The probability that the sample proportion of the number of people using the courier will differ from the population proportion by greater than 0.03 is 0.0504
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 0.05
sample size, n = 202
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.05(1 - 0.05)) / 202}
= √{(0.05 * 0.95) / 202}
= 0.01533
The probability
differ from the population proportion by less than 3%
|X - 0.05| > 0.03
X < 0.02 OR X > 0.08
P(z < 0.02) + P(z > 0.08 )
z score for z < 0.02
z = (0.02 - 0.05) / 0.01533
= -1.9569
p value for z < -1.9569 = 0.02518
z score for z > 0.08
z = (0.08 - 0.05) / 0.02196
= 1.9569
p value for z > 1.9569 = 1 - 0.9748 = 0.02518
The probability required = 0.02518 + 0.02518 = 0.0504 = 5.04%
Learn more about p - values at:
https://brainly.com/question/28940355
#SPJ1
Consider the equation and the following ordered pairs: (−3,y) and (x,2). y=−3x−1 Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation. Answer Keyboard Shortcuts Complete the table below. x y row 1−3 Answer row 2 Answer 2
Using the equation y = -3x - 1, the missing values are in the ordered pairs, (−3,y) and (x,2), are: x = -1 and y = 8.
How to Compute Missing Values that Satisfies an Equation?An algebraic equation is an expression that has variables. The values of those variables, when plugged into the equation would make the equation true.
Given the equation, y = -3x - 1, substitute x = -3 into the equation to find y:
y = -3(-3) - 1
y = 9 - 1
y = 8
The missing value in the ordered pair is: (-3, 8).
To find the missing value of x in (x, 2), substitute y = 2 into the equation, y = -3x - 1:
2 = -3x - 1
2 + 1 = -3x
3 = -3x
3/-3 = x
x = -1
The missing value is (-1, 2).
Learn more about equations on:
https://brainly.com/question/21287234
#SPJ1
Fewer than %97 of adults have a cell phone. In a reputable poll of 1160 adults, %88
said that they have a cell phone. Find the value of the test statistic
The value of the test statistic of the hypotheses is; -17.969
How to find the test statistic?
The test statistic is defined as a number, calculated from a statistical test, which is used to find if your data could have occurred under the null hypothesis.
We are given;
Sample size; n = 1160
Sample proportion; p^ = 88% = 0.88
Population proportion; p = 97% = 0.97
The claim is about the population proportion (p) in the hypotheses. Since we are told that fewer than 97% of adults have a cell phone, then the claim is; p < 0.97
The null hypothesis is expressed as;
H₀: p = 0.97
The alternative hypothesis is expressed as;
Hₐ: p < 0.97
The value of the test-statistic is gotten from the formula;
z = (p^ - p)/(√(p(1 - p)/n))
z = (0.88 - 0.97)/(√(0.97(1 - 0.97)/1160))
z = -17.969
Read more about Test statistic at; https://brainly.com/question/4621112
#SPJ1
A small rectangle has a width of 5cm and a length of 7cm. using the same ratio, what will be the length of a bigger rectangle it its width is 90cm?
According to the local weather report, the probability of rain in Chicago on October 14 is 57%.
The fraction that represents the percentage of 57% is presented as follows:
57/100.
How to convert a percentage to a fraction?A fraction is represented by the division of a term x by a term y, according to the equation presented as follows:
Fraction = x/y.
The terms are know as numerator and denominator, respectively, as follows:
Numerator: the top term of the fraction, in our example x, is called the numerator of the fraction.Denominator: the bottom term of the fraction, in our example y, is called the denominator of the fraction.For a percentage of a%, the equivalent fraction is obtained as follows:
The numerator is the percentage of a.The denominator is of 100.Hence, for a percentage of 57%, as is the case in this problem:
The numerator is 57.The denominator is 100.Hence the fraction is:
57/100.
Missing InformationThe problem asks to represent the percentage as a fraction.
A similar problem, also featuring fractions, is presented at brainly.com/question/1622425
#SPJ1
Given that capital is fixed, what do you figure is the marginal cost or additional cost of producing another:
haircut
sandwich
Ferris Wheel ride
The marginal cost is the labor utilized in order to provide an additional cost of a haircut.
What is the marginal cost?The marginal cost is the extra cost of generating one additional unit of output.
The example of a haircut, the marginal cost is the labor utilized in order to provide an additional haircut; employees offer their time, which is valued in pay, resulting in the marginal cost of labor.
Thus, in all circumstances, such as the sandwich and Ferris Wheel, there will be an additional labor cost because labor is necessary to make each of the items.
Change in cost / Change in quantity Equals Marginal cost.
The firm will incur an increased labor expense because of one more haircut, and the laborer will be paid more because of the rise in one more quantity of haircut delivered. This pay rise is the marginal cost.
Thus, the marginal cost is the labor utilized in order to provide an additional cost of a haircut.
To learn more about the marginal cost here:
https://brainly.com/question/7781429
#SPJ1
there are 32 steps in one floor of a tower max lives .he climbs 6 floors of his building. if he clims 6 floor every day , how many steps does he climb every week
Answer:
1,344
Step-by-step explanation:
First, find how many steps he climbs every day
32*6=192
Now, multiply that by 7 to see how many he climbs in a week
192*7=1,344
Two buses leave a station at the same time and travel in opposite directions. On bus travels 17 km/h faster than the other. If the two buses are 836 kilometers apart after 4 hours, what is the rate of each bus
Step-by-step explanation:
speed = distance / time
to get distance, we have to multiply by time.
the speed the 2 busses are moving seat from each other is
x + (x + 17) = 2x + 17
x = the speed of one bus
x + 17 = the speed of the other bus.
so, after 4 hours the distance between them is
(2x + 17) × 4 = 836
2x + 17 = 209
2x = 192
x = 96 km/h
bus 1 travels at 96 km/h.
bus 2 travels at 96+17 = 113 km/h.
Factor: 64x³ + 125y³
64x³+125y³
= (4x+5y)( 16x²-20xy+25y²)
a³ + b³ = ( a + b )( a² - ab + b² )
64x³ + 125y³
= ( 4x )³ + ( 5y )³
= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]
= (4x+5y)( 16x²-20xy+25y² )
6 books weigh 1.260 kg. How many books will weigh 3.150 kg?
Answer: 15 books
Step-by-step explanation:
Given that the weight of 6 books is 1.260 kg
⟹ weight of each book is [tex]\frac{1.260}{6}[/tex] = 0.210kg
Let the number of books that will weigh 3.150 kg be x
as we know that
weight of x books is 0.210x kg
⟹0.210x=3.150
⟹x= [tex]\frac{3.150}{0.210}[/tex] = 15
The number of books is 15
15 books will weigh 3.150 kg.
Given the weight of 6 books is 1.260 kg
⟹ weight of each book is
1.260/6
=0.210 kg
Let x be the total number of books that weigh 3.150 kg.
as we are aware
weight of x books is 0.210x kg
⟹0.210x=3.150
⟹x= 3.150/0.210
=15
So, the number of books is 15.
know more about weight numerical at :
https://brainly.com/question/17490356
Simplify the variable expression by evaluating its numerical part, and enter
your answer below.
g- 16/4 +2
simplification of expression will be g - 2
Our expression is g - 16/4 + 2
16/4 = 4
so we c will write it as
g - 4 + 2
which can be further simplified to
g - 2
Therefore, our simplified expression comes out to be g - 2.
For more questions related to simplification
https://brainly.com/question/2804192
#SPJ1
Use I=PRT
p=12,000
r=4%
t=3year
find I
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (12000)(0.04)(3) \implies I = 1440[/tex]
A fish tank has a capacity of 154L.
What is the volume of the fish tank?
The volume of the fish tank required = 0.154 m^3.
A fish tank has a capacity = 154L.
Capacity of fish tank in Litre = Volume of the fish tank in meter cube
So the volume of the fish tank required in cubic meter.
For the volume we required a conversion of litre into meter cube.
Cubic meters and liters are two common metric units of volume.
1 cubic meter is 1000 liters.
To convert liters to cubic meters, you simply need to move the decimal point three places to the left. In other words, divide a value in liters by 1000 to get an answer in cubic meters.
1L = 0.001 m^3
So 154L = 0.154 m^3
So the volume of the fish tank required = 0.154 m^3.
To know more about volume here.
https://brainly.com/question/19908969
#SPJ1
What Did the Baby Porcupine Say
When It Backed Into a Cactus?
each
Answer:
As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give call to its mother.
Step-by-step explanation
He said hi Ma.
