Answer:
33 web pages (at least)
Step-by-step explanation:
We can set up an inequality to represent this, where x represents the number of web pages made.
1.5x > 1.25x + 8
1.5x represents the number of hours it will take normally, and 1.25x + 8 represents the time with the new software. 1.5x (amount of hours using old software) needs to be larger than the time it takes with the new software.
Solve for x:
1.5x > 1.25x + 8
0.25x > 8
x > 32
So, the designer would have to make at least 33 pages.
The number of web pages would the designer have to make in order to save time using the new software will be 33 web pages (at least).
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
We can set up an inequality to represent this, where x represents the number of web pages made.
1.5x > 1.25x + 8
The time with the new software is represented by 1.25x + 8 and the normal time is represented by 1.5x. The number of hours spent using the old software must be 1.5 times greater than the time spent using the new product.
Solve for x:
1.5x > 1.25x + 8
0.25x > 8
x > 32
Therefore, the number of web pages would the designer have to make in order to save time using the new software will be 33 web pages (at least).
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Write a variable expression for a number w increased by 4 (A) 4 ÷ w (B) w + 5 (C) w + 4
Answer:
C) w+4
Step-by-step explanation:
w=the variable
+4= increased by 4
HOPE THIS HELPS!!!!!! :)
<33333333333
2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)
Answer:
16/45x-11/12
Step-by-step explanation:
Multiply across
2/15x-30/40-1/6+2/9x=
Get common denominators of like terms
6/45x+10/45x-9/12-2/12=
Combine like terms
16/45x-11/12
The simplified expression is: (16/45)x - (11/12)
To simplify the given expression, we'll follow the steps:
Step 1: Distribute the fractions through the parentheses.
Step 2: Simplify the expression by combining like terms.
Let's proceed with the simplification:
Step 1: Distribute the fractions through the parentheses:
2/5 * (1/3x - 15/8) - 1/3 * (1/2 - 2/3x)
Step 2: Simplify the expression:
To distribute 2/5 through (1/3x - 15/8):
2/5 * 1/3x = 2/15x
2/5 * (-15/8) = -15/20 = -3/4
So, the first part becomes: 2/15x - 3/4
To distribute -1/3 through (1/2 - 2/3x):
-1/3 * 1/2 = -1/6
-1/3 * (-2/3x) = 2/9x
So, the second part becomes: -1/6 + 2/9x
Now, the entire expression becomes:
2/15x - 3/4 - 1/6 + 2/9x
Step 3: Combine like terms:
To combine the terms with "x":
2/15x + 2/9x = (2/15 + 2/9)x
Now, find the common denominator for (2/15) and (2/9), which is 45:
(2/15 + 2/9) = (6/45 + 10/45) = 16/45
So, the combined x term becomes:
(16/45)x
Now, combine the constant terms:
-3/4 - 1/6 = (-18/24 - 4/24) = -22/24
To simplify -22/24, we can divide both numerator and denominator by their greatest common divisor (which is 2):
-22 ÷ 2 = -11
24 ÷ 2 = 12
So, the combined constant term becomes:
(-11/12)
Putting it all together, the simplified expression is:
(16/45)x - (11/12)
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Complete question is:
Simplify the given expression: 2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
Answer:the mean is greater than the median
Step-by-step explanation:
The mean is less than the median. Then the correct option is A.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
Half the students scored 87.
The next highest score is 71.
Then the median will be
(71+ 87) / 2 = 79
A few students scored 52, so the mean is slightly lower than the mean of 71 and 87.
Thus, the mean is less than the median.
Then the correct option is A.
The missing options are given below.
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
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“Type ‘equal, supplementary, complementary, or vertical in the space provided’”
Answer:
Supplementary
Step-by-step explanation:
When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.
<AOB (40°) and <BOC (140°) are not equal angles.
<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.
<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.
<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.
A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. Exactly 3 fours.
A. 0.161
B. 0.002
C. 0.116
D. 0.216
Answer:
0.0321
Step-by-step explanation:
This can be found by binomial probability distribution as the probability of success is constant. There are a given number of trials. the successive tosses are independent.
