in a survey, 32 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $48 and standard deviation of $7. construct a confidence interval at a 80% confidence level. give your answers to one decimal place.
The required 80% confidence interval is (46.15, 49.85).
What is a confidence interval?In frequentist statistics, a confidence interval is a range of estimates for an unknown quantity.
The most common confidence level is 95%, but when calculating confidence intervals, other levels, such as 90% or 99%, are also occasionally employed.
So, we know that:
n = 32
χ' = 48
s = 8
Create an 80% confidence interval using the equation below:
[tex]\left(\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}\right)[/tex]
To determine the critical value t for n-1 degrees of freedom and 1 -cl level of significance, use the formula below:
[tex]t_{0.2, d f=31}=\pm 1.309[/tex]
Create the confidence interval now:
[tex]\begin{aligned}& \left(48 \pm 1.309 \times \frac{8}{\sqrt{32}}\right) \\& (48 \pm 1.85) \\& (46.15,49.85)\end{aligned}[/tex]
Therefore, the required 80% confidence interval is (46.15, 49.85).
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Is DEF = ABC? If so, type the reason, if not type no.
Answer:
Yes
Step-by-step explanation:
All you need to do is figure out the missing angles. We know that the three angles in a triangle add up to 180 degrees.
For angle B in ABC, 180-52-39= 89. So angle B = 89 degrees.
For angle D in DEF, 180-39-89= 52. So angle D = 52 degrees.
Then see if the order of the angles match up.
DEF = 52 degrees, 89 degrees, 39 degrees
ABC = 52 degrees, 89 degrees, 39 degrees
The order of the same angles match, so triangle DEF and triangle ABC are equal.
Answer:
Yes, triangle DEF is similar to triangle ABC because their corresponding angles are the same size.
Step-by-step explanation:
Interior angles of a triangle sum to 180°.
⇒ ∠A + ∠B + ∠C = 180°
⇒ 52° + ∠B + 39° = 180°
⇒ ∠B = 89°
⇒ ∠D + ∠E + ∠F = 180°
⇒ ∠D + 89° + 39° = 180°
⇒ ∠D = 52°
Two triangles are similar if their corresponding angles are the same size.
If ΔDEF ~ ΔABC then:
∠D = ∠A∠E = ∠B∠F = ∠CFrom inspection of the given diagram:
∠D = 52° and ∠A = 52° so ∠D = ∠A∠E = 89° and ∠B = 89° so ∠E = ∠B∠F = 39° and ∠C = 39° so ∠F = ∠CTherefore, the triangles are similar because their corresponding angles are the same size.
A basketball team has 12 players. For the last game of the season the coach will randomly select 5 players to start the game. The first player selected is the center, the second player selected is the power forward, the third player selected is the forward, the fourth player selected is the shooting guard, and the fifth player selected is the point guard. Determine the number of different ways the coach can pick up he line of the game
The number of different ways the coach can pick up the line of the game is 792 ways
Step-by-step explanation:
Let n- number of players, r-selection of players.
We can select them using Combination: nCr = 12C5
Combination formula nCr =[tex]\frac{n!r!}{ (n-r)!}[/tex] = 12C5 = [tex]\frac{12!5!}{(12-5)! }[/tex]
=[tex]\frac{12!5!}{ 7!}[/tex]
= 792ways
The number of different ways the coach can pick up the line of the game is 792 ways.
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Let a,b,c,d be real numbers such that 1/a+Ï + 1/b+Ï + 1/c+Ï = 2/Ï
where Ï is non real cube root of unity choose the correct answer. abc+bcd+acd+abd is equal to
First, we can rewrite the given equation as:
1/a+Ï + 1/b+Ï + 1/c+Ï = (1/Ï)(1/a + 1/b + 1/c)where Ï is the non real cube root of unity.
We can then multiply both sides of the equation by Ï to get:
1/a + 1/b + 1/c = 2(1/a + 1/b + 1/c)This simplifies to:
1/a + 1/b + 1/c = 0Since a, b, and c are all real numbers, we know that 1/a, 1/b, and 1/c are also real numbers. Therefore, the sum of these three real numbers must also be a real number. The only way that 1/a + 1/b + 1/c can equal 0 is if all three of these terms are equal to 0.
Thus, we can conclude that a = b = c = 0.
Since a, b, and c are all equal to 0, we know that abc + bcd + acd + abd must also equal 0. Therefore, the answer is 0.
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How much would you need to deposit in an account now in order to have $3,000.00 in the account in 1607 days?
Assume the account earns 3% simple interest.
You would need to deposit_____ in your account now.
Answer:
$ 2649.98
Step-by-step explanation:
1607 days = 1607/365 yrs
3000 = (deposit) + deposit * i * 1607/365 where i = decimal interest 3000 = deposit ( 1 + .03 * 1607/365)
3000/(1 + .03 * 1607/365) = deposit = $ 2649.98
Fill in the blanks 30 = 27 __ ___x 9 = 54 81 / ___ = 9 2 = ___ / 5 8 x ___ = 32 72 / ___ = 8 7* __ = 49
Step-by-step explanation:
this is a college level question, and you need help with that ? elementary school students have to be able to answer this.
30 = 27 + 3
6 × 9 = 54
81 / 9 = 9
2 = 10 / 5
8 × 4 = 32
72 / 9 = 8
7 × 7 = 49
Select all of the following equation(s) that are quadratic in form.
x4 – 6x2 – 27 = 0
3x4 = 2x
2(x + 5)4 + 2x2 + 5 = 0
6(2x + 4)2 = (2x + 4) + 2
6x4 = -x2 + 5
8x4 + 2x2 – 4x = 0
Answer:
Step-by-step explanation:
x4 – 6x2 – 27 = 0
x=2.49,-2.49
3x4 = 2x
x=6
I’ll give BRAINLIEST if correct need asap question is in the photo attached
Graph the line using the slope and y-intercept, or two points.
Slope:
1
y-intercept: (0,3)
x y
0 3
1 4
1. Mr. C has a square soccer field. The length of the soccer field is 18 feet.
What is the area of the soccer field:,
What is the perimeter of the soccer field
Answer:
Area = 324ft²
Perimeter = 72ft
Step-by-step explanation:
Area of a square = length²
Area of a square = (18ft)² = 324ft²
Perimeter of a square = 4*length
Perimeter of a square = 4ft*18 = 72ft
Evaluate the following 14/2+4*4-4
Answer:
14/2+4x4-4= 19
Step-by-step explanation:
calculate
7+19-4
which is 19
(BODMAS rule is used here)
14/2 + 4 × 4 - 4
7 + 4 × 4 - 4
7 + 16 - 4
7 + 12
19
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What is 1.8 rounded to the nearest tenth
Answer: 1.8 rounded to the nearest tenth will remain as 1.8 because 0.8 is 8 tenths
Answer:
Step-by-step explanation:
11.3
work out and simplify where possible 9/10 - 7/10
Answer:
1/5
Step-by-step explanation:
(9-7)/10
2/10
(2:2) / (10:2)
1/5
A bag contains 3 gold marbles, 7 silver marbles, and
28 black marbles. Someone offers to play this game:
You randomly select one marble from the bag. If it
is gold, you win $3. If it is silver, you win $2. If it is
black, you lose $1.
What is your expected value if you play this game?
To calculate the expected value of playing this game, we need to multiply the value of each possible outcome by its probability of occurring and then add these values together. In this case, there are 3 gold marbles, 7 silver marbles, and 28 black marbles in the bag, for a total of 38 marbles. So, the probability of selecting a gold marble is 3/38, the probability of selecting a silver marble is 7/38, and the probability of selecting a black marble is 28/38. The value of winning $3 if a gold marble is selected is $3 * (3/38) = $0.21. The value of winning $2 if a silver marble is selected is $2 * (7/38) = $0.37. And the value of losing $1 if a black marble is selected is -$1 * (28/38) = -$0.74. Adding these values together, we get $0.21 + $0.37 - $0.74 = -$0.16. Therefore, the expected value of playing this game is approximately -$0.16.
Find (f - g)(x), if f(x) = 2x2 + 2 and g(x) = 6x2 + 6.
