Answer:
Tn = 34-3nStep-by-step explanation:
The formula for calculating the nth term of an arithmetic sequence is given as;
Tn = [tex]a+(n-1)d[/tex]
a is the first term
n is the number of terms
d is the common difference
If two terms of an arithmetic sequence are a12=70 and a30=124 then;
T12 = a+(12-1)d = 70
T12 = a+11d = 70...(1)
T30 = a+(30-1)d = 124
T30 = a+29d = 124...(2)
Solving equation 1 and 2 simultaneously to get a and d;
Taking the difference of both equation we have;
29d - 11d = 124-70
18d = 54
d = 54/18
d = 3
Substituting d=3 into equation 1 to get the value of 'a' we have;
a+11(3) = 70
a+33=70
a = 70-33
a = 37
To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3
Tn = 37+(n-1)3
Tn = 37+3n-3
Tn = 34-3n
This gives the required nth term
Franco freezes the vegetables he grows in the summer so he can eat them all year long. He packs the vegetables into cube-shaped boxes that each have a volume of one cubic foot. Then, he places the boxes into a freezer that is shaped like a rectangular prism. The bottom of the freezer can be completely covered by a layer of 6 boxes. If the volume of the freezer is 18 cubic feet, what is its height?
Answer:
3 feet
Step-by-step explanation:
If there are 6 boxes in each layer, there are 3 layers to have a total of 18 boxes, each of which is 1 cubic foot.
Three layers of boxes that are 1 ft high will be 3 ft high.
The height of the freezer space is 3 feet.
What is 1/3 of 5 1/2
Answer:
im so sorry
Step-by-step explanation:
Answer:
(1/3)*(5 1/2) = 1.83333333333 or 1.8
Step-by-step explanation:
The admission fee at a carnival is $5 for children and $8 for adults on Friday, 1250 people attended the carnival and $7300 was collected. Write a system on equations to represent the situation. Then solve the system of equations by substitution. Explain what the solution means.
Answer:
-> a + c = 1250 ____________ (1)
-> 8a + 5c = 7300 __________(2)
There were 900 children and 350 adults.
Step-by-step explanation:
Let the number of children at the carnival be c.
Let the number of adults at the carnival be a.
The admission fee at a carnival is $5 for children and $8 for adults on Friday.
1250 people attended the carnival and $7300 was collected. This means two things:
-> a + c = 1250 ____________ (1)
-> 8a + 5c = 7300 __________(2)
We now have a system of equations representing the problem.
To solve, make a subject of formula in (1):
a = 1250 - c _______(3)
Put (3) in (2):
8(1250 - c) + 5c = 7300
10000 - 8c + 5c = 7300
10000 - 7300 = 3c
3c = 2700
c = 2700 / 3 = 900
Put the value of c back in (3):
a = 1250 - 900 = 350
Therefore, there were 900 children and 350 adults at the carnival.
find all of the polar coordinatesof the point p if p=(7, pi/3)
Answer:
(7, π/3 +2kπ) . . . for any integer k(-7, 4π/3 +2kπ) . . . for any integer kStep-by-step explanation:
Adding any multiple of 2π radians to the angle will result in the same point. So, one set of coordinates of the same point can be ...
(7, π/3 +2kπ) . . . . for any integer k
The value of the radius can be negated, and an odd multiple of π can be added to the angle to get the same point. Another set of coordinates of the same point can be ...
(-7, 4π/3 +2kπ) . . . . for any integer k
can someone please answer this fast, ty
Answer:
13p
Step-by-step explanation:
12p+p
Factor out the p
p(12+1)
p (13)
13p
Find the lcm of 10 and 3
Answer:
30
Step-by-step explanation:
least common multiple
10 = 2*5
3 = 3
2*3*5 = 30
The least common multiple is 30
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! Show your work!
