Answer:
Perimeter=60.18cm
Area=215.495cm^2
Step-by-step explanation:
Given:
Length of book=18.34cm
Breadth=11.75cm
Solution:
Perimeter=2(l +b)
P=2(18.34+11.75)
P=2 x 30.09
P=60.18cm
Area=l x b
A=18.34 x 11.75
A=215.495 cm^2
Thank you!
what is 12x^3-9x^2-4x+3 in factored form?
Answer: (3x^2-1)(4x-3)
============================
Work Shown:
Use the factor by grouping method
12x^3-9x^2-4x+3
(12x^3-9x^2)+(-4x+3)
3x^2(4x-3)-1(4x-3)
(3x^2-1)(4x-3)
What are the slope and y-intercept of the equation 2x - 5y = -10?
Answer:
Step-by-step explanation:
y=2/5x+2
x= 5/2y-5
hopefully this works
5.39 jings =15.4 hings
4.9 hings = 2.8 gings
According to the conversion rates above, how
many jings equal 1 ging?
E. 7/40
F. 5/8
G. 49/80
H. 20/7
Step-by-step explanation:
It is given that,
5.39 jings =15.4 hings ....(1)
4.9 hings = 2.8 gings ...(2)
From equation (2), the value of 1 ging is :
[tex]1\ \text{ging} = \dfrac{4.9}{2.8}\ \text{hing}\ .....(3)[/tex]
From equation (1), the value of 1 jing is :
[tex]1\ \text{jing} = \dfrac{15.4}{5.39}\ \text{hing}\ .....(4)[/tex]
From equation (3) and (4), we get :
[tex]\dfrac{\text{1 ging}}{\text{1 jing}}=\dfrac{4.9}{2.8}\times \dfrac{5.39}{15.4}\\\\\dfrac{\text{1 ging}}{\text{1 jing}}=\dfrac{49}{80} \\\\1\ \text{ging}=\dfrac{49}{80}\ \text{ jings}[/tex]
Hence, the correct option is (g) "49/80"
An operator wants to determine the standard deviation for a machine relative to its ability to produce windshield wipers conforming within their specifications. To do this, she wants to create a p-chart. Over a month's time, she tests 100 units every day and records the number of manufacturing defects. The average proportion of non-conforming windshield wipers is found to be 0.042. What is the standard deviation of this sample
Answer:
the standard deviation of the sample is less than 0.1
Step-by-step explanation:
Given that :
The sample size n = 100 units
The average proportion of non-conforming windshield wipers is found to be 0.042 which is the defective rate P-bar
The standard deviation of the machine([tex]S_p[/tex]) can be calculated by using the formula:
[tex]S_p =\dfrac{ \sqrt{ \overline P \times (1 - \overline P)} }{n}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (1 -0.042)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (0.958)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.040236} }{100}[/tex]
[tex]S_p =\dfrac{ 0.2005891323 }{100}[/tex]
[tex]S_p =0.002[/tex]
Thus , the standard deviation of the sample is less than 0.1
The time is 8:08 and subract that to 27 minutes ago what time was it?
Answer:
7:41
Step-by-step explanation:
8:08 - 7 Minutes = 8:01
8:01 - 20 Minutes = 7:41
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Suppose that it rains in Spain an average of once every 9 days, and when it does, hurricanes have a 2% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 1% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford? (Round your answer to four decimal places.)
Answer:
I found the answer on Yahoo
Step-by-step explanation:
P[rains in spain] = 1/9
P[hurricane in hartford & rain in spain] = 0.03*1/9 = A
P[hurricane in hartford & no rain in spain] = 0.02*8/9
P[hurricane in hartford] = 0.03*1/9 + 0.02*8/9 = 0.19/9 = B
P[rain in spain | hurricane in hartford] = A/B = 3/19 <---------
Find the equation with the given slope through the given point. Write the equation in the given form AX+BY=C m=1/9 (-6,2)
Answer:
x - 3y = 12
Step-by-step explanation:
Find the point-slope form of this equation and then convert the point-slope form into standard form (ax + by = c):
y - k = m(x - h) becomes y - 2 = (1/9)(x + 6).
