Answer:
slope = 3/4
Step-by-step explanation:
Select the correct answer.
Select the function that defines the given sequence.
-8, -20, -50, –125, 625,...
ОА
- 1)
f(n) = -8-()
n-
OB.
- 1)
= -8.(29)
OC f(1) = -8
f(n) = f(n − 1), for n = 2, 3, 4, ...
OD. (1) = 8
f(n) = - . 1(n − 1), for n = 2, 3, 4, ...
Answer:
Option C
Step-by-step explanation:
f(1) = -8
f(2) = -5/2×-8 = -20
f(3) = -5/2×-20 = -125
.
.
.
So option C is the answer
Answer:
C. a1 = -8
an = an-1 * 5/2 for n >1
Step-by-step explanation:
-8, -20, -50, –125, 625,...
We need to find the common ratio
Take the second term and divide by the first term
-20/-8 = 5/2
Take the third term and divide by the second term
-50/-20 = 5/2
The common ratio is 5/2
A geometric sequence is
an = a1 * r^(n-1)
an = -8 *(5/2)^(n-1)
We can also write a recursive formula
a1 = -8
an = an-1 * 5/2 for n >1
[tex]4 + \frac{4}{4 } \: = [/tex]
what is answer
Answer:
5Step-by-step explanation:
[tex]4 + \frac{4}{4} [/tex]
= 4 + 1
= 5 (Ans)
Solve this inequality: 4x-8>-40
Answer:
x > - 8
Step-by-step explanation:
4x - 8 > - 40
4x > - 40 + 8
4x > - 32
Divide 4 on both sides,
4x / 4 > - 32 / 4
x > - 8
Find the area AND perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
a=40+8pi, p=4pi+4(sqrt of 29)
Step-by-step explanation:
rsm geometry class 122?
The organic garden at a restaurant is rectangular in shape and has a perimeter of 84 feet. If the length of the garden is 24 ft longer than the width of the garden what is the area of the garden in sq ft
Answer:
297 square feet
Step-by-step explanation:
Let w represent the width of the garden.
Since the length is 24 ft longer than the width, it can be represented by w + 24.
Use the perimeter formula, p = 2l + 2w. Plug in the perimeter and w + 24 as l, then solve for w:
p = 2l + 2w
84 = 2(w + 24) + 2w
84 = 2w + 48 + 2w
84 = 4w + 48
36 = 4w
9 = w
So, the width is 9 ft. Add 24 to this to find the length:
24 + 9 = 33
So, the length is 33 ft.
Find the area of the garden with the formula A = lw:
A = lw
A = (33)(9)
A = 297
The area of the garden is 297 square feet.
x^ 3 +x^ 2 +4x/x^ 2 +x-2
into partial
fractions
Answer:
x + (4/ x-2) + (2/ x-1)
Step-by-step explanation:
x + (6x/ x^2 + 2x - x -2)
x + (6x/ (x + 2) X (x - 1))
(6x/ (x + 2) X (x - 1))
(A/ x+2) + (B/ x-1)
(6x/ (x + 2) X (x - 1)) = (A/ x+2) + (B/ x-1)
6x = Ax + Bx - A + 2B
6x = (A+B)x + (-A+2b)
{0 = -A+2B
{6 = A+B
(A,B) = (4, 2)
(4/ x+2) + (2/ x-1)
x + (4/ x-2) + (2/ x-1)
Which sequence is arithmetic?
O 2, 6, 18, 54, ...
O 3, 6, 12, 24, ...
O 11, 14, 17, 20, ...
O 7, 11, 13, 18, ...
Answer:
11, 14, 17, 20, ...
Step-by-step explanation:
An arithmetic sequence is one where each term increases by the same number every time. This is called the common difference and is always added to the previous term to get the current term. The only sequence that follows this is the third once. Every term increases by 3; therefore, it is an arithmetic sequence.
I need help completing this problem ASAP
Answer:
D. [tex]3x\sqrt{2x}[/tex]
Step-by-step explanation:
The problem gives on the following equation:
[tex]\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}[/tex]
Alongside the information that ([tex]x\geq0[/tex]).
One must bear in mind that the operation ([tex]\sqrt[/tex]) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,
[tex]\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}[/tex]
Now remove the duplicate factors from underneath the radical,
[tex]2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}[/tex]
Simplify,
[tex]4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}[/tex]
[tex]3x\sqrt{2x}[/tex]
What is the slope of the line passing through the points (6,1) and (-3,-4)?
