12-6 1. What is the value of a÷a−4 when a=22÷2−4=2 2. For x=1 and y=−1, give the value of the expression 15x2y−3+18yx−1+27xy4 3. Find the integer k such that 33+33+33=243⋅3k (Hint: Express 243 as a power of 3 .) 4. Let a and b be nonzero numbers. Simplify (6a2b)2÷(3a2b3). Express your answer as a number times a power of a times a power of b. 5. 4−8((−2)2−4(−3)) 6. 5⋅25−(2⋅3)2
4 Find the following products:
a (2x2−3x+5)(3x−1)
b (4x2−x+2)(2x+5)
c (2x2+3x+2)(5−x)
d (x−2)2(2x+1)
e (x2−3x+2)(2x2+4x−1)
f (3x2−x+2)(5x2+2x−3)
g (x2−x+3)2
h (2x2+x−4)2(2x+5)3
) (x3+x2−2)2
3. A large tank is partially filled with a solution. The tank has a faucet that allows solution to enter the tank rate of 1643 liters per minute. The tank also has a drain that allows solution to leave the tank at a rate 1954 liters per minute.
(a) What expression represents the change in volume of solution in the tank in 1 minute?
(b) What is the change in volume of the solution after 15 seconds? Show necessary work.
(c) What does the change in volume after 15 seconds mean in the real world? Answer in complet sentences.
Answer:
A fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If Jeff keeps playing until he wins a prize, what is the probability that he has to play the game exactly 5 times?
(0.75)5(0.25)5(0.75)4(15)(0.75)4(0.25)(0.75)4(0.25)
Factor completely. Remember to look first for a common factor. Check by multiplying. If a polyno
−a6−4a5+96a4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. −a6−4a5+96a4=□
B. The polynomial is prime.
Each license plate in a certain state has six characters (with repeats allo
Here are the possibilities for each character.
\begin{tabular}{|c|l|}
\hline Character & \multicolumn{1}{|c|}{ Possibilities } \\
\hline First & The digits 1, 2, 3, 4, or 5 \\
\hline Second & The 26 letters of the alphabet \\
\hline Third & The 26 letters of the alphabet \\
\hline Fourth & The 10 digits 0 through 9 \\
\hline Fifth & The 10 digits 0 through 9 \\
\hline Sixth & The 10 digits 0 through 9 \\
\hline
\end{tabular} How many license plates are possible in this state?
NAME DATE PERIOD Lesson 1 Homework Practice
Estimate Products of Fractions
Estimate each product. 1. 31×28 ' 2. 71×20772 4. 111 of 47
(4) 5. 85×23 N 9. 53×92 7. 52 of 37 8. 76 of 51
el, 10. 87×54 11. 1910×87 12. 43×73
13. 276×341 14. 12109×641 15. 483×1772 Estimate the area of each rectangle.
16.
17. 18. SCULPTURE Trevor is using the recipe for sculpture-carving material shown at the right.
a. About how many cups of cement would he need to make 94 batch of the recipe?
b. About how many cups of sand would he need to make
\begin{tabular}{|l|}
\hline \multicolumn{1}{|c|}{ Girostone Recipe } \\
\hline 5 cup vermiculite \\
141 cup cement \\
85 cup sand \\
water to form thick paste \\
\hline
\end{tabular}
176 batches of the recipe?
Course 1 - Chapter 4 Multiply and Divide Fractions
53
II in the blank with the appropriate word or phrase. If p^ is the sample proportion and n is the sample size, then np^(1−p^) is the (Choose one)
sample standard deviation population standard deviation standard error sample proportion
Factor the trinomial completely.
x2−10x+9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice
A. x2−10x+9=□ (Type your answer in factored form:)
B. The polynomial is prime.
Jelissa and Yari are both computing the product of 0.05 and 0.3. Their work is below:
\begin{tabular}{|c|c|}
\hline Jelissa's Work & Yari's Work \\
\hline1005×103=100015 & 0.05×100=5 \\
& 0.3×10=3 \\
& 5×3=15 \\
& 15÷1,000=0.015 \\
\hline
\end{tabular}
a. Explain the similarities shown in Jelissa and Yari's work.
b. Explain the differences shown in Jelissa and Yari's work.