Multiplying all three terms by 9 removes the fraction:
3y - 6 = x + 6, or x - 3y = 12
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste?
A. none of these
B. Let “1,2,3” represent preferring the toothpaste and “0,4,5,6,7,8,9” represent not recommending the toothpaste.
C. Let “1,2,3” represent preferring the toothpaste and “4,5,6,7,8,9” represent not recommending the toothpaste.
D. Let “0,1,2” represent preferring the toothpaste and “3,4,5,6,7,8” represent not recommending the toothpaste.
Reset Selection
Answer:
b
Step-by-step explanation:
only b has 10 didgets. it could be a since the didgets aren't very random, but then again, i think it's b
Let favorable event“1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste to determine.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
While going throughout the option in options C and D number so the sample is not equal to 10 so both the statement is false. Option B is the correct option because the sample space is also equal to 10 and the number of the favorable events is also 3 which is mentioned in the question.
Thus, let favorable event “1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.
Learn more about probability here:
brainly.com/question/14290572
#SPJ5
For this problem, use the tables and charts shown in this section. (Use picture provided)
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
0 $0.00
$5.00
$10.00
$300
Answer:
0
Step-by-step explanation:
0 because there is a $100 duty free exemption.
answer:
For this problem, use the tables and charts shown in this section.
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
$0.00 !
$5.00
$10.00
$300
If √2x - 1 + 2=5, then x is equal to?
Answer:
x = 5
Step-by-step explanation:
Remove the radical by raising each side to the index of the radical.
x = 5
This was done assuming that 2x-1 was under the radical and that +2 wasn't.
2 divided by ___=42 two divided by what equals 42?
The circumference of a redwood tree trunk is 16π ft, and it is 100 ft tall. What is the approximate volume of the redwood tree trunk? 2,560π ft3 640π ft3 25,600π ft3 6,400π ft3
Answer:
volume of redwood tree is 6400 π ft^3(option 4)
Step-by-step explanation:
concept =
volume of cylinder = πr^2l
where r is the radius and l is the length of cylinder
circumference of cylinder = 2πr
_____________________________________
shape of redwood tree can be taken as cylindrical
given
circumference of a redwood tree trunk is 16π ft
2πr = 16π
=> r = 16π/2π = 8
Thus, radius is 8 feet
Therefore volume of redwood tree = πr^2l = π8^2*100 = π*64*100
volume of redwood tree =6400 π ft^3
Answer:
6,400π ft3
Step-by-step explanation:
took test and got it right
Find the value of x.
Answer:
x=3
Step-by-step explanation:
I guessed and checked which x value would make ABC proportional to DBE. If x=3, than DB=8 which is double BE. If x=3, than AB=14 which is double BC. Since it is proportional, It should be correct. I don't remember the actual way you solve this with a formula but this makes sense to me.
Answer:
x=3
Step-by-step explanation:
We can use ratios to solve since the triangles are similar
x+5 4
------------ = ---------------
x+5 +2x 4+3
Simplifying
x+5 4
------------ = ---------------
3x+5 7
Using cross products
7(x+5) = 4(3x+5)
Distribute
7x+35 = 12x+20
Subtract 7x from each side
35 = 5x+20
Subtract 20 from each side
15 = 5x
Divide by 5
3 =x
A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 210 students who averaged 28 texts per day. The standard deviation was 21 texts.A. The sampling distribution follows a_______.1. "F"2. "normal"3. "T"4. "Chi-square" B. With 95% confidence the population mean number of texts per day of is between_______and______texts. A. 1. "24.92"2. "25.79"3. "27.37"4. "25.14"B. 1. "31.19"2. "31.20"3. "29.28"4. "30.86" C. If many groups of 210 randomly selected students are studied, then a different confidence interval would be produced from each group. About_______% of these confidence intervals will contain the true population mean number of texts per day and about______% will not contain the true population mean number of texts per day.A. 1. "5"2. "95"3. "1"4. "99"B. 1. "95"2. "99"3. "5"4. "1"
Answer: A. The sampling follows a normal distribution.
