Answer:
a) The 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report is (0.3798,0.4602). This means that we are 99% sure that the true population proportion is in this interval.
b) No, since May is a month with a wide range of possible weather.
Step-by-step explanation:
a)
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong.
This means that [tex]p = 0.42, n = 1001[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{1001}} = 0.3798[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{1001}} = 0.4602[/tex]
The 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report is (0.3798,0.4602). This means that we are 99% sure that the true population proportion is in this interval.
b. Do you think it is reasonable to generalize this estimate to other months of the year
No, since May is a month with a vast number of possible outcomes, as it is in the spring, not being in the winter(cold) or summer(hot), which means that it can be both hot or cold, wet or dry,...
B(2, 1) and C(–8, –4) are the endpoints of a line segment. What is the midpoint M of that line segment?
Write the coordinates as decimals or integers.
You don't need to give me steps if you don't want to, I'm fine with that
Point M has the coordinates (-3, -1.5) which are written as decimals.
What is the midpoint of the line segment?
The midpoint of a line segment is the point that is exactly in the middle of the line segment. It is the point that divides the line segment into two equal parts.
To find the midpoint of a line segment, you can use the formula:
Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
Where x1, y1 and x2, y2 are the coordinates of the two endpoints of the line segment.
In this case, the endpoints of the line segment are B(2, 1) and C(–8, –4).
So we can substitute the coordinates of B and C in the midpoint formula:
Midpoint = ( (2 + -8) / 2 , (1 + -4) / 2 )
Midpoint = ( -3 , -1.5)
The midpoint of the line segment is (-3, -1.5).
Hence, point M has the coordinates (-3, -1.5) which are written as decimals.
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Which expression is equivalent to
The equivalent expression to 4y²(6x³ + 4xy + 3y) is 24x³y² + 16xy³ + 12y³
Equivalent expressions:A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.
In general, something is considered equal if two of them are the same. Similar to this, similar expressions in mathematics are those that hold true even when they appear to be different.
However, both forms provide the same outcome when the values are entered into the equation.
Here we have
4y²(6x³ + 4xy + 3y)
Simplify the given expression as follows
=> 24x³y² + 16xy³ + 12y³
Therefore,
The equivalent expression to 4y²(6x³ + 4xy + 3y) is 24x³y² + 16xy³ + 12y³
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5x-y=54 x=10 what is the answer
Answer:
Y = 4
Step-by-step explanation:
5x-y=54
50-y=54
circle y and subtract 50 from itself then subtract 50 from 54.
after subtracting you should have y=4
What are the solutions to sin theta=-sqrt3/2, where 0 ≤ 0≤ 2n?
The solutions to sin(θ) = -√3/2 in the interval 0 ≤ θ ≤ 2π are approximately θ = 5π/3 and θ = 4π/3.
What is an interval?
An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers. This range includes all the real numbers between those two numbers.
The equation sin(θ) = -√3/2 has two solutions in the interval 0 ≤ θ ≤ 2π.
Since the sine function has a range [-1, 1], the value of -√3/2 lies in the range of the sine function, so there are solutions in the specified interval.
Using the unit circle, we can find the values of θ that satisfy the equation. In the unit circle, the sine of an angle is equal to the y-coordinate of the point on the circle that corresponds to that angle.
The point (-√3/2, -1/2) lies on the unit circle and has an angle θ that satisfies the equation.
The other solution can be found by adding π to θ, since the sine function has a period 2π.
Hence, the solutions to sin(θ) = -√3/2 in the interval 0 ≤ θ ≤ 2π are approximately θ = 5π/3 and θ = 4π/3.
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A retailer has some sweaters that cost her$38 each she wants to make a profit of 20% of her cost. What price should she charge for each sweater
The retailer's selling price per sweater should be $45.60 if she wants to make a profit of 20% of her cost price (markup) of $38.
How is the selling price determined?The selling price is the marked-up cost.
The markup is the percentage added to the cost price to achieve a target profit percentage.
Cost price per unit = $38
Target profit = 20%
Selling price = $45.60 ($38 x 1.2)
Thus, for the retailer to make a profit of 20% of her cost, she must sell each sweater for $45.60.
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Please help 31 +5/9y =
y=-6x-7 7x+y=-3 substitution
By substitution; x = 4 and y = -31
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity.
y=-6x-7 --- 1
7x+y=-3 --- 2
Substituting y as 6x - 7 in equation 2
7x + (-6x - 7) = -3
7x - 6x - 7 = -3
x - 7 = -3
x = -3 + 7
x = 4
Substitute x as 4 in equation 1
y = -6x - 7
y = -6(4) - 7
y = -24 - 7
y = -31
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Write the equation of the line shown.
