==================================================
Work Shown:
h(x) = 7x-5
h(2) = 7(2)-5
h(2) = 14-5
h(2) = 9
f(h(2)) = f(9)
f(x) = x^2-7
f(9) = 9^2-7
f(9) = 81-7
f(9) = 74
f(h(2)) = 74
-----------
Here's a slightly alternative approach:
f(x) = x^2 - 7
f(h(x)) = ( h(x) )^2 - 7
f(h(x)) = ( 7x-5 )^2 - 7
f(h(2)) = ( 7*2-5 )^2 - 7
f(h(2)) = ( 14-5 )^2 - 7
f(h(2)) = ( 9 )^2 - 7
f(h(2)) = 81 - 7
f(h(2)) = 74
your friend claims that the average maximum amount of time people can hold their breath is less than 60 seconds. to check whether your friend's claim is true, you take a random sample of the maximum amount of time 10 people can hold their breath. 42 45 47 50 58 60 61 63 64 68 assume the population is approximately normal. perform a hypothesis test to determine whether the average maximum amount of time people can hold their breath is less than 60 seconds. use the alpha =0.05 level of significance.
a. state the null and alternate hypothesis
b. compute the value of the test statistic. round your intermediate calculations and final answer to at least three decimal places.
c. give the p-value
d. determine whether to reject the null hypothesis
e. state a conclusion in the context of the question (in the story of the problem)
Using the t-distribution, it is found that:
a)
The null hypothesis is: [tex]H_0: \mu \geq 60[/tex]
The alternative hypothesis is: [tex]H_1: \mu < 60[/tex]
b) t = -1.47
c) 0.0878.
d) Do not reject the null hypothesis.
e) Not enough evidence to conclude that the average maximum amount of time people can hold their breath is less than 60 seconds.
Item a:
At the null hypothesis, it is tested if the mean is not less than 60 seconds, that is:
[tex]H_0: \mu \geq 60[/tex]
At the alternative hypothesis, it is tested if the mean is less than 60 seconds, that is:
[tex]H_1: \mu < 60[/tex]
Item b:
We can find the standard deviation for the sample, hence, the t-distribution is used to solve this question.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.With the help of a calculator to find the sample mean and the standard deviation, the values of the parameters are:
[tex]\overline{x} = 55.8, \mu = 60, s = 9.04, n = 10[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{55.8 - 60}{\frac{9.04}{\sqrt{10}}}[/tex]
[tex]t = -1.47[/tex]
Item c:
The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -1.47.
Using a t-distribution calculator, this p-value is of 0.0878.Item d:
The p-value is of 0.0878 > 0.05, hence, we do not reject the null hypothesis.
Item e:
Since the null hypothesis is not rejected, there is not enough evidence to conclude that the average maximum amount of time people can hold their breath is less than 60 seconds.
A similar problem is given at brainly.com/question/24826023
Mariana's office recycled a total of 9 kilograms of paper over 3 weeks. After 4 weeks,
how many kilograms of paper will Mariana's office have recycled? Solve using unit rates.
Answer:
9 kg per 3 weeks = 3 kg per week
Therefore, after 4 weeks it is (4 * 3) kilograms or 12 kilograms
Step-by-step explanation:
A 67-kilogram cannon fires a 1 kilogram cannonball at 45 m/sec. If the cannon is on wheels, at what speed does it move backward?
Answer:
-1.4 m/sec [backwards]
Step-by-step explanation:
The energy of the cannon moving should be equal to the energy contained in the cannonball. Kinetic energy for each is calculated using KE = (1/2)m[tex]v^{2}[/tex]
Let x be the speed of the cannon.
Cannonball:
KE = (1/2)m[tex]v^{2}[/tex]
KE = (1/2)(1kg)(45 m/sec)^2
KE = 22.5 kg*m/sec^2
Cannon: [The cannon will have the reverse energy]
KE = - (1/2)m[tex]v^{2}[/tex]
22.5 kg*m/sec^2 = -(1/2)(67 kg)x^2
22.5 kg*m/sec^2 = -(33.5 kg)x^2
x^2 = (33.5 kg)/(22.5 kg*m/sec^2)
x^2 = -1.4 m/sec [backwards]
What is the solution to the system of equations?
{2x + 3y = 6
x+y=1
Answer: {x,y} = {-3,-4}
Step-by-step explanation:
factor this polynomial completely x^2-10x+25
x^2-10x+25
=x^2-5x-5x+25
x(x-5)-5(x-5)
=(x-5)(x-5)
x=5 , x=5
hope it's helpful to you
[tex]x^2 -10x +25\\\\=x^2 -2 \cdot 5 \cdot x +5^2\\\\=(x-5)^2\\\\=(x-5)(x-5)[/tex]
Select the correct answer. This table represents the boiling point of water at different altitudes.Which equation represents water's boiling point (y) based on the change in altitude (x)? Altitude (thousands of feet) Boiling Point of Water (Fahrenheit) (sea level) 0 212 0.5 211.1 1.0 210 2.0 208.4 2.5 207.5 3.0 206.6 4.0 204.8 4.5 203.9
Answer:
Step-by-step explanation:
The net income reported on the income statement for the current year was $135,500 depreciation recorded on store equipment for the year amounted to $22,400 balances of the current asset and current libaility accounts at the beginning and end of the year are as follows
PLS HELP BEST ANSWER=BRAINLIEST
3a² - ac + 2c - 6a/ 3a - c = a - 2
i have been looking everywhere but i cannot find the steps on how to simplify/solve this
PLS SHOW STEPS
Answer:
a-2=a-2
Step-by-step explanation:
Here it is, you just have to notice that the numerator has common factors alternated. You will then collect the same parentheses and simplify with the denominator.
Answer:
Step-by-step explanation:
Parentheses are missing in your problem statement if you intend to simplify ...
[tex]\dfrac{3a^2-ac+2c-6a}{3a-c}\\\\=\dfrac{a(3a-c) -2(3a-c)}{3a-c}\qquad\text{factor pairs of terms}\\\\=\dfrac{(a-2)(3a-c)}{(3a-c)}\\\\=\boxed{a-2}\qquad\text{cancel common factors}[/tex]
The "steps" are ...
factor numerator (and denominator, if necessary)cancel common factorsPLEASE HELP
solve for x?
Explain how the ratios 5 tacos for every 2 guest and 2 tacos for every 5 guests are different. Include a model in your explanation.
Answer:
5 tacos for 2 guests would mean more for each person, while 2 tacos for 5 guests would mean less for each person
Suppose theta is an angle in the standard position whose terminal side is in Quadrant II and tan0= -sqrt3 Find the exact values of the remaining five trigonometric functions of theta
The exact values of the remaining five trigonometric functions of theta are
sinθ = √3/2cosecθ = 2/√3cosθ = -1/2secθ = -2 cotθ = -1/√3Since tanθ = -√3.
The remaining five trigonometric functions of theta are sinθ, cosecθ, cosθ, secθ and cotθ.
The next trigonometric function of θ is cotθ.
cotθ = 1/tanθ
= 1/-√3
= -1/√3.
Also, tan²θ + 1 = sec²θ
Substituting tanθ = -√3 into the equation, we have
(-√3)² + 1 = sec²θ
3 + 1 = sec²θ
sec²θ = 4
secθ = ±√4
secθ = ±2
Since θ is in the quadrant II,
secθ = -2
Also, cosθ = 1/secθ
= 1/-2
= -1/2
Also, cot²θ + 1 = cosec²θ
Substituting cotθ = -1/√3 into the equation, we have
(-1/√3)² + 1 = cosec²θ
1/3 + 1 = cosec²θ
cosec²θ = 4/3
cosecθ = ±√(4/3)
cosecθ = ±2/√3
Since θ is in the quadrant II,
cosecθ = +2/√3
Also, sinθ = 1/cosecθ
= 1/2/√3
= √3/2
So, the exact values of the remaining five trigonometric functions of theta are
sinθ = √3/2cosecθ = 2/√3 cosθ = -1/2secθ = -2cotθ = -1/√3.Learn more about trigonometric functions here:
https://brainly.com/question/4515552
A local band sells out for their concert. They sell all 1,175 tickets for a total purse of $28,112.50. The tickets were priced at $20 for student tickets, $22.50 for children, and $29 for adult tickets. If the band sold twice as many adult as children tickets, how many of each type was sold
Answer:
225 children tickets, 450 adult tickets and 500 student tickets were sold
BraniliestBraniliestBraniliestBraniliest Braniliest
Answer:
-20.54 C
Step-by-step explanation:
Form an equation
-12.94 C = initial temperature
changes -1.9 per hour = -1.9h
h = hour
x = temperature after 4 hours
-12.94 -1.9h = x
substitute 4 for "h"
-12.94-1.9(4) = x
x = -20.54C
Answer:
-20.54Step-by-step explanation:
Just multiply -1.9 by 4 then add it to 12.94
A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is
if we can assume the ball is being thrown from the ground upwards, then we can say that the inital height of it is 0, whilst its initial velocity is 80 ft/s, thus
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+80t+0\implies h(t)=-16t^2+80t[/tex]
12POINTS PLEASE HURRY ASAPPPPP <3
ITS SQAURE 6
6 SQAURE OFTHE 6
5 x (3+H) = 15+45. What is H?