Answer:
P represents the population in year 0
Step-by-step explanation:
The exponential growth function is f(x) = a (1 + r)^t, where a is the initial
amount (at t = 0), (1 + r) is the factor of growth , r is the rate of growth
in decimal ant is the time of growth
the function C(t) = P(1 + r)^t represents the population of
centerville at year t, where P is the initial population and r is the
rate of increase
If your investment is increased 10% annually, then that means
each year, your total has multiplied itself by 110% (the growth factor
is 1 + 10/100 = 1.1)
(1 + r) is the factor grows each year
C(t) = P(1 + r)^t
C depends on P(starting population) , r(the increasing rate and
t(the time in year)
r is the rate of increase means the percentage of increasing , then
0 < r < 1
r is not less than 0
P is the initial amount when t = 0
P represents the population in year 0
Answer:
P represents the population in year 0
Step-by-step explanation:
Help asap! Giving brainliest!
Answer:
A D E
Step-by-step explanation:
Answer:e
Step-by-step explanation:
Start at 4, 13 move 2 units left and 9 units down where do you end up
Answer:
( 2, 4 )
Step-by-step explanation:
Look at the attachment
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply
130 cars are parked in a parking lot. Each row holds 8 cars. If every row is full except for the last, how many cars are in the last row?
Answer:
2 are in the last row
Which is the simplified form of m ^-8 p^0
Answer:
Step-by-step explanation:
m−^8p^0
=1/m^8
Complete A and B for 5-8 points.
Answer:
a) 4 hours
b) 11 am
Step-by-step explanation:
So say the number of hours is x
a) 72 + 6x = 96
6x = 24
x = 4
b) 7am + 4 hours = 11am
Reese's truck can go 1,040miles on a full tank of 52gallons of gas. Find the rate of miles per gallon.
Answer:
20
Step-by-step explanation:
Since the truck goes 1040 miles and costs 52 gallons of gas every tiime it goes 1040 miles, we can divide 1040 by 52 to see how far 1 gallon of gas will get you. 1040/52=20 so every 20 miles cost 1 gallon of gas
The difference of two supplementary angles is 70 degrees. Find the measures of the angles.
Answer:
DUEDY A. 32 degrees
Step-by-step explanation:
PATROLLING WEE WOOO
Xd
Answer:
55 125
Step-by-step explanation:
Let the smaller angle = x
Let the larger angle = x + 70
They are supplementary so the total of the two angles, by definition must be 180 degrees. Note that you should understand that any number of angles can but supplementary as long as they all add up to 180 degrees.
x + x + 70 = 180
2x + 70 = 180
2x + 70 - 70 = 180 - 70
2x = 110
2x/2 = 110/2
x = 55
the smaller angle = 55 degrees
The larger angle = 55 + 70 = 125
The number of new contributors to a public radio station's annual fund drive over the last ten years is 63, 58, 61, 72, 98, 103, 121, 147, 163, 198 Using Microsoft Excel, develop a linear regression model that predicts the number of new contributors. Explain the slope of this model. Based on this model, how many new contributors would you predict for the following year?
Answer:
The number of potential members predicted in next year's estimate becomes 193. The further explanation is given below.
Step-by-step explanation:
The slope of the model,
m = 15.345
c = 24
After comparing with the equation,
⇒ [tex]y=mx+c[/tex]
we get,
⇒ [tex]=15.345x + 24[/tex]
The slope seems to be a positive value which also means that another always improves this as component decreases. Which ensures that perhaps the number of contributors rising as time went by.
So that the above is the right answer.
Which images below are scalene triangles?
Triangles A and D
Triangles B and D
Triangles A and C
Triangles C and D
Answer: C & D
Step-by-step explanation:
I took the test and got it right (:
Hope this helps
A scalene triangle has NO equal sides A has 3 equal sides and B has 2 equal sides, so that means Triangles C & D are your answer!
Find the area of a circle with a diameter of 15 feet
Answer:
15[tex]\pi[/tex]
Step-by-step explanation:
with diameter
A=[tex]\pi[/tex]d
A=[tex]\pi[/tex](15)
A=15[tex]\pi[/tex]
Find the equation of the line that has the given properties. Write the equation in slope-intercept form, if possible.
Contains (3, 3); perpendicular to the line y = 2x - 1
Answer:
y = (-1/2)x + 9/2
Step-by-step explanation:
the equation of a straight line can be written as;
y = mx + c ......1
Where;
m = slope
c = intercept
For two lines to be perpendicular their slope must be opposite reciprocal of each other.
m1 × m2 = -1 .....2
Given;
The equation Contains (3, 3); and perpendicular to the line y = 2x - 1
Slope of the given equation m1 = 2
Slope of the line m2; substituting m1 to equation 2.
2 × m2 = -1
m2 = -1/2
So,
y = (-1/2)x + c
To solve for c, let's substitute the given point on the line; (3,3).
3 = (-1/2)(3) + c
3 = -3/2 + c
c = 3 + 3/2
c = 9/2
Therefore, the equation of the line that has the given properties is;
y = (-1/2)x + 9/2
Your teacher has 50 pencils. 9 of the pencils are green, 10 are yellow, 7 are
blue and the rest are red. Once a pencil is picked, assume it is not given
back to the teacher. What is the probability that the first 3 students pick a
yellow pencil, a blue pencil and a red pencil in that order? Is this a
dependent or independent event? *
A. Independent, 1/70
B. Dependent, 1/70
C. Independent, 41/3125
D. Dependent, 41/3125
Answer:
B. Dependent, 1/70
Step-by-step explanation:
The probability that the first pencil is yellow is 10/50.
There are now 49 pencils, so the probability that the second pencil is blue is 7/49.
There are now 48 pencils, so the probability that the third pencil is red is 24/48.
The total probability is (10/50) (7/49) (24/48) = 1/70.
Since the pencils aren't replaced after selection, each event changes the probability of the next, so the events are dependent.
6th grade math ! Help me please :))
Answer:
120
Step-by-step explanation:
20 ÷2=10 10×12=120
or 20×6=120
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answer:
0,8,5
Step-by-step explanation:
x+22 <32
Subtract 22 from each side
x+22-22 <32-22
x <10
The choices that fit
0,8,5
Answer:
Therefore, our applicable set is: 0, 8, and 5. All of these numbers make the inequality true.
Step-by-step explanation:
x + 22 < 32
This problem is fairly simple! All we need to do is substitute each number given for x and compute to find out if the equation will be true! First what we need to do is plug in each number given into our variable x. Our numbers are: 0, 10, 8, 71, 15, and 5
x = 0
0 + 22 < 32
22 < 32
Is 22 less than 32? It is! So it belongs to the solution set.
x = 10
10 + 22 < 32
32 < 32
32 is equal to 32, not less than 32. A number cannot be itself and less than itself, thus x = 10 does not belong to the solution set.
x = 8
8 + 22 < 32
30 < 32
Is 30 less than 32? Yes! Since the inequality is true (that's what these kinds of equations are called) it belongs to the solution set.
x = 71
71 + 22 < 32
94 < 32
Is 94 less than 32? No. 71 does not belong to this solution set.
x = 15
15 + 22 < 32
37 < 32
37 is not less than 32. Therefore it doesn't belong to the solution set.
x = 5
5 + 22 < 32
27 < 32
Is 27 less than 32? Yes. Therefore, it belongs to the solution set.
Therefore, our applicable set is: 0, 8, and 5. All of these numbers make the inequality true.
Joanie has $14. Then she got $23 for her birthday. Later she spend $5 on a book. Which number sentence can be used to find m, the amount of money Joanie has now?
A.
14+23-5=m
B.
14+23+5=m
C.
23-14+5=m
D.
23-14-5=m
Answer A
Step-by-step explanation:14+23-5
Which expression has the same value as the one below?
22+(-32)
○ 22+(-22)+(-10)
○22+(22)+(-10)
○22+(-22)+(10)
○22+0+32
Answer:
Option A
Step-by-step explanation:
22+(-32) is the same thing as 22-32.
[tex]22-32=-10[/tex]
Let's see if the given options are equal:Option A:
[tex]22+(-22)+(-10) \\22-22-10\leftarrow \text{Distribute -1 into the Parentheses.} \\0-10\\\boxed {-10}[/tex]
Option A's expression has the same value as the expression given.
Option B:
22+(22)+(-10)
[tex]22+22-10\\44-10\\\boxed {34}[/tex]
Option B's expression does not have the same value as the expression given.
Option C:
[tex]22+(-22)+(10)\\22-22+10\\0+10\\\boxed {10}[/tex]
Option C's expression does not have the same value as the expression given.
