
A cake recipe is baked until the center is 180 °F
T₀=180 ⇒ initial temperature
The room temperature is 69 °F
C = 69 ⇒ surrounding temperature
By using the table, substitute t and T to find the constant k
At t = 5 minutes, T = 125 °F
[tex]125=69+(180-69)e^k^t[/tex]
By subtracting 69 on both sides
[tex]56=(111)e^k^t[/tex]
Dividing both sides by 111
[tex]\frac{56}{111} =e^k^t[/tex]
Add ㏑ for both sides
[tex]ln(\frac{56}{111} )=ln(e^k^t)[/tex]
Dividing both sides by 5
k=- 0.1368357021
The exponential model is [tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
The cake cools at 100 °F and the desired temperature is 100°
T(t) = 100 ⇒ cake's temperature at t minute
Using the model above to find t
[tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t\\\\100=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
Subtract 69 from both sides
[tex]39=(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
Divide both sides by 111
[tex]\frac{39}{111} =e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
Applying ㏑ for both sides
[tex]ln(\frac{39}{111}) =e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
Dividing both sides by - 0.136835702
t=9.321711938
t ≅ 9.32 minutes
It takes the cake 9.32 minutes to cool to the desired temperature.
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Help ASAP please !!!!!!!!,,
The exponential function shown in the graph is f(x) = 2ˣ
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
The standard form of an exponential function is:
y = abˣ
where a is the initial value and b is the multiplication factor.
The graph shown is an exponential function.
At the point (0, 1):
y = abˣ
substituting:
1 = ab⁰
a = 1
At the point (2, 4):
y = abˣ
substituting x = 2, y = 4 and a = 1:
4 = b²
b = 2
The exponential function is y = 2ˣ
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The exam results for the students in a class are shown in the frequency tree below
Given that the student did not pass the exam, the probability that they revised is 24%.
What is the probability?Probability refers to the likelihood, odds or chance of an expected outcome given many possible outcomes.
Probability is the quotient of expected outcomes over total outcomes.
The total number of students in the class = 33
The total number of students who revised = 19
The total number of students who revised and failed the exam = 8
The probability that the student revised but failed the exam = 8/33 = 24%
or (8/19 x 19/33)
Thus, the probability that a student chosen at random from the class revised but failed the exam is 24%.
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Is the midpoint rule an overestimate or underestimate?
The midpoint rule is an overestimate.
This is because the midpoint rule is a form of numerical integration which approximates the area under a curve by summing the areas of rectangles that are divided into equal intervals. These rectangles are centered on the midpoints of the intervals.
Because the rectangles are centered on the midpoints instead of the endpoints of each interval, the midpoint rule overestimates the area under the curve as the rectangles are wider than the intervals.
This means that the midpoint rule produces a larger area than the exact area under the curve. This is why the midpoint rule is an overestimate.
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The midpoint rule is an overestimate of the definite integral. The midpoint rule is a numerical integration method used to approximate the definite integral of a function.
It works by dividing the interval of integration into smaller subintervals and approximating the integral by summing the areas of rectangles whose heights are determined by the function evaluated at the midpoint of each subinterval.
Since the rectangles in the midpoint rule are taller at the midpoint and shorter at the endpoints, this method generally overestimates the true area under the curve. However, if the function is well-behaved and the subintervals are small enough, the error between the midpoint rule approximation and the true definite integral can be made arbitrarily small.
In conclusion, the midpoint rule is an overestimate of the definite integral, but the error can be made small by using smaller subintervals.
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find the product 5^56 × 5^22 × 5^-96
Answer:
5^-18
Step-by-step explanation:
here is the answer please mark me as the brainliest
What is the most simplified expression for 4 c squared d + 3 d c minus 2 (d c squared + c d) + 6 c squared d squared?
2 c squared d + d c + 6 c squared d squared
2 c squared d + 5 d c + 6 c squared d squared
3 c squared d + 3 d c + 6 c squared d squared + c d
3 c squared d + 2 d c + 6 c squared d squared minus 2 cd
Answer: 2 c squared d + d c + 6 c squared d squared
Step-by-step explanation: I looked it up
1. A function that has a V-shaped graph that opens up or
down is a(n)
2. The lowest or highest point on the graph of an absolute value
function is the
3. The line that divides the graph of an absolute value function
into two sections that are reflections of each other is the
1. A function that has a V-shaped graph that opens up or down is the absolute value function.
2. The lowest or highest point on the graph of an absolute value function is the vertex.
3. The line that divides the graph of an absolute value function into two sections that are reflections of each other is the line of symmetry.
What is the absolute value function?
The absolute value function of vertex (h,k) is given by the equation presented as follows:
y = |x - h| + k.
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What are the Multiples of 8 ?
Answer: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80…
Step-by-step explanation:
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so on. It is a sequence where the difference between each next number and the preceding number, i.e. two consecutive results, is 8.
