Answers
Answer:
1. [tex]2^{3}[/tex] x [tex]3^{6}[/tex]
ii. 18
b. -12
2. nth = a + (n - 1)d
ii. k = 103
3. [tex]x^{o}[/tex] = [tex]27^{o}[/tex]
4. Volume = 25.025 [tex]m^{3}[/tex]
Step-by-step explanation:
1. Prime factors of 5832 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
= [tex]2^{3}[/tex] x [tex]3^{6}[/tex]
ii. [tex]\sqrt[3]{5832}[/tex] = 18
b. 2[tex]a^{2}[/tex] - 3[tex]b^{2}[/tex] + 3abc
a = 3, b = 2, c = -1
Thus,
2[tex](3)^{2}[/tex] - 3[tex](2)^{2}[/tex] + 3(3 x 2 x -1)
= 18 - 12 - 18
= -12
2. The required formula is;
nth = a + (n - 1)d
where: a is the first term, n is the number of terms in the sequence and d is the common difference.
b. kth term = 304, then
304 = -2 + (k - 1) 3
= -2 + 3k -3
= 3k - 5
3k = 304 + 5
3k = 309
k = [tex]\frac{309}{3}[/tex]
= 103
k = 103
3. Comparing <DAB and < EBC;
<DAB ≅ <EBC = [tex]x^{o}[/tex]
<BEC = [tex]90^{o}[/tex] (right angle property)
<C = [tex]63^{o}[/tex]
Thus,
<B + <C + <E = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]x^{o}[/tex] + [tex]63^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex]
[tex]x^{o}[/tex] + 153 = [tex]180^{o}[/tex]
[tex]x^{o}[/tex] = 180 - 153
= 27
[tex]x^{o}[/tex] = [tex]27^{o}[/tex]
4. Volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius and h is the height of the cylinder.
Diameter = 3.5 m, h = 2.6 m
r = [tex]\frac{3.5}{2}[/tex]
r = [tex]\frac{7}{4}[/tex] m
So that,
Volume = [tex]\frac{22}{7}[/tex] x [tex](\frac{7}{4}) ^{2}[/tex] x 2.6
= [tex]\frac{22}{7}[/tex] x [tex]\frac{49}{16}[/tex] x [tex]\frac{13}{5}[/tex]
= 25[tex]\frac{1}{40}[/tex]
Volume = 25.025 [tex]m^{3}[/tex]
Related Questions
how to write expression for The product of ten less than a number and the number
Answers
Answer:
x-10
Step-by-step explanation:
ten is less than x
follow me for more answer
What is the factorization of the trinomial below?
x2 - 6x + 5
O A. (X - 4)(x - 2)
O B. (X - 5)(x - 1)
O C. (x + 4)(x - 2)
O D. (x + 5)(x - 1)
Answers
B. [tex](x - 5)(x - 1)[/tex] ✅
Step-by-step explanation:
[tex] {x}^{2} - 6x + 5 \\ \\ = \:{x}^{2} - 5x - x + 5 [/tex]
Taking [tex]x[/tex] as common from first two terms and 1 from last two terms, we have
[tex] =\: x(x - 5) - 1(x - 5)[/tex]
Taking the factor [tex](x-5)[/tex] as common,
[tex]=\:(x - 5)(x - 1)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Which expression and diagram represent “three times a number”?
3 x right-arrow 3 boxes with x and 3 boxes with minus signs
3 x right-arrow 3 boxes with x
3 + x right-arrow 2 boxes with x and 3 boxes with plus signs
x + 3 right-arrow 3 boxes with plus signs
Answers
Answer:
b
Step-by-step explanation:
Answer:
took the test, it is B like the other person said!!
A flower garden is the shape of a circle. The circumference of the garden is 20 meters. What is the area of the garden. Use 3.14 for pie and round your answer to the nearest whole number.
Answers
Answer:
Circumference = 2 pi r = 2*3.14 *r = 20
radius r = 20 / 2*314 = 3.185
Area = pi r^2 = 3.14 * 3.185^2 = 32 m^2 to nearest whole number
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint 1: (−1,2) Midpoint: (9,−6) Endpoint 2=
Answers
PT=3x+3 and TQ=6x-6
Use the figure to the right to find the value of PT. T is the midpoint of PQ
Answers
Answer:
PT = 12 units
Step-by-step explanation:
Given that,
PT=3x+3 and TQ=6x-6
T is the midpoint of PQ.
If T is mindpoint of PQ, it means,
PT = TQ
Substitute all the values,
3x+3 = 6x-6
Taking like terms together,
3x-6x = -6-3
-3x = -9
x = 3
So,
PT = 3x+3
= 3(3) + 3
= 9+3
= 12
So, the value of PT is equal to 12 units.
