Answer:
3p + 8n, 12p + 2n, 9p+4n, 6p+6n
8 columns bar graph.
Step-by-step explanation:
$2 = pen
$3 = notebook
This could be written as a bar graph in multiples of $6.00 along y axes.
3 pens + 8 notebooks. Then 12 pens + 2 notebooks.
Then 9 pens + 4 notebooks . Then 6 pens + 6 notebooks
3p + 8n, 12p + 2n, 9p+4n, 6p + 6n
3p = $6
8n = $24
12p = $24
2n = $6
9p = $18
4n = $12
6p = $12
6n = $18
and so on...
simplify the following 4√28÷3√7
[tex]\displaystyle\bf 4\sqrt{28} :3\sqrt{7} =4\sqrt{4} \cdot \sqrt{7} :3\sqrt{7} =4\cdot2:3=\boxed{\frac{8}{3} }[/tex]
David has available 240 yards of fencing and wishes to enclose a rectangular area.
(a) Express the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?
Answer:
Below in bold.
Step-by-step explanation:
Perimeter = 2*width + 2*length
So
240 = 2w + 2l
120 = w + l
l = 120 - w
(a) Area = w*l
Substituting for l:
A = w(120 - w)
A = 120w - w^2
(b)
Finding the derivative:
A = 120w - w^2
A' = 120 - 2w
For a maximum area A' = 0, so:
120 - 2w = 0
2w = 120
w = 60 yards for maximum area.
(c)
Maximum area
= 120*60 - 60^2
= 3600 yd^2.
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
A. In 2 - In x
B. In 1 + In 2 - ln x
C. 1 + In 2 - In x
D. In 2 + ln x
Answer:c
Step-by-step explanation:
The equivalent expression is 1 + In 2 - In x.
How to estimate an equivalent to the given expression?Given:
[tex]$\ln \left(\frac{2 e}{x}\right)$[/tex]
Apply log rule:
[tex]$$\log _{C}\left(\frac{a}{b}\right)=\log _{c}(a)-\log _{c}(b)$[/tex]
[tex]$&\ln \left(\frac{2 e}{x}\right)=\ln (2 e)-\ln (x) \\[/tex]
= ln (2e) - ln (x)
Apply log rule:
[tex]$\log _{c}(a b)=\log _{c}(a)+\log _{c}(b)$[/tex]
ln (2e) = ln (2) + ln (e)
= ln (2) + ln (e) - ln (x)
Apply log rule:
[tex]$\log _{a}(a)=1$[/tex]
= ln (2)+1-ln (x)
Therefore, the correct answer is option C. 1 + In 2 - In x.
To learn more about log rule
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Eden has a part-time job
She is paid £7.20 per hour
This week she worked for 18½ hours
Work out Eden's total pay for this week
Answer:
$133.20
Step-by-step explanation:
You make 7.20 an hour for 18 1/2 hours. You must multiply to know how much she made that week
7.20/hr = ?/18 1/2 hr
7.20 x 18 1/2
7.20 x 18.5=
133.20
Write down the equation of the function whose graph is shown.
will mark brainliest
Answer:
y = 1(x - 5)² + 3
Step-by-step explanation:
The general formula of a quadratic equation is written as;
y = a(x − h)² + k
Where (h, k) are the x and y coordinates at the vertex.
Our vertex coordinate is (5, 3)
Thus;
y = a(x - 5)² + 3
Now,we are given another coordinate as (8, 12)
Thus;
12 = a(8 - 5)² + 3
12 = 9a + 3
9a = 12 - 3
9a = 9
a = 9/9
a = 1
Thus,the equation is;
y = 1(x - 5)² + 3
Suppose a researcher found an rs of .89 between amount of blood cholesterol and the severity of the heart attack. Based on an N of 6 and a two-tailed test, the researcher should conclude:_________.a. not significantb. significant at the .05 levelc. p > .05d. higher blood cholesterol causes more severe heart attacks
Answer:
d. higher blood cholesterol causes more severe heart attacks.