Rewrite 1/4 book as a unit rate
A.1/12. 1/3hour
B.3/4
C.12
D. 1 1/3
The required unit rate is [tex]\frac{3}{4}[/tex] book/ hour
What is Unit rate:When two different types of quantities with various units are being compared, the ratio of rate is applied. On the other hand, the unit rate shows how many units of one quantity are equivalent to one unit of another. A unit rate is a ratio between two separate units with 1 as the denominator.
Here we have
1/4 book/ 1/3 hour
We can convert the given fraction into a unit rate as given below
=> 1/4 book/ 1/3 hour
=> [tex]\frac{1}{4} \times (\frac{3}{1})[/tex] book/ hour
=> [tex]\frac{3}{4}[/tex] book/ hour
Therefore,
The required unit rate is [tex]\frac{3}{4}[/tex] book/ hour
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Evaluate the expression for the given value of the variable.
41 + 5/7t =
t= -1/2
41 + 5.7t= Answer?
The value of the expression is 40.64.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
41 + (5/7)t
When t = -1/2
41 + (5/7)t
= 41 + 5/7 x (-1/2)
= 41 - 5/14
= (574 - 5) / 14
= 569/14
= 40.64
Thus,
The value is 40.64.
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A cylinder shaped pipe is 24 inches long and has a diameter of 6 inches. Witch measurements is closest to the lateral surface area of the pipe in square inches?
The lateral surface area of the cylinder for the given measurements is equal to 452.16 square inches.
Pipe is in form of cylinder
Diameter of the cylinder = 6 inches
Height of the cylinder 'h' = 24 inches
Radius of the cylinder 'r' = diameter / 2
= 6/ 2
= 3inches
lateral surface area of the cylinder = 2πrh
value of π = 3.14
Substitute the value we get,
⇒lateral surface area of the cylinder = 2 × π × 3 × 24
⇒lateral surface area of the cylinder = 144π square inches
⇒lateral surface area of the cylinder = 144 × 31.4
⇒ lateral surface area of the cylinder = 452.16 square inches
Therefore, the lateral surface area of the cylindrical pipe is equal to 452.16 square inches.
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Find the value of x in the supplement
The value of 'x' in the linear pair of angles is 126°.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
We know the sum of linear pair of angles is 180°.
Therefore, From the given information
(x - 6)° + 60° = 180°.
x + 54° = 180°.
x = 180° - 54°.
x = 126°.
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The points (-8, -3) and (-1, -2) fall on a particular line. What is its equation in point-slope form?
Answer: y+3= 1/7 * (x+8)
Step-by-step explanation:
(8^x/4+4)=(8^-19x/4)
Answer:x = 1/60
Step-by-step explanation:
(8^x/4+4)=(8^-19x/4)
Apply fraction cross multiply: a/b = c/d then a*d = c*b
8^x * 4 = (4+4) * 8^-19x
simplify
8^x * 4 = 8 * 8^-19x
Apply exponet rules
xln(8) + ln(4) = (-19x +1) ln(8)
then just solve
x= 1/60
while y = -1/8
or
Rudy has run many marathons and keeps track of all of his finishing times. At a race last month, he finished in 260 minutes. At his next race, he finished with a time that was 20% longer. What was his finishing time at the most recent race?
Rudy's timing in the most recent race is 312 minutes.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that Rudy has run many marathons and keeps track of all of his finishing times. At a race last month, he finished in 260 minutes. At his next race, he finished with a time that was 20% longer.
Rudy's timing in the most recent race can be calculated as -
{x} = 260 + 20% of 260
{x} = 260 + (20/100) x 260
{x} = 260 + 20 x 2.6
{x} = 260 + 52
{x} = 312
Therefore, Rudy's timing in the most recent race is 312 minutes.
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Nolan had 20 dollars to spend on 3 gifts. He spent 9 34 dollars on gift A and 3 12
dollars on gift B. How much money did he have left for gift C?
Therefore, Nolan has 8 dollars left to spend on gift C.
Nolan spent 9 dollars and 34 cents on gift A,
and 3 dollars and 12 cents on gift B,
for a total of
9 + 3 = 12 dollars and
34 + 12 = 46 cents spent so far.
Nolan started with 20 dollars, so he has 20 - 12 = 8 dollars remaining for gift C.
By using wildcards (such as "x" and "y") that are replaced with random values when the quiz is taken, simple calculated questions provide a technique to build individual numerical questions whose response is the result of a numerical formula that contains changeable numerical values.
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find the minimum value c=x+3y
Answer: To find the minimum value of c = x + 3y, you need to solve the optimization problem with a constraint or without any constraint.
Without a constraint:
The minimum value of c = x + 3y without a constraint is achieved when the partial derivatives of c with respect to x and y are equal to zero.
Let's take the partial derivative of c with respect to x:
dc/dx = 1
And with respect to y:
dc/dy = 3
Setting these equal to zero, we have:
1 = 0 and 3 = 0
Since the partial derivatives are not equal to zero, there is no minimum value of c without a constraint.
With a constraint:
If there is a constraint, such as a limit on x or y, then the minimum value of c can be found by using optimization techniques, such as the method of Lagrange multipliers.
Step-by-step explanation: