Answer:
[tex](x+6.2)^2 + (y-5.8)^2 = \frac{16}{81}[/tex]
Step-by-step explanation:
The vertex form of the equation of a circle is [tex](x-h)^2 + (y-k)^2 = r^2[/tex] where (h,k) is the center of the circle and r is the radius. This circle has center (-6.2, 5.8) and r= 4/9. Substitute h = -6.2, k = 5.8 and r = 4/9 into the vertex form. Then simplify for the equation.
[tex](x-h)^2 + (y-k)^2 = r^2\\(x--6.2)^2 + (y-5.8)^2 = \frac{4}{9}^2\\ (x+6.2)^2 + (y-5.8)^2 = \frac{16}{81}[/tex]
A container is in the shape of a rectangular prism with a square base. It has a volume of 99 cubic inches and a height of 11 inches. How many softballs with a diameter of 3.8 inches will fit into the container? Use the drop-down menus to explain your answer.
Answer:
A total of zero softballs will fit into the container
Step-by-step explanation:
step 1
Find the dimensions of the base of the prism
we know that
The volume of the prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
In this problem we have
[tex]V=99\ in^{3}[/tex]
[tex]h=11\ in[/tex]
substitute in the formula and find the area of the base B
[tex]99=B(11)[/tex]
[tex]B=99/11=9\ in^{2}[/tex]
the length side of the square base is the square root of the area
so
[tex]\sqrt{9}=3\ in[/tex]
we have that
The diameter of the softball 3.8 inches will fit (11/3.8=2.89 ) 2 times in the length of the container
The diameter of the softball 3.8 inches will fit 0 times in the width of the container
so
A total of 0 times of softballs will fit in the width of the container
therefore
A total of zero softballs will fit into the container
Answer:
Zero softballs with a diameter of 3.8 inches will fit into the container as length of the container is less the diameter of the softball.
Zero softballs can fit in length and zero softballs will fit in width.
Step-by-step explanation:
Length of the square base in rectangular pyramid = s
Breadth of the square base in rectangular pyramid = s
Height of the square base in rectangular pyramid ,l = 11 inches
Volume of the square base in rectangular pyramid ,V=[tex]99 inches^3[/tex]
Volume of the cuboid = l × b × w
V= s × s × l
[tex]99 inches^3=s^2\times 11 inches[/tex]
s = 3 inches
Softballs with a diameter of 3.8 inches.
But the length of the container is less the diameter of the softball which means not even single ball will not be able to get into the container. So zero softballs can fit in length and zero softballs will fit in width.
PLZ HURRY Part A:
Find the measure of the following angles:
<1
<2
<3.
Show your work to justify your answers. Earn up to 1 point for each missing angle with the correct answer and work shown.
Part B:
Answer the following question in 1-2 complete sentences. How is the measure of <1 and the measure of <2 related to the exterior 123° angle?
Answer:
<1:88
<2:65
<3:115
Step-by-step explanation:
Since we know that a line and the inside of a triangle equals 180 than we can use that to identify the missing angles.Using what we know about a line we can subtract 92 from 180 and we get 88, knowing that angle 1(<1)is the only angle that rest on that line than we know that <1 is 88.(to check this you can add 92 plus 88 and you get 180)Then switching hands,we can now figure out the interior missing angle 2(<2).There are two ways you can do this,Add all the interior angles together and then subtract from 180(88+57=145 then 180-145=35)or you can subtract all the known interior angles and then the answer is your missing angle(180-57-88=35).Now switching again, in order to find <3 then you have to find which number falls on the angle which we are looking for.Which would be 35 or <2.Now all you have to do is subtract 180-35=145
Part B:
I agree with the other person below⬇⬇⬇
Answer:
Step-by-step explanation:
(A) From the given figure, we have
[tex]{\angle}1+92^{\circ}=180^{\circ}[/tex] (Linear pair)
⇒[tex]{\angle}1=180^{\circ}-92^{\circ}[/tex]
⇒[tex]{\angle}1=88^{\circ}[/tex]
Thus, the measure of [tex]{\angle}1[/tex] is [tex]88^{\circ}[/tex].