Step-by-step explanation:
Two tailed tests are a method for hypothesis testing when data is distributed on the two sides. P value is determined to identify whether the hypothesis is true or false. When rs is 0.89 between blood cholesterols and severity of heart attacks then these is significant relation between them.
Sadie brought $28.00 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/3 as much as the sketchbook, and the sketchbook cost 1/2 the cost of the paint set. Sadie had $3.00 leftover after buying these items. What was the cost of each item?
Answer:
cost of paint set = $ 13.64
cost of sketch book = $ 6.82
cost of brush = $ 4.55
Step-by-step explanation:
Let the cost of paint set is s.
cost of sketch book = s/2
cost of brush = s/3
Money spent = $ 28 - $ 3 = $ 25
So,
s + s/2 + s/3 = 25
6 s + 3 s + 2 s = 150
11 s = 150
s = $ 13.64
cost of paint set = $ 13.64
cost of sketch book = $ 6.82
cost of brush = $ 4.55
Which of the following statistics would provide a good comparison between data sets?
Group of answer choices
all of these
correlation
interquartile range
mean
The following statistics which would provide a good comparison between data sets is all of the above and is denoted as option A.
What is Statistics?This refers to the branch of science which involves the collection and interpretation of data sets or variables. There are different ways or techniques which are used and they vary according to the features of the data set.
There are statistics which provide a good comparison between data sets include the following below:
correlationinterquartile rangemeanThis comparison is done so as to to prove that there are no differences between them and other reasons.
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rosa can run 400 meters in one min. if she runs at the same rate how may meters can she run in 5 min
Answer:
2000 meters
Step-by-step explanation:
400 * 5
Listed below are the top 10 salaries (in millions of dollars) of television personalities in a recent year.
38 36 35 27 15 13 12 10 9.6 8.4
Use the sample data to construct a 95% confidence interval for the population mean and correctly interpret your answer.
Answer:
The correct answer is "(11.69, 29.11)".
Step-by-step explanation:
Given:
[tex]38 \ 36\ 35\ 27\ 15\ 13\ 12\ 10\ 9.6\ 8.4[/tex]
[tex]n=10[/tex]
As per the question,
Mean,
[tex]\bar x=20.40[/tex]
Standard deviation,
[tex]s=12.17[/tex]
or,
[tex]df=10-1[/tex]
[tex]=9[/tex]
For 95% confidence interval,
[tex]t^*=2.262[/tex]
hence,
The 95% confidence interval will be:
= [tex]\bar x \pm \ t^*\times \frac{s}{\sqrt{10} }[/tex]
By substituting the values, we get
= [tex]20.40 \pm 2.262\times \frac{12.17}{\sqrt{10} }[/tex]
= [tex](11.69, 29.11)[/tex]
Show that the number 6 is a rational number by finding a ratio of two integers equal to the number
9514 1404 393
Answer:
6 = 6/1 = 12/2 = 18/3
Step-by-step explanation:
The simplest ratio of integers with a value of 6 is ...
6 = 6/1
We can multiply numerator and denominator by any non-zero integer value to obtain an equivalent:
6 = 12/2 = 18/3 = -54/-9
When comparing two box-plots that show the same type of information, what determines agreement within the data?
A.the range of the quartiles in each data set
B.the median of each data set
C.the mean of each data set
D.the number of values in each data set
Answer:
c.the mean of each data set
Answer:
A
Step-by-step explanation:
How many side of the triangle are congruent? Explain.
A) 0
B) 2
C)3
D) not enough information given
Answer:
Option B
Step-by-step explanation:
In the given triangle,
Two sides of the triangle measure 2 cm and one side measures 3 cm.
Therefore, in this triangle two sides measuring 2 cm are congruent.
Option B is the correct option.
simpify 20/[(5-{24/2-(7-5of3)}]
Answer:
Why do we need an order of operations?
