Answer:
The critical region is t ≥ t(0.025, 7) = 2.365
Since the calculated value of t= 18.50249 falls in the critical region we reject the null hypothesis and conclude that there is sufficient reason to support the claim of a linear relationship between the two variables.
Step-by-step explanation:
We set up our hypotheses as
H0: β= 0 the two variable X and Y are not related
Ha: β ≠ 0. the two variables X and Y are related.
The significance level is set at α =0.05
The test statistic if, H0 is true, is t= b/s_b
Where Sb =S_yx/√(∑(X-X`)^2 )
Syx = √((∑(Y-Y`)^2 )/(n-2))
In the given question we have the estimated regression line as y= 0.449x - 30.27
X Y X2 Y2 XY
72 3 5184 9 216
85 7 7225 49 595
91 10 8281 100 910
90 10 8100 100 900
88 8 7744 64 704
98 15 9604 225 1470
75 4 5625 16 300
100 15 10000 225 1500
80 5 6400 25 400
∑779 77 68163 813 6995
Now finding the variances
∑(Y-Y`)^2 = ∑〖Y^2- a〗 ∑Y- b∑XY
= 813 – (- 30.27)77 - 0.449(6995)
= 813+2330.79 – 3140.755
= 3.035
∑(X-X`)^2 = ∑X^2 – (∑〖X)〗^2 /n
= 68163 – (779)2/9
= 736.22
Syx = √((∑(Y-Y`)^2 )/(n-2)) = √(3.035/7) = 0.65846 and
Sb =S_yx/√(∑(X-X`)^2 ) = (0.65846 )/27.13337 = 0.024267
t= b/s_b = 0.449/ 0.024267 = 18.50249
The critical region is t ≥ t(0.025, 7) = 2.365
Since the calculated value of t= 18.50249 falls in the critical region we reject the null hypothesis and conclude that there is sufficient reason to support the claim of a linear relationship between the two variables.
PLEASE HELP IMMEDIATELY!!! (Emergency)
Isaac owes $474.43 on his credit card. He returns two items, one for $48.90 and the other for $45.38. Then he makes purchases of $38.39 and $31.03. What is the new balance on the card?
Answer:
The new balance on his card is $-449.57
Step-by-step explanation:
He starts by owing $474.43 which is -474.43
First, he returns $48.90 and $45.38 which means that we are going to add 48.9 and 45.38 to -474.43
, he returns $48.90 and $45.38 which means that we are going to add 48.9 and 45.38 to -474.43-474.43 + 48.9 + 45.38 = -380.15
, he returns $48.90 and $45.38 which means that we are going to add 48.9 and 45.38 to -474.43-474.43 + 48.9 + 45.38 = -380.15Now he owes the bank $380.15
Next, he purchased 2 more items for $38.39 and $31.03 which indicates -380.15 - 38.39 - 31.03.
-380.15 - 38.39 - 31.03 = -449.57
Therefore he owes the bank $449.57 now
Hope this helped ~
Your local smart crackhead
a 50 litre ice cream bucket is to be emptied in 750 ml ice cream term find the number of tubs
required
Answer:
Quantity of ice cream = 50 litre
Quantity of ice cream contained in one ice cream tub = 750 ml
1 litre = 1000 mL
Quantity of one ice cream tub in litres = 0.75 litres
we need to calculate the number of ice cream tubs filled by using 50 litres of ice cream
Number of ice cream tubs filled = 66 tubs 500 ml
hope it helps :)
please mark it the brainliest!
Which of the following is an irrational number?
Answer:
A.
Step-by-step explanation:
Which one is greater? -14 or 11
Answer:
Hey there!
11 is greater than 14.
Positive numbers are greater than negative numbers.
Hope this helps :)
6. Out of 300 students in a class. 60% students study Physics, 35% students study
Chemistry and 20% students do not study both of the subjects.
1. How many students study both subjects?
ii. How many students study Physics only?
iii. How many students study Chemistry only?
iv. What is the number of students who study only one subject? Find it.
Answer:
HOPE THIS WILL BE HELPFUL FOR YOU
Write an absolute value inequality that represents the situation.
The length of a standard basketball court can vary from 84 feet to 94 feet, inclusive.
