Answer:
total surface area = 298.45105 m2
lateral surface area = 141.37155 m2
top surface area = 78.53975 m2
bottom surface area = 78.53975 m2
Step-by-step explanation:
Joanna will need approximately 298.3 square inches of frosting to cover the entire cake.
To calculate the amount of frosting Joanna will need for the entire cake, we first need to find the surface area of the cylindrical cake.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
Where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of the cake is 10 inches, we can find the radius by dividing it by 2: r = 10/2 = 5 inches.
Plugging in the values, we have:
Surface Area = 2π(5)² + 2π(5)(4.5)
Simplifying the equation:
Surface Area = 2π(25) + 2π(22.5)
Surface Area = 50π + 45π
Surface Area = 95π
To find the actual numerical value, we can approximate π as 3.14:
Surface Area ≈ 95 * 3.14
Surface Area ≈ 298.3 square inches
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Introduction to area of a piecewise rectangular figure
Given:
The piecewise rectangular figure.
To find:
The area of the piecewise rectangular figure.
Solution:
Draw a line and divide the given figure in two parts (a) and (b) as shown in the below figure.
Figure (a) is a rectangle of length 5 yd and width 3 yd. So, the area of the rectangle is:
[tex]Area=length\times width[/tex]
[tex]A_a=5\times 3[/tex]
[tex]A_a=15[/tex]
Figure (b) is a square of edge 2 yd. So, the area of the square is:
[tex]Area=(edge)^2[/tex]
[tex]A_b=(2)^2[/tex]
[tex]A_b=4[/tex]
The area of the given figure is:
[tex]A=A_a+A_b[/tex]
[tex]A=15+4[/tex]
[tex]A=19[/tex]
Therefore, the area of the given figure is 19 square yd.
Steel rods are manufactured with a mean length of 29 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.07 cm. (a) What proportion of rods has a length less than 28.9 cm? (b) b) Any rods that are shorter than 24.84 cm or longer than 25.16 cm are discarded. What proportion of rods will be discarded?
Solution :
Given data :
The mean length of the steel rod = 29 centimeter (cm)
The standard deviation of a normally distributed lengths of rods = 0.07 centimeter (cm)
a). We are required to find the proportion of rod that have a length of less than 28.9 centimeter (cm).
Therefore, P(x < 28.9) = P(z < (28.9-29) / 0.07)
= P(z < -1.42)
= 0.0778
b). Any rods which is shorter than [tex]24.84[/tex] cm or longer than [tex]25.16[/tex] cm that re discarded.
Therefore,
P (x < 24.84 or 25.16 < x) = P( -59.42 < z or -54.85)
= 1.052
Please help!
A line intersects the points (-2, 8) and
(4, 12). Find the slope and simplify
completely.
Help Resource
Slope
[?]
= +
Hint: m =
y2-yi
X2-X1
Enter
Answer:
2/3
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (12-8)/(4 - -2)
(12-8)/(4+2)
4/6
2/3
Please need help explanation need it
Answer:
308 m^3
Step-by-step explanation:
The volume is given by
V = l*w*h where l is the length , w is the width and h is the height
V = 7*4*11
V = 308 m^3
Perform the indicated operation. Be sure the answer is reduced.
4x/2x+y + 2y/2x+y
4
2
1
Answer:
2y + y/x + 2
Step-by-step explanation:
is the answer.....
7/12 - ( 1- ( 2/3 - 3/4 ) ) =
The solution couldn't fit but I can explain
You basically solve the sum in the brackets first
multiply the sign in the brackets after the sum
9/37 is changed to a decimal. What digit lies in the 2005th place to the right of the decimal point?
Answer:
2
Step-by-step explanation:
Divide 9/37 and you get repeating decimal of 0.243
Divide 2005 by 3 because the decimal repeats 3 numbers
You will get reminder of 1 from dividing 2005 by 3
Move 1 place from the decimal point and you get 2
Which of the following is a correct tangent ratio for the figure? A) tan (24) 76 B) tan(76°) °= 2 C) tan(76°) = D) tan(8") = 24 76
Given question is incorrect; here is the complete question.
"Which of the following is a correct tangent ratio for the figure attached"
A) tan(76°) = [tex]\frac{24}{8}[/tex]
B) tan (76°) = [tex]\frac{8}{24}[/tex]
C) tan (24°) = [tex]\frac{76}{8}[/tex]
D) tan (8°) = [tex]\frac{24}{76}[/tex]
Option A will be the correct option.
