The test statistic for this hypothesis test is; t = 1.5
What is the Test Statistic?
The formula for test statistic is;
t = (x' - μ)/(σ/√n)
where;
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
We are given;
Sample mean; x' = 8.12 hours
Population mean; μ = 8 hours
Standard deviation; σ = 0.72 hours
sample size ; n = 81 pilots
Thus;
t = (8.12 - 8)/(0.72/√81)
t = 0.12/0.08
t = 1.5
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a number divided by 3 decreased by 7 is less than 4 times the number increased by 5
If we solve for the value of x we find that x is any value which is greater than -36/11.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given in question that a required number divided by 3 decreased by 7 is less than 4 times the number increased by 5.
Let's assume the number be x.
So , x divided by 3 is x / 3 and if we subtract it by 7 , we get :
x/ 3 - 7
Also , this value is less than 4 times the number added with 5.
i.e.,
4x + 5
So , the inequality can be written as :
[tex]\frac{x}{3}[/tex] - 7 < 4x + 5
or
x - 21 < 12x + 15
-36 < 11x
or
-36 /11 < x
or
x > -36/11
or
x is greater than -36/11.
Therefore , if we solve for the value of x we find that x is any value which is greater than -36/11.
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17. Scarlet made a dive off a 10-ft platform. Her height above the surface of the pool t
seconds after leaving the platform can be modeled in the graph shown. Which of these
statements is NOT true about Scarlet's dive?
A. After 1 second, her height is 42 meters.
B. She reaches her maximum height at 1.5
C. Her maximum height is 46 meters.
D. She hits the water at 3 seconds.
O A
OB
O C
OD
40
30
20
10
1
2
3
Given the attached graph, the statement that is NOT true about scarlet's dive is that "She hits the water at 3 seconds." (Option D) See the explanation below.
What is a graph?In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.
In this scenario, the relationship represented is between Scarlet's descent from a 10-foot platform and the time it takes her to complete the trajectory from point of dive to point of reaching the water.
Hence, it is clear from the graph attached that Scarlet hits the water at 3.25 seconds.
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Solve y3 = −125.
answers are
y = −5
y = ±5
y = −25
y = ±25
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y
=
−
16
x
2
+
170
x
+
61
Answer:
10.97 seconds
Step-by-step explanation:
You want to know when a rocket will hit the ground if its height is given by y = -16x² +170x +61, where x is seconds after launch.
Quadratic FormulaThe formula for the solutions of a quadratic equation is ...
[tex]\text{for }ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
When we apply this to the equation y=0, we have ...
[tex]x=\dfrac{-170\pm\sqrt{170^2-4(-16)(61)}}{2(-16)}=\dfrac{170\pm\sqrt{32804}}{32}\\\\x\approx 10.97\quad\text{seconds}[/tex]
The rocket will hit the ground after about 10.97 seconds.
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The table below shows the gender and type of movies they prefer to watch.MaleFemale829418464891Horror MoviesSuspense MoviesComedy MoviesWhat is the approximate probability that a person will be a female and prefer suspense movies?
First, we must find the total of females, it will be
[tex]T=94+46+91[/tex]Now we must look at the table how many females prefer suspense movies, it's
[tex]S=46[/tex]Now we do the quotient between the females that prefer suspense by the total of females:
[tex]\begin{gathered} P=\frac{46}{94+46+91} \\ \\ P=\frac{46}{231} \\ \\ P=0.199134199 \end{gathered}[/tex]Rounding it, we can say that approximately,
[tex]P\approx0.2[/tex]Or 20% of the females prefer suspense movies
Will give brainlest:)
Answer:
1/9
Step-by-step explanation:
-1/9 + 2/9
Since the denominator is the same, we can add the numerators
(-1+2)/9 = 1/9
The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.
A.-4
B.25
C.-18
D.0
In the quadratic function, the discriminants with no x-intercepts are (A) -4 and (C) -18.
What is a quadratic function?f(x) = ax² + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" shape.So, there are no x-intercepts on the graph of a particular quadratic function.
As is common knowledge, if a graph lacks an x-intercept, it will either end above or below the x-axis.This quadratic function has imaginary zeros.Discriminant= D
y = ax² + bx + cD = b² - 4acFor imaginary zeros, D must be negative.
The given option (A) and (C) which are -4 and -18 are negative and hence are the Discriminant with no x-intercepts.
Therefore, in the quadratic function, the discriminants with no x-intercepts are (A) -4 and (C) -18.
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Convert degrees to radians:144° = __ πEnter your answer as a decimal to the tenths place
Answer:
To convert the degrees to radians
[tex]144^{\circ}[/tex]we know that,
Radian is equivalent to the angle subtended at the centre of a circle by an arc equal in length to the radius.
we get that,
[tex]1\text{ radian}=\frac{180^{\circ}}{\pi}\text{ degrees}[/tex]That is,
[tex]1\text{ degree}=\frac{\pi^{}}{180^{\circ}}\text{ radians}[/tex]we get that,
[tex]144^{\circ}=144^{\circ}\times\frac{\pi}{180^{\circ}}\text{ radians}[/tex][tex]=\frac{4}{5}\pi\text{ radians}[/tex][tex]=0.8\pi\text{ radians}[/tex]Answer is: 0.8
Then, find an equivalent ratio where the number of skateboards is 50.
The equivalent ratio of longboard 3 : 10
What is Ratio ?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
Given:
Long-boards A 30
Skateboards 50 100
Find:
An equivalent ratio where the number of skateboards is 50.
Now,
⇒ Equivalent ratio = Long-boards / Skateboards
⇒ Equivalent ratio = 30 / 100
⇒ Equivalent ratio = 3 / 10
Now, Equivalent value of Long-boards = Equivalent ratio × Number of skateboards
Equivalent value of Long-boards = [3 / 10] × 50
Equivalent value of Long-boards = 15
Then the ratio will be :
15 / 50 = 3 / 10
or, 3:10
Hence, equivalent ratio where the number of skateboards is 50. will be 3:10
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The blueprint for the moreno’s living room has a scale of 2 inches= 5 feet. The family wants to use a scale of 1 inch= 3 feet. What is the width of the living room on the new blueprint
Please help me it’s due at 11:59pm!!!
The width of the living room on the new blueprint is 15 feet.
How to calculate the width?Based on the information, the scale of the original blueprint will be:
= 2 in / 5 ft
The width of the original blueprint is 6 inches, the actual width of the living room will be:
2/5 = 6/x
where x = width of living room
Cross multiply
x = 5 × 6 / 2
x = 15 feet.
The width is 15 feet.
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please I need help with algebra 2!
photo for questions
8 and 9!
Answer:
I need more information to solve this.
Step-by-step explanation:
PLEASE HELP FAST PLEASE
Given:BC=AD and BC||AD Prove: BEC=DEA
Answer: ad bc is the answer
Step-by-step explanation:
In a game
of ice hockey, the hockey puck took 0.6 second to travel 66 feet to the goal line. Determine the
the average speed of the puck in feet per second.
Answer:
The average speed of the puck is 110 ft per second.
Step-by-step explanation:
Using the d = st formula to find distance when given the speed and time, you can rewrite it to be s = d/t.
When you substitute the values in, you get s = 66/0.6, which is 110.
Hope this helps.
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Bette used 3 jumbo cans of frosting to frost 105
cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an
additional 175 cupcakes. How many jumbo cans of frosting would she need to frost 280
cupcakes?
The jumbo cans of frosting would she need to frost 280 cupcakes is 8 cans.
What is addition?Addition simply means the sum of the numbers that are given.
In this case, Bette used 3 jumbo cans of frosting to frost 105 cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an additional 175 cupcakes. This implies that the total cupcakes will be:
= 105 + 175 = 280
In this case, the cans used will be the addition of the cans above. This will be:
= 3 + 5
= 8 cans
This shows the concept of addition.
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what is 6000 divided by 40
Answer:
150
Explanation:
Alright so basically, 150 x 40 = 6000, right? So you want to find out how to find it using the division process. It is a whole number with no fractional part. As division with remainder the result of 6000 ÷ 40 = 150 R 0.
6000 divided by 40 ⇒ 150.
Here given that,
6000 is divisible by 40
since we know that,
Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.
6000 is divisible by 40 we get,
⇒ 6000/40
⇒ 150
So, the quotient is 150
Hence,
After dividing 6000 by 40 we get 150.
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Lin knows that angle A is congruent to angle D. She claims that triangles ABC and DEF
must be similar. Convince Lin that the triangles are not similar.
d) Work out 7½ ÷ 3 ²/3
Give your answer as a mixed number.
The answer is given above
12:36=21 :
Fill in the blank I don't understand it ?
Answer:
63
Step-by-step explanation:
12:36
36/12=3
21(3)=63
a restaurant offers 4 appetizers, 8 salads, 9 entrees and 7 desserts. in how many ways can a customer select a meal, if a meal consists of an appetizer, a salad, an entree and a dessert? a) 28 b) 491,400 c) 20,475 d) 112 e) 2,016 f) none of the above.
The customer can select the meal in 2016 ways.
There are four different methods to choose an appetizer, eight different ways to choose a salad, nine different ways to choose an entree, and seven different ways to choose a dessert. Customers can choose a meal in the range of 4*8*7*9 if, according to the multiplication rule, a meal includes an appetizer, a salad, an entree, and a dessert.
x = 4 * 8 * 7 * 9 = 2016 ways.
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Marie’s age is 12 less than triple Carl's’s age. When you add Marie's age to Carl’s age, you get 68. How old is Marie and how old is Carl? Show work.
A.) Use x to represent Carl's age. If x is Carl's age, write an expression for Marie's age using Carl's age x.
B.) Write an equation for the situation.
