Answer:
Null Hypothesis, [tex]H_0[/tex] : P = 4.1%
Alternate Hypothesis, [tex]H_A[/tex] : P > 4.1%
Step-by-step explanation:
We are given that a psychologist claims that more than 4.1% of the population suffers from professional problems due to extreme shyness.
Let p = true percentage of the population that suffers from extreme shyness.
So, Null Hypothesis, [tex]H_0[/tex] : P = 4.1%
Alternate Hypothesis, [tex]H_A[/tex] : P > 4.1%
Here, null hypothesis states that % of the population who suffers from professional problems due to extreme shyness is equal to 4.1%.
On the other hand, alternate hypothesis states that more than 4.1% of the population suffers from professional problems due to extreme shyness.
So, the above hypothesis would be appropriate for conducting the test.
Round numerical answers to the nearest hundredth, if necessary.
A water bottle rocket is shot upward with an initial velocity of vi = 40 ft/s from the roof of a school, which is at hi = 70 ft above the ground. The equation h = −
1
2
at2 + vit + hi models the rocket's height as a function of time. The acceleration due to gravity a is 32 ft/s2.
We are to find how long will it take to return to the ground?
Answer:
t = 0.48 sec
Step-by-step explanation:
We are given;
initial velocity; vi = 40 ft/s
hi = 70 ft
acceleration due to gravity; a = 32 ft/s²
Now, we are given that the rocket's height as a function of time is;
h = -12at² + vit + hi
At ground, h = 0
Plugging in the relevant values to obtain ;
0 = -12(32)t² + 40t + 70
-384t² + 40t + 70 = 0
The roots of the equation gives; t = 0.48 sec
What is the median of the following data 2,3,1,1,0,4
Answer:
1.5
Step-by-step explanation:
0,1,1,2,3,4 - rearrange in order
2+1=3
3/2=1.5
I hope this helps!
Answer:
1.5
Step-by-step explanation:
Arrange the data in order from least to greatest
2,3,1,1,0,4
Least to greatest:
0,1,1,2,3,4
Then, find the number in the middle
In this case, there is 2 numbers in the middle, so we will take the average of those 2
1,2
To find the average, add up the numbers and divide by the number of terms
1+2=3
3/2=1.5
1.5 is the median
which equation has a constant of proportionality equal to 9?
Answer: 9y = 2x is the constant proportionality of 9
Step-by-step explanation:
Answer:
9y = 2x is the constant proportionality of 9
Step-by-step explanation:
Line
a
is parallel to line
b
. Which statement about lines
a
and
b
is true?
Math item stem image
Answer:
?
Step-by-step explanation:
Evaluate each logarithm. Round your answer to the nearest ten thousandth.
1. Log5 15
2. -3ln(1/e4/5)
Answer:
1. 1.685
2. 16.828
Step-by-step explanation:
1. log_5 15
To evaluate this logarithm you use the following formula:
[tex]Log_ab=\frac{log_{10}b}{log_{10} a}[/tex]
by replacing you obtain:
[tex]log_5 15=\frac{log_{10} 15}{log_{10}5}=\frac{1.176}{0.698}=1.685[/tex]
hence, the answer is 1.685
2. -3ln(1/e4/5)
to solve this logarithm you use the following properties:
[tex]ln(a^m)=m\ ln(a)\\\\ln(\frac{a}{b})=ln(a)-ln(b)\\\\ln(e^m)=m[/tex]
[tex]ln(1)=0[/tex]
By applying all these properties you obtain:
[tex]-3ln(\frac{1}{\frac{e^4}{5}})=-3[ln(\frac{1}{e^4})-ln(5)]=-3[ln(1)-ln(e^4)-ln(5)]\\\\-3ln(\frac{1}{\frac{e^4}{5}})=-3[0-4-1.609]=16.828[/tex]
hence, the answer is 16.282
Which of the following is a property of all squares?
A
No sides are parallel.
B
Opposite sides are not congruent.
C
Opposite vertex angles are not congruent.
D
The diagonals bisect each other.
Answer:
D. the diagonals bisect each other
Final answer:
The property of all squares is that their diagonals bisect each other. Other options are incorrect as squares have parallel and congruent sides as well as congruent angles. Therefore, the correct answer is D.
Explanation:
The question asks which of the following is a property of all squares. The correct answer is option D: The diagonals bisect each other. In every square, this property holds true, as squares are a type of rectangle, and in rectangles, the diagonals are congruent and bisect each other. We know that a square has four equal sides and four equal angles, which are right angles.
