Timex can survey at least 384 consumers to guarantee a margin of error of 0.05 or less at a 99% confidence level.
What is proportion ?
A proportion is a way to express the relationship between two or more quantities or values. It is a statement that asserts that two ratios or fractions are equal, such as "2/5 is equal to 4/10".
To estimate the true proportion p of consumers who believe what is shown in Timex television commercials, Timex can use a sample proportion formula which is:
p = (number of positive responses) / (sample size)
To guarantee a margin of error of 0.05 or less at a 99% confidence level, Timex can use a sample size calculator. The sample size calculator takes into account the margin of error, confidence level, and the proportion of the population that is expected to be positive.
The sample size can be calculated using the formula :
n = (z^2 * p * (1-p)) / E^2
Where z is the z-score for the desired confidence level (z = 2.576 for 99% confidence level), p is the estimated proportion of the population that is expected to be positive (0.5 if the true proportion is unknown), and E is the desired margin of error (0.05).
Timex can survey at least 384 consumers to guarantee a margin of error of 0.05 or less at a 99% confidence level.
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Eva deposited $50 in an account earning 10% cents interest compounded annually. to the nearest cent, how much interest will she earn in 2 years
Eva will earn $10.50 interest.
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P(1 + r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
Eva deposited $50 in an account earning 10% interest compounded annually.
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n[tex])^{nt}[/tex]
A = 50.00(1 + 0.1/1[tex])^{2}[/tex]
A = $60.50
Therefore, she will earn $10.50 of interest.
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Round 0.814 to the nearest hundredth.
Answer: 0.81
Step-by-step explanation:
We will look at the thousands place to round to the hundredth. If the thousands place is at or above 5, we will round up. If it is 4 or below, we will round down.
[tex]\displaystyle 0.814\\0.81\boxed{4}\\\\4 < 5\\\\0.81[/tex]
4X+3 2x+9 linear pairs of angles
Answer:
x = 28°
Step-by-step explanation:
4x+3 and 2x+9 are on a straight line, so the sum is 180°, we solve with an equation
4x + 3 + 2x + 9 = 180°
6x + 12 = 180
6x = 180 - 12
6x = 168
x = 168 : 6
x = 28°
-------------------------------
check4 × 28 + 3 + 2 × 28 + 9 = 180 (remember PEMDAS)
112 + 3 + 56 + 9 = 180
180 = 180
Learning Task 1: Solve for n. Write your answer in your notebook.
1. 7. 26 x 0. 22 =n
2. 17. 92 x 0. 64 = n
3. 7. 65 x 0. 85 =n
4. 36. 20 x 0. 05 = n
5. 31. 85 x 0. 91 = n
The solutions of each expression for n are given as follows:
1. n = 1.5972.
2. n = 11.4688.
3. n = 6.5025.
4. n = 1.81.
5. n = 28.9835.
How to solve the expressions?
All the five expressions in this problem are multiplication operations involving two decimal numbers.
Hence, to obtain the solution for n of each expression, we must simply apply the multiplication operation of the two decimals, using a calculator.
The result of each expression is given at the beginning of the answer.
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a cat's heart beats approximately 45 times and 15 seconds. at this rate how many times does the cat's heartbeat per second?
help.
Answer:
Step-by-step explanation:
For the cat's heart to beat 45 times in 15 seconds
for 1 second, we must divide 45 by 15
the answer will be 3 beats per second
Use Similar Polygons to Find x
Answer:
x = 8--------------------------
We know that corresponding sides of similar figures are proportional.
Thus we have equal ratios:
7x/9x = (8x - 1)/(10x + 1)Solve it for x:
7x/9x = (8x - 1)/(10x + 1) Cancel x on the left side as x ≠ 07/9 = (8x - 1)/(10x + 1) Cross- multiply7(10x + 1) = 9(8x - 1) Distribute70x + 7 = 72x - 9 Collect like terms72x - 70x = 7 + 9 Simplify2x = 16 Divide by 2x = 8 AnswerFormative REDO
1. Find the slope and y-intercept from the equation: y = -2x + 7
b=_
m=
2. Find the slope and y-intercept from the graph:
b=
m=
The equation in the problem is in slope intercept form. The slope-intercept form of a linear equation is: y = mx + b
What is meant by slope?
Slope is a numerical representation of how inclined a line is with respect to the horizontal. The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment.A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.The foundation of differential calculus is the idea of a slope. The rate of change for non-linear functions varies along the curve.Both the slope and the y intercept can have a positive or negative value. Slope is defined as the y-axis divided by the x-axis.The slope-intercept form of a linear equation is: y = mx + b
Where m is the slope and b is the y-intercept value.
Therefore, for this equation y = -2x - 7
The Slope is: m = -2
The Y=Intercept is b = -7 (or)
slope and y-intercept from the graph: (0, -7)
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Enter the statement, with the values in the same order, but with parentheses so that the statement is true.
7x5-4x5+16+4-26 when
(select) (select) (select) (select)+(select)=(select)-26
The statement "7x5-4x5+16+4-26 when
(select) (select) (select) (select)+(select)=(select)-26", with the values in the same order, but with parentheses such that the statement is true is 7x(5-4x+4)-26 = (7x)(1) - 26
What is factorization?Factorization is the process of finding the factors, or integers that multiply together to give a specific number. It is also known as factoring or prime factorization when the factors are prime numbers. For example, factorization of 12 is 2x2x3, which are the prime factors that multiply to give 12. The process of factorization is used in a variety of mathematical and scientific fields, such as number theory, algebra, and computer science.
It can also refer to a mathematical expression where an algebraic expression can be written as a product of two or more expressions.
In general, factorization is a way of breaking down a number or an expression into smaller parts that can be used to understand or simplify it.
Therefore, when plugged in those values in the same order, the statement become true.
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Find two other points on the line passing through (1,5) and (3,-1)
Answer:
We can find two other points on the line passing through (1,5) and (3,-1) by using the slope-intercept form of a line: y = mx + b where m is the slope of the line, and b is the y-intercept.
To find the slope (m) of the line, we can use the formula: m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two given points: m = (-1 - 5) / (3 - 1) = -6 / 2 = -3
To find the y-intercept (b) of the line, we can use one of the given points and substitute the values of x, y and m into the equation y = mx + b.
Plugging in the coordinates of the point (1,5) and the value of m: 5 = -3(1) + b, b = 8
So the equation of the line is y = -3x + 8
We can use this equation and any x value to find two other points on the line. For example, if we choose x = -2, we get y = -3(-2) + 8 = 2
so the point (-2,2) is on the line.
If we choose x = 0, we get y = -3(0) + 8 = 8
so the point (0,8) is on the line.
So two other points on the line passing through (1,5) and (3,-1) are (-2,2) and (0,8)
If I helped you, could you please make my answer best?
Answer:
x + y = 4
m = -1
Step-by-step explanation:
(3 - 5) / (1 - (-1))
m = -2/2
(y - 5) = -1 × (x - (-1))
y - 5 = - x - 1 = 0
a. Are the integers closed under addition and subtraction? In other words, when you add or subtract two integers, is the result always an integer? Justify your response.
b. Give a counterexample to show that the whole numbers are not closed under subtraction.
Answer:
a. The result is always an integer because integers are not fractions or decimals.
b. Sorry I don't have an answer for b i don;t know what that means. :(
a basket holds at most 14 pounds of apple and oranges. there are atleast 3 pounds of apples in the basket
The point (4, 3) is a viable solution.
What are systems of inequalities?At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.
Given:
A basket holds at most 14 pounds of apples and oranges.
There are at least 3 pounds of apples in the basket.
This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges.
That means, we have the system of inequalities,
x + y ≤ 14,
x ≥ 3
Option B and C are discarded.
And y ≥ 0.
Option A is also discarded.
Substituting (4, 3),
x + y ≤ 14,
7 ≤ 14.
Therefore, (4, 3) is a solution.
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The complete question:
A basket holds at most 14 pounds of apples and oranges. There are at least 3 pounds of apples in the basket. This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges. Which point represents a viable solution?
Please help I need the answers ASAP.
Answer:
Refer to the step-by-step
Step-by-step explanation:
∠1 and ∠2 lie in the alternate interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal angles.
E is the encoding matrix.
Use E to decode the coded message matrix.
Encoding simply means the process of putting a sequence of characters like letters, numbers and other special characters into a specialized format.
What is an encoding matrix?It should be noted that a type of code, that is extremely difficult to break, and one which makes use of a large matrix to encode a message is the encoding matrix.
Here, the receiver of the message decodes it by using the inverse of the matrix. In their case, the first matrix is the encoding matrix and the inverse is the decoding matrix.
To decode the message, we simony have to take the string of coded numbers and then multiply it by the inverse of the matrix in order to get the original string of numbers.
Encoding simply means the process of putting a sequence of characters like letters, numbers and other special characters into a specialized format.
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how many different batting orders can a baseball coach create from a team of 15 players, if there are nice positions to fill?
15 x 14 x 13 x ... x 3 x 2 x 1 is the possible batting orders.
A baseball coach can create 15! (15 factorial) different batting orders for a team of 15 players if there are nine positions to fill in the lineup. This is because, for the first spot in the lineup, there are 15 options, for the second spot there are 14 options, and so on, leading to 15 x 14 x 13 x ... x 3 x 2 x 1 possible batting orders.
The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.
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Please help please help
For geometric shape no.4,∠1=26°,∠2=154°,∠3=26°,∠4=26°,
∠5=154°,∠6=154°,∠7=26°.
What are geometric shapes?
In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.
Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.
In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc. In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.
Now,
∠1+154°=180° -->∠1=26° (supplementary angles)
∠1=∠3 (opposite angles) -->∠3=26°
∠2+∠3=180°
∠2=154°
∠1=∠7 --->∠7=26°
∠7+∠6=180° (supplementary angles)
∠6=154°
∠5+∠7=180° (supplementary angles)
∠5=154°
∠4+∠5=180° (supplementary angles)
∠4=26°
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Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not a/d=j
The expression in terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.
What exactly is a phrase?
It is described as blending mathematical operators, constants, and variables.
It follows that:
The sentence is:
hD = m
To account for D Declare D as the subject.
As we know, an arithmetic operation can be defined as an operation in which we add, subtract, multiply, and divide integers. It has four basic operators that are +, -, ×, and ÷.
By dividing both sides by h:
hD/h = m/h
Here h ≠ 0
D = m/h
As a result, if the statement is hD = m, then the expression in terms of m and h is D = m/h, and the solution is D = m/h.
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Substitute each variable to determine whether the inequality statement is true or false j/6 >3 if j =24
The inequality statement j/6 > 3 is true when j = 24.
How to Determine if an Inequality Statement is True?To substitute the value of j into the inequality statement, you will replace j with 24 and then simplify the expression.
j / 6 > 3
24 / 6 > 3
Simplifying, we get
4 > 3
Since 4 is greater than 3, the inequality statement is true.
You can also check by multiplying both sides of inequality by 6
j > 18
24 > 18
This is true because 24 is greater than 18. Therefore, the inequality statement j/6 >3 if j =24 is true.
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Write an explicit formula for
�
�
a
n
, the
�
th
n
th
term of the sequence
28
,
14
,
7
,
.
.
.
28,14,7,....
Answer:
This equation makes no sense post in better quality
Step-by-step explanation:
For the translation below, give the vertices of ABC
Answer:
see explanation
Step-by-step explanation:
A translation of [tex]T_{(5,2)}[/tex] means
add 5 to the original x- coordinate and add 2 to the original y- coordinate.