Answer:
y = 3x
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
The slope = rise/run
Let's pick 2 points (0,0) (2,6), we see that the y increase by 6 and the x increase by 2, so our slope is
m = 6/2 = 3
Y-intercept is when the x = 0, we see that the y-intercept is located at (0,0)
So, our equation is
y = 3x
please help asap !! due at 11
Answer:
x=6x okay that should help
Please state which property allows each of the statements to be true. A list of properties
has been given to you. Please use those letters to fill in the blanks.
1.
2.
3.
4.
5.
6829)
6.
7.
8.
9.
If 9x - 2 = 21, then 9x = 23.
If 3(x + 5) = 24, then 3x + 15 = 24.
If 3x + 15 = 24, then 3x = 9.
If 3x = 9, then x = 3.
If a = 7, then 7 = a.
If x/2 = 3, then x = 6.
If 2x + y = 3 and x = 9, then 2(9) + y = 3.
X = X.
If a = b and b = 2, then a = 2.
A.
B.
Addition Property of Equality
Subtraction Property of Equalit
Multiplication Property of Equa
Division Property of Equality
Reflexive Property of Equality
Symmetric Property of Equalit
Transitive Property of Equality
H. Substitution Property of Equa
Distributive Property
F.
G.
1.
C.
D.
E.
Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root qualities are the main nine properties of equality.
What is the properties of equality?The nine basic characteristics of equality are addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root. Real number-based algebraic problems can be resolved with the aid of the addition, subtraction, multiplication, and division properties of equality.
When you add the same amount to both sides of an equation that has two equal expressions, the equation will stay equal. Finding the value of the variable that makes an equation true is the process of solving an equation.
The Subtraction Property of Equality asserts that when an equal value is subtracted from or removed from two equal objects, a new equal quantity is created. A mathematical statement with two equivalent sides is denoted by an equal sign. The formula for the subtraction property is if a = b, then a - c = b - c.
According to the equality's multiplication property, an equation's two sides stay equal when multiplied by the same amount.
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Help bc it’s due in a couple hours and im nowhere near done
Answer: -9 1/4
Step-by-step explanation:
Mr. Sehmi is making an array to display 9 pictures. For each pair of different factors, there are two arrays he can make. How many different arrays can Mr.Sehmi make? Is the number of arrays odd or even ? Explain.
Hi Bixby can you help me with this Mr. CV is making an area to display 9 pictures for for each pair of different functions there are 2 Irish he can we how many different areas can Mr. Semi make is in the number of a rice old number odd or even
Denise has $10 and wants to buy pens that cost
$0.80 each. How many pens can Denise buy and
have at least $6 left?
Answer:
5 pens
Step-by-step explanation:
$10 - 6$ = $4
$4/$0.80
she can afford 5 pens
Write your answer in simplest form.
-\dfrac{3}{2} \div \dfrac{7}{4} = {?}−
2
3
÷
4
7
=?\
The solution of the equation - (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7) will be 13 / 42.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given as,
- (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7)
Simplify the equation, then we have
- (3/2) x (4/7) = x - (2/3) x (7/4)
- 6/7 = x - 7 / 6
x = 7/6 - 6/7
x = (49 - 36)/42
x = 13 / 42
The solution of the equation - (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7) will be 13 / 42.
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You answer 21 out of 25 questions correctly on a test. Did you reach your goal of getting 80% or better? Explain your reasoning.
Answer: yes, you did
Step-by-step explanation:
21 divided by 25 is 0.84
the you times 0.84 with 100 and you would get 84%
i-Ready
Divide by Two-Digit Numbers, Part 2- Quiz - Level E
→Yumi has 6,720 coins to plant apple trees in her village. It costs 21 coins to plant an
apple tree. Find how many apple trees Yumi can plant if she uses all her coins.
Which division equation represents the problem?
21 ÷ 6,720 = ?
21 ? = 6,720
6,72021?
? 216,720
The answer is 21/6720
8 to the power of X over 2 divided by 4 to the power of X over 3 = 2 to the power of -5 over 2
The value of x = -3 in the given quadratic equation.
What is quadratic equation?In mathematics, a quadratic equation is defined as an equation of degree 2, which means that the highest exponent of this function is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are numbers and a cannot be 0.
Quadratic equations are unique in that they can have up to two real solutions. Solutions are found where the quadratic equals 0. Real solutions are those that are not fictitious and have real numbers.
8 to the power of X over 2 divided by 4 to the power of X over 3 = 2 to the power of -5 over 2.
In equation it will be written as
[tex]$ 8^{x/2} \div 4^{x/3} = 2^{-5/2}[/tex]
[tex]$ (2^3)^{x/2} \div (2^2)^{x/3} = 2^{-5/2}[/tex]
[tex]$ (2)^{3x/2} \div (2)^{2x/3} = 2^{-5/2}[/tex]
[tex]$ (2)^{\frac{ 3x}{2} -\frac{ 2x}{3} } = 2^{-5/2}[/tex]
[tex]$ (2)^{\frac{ 5x}{6} } = 2^{-5/2}[/tex]
By solving this
x = -3
Thus, the value of x = -3 in the given quadratic equation.
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A different customer wants Ellie to spread fertiliser on a lawn.
A shop sells these bags of fertiliser.
Lawn fertiliser 750 grams £2.95
Ellie uses 40 grams of fertiliser for every square metre of lawn.
The area of the lawn is 145 square metres.
She needs to buy enough bags for the whole lawn.
Work out the total cost of the fertiliser Ellie needs.
Ellie needs 5050 grams extra fertilizer and total cost of fertilizer = 22.81-pound sterling.
what is multiplication and division?Multiplication is the product of two or more numerical terms. Division is the process of dividing any numbers into equal parts.
What is the total cost of fertilizer that Ellie needs?
Cost of 750 grams fertilizer = 2.95-pound sterling,
the area of the lawn = 145 square meters.
Ellie uses 40 grams fertilizer for every square meter of lawn.
So, fertilizer needed for the 145 square meters of land = (145 × 40)
= 5800 grams
it stated earlier that 750-gram fertilizer was bought but Ellie needs 5800 grams fertilizer.
the extra amount of fertilizer that Ellie needs = (5800 - 750) = 5050 grams.
cost of 750 gram fertilizer = 2.95-pound sterling
cost of 5050-gram fertilizer = (2.95 × 5050) / 750 = 19.86-pound sterling
cost of extra fertilizer = 19.86-pound sterling.
Total cost of fertilizer = (2.95 + 19.86) pound sterling
= 22.81-pound sterling
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Graph the function.
y=−2/3x+2
The graph of y = -(2/3)x + 2 is shown, having a slope of -2/3 and y intercept of 2
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
The equation y = -(2/3)x + 2 have a negative slope of -2/3 and y intercept of 2
The graph of y = -(2/3)x + 2 is shown
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Polygon ABCD with
A (0, 4), B (-4, 8), C (3, 3), and D (4, -2), is dilated by a scale factor of ½. Find A’B’.
Explain please!!!
The length of A'B' after undergoing the dilation is; A'B' = 2√2
How to interpret scale of dilation?The scale factor in the dilation of an object tells us how much larger or smaller the image will be when compared to the original object. Thus, the coordinates will be multiplied by the scale of dilation to get the new coordinates.
We are given the coordinates of Polygon ABCD as A(0, 4), B(-4, 8), C(3, 3), and D(4, -2). With a scale of dilation of ½, we will have the new coordinates as;
A'(0, 2), B'(-2, 4), C'(1.5, 1.5), and D'(2, -1)
The formula to find the distance between two coordinates is;
Distance = √[(y₂ - y₁)² + (x₂- x₁)²]
Thus;
A'B' = √[(4 - 2)² + (-2 - 0)²]
A'B' = √8
A'B' = 2√2
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Alicia bought 4 sandwiches and 5 cups of soup, spending $38.50. Adam spent $47.25 to buy 3 sandwiches and 9 cups of soup. Write and solve a system of
equations to find out the cost of each sandwich, 8, and each cup of soup, C.
On solving the provided question, we can say that the equation that can be formed are 4x+5y=38.50 and 3x+9y=47.25
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation that can be formed are
Sandwiches are $5.25 Bowls are $3.50
4x+5y=38.50
3x+9y=47.25
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What is (6 − 2) ÷ 1/4 = ???
Answer: your answer is 16!
Step-by-step explanation:
Factor
2x2 + 7x + 5.
The solution to the quadratic equation are x = 1 and -5/2
How to determine the valueWe have the quadratic function;
2x² + 7x + 5
Using the factorization method of solving quadratic equation. We need to multiply the coefficient of x² and the constant 5.