Write the expression log5(x83y13) as a sum of logarithms with no exponents or radicals.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline Basic & Funcs & Tri & & & & & × \\
\hline x & B & x & x□ & & n & ↑ & ↓ \\
\hline y & ( □ & |ㅁ| & π & ∞ & DNE & ← & ⟶ \\
\hline \multicolumn{6}{|l|}{Enter an algebraic expression [more.]} & \multicolumn{2}{|c|}{Q} \\
\hline
\end{tabular}
Select the correct answer. In a right triangle, if ∠θ=39∘ and the side adjacent to ∠θ is equal to 12.0 centimeters, what is the approximate length of the opposite side?
A. 7.6 centimeters
B. 9.3 centimeters
C. 9.7 centimeters
D. 14.8 centimeters
Example
Hummingbirds sip221flOz of the liquid food in a feeder. Then 121floz of food is added to the feeder. Last, hummingbirds sip another 341floz of food. What is the overall change in the amount of food in the feeder?
You can write an expression to represent the situation.
−221+121−341 To simplify the expression, you can first reorder the terms.
−221+121−341=−221−341+121=−543+121=−441 The overall change in the amount of food in the feeder is −441floz. The feeder in the Example had 16 fl oz of food in it to start. How much food does it have now? Show your work.
d. The p-value = 0.0735
(Please show your answer to 4 decimal places.)
e. The p-value is □α
f. Based on this, we should
fail to reject 0 the null hypothesis.
g. Thus, the final conclusion is that ...
The data suggest the populaton proportion is significantly smaller than 53% at α=0.05, so there is sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is smaller than 53%
The data suggest the population proportion is not significantly smaller than 53% at α=0.05, so there is not sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is smaller than 53%.
The data suggest the population proportion is not significantly smaller than 53% at α=0.05, so there is sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is equal to 53%.
h. Interpret the p-value in the context of the study.
If the population proportion of students who played intramural sports who received a degree within six years is 53% and if another 257 students who played intramural sports are surveyed then there would be a 10.1% chance fewer than 49% of the 257 students surveyed received a degree within six years.
There is a 53\% chance of a Type I error.
If the sample proportion of students who played intramural sports who received a degree within six years is 49% and if another 257 such students are surveyed then there would be a 10.1% chance of concluding that fewer than 53% of all students who played intramural sports received a degree within six years.
There is a 10.1% chance that fewer than 53% of all students who played intramural sports graduate within six years.
i. Interpret the level of significance in the context of the study.
If the population proportion of students who played intramural sports who received a degree within six years is 53% and if another 257 students who played intramural sports are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all students who played intramural sports who received a degree within six years is smaller than 53\%
There is a 5% chance that the proportion of all students who played intramural sports who received a degree within six years is smaller than 53%.
If the population proportion of students who played intramural sports who received a degree within six years is smaller than 53% and if another 257 students who played intramural sports are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all students who played intramural sports who received a degree within six years is equal to 53%.
There is a 5% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.
The township of Pee Pee, Ohio has a population of 7,500 people. Recently an outbreak of Cholera was documented for the first three months of 2021. In January, 1500 of the population contracted Cholera, in February 500 more residents contracted Cholera, and in March 100 residents contracted Cholera. No deaths were reported from the outbreak! 1. What is the initial prevalence? 2. What is the overall prevalence? 3. What was Jan's incidence? 4. What was Feb.'s incidence? 5. What was March's incidence?
g. Thus, the final conclusion is that ...
The data suggest the population proportion is not significantly larger 60% at α=0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 60%.
The data suggest the population proportion is not significantly larger 60% at α=0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger 60\%.
- The data suggest the populaton proportion is significantly larger 60% at α=0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger 60\%
h. Interpret the p-value in the context of the study.
There is a 0.33% chance that more than 60% of all voters prefer the Democratic candidate.
- If the population proportion of voters who prefer the Democratic candidate is 60% and if another 222 voters are surveyed then there would be a 0.33% chance that more than 69% of the 222 voters surveyed prefer the Democratic candidate. O
If the sample proportion of voters who prefer the Democratic candidate is 69% and if another 222 voters are surveyed then there would be a 0.33% chance of concluding that more than 60% of all voters surveyed prefer the Democratic candidate.
There is a 0.33% chance of a Type I error.
i. Interpret the level of significance in the context of the study.
If the population proportion of voters who prefer the Democratic candidate is 60% and if another 222 voters are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is larger 60\%
There is a 5% chance that the proportion of voters who prefer the Democratic candidate is larger 60\%.
There is a 5% chance that the earth is flat and we never actually sent a man to the moon.
If the proportion of voters who prefer the Democratic candidate is larger 60\% and if another 222 voters are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 60%.
Use scientific notation to determine which of these numbers has the greatest value: 654,987,034;645,897,430; or 546,789,340. Write your answer in scientific notation, expressed to the exact decimal place. (1 point)
Greenville County, South Carolina, has 396,183 adult residents, of which 80,987 are 65 years or older. A survey wants to contact n=689 residents. These are 2018 population counts, found online
at datausa.io/profile/geo/greenville-county-sc.
Find p, the proportion of Greenville county adult residents who are 65 years or older. Give your answer to four decimal places.
p=□
A survey of 2279 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 421 have donated blood in the past two years. Complete parts (a) through (c) below.
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
p^=0.185
(Round to three decimal places as needed.)
(b) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample □ a simple random sample, the value of p^(1−p^) is □ , which is
□□ less than or equal to 5% of the □ (Round to three decimal places as needed.)
(c) Construct and interpret a 90\% confidence interval for the population proportion of adults in the country who have donated blood in the past two years. Select the correct choice below and fill in any answer boxes within your choice.
(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)
A. There is a □ \% probability the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between □ and □ .
B. We are □ \% confident the proportion of adults in the country aged 18 and older who have donated blood in the
Cesimplfy
Q(P⇒P)⇒¬(Q⇒(Q)T⇒¬(¬6⇒Q)T⇒¬(¬T)T⇒¬FT⇒I always true
(2) (7P∧φ)∨(¬P∧Q) Q/Find the converse and contrapositive "If Muna is studing for the mid-term exam then it is not hoilday time
Самостоятельная работа по теме: «Свойства степеней» ВАРИАНТ 2
o 1. Представьте в виде степени произведение:
1) x9x2;
2) 711⋅73
3) (a+b)(a+b)7
4) aa7;
5) m4m5m11
Вариант 2
1) Выполните умножение одночленов
a) 43xy2⋅16y
б) 1,6a2c⋅(−2ac2)
в) −x3y4⋅1,4x6y5
2) Возведите одночлен в указанную степень
a) (−10x2y6)3
б) (−31xy)4
в) −(3a2b)3
3) Выполните действия
a) 35a⋅(2a)2
в) (−81x2y3)⋅(2x6y)4
Вариант 1
1) Выполните умножение одночленов
a) 32a⋅12ab2
б) 0,5x2y⋅(−xy)
в) −0,4x4y2⋅2,5x2y4
2) Возведите одночлен в указанную степен
а) (−21ab)3
б) −(2kx2)2
B) (−10s3b2)4
3) Выполните действия
a) 20a3⋅(5a)2
б) −0,4x5(2x3)4
в) (3x6y3)4⋅(−811xy2)
Aufgabe 1:
Handelt es sich um eine Bernoulli-Kette? Geben Sie gegebenenfalls ihre Länge n und die Trefferwahrscheinlichkeit p an.
a) Eine ideale Münze wird zehnmal geworfen und es wird jedes Mal notiert, ob „Zahl" erscheint.
b) Eine "Münze" aus Knetmasse wird zehnmal geworfen und es wird jedes Mal notiert, ob „Zahl" erscheint.
c) Ein idealer Würfel wird siebenmal geworfen und es wird jedes Mal die Augenzahl notiert.
d) Ein idealer Würfel wird siebenmal geworfen und es wird jedes Mal notiert, ob eine Drei erscheint. Aufgabe 2: Das abgebildete Glücksrad wird dreimal gedreht.
a) Begründe, dass es sich dabei um eine Bernoullie-Kette handelt und gib die Länge n sowie die Trefferwahrscheinlichkeit p an.
b) Gib alle Ergebnisse an, die zu den folgenden Ereignissen gehören (in der Form bgb usw.). Berechne außerdem die Wahrscheinlichkeit dieser Ereignisse.
A: dreimal blau
B: zuerst blau, dann zwei mal gelb
C: genau ein mal blau Aufgabe 3: Eine verbeulte Münze wird vier mal geworfen.
a) Begründe, dass es sich dabei um eine Bernoullie-Kette handelt und gib die Länge n sowie die Trefferwahrscheinlichkeit p an.
b) Berechne die Wahrscheinlichkeit der folgenden Ereignisse. A: Es fällt einmal Zahl.
B: Es fällt dreimal Zahl.
C: Es fällt zweimal Zahl.