Finding the radius from it's surface area, the volume of the sphere is of 268.08 cm³.
What are the surface area and the volume of an sphere?For an sphere of radius r, we have that the surface area is given by:
[tex]S = 4\pi r^2[/tex]
The volume is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Considering the surface area of 200.96 cm², the radius is given by:
[tex]S = 4\pi r^2[/tex]
[tex]200.96 = 4\pi r^2[/tex]
[tex]r = \sqrt{\frac{200.96}{4\pi}}[/tex]
r = 4 cm
Hence the volume is given by:
[tex]V = \frac{4\pi \times 4^3}{3} = 268.08 \text{cm}^3[/tex]
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Two sides of an obtuse triangle measure 9 inches and 14 inches. The length of longest side is unknown.
What is the smallest possible whole-number length of the unknown side?
The smallest possible whole-number length of the unknown side is 17 inches.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
From the information given, the sides of an obtuse triangle measure 9 inches and 14 inches.
Therefore, the third side will be:
c² = 9² + 14²
c² = 81 + 196
c² = 277
c = ✓277
c = 16.64
c = 17
Hence, the smallest possible whole-number length of the unknown side is 17 inches.
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If f ( 1 ) = 5 f(1)=5 and f ( n ) = − 2 f ( n − 1 ) − 5 f(n)=−2f(n−1)−5 then find the value of f ( 4 ) f(4).
Answer:
f(4) = -55
Step-by-step explanation:
Given
f(1) = 5
f(n) = -2f(n-1) - 5
If you substitute n with 4 you get:
f(n) = -2f(n-1) - 5
f(4) = -2f(4-1) - 5
= -2f(3) - 5
This shows that you have to calculate the value of f(3) before we can get the value of f(4). To calculate f(3) we have to know f(2) and to calculate f(2) we have to know f(1), which is given.
Let's start from the bottom.
f(1) = 5
f(2) = -2f(n-1) - 5
= -2f(2-1) - 5
= -2f(1) - 5 // substitute f(1) with the value 5 (given)
= -2(5) - 5
= -15
f(3) = -2f(n-1) - 5
= -2f(3-1) - 5
= -2f(2) - 5
= -2(-15) - 5
= 25
Now we can finally calculate f(4)!
f(4) = -2f(n-1) - 5
= -2f(4-1) - 5
= -2f(3) - 5
= -2(25) - 5
= -55
The solution to an absolute value inequality is shown on the graph below.
71
++
-54-3-2-1 0 1 2 3 4 5
What is another way to show the solution?
O x>-3 orx<2
O {xx<-3orx<2}
4
O [-3, 2]
O (-3,2)
The solution to show the absolute value inequality is (-3,-2)
What is absolute inequality?An absolute value inequality is an expression with absolute functions as well as inequality signs
Interval = -3 to 2
The intervals are represented with open parenthesis, which shows that -3 and 2 are excluded values of the inequality.
So, we have:
-3 < x < 2
As an interval notation,
(-3,-2)
Hence, the solution to the absolute value inequality is (-3,-2)
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Find the surface area of the image below
The surface area of the provided figure is 1051.2 square ft after calculating the area separately.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
We have given a three-dimensional figure with dimensions.
The surface area = area of seven rectangles + area of two triangle
= 15×9 + 2(15×12) + 2(9×12) + 2(9×15) + 2(1/2)[9(19.8-12)]
= 135 + 360 + 216 + 270 + 70.2
= 1051.2 square ft
Thus, the surface area of the provided figure is 1051.2 square ft after calculating the area separately.
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Bruno uses a piece of wrapping paper with dimensions 1 and one-fourth feet by 3 feet to wrap a gift. What is the total area of the paper used to wrap the gift?
One-fourth square feet
Three-fourths square feet
3 and one-fourth square feet
3 and three-fourths square feet
The area of the paper used to wrap the gift is 3 3/4 square feet
How to determine the total area?The dimension is given as:
1 1/4 by 3
The area is the product of the dimensions.
