By applying the simple concept of algebra, the equation showing the number of Kenny's baseball cards (b) is b = 82 + 159. So it can be concluded that the number of Kenny's baseball cards is 241 cards.
The use of algebra in everyday life.
Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used, starting from simple mathematical operations, to financial planning, calculating time/mileage, and so on.
In the above questions, we can take some notes as follows:
Baseball cards sold (x) = 82 cards.
Remaining baseball cards (y) = 159 cards.
The number of baseball cards owned by Kenny (b):
b = x + y
= 159 + 82
= 241 cards
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at confidence, what is the margin of error and the interval estimate of the number of eligible people under years old who had a driver's license in ?
Part a: The margin of error and the interval estimate is E = 0.027 and 0.6120 < p < 0.666 respectively.
Part b: The margin of error and the interval estimate is E = 0.027 and 0.3900 < p < 0.4440 respectively.
Explain the term margin of error?Your results will deviate by various percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.Considering the first query;
The 1995 sample proportion is; P₁ = 0.693.The size of the sample is; n = 1200Since the confidence level for the question is 95%, the level of importance is;
α = (100 - 95)%
α = 0.05
Typically, the crucial value of comes out from normal distribution table of α/2 is;
Z(α/2) = 1.96
Typically, this margin of error is denoted mathematically as follows:
E = Z(α/2)*√P₁(1 - P₁)/n
E = 1.96*√0.639(1 - 0.639)/1200
E = 0.027
Mathematically, a 95% Interval estimate is typically written as;
P₁ - E < p < P₁ +E
0.639 - 0.027 < p < 0.639 + 0.027
0.6120 < p < 0.666
Thus, the margin of error and the interval estimate is E = 0.027 and 0.6120 < p < 0.666 respectively.
Part (b)
The 1995 sample proportion is; p₂ = 0.417Sample size: n = 1200Since the confidence level for the question is 95%, the level of importance is;
α = (100 - 95)%
α = 0.05
Typically, the crucial value of comes from the normal distribution table and is;
Z(α/2) = 1.96
Typically, the margin of error is denoted mathematically as follows:
E = Z(α/2)*√p₂(1 - p₂)/n
E = 1.96*√0.417(1 - 0.417)/1200
E = 0.027
Mathematically, a 95% Interval estimate is typically written as;
P₁ - E < p < P₁ +E
0.417 - 0.027 < p < 0.417 + 0.027
0.3900 < p < 0.4440
Thus, the margin of error and the interval estimate is E = 0.027 and 0.3900 < p < 0.4440 respectively.
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The complete question is-
Fewer young people are driving. In 1995, 63.9% of people under years 20 old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample 1,200 of people under 20 years old who were eligible to have a driver's license in 1995 and again in 2016.
a. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 1995?
Margin of error(to four decimal places)
Interval estimate (to four decimal places)
b. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 2016?
Which expression is equivalent to (ab8)4?
a5b12
ab12
a4b32
ab32
Answer:
The answer is ab32
Step-by-step explanation:
ab x 8 x 4 = ab32
Answer: a^4b^32
Step-by-step explanation: (ab^8)^4 = (ab^8)(ab^8)(ab^8)(ab^8) = a^4b^32
Find an equation of the tangent to the curve at the given pointx=cos(t)+cos(2t)y=sin(t)+sin(2t)(-1,1)y=?
Answer:
y = -0.11x + 0.89
Step-by-step explanation:
First find the slope of the tangent line, which is equal to dy/dx
Find the derivative of y at 1:
dy = cos(t) + 2cos(2t)
dy = cos(1) + 2cos(2)
dy = -0.292
Then the derivative of x at -1:
dx = -sin(t) - 2sin(2t)
dx = -sin(-1) - 2sin(-2)
dx = 2.66
So now calculate dy/dx:
dy/dx = -0.11
Now use point slope form to find the equation of the tangent line:
y - 1 = -0.11(x + 1)
y - 1 = -0.11x - 0.11
y = -0.11x + 0.89
Please help me respond this question
Check the picture below.
Answer:
14.1
Step-by-step explanation:
You add all of your numbers up, and then you divide by how many numbers you have.
(12a - 5b) - (a + 6b)
The answer is 11(a - b), To solve this expression, we need to perform the subtraction operation on the terms inside the parentheses. First, we subtract the term "a + 6b" from "12a - 5b". This gives us 11a - 11b. Then, we can simplify this expression by combining the like terms 11a and -11b to get 11a - 11b = 11(a - b). This is the final answer.
mr. yates picked up a dozen items in the grocery store with a mean cost of $3.25. then he added an apple pie for $6.50. the new mean for all 13 items is
The new mean cost for all 13 items purchased by Mr. Yates is found to be $3.50.
