Answer:
a = 1875
Step-by-step explanation:
Sum of geometric series formula:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Geometric series formula:
[tex]a_n=ar^{n-1}[/tex]
Given:
[tex]S_n=3045[/tex][tex]r=\dfrac25=0.4[/tex][tex]a_n=120[/tex][tex]\implies 120=a(0.4)^{n-1}[/tex]
[tex]\implies a=\dfrac{120}{(0.4)^{n-1}}[/tex]
[tex]\implies 3045=\dfrac{a(1-0.4^n)}{1-0.4}[/tex]
[tex]\implies 3045=\dfrac{a(1-0.4^n)}{0.6}[/tex]
[tex]\implies 1827=a(1-0.4^n)[/tex]
[tex]\implies a=\dfrac{1827}{1-0.4^n}[/tex]
Equate equations for a:
[tex]\implies \dfrac{120}{(0.4)^{n-1}}=\dfrac{1827}{1-0.4^n}[/tex]
Apply exponent rule [tex]a^{b-c}=\dfrac{a^b}{a^c}[/tex]
[tex]\implies \dfrac{120}{\frac{0.4^n}{0.4^1}}=\dfrac{1827}{1-0.4^n}[/tex]
[tex]\implies \dfrac{48}{0.4^n}=\dfrac{1827}{1-0.4^n}[/tex]
[tex]\implies 48(1-0.4^n)=1827(0.4^n)[/tex]
[tex]\implies 48-48(0.4^n)=1827(0.4^n)[/tex]
[tex]\implies 48=1875(0.4^n)[/tex]
[tex]\implies 0.4^n=\dfrac{48}{1875}[/tex]
[tex]\implies 0.4^n=0.0256[/tex]
Taking natural logs:
[tex]\implies \ln0.4^n=\ln0.0256[/tex]
[tex]\implies n\ln0.4=\ln0.0256[/tex]
[tex]\implies n=\dfrac{\ln0.0256}{\ln0.4}[/tex]
[tex]\implies n=4[/tex]
Substituting found value for n into one of the equations and solving for a:
[tex]\implies a=\dfrac{120}{(0.4)^{4-1}}[/tex]
[tex]\implies a=\dfrac{120}{0.4^3}[/tex]
[tex]\implies a=\dfrac{120}{0.064}[/tex]
[tex]\implies a=1875[/tex]
Solving Linear Equations Unit Test 16 of 20Items Item 16 Gold has a density of 0.70 pounds per cubic inch and copper has a density of 8.96 grams per cubic centimeter. How much will 1 cubic foot of each metal weigh? 1 ft3 = 1728 in3, 1 ft3 = 28,316.8 cm3, and 1 lb=453.5 g. Use the equation rho=mV. (1 point) The gold will weigh 4063.4 pounds and the copper will weigh 12,096 pounds. The gold will weigh 559 pounds and the copper will weigh 1209.6 pounds. The gold will weigh 12,096 pounds and the copper will weigh 4063.4 pounds. The gold will weigh 1209.6 pounds and the copper will weigh 559 pounds.
Answer:
1 ft³ of gold will weigh 1209.6 pounds
1 ft³ of copper will weigh 559 pounds.