Answer:
9
Step-by-step explanation:
5 x 3 = 15 and 5 x H = 45
45 / 5 = 9
Who are you favorite male country singers?
Answer:
kanye west
Step-by-step explanation:
Which variable would you eliminate first to solve this system using the elimination method? 3x+7y=2 -3x-y=10
Answer:
x
Step-by-step explanation:
Since the x- terms are opposites , that is 3x and - 3x , then when the 2 equations are added the x- term will be eliminated.
plz help me to answer
Answer:
if you can only pick one it's e
Step-by-step explanation:
Im 90% sure a and c are both true answers while 70% sure that b and d are both true answers so unless someone says otherwise e is your best bet
someone help please i don’t want to fail math
Answer:
Image below!
Step-by-step explanation:
Plotting [tex]\underline{y=2x+3}[/tex]
Step 1: determine the y-intercept
[tex](0,3)[/tex]
plot the point as the first point on the graphStep 2: Move 2 units up, and 1 unit left (keep repeating this process until you have reached the limit of the graph)
Step 3: Go to the other side of the graph of the first point (y-intercept)
move 2 units down, and 1 unit right keep repeating this process until you have reached the limit of the graph)When you've completed this process, it should look like this:
Solve the following exponential equation:
5^x=2
e^x=10
Number 1.
[tex]5^x=2[/tex], first we will take the [tex]log[/tex] of both of these numbers getting us,
[tex]x=\frac{log(2)}{log(5)}[/tex], which then gives us that [tex]x=0.4306777777....[/tex]
Number 2
[tex]e^x=10[/tex], solve for our exponent, [tex]2.718282^x=10[/tex], use the logarithmic formula, and we get,
[tex]x=\frac{log(10)}{log(2.718282)}[/tex], which then we get that [tex]x=2.302585[/tex]
Plz solve this its urgent
Options are 6cm
3cm
1.5cm
ΔPQR has: PM is a median
So: MR = QM = 3 cm
ANSWER: MR = 3 cm
Ok done. Thank to me :>
I need help on this math question
Answer:
84
Step-by-step explanation:
7 Sizes * 3 Lengths * 4 Colors = 84
Help help help math math math math
Answer:
66 degrees.
Step-by-step explanation:
angle 4 is 124, and angle 1 and 4 make 180 degrees. that means angle 1 is 56 degrees (180-124). and the total angle in a triangle is also 180 degrees.
Add 56 and 58, you'd get 114.
180-114=66
angle 2=66 degrees.
Answer:
66
Step-by-step explanation:
1. The exterior angle theorem states that the measure of an exterior angle of a triangle is congruent to the sum of the two opposite interior angles.
Basically, exterior angle = opposite interior angle + opposite interior angle2. Now, let's see what information we have so far, and what we don't have.
m∠4 is 124 degrees, is the exterior angleThe angle with 58 degrees is one of the opposite interior angles∠2 is the other opposite interior angle, but we don't know its measure3. Now, let's set up the equation and solve it.
Step 1: Set up the equation.
[tex]124 = x + 58[/tex]Step 2: Subtract 58 from both sides.
[tex]124-58=x+58-58[/tex] [tex]66 = x[/tex]Step 3: Check if solution is correct.
[tex]124=66+58[/tex] [tex]124=124[/tex]Therefore, the answer is 66.
the orthocenter of a triangle is at the origin, and two of the vertices of the triangle are at (-5,0) and (3,4) Find the third vertex of the triangle
Answer:
(3, -6)
Step-by-step explanation:
The orthocenter is the point of intersection of the altitudes of the triangle. That is, each altitude goes through the orthocenter. Hence, the line from any given vertex through the orthocenter is perpendicular to the opposite side.
The attached figure shows the given points labeled A and B. Point A lies on the x-axis, as does the orthocenter, so the side opposite will be a vertical line (perpendicular to the x-axis).
The remaining side of the triangle will be perpendicular to the line from B through the origin. The line through B has slope 4/3, so the line containing side AC will have slope -3/4 and will go through point A. Its point-slope equation will be ...
y -0 = -3/4(x +5)
We already know the x-coordinate of vertex C is the same as that of vertex B, so is x=3. Using this in the equation for side AC, we find the y-coordinate to be ...
y = -3/4(3 +5) = -6
The coordinates of point C, the third vertex, are (3, -6).
_____
Additional comments
The slope of a line is given by ...
m = (y2 -y1)/(x2 -x1)
When (x1, y1) = (0, 0), this reduces to ...
m = y2/x2 . . . . . . the relation we used for the slope of line OB
__
The slope of a perpendicular line is the opposite reciprocal of the slope of a line. The line perpendicular to the one with slope 4/3 will be -1/(4/3) = -3/4.
__
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
A jet plane can carry up to 200,000 liters of fuel. It used 130,000 liters of fuel during a flight. What percentage of the fuel capacity did it use on this flight?
Answer:
Step-by-step explanation:
65%
Step-by-step explanation:
Given: Full capacity= 200000 litres
Amount of fuel used during flight= 130000 litres
Now, finding percentage of fuel used on the flight.
∴ Percentage of fuel used=
Solving it, we will get
∴ 65% of fuel capacity been used in this flight.
Answer:
65%.
Step-by-step explanation:
(130,000/200.000) * 100
= 0.65 * 100
= 65%.
please help me on this one would be great help.
Answer:
60
Step-by-step explanation:
Marty has 6 cans of pain that he can use for the 3 bedrooms he needs to paint. How much paint can Marty use in each bedroom?
There are 5 boxes of chocolates. If taking 200g out of each box, the remaining chocolates in the 5 boxes are exactly the same weight as the original 4 boxes. How many grams of chocolate is in each box?
Answer:
1000
Step-by-step explanation:
So the taken chocolate weight equals to the original 1 box of chocolate.
Thus there are 200 x 5 = 1000g.
The orginal chocolate has 1000g each.
What is (3*7) divided by 5
Answer:
The answer is 4.2,
Hope that helped. x
Step-by-step explanation:
3 x 7 (3*7) = 21
21 divided by 5 = 4.2.
Answer:
4.2
Step-by-step explanation:
Using PEMDAS,
ParenthesisExponentsMultiplicationDivisionAdditionSubtractionWe know that to solve (3*7) divided by 5, we will need to solve what is in the parenthesis.
So, we need to figure out what is 7*3, which is 21.
This is what we have right now:
21 divided by 5
The next step is dividing,
We divide 21 by 5 to get 4Multiply the quotient digit (4) by the divisor 5Subtract 20 from 21Add a decimal place and a zero to the dividend, bring down the zero from the dividendDivided 10 by 5 to get 2Multiply the quotient digit (2) by the divisor 5Subtract 10 from 10The solution for the division is 4.2In the end, the answer is 4.2, hope this helped!
Find the value of .
X
100°
Y
130°
x
66°
w
Z
The measure for angle W is 80 degree.
What is Trapezium?A unrestricted polygon or figure with four sides, four corners, and four angles is called a trapezium. Each brace of a trapezium's opposing sides is resemblant to the other.
Similar to other quadrilaterals, the trapezium's four angles add up to 360°. Two of the sides of a trapezium are parallel, and the other two are not. Regular trapezium diagonals cut each other in half.
Given:
We have angles <X= 100, <Y = 130 and <Z= 66.
As, we know that in Trapezium the sum of adjacent angle is 180.
So, <X + <W = 180
100 + <W =180
<W= 180- 100
<W = 80 degree.
Learn more about Trapezium here:
https://brainly.com/question/22607187
#SPJ2