So, we have
Area = 1 1/4 * 3
Express as an improper fraction
Area = 5/4 * 3
Evaluate
Area = 15/4
Rewrite as:
Area = 3 3/4
Hence, the area of the paper used to wrap the gift is 3 3/4 square feet
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Answer: D
Step-by-step explanation: E2022
graph the system below
2x-3y=-18
3x+y=-5
Answer:
[tex]x = 3 \frac{(y - 6)}{2} \\ \\ x = \frac{ - 5 - y}{3} [/tex]
Step-by-step explanation:
[tex]2x = - 18 + 3y \\ 2x = 3y - 18 \\ x = \frac{3y - 18}{2} \\ x = \frac{3(y - 6)}{2} \\ \\ 3x = - 5 - y \\ x = \frac{ - 5 - y}{3} [/tex]
Which values are in the solution set of the compound inequality? Select two options
4(x + 3) ≤0 orx+1>3
0-6
0-3
0
3
8
The values are in the solution set of the compound inequality are (-6, -3), (3, 8).
What is inequality?Inequality is the phenomenon of unequal distribution of resources and opportunities among the given function.
To find the number that are solutions to the compound inequalities, the value of x is
First inequality:
4(x +3) ≤0
4x +12 ≤0
4x ≤-12
x ≤-3
The value of x lies in the interval = (-∞ , -3]
Second inequality:
x +1 >3
x>2
The value of x lies in the interval = (2 , ∞)
So, the interval solution is (-∞ , -3] U (2 , ∞)
Thus, the values are in the solution set of the compound inequality are (-6, -3), (3, 8).
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A tower that is 159 feet tall casts a shadow 172 feet long. Find the angle of elevation of the sun to the nearest degree
helppp pleasee quick points no wrong answers
Answer:
A.) 6π/5
B.) 756°
Step-by-step explanation:
A.) [tex]216*\frac{\pi }{180} = \frac{6\pi }{5}[/tex]
B.) [tex]\frac{21\pi }{5} *\frac{180}{\pi } = 756 ^{0}[/tex]
Hope this helps!
Betty wants to bake the perfect cookie. She wants to determine the ideal temperature at which to bake the cookies. She has enough batter to make 60 cookies. She decides to randomly assign 15 cookies to be baked at 300°, 15 at 325°, 15 at 350°, and 15 at 375°. The baking time for each batch is 12 minutes. Use the diagram to identify the components of the completely randomized design.
The true option about the randomized design is (c) Betty should prepare all 60 cookies.
Each cookie will receive a number.
The numbers will be written on slips of paper, put into a hat, and shuffled well.
The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated.
The given parameters are:
n=60
batches=4
cookies=15 ---- the number of cookies in each batch
Temperature=300,325,350,375.
To randomly assign the cookies to the given temperatures, all cookies have to be subjected to the same conditions (except for the difference in the temperature).
What is the temperature?Normal human body temperature is the typical temperature range found in humans. The normal human body temperature range is typically stated as 36.5–37 °C. Human body temperature varies.
This means that she can bake all the cookies at once at different temperatures while noting down the cookies with a given number.
Hence, the true option is (c)
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Answer: C : completely randomized experimental design
Step-by-step explanation: edge 2023
2) Find the 10th term of the Harmonic progression,
1/2,1/4,1/6............. 10th term
========================================================
Explanation:
The denominators 2, 4, 6, ... are in an arithmetic progression
first term = 2common difference = 2We have the multiples of 2.
first denominator = 1*2 = 2second denominator = 2*2 = 4third denominator = 3*2 = 6And so on.
The tenth denominator is 10*2 = 20
Therefore, the tenth term of the harmonic progression is 1/20
---------
Side note:
An arithmetic progression is of the form [tex]a, a+d, a+2d, a+3d, \ldots[/tex]
A harmonic progression is of the form [tex]\frac{1}{a}, \frac{1}{a+d}, \frac{1}{a+2d}, \frac{1}{a+3d}, \ldots[/tex]
I.e. take the reciprocal of the arithmetic sequence to get the harmonic sequence, or vice versa.
Help me please !!
The sum of 5th and 9th terms of an A.P. is 72 and the sum of 7th and 12th terms is 97. Find the A.P.
