Answer:
y = 33.6
Step-by-step explanation:
1/2 y + 3.2 = 20 subtract 3.2 from both sides of the equation
1/2y = 16.8 multiply both sides by 2
y = 33.6
Find the surface area of the prism. Round to the nearest tenth if necessary.
The surface area of the prism according to the segment labels is; 480mm².
What is the surface area of the prism?The prism given in the task content is five-faced and hence, its surface area can be evaluated as follows;
Surface area = 2(0.5×15×8)+(15×9)+(8×9) + (17×9).
Hence, the surface area of the prism upon evaluation is; 480mm².
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A candy distributor needs to mix a 10% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 25% fat-content chocolate. How many kilograms of each kind of chocolate must they use
The candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.
How to find the correct quantity of chocolate that should be used?Let x be the quantity of 10% fat-content chocolate.
Fat in 10% fat-content chocolate + Fat in 60% fat-content chocolate = Total fat in 25% fat-content chocolate
0.10x + 0.60(100 - x) = 0.25*100
10x + 60*100 - 60x = 25*100
-50x = 25*100 - 60*100
-50x = 100(25 - 60)
50x = 3500
x = 3500/50
x = 70 kg
This is the quantity of 10% fat-content chocolate required.
100 - x = 30 kg
This is the quantity of 60% fat-content chocolate required.
Therefore, we have found that the candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.
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The diameter of a semicircle is 26 meters. What is the semicircle's perimeter? Use 3.14 for .
The perimeter of the semicircle is 66. 846 meters
How to find the perimeterThe formula for finding the perimeter of a semicircle is
Perimeter = πr + 2r
We were given diameter = 26meters
Radius, r = diameter/2
radius = 26/ 2 = 13 meters
π = 3. 142
Substitute value into the formula
Perimeter = 3. 142 × 13 + 2 × 13
Perimeter = 40. 846 + 26
Perimeter = 66. 846 meters
Thus, the perimeter of the semicircle is 66. 846 meters
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There is a total of 32 cubic centimeters of a liquid in two beakers. one of these beakers contains 15 cubic centimeters of the liquid. how much liquid does the other beaker contain? a. 13 cc b. 15 cc c. 16 cc d. 17 cc
The correct option is (d).
The other beaker contains 17 cc (cubic centimetres) of the liquid.
What is cubic centimetres of liquid mean?The volume of a cube with dimensions of 1 cm ×1 cm× 1 cm is equal to one cubic centimetre (or cubic centimetre in US English) (SI unit symbol: cm³; non-SI abbreviations: cc and ccm). A millilitre's volume is equal to one cubic centimetre.
According to the question,
The total liquid is 32 in cubic centimetres which is stored in the two beakers.
In the first beaker the liquid stored is 15 cubic centimetres.
The second beaker will contain the liquid = total liquid stored in both beakers - liquid stored in the first beaker.
Liquid in second beaker = 32 - 15
= 17
Therefore, the liquid stored in the second beaker is 17 cc (cubic centimetres).
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A rectangular paperboard measuring 20 invhes long and 15 inches wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.)
The perimeter of the rectangle is 70 Inches square
How to determine the perimeterThe formula for perimeter of a rectangle is given as;
Perimeter = 2 ( l + w)
length = 20 inches
width = 15 inches
Perimeter = 2 ( 20 + 15 )
Perimeter = 2 ( 35)
Perimeter = 70 Inches square
Thus, the perimeter of the rectangle is 70 Inches square
Note that it is a general knowledge on the given question.
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What is the radius for a circle whose equation is x² + y² = 16?
OA. 4
OB. 16
C. 8
OD. 256
Answer:The radius is √16.
Step-by-step explanation:
What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89
The value of the sum of squares due to regression is 18.43.
Given the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89.
A common measure used in regression analysis is the sum of squares total (SST). The square of each difference is added to the sum of squares to obtain the squared disparities between individual data points and their mean. The variance is calculated using the sum of squares, which is also used to assess how well a regression curve fits the data.
We will use the total sum of squares (SST) is given as the summation of the sum of squares due to regression (SSR) and sum of squares error (SSE);
SST = SSR + SSE
Here, SST=25.32 and SSE=6.89
Substitute the values in the formula, we get
25.32=SSR+6.89
Now, we will subtract 6.89 from both sides, we get
25.32-6.89=SSR+6.89-6.89
18.43=SSR
Hence, the value of the sum of squares due to regression (SSR) when the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89 is 18.43.
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find area and perimeter show your work
Answer:
A= 16
P=16
Step-by-step explanation:
A=h^bxb/ 2
P= side+base+side
At a coffee shop, the manager recorded the number of customers who visited the store at the end of each hour. The graph shows the recordings for a 24-hour period. The function describing this graph is a transformation of the parent sine function, y=sin(x)
Which value is closest to the amplitude of the transformed function?
O 83 customers
O 27 customers
O 54 customers
O 30 customers
Answer:
Step-by-step explanation:
The amplitude of a sine function is equal to one-half the distance between the maximum and minimum values of the function.
In this case, the maximum value is approximately 84 customers, and the minimum value is approximately 30 customers
Therefore, the value that is closest to the amplitude of the transformed function is 27 customers.
Suppose . has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if or if and . Also, determine whether the critical point a local maximum, a local minimim, or a saddle point.
The points are (0,0) Minimum and (1/6, 1/18) is the saddle point.
What is the saddle point?
A saddle point, also known as a minimax point, is a place on the surface of a function's graph where the slopes in orthogonal directions are all zero but the function does not have a local extremum.To solve the question we have:
f(x,y) = xy(1-2x-6y)
Therefore, f(x,y) = xy-2x²y-6xy²
Finding the partial derivative of the above gives:
fₓ = y - 4xy-6y²
= x - 2x²-12xy
Therefore, when the above equations are set to 0 we get:
y - 4xy-6y² = 0.......(1)
x - 2x²-12xy = 0......(2)
Dividing equations (1) and (2) by y and x respectively give:
1 - 4x - 6y = 0
1 - 2x - 12y = 0
Solving gives:
x = 0.167 = 1/6
y = 0.056 = 1/18
When we place x in equation (1) we have:
y - 4(1/6)y-6y² = 0
y = 0 or y = 1/18
Similarly, x = 0 or 1/6
Therefore, the four critical points are:
(0,0) (1/6,1/18)
When x = 0 and y = 0
f(x,y) = 0 Hence this is a minimum
When x = 1/6 and y = 1/18
f (x,y) = 1/324 Which is a saddle point.
Therefore, the points are (0,0) Minimum, and (1/6, 1/18) is the saddle point.
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The question you are looking for is here:
(1 point) The function f(x,y)=xy(1−2x−6y) has 4 critical points. List them and select the type of critical point. Points should be entered as ordered pairs and listed in increasing lexicographic order. By that, we mean that (x,y) comes before (z,w) if x
Find the lateral surface area of the
following prism:
5 cm
5 cm
apothem = 3.44 cm
cm
5 cm
10 cm
5 cm
LSA = [?] cm2
The laterals surface area of the given hexagonal prism is: 250 cm².
How to Find the Lateral Surface Area of Hexagonal Prism?Lateral surface area = 5ah, where:
a = edge length of the baseh = height of the prism.Given the following:
a = 5 cm
h = 10 cm
Lateral surface area of the hexagonal prism = 5ah = 5(5)(10)
Lateral surface area of the hexagonal prism = 250 cm²
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What are the coordinates of the terminal point corresponding to 0=-120?
Using the unit circle, the coordinates of the terminal point corresponding to [tex]\theta = 120^\circ[/tex] is: (-0.5, 0.866).
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
In this problem, the angle is of [tex]\theta = 120^\circ[/tex], hence:
[tex]\cos{\theta} = \cos{120^\circ} = -0.5[/tex].[tex]\sin{\theta} = \sin{120^\circ} = 0.866[/tex].Hence the terminal point is:
(-0.5, 0.866).
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PLEASE HELP URGENT!!!
From-
~xXIndieKidXx~
Answer:
C. 9
Step-by-step explanation:
The cubed root of 729 is the number that is multiplied 3 times to get 729. In this case, it's 9.
9*9*9 = 81*9
81*9 = 729
Prove by induction:
5| (21^n+9)
It's kind of self-evident. Any power of 21 will have a 1 in the units place, and adding 9 to it makes it 0 and hence the number is divisible by 5.
To prove the claim by induction, first establish the base case. I assume [tex]n\in\Bbb N[/tex], so for [tex]n=1[/tex] we have
[tex]21^1 + 9 = 21 + 9 = 30[/tex]
and of course 30 = 5×6 is divisible by 5.
Assume the claim is true for [tex]n=k[/tex], that [tex]5 \mid 21^k + 9[/tex]. This means that for some integer [tex]\ell[/tex], we can write
[tex]21^k + 9 = 5\ell[/tex]
Now the induction step: when [tex]n=k+1[/tex], we have
[tex]21^{k+1} + 9 = \bigg(21\times(21^k + 9) - 9\times21\bigg) + 9 \\\\ ~~~~~~~~~~~~~~ = 21\times5\ell - 9\times20 \\\\ ~~~~~~~~~~~~~~= 5\times(21\ell - 9\times4)[/tex]
which is divisible by 5. QED
When she adds 2 to both sides, the equation 4x = 3x results. Which solution will best illustrate what happens to x ?
The solution will illustrate that the equation has one solution at x=0.
Given that adds 2 to both sides, the equation 4x = 3x results.
An algebraic equation may be described as a mathematical declaration wherein expressions are set the same as every other.
The equation is 4x=3x.
As given that add 2 on both sides, we get
4x+2=3x+2
Now, we will subtract 3x from both sides, we get
4x+2-3x=3x+2-3x
x+2=2
Further, we will subtract 2 from both sides, we get
x+2-2=2-2
x=0
Hence, When adds 2 to both sides, the equation 4x = 3x results that the equation has one solution x=0.
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Find the equation of a line perpendicular to 2x+4y=8 which cross the y intercept
Answer: [tex]y=2x+2[/tex]
Step-by-step explanation:
[tex]2x+4y=8\\\\x+2y=4\\\\2y=-x+4\\\\y=-\frac{1}{2}x+2[/tex]
So, the slope of the given line is -1/2, meaning the slope of the line we want to find is 2.
Since the y-intercept is the given line is (0,2), the equation is [tex]y=2x+2[/tex]
Round 18.57631 to three decimal places.
❄ Hi there,
let us revise the rounding rules and then, get down to rounding the number.
[tex]\sf{Rounding \ Rules:}[/tex]
If the number you need to round is followed by a number from 0 to 4, you round down.If the number you need to round is followed by a number that's 5 or more, you round up.Now we can start the rounding process.
Reading the problem & the directions, we notice that we need to round to 3 decimal places (3 numbers after the decimal point).
Looking at the fourth number, we notice that it's less than 5.
∴ we need to round down ↡
↬[tex]\sf{18.57631 \ rounded \ to \ 3 \ DP \ = \bf{18.576}}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
❄
A super sundae ice cream cone has a radius of 0. 5 in and a depth of 4 in. A wonderful waffle cone has a radius 0. 9 in and a depth of 3 in. Which cone holds more ice cream?
The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer:
{x:x is a real number}
Since any value can replace x to give an integer.
{x:x is a real number}
The graph shows a system of inequalities.
The graph shows a dashed upward opening parabola with a vertex at 0 comma 0 that passes through negative 3 comma 9 and 3 comma 9, with shading inside the parabola. It also shows a graph of a downward opening parabola with a vertex at 4 comma 22 that passes through 0 comma 6 and 8 comma 6, with shading inside the parabola.
Which point is a solution to the system?
(–1, 6)
(0, 22)
(2, 9)
(8, 2)
The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation of the parabola passing through (0, 0), (-3, 9) and (3, 9) is y = x²
The equation of the parabola with vertex at (4, 22) passing through (0, 6), (8, 6) and (3, 9) is y < -x² + 8x + 6
The solution to the system of equation is the darker region and it contains the point (-1, 6)
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Answer:
(2,9)
Step-by-step explanation:
Got it on FlVS
I'm not sure what theorem to use for this question
The statement that <A > <C and <B > <D has been proved
How to prove that <A > <C and <B > <D?In geometry, the side length opposite the largest angle is the longest side.
Similarly, the side length opposite the smallest angle is the shortest side.
From the given figure of quadrilateral, we have the following sides in increasing order:
Side length ABSide length BCSide length ADSide length CDThe angles opposite the side lengths are:
Angle DAngle BAngle CAngle AThis means that:
<A > <C and <B > <D
Hence, the statement that <A > <C and <B > <D has been proved
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Question 6 of 20
What is the common difference between consecutive terms in the following
arithmetic sequence?
51, 47, 43, 39, ...
OA. 3
B. -3
O C. -4
D. 4
Common difference formula
[tex]\boxed{\sf d=t_2-t_1}[/tex]
So
Here
[tex]\\ \tt{:}\longrightarrow d=47-51[/tex]
[tex]\\ \tt{:}\longrightarrow d=-4[/tex]
Option C
Answer:
C. -4
Step-by-step explanation:
Given sequence: 51, 47, 43, 39, ...
To find the common difference (d) between consecutive terms in an arithmetic sequence, subtract the previous term from the next term:
[tex]\implies \sf d=47-51=-4[/tex]
[tex]\implies \sf d=43-47=-4[/tex]
[tex]\implies \sf d=39-43=-4[/tex]
Therefore, the common difference for the given arithmetic sequence is -4.
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A certain quadratic function has the factors
3,
(x+2)，
and
(x - 5)
. What are the zeros of this function?
a. x=2 and x=-5
b. x=2, x=5, and x=-3
c. x=-2 and x=5
d. x=-2, x=5, and x=3
[tex]f(x) = 3(x + 2)(x - 5)[/tex]
[tex]solving \: f(x) = 0 \\ 3(x + 2)(x - 5) = 0 \\ (x + 2)(x - 5) = \frac{0}{3} \\ (x + 2)(x - 5) = 0 \\ x + 2 = 0 \: \: \: \: \: \: \: \: \: \: x - 5 = 0 \\ x = - 2 \: \: \: \: \: \: \: \: \: \: x = + 5[/tex]
Option CPlease help! i will give you a lot of points if you do!
i don't understand how to solve number 19 through 31, only the odd numbers.
please show work
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Tyler's playlist has 36 songs. Noah’s playlist has one quarter as many songs as Tyler's playlist. How many songs are on Noah’s playlist?
Answer: 9
Step-by-step explanation:
Answer:
9 songs
Step-by-step explanation:
a quarter is basically a fourth of a number so you need to just divide the number by four
One of the criticisms of the Social Readjustment Rating Scale is that it does NOT take into account:
What is one major limitation of the Social Readjustment Rating Scale?
The Social Readjustment Rating Scale has severe limitations, despite being a helpful tool for the research of life transition and disease. The current measure cannot be used to assess the impact of various life changes (such as positive or negative ones) on the development of sickness.Learn more about Social Readjustment Rating Scale brainly.com/question/13044228
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A metallurgist has one alloy containing 39% copper and another containing 65% copper. How many pounds of each alloy must he use to make 48 pounds of a third alloy containing 62% copper? (Round to two decimal places if necessary.)
The metallurgist must use 5.538 pounds of an alloy with 39 % copper and 42.462 pounds of an alloy with 62 % copper.
How to calculate proportions of components associated to an alloy
Herein we must create a new alloy by using correct quantities of two alloys with distinct copper concentrations. All required information can be found by concept of weighted averages:
(62/100) · (48 lb) = (39/100) · x + (65/100) · (48 - x)
62 · 48 = 39 · x + 65 · 48 - 65 · x
3 · 48 = 26 · x
x = 5.538 lb
The metallurgist must use 5.538 pounds of an alloy with 39 % copper and 42.462 pounds of an alloy with 62 % copper.
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What is f[g(7)] for the following functions?
f(x) = 3x2 − 4
g(x) = 2x − 5
f[g(7)] = 9
f[g(7)] = 143
f[g(7)] = 239
f[g(7)] =281
Answer: 239
Step-by-step explanation:
[tex]g(7)=2(7)-5=9\\\\f[g(7)]=f(9)=3(9)^2 - 4=239[/tex]
Describe the difference between plots that show a strong correlation and plots that show a weak correlation.
We need to find the difference between plots that show a strong correlation and plots that show a weak correlation.
The point of creating a scatter plot is to determine if there is a correlation. Correlation means the relationship between two quantities. For example, there is a correlation between how much a person studies and the grade they get on a test, but there is no correlation between how much money a person earns and what pets they own. In mathematics, correlation between data means that the points follow a pattern and go in the same direction. There are two types of correlation:
Positive: the trend is rising from left to right
Negative: the trend is decreasing from left to right
If the dots on the scatter plot do not follow a pattern, there is no correlation.
All correlations have two properties: strength and direction. The strength of the correlation is determined by its numerical value. The direction of the correlation is determined by whether the correlation is positive or negative.
The strength of the correlation indicates how strong the relationship is between the two variables. The strength is determined by the numerical value of the correlation. A correlation of 1, whether +1 or -1, is a perfect correlation. In perfect correlations, the data points lie directly on the fit line. The further the data is from the fit line, the weaker the correlation. A correlation of 0 means there is no correlation
If the value of correlation coefficient is nearer to to 1 or -1 , then there exist a strong correlation.
If the value of correlation coefficient is nearer to to 0 , then there exist a weak correlation.
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The data points are a little closer for a weak correlation, and you can see that there is some sort of relationship between these factors.
Data points for a strong correlation are in close proximity to one another, making it possible to build a line by imitating their pattern.
A statistic called correlation gauges how much two variables change in connection to one another.
Correlation and diversification, the idea that certain types of risk can be reduced by investing in assets that are not connected, are closely related concepts.
Correlation cannot determine whether x causes y or vice versa, or whether a third component is responsible for the association.
A scatter plot may make it easier to spot correlation, particularly when the variables have a non-linear but nevertheless significant association.
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i need help please! I think I know the answer but for some reason my brain's telling me that it's wrong so if someone could explain how to get the answer so I can check that would be great.
Considering the slopes of the segments, the correct option is:
D. No, because the triangle ABC doesn't have a pair of perpendicular sides.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.Here, we have to find if there are perpendicular segments, that is, if two slopes multiplied have a value of -1, then:
mAB = (-7 - 9)/(11 - 1) = -8/5.mAC = (3 - 9)/(-9 - 1) = 3/5.mBC = (3 - (-7))/(-9 - 11) = -1/2.No sides are perpendicular, hence option D is correct.
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