Answer:
|x - 89| ≤ 5
Step-by-step explanation:
Here the range is 84 to 94 ft, with the midpoint being 89 and the greatest variation from the midpoint being ±5.
We adapt |x| ≤ a as follows: replace x with 'x - 89' and a with 5:
|x - 89| ≤ 5
It is customary to regard '89' as the 'center' of the solution interval and 5 as the 'maximum difference' or 'radius' separating x from this center.
find the sum to infinity of a geometric series having a second term of -9 and fifth term of 1/3 g
Answer:
S infinity= -51/4
Step-by-step explanation:
First term
ar= -9
Fifth term
ar⁴= 1/3
Solving for the value of the r and a
ar= -9
ar⁴= 1/3
Dividing each other
r³=1/3 * -1/9
r³=-1/27
r= 3√-1/27
r= -1/3
Solving for a
ar= -9
a(-1/3)= 9
a= 9*-3
a= -27
Sum of a go to infinity is given by the formula
S infinity= a/(1-r)
S infinity= -27/(1-(-1/3))
S infinity= -27/(1+1/3)
S infinity= -27 * 3/4
S infinity= -51/4
The travelers are adding a new room to their house. the room will be a cube with volume 3375 ft.³.they are going to put in hardwood floors, the contractor charges $10 per square foot. how much will the hardwood floors cost?
Answer:
$ 2250
Step-by-step explanation:
3375 = s³
s = ∛3375
s = 15 ft.
floor area = s² = (15 * 15)
floor area = 225 ft²
the contractor charges $10 per ft².
therefore,
the hardwood cost = 225 x $10 = $2250
Answer:
$2,250.
Step-by-step explanation:
So first, we need to find the area of the floor (the side shaded green). To do so, we first need to find the length of the one side of the room.
Since we know that the room is a cube, all side lengths are equivalent. And since we are given that the volume of the room is 3375, we can find the length of the side.
The volume of a cube is given by the formula:
[tex]V=s^3[/tex]
Substitute 3375 for V:
[tex]s^3=3375[/tex]
Take the cube root of both sides:
[tex]s=\sqrt[3]{3375}=15[/tex]
So, the side length of the room is 15.
This means that the area of the floor is:
[tex]A=(15)^2\\A=225\text{ in}^2[/tex]
They charge $10 per square foot. There are 225 square feet. Thus, the total cost will be:
[tex]10(225)=$2250[/tex]
$2,250.
Solve x(x+9)+12=0 by using the Quadratic Formula.
Answer:
Answer: approximately -1.63 and -7.37
Step-by-step explanation:
First of all, let's expand the parenthesis by multiplying x into both of its terms.
[tex]x(x+9)+12 = 0\\x^2+9x+12=0[/tex]
We get the equation:
[tex]x^2+9x+12=0[/tex]
The quadratic formula looks like this
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
where the equation is of the form
[tex]ax^{2}+bx+c=0[/tex]
Comparing this to our equation above,
[tex]x^2+9x+12=0[/tex]
we can see that
[tex]a = 1\\b= 9\\c= 12[/tex]
Let's put these values into the quadratic formula.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-9\pm\sqrt{9^2-4*1*12}}{2*1}\\x=\frac{-9\pm\sqrt{9^2-48}}{2}\\x=\frac{-9\pm\sqrt{81-48}}{2}\\x=\frac{-9\pm\sqrt{33}}{2}\\x=\frac{-9\pm\ 5.744...}{2}\\x=\frac{-9\pm\ 5.744...}{2}\\x_{1}=\frac{-9+5.744...}{2}=\frac{-3.255...}{2}=-1.62771867\\x_{2}=\frac{-9-5.744...}{2}=\frac{-14.744...}{2}=-7.3722813\\[/tex]
Answer: approximately -1.63 and -7.37
You can also choose not to approximate the square root of 33, and you'd receive the answers:
[tex]x_{1}=\frac{-9+\sqrt{33}}{2}\\x_{2}=\frac{-9-\sqrt{33}}{2}[/tex]
Divide (6.3 × 103) by (1.8 × 105) giving your answer in Scientific Notation.
Answer:
(6.3*10³) ÷ (1.8*10⁵)
6.3*10³ = 0.063*10⁵
then:
(6,3*10³) ÷ (1.8*10⁵) = (0.063*10⁵) ÷ (1.8*10⁵)
= 0.063/1.8
= 0.035
0.035 = 3.5 *10⁻² = 35*10⁻³
Suppose C = 30y + 15 and y = 40x + 25.
Which of the following is equivalent to C = 30y + 15, but written only in terms of x?
Answer:
d.)
C = 1200x + 765
Step-by-step explanation:
The substitution property of equality allows you to substitute an expression for a variable. Since y equals 40x + 25, you can substitute (40x + 25) for y in the C = 30y + 15 equation:
C = 30y+ 15
y = 40x + 25
C = 30y + 15
C = 30(40x + 25) + 15
C = 1200x + 750 + 15
C = 1200x + 765
The equivalent expression for C = 1200x+765.
C = 30y+15; y = 40x+25 Equivalent relation between C and x to determine.
Equations are defined as the mathematical expression intended meaning to something that contains an equal sign.
Here, C=30y+15
y = 40x+25
Putting y in C = 30y+15
C= 30(40x+25)+15
C = 1200x + 750 +15
C = 1200x +765
Thus, the equivalent expression for C = 1200x+765.
learn more about the equation here:
https://brainly.com/question/10413253
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Big Ben is the largest clock tower in England and overlooks the Houses of Parliament and the Thames River. The minute hand of the clock measures 36 feet in length. How far does the tip of the minute hand move in 20 minutes
Answer:
75.408 ft
Step-by-step explanation:
In 20 minutes, the angle swept by a minute hand is calculated as
(20/60) x 360° = 120°
The length of the minute hand = 36 ft
To calculate the distance moved by the minute hand, we solve for the fraction of the circumference of a circle swept by the minute hand in going through this 20 min.
we use the expression
Distance moved by the tip of the minute hand d = (θ/360) x 2πR
where
θ is the angle swept in the 20 minutes = 120°
R is the length of the minute hand, which is the radius of the circle formed if the minute hand moves completely in a 360° motion round the clock.
R = 36 ft
substituting values, we have
d = (120/360) x (2 x 3.142 x 36) = 75.408 ft
The tip of the minute hand moves 0.21 ft in 20 minutes.
Length of an arc
The minute hand sweeps an arc of length L given by
L = Ф/360° × 2πR where
Ф = angle moved by minute hand in 20 minutes = 20' × 1°/60' = 1/3° and R = length of minute hand = 36 ftDistance moved by tip of minute handSo, substituting the values of the variables into the equation, we have
L = Ф/360° × 2πR
L = 1/3°/360° × 2π × 36 ft
L = 1/(3 × 360) × 2π × 36 ft
L = 1/(3 × 10) × 2π ft
L = 1/30 × 2π ft
L = 1/15 × π ft
L = 3.1416/15 ft
L = 0.2094 ft
L ≅ 0.21 ft
So, the tip of the minute hand moves 0.21 ft in 20 minutes.
Learn more about length of an arc here:
https://brainly.com/question/8402454
Which graph represents the solution to the compound inequality? 4x + 8 < –16 or 4x + 8 ≥ 4 A number line with an open circle at negative 6 with a bold line pointing to the right ending at the point at negative 1. A number line with a point at negative 6 with a bold line pointing to the right ending at the open circle at negative 1. A number line with an open circle at negative 6 with a bold line pointing to the left. A point at negative 1 with a bold line pointing to the right. A number line with a point at negative 6 with a bold line pointing to the left. An open circle at negative 1 with a bold line pointing to the right.
Answer:
a line starting at -6 going to the left of this number, and with an open circle around the -6.
Step-by-step explanation:
To solve for this inequality, we need to isolate "x" on one side of the inequality symbol (<):
4 x + 8 < -16
subtract 8 from both sides:
4 x < -16 - 8
4 x < - 24
now divide both sides by 4 to get rid of the 4 that appears multiplying "x":
x < - 24/4
x < - 6
To graph this inequality one needs to highlight all the real numbers of the number line to the left of the value -6, making sure that one draws an open circle around the -6 because we don't want this number to be included (notice that x < -6 implies x-values strictly smaller than -6)
Then one would draw a line starting at -6 going to the left of this number, and with an open circle around the -6.