All of the following solid figures except a _____ have two bases.
Answers
Answer:
All of the following solid figures except a square pyramid have two bases.
A box has seven orange hats and 19 yellow hats if you pick three hats without replacement what is the probability that you pick at least two orange hats from the box?
Answers
Answer:
a chance of 3.16
Step-by-step explanation:
PLEASE HELP ASAP NO LINKS OR WILL BE REPORTED I NEED THIS LIKE RIGHT NOW PLEASE HURRY SHOW ALL OF YOUR WORK! (b) What is 1.363636... expressed as a fraction in simplest form? SHOW ALL OF YOUR WORK ( c) what is 5.152 expressed as a fraction in simplest form? SHOW ALL OF YOUR WORK
Answers
Answer:
1.3636363636...
can be expressed as
1 + 4/11
I tried out different fractions
1/11 is just 0.09090909...
4/11 is 4 times thar
1 = 11/11
so it's just 15/11
5.152
can be written as
[tex] \frac{5.152}{1} [/tex]
or as
[tex] \frac{5152}{1000} [/tex]
simplified with 8
[tex] \frac{644}{125} [/tex]
What is the Answer
Please Help
Answers
Answer:
Step-by-step explanation:
circumference=2πr
=2*3.14*2
=12.56 km
I NEED IT FASTTTTTTTTTTTTTTT
Answers
Answer:
17
Step-by-step explanation:
2x^2=50 solve the equation algebraically?
Answers
define prism and itz color
Answers
Answer:
triangle piece of glass that different colors of light travel through
BRAINLIEST PLS HELP
(05.03)
Identify the initial value and rate of change for the graph shown
initial value:1,rate of change 3/5
initial value:3/5 ,rate of change 5/3
initial value :1,rate of change 5/3
initial value:5/3,rate of change:0
Answers
Answer:
the initial value is 1, rate of change 3/5
Step-by-step explanation:
rate of change is the slope, which is not zero and is def not 5/3
it started at 1, so thats the initial value
which expresion is equivalent to-12(3x-3/4)
A -36x-8
B -36x+8
C -36x-9
D -36x+9
Answers
8. In rural third world countries, farmers use a
conical bucket, the "Gầu Dây” to drain/transfer
water from one rice field to another. If the height
is 20" & the diameter of the opening is 15”, how
much cubic feet of water can two farmers drain
in three hours if their rate is 28 “gầu" per
minute?
Answers
9514 1404 393
Answer:
6872 cubic feet
Step-by-step explanation:
The volume of the conical bucket is ...
V = 1/3πr²h
V = 1/3π(15/2 in)²(20 in) = 375π in³
There are 60 minutes in 1 hour, so 3×60 = 180 minutes in 3 hours.
If each of 2 farmers can transfer 28 buckets per minute the total amount transferred is ...
(375π in³)(180 min)(2 farmers)(28/min/farmer) = 3,780,000π in³
There are 1728 in³ in 1 ft³, so this is ...
(3,780,000π/1728) ft³ = 2187.5π ft³, about 6872 cubic feet.
Calculate a critical z-score for a left-tailed, right-tailed, or two-tailed test.
a. The critical z-score for a left-tailed test at a 12% significance level is -0.45.
b. The critical z-score for a right-tailed test at a 9% significance level is 1.34.
c. The critical z-score for a two-sided test at a 4% significance level is 1.75.
d. The critical z-score for a two-sided test at a 20% significance level is 0.85.
Answers
Answer:
a. Z = -1.175.
b. Z = 1.34.
c. |Z| = 2.054.
d. |Z| = 1.28.
Step-by-step explanation:
Z-score:
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.
a. The critical z-score for a left-tailed test at a 12% significance level
Left-tailed test: The region of interest is the 12th percentile or below.
Thus, the critical z-score is Z with a p-value of 0.12, so Z = -1.175.
b. The critical z-score for a right-tailed test at a 9% significance level
Right-tailed test: The region of interest is the 100 - 9 = 91th percentile and above.
Thus, the critical z-score is Z with a p-value of 0.91, so Z = 1.34.
c. The critical z-score for a two-sided test at a 4% significance level is 1.75.
Two-tailed test: The region of interest is between the 4/2 = 2th percentile and the 100 - (4/2) = 98th percentile.
Thus, the critical z-score is |Z| with a p-value of 0.02 or 0.98, so |Z| = 2.054.
d. The critical z-score for a two-sided test at a 20% significance level is 0.85.
Region of interest is between the 20/2 = 10th percentile and the 100 - (20/2) = 90th percentile.
Thus, the critical z-score is |Z| with a p-value of 0.1 or 0.9, so |Z| = 1.28.