Here n= 5
The probability of getting a four in a roll of a die = 1/6
The probability of not getting a four in a roll of a die = 5/6
The probability of getting exactly three 4s in five throws is given by
5C3 (1/6)³ (5/6)² = 10 (0.0046) (0.694)= 0.0321
PLLLEEEASSSSEEEE ANSWER FAST
The shape is based only on squares, semicircles, and quarter circles. Find the area of each shaded part.
Answer:
36.48 cm²
Step-by-step Explanation:
If you take a careful look at the figure given, you'd realise that the area of the shaded portion is actually created by 2 overlapping quarter circle.
The area of the shaded portion = Area of Square - Area of Unshaded part
Area of square = s² = 8² = 64 cm²
Area of the Unshaded portion = 2(Area of Square - Area of Quarter Circle)
= 2(s² - ¼*πr²)
Where, radius (r) = s = 8 cm, take π as 3.14
Area of unshaded part = 2(8² - ¼*3.14*8²)
= 2(64 - ¼*3.14*64)
= 2(64 - 1*3.14*16)
= 2(64 - 50.24)
= 2(13.76)
Area of unshaded part = 27.52 cm²
Area of shaded part = Area of Square - Area of Unshaded part
Area of shaded part = 64 - 27.52 = 36.48 cm²
The mean area of 7 halls is 55m².If the mean of 6 of them be 58m², find the area of the seventh all.
Answer:
Area of 7th hall = 37 m^2
Step-by-step explanation:
Total area of 7 halls = 7*55 = 385
Total area of 6 halls = 6*58 = 348
Area of 7th hall = 385-348 = 37 m^2
Answer:
The area of the seventh hall = 37m²
Step-by-step explanation:
for 6 halls
Mean area of 6 halls = 58m²
[tex]Mean\ area = \frac{sum\ of\ areas}{Number\ of\ halls} \\58\ =\ \frac{sum\ of\ areas}{6} \\sum\ of\ areas\ of\ 6\ halls\ = 58\ \times\ 6 = 348\\sum\ of\ areas\ of\ 6\ halls\ = 348[/tex]
Let the area of the 7th hall be x
The sum of the areas of 7 halls = 348 + x - - - - - - (1)
[tex]Mean = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\55 = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\sum\ of\ the\ areas\ of\ 7\ halls\ = 55\ \times\ 7\ = 385\\sum\ of\ the\ areas\ of\ 7\ halls\ =\ 385 - - - - (2)[/tex]
notice that equation (1) = equation (2)
348 + x = 385
x = 385 - 348 = 37m²
Therefore, the area of the seventh hall = 37m²
determine x in the following equation 2x - 4 = 10
Answer:
7
Step-by-step explanation:
10+4 = 14
14/2 = 7
x = 7
a kicker starts a football game by "kicking off". The quadratic function y = -10x^2 + 25x models football's height after x seconds. How long, in seconds, is the football in the air?
Answer: 2.5 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)
0 = -10x² + 25x
0 = -5x(2x - 5)
0 = -5x 0 = 2x - 5
[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]
x = 0 seconds is when the ball was kicked
x = 5/2 --> 2.5 seconds is when the ball landed on the ground
Mary states, "If the diagonals of a parallelogramare congruent, then the
parallelogram is a rectangle." Decide if her statement is wue or false.
A. True
B. False
Answer:
True
Step-by-step explanation:
A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,
AD ≅ BC (opposite side property)
AB ≅ CD (opposite side property)
<ABC = <BCD = <CDA = <DAC = [tex]90^{0}[/tex] (right angle property)
Thus,
<ABC + <BCD + <CDA + <DAC = [tex]360^{0}[/tex]
AC ⊥ BD (diagonals are perpendicular to each other)
AC ≅ BD (congruent property of diagonals)
Therefore, the parallelogram is a rectangle.
The time required for workers to produce each unit of a product decreases as the workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit. Find the time required for a new worker to produce units 10 through 19.
Answer: 2.79 hours.
Step-by-step explanation:
Given that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit
To calculate the time for the new worker to produce 10 units, substitute 10 for x in the equation above.
T(x) = 2 + 0.31 (10)
T(x) = 2 + 3.1
T(x) = 5.1 hours
To calculate the time for the new worker to produce 19 units, substitute 19 for x in the equation above.
T(x) = 2 + 0.31(19)
T(x) = 2 + 5.89
T(x) = 7.89 hours
The time required for a new worker to produce units 10 through 19 will be
7.89 - 5.1 = 2.79 hours
Is 55/22 a rational
Answer:
The fraction [tex]\displaystyle \frac{55}{22}[/tex] is indeed a rational number.
Step-by-step explanation:
A number [tex]x[/tex] is rational if and only if there exist two integers [tex]p[/tex] and [tex]q[/tex] (where [tex]q \ne 0[/tex]) such that [tex]x = \displaystyle \frac{p}{q}[/tex].
[tex]\displaystyle \frac{55}{22}[/tex], the number in question here is already written in the form of a fraction. The two integers [tex]p = 55[/tex] and [tex]q = 22[/tex] ([tex]q \ne 0[/tex]) meet the requirement that [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]. Therefore, [tex]\displaystyle \frac{55}{22}\![/tex] is indeed a rational number.
Side note: the [tex]p[/tex] and [tex]q[/tex] here ([tex]q \ne 0[/tex]) don't have to be unique. For example:
because [tex]\displaystyle \frac{55}{22} = \frac{5 \times 11 }{2 \times 11} = \fraac{5}{2}[/tex], both of the following pairs could satisfy [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]:
[tex]p = 55[/tex] and [tex]q = 22[/tex];[tex]p = 5[/tex] and [tex]q = 2[/tex].Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.
Answer:
The chi - square test can be [tex]\approx[/tex] 0.667
Step-by-step explanation:
From the given data :
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis: The number of customers does follow a uniform distribution
Alternative hypothesis: The number of customers does not follow a uniform distribution
We learnt that: Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
The above given data was the observed value.
However, the question progress by stating that : He expected to have 15 customers each day.
Now; we can have an expected value for each customer as:
Observed Value Expected Value
Day Customers
Monday 17 15
Tuesday 13 15
Wednesday 14 15
Thursday 16 15
The Chi square corresponding to each data can be determined by using the formula:
[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]
For Monday:
[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Tuesday :
[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Wednesday :
[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
For Thursday:
[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
Observed Value Expected Value chi - square
Day Customers
Monday 17 15 0.2666666667
Tuesday 13 15 0.2666666667
Wednesday 14 15 0.06666666667
Thursday 16 15 0.06666666667
Total : 0.6666666668
The chi - square test can be [tex]\approx[/tex] 0.667
At level of significance ∝ = 0.10
degree of freedom = n - 1
degree of freedom = 4 - 1
degree of freedom = 3
At ∝ = 0.10 and df = 3
The p - value for the chi - square test statistics is 0.880937
Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis
Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.
Answer:.67
Step-by-step explanation:
If x represents the rate that Joy traveled at for the first half of the trip, write an
expression that represents the amount of time it takes Joy to complete the second half of the
trip at the slower rate.
Answer:
time taken for trip 2nd half > time taken for trip 1st half
Step-by-step explanation:
Let the total distance of Joy's trip be = D
Then, the first half distance travelled = D/2
The rate (speed) at which Joy travels during first half = x
So, time taken to travel first half = Distance / Speed
= (D/2) / x = D / 2x
Second half of trip distance travelled = remaining D/2Let the rate (speed) at which Joy travels during second half = x'
As given, x' (second half speed) < x (first half speed)
So, time taken to travel first half = Distance / Speed
(D/2) / x' = D / 2x'
As x' < x : D / 2x' > D / 2x .
Trip 1st half Time taken trip < 2nd half ; or trip 2nd half time taken > 1st half
What is an equation of the line that passes through the points (-5, 8) and (5,0)?
Answer:
y= -0.8x + 4
Midpoint is 0,4
please help me to answer this question
Answer:
I can not see any questions
800,000+700 standard form
Answer:
800700
Step-by-step explanation:
800000 + 00000 + 0000 + 000 + 00 + 0
000000 + 00000 + 0000 + 700 + 00 + 0
------------------------------------------------------------
= 800700
Answer:
Hey there!
