Answer:
1st term: -45th term: 8Step-by-step explanation:
Put the appropriate values of n in the formula and do the arithmetic.
a(1) = 3·1 -7 = -4
a(5) = 3·5 -7 = 8
The 1st and 5th terms are -4 and 8.
_____
The first few terms of the sequence are ...
-4, -1, 2, 5, 8, 11, 14, ...
To find the sum of the 1st and 5th terms of the sequence defined by the function a(n) = 3n - 7, calculate each term using their respective n value and add the results together, resulting in a sum of 4.
Explanation:When you are given the function a(n) = 3n - 7, which represents the value of the nth term in a sequence, the sum of the 1st and 5th terms of the sequence can be calculated by plugging in the values for n into the function for each term and adding the results.
For the 1st term (n = 1):
For the 5th term (n = 5):
The sum of the 1st and 5th terms is then:
-4 + 8 = 4
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Randy does 200 Newton-meters of work moving a 100 pound piano a distance of 5 meters. How much force did he use?
The force used by Randy is 40 N.
What is work done?When a force moves anything over a distance, it is said to be doing work.
Work = Force * Displacement
Work done given in the question = 200 N.m
Distance moved by the piano = 5m
W = F * d
200 = F * 5
F = 40N
Hence, the force used by randy is 40N.
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Graph the polar equation. r = 2 + 2sin θ
Answer:
The graph attached below is for r=2+ 2sin θ where θ=pi
Step-by-step explanation
The coordinates in a polar equation are written as (r,θ)
r= radius and θ is the angle
⇒⇒⇒ so this mean we rotate θ radians and of the size r units
In our case assume θ=[tex]\pi[/tex] where 0≤θ≤2[tex]\pi[/tex]
1. In a closet, Jeremy has 5 blue uniform shirts and 5 red uniform shirts for school. Jeremy says that selecting a blue uniform shirt is equally as likely as selecting a red uniform shirt, so the probability of selecting a blue shirt is 50/50. What is wrong with Jeremy's statement? Justify your answer.
Answer:
Step-by-step explanation:
Let's calculate the probability of selecting a blue shirt from a total of 10 shirts:
It's 5/10, or 0.5, which stems from there being 5 blue shirts among the 10 Jeremy owns. 50/50 is not a standard way of expressing probability; 0.5 is proper.
A recent poll taken by the national ice cream industry shows that 32% of the population names vanilla as its favorite ice cream flavor. A sample of 200 people shows that only 20% of those polled names vanilla as their favorite ice cream flavor.
To determine whether this sample supports the population proportion of 0.32, a simulation of 100 trials is run, each with a sample size of 50 and a point estimate of 0.20. The minimum sample proportion from the simulation is 0.16, and the maximum sample proportion from the simulation is 0.28.
What is the margin of error of the population proportion using half the range?
Hence margin of error for population proportion is option c which is 0.6
What is margin of error ?MoE refers to estimated point value that tells us how much difference is there from actual value.
How to calculate?critical value * SD of population
Given max sample proportion =0.28 and min sample proportion=0.16
Hence we can directly calculate MOE by subtracting both = 0.28=0.16=0.6
which is option no. c
Hence option c is 0.6 which is correct.
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Answer:
0.6 is the answer
Which linear inequality is represented by the graph?
Answer:
The required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].
Step-by-step explanation:
From the given graph it is clear that the related line passes through the points (-3,-3) and (3,1).
If a line passes through two points, then the equation of line is
[tex]y-y_1=\frac{y-y_1}{x-x_1}(x-x_1)[/tex]
The equation of related line is
[tex]y-(-3)=\frac{1-(-3)}{3-(-3)}(x-(-3))[/tex]
[tex]y+3=\frac{4}{6}(x+3)[/tex]
[tex]y+3=\frac{2}{3}(x+3)[/tex]
[tex]y+3=\frac{2}{3}(x)+2[/tex]
Subtract 3 from both the sides.
[tex]y=\frac{2}{3}(x)+2-3[/tex]
[tex]y=\frac{2}{3}(x)-1[/tex]
The equation of related line is [tex]y=\frac{2}{3}(x)-1[/tex]. The related line is a dotted and the shaded region is below the line. So, the sign of inequality is <.
The required inequality is
[tex]y<\frac{2}{3}(x)-1[/tex]
Therefore the required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].
If the temperature changes from 64 degrees to 72 degrees, what is the percent increase in temperature
Answer:
8% difference I think.
Step-by-step explanation:
72 - 64 = 8.
The temperature increase from 64 degrees to 72 degrees represents a 12.5% increase. You calculate this by dividing the difference in temperature by the original temperature and then multiplying by 100.
To calculate the percent increase in temperature from 64 degrees to 72 degrees, you subtract the original temperature from the new temperature and divide by the original temperature. Then, multiply the result by 100 to get the percentage.
Here is the calculation:
Percent Increase = ((New Temperature - Original Temperature) / Original Temperature) × 100
Percent Increase = ((72 - 64) / 64) × 100
Percent Increase = (8 / 64) × 100
Percent Increase = 0.125 × 100
Percent Increase = 12.5%
Therefore, the temperature has increased by 12.5%.
Asher solved the equation below: 4x = 64 4x − 4 = 64 − 4 x = 60 Is Asher's solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
No. Asher figured that just subtracting 4 from 4x, which is 64, would get him the value of x. However, since 64=4x, one needs to divide 64 by the number of x's to get x's value. 64/4= 16, which is the value of x.
The method of solving the equation by asher is; Incorrect because she is supposed to divide directly and not subtract.
What is the method of solving an equation?We are told that she wants to solve the equation;
4x = 64
Now, she decided to subtract 4 from both sides to get the value of x. That will not be correct because she is meant to divide both sides by the coefficient of x to get the value of x.
4x = 64
x = 64/4
x = 16
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Clarissa and her friends are playing a game by throwing sticky darts onto the board shown below.
What is the likelihood of a sticky dart landing in the green section of the board, assuming that the sticky dart lands on the board?
t is certain.
It is impossible.
It is likely.
It is unlikely.
Answer:
It is unlikely
Step-by-step explanation:
The probability of a sticky dart landing in the green section of the board, assuming that it lands on the board is possible but very unlikely.
The green section of the board has the least area compare to an other section of the board. Therefore, the dark is unlikely to land in this section.
Answer:
it is unlikey
Step-by-step explanation:
the possibility of the sticky dart landing on the green part is unlikley
Suppose that a typical household in the United States has an average after-tax income of $41,100. The circle graph below represents how this annual income is
(Vote it is because of rounding that the percents do not add up to 100.) How much more is spent on insurance/pensions than on health care?
Entertainment
Health Care en
5%
5%
Clothing
Housing
33%
Insurance/
Pensions
9%
Other
11%
Food
14%
Transportation
17%
Answer:
9% + 5%
Step-by-step explanation:
Answer:
$1644.
Step-by-step explanation:
We have been a typical household in the United States has an average after-tax income of $41,100. We are asked to find how much more is spent on insurance/pensions than on health care.
We have been given that 5% is spent on health care and 9% is spent on insurance/pensions. This means that 4% (9%-5%) is more on insurance/pensions than on health care.
Now, we need to find 4% of $41,100.
[tex]\text{Amount more spent on insurance/pensions than on health care}=\frac{4}{100}\times \$41,100[/tex]
[tex]\text{Amount more spent on insurance/pensions than on health care}=4\times \$411[/tex]
[tex]\text{Amount more spent on insurance/pensions than on health care}=\$1644[/tex]
Therefore, $1644 is more spent on insurance/pensions than on health care.
Please explain the process!
Moira has a collection of nickels (5 cents) and dimes (10 cents). She has 630 coins totaling a value of $48. Moira challenges her friend, Mark, to determine how many nickels and how many dimes she has.
Mark sets up the correct system of equations, {n+d=630 & 0.05n+0.10d=48, where n represents the number of nickels Moira has and d represents the number of dimes she has.
He correctly determines that she has _[blank A]_ nickels and _[blank B]_ dimes.
Answer:
He correctly determines that she has 300 nickels and 330 dimes.
Step-by-step explanation:
I'll first explain how Mark got that system of equations. Then I'll solve the system of equations to find the numbers of coins.
Moira has a collection of nickels and dimes. We don't know the number of nickels and the number of dimes she has.
First, we define two variables to represent the unknowns in this problems, the numbers of coins.
Let n = number of nickels.
Let d = number of dimes.
The sum of the numbers of coins is n + d. We are told she has 630 coins, so the first equation is
n + d = 630
Since we have two unknowns, we need two equations. Now we write an equation based on the values of the coins. A nickel is worth $0.05. A dime is worth $0.1. n nickels are worth 0.05n, and d dimes are worth 0.1d. The total value of the coins is 0.05n + 0.1d. We are told the value of the coins is $48. Now we can write the second equation.
0.05n + 0.1d = 48
Our system of equations is:
n + d = 630
0.05n + 0.1d = 48
These are the same equations Mark got.
Now we solve the system of equations. We will use the substitution method. First, we solve one equation for one variable. Then we substitute that into the other equation.
Let's solve the first equation for n:
n + d = 630
Subtract d from both sides:
n = 630 - d
Now that we know that n is the same as 630 - d, we replace n of the second equation with 630 - d.
0.05n + 0.1d = 48
0.05(630 - d) + 0.1d = 48
Distribute the 0.05:
31.5 - 0.05d + 0.1d = 48
Combine the terms in d:
0.05d + 31.5 = 48
Subtract 31.5 from both sides.
0.05d = 16.5
Divide both sides by 0.05.
d = 330
Now that we know d is 330, we substitute d with 330 in the first original equation and solve for n.
n + d = 630
n + 330 = 630
Subtract 330 from both sides.
n = 300
Since we let n = the number of nickels, and d = the number of dimes, now we can fill in the blanks.
n = number of nickels = 300
d = number of dimes = 330
Answer: He correctly determines that she has 300 nickels and 330 dimes.
*******************************************************************
The question is already answered, but we can check with the given information to confirm that our answer is correct.
We check the number of coins:
300 nickels + 330 dimes = 630 coins (the number of coins checks out.)
Now, we check the value of the coins:
300 * $0.05 + 330 * $0.1 = $15 + $33 = $48 (the value of the coins checks out.)
Since both the number of coins and the value of coins check correctly, our answer, 300 nickels and 330 dimes, is correct.
To find the number of nickels and dimes Moira has, start by simplifying the system of equations and solve for the variables. The solution to the given system of equations reveals that Moira has 300 nickels and 330 dimes.
Explanation:The subject of this question is about solving a system of equations. The system in this case is given as {n+d=630 & 0.05n+0.10d=48}, where n represents the number of nickels Moira has and d represents the number of dimes she has.
First, we clear the decimals in the second equation by multiplying every term by 100, which gives us 5n + 10d = 4800. This can be simplified to n + 2d = 960 after dividing each term by 5.
Now, we have a new system of equations: {n + d = 630 & n + 2d = 960}. Subtraction of the first equation from the second will give us d = 330. Substituting d = 330 into the first equation will give us n = 300. Therefore, Moira has 300 nickels and 330 dimes.
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Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
Find sin B and tan B.
For this case we have that by definition of trigonometric relations of a rectangular triangle, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. While the tangent of the same angle is given by the leg opposite the angle on the leg adjacent to the angle.
Then, according to the figure we have:
[tex]sin (B) = \frac {7} {25} = 0.28\\tg (B) = \frac {7} {24} = 0.2917[/tex]
Answer:
[tex]sin (B) = \frac {7} {25}\\tg (B) = \frac {7} {24}[/tex]
Answer:
[tex]\text{sin}(B)=\frac{7}{25}[/tex]
[tex]\text{tan}(B)=\frac{7}{24}[/tex]
Step-by-step explanation:
We have been given a right triangle. We are asked to find the [tex]\text{sin}(B)[/tex] and [tex]\text{tan}(B)[/tex] for our given triangle.
We know that sine relates opposite side of right triangle to its hypotenuse.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
We can see that AC is opposite side to angle B and AB is hypotenuse of the given triangle.
[tex]\text{sin}(B)=\frac{AC}{AB}[/tex]
[tex]\text{sin}(B)=\frac{7}{25}[/tex]
We know that tangent relates opposite side of right triangle to its adjacent.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
We can see that AC is opposite side to angle B and BC is adjacent side of the angle B.
[tex]\text{tan}(B)=\frac{AC}{BC}[/tex]
[tex]\text{tan}(B)=\frac{7}{24}[/tex]
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!!
Solve the inequality for x:
5x - 3 ≤ 7x +7
Subtract 7x from each side:
-2x -3 ≤ 7
Add 3 to each side:
-2x ≤ 10
Divide both sides by -2, also when dividing both sides of an inequality you flip the direction of the inequality sign:
x ≥ -5
The dot will be on -5, because the inequality includes equal to, the dot is solid and is greater than, the arrow will point to the right.
The correct answer is D.
A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of enclosed area. What is the maximum area that can be enclosed by fencing?
11125 ft2. I hope i got it right
Consider the function f(x) = x2 + 2x – 15. What are the x-intercepts of the function? Left-most x-intercept: ( , 0) Right-most x-intercept: ( , 0)
Answer:
(- 5, 0) and (3, 0)
Step-by-step explanation:
Given
f(x) = x² + 2x - 15
To find the x- intercepts let f(x) = 0, that is
x² + 2x - 15 = 0 ← in standard form
(x + 5)(x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5 ← left x- intercept
x - 3 = 0 ⇒ x = 3 ← right x- intercept
Answer:
Left-most x-intercept: (-5, 0)
Right-most x-intercept: (3, 0)
Please answer this multiple choice question for 30 points and brainliest!!
Answer:
B. s = 0.85r
Step-by-step explanation:
The sale price is 15% off the regular price. In equation form, that is ...
s = r - 15%×r
s = r(1 - 0.15) = 0.85r
The equation that can be used to calculate the sale price is s = 0.85r.
What is the ratio of the corresponding sides of ABCD to LMNO?
3/2
1/2
2/3
2/1
Answer:
2 : 3
Step-by-step explanation:
Calculate the ratio of corresponding sides
AB : LM = 4 : 6 = 2 : 3
AD : LO = 2 : 3
DC : ON = 4 : 6 = 2 : 3
CB : NM = 2 : 3
The ratio of corresponding sides is 2 : 3
Which property of real numbers is shown below? 3 + ((-5) + 6) = (3 + (-5)) + 6
Answer:
the associative property
Step-by-step explanation:
The associative property of addition lets you move the parentheses without changing the order of the operands.
Ten thousand marbles were produced on a production line the first 100 marbles off the line were taken and tested for roundness does this sampling result in a simple random sample
Answer:
No, because each group of n items does not have an equal chance of being selected.
Step-by-step explanation:
After two half-lives, what fraction of a radioactive sample has decayed?1/2 2/3 3/4 5/6
A half life means that half the sample decays.
If the sample size is 1 , then after one half life there would be x * 1/2 = 1/2 of the sample left.
For the 2nd half life, multiply 1/2 by 1/2 to get 1/4.
So after 2 half lives, there is 1/4 of the sample left, which means 3/4 of the sample decayed.
The answer is 3/4
Need help with fill in the exponent #9
When you raise something to the power of -1, all that happens is that thing turns upside down.
For example: (x^3 / y^4)^-1 will become (y^4 / y^3), basically the same fraction but just swap the numerator and denominator.
In your example, the first exponent is 4 and the second exponent is 3.
Answer: y^4 and x^3
A conveyor belt leads from the ground to a bar door24 feet high. The angle between the belt and the ground is 32 degree. What is the length of the conveyor nearest foot?
Answer:
45 feet
Step-by-step explanation:
This is a classic right triangle trig problem. We have a reference angle, which is the angle made between the ground and the belt, of 32 degrees. The height up the side of the barn, which is the side across from the reference angle, is 24 feet. Which of our trig ratios relates side opposite to the hypotenuse? It's the sin ratio, so let's set it up and solve for the length of the belt, which is the hypotenuse of the right triangle.
[tex]sin(32)=\frac{24}{x}[/tex]
Doing some algebraic acrobatics that with we get
[tex]x=\frac{24}{sin(32)}[/tex]
Plug that into your calculator in degree mode and you'll get 45.28991. Rounded to the nearest foot is 45 feet.
The length of the conveyor is approximately 45 feet.
The subject of the question is Mathematics, and it deals with determining the length of a conveyor belt that makes an angle with the horizontal. This type of problem involves trigonometry, specifically the use of sine, cosine, or tangent functions to find the length of the hypotenuse of a right-angled triangle.
To find the length of the conveyor belt, we consider the belt as the hypotenuse of a right-angled triangle, with the vertical height of the barn door as the opposite side, and the angle given as the angle between the belt (hypotenuse) and the ground (adjacent side).
The height of the barn door is 24 feet, and the angle between the belt and the ground is 32 degrees. We can use the sine function (sin) since we have the opposite side and need to find the hypotenuse (length of the conveyor belt).
The formula to find the length (L) of the conveyor belt is:
L = height / sin(angle)
L = 24 feet / sin(32 degrees)
L = 24/0.5299
L = 45.29 feet
Please help! ASAP ty!
Answer:0.1
Step-by-step explanation:
4^3 * 4^4 =
A) 4^-1
B) 4^1
C) 4^7
D) 4^12
The answer is:
The correct option is:
C) [tex]4^{3}*4^{4}=4^{7}[/tex]
Why?To solve the problem, we need to remember the product of powers with the same base property, the property is defined by the following relation:
[tex]a^{m}*a^{n}=a^{m+n}[/tex]
If we are multiplying two or more powers with the same base, we must keep the base and add/subtract the exponents.
So, we are given the expression:
[tex]4^{3}*4^{4}[/tex]
We can see that both powers have the same base (4), so solving we have:
[tex]4^{3}*4^{4}=4^{4+3}=4^{7}[/tex]
Hence, we have that the correct option is:
C) [tex]4^{3}*4^{4}=4^{7}[/tex]
Have a nice day!
Answer:
The correct answer is option C
4^7
Step-by-step explanation:
Points to remember
Identities
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾
xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
x⁻ᵃ = 1/xᵃ
To find the correct option
It is given that,
4^3 * 4^4
⇒ 4³ * 4⁴
By using identities we can write,
4³ * 4⁴ = 4⁽³ ⁺ ⁴)
= 4⁷
Therefore the correct option is option C. 4^7
Please help me please
Answer:
y = 3.4
Step-by-step explanation:
Given 2 secants and a tangent drawn to the circle from an external point then
The square of the measure of the tangent is equal to the product of the external part of the secant to the entire secant.
Using the secant with measure y + 11, then
y(y + 11) = 7²
y² + 11y = 49 ( subtract 49 from both sides )
y² + 11y - 49 = 0 ← in standard form
with a = 1, b = 11 and c = - 49
Using the quadratic formula to solve for y
y = ( - 11 ± [tex]\sqrt{11^2-4(1)(-49)}[/tex] ) / 2
= ( - 11 ± [tex]\sqrt{121+196}[/tex] ) / 2
= ( - 11 ± [tex]\sqrt{317}[/tex] ) / 2
y = [tex]\frac{-11-\sqrt{317} }{2}[/tex] or y = [tex]\frac{-11+\sqrt{317} }{2}[/tex]
y = - 14.4 or y = 3.4
However y > 0 ⇒ y = 3.4 ( nearest tenth )
A cylinder has an elliptical base with major semiaxis length of 6 cm and minor semiaxis length of 4 cm. its altitude is 7.5 cm. find the volume of the cylinder. (hint: volume of the cylinder = area. of base × altitude.) volume (to the nearest tenth) = a0 cm 3.
Answer:
180π cm³
Step-by-step explanation:
The formula for the area of an ellipse with major axis a and minor axis b is
A = π·a·b.
Here, that area is A = π(6 cm)(4 cm) = 24π cm².
Multiplying this base area by the altitude, 7.5 cm, results in the volume:
V = (24 cm²)·π·(7.5 cm) = 180π cm³
Answer:
565,5 cm³
Step-by-step explanation:
To calculate the volume of a cylinder we have to found the area of the base and multiply by the altitude of the cylinder. As the base is elliptical, the area is given by:
[tex]A = a*b*\pi[/tex], where a is the major axis and b the minor axis. Thus:
[tex]A=6*4*\pi =75.39 cm^2[/tex]
And,
[tex]V = A*h = 75.39*7.5 = 565.48 cm^3[/tex].
Rounding to the nearest tenth: 565.5 cm³
Enter the explicit rule for the geometric sequence.
15, 3, 3/5, 3/25, …
Answer:
an = 15 (1/5)^(n-1)
Step-by-step explanation:
In a geometric series, each term is multiplied by a common ratio to get the next term. Such that:
an = a₁ (r)^(n-1)
Here, the first term, a₁, is 15. The common ratio, r, is 1/5, because each term is divided by 5 to get the next term. So:
an = 15 (1/5)^(n-1)
Your answer is correct, well done!
I think this is an example of it
The area of a triangle is 33.6 square inches. If the height of the triangle is 4 inches, what is the length of the base? b = a0 in.
[tex]a = \frac{b \times h}{2} [/tex]
33.6 × 2 = b×h
67.2 = b×h
h=4
67.2÷4 =b
16.8=b
answer: b=16.8inches
Which of the following statements follows from
(x - 3)^2 = 5?
A. x^2 + 9 = 5
B. x - 3 = +- Square root of 5
C. x - 3 = +-25
Answer:
Option B.
Step-by-step explanation:
we have
[tex](x-3)^{2}=5[/tex]
take square root both sides
[tex](x-3)=(+/-)\sqrt{5}[/tex]
[tex]x=3(+/-)\sqrt{5}[/tex]
evaluate the function f(x)=-2x^2-3x+5 for the input value -3
Answer:
the answer should be f(x)=-4
Substitute x=-3 in the equation
F(x)= -2(-3)^2 -3(-3) +5
-18+9+5=-4
The answer is -4
PLEASE HELP ASAP 40 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Zoom in a bit, the answers are a tad glitched ):
Answer:
see explanation
Step-by-step explanation:
Using the coefficients of the polynomial and evaluating for h = - 3
- 3 | 1 - 4 - 9 36
↓ - 3 21 - 36
-------------------------
1 - 7 12 0 ← remainder
Since remainder is 0 then (x + 3) is a factor, so
y = (x + 3)(x² - 7x + 12)
To factor the quadratic
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (- 7)
The factors are - 4 and - 3, since
- 4 × - 3 = + 12 and - 4 - 3 = - 7, then
x² - 7x + 12 = (x - 4)(x - 3), and
y = (x + 3)(x - 4)(x - 3)