Also, using the angle sum property in the given triangle, we get
[tex]{\angle}1+{\angle}2+57^{\circ}=180^{\circ}[/tex]
⇒[tex]88^{\circ}+{\angle}2+57^{\circ}=180^{\circ}[/tex]
⇒[tex]{\angle}2+145^{\circ}=180^{\circ}[/tex]
⇒[tex]{\angle}2=35^{\circ}[/tex]
Thus, the measure of [tex]{\angle}2[/tex] is [tex]35^{\circ}[/tex].
And, [tex]{\angle}2+{\angle}3=180^{\circ}[/tex]
⇒[tex]35^{\circ}+{\angle}3=180^{\circ}[/tex]
⇒[tex]{\angle}3=145^{\circ}[/tex]
Thus, the measure of [tex]{\angle}3[/tex] is [tex]145^{\circ}[/tex].
(B) Exterior angle theorem states that the exterior angle is equal to the sum of the two interior angles, thus from the given figure, we have
[tex]{\angle}1+{\angle}2=123^{\circ}[/tex]
Therefore, the relationship between the measure of [tex]{\angle}1[/tex] and [tex]{\angle}2[/tex] to exterior angle is [tex]{\angle}1+{\angle}2=123^{\circ}[/tex].
Need help ASAP!!
2. The Geo Air pilot is looking at SCCA from the plane. From the aircraft the angle of depression is 17 degrees. If the plane is at an altitude of 10,000 feet, approximately how far is the plane to SCCA? Round your answer to the nearest tenth. The image is not drawn to scale.
Answer:
The horizontal distance from the plane to SCCA is [tex]32,708.5\ ft[/tex]
Step-by-step explanation:
Let
x-----> the horizontal distance from the plane to SCCA
we know that
see the attached figure to better understand the problem
[tex]tan(17\°)=\frac{10,000}{x}[/tex]
[tex]x=\frac{10,000}{tan(17\°)}[/tex]
[tex]x=32,708.5\ ft[/tex]
What are the values of the variables in the triangle below? if the answer is not an integer, leave it in simplest radical form. the diagram is not drawn to scale
Answer:
x = 69 and y = [tex]23\sqrt{3}[/tex]
Step-by-step explanation:
Firstly the hypotenuse is the side opposite the 90 degree angle. So hypotenuse is [tex]46\sqrt{3}[/tex]
Since the angle given is 30 degree, with respect to this angle, the side length y is opposite and the side length x is adjacent.
Now, we can use trigonometric ratios to solve for x and y. Sine is defined as [tex]sin\theta=\frac{Opposite}{Hypotenuse}[/tex] and Cos is defined as [tex]Cos\theta=\frac{Adjacent}{Hypotenuse}[/tex]
Hence, we can write:
[tex]Sin(30)=\frac{y}{46\sqrt{3} }\\y=46\sqrt{3}*Sin30 \\y=46\sqrt{3}*\frac{1}{2}\\y=23\sqrt{3}[/tex]
Also, we can figure out:
[tex]Cos(30)=\frac{x}{46\sqrt{3} }\\Cos(30)*46\sqrt{3}=x\\ x=\frac{\sqrt{3} }{2}*46\sqrt{3} \\x=\frac{46*3}{2}\\x=69[/tex]
2nd answer choice is right.
ANSWER
[tex]x = 69,y = 23 \sqrt{3} [/tex]
EXPLANATION
Recall and use the mnemonics SOH CAH TOA.
We use the cosine ratio to find x.
[tex] \cos(30 \degree) = \frac{adjacent}{hypotenuse} [/tex]
[tex] \cos(30 \degree) = \frac{x}{46 \sqrt{3} } [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{x}{46 \sqrt{3} } [/tex]
Cross multiply,
[tex]2x = 46 \sqrt{3} \times \sqrt{3} [/tex]
[tex]2x = 46(3)[/tex]
[tex]x = 23(3)[/tex]
[tex]x = 69[/tex]
We use the sine ratio, to find y.
[tex] \sin(30 \degree) = \frac{opposite}{hypotenuse} [/tex]
[tex]\sin(30 \degree) = \frac{y}{46 \sqrt{3} } [/tex]
[tex] \frac{1}{2} = \frac{y}{46 \sqrt{3} } [/tex]
Solve for y.
[tex] \frac{1}{2} \times 46 \sqrt{3} = y[/tex]
[tex]23 \sqrt{3} = y[/tex]
Therefore,
[tex]x = 69,y = 23 \sqrt{3} [/tex]
Help me with #32 develop an inverse relationship and graph it on the graph
Step-by-step explanation:
Inverse is x · y = k
Since k = 20, then you are looking for x,y coordinates whose product is 20.
Answer:
The following are possible solutions:
[tex]\left\begin{array}{c|c|c}\underline{\quad x\quad }&\underline{\quad y\quad }&\underline{\qquad k\qquad }\\1&20&1\cdot 20=20\\2&10&2\cdot 20=20\\4&5&4\cdot 5=20\\10&2&10\cdot 2=20\\20&1&20\cdot 1=20\end{array}\right[/tex]
(See attached for graph)
A circle has a circumference of 615.44615. point, 44 units. What is the radius of the circle?
Answer:
The radius is 98
Step-by-step explanation:
The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. You have the circumference so substitute C = 615.44. Then solve for r.
C = 2πr
615.44 = 2πr
98 = r
Answer: 98 units
Step-by-step explanation:
PLEASE HELP ME ASAAAAAPPPPPPPPPPPP PLEASE HELP ME FAST What is 5 x 2/3 ? A) 3 1/3 B) 3 2/5 C) 5 2/3 D) 10/15
Answer:
A) 3 1/3
Step-by-step explanation:
5 x 2 = 10
10/3= 3 with a remainder of 1. That gives you 3 1/3
Answer:
Step-by-step explanation:
IF you calculate it right it is 3.3333333 or 3 1/3
Please answer this question! Will give brainliest!
Step-by-step answer:
Angle ECF = 110 = angle of intercepted (minor) arc EF.
The inscribed angles (angles EDF and EHF) are equal to half the angle of the inscribed arc, namely 110/2 = 55 degrees.
For your information, an inscribed angle is an angle with its vertex on (circumference of) the circle, formed by two intersecting chords, with a base on the inscribed arc.
Answer:
m∠EHF = m∠EDF = 55°Step-by-step explanation:
Look at the pictures.
(the picture 1)
Inscribed angle and central angle.
(the picture 2)
In a circle, central angle is two times larger than inscribed angle that intercept the same arc.
In a circle, inscribed angles that intercept the same arc are congruent.
We have the central angle C = 110°. The inscribed angle EHF is two times smaller than ∠C. Therefore m∠EHF = 110° : 2 = 55°.
The inscribed angles EHF and EDF that intercept the same arc. Therefore are congruent. m∠EHF = m∠EDF.
Mia has 7/8 ponds of bird food. She puts an equal portion into 4 bird feeders how much bird food in pounds does she put into each bird feeder
Answer:
B
Step-by-step explanation:
first you wanna multiply and sehow many mutiplesof 4 will go into 8.
The equal amount of bird food put into the 4 feeders is 7 / 32 pounds.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Mia has 7/8 pounds of bird food. She puts an equal portion into 4 bird feeders.
The amount of bird food for each feeder will be calculated as,
Bird food = (7/8) / (4)
Bird food = [ 7/ (8 x 4 )]
Bird food = 7 / 32 pounds
Therefore, the equal amount of bird food put into the 4 feeders is 7 / 32 pounds.
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(10CQ) The series 1/49+1/64+1/81+ ... is divergent.
