Answer:
[tex]a_{n}[/tex] = 100n - 78
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₄ = 1322 and a₃₈ = 3722 , then
a₁ + 13d = 1322 → (1)
a₁ + 37d = 3722 → (2)
subtract (1) from (2) term by term to eliminate a₁
24d = 2400 ( divide both sides by 24 )
d = 100
substitute d = 100 into either of the 2 equations and solve for a₁
substituting into (1)
a₁ + 13(100) = 1322
a₁ + 1300 = 1322 ( subtract 1300 from both sides )
a₁ = 22
then nth term formula is
[tex]a_{n}[/tex] = 22 + 100(n - 1) = 22 + 100n - 100 = 100n - 78
Evaluate the function: g(x) = -x +4 Find: g(b-3)
Answer:
g(b-3) = -b + 7
Step-by-step explanation:
Plug in the value (b-3) as x into the equation
g(b-3) = -(b-3) + 4
distribute the negative sign
g(b-3) = -b + 3 + 4
combine like terms
g(b-3) = -b + 7
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:
−−→AB=(xy)
What values should x an y take?
The values x and y take are 5 and 0 respectively.
We know that in mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way.
The relationships between two or more things are frequently represented by the points on a graph.
In this case, we have to determine the values of x and y.
Notice that in this graph, point A is located at A = 5 and point B is located at B = 0.
So, we can write (A, B) = (x, y) = (5, 0)
Therefore, the values x and y take are 5 and 0 respectively.
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Jada is comparing membership costs for two gyms. What is the difference in membership costs after m months if she joins Be strong instead of Zippy Health Club?
Write an expression for each membership cost for m months and subtract them.
Answer: Difference in membership costs after m months = -($24.96m + $34.94)
Step-by-step explanation:
Cost of Zippy health club = $49.95 + $19.95 per month
Cost of Be strong = $24.99 per month and $10 off the first month
Total cost after m months of Zippy health club = $49.95 + $19.95m
Total cost after m months of Be strong = $24.99 (m - 1) + $ 10
Difference in membership costs after m months ={ $24.99m - $24.99 + $10 ]-[$49.95m + $19.95}
=$(24.99 - 49.95) m -$14.99 - $19.95
= -$24.96m - $34.94
=-($24.96m + $34.94)
So Difference in membership costs after m months =-($24.96m + $34.94)
therefore jada have to pay more if she joins Be strong.
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The depreciation method that does not initially use the residual value in depreciation calculations is the.
An asset loses value over time as a result of use, damage, or obsolescence.
What is depreciation?An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline.
The depreciation method that does not initially use the residual value in depreciation calculations is the depreciating balance.
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In △ABC, ∠C = 2∠B and ∠A = 540, find the measure of ∠B.
Answer:
B = 42°
Step-by-step explanation:
All of the internal angles of a triangle sum to 180°
x + 2x + 54 = 180
3x = 180 - 54
x = 42 ° which is angle B
What is the midpoint of the segment (-6.-9)(16.5)
Answer:
M=(11,−2)
Step-by-step explanation:
Find the midpoint for [tex]P = \left(6, -9\right)P=(6,-9) \text{and} Q = \left(16, 5\right)Q=(16,5).[/tex]
The midpoint for two points P and Q is a point M whose coordinates is the half-sum of the corresponding coordinates of the two points.
Thus, [tex]M = \left(\frac{6 + 16}{2}, \frac{-9 + 5}{2}\right) = \left(11, -2\right)[/tex]
M=(11,−2)
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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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]
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!
Find the measure of angle 1.
5)
AB is a straight line.
A
152⁰
B
Let that angle be x
Linear pairs are supplementary
So
152+x=180x=180-152x=28°If f(x) = √2x, then f'(8) =
Answer:
√2
Step-by-step explanation:
Comment
You have differentiated the given equation. When you do that the x becomes 1. F'(x) is going to be √2 no matter what x is.
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
A sector of a circle of radius 14cm containing
an angle 60° is folded to forma cone
Calculate the radius of the base of the circle
}
answer is 2 ⅓
Explanation
Length of arc = circumference of the base of the
cone
is β/360 x 2πR=2πr
make r the subject of formula
r =βR/360
r=60 x 14/360
r=2⅓cm
please mark as brainliest if i am right
Using p as the variable for the problem below, solve for p. Submit your answer
as an inequality, using "<=" for < or ">" for ≥ if necessary. Round to two
decimal places.
Hosting a dinner party for 38 people, you plan to serve peach pie for dessert.
Each pie has 8 slices. How many pies must you buy to ensure each guest
gets 1 slice?
Answer:
Step-by-step explanation:
As host, we want to insure each guest has at least one slice of pie. We can say (1 Slice/Guest) and use this as a conversion factor. We also know each pie has 8 slices: (8 Slices/1 Pie). Since this is a conversion factor, we can invert it to (1 Pie/8 Slices). We expect 38 people and want to convert that number of people to the number of pies, p, we need.
p (pies) [tex]\geq[/tex] (38 Guests)*(1 Slice/Guest)*(1 Pie/8 Slices)
We use the [tex]\geq[/tex] sign to note that we need a minimum of pies to be sure everyone is served.
p (pies) [tex]\geq[/tex] (38 )*(1 /)*(1 Pie/8 )
Note how the units cancel:
Guests and Slices both cancel and we are left with pies as the only remaining unit, as we hoped we'd see.
p [tex]\geq[/tex] (38/8) pies
p = 4 +(6/8) pies
Since we cannot purchase 6/8 of a pie, we need to round up to 5 pies.
5 pies, at 8 slices per pie, will provide 40 servings, enough for the 38 guests.
This question was confusing 15 for whoever answers
Answer:
Refer to the attached image. I'm not clear on one point. Yes, it is confusing.
Step-by-step explanation:
See attached image.
5|2x+6|=26...can someone answer this please
Answer:
x = -2/5 or x = -28/5
Step-by-step explanation:
Let's solve your equation step-by-step.
5(|2x+6|)=26
Step 1: Divide both sides by 5.
5(|2x+6|)/5 = 26/5
|2x+6|=26/5
Step 2: Solve Absolute Value.
|2x+6|=26/5
We know either2x+6= 26/5 r2x+6=−26/5
2x + 6 = 26/5(Possibility 1)
2x+6−6= 26/5 - 6 (Subtract 6 from both sides)
2x = -4/5
2x/2 = -4/5/2 (Divide both sides by 2)
x = -2/5
2x + 6=-26/5 (Possibility 2)
2x+6= -26/5 (Simplify both sides of the equation)
2x + 6 - 6 = -26/5 - 6 (Subtract 6 from both sides)
2x = -56/5
2x/2 = -56/5/2(Divide both sides by 2)
x = -28/5
Answer:
x = -2/5 or x = -28/5
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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PLEASE HELP !!! which choices are equivalent to square root of -4???
Answer:
-2
Step-by-step explanation:
just a guess but it's right
I NEED HELP !!! Right now!!!
Answer:
Step-by-step explanation:
Rosa has $12.29 and spends $4.85. To the nearest dollar, about how much does she have left?
A $3
B $5
C $7
D $9
22.
(05.07 MC)
The table shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The correlation coefficient for the data is −0.9847. Which statement is true about the data in the table? (1 point)
There is no relationship between x and y.
There is a weak negative relationship between x and y.
There is a strong positive relationship between x and y.
There 22.
(05.07 MC)
The table shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The correlation coefficient for the data is −0.9847. Which statement is true about the data in the table? (1 point)
There is no relationship between x and y.
There is a weak negative relationship between x and y.
There is a strong positive relationship between x and y.
There is a strong negative relationship between x and y.
The option fourth "There is a strong negative relationship between x and y" is correct.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
The options are:
There is no relationship between x and y.There is a weak negative relationship between x and y.There is a strong positive relationship between x and y.There is a strong negative relationship between x and y.We have data:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The value of correlation r = -0.9847
As we know the value of r between -1 to +1
If r = 1 (perfect and positive correlation)
if r = -1 (perfect and negative correlation)
We have r = -0.9847
The value is near to -1 which means there is a strong negative relationship between x and y.
Thus, the option fourth "There is a strong negative relationship between x and y" 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.
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 concreteIf+you+invest+$100+at+an+interest+rate+of+15%,+how+much+will+you+have+at+the+end+of+eight+years?
Answer:
$305.9022863 or $305.90 (rounded to 2 decimal places)
Step-by-step explanation:
It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula
A= P(1+R)^n
A= the total amount P=Initial amount R= rate n=time period
P=$100 R=15% or 0.15(decimal) n=8 (years)
A= 100 (1.15)^8
A= 100(3.059022863)
A=305.9022863
The amount you will have after 8 years is $220
Calculating simple interestThe formula for calculating simple interest is expressed as:
SI =PRT
P is the principal = $100
T is the time = 8 years
R is the rate. = 15%
SI = 100 * 8 * 0.15
SI = $120
Amount after 8years = $100 + $120
Amount after 8years = $220
Hence the amount you will have after 8 years is $220
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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
In your notebook, set up the following subtraction in a vertical format and select the correct answer.
Find 2p 2 + 3p - 4 less - 2p 2 - 3p + 4.
1. 4p2 + 6p + 8
2. 4p2 - 6p - 8
3. 4p2 + 6p - 8
4. 0
The answer is 4p² + 6p - 8 which is subtraction of one equation from the other in vertical format.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have two polynomial:
2p² + 3p - 4 and -2p² - 3p + 4
Subtraction in a vertical format:
2p² + 3p - 4
- -2p² - 3p + 4
-------------------------
Changin sign of the expression -2p² - 3p + 4:
2p² + 3p - 4
+ 2p² + 3p - 4
-------------------------
Now adding like terms.
2p² + 3p - 4
+ 2p² + 3p - 4
-------------------------
4p² + 6p - 8
Thus, the answer is 4p² + 6p - 8 which is the subtraction of one equation from the other in vertical format.
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Which of the following is equivalent to
Answer:
The first one
Step-by-step explanation:
[tex]n^{2} - 6n + 9 = (n-3)^{2}\\\\[/tex]
The expression removes the first 9 terms of the summation so the summation goes from 10 to 19
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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You are heading to a drive-in movie and will need exact cash at the entrance for everyone in your car to get in. The cost is $6.50 per person. Write an expression that represents the total cash needed for your car based on the number of people, p, in your car.
Answer:
Using the concept of equation of line, we find that the relationship will be
C = $6.5p.
Step-by-step explanation:
If the cost per head is $6.5 and there are p persons entering the car, then the total amount would be $6.5p.
The final equation would resemble the equation of line y = mx + c.
The expression for the total cost C, would be
C = 6.5p.
Here y = C, x = p, m = 6.5 and c = 0.
So, the expression for the total cost will be the equation of line C = 6.5p.
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