[tex] \star\:{\underline{\underline{\sf{\purple{Given ::}}}}}[/tex]
❖ [tex]\sf a_{5} + a_{9} = 72 [/tex]
❖ [tex]\sf a_{7} + a_{12}= 97 [/tex]
[tex] \star\:{\underline{\underline{\sf{\purple{To \: Find ::}}}}}[/tex]
❖ The A.P
[tex] \star\:{\underline{\underline{\sf{\purple{Solution ::}}}}}[/tex]
Let,
[tex]a[/tex] be the first term and [tex]d[/tex] be the common difference of the A.P
According to the question,
[tex]\sf a_{5} + a_{9} = 72 [/tex] and [tex]\sf a_{7} + a_{12}= 97 [/tex]
[tex]\longrightarrow \sf (a + 4d) + (a + 8d) = 72[/tex] and [tex]\sf (a + 6d) + (a + 11d) = 97[/tex]
Thus, we have
[tex] \longrightarrow \sf 2a + 12d = 72 - - (i)[/tex]
[tex] \longrightarrow \sf 2a + 17d = 97 - - (ii) [/tex]
Subtracting (i) from (ii), we get
[tex] \implies \sf 5d = 25[/tex]
[tex] \implies \sf d = \dfrac{25}{5} [/tex]
[tex]\implies {\star{ \underline{\boxed{\sf{\pink{\sf d = 5}}}}}}[/tex]
Now,
Putting d=5 in (i), we get
[tex] \longrightarrow \sf 2a + 12(5) = 72 [/tex]
[tex] \longrightarrow \sf 2a + 60= 72 [/tex]
[tex]\longrightarrow \sf 2a= 72 - 60[/tex]
[tex]\longrightarrow \sf 2a= 12[/tex]
[tex]\longrightarrow \sf a= \dfrac{12}{2} [/tex]
[tex]\longrightarrow{\star{ \underline{\boxed{\sf{\pink{\sf a = 6}}}}}}[/tex]
[tex] \therefore[/tex] a=6 and d=5
Hence, the A.P is 6,11,16,21,26...
[tex]\rule{250pt}{2.5pt}[/tex]
¿Cuál es la probabilidad de que, al lanzar dos dados, uno blanco y uno rojo, obtener en el dado blanco un número menor que tres y en el rojo un valor mayor a tres?
La probabilidad de obtener en el dado blanco un número menor que tres y en el rojo un valor mayor a tres es:
p = 1/6.
¿Como obtener la probabilidad?
Tiramos dos dados, uno blanco y uno rojo, y queremos obtener la probabilidad de obtener un número menor a 3 en el dado blanco y un numero mayor a 3 en el dado rojo.
Primero, el dado blanco tiene los posibles valores {1, 2, 3, 4, 5, 6}, los valores menores que 3 son {1, 2}
Entonces 2 de 6 resultados son menores que 3, es decir, la probabilidad es:
P = 2/6 = 1/3.
Para el dado rojo los posibles valores son los mismos, y los valores mayores que 3 son {4, 5, 6}, entonces 3 de 6 resultados son mayores que 3, es decir, la probabilidad es:
Q = 3/6 = 1/2.
La probabilidad conjunta es el producto de la dos probabilidades individuales:
p = P*Q = (1/3)*(1/2) = 1/6.
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Calculate for the area of the shaded portion. Take π=22/7.
100 PTS TO THE FIRST PERSON WHO ANSWERS IT CORRECTLY
Step-by-step explanation:
the point coordinates at the end of their flights are
x = cos(angle) × distance
y = sin(angle) × distance
remember, cosine is on the x-axis (left and right values), sine is on the y-axis (up and down values).
and the values of sine and cosine are standard for the norm circle with radius = 1.
but in such cases the radius is much larger that 1, and we have to multiply it with the trigonometric functions for scaling reasons.
the radius is always the angled connection from the center of the circle to the point on the arc of the circle. in our cases the travel distances of the shuttles.
so, if we consider the central staffing point as (0, 0), they end up at the following coordinates :
the inner (lower) angle for Mr. Scotts trip is
90-30 = 60°
and his coordinates are
(cos(60)×100, sin(60)×100) =
= (0.5×100, 86.60254038...) = (50, 86.60254038...)
the inner (lower) angle for Mr. Spock's trip is
90-62 = 28°
and his coordinates are
(cos(28)×110, sin(28)×110) =
= (97.12423521..., 51.64187191...)
the distance between these 2 points is
distance² = (Spockx - Scottx)² + (Spocky - Scotty)² =
= (47.12423521...)² + (-34.96066847...)² =
= 2,220.693545... + 1,222.24834... =
= 3,442.941885...
distance = 58.67658719... km
How can you find the magnitude of a vector v→=
, where the horizontal change is x and the vertical change is y?
Answer:
The magnitude of a vector is its length.