Answer:
False
Step-by-step explanation:
We have the serie:
[tex]\frac{1}{49}+ \frac{1}{64} + \frac{1}{81}+...[/tex]
To test whether the series converges or diverges first we must find the rule of the series
Note that:
[tex]7^2 = 49\\\\8^2 = 64\\\\9^2 = 81[/tex]
Then we can write the series as:
[tex]\frac{1}{7^2}+ \frac{1}{8^2} + \frac{1}{9^2}+...[/tex]
Then:
[tex]\frac{1}{7^2}+ \frac{1}{8^2} + \frac{1}{9^2}+... = \sum_{n=7}^{\infty}\frac{1}{n^2}\\\\\sum_{n=7}^{\infty}\frac{1}{n^2} = \sum_{n=1}^{\infty}\frac{1}{(n+6)^2}[/tex]
The series that have the form:
[tex]\sum_{n=1}^{\infty}\frac{1}{n^p}[/tex]
are known as "p-series". This type of series converges whenever [tex]p > 1[/tex].
In this case, [tex]p = 2[/tex] and [tex]2 > 1[/tex]. Then the series converges
according to the graph, what is the value of the constant in the equation below? apex
Answer:
Option B. 36
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
The graph of the figure represent an inverse variation
so
In this problem
Constant=Height*Width
Take any point in the graph
example -----> the point (4,9)
Constant=4*9=36
Taylor was earning an income of $1,000 a week. Then his income was reduced by 10%. Two months later, his income increases by 10%. How much is Taylor earning, in dollars, after his income increases?
Wouldn't he be making $1,000 a week again? Since it was reduced by 10% but then raised by 10%.....
A father is four times as old as his son. In 4 years, the father will be three times as old as the son. How old is each now?
Answer:
M = 4S
In three years
M + 3 = 3(S + 3)
So you put the 4S in to substitute for the M.
4S + 3 = 3(S + 3)
4S + 3 = 3S + 9
S = 6
If the son is 6, the father must be 24.
We can check this by adding three to both ages. Then, the son will be 9 and the father will be 27, which is three times 9.
Step-by-step explanation:
A point is on a circle if the difference from the center of the circle to the point is equal to the
it should be the radius
At this rate, would a person your age (18 years old) have contributed a ton of garbage? On average, how long does it take for each person to throw away a ton, or 2000 pounds of garbage?
Answer: Yes. On average, it takes about 455 days for 1 person to throw away 1 ton of garbage, so just over 1 year.
Step-by-step explanation: The average person throws away 4.4 pounds of trash daily. So, the way to figure this out is 2,000 divided by 4.4 to find out the number of days it would take to throw away 2,000 pounds of trash.
Find the area of the regular polygon below. leave your answer in simplest radical form.
Answer:
384√3 in²
Step-by-step explanation:
Given in the question a regular 6 sided polygon
To find it's area you have to use the following formula
1/2 x perimeter x apothemPerimeter = the sum of the lengths of all the sides
Suppose length of one side = x
Apothem = a segment that joins the polygon's centre to the midpoint of any side that is perpendicular to that side = 8√3
Since the polygon have 6 sides so
perimeter = 6x
x = 2(8√3)/√3x = 2(8)
x = 16
perimeter = 6(16) = 96 in
plug values in the formula of area
1/2 x 96 x 8√3384√3 in²
Answer:
= 384√3 In²
Step-by-step explanation:
The polygon is a hexagon ; thus the angle subtended by each side at the center will be given by;
θ = 360/6
= 60°
Therefore; we can calculate the length of each side;
Tan θ = opp/Adj
Tan θ = x /8√3
Tan 30 = x /8√3
Therefore; 1/√3 =x /8√3
x = 8√3× 1/√3
= 8
The length of each side is 8 × 2 = 16 In
The area of the polygon will be;
Area of one triangle multiplied by the number of a triangle;
= 1/2 × 16 × 8√3 ×6
= 384√3 In²Find the polar equation of the conic with the focus at the pole, directrix y = -6, and eccentricity 4 (picture provided)
Answer:
Choice B is correct
Step-by-step explanation:
The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.
Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;
[tex]r=\frac{k}{1-4sin(theta)}[/tex]
The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;
k= 4*6 = 24
The polar equation is thus given by alternative B
Answer:
b on edge
Step-by-step explanation:
Determine the graph of the polar equation r =6/2-2cos theta
(picture provided)
Answer:
Choice D is correct
Step-by-step explanation:
The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;
[tex]r=\frac{3}{1-cos(theta)}[/tex]
The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.
The value of the directrix is determined as;
d = k/e = 3/1 = 3
The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;
x = -3
Thus, the polar equation represents a parabola that opens towards the right with a directrix located at x = -3. Choice D fits this criteria
Please answer this question, will give brainliest!
Answer:
10.1
Step-by-step explanation:
i divided the numbers now mark brainliest if its wrong or right
Find the midpoint of the chord:
9 / 2 = 4.5 cm
Now we can find the radius:
Radius = √(4.5^2 + 3.7^2)
Radius = √(20.25 + 13.69)
Radius = √33.94
Radius = 5.8 cm
Which shows the correct way to evaluate 10 × 4 – (5 – 3) + 2? 10 × 4 – (5 – 3) + 2 10 × 4 – (2 + 2) 10 × 4 – 4 10 × 0 0 10 × 4 – (5 – 3) + 2 10 × 4 – (2 + 2) 10 × 4 – 4 40 – 4 36 10 × 4 – (5 – 3) + 2 10 × 4 – 2 + 2 10 × 2 + 2 20 + 2 22 10 × 4 – (5 – 3) + 2 10 × 4 – 2 + 2 40 – 2 + 2 38 + 2 40
Answer:
10 × 4 – (5 – 3) + 2
10 × 4 – 2 + 2
40 – 2 + 2
38 + 2
40
Step-by-step explanation:
To solve;
10 × 4 – (5 – 3) + 2
We use BODMAS
We start by removing brackets, to get
10 × 4 – 2 + 2
Then we proceed to multiplication to get;
40 – 2 + 2
Then subtraction to get;
38 + 2
The answer is 40
The correct answer to evaluate is 10 × 4 – (5 – 3) + 2 is 40
What is the evaluationThe correct way to evaluate the expression 10 × 4 – (5 – 3) + 2 is as follows:
10 × 4 – (5 – 3) + 2
= 40 – (5 – 3) + 2
= 40 – 2 + 2
= 38 + 2
= 40
Therefore, the correct evaluation is 40.
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Look at the tally chart or line plot from Exercise 2 above. What was the total distance ridden by all of the children?
The data and summary given in the represents a random sample of twelfth-grade girls and bots in a school district. Is there an overlap between the two data sets?
Answer:
it is A) No, there is not an overlap between the two data setsStep-by-step explanation:
i did it on usatestprep
Answer:
A-No, there is not an overlap between the two data sets.
Step-by-step explanation:
Plz help me
WILL GIVE BRAINLIEST
Factor 3x^3−12x
3x^3−12x
=3x(x+2)(x−2)
Answer:
3x(x+2)(x−2)
3x^3 - 12x //Common factor: 3x
3x (x^2 - 4)
3x (x - 2) (x + 2)
Answer: C
//Hope this helps.
You can spend no more than $20. You have already spent $6. Let s be the amount of money (in dollars) you can spend now. Which inequality and solution represent this situation?
Complete the square to transform the quadratic equation into the form (x – p)2 = q. X2 - 8x - 10 = 18 A) (x - 8)2 = 14 B) (x - 4)2 = 44 C) (x - 8)2 = -14 D) (x - 4)2 = -44
Answer:
Option B. [tex](x-4)^{2}=44[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-8x-10=18[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-8x=18+10[/tex]
[tex]x^{2}-8x=28[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2}-8x+16=28+16[/tex]
[tex]x^{2}-8x+16=44[/tex]
Rewrite as perfect squares
[tex](x-4)^{2}=44[/tex]
Answer:
b
Step-by-step explanation:
Based on this data what is a reasonable estimate of the probability that the next tucker family vacation lasts less than 3 days
A. 0.24
B. 0.44
C. 0.56
D. 0.89
Answer:
I am assuming it is the same table as mine. So it would be 0.56
Step-by-step explanation:
Select the correct answer from each drop-down menu. Determine the dependence between the quantities for the given graph.
