Answer:
[tex]a_{n} = 27 - 3(n-1)[/tex]
Step-by-step explanation:
Arithmetic sequences concepts:
The general rule of an arithmetic sequence is the following:[tex]a_{n+1} = a_{n} + d[/tex]
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
[tex]a_{n} = a_{1} + (n-1)*d[/tex]
And also:
[tex]a_{n} = a_{m} + (n-m)*d[/tex]
In this question:
[tex]a_{4} = 18, a_{7} = 9[/tex]
Finding the common ratio:
[tex]a_{n} = a_{m} + (n-m)*d[/tex]
[tex]a_{7} = a_{4} + (7-4)*d[/tex]
[tex]9 = 18 + 3d[/tex]
[tex]3d = -9[/tex]
[tex]d = \frac{-9}{3}[/tex]
[tex]d = -3[/tex]
Finding the first term:
[tex]a_{4} = a_{1} + (4-1)*d[/tex]
[tex]18 = a_{1} + 3*(-3)[/tex]
[tex]a_{1} = 27[/tex]
General rule:
[tex]a_{n} = a_{1} + (n-1)*d[/tex]
[tex]a_{n} = 27 - 3(n-1)[/tex]
SOMEONE PLEASE HELP ???
Which of the following proportionality statements is correct ?
Answer:
The third one is correct
Step-by-step explanation:
Standard Cost Journal Entries Bellingham Company produced 4,600 units that require five standard pounds per unit at a $10.5 standard price per pound. The company actually used 22,500 pounds in production. Journalize the entry to record the standard direct materials used in production. For a compound transaction, if an amount box does not require an entry, leave it blank.
Answer:
Dr work-in-process $ 241,500.00
Cr materials $236,250
Cr direct material quantity variance $ 5,250.00
Step-by-step explanation:
The cost of the materials using standard price per pound of $10.5 is computed below:
standard cost=4,600*5*$10.5=$241,500.00
The above is debited to work in process account.
The actual cost of materials used =22,500*$10.5=$236,250.00
Since the actual cost materials is $ 236,250.00 ,the materials ledger is credited with $ 236,250.00
The direct material quantity variance=$241,500-$236,250=$5,250
what’s the length of the tunnel?
Answer:
3.40 km
Step-by-step explanation:
Given two sides and the angle between them, the Law of Cosines is useful for finding the remaining side of the triangle.
If we call the vertices of the triangle H, P, Y, then the Law of Cosines tells you ...
HY² = HP² +YP² -2HP·YP·cos(P)
HY² = 6² +7² -2·6·7·cos(29°) = 85 -84·cos(29°) ≈ 11.531944
HY ≈ √11.531944 ≈ 3.40 . . . . km
The length of the tunnel is about 3.40 km.
An outdoor club conducted a survey of its members. The members were asked to state their preference between skiing and snowboarding. Each member had to pick one. Of the 60 males, 45 stated they preferred to snowboard. Twenty-two of the 60 females preferred to ski. What is the relative frequency that a male prefers to ski?
Answer:
Answer:
0.25
Step-by-step explanation:
Data provided in the question
Number of males = 60
Number of stated preferred to snowboard = 45
Number of females preferred to ski = 22
Based on the above information, the relative frequency male preferred to ski is
Before computing this first we have to calculate the number of ski picked which is
= Number of males - Number of stated preferred to snowboard
= 60 - 45
= 15
Now the relative frequency is
[tex]= \frac{Number\ of\ ski}{Number\ of\ males}[/tex]
[tex]= \frac{15}{60}[/tex]
= 0.25
A birthday party caterer counted the number of juice cups on the table. The cups contained different flavored juices and different shaped straws.
Heart-shaped straw Star-shaped straw
Orange juice 9 3
Grape juice 4 4
Pineapple juice 5 8
What is the probability that a randomly selected cup contains orange juice or contains a heart-shaped straw?
Simplify any fractions.
HELp PLEASE WITH CORRECT ANSWER I NEED HELP I
find the area of the triangle the height is 12 in and the base is 3 in.
will mark brainliest
Answer:
18in²
Step-by-step explanation:
Answer: I know da way hehhe
Step-by-step explanation:
Base times height / 2
12*3= 36/2 =18
Roblox:Supertasticgg just follow me on roblox
SUB TO FLAMINGO IF U GET IT RIGHT hehehheheh
1f 3/4 gallon of paint can cover 1/8 of the fence how many gallons will he need to paint the whole fence
Answer:
He will need 6 gallons of painting to paint the whole fence.
Step-by-step explanation:
Since 3/4 gallon of paint covered 1/8 of the fence, we have to multiply 3/4 by 8 in order to find the number of gallons that will paint the whole fence (because 8 x 1/8 = 1)
[tex]\frac{3}{4}[/tex] x [tex]\frac{8}{1}[/tex] = [tex]\frac{24}{4}[/tex] = 6
Hope this helps!
in schools lesson are 55 minutes long A Science lesson ends At 2:30 PM What time does it start
Answer:
1:35
Step-by-step explanation:
Answer:
1: 35pm
Step-by-step explanation:
Find the distance between the points (-8,-11) and (14,-11).
Answer:
Distance =(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√
Step-by-step explanation:
The answer is provided above.
Distance =(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√
Hope this helps.
What is the slope of a line that passes through the points (-1,9) and (3,6)
Answer:
-3/4
Step-by-step explanation:
Between these two points, the x value changes by 4, and the y value changes by -3. Therefore, the slope of this line is -3/4. Hope this helps!
What equation relates a and s to the $ 400 income total? Explain what
each term of the equation represents.
Answer:
You would need to show us what terms there are by taking a picture
Joel had 4 liters of water. He drank 2.7 liters of water while he was hiking. How many liters does Joel have left?
Answer:
1.3 liters are left
Step-by-step explanation:
Take the amount of water he had and subtract the amount of water he drank
4.0
-2.7
-----------
Borrow
3.10
-2.7
-----------
1.3 liters are left
Answer:
1.3 liters
Step-by-step explanation:
In the given question: "Joel had 4 liters of water, and drank 2.7 liters of water while he was hiking. "
Subtract the total before the hike by the amount he drank during the hike.
[tex]4-2.7=1.3[/tex]
Joel should have 1.3 liters left.
Which statements about the cone are true? Check all that apply. The radius is double the diameter. The radius is 9 mm. The base area is calculated using the radius. The volume is one-third the volume of a cylinder with the same height and diameter. The volume of the cone is
Step-by-step explanation:
I think the question is incomplete without an attachment of the diagram of the cone, but we can make do with the information provided.
This problem test our knowledge on the mensuration of solid shape, cone and cylinder.Back to our question. the statements that apply are
The base area is calculated using the radiusThe volume is one-third the volume of a cylinder with the same height and diameter .the volume of the cone is expressed as [tex]v= \frac{1}{3}\pi r^{2}h[/tex]Answer:
2 3 4 5
Step-by-step explanation:
Multiple choices answer and explain the solution?
Answer:
associative property of multiplication
Step-by-step explanation:
You cant rlly explain, you just have to know your properties
Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.
Two angles measuring 180 are supplementary.
Answer: A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.
Step-by-step explanation:
A video company randomly selected 100 of its subscribers and asked them how many hours of shows they watch per week. Of those surveyed 35 watch more than 10 hours per week. Based on the data, if the company has 3,000 subscribers, how many watch more than 10 hours per week?
Hello there!
35/100 watch more then 10 hours a week
3000 is 30 times greater than 100 so we can simply multiply 35/100 by 30.
35/100 x 30 = 1050/3000
Therefore, if the company had 3,000 subscribers, 1,050 subscribers would be watching more than 10 hours a week.
Find ,H assuming the triangles formed are similar.
Answer:
15
Step-by-step explanation:
if you divide 20 by 8, then you get 2.5. multiply that by six, and you get your answer.
AB=6CM AC= 12cm
calculate the length of CD
AB=6cm AC=12cm
AC² = AB + BC²
12² = 6² + CB²
CB² = 12² - 6²
CB² = 144 - 36
CB² = 108
CB = √ 108 cm.
sin 55° = CB / CD
0.81915 = √108 / CD
CD = 10.392 / 0.81915
CD = 12.686 cm
Answer:
Step-by-step explanation:
This was a question on mathswatch, so I’ve done this.