To calculate the magnitude of a vector in any number of dimensions, square root the sum of the squares of each dimension.
Therefore, if [tex]\vec v=(x,y)[/tex] then its magnitude is:
[tex]|v|=\sqrt{x^2+y^2}[/tex]
Similarly, if [tex]\vec v=(x,y,z)[/tex] then its magnitude is:
[tex]|v|=\sqrt{x^2+y^2+z^2}[/tex]
pls help me it geometry
Let's solve this problem step-by-step:
First let's convert 1 to 1/1:
⇒ Sequence: [tex]\frac{1}{1},\frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25} ,..[/tex]
Now let's consider a few things:
the numerator of each of the fractions don't changethe denominators are all perfect squares:⇒ 1, 4, 9, 16 ,25, 36
The perfect square that comes after 25:
⇒ is 36
⇒ which is the denominator of the fraction that comes after [tex]\frac{1}{25}[/tex]
Answer: [tex]\frac{1}{36}[/tex]
Hope that helps!
Answer:
1/36
Step-by-step explanation:
If you write the first number as a fraction also, 1/1, then every term has a 1 on top of a fraction.
The denominators (number on the bottom) are
1, 4, 9, 16, 25, this is a list of perfect squares. That is
1 = 1×1 = 1^2
4 = 2×2 = 2^2
9 = 3×3 = 3^2
16 = 4×4 = 4^2
25 = 5×5 = 5^2
So the next number is
6×6 = 6^2
= 36
36 is on the bottom. 1 is on the top.
The next number is 1/36.
You have at most $20.25 to spend at a market. Apples cost $0.30 each, and pears cost $0.70 each. Let [tex]a[/tex] be numbers of apples and [tex]p[/tex] be numbers of pears. Write an inequality that represents the numbers of apples and pears you can afford.
Answer:
See below
Step-by-step explanation:
.30 a + .70 p ≤ 20.25 where a = # apples p = # pears
Which table of ordered pairs represents a proportional relationship?
X
0
5
10
X246
123
2
3
134
3
4
10
20
30
10
20
30
234
4
10
13
Answer:
The second option
Step-by-step explanation:
The second option is a proportional relationship since the ratio between y and x is constant.
10/2 = 5
20/4 = 5
30 / 6 = 5
What is
a situation in which a polynomial model might make sense, and why
Answer:
variety of functions types can model situations in the real world. Properties or key features of functions make them more or less appropriate models, depending on the situation. You might already know about these types of functions.
Step-by-step explanation:
3. Zach is preparing for an interview and needs to
purchase 2 ferns and 7 balloons. Each balloon costs
$2.30, and he has $50 total to spend. What is the
maximum amount he could spend on each fern?
[~Answer~} (7.):
Hey there. I'm Avery, and I'm here to help you with your amazing question! <33
I believe the answer is: $16.95 per fern tree.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[~Answer Explanation~]:
first, you want to find how much money the 7 balloons cost:
7(2.30) = 16.10
second, you want to find how much money you have left AFTER buying 7 balloons:
50 - 16.10 = 33.90
third, divide the money you have left by 2 (2 fern trees) to find the final answer:
33.90/2 = 16.95
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[~Last Messages~]
Okay, I really hope my answer is correct.
I am truly sorry if it's wrong :(
Have a great morning, afternoon, or night. <333
[-!AveryIsSomehowAlive!-]
solve the given system of equations
2x+8y=5
24x-4y=-15
The value of x and y is y= 3/4 and x= -1/2
What is equation?
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given equations:
2x+8y=5........(1)
24x-4y=-15...........(2)
Multiply equation (1) by 12, we get
24x + 96y = 60.....(3)
From (2) and (3), we get
-4y-96y= -15-60
-100 y= -75
y= -75/-100
y= 3/4
and 2x+8y=5
2x + 8 (3/4) =5
2x + 6 = 5
2x= -1
x= -1/2
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A basket contains 56 mangoes out of which 14 are rotten. find the percentage of the mangoes that are in good condition?
Answer:
75%
Step-by-step explanation:
56-14=42, so 42 is the number of mangoes that are still in good condition. To find the percentage of 42/56 use this equation:
42/56=x/100
cross multiply to get:
4200=56x
divide 4200 by 56:
x=75
Help please
Solve the equation:
2x + 6-12 = 26
Answer:
x=16
Step-by-step explanation:
2x+6-12=262x-6=262x=26+62x=32, divide both sides by 2x=16Answer:
x = 16Step-by-step explanation:
Solve the equation:
2x + 6-12 = 26
2x = 26 - 6 + 12
2x = 20 + 12
2x = 32
x = 32 : 2
x = 16
--------------------------------
check
2 * 16 + 6 - 12 = 26
32 + 6 - 12 = 26
38 - 12 = 26
26 = 26
the answer is good
In ΔABC, m angle CAB = 60°, AD is the angle bisector of angle BAC with D∈BC and AD = 8ft. Find the distances from point D to the sides of the triangle. PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
As D lies on BC, the distance from D to BC is 0.
If we let the distance from D to AB be x, then in the right triangle,
[tex]\sin 30^{\circ}=\frac{x}{8}\\\\\frac{1}{2}=\frac{x}{8}\\ \\ x=4[/tex]
This means the distance from D to side AB is 4.
We can note that [tex]\sin 30^{\circ}=\frac{x}{8}=\frac{y}{8}[/tex], meaning y=4 as well, and thus the distance from D to side AC is 4
Find the ratio of RMS speed of an ideal gas at 235k and 37k.
The ratio of RMS speed of an ideal gas at 235K and 37K is 2.52011.
What is the RMS speed of an ideal gas?The equation V = √((3RT)/M), where R is the universal gas constant, T is the absolute (Kelvin) temperature, and M is the molecular mass, gives the root mean square (R.M.S.) speed V of the molecules of an ideal gas.
How to solve the question?In the question, we are asked to find the ratio of the RMS speed of an ideal gas at 235K and 37K.
We are given two temperatures, T₁ = 235K and T₂ = 37K
We calculate the ratio V₁:V₂ in the following way:
V₁:V₂
= √((3RT₁)/M)/√((3RT₂)/M)
= √((3R(235))/M)/√((3R(37))/M)
= √(235/37) {Since, 3, R, and M, cancel off each other}
= √6.351 = 2.52011.
Thus, the ratio of RMS speed of an ideal gas at 235K and 37K is 2.52011.
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Someone discovers that we are all actually robots — who created us and why?
(pls what do you think)
Type the correct answer in each box. Use numerals instead of words. Function f is given by the table of values shown. x 0 1 2 3 f(x) 7 0 -5 -8 If function f is reflected across the x-axis to obtain function g, complete the table of values which represents function g. x 0 1 2 3 g(x)
Using translation concepts, it is found that the table of values for function g(x) is given as follows:
x 0 1 2 3
g(x) -7 0 5 8
What happens when a function is reflected across the x-axis?When a function is reflected across the x-axis, all it's values are multiplied by -1.
Hence, considering the values of f(x) given in the problem, the table of values for function g(x) is given as follows:
x 0 1 2 3
g(x) -7 0 5 8
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Find the slope of the line passing through the points (-1,5) and (-8,2)
To determine the slope of the line, use the formula
[tex] \boxed{ \rm{m = \frac{y_2 - y_1}{x_2 - x_1} }}[/tex][tex]\\[/tex]
Representation:
[tex]\\[/tex]
[tex]\rm{(x_1, y_1) = (-1, 5)}[/tex][tex]\rm{(x_2, y_2) = (-8, 2)}[/tex][tex]\\[/tex]
Solution:
[tex]\rm{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex][tex]\rm{m = \frac{2 - 5}{((-8) - (-1)}}[/tex][tex]\rm{m = \frac{-3}{((-8) - (-1)}}[/tex][tex]\rm{m = \frac{-3}{-7}}[/tex][tex]\rm{m = \frac{3}{7}}[/tex][tex]\\[/tex]
Answer:
The slope is 3/7.[tex]\\[/tex]
[tex]\\[/tex]
[tex]\\[/tex]
Wxndy~~
Which statement is true about the end behavior of the
graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero
As the x-values go to positive infinity, the function's values go to positive infinity.
As the x-values go to positive infinity, the function's values go to positive infinity, Option D is the correct answer.
What is a Function ?A function is a mathematical statement that relates an independent variable with a dependent variable .
The graph is given in the question and the statement that correctly matches to the behaviour shown is asked .
When X values is increasing , the y value is increasing and
when the x value is decreasing the y value is also decreasing
Therefore the correct Option that can be chosen from the given is Option D
As the x-values go to positive infinity, the function's values go to positive infinity.
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