800000+700=800700
Hope this helps :)
Joy is preparing 20 liters of a 25% saline solution. She has only a 40% solution and a 10% solution in her lab. How many liters of the 40% solution and how many liters of the 10% solution should she mix to make the 25% solution?
Answer:
10 Liters of 40% solution
Step-by-step explanation:
Answer:
10 liters of the 40% solution, and 10 liters of the 10% solution
Step-by-step explanation:
Let us say that x = the liters of the 40% solution, and y = liters of the 10% solution in her lab. We know that Joy is preparing a solution containing a total 20 liters, so x + y = 20. We can respectively create the following system of equations,
x + y = 20,
0.40x + 0.10y = 0.25 ( 20 )
And now we have to solve this system of equations for x and y, the liters of the 40% solution and the liters of the 10% solution,
[tex]\begin{bmatrix}x+y=20\\ 0.4x+0.1y=0.25\left(20\right)\end{bmatrix}[/tex] ( Substitute x as 20 - y )
[tex]0.4\left(20-y\right)+0.1y=0.25\cdot \:20\end{bmatrix}[/tex] ( Isolate y )
[tex]8-0.3y=5[/tex] ⇒ [tex]80-3y=50[/tex] ⇒ [tex]-3y=-30[/tex] ⇒ y = 10
[tex]x=20-10 = 10[/tex] ⇒ x = 10
Therefore, there are 10 liters of both the 40% and 10% solution.
The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of and use a class width of . Does the frequency distribution appear to be roughly a normal distribution?
Answer:
The frequency distribution does not appear to be normal.
Step-by-step explanation:
The data provided is as follows:
S = {0.38 , 0 , 0.22 , 0.06 , 0 , 0 , 0.21 , 0 , 0.53 , 0.18 , 0 , 0 , 0.02 , 0 , 0 , 0.24 , 0 , 0 , 0.01 , 0 , 0 , 1.28 , 0.24 , 0 , 0.19 , 0.53 , 0 , 0, 0.24 , 0}
It is provided that the first lower class limit should be 0.00 and the class width should be 0.20.
The frequency distribution table is as follows:
Class Interval Count
0.00 - 0.19 21
0.20 - 0.39 6
0.40 - 0.59 2
0.60 - 0.79 0
0.80 - 0.99 0
1.00 - 1 . 19 0
1.20 - 1. 39 1
The frequency distribution does not appear to be normal. This is because the frequencies does not start and end at almost equivalent points and the mid-distribution does not consist of the highest frequency.
Thus, the frequency distribution does not appear to be normal.
Find the intervals on which the function f(x) = ax2 + bx + c (where "a" doesn't = 0) is increasing and decreasing. Describe the reasoning behind your answer.
Answer:
Step-by-step explanation:
Given that:
[tex]\mathtt{f(x) = ax^2 + bx + c}[/tex]
The derivative of the function of x is [tex]\mathtt{f'(x) = 2ax + b}[/tex]
Thus; f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
i.e
f'(x) > 0 , when b > 0 and a < 0
∴
2ax + b < 0
2ax < - b
[tex]\mathtt{x < \dfrac{-b}{2a}}[/tex]
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
[tex]\mathtt{x > \dfrac{-b}{2a}}[/tex]
Can somebody please solve this problem for me!
Answer:
x = 200.674
Step-by-step explanation:
tan∅ = opposite/adjacent
Step 1: Find length of z
tan70° = 119/z
ztan70° = 119
z = 119/tan70°
z = 43.3125
Step 2: Find length z + x (denoted as y)
tan26° = 119/y
ytan26° = 119
y = 119/tan26°
y = 243.986
Step 3: Find x
y - z = x
243.986 - 43.3125 = x
x = 200.674
A middle school has 470 students. Regina surveys a random sample of 40 students and finds that 28 have cell phones. How many students at the school are likely to have cell phones? A. 132 students B. 188 students C. 329 students D. 338 students Please include ALL work! <3
Answer:
C. 329
Step-by-step explanation:
So 28 is 70% of 40
so we know that 70% percent of students have phones
70% of 470
329
Thats how I solved it have a great day :)
Jamar rolls a 6-sided number cube with the numbers 1 through 6 on it. What is the
probability that he does not roll a prime number?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
In a 6 sided die, the numbers that are possible to be rolled are
1, 2, 3, 4, 5, and 6.