Explain the term mean value of the data?The mean of a dataset seems to be the sum of all numbers divided by a total number of values, also known as the arithmetic mean, which differs from the geometric mean. The term "average" is frequently used to describe this measure of central tendency.The given data is-
mean cost = $3.25
Number of items = 12.
When added with apple pie of $6.50.
Total number of items becomes = 13.
So,
New mean = 6.50x12 + 3.25 / 13
New mean = 3.50
Thus, the new mean for all 13 items purchased by Mr. Yates is found to be $3.50.
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helpppppppppppppppppppppppppppppppppppppppppppppppp asap
Answer: It should be 3rd onem 3/4n=5/8
Step-by-step explanation: if not my bad-
two students are chosen at random from a group of two girls and five boys, all of different ages. find the probability
From a group of two girls and five boys, all of the various ages, two pupils are randomly selected. The likelihood that the two selected students will be boys is 10/21.
In probability theory and other branches of mathematics, the term "combination" designates a series of results in which the order of the results is irrelevant.
Here given the total number of girls is 2 and boys is 5. Then, the total number of students is 7. The number of ways of selecting 2 students from 7 students is,
[tex]\begin{aligned}n(S)&=\frac{7C2}{2}\\&= \frac{7\times6}{2}\\&=\text{21 ways}\end{aligned}[/tex]
The number of ways of selecting 2 boys from 5 boys is,
[tex]\begin{aligned}n(E)&=\frac{5C2}{2}\\&=\frac{5\times4}{2}\\&=\text{10 ways}\end{aligned}[/tex]
Then, the required probability is calculated as,
[tex]\begin{aligned}P(E)&=\frac{n(E)}{n(S)}\\&=\frac{10}{21}\end{aligned}[/tex]
Therefore, the required answer is 10/21.
The complete question is -
Two students are chosen at random from a group of two girls and five boys, all of the different ages. Find the probability that the two students chosen will be: two boys
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The functions f(x) and g(x) are shown on the graph.
f(x) = x²
What is g(x)?
10
A. g(x) = 2x²
B. g(x) = (x - 2)²
C. g(x) = (¹ x)²
D. g(x) = (x + 2)²
f(x)
(2,8)
The equation of the transformed function is g(x) = -x² - 2
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x² -- parent root function
When the graph is examined (see attachment), we have the transformation to be
g(x) = reflect f(x) across the x-axis and a downward shift of 2 units.
Mathematically, this can be represented as
g(x) = -f(x) - 2
Substitute the known values in the above equation, so, we have the following representation
g(x) = -x² - 2
Hence, the transformed function is g(x) = -x² - 2
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12)
60°
-5+ 13x
Please help
-5 + 13x = 60
13x = 65
x = 5
CHECKING:
-5 + 13(5) = 60
-5 + 65 = 60
60 = 60
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Which expression is equivalent to 3(−4.2y − 13.6)?
A. 1.2y − 13.6
B. 1.2y − 10.6
C. −12.6y − 13.6
D. −12.6y − 40.8
Answer:
the anwser is b
Step-by-step explanation:
What is a reflection rule that maps each triangle and its image?
The equation of the line is y = x. Then the rule of reflection is (x, y) ⇒ (y, x).
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the refection is given will be
Firstly, the rule for reflecting a point about the line y = x is;
While reflecting on the line y = x, we get the reflected points by swapping the coordinates.
The equation of the line that passes through (0, 0) and (1, 1) is given as,
y - 0 = [(1 - 0) / (1 - 0)](x - 0)
y = x
The equation of the line is y = x. Then the rule of reflection is given as,
(x, y) ⇒ (y, x)
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the tangent line to a certain curve at any point p(x, y) has an x-intercept equal to 3 4 x. this curve also passes through the point (1, 16). find the equation of this curve.
At any point p(x, y), the tangent line to a particular curve has an x-intercept of 3 4 x. The point is also traversed by this curve (1, 16). The equation of the curve is y - 16 = (3/4)(x - 1)^2
To find the equation of the curve, we first need to find the equation of the tangent line at point P(x, y).
Since the x-intercept is 3/4x, the equation of the tangent line is
y - y_p = (3/4)(x - x_p).
We substitute the given point (1, 16) in the equation to find the value of y_p and x_p which are 16 and 1 respectively.
y - 16
= (3/4)(x - 1).