(7.3 × 10-9) + (1.5 × 10−9) in standard form
Answers
Answer:
The answer in standard form is 70.
Answer:
(7.3*10-9)+(1.5*10-9)
(73-9)+(15-9)
64+6=70
Step-by-step explanation:
Question #7: Which revolution resulted from the division of society shown in this diagram?
(5 Points)
First Estate Second Estate
Third Estate
Magd
。
KUIN
பரிழப்பாகத் AARA
annu
MIA
AACAAN
Clergy
Nobles
Atées en
be eagere
1% of the people
owned 10%
of the land
2% of the people
owned 25%
of the land
Bab 2 828
Anu
AR SALE
M
Middle class, peasants, city workers
97% of the people owned 65% of the land
Source Schwartz and O'Connor Democracy and Nationalism Globe Book Company (adapted from the NYS Global History and Geography Regents
Exam August 2007
Puritan (1642)
French (1789)
Mexican (1910)
Russian (1917
Answers
Answer: French (1789)
Step-by-step explanation:
using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation 10.0y-4.55x=581. where x is the number of years after 2000 what is projected population in 2026?
Answers
Answer:
The projected population in 2026 is of 699.3 million.
Step-by-step explanation:
Population:
The population, in x years after 2000, is given by the follwing equation:
[tex]y - 4.55x = 581[/tex]
That is:
[tex]y(x) = 4.55x + 581[/tex]
What is projected population in 2026?
2026 - 2000 = 26, so this is y(26).
[tex]y(26) = 4.55(26) + 581 = 699.3[/tex]
The projected population in 2026 is of 699.3 million.
Which equation demonstrates the additive identity property?
(7 + 4 i) + (7 minus 4 i) = 14
(7 + 4 i) + 0 = 7 + 4 i
(7 + 4 i) (1) = 7 + 4 i
(7 + 4 i) + (negative 7 minus 4 i) = 0
Answers
Answer:
b. on edge
Step-by-step explanation: just did the quiz and got it right
Recounting Rectangles
How many rectangles are
there in the figure below?
Answers
Answer:
gimme a second, I'll comment
Someone help me please
whats the square root of 0.0025
Answers
Explanation: √0.0025=0.05
100 students attended a revision lesson at the weekend.
Each student went to Maths or English or Science.
55 of these students attended on Saturday.
Over the weekend a total of 40 students went to Maths.
12 of the 27 students that went to Science went on Sunday.
10 students went to English on Saturday.
How many students went to the Maths revision lesson on Saturday?
Answers
Answer:
I am pretty sure its 30 students
11
12
13
14
15
16
18
19
20
What is the value of x in the equation (3x + 12) = {(x + 14) – 3?
0
-24
46
0 0
Answers
Answer:
x = -24
Step-by-step explanation:
(2/3)(x/2 + 12) = (1/2)(x/3 + 14) - 3
2x/6 + 24/3 = x/6 + 14/2 - 3
2x/6 + 8 = x/6 + 7 - 3 = x/6 + 4
x/6 + 8 = 4
x/6 = -4
x = -24
Can someone help me solve this
Answers
Answer:
Yup! There are 6 possible 0s, 4 actual 0s, and the factored form is -2x^5-6
Step-by-step explanation:
Consider the graphs shown below. Look at each trend line.
Which line does a better job capturing the trend of the data? Explain.
Answers
Answer:
GraphB
Step-by-step explanation:
To obtain the best line of fit, we need the line which minimizes the sum of the squared distances, Therefore, from visual inspection, we can conclude that the best line of fit will be one in which the distance between each individual distance and the line of best fit is minimized, for the first graph, only the upper points are close to the regression line leaving the lower values further away, however, the secubd graph gives a more uniform distance between all the data values and the regression line. Hence, it does a better job at capturing the trend in the data.
Use the intercepts to graph the equation x-5=y
Answers
9514 1404 393
Answer:
see beow
Step-by-step explanation:
When x=0, y=-5. The y-intercept is (0, -5).
When y=0, x-5=0, so x=5. The x-intercept is (5, 0).
Plot these two points and draw the line through them.
Simplify the given expression and enter in numerical form.6+5
Answers
Answer:
6+5=11
Step-by-step explanation:
6 is added to 5
i am sorry if i am wrong
Max has 4/5 qt of apple juice. He drinks 1/2 qt of it. How many apple juice does he have left? (Give your answer in quarts)
Answers
Answer:
3/10 quarts.
Step-by-step explanation:
Set the denominators equal to one another.
4/5 = 8/10 (multiplied by a factor of 2)
1/2 = 5/10 (multiplied by a factor of 5)
Subtract the 5/10 from the 8/10
3/10 qt