Example: In a room there are 2 teacher's chairs and 3 tables each with 4 chairs for the students. How many chairs are in the room?
We know there are 14, but how do we write this calculation? If we just write
2 + 3 x 4
how does a reader know whether the answer is
2 + 3 = 5, then multiply by 4 to get 20 or
3 x 4 = 12, then 2 + 12 to get 14?
There are two steps needed to find the answer; addition and multiplication. Without an agreed upon order of when we perform each of these operations to calculate a written expression, we could get two different answers. If we want to all get the same "correct" answer when we only have the written expression to guide us, it is important that we all interpret the expression the same way.
One way of explaining the order is to use brackets. This always works. To say that the 3 x 4 is done before the adding, we would use brackets like this:
2 + (3 x 4)
The brackets show us that 3 x 4 needs to be worked out first and then added to 2. However, we can also agree on an order of operations, which is explained below.
Another example: Calculate 15- 10 ÷ 5
If you do the subtraction first, you will get 1. If you do the division first, which is actually correct according to the rules explained below, you will get 13. We need an agreed order.
The shortest route from London to Oxford is 55 miles.
A lorry is expected to take 1.1 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 1.1 hours.
By how many more mph than the expected speed does the lorry travel?
Answer:
so to find the mph of the lorry for the original route we divide 66 by 55 since it 66 is 1.1 of 60
66 divided by 55=1.2
so it takes 1 minutes 12 seconds for the lorry to go a mile
now we multiply 55 by 1.15=63.25
so we divide 66 by 63.25=1.04347826087
so it takes 1 minute and 1 second for the the lorry to go a miles
1 minute 1 second is 59 miles per hour
1 minute 12 seconds is 50 miles per hour
so the lorry travels 9 mph over its expected speed
Hope This Helps!!!
=================================================
Explanation:
distance = rate*time
d = r*t
r = d/t
r = 55/1.1
r = 50
The lorry's original speed is 50 mph when going the original route.
-----------------
Now consider the longer route, which is 15% longer compared to the original 55 mile route. So the longer route is 1.15*55 = 63.25 miles exactly. Or you could say 15% of 55 = 0.15*55 = 8.25 which adds onto the original 55 to get 55+8.25 = 53.25; either way the longer distance is 63.25 miles.
Computing the new rate or speed gets us
r = d/t
r = 63.25/1.1
r = 57.5
-----------------
When traveling the original route, the lorry goes 50 mph. When traveling the longer route, the lorry goes 57.5 mph. This is a difference of 57.5 - 50 = 7.5 mph
Meaning that the lorry must drive 7.5 mph faster on the longer route compared to the shortest route. This is if the driver wants to make the trip in the same 1.1 hour timeframe.
Note: 1.1 hours = 1.1*60 = 66 minutes = 1 hour, 6 minutes.
A scale model of a building has a scale of 3 : 79.
The height of the real building is 24 m.
Find the height of the scale model.
Give your answer in cm to 2 dp.
Answer:
The height of the scale model is of 91.14 cm.
Step-by-step explanation:
Scale problems are solved by proportions, using rule of three.
A scale model of a building has a scale of 3 : 79.
This means that 3m on the drawing represent 79m of real height.
The height of the real building is 24 m.
3m - 79m
xm - 24m
Applying cross multiplication
[tex]79x = 72[/tex]
[tex]x = \frac{72}{79}[/tex]
[tex]x = 0.9114[/tex]
In centimeters:
Multiplying by 100:
0.9114*100 = 91.14 cm.
A rectangular room is 1.2 1.2 times as long as it is wide, and its perimeter is 35 35 meters. Find the dimension of the room.