This equation is the equation of the curve.
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Is this a function or not a function?
answer:
if because x does not have two y
Step-by-step explanation:
I hope it works
The point-lope form of the equation of the line that pae through (–4, –3) and (12, 1) i y – 1 = y-1=1/4(x – 12). What i the tandard form of the equation for thi line?
An equation of line having slope 1/4 and passes through the point (-4,-3) is y = 1/4x - 2
We know that the slope-point form of line is:
(y - y1) = m(x - x1)
Here, we need to find an equation of line having slope 1/4 and passes pae through the point (-4,-3)
let (x1, y1) = (-4, -3)
and m = 1/4
substitute values in above formula,
(y - (-3)) = 1/4 (x +4)
y + 3 = 1/4 (x+4)
y = 1/4x -2
which is slope-intercept form of line (y = mx + b)
Therefore, equation of line is y = 1/4x - 2
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Evaluate the expression for t = 9 and u = 2.
t + u =
A cylinder has a radius of 14 m and a height of 6 m. what is the exact volume of the cylinder? responses 84π m³ 84 pi, m³ 168π m³ 168 pi, m³ 504π m³ 504 pi, m³ 1176π m³
Answer:
answer is on the photo......
Write
38
46
in lowest terms.
The lowest term of 38/46 can be expressed as a decimal as 0.826087 and percentage as 82.6087%.
How to estimate the lowest term of 38/46?The fraction 38/46 is equivalent to 19/23.
Once the absolute value of the top number, or numerator, (38) is less than the absolute value of the bottom number, or denominator, the fraction is considered to be correct (46).
The fraction 38/46 can be reduced.
To make things simpler, we'll employ the Greatest Common Factor (GCF) technique.
The GCF is the largest number equally divisible by two or more other numbers.
The numerator and denominator factors are listed, and the greatest number repeated in both lists is used to calculate the GCF:
The factors of 38 exists 1,2,19,38;
The factors of 46 exists 1,2,23,46.
We can see that the GCD is 2 because it is the largest number by which 38 y 46 can be divided without leaving any residue.
Simply divide the numerator and denominator by 2 to lower this fraction (the GCF).
So, [tex]$\frac{38}{46}=\frac{38 \div 2}{46 \div 2}=\frac{19}{23}$[/tex]
Therefore, 38/46 exists equivalent to 19/23 in the reduced form.
The factors exists numbers that multiply each other to get another number.
The fraction 38/46 exists even equivalent to 38÷46 and can also be expressed as a decimal as 0.826087 and expressed as a percentage as 82.6087%.
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Is this a function or not a function?
(6, 3) (5, 3) (4, 3) (3, 3)
Maria had $150 in gift certificates to use at a record store. She bought no more than 20 recordings. Each tape cost $5.95 and each CD cost $8.95. How many of each type of recording might she have bought?
Maria might have bought 9 tapes and 10 CDs of each type with her gift
certificate.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let,The no. of tapes be 'x' and the no. of CD be 'y'.
Given, She bought no more than 20 recordings.
Therefore, x + y ≤ 20.
And,
Each tape cost $5.95 and each CD cost $8.95.
Therefore,
5.85x + 8.95y ≤ 150.
By graph intersection method we find that (9.355, 10.645) is a solution.
But the numbers should be in integers so, 9 tapes and 10 CD recordings
she might have bought.
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Use the image below to answer the identify the following. Please show ur work Bc I have too !!
One pair of vertical angles
One pair of adjacent angles
One pair of supplementary angles
∠1 and ∠4 are vertical angles
∠1 and ∠3 are adjacent angles
∠1 and ∠2 are supplementary angles
Vertical Angles:Vertically opposing angles are established when two lines intersect at a single place and the angles opposite to each other are created using the two intersecting lines. There is never a difference between these angles.
Adjacent Angles:Those angles are referred to as vertical angles if they share an arm and a vertex. Additionally, the nearby angles are those that are produced side by side. The primary characteristic of these angles is that they never cross over.
Supplementary Angles:When two angles add up to 180 degrees, they are said to be supplementary. Angles are referred to be supplementary angles when two of them are next to one another.
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Given that the measurement is in inches find the circumference of the circle to the nearest tenth use 3.14 for. Please show ur work Bc I have too !!
Answer:
25.12 in.
Step-by-step explanation:
C = 2πd
C = 2 × 3.14 × 4 in.
C = 25.12 in.