Step-by-step explanation:
We know the formula for:
Density = Mass/Volume
Hence, making mass the subject of the formula:
Mass = Density × Volume
From the question we are told:Volume of each metal = 1 ft³
1) Metal: Gold
Density of Gold = 0.70 pounds per cubic inch(lb/in³)
We convert the Volume of gold from ft³ to in³
The Volume of gold given in the question = 1 cubic foot = 1 ft³
1 cubic foot = 1728 cubic inches
Hence, the volume of Gold = 1728 in³
Mass of Gold = Density of Gold × Volume of Gold
Mass of Gold = 0.70Ib/in³ × 1728 in³
= 1209.6 lb(pounds)
2) Metal : Copper
Density of copper given in the question = 8.96 grams per cubic centimeter
Ib = pounds
We convert this density in g/cm³ to ib/in³
453.5g = 1 Ib
8.96g = a Ib
Cross Multiply
= 453.5g × a Ib =8.96g × 1 Ib
= a Ib = 8.96g × 1 Ib/453.5g
a Ib = 0.0197574421 Ib
Density of Copper = 0.0197574421 Ib/cm³
28,316.8 cm³ = 1 ft³
1 cm³ = b ft³
b ft³ = 1 cm³ × 1 ft³/28,316.8cm³
b ft³ = 0.0000353147 ft³
1 cm³ = 0.0000353147 ft³
We have to convert the density of Copper from Ib/cm³ to Ib/ft³
0.0197574421 Ib/cm³ = 0.0197574421 Ib/0.0000353147 ft³
559.46793026 Ib/ft³
Volume of copper = 1ft³
Mass = Density × Volume
Mass of copper = 559.46793026 Ib/ft³ × 1 ft³
= 559.46793026 Ib or pounds
≈ 559 pounds
Therefore , the weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.
Answer:
Gold
Density of Gold = 0.70 pounds per cubic inch
1 cubic foot = 1728 cubic inches
Hence, the volume of Gold = 1728 in³
Mass of Gold = Density of Gold × Volume of Gold
Mass of Gold = 0.70Ib/in³ × 1728 in³ = 1209.6 lb(pounds)
2) Metal : Copper
Density of copper given in the question = 8.96 grams per cubic centimeter
We convert this density in g/cm³ to ib/in³
453.5g × a Ib =8.96g × 1 Ib = 8.96g × 1 Ib/453.5g = 0.0197574421 Ib
Density of Copper = 0.0197574421 Ib/cm³
Volume of copper = 1ft³
Mass = Density × Volume
Mass of copper = 559.46793026 Ib/ft³ × 1 ft³ = 559.46793026 Ib or pounds
≈ 559 pounds
The weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.
How to you round 6 3/7 to the nearest hundred s
Answer:
0
Step-by-step explanation:
63/7 = 9
We know,
If any number smaller then fifty told to be rounded to its nearest hundred then the answer is ' 0 '
Similarly the nearest hundred of 9 is 0.
Hope it helps
Mark me brainliest.
80 is M% of 25. What is M? Explain your answer
Please answer correctly !!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!
Answer:
bc=12x
ab=17
ac=141
Step-by-step explanation:
What is the approximate length of the diameter, d? Use 3. 14 for. Round to the nearest tenth of a centimeter. 4. 0 centimeters 8. 0 centimeters 15. 9 centimeters 31. 8 centimeters.
Larry started out the week in a new job. He was paid $10 to attend job orientation.
After that he made $6.25 per hour for each hour he worked. Write the equation in
slope-intercept form that represents the equation.
Answer:
y=6.25x+10
Step-by-step explanation:
6.25 is the rate of change so it is the slope. 10 is what you start with so it is the y- intercept
The temperature on Monday was 64.8 degrees and the temperature on Tuesday was 7.65 degrees warmer. What was the temperature on tuesday?
Answer:
72.45°
Step-by-step explanation:
Add 7.65° to 64.8°
The temperature is 72.45° on Tuesday.
Hope I helped :)
Please consider Brainliest :)
Answer:
Step-by-step explanation:
Monday=64.8
Tuesday= 64.8+7.65
=72.45
What is the factored form of 3x+24y?
O 3(x+8y)
0 3xy(x+8y)
O 3(3x+24y)
O 3xy(3x+247)
Plzz helpp
Answer:
3(x + 8y)
Step-by-step explanation:
3 is the highest term that can be factored out; there are no other numbers/variables in common.
Factor out 3 from 3x + 24y.
= 3(x+8y)
The factored form of the given expression is 3(x+8y).
What are factors?A factor is a number that divides into another number without a remainder. So, for example, 5 is a factor of 20 because 20/5 = 4. There is no remainder. You can also think of factors as the numbers that you multiply together in order to obtain a product.
Given is an expression 3x+24y, we need to find the factors of the given expression,
3x+24y
Since, 3 is the highest term that can be factored out; there are no other numbers/variables in common.
Factor out 3 from 3x + 24y.
= 3(x+8y)
Hence, the factored form of the given expression is 3(x+8y).
Learn more about factors, click;
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Does the graph represent y as a function of x?
Answer:
No this is not a function
Step-by-step explanation:
If you use the vertical line test which is just a line used across the graph. If we can draw any vertical line that intersects a graph more than once then it is not a function.
Point (2, 4) is reflected across the x-axis. What are
the coordinates of its image?
Answer:
The coordinates of its image are (2, -4)
Step-by-step explanation:
Let us revise the rules of reflection across the axes
If the point (x, y) reflected across the x-axis, then its image is (x, -y), the rule of reflection is rx-axis (x, y) → (x, -y) If the point (x, y) reflected across the y-axis, then its image is (-x, y), the rule of reflection is ry-axis (x, y) → (-x, y)∵ The point (2, 4) is reflected across the x-axis
→ By using the first rule above rx-axis (x, y) → (x, -y)
∴ Change the sign of its y-coordinate
∴ Its image is (2, -4)
∴ The coordinates of its image are (2, -4)
A recycling bin is shaped like a trapezoid. The bottom 2 angles are 108 degrees. The top left angle is 72 degrees. The front view of a recycle bin is shaped like a trapezoid. What is the measure of the remaining angle? 72° 144° 198° 252°.
The measure of the remaining angle is 72 degree, the correct option is A.
What is the trapezoid?A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.
Given
A recycling bin is shaped like a trapezoid.
The bottom 2 angles are 108 degrees.
The top left angle is 72 degrees.
The front view of a recycle bin is shaped like a trapezoid is given by;
[tex]\rm \angle 1+ \rm \angle 2+ \rm \angle 3+ \rm \angle4= 360\\\\108+108+72\rm +\angle 4=360\\\\\rm 288+\angle 4 = 360 \\\\\rm \angle 4=360-288\\\\\rm \angle 4=72[/tex]
Hence, the measure of the remaining angle is 72 degree.
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Answer: A) 72
Step-by-step explanation: I got it right
When soling a system of liner equations, try to algebraically form one equation that has only one variable
Answer:
Yes
Step-by-step explanation:
It helps you to understand the equation easily
HOPE IT HELPED
which is larger -17/24 or -11/12
Answer:
-17/24
Step-by-step explanation:
Because they are negative numbers, the smaller fraction (when disregarding the negative sign) is always a larger number. -11/12 could be changed to -22/24, and therefore since it is a larger number when disregarding the negative (22/24), it is a smaller number altogether.
-17/24 > -22/24
2. Find f(2) for
the function
below.
f(x) = 1/8•5^x
Answer:
f(2) = [tex]\frac{25}{8}[/tex]
Step-by-step explanation:
To evaluate f(2) substitute x = 2 into f(x) , that is
f(2) = [tex]\frac{1}{8}[/tex] × 5² = [tex]\frac{1}{8}[/tex] × 25 = [tex]\frac{25}{8}[/tex]
Answer:
24/8
Step-by-step explanation:
BIG BRAIN
PLEASE HELP! I WILL MAKE BRAINLIST!
Answer:
the answer is b because that's the slope
Answer:
B
Step-by-step explanation:
you can try each answer or you can just use number of plants and divide it by number of seed packets which is 10 so B
What are the values of v and w?
Answer: i think 130 and 80
Step-by-step explanation: sorry if wrong
The medium sushee has 17 more ounces than the small slushee
The large slushee has 6 times as many ounces than the small slushee
The Slushee Company says there are 113 ounces total in the small, medium, and large drinks
How many ounces are in cach size slushee?
Answer:
A small slushee has 12 ounces.
A medium 29 ounces.
And a large 72 ounces.
Step-by-step explanation:
Let s represent the size of the small slushee, m the medium slushee, and l the large slushee.
We know that the medium slushee has 17 more ounces than the small slushee. So:
[tex]m=s+17[/tex]
We also know that the large slushee l has 6 times as many ounces than the small slushee. Therefore:
[tex]l=6s[/tex]
Finally, we know that there are a total of 113 ounces in the small, medium, and large drinks combined. So:
[tex]s+m+l=113[/tex]
We can solve this triple system of equations using substitution. Let's substitute l for 6s and m for (s+17). This yields:
[tex]s+(s+17)+(6s)=113[/tex]
Combine like terms:
[tex]8s+17=113[/tex]
Subtract 17 from both sides:
[tex]8s=96[/tex]
Divide both sides by 8:
[tex]s=12\text{ oz}[/tex]
So, the small slushee is 12 ounces.
So, the medium slushee is [tex]12+17=29\text{ oz}[/tex]
And the large slushee is [tex]6(12)=72\text{ oz}[/tex]
And we're done!
Write 5/2 as a mixed number
5/2 can be written as 2 1/2
2*2 = 4 + 1 = 5
Answer:
2 1/2
Step-by-step explanation:
you divide 5 into 2, to get 2 and 1 left over
THIS ID DUE TODAY! MATH.
Answer: Inverse
Explanation: Any conditions that doesn't fit the requirement of the conditional statement would make the statement false, therefore it is inverse.
What is the equation in slope-intercept form of a line with
а
slope - and y-intercept -2?
3
4
OA) y=_x+2
)
3
4
4.
OB) y=2x +
3
4
OC) y=-x+2
3
v
=x+2
4.
OD) y=-x-2
3
-
Answer:
D
Step-by-step explanation:
sorry about last time 100% sure about this one
Answer: D, because y =mx + b
X + 2x - 9 + xy - 2 - 3x + 2xy - 4
Answer:
3xy-15 thats the simplified form
3 times x plus 4 is greater than or equal to 4 times the sum of x and 1. (Hint: 4 times the sum means you should write a distributive property problem)
Given:
3 times x plus 4 is greater than or equal to 4 times the sum of x and 1.
To find:
The inequality for the given statement and solution of the inequality.
Solution:
4 times the sum means a distributive property problem.
Now,
3 times x : 3x
3 times x plus 4 : 3x+4
Greater than or equal to : ≥
4 times the sum of x and 1 : 4(x+1)
So, the inequality is
[tex]3x+4\geq 4(x+1)[/tex]
Using distributive property, we get
[tex]3x+4\geq 4x+4[/tex]
Isolate variable terms.
[tex]4-4\geq 4x+3x[/tex]
[tex]0\geq x[/tex]
It can be written as
[tex]x\leq 0[/tex]
Therefore, the required inequality is [tex]3x+4\geq 4(x+1)[/tex] and the solution is [tex]x\leq 0[/tex].
mont 10: The diagonals of a square bisect the vertical engles yp 1: Draw a square ABCD. Draw diagonals AC and BD. D B A | 2: of each vertical angle by the diagonals. Write the measurements in the table. Vertical angles Other angles formed by diagonals at Result each vortex ZBAD = ROZBAC ZCAD ZBAC = CAD LABD = ZCBD = ZABD = ZCED ZBCA ZACD ZBCA ZACD ZADB BDC = ZADE - EDC ABC = BCD ADC Conclusion: The diagonals of a square bisect the vertical angles.
Answer:
square the vertical starting from bisect angle !
In a bird sanctuary, 30% of the birds are
hummingbirds. If there are about 350 birds in
the sanctuary at any given time, how many are hummingbirds?
Answer: 105 of them are hummingbirds.
Step-by-step explanation:
I there are a total of 350 birds then 30% o 350 will give the number o hummingbirds.
350 of 30%
350 * 0.3 = 105
Which point has the coordinates (-2.5, 5.5)?
A.
point E
B.
point F
C.
point G
D.
point H
Out of 28 people, 12 adults attended a play. What is the ratio of children to attendees
Answer: 7:3 is the ratio of the problem
Step-by-step explanation:
(u + 9) 10 distributive property
= 10 (u + 9)
= 10 x u + 10 x 9
= 10u + 90
Find the magnitude of the vector <5, −3>.
1. 5.8
2. 6.1
3. 5.2
4. 4
Answer:
5.8
Step-by-step explanation:
[tex]\sqrt{5^{2} + (-3)^{2} } \\\sqrt{25 + 9} \\\sqrt{34}[/tex]
5.83
hope it helps
Answer:
5.8
Step-by-step explanation:
well, you use the distance formula to find the magnitude of this vector.
Hope this helps!
Grace, Jessica and Mia went out to dinner after the Volleyball game. Jessica bought two tacos, a coke and a mango smoothie and spent $14.74. Grace bought Mia's dinner. She bought 5 tacos, 2 cokes and 1 mango smoothie and spent $29.05. The mango smoothie cost three times as much as the coke. Determine the price of each item. Answer in a complete sentence.
Answer:
A mango costs $4.68, a coke costs $1.56 and a taco costs $4.25
Step-by-step explanation:
Given
Represent Tacos with T, Coke with C and Mango with M
For Grace:
[tex]2T + C + M = 14.74[/tex] --- (1)
For Mia:
[tex]5T + 2C + M = 29.05[/tex] -- (2)
[tex]M = 3C[/tex]
Required
Determine the cost of each item
Substitute 3C for M in (1) & (2)
[tex]2T + C + M = 14.74[/tex]
[tex]2T + C + 3C = 14.74[/tex]
[tex]2T + 4C = 14.74[/tex] --- (4)
[tex]5T + 2C + M = 29.05[/tex]
[tex]5T + 2C + 3C = 29.05[/tex]
[tex]5T + 5C = 29.05[/tex] --- (5)
Divide through (5) by 5
[tex]T + C = 5.81[/tex]
Solve for C
[tex]C= 5.81 - T[/tex]
Substitute 5.81 - T for C in (4)
[tex]2T + 4C = 14.74[/tex]
[tex]2T + 4(5.81 - T) = 14.74[/tex]
[tex]2T + 23.24 - 4T = 14.74[/tex]
Collect Like Terms
[tex]2T - 4T = 14.74 - 23.24[/tex]
[tex]-2T= -8.5[/tex]
Solve for T
[tex]T = -8.5/-2[/tex]
[tex]T = 4.25[/tex]
Recall that:
[tex]C= 5.81 - T[/tex]
[tex]C = 5.81 - 4.25[/tex]
[tex]C = 1.56[/tex]
Recall that
[tex]M = 3C[/tex]
[tex]M = 3 * 1.56[/tex]
[tex]M = 4.68[/tex]
Hence:
A mango costs $4.68, a coke costs $1.56 and a taco costs $4.25
Lance has 3 time as many pencils as Nick, and they have 84 pencils together. How many pencils does each of them have?
Answer:
21 pencils for Nick and 63 pencils for Lance
Step-by-step explanation:
Lance is said to have 3 times the pencils Nick has.Let's keep the number of pencils Nick has as x.If Nick has x pencils that means Lance has 3x pencils. The total number of pencils present is 84.Now let's make an equation out of the information above:
3x + x = 84
Now solve for x.
3x + x = 84
4x = 84
x = 84/4
x = 21
So Nick has 21 pencils
Now for Lance:
3x
3 * (21) = 63
So Lance has 63 pencils
63 + 21 = 84 pencils