No, the difference between the sample result and what we expected is not extreme enough. The probability of it occurring by chance alone is not unlikely (0.3664 > 0.05).
The correct option is A.
What is a distribution?The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.
Given:
According to a recent national poll, 22% of US adults get an average of 7 or more hours of sleep per night.
Let x = Number of US adult get an average of 7 or more hours of sleep per night.
Assume this is the parameter value for the population.
That means,
Proportion of number of US adults get an average of 7 or more hours of sleep per night in population = p =0.22
Suppose you select a random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night.
1) The shape of this sampling distribution is approximately normal.
2) Let a = Number of US adults get an average of 7 or more hours of sleep per night in sample = 10
Sample size n = 50.
So, [tex]\hat {p}[/tex] = 10/50
[tex]\hat {p}[/tex] = 0.2
Option a) is correct.
3) σ[tex]_{\hat p}[/tex] = √(pq)/n
= √(0.22)(1 -0.22)/50
= 0.0586
The difference between the sample result and what we expected is not extreme enough.
Therefore, the probability of it occurring by chance alone is not unlikely (0.3664 > 0.05).
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You start at (-3, 2). You move left 1 unit and right 6 units. Where do you end?
13 quarts of soil are used to completely fill 4 flower pots. If each pot holds the same amount of soil, how many quarts will each pot hold? Solve on paper and check your w
The number of quarts of soil in each pot will be 3.25 quarts.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
13 quarts of soil are used to completely fill 4 flower pots. If each pot holds the same amount of soil.
Then the number of quarts of soil in each pot will be given as,
⇒ 13 ÷ 4
⇒ 13 / 4
⇒ 3.25
The number of quarts of soil in each pot will be 3.25 quarts.
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Jill is studying a strange bacterium. When she first
looks at the bacteria, there are 1000 cells in her
sample. The next day, there are 2000 cells. Intrigued,
she comes back the next day to find that there are
4000 cells!
Create a table and a graph for this situation. The
inputs (x) are the days that have passed after she
first began to study the sample, and the outputs (y)
are the number of bacteria cells.
We have prepared the table and drawn the graph.
What is a graph of a function?
A graph of a function is a visual representation of the relationship between the inputs (x-coordinates) and the outputs (y-coordinates) of a function. The inputs are typically represented on the x-axis and the outputs are represented on the y-axis.
Table:
x (days) y (number of cells)
0 1000
1 2000
2 4000
Graph:
The graph would be a line graph with x-axis showing the day passed and y-axis showing the number of bacteria cells,
The point (0,1000) would be plotted on the graph, representing the initial number of bacteria cells on the first day.
The point (1,2000) would be plotted on the graph, representing the second day and the number of bacteria cells.
The point (2,4000) would be plotted on the graph, representing the third day and the number of bacteria cells.
The graph would be a upward sloping line, representing the growth of bacteria cells.
Hence we have prepared the table and drawn the graph.
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What is the perform indicated operation for 1/3 × 6/7
The indicated operation 1/3 x 6/7 can be performed as 2/7.
What is multiplication operation?The concept that will be used in this operation is the multiplication operation.
One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream. By multiplying their outputs, you can multiply one function by another.
Given operation is 1/3 x 6/7
1/3 x 6/7
=[ (1 x 6)/(3 x 7) ]
= (6/21)
= 2/7
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check the correct question:
Perform the indicated operation. 1/3 x 6/7
Which exponential function models the situation?
A function has an initial amount of 22 and a rate of increase of 9%.
g(t) = 22(1.09)t
g(t) = 0.09(22)t
g(t) = 1.09(22)t
g(t) = 22(0.09)t
Answer:
g(t) = 22(1.09)t
Step-by-step explanation:
formula is y = a(1 + r)t
staticbigideasmathcom
Solve the quadratic equation graphically using at least two different approaches. When necessary, give your solutions to
the nearest hundredth.
16x²-400-0
The value of x = ±5.
What is Quadratic Equation?
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x).
Method 1 :
⇒ 16x² - 400 = 0
⇒ 16x² = 400
⇒ x² = 400/16
⇒ x² = 25
⇒ x = ±5
Method 2 :
⇒ 16x² - 400 = 0
⇒ 16(x² - 25) = 0
⇒ x² - 25 = 0
⇒ x² = 25
⇒ x = ±5
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Translate the sentence into an equation.
Two more than the quotient of a number and 4 is 8.
Use the variable b for the unknown number.
The Equations is b/4 + 2= 8 and b = 24.
What is expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.
Mathematical statements called expressions must contain at least two phrases including numbers, variables, or both, and they must be joined by an operator.
Given Two more than the quotient of a number and 4 is 8,
Let number be b
b/4 + 2= 8
b/4 = 8 -2
b/4 = 6
b = 24
Hence, two more than the quotient of a number is 24.
Hence the equation for phrase is b/4 + 2= 8 and b = 24.
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48.
1. (2 x+1)⁰+67
2x+68
The measure of the value of x in the expression for the angle (2·x + 1)°, obtained using vertical angles theorem is; x = 33°
What are vertical angles?Vertical angles are angles formed when two lines intersect. Vertical angles are the angles vertically opposite each other, formed by the intersection of the two lines.
Vertical angles theorem states that the vertical angles formed by the intersection of two straight lines are congruent.
The angles (2·x + 1)° and 67° are vertical angles. therefore;
(2·x + 1)° ≅ 67° (Vertical angles theorem)
(2·x + 1)° = 67°, by the definition of congruency
(2·x)° = 67° - 1° = 66°
x = 66° ÷ 2 = 33°
The measure of x is 33°Therefore, plugging in the value of x = 33°, in the expression; (2·x + 1)° + 67°, we get;
(2·x + 1)° + 67° = (2 ×33 + 1)° + 67°
(2 ×33 + 1)° + 67° = 67° + 67° = 134°
The measure of the sum of the angles, (2 ×33 + 1)° and 67° is 134°
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What ratio is equivalent to 8/6
Answer:
3rd option: 32/24
Step-by-step explanation:
8/6 = 4/3
1st option: Now let's change the denominator to 24:
4/3 ==> ?/24
4/3 =
4*8 / 3*8 = 32/24, not 3/24.
2nd option: Now let's change the numerator to 24:
4/3 ==> 24/?
4/3 =
4*6 / 3*6 = 24/18, not 24/32
24/32 = 3/4, not 4/3 ==> don't get confused by this
3rd option: 32/24 is correct [Look at the explanation for 1st option]
4/3 ==> ?/24
4/3 =
4*8 / 3*8 = 32/24, not 3/24.
Hence, the 3rd option is correct.
simplify 125 xy^3/5x^3y^3 simplify
Answer:
[tex]\frac{25}{3x^{2} }[/tex]
Step-by-step explanation:
[tex]\frac{125xy^{3} }{5x^{3}3y^{3} }[/tex] = [tex]\frac{25}{3x^{2} }[/tex]
125/5 = 15
[tex]\frac{xyyy}{xxxyyy}[/tex] We can cancel out one x in the numerator and the denominator. That leaves [tex]x^{2}[/tex] in the denominator.
We can cancel out the 3 y's in the numerator and the denominator and that leaves no y's
resolve the equation:
6*(9^3x)-13*(6^3x)+6*(4^3x)=0
The solution to the equation 9(6^3x) - 13(6^3x) + 4(6^3x) = 0 is x = 0.
What is the equation?Generally, To solve the equation we try to get the values to be coherent by writing as
9(6^3x)-13*(6^3x)+4*(6^3x)=0
Therefore we solve the coefficients of the solution
To solve this equation, we can first distribute the constants in front of the parentheses:
9(6^3x) - 13(6^3x) + 4(6^3x) = 0
This simplifies to:
(9 - 13 + 4)(6^3x) = 0
Then, we can simplify the expression in the parentheses:
(0)(6^3x) = 0
This means that either (0) = 0 or (6^3x) = 0.
The second case is not possible, because the base of an exponent can't be zero. So, the only solution to this equation is x = 0.
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IF each term in the sum a1+a2+a3..._an . . . an is either 7 or 77 and the sum equals 350, which of the following could be equal to n ?
A. 38
B. 39
C. 40
D. 41
E. 42
If each term in the sum a1+a2+a3...+an is 7 and the sum equals 350, C: 40 would be equal to n.
In equation form, it is:
7s + 77t = 350
In this equation,
s represents the number of 7's
t represents the number of 77's
thus, the number of terms i.e n = s + t =?
now solving the equation,
7 (s + 11t) = 350
7 (s + 11t) = 350
s + 11t = 50
s + 11t = 50
now, if
s=39 & t =1
then
s + 11t = 50 -> 39 + 11 (1) = 50
Since the number of terms n = s + t
n = s + t
n = 39 + 1
n = 40
Hence, the if each term in the given sum is 7 which gives a total sum as 350, then number of terms in the given series is 40.
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What would the surface area of this shape be?
What value in the replacement set is a solution to this equation? 3(n+7)=48 Replacement set: {8, 9, 10} Drag the solution into the box. Put responses in the correct input to answer the question.
In the replacement set, 9 is the solution to this equation 3 (n+7) = 48.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 3 (n + 7) = 48
And, Replacement set: {8, 9, 10}
Now, We can solve the expression as;
⇒ 3 (n + 7) = 48
Divide by 3,
⇒ n + 7 = 48/3
⇒ n + 7 = 16
Subtract 7, we get;
⇒ n = 16 - 7
⇒ n = 9
Thus, The solution of the equation is, 9.
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Find the sum.
1. 1/3+1/5=
2. 1/8+2/6=
3. 8/9+11/12=
4. 1/7+5/8=
5. 1/4+2/4=
6. 1/2+3/9=
7. 1/10+1/4=
8. $3/11+11/12=
a. The sum of 1/3+1/5= 8/15
b. The sum of 1/8+2/6 = 3/8
c. the sum of 8/9+11/12= 1 87/108
d. the sum of 1/7+5/8= 1 7/36
e. the sum of 1/4+2/4= 3/4
f. the sum of 1/2+3/9= 5/6
g. the sum of 1/10+1/4= 7/20
h. the sum of 3/11+11/12 = 1 25/132
What is sum of fractions?Sum of fractions is the addition of fractions. This is obtained by by using the L.C.M of the denominator method.
a. 1/3 + 1/5 = (5+3)/15 = 8/15
b. 1/8+2/6 = (3+6)/24 = 9/24 = 3/8
c. 8/9 + 11/12 = (96+99)/108 = 195/108 = 1 87/108
d. 1/7+ 5/8 = (8+35)/56 = 43/36 = 1 7/36
e. 1/4+ 2/4 = (2+1)/4 = 3/4
f. 1/2 + 3/9 = (9+6)/18 = 15/18 = 5/6
g. 1/10+1/4 = (2+5)/20 = 7/20
h. 3/11+ 11/12 = (36+121)/132 = 157/132 = 1 25/132
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Which ordered pair(s) are solutions to the system of inequalities?
2х + 3у > 2
3x + 5y > 1
(1,1)
(-2,-1)
(-2,3)
(7,-4)
the solutions to the system of inequalities are (1,1) and (-2,3).
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
2х + 3у > 2
3x + 5y > 1
for (1,1):
2+3 > 2 (true)
3+5 > 1 (true)
for (-2,-1)
-4-3 > 2 (false)
for (-2,3):
-4+9 >2 (true)
-6+15>1 (true)
for (7,-4):
14-12>2(false)
Hence, the solutions to the system of inequalities are (1,1) and (-2,3).
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help PLEASE!!!!!
i need to pass math
Answer:
Step-by-step explanation:
pass it then
when solving a system of equations, which of the following is a possible outcome? select all that apply. please help i will mark you brainliest.
When solving a system of two equations there are three possible outcomes for the solution of a system of three variables and two solutions for two variables.we can say that system of equation have infinite solutions.
What are the ways to solve system of equations?There are three methods used to solve systems of equations graphing, substitution, and elimination. To solve a system by graphing you simply graph the given equations and find the point(s) where they all intersect.Solve the linear equation for the remaining variable.
How do you find the solution to a system of equations?To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.
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Which choice is equivalent to the quotient below?
√32
OA.
√2
B. 4
C. 2
D. 24
SUBM
Answer:
C (2)
Step-by-step explanation:
• √32 = 4√2 ( bc √32 = √16×2 = √16×√2 = 4×√2 )
• √8 = 2√2 ( bc √8 = √4×2 = √4×√2 = 2×√2 )
So √32 ÷ √8 is equal to 4√2 ÷ 2√2
And there √2 cancels for both
So what you're left with is 4 ÷ 2
And 4÷2 = 2
We are looking at rectangles where one side is of length 5.0 cm. Amongst those are some that can be cut into a square and a rectangle one of which has an area of 4,0 cm². How many such rectangles are there?
A: 1
B: 2
C: 3
D: 4
E: 5
Spoiler: According to the answer key it is D but I could only find 3 variations.
the answer is D : 4
How to calculate how many of these rectangles are there?According to the problem statement, one side of the rectangle is of length 5 cm. The other side can have any length greater than 4 cm (since the area of the rectangle should be greater than 4 cm^2).
Let's call this other side "x".
We know that the area of a rectangle is given by the formula A = l*w, where l is the length and w is the width.
Therefore, we can write the equation: 5*x = A, where A is the area of the rectangle.
We can also say that the area of the square and the rectangle is equal to 4 cm^2.
If we call the side of the square "y", then we can write the equation: y^2 = 4 cm^2.
Solving for y, we get: y = 2 cm.
Therefore, the length of the rectangle that can be cut into a square and a rectangle of area 4 cm^2 is 5 cm - y = 5 cm - 2 cm = 3 cm.
So, there are 4 possible rectangles that can be cut into a square and a rectangle of area 4 cm^2: (5,3), (3,5), (6,4), and (4,6).
So the answer is D : 4
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14. What is the equation of a circle with a center at (4,−9) and a radius of 5?
A) (x+4)^2+(y−9)^2=5
B) (x+4)^2+(y−9)^2=25
C) (x−4)^2+(y+9)^2=25
The equation of a circle with a center at (4,−9) and a radius of 5 is
(x−4)^2+(y+9)^2=25. The correct Option C.
How to find equation of a circle?A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.
The equation of a circle with center (h, k) and radius r units is
(x−h)^2+(y−k)^2=r^2 .
where h = 4
k = -9
r = 5
The equation of the circle
(x−4)^2+(y−(-9))^2 = 5^2
The equation of the circle
(x−4)^2+(y+9)^2 = 25
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What is the factorization of the trinomial below?
12x2 - x-35
O A. (6x-7)(x+ 5)
O B. (4x + 7)(3x-5)
O C. (4x- 7)(3x+ 5)
O D. (6x + 7)(x- 5)
(4x + 7)(3x-5) are the factors of trinomial 12x²-x-35
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 given trinomial is 12x²-x-35
Break the expression into groups
(12x²+20x)+(-21x-35)
12x²+20x-21x-35=0
Now take the gcf of first two terms
4x(3x+5)-7(3x+5)=0
(4x-7)(3x+5)=0
Hence, (4x + 7)(3x-5) are the factors of trinomial 12x²-x-35
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Henry ran 1 5_8 miles in the morning and 9_10 miles in the afternoon. About how many miles did he run in all?
When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles
How to find the number of miles that Henry ranThe number of miles Henry ran is calculated by addition operation
The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all
The procedure involves addition of tractions and done as follows
= 1 5/8 + 9/10
= 13/8 + 9/10
adding both fractions will result to
= 101/40 miles
= 2 21/40 miles (as a mixed number)
Henry ran a sum of 2 21/40 miles
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On Monday Paolo so 21 tickets to the dance on Tuesday he sold three times as many tickets as he sold on Monday on Wednesday he's so twice as many tickets as he sold on Tuesday how many total tickets did Paulo sell in the three days
Using the given conditions and the value provided to us, The answer is Paolo sold 210 tickets in 3 days.
What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.
What are word problems in mathematics?Word problems in mathematics are problems that are presented in a narrative format, rather than as a mathematical equation. They often describe a real-world situation, such as a person buying items at a store, and ask the student to use mathematical concepts to solve the problem. This can include concepts such as addition, subtraction, multiplication, division, fractions, and percentages. Word problems can be challenging for students because they require not only mathematical knowledge, but also the ability to understand and interpret the problem, and to translate the information given into mathematical equations.
On Tuesday, Paolo sold 3 * 21 = 63 tickets.
On Wednesday, he sold 2 * 63 = 126 tickets.
So in total, Paolo sold 21 + 63 + 126 = 210 tickets.
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Answer: Using the given conditions and the value provided to us, The answer is Paolo sold 210 tickets in 3 days.What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.What are word problems in mathematics?Word problems in mathematics are problems that are presented in a narrative format, rather than as a mathematical equation. They often describe a real-world situation, such as a person buying items at a store, and ask the student to use mathematical concepts to solve the problem. This can include concepts such as addition, subtraction, multiplication, division, fractions, and percentages. Word problems can be challenging for students because they require not only mathematical knowledge, but also the ability to understand and interpret the problem, and to translate the information given into mathematical equations.On Tuesday, Paolo sold 3 * 21 = 63 tickets.On Wednesday, he sold 2 * 63 = 126 tickets.So in total, Paolo sold 21 + 63 + 126 = 210 tickets.
Step-by-step explanation:
The circumference of a circle is 9pi cm. What is the area, in square centimeters? Express answer in terms of pi.
==============================================
Work Shown:
C = 2pi*r
9pi = 2pi*r
r = (9pi)/(2pi)
r = 4.5
A = pi*r^2
A = pi*(4.5)^2
A = 20.25pi square cm
------------------
Explanation:
The first portion involves using the circumference C = 9pi to determine the radius r. The circumference is the perimeter around the circle.
Once we know that r = 4.5 cm, we then plug that into the area of a circle formula A = pi*r^2
Side notes:
4.5 = 9/220.25 = 81/4pls help this is confusing and i dont get it at all......
Completing the table with the appropriate percentage and decimals will be:
Fraction Decimal Percentage
1/4. 0.25. 25% of 1
1/10. 0.1. 10% of 1
3/4. 0.75. 75% of 1
1/5. 0.2. 20% of 1
3/2. 1.5. 150% of 1
7/5. 1.4. 140% of 1
How to calculate the percentage be decimal?It should be noted that based on the information, 0.1 will be 1/10. The percentage will be:
= 1/10 × 100
= 10%
0.1 to fraction will be:
= 1/10
The percentage for 1/5 will be:
= 1/5 × 100
= 20%
1/5 to decimal will be:
= 1/5
= 0.2
The decimal 1.5 will give 150%
The fraction for 1.5 will be:
= 1.5 / 1
= 15 / 10
= 3/2
Also 3/4 as percentage will be:
= 3/4 × 100
= 75%
75% to decimal will be:
= 75 / 100
= 0.75
140% to fraction will be:
= 140 / 100
= 7 / 5.
The decimal for 140% will be:
= 140 / 100
= 1.4
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The relationship between pressure (P),
volume (V), and temperature (T) for
an ideal gas is stated by the Ideal Gas
Law: PV = nRT, where n is the number
of moles and R is the universal gas
constant. If n is kept constant, which of
these statements is not true according to
the equation?
A Decreased volume at constant
pressure reduces temperature.
B Decreased volume at constant
temperature increases pressure.
C Decreased temperature at constant
volume reduces pressure.
D Decreased temperature at constant
volume increases pressure.
Answer:
A
Step-by-step explanation:
For an ideal gas : PV=RT
And the internal energy of an ideal gas:
E
in
=
2
3
RT
E
in
=
2
3
PV
V
E
in
=
2
3
P
Energy density (E)=
2
3
P
P=2/3E
Need help doing this math problem the one that says AE is the one I need to do.
Check the picture below.
need the answer asap!!!
The length in centimeters of AB is 125/360 x 42cm.
What is the circumference of the circle?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
Here, we have
Given: The circumference of the circle is 42 centimeters
AB is an arc, the formula for calculating the length of an arc is given as
L = Ф/360 X 2πr
where Ф is the angle subtended by the arc, and 2πr is the circumference of the circle.
Substituting the given values into the formula, we have
L = 125/360 x 42
L = 14.5
Hence, the length in centimeters of AB is 125/360 x 42cm.
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Find the value of X. (please no spamming and do both problems) I'll make brainliest.
Answer:
13. x=4
14. x=8
Step-by-step explanation:
We know that these are both isosceles triangle because the two base angles are the same on #13, and the two sides are the congruent on #14. So all we need to do is make equations of equivalence. So #13 9x-8=28 and #14 11x-18=70. Look at the work shown in the image and follow those steps.
-Hope this helped & Happy New Year!