To find (f - g)(x), you can subtract g(x) from f(x):
(f - g)(x) = f(x) - g(x)
= (2x2 + 2) - (6x2 + 6)
= -4x2 + (-4)
= -4(x2 - 1)
Therefore, the result of (f - g)(x) is -4(x2 - 1).
7. Sketch a model to represent the equation
2x + 2 = 12. Then, solve the equation.
x = 5 will be the correct answer and Model is provided in attachment don't look at the beauty of my figure.
The solution of the equation 2x + 2 = 12 is x = 5. And the model and the graph are given.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
Equation 2x + 2 = 12
The model for the equation is given in the attached image.
And the graph is also given in the attached image.
To solve for x:
2x + 2 = 12
Simplifying,
2x = 12 -2
2x = 10
Divide by 2,
2x / 2 = 10 / 2
x = 5.
Therefore, the solution of the equation is x = 5
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Emily loves to go the spa she and her friends go twice a month each visit she gets a 90 minute massage for $125 and a deluxe manicure and pedicure for $65. How much does she spent at the spa each month?
Answer: $380
Step-by-step explanation:
First, we will find the price per visit using addition.
$125 + $65 = $190
Next, we notice it says "twice a month" in the question. We will multiply the value above by two to find the price per month.
$190 * 2 = $380
Answer:
twice a month of 125 + 65
2($125 + $65)
= 2($190)
= $380
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answer: a is a rational number
Step-by-step explanation
Rational numbers are written in p/q form.
work out and simplify where possible 7/8 - 1/4
Answer:
5/8
Step-by-step explanation:
1/4=2/8
7/8-2/8=5/8
5/8 cannot be simplified
Answer:
5/8
Step-by-step explanation:
(7-2)/8
5/8
which of the following is false about probability distributions? O point the probabilities must total O. each probability should be greater than or equal to O. each probability should be positive, less than or equal to O. the outcomes listed must be independent.
The outcomes listed must be independent is false about probability distributions.
In probability theory, statistics, and the theory of stochastic processes, independence is a key concept. Informally speaking, two occurrences are independent, statistically independent, or stochastically independent if their occurrence has no bearing on either their chances or probability of occurring. Similarly to this, two random variables are independent if the probability distribution of either one is unaffected by the realization of the other.
It is important to distinguish between two definitions of independence when working with collections of more than two occurrences. Informally, mutual independence of events refers to each event being independent of any combination of other events in the collection, whereas pairwise independence of events refers to any two events in the collection being independent of each other.
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11/3 of x is 55 find x
Answer:
16.5
Step-by-step explanation:
11/3 =3 and 1/3 so 55/3 and 1/3 = 16.5 or 16 and 1/2
what is the translation rule
Answer:
A translation is a type of transformation that moves each point in a figure the same distance in the same direction
Step-by-step explanation:
Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.
pls help with both questions
In an experiment studying the effects of alcohol on social anxiety, alcohol is the ______ variable. A.) independent. B.) confounding. C.) random. D.) dependent.
In an experiment studying the effects of alcohol on social anxiety, alcohol is the dependent variable. So, correct option is option D.
What is Dependent variable ?Variables: The goal of all research is to describe and explain global dispersion. Variance is just the difference. That is, the fluctuations that occur naturally in the world, or the changes that occur as a result of manipulation. A variable is the name given to the variance you want to describe. A variable is the result of a force or is itself a force that changes another variable. There are two types of variables.
DependentIndependentWhen researchers administer an active drug to one group of people and placebo or an inactive drug to another group of people, the independent variable is drug treatment. Each person's response to active drug or placebo is called the dependent variable.
In this case, an experiment examining the effects of alcohol on social anxiety. Alcohol is the dependent variable here.
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determine the longest wavelength photon (in nm) which can remove an electron from mercury metal if the work function of the metal is 4.475 ev (1 ev
To determine the longest wavelength photon which can remove an electron from mercury metal, we need to use the equation:
wavelength = hc/work function
What are photons?Photons are just light particles. Photons are basic subatomic particles that convey the electromagnetic force (and so much more). The photon is the basic unit of electromagnetic radiation, or the "quantum."
What is wavelength?A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is often defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm).
