Solution
We are given the following
Diameter = 10cm
Radius = 10/2 = 5cm
Height = 12cm
Therefore, the Volume will be
[tex]\begin{gathered} Volume=\pi r^2h \\ \\ Volume=\pi(5^2)(12) \\ \\ Volume=\pi\times25\times12 \\ \\ Volume=300\pi \\ \\ Volume=942.5cm^3\text{ \lparen to the nearest tenth\rparen} \end{gathered}[/tex]Therefore, the answer is
[tex]\begin{equation*} 942.5cm^3\text{ } \end{equation*}[/tex]A plan for a park has a rectangular plot of wild flowers that needs to be enclosed by 54 feet of fencing. Only three sides need to be enclosed because one side is bordered by the parking lot. use Desmos to get your answers. 1. What is the largest area possible for the garden? DO NOT ROUND YOUR ANSWER. ____ squared feet2. What width will produce the maximum area? ____ feet3. What is the length of the garden that will produce the maximum area?
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
a) What is the largest area possible for the garden?
Now, let the length of the rectangular plot be 54 -2x,
and the width of the rectangular plot be x,
so that:
[tex]\begin{gathered} \text{Area = (54 -2x) x = 54 x -2x}^2 \\ \frac{dA}{dx}=\text{ 54 - 4x = 0} \\ We\text{ have that:} \\ 54\text{ = 4x } \\ \text{Divide both sides by 4, we have that:} \\ \text{x = }\frac{54}{4} \\ \text{x = 13. 5} \end{gathered}[/tex]Then, the largest area possible for the garden will be:
[tex]\text{Area = 54x -2x}^2=54(13.5)-2(13.5)^2=729-364.5=364.5ft^2[/tex]b) What width will produce the maximum area?
[tex]Width,\text{ x = 13. 5 fe}et[/tex]c) The length of the garden that will produce the maximum area:
[tex]\text{Length = 54 - 2x = 54 - 2( 13. 5) = 54 -27 = 27 fe}et[/tex]The table below shows the average amount of time spent per person on entertainment per year from 2000 to 2005.Year Hours2000 34922001 35402002 36062003 36632004 37572005 3809(a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data. Let t represent the year, with t=0 in 2000. Round each coefficient to two decimal places.Pt =(b) Based on this model, how many hours would you expect the average person to spend on entertainment in 2012? Round your answer to the nearest whole number.hours(c) When would you expect the average amount of entertainment time to reach 4000? Give your answer as a calendar year (ex: 1997).During the year
EXPLANATION
Given the table,
Year Hours
2000 3492
2001 3540
2002 3606
2003 3663
2004 3757
2005 3809
Plugging in the data into a graphing calculator with a quadratic regression model AX^2+BX+C:
The function is:
P(t) = 2.35714 X^2 -9376.16 X +9325921.701
B)
When the time is 2012 substituting on the function:
P(t) = 2.357*(2012)^2 - 9,374.84*(2012) + 9.3246X10^6 = 3897.32
Hence, the number of hours spent in 2012 would be 3897 hours.
C) By using the graph, we can expect that the average amount of entertainment time to reach 4000 would be 9,540,465 hours.
Michelle earned some money doing odd jobs last summer and put it in a savings account that earns 10% interest compounded quarterly after 6 years there is $100.00 in the account. how much did Michelle earn doing odd jobs
The amount she earned doing the odd job is her principal. The principal can be calculated below
[tex]\begin{gathered} p=\frac{A}{(1+\frac{r}{n})^{nt}} \\ A=\text{accrued amount=100} \\ r=\text{rate}=10\text{ \%=}\frac{10}{100}=0.1 \\ t=6\text{ years} \\ n=4 \\ p=\frac{100}{(1+\frac{0.1}{4})^{24}} \\ p=\frac{100}{(1.025)^{24}} \\ p=\frac{100}{1.80872594958} \\ p=55.2875354186 \\ p=\text{ \$55.29} \end{gathered}[/tex]Select the values that make the inequality u≥8u≥8 true.(Numbers written in order from least to greatest going across.)
To make u >= 8 true, we need to select all of the values that are either equal to OR greater than 8. This means that we must check the following:
8
8.001
8.01
8.1
9
11
13
16
I’m in AP Calc AB and can’t figure this out. Any idea?
Answer::
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]Explanation:
Given f(x) defined below:
[tex]f(x)=\ln x+7x\sec x[/tex]The derivative is calculated below.