Answer:
I. Length, L = 9.552 meters
II. Width, W = 7.96 meters
Step-by-step explanation:
Let the length = L
Let the width = W
Given the following data;
Perimeter = 35 m
Translating the word problem into an algebraic equation, we have;
Length = 1.2W
To find the dimension of the room;
The perimeter of a rectangle is given by the formula;
P = 2(L + W)
Substituting into the formula, we have;
35 = 2(1.2W + W)
35 = 2(2.2W)
35 = 4.4W
Width, W = 7.96 meters
Next, we would find the length of the rectangle;
L = 1.2*W
L = 1.2 * 7.96
Length, L = 9.552 meters
What should the m<3 be for —- ?
9514 1404 393
Answer:
m∠3 = 63°
Step-by-step explanation:
Where a transversal crosses parallel lines, all of the obtuse angles are congruent, and all of the acute angles are congruent. The obtuse and acute angles are supplementary.
Angle 1 is an obtuse angle; angle 3 is an acute angle.
angle 3 = 180° - angle 1 = 180° -117° = 63°
The measure of angle 3 is 63°.
_____
Additional comment
There are a number of applicable theorems describing the different angle relationships. Taken together, they are summarized by the first statement above. For example, we could declare angles 1 and 4 to be "corresponding" (hence, congruent), and angles 4 and 3 to be a "linear pair", hence supplementary. The net result is that angle 1 is supplementary to angle 3, as we said above.
We could also get there via relations between alternate exterior angles, alternate interior angles, consecutive exterior or interior angles, and other ways. While that terminology is useful to understand in some problems, it is largely irrelevant here.
Rewrite the equation by completing the square.
x^2 + 7x + 12 = 0
Answer:
x^2 + 7x + 12 = 0
x^2 + 7x = -12
(+3)(+4)=0
=−3
=−4
I also love r o blox
Hope This Helps!!!
Answer:
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
Step-by-step explanation:
Given
x² + 7x + 12 = 0
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 7x
x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials. Suppose you are a news reporter following twelve criminal trials.
(a) If the trials were in Japan, what is the probability that all the defendants would be found guilty? What is this probability if the trials were in the United States?
(b) Of the ten trials, what is the expected number of guilty verdicts in Japan? What is the expected number in the United Sates? What is the standard deviation in each case?
Answer:
a) Japan =0.599
US= 0.006
b) Japan
Variance= 0.475
Standard Deviation =0.69
USA
Variance =2.4
Standard Deviation= 1.55
Step-by-step explanation:
A represents the number of defendants found guilty in Japan in 10 trials
B represents the number of defendants found guilty in US in 10 trials
A represents a binomial function such that n=10,p=0.95 and B represents a binomial function such that n=10,p=0.60
a) Japan: P(A=10)=0.95^10=0.599
US: P(B=10)=0.60^10=0.006
b) Japan:
Expected number of guilty verdicts in 10 trials in Japan = np=10*0.95=9.5
Variance: Var(A) = np(1-p) = 10*0.95*(1-0.95) = 0.475
Standard Deviation = sd(A)=√0.475=0.69
US:
Expected number of guilty verdicts in 10 trials in USA = np=10*0.60=6
Variance: Var(B)=np(1-p)=10*0.6*0.4=2.4
Standard Deviation sd(B)=√2.4=1.55
find the coordinates of 6x² + 6x = 12
Answer:
1 , -2
Step-by-step explanation:
6x^2 + 6x = 12
6x^2 + 6x - 12 = 0
using middle term break method
6x^2 + (12 - 6)x - 12 = 0
6x^2 + 12x - 6x - 12 = 0
6x(x + 2) - 6(x + 2) = 0
(x + 2)(6x - 6) = 0
either (x + 2) = 0 OR (6x - 6) = 0
x + 2 = 0
x = 0 -2
x = -2
6x - 6 = 0
6x = 6
x = 6/6
x = 1
therefore , x = 1 , -2
Type the correct answer in each box. Functions h and K are inverse functions, and both are defined for all real numbers Using this relationship, what is the value of each function composition?