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
f(x) is decreasing for all x < 6
f(x) is increasing for all x > 6
f(x) is decreasing for all x < 3
f(x) is increasing for all x < 3
The correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6
How to determine the correct statementInformation given in the question
f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity
This is written as (x + 6) / ( x² - 9x + 18 )
factorizing the denominator gives
(x + 6) / {( x - 6)( x - 3)}
In the denominator
At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:
f(x) is decreasing for all x < 6: contains x = 3 and result to a higher value
f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing
f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4
Therefore the correct option is f(x) is increasing for all x > 6
Learn more on polynomial functions here:
https://brainly.com/question/29241065
#SPJ1
A certain disease has an incidence rate of 0.2%. If the false negative rate is 8% and the false positive rate is
1%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places
According to the solving the probability will be 0.159.
What is probability?The area of mathematics known as probability deals with numerical assessments of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
In statistics, what exactly is a probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed in percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.
According to the given data:The incidence rate is = 0.2% or 0.002
The false negative rate is = 8% or 0.008
The false positive rate is = 1% or 0.001
The probability is
0.01*(1-0.002) + 0.95*0.002
= 0.00998 + 0.0019 = 0.01188
Probability that a person who tests positive actually has the disease would be represented as:
Let the probability be represented by = p
p * 0.01188 = 0.95 * 0.002
p = 0.0019/0.01188
p = 0.159
Hence, probability is 0.159
According to the solving the probability will be 0.159.
To know more about probability visit:
https://brainly.com/question/11530879
#SPJ1
What is the equation in slope-intercept form of the line that passes through the point (2, -1) and is perpendicular to the line represented by y=x+4?
y=32-4
y=3x+4
y=-32-2
y=-3x+2
The slope-intercept form is
y = - x + 1
Given points are (2, - 1)
and y = x + 4
The product of slopes of perpendicular lines is - 1
so , m = - 1/1 = -1
y = mx + b-1 = (-1) (2) + b -1 = -2 + b-1 + 2 = b b = 1∴ y = -1 (x) + b
y = - x + 1
Learn more about Slop -intercept form at
brainly.com/question/25024332
Solve 2x-7 = 3x-2(x+8) for x
Answer:
x = -11
Step-by-step explanation:
2x - 7 = 3x - 2x - 18
2x - 7 = x - 18
collect like terms
2x - x = 7 - 18
x = -11
←
Suppose a bunny farm initally has 20 bunnies. After 2 years the population grew to 80 bunnies.
A) Find f(T)=mT+b, where f(T) is the bunny population after every 2 months. Answers must be in Exact Form, Round 3 decimals, and Change of Base
B) What is the bunny population after 16 weeks?
C) How many months will it take for the bunny population to reach 300 bunnies? Answers must be in Exact Form, Round 3 decimals, and Change of Base
A) The bunny population after every 2 months is f(T)=5T+20
B) The bunny population after 16 weeks is x=29.205
C) The number of months that the bunny population to reach 300 bunnies is 112 months.
What is meant by population?All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.
Given,
0 months -------- 20 bunnies
2 years ------- 80 bunnies
In two years, bunnies are increased by,
=80-20
=60
2 years ------>60
1 year ------>30
A) f(T)=mT + b
1 year -----> 12 months -----> 30 bunnies
12/6 months ------>30/6 bunnies
2 months -----> 5 bunnies
f(T)= initial population+ increased population in two months
f(T)=20+5
f(T)==25
f(T)= 2.5T+20
f(T)=5T+20
Where T =time in months
B) For 10 years ------> 10 bunnies
52 weeks -------->30 bunnies
16 weeks ------?
x=(16*30)/52
x=29.205
C) 1 month -------> 2.5 bunnies
? ---------------->280 bunnies
x=280/2.5
x=112 months
To know more about population, visit:
https://brainly.com/question/27991860
#SPJ1
Answer:
A) The bunny population after every 2 months is f(T)=5T+20
B) The bunny population after 16 weeks is x=29.205
C) The number of months that the bunny population to reach 300 bunnies is 112 months.
What is meant by population?
All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.
Given,
0 months -------- 20 bunnies
2 years ------- 80 bunnies
In two years, bunnies are increased by,
=80-20
=60
2 years ------>60
1 year ------>30
A) f(T)=mT + b
1 year -----> 12 months -----> 30 bunnies
12/6 months ------>30/6 bunnies
2 months -----> 5 bunnies
f(T)= initial population+ increased population in two months
f(T)=20+5
f(T)==25
f(T)= 2.5T+20
f(T)=5T+20
Where T =time in months
B) For 10 years ------> 10 bunnies
52 weeks -------->30 bunnies
16 weeks ------?
x=(16*30)/52
x=29.205
C) 1 month -------> 2.5 bunnies
? ---------------->280 bunnies
x=280/2.5
x=112 months
In Alex's drawer she has 10 pairs of socks, 8 of which are white, and 9 tee shirts, 2 of which are white.
The probability of choosing a white pair of socks is
The probability of choosing a white tee shirt is
The probability of both being white is
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total socks= 10
White socks= 8
Total T- shirts= 9
White T- shirts = 2
Now, The probability of choosing a white pair of socks is
= 8/10
= 4/5
and, The probability of choosing a white tee shirt is
= 2/9
and, The probability of both being white is
= 4/5 x 2/9
= 8/45
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ1
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 220 numerical entries from the file and r = 52 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.
(i) Test the claim that p is less than 0.301. Use = 0.05.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p < 0.301; H1: p = 0.301
H0: p = 0.301; H1: p ≠ 0.301
H0: p = 0.301; H1: p > 0.301
H0: p = 0.301; H1: p < 0.301
Correct: Your answer is correct.
(b) What sampling distribution will you use?
The Student's t, since np > 5 and nq > 5.
The standard normal, since np > 5 and nq > 5.
The Student's t, since np < 5 and nq < 5.
The standard normal, since np < 5 and nq < 5.
Correct: Your answer is correct.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
The hypothesis are given as follows:
H0: p = 0.301; H1: p ≠ 0.301.
a) The level of significance is of 0.05.
b) The sampling distribution is given by: The standard normal, since np > 5 and nq > 5.
The test statistic is of: z = -2.09.
c) The p-value is of: 0.0366.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence to conclude that the proportion has changed, hence:
[tex]H_0: p = 0.301[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion has changed, hence:
[tex]H_1: p \neq 0.301[/tex]
What is the test statistic?The test statistic is given by the equation presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
The parameters of the equation are listed as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters for this test are:
[tex]\overline{p} = \frac{52}{220} = 0.2364, p = 0.301, n = 220[/tex]
Hence the value of the test statistic is of:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.2364 - 0.301}{\sqrt{\frac{0.301(0.699)}{220}}}[/tex]
z = -2.09.
What is the p-value?We have a two-tailed test, as we are testing if the proportion is different of a value.
Hence, using a z-distribution calculator, with z = -2.09, the p-value is of 0.0366.
More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
#SPJ1
sin cos tan
( )
0
7
ans
Submit Question
I
+
One side of a rectangle is 24 m longer than four times another side. Find the length of the sides, given that
the area of the rectangle is 1408 m². Enter both sides, separated by a comma.
Length of the sides:
Question Help: D Post to forum
1
m
Length= 80 and width = 16 cm in the rectangle .
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.let side = x cm
= x( 24 + 4x) = 1408
= 24x + 4x² = 1408
⇒ 4x² + 24x - 1408 = 0
4 ( x² + 6x - 352 ) = 0
x² + 6x - 352 = 0
x² + 22x - 16x - 352 = 0
x( x + 22 ) - 16 ( x + 22) = 0
( x - 16 ) ( x + 22 ) = 0
x= 16 , -22
we take x = 16 because distance never be negative
length = 16 + 4 * 16 = 80 cm
width = 16 cm
Learn more about rectangle.
brainly.com/question/15019502
#SPJ13
4.
Consider the following diagram:
What is the value of m?
56°
m
68°
According to the solving the Angle m = 124
What is the name for a straight angle?An angle with something like a vertex point at 180 degrees is considered to be a straight angle in geometry. Basically, it produces a straight line with sides that are turned away from the vertex. "Flat angles" is another term for it.
How do you see a straight angle?A straight line appears to have a straight angle. Here's an illustration of a straight angle. a straight line that has a half circle in the middle and at the top to symbolize a straight angle.
According to the given data:The sum of all angles in triangle = 180.
Angle A = 56
Angle B = 68
Angle C =
A + B + C = 180
56 + 68 + C = 180
124 + C = 180
C = 180 - 124
C = 56
if Angle C = 56
so we know the property of straight angle:
= Angle m + 56 = 180
Angle m = 180 - 56
Angle m = 124
According to the solving the Angle m = 124
To know more about straight angle visit:
https://brainly.com/question/9662298
#SPJ1
SOMEONE PLEASE HELP!
I WILL GIVE BRAINLIEST TO THE FIRST CORRECT ANSWER!! Just Need Help!!!
Represent the following expressions as a power of the number a where a ≠ 0: (a^3)^-2. PLEASE ANSWER I WILL GIVE BRAINLYEST
Answer:
a^-6 or 1/a^6
Step-by-step explanation:
(a³)-²
=a^-6
=1/a^6
HELP PLEASE QUICKLY!!!!
The expression that shows the result of applying the distributive property is 21y - 7/11 (option D).
What is the expression?The distributive property states that an expression that has this form a(b + c) can be solved as a x (b + c) which becomes ab + ac.
Thus, to solve an expression using the distributive property, multiply the term in the brackets by the term outside the brackets. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is x.
7(3y - 1/11)
= 7 x (3y - 1/11)
= 21y - 7/11
To learn more about the distributive property, please check: https://brainly.com/question/6276874
#SPJ1
Please help me verify. I am stuck.
The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.
Proving the identityThe identity is presented as follows:
[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]
Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:
[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]
The following identity relates the square of the secant and of the tangent:
[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]
Hence:
[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]
Thus the remaining expression is:
[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]
The equations of the cotangent, secant and tangent are given as follows:
Cotangent: cosine/sine.Secant: 1/cosine.Tangent: sine/cosine.Hence:
[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]
One divided by the sine is the cosecant, as follows:
[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]
Hence the simplified expression is:
[tex]\csc{\beta} + 1[/tex]
Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.
More can be learned about trigonometric identities at https://brainly.com/question/7331447
#SPJ1
kind of suck help please ? brianslest
Answer:
[tex]d=7[/tex]
[tex]a_9=59[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]3[/tex] and the second term is [tex]10[/tex], then each successive term in the sequence is [tex]7[/tex] more than the previous term. The common difference is [tex]7[/tex] ( [tex]d=7[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=7n-4[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=7(9)-4[/tex]
[tex]a_9=63-4[/tex]
[tex]a_9=59[/tex]
Daniel has invested $300 in an annuity each month, earning 4% interest for 20 years.
Sarah has invested $150 in an annuity each month, earning 4% interest for 40 years.
Which of the following must be true?
Answer: daniel and sarah will deposit the same amount
The table below shows a proportional relationship between h and j.
h
18
27
48
j
6
9
16
Find the constant of proportionality from h to j. Express
your answer as a fraction in reduced terms.
As per the proportional relationship, the constant of the proportionality is 1/3
Proportional relationship
A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.
The standard form of proportional relationship is written as.
y = k x
where k refers the constant of proportionality.
Given,
The table shows the proportional relationship between h and j.
Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.
We know that the standard form of the proportionality is written as,
y = k x
So, here y takes the value of j and x takes the values of h.
Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,
=> 6 = k (18)
Here we need the value of k, so move the number to the other side then we get,
=> k = 6/18
When we reduce this, then we get,
=> k = 1/3
Therefore, the constant of proportionality is 1/3.
To know more about Proportional relationship here.
https://brainly.com/question/7096655
#SPJ1
Tim needs 6 lb of a metal that contains 54 % silver. If Tim combines one metal with 29%
silver, and another with 80 % silver, how much of each metal does Tim need?
After solving the Algebraic expression we gets Tim needs 3.05 lbs. and 2.95 lbs. Metal.
What is algebra ?Algebraic expressions are constructed using integer constants, variables, and the addition, subtraction, multiplication, and division operations of basic arithmetic.
To form the Algebraic expression
Let x be the quantity of silver at 29% and y the quantity at 80%
Then x*28% + y*61% = 6*54%
and x + y = 6
Let y = 6-x then
29*x + (6-x)*80= 324
29*x + 480- 80*x = 324
51*x = 156 and x = 156/51 = 3.05 lbs.
so y = 6 - x = 2.95 lbs.
Hence,
Tim needs 3.05 lbs. and 2.95 lbs. Metal.
To learn more about Algebraic expression refer,
https://brainly.com/question/2164351
#SPJ13