Scott is 72 inches tall. How many feet is Scott? Use a conversion factor to show your work.
Answers
Answer
6 feet
Explanation
Note: The conversion rate of inches to feet is given below
1 inches = 0.0833333 foot
Since Scott is 72 inches tall, His height in feet will be
[tex]72\times0.0833333=6\text{ fe}et[/tex]Related Questions
Suppose Deon places $4000 in an account that pays 12% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.
Answers
The formula for compounded interest is
[tex]A=P(1+r)^t[/tex]We have
P = 4000
r = 12% = 0.12
t = time in years
Therefore
[tex]\begin{gathered} A=4000(1+0.12)^t \\ \\ A=4000\cdot(1.12)^t \end{gathered}[/tex]a)
Now let's evaluate that function at t = 1
[tex]\begin{gathered} A=4000\cdot(1.12)^t \\ \\ A=4000(1.12)^1 \\ \\ A=4000\cdot1.12 \\ \\ A=4480 \end{gathered}[/tex]Therefore at the end of 1 year, he would have $4480
b)
Now let's do it for t = 2, we have
[tex]\begin{gathered} A=4000\cdot(1.12)^t \\ \\ A=4000\cdot(1.12)^2 \\ \\ A=4000\cdot1.2544 \\ \\ A=5017.6 \end{gathered}[/tex]At the end of 2 years, he would have $5017.6
The following table gives the probability distribution of a distribute random variable X use the table to find the following probability round solution at 3 festival places
Answers
The right column of the table represents the probability of
x being 0, 1, 2, 3, 4 or 5.
x=0, x=1, x=2, x=3, x=4 or x=5.
P(x = 2)We have that P(x=2) is the probability of x being 2. The space to the right of x=2:
Then,
P(x = 2) = 0.153
P(x ≤ 1)We have that x ≤ 1 if x=0 or x=1.
Then, the probability of x ≤ 1 is the addition of the probability of x=0 and x=1:
P(x ≤ 1) = P(x = 0) + P(x = 1)
= 0.305 + 0.185 = 0.490
P(x ≤ 1) = 0.490
Then,
P(x ≤ 1) = 0.490
P(x ≥ 4)We have that x ≥ 4 if x=4 or x=5.
Then, the probability of x ≥ 4 is the addition of the probability of x=4 and x=5:
P(x ≥ 4) = P(x = 4) + P(x = 5)
= 0.136 + 0.085
= 0.221
Then,
P(x ≥ 4) = 0.221
P(1 ≤ x ≤ 3)We have that 1 ≤ x ≤ 3 if x=1, x=2 or x=3.
Then, the probability of1 ≤ x ≤ 3 is the addition of the probability of x=1, x=2 and x=3:
P(1 ≤ x ≤ 3) = P(x = 1) + P(x = 2) + P(x = 3)
= 0.185 + 0.153 + 0.136
= 0.474
Then,
P(1 ≤ x ≤ 3) = 0.474
Type of distributionWe observe that the probability decreases when x increase.
Then, this can be a geometric distribution
Elizabeth brought a box of donuts to share. there are two dozens (24) donuts in the box. all identical in size shape and color. four are jelly filled, six are lemon filled and 14 are custard filled. you randomly select one donut and eat it. and select another donut. find the probability of selecting two custard filled donuts in a row
Answers
Total donut = 24
donut with lemom=6
donut with jelly=4
donut with custard = 14
[tex]\begin{gathered} \text{Probability =}\frac{Required\text{ outcome}}{\text{Total outcome}} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Hence} \\ \text{prb(custard) = }\frac{14}{24}=\frac{7}{12} \end{gathered}[/tex]Since you are taking donuts and eating them. Hence you are not replacing the donut you have taken.
The probability of taking a second custard without replacement will be
[tex]\text{Prb(custard)}=\frac{13}{23}[/tex]Hence the probability becomes
[tex]\frac{7}{12}\times\frac{13}{23}=\frac{91}{276}[/tex]The probability of selecting two custard-filled donuts in a row is 91/276
Categorize the following logical fallacy.We can go to the amusement park or the library. The amusement park is too expensive, so we must go to the library.The options are listed in the picture
Answers
False dilemma fallacy
The argument either misrepresents the consequences of choices that are available when making a decision, or else it fails to present all the choices available.
The given statement is:
We can go to the amusement park or the library. The amusement park is too expensive, so we must go to the library.
Therefore, the correct answer is the False dilemma.
What is the measure of n?mnn =8.4= [?]VGive your answer in simplest form.Enter
Answers
We have 3 similar triangles. We will use the two inner triangles.
Using the ratio of similar sides
8 n
---- = ------
n 4
Using cross products
8*4 = n^2
32 = n^2
Taking the square root of each side
sqrt(32) = sqrt(n^2)
sqrt(16 *2) = n
4 sqrt(2) = n
[tex]n=4\sqrt[]{2}[/tex]On the coordinate grid, the graph of y = √√x - 1 + 3 isshown. It is a translation of y = 3√x.6543-7-6-5-4-3-2-1₁-2-3N& b w-4-5up my2 345 6 7 XWhat is the domain of the graphed function?O {x|1
Answers
The domain is the set of all values of x that satisfies the function. On the graph, it is between the minimum value of x on the left and the maximum value of x on the right. Looking at the graph, the minimum value of x is negative infinity on the left and the maximum is positive infinity on the right. Thus, the domain is
{x/x is a real number}
Calculate the volume of a regular pyramid if the area of the base and the altitude lenght are given.
Answers
Solution:
Given regular pyramids;
The volume, V, of a regular pyramid is;
[tex]\begin{gathered} V=\frac{1}{3}bh \\ \\ \text{ Where }b=area\text{ of base},h=height \end{gathered}[/tex](a)
[tex]\begin{gathered} S_{ABCD}=9cm^2,SO=5cm \\ \\ V=\frac{1}{3}(9)(5)cm^3 \\ \\ V=15cm^3 \end{gathered}[/tex](b)
[tex]\begin{gathered} S_{ABCDEF}=500mm^2,SO=3cm \\ \\ S_{ABCDEF}=50cm^2 \\ \\ V=\frac{1}{3}(50)(3)cm^3 \\ \\ V=50cm^3 \end{gathered}[/tex]graph the line that passes through the points (3,-7) and (-3,1) and determine the equation of the line
Answers
Given: Two points (3,-7) and (-3,1).
Required: Graph the line that passes through the points (3,-7) and (-3,1) and determine the equation of the line.
Explanation:
Graph can easily be drawn, using the two given points (3,-7) and (-3,1).
Further, equation of line can be found using two point form. The line passing through two points (3,-7) and (-3,1) is
[tex]\begin{gathered} y-1=\frac{-7-1}{3-(-3)}(x-(-3)) \\ y-1=\frac{-8}{6}(x+3) \end{gathered}[/tex]Solving further,
[tex]\begin{gathered} y-1=-\frac{4}{3}(x+3) \\ 3(y-1)=-4(x+3) \end{gathered}[/tex]So
[tex]\begin{gathered} 3y-3=-4x-12 \\ 4x+3y+9=0 \end{gathered}[/tex]Final Answer: The graph is drawn and equation of line passing through the points (3,-7) and (-3,1) is 4x+3y+9=0.
3All 6 members of a family work. Their hourly wages (in dollars) are the following.26, 11, 12, 40, 21, 22Send data to calculatorAssuming that these wages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
Answers
Bearing in mind that the formula for the population standard deviation is
[tex]{\sigma={\sqrt{{\frac{1}{N}}\sum_{i=1}^{N}(x_{i}-\mu)^{2}}}}[/tex]Using the calculator and remembering that we are assuming that the information is about the whole population.
The standard deviation requested is equal to 10.60.
Two circles have their centers at (2, 4) and (-14, 2) and they intersect at the point (-2, 7). What is the radius of each circle?
Answers
To determine the radius of each circle, find the distance of the intersection and the center of the circles.
Thus, the radius of the circle with center (2,4) is as follows:
[tex]\begin{gathered} r_1=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt[]{(-2-2)^2+(7-4)^2} \\ =\sqrt[]{(-4)^2+(3)^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5 \end{gathered}[/tex]Thus, the radius of the circle with center (-14,2) is as follows:
[tex]\begin{gathered} r_2=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt[]{\lbrack-2-(-14)\rbrack^2+(7-2)^2} \\ =\sqrt[]{(-2+14)^2+(7-2)^2} \\ =\sqrt[]{(12)^2+(5)^2} \\ =\sqrt[]{144+25} \\ =\sqrt[]{169} \\ =13 \end{gathered}[/tex]Thus, the radius of the circles with centers at (2,4) and (-14,2) passing through (-2,7) are 5 and 13, respectively.
name the type of transformation that will result from applying the given rule.a. (x,y)-->(7x,y)b.(x,y)-->(-x,-y)c.(x,y)-->(x+2,1/2y)
Answers
We have the following:
a. (x,y)-->(7x,y)
Dilation
b.(x,y)-->(-x,-y)
Reflection
c.(x,y)-->(x+2,1/2y)
Translation and Dilation
Find the value of cos(-90).
Answers
We know,
[tex]\cos (-\theta)=\cos \theta[/tex]Therefore,
[tex]\cos (-90^{\circ})=\cos 90^{\circ}[/tex]We also know,
[tex]\cos 90^{\circ}=0[/tex]Hence,
[tex]\begin{gathered} \cos (-90^{\circ})=\cos 90^{\circ}=0 \\ \cos (-90^{\circ})=0 \end{gathered}[/tex]So, the value of cos(-90) is zero.
Arnold has recorded the number of chirps per minute ( x) that crickets make at different temperatures (y). He has determined that the association is linear and that the line of best fit is y = 1 + 50. What is the interpretation of the slope and yintercept of this equation?
Answers
Answer:
Choice D
Explanation:
The slope of the line is
[tex]\frac{\delta\text{temperature}}{\#ofchirps}=\frac{60-50}{40-0}=\frac{1}{4}\frac{temperature}{\text{chirp}}[/tex]This says that for every 1 chirp there is a temperature increase of 1/4.
The y-intercept of the line is (0, 50) meaning when there are no chirps the temperature is 50 degrees.
Therefore, choice D is correct.
Section 2.4 question: 2 Suppose 27 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 80% a month. If the yard can only sustain 140 plants, use a logistic growth model to estimate the number of plants after 5 months. plants
Answers
The question indicates that we should use a logistic model.
This can be given as
[tex]P(t)=\frac{K}{1+Ae^{-kt}};A=\frac{K-P_o}{P_0}[/tex]In this case. K is the carrying capacity =140
Po is the initial population=27
[tex]\begin{gathered} \therefore A=\frac{140-27}{27} \\ A=4.185 \end{gathered}[/tex]This then brings the model to be
[tex]P(t)=\frac{140}{1+4.185e^{-kt}}[/tex]The next step would be to find the value of k
Since the blackberry plants increase by 80% every month. Therefore, for 1 month we would have
[tex]27+\frac{80}{100}\times27=48.6[/tex]This implies that for that first month we would have
[tex]\begin{gathered} \frac{140}{1+4.185e^{-k\times1}}=48.6 \\ \frac{140}{1+4.185e^{-k}}=48.6 \\ 140=48.6+203.391e^{-k} \\ 91.4=203.391e^{-k} \\ e^{-k}=\frac{91.4}{203.391} \\ e^{-k}=0.44938 \\ \ln (e^{-k})=\ln 0.44938 \\ -k=-0.7999 \\ k=0.7999 \end{gathered}[/tex]Therefore for 5 months, we would have
[tex]\begin{gathered} P(5)=\frac{140}{1+4.185e^{-0.7999\times5}} \\ P(5)=\frac{140}{1+4.185e^{-3.9995}} \\ P(5)=\frac{140}{1.0770352} \\ P(5)=129.986\approx130 \end{gathered}[/tex]Answer: Using the logistic model the estimated number of plants after 5 months becomes
[tex]130[/tex]how do you estimate 32% of 91
Answers
To solve the exercise, we can use a rule of three:
[tex]\begin{gathered} 91\rightarrow100\text{\%} \\ x\leftarrow32\text{\%} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{91\cdot32\text{\%}}{100\text{\%}} \\ x=\frac{91\cdot32}{100} \\ x=\frac{2912}{100} \\ x=29.12 \end{gathered}[/tex]Therefore, 32% of 91 is 29.12.
Making an inference using a two-way frequency table A group of 200 adults were asked whether they exercise and whether they are vegetarian. Their responses are summarized in the following table.
Answers
Given:
Total adults=200
Total vegetarian who exercise=35
Total vegetarian who don"t exercise=25
Total non-vegetarian who exercise=77
Total non-vegetarian who don't exercise=63
To find:
percentage of given data
Explanation:
((Required percentage of the data)/Total data)*100
Step:1
To find the percentage of the adults who exercise=((Total adult who exercise)/Total adult)*100
=((35+77)/200)*100
=56%
Step:2
To find the percentage of the adults who are non vegetarian=((Total non veg adults)/Total adult)*100
=((77+63)/200)*100
=70%
Step:3
To find the percentage of the adults who are non vegetarian exercise=((Total not vegetarian exercise)/Total adults)*100
=(77/200)*100
=38.5%
Step:4
Option c is correct
This is our required answer.
Final answer=56%, 70%, 38.5%, option c
10) Which statement is true about the following pentagon?Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the originas the center of dilation using the rule (x,y) → (n) to create pentagon M'N+PQR.NMPentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.Pentagon M'N'PQ'R' is smaller r than pentagon MNPQR, because the scale factor is less than 1.Pentagon M'N'PQ'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.