From the figure attached,
Given triangle is a right triangle.Measure of one angle = 76°Measure of two sides of the triangle are 24 and 8units.By applying tangent ratio of angle having measure 76°.
tan(76°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{24}{8}[/tex]
Therefore, Option (A) is the correct option.
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Find the altitude of an equilateral triangle whose perimeter is 18
Answer:
3√3 units
Step-by-step explanation:
We are asked to find the altitude of the equilateral triangle whose perimeter is 18 . Firstly let us find the side of the∆.
[tex]\rm \implies a + a + a = 18 \\\\\rm\implies 3a = 18 \\\\\rm\implies a = 6 [/tex]
Now we know that in a equilateral triangle , the altitude of the triangle with side length a is ,
[tex]\rm\implies Altitude =\dfrac{\sqrt3}{2} a [/tex]
Plug in the value of a that is 6 , we will get ,
[tex]\rm\implies Altitude =\dfrac{\sqrt 3}{2} a \\\\\rm\implies Altitude =\dfrac{ \sqrt3}{2}\times 6 \\\\\rm\implies Altitude = \sqrt3 \times 3 \\\\\rm\implies\boxed{ \bf Altitude = 3\sqrt3 \ units }[/tex]
Which of the following is true of the discriminant for the graph below?
Considering that the quadratic equation has no solutions, the discriminant is classified as:
C. Negative.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], it has 2 real solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has 1 real solutions.If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.Looking at the graph, the equation has no solutions, hence [tex]\Delta < 0[/tex] and option C is correct.
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Thank you so much for your help
Answer:
1.1x
Step-by-step explanation:
that is the procedure above
juans pencil box measures 6 cm long. if the length of the diagonal is 10 cm what is the width of the pencil box
Answer:
8 cm
Step-by-step explanation:
We can use the Pythagorean theorem to solve since we have a right triangle
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 +6^2 = 10^2
a^2 +36 = 100
a^2 = 100-36
a^2 = 64
Taking the square root of each side
sqrt(a^2) = sqrt(64)
a =8
Answer:
8 cm
Step-by-step explanation:
Use the Pythagorean theorem- [tex]a^{2} +b^{2} =c^{2}[/tex]
leg a: 6cm
leg b: unknown
hypotenuse: 10cm
Therefore [tex]6^{2} +x^{2} =10^{2} = 36+x^{2} =100[/tex]
Subtract 36 to 100 to isolate the [tex]x^{2}[/tex]. [tex]x^{2} =64[/tex]
Square root both sides and get your answer of 8cm
Tim has 17 marbles bob has 36 marbles and Jeffery has 49 marbles if they share all their marbles equally among themselves how many marbles will each boy get
Let f(x) = 2x - 7 and g(x) = -6x - 3. Find f(x) + g(x) and state its domain.
HELP PLSSSSS!!!!!!!!!!!!!!!!!!!!!!!!!!!
A : 12x2 - 48x + 21; all real numbers
B: -14x2 + 36x - 18; all real numbers except x = 7
C: 12x2 - 48x + 21; all real numbers except x = 1
D: -14x2 + 36x - 18; all real numbers
Answer:
Step-by-step explanation:
f(x) + g(x) = 2x - 7 - 6x - 3
f(x) + g(x) = -4x - 10
The domain is any real number.
I think you have mixed up the question. None of the choices are correct. They look like they belong to another choice.
It could be f(x)*g(x)
(2x - 7) (-6x - 3)
-12x^2 - 42x - 6x + 32
-12x^2 - 48x + 21
Well it could be either A or C since they are identical.
