The mean of the numbers 21, 6, 13, 36, 22, 48, 104, 73, 158, and 17 is 49.8.
What is the mean?The mean is the average value of a data set.
The mean is one of the measures of central tendency, like the mode and the median.
To compute the mean, we sum the data values and divide the result by the number of items in the data set.
The mean is simply the quotient found by dividing the sum of the data values by the number of items.
Sum:S/No. Value
1 21
2 6
3 13
4 36
5 22
6 48
7 104
8 73
9 158
10 17
Total 498
Average = 49.8 (498/10)
The sum of the data values is 498.
The number of the numbers (items) in the data set is 10.
Therefore, the average or mean equals 49.8.
Thus, in that recent math test, the students can answer the teacher that the mean of the given values is 49.8.
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Question Completion:On a recent math test, a teacher asked the students for a measure of the mean of 21, 6, 13, 36, 22, 48, 104, 73, 158, and 17. What is the mean?
How much money would i need to invest for six years at 4 ¼% simple interest to earn 400.00 kina?
ANSWER:
1568.63
STEP-BY-STEP EXPLANATION:
We have that the simple inteters formula is the following:
[tex]I=Prt[/tex]Where I is the interest earned, P is the principal, that is, the amount invested, r the rate and t the time. We substitute and calculate for P, like this:
[tex]\begin{gathered} r=4\frac{1}{4}\text{\%}=4.25\text{\%}=\frac{4.25}{100}=0.0425 \\ t=6 \\ I=400 \\ \text{ replacing} \\ 400=P\cdot0.0425\cdot6 \\ P=\frac{400}{6\cdot0.425} \\ P=1568.63 \end{gathered}[/tex]Therefore, for a profit of 400 under these conditions, 1568.63 must be invested
The data set lists the number of tickets purchased for a school dance each day for 9 days. {13, 6, 13, 8, 2, 19, 11, 16, 17}If 32 is added to the data set, which statement will be TRUE?
D
1) The median is by nature more consistent and resistant to changes when some value is added to the data set. Let's visualize how that happens:
2) Mean
[tex]\begin{gathered} \left\{13,6,13,8,2,19,11,16,17\right\} \\ \bar{x}=\frac{13+6+13+8+2+19+11+16+17}{9}=11.67 \\ 2)\operatorname{\{}13,\:6,\:13,\:8,\:2,\:19,\:11,\:16,\:17,32\operatorname{\}} \\ \bar{x}=\frac{\sum_{i=1}^na_i=137}{10}=13.7 \end{gathered}[/tex]As we can see, the addition of 32 to the data set changes the mean.
3) Now, let's check the Median. Rewriting that into the ascending order:
[tex]\begin{gathered} 2,\:6,\:8,\:11,\:13,\:13,\:16,\:17,\:19 \\ Median:13 \end{gathered}[/tex]Note that 13 divides the distribution into two halves.
Now, let's add 32 to that dataset and check it:
[tex]\begin{gathered} 2,\:6,\:8,\:11,\:13,\:13,\:16,\:17,\:19,\:32 \\ Md=\frac{13+13}{2}=13 \end{gathered}[/tex]Thus, we can tell that the answer is:
Please help: write the equation in logarithmic form 1/64 = (1/4)^3
Recall the equation,
x = a^y
This is an exponential equation. To write it as a logarithmic function, it becomes
y = loga x
where
a is the base of the logarithm
The given exponential equation is
1/64 = (1/4)^3
By comparing both equations, we have
a = 1/4, y = 3, x = 1/64
Thus, in logarithmic form, the equation is
3 = log(1/4) 1/64
where
1/4 is the base of the logarithm
based on a survey of random samples from Saint Joseph citizens the proportion of citizens interested in creating a Riverfront tourist area is 71 with a margin of error of .04 what interval contains the margin of error of 95% of the sample proportions?
In order to find the interval for 95% of the sample proportions, we need to find the z-scores for the interval of 95% in the normal distribution.
To do so, we can find the z value for 2.5% and 97.5% (this way, we can subtract then and find the interval of 95%).