Answers
Since the scale factor is a fraction of 1, the scale factor less than one.
When the scale factor is less than one, the result of the dilation is smaller than the original figure.
So, the correct answer is:
Pentagon M'N'PQ'R' is smaller r than pentagon MNPQR, because the scale factor is less than 1.
4.4 cm3.4 cmWhat is the surface area of the square pyramid, in squarecentimeters?Answer: AcmSubmit Answer
Answers
The surface area is the sum of the area of the square plus the area of the 4 equal triangles. So, we need to find the area of one triangle multiply by 4 and add the area of the square.
Then, the area of one triangle is
[tex]\begin{gathered} A_T=\frac{1}{2}(3.4)(4.4) \\ A_T=7.48cm^2 \end{gathered}[/tex]and the area of the square is
[tex]\begin{gathered} A_S=(3.4)^2 \\ A_S=11.56cm^2 \end{gathered}[/tex]Then, the surface S is
[tex]\begin{gathered} S=4\times A_T+A_S \\ S=4\times7.48+11.56 \\ S=41.48cm^2 \end{gathered}[/tex]And the answer is 41.48 centimeters squared.
This is Geometry so can you please help me out!
Answers
To map the purple figure onto the white figure we have to
• Translate ,10 units right side.
,• Translate, 8 units up.
Hence, both transformations are translations.
Certain ball bearings are packed in boxes that hold 500. 25 boxes of ball bearings are then packed each crate for shipping. To make sure that theball bearings being prepared for shipping were being produced with the correct measurements, asupervisor decided to conduct asample for quality-control purposes.He randomly picked one crate,opened it up, and then randomlychose two boxes of ball bearingsfrom that crate. He measured all ofthe ball bearings from the two boxes.This is an example of a:Answer Choices:convenience sample.systematic sample.cluster samplestratified random sample.
Answers
Given:
Number of balls packed in a box = 500
Number of boxes packed for shipping = 25
Given that the supervisor randomly picked one crate, opened it up, then randomly chose two boxes from the crate.
He then measures all of the ball bearings from the two boxes.
Let's determine the type of sampling method used here.
Here, we can see that the balls were packed in boxes, then into crates.
Since the manger then chooses one crate out of all crates, then picks only two boxes and sampled all balls in the tow boxes, the type of sampling technique used here can be said to be the cluster sampling technique.
Cluster sampling involves a sampling method where by the population is divided into clusters(small groups), then they randomly select select among these clusters to form a sample.
The cluster sampling is used mostly when the population is large.
ANSWER:
Cluster sampling.
During the summer, Martin estimates that he must earn between $600 and 1000 inorder to pay for his car insurance. If he earns $8 an hour, how many hours must hework? Variable Represents:Inequality:Solve:Sentence:
Answers
Answer:
75≤h≤125
Explanation:
Let the variable = h
Variable h represents: the number of hours which he must work
If he works for h hours and earns $8 an hour, his income = $8h.
Since he must earn between $600 and 1000 in order to pay for his car insurance, we have the inequality
[tex]600\leq8h\leq1000[/tex]Next, we solve for h.
[tex]\begin{gathered} \frac{600}{8}\leq\frac{8h}{8}\leq\frac{1000}{8} \\ 75\leq h\leq125 \end{gathered}[/tex]Martin must work between 75 to 125 hours in order to be able to pay for his car insurance.
Find the volume of the given solid. Round to the nearest 10th, if necessary.
Answers
SOLUTION:
Case: Volume of a Sphere
The volume of a sphere is the capacity it has. It is the space occupied by the sphere. The volume of a sphere is measured in cubic units, such as m3, cm3, in3, etc. The shape of the sphere is round and three-dimensional. It has three axes as x-axis, y-axis and z-axis which defines its shape. All the things like football and basketball are examples of the sphere which have volume.
Given:
The radius of the sphere is 2.2cm
Method:
The Volume of a sphere is given as:
[tex]V=\frac{4}{3}\pi r^3[/tex][tex]\begin{gathered} V=\frac{4}{3}\pi(2.2)^3 \\ V=\frac{4}{3}\pi\times2.2\times2.2\times2.2 \\ V=\frac{42.592}{3}\pi \\ V=14.1973\pi \\ V=44.6 \end{gathered}[/tex]Final answer:
The Volume of the Sphere to the nearest tenth is 44.6 cubic centimeters
Find the slope of each line.Y=5/4x+1
Answers
The general slope-intercept equation of a line is:
[tex]y=m\cdot x+b\text{.}[/tex]Comparing this equation with:
[tex]y=\frac{5}{4}\cdot x+1.[/tex]We see that the slope of the line is:
[tex]m=\frac{5}{4}\text{.}[/tex]Answer
The slope of the line is m = 5/4.