[tex]\begin{gathered} \frac{d}{dx}\lbrack f(x)\rbrack=\frac{d}{dx}\lbrack\ln x+7x\sec x\rbrack \\ =\frac{d}{dx}\lbrack\ln x\rbrack+\frac{d}{dx}\lbrack7x\sec x\rbrack \\ Take\text{ the constant 7 outside the derivative sign.} \\ =$$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack \\ \text{The derivative of }\ln (x)=\frac{1}{x},\text{ therefore:} \\ $$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack=$$\textcolor{red}{\frac{1}{x}}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack\cdots(1) \end{gathered}[/tex]Next, we find the derivative of x sec x using the product rule.
[tex]\begin{gathered} \frac{d}{dx}\lbrack x\sec x\rbrack=x$$\textcolor{blue}{\frac{d}{dx}\lbrack\sec x\rbrack}$$+\sec x\frac{d}{dx}\lbrack x\rbrack\text{ } \\ The\text{ derivative of sec(x), }\text{\textcolor{red}{ }}\textcolor{red}{\frac{d}{dx}\lbrack\sec x\rbrack=\sec x\tan x} \\ =x$$\textcolor{blue}{\lbrack\sec x\tan x\rbrack}$$+\sec x \end{gathered}[/tex]Substitute the result into equation (1) above.
[tex]\begin{gathered} \frac{1}{x}+7\frac{d}{dx}\lbrack x\sec x\rbrack=\frac{1}{x}+7(x\sec x\tan x+\sec x) \\ =7x\sec x\tan x+7\sec x+\frac{1}{x} \end{gathered}[/tex]Therefore:
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]A company wants to estimate the mean net weight of all 32-ounce packages of its Yummy Taste cookies at a 95% confidence level. The margin of error is to be within 0.026 ounces of the population mean. The population standard deviation is 0.108 ounces. The sample size that will yield a margin of error within 0.026 ounces of the population mean is:
Explanation
Given that the company wants to estimate the mean net weight of all 32-ounce packages of its Yummy Taste cookies at a 95% confidence level. The margin of error is to be within 0.026 ounces of the population mean. The population standard deviation is 0.108 ounces. The sample size that will yield a margin of error within 0.026 ounces of the population mean is:
Steps
2. Write the equation of the graph below. y 57 4 3 2 1 -5 -4 -3,2 -1 0 1 2 .
a total of 200 video game players take a survey on their favorite game unknown Kingdom gets 55% of the votes the video game designer wants to know how many players voted for unknown Kingdom write 55% as a rate per hundred
to find out how many players are on the 55% of 200, we can multiply the total players by 55% in decimal form:
[tex]undefined[/tex]The area of a field can be expressed as A [tex] = \frac{2x + 6}{x + 1} [/tex]square yards. if the length is[tex]l = \frac{ {x}^{2} - 9 }{2x + 10} [/tex]what is the width? show all work.
Solution
Note: Formula To Use
[tex]Area=lw[/tex][tex]\begin{gathered} A=\frac{2x+6}{x+1} \\ \\ A=\frac{2(x+3)}{x+1} \\ \\ l=\frac{x^2-9}{2x+10} \\ \\ l=\frac{(x-3)(x+3)}{2(x+5)} \\ \\ w=? \end{gathered}[/tex]Substituting the parameter
[tex]\begin{gathered} Area=lw \\ \\ \frac{2(x+3)}{x+1}=\frac{(x-3)(x+3)}{2(x+5)}\times w \\ \\ divide\text{ both side by }(x+3) \\ \\ \frac{2}{x+1}=\frac{x-3}{2(x+5)}\times w \\ \\ w=\frac{2}{x+1}\times\frac{2(x+5)}{(x-3)} \\ \\ w=\frac{4(x+5)}{(x+1)(x-3)} \end{gathered}[/tex]Therefore, the width is
[tex]\frac{4(x+5)}{(x+1)(x-3)}[/tex]-Convert the following into given base units of measurement. (Refer to slide 21 &27 on uploaded ppt).
1. 3.65 mg =______ dg
2. 9.987 g =______ hg
3. 12.203 km =______ mm
The conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
Part 1
The given quantity is 3.65 mg
mg is the milligram and dg is the decigram
We know
1 mg = 0.01 dg
Then,
3.65 mg = 3.65×0.01
Multiply the terms
3.65 mg = 0.0365 dg
Part 2
The given quantity is 9.987 g
g is the gram and hg is the hectogram
1 g = 0.01 hg
Then,
9.987 g = 0.09987 hg
Part 3
The given quantity is 12.203 km
km is the kilometer and mm is the millimeter
1 km = 1000000 mm
12.203 km = 12203072.2 mm
Hence, the conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
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what will the inflation-adjusted cost of a $154,600 house be in 5 years? round to two decimal places.
The inflation-adjusted cost of the house is $166,548.11
Explanation:[tex]\begin{gathered} The\text{ funcion the inflation adjusted cost:} \\ C(t)\text{ = C}_0(1\text{ + r\rparen}^t \\ r\text{ = rate} \\ \text{t = time} \\ C_0\text{ = cost of product} \end{gathered}[/tex][tex]\begin{gathered} From\text{ the information in the question:} \\ C_0\text{ = cost of house =\$154600} \\ r\text{ = 1.5\% = 0.015} \\ t\text{ = 5 years} \\ C(t)\text{ = ?} \\ We\text{ need to find the inflation adjusted cost using the function we were given in the question} \end{gathered}[/tex]substitute the values into the formula:
[tex]\begin{gathered} C(t)\text{ = 154600\lparen1 + 0.015\rparen}^5 \\ C(t)\text{ = 154600\lparen1.015\rparen}^5 \\ C(t)\text{ = 166548.107} \\ \\ To\text{ 2 decimal place, C\lparen t\rparen = 166548.11} \end{gathered}[/tex]The inflation-adjusted cost of the house is $166,548.11
Find the y-intercept of the line.y = 3.1x+2.6y-intercept:
To find the y-intercept in any equation equate x by 0
The given equation is
[tex]y=3.1x+2.6[/tex]Substitute x by 0 to find the y-intercept
[tex]\begin{gathered} y=3.1(0)+2.6 \\ \\ y=0+2.6 \\ \\ y=2.6 \end{gathered}[/tex]The y-intercept is 2.6
If Tia also leaves an 18% tip on the $22 cost of the meal, then how much does she spend on the meal altogether, including both tax and tip?
We have the next information
Cost of the meal
$22
Tip
18%
First, we need to calculate the tip that is 18% of 22
22(.18)= 3.96
the total cost will be
$22+$3.96=$25.96
In a class of 10 students, the ratings are given based on their performance on a test. The following data was taken from ratings given by the class teacher:5, 1, 2, 4, 2, 3, 5, 3, 3, 4Do the ratings earned by the students follow a normal distribution? aNo, because the mean and mode are same bYes, because the data is symmetrical about the mean 3 cNo, because the data is not symmetrical dYes, because the mean is greater than the mode of the data set
Given:
In a class of 10 students, the ratings are given based on their performance on a test. The following data was taken from ratings given by the class teacher:
5, 1, 2, 4, 2, 3, 5, 3, 3, 4
Required:
To choose the correct option
Examine the sequence of integers below.26, 17, 8, -1, -10, -19Which algebraic expression represents the nth integer in this sequences
Explanation:
Each number in this sequence is the previous number minus 9. This is an arithmetic sequence.
In arithmetic sequences the rule is:
[tex]x_n=a+d(n-1)[/tex]Where a is the first term and d is the distance between terms. In this case the distance is -9 and the first term is 26
Answer:
The algebraic expression that represents the nth integer in the sequence is:
[tex]x_n=26-9(n-1)[/tex]Express the given Hindu-Arabic numeral in expanded form 26
Given:
The numeral is 26.
To find: The expanded form
Explanation:
As we know,
Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits.
Separating the numbers into the individual place values, we get
[tex]26=(2\times10)+(6\times1)[/tex]Final answer: The expanded form of 26 is,
[tex](2\times10)+(6\times1)[/tex]when students enter the library they are able to walk anywhere in the library where a bookcase is not present all for bookcases are the same size a diagram below shows the dimensions of the library bookcases what is the area in square feet the available carpet for students to walk
4 rectangles each of dimensions 6ft by 2.5ft: Area of bookcases = 4(L x B) = 4(6x2.5) = 4x15 = 60 square feet
Area of the library = L x B = 40 x 17 = 680 square feet
Area of available carpet to walk on = Area of the library - Area of bookcases = 680 - 60 = 620 square feet
ylinders, cone Justin uses the mold picture cement column posts to use a height of the Cylinder = 18 in To make a post, Justin completel wet cement How much wet cement, in cubic inche make 4 posts? dus 3 in Formula Sheet
solve for the value of s
110°
(8s-2)°
The value of s for equation 110=8s-2 will be 14 by solving the linear equation.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. a formula that expresses the connection between two expressions on each side of a sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Here,
110=8s-2
8s=112
s=14
By resolving the linear equation, we obtain the value of s for equation 110=8s-2 as 14.