Option D:
[tex]22+0+32\\22+32\\\boxed{54}[/tex]
Option D's expression does not have the same value as the expression given.
The correct answer should be A: 22+(-22)+(-10).Answer:
the answer is A
hoped this helped
A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. a) Estimate the percentage of all males who identify themselves as the primary grocery shopper. Use a 98% confidence interval. Check the conditions first. b) A grocery store owner believed that only 43% of men are the primary grocery shopper for their family, and targets his advertising accordingly. He wishes to conduct a hypothesis test to see if the fraction is in fact higher than 43%. What does your confidence interval indicate? Explain. c) What is the level of significance of this test? Explain.
Answer:
a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.
b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.
c) [tex]\alpha =1-0.98=0.02[/tex]
Step-by-step explanation:
If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:
[tex]p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }[/tex]
Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and [tex]z_{\alpha/2}[/tex] is the z-value that let a probability of [tex]\alpha/2[/tex] on the right tail.
Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, [tex]\alpha[/tex] by 0.02 and [tex]z_{\alpha/2}[/tex] by 2.33
Where p' and [tex]\alpha[/tex] are calculated as:
[tex]p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02[/tex]
So, replacing the values we get:
[tex]0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438[/tex]
With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.
The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.
Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence [tex]1-\alpha[/tex] is equal to 98%
It means the the level of significance [tex]\alpha[/tex] is:
[tex]\alpha =1-0.98=0.02[/tex]
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
D. Vertx: (3,-16); Intercepts: x = -1, 7
Step-by-step explanation:
I graphed the equation on the graph below.
Six minus a number divided by 3 equals 8. What is the number?
Answer:
-18
Step-by-step explanation:
let n be the number
(6-n)/3 = 8
6-n = 24
6-24 = n
-18 = n
Answer:
The number is 30
Step-by-step explanation:
Six minus a number divided by 3 equals 8
x-6/3 = 8
x-6 = 8*3
x = 24 +6
x = 30
perform the following operations on matrices (1 8 0 7) (7 6 7 4) = ( )
Answer:
[tex]\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{cc}1&8\\0&7\end{array}\right]\left[\begin{array}{cc}7&6\\7&4\end{array}\right]=\left[\begin{array}{cc}(1)(7)+(8)(7)&(1)(6)+(8)(4)\\(0)(7)+(7)(7)&(0)(6)+(7)(4)\end{array}\right]\\\\=\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Each element of the product matrix is the dot product of the corresponding row in the left matrix and the corresponding column in the right matrix.
For example, the element at row 2, column 1 of the product is [0 7]·[7, 7], the dot product of row 2 of the left matrix with column 1 of the right matrix.
_____
Many calculators, spreadsheets, and web sites can do this tedious math for you.
Algebraic exspression of
15x +8
Answer:
15x-8=0
x=8/15
Step-by-step explanation:
What is an equation of the line that passes through the point (- 5, - 6) and is parallel to the line 4x - 5y = 35
Answer:
4x - 5y = 10
Step-by-step explanation:
Any line parallel to 4x - 5y = 35 will have the same equation EXCEPT that the constant will be different.
Starting with 4x - 5y = 35, replace x with the given x-coordinate -5 and the given y-coordinate -6, and finally the given 35 with the constant C:
4(-5) - 5(-6) = C, or
-20 + 30 = C. Thus, C = 10, and the equation of the new line is
4x - 5y = 10
The equation of line is 4x - 5y = 10
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient. On the y-axis, this number c is referred to as the intercept. Key Point y = mx + c is the equation for a straight line with a gradient of m and an intercept of c on the y-axis.
Given the points (-5,-6)
and parallel to line 4x - 5y = 35...…..(1)
the equation of line is (y - y₁) = m( x - x₁)
for parallel line condition the value of m is equal to both equations
converting eq. 1 in the form of y = mx + c
4x - 5y = 35
we get y = 4/5x -7
here m = 4/5 and c = -7
substitute the value of m in equation of line
where y₁ = -6; x₁ = -5
(y - (-6)) = 4/5(x - (-5))
y +6 = 4/5(x+5)
simplify above eq. we get
4x - 5y = 20
Hence the equation of the line that passes through the point (- 5, - 6) is 4x - 5y = 20
Learn more about equation of line
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