At the movie theatre, child admission is $5.10 and adult admission is $9.00 . On Monday, 163 tickets were sold for a total sales of $1088.70 . How many adult tickets were sold that day?
a = adult tickets
c = child
c + a = 163 tickets total
rewrite as c = 163-a
5.10c + 9.00a = 1088.70
5.10(163-a) + 9.00a = 1088.70
831.30-5.10a + 9.00a = 1088.70
831.30 +3.9a = 1088.70
3.9a = 1088.70-831.30
3.9a = 257.40
a = 257.40 / 3.9 = 66
66 adult tickets were sold
EASSSSSSSSSSSSSSSSSSY
A coin is weighted so that the probability of obtaining a head in a single toss is 0.3. if the coin is tossed 35 times, what is the probability of obtaining between 9 and 14 heads, exclusive.
The probability of obtaining between 9 and 14 heads , exclusive is 0.510
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the probability of obtaining a head in a single toss be p = 0.3
Let the number of times the coin is tossed be n = 35
Now , the mean and the standard deviation is calculated by
Mean M = np
Substituting the values of n and p , we get
Mean M = 0.3 x 35
Mean M = 10.5
Now , the standard deviation S = √M ( 1- p )
Substituting the values in the equation , we get
Standard Deviation S = √10.5 ( 1 - 0.3 )
Standard Deviation S = √10.5 x 0.7
Standard Deviation S = 2.71
Now , the probability of obtaining between 9 and 14 heads , exclusive is represented as P ( 9 < x < 14 ) = P ( 8.5 < x < 14.5 )
And , the z - scores of 8.5 and 14.5 are
z ( 8.5 ) = ( x - M ) / S
= ( 8.5 - 10.5 ) / 2.71
= -0.3688
z ( 14.5 ) = ( x - M ) / S
= ( 14.5 - 10.5 ) / 2.71
= 1.1066
So , the probability of obtaining between 9 and 14 heads , exclusive is represented as P ( 9 < x < 14 ) = P ( -0.3688 < x < 1.1066 )
So , the equation can be written as
P ( 9 < x < 14 ) = P ( z < 1.1066 ) - P ( z < -0.3688 )
Using z-scores of probabilities, we have:
P ( 9 < x < 14 ) = 0.86577 - 0.3561
P ( 9 < x < 14 ) = 0.50967
P ( 9 < x < 14 ) = 0.510
Therefore , the value of P ( 9 < x < 14 ) is 0.510
Hence,
The probability of obtaining between 9 and 14 heads , exclusive is 0.510
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Suzanne works 25 hours a week for four weeks at $9.50 per hour. how much does she earn at the end of four weeks?
What are the coordinates of the point (x,y) after being translated m units left and n units up?
How do you find the x intercepts of a polynomial function with a zero constant?
To find the x-intercepts of a polynomial function, set y equal to zero and solve for x. Use the quadratic formula -b±sqrt(b²-4ac)/2a to solve, where a, b, and c are coefficients of the function.
Explanation:The 'x' intercepts of a function are the values of 'x' where 'y' equals zero. Take the given polynomial equation x² +0.0211x -0.0211 = 0; here a=1, b=0.0211 and c=-0.0211. We can solve this using the quadratic formula which states: x = -b ± sqrt(b² - 4ac) / 2a. Plugging the values in we get: x = -0.0211 ± sqrt((0.0211)² - 4(1)(-0.0211)) / (2*1). Solve this to get the x-intercepts.
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What is a reasonable percent error in chemistry?
The distance between the baseball stadium and the airport is 1.6×106 centimeters. Which unit of measurement is most appropriate to measure this distance? inches kilometers feet milimeters
The correct answer would be kilometers
Answer:
Kilometers
Step-by-step explanation:
I took the test.
Dawn Lingua bought three yards of cloth to make some curtains. The cloth was on sale for $2.25 per yard. How much did Dawn pay for the cloth if the sales tax was 5%?
Answer:
Dawn paid $7.09.
Step-by-step explanation:
Dawn Lingua bought cloth to make curtains = 3 yards
Cost of the cloth = $2.25 per yard
Cost of 3 yard cloth = $2.25 × 3 = $6.75
Sales tax was = 5%
Sales tax on the total cost = 5% of 6.75
= (5/100) × 6.75 = 0.05 × 6.75 = $0.3375
Now we add sales tax to the total cost
= 6.75 + 0.3375 = $7.0875 rounded to $7.09
Dawn paid for the cloth with sales tax was $7.09
Which should be the first step in solving the equation 1.2 w -3.8= 12.4
1. Add 3.8 to both sides of the equation.
2. Subtract 1.2 from both sides of the equation.
3. Multiply both sides of the equation by 1.2.
4. Divide both sides of the equation by 3.8.
Answer:
Option 1 - Add 3.8 to both sides of the equation.
Step-by-step explanation:
Given : Equation [tex]1.2w-3.8=12.4[/tex]
To find : Which should be the first step in solving the equation?
Solution :
Equation [tex]1.2w-3.8=12.4[/tex]
Step 1 - Adding 3.8 both side,
[tex]1.2w-3.8+3.8=12.4+3.8[/tex]
[tex]1.2w= 16.2[/tex]
Step 2 - Divide 1.2 both side,
[tex]\frac{1.2w}{1.2}=\frac{16.2}{1.2}[/tex]
[tex]w=13.5[/tex]
Therefore, The first step in solving the equation is 'Add 3.8 to both sides of the equation.'
So, Option 1 is correct.
Between which two integers does √64 lie?
In a standard deck of 52 playing cards, which king does not have a mustache?
The King of Hearts is the card without a mustache. Whether you should play a game where you draw cards for money depends on the expected value calculation. Understanding the difference between sampling with and without replacement is key in card probability problems.
Explanation:In a standard deck of 52 playing cards, the king without a mustache is the King of Hearts. Now, regarding the different scenarios involving card games with a standard deck:
When you play a game where drawing a face card wins you $30, and a non-face card makes you pay $2, you need to consider the expected value of the game. With 12 face cards and 40 non-face cards, your expected winnings would be (12/52) * $30 - (40/52) * $2, which may or may not be positive. You should calculate this to decide if you should play the game.When drawing two cards without replacement from a standard deck, the probabilities will change after the first draw since there are fewer cards remaining in the deck. You would create and use a tree diagram to calculate the precise probabilities of each combination.The probability of being dealt a bridge hand that does not contain a heart would require calculating the combinations of all possible non-heart cards from the remaining three suits.When comparing scenarios a. and b. above, scenario a represents sampling without replacement because once a card is drawn, it is not put back into the deck, whereas scenario b represents sampling with replacement as each card is put back before the next one is drawn.1. Which statement about subatomic particles is not true?
Protons and electrons have opposite charges.
Neutrons have no electrical charge.
Protons and neutrons have the same charge.
Protons and neutrons have nearly the same mass.
2.
Which term describes the sum of the number of protons and neutrons in an atom?
mass number
nuclear charge
atomic charge
atomic number
3.
Which is not part of John Dalton’s atomic theory?
All elements are composed of atoms.
Atoms are made up of smaller particles.
Atoms of different elements have different masses.
4.
All atoms of the same element have the same mass.
Dalton’s model of an atom is best described as _____.
a scoop of chocolate chip ice cream
a solar system
a cloud
a solid sphere
5.
Who provided the first evidence that atoms contain subatomic particles?
J. J. Thomson
Ernest Rutherford
John Dalton
6.
Which statement about electrons and atomic orbitals is not true?
An atom’s lowest energy level has only one orbital.
An electron has the same amount of energy in all orbitals.
An electron cloud represents all the orbitals in an atom.
An orbital can contain a maximum of two electrons.
7.
How is heavy water different from normal water?
A hydrogen atom in heavy water has an extra proton.
A hydrogen atom in heavy water has an extra neutron.
An oxygen atom in heavy water has an extra neutron.
An oxygen atom in heavy water has an extra proton.
8.
What experimental evidence did Thomson use to support his hypothesis that atoms are made up of even smaller, charged particles?
The glowing beam was always deflected by charged plates.
Identical particles were produced no matter which metal he used.
The particles all had the same mass as a hydrogen atom.
9.
Atoms may emit light energy when _____.
electrons move to a higher energy level
protons move to a higher energy level
protons move to a lower energy level
electrons move to a lower energy level
10.
Which term describes the region in which an electron is most likely to be found?
isotope
path
orbital
cloud
11.
According to Dalton, if 2 grams of element X combine with 4 grams of element Y to form compound XY, how many grams of element X would combine with 28 grams of element Y to form the same compound?
28
14
7
56
12.
An electron is a particle with a _____.
positive charge, found outside the nucleus
negative charge, found in the nucleus
positive charge, found in the nucleus
negative charge, found outside the nucleus
13.
The glow of a neon light is caused by electrons emitting energy as they _____.
move from higher to lower energy levels
collide with the nucleus
move from lower to higher energy levels
collide with other electrons
14.
To find the number of neutrons in an atom, subtract its _____.
atomic number from its mass number
mass number from its atomic number
isotope number from its atomic number
15.
Which is the best analogy describing the location of an electron in an atomic orbital?
pins on a map plotting your location every minute of a school day
the path of a bee moving from flower to flower in a garden
free-thrown basketballs bouncing on a basketball court
Answer:
12 is a negative charge outside the nucleu
Step-by-step explanation:
if x is 50 then what is x4+44+3.5
Jacob held different part-time jobs during his summer holiday. The table below shows the total money he earned for different amounts of time, in hours: Hours Worked 1 2 3 4 5 6 7 8 9 Money Earned (dollars) 4 8 12 16 20 24 28 32 36 What type of association will the scatter plot for this data represent between the number of hours worked and the total money earned?
The type of association scatter plot for this data represents the number of hours worked and the total money earned is a positive correlation.
How to find the type of association that represent the data?The number of hours and the amount of money increases at an even rate, 4 dollars for each hour.
The given table;
Hours Worked 1 2 3 4 5 6 7 8 9
Money Earned (dollars) 4 8 12 16 20 24 28 32 36
We can see here as the number of hours increases the amount of money is increasing, so it indicates that there is a positive association.
Also, there is an unequal change in equal intervals of time, so it represents a positive nonlinear association.
Hence, the graph is a line, y=4x,
The type of association scatter plot for this data represents the number of hours worked and the total money earned is a positive correlation.
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What equation allows you to calculate the force acting on an object
What is the area of the rectangle?
60 units²
66 units²
70 units²
74 units²
What is the answer to 3n-5=7n+11 with work shown
The sum of twice a number and 17 less than the number is the same as the difference between -5 and the number. What is the number?
Find the average rate of change for the given function from x = −1 to x = 2.
Graph of f of x equals negative three x plus 2
Answer:
Average rate of change: [tex]-3[/tex]
Step-by-step explanation:
We are asked to find average rate of change for our given function [tex]f(x)=-3x+2[/tex].
We will use average rate of change formula to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\text{Average rate of change}=\frac{f(2)-f(-1)}{2-(-1)}[/tex]
[tex]\text{Average rate of change}=\frac{(-3(2)+2)-(-3(-1)+2)}{2-(-1)}[/tex]
[tex]\text{Average rate of change}=\frac{(-6+2)-(3+2)}{2+1}[/tex]
[tex]\text{Average rate of change}=\frac{(-4)-(5)}{3}[/tex]
[tex]\text{Average rate of change}=\frac{-4-5}{3}[/tex]
[tex]\text{Average rate of change}=\frac{-9}{3}[/tex]
[tex]\text{Average rate of change}=-3[/tex]
Therefore, the average rate of change for our given function from [tex]x=-1[/tex] to [tex]x=2[/tex] is [tex]-3[/tex].
What is the first step in solving a quadratic equation of the form given below? (ax + b)2 = c
Answer:
The answer on apex is: Take the Square Root of both sides.
Step-by-step explanation:
Find the inverse function for
\(\large\bf{f(x)= \sqrt{2x-6}}\)
I found that it was
\(\large\bf{\color{Red}{y=\frac{1}{2}x^{2} + 3}}\)
but I am to restrict the function would it be \(\bf{x \ge 0}\)?
How to order decimals from least to greatest with different decimals places?
What is the answer to the question above? I need help with it.
Simplify: √5 x √12 x √50
a: 10√10
b: 7√30
c:10√30
d: 7√10
According to bmi, a woman who is 5 feet 6 inches tall and weighs 175 pounds is considered to be
A woman who is 5 feet 6 inches tall and weighs 175 pounds has a BMI of 28.2 and would be classified as overweight.
The Body Mass Index (BMI) is a tool commonly used to assess whether a person has a healthy weight relative to their height. To calculate BMI, you divide a person's weight in pounds by their height in inches squared and multiply by 703.
For a woman who is 5 feet 6 inches tall and weighs 175 pounds:
Height: 66 inchesWeight: 175 poundsThe calculation for BMI would be:
BMI = (175 / (66×66)) × 703
BMI = 28.2
According to the BMI weight status categories:
BMI between 25 and 29.9 is considered overweight, and a BMI of 30 or higher is considered obese.
Therefore, a woman who is 5 feet 6 inches tall and weighs 175 pounds would be classified as overweight.
Two angles of an isosceles triangle measure 70° and x°. What is the sum of three possible values of x? A. 95 B. 125 C. 140 D. 165 E. 180
The sum of three possible values of x° in the isosceles triangle is 180°. The angles are 40°, 70°, and 70°. The correct answer is E. 180.
In an isosceles triangle, two angles are congruent (equal). So, if one angle is 70°, the other angle must also be 70°.
Let's denote the third angle as y°.
Since the sum of the angles in any triangle is 180°, we can write the equation:
70° + 70° + y° = 180°
Solving for y:
2 × 70° + y° = 180°
y° = 180° - 140°
y° = 40°
So, the three possible values of x° are 40°, 70°, and 70°.
Now, let's find the sum of these three possible values:
Sum = 40° + 70° + 70°
Sum = 180°
Therefore, the sum of three possible values of x° is 180°. The correct answer is E. 180.
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When converting from binary to hexadecimal, 4 binary digits is equivalent to _____ hexadecimal digit(s)?
Final answer:
In conversions from binary to hexadecimal, 4 binary digits are equivalent to 1 hexadecimal digit due to the fact that the base-16 system of hexadecimal can represent any combination of 4 binary digits (base-2 system).
Explanation:
When converting from binary to hexadecimal, 4 binary digits are equivalent to 1 hexadecimal digit. This is because binary is a base-2 system and hexadecimal is a base-16 system. Each hexadecimal digit can represent 4 binary digits since 24 = 16. Here's a quick conversion table for single binary digits to hexadecimal:
0000 = 0
0001 = 1
0010 = 2
0011 = 3
0100 = 4
0101 = 5
0110 = 6
0111 = 7
1000 = 8
1001 = 9
1010 = A
1011 = B
1100 = C
1101 = D
1110 = E
1111 = F
Therefore, when performing this conversion, group the binary numbers into sets of 4 digits from right to left and then convert each group to the corresponding hexadecimal digit.
What is the length of leg s of the triangle below
Answer: The correct option is (B) 3.
Step-by-step explanation: We are given to find the length of the leg s in the triangle shown in the figure.
From the figure, we note that
the given triangle is a right-angled one, where
length of the hypotenuse, H = √18 units,
length of one leg, P = 3 units
and
length of the other leg, s = B =?.
From Pythagoras theorem, we have
[tex]H^2=P^2+B^2\\\\\Rightarrow (\sqrt{18})^2=3^2+B^2\\\\\Rightarrow 18=9+B^2\\\\\Rightarrow B^2=18-9\\\\\Rightarrow B^2=9\\\\\Rightarrow B=3.[/tex]
Thus, the length of the leg s is 3 units.
Option (B) is CORRECT.
Find the measure of z.