C.) Solve the equation from part a. Show your work. What is Marie's age and Carl's age.
30 Points for answering!
1.8.7 Check Your Understanding
Amala is copying XY.
After drawing an arc with the compass from the first point of the construction, the next step is [DROP DOWN 1].
Drop Down 1
Y
pick a point on the arc that will be the second endpoint of the new segment
Select a Value
adjust the compass width to equal the length of XY
use a straightedge to draw a line segment from the new points
pick a point on the arc that will be the second endpoint of the new segment
The next step after drawing an arc with the compass from the first point of the construction will be, to pick a point on the arc that will be the second endpoint of the new segment. (a)
To copy a line we have to follow a few steps of the procedure.
The steps are;
Adjust the compass width to equal the length of XY.Draw an arc with the compass from the first point of the construction.Pick a point on the arc that will be the second endpoint of the new segment. Use a straightedge to draw a line segment from the new points.The newly constructed line is exactly equal to the given line.To know more about the construction of copied structure visit,
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Find the nth term of this quadratic sequence
2, 8, 18, 32, 50,
Step-by-step explanation:
+6,+10,+14,+18
+4+4+4
therefore quadratic 4/period function=2
[tex]y = 2{x}^{2} + bx + c[/tex]
y=2 x=1
[tex] 0 = b + c[/tex]
y=8 x=2
8=8+2b+c
0=2b+c
y=18 x=3
0=3b+c
therefore
the equation is 2x^2=y
How to solve the blank
Answer:
blank = - 3
Step-by-step explanation:
let x represent the blanks , then
[tex]\frac{2}{3}[/tex] ([tex]\frac{9}{5}[/tex] + x) = [tex]\frac{2}{5}[/tex] x + [tex]\frac{2}{5}[/tex]
multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions
10([tex]\frac{9}{5}[/tex] + x) = 6x + 6 ← distribute parenthesis on left side
[tex]\frac{90}{5}[/tex] + 10x = 6x + 6
18 + 10x = 6x + 6 ( subtract 6x from both sides )
18 + 4x = 6 ( subtract 18 from both sides )
4x = - 12 ( divide both sides by 4 )
x = - 3
I NEED HELP WITH THIS QUESTION
Answer:
KML and LMK
Step-by-step explanation:
Tyler has 500 counters in a bag.
He gives
15 of the counters to Sam
52 of the counters to Peter
43 of the counters to Lakhdar
What fraction of the 500 counters is left in Tyler's bag?
Give your fraction in its simplest form.
Hamza is graphing the parabola represented by this equation. 3x-6y^2+6y=0
The answer is below!!!
Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right
The given equation is 3x-6y²+6y=0.
What is the parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Right
Vertex: (-1/2, 1/2)
Focus: (-3/8, 1/2)
Axis of symmetry: y=1/2
Directrix: x=-5/8
The coordinate points to plot (-1/2, 1/2), (0.5, 1.21), (0.5, -1.21), (1.5, 1.5) and (1.5, -0.5).
Therefore, Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right.
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If p and q vary inversely and p is 5 when q is 4, determine q when p is equal to 10.
If p and q vary inversely and p is 5 when q is 4, the value of q when p is equal to 10 is 2.
What is an inverse variation?An inverse variation can be defined as a type of proportionality which shows the relationship that exist between two (2) distinct variables, wherein, as the value of one variable increases, the value of the other variable decreases and vice-versa.
Mathematically, an inverse variation can be modeled or represented by this expression:
p ∝ 1/q
p = k/q
Where:
p and q are the variables.k represents the constant of proportionality.
Next, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:
k = pq
k = 5(4)
k = 20
Now, we can determine the value of q:
q = k/p
q = 20/10
q = 2.
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Pls tell me the answer thank you
Answer:
Third option
Step-by-step explanation:
The intercept x-intercept of f¹(x) is 1 and y-intercept of f(x) is also 1.
Set up a system of equations and solve using substitution or elimination. You must show all work You have 258 coins in a jar. They are a combination of dimes and quarters. If the money in the jar equals $36.75, how many of each type of coin is there?
Answer:
185 dimes and 73 quarters
Step-by-step explanation:
q + d = 258
25(q) + 10(d) = 3675
Write an equation and the answer.
A certain number was multiplied by 5, then decreased by 3, then halved. The result was 0.3 less than the original number. What was the original number?
Write in this format:
If the original number is x, the equation will be _; x=_.
I hope this was helpful.
The original number is 0.8.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number be x.
A certain number was multiplied by 5, then decreased by 3, then halved. The result was 0.3 less than the original number.
So, the mathematical expression is
1/2( 5x- 3) = x- 0.3
Now, solving for x
Multiply both side by 2
5x-3 = 2x- 0.6
5x- 2x= -0.6 + 3
3x= 2.4
Divide both side by 3
3x/3 = 2.4/3
x= 0.8
Hence, the original number is 0.8.
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