(h o k) (3)=
(k o h)(-4b) =
Answer:
(h o k) (3) = 3
(k o h) (-4b) = -4b
Step-by-step explanation:
An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.
This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.
calculus help needed!
Answer:
No
Not continous at x = 6
Step-by-step explanation:
When x = 6
G(6) = 1/(6 - 6) = 1/0
Dividing by 0 creates a discontinuity
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
An inverse function is y = k/x
replace x and y with the given values:
6 = k/18
Solve for k by multiplying both sides by 18:
k = 108
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
Solution:-[tex]\sf{The \: relation \: y \: varies \: inversely \: as \: x \: translates \: to \: y = \frac{k}{x}.}[/tex]
Substitute the values to find k:
[tex]\sf\rightarrow{y= \frac{k}{x} }[/tex]
[tex]\sf\rightarrow{6= \frac{k}{18} }[/tex]
[tex]\sf\rightarrow{k=(6)(18)}[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{108}}}[/tex]
Answer:-[tex]\sf{The \: equation \: of \: variations \: is \: y={ \color{red}{ \frac{108}{x} }}}[/tex]
[tex]{\huge{\color{blue}{━━━━━━━━━━━━}}}[/tex]
#CarryOnMath⸙
Which values are NOT in the domain of the function?
f(x)
x +4
x2 – 25
O
A) x = -4,4
B) 2 = -5,4
C) x = -4,5
OD) X = -5,5
Given:
The function is:
[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]
To find:
The values that are NOT in the domain of the given function.
Solution:
We have,
[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]
This function is a rational function and it is defined for all real values of x except the values for which the denominator is equal to 0.
Equate the denominator and 0.
[tex]x^2-25=0[/tex]
[tex]x^2=25[/tex]
Taking square root on both sides, we get
[tex]x=\pm \sqrt{25}[/tex]
[tex]x=\pm 5[/tex]
So, the values [tex]x=-5,5[/tex] are not in the domain of the given function.
Therefore, the correct option is D.
The student council has 30 male members and 25 female members. What is the ratio of male student council members to female?
Weekly demand for a certain brand of a golf ball at The Golf Outlet is normally distributed with a mean of 35 and a standard deviation of 5. The profit per box is $5.00. Write an Excel formula that simulates the weekly profit:
= 5 * 35 * NORMSINV(RAND())
= 5* NORMINV(RAND(), 35, 5)
= 5 * RANDBETWEEN(5, 35)
= NORMINV(RAND(), 5 * 35, 5)
Answer:
= 5 * NORMINV(RAND(), 35, 5)
Step-by-step explanation:
From the given information:
The total weekly profit is achieved by the multiplication of the unit profit (5) and the weekly demand.
Here, the weekly demands obey a normal distribution where the mean = 35 and the standard deviation = 5.
Using the Excel Formula:
The weekly profit can be computed as:
= 5 * NORMINV(RAND(), 35, 5)
The area of a circle is 64 pi ft squared. What is the circumference, in feet? Express your answer in terms of pi
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
Answer:
|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
If [tex]|Z| > 2[/tex], the value of X is considered to be unusual.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
Sample of 3
This means that [tex]n = 3, s = \frac{15}{\sqrt{3}}[/tex]
Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
We have to find the z-score.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{115 - 100}{\frac{15}{\sqrt{3}}}[/tex]
[tex]Z = 1.73[/tex]
|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.
One evening Papa John’s sold a total of 33 pizzas topped with pepperoni, sausage, or pepperoni and sausage. There were 29 pizzas that had pepperoni. Of these, 15 also had sausage. How many more pizzas had pepperoni only than had sausage only?
Answer:
10
Step-by-step explanation:
Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33
Number of pizzas with pepperoni = 29
Number of pizzas with pepperoni and sausage = 15
Pizza with pepperoni only = 29 - 15 = 14
Pizza with sausage only = 33 - 29 = 4
Pepperoni only than sausage only :
14 - 4 = 10