In edg:
A & B
A: StartFraction x over 2 EndFraction less than 1 or StartFraction 4 x minus 2 over 2 EndFraction greater than or equal to 13.< 1 or ≥ 13
B: 3x – 3 < 3 or 2x + 8 ≥ 22
Mrs.torres class has 28 students. The class includes 12 boys. What is the ratio of girls to boys?
Answer:
16:12
Step-by-step explanation:
if there is 12 boys, that leaves the other 16 to be girls
Answer:
4:3
Step-by-step explanation:
If there are 12 boys then 28-12=16
So there are 16 girls
The girls to boys ratio is 16:12 and you simplify
Now it's 4:3
For the equation below, x is the input and y is the output. Choose the ordered pair that makes a true statement for
the equation
y=-4x+ 3
O (-1,1)
O (0, 3)
O (1,-1)
O (2, 11)
HELP ASAP
Answer:
(0,3) and (1,-1)
Answer:
C on edge 2020
Step-by-step explanation:
For the equation below, x is the input and y is the output. Choose the ordered pair that makes a true statement for the equation.
y = -4x + 3
A-(-1, 1)
B-(0, -3)
C-(1, -1)
D-(2, 11)
Question 1 of 15
Which of the following is a trinomial with a constant term?
A. x + 64
B. x + 4y
C. y5+ 13x +12
D. A + 3y2 + 2y
E. x
F. x(10-2) + 7
SUBMIT
Answer: C, y^5 + 13x + 12
Step-by-step explanation:
A trinomial is a polynomial that consists of three terms. y^5 is one term, 13x is the second, and 12 is the third term. Each term is separated by an operator (ie +,-,*, etc). Constant terms are terms that do not change. In this case, your constant term is 12.
Answer:
C
Step-by-step explanation: A trinomial has 3 terms and a constant term is just a number.
Use front-end estimation to estimate the difference.
92.1 - 18.56
80
70
60
50
Answer:
70
Step-by-step explanation:
Here, you're expected to round the numbers to the nearest 10, then do the subtraction:
92.1 -18.56 ≈ 90 -20 ≈ 70 . . . estimated answer
The manager suggests that Darryl should purchase the deli’s bread from Store D because they sell the most loaves of bread for the best price. Is this true? Why or why not? Explain your reasoning. please i need help
Answer:
yes
Step-by-step explanation:
because it sells the best price
Answer:
No
Step-by-step explanation:
Stores D dose not have the best deal when you compare the unit prices. The best deal isn't from having more loaves. The best deal from store B because the unit price is the lowest.
If the principal is $350 and the interest rate is 3 percent, what is the simple interest earned in one year?
simple interest = Pxrxt
Answer:
The simple interest was found to be $9.6 after 1 year at 3%
Step-by-step explanation:
Given that
principal p= $350
rate r= 3%= 3/100= 0.03
time t= 1 year
The expression for the simple interest is given as
SI= p*r*t
SI= 320*0.03*1
SI= $9.6
After 1 year at 3% the simple interest is $9.6
Simply put the extra money earned after an investment is called the simple interest
Tom earns $12.50 per hour at the Yankee Bowling Alley. He regularly works 40 hours per week. He is paid time and a half for each hour of overtime work. Last week he worked 42 hours. What is his pay for the week?
Answer:
Tom's pay for the week should be over 500 dollars. Sorry if this isn't very helpful. :(
Step-by-step explanation:
Solve for z
5 = z/-4 -3.
Answer:
The answer is z=-35.
5=z/-4-3.=-35.
And if the question is the other way around that the -3 is for the whole question and not with the -4 like if they are not together then the answer is -32.
Eight subtracted from seven times a number is -43. What is the number?
Answer:
8-7x=-43.
-7x= -43-8.
-7x= -51.
x= 7.285714286~7.3
Answer: The number is -5 or its value is equivalent to -5.
Step-by-step explanation:
So we are given the equation:
eight subtracted from seven times a number is -43
So we have to find what that unknown number is. We can do this by adding 8 to -43 which gives us -35. Now divide -35 by 7, and your answer is -5.
So the number is -5 or its value is equivalent to -5.
Which expressions have a value of -1/64?
Answer:
Step-by-step explanation:
Please, share any answer choices that were given to you.