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Use the Pythagorean Theorem to find the length of the unknown side in the righttriangle shown below. (Round your answer to the nearest tenth.)817
pythagorean theorm is a^2 + b^2 = c^2
side lengths 8 and 17
8 is a base and 17 is the hypotenuse, the other side is 15
8 15 17 is one of the first 10 Pythagorean triples
8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
Saul reads every week. In his first week of reading, he read 50 pages. Each week after that, he read 65 pages. Which expression represents the total number of pages Saul has read, where w represents the number of weeks since he first started reading.
Given
In first week , he read 50 pages.
After first week , he read 65 pages.
Find
Expression represents the total number of pages Saul has read
Explanation
Let w represents the number of weeks since he first started reading.
Assume y represent number of pages.
when w = 1 then y = 50 ; w = 2 then y = 65+50=115
we know the equation of line
y = mw + c
so ,
50 = m + c .........(1)
and
115 = 2m + c ............(2)
on solving equation (1) and (2) , we get m = 65 and c = -15
so ,
y = 65w - 15
Final Answer
Therefore , the correct option is 3rd
this is a practice problem with more than one answer. it won't allow to me to send the whole picture so the question got cut off and another potential answer. I'll put it here. In the diagram, which of these objects is a radius? Select all that apply. the other option for an answer was EG
We are asked to determine which of the objects are a radius. To do that, let's remember that a radius is a line segment that has one end at the center of a circle and the other end at any circumference point of the circle. Therefore, the segments that are radii are:
[tex]\begin{gathered} \bar{CD} \\ \bar{CB} \\ \bar{CH} \\ \bar{GE} \\ \bar{GF} \end{gathered}[/tex]I NEED SOME HELP PLEASE ;n; .Zan took her dog, Simba, to the dog park on Saturday afternoon. There were less than 15 dogs running around the park when they arrived.
Determine which inequality describes the dogs at the park.
d < 15
d > 15
d ≤ 15
d ≥ 15
Answer:
I am pretty sure that it is d < 15
Explanation:
> means greater than
< means less than
≤ means less than or equal too
≥ means greater than or equal to
So the only only one that makes sense is <
A scale for a skyscraper blueprint is 1 inch = 40 feet. The height of theskyscraper is 640 feet and the width is 540 feet. What are the height andwidth in inches of the scale drawing of the skyscraper
Answer:
The height of the scale drawing of the skyscraper is 16 inches.
The width of the scale drawing of the skyscraper is 13.5 inches.
Explanation:
Given the scale of the model as 1 inch = 40 feet.
Let h represent the height of the scale drawing of the skyscraper. Given the actual height of the skyscraper as 640 feet, we can go ahead and determine h by setting up proportions as shown below;
[tex]\begin{gathered} \frac{1\text{inch}}{40\text{ ft}}=\frac{h\text{ in}}{640ft} \\ h=\frac{640\times1}{40} \\ h=16\text{inches} \end{gathered}[/tex]Let w represent the width of the scale drawing. Given the actual width of the skyscraper as 540 feet, we can go ahead and solve for w by setting up proportions as shown below;
[tex]\begin{gathered} \frac{1in}{40ft}=\frac{w\text{ in}}{540ft} \\ w=\frac{540\times1}{40} \\ w=13.5\text{inches} \end{gathered}[/tex]the total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)Find the expression that represents the scenario
Answer:
(3/10)x
Explanation:
The expression that represents the scenario is an expression that we can use to calculate the total amount of flour, so the correct expression is:
[tex]\frac{3}{10}x[/tex]Because the amount of flour is 3/10 of x ( the current stock)
е A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 3 hours. The inlet pipe alone can complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone. ntents Library The time that the hose can complete the job alone is (?) hours. (Round to the nearest tenth.) The time that the inlet pipe can complete the job alone is (? )hours. (Round to the nearest tenth.) nizer
SOLUTION
