Answer:
[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]
Step by step explanation:
[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]
if 6 men. 8 women and 16 boys together can do a piece of work in 288 days by working 6 hours each day in how many days can 12 men, 18 women and 28 boys complete the same & work by working 8 hours each day? The work efficiency of men, women and boys proportion 3:2:1 respectively?
Answer:
144 days
Step-by-step explanation:
Let's put the efficiency in terms of b
m = 3b w = 2b b=b
starting with 6 m = 18 b
8w = 16 b
16b = 16 b total 50 b
then increase 12m = 36b
18w = 36b
28b = 28 b total = 100 b
You doubled 'b' workers so work time will be halved to 144 days
.
A grab-bag contains 20 packages worth $.70 each, 15 packages $.60 cents each, and 5 packages worth $.30 each. What is the expected value if you have to pay $.50 to pick one package at random?
about $0.53
about $0.00
about $0.60
about $0.11
The expected value if I have to pick one package given the price I would have to pay is $0.11.
What is the expected value?The expected value is the cost you would have to pay subtracted from the total value of one package.
Total value of one package =[ (15 x 0.60) + (5 x 0.3) + (20 x 0.7)]/ (20 + 15 + 5) = $0.61
Expected value = $0.61 - $0.50 = $0.11
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Let f(x) = -3x³ + 4 and g(x) = -8x² + 2x. What is f(x) g(x)?
·
Answer:
[tex]{ \tt{f(x).g(x) = ( - 3 {x}^{2} + 4)( { - 8x }^{2} + 2x) }} \\ = { \tt{( - 3 \times - 8) {x}^{(2 + 2)} + (2 \times - 3) {x}^{(2 + 1)} + ( - 8 \times 4) {x}^{2} + (4 \times 2)x }} \\ = { \tt{24 {x}^{4} - 6 {x}^{3} - 32 {x}^{2} + 8x}}[/tex]
At each point (x, y) on a graph of function f, the graph has a slope equal to 4x - 4. If the
graph of f goes through the point (2, 3), then f(x) =
A)
2x² - 4x - 4
B)
2x² - 4x
C)
2x² - 1
D)
2x² - 4x + 3
E)
16x - 12
Answer:
f(x)= 2x² - 4x + 3
Step-by-step explanation:
dy/dx = 4x - 4
y = integrate dy/dx
y = 4x²/2 - 4x + c
y = 2x² - 4x + c
at (2,3)
3 = 2(2)² - 4(2) + c
3 = 8 -8 + c
c = 3
therefore f(x)= y = 2x² - 4x + 3
The graph of the function is given by f ( x ) = 2x² - 4x + 3
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
At each point (x, y) on a graph of function f, the graph has a slope equal to 4x - 4
So , dy/dx = 4x - 4
On integrating , we get
f ( x ) = 2x² - 4x + c
where the function passes through P ( 2 , 3 )
So , 3 = 2 ( 2 )² - 4 ( 2 ) + c
c = 3
Hence , the function is f ( x ) = 2x² - 4x + 3
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What type of function is represented by the table of values below?
y
4
8
12
16
20
A. exponential
B. cubic
C. linear
D. quadratic
X12345
X
Answer
The type of function that is represented by the table of values below is C. linear
Does this graph represent a function? Why or why not?
10-
8-
6-
2
--8-
-10-
O A. No, because it fails the vertical line test.
OB. Yes, because it passes the vertical line test.
OC. Yes, because it is a curved line.
OD. No, because it is not a straight line.
-1080
Evaluate each function at the given value using the remainder theorem.
F(x)=x^4+5x^3-18x+1 at x=-4
Please show work , I give brainliest. :)
Answer:
9
Step-by-step explanation:
[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]
Would the answer for c be 21 square root of 3?
Answer:
c = 14√3 km
Step-by-step explanation:
[tex]x\sqrt{3} =42\Longrightarrow x=\frac{42}{\sqrt{3} } = \frac{42 \times \sqrt{3} }{\sqrt{3}\times \sqrt{3} }=\frac{42 \times \sqrt{3} }{3 }=14 \sqrt{3}[/tex]
Since c = x
Then
c = 14√3
HELLPPP!!! ASAPPP WHAT IS THE EQUATION FOR THE RED GRAPH?!?!
Answer: The correct answer is D.
Step-by-step explanation: A and B is incorrect because the x value is 0. C is incorrect because the y-intercept is 3, not -3. Hence, it is D.
This histogram represents a sampling of recent visitors to the mall on a Friday night, grouped by their ages.
Which of the following describes the overall shape of the distribution?
The distribution is nearly symmetrical.
The distribution is skewed left.
The distribution is skewed right.
The distribution is symmetrical.
Answer:
skewed to the right
Step-by-step explanation:
Question 1 of 10
What is the effect on the graph of f(x) = x² when it is transformed to
h(x) = x² +12?