This implies that not only are the diagonals congruent, but they also divide the square into four congruent right triangles, bisecting one another at their midpoint. Options A, B, and C describe properties that are incorrect for squares, as all sides of a square are parallel and congruent, and all angles are congruent as well.
68 is 17% of what number?
Enter
Answer:
400
Step-by-step explanation:
Is means equals and of means multiply
68 = 17% * what number
Change to decimal form
68 = .17 * what number
Divide each side by .17
68/.17 = .17/.17 what number
400 = what number
The number is 400
68 is approximately 17 percent of 400.
To find out what number 68 is 17% of, we can use the following formula:
(17 / 100) x = 68
Let's solve for x:
(17 / 100) x = 68
To isolate x, we can multiply both sides of the equation by (100 / 17):
x = (68 × 100) / 17
x ≈ 400
Therefore, 68 is approximately 17% of 400.
To understand this calculation, think of the percentage as a proportion or ratio. In this case, we are trying to find the ratio of 68 to the unknown number. The result, 0.17, represents how much of the unknown number 68 comprises. By multiplying this ratio by the unknown number, we obtain the value of x, which is approximately 400. Thus, 68 is roughly 17% of 400, indicating that 68 represents 17% of the value 400.
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vTriangles 1 and 2 are similar. What ratio relates a side length of triangle 1 to the corresponding side length of triangle 2? Fill in the box to complete the ratio.
Answer:
a
Step-by-step explanation:
Lin need need to mix a specific shade of orange for the set of the school play. The color uses 3 parts yellow for ever 2 parts red.
So I understand that for example: cups of red paint=6 and you have to multiply 6 by 3 to get 21 put I don’t know how to get the total cups of paint
Answer:
Could you provide more detail so that I can help. Perhaps a screenshot or photo of the problem?
Step-by-step explanation:
The solution to the system of equations is (-1, -7)
5x + y = -12
4x - y = 3
true or false
Answer:true
Step-by-step explanation:
Find the area of a circle with a
circumference of 11(3.14) feet.
Answer:
Approximately: 9.63
Step-by-step explanation:
Simon calculated the volume of the prism. His work is shown here. area of base = B = 1 2 bh = 1 2 (5)(13) = 32.5 m2 volume = Bh = 32.5(12) = 390 m3 A triangular prism. The triangular base has a base of 5 meters and height of 12 meters. The height is 4 meters. What errors did he make? Check all that apply. The area of the base is 30 m2, not 32.5 m2. The area of the base is 60 m2, not 32.5 m2. The area of the base is 78 m2, not 32.5 m2. The volume of the prism is 108 m3, not 390 m3. The volume of the prism is 120 m3, not 390 m3.
Answer:
A and E
Step-by-step explanation:
Answer:
a and e
Step-by-step explanation:
i got it right :)
14. A woman looks down from a hot air balloon. She sees a sheep below and
measures the angle of depression as 35º. If the sheep is 125 ft from where
the woman is looking down from the balloon, how high off the ground is the
balloon? Round to the nearest foot.
Answer:
80 feet
Step-by-step explanation:
Kindly refer to the attached image for explanations
plz help worth 40 points
Answer:
Answer is B
Answer:
B
Step-by-step explanation:
wHaT iS 203892489897238748 pLuS 2385938749757437186791879867949382
I’m stuck on this I need the correct answer ASAP !
Answer:
S is the center of the circle shown below. The correct answer choice is A.
Step-by-step explanation:
I need help please thank u sm
The length of the shortest side of a 30-60-90 triangle is 2 cm. Which of the following is the length of the hypotenuse?
2cm
√3cm
4cm
2 √3cm
Answer:
4 cm
Step-by-step explanation:
The ratios of sides in a 30-60-90 triangle are ...
1 : √3 : 2
The hypotenuse is double the length of the shortest side, so is 4 cm in your triangle.
Final answer:
In a 30-60-90 triangle, if the shortest side is 2 cm, the hypotenuse is twice that length, resulting in a hypotenuse of 4 cm.
Explanation:
The 30-60-90 right triangle has sides in a specific ratio. The lengths of the sides opposite the 30°, 60°, and 90° angles are in the ratio 1:√3:2. If the shortest side is 2 cm, which is opposite the 30° angle, the hypotenuse is twice the length of the shortest side because it is opposite the 90° angle. Therefore, the length of the hypotenuse is 4 cm.
Harry took a loan from the bank.
D represents Harry's remaining debt (in dollars) after t months.
What was the size of Harry's loan?
Answer:
Step-by-step explanation:
The " -200 " decreases the amount owed by $200 every month
So...he pays $200 per month
True or false 6/10 is equivalent to 0.60.
Answer:
Yes. 1/10 is equal to 0.10. So 6/10 is equal to 0.60.
Which model shows a ratio of 2 unshaded parts to 3 shaded parts?
6 shaded squares and 4 unshaded squares.
4 shaded squares and 6 unshaded squares.
9 shaded squares and 3 unshaded squares.
3 shaded squares and 9 unshaded squares.
Answer: The answer is A
Step-by-step explanation:
Because it said, 2 unshaded parts and 3 shaded parts. And you have to multiply by 2 for 2 and 3
Find the value of x in the figure
Answer:
x=85
Step-by-step explanation:
The angles are vertical angles, therefore they are congruent. This means we can set them equal to each other.
x+5=90
Solve for x by isolating x. To do this, subtract 5 from both sides
x+5-5=90-5
x=85
So, x=85, and the second choice is correct.
Answer:
It is 85.
Step-by-step explanation:
The angles are vertical from each other so they are equal. 85+5=90.
Add.
(8y + 6) + (4y + 5)
Submit
Answer:
12y + 11
Step-by-step explanation:
To add them you would add like terms. That means you would add those with y together and those without together.
8y + 4y + 6 + 5 = 12y + 11
If you want to solve for y, subtract 11 from both sides then divide both sides by 12.
Answer:
Step-by-step explanation:
hello :
(8y + 6) + (4y + 5)=12y+11
PLEASE HELP ASAP
Select the correct answer from the drop-down menu.
Find the polynomial.
{5} is the solution set of
Reset
Next
Answer:
the third one down is the answer
Option C is correct, x² - 10x + 25 = 0 is the polynomial for the solution set of {5}.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The polynomial with a solution set of {5} for the equation
x²-5x+25=0
x is the variable of the given polynomial
We know that (a-b)²=a²+b²-2ab
x²-5x+25 can be converted to (x-5)²
(x-5)² = 0
Expanding the square, we get:
x² - 10x + 25 = 0
Hence, x² - 10x + 25 = 0 is the polynomial for the solution set of {5}.
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Apollo traveled 84 leagues in 6 days. Then he doubled his rate. How long would it take him
at this new speed?
Answer:
168 leagues in 12 days
Step-by-step explanation:
84 : 6
if doubled, 6 x 2 = 12 and 84 x 2 = 168
168 : 12
What is the volume of this container
Answer:
1,875 cm^3
Step-by-step explanation:
To find the volume of the big square you would multiply 20x5x20= 2,000
to find the volume of the little square you would multiply 5x5x5= 125
Then to find the Volume of the square with the hole in it you would subtract 2,000 and 125 which = 1,875 cm^3
Help Plz! Sam has to read a 144-page book for his literature class.He has 8 days to finish it.He wants to read about the same number of pages each day.How many pages per day must he read to finish the book in 8 days?
Answer:
18 pages per day
Step-by-step explanation:
Take the number of pages in the book and divide by the number of days he has to read to determine the number of pages per day
144/8 =18 pages per day
Find the product.
2y2(3x+52)
Answer:
this might be it : 12xy+228y
Step-by-step explanation:
you multiply 2 by 3 and get 6 and then multiply by 2 again and add they y
and then multiply 52 by 2 and gte 104 and them multiply by 2 and get 228 and add they y
Answer:
6xy² + 10y²z
Step-by-step explanation:
I did it and I got it right
Find the length of the missing side
The length of the missing side is
Answer:
52 m
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 + 39^2 = 65^2
a^2 + 1521 = 4225
4225 - 1521 = 2704
Square root of 2704 = 52
Answer:
52m
Step-by-step explanation:
as this is a right angled triangle (has a 90° angle), you can use the Pythagoras theorem to work out the missing side.
Pythagoras theorem:
[tex]a^{2} + b^{2} = c^{2}[/tex]
side A squared (labeled on diagram below)
+ side B squared
= side C squared
for this example though, we don't know the length of side B so we need to swap around the formula.
[tex]c^{2} - a^{2} = b^{2}[/tex]
replace the letters for their numbers,
[tex]65^{2} - 39^{2} = b^{2}[/tex] (calculate)
[tex]65^{2} - 39^{2} = 2704[/tex]
2704 = b² but we want b by itself so we will square root b² (2704)
[tex]\sqrt{2704} = 52[/tex]
∴ side B = 52m (remember we were calculating in meters)
I hope this was helpful :-)
Which step should be used to find the value of n?
2.3n = 10.35
A.
multiply both sides by 2.3
B.
add 2.3 to both sides
C.
subtract 2.3 from both sides
D.
divide both sides by 2.3