When broken open Austins jawbreaker will make a hemisphere, what is it surface area if the diameter is 16.4 inches?
Answers
When broken open Austen's jawbreaker will make a hemisphere.
Recall that the total surface area of a hemisphere is given by
[tex]TSA=3\pi r^2[/tex]Where r is the radius of the hemisphere.
We are given the diameter of the hemisphere that is 16.4 inches.
The radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{16.4}{2}=8.2\: in[/tex]So, the radius is 8.2 inches
Substitute the radius into the above formula of total surface area
[tex]TSA=3\pi r^2=3\pi(8.2)^2=3\pi(67.24)=633.72\: in^2[/tex]Therefore, the total surface area of the hemisphere is 633.72 square inches.
Please note that if you want to find out only the curved surface area then use the following formula
[tex]CSA=2\pi r^2=2\pi(8.2)^2=453.96\: in^2[/tex]For the given case, the curved surface area is 453.96 square inches.
Related Questions
What concentration of mixture would need to be added to protect the cars engine from the coolant boiling away at 230 F
Answers
The mixture should be at a concentration of 65.5% to protect the cars from the coolant boiling away at 230°F .
The given table has the concentration percentages and the boiling points of the antifreeze.
So the coolant boils away at 230F, so we need to find the concertation whose boiling point is higher than 230F .
From the table it is evident that the boiling point of 236 is good to protect the coolant as it is higher and closest to the given temperature.
Corresponding to the temperature we have , the percentage at 65.5%.
As 236F > 230F , so it is evident that we need the concentration of 65.5%.
1. a break will be needed for the x axis.
2. The graph of the table is attached below.
the red line indicates 230F, so the value above it is the required data.
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Write expression in terms of sine and cosine, and simplify so that no quotients appear in final expression.
Answers
Use the identity
[tex]1+\tan ^2x=\sec ^2x[/tex]Then the expression becomes
[tex]\frac{\sec^2x}{\sec x}=\sec x[/tex]Now, sec x is the reciprocal of cos x.
[tex]\frac{1+\tan^2x}{\sec x}=\frac{1}{\cos x}[/tex]Simplify by finding the sum or difference of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (6w^2+24w+24)-(3w^2-26w+3) This simplifies to: AnswerThe degree of our simplified answer i
Answers
Start by distributing the negative sign
[tex]6w^2+24w+24-3w^2+26w-3[/tex]Then group terms that have the same literal parts
[tex]\begin{gathered} (6w^2-3w^2)+(24w+26w)+(24-3) \\ \text{The resulting operation simplifies to} \\ 3w^2+50w+21 \\ \text{the degree of the polynomial is 2 since its the highest exponent.} \end{gathered}[/tex]Which relationships can be represented by the equation y=1/5x?
Answers
First, notice that 1/5 = 0.20. With this in mind, the examples that can be represented by the equation y = 1/5x are the following:
1.-Bananas are on sale for $0.20. Let x represent the number of bananas and y represent the total cost,in dollars
2.-For every 10 gallons of water, Jasmine adds 2 cups of Soap. Let x be the gallons of water and y the cups of soap.
Oliver and Robin have different stride lengths and want to compare them. Oliver uses a table to represent the distance he travels in feet related tothe number of strides he takes. Question 2 Using Robin's graph, how can you find the unit rate?
Answers
The grpah is plotted with the number of strides along the x axis and the distance travelled along the y axis.
So, the slope of the graph gives the distance travelled by Robin per stride or the stride length. The approximate value of slope of the graph is,
[tex]\text{Slope}=\frac{\Delta y}{\Delta x}=\frac{8-0}{3-0}=\frac{8}{3}=2.67[/tex]So, the stride length or the unit rate of Robin is approximately 2.67 feet.
graph the image of the figure after the given rotation. all rotations have a center of rotation at the origin180 degree rotation
Answers
Since all rotations have a center of rotation at the origin, let us first give the coordinates of the vertices of the original figure
If an object M(x, y) is rotated about the origin, the image will have the coordinates M'(-x, -y)
F(-4, 2)
N(-1, -2)
K(3, 0)
P(2, 4)
The coordinates of the new vertices after rotation will be:
F'(4, -2)
N'(1, 2)
K'(-3, 0)
P'(-2, -4)
The graph is shown below:
points (k,-3) lies on the line whose equation is X-2y=-2 what is the value of k
Answers
(k,-3)
x-2y=-2
replace (x,y ) for (k,-3) and solve for k
k-2(-3)=-2
k+6 =-2
k= -2-6
k=-8
0.16 whole number , integer, rational number (can be more than one set)
Answers
Answer : 0.16 is a rational number
Rational number is a number such that can be expressed as the quotient or fraction of two integers
An integer is a number that can be written without a fractional component
0. 16 can be written as
16 / 100
16 and 100 are both integers but 0.16 is not an integer but a rational number
16 / 100 = 0.16. This means that fraction of two integers that does does not gives an integer is a rational number
Hence, 0.16 is a ratioanal number
14 3/4% as a decimal
Answers
ANSWER
14.75
EXPLANATION
To write a fraction as a decimal we have to do the division. In this case we have a mixed number, so we have the whole part of the decimal and we just have to find the decimal part - which is 3/4.
3/4 is 0.75:
So 14 3/4 is:
[tex]14\frac{3}{4}=14+\frac{3}{4}=14+0.75=14.75[/tex]x2 - 4x + 4 = 0 following quadratic equations graphically
Answers
Since we have to solve it graphically, we need to plot the function:
Here, we can see that the point where the graph touches the y axis is when x = 2
The solution to the equation is x = 2
Point A is located at coordinates (-4,3). у. А 2 1 -3 -2 2. 3 $ X 1 2 3 What are the coordinates of each point? 1. Point B is the image of A after a rotation of 180° using (0,0) as center. 2. Point C is the image of A after a translation two units to the right, then a reflection using the c-axis. 3. Point D is the image of A after a reflection using the y-axis, then a translation two units to the right.
Answers
1. The rotation of a point in 180 degrees is given by reflecting both of its coordinates. In this case the original point is (-4, 3), so the rotated point will be (4, -3).
2. When we reflect a point around the x-axis we need to invert the signal of the y-coordinate. When we make a translation to the right we need to add the number of units to the x-coordinate of the point, therefore.
Translation:
A' = (-4 + 2, 3) = (-2, 3)
Reflection x-axis:
C = (-2, -3)
3. When we reflect a point around the y-axis we invert the signal of x-coordinate. To perform a translation to the right we add the number of units to the x-coordinates, therefore:
Reflection y-axis:
A'' = (4, 3)
Translation:
D = (4 + 2, 3) = (6,3)
Find an equation of the line passing through point (4, -5) and perpendicular to the line whose equation is y= 1/2x + 11/6. *In Slope-Intercept Form
Answers
Explanation:
Given the equation:
[tex]y=\frac{1}{2}x+\frac{11}{6}[/tex]Comparing it with the slope-intercept form: y=mx+b
[tex]\text{Slope,m}=\frac{1}{2}[/tex]Definition: Two lines are perpendicular if the product of the slopes is -1.
Let the slope of the new line = n
[tex]\begin{gathered} \frac{1}{2}n=-1 \\ n=-2 \end{gathered}[/tex]Substitute the slope, -2 and point (4,-5) in the slope-point form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-2(x-4) \end{gathered}[/tex]We then express it in the slope-intercept form:
[tex]\begin{gathered} y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]The equation of the perpendicular line is y=-2x+3.
Answer:
[tex]y=-2x+3[/tex]The value of y is directly proportional to the value of x. If y = 3 whenx = 7, what is the value of x when y= 10.5? *Hint: Now you are looking for the "X". (show work)
Answers
we have that y=k*x, therefore we can say that k=y/x
[tex]k=\frac{3}{7}[/tex]so, if we have y= 10.5 we get that
[tex]x=\frac{y}{k}=\frac{10.5}{\frac{3}{7}}=24.5[/tex]x=24.5
There were 24 participants in a recent study on personality traits. After being shown five images (1, 2, 3, 4, and 5), each participant selected the one that was most appealing to them. (a) The image each participant selected appears below. Complete the frequency distribution for the data.
Answers
The given images are 1, 2, 3, 4, 5
The total number of participants = 24
The frequency of each image is the number of times it appears in the distribution
Frequency of 1 = 6
Frequency of 2 = 5
Frequency of 3 = 4
Frequency of 4 = 3
Frequency of 5 = 6
The frequency distribution table is therefore shown below:
Find the length of XY if W is between X and Y, WX = 38 and WY = 16.XY =
Answers
Answer
XY = 54 units
Explanation
We are told that W is in between X and Y. This means that
XY = XW + WY
WX = XW = 38
WY = 16
XY = ?
We just make the necessary substitutions
XY = XW + WY
XY = 38 + 16 = 54 units
Hope this Helps!!!
zero, depending on your answer.|A flashlight is projecting a triangle onto a wall, as shown below.20nThe original triangle and its projection are similar. What is the missing length n on the projection?C 19.230O13.328
Answers
If two triangles are similar, it means that the ratio of their corresponding sides is the same. By applying this to the given triangles, it means that
20/n = 16/24
By crossmultiplying, we have
n x 16 = 20 x 24
16n = 480
n = 480/16
n = 30
The second option is correct
The function f is defined as follows for the domain given. f(x)= 1-3x domain = (-1, 0, 1, 2)(a)Write the range of f using set notation. (b)Then graph f.
Answers
Answer:
(a)Range: {-5, -2 ,1 ,4}
Explanation:
The function f is defined below:
[tex]f\mleft(x\mright)=1-3x[/tex]The domain of f(x) = {-1, 0, 1, 2}.
(a)To find the range of f(x), we evaluate f(x) for each value in the domain.
[tex]\begin{gathered} f\mleft(-1\mright)=1-3\left(-1\right)=1+3=4 \\ f\mleft(0\mright)=1-3(0)=1-0=1 \\ f\lparen1)=1-3(1)=1-3=-2 \\ f\mleft(2\mright)=1-3(2)=1-6=-5 \end{gathered}[/tex]Therefore, the range of f is:
[tex]\{-5,-2,1,4\}[/tex](b)Next, we graph f.
If you were to make a relative frequency table, which percent would go in the cell for red cars?1. 23.6%2. 27.3%3. 18.2%4. 30.9%
Answers
Answer:
23.6%
Explanation:
A relative frequency table shows the number of times a specific event occurs compared to the total number of events.
First, we calculate the total number of vehicles.
[tex]15+13+10+17=55[/tex]Next, the number of red cars = 13.
Therefore, the relative frequency for red cars will be:
[tex]\frac{13}{55}=0.236=23.6\%[/tex]The percent that would go in the cell for red cars is 23.6%.
In the scenarios you have explored so far, the angle measures were given, and you used trigonometric ratios to find missing side lengths. To determine the angle measures when only the side lengths are given, you can use inverse trigonometric functions. The input of each function is a number, which represents a ratio of two of the sides. The output of each function is an acute angle measure.Inverse sine: If sin A = z is given, then angle A can be determined by sin ¹2 = A.Inverse cosine: If cos A = x, is given, then angle A can be determined by cos ¹ = A.Inverse tangent: If tan A = z, is given, then angle A can be determined by tan ¹ = A.Let's explore this idea using the familiar 45°-45°-90° isosceles right triangle.
Answers
Given:-
A right angled triangle with side length 1.
To find the required angle value.