-1 -1 -1
-1/64 is equivalent to -------- and ---------- and ---------
4^3 2^6 8^2
What numbers belongs with what
Answer:
1.) 10 is R, Q, Z, W, N
2.) 5/6 is R,Q,
3.) sqrt 24 is I
4.) 0 is R, Q, Z, W
5.) none, neagative sqrt are imaginary.
F(x) = x + 1, find f(x+3)
Answer:
Step-by-step explanation:
f(x) = x + 1, find f(x+3)
f(x+3) = x + 3 + 1 = x + 4
Answer: f(x+3)=x+4
Step-by-step explanation:
f(x)=x+1
f(x+3)=(x+3)+1 ⇔ substitute x
f(x+3)=x+3+1 ⇔ take of parentheses
f(x+3)=x+4 ⇔ simplify
Hope this helps!! :)
Please let me know if you have any question
What is 7/8- 5/8?
Answer
Answer:
1/4
Step-by-step explanation:
Since the denominatior is the same, we can look at only the numerator. So 7/8 - 5/8 is basically 7 - 5 which is 2.
The denominator doesn't change so it's 2/8. We can further simplify this into 1/4.
Given a right triangle with legs 5cm and 12cm, find the length of the hypotenus. Show work please
Answer:
13 cm
Step-by-step explanation:
We can use the Pythagorean Theorem to find the length of the hypotenuse. The Pythagorean Theorem is used to find a missing side to a right triangle.
The theorem states that [tex]a^2 + b^2 = c^2[/tex], where a and b are the legs, and c is the hypotenuse.
The legs of this triangle are already states - 5 and 12, so we can plug it's values into the formula.
[tex]5^2 + 12^2 = c^2\\\\25 + 144 = c^2\\\\169 = c^2\\\\c = \sqrt{169}\\\\c=13[/tex]
So the hypotenuse of this triangle is 13 cm.
Hope this helped!
The Florida Turnpike is a 312-mile stretch of highway running from Central Florida to South Florida. Drivers who use a SunPass pay discounted toll rates. For 2-axle passenger vehicles with a SunPass, the toll at the Orlando (I-4) Mile Post is͵, and the toll at the Okeechobee Plaza exit in West Palm Beach is a. A 2-axle passenger vehicle with a SunPass drives through the Orlando (I-4) Mile Post five times. Determine the total amount of money that will be deducted from this vehicle’s SunPass account. b. Create an algebraic expression to describe the total amount of money that will be deducted from this vehicle’s SunPass account for any given number of drives through the Orlando (I-4) Mile Post. c. The same 2-axle passenger vehicle drives through the Okeechobee Plaza exit in West Palm Beach seven times. Determine the total amount of money that will be deducted from its SunPass account. d. Create an algebraic expression to describe the total amount of money that will be deducted from this vehicle’s SunPass account for any given number of drives through the Okeechobee Plaza exit. e. Write an algebraic expression to describe the combined total amount of money that will be deducted from this vehicle’s SunPass account after it passes through the Orlando (I-4) Mile Post and the Okeechobee Plaza exit any given number of times. f. What is the total amount of money that will be deducted from this vehicle’s SunPass account after it passes through the Orlando (I-4) Mile Post eight times and Okeechobee Plaza exit four times?
Answer:
2.65
Step-by-step explanation:
3. Define a variable, write an equation, and solve the problem. Carla began a
running program to prepare for track team try-outs. On her first day she ran
3 miles, and on her second day she ran 5 miles. Since then, Carla has run 7 miles
each day. If her log book shows that Carla has run a total of 99 miles, for how
many days has Carla been running 7 miles?
Answer:
Carla has been running 7 miles each day for 13 days.
Step-by-step explanation:
Carla ran 3 miles on her first day, 5 miles on her second day and then 7 miles each day onward.
Let the number of days she ran 7 miles each day = x
Total distance run by Carla = 3 + 5 + 7(x)
= 8 + 7x
If her log book shows that she has run total distance = 99 miles
Equation representing her total run will be,
8 + 7x = 99
7x = 99 - 8
7x = 91
x = [tex]\frac{91}{7}[/tex]
x = 13 days
Therefore, Carla has been running 7 miles each day for 13 days.
Find three consecutive numbers whose sum is 675.
Answer:
three consecutive integers that add up to 675 are 224, 225, and 226.
Step-by-step explanation: