A 65 ft. long swimming pool is to be constructed. The pool will be 4 ft. deep at one end and 11 ft. deep at the other. To the nearest degree, what will be the measure of the acute angle the bottom of the pool makes with the wall at the deep end
Answers
Answer:
Measure of the acute angle = 84°
Step-by-step explanation:
In the figure attached,
ABDE is a swimming pool having length 'AB' = 65 feet
Depth of one end of the pool is BE = 4 feet
And depth of the other end AD = 11 feet
Acute angle between the bottom of the pool (DE) and wall of the deep end (AD) is ∠ADE.
Now from ΔCDE,
tanx = [tex]\frac{EC}{DC}[/tex]
tanx = [tex]\frac{7}{65}[/tex]
x = [tex]\text{tan}^{-1}(\frac{7}{65})[/tex]
x = 6.15°
Now measure of acute angle the bottom of the pool makes with wall at he deep end,
m∠ADE = (90 - 6.15)°
= 83.85°
≈ 84°
Related Questions
Explain what the difference between a tangent and a secant segment is?
Answers
Answer:
A tangent line touches a curve at one point and has the same slope as the curve at that point. A secant line intersects at 2 or more points and has a slope equal to the average rate of change between those points.
Answer:
A Tangent of a circle is found outside of the circle but touching 2 points of the circle on the outside. But a Secant is found inside the circle and it touches 2 points in the circle. A Chord can always be Secant, but a secant can not always be a chord because it may pass through the circle.
Step-by-step explanation:
What’s the correct answer for this?
Answers
Answer:
AP = 14
Step-by-step explanation:
According to secant-secant theorem
(CP)(PD)=(BP)(AP)
7×12=6×AP
AP = 84/6
AP = 14
Read the problem and decide whether it has too much or too little
information,
Every day, Ellie the Elephant eats 150 pounds of hay, eats 200
pounds of fruit, and drinks 50 gallons of water. How many gallons
of water does she drink each week?
A. too much
B. too little
Answers
Answer:
A. too much
Step-by-step explanation:
If we are only looking for how much water she drinks, we do not need to know the amount of hay or the amount of fruit
Polluted water is passed through a series of filters. Each filter removes 90% of the remaining impurities from the water. If you have 10 million particles of pollutant per gallon originally, how many filters would the water need to be passed through to reduce the pollutant to below 500 particles per gallon? You can only use a whole number of filters.
Answers
Answer:
5 filters
Step-by-step explanation:
1 filter = 1 million remain
2 filter =100,000 remain
3 filter =10,000 remain
4 filter =1,000 remain
5 filter = 100 remain which is below to 500
To reduce the pollutant to below 500 particles per gallon, the water would need to be filtered through 13 filters.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Let's first define a variable, p, to represent the number of filters. We can then say that the number of particles remaining in the water after the first filter is applied is 0.9 x 10,000,000 = 9,000,000 particles per gallon.
After the second filter is applied, the number of particles remaining is 0.9 x 9,000,000 = 8,100,000 particles per gallon, and so on.
This equation would be [tex]0.9^p \times 10,000,000[/tex]. We want to find the smallest value of p that makes this expression less than 500.
We can solve this by setting the expression equal to 500 and solving for p. This gives us the equation [tex]0.9^p \times 10,000,000=500[/tex].
Solving for p, we get p = log(500/10,000,000) / log(0.9), which is approximately 12.39.
Since we can only use a whole number of filters,
Thus, we would need to use 13 filters to reduce the pollutant to below 500 particles per gallon.
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What is the measure of arc WXY
Answers
Answer:
152°
Step-by-step explanation:
Let P be any point on tangent [tex] \overleftrightarrow{YZ} [/tex] and WY is secant or chord of the [tex] \odot J[/tex] .
[tex] \therefore m\angle WYZ + m\angle WYP = 180°\\(Straight \: line \: \angle 's) \\
\therefore 104° + m\angle WYP = 180°\\
\therefore m\angle WYP = 180°- 104° \\
\red{\boxed {\bold {\therefore m\angle WYP = 76°}}} \\[/tex]
NOW, by tangent secant theorem:
[tex] m\angle WYP =\frac{1}{2}\times m(\widehat{WXY}) \\\\
76°=\frac{1}{2}\times m( \widehat{WXY}) \\\\
76°\times 2 =m( \widehat{WXY}) \\
\huge \purple {\boxed {\therefore m(\widehat{WXY}) = 152°}} [/tex]
What’s the correct answer for this?
Answers
Answer:
36
Step-by-step explanation:
In circle with center O,
[tex] chord\overline {EF} \cong chord\overline {WV}... (Given) [/tex]
Since, congruent chords are equidistant from the center of the circle.
[tex] \therefore PG = GO\\
\therefore - x +10 = - 3(x+2)\\
\therefore - x + 10 = - 3x - 6\\
\therefore 3x - x = - 6-10\\
\therefore 2x = - 16\\\\
\therefore x = \frac{-16}{2} \\\\
\huge \red {\boxed {\therefore x = - 8}} \\\\
\because \overline {PO} = \overline {PG} + \overline {GO} \\
\therefore \overline {PO} = - x + 10 + \{-3(x + 2)\}\\
\therefore \overline {PO} = - x + 10 - 3x - 6\\
\therefore \overline {PO} = - 4x + 4 \\
\therefore \overline {PO} = - 4\times (-8)+ 4 \\
\therefore \overline {PO} =32+ 4 \\
\huge \orange {\boxed {\therefore \overline {PO} =36}} \\[/tex]
Pls answer anyone out there pls pls pls
Answers
Answer:
See below.
Step-by-step explanation:
9.
Property of a rhombus:
In a rhombus, the diagonals are perpendicular.
The sum of the measures of the angles of a triangle is 180 deg.
Since the diagonals are perpendicular, the angles formed by the intersection of the diagonals are right angles and measure 90 deg.
m<ABD + m<CAB + 90 = 180
50 + m<CAB + 90 = 180
m<CAB + 140 = 180
(i) m<CAB = 40
The diagonals of a rhombus divide the rhombus into 4 congruent triangles.
Call the point of intersection of the diagonals E.
Triangles CEB and AEB are congruent.
m<BCA = m<DCA = 40
m<BCD = m<BCA + m<DCA = 40 + 40
(ii) m<BCD = 80
m<CDB = m<ADB = 50
m<ADC = m<CDB + m<ADB = 50 + 50
(iii) m<ADC = 100
10.
There are two angles labeled z. One is near point E and one is near point O. One of them probably is x.
Two angles measure 60 and 80. Add them to get 140.
z (near point O) and the 140 deg angle are a linear pair. their measures add to 180 deg.
z + 140 = 180
z = 40 (This is the z near point O.)
z (near point O) and 60 deg add to an interior angle of the parallelogram.
z + 60 = 40 + 60 = 100
The interior angle at vertex O measures 100 deg.
Adjacent interior angles of a parallelogram are supplementary.
100 + y = 180
y = 80
The two angles labeled z are alternate interior angles. Since the sides of a parallelogram are parallel, the two angles labeled z are congruent and measure 40 deg.
z = 40 (This is angle z near point E)
Simplify the expression.
[tex]\frac{19}{3} +\frac{y}{2} + \frac{91}{13}[/tex]
Answers
Simplify the expression.
[tex]\frac{y}{2} +\frac{40}{3}[/tex]
(19*2*13)+(y*2*13)+(91*3*2)
= 45+y*26+91*6
= 591+26*y
Evaluate the expression y - x + z for x = 22, y = 4, and z = 0.15
y - X + z =
(Type an integer or a decimal.)
S
Answers
Answer:
-17.85
Step-by-step explanation:
=> y-x+z
Putting y = 4, x = 22 and z = 0.15
=> 4-22+0.15
=> -18+0.15
=> -17.85
Answer:
the answer is -17.85
Step-by-step explanation:
to find the answer first substitute x, y and z by the numbers 22, 4 and 0.15 respectively.
y-x+z
4-22+0.15
-18+0.15=-17.85
An epidemiologist found five cases of "big toe cancer" in the Yukon Territory. Because there were only a few cases, the epidemiologist decided to conduct a matched case-control study to determine whether shoe size larger than 9 is a risk factor for big toe cancer. Cases were individually matched to one control for daily activity, history of athlete’s foot, and history of ingrown toenails. The following data were gathered:
Shoe size > 9
Pair Case Control
1 Yes No
2 No No
3 No Yes
4 Yes Yes
5 No Yes
Compute the proper measure of association.
Interpret your results.
If you were to investigate a rare cancer in Lynchburg, where might you look for data?
What would be necessary legally and ethically to be able to utilize this data set(s)?
Submit your thread by 11:59 p.m. (ET) on Thursday of Module/Week 3, and submit your replies by 11:59 p.m. (ET) on Sunday of the same module/week.
Answers
Answer:
Step-by-step explanation:
Given that:
An epidemiologist found five cases of "big toe cancer" in the Yukon Territory.
Therefore, shoe size > 9
1) From the required data given below
Case Control Total
Yes 2(a) 3(b) 5
No 3(c) 2(d) 5
Total 5 5 10
∴ odds ratio = ad/bc
= 4/9
=0.444
2) From the less than 1.0 mean that the odds of cancer among case is lower than the odds of cancer among controls
These lines are parallel. Is this statement true or false? y = - 2 3 x + 8 y = 2 3 x − 5 A. true B. false
Answers
Answer:
This statement would be false.
Step-by-step explanation:
The given equations have slopes that are positive and negative. Therefore, we know that they will intersect at some point because the slopes are not the same. In fact, they intersect at the point (9 3/4, 1 1/2).
I have attached an image of the graph of these two equations for your reference.
Please answer this correctly
Answers
Answer:
19.4ft
Step-by-step explanation:
A parallelogram has two sides parallel and equal meaning the top and bottom length are the same;
Meaning if the top is C, the bottom is C.
Similarly the length at the right side equals that on the left;
That means the the left = 60.4ft
Perimeter means distance round
And perimeter =157.6ft
Meaning if we start from the Top, it means:
C+ 60.4ft + C + 60.4ft= 157.6ft
C + C + 60.4ft+ 60.4ft = 157.6ft
2C + 120.8 = 157.6
2C = 157.6 - 120.8
2C= 36.8
C = 36.8/2
C= 19.4ft
You can calculate C from here
The cone pictured has a surface area of____a0 square meters. (Use 3.14 for π .)
Answers
Answer: A=286.2 m²
Step-by-step explanation:
The surface area of a cone is [tex]A=\pi r(r+\sqrt{h^2+r^2} )[/tex].
We are given h=11 m and r=5 m. With these values, we can plug them into the equation to find the surface area.
[tex]A=\pi (5)(5+\sqrt{11^2+5^2} )[/tex]
[tex]A=5\pi (5+\sqrt{146} )\\[/tex]
[tex]A= 268.2 m^2[/tex]
Answer:
The cone pictured has a surface area of_268.2___a0 square meters
Step-by-step explanation:
SA of a cone = πr² + πrs
s = slant height
s = √h² +r²
so combined together
SA of a cone = πr² + πr(√h² + r²) = πr(r +√h² + r²)
SA of a cone = 3.14*5(5+[tex]\sqrt{11^{2}+ 5^{2} }[/tex] ) =268.2038
When a deposit of $1000 is made into an account paying 2% interest, compounded annually, the balance, $B, in the account after t years is given by B = 1000(1.02)t. Find the average rate of change in the balance over the interval t = 0 to t = 5. Give units and interpret your answer in terms of the balance in the account.
Answers
Answer:
The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.
Step-by-step explanation:
Given a function y, the average rate of change S of y=f(x) in an interval [tex](x_{s}, x_{f})[/tex] will be given by the following equation:
[tex]S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}[/tex]
In this problem, we have that:
[tex]B(t) = 1000(1.02)^{t}[/tex]
Find the average rate of change in the balance over the interval t = 0 to t = 5.
[tex]B(0) = 1000(1.02)^{0} = 1000[/tex]
[tex]B(5) = 1000(1.02)^{5} = 1104.08[/tex]
Then
[tex]S = \frac{1104.08 - 1000}{5-0} = 20.82[/tex]
The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.
Find the gradient of the line segment between the points (8,6) and (10,14).
Answers
Answer:
4
Step-by-step explanation:
Gradient= [tex] \frac{y1 - y2}{x1 - x2} [/tex]
Gradient of line segment
[tex] = \frac{14 - 6}{10 - 8} \\ = \frac{8}{2} \\ =4[/tex]
Solve for x. Show or explain your work.
Then, verify that your solution is correct.
-15 = 2x + 1
Answers
Answer:
-8 = x
Step-by-step explanation:
-15 = 2x + 1
-1 - 1 Subtract 1 from both sides
-16 = 2x Divide both sides by 2
-8 = x
To make sure this answer is correct, plug it into the equation to see if it works.
-15 = 2(-8) + 1 Multiply
-15 = -16 + 1 Add
-15 = -15
Solve the following absolute value equation for the unknown. Show all of your work for full credit. |-3h – 6| ≤ 3
Answers
Answer:
[tex]-3 \le h \le 1[/tex].
Step-by-step explanation:
Apply the property of absolute values: if [tex]a \ge 0[/tex], then [tex]|x| \le a \iff -a \le x \le a[/tex]. By this property, [tex]|- 3\, h - 6 | \le 3[/tex] is equivalent to [tex]-3 \le -3\, h - 6\le 3[/tex]. That's the same as saying that [tex]-3\, h - 6 \ge -3[/tex] and [tex]-3\, h - 6 \le 3[/tex].
Add [tex]6[/tex] to both sides of both inequalities:
[tex]-3\, h \ge 3[/tex] and [tex]-3\, h \le 9[/tex].
Divide both sides of both inequalities by [tex](-3)[/tex]. Note that because [tex]-3 < 0[/tex], dividing both sides of an equality by this number will flip the direction of the inequality sign.
[tex]-3\, h \ge 3[/tex] would become [tex]h \le -1[/tex].[tex]-3\, h \le 9[/tex] would become [tex]h \ge -3[/tex].Both inequalities are supposed to be true. Combining the two inequalities to obtain:
[tex]-3 \le h \le 1[/tex].
Stan ran 4 7/10 miles , which was 1 3/10 fewer miles than Matt ran. For students wrote and solve the equation to find him the number of miles that Matt Ryan which student wrote and solve the equation correctly
Answers
Answer:
Matt ran 6 miles.
Step-by-step explanation:
Stan ran 4 and 7/10 miles, and this is 1 and 3/10 fewer miles than Matt.
this means that Matt ran the following amount of miles
4 and 7/|0 + 1 and 3/10 miles:
(4 + 1) + (7/10 + 3/10) = 5 + 10/10 = 6 miles.
This would be the correct way to solve this equation.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
The box plot compares the monthly average temperature (in degrees Fahrenheit) recorded in the towns of Springwood and Meadows from April
to October Match each phrase to its correct value.
Meadows
Springwood
60
65
70
75
30
85
00
95
91
86
80
73
14
12
6
1
2
the median of the temperatures at Springwood
the median of the temperatures at Meadows
the interquartile range of the temperatures at Springwood
the interquartile range of the temperatures at Meadows
(ANSWER ASAP FOR 30 POINTS.)
Answers
Answer:
12
Step-by-step explanation:
For a certain instant lottery game comma the odds in favor of a win are given as 19 to 81. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is nothing.(Round to two decimal places as needed.)
Answers
Answer:
The probability is 0.19.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Odds in favor of a win are given as 19 to 81.
This means that for each 19 + 81 = 100 games played, there are expected to be 19 wins.
Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Desired outcomes:
19 wins, so D = 19.
Total outcomes:
100 games, so T = 100:
Probability:
[tex]p = \frac{D}{T} = \frac{19}{100} = 0.19[/tex]
The probability is 0.19.
through (8.-8) and has a slope of 3/4
Answers
Step-by-step explanation:
work is shown and pictured
What is the solution to the system of equations?
y=-3x + 6
y= 9
O (-21,9)
O (9,-21)
0 (-1,9)
O (9.-1)
Answers
Answer:
(-1,9)
Step-by-step explanation:
y=-3x + 6
y= 9
Set the two equations equal
-3x + 6 = 9
Subtract 6 from each side
-3x+6-6 = 9-6
-3x =3
Divide by -3
-3x/-3 = 3/-3
x =-1
y = 9
(-1,9)
The solution to the system of equations is (-1, 9). Therefore, option C is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are y=-3x+6 ----(i) and y=9 ----(ii).
From equation (i) and (ii), we get
9=-3x+6
-3x=3
x=-1
Substitute x=-1 in equation (i), we get
y=-3(-1)+6
y=3+6
y=9
So, the solution is (-1, 9)
Therefore, option C is the correct answer.
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Un sfert din numărul porcinelor din fermă, fiind de rasă superioară, aduc la sfârşitul anului, in medie,
o productie de 9.6 kg de carne pe cap de animal. Productia astfel obținută reprezintă jumătate din
totalul productiei de carne,
5 Determinati productia de carne pe cap de animal obținută de la un porc ce nu este de rasă supe-
noara
Answers
Answer:
The meat production per animal obtained from a non-superior breed pig = 4.8 kg of meat per non superior breed of pig.
Producția de carne pe animal obținută de la un porc de rasă non-superioară = 4,8 kg de carne pe o rasă de porc non-superioară.
Step-by-step explanation:
English Translation
A quarter of the number of pigs on the farm, being of superior breed, bring at the end of the year, on average, a production of 9.6 kg of meat per animal. The production thus obtained represents half of total meat production, Determine the meat production per animal obtained from a non-superior breed pig.
Solution
Let the meat production per animal for the non superior breed of pig be y
Let the total number of pigs be x
A quarter of the pigs are superior breed, 0.25x, bring in 9.6 kg of meat per superior breed of pigs.
Total amount of meat produced by the superior breed of pigs = 0.25x × 9.6 = (3.6x) kg
This means that there are three quarter pigs from the less superior breed, 0.75x, making y kg of meat per animal.
Total amount of meat produced by the non superior breed of pigs = 0.75x × y = 0.75xy kg
Total meat production = (3.6x + 0.75xy) kg
It is then given that the total amount of meat from the superior breed is half of the total meat production.
That is,
3.6x = (3.6x + 0.75xy)/2
7.2x = 3.6x + 0.75xy
7.2x - 3.6x = 0.75xy
3.6x = 0.75xy
y = (3.6/0.75) = 4.8 kg
Hence, the meat production per animal obtained from a non-superior breed pig = 4.8 kg of meat per non superior breed of pig.
In Romanian/In limba romana
Permiteți producția de carne pe animal pentru rasa non superioară de porc
Fie numărul total de porci x
Un sfert din rasa superioară, 0,25x, aduce 9,6 kg de carne pentru fiecare rasă superioară de porci.
Un sfert din porci sunt de rasa superioară, 0,25x, aduc 9,6 kg de carne pe rasă superioară de porci.
Cantitatea totală de carne produsă de rasa superioară de porci = 0,25x × 9,6 = (3,6x) kg
Aceasta înseamnă că există trei sferturi de porci de la rasa mai puțin superioară, 0,75x, ceea ce face y kg de carne pe animal.
Cantitatea totală de carne produsă de rasa non superioară de porci = 0,75x × y = (0,75xy) kg
Producția totală de carne = (3,6x + 0,75xy) kg
Se consideră că cantitatea totală de carne de la rasa superioară este jumătate din producția totală de carne.
Acesta este,
3,6x = (3,6x + 0,75xy) / 2
7,2x = 3,6x + 0,75xy
7,2x - 3,6x = 0,75xy
3,6x = 0,75xy
y = (3,6 / 0,75) = 4,8 kg
Prin urmare, producția de carne pe animal obținută de la un porc de rasă non-superioară = 4,8 kg de carne la o rasă de porc ne superioară.
Hope this Helps!!!
Sper că acest lucru vă ajută!!!
Given the speeds of each runner below, determine who runs the fastest. \text{Noah runs 11 feet per second.} Noah runs 11 feet per second. \text{Katie runs 423 feet in 33 seconds.} Katie runs 423 feet in 33 seconds. \text{Jake runs 1 mile in 396 seconds.} Jake runs 1 mile in 396 seconds. \text{Liz runs 638 feet in 1 minute.} Liz runs 638 feet in 1 minute.
Answers
Answer:
Jake
Step-by-step explanation:
Noah: 11 feet per second
Katie: 423 feet / 33 seconds = 12.82 ft/sec (just divide the feet / seconds)
Jake:
1 mile = 5280 feet
Adam runs 5280ft / 396 seconds = 13.34 ft/sec
Liz:
1 minute = 60 second.
Liz runs 638 feet / 60 seconds = 10.63 ft / sec
From the above results we find that Jake runs the fastest
Table of grams and ounces
A 2-column table with 5 rows. Column 1 is labeled Grams, x with entries 1, 2, 3, 4, 5. Column 2 is labeled Ounces, y with entries 0.035, 0.07, 0.105, 0.14, 0.175.
Choose the equation and description for the relationship given in the table.
Answers
Answer:
B) y = 0.035x. There are 0.035 ounces in every gram.A frozen yogurt shop offers scoops in cake cone, waffle cones, or cups. You can get vanilla, chocolate, strawberry, pistachio, or coffee flavored frozen yogurt. If you order a single scoop, how many outcomes are in the sample space?
Answers
Answer:
15 possible outcomes
Step-by-step explanation:
Given;
A frozen yogurt shop offers scoops in cake cone, waffle cones, or cups.
N1 = 3 possible options
You can get vanilla, chocolate, strawberry, pistachio, or coffee flavored frozen yogurt.
N2 = 5 possible options
The total number of possible outcomes in the sample space when you order a scoop of yogurt is the product of the available options;
N = N1 × N2 = 3 × 5
N = 15 possible outcomes
Joe is a waiter of a local pizza parlor. He usually gets a tip from the tables he waits on. The bill for one table comes to $34. Write a formula that will help Joe determine how much of a tip he'll receive from that table.
Answers
Answer:
Step-by-step explanation:
I remember leaving a top of ten percent (15%)
lets convert 15% into a decimal
15%=0.15
Tip=0.15x, where x is the bill price
Tip=0.15*34
Tip=5.1
So he could get 5$ and 10 cents as a tip
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answers
Answer:
Rhombus
Step-by-step explanation:
Answer:
Step-by-step explanation:
rhombus
What is the value of the expression below?
Answers
Answer:
(7÷2)-(4.5*3)+8
(3.5)-(13.5)+8
3.5-5.5=-2
A well-known brokerage firm executive claimed that 40% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 500 people, 38% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is smaller than 40% at the 0.025 significance level. The null and alternative hypothesis would be: H 0 : μ ≤ 0.4 H 1 : μ > 0.4 H 0 : p ≤ 0.4 H 1 : p > 0.4 H 0 : p = 0.4 H 1 : p ≠ 0.4 H 0 : μ = 0.4 H 1 : μ ≠ 0.4 H 0 : μ ≥ 0.4 H 1 : μ < 0.4 H 0 : p ≥ 0.4 H 1 : p < 0.4 1. The test is:______ a. left-tailed b. two-tailed c. right-tailed 2. The test statistic is:______ (to 3 decimals) 3. The p-value is:______ (to 4 decimals) 4. Based on this we:_______ a. Fail to reject the null hypothesis b. Reject the null hypothesis
Answers
Answer:
1) Null hypothesis:[tex]p \geq 0.4[/tex]
Alternative hypothesis:[tex]p < 0.4[/tex]
2) [tex]z=\frac{0.38 -0.4}{\sqrt{\frac{0.4(1-0.4)}{500}}}=-0.913[/tex]
3) [tex]p_v =P(z<-0.913)=0.1806[/tex]
4) For this case since the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly less than 0.4
a. Fail to reject the null hypothesis
Step-by-step explanation:
Information given
n=500 represent the random sample taken
[tex]\hat p=0.38[/tex] estimated proportion of if the people they are confident of meeting their goals
[tex]p_o=0.4[/tex] is the value to test
represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Part 1
We want to test if the true proportion is less than 0.4, the system of hypothesis are.:
Null hypothesis:[tex]p \geq 0.4[/tex]
Alternative hypothesis:[tex]p < 0.4[/tex]
a. left-tailed
Part 2
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.38 -0.4}{\sqrt{\frac{0.4(1-0.4)}{500}}}=-0.913[/tex]
Part 3
The p value for this case can be calculated like this:
[tex]p_v =P(z<-0.913)=0.1806[/tex]
Part 4
For this case since the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly less than 0.4
a. Fail to reject the null hypothesis