Answer:
5/9
Step-by-step explanation:
y2-y1/x2-x1 = 5/9
Find f′ in terms of g′
f(x)=x2g(x)
Select one:
f′(x)=2xf′(x)+2xg′(x)
f′(x)=2xg′(x)
f′(x)=2x+g′(x)
f′(x)=x2g(x)+2x2g′(x)
f′(x)=2xg(x)+x2g′(x)
f(x)g(x) if you find the derivative of two products, you get f(x)g’(x)+f’(x)g(x). Let’s say x^2 = f(x).
(x^2)(g’(x))+2x(g(x)) so it would be your last option, 2x(g(x))+x^2(g’(x))
Hello Pls help and thanks
Answer:
c.) in the correct answer
How many more cherry pies have 60 to 89 cherries than 90 to 119 cherries?
Answer:
6 pies
Step-by-step explanation:
For 60 - 89 cherries there are 10 pies
For 90 -119 cherries there are 4 pies
10 -4 = 6
There are 6 more pies in the 60 -89 cherries category than in the 90-119 category
4. Work out the area.
Answer:
90m^2
Step-by-step explanation:
image shows a trapezium,
area of trapezium = h(a+b)/2 = 9(8+12)/2 = 90
Answer:
29
12+8+9 =29
Step-by-step explanation:
additional question
add tose measure
A certain drug is used to treat asthma. In a clinical trial of theâ drug, 17 of 258 treated subjects experienced headachesâ (based on data from theâ manufacturer). The accompanying calculator display shows results from a test of the claim that less than 11â% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete partsâ (a) throughâ (e) below. â
1-PropZTest
prop<0.11
z=â2.264337000
p=0.0117766978
p=0.0658914729
n=258
a. Is the testâ two-tailed, left-tailed, orâ right-tailed?
b. What is the best statistics?
c. What is the P-value?
d. What is the nut hypothesis and what do you conclude who det hypothesis?
Identify the null hypothesis.
A. H0: pâ 0.11.
B. H0: p=0.11.
C. H0: p<0.11.
D. H0: p>0.11.
Decide whether to reject the null hypothesis.
A. Reject the null hypothesis because theâ P-value is greater than α.
B. Fail to reject the null hypothesis because theâ P-value is less than or equal to α.
C. Reject the null hypothesis because theâ P-value is less than or equal to α.
D. Fail to reject the null hypothesis because theâ P-value is greater than α
e. What is the finalâ conclusion?
A. There is not sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
B. There is not sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
C. There is sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
Solution :
a). The test is a left tailed test.
b). The sample proportion is :
[tex]$\hat p = \frac{x}{n}$[/tex]
[tex]$\hat p = \frac{17}{258}$[/tex]
= 0.065
Determining the Z statistics using the formula :
[tex]$Z=\frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]
[tex]$Z=\frac{0.065 - 0.11}{\sqrt{\frac{0.11(1-0.11)}{258}}}$[/tex]
= -2.31
∴ Z statistics value is -2.31
c). Using the excel function, the P-value is :
P-value = Normsdist(-2.31)
= 0.0104441
d). The null hypothesis is [tex]$H_0: P = 0.11$[/tex]
The level of significance is 0.01
We fail to reject the null hypothesis as the P value is less than or equal to the significant level.
Part III- Percentage Problems
1. You currently have $4,500 saved in your bank account. You have decided to use $2700.
What percentage of your savings did you use? Show all your work to justify your answer.
2. An organization raises money for students who attend Berkeley College every year.
Currently, they have raised $11,250 which represents 45% of the money they raise.
Determine the amount of money the organization will raise in total. Show all your work
to justify your answer.
The percentage of your savings that I use is 60%
This shows that the amount of money the organization will raise in total is $25,000.
1) Given
Total amount saved = $4500
Amount used = $2,700
Percentage of money used = Amount used/Total amount saved × 100%
[tex]Percentage \ of \ money \ used = \frac{2700}{4500} \times 100\\Percentage \ of \ money = \frac{27}{45} \times 100\\Percentage \ of \ money \ used = \frac{2700}{45} \\Percentage \ of \ money \ used = 60 \%[/tex]
Hence the percentage of your savings that I use is 60%
2) Let the amount of money the organization will raise in total be x
Since the 45% of the money they raise represents $11,250, hence:
[tex]45\% \ of \ x = \$11,250\\0.45x = 11,250\\x = \frac{11250}{0.45}\\ x = 25,000[/tex]
This shows that the amount of money the organization will raise in total is $25,000
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The vertex form of the equation of a vertical parabola is given by , where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra. Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part F
What is the value of p for your parabola?
