Answer:
The sum of the first 70 terms of the sequence [tex]-6, -3,0,3,6, ...[/tex] is 6825.
Step-by-step explanation:
A sequence is a set of numbers that are in order.
In an Arithmetic Sequence the difference between one term and the next is a constant.
[tex]-6, -3,0,3,6, ...[/tex] This sequence has a difference of 3 between each number.
The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms.
[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]
where [tex]n[/tex] = the number of terms, [tex]a_1[/tex] = the first term, and [tex]d[/tex] = the common difference.
For our arithmetic sequence, the values of a, d and n are:
[tex]a_1 =-6[/tex][tex]d=3[/tex][tex]n = 70[/tex]So:
[tex]S_{70}=\frac{70}{2}(2(-6)+(70-1)3)\\\\S_{70}=35\left(3\left(70-1\right)-2\cdot \:6\right)=35\left(207-12\right)=35\cdot \:195)=6825[/tex]
given that the quadratic equation (k^2-1)x^2-2kx+3k+1=0 has equal roots show that 3K^3-3K-1=0
Step-by-step explanation:
The roots are equal, so the discriminant equals 0.
b² − 4ac = 0
(2k)² − 4 (k²−1) (3k+1) = 0
4k² − 4 (3k³ + k² − 3k − 1) = 0
k² − (3k³ + k² − 3k − 1) = 0
k² = 3k³ + k² − 3k − 1
0 = 3k³ − 3k − 1
Ann desires to grow tall sunflower plants. She wonders how the amount of water she provides the sunflowers will affect their growth. One spring Ann planted 25 sunflower plants, making sure each one had the same soil, amount of space, and exposure to sunlight. The first one received one ounce of water per day. The second one received 2 ounces of water per day, and so on.
To determine the ideal amount of water needed, she consistently watered her sunflowers this way and at the end of the summer recorded the height of each sunflower (in cm). Then she performed a regression analysis on the data.
She conducts a significance test to determine if there is convincing evidence of a positive linear relationship between the amount of water her sunflower plants received and how tall they grew. What is the correct test statistic and conclusion? Assume all conditions for inference are met.
(A)
t=2.68\textit{t}=2.68
t=2.68. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
(B)
t=2.68\textit{t}=2.68
t=2.68.There is not convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
(C)
t=5.10\textit{t}=5.10
t=5.10. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
(D)
t=5.10\textit{t}=5.10
t=5.10.There is not convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
(E)
t=5.875\textit{t}=5.875
t=5.875.There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
Answer: a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The appropriate test is a t-test for slope. The test statistic is t = 2.68 and the p-value is 0.005. Because the p-value, 0.005, is less than α=0.05 we have convincing evidence that there is a positive linear relationship between the amount of water received and how tall the sunflower plants grew.
Temperature (x) 65 70 75 80 85 90 95 100 105
Number of ice cream cones sold per hour (y) 8 10 11 13 12 16 19 22 23
Note: Critical Value for n = 9 is 0.666
Calculate the linear correlation coefficient r, for temperature (x) and the number of ice cream cones sold per hour (y). (round to 3 decimal place)
Is there a linear relation between the two variables x, and y? Why? If yes, indicate if the relationship is positive or negative. (Hint: Compare the absolute value of r and critical value)
Construct the least-squares regression line for temperature (x) and the number of ice cream cones sold per hour (y) and interpret its slope. (round to 3 decimal place)
Predict the number of ice cream cones sold per hour when the temperature is 80 and calculate the residual for x = 80º. (round to nearest whole number)
Would it be reasonable to use the least-squares regression line to predict the number of ice cream cones sold when it is 50 degrees? Explain your answer.
Answer:
Step-by-step explanation:
Hello!
You have to calculate the linear correlation coefficient (r) between the variables
X₁: temperature
X₂: Number of ice cream cones sold per hour.
The formula to calculate the coefficient of linear correlation between the two variables is the following:
[tex]r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{\sqrt{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2\frac{(sumX_2)^2}{n} ]} }[/tex]
∑X₁= 765; ∑X₁²= 66525 ∑X₂= 134 ∑X₂²= 2228 ∑X₁X₂= 11965 n=9
[tex]r= \frac{11965-\frac{765*134}{9} }{\sqrt{[66525-\frac{(765)^2}{9} ][2228-\frac{(134)^2}{9} ]} }[/tex]
r= 0.97
To test if there is a positive linear association between both variables the statistical hypotheses are:
H₀: ρ ≤ 0
H₁: ρ > 0
critical value 0.666
r= 0.97
The decision is to reject the null hypothesis, there is a positive linear correlation between the temperature and the number of ice cream cones sold per hour.