B. Between 25.14 and 30.86
C. About 95% will contain the true mean and about 5% won't
Step-by-step explanation: A. The sampling is normally distributed because:
it has a symmetric bell shape, mean and median are both the same and located at the center of graphic, approximately 68% of the data falls within one standard deviation;95% falls within two standard deviations;99.7% within 3 standard deviations;B. For a 95% confidence interval: α/2 = 0.025
Since n = 210, use z-score = 1.96
To calculate the interval:
mean ± [tex]z.\frac{s}{\sqrt{n} }[/tex]
Replacing for the values given:
28 ± [tex]1.96.\frac{21}{\sqrt{210} }[/tex]
28 ± [tex]1.96*1.45[/tex]
28 ± 2.84
lower limit: 28 - 2.84 = 25.14
upper limit: 28 + 2.84 = 30.86
Confidence Interval is between 25.14 and 30.86.
C. Confidence Interval at a certain percentage is an interval of values that contains the true mean with a percentage of confidence. In the case of number of times per day students text, 95% of the interval will contain the true mean, while 5% will not contain it.
Find the length S of the spiral (t cos(t), t sin(t)) for 0 ≤ t ≤ 3π. (Round your answer to three decimal places.) S =
The arc length is
[tex]S=\displaystyle\int_C\mathrm ds[/tex]
where C is the given curve and ds is the line element. C is defined on 0 ≤ t ≤ 3π by the vector function,
[tex]\mathbf r(t)=(t\cos t,t\sin t)[/tex]
so the line element is
[tex]\mathrm ds=\left\|\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}\right\|\,\mathrm dt[/tex]
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm d(t\cos t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm d(t\sin t)}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
[tex]\mathrm ds=\sqrt{1+t^2}\,\mathrm dt[/tex]
So we have
[tex]S=\displaystyle\int_0^{3\pi}\sqrt{1+t^2}\,\mathrm dt\approx46.132[/tex]
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
Answer:
Both functions have the same slope.The origin is the y-intercept for the function expressed in the table.The table and the graph express an equivalent function.Step-by-step explanation:
Both functions have the same slope
The slope is m in the equation; y =mx+c which is the formula for a straight line.
m = change in Y/change in x
Using 2 points: (1,3/4) and ( 4,3) from the table;
= (3 - 3/4) / ( 4 - 1)
= 2.25/3
= 0.75 which is 3/4 which is the same as the slope of the function in the equation.
The origin is the y-intercept for the function expressed in the table.
Slope of function in table is known to be 0.75. Find c to complete equation.
3 = 0.75 ( 4) + c
3 = 3 + c
c = 0
c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.
The table and the graph express an equivalent function.
The function for the table as calculated is;
y = 0.75x + 0
y = 0.75x
This is the same as the function for the equation for the graph which is y = 3/4x.
Answer:Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The table and the graph express an equivalent function.
Step-by-step explanation:
Compare the linear functions expressed below by data in a table and by an equation.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
5/2 + 6g = 11/4 solve it
Answer:
g = [tex]\frac{1}{24}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{2}[/tex] + 6g = [tex]\frac{11}{4}[/tex]
Multiply through by 4 to clear the fractions
10 + 24g = 11 ( subtract 10 from both sides )
24g = 1 ( divide both sides by 24 )
g = [tex]\frac{1}{24}[/tex]
the fourth term of an AP is 5 while the sum of the first 6 terms is 10. Find the sum of the first 19 terms
Answer: S₁₉ = 855
Step-by-step explanation:
T₄ = a + ( n - 1 )d = 5 , from the statement above , but n = 4
a + 3d = 5 -------------------------1
S₆ = ⁿ/₂[(2a + ( n - 1 )d] = 10, where n = 6
= ⁶/₂( 2a + 5d ) = 10
= 3( 2a + 5d ) = 10
= 6a + 15d = 10 -----------------2
Now solve the two equation together simultaneously to get the values of a and d
a + 3d = 5
6a + 15d = 10
from 1,
a = 5 - 3d -------------------------------3
Now put (3) in equation 2 and open the brackets
6( 5 - 3d ) + 15d = 10
30 - 18d + 15d = 10
30 - 3d = 10
3d = 30 - 10
3d = 20
d = ²⁰/₃.