You need to round to 3 significant numbers
AB=6cm AC=12cm
AC² = AB + BC²
12² = 6² + CB²
CB² = 12² - 6²
CB² = 144 - 36
CB² = 108
CB = √ 108 cm.
sin 55° = CB / CD
0.81915 = √108 / CD
CD = 10.392 / 0.81915
CD = 12.686 cm
CD = 12.7 cm
What is the slope of the line whose equation is y -2/3 = 0?
Answer: The slope is 0.
Step-by-step explanation:
y -2/3=0
+2/3. +2/3
y=2/3
what does 5 1/2 * 4 equal
Answer:
22
Step-by-step explanation:
5 1/2 = 11/2
11/2 * 4/1
44/2
22
Answer:
22
Step-by-step explanation:
5.5 times 4 = 22
(5.5 = 5 1/2)
therefore the answer is
22
hope this helps!! ;)
Working alone, Dan can sweep a porch in
15 minutes. Alberto can sweep the same
porch in 11 minutes. If they worked
together how long would it take them?
Answer:
It will take them 6.35 minutes
Step-by-step explanation:
The question can be solved when you know how much of the job can be done in minutes.
Therefore if Dan can do the job in 15 minutes he will be to sweep 1/15 of the porch in 1 minutes. Alberto can do the same job in 11 minutes, in 1 minutes he will do 1/11 of the job.
let
a = combined time together
1/15 + 1/11 = 1/a
(11 + 15)/165 = 1/a
26/165 = 1/a
cross multiply
26a = 165
divide both sides by 26
a = 165/26
a = 6.34615384615
a ≈ 6.35 minutes
It will take them 6.35 minutes
The Department of Highway Improvements, responsible for repairing a 25-mile stretch of interstate highway, wants to design a surface that will be structurally efficient. One important consideration is the volume of heavy freight traffic on the interstate. State weigh stations report that the average number of heavy-duty trailers traveling on a 25-mile segment of the interstate is 72 per hour. However, the section of highway to be repaired is located in an urban area and the department engineers believe that the volume of heavy freight traffic for this particular section is greater than the average reported for the entire interstate.
To validate this theory, the department monitors the highway for 50 1-hour periods randomly selected throughout the month. Suppose the sample mean and standard deviation of the heavy freight traffic for the 50 sampled hours are:
Sample mean = 74.1 standard deviation = 13.3
a) Do the data support the department's theory? Use α = 0.10 to come to a conclusion based on a large sample test.
Answer:
[tex]t=\frac{74.1-72}{\frac{13.3}{\sqrt{50}}}=1.116[/tex]
The degrees of freedom are given by:
[tex]df=n-1=50-1=49[/tex]
Now we can calculate the p value with the following probability:
[tex]p_v =P(t_{(49)}>1.116)=0.135[/tex]
Since the p value is higher than the significance level provided of 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 72 per hour.
Step-by-step explanation:
Information provided
[tex]\bar X=74.1[/tex] represent the sample mean
[tex]s=13.1[/tex] represent the sample standard deviation
[tex]n=50[/tex] sample size
[tex]\mu_o =72[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to analyze if the true mean for this case is higher than 72, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 72[/tex]
Alternative hypothesis:[tex]\mu > 72[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{74.1-72}{\frac{13.3}{\sqrt{50}}}=1.116[/tex]
The degrees of freedom are given by:
[tex]df=n-1=50-1=49[/tex]
Now we can calculate the p value with the following probability:
[tex]p_v =P(t_{(49)}>1.116)=0.135[/tex]
Since the p value is higher than the significance level provided of 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 72 per hour.
Check all of the expressions that are equal to the one below.
(8 + 7). 11
A. 11. (8 + 7)
B. 8•(11)-7•(11)
C. 11•(7) + 11 (8)
D. 8+ (711)
Answer:
A. 11•(8 + 7)
B. 8•(11)-7•(11)
C. 11•(7) + 11•(8)
Step-by-step explanation:
The commutative property of multiplication lets you swap the order of the factors in the product:
(8 +7)•11 = 11•(8 +7)
The distributive property lets you eliminate parentheses:
(8 +7)•11 = 8•11 +7•11
And the commutative properties of addition and multiplication let you rearrange this sum of products to ...