Looking at the table, we have that z1 = -1.96 for 0.025 and z2 = 1.96 for 0.975.
Now, finding the interval, we have that:
[tex]\begin{gathered} \text{interval}=\lbrack\mu+\sigma\cdot z1,\mu+\sigma\cdot z2\rbrack \\ \text{interval}=\lbrack71+0.04\cdot(-1.96),71+0.04\cdot1.96\rbrack \\ \text{interval}=\lbrack71-0.0784,71+0.0784\rbrack \\ \text{interval}=\lbrack70.9216,71.0784\rbrack \end{gathered}[/tex]So the interval is from 70.9216 to 71.0784.
Select all the expressions that equivalent to 5(f + 7)
Answer
Options A and B are correct.
5 (f + 7)
= (f + 7) 5
= 5f + 35
Explanation
5 (f + 7)
This expression can be rewritten as
5 (f + 7)
= (f + 7) 5
Since multiplication is commutative, that is a × b = b × a
And it can be further simplified by opening the bracket
5 (f + 7)
= 5f + 35
Hope this Helps!!!
Suppose that $2060 is deposited into an account where the interest is compounded annually. This situationcan be modeled by the function.P(t) = 2060(1.019)where P(t) represent the value (in dollars) of the account at t years afterdepositing the $2060.According to this model, what is the earning interest rate in percent?
Notice that:
[tex]1.019=1+0.019,[/tex]therefore, the interest rate is
[tex]0.019[/tex]which in percent corresponds to:
[tex]0.019\times100=1.9\%.[/tex]Answer:[tex]1.9\%[/tex]sam is cutting 5 sq.ft of grass with scissors. He caan cut 3/4 sq ft an hour. how long will it take him to cut it all
Let X be the time taken to cut all the 5 sq ft
3/4 sq ft = 1hour
5 sq ft = X
cross-multiply
3/4 X = 5
Multiply both-side of the equation by 4/3
X= 5 x 4/3
X = 20/3
X=6.667 hours
X= 6 hours 40 minutes
It will take Sam 6hours40 minute to cut it all
Question 3 of 5 Which math expression means "the sum of 270 and 180"? O A. 270 + 180 B. 270 : 180 O C. 270 = 180 O D. 270 - 180
Sum of 270 and 180
270+180 (option A)
use one unit multiplier to change 840 inches to feet
Recall that
12 inch = 1 foot
Hence
840 inches = 840/12
= 70 feet
solve the equation for x. -x/8=7
Use the properties of equalities to solve the given equation:
[tex]-\frac{x}{8}=7[/tex]Multiply both sides by -8:
[tex]\begin{gathered} -\frac{x}{8}\times-8=7\times-8 \\ \Rightarrow x=-56 \end{gathered}[/tex]Therefore:
[tex]x=-56[/tex]i need help with my homewrok PLEASE CHECK WORK number 1
Answer
D
[tex]C(t)=84(1.02)^{t}[/tex]Step-by-step explanation
Given that the price of the tickets each year is 2% more than the previous year, then the function that represents the price is an exponential growth function.
Exponential growth formula
[tex]C(t)=a(1+r)^t[/tex]where
• C(t): ticket's price after t years
,• a: initial price
,• r: growth rate, as a decimal
,• t: time in years
Substituting a = $84, r = 0.02 (= 2/100):
[tex]\begin{gathered} C(t)=84(1+0.02)^t \\ C(t)=84(1.02)^t \end{gathered}[/tex]How do I solve inequalities and graph their solutions afterwards
Solve for x, by dividing both sides by 6
[tex]\begin{gathered} 6x<-11 \\ \frac{6x}{6}<\frac{-11}{6} \\ x<-\frac{11}{6} \end{gathered}[/tex]Now that we know that the solution is x < -11/6, to graph it, create a number line, and then locate -11/6, which is approximately -1.833, which is between -2, and -1, but closer to -2.
Since the inequality is less than ( < ), draw a hole at the starting point -1.833, and then draw an arrow towards the left. Notice that the direction of the inequality sign less than ( < ), is the same direction of the arrow ( <=== ) that we also drew on the number line.
I don't know how to order them from greatest to least , could you help?
According to the given data, we have the following numbers to order:
3, 1.5%, π, √4, -1 3/4, -157%
To order them from greatest to least, we use logic and common sense as follows:
Number 3 is in this case no problem.
1.5%. This number is express as a percentage, hence, when you have a percentage you have to divide the coefficient to 100, therefore in this case would be 1.5/100 and this is equal to 0.015
π. The number pi is equal mathematically to 3.14159 26535
√4=2
-1 3/4= -1 * 0.75=-0.75
-157%=-157/100=-1.57
Therefore, given the results calculated above, the order from greatest to least would be:
π, 3, √4, 1.5%, -1 3/4, -157%
If an item that originally cost $19 is decreased to $16, what is the percentage of decrease in the item?
Round your answer to 3 decimal places.
15.789% is the percentage decrease of the item with an originally cost of $19 and decreasing to $16
What is the percentage decrease of the item?Percentage decrease is simply the amount of decrease from the original value to the new value in terms of 100 parts of the original value.
The formula for percentage decrease is expressed as;
D = ((x₁ - x₂) / x₁)100%
Given the data in the question;
original value x₁ = $19New value x₂ = $16Percentage decrease D = ?To determine the percentage decrease, plug the given values into the percentage decrease formula above.
D = ((x₁ - x₂) / x₁)100%
D = (( 19 - 16 ) / 19 )100%
D = (( 3 ) / 19 )100%
D = ( 0.1578947 )100%
D = 15.789%
Therefore, the percentage decrease of the item is 15.789%.
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Which of the lines on the graph represents a proportional relationship with a greater constant of proportionality? and why?
From the graph given,
A has a greater constant of proportionality
Reason is that:
In line A, the y values is larger compared to the x value
But in B the y value is not as large as the y value in A and the x-value is larger than tha x-values in B. Also the difference between the x and y-values is not that large as compared to A
-Using a ruler and what you know about the Golden Ratio, which image has a length-to-width ratio of about 1.618? Show your measurements below.
1)
a = 3.3
b = 1.1
φ = 3.3/1.1 = 3
2)
a = 3.3
b = 2.1
φ = 3.3/2.1 = 1.5714
3)
a = 3.3
b = 3.1
φ = 3.3/3.1 = 1.06
If cos A = 1/3 with A in QIV, then sin A/2=
The question gives us the value of
[tex]\cos A=\frac{1}{3}[/tex]We are then required to find
[tex]\sin (\frac{A}{2})[/tex]In order to find the value of this expression, we need to use the following trigonometric identity:
[tex]\begin{gathered} \cos A=\cos ^2(\frac{A}{2})-\sin ^2(\frac{A}{2}) \\ \\ \cos ^2(\frac{A}{2})=1-\sin ^2(\frac{A}{2}) \\ \\ \therefore\cos A=1-\sin ^2(\frac{A}{2})-\sin ^2(\frac{A}{2}) \\ \cos A=1-2\sin ^2(\frac{A}{2}) \end{gathered}[/tex]With this derived identity for cos A, we can proceed to solve the question.
The identity expresses cos A in terms of sin (A/2). Since we already know the value for cos A, we can proceed to find
the value of sin(A/2)
This is done below:
[tex]\begin{gathered} \cos A=1-2\sin ^2(\frac{A}{2}) \\ \\ \text{Making sin(}\frac{A}{2})\text{ the subject of the formula;} \\ \text{subtract 1 from both sides}S \\ \cos A-1=-2\sin ^2(\frac{A}{2}) \\ \\ \text{Divide both sides by -2} \\ \frac{\cos A-1}{-2}=\sin ^2(\frac{A}{2}) \\ \\ \text{ Find the square root of both sides} \\ \\ \therefore\sin (\frac{A}{2})=\sqrt[]{\frac{\cos A-1}{-2}} \end{gathered}[/tex]Now that we have the final expression for calculating sin(A/2), let us substitute the value of cos A into the expression.
This is done below:
[tex]\begin{gathered} \sin (\frac{A}{2})=\sqrt[]{\frac{\cos A-1}{-2}} \\ \cos A=\frac{1}{3} \\ \\ \sin (\frac{A}{2})=\sqrt[]{\frac{\frac{1}{3}-1}{-2}} \\ \\ \sin (\frac{A}{2})=\sqrt[]{\frac{1}{3}} \\ \\ \end{gathered}[/tex]
Question 3 (1 point)Give the algebraic representation of the transformation.Xy)ddf7ec519c24031717c638db9c8e1382.webmBlank 1:Blank 2:
Problem
Solution
For this case we see that A = (-6,-6) and A'= (-2,-2)
then we can find the transformation on this way:
kx = -2/-6 = 1/3
ky = -2/-6= 1/3
Then the correct answer is:
(1/3 x , 1/3y)
51) Write the equation of the line passing through (-2, 5) and perpendicular x + 3y = 15.
The genral equation of straight line is y=mx+c, where m is the slope of the line and c is the y intercept.
The given line is x+3y=15. Rewrite this equation in the form y=mx+c.
[tex]\begin{gathered} x+3y=15 \\ 3y=-x+15 \\ y=\frac{-1}{3}x+\frac{15}{3} \\ y=\frac{-1}{3}x+5 \end{gathered}[/tex]Comparing above equation with y=mx+c, we can write
[tex]\text{Slope, m=}\frac{-1}{3}[/tex]The slope of a line perpendicular to x+3y=15 is the negative reciprocal of the slope m. Hence, the slope of the perpendicular line can be written as,
[tex]m_1=-\frac{1}{m}=-(\frac{1}{\frac{-1}{3}})=3[/tex]Let (x1,y1)=( -2,5). Now, the equation of the line with slope m1 and passing through (x1,y1) can be written as,
[tex]\begin{gathered} m_1=\frac{y_1-y}{x_1-x} \\ 3=\frac{5-y}{-2-x} \\ 3(-2-x)=5-y \\ -6-3x=5-y \\ y=3x+11 \end{gathered}[/tex]Theefore, the equation of aline passing through (-2,5) and perpendicular to x+3y=15 is y=3x+11.
Let me know if you need a better picture it’s bad quality but readable
Given data:
The given table.
The expression for given table can be written as,
[tex]t(p)=a+bp[/tex]Substitute the given ( 1,6) in the above expression.
[tex]\begin{gathered} 6=a+b(1) \\ b=6-a \end{gathered}[/tex]Substitute (5, 20.4) in the expression.
[tex]20.4=a+5b[/tex]Substitute (6-a) in above expression.
[tex]\begin{gathered} 20.4=a+5(6-a)) \\ -9.6=-4a \\ a=2.4 \end{gathered}[/tex]The value of b is,
[tex]\begin{gathered} b=6-2.4 \\ =3.6 \end{gathered}[/tex]The expression is t(p)=3.6p+2.4.
Thus, the third option is correct.
a triangle has side lengths of 6 8 and 10 . Is it a right triangle? explain
For a triangle to be right angled triangle, it muist satisfy the pythagoras theorem,
[tex]\begin{gathered} H^2=P^2+B^2 \\ 10^2=6^2+8^2 \\ 100=36+64 \\ 100=100 \\ \text{left hand side = right hand side} \end{gathered}[/tex]Hence, It is a right angle.
Rewrite in simplest terms: -4(-0.7w – 3w + 0.1) - 0.1w
Step 1: Problem
Rewrite in simplest terms: -4(-0.7w – 3w + 0.1) - 0.1w
Step 2: Concept and method
Use the associative method to open the bracket.
= -4( -0.7w - 3w + 0.1 ) - 0.1w
= -0.7w(-4) -3w(-4) + 0.1(-4) - 0.1w
= - 2.8w + 12w - 0.4 - 0.1w
Collect like terms
= - 2.8w + 12w - 0.1w - 0.4
= 9.1w - 0.4
Step 3: Final answer
= 9.1w - 0.4
The domain of the following relation R {(6, -2), (1, 2), (-3,-4), (-3, 2)} is (1 point) O {-3, -3, 1,6) {-4,-2, 2, 2) O {-4,-2, 2) O {-3, 1,67
The domain of a function are all the input values of a function.
These are the x coordinate values.
In this case;
{(6, -2), (1, 2), (-3,-4), (-3, 2)}
The domain is { -3,-3,1, 6}
Answer
A. {-3, -3, 1 , 6 }
congruence - SSS theoremIll send a picture of the question
From the figure,
We need to prove that,
[tex]\Delta\text{MNO}\cong\Delta\text{PQR}[/tex]By SSS theorem,
[tex]\begin{gathered} MN\cong PQ(\text{Given)} \\ NO\cong QR(\text{Given)} \end{gathered}[/tex]So, the third side must be,
[tex]MO\cong PR[/tex]Hence, the correct option is D.
Consider the sets, A={x€N:P(x)} and B={x€N:O(x)} 1. Examine A and B with respect to the subset relation. What can you conclude? Justify your answer. 2. Are A and B equal? Justify your answer
Solution:
Consider the set A and set B;
[tex]A=\mleft\lbrace x\in N\colon P(x\mright)\},B=\mleft\lbrace x\in N\colon O(x)\mright\rbrace[/tex]Let P be the property "is a prime number" and O be the property "is an odd integer".
[tex]\begin{gathered} A=\mleft\lbrace2,3,5,7,11,\ldots\mright\rbrace,B=\mleft\lbrace1,3,5,7,9,11,\ldots\mright\rbrace \\ A\text{ is not a subset of set B} \end{gathered}[/tex]Also;
[tex]undefined[/tex]1 12 cm Find the area of the figure, (15 Points) 4.5 cm 2 cm 5 cm
area large rectangle:
[tex]A=\text{length}\times width=12\times4.5=54[/tex]area small rectangle:
[tex]A=5\times2=10[/tex]area figure = area large rectangle + area small rectangle
[tex]A=54+10=64[/tex]asnwer: 64 sq cm
Avenue B makes a 70 degree angle with Center Street what are the measures of the angles at South Street makes with Avenue B
1.- They are also perpendicular.
2.- It is also 70° .
3 expression equivalent to: 10(2+3)-8 × 3
We want to know about 3 expression equivalent to
[tex]10\mleft(2+3\mright)-8\times3\text{ }[/tex]you have to do the parenthesis operations first, that is: (2+ 3) = 5
Now:
10 (2+3) = 10 (5)= 50
the we apply the following operations to the previous equation
50 - 8 x 3 = 50- (8x3) = 50 - (24) = 50-24 = 26.
the first equivalent equation is
1. 10(5) - (8 x3)
the second equivalent equation is
2. 50 - 24
the third equation is
3. 10(5) - (24)
What is the difference in high temperatures between the coldest day and the warmest day?
The temperature of the coldest day is -2.1 degree celcius
and the temperature of the warmest day is 3.4-degree celcius
so the difference in the temperature is
3.4-(-2.1)
3.4+2.1=5.5
so the answer is 5.5 degrees celsius.
here the warmest day is Saturday with 3.4 degree celcius
Annual sales for a company are $375,000 and they increase at a rate of 7% each year. Find the company’s sales after 6 years.
Notice that 7%=7/100=0.07
After the first year, the annual sales are
[tex]375000+0.07(375000)=375000(1+0.07)[/tex]After the second year,
[tex]\begin{gathered} (375000+0.07(375000))+0.07(375000+0.07(375000))=(1+0.07)(375000+0.07(375000)) \\ =(1+0.07)^2375000 \end{gathered}[/tex]Therefore, in general, after n years, the annual sales are
[tex]f(n)=375000(1+0.07)^n[/tex]Set n=6; then,
[tex]\begin{gathered} f(6)=375000(1.07)^6=562773.881943375 \\ \Rightarrow f(6)\approx562773.88 \end{gathered}[/tex]The answer is approximately $562773.88, the exact answer is $562773.881943375