Which expressions are equivalent to the given expression?510810 I + 108,g 20 - 10810 10
Answers
Given the following properties for logarithms:
[tex]\begin{gathered} b\log_{10}a=\log_{10}a^b...(1) \\ \\ \log_{10}a+\log_{10}b=\log_{10}a\cdot b...(2) \\ \\ \operatorname{\log}_{10}a-\operatorname{\log}_{10}b=\operatorname{\log}_{10}\frac{a}{b}...(3) \end{gathered}[/tex]Then, from the problem, using (1):
[tex]\begin{gathered} 5\log_{10}x+\log_{10}20-\log_{10}10 \\ \\ \log_{10}x^5+\log_{10}20-\log_{10}10 \end{gathered}[/tex]Now, using (2):
[tex]\log_{10}20\cdot x^5-\log_{10}10=\log_{10}(20x^5)-1[/tex]Finally, using (3):
[tex]\begin{gathered} \log_{10}\frac{20x^5}{10} \\ \\ \therefore\log_{10}(2x^5) \end{gathered}[/tex]Answer: Third and last options
Please help me find the value of x for this
Answers
Given:-
A triangle with hypotneus value 15 and angle value 23.
To find the value of x.
So now we use the formula,
[tex]sin\theta=\frac{Opposite\text{ side}}{Hypotneus}[/tex]Substituting the values. we get,
[tex]sin23=\frac{x}{15}[/tex]So the value of sin23 = 0.3907.
Substituting the value,
[tex]\begin{gathered} 0.3907=\frac{x}{15} \\ x=0.3907(15) \\ x=5.86 \end{gathered}[/tex]So the value is approximatly 5.9
Determine the domain and range of the function using the graph below. Give your answer as an inequality using the appropriate variables.12345-1-2-3-4-51234567-1-2-3-4-5-6-7-8-9-10-11-12-13-14-15Domain: Range:
Answers
Remember that
The Domain is the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).
The Range is the set of all output values, which are the y-coordinate of each ordered pair (the second number in each pair).
in this problem
the domain is the interval (0,5]
[tex]0\text{ < x }\leq\text{ 5}[/tex]and the range is the interval [-3,6]
[tex]-3\leq\text{ y }\leq6[/tex]Which expression matches the statement? seventeen is two more than the product of 8 and y.a. 17+2=8yb. 17=8y+2 c. 17=y(8+2)
Answers
ANSWER
b. 17 = 8y + 2
EXPLANATION
We want to find the correct equation for the statement:
Seventeen is two more than the product of 8 and y
First, the product of 8 and y is:
8 * y
= 8y
"17 is two more than" means that 17 is greater than 8y by 2.
This means that:
17 = 2 + 8y
or 17 = 8y + 2
So, the correct answer is b
Solve for x and graph.|35-7x| less then or equal to 70And/Or
Answers
Solving for x
[tex]\begin{gathered} \text{Apply the absolute rule:} \\ \text{If }|u|\le a,a>0,\text{ then }-aCombine the two solutions, the solution for the inequality | 35 - 7x | ≤ 70 is[tex]-5\le x<15[/tex]Using this interval, draw a solid vertical line at x = -5, and x = 15, and shade the interval in between which gives us
part a: bases on the imformation collected, who will have the higher mean annual salarypart b: if you were to graph this data what would be important to consider
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Table:
annual salaries (thousands of dollars)
Step 02:
higher mean annual salary:
College grad:
[tex]\operatorname{mean}\text{ =}\frac{41+67+53+48+45+60+59+55+52+52+50+59+44+49+52}{15}[/tex]mean = 52.4
High School grad:
[tex]\text{mean = }\frac{23+33+36+29+25+43+42+38+27+25+33+41+29+33+35}{15}[/tex]mean = 32.8
The answer is:
The College grad will have a higher mean annual salary.
Sam borrowed Php14,500.00 for 2 years and had to pay Php2320.00 simple interest at the end of that time. What rate of interest did he pay?
Answers
We will use the next formula
[tex]I=P\cdot r\cdot t[/tex]Where
P is the principal
r is the rate
t is the time
I is the interest
we have the next information
P=14,500
t=2
I=2320
we substitute in the formula
[tex]2320=14500(r)(2)[/tex]We isolate the rate
[tex]r=\frac{2320}{14500(2)}=0.08[/tex]The rate of interest is 8%
ANSWER
the rate of interest did he pay is 8%