Let the time for the pipe to complete the Job be represented as
[tex]p[/tex]Let the time for the hose to complete the Job be represented as
[tex]h[/tex]The pipe and the hose completed the job in 3hours
Hence we have the equation
[tex]p+h=3[/tex]The inlet pipe alone can complete the job in one hour less time than the hose alone implies that
[tex]h-p=1[/tex]This leads to a system of equation which we now solve simultaneously
[tex]\begin{gathered} h+p=3\ldots\text{.eq}1 \\ h-p=1\ldots\text{.}\mathrm{}eq2 \end{gathered}[/tex]Adding eq1 and eq2, we o btain
[tex]\begin{gathered} 2h=4 \\ h=\frac{4}{2}=2 \end{gathered}[/tex]Substituting the value of h into eq1 we have
[tex]\begin{gathered} h+p=3 \\ 2+p=3 \\ p=3-2 \\ p=1 \end{gathered}[/tex]Therefore
[tex]h=2,\text{ p=1}[/tex]The time that the inlet pipe can complete the job alone is 1 hours
The time that the hose can complete the job alone is 2 hours
When the members of a family discussed where their annual reunion should take place, they found that out of all the family members, 10 would not go to a park, 9 would not go to a beach, 11 would not go to the family cottage, 3 would go to neither a park nor a beach, 4 would go to neither a beach nor the family cottage, 6 would go to neither a park nor the family cottage, 1 would not go to apark or a beach or to the family cottage,and 2 would go to all three places. What is the total number of family members?
Answer:
20
Explanation:
Let:
• NP = The non-park goers.
,• NB = The non-beach goers.
,• NC = The non-cottage goers.
The Venn diagram below is used to represent the given information:
Given:
• There are 10 non-park goers: a+b+c+g=10
,• There are 9 non-beach goers: b+d+e+g=9
,• There are 11 non-cottages goers: c+e+f+g=11
,• There are 3 non-park and non-beach goers: b+g=3
,• There are 4 non-beach and non-cottage goers: e+g = 4
,• There are 6 non-park and non-cottage goers: c+g=6
,• There is 1 non-park, non-beach, and non-cottage goer: g=1
,• There are 2 who are neither a non-park, non-beach, or non-cottage goer: h=2
So, the total number of family members will be:
[tex]Total=a+b+c+d+e+f+g+h[/tex]Since g=1:
[tex]\begin{gathered} b+g=3\implies b+1=3\implies b=2 \\ c+g=6\operatorname{\implies}c+1=6\operatorname{\implies}c=5 \\ e+g=4\operatorname{\implies}e+1=4\operatorname{\implies}e=3 \end{gathered}[/tex]Next:
[tex]\begin{gathered} c+e+f+g=11 \\ 5+3+f+1=11 \\ f+9=11 \\ f=11-9 \\ f=2 \end{gathered}[/tex]Next:
[tex]\begin{gathered} b+d+e+g=9 \\ 2+d+3+1=9 \\ d+6=9 \\ d=9-6 \\ d=3 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} Total=(a+b+c+g)+d+e+f+h \\ =10+3+3+2+2 \\ =20 \end{gathered}[/tex]The total number of family members is 20.
which fraction correctly shows the probability of 7 favorable outcomes and 28 possible outcomes?
Probability is calculated as follows:
[tex]P=\frac{\text{ number of favorable outcomes}}{\text{ number of total possible outcomes}}[/tex]In this case:
[tex]P=\frac{7}{28}=\frac{1}{4}[/tex]Determine if the table is linear or exponential. Tables 2 , 3 and 4 are the same
Exponential and linear relations differ in the way the y-values change when the x-values increase by a constant amount, that is, in a linear relationship, the y-values have equal differences and in an exponential relationship, the y-values have equal ratios.
In our first table, when the x-values increase one unit, the y-values decreses 2 units. Similarly, when the x-values increase 2 units, the y-values decrease 4 units and so on:
. Therefore, the first table shows a linear behavior.
On the other hand, table 2,3 and 4 are the same. In those cases, when the x-values increase one unit the, the y-values have a ratio of 2. Similarly, when the x-values increase 2 units the corresponding ratio for the y-values in 4 and so on.
This means that tables 2, 3 and 4 denote an exponential relationship.
The directions says state if the two triangles are congruent. If they are state how you know
From the diagram, we see that the triangles have:
• equal hypotenuse,
,• equal base.
HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
We conclude that the triangles are congruent because of HL Theorem.
AnswerB) HL