(8 +7)•11 = 11•7 +11•8
What is the surface area of a rectangular prism with a length of 16 cm, a width of 8 cm, and a height of 4 cm? (show your work in numbers)
Answer:
Step-by-step explanation:
Multiply base area * height
= 16 * 8 * 4 = 512 cm^3
Answer:
448
Step-by-step explanation:
it is correct trust me
There is a bag filled with 3 blue, 4 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of exactly 1 red?
Answer:
22.22%
Step-by-step explanation:
If it is exactly a red, it means that it is removed on the first or second attempt, but only once, in this case it does not matter if it is on the first or second attempt because the marble is returned to the bag.
So suppose that on the first attempt red is drawn, the probability would be:
4 / (3 + 4 + 5) = 4/12 = 1/3
Now, on the second attempt, it is not to draw a red, it must be green or blue, so it would be:
(5 + 3) / (3 + 4 + 5) = 8/12 = 2/3
The final probability then is:
1/3 * 2/3 = 0.2222
that is, the probability is 22.22%
5. Which is equivalent to 1/2
? Select all that apply.
A sin 30°
B sin 45°
C cos 45°
D cos 60°
E tan 30°
F tan 45º
Answer:
A sin 30°D cos 60°Step-by-step explanation:
Attached is a short table of trig function values. There are really only three you need to remember if you keep an image of the sine and cosine graphs in your head (for 0° and 90° values).
sin(α) = cos(90°-α)
tan(α) = sin(α)/cos(α)
__
sin(30°) = cos(60°) = 1/2 . . . . . . . the answer to this question
sin(45°) = cos(45°) = 1/√2 = (√2)/2
sin(60°) = cos(30°) = (√3)/2
__
I find it just as easy to remember SOH CAH TOA and the side ratios in isosceles and half-equilateral right triangles: 1:1:√2 and 1:√3:2, respectively.
Two models of the same compound are shown.

In what way is Model A better than Model B?
Model A shows the types of elements in the compound, but Model B does not.
Model A shows the total number of atoms in the molecule, but Model B does not.
Model A shows the three-dimensional shape of the molecule, but Model B does not.
Model A shows the number of atoms of each element in the molecule, but Model B does not.
Answer:
Step-by-step explanation:
Model B shows how the atoms in the molecule are connected, but Model A does not.
it is C
just did the test
A copy machine makes 84 copies in 3 minutes and 30 seconds. How many copies does it make per minute
Answer:
24
Step-by-step explanation:
30 secs = 0.5 min
thus 84 / 3.5 min = 168 / 7 = 24
the perimeter of this quarter circle with radius, r = 32mm. Give your answer as an expression in terms of π.
Answer:
16π + 64
Step-by-step explanation:
So the whole circumference is 64π
A quarter is 16π
Then you just have to account for the two radii.
16π + 64
Answer:
C≈201.06
16π + 64
Step-by-step explanation:
Radius: 32mm.
Solved for perimeter
Shape: Circle.
The correct answer to this question is C≈201.06.
You asked for 16π + 64.
Hope this helps.
An element with a mass of 740 grams decays by 28.4% per minute. To the nearest minute, how long will it be until there are 30 grams of the element remaining?
Answer:t=9.6 minutes
Step-by-step explanation:
Given
mass of element is [tex]A_o=740\ gm[/tex]
Decay rate [tex]r=28.4\%\ \text{per minute}[/tex]
and we know
Amount of exponential decay is given by
[tex]A=A_o[1-r]^t[/tex]
Where [tex]A_0=\text{Initial amount}[/tex]
[tex]\text{A=Accumulated amount}[/tex]
[tex]\text{r=rate}[/tex]
[tex]\text{t=time}[/tex]
Substituting values we get
[tex]\Rightarrow 30=740[1-0.284]^t[/tex]
[tex]\Rightarrow \dfrac{30}{740}=0.716^t[/tex]
[tex]\Rightarrow 0.0405=0.716^t[/tex]
taking log both sides we get
[tex]\Rightarrow\ \ln (0.0405)=t\times \ln (0.716)[/tex]
[tex]\Rightarrow t=\dfrac{\ln (0.0405)}{\ln (0.716)}[/tex]
[tex]\Rightarrow t=9.598\approx 9.6\ \text{minutes}[/tex]
Answer:
Delta math it’s 10
Step-by-step explanation: