The number of lines that can be drawn parallel to plane P that passes through point A is 1.
How to depict the information?From the information given, we are told that Point A lies outside of plane P. It should be noted that when a line is drawn from a point to another, it can only be one.
Therefore, the number of lines that can be drawn parallel to plane P that passes through point A is 1.
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find the equation of the arithmetic sequence in which t(5)=40 and t(10)=70.
The equation of the arithmetic sequence in which t(5)=40 and t(10)=70 is tₙ = 10 + 6n
How to find the equation of an arithmetic sequence?The equation of an arithmetic sequence can be represented as follows;
tₙ = a + (n -1)d
where
a = first termd = common differencen = number of termsHence,
70 = a + 9d
40 = a + 4d
30 = 5d
d = 30 / 5
d = 6
Therefore,
40 = a + 4(6)
40 - 24 = a
a = 16
Hence, the equation is as follows:
tₙ = 16 + (n - 1)6
tₙ = 16 + 6n - 6
tₙ = 16 - 6 + 6n
tₙ = 10 + 6n
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I think my other question might've been deleted for some reason
We know that if (x,y) lies on the graph of a function, then (y,x) lies on the graph of its inverse.
This means you need to draw the segment with endpoints (9,1) and (2,3).
Using a left endpoint riemann sum approximation with four equal subintervals, the approximate value of integral from 0 to 8 g(x) dx is:
Subdividing [0, 8] into 4 equally-spaced subintervals, each one will have length ∆x = (8 - 0)/4 = 2, and the partition is
[0, 2] U [2, 4] U [4, 6] U [6, 8]
We approximate the integral with a left endpoint sum. The left endpoint of the i-th subinterval is
[tex]\ell_i = 2(i-1)[/tex]
where 1 ≤ i ≤ 4.
Then the integral is approximated by
[tex]\displaystyle \int_0^8 g(x) \, dx \approx \sum_{i=1}^4 g(\ell_i) \Delta x \\\\ = 2 (g(0) + g(2) + g(4) + g(6)) \\\\ = 2 (-1 - 3 - 1.25 - 1.5) = \boxed{-13.5}[/tex]
Students are selling T-shirts for a school fundraiser. The table shows the amount they raise from the T-shirt sales.
Shirts Sold 1 2 3 4
Amount Raised (dollars) 4 8 12 16
Complete each statement.
The amount raised ? proportional to the number of shirts sold.
is
is not
Answer:..
Step-by-step explanation: what is is not?
Answer:
1. is
2. amount raised, number of shirts sold
3. dependent, independent
4. 4
5. 4x
Step-by-step explanation:
The radius is
cm.
The circumference in terms of is
✓ cm.
7
Using 3.14 for л, the approximate circumference of the
circle is
cm.
The circumference of this circle with a radius of 7 cm is equal to 44 cm.
Given the following data:
Radius of circular rug = 7 cm.π = 3.14.How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this formula:
Circumference = 2πr
Where:
r is the radius of a circle.
Substituting the given parameters into the formula, we have;
Circumference = 2 × 3.14 × 7
Circumference = 43.96 ≈ 44 cm.
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Solve:
x-1
——— < 0
x²-4
Answer: x≠±2, x<±2, x>1, x<1, and x>±2
explanation:
for this equation to be true
Case 1
either (x-1) should be a negative while (x²-4) should be positive
which gives:-
x-1<0
so, x<1
also, x²-4>0
so, x²>4
⇒x>±2
Case 2:-
x-1>0 and x²-4<0
which gives
x>1 and x²-4<0
so, x>1 or x<±2
Case 3:-
either way, the denominator can't be 0
so, x²-4≠0
which gives,
x≠±2
compiling all, we have,
x≠±2, x<±2, x>1, x<1, and x>±2
These solutions can be pointed to as points on a number line and the behavior shows their discontinuity.
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Please help answer this question asap 4/11
Match the terms to their correct definitions.
1. Adjusted balance
planning for the distribution of one's estate after death
2. ATM Automatic (or Automated) Teller Machine
the annual interest ÷ cost
3. Bond
a share in the ownership of a company
4. Certificates of deposit (CD's)
document that specifies how one desires his estate to be distributed upon his death
5. Checking account
a share of money earned as profits by a company and distributed to its stockholders
6. Club account
a sum on deposit usually for a given period of time at a fixed interest rate
7. Compound interest
accounts are set up to save for specific purchases
8. Debit card
can be used like a credit card, but money is deducted directly from bank account
9. Dividend
a trust established while the owner of the trust is still alive
10. Estate planning
interest figured only on the amount of money in the savings account
11. Interest
interest figured on the amount of money in the savings account plus the amount of interest already earned
12. Intestate
permits the customer to make transactions by using a special computer terminal
13. Investment
an estate, or other property or money, given to a person or institution to manage
14. Living trust
like loaning money to the company for interest
15. Mutual fund
account allows you to write an instruction to the bank, as a check, to make a payment from that account
16. Simple interest
without a will
17. Stocks
a commitment of money in order to gain a financial return
18. Trust
investment instrument in which you purchase a part of a collection of investments
19. Will
balance after adding the outstanding deposits and subtracts the outstanding checks to the balance on the statement
20. Yield
the fee a bank pays you to keep your money
Lets try to figuring out the definition of it.
1. Planning for the distribution of one's estate after death is Estate planning.
2. Trust: an estate, or other property or money, given to a person or institution to manage.
3. Compound interest: figured on the amount of money in the savings account plus the amount of interest already earned.
4. Dividend: a share of money earned as profits by a company and distributed to its stockholders.
5. Checking account: account allows you to write an instruction to the bank, as a check, to make a payment from that account.
6. Will a legal document that describes how your estate should be distributed upon.
8. Purchasing a bond is like loaning money to the company for interest.
9. Club accounts: accounts are set up to save for specific purchases.
11. Mutual fund: instrument in which you purchase a part of a collection of investments.
12. A debit card can be used like a credit card, but money is deducted directly from bank account.
13. Automatic Teller Machine: permits the customer to make transactions by using a special computer terminal.
14. Adjusted balance: balance after adding the outstanding deposits and subtracts the outstanding checks to the balance on the statement.
15. Certificate of deposit (CD) is a sum on deposit usually for a given period of time at a fixed interest rate.
18. A trust created while a person is still alive is called a Living Trust.
19. Intestate: without a will.
20. Interest is the fee a bank pays you to keep your money.
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Answer:
1. Planning for the distribution of one's estate after death is Estate planning.
2. Trust: an estate, or other property or money, given to a person or institution to manage.
3. Compound interest: figured on the amount of money in the savings account plus the amount of interest already earned.
4. Dividend: a share of money earned as profits by a company and distributed to its stockholders.
5. Checking account: account allows you to write an instruction to the bank, as a check, to make a payment from that account.
6. Will a legal document that describes how your estate should be distributed upon.
8. Purchasing a bond is like loaning money to the company for interest.
9. Club accounts: accounts are set up to save for specific purchases.
11. Mutual fund: instrument in which you purchase a part of a collection of investments.
12. A debit card can be used like a credit card, but money is deducted directly from bank account.
13. Automatic Teller Machine: permits the customer to make transactions by using a special computer terminal.
14. Adjusted balance: balance after adding the outstanding deposits and subtracts the outstanding checks to the balance on the statement.
15. Certificate of deposit (CD) is a sum on deposit usually for a given period of time at a fixed interest rate.
18. A trust created while a person is still alive is called a Living Trust.
19. Intestate: without a will.
20. Interest is the fee a bank pays you to keep your money.
Step-by-step explanation:
NEED HELP ASAP PLS!! Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. With reference to the figure, match the angles and arcs to their measures?
Answer:
1) 122 = Angle DFA
2) 144 = Angle COB
3) 124 = CE
4) 58 = EOB
Step-by-step explanation:
I think this is correct. Correct me if im wrong
What is the best name for the part of the figure
identified by the arrow?
O line of reflection
O line of symmetry
O plane of reflection
O axis of symmetry
The best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have given a three-dimensional figure.
As we can see the arrow is pointing at the plane.
A triangular prism is reflected over the given plane and creates a mirror image of a triangular prism.
A plane is a plane of symmetry.
Thus, the best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
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is the number there three? if you answer to me i will give you twenty Points.
Answer:
t = 2
Step-by-step explanation:
Look at the fraction on the left, 1/3.
Notice that the denominator is 3 times the numerator.
Since the fractions are equal, for the second fraction, you also need the denominator to be 3 times the numerator. Since the denominator is 6, the numerator must be 2 since 6 is 3 times 2.
Answer: t = 2
Of course, since you have two fractions that are equal, and fractions are also ratios, you have a proportion.
You can solve the problem as a proportion.
1/3 = t/6
Cross multiply:
3t = 1 × 6
3t = 6
t = 6/3
t = 2
Either way, you get t = 2.
Dexter makes 40 cookies.
He eats 16 of the cookies and take the rest to school.
What percentage of the cookies does he take to school?
In a class of 20 students:
11 have a brother
9 have a sister
6 have neither
Fill in the Venn Diagram.
The Venn diagram is given below. Then the number of students who have brother and sister will be 6.
What are sets?A set is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
In a class of 20 students:
11 have a brother, 9 have a sister, and 6 have neither.
Then the Venn diagram will be
11 – a + a + 9 – a = 20 – 6
20 – a = 14
a = 6
The Venn diagram is given below.
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Here are the results of a survey that students conducted at a mall. the students conducted this survey as part of a statistics project to determine if younger adults are more likely to have tattoos. at least one tattoo no tattoo row totals age 18-19 170 320 490 age 30-50 60 445 505 column totals 230 765 995 we randomly select a person who responded to this survey. which calculation gives the probability that the person has a tattoo
Using it's concept, it is found that there is a 0.2312 = 23.12% probability that the person has a tattoo.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 995 people were surveyed, out of which 230 have tattoos, hence the probability is given by:
p = 230/995 = 0.2312.
0.2312 = 23.12% probability that the person has a tattoo.
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Pls help i give 25 points
Answer:
[tex]\mathsf {11 \frac{1}{5} }[/tex] tons of concrete
Step-by-step explanation:
Here we need to divide fractions.
Concrete made :
Tons of total sand / Tons used to make a ton of concrete[tex]\mathsf {4\frac{4}{5} \div \frac{3}{7} }[/tex][tex]\mathsf {\frac{24}{5} \div \frac{3}{7} }[/tex][tex]\mathsf {\frac{24}{5} \times \frac{7}{3} }[/tex][tex]\mathsf {\frac{56}{5}}[/tex][tex]\mathsf {11 \frac{1}{5} }[/tex] tons of concreteWhat is the surface area of the cylinder with height 4 yd and radius 5 yd? Round your answer to the nearest thousandth.
Answer:
282.743 yd²
Step-by-step explanation:
Surface Area of the Cylinder: Top Base + Bottom Base + Side
Area of Top Base (Circle): πr² = π(5 yd)² = 25π yd²
Area of Bottom Base (Circle): same as top base = 25π yd²
Area of Side (Rectangle): Circumference*Height = (2πr)*(4 yd) =
2π(5 yd)*(4 yd) = 40π yd²
Total Surface Area = 25π yd² + 25π yd² + 40π yd² = 90π yd² = 282.743 yd²
The height of a cone is twice the radius of its base. a cone has a height of 2 x and a radius of x. what expression represents the volume of the cone, in cubic units?
Answer:
Step-by-step explanation:
The volume of a cone is V = 1/3 [tex]\pi[/tex] * h * r^2
The height of the cone = the diameter of its circle.
Here is the expression:
Volume = 1/3 π * 2x * x^2
[tex]\frac{\pi *x^{2} *2x}{3}[/tex]
Hope I helped!
please help!!!
picture below
Answer:
4^3x=4^(4x+4)
Step-by-step explanation:
You can eliminate the first 2 options since those don’t make sense already, and the last option changed 64 to 2^6 which is correct, but when they changed the other side. They should have multiplied 8 to both x and 1 which would have made the whole term 2^(8x+8) and not 2^(8x+1). Left with the third option, 4 to the power of 3 is 64 so the left side makes sense, 4^3x=64^x, on the right side, 4^4 equals 256, so the whole exponent should multiply by 4 so from 256^(x+1) you get 4^4(x+1) giving 4^(4x+4) making the third choice the right answer.
0.27 recurring as a fraction please
Answer:
[tex]\frac{3}{11}[/tex]
Step-by-step explanation:
assuming the recurring digits are 0.272727.... , then
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.2727.... (1) ← multiply both sides by 100
100x = 27.2727... (2)
subtract (1) from (2) thus eliminating the repeating digits
99x = 27 ( divide both sides by 99 )
x = [tex]\frac{27}{99}[/tex] = [tex]\frac{3}{11}[/tex] ← in simplest form
Answer:
Jimrgrant1 has already answered this correctly, 3/11.
Step-by-step explanation:
I took 1.0 and divided it by 0.272727 to give 3.666666 . . .
I looked for value that would convert this into a whole number when multiplied. 3 times 3.666666 . . . is equal to 11.
That would mean a fraction equal to 0.272727 . . . would be 3/11
the amount a gardener gets paid is directly proportional to the number of hours it takes for him to complete the job.
the gardener got paid £70 for a 12 hour job.
how much would he get paid for a job that took a total of 18 hours?
Answer:
£105
Step-by-step explanation:
The pay is proportional to the time, so working 18/12 = 3/2 times as long will gain the gardener 3/2 times the pay:
3/2 × £70 = £105
He would get paid £105 for an 18-hour job.
__
Here are a couple of other solution methods.
as a proportionpay/hours = ?/(18 hours) = £70/(12 hours)
Multiplying by 18 hours, we get ...
? = £70×(18 hours)/(12 hours) = £70×(18/12)
? = £105 . . . . pay for 18 hours
He would get paid £105 for 18 hours.
__
as direct proportion equationThe equation for a directly proportional relationship is ...
y = kx
If we let y represent pay and x represent hours, then we have ...
70 = k(12) ⇒ k = 70/12 = 35/6
Then for 18 hours, the pay is ...
y = (35/6)x
y = (35/6)(18) = 35(3) = 105
He would get paid £105 for 18 hours.
PLEASE HELP !!! which choices are equivalent to square root of -4???
Answer:
-2
Step-by-step explanation:
just a guess but it's right
x2 - x - 42
a=?
b=?
C=?
help me
Step-by-step explanation:
thr standard form for a quadratic equation is:
ax²+bx+c
in this example, a=1, b=(-1), c=(-42)
Please help me with this
Exponential functions are typically organized in this format:
[tex]f(x) = a*c^x[/tex]
To find the equation given the graph of an exponential function:
Identify the horizontal asymptoteSolving the Question
Identify the horizontal asymptote
In this question, it appears to be x = 0.
Identify the y-intercept
The y-intercept is the value of y at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our a value. Plug this into [tex]f(x) = a*c^x[/tex]:
[tex]f(x) = 100*c^x[/tex]
Solve for c
We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for c:
[tex]f(x) = 100*c^x\\50 = 100*c^1\\50 = 100*c\\\\c=\dfrac{1}{2}[/tex]
Plug c back into our original equation:
[tex]f(x) = 100*(\dfrac{1}{2})^x[/tex]
Answer[tex]f(x) = 100*(\dfrac{1}{2})^x[/tex]
I read 1/3 of a book in an hour.
How much more of the book will I read in 2 1/5 hours
Answer:
Step-by-step explanation:
To find the number of pages of the book in the given hour:
To find the number of pages in 2 1/5 hours, multiply the number of pages read in 1 hour by 2 1/5 hours.
[tex]\sf \text{ Number of pages read in 2 $\dfrac{1}{5}$ hours = $\dfrac{1}{3}*2\dfrac{1}{5}$ }[/tex]
[tex]\sf = \dfrac{1}{3}*\dfrac{11}{5}\\\\=\dfrac{11}{15}[/tex]
[tex]\sf \text{Number of pages read more in 2 $\dfrac{1}{5}$ hours = $\dfrac{11}{15}-\dfrac{1}{3}$}[/tex]
[tex]\sf =\dfrac{11}{15}-\dfrac{1*5}{3*5}\\\\=\dfrac{11}{15}-\dfrac{5}{15}\\\\=\dfrac{6}{15}[/tex]
Answer:
see below
Step-by-step explanation:
Here is another way
1/3 book / hr * 2 1/5 hr =
1/3 * 11/5 = 11/15 read in 2 1/5 hr
1/3is the same as 5 /15
11/15 - 5 /15 = 6/15 = 2/5 more read in 2 1/5 hr that 1/3 hr
please help
(a) Is it safe to place the plant box on a window ledge that can support a maximum weight of 2400 grams? Explain why or why not.
(b) Would the density of the soil change if the plant box was only half full? Explain.
Answers:
(a) The ledge can support the plant box. It is safe to put it there.
(b) No the density would not change.
=========================================================
Explanation for part (a)
We'll need the volume of the cube.
volume = side*side*side
volume = 13*13*13
volume = 2,197
Or you could do
volume = (side)^3
volume = (13)^3
volume = 2,197
The volume of the cube is 2,197 cubic cm. Multiply this with the density to determine its weight.
1.33*2197 = 2,922.01
The soil weighs 2,922.01 grams which is below the 2400 gram weight limit. Therefore, the ledge can support the planter.
------------------------------------
Explanation for part (b)
The weight would go down if you only put in half the soil, but the density would not change regardless of how much soil is in there. Why doesn't the density change? Because the density is the amount of stuff per unit volume. The density tells us how packed in a material is. We can scale the amount of material up or down, and retain the same density.
This is based off physics concepts which are bit beyond the scope of this math course, but different materials have different densities. It's common to use a reference table to look up densities of various materials. For instance, ice is less dense than water. This is why ice floats rather than sinks. As another example, gold is more dense than iron. So 1 cubic unit of gold will weigh more compared to 1 cubic unit of iron.
Please help! I'm not understanding this question. Giving 75 points! Please provide an explanation as to why that is the answer as well. Thank you!
What is i* if i = 0?
A. 0
B. 6
C. 8
D. 9
E. none of these
Answer:
A, the answer is A
The answer is a because the question say what is I if I = 0. The question basically gave you the answer. In other words the question said, I = 0 what is I? Sorry if this is a bit confusing, I’m not that good at explaining.
Hope this helps!
What is the intermediate step in the form (x+a)^2=b as a result of completing the square
for the following equation? 4x^2+64x+467=15
The intermediate step in the following equation is (4x + 16)² = - 196
What is an Equation ?An Equation is the mathematical statement formed when two algebraic expressions are equated using an equal sign.
The given equation is
4x² +64x+467 = 15
4x² + 2 * 2x *16 + 256 -256 +467 = 15
(4x + 16)² +211 = 15
(4x + 16)² = - 196
Therefore the intermediate step in the following equation is
(4x + 16)² = - 196
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Which of the following is equivalent to the sum of expressions 2a^2 + 2 and a – 2
A = 2a^2+a
B = a^3-2
C = 2a^2
D = a^2-2
Answer:
A
Step-by-step explanation:
2a² + 2 + a - 2
+2 and -2 cancel
a² and a aren't like terms
final = 2a² + a
Which function is graphed?
Answer:
science type of food group : fibre
A triangle has a base length of 3ac2 and a height 5 centimeters more than the base length. Find the area of the triangle if a = 4 and c = 5.
Answer:
45750 cm²
Step-by-step explanation:
Area of triangle:a = 4 and c = 5
base length = 3ac²
= 3 * 4 * 5 * 5
= 300 cm
height = 5 cm more than the base length
= 300 + 5
= 305 cm
[tex]\sf \boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*base \ length * height}[/tex]
[tex]\sf =\dfrac{1}{2}*300*305\\\\= 150 * 305\\\\= 45750 \ cm^2[/tex]