The regression line is
^Y= a + bX
where
a: represents the estimation of the y-intercept
b: represents the estimation of the slope
[tex]b= \frac{sumXY-\frac{sumXsumY}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]
b= 0.38
a= Y[bar]-bX[bar]
a= -17.69
The estimated regression line for the number of ice cream cones and the temperature is ^Y= -17.69 + 0.38Xi
To estimate the number of ice cream cones sold when the temperature is 80º you have to replace the value of X in the estimated regression line:
^Y= -17.69 + 0.38*80= 12.71
It is expected that they will sell 12.71 ≅ 13 ice cream cones when the temperature is 80º
You can use the estimation of the regression line to predict values within the range of definition of the independent variable, in this case from 65º to 105º of temperature, because it is within those values that you can be sure they have a linear association. Below or above you are not certain that their association is linear, it may be, for example exponential, or there may be no association between them.
Example: If the temperature is comfortable or cold, it is more likely that people won't buy ice creams, so for those values it will be no linear association between them.
I hope this helps!
Farmer Smith Jr is putting together fruit baskets. He has 240 oranges and 150 grapefruits. What is the largest number of baskets he can put together so that he can have the same number of oranges in each basket and the same number of grapefruits in each basket?
Answer:
why does it say college even tho this is a question on my homework
Step-by-step explanation:
and i'm in 7th grade.
The function Fx) = log5 xis increasing.
Answer:
Yes
Step-by-step explanation:
If F(x)= log base 5 of x, then yes, it is increasing.
Answer: True
Step-by-step explanation: Got it correct on a-p-e-x
Help !!! I got -15 & it’s wrong !
Answer:
-11
Step-by-step explanation:
I substitute x in ( put parenthesis around x so it makes it clear)
-9-6-18+9+4+9
simplify
-33+22
-11
Answer: -11
Step-by-step explanation:
That polynomial simplifies to -2x^2-x+4
If we plug in -3 for x, we get -2(-3)^2-(-3)+4 and thats -11
Drag the item from the item bank to its corresponding match.
Match the prism or cylinder with its volume.
Answer:
i cant help you because i cant see the things on the picture if u get a better picture i can help
Step-by-step explanation:
what is the area of the figure below
Answer:
58
Step-by-step explanation:
Answer: 58 in.^2
Step-by-step explanation:
A 14-foot ladder is leaning against the side of a house.The angle the ladder makes with the ground is 50 degrees. How far is the base of the ladder from the house to the nearest tenth of a foot
Answer:
9 ft
Step-by-step explanation:
You can use cosine to solve this, which is adjacent over hypotenuse. The ladder forms a triangle with the house, and the side you need to solve for is adjacent to the angle. You can set up the equation:
cos(50)=x/14
Then you multiply 14 by cos(50) and get almost 9 ft (rounding to the nearest tenth of a foot).
Is a temperature of 0.67 degrees a positive number or a negative number.
Answer:
It is a positive number.
Step-by-step explanation:
Numbers that are above 0 are considered positive and numbers below 0 are considered negative.
~Anna
The product of two consecutive natural numbers is 19 greater than their sum. Find thee numbers.
Answer:
The numbers are suppose to be natural numbers that is positive integers form 1 upward. So the numbers will be 5 and 6.
Step-by-step explanation:
The product of 2 consecutive natural numbers is 19 greater than their sum . We need to understand important terms in this question like consecutive and natural numbers.
Consecutive numbers are numbers that follows each other continuously from smallest to largest. Natural numbers are numbers that includes all the positive numbers from 1 to infinity example 1, 2, 3, 4............infinity.
Let the consecutive number be a and a+1.
The product of this 2 numbers are when you multiply them. Therefore,
a(a + 1) = a² + a
The sum of the 2 numbers are their addition. Therefore,
a + (a + 1) = 2a + 1
The product is 19 greater than the sum. This means the product of this numbers minus the sum of this numbers is equals to 19.
a² + a - (2a + 1) = 19
a²+ a - 2a - 1 = 19
a²- a - 20 = 0
Find the numbers that can be multiplied to get -20 and added together to get -1. The numbers are 4 and -5
a² + 4a - 5a - 20 = 0
a(a + 4) - 5(a + 4) = 0
(a + 4)(a - 5) = 0
a = - 4 and a = 5
The numbers are suppose to be natural numbers that is positive integers from 1 upward. So the numbers will be 5 and 6.
To prove it
5 × 6 = 30(products)
5 + 6 = 11(sum)
30 - 11 = 19
Which description matches finding the volume of the solid ?
Square prism + Triangular prism. Hope it helps.
Can someone help me with this
Answer:
(y-b) /x = m
Step-by-step explanation:
y = mx+b
Subtract b from each side
y -b = mx+b-b
y-b = mx
Divide each side by x
(y-b) /x = mx/x
(y-b) /x = m
Consider this quadratic equation
X^2+2x+7=21
Answer:
x = sqrt(15) - 1 or x = -1 - sqrt(15)
Step-by-step explanation:
Solve for x:
x^2 + 2 x + 7 = 21
Subtract 7 from both sides:
x^2 + 2 x = 14
Add 1 to both sides:
x^2 + 2 x + 1 = 15
Write the left hand side as a square:
(x + 1)^2 = 15
Take the square root of both sides:
x + 1 = sqrt(15) or x + 1 = -sqrt(15)
Subtract 1 from both sides:
x = sqrt(15) - 1 or x + 1 = -sqrt(15)
Subtract 1 from both sides:
Answer: x = sqrt(15) - 1 or x = -1 - sqrt(15)
Write the following number in standard decimal form.
six thousand five hundred thirty-four ten-thousandths
Answer: 6.534 x 10^(-1)
Step-by-step explanation:
Six thousand five hundred and thirty four ten thousandth
6534/10000
Convert to decimal
6534/10000=0.6534
Then convert to standard form
0.6534=6.534 x 10^(-1)
the sum of three consecutive even numbers is 114 what's the smallest of these numbers
Answer:
36
Step-by-step explanation:
consecutive even numbers are 2,4, 6...
Let the smallest of the 3 numbers be x.
2nd number= x+2
3rd number
=x+2+2
= x+4
sum of the 3 numbers= x +x+2 +x+4
114= 3x+6
3x= 114 -6 (-3 on both sides)
3x= 108 (simplify)
x= 108 ÷3
x= 36
Thus, the smallest number is 36.
Let's check!
36+38+40= 114 ✓
Which statement describes a cause of screwed data
a sample that excludes subjects that are not part of the population being measured.
a(b+c) =a.b+a.c, where a, b, and c are real numbers. Use the distributive property to simplify the expression 8(3+4)=24+ ?
Answer: 32
Step-by-step explanation:
All you have to do is is multiply 8 by the numbers in the parentheses. So you multiply 8 by 3, which equals 24. Then multiply 8 by 4, which is 32. Hope this helps! :)
Answer:
The answer is 32 and the next one is C, 24x+32.
Step-by-step explanation:
The quarterback Tom Brady completes 60% of his passes. To simulate the outcome of a single pass we use the digits 0, 1, 2, 3, 4, and 5 to represent the outcome "the pass is completed" and the digits 6, 7, 8, and 9 to represent the outcome "the pass is not completed." To be confident that our simulation is accurate, one needs to :
A. Repeat the simulation several more times
B. Assign new digits to represent outcomes
C. Take the average of the results of Line 134 and Line 101
Answer:
A. Repeat the simulation several more times
Step-by-step explanation:
The purpose of the simulation model is to represent the effectivity of the passes.
The proportion of successful passes is 60%.
As we have 10 digits available, 6 (digits from 0 to 5) are used for the outcome "the pass is completed" and 4 (digits 6, 7, 8, and 9) to represent the outcome "the pass is not completed". This is correct, as it represents a probability of 60% of having a successful pass.
But to have a representative distribution of the possible and probable results, the simulation have to run enough times to have a stable distribution of the results.
The area of a circle is 286 cm2. Use the π button on your calculator for π in your calculations.
8a
If its radius is r cm, find r, correct to 2 decimal places.
Be careful not to round your answer until the very end.
Answer:
9.54 cm
Explanation:
area = πr^2
286 cm^2= πr^2
=>πr^2= 286 cm^2
=>r^2= 286÷π
=>r= √286÷π
: 9.54. m
circumference=2πr
=> circumference=2×π×9.54
=60 cm
Nora wants to put new glass in her window
If her window measures 34 inches by 48 inch
What is the area of the glass that she will need
Answer:
1632 inches squared
Step-by-step explanation:
Hi!
So the formula for area is length times width.
So you would multiply the length by the width which is 34 times 48 to get the area which is 1632 in squared.
Hope this helps!
h(t)= -20 + 11t
h(11) =
Answer:
h(11) = -20 + 11(11)
h(11) = -20 + 121
h(11) = 101
Step-by-step explanation:
replace t by 11
do multiplication
add them together
Answer:
h(t) =−20+11t h(11)= 101
Step-by-step explanation:
write an equation of a line that is parellel to x=8 and that passes through the point -3,-2
Since the line is parallel to x = 8, the slope doesn't change.
In this case, the slope is undefined so nothing changes.
All we need to do is find the x-coordinate in (-3, -2). The x-coordinate is -3.
So, the equation will be x = -3
Best of Luck!
Find the area of each face of the triangular prism and the total surface area.
Drag each tile to its matching measurement. Each number may be used once or not at all.
9514 1404 393
Answer:
24160120200528Step-by-step explanation:
The area of each triangular face is given by the formula ...
A = 1/2bh
The triangular faces have a base of b=8 cm, and a height of h=6 cm. Their area is ...
A = 1/2(8 cm)(6 cm) = 24 cm²
__
Each of the rectangular faces has a length of 20 cm. The width depends on which face is of interest. In each case, the area is given by ...
A = LW
Bottom face: A = (20 cm)(8 cm) = 160 cm²
Back face: A = (20 cm)(6 cm) = 120 cm²
Sloped face: A = (20 cm)(10 cm) = 200 cm²
__
The total area is the sum of the areas of all of the faces and bases. There are two triangular bases, so the total area is ...
(2×24 + 160 +120 +200) cm² = 528 cm²
Mark wants a new car that costs $30000. He only has $500 in his savings account and $300 in his checking account. Which financing option should he chose
Answer: He should choose the savings account because he can earn more interest and the money in his savings account is more than the money in his checking account.
Step-by-step explanation:
A 25 lb. bag Balkfoods Small Red Beans cost $52.92. What is the unit price
per Ib?
Answer:
$2.1 per pound
Step-by-step explanation:
price/pounds
52.92 / 25 = 2.1
She used 25 equally sized stones to make a path that is 12 feet long. How long is each stone
Answer:
The length of each stone is
L = 12/25 = 0.48 ft
Hope this helps!
:)
Each stone measures 0.48 feet.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here, the number of stones is 25 and it is used to construct 12 feet long then measure of each stone =12/25
=0.48 feet
Hence, Each stone measures 0.48 feet.
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ2
Multiply (2m+3)(m^2-2m+2)
A) 2m^3-m^2-8m+3
B) 2m^3-m^2-10m+3
C)2m^3-m^2-4m+3
D)2m^37m^2-4m+2
Answer:
Step-by-step explanation:
The first step is to distribute the 2m and 3 to ([tex]m^2-2m+2[/tex]), like so:
[tex](2m+3)(m^2-2m+2)[/tex]
[tex]2m^3-4m^2+4m+3m^2-6m+6[/tex]
Then, add like terms:
[tex]2m^3 -m^2 -2m + 6[/tex]
148, 139, 109, 146, 141, 179, 187, 131, 149, 141 What is the mean absolute deviation of the data set
Answer:
The mean absolute deviation is 15
Step-by-step explanation:
First you have to find the mean, which in this case is 147.
Then you need to find the difference between each individual number and the mean. Once you have all the diffences written down, you need to add all the differences together. If you take the sum of the differences and divide them by the mean, you'll get your answer!
Let me know if that makes sense! :)
BRAINLIEST for anyone who gets this correct! Factor the expression below.
16x^2 + 40x+ 25
A. (2x+5)(8x+5)
В. (4х+5)(8х+3)
C. (4x - 5)(4x-5)
D. (2x - 5)(8x-5)
(4x+5)2
Expand the polynomial using the FOIL method.
16x^2−40x+25
c(4x - 5)(4x-5)