I’m pretty sure the answer is c but I need further help to understand if I am right or not
Answer:
you are correct'v'
Step-by-step explanation:
in the first column it adds the next odd number, 1, 3, 5,7
and in the 2nd it mutiplies by 2 so it would be faster by a whole lot
Determine the period
Answer:
3 units
Step-by-step explanation:
The period of a wave is the time taken to complete a cycle of motion of the wave
In the given figure, the graduations of the x-axis, which is the usually time axis = 1 unit
At the origin, (0, 0), the vertical displacement of the wave = 0
The maximum value of the wave function is between x = 0 and x = 1
The minimum value of the wave function is between x = 2 and x = 3
At the point (3, 0) the value of the wave function is again 0, and a cycle of the wave is completed
Therefore, the period of the wave = 3 units of the x-variable
Can some help me with 12 and 13 and 14
If you don’t know the answer please don’t answer
Answer:
[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ { \tt{ \sin(55 \degree) = \frac{x}{15} }} \\ x = 15 \sin(55 \degree) \\{ \boxed{ \bf{ x = 12.29 \: }}} \: feet[/tex]
If a 750 ml bottle of juice costs £1.90 and a 1 litre bottle of the same juice costs £2.50 then the 750 ml bottle is better value.
Answer:
The 1 liter bottle is better value
Step-by-step explanation:
Cost of 750 ml = £1.90
Cost of 1 liter = £2.50
1000 ml = 1 liter
Cost per 250 ml
750 ml / 3 = £1.90 / 3
250 ml = £0.6333333333333
Approximately,
£ 0.633
Cost per 250 ml
1 liter / 4 = £2.50 / 4
250 ml = £0.625
The 750 ml bottle is not a better value
The 1 liter bottle is better value
Lisa runs 6 miles in 50 minutes. At the same rate, how many miles would she run in 35 minutes?
Answer:
6/50 = .12 m/min
.12 * 35 =4.2 miles
Step-by-step explanation:
Which expressions are equivalent to the equation below
Answer:
Polynomial Expression.
Step-by-step explanation:
PLS HELP QUESTION ATTACHED
Answer:
A
Step-by-step explanation:
the -1 represents the graph going down by 1
convert 4 seconds to hour
Answer:
0.00111111 hrs
Step-by-step explanation:
Have a nice day
Answer:
4/3600 = .001111 hr
Step-by-step explanation:
4 seconds * 1 hour * 1 minute = 4/3600 = .001111 hr
60 minutes 60 seconds
Simplify this algebraic expression completely
8-y-2(y+4)
A. 6y+4
B.6y-8
C.6y+2
D.6y-4
the answer for your question is A :>
What is the period 3 pi and 4 pi
Answer:
i think i know the answer sorry if im wrong but i would say B
Step-by-step explanation:
On Monday morning at 8:00 a.m. the temperature is – 14 o C. Over the
next 6 hours the temperature rises 6 o C. Between 2:00 p.m. on Monday
and 8:00 a.m. on Tuesday the temperature drops 9 o C. Over the next 6
hours the temperature rises only 4 o C. What is the temperature at 2:00
p.m. on Tuesday?
Which statements are true of functions? Check all that apply.
All functions have a dependent variable.
All functions have an independent variable.
The range of a function includes its domain.
A vertical line is an example of a functional relationship.
A horizontal line is an example of a functional relationship.
Each output value of a function can correspond to only one input value.
Answer:
All functions have a dependent variable.
All functions have an independent variable.
A horizontal line is an example of a functional relationship.
Step-by-step explanation:
I have solved a), please help!
Answer:
Step-by-step explanation:
GHLM is a rectangle
MG = LH
MG = 14
ΔMXG ~ ΔKXL
In similar triangles, corresponding side are in same ratio.
[tex]\frac{MG}{MX}=\frac{XL}{XK}\\\\\frac{14}{7}=\frac{x}{8}\\\\\frac{14}{7}*8=x\\\\x = 8*2\\\\x= 16[/tex]
- CA Geometry A Illuminate Credit 4 FF.pdf
Answer:
hii
Step-by-step explanation:
Solve. -7x+1-10x^2=0
Answer:
[tex]-7x+1-10x^2=0[/tex]
[tex]-10x^2-7x+1=0[/tex]
[tex]quadratic\:equation:-[/tex] [tex]ax^2+bx+c=0[/tex]
[tex]solutions:-\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]For \\A=-10\\B=-7\\C=1[/tex]
[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}}{2\left(-10\right)}[/tex]
[tex]\sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}=\sqrt{89}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{89}}{2\left(-10\right)}[/tex]
[tex]x_1=\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)},\:x_2=\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}[/tex]
[tex]\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)}=-\frac{7+\sqrt{89}}{20}[/tex]
[tex]\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}=\frac{\sqrt{89}-7}{20}[/tex]
[tex]x=\frac{\sqrt{89}-7}{20}[/tex]
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