To determine the longest wavelength photon which can remove an electron from mercury metal, you need to use the equation:
wavelength = hc/work function
where h is the Planck constant (6.626 x 10^-34 Js), c is the speed of light (2.998 x 10^8 m/s), and work function is the minimum energy needed to remove an electron from the metal, in this case 4.475 eV.
Plugging these values into the equation gives:
wavelength = (6.626 x 10^-34 Js)(2.998 x 10^8 m/s)/(4.475 x 1.602 x 10^-19 J/eV)
This simplifies to:
wavelength = 404.4 nm
So, the longest wavelength photon which can remove an electron from mercury metal is 404.4 nm.
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100 POINTS!!!!
a) The next event requires each runner to jump 10 hurdles that are spaced 8.5 meters apart. If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line, how long is the race? Show your work. (3 points)
PLEASE QUICK
Answer:
100.72
Step-by-step explanation:
[tex]Given,[/tex]
event requires each runner to jump 10 hurdles that are spaced 8.5 meters apart.
If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,
To Find: how long is the raceSolution:
runner to jump 10 hurdles that are spaced 8.5 meters apart.
Distance between 10 hurdles
=(10-1)* 8.5
=9*8.5
=76.5
If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,
Hence length of race = 13.72+76.5+10.5
=100.72
Mark me Brainliest pls
Answer:
100.72 meters
Step-by-step explanation:
To find the total length of the race, we need to sum:
The distance from the starting line to the first hurdle.The distances between the hurdles.The distance from the last hurdle to the finish line.The distance from the starting line to the first hurdle is 13.72 meters.
The distance between each of the 10 hurdles is 8.5 meters.
There are 9 spaces between hurdles 1 and 10, so the distance between the hurdles is 9 × 8.5 = 76.5 meters.
The distance from the last hurdle to the finish line is 10.5 meters.
To find the total length of the race, add these distances together:
[tex]\begin{aligned}\textsf{Total length of the race} &=\sf 13.72\; meters + 76.5\; meters + 10.5 \;meters\\\\&=\sf 100.72\; meters\end{aligned}[/tex]
Therefore, the race is 100.72 meters long.
A company has found that the demand for its product varies inversely as the price of the product. When the price x is 4.75 dollars, the
demand y is 500 units.
Find a mathematical model that gives the demand y in terms of the price x in dollars.
With the help of algebra mathematical model equation for demand of company's product is given by the equation d = 1800 / p.
What is algebra?
The area of mathematics known as algebra deals with the representation of problems as mathematical expressions. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.
Let demand for company's product d vary inversely with its price p, which means
d ∝ ( 1/p ) or d = k * ( 1/ p) = k / p ----- 1
As when p = 4.5, d = 400
Putting these in (1), we get 400 = k/ 4.5
Hence #k=400 x 4.5=1800 and our model equation is
d = 1800/p
Hence mathematical model equation for demand of company's product is given by the equation d = 1800 / p.
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Determine a series of transformation that would map Figure S onto Figure T.
Answer:
reflection then rotation
Step-by-step explanation:
A shoe store uses a 60% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $55?
Answer:The selling price of shoes after a markup of 60% of the price will be equal to $81.60
Step-by-step explanation:
i don't think this is right
graph the line y=3/2x
The equation of the line passes the origin. And the inclination of the line with the x-axis is 3/2. And the graph is given below.
What is a linear equation?An association between various factors brings about a straight model when a diagram is shown. The variable will have a level of one.
The straight condition is given as,
y = mx + c
Where m is the incline of the line and c is the y-block of the line.
The equation of the line is given below.
y = (3/2)x
The y-intercept is zero. Then the condition of the line passes the beginning. Furthermore, the tendency of the line with the x-pivot is 3/2.
The graph of the line is drawn below.
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what is the measure of X
The measure of an angle X is 11° and 3X+2°=35° , 4X-9° =35° .
What is meant by an angle?In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.
∠QPA = ∠UPA
3X+2 =4X- 9
4X-3X= 9 + 2
X= 11
The measure of X is 11
3X+2°=3(11)+2°
=35°
(4X-9)°=(4(11)-9)°
=35°
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