We know that the numbers 2, 3, and 5 are prime, while 1, 4, and 6 are not.
3 out of the 6 numbers are prime, therefore 3 out of the 6 numbers are not prime.
So the fraction is [tex]\frac{3}{6}[/tex]
This simplifies to [tex]\frac{1}{2}[/tex].
Hope this helped!
Answer:
1/2
Step-by-step explanation:
the prime numbers between 1 and 6 inclusive are: 2, 3, 5 (i.e 3 possible outcomes)
the non prime numbers are : 1, 4 and 6 (i.e 3 possible outcomes)
for each roll, the total number of possible outcomes is 6 (because its a 6-sided die)
P(does not roll a prime number) = P (rolls 1, 4 or 6)
= number of possible non-prime outcomes / total number of outcomes
= 3/6
= 1/2
ASAP HELP WILL MARK BRAINLIEST
Answer:
c(x)=(3/4)^x
(3/4)^-2= 16/9
(3/4)^-1 =4/3
(3/4)^0=1
(3/4)^1 = 3/4
(3/4)^2= 9/16
In what order should you evaluate problems?
Answer:
(4) → (1) → (3) → (2)
Step-by-step explanation:
Order of operations in any question are decided by the rule,
P → Parentheses
E → Exponents
D → Division
M → Multiplication
A → Addition
S → Subtract
Following the same rule order of operations will be,
- Take care of anything inside the parentheses.
- Evaluate and raise the exponents
- Multiply or divide. Make sure to do whichever one comes first from left to right.
- Add or Subtract from left to right.
Options are arranged in the order of,
(4) → (1) → (3) → (2)
Help someone please!!
Answer:
A. 5:4
Step-by-step explanation:
Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.
Q-The general solution of inequality cos 2 x≤- sin x is
Answer:
x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
Step-by-step explanation:
1−2sin2 x≤−sin x ⇒ (2sin x+1)(sin x−1)≥0
sin x≤−1/2 or sin x≥1
−5π/6+2nπ≤x≤−π/6+2nπ or , n ϵ I x=(4n+1)π/2, n ϵ I⇒ -5π6+2nπ≤x≤-π6+2nπ or , n ϵ I x=4n+1π2, n ϵ I (as sin x = 1 is valid only)
In general⇒ In general x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
The fastest fish in the world is the sailfish. If a
sailfish could maintain its speed, as shown in the
table, how many miles could the sailfish travel in 6
hours?
p.s the top is hour traveled and the bottom is miles traveled
Answer:
(C) 408 miles
Step-by-step explanation:
Looking at this table, we can see that the beginning point is (0,0) so this is a linear slope, meaning we won’t have to add anything.
This means that for every time we rise in x, y will rise by the same amount.
When x is 1, y is 68 - so the constant of proportionality here is 68.
So, to find how much 6 hours would be we just multiply.
[tex]6\cdot68=408[/tex]
Hope this helped!
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Complete Question
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive
Answer:
Yes the company conclude that the correlation is positive
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The correlation is r = 0.65
The null hypothesis is [tex]H_o : r < 0[/tex]
The alternative hypothesis is [tex]H_1 : r > 0[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]Sr = \sqrt{1- r}[/tex]
[tex]Sr = \sqrt{1- 0.65}[/tex]
[tex]Sr = 0.616[/tex]
The degree of freedom for the one-tail test is
[tex]df = n- 2[/tex]
[tex]df = 14- 2[/tex]
[tex]df = 12[/tex]
The standard error is evaluated as
[tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]
[tex]SE =0.1779[/tex]
The test statistics is evaluated as
[tex]t = \frac{r }{SE}[/tex]
[tex]t = \frac{0.65 }{0.1779}[/tex]
[tex]t = 3.654[/tex]
The p-value of of t is obtained from the z table, the value is
[tex]p-value = P(t < 3.654) = 0.00012909[/tex]
Given that [tex]p-value < \alpha[/tex] then we reject the null hypothesis
Hence the company can conclude that the correlation is positive
What is the x-intercept?