So now we use different trigonometric ratios such as,
[tex]sin,cos,tan[/tex]So we get,
[tex]sin^{-1}(\frac{1}{\sqrt{2}})=cos^{-1}(\frac{1}{\sqrt{2}})=tan^{-1}(\frac{1}{1})=45[/tex]So the required angle is 45 degree.
Selma and Didi both have parents that live far away. One weekend, both women decide to visit their parents. They each decide to leave for their trips at the same time.
Selma's distance from home is shown in the graph.
Unfortunately, Didi's route has a lot of traffic at the beginning of her trip. Didi's distance from home, in miles, is represented by the function f(x)=12(1.63)x, where x represents the hours she has been traveling.
How do the distances each woman is from home compare during their journeys?
Responses
After 3 hours, Selma is approximately 130 miles from home, and Didi is approximately 52 miles from home.
After 3 hours, Selma is approximately 130 miles from home, and Didi is approximately 52 miles from home.
After 2 hours, Selma is 91 miles from home, and Didi is approximately 20 miles from home.
After 2 hours, Selma is 91 miles from home, and Didi is approximately 20 miles from home.
After 2 hours, Didi is 91 miles from home, and Selma is approximately 20 miles from home.
After 2 hours, Didi is 91 miles from home, and Selma is approximately 20 miles from home.
After 3 hours, Didi is approximately 130 miles from home, and Selma is approximately 52 miles from home.
Answers
After 3 hours, Selma is approximately 130 miles from home and Didi is approximately 52 miles from home
Rewrite x^2+9 in factored form
Answers
The factored form is, x =3i and x = -3i
Given:
The objective is to write x^2+9 in factored form.
The factored form can be written as,
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\sqrt[]{-9} \\ x=\pm3i \end{gathered}[/tex]Here, i stands for imaginary term due the square root of (-1).
Hence, the factored form is, x =3i and x = -3i.
If you vertically compress the absolute value parent function, f(x) = lxl, by afactor of 5, what is the equation of the new function?OA. g(x) = 51x|OB. g(x)=x-51OC. g(x) = 15x|O D. g(x) = x
Answers
When the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .
The given function is of the form f(x) = ·|x| .
Therefore we can say that this function will be vertically compressed.
From the properties of transformation of graphs we know that when a function is vertically compressed by a factor of a we get the transformed function as 1/a times the original function.
given function:
f(x) = |x|
vertically compressed by 5.
therefore new function = 1/5 |x|
Hence the transformed function is g(x) .
g(x) = 1/5 |x|
Let us take a few coordinates along the x-axis to get the values of the y and the graph of both modulus function pass through origin .
f(x) = |x|
at x = 10 , f(x) = 10
and g(x) = 2
Here we see that the function is compressed.
Therefore when the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .
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Choose the option with the proper number of sig figs
Answers
let's break down the expression to get the final result:
[tex]\begin{gathered} \frac{9\text{ }\times10^9}{4.5\text{ }\times10^1}\text{ = }\frac{9}{4.5}\times\text{ }\frac{10^9}{10^1} \\ \frac{9}{4.5}\text{ = }\frac{9\text{ }\times\text{ 10}}{4.5\text{ }\times\text{ 10}}\text{ = }\frac{90}{45} \\ \frac{9}{4.5}\text{ = }2 \\ \\ \frac{10^9}{10^1}\colon\text{ when we divide exponents with same base, } \\ we\text{ take one of the base and combine the exponents by subtracting them:} \\ \frac{10^9}{10^1}=10^{9-1} \\ \frac{10^9}{10^1}=10^8 \end{gathered}[/tex][tex]\begin{gathered} \frac{9}{4.5}\times\text{ }\frac{10^9}{10^1}\text{ = 2 }\times10^8 \\ \\ \text{when dividing decimals, }the\text{ least number of }significant\text{ }figures\text{ in the problem}, \\ \text{ }\det ermines\text{ the significant figures in the answer} \\ 9\text{ = 1 significant, 4.5 = 2 significant} \\ \text{The least significant is 1} \\ \\ \frac{9\text{ }\times10^9}{4.5\text{ }\times10^1}\text{ = 2 }\times10^8 \end{gathered}[/tex]Drag numbers in the box to make each comparison true
Answers
1) Let's find the results of each inequality/equality so that we write out the right choices.
2) Let's begin with the equation. We're going to resort to Algebra:
[tex]\begin{gathered} 12\times\frac{4}{x}=8 \\ 12\times4=8x \\ 48=8x \\ 8x=48 \\ \frac{8x}{8}=\frac{48}{8} \\ x=6 \\ 12\times\frac{4}{6}=8{\color{DarkBlue} } \end{gathered}[/tex]Based on that, we can tell that and filling in the gap with other whole numbers the following:
[tex]\begin{gathered} 12\times\frac{4}{8}<8 \\ 6<8 \\ 12\times\frac{4}{6}=8 \\ 12\times\frac{4}{3}>8 \\ 16>8 \end{gathered}[/tex]Note that we picked whole numbers and it is clear that the greater the denominator the lesser the value.
there are 4 sets of balls numbered 1 through 12 placed in a bowl. if 4 balls are randomly chosen without replacement, find the probability that the balls have the same number. express your answer as a fraction
Answers
The probability is 12/194580
Explanation:The balls numbered 1 through 12 are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
If 4 balls have the same number, then there are 12 types of this arrangement:
1, 1, 1, 1
2, 2, 2, 2
3, 3, 3, 3
and so on.
There is also 4 * 12 = 48 total number of balls.
We have a permutation:
[tex]\begin{gathered} 48C4=\frac{48!}{(48-4)!4!} \\ \\ =\frac{48!}{44!4!}=194580 \end{gathered}[/tex]Finally, we
[tex]\frac{12}{194580}[/tex]This is the required probability.
the sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2. find the number
Answers
The required number would be 2 which represents "the sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2."
The sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2.
Let's assume the number would be x
As per the given condition, the algebraic form would be as
⇒ 4(x - 2) = 5(x - 2)
Apply the distributive property of multiplication,
⇒ 4x - 8 = 5x - 10
Rearrange the terms of variable x,
⇒ 5x - 4x = 10 - 8
Apply the subtraction operation,
⇒ x = 2
Therefore, the required number would be 2.
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10. What is 7/4 as a mixed number?
Answers
Solution:
Given;
What is 7/4 as a mixed number?
7/4 as a mixed number can be expressed as
[tex]1\frac{3}{4}[/tex]Hence, the answer is 1 3/4
The seventh decile is the ___ percentile in terms of the data set.
Answers
The statement is given as
The seventh decile is the ___ percentile in terms of the data set.
ExplanationThe seventh decile is the 70-th percentile in terms of the data set.
AnswerHence the answer is 70th percentile in terms of data set.
The Obama family is building a circular swimming pool. If the radius of the pool is 15 feet, What is its circumference? Use I = 3.14 to solve.
Answers
The formula for circumference is given by
C = pi *d where pi = 3.14 and d is the diameter
We can find the diameter from the radius
d = 2*r where r is the radius
C = pi * 2 *r
C = 3.14 * 2 * 15
C =94.2 ft
Which of the following numbers is irrational?Select all that apply.(A)8/9(B)pi(C)2.3(Recur)(D)1.5
Answers
Answer:
B) π
Definition
A number is said to be Irrational if it cannot be expressed as a terminating or repeating decimal.
[tex]\begin{gathered} \frac{8}{9}=0.8888888\cdots=0.\bar{8} \\ 2.\bar{3}=2.3333333\cdots \\ \pi=3.1415926535\cdots \end{gathered}[/tex]From the given options
• Option A when converted to a decimal number is a repeating decimal.
,• Option C is also a repeating decimal
,• Option D (1.5) is a Terminating decimal.
Therefore, the only number which is Irrational is π since it neither terminates nor repeats (or recur).