The cost per package depends on the weight of the package.
Step-by-step explanation:We know that a dependent variable is one which depends on some other variable or the value of the variable is calculated corresponding to the independent variable.
Generally we consider the values on the y-axis or the vertical axis as the dependent values because they are dependent upon the x-value or the value on the horizontal axis.
Here from the graph we may observe that the cost of the package depends on the weight of the package.
The cost per package depends on the weight of the package.
We know that a dependent variable is one which depends on some other variable or the value of the variable is calculated corresponding to the independent variable.
Generally we consider the values on the y-axis or the vertical axis as the dependent values because they are dependent upon the x-value or the value on the horizontal axis.
Here from the graph we may observe that the cost of the package depends on the weight of the package.
Please help me out :)
79-y=2y+22
Add y on both sides
79=3y+22
Subtract 22 from both sides
57=3y
Divide by 3 on both sides
19=y
"Which number can be inserted in the parentheses so the numbers are ordered from least to greatest?" -3,(),-1 1/8 A. -3 1/2 B. 0 C. -2 1/4 D 1 1/2
Answer:
Option C
Step-by-step explanation:
The first number is - 3, then we have a blank and the third number is - 1 1/8
In order for the numbers to be arranged from least to greatest, the number in the center should be greater than -3, and lesser than -1 1/8
Note that for negative numbers, the larger the constant, the smaller the number. i.e. -5 is smaller than -4.
So from the given options, the only number that is greater than -3 and lesser than -1 1/8 is - 2 1/4
So, option C gives us the correct answer to have the numbers ordered from least to greatest.
Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample of n = 25 light bulbs and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below. Test of H0: f$mu leq f$ 1500 versus H1: f$ mu f$ > 1500 Sample mean 1509.5 Sample standard deviation 24.27 Assuming the life length of this type of lightbulb is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, .123 would be a legitimate entry.
Answer:
p score = 0.031
Step-by-step explanation:
We will be running a hypothesis test to find the p-value. See attached photo for the work needed and the running of the test.
Our hypothesis are:
H0: µ = 1500
HA: µ > 1500 (claim)
They say that the life of the light bulbs are more than 1,500 hours, so that is the alternate hypothesis since it's strictly more than, not equal to or greater.
we have a sample mean of: 1509.5
we have a sample standard deviation of: 24.27
We just need to find the p-value, we don't need to make a conclusion about the test results.
The p-value of the hypothesis test that the light bulbs last more than 1500 hours is estimated to be less than 0.05, supporting the company's claim. The calculation involved computing a t-statistic from the sample data and then finding the probability of getting a t-statistic larger than the computed value.
Explanation:The question involves conducting a hypothesis test for the claim that the company's light bulbs last more than 1500 hours. The null hypothesis H0 for this test would indicate that the population mean longevity is less than or equal to 1500 hours (H0: μ ≤ 1500), while the alternative hypothesis H1 posits that the mean exceeds 1500 hours (H1: μ > 1500). The company collected a sample (n=25) and computed the sample mean ( = 1509.5 hours) and the sample standard deviation (s = 24.27 hours). To calculate the p-value for this test, we need to first calculate the test statistic (z or t) by using the given sample data and then find the area to the right of this test statistic in the relevant distribution.
Using the formula for calculating the test statistic in t-tests: t = ( - μ0)/(s / √n), where μ0 is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size. Here, t = (1509.5 - 1500)/(24.27 / √25) = approximately 1.96.
Since the alternative hypothesis is looking for values greater than 1500, we seek the probability that a test statistic is greater than what we observed (i.e., t > 1.96). This probability is equal to the p-value. To obtain it, we use the t-distribution with n-1 = 24 degrees of freedom. Since exact p-values can be challenging to retrieve without a statistical software or detailed tables, it's typically adhered to note if the p-value is less than or greater than the significance level, which is 0.05 in this case. Due to the calculated t-statistic, our p-value is approximately less than 0.05. Hence, this result supports rejecting the null hypothesis and lends credibility to the company's claim that its light bulbs typically last more than 1500 hours.
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