Font Sizes
Characters used: 0 / 15000
Part G
Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
Font Sizes
Characters used: 0 / 15000
Part H
Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
Font Sizes
Characters used: 0 / 15000
Part I
Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.
Font Sizes
Characters used: 0 / 15000
Part J
To practice writing the equations of vertical parabolas, write the equations of these parabolas in vertex form:
focus at (-5, -3), and directrix y = -6
focus at (10, -4), and directrix y = 6.
Answer:
Step-by-step explanation:
Focus: (6,4)
Directrix lies 6 units below the focus, so the parabola opens upwards and focal length p = 6/2 = 3.
The equation of the directrix is y = -2.
The vertex is halfway between focus and directrix, at (6,1).
Equation of the parabola:
y = (1/(4p))(x-6)²+1 = (1/12)(x-6)²+1
The equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
What are parabolas?Parabolas are used to represent a quadratic equation in the vertex form
The given parameters are:
Focus = (6,4)
Directrix (x) = 6 units below the focus,
Start by calculating the focal length (p)
[tex]p = \frac x2[/tex]
This gives
[tex]p = \frac 62[/tex]
[tex]p = 3[/tex]
Next, calculate the vertex as follows:
[tex](h,k) = (6,2/2)[/tex]
Simplify
[tex](h,k) = (6,1)[/tex]
The equation of the parabola is then calculated a:
[tex]y = \frac{1}{4p}(x - h)^2 + k[/tex]
So, we have:
[tex]y = \frac{1}{4*3}(x - 6)^2 + 1[/tex]
Simplify
[tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Hence, the equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Read more about parabola at:
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The point p=(2/5,y) lies on the unit circle below what is the value of y in simplest form
Step-by-step explanation:
distance of (1,0) from the origin is,
√{(1-0)²+(0-0)²}
= √1
= 1
So the radius of the circle is 1,
now for the point (2/5,y) distance from origin should be the same since it's the radius
so,
√{(2/5-0)²+(y-0)²} = 1
or, √(4/25+y²)=1
or, 4/25+y²=1
or, y² = 1-4/25
or, y²=21/25
or, y=√(21/25)
or, y=√21/5
so, the simplest form of y is,
[tex] \frac{ \sqrt{21} }{5} [/tex]
If the average(arithmetic mean) of g and 100 is 75,what is the value of g + 100?
The value of g + 100 is 150.
Given that,
The average of g and 100 is 75.
And we have to determine the value of g + 100.
So that means
The arithmetic mean of g and 100 is 75.
So, mathematically it should be
[tex]\frac{g + 100}{2} = 75\\\\[/tex]
So, g + 100 = 150
Therefore we can conclude that the value of g + 100 is 150
Learn more about the mean here: brainly.com/question/11230531
Janet invests a sum of EUR in an account that offers 3.5% simple interest. After ten years her investment is worth 7425 EUR. How much did she invest?
We need to find the amount of money Janet invested in 10 years to yield 7425 EUR
She invested EUR 21,214.29
Simple interest = P × R × T
Where,
P = principal = ?
R = interest rate = 3.5% = 0.035
T = Time = 10 years
Simple interest = 7425 EUR
Simple interest = P × R × T
7425 = p × 0.035 × 10
7425 = p × 0.35
7425 = 0.35p
Divide both sides by 0.35
P = 7425 / 0.35
= 21,214.285714285
Approximately,
P = EUR 21,214.29
https://brainly.com/question/10936433
A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 8 questions on the survey
Answer:
40320 different surveys would be necessary ...
Step-by-step explanation:
let's start small :
how many are required for 2 questions ?
well, 2 (we can either ask question 1 first and then question 2, or question 2 first and then question 1).
how many for 3 questions ?
well, we have a choice of 3 questions to be asked first. but then for the second and third question we are back in the previous problem of 2 (remaining) questions.
so, we multiply the 3 initial options with the 2 following options. 3×2 = 6
how many for 4 questions ?
well, we have a choice of 4 questions as first question, and then fit the rest we are back in the previous problem of 3 questions. 4×3×2 = 24
you see the pattern ?
yes, that continues as far as we want to go.
for our example the problem was about 8 questions.
so,
8×7×6×5×4×3×2 = 8! = 40320
find the midpoint of the segment with the following endpoints (10,6) and (3,1)
Answer:
(6.5,3.5)
Step-by-step explanation:
To find the x coordinates of the midpoint, average the x coordinates of the endpoints
(10+3)/2 = 13/2 = 6.5
To find the y coordinates of the midpoint, average the y coordinates of the endpoints
(6+1)/2 = 7/2 = 3.5
(6.5,3.5)
Which equation shows a slope of 3 and a y-intercept of (0,7)?
y = 7x + 3
y = −7x + 3
y = 3x
y = 3x + 7
Answer:
[tex]{ \tt{y = 3x + 7}}[/tex]
Step-by-step explanation:
General equation of a line:
[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]
m is the slope, and c is the y-intercept:
m = 3, and c = 7
You are trying to get an important customer order out the door, but your boss keeps coming over to ask you about the status of this order and several other orders. He's just nervous and wants to be
Identify the triangle, ABC, which has a 72∘ angle and a 36∘ angle.