A (1, - 2 ) → A' (1 + 5, - 2 + 2 ) → A' (6, 0 )
B (- 3, - 3 ) → B' (- 3 + 5, - 3 + 2 ) → B' (2, - 1 )
C (3, 5 ) → C' (3 + 5, 5 + 2 ) → C' (8, 7 )
Cody hiked at an average speed of 1 mile per hour for 5 hours on Saturday. He hiked an average speed of 2 miles per hour for 3 hours on Sunday. Which explanation correctly tells how to calculate the total number of miles that Cody hiked in two days?
The correct explaination to calculate the total number of miles that Cody hiked in two days is Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products.
First of all, we must know the formula of average speed. The formula is as follows -
Average speed = distance ÷ time
Using this formula, we can calculate distance for Saturday and Sunday and subsequently add the distance to find the number of miles that Cody hiked in two days.
For Saturday -
Distance = 1 × 5
Performing multiplication
Distance = 5 miles
For Sunday -
Distance = 3 × 2
Performing multiplication
Distance = 6 miles
Total distance hiked = 5 + 6
Performing addition
Total distance hiked = 11 miles
Thus, the correct explaination is Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products.
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The complete question is -
Cody hiked at an average speed of 1 mile per hour for 5 hours on Saturday. He hiked an average speed of 2 miles per hour for 3 hours on Sunday. Which explanation correctly tells how to calculate the total number of miles that Cody hiked in two days? Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Subtract the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products. Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Add the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Subtract the two products.
Javier is ordering a sandwich from a deli. There are 3 types of meat to choose from and 4 cheeses, and Javier must pick one of each. How many different sandwiches can Javier order?
The number of different sandwiches that Javier can order, given the number of types of meat and cheeses, is 12 sandwiches.
How to find the number of sandwiches ?Javier has 3 choices for the type of meat and 4 choices for the cheese, so the total number of different sandwiches he can order is the product of the number of choices for each ingredient.
To find the total number of different sandwiches, you can multiply the number of meat choices by 4 the number of cheese choices.
The number of sandwiches Javier can order are:
= 3 x 4
= 12 sandwiches
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expresa con una fracción cada situacion. a) la temperatura ambiente es un tercio bajo cero
Answer:
a) La temperatura ambiente es -1/3.
the difference between the squares of two positive integers is 2009. what is the maximum possible difference between these two integers?
Answer:
Step-by-step explanation:
i dont knpw
A small town has two local high schools. High School A currently has 800 students
and is projected to grow by 35 students each year. High School B currently has 550
students and is projected to grow by 85 students each year. Let A represent the
number of students in High School A in t years, and let B represent the number of
students in High School B after t years. Write an equation for each situation, in terms
of t, and determine the interval of years, t, for which High School A will have more
students than High School B.
Answer:
T < 5
Step-by-step explanation:
High School A: A(t) = 800 + 35t
High School B: B(t) = 550 + 85t
To find the interval of years in which High School A will have more students than High School B, we need to find the years in which A(t) > B(t).
So, we need to solve the inequality A(t) > B(t)
800 + 35t > 550 + 85t
250 > 50t
t < 5
Therefore, High School A will have more students than High School B for the first five years.
The interval of years, t, for which High School A will have more students than High School B is t < 5
Put the following equation of a line into slope-intercept form, simplifying all fractions.
2x+4y=16
Answer:
Step-by-step explanation: I do these in 2 steps:
1. isolate the y term ----- 4y = -2x + 16
2. divide each term by the coefficient of the y-term
y = (-2/4)x + 4
y = (-1/2)x + 4
The statement, 81:135 = 36:60 is a proportion.
If a and b are non-zero numbers and c = 0, then a/c = b/c is a proportion.