Now substitute for d to get a in equation 3
a = 5 - 3( ²⁰/₃)
a = 5 - 3 ₓ ²⁰/₃
= 5 - 20
a = -15.
Now to find the sum of the first 19 terms,
we use the formula
S₁₉ = ⁿ/₂( 2a + ( n - 1 )d )
= ¹⁹/₂( 2 x -15 + 18 x ²⁰/₃ )
= ¹⁹/₂( -30 + 6 x 20 )
= ¹⁹/₂( -30 + 120 )
= ¹⁹/₂( 90 )
= ¹⁹/₂ x 90
= 19 x 45
= 855
Therefore,
S₁₉ = 855
Find the radius of the circle with equation x^2 + y^2 - 10x - 16y + 53 = 0.
Answer:
radius = 10.5 unitsStep-by-step explanation:
Equation of a circle is given by
x² + y² + 2gx + 2fy + c = 0
To find the radius of the circle we use the formula
[tex]r = \sqrt{ {g}^{2} + {f}^{2} - c } [/tex]
where g and f is the center of the circle
From the question
x² + y² - 10x - 16y + 53 = 0
Comparing with the general equation above we have
2g = - 10 2f = - 16
g = - 5 f = - 8
c = 53
Substitute the values into the above formula
That's
[tex]r = \sqrt{ ({ - 10})^{2} + ( { - 8})^{2} - 53 } [/tex]
[tex]r = \sqrt{100 + 64 - 53} [/tex]
[tex]r = \sqrt{111} [/tex]
We have the final answer as
radius = 10.5 unitsHope this helps you
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 35% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality.
Answer:
The conclusion about p using an absolute value inequality is
[tex]0.325 < p < 0.375[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.35[/tex]
The margin of error is [tex]E = 0.025[/tex]
The confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.35 - 0.025 < p < 0.35 + 0.025[/tex]
=> [tex]0.325 < p < 0.375[/tex]
Find the distance between (8,4) and (8,8).
Answer:
From the given points above, the distance between them is 4 units.
Step-by-step explanation:
In order to find the distance between the two points, we must know the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now, we plug in our numbers from the coordinate points that we are given to their respectful places.
[tex]d=\sqrt{(8-8)^2+(8-4)^2}[/tex]
Now, we solve. First, simplify the terms in parentheses. So, subtract 8 from 8 and subtract 4 from 8.
[tex]d=\sqrt{(0)^2+(4)^2}[/tex]
Next, solve for the exponents.
[tex]d=\sqrt{0+16}[/tex]
Add the numbers in the radical.
[tex]d=\sqrt{16}[/tex]
Solve the radical.
[tex]d=4[/tex]
So, the distance between the two given points is 4 units.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Years in which U.S. presidents were inaugurated
Answer:
Interval Level of Measurement
Step-by-step explanation:
The Interval level of measurement highlights the distances between two measurements. These distances are meaningful and could be rated as low intervals or high intervals. Intervals also indicate class and order between measurements. The inauguration of the United States President is an event that occurs 72 to 78 days after the presidential election. It is usually done as a private and public oath-taking ceremony on January 20, four years after the last presidential election. So, even if the president is on a second term, this event must be held.
The last U.S presidential election occurred on January 20, 2017, and the next one will be held on January 21, 2021. So there is an interval of four years between the last and next U.S presidential inauguration ceremony.
what is the prime factorization of 55^5 x 65 x 9^15 and why? A. 3^15 * 5^6 *11^5*13 B. 3^30 *5^6 *11^5 *13 C.3^30 * 5^6 *11 * 13 D. 3^30 *5^5*11^5*13
Answer:
B
Step-by-step explanation:
1. Lets focus on 55^5
55^5 = 11^5 * 5^5
2. now on 65
65 = 5 * 13
3. now on 9^15
9^15=(3^2)^15 = 3^30
4. combine all three parts
11^5 * 5^5 * 5 * 13 * 3^30 = 11^5*5^6*13*3^30
so our answer is B
-x + 3y = 3
x - 3y = 3
Does this system have a solution?