Answer:
isosceles acute
Step-by-step explanation:
sum of angles in a triangle = 180
to find third angle, subtract 72 & 36 from 180 and you get 72
72, 36, and 72 are all less than 90 so it will be an acute triangle
It will also be isosceles bc there are 2 angles of the same measure
Sarah has two similar rectangular boxes. The dimensions of Box 1 are four times those of Box 2.
How many times greater is the surface area of Box 1 than the surface area of Box 2?
8
64
4
16
Answer:
16
Step-by-step explanation:
an area is always calculated by multiplying 2 dimensions.
when changing the dimensions, then the change factors for EACH dimension go into the calculation too.
therefore, when both dimensions of an area are enlarged 4 times, then the area is enlarged 4×4 = 16 times.
this just propagates to the whole surface area of an object, as each individual area of the overall surface area is enlarged by the same factor. and so, the sum of all the individual areas (= altogether the surface area of the object) is also enlarged in total by the same factor.
just think
16×a + 16×b + 16×c ... = 16×(a+b+c+...)
and you understand why.
Value of x
1\5(x)(1/5)=6/3(5/1)
Answer:
1/25=3/30
1250=
2501
2389
5552
factorise m^2 - 12 m + 24
Answer:
(m-6+2root3)(m-6-2root3)
Step-by-step explanation:
m^2 - 12m +36 -12
= (m-6)^2 - 12
= (m-6+2root3)(m-6-2root3)[root 12 = 2root3]
PQRS is a parallelogram of area 18 cm. if PQ = 5 cm & QR = 4 cm. calculate the lengths of corresponding heights ?
Answer:
2cm
Step-by-step explanation:
area of parallelogram=b*h=18cm
5*4=20
length of corresponding heights=20-18
=2cm
the length of corresponding height of the parallelogram is : 2cm
Meaning of a parallelogramA parallelogram can be defined as a simple quadrilateral that is it possesses four sides and two pairs of parallel sides.
A opposite sides of a parallelogram are equal and the opposite angles of a parallelogram are equal.
In conclusion, the length of corresponding height of the parallelogram is : 2cm
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Wyatt is making a salad using tomatoes, cucumbers, and carrots. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Wyatt uses:
Ingredient Price per kilogram Amount
Tomatoes 3.30dollars per kilogram 0.3
Cucumbers x dollars per kilogram y kilograms
Carrots z dollars per kilogram 0.20
The total amount Wyatt spends on ingredients is C dollars.
Write an equation that relates x, y, z, and C.
According to the given information, we build the equation for the cost. After we build the equation, the equation that relates these measures is:
[tex]C = 0.99 + xy + 0.2z[/tex]
Cost:
0.3 kilograms of tomatoes, at 3.30 dollars per kilogram.
Thus, the cost starts at:
[tex]C = 0.3*3.3 = 0.99[/tex]
y kilograms of cucumbers, at x dollars per kilogram.
Considering this, the cost will now be of:
[tex]C = 0.99 + xy[/tex]
0.2 kilograms of carrots, at z dollars per kilogram:
Now, we have to consider this for the cost, so:
[tex]C = 0.99 + xy + 0.2z[/tex]
A similar example is given at https://brainly.com/question/14544759
Consider a credit card with a balance of $7000 and an APR of 16.5 %. If you want to make monthly payments in order to pay off the balance in 1 year, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.
9514 1404 393
Answer:
$7641.24
Step-by-step explanation:
The amortization formula tells the payment amount.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where principal P is paid off in t years with n payments per year at interest rat r.
Using the given values, we find ...
A = $7000(0.165/12)/(1 -(1 +0.165/12)^-12) = $7000×0.01375/(1 -1.01375^-12)
A = $636.77
The total of 12 such payments is ...
$636.77 × 12 = $7641.24
You will pay a total of about $7641.24.
_____
Additional comment
Since the payment amount is rounded down, the actual payoff will be slightly more. Usually, the lender will round interest and principal to the nearest cent on each monthly statement. The final payment will likely be a few cents more than the monthly payment shown here.