While looking at some reports, a
store manager notes that gold
rings that retail for $688 end up
costing customers $731 once the
sales tax is added. What is the
sales tax percentage?
(round your answer to the nearest hundreths)
6.25% is the the sales tax.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given that a store manager notes that gold rings that retail for $688 end up
costing customers $731 once the sales tax is added.
We need to find the sales tax percentage.
The percentage we can calculate by subtracting original amount minus new amount by original amount and multiplied with 100.
731-688/688
0.0625
Multiply 0.0625 with 100 as it is a hundredth part.
0.0625×100
6.25%
Hence, the sales tax percentage is 6.25%.
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Complete the equation for a line through point A(-3, 3) and perpendicular to the line passing through (0, -2) and (4, 1).
Answer: Zeli shan tel
Step-by-step explanation:
Complete the statements. Explain.
Question 1
Part A
Enter the correct answers in the boxes.
−4(5+(−2))= (
) (5)+ (
)(−2)
−4 (
) =−20+
The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.
Given that,
The expression is -4(5+(-2))
We have to find what is the solution for the given numerical expression.
We know that,
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Take the numerical expression
-4(5+(-2))
Adding 5+(-2)
Multiply + - we get -
So,
5-2=3
-4(5-2)=-4(3)
Multiply 4 to 3
-4(3)=-12
Therefore, The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.
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Drag each tile to the correct location on the inequality. Each tile can be used more than once.
Consider the graphed function.
The domain of the function y = 2x + 5 is [-4, 1), and the range of the function is [5, 7). The graph is also attached below.
What is a graph?A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.
Given:
As you can see from the graph, the coordinates of the line are (0, 5) and (1,7),
Calculate the equation of the line as shown below,
y - 5 = (7 - 5) / (1 -0) (x-0)
y - 5 = 2 (x +0)
y = 2x + 5
The domain of the above equation can be determined from the graph,
Domain = [-4, 1)
Range = [5, 7)
The graph is also attached below.
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Machine fills rate 135 containers per minute how long will it take to fill 1000 containers at the same rate
HOW?
HOW?
7.4
Answer:
7.4 mins
Step-by-step explanation:
135 -----> 1 min
1000 ----> x
1000/135 mins = x
= 7.4 mins
Answer:
To determine how long it will take to fill 1000 containers at a rate of 135 containers per minute, you can use the formula: time = number of containers / filling rate. In this case, the filling rate is 135 containers per minute, and the number of containers you want to fill is 1000. Plugging these values into the formula, we get: time = 1000 / 135 = 7.41 minutes.
Tyler’ firt and correct equation : 0. 65p 0. 10t = 1. 70
Tyler’ econd and incorrect equation: t =(1. 70. 0. 65p). 0. 10
This equation is incorrect because it is missing a division sign between 1.7 and 0.65p. The correct equation should be t = (1.7 / 0.65p) * 0.10
First, we need to isolate the variable 't' in the equation. To do this, we need to divide both sides of the equation by 0.10. This will give us 0.65p/0.10 = 1.70/0.10, which simplifies to t = (1.7 / 0.65p) * 0.10. This is the correct equation that we need to solve for 't'.
t = (1.7 / 0.65p) * 0.10
t = (1.7 / (0.65 * p)) * 0.10
t = (17 / (6.5 * p)) * 0.1
t = (17 * 0.1) / (6.5 * p)
t = (1.7) / (6.5 * p)
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A boa constrictor slithers 2/6 kilometers in 4/5 hours. What is the distance the boa constrictor travels in 16 hours?
10 kilometres
Explanation
1/3 + 4/5 = 5/8
5÷8 = 0.625
0.625 * 16 = 10
Find the sum of the first 20 terms of the sequence below.
27, - 9, + 3, - 1, ...
The sum of the first 20 terms of the geometric sequence is 20.25.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16, 32 is a geometric sequence.
We have,
27, -9, 3, -1,.....
a = 27
Common ratio:
= -9/27 = -1/3
= 3/-9 = -1/3
The sum of the geometric sequence.
S(n) = a (1 - [tex]r^n[/tex]) / (1 - r)
Now,
a = 27,
r = -1/3
S(20):
= 27 (1 - [tex](-1/3)^{20}[/tex]) / (1 + 1/3)
= 27 (1 + 1/[tex]3^{20}[/tex]) / (4/3)
[ (1 + 1/[tex]3^{20}[/tex]) = 1 ]
= 27 x 3/4 x 1
= 20.25
Thus,
The sum of the geometric sequence is 20.25.
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