Answer:
No solution
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write out systems of equations
-x + 3y = 3
x - 3y = 3
Step 2: Rewrite equations into slope-intercept form
3y = 3 + x
y = 1 + x/3
-3y = 3 - x
y = -1 + x/3
Step 3: Rewrite systems of equations
y = x/3 + 1
y = x/3 - 1
Since we have the same slope for both equations but different y-intercepts, we know that both lines are parallel. If that is the case, they will never touch or intersect each other. Therefore, we have no solution.
Consider the age distribution in the United States in the year 2075 (as projected by the Census Bureau). Construct a cumulative frequency plot and describe what information the plot communicates about the distribution of ages in the future.
Answer:
The cumulative frequency plot is also attached below.
Step-by-step explanation:
The data provided is as follows:
Age Group Frequency
0 - 9 34.9
10 - 19 35.7
20 - 29 36.8
30 - 39 38.1
40 - 49 37.8
50 - 59 37.8
60 - 69 34.5
70 - 79 27.2
80 - 89 18.8
90 - 99 7.7
100 - 109 1.7
Consider the Excel output attached.
The cumulative frequency are computed in the Excel sheet.
The cumulative frequency plot is also attached below.
From the cumulative frequency plot it can be seen that in the future most people will belong to a higher age group rather then the lower ones.
Jessica just bought a refrigerator for $799. She paid $79.80 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
$179.80
Step-by-step explanation:
799-79.80=719. That's the down payment subtracted from the total price of the refrigerator. 719/4, since there's four equal installments, gives you 179.8. Since cents go in 10s, you make it 179.80 and slap a dollar sign in front of that.
Apply the square root property of equality.
x + =
Answer:
Step-by-step explanation:
Answer:
+ 1/16 = +- 2/3
Simplify to create an equivalent expression. 7n-(4n-3) a=3n+3 b=3n−3 c=11n+3 d=11n−3 I will rate you brainliest. :)
Answer:
3n +3
Step-by-step explanation:
7n-(4n-3)
Distribute the minus sign
7n -4n +3
3n +3
Consider the following two questions designed to assess quantitative literacy: a. What is 15% of 1000? b. A store is offering a 1596 off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale? Suppose the first question is asked of 200 randomly selected college students, with 165 answering correctly; the second one is asked of a different random sample of 200 college students, resulting in 142 correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Use p1 for the true proportion students who answered the question without context correctly and p2 for the true proportion of students who answered the question with context correctly.) Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context.
Answer:
The calculated value of z= 2.7225 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.
Step-by-step explanation:
a: 15 % of 1000= 150
b. 15.96 % of $ 1000= $ 159.6
The customer would pay = $ 1000- $ 159.6= $ 840.4 and save $ 159.6
Formulate the hypotheses as
H0: p1= p2 true proportion of correct responses to the question without context is equal that for the one with context.
Ha : p1≠ p2
We choose the significance level ∝= 0.05
The critical value for two tailed test at alpha=0.05 is ± 1.96
The test statistic is
Z = p1-p2/ √pq (1/n1+ 1/n2)
p1= true proportion students who answered the question without context correctly = 165/200=0.825
p2= true proportion of students who answered the question with context correctly = 142/200= 0.71
p = an estimate of the common rate on the assumption that the two proportions are same.
p = n1p1+ n2p2/ n1 + n2
p =200 (0.825) + 200 (0.71) / 400
p= 165+ 142/400= 307 /400 =0.7675
now q = 1-p= 1- 0.7675= 0.2325
Thus
z= 0.825- 0.71/ √0.7675*0.2325( 1/200 + 1/200)
z= 0.115/√ 0.17844( 2/200)
z= 0.115/0.04224
z= 2.7225
The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.
