Answer:
Height = 6000 m
Step-by-step explanation:
[tex]Volume = length \times breadth \times height \\\\480000 = 10 \times 8 \times height\\\\480000 = 80 \times height\\\\height = \frac{480000}{80} = 6000 \ m[/tex]
The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240. A) Find the first term. B) Find the common ratio. C) Justify your answers by showing steps that demonstrates your answers generate S8=19680 and S4=240.
Answer:
First Term = 6
Common Ratio = 3
Step-by-step explanation:
According to the Question,
Given, The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240 .Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .
The Sum of n-term of Geometric Mean is [tex]S_{n} = \frac{a(r^{n-1)} }{r-1}[/tex] Where, r>1 , a=First term of G.P & r=common Ratio .Now, on solving [tex]\frac{S_{8} }{S_{4} }[/tex] we get,
[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]
[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]
[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )
So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .
Seventh Grade Students
Instrument # of Students
Guitar 12
Bass 10
Drums 9
Keyboard 12
Eighth Grade Students
Instrument # of Students
Guitar 5
Bass 6
Drums 15
Keyboard 5
Based on these results, express the probability that a seventh grader chosen at random will play the drums as a fraction in simplest form.
Answer:
3/11Step-by-step explanation:
FORMULA= P(A)=
NUMBER OF FAVORABLE OUTCOMES
-------------------------------------------------------------
NUMBER OF POSSIBLE OUTCOMES
GIVEN: 12 Guitars, 10 Bass, 9 Drums, 12 Keyboards
WANT: The probality a seventh grader chosen at randome will play drums
add all the instruments
12+10+9+12=33
there are 9 drums
FOLLOW THE FORMULA
9 3
---- = ---- SIMPLIFIES FORM
33 11
1. Which two points fail the VLT here in this graph?
PLEASE HELP!!!!
(1.3) Sequence A: 4; 7; 10; 13; 16; Sequence B: 5; 10; 20; 40; 80; .......... Sequence C: 2; 5; 10; 17; 26; (1.3.1) Write down the next three numbers in each of given sequences. (3) Sequence A Sequence B: Sequence C: (1.3.2) Write down how you decided what the next number would be in each of the three sequences. (3) Sequence A: Sequence B: Sequence C
Answer with Step-by -step explanation:
Sequence A;4,7,10,13,16
[tex]a_2-a_1=7-4=3[/tex]
[tex]a_3-a_2=10-7=3[/tex]
The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.
Common difference, d=3
a=4
[tex]a_n=a+(n-1)d[/tex]
[tex]a_6=a+5d=4+5\times 3=19[/tex]
[tex]a_7=a+6d=4+6(3)=22[/tex]
[tex]a_8=a+7d=4+7(3)=25[/tex]
Sequence B: 5,10,20,40,80,...
[tex]a_1=5,a_2=10,a_3=20[/tex]
[tex]\frac{a_2}{a_1}=\frac{10}{2}=2[/tex]
[tex]\frac{a_3}{a_2}=\frac{20}{10}=2[/tex]
The ratio of two consecutive terms is equal. Therefore, it forms geometric sequence.
Common ratio, r=2
a=5
[tex]a_n=a r^{n-1}[/tex]
[tex]a_6=ar^5=5(2)^5=160[/tex]
[tex]a_7=ar^6=5(2^6)=320[/tex]
[tex]a_8=ar^7=5(2^7)=640[/tex]
Sequence C:2,5,10,17,26,..
a1=2
[tex]a_2=5=2+3=a_1+3[/tex]
[tex]a_3=10=5+5=a_2+5[/tex]
[tex]a_4=17=10+7=a_3+7[/tex]
[tex]a_5=26=17+9=a_4+9[/tex]
From the following pattern
We can get
[tex]a_6=a_5+11=26+11=37[/tex]
[tex]a_7=a_6+13=37+13=50[/tex]
[tex]a_8=a_7+15=50+15=65[/tex]
Financial software can do all of the following except ____.
A.
prepare your taxes
B.
apply for loans
C.
keep track of expenses
D.
monitor your savings
Answer: Apply for loans
Step-by-step explanation:
I just took the quiz off gradpoint :) trust me its right!!!!
Which equation represents a line that passes through the two points in The table
Answer:
y = mx + by= mx+ b
Step-by-step explanation:
since we know the two points on the line. we use the two points formed to find its equation. the final equation.the slope intercept form ,y=mx+by = mx+b
In triangle ABC, b = 600, ∠B = 11°, and ∠C = 75°. Find a.
Answer:
Step-by-step explanation:
We could use the Law of Sines if we only knew what angle A was. It just so happens that by the Triangle Angle-Sum Theorem, angle A is equal to
180 - B - C. Therefore,
angle A = 180 - 11 - 75 so
angle A = 94. And the Law of Sines is
[tex]\frac{sin94}{a}=\frac{sin11}{600}[/tex] and cross multiply to get
600sin94 = asin11 and solve for a:
[tex]a=\frac{600sin94}{sin11}[/tex] gives you that
a = 3136.85
If a is an odd number, b is not divisible by 3 and LCM of a and b is P, what is the LCM of 3a and 2b?
Answer:
The LCM of 3a and 2b = 6P
Step-by-step explanation:
LCM of 3 a and 2 b will be 6 p
Since a is odd, which means it's not divisible by 2. Therefore a can be number 1, 3, 5, 7, 9, 11, .......
b is not divisible by 3, which means b can be number 1, 2, 4, 5, 7, 8, 10, 11, .....
LCM of a and b is P
Factors of 2b can be 2 multiplied by (1, 2, 4, 5, 7, 8, 10, 11, ..... )
Factors of 3a can be 3 multiplied by (1, 3, 5, 7, 9, 11, .......)
So, to get the LCM of 3a and 2b, since we already show the factors of a and b, Then, 3 X 2 X P (remember P is the LCM of a and b)
The LCM of 3a and 2b = 6P
Line x line y find the measures of angle 4
Answer: The measure of angle 4 is 95 degrees.
Step-by-step explanation:
Knowing that the lines are parallel that means the alternate exterior angles are congruent. The alternate exterior angle of the angle marked with 95 degrees is angle 1. That means angle one is 95 degrees. Angle 1 and Angle 4 are vertical angles. All vertical angles are congruent so this mean angle 4 is also 95 degrees.
When 345 is multiplied by a power of 10 the number of zeros in the product is related to the power of 10. Explain how the number of zeros relates to the power of 10.
Answer:
The Number of Zeroes In The Results is Always equal To the Powers of 10.
Step-by-step explanation:
Example:-
345*[tex]10^{2}[/tex] = 34500
345*[tex]10^{5}[/tex] = 34500000
345*[tex]10^{7}[/tex] = 3450000000
345*[tex]10^{8}[/tex] = 34500000000
(In the Above examples, There is All The Numbers of Zeroes In The Results is equal To the Powers of 10)
Edna has a new St. Bernard puppy. He found a mud puddle on their last walk, so Edna needs to give him a bath. She buys a bottle of dog shampoo that costs $3.99. The bottle contains 28.5 ounces of shampoo. What is the cost per ounce of shampoo?
Answer: 7.142857142857143
Step-by-step explanation: all you have to do is divide 28.5 by 3.99
The cost per ounce of shampoo is 7.15 ounce.
Assume that the cost per ounce of shampoo is ${x}.
Total cost of bottle of a dog shampoo is $3.99.
Amount of shampoo in the bottle is 28.5 ounces.
So, we can write the cost per ounce of shampoo as
x = 28.5/3.99
x = 7.15 ounce
The cost per ounce of shampoo is 7.15 ounce.
To solve more questions on division, visit the link below-
https://brainly.com/question/15381501
#SPJ2
classify the expression by both degree and terms 2x4 - x +5
Answer:
x=3
Step-by-step explanation:
I need help on this hurry please
Answer:
x=70
Step-by-step explanation:
sum is angles of a Pentagon=540°
x°+138°+2x°+80°+112°=540°
3x°+330°=540°
3x°=540°-330°
3x°=210°
3x°/3°=210°/3°
x=70
hope this is helpful
What is the value of the 9 in the number 0.09432
Answer:
hundredths
Step-by-step explanation:
Numbers after the decimal start with
tenth
hundredth
please give answer of 6 number
Answer:
[tex]7,500[/tex]
Step-by-step explanation:
Let's solve this problem step-by-step. The library had 1,500 books in 2011. The ratio of books in 2011 and in 2012 is 1:2. Therefore, let the number of books in 2012 be [tex]x[/tex].
We have the following proportion:
[tex]\frac{1}{1,500}=\frac{2}{x},\\x=2\cdot 1,500=3,000[/tex]
Therefore, there were 3,000 books in 2012. The ratio of books in 2012 and in 2013 is 2:5. Let the number of books in 2013 be [tex]y[/tex].
We have:
[tex]\frac{2}{3,000}=\frac{5}{y},\\2y=5\cdot 3,000,\\2y=15,000\\y=\boxed{7,500}[/tex]
Therefore, there were 7,500 books in 2013.
Answer:
7,500 books
Step-by-step explanation:
is 15 over -4 negative
Answer:
15 is larger than -4
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
15 ÷ (-4) = -3.75
the question is on the image
Answer:
70
Step-by-step explanation:
the fraction 7/10 turns into 70% which means 70 out of 100 tickets were sold.
Answer:
70 tickets sold
Step-by-step explanation:
Multiply the number of tickets by the fraction of tickets sold
100 *7/10
Rewriting
100/10 * 7
10*7
70
Please help I wanna pass
Answer:
Everything is correct except for the second one and the ones you checkmarked.
Step-by-step explanation:
What is the angle measure ?
Answer:
140 degrees
Step-by-step explanation:
Kate is 1 year and six months younger than her sister. If her sister is 14 years and 2 months old, how old is Kate?
Answer:
Kate is 13years and 4 months old,I suggest.
Which conversion factor would you use to convert from meters to feet?
Answer:
To convert a meter measurement to a foot measurement, multiply the length by the conversion ratio. The length in feet is equal to the meters multiplied by 3.28084.
Step-by-step explanation:
URGENT: If θ is a second-quadrant angle and cosθ = -2/3, then tanθ = _____.
In the second quadrant, both cos and tan are negative while only sin is positive.
To find tan, we will use the following property below:
[tex] \large \boxed{ {tan}^{2} \theta = {sec}^{2} \theta - 1}[/tex]
Sec is the reciprocal of cos. If cos is a/b then sec is b/a. Since cos is 2/3 then sec is 3/2
[tex] \large{ {tan}^{2} \theta = {( - \frac{3}{2}) }^{2} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - \frac{4}{4} \longrightarrow \frac{5}{4} } \\ \large{tan \theta = \frac{ \sqrt{5} }{ \sqrt{4} } } \\ \large \boxed{tan \theta = \frac{ \sqrt{5} }{2} }[/tex]
Since tan is negative in the second quadrant. Hence,
[tex] \large{ \cancel{ tan \theta = \frac{ \sqrt{5} }{2} } \longrightarrow \boxed{tan \theta = - \frac{ \sqrt{5} }{2} }}[/tex]
Answer
tan = -√5/27. From eye level 5 feet off the ground, a person has to look up at an angle of 35
degrees to see the top of a tree 60 feet away. How tall is the tree.
Answer:
47.01 ft
Step-by-step explanation:
answer in photo above
can you help me do this Q I can't seem to get it :)
9514 1404 393
Answer:
x = 3∠IEH = 61°∠IHE = 35°Step-by-step explanation:
There are a couple of useful facts about parallelograms that can be used here.
1) The diagonals bisect each other.
2) Opposite sides are parallel, so each diagonal can be considered a "transversal" with respect to parallel lines. That means all of the angle relationships involving parallel lines apply.
__
The two marked sections of diagonal GIE are congruent, so you have ...
3x +1 = 10
3x = 9 . . . . subtract 1
x = 3 . . . . . divide by 3
__
Angles IEH and IGF are "alternate interior" angles, so are congruent.
angle IEH = 61°
__
Angles IHE and IFG are "alternate interior" angles, so are congruent.
angle IHE = 35°
1. Solve for x.
55°
(3r + 23)
75°
Answer:
The value of x is 9.
Step-by-step explanation:
55°
(3 x + 23)
75°
The sum of all the angles of triangle is 180°.
55 + 3 x + 23 + 75 = 180
3 x = 27
x = 9
So, the value of x is 9.
A fair dice is rolled 3 times in a row. The outcomes are shown below.
Calculate the probability of all three events occurring.
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{1}{6} + \frac{1}{6} + \frac{1}{6} =\frac{1}{2}[/tex]
ONE reason why people loan money from banks.
Answer:
to use the money when in an emergency
pls ans this
its urgent
What's the domain of the graph?
Step-by-step explanation:
In interval form, the domain of f is (−∞,∞).
30 POINTS + BRAINLIEST!!! PLEASE HELP ASAP!!!
Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule.
Answer:
CNBD
Step-by-step explanation:
From the diagram, we can see that:
[tex]\displaystyle BL\parallel CA[/tex]
Then by Alternate Interior Angles:
[tex]\angle LBA\cong \angle CAB\text{ and } \angle BLC\cong \angle ACL[/tex]
From vertical angles, we also know that:
[tex]\displaystyle \angle BKL\cong \angle AKC[/tex]
This is all we can gather from the given image. Knowing only three pairs of angles cannot prove congruence, as proving congruence requires at least one side.
Congruence cannot be determined.
Answer:
Cannot be determined
Step-by-step explanation:
With BL and AC being parallel, we can deduce that the two triangles in question share all three of their angles. However, there is no information given that implies any of the sides are equal. AAA (Angle-Angle-Angle) is a proof of similarity, but not congruence, therefore the two triangles cannot be determined to be congruent.