Then find the pair factors and substitute the values into the function.
Substitute the values, we have;
2x² + 2x + 5x + 5
Factor the expression in pairs
(2x² + 2x) + (5x + 5)
Factor the common terms, we get;
2x(x + 1) + 5( x+ 1)
We have the equations;
2x + 5 = 0
x = -5/2
And
x + 1 = 0
x = -1
Thus, the values are x = -5/2 and -1
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calculate the density of a cube with a mass of 135 grams and a length width and height of 3 cm
Answer:
ρ= 5 g/cm³
Step-by-step explanation:
density= mass/volume
ρ= m/v
As all side of the cube is equal so the formula for volume is a³ 3³
which gives us volume 27.
ρ= 135g/27cm³
ρ= 5 g/cm³
Melanie runs 2.6 miles each weekday morning before going to work to prepare for a marathon race. If the race is approximately 26 miles, what percent of the distance does Carol run each week?
A) 10%
B) 20%
C) 40%
D) 50%
I have the right answer, show work please.
Answer:
D) 50%
Step-by-step explanation:
There are 5 weekdays, Monday through Friday.
In each of the 5 weekdays she runs 2.6 miles.
In a week, she runs 5 × 2.6 miles = 13 miles by running only on weekdays.
Now we need to find out what percent of 26 miles is 13 miles.
percent = part/whole × 100%
percent = 13/26 × 100%
percent = 0.5 × 100%
percent = 50%
Answer: D) 50%
A farmer has 30 boxes of eggs. There are 6 eggs in each box. Write, as a ratio, the number of eggs in three boxes to the total number of eggs Give your answer in its simplest form.
Answer:
1:10
Step-by-step explanation:
30 boxes = 180 eggs
3 boxes = 18 eggs
18:180 = 1:10
in the diagram, ABC = FDE.
Find the value of x.
Find the value of y.
x = 27
y = 50
Step-by-step explanation:
ABC=FDE
We need x first.
AC=EF
108=2x-y
54=x -1 . . . . . divide by2
27=x
x=27
Now, we can find y.
∠B = ∠F
2X-Y=48
Y=48+2X=50
Y=50
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Simplify the product. 8x(x-5/4x)
The product of the expression is 8x²-10x
What are expressions?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Given that, an expression 8x(x-5/4x) we are asked to find its product,
8x(x-5/4x)
= 8x²-10x
Hence, the product of the expression is 8x²-10x
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Which inequality represents this sentence? Six plus two is less than nine plus three. Responses 6+2>9+3 6 addition symbol 2 inequality symbol with narrow side pointing to right and wide side opening to the left 9 addition symbol 3 6+2<9+3 6 addition symbol 2 inequality symbol with narrow side pointing to left and wide side opening to the right 9 addition symbol 3 6+2≤9+3 6 addition symbol 2 inequality or equal to symbol with narrow side pointing to left and wide side opening to the right 9 addition symbol 3 9+3<6+2 9 addition symbol 3 inequality symbol with narrow side pointing to left and wide side opening to the right 6 addition symbol 2
The inequality that represents this sentence is 6 + 2 < 9 + 3
How to determine the inequality?From the question, we have the following parameters that can be used in our computation:
Six plus two is less than nine plus three
Express as numbers
So, we have
6 plus 2 is less than 9 plus 3
Introduce the operators
6 + 2 < 9 + 3
Hence, the inequality is 6 + 2 < 9 + 3
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mark has 5 quarters 25 dimes and 20 nickels in his coin box. he randomly takes out a coin and replaces it and randomly takes out another what is the probability that he picked a dime and a nickel
When he replaces a coin that was taken out randomly, there is a 50% chance that he chose a dime and a nickel.
what is probability ?A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A chance is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or probability that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as a percentage form 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain occurrence relative to all possible outcomes.
given
There are six possible methods to select two coins (sequence is irrelevant): 1, 5, 1, 10, 1, 25, 5, 10, and 1, 25. (10,25).
Three of these add up to at least 25, thus 3/6 or 1/2 of them.
Alternatively, there are 4 ways to choose 2 coins from 4, or 4 C 2 = 6.
You then select one of the three remaining coins and the quarter (required to reach at least 25) as follows: 3 C 1= 3 ways.
When he replaces a coin that was taken out randomly, there is a 50% chance that he chose a dime and a nickel.
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