State whether the following statements are proportions or not. If it is a proportion, then prove by the definition of proportion. If not, then solve the correct value of x. Be sure to show the complete steps in solving for x.
a) The value of x from the proportion is x = 2/5
b) The value of x from the proportion is x = 8
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
a)
3 / ( x + 2 ) = ( 5 / 4 ) be equation (1)
On simplifying the equation , we get
Multiply by ( x + 4 ) on both sides of the equation , we get
( 5/4 ) ( x + 2 ) = 3
Multiply by 4 on both sides of the equation , we get
5 ( x + 2 ) = 12
On further simplification , we get
5x + 10 = 12
Subtracting 10 on both sides of the equation , we get
5x = 2
Divide by 5 on both sides of the equation , we get
x = 2/5
Therefore , the value of x is 2/5
b)
( x + 2 ) / 5 = ( x - 2 ) / 3 be equation (2)
On simplifying the equation , we get
Multiply by 5 on both sides of the equation , we get
( x + 2 ) = 5( x - 2 ) / 3
Multiply by 3 on both sides of the equation , we get
3 ( x + 2 ) = 5 ( x - 2 )
On further simplification , we get
3x + 6 = 5x - 10
Subtracting 3x on both sides of the equation , we get
2x - 10 = 6
Adding 10 on both sides of the equation , we get
2x = 16
Divide by 2 on both sides of the equation , we get
x = 8
Therefore , the value of x is 8
Hence , the proportion is solved
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A statistics professor asked her students whether or not they were registered to vote. In a sample of
50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.
1. Find a 95% confidence interval for the true proportion of the professor's students who were
registered to vote. (Make sure to check any necessary conditions and to state a conclusion in
the context of the problem. )
As per the 95% confidence interval, the true proportion of the professor's students who were registered to vote is between 57.3% and 82.7%
The term called confidence interval is defied as the mean of your estimate plus and minus the variation in that estimate.
Here we know that sample of 50 of her students randomly sampled from her 700 students, 35 said they were registered to vote.
Here we have to calculate the true proportion of the professor's students who were registered to vote with 95% confidence interval is,
Here we have a random sample of less than 10% of the professor's students with 35 expected successes and 15 expected failures
Here we have know that both of which are at least ten, so a Normal model applies.
Then the value of n = 50,
=> P =35/50 = 0.70
Then the value of q = 1 - p = 1 - 0.70 = 0.30
Then the value of SE is
=> √(0.70 0.30)/ 50 = 0.065
Then with 95% confidence interval is calculated as,
=> p± SE(p)
Apply the values on it, then we get
=> 0.70±1.96 (0.065)=0.70±0.127
=> 0.573 to 0.827
hence the 95% confident that between 57.3% and 82.7% of the professor's students are registered to vote.
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a measure computed from the entire population is called __________.
A measure computed from the entire population is called parameter.
A limit is a parameter. A parameter is a constant in an equation in mathematics, however today, any system can include parameters that control how it functions. You can provide guidelines for your class discussion.
Greek words para-, which means "beside," and metron, which means "measure," are combined to form the term parameter. Gravity and time are two boundaries that the natural world establishes. The law establishes the boundaries of appropriate conduct in court. While parameters and perimeters are similar, a parameter can contain or define something that is either physically present or abstractly defined, whereas a perimeter is the physical space that surrounds an entity.
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(-xy)^2 * (2x^9y^5)^4
please show me the steps on how to get the answer
Answer: 16x^38y^22
Step-by-step explanation:
Re-order terms so constants are on the left
(−xy)2(2x9y5)4(−)2(295)4
Distribute exponent
(−xy)2(2x9y5)4(−)2(295)4
Evaluate the exponent
(−1)2(xy)2⋅(2x9y5)4(−1)2()2⋅(295)4
Question
True or False... (8, -7) is a solution to the inequality y<12x−9
The statement is true, the point (8, 7) is a solution to the inequality.
Is the statement true or false?Here we have the following statement:
"(8, -7) is a solution to the inequality y < 12x − 9"
To check if that is true, we just need to replace the values of the point on the inequality and check if the ienquaity becomes true.
We will get:
-7 < 12*8 - 9
-7 < 87
This is true, 87 is a number larger than -7, then the statement is true, (8, -7) is a solution of the inequality.
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