Julia made a model of a square pyramid. She used cardboard to construct the model with the dimensions shown. It has an open bottom.
A square pyramid has a square base with side lengths of 8 centimeters, and 4 triangular sides with a height of 5 centimeters.
What is the surface area of the model?
A. 80 cm2
B. 144 cm2
C. 224 cm2
D. 320 cm2
Answer:
A. 80 cm²
Step-by-step explanation:
If a square pyramid has an open base, then the surface area is made up of the 4 congruent triangular sides only.
Area of a triangle = 1/2 × base × height
Given:
Base = 8 cmHeight = 5 cm⇒ Area of one triangular face = 1/2 × 8 × 5
= 20 cm²
⇒ Total surface area = 4 triangular faces
= 4 × 20
= 80 cm²
Answer:
80 cm²
Step-by-step explanation:
I did it and I got it right
184 is 130% more than what number?
Answer:
80
Step-by-step explanation:
The wording "130% more" suggests that we have the result of adding 130% of the original number to the original number.* This can be expressed as an equation to be solved for the original number.
__
Let x represent the original number. The given relation is ...
184 = x + 130% × x
184 = 2.30x . . . . . . . . . collect terms (130% = 1.3)
80 = x . . . . . . . divide by 2.3
184 is 130% more than 80.
_____
* One needs to be a little careful here. You will often see the wording ...
"<some number> times more".
Usually the intention there is that the result is <some number> times the original amount. That is, percentages are often treated differently from other number expressions in problems like this.
Tim needs 18 pens. He can buy them in packages containing 6,9, or 12 pens each. He will buy only one type of package. Which packages could Tim buy? Write two different ways of how Tim can buy exactly 18 pens. (Goodluck)
Answer:
9 and 6
Step-by-step explanation:
You see, 9x2=18 and 6x3=18
The probability distribution for a
random variable x is given in the table.
X
-10 -5 0
5
10 15 20
Probability ,20 15.05 .1
25 .1 .15
Find the probability that -5 ≤x≤5
The correct answer is 0.3
Given as:X : -10 -5 0 5 10 15 20
P(X)=f(x): 0.20 0.15 0.05 0.1 0.25 0.1 0.15
To find:probability of -5≤x≤5
Solution: ∑f(x)= f(-5)+f(0)+f(5)⇒ P(-5≤x≤5) = 0.15 +0.05+0.1 = 0.3
Hence, the answer of the given question is 0.3.
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https://brainly.com/question/16730693. Which volume-to-surface-area ratio would be better for an ice cube— the lowest possible or the highest possible? Use the table to help you try different shapes and sizes to make your selection (You can show your work on a separate piece of paper.):
The volume-to-surface-area ratio would be better for an ice cube is the highest possible one.
How to explain the volume?When you put ice into your drink, the goal is to have the ice chill your drink. This takes time. Therefore, you would want the ice to slowly melt and cool the drink for as long as you can.
You would want to have the highest possible volume to surface area ratio in an ice cube. If your ice cube is mostly surface area with less volume, it will melt quickly and water down your drink. If your ice cube has a higher ratio of volume to the surface area, it will stay solid longer and chill your drink longer.
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Devaughn earns $7.25 per hour working as a waiter at TGI Fridays. He typically pays a total of $89.76 towards deduction. If he works 37 hours, what will Devaughn net?
Hello, the answer should be $178.49.
If Devaughn earns $7.25 an hour at his job, we need to find out how much money he will make if he works for 37 hours.
[tex]37.(7.25)=268.25[/tex]
Next, we need to subtract the deduction amount from the total amount.
Net Equation will be defined as;
[tex]N=T-D[/tex]
[tex]N=(268.25)-(89.76)=178.49[/tex]
Good luck! If you have any questions, then feel free to ask in comments!
←
How many solutions does this linear system have
y =
x+2
6x - 4y = -10
Answer:
This linear system has one solution.
Step-by-step explanation:
First equation: y = x + 2
Second equation: 6x - 4y = -10
Let's change the second equation in slope-intercept form y = mx + b.
Slope-intercept form
y = mx + b
m ... slope
b ... y-intercept
[tex]6x - 4y = -10[/tex]
[tex]6x + 10 = 4y[/tex]
[tex]\frac{6}{4}x + \frac{10}{4} = y[/tex]
[tex]\frac{3}{2}x + \frac{5}{2} = y[/tex]
If two lines have the same slope but different y-intercept, they are parallel - system has no solutions.
If two lines have the same slope and the same y-intercept, they are the same line and are intersecting in infinite many points - system has infinite many solutions.
If two lines have different slopes then they intersect in one point - system has one solution.
We see that lines have different slopes. First line has slope 1 and the other line has slope [tex]\frac{3}{2}[/tex]. So the system has one solution.
You can also check this by solving the system.
Substitute y in second equation with y from first.
6x - 4y = -10
6x - 4(x + 2) = -10
Solve for x.
6x - 4x - 8 = -10
2x = -2
x = -1
y = x + 2
y = -1 + 2
y = 1
The lines intersect in point (-1, 1). <-- one solution
3 x 10³ - 7000
(8 × (-5)) + (4² + 22)
please help!
solve as simplest answer!
Answer:
283038 or 2.83038×10⁵
Step-by-step explanation:
3×10³-7000(-40)+(16+22)3×10³+280000+383×1000+2800383000+280038283038
In a class there are two girls for every three boys. The ratio 2 : 3 compares the
number of girls to the number of boys.
a) What is the ratio of boys to the whole class? - 3:5
b) If this class has eight girls, determine how many boys there are using the ratio that there are two girls for every three boys
Answer:
a. I'm not sure if there's more to the question but I can't answer without knowing how many is the whole class
B. 12 boys
can someone do this for me please?! Just the answer pls
The time taken that the aliens on Vormir will be waiting is 6 days.
How to calculate the distance?From the information given, the speed ia given as 0.7 and the time taken is given as 8.5. It should be noted that the formula for calculating distance will be:
Time = Speed × Distance
Time = 0.7 × 8.5
Time = 6 days approximately.
Therefore, the correct option is D.
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An 80-centimeter ramp connects the sidewalk to the bed of a truck. If the ramp
forms a 30-degree angle with the ground, the truck bed is centimeters off the ground.
The truck bed is 40cm .
What is a right-angled triangle?A right-angled triangle is a triangle with one of its angle 90°.
Analysis:
The ramp, the height of the truck bed from ground and the distance of truck bed to the point the ramp makes contact with the ground form a right angle triangle.
So that sin 30 = height of truck bed above ground/length of ramp
sin 30 = height/80
height of the truck = 0.5 x 80 = 40cm
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how many minutes does the white vacuum need to clean 86.25 square feet?
black vacuum cleans 8 square feet per min
white vacuum cleans 60 square feet for 8 min
red vacuum cleans 150 square feet for 25 min
Answer:
1.5 hours
As a general rule, 1,000 square feet of the house should take 1.5 hours to clean, according to Cleaning 4 Profit. So a 3,000 square feet home should take 3 hours to clean, and so on.
A box 10 centimeters high, 5 centimeters long, and 5 centimeters wide.Find the volume of a box with a length of 5 cm, a width of 5 cm, and a height of 10 cm.
Answer:
250 [tex]cm^{3}[/tex]
Step-by-step explanation:
First, start with the formula for the volume of a rectangular prism (aka a box):
V=length*width*height
Then, plug in your values:
V=5*5*10
V=25*10
V=250
Don't forget your units!
250 [tex]cm^{3}[/tex]
A light bulb consumes 1440 watt-hours per day. How long does it take to consume 6480 watt-hours?
The number of days it will take to consume the given power = 4.5 days
Calculation of energy consumptionThe amount of power consumed per day = 1440watt-hours
Therefore X days = 6480 watt-hours?
Make X the subject formula;
X = 1 × 6480/1440
X = 4.5 days
Therefore, The number of days it will take to consume the given power = 4.5 days.
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PRECISION In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was the average cost for 16 gallons of gasoline?
Answer:
$46.272
Step-by-step explanation:
what is 14 divided bye 3
Answer:
4.66
14÷ 3 = 4 r 2
add 0 to 2 ( this attracts a decimal point in your answer)
20 ÷ 3 = 6r 2
and = 4.66
Anyone know the answer
Step-by-step explanation:
-2g(1+g)
-2g - 2g²
(-2)g - (2)g²
The formula for the nth term of an arithmetic sequence can be found using the formula a Subscript n Baseline = a Subscript 1 Baseline + (n minus 1) d. Which of the following is equivalent to this equation?
The equation of nth term will be written as for n as will be ([tex]\rm a_n[/tex] - a₁ + d) / d. Then the correct option is D.
The missing options are attached to the picture given below.
What is a sequence?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
The formula for the nth term of an arithmetic sequence can be found using the formula given below.
[tex]\rm a_n = a_1 + (n-1)d[/tex]
Then arrange the equation for n, we have
[tex]\begin{aligned} \rm a_n - a_1 & \rm = nd - d\\\\\rm a_n - a_1 + d & \rm =nd\\\\\rm n & \rm = \dfrac{a_n - a_1 + d}{d} \end{aligned}[/tex]
Then the correct option is D.
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Answer: The answer is D
Step-by-step explanation:
took the test
a sticker shaped like a rectangle has an area of 56 square centimeters. it has a width of 7 centimeters.
Step-by-step explanation:
Soln:-
Given,
Area of sticker=56 cm^2
Width of sticker=7 cm
Length of sticker=?
We know that,
Area of rectangle=l×b
or,56=l×7
or,l=56÷7
•°•l=8
Hence,the required length of the sticker is 8 cm.