Watch help videoIan is working two summer jobs, making $19 per hour lifeguarding and making $9per hour clearing tables. In a given week, he can work no more than 14 total hoursand must earn a minimum of $180. If e represents the number of hours lifeguardingand y represents the number of hours clearing tables, write and solve a system ofinequalities graphically and determine one possible solutionInequality 1: y zInequality 2; y 2
Answers
Given:
Amount he earns lifeguarding = $19 per hour
Amount he earns clearing table = $9 per hour
Maximum amount of hours he can work in a week = 14 hours.
This is expressed as: e + y ≤ 14
Minimum amount he must earn = $180.
This is expressed as: 19e + 9y ≥ 180
Let e represent the number of hours lifeguarding
Let y represent the number hours clearing tables.
We have the system of inequaties:
19e + 9y ≥ 180......................inequality 1
e + y ≤ 14................................inequality 2
Let's solve for y using substitution method.
Subtract y from both sides in inequality 1:
e + y - y ≤ 14 - y
e ≤ 14 - y
Substitute (14 - y) for e in inequality 1:
19(14 - y) + 9y ≥ 180
266 - 19y + 9y ≥ 180
266 - 10y ≥ 180
Subtract 266 from both sides:
266 - 266 - 10y ≥ 180 - 266
-10y ≥ -86
Divide both sides by -10:
\(\frac{-10y}{-10}\ge\frac{-86}{-10}\)Solving further:
\(y\le8.6\)Therefore, the number of hours Ian must use in clearing the tables should be no more than 8.6 hours
To solve for e, substitute 8.6 for y in either of the inequalities.
Substitute 8.6 for y in inequality 2:
The graph of the inequalities is below:
e + y ≤ 14
e + 8.6
Related Questions
Which type of data would be BEST displayed in a dot plot?
Answers
Answer:
Fourth Option
Step-by-step explanation:
The graph shows the distance (d) in miles that an animal runs at a constant speed in (t) minutes. Which equation represents this situation.
Answers
. Where is the vertex of the graph that represents y=(x−2)2−8 ? Type the answers in the boxes below. ( , ) b. Where is the y -intercept? Type the answers in the boxes below.
Answers
The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
Given equation :
y=(x−2)2−8
y = 2x - 4 - 8
= 2x - 12
The final equation is y = 2x - 12.
Compare this equation with slope and y-intercept formula :
y = mx+c
So that c = -12
The value of y-intercept according to the solution is -12.
To find the vertex. Let's assume x=0; Substitute in the equation
y = 2(0) -12
y = -12
The first vertex will be (0, -12)
If x = 1; y = 2(1) -12
y = -10
Then the second vertex will be (1, -10).
Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
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There are 20 circles and 12 triangles. What is the simplest ratio of triangles to total shapes
Answers
Answer:
3:8
Step-by-step explanation:
You can divide both numbers by 4, that gets you to your simplest ratio. :)
The ratio of the triangles to the total shape will be equal to 3: 8.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.
For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.
Given that there are 20 circles and 12 triangles. The ratio will be calculated as,
Ratio = triangles / total shape
Ratio = 12 / ( 20+ 12 )
Ratio = 12 / 32
Ratio = 3 / 8
Therefore, the ratio of the triangles to the total shape will be equal to 3: 8.
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Translate the sentence into an equation.
The square of a number is equal to the square root of that number.
Answers
The equation of the sentence, the square of a number is equal to the square root of that number, is \(x^{2} =\sqrt{x}\).
According to the question,
We have the following information:
The square of a number is equal to the square root of that number.
Now, let's take this number to be x.
Now, square of this number will be \(x^{2}\) and the square root of this number will be \(\sqrt{x}\).
Now, according to the sentence, we will have the following expression:
\(x^{2} =\sqrt{x}\)
Hence, the equation of the sentence, the square of a number is equal to the square root of that number, is \(x^{2} =\sqrt{x}\).
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y=x^2-2x+7
i need help finding the axis of symmetry,the domain, the y-intercept and x intercept
Answers
The axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .
Explain about the features of parabolic function?A parabolic function is one that satisfies the formula f(x) = ax2 + bx + c and, when represented graphically in two dimensions, has the shape of a parabola. Any quadratic equation with just a second degree in x is the equation for a parabolic function.
The following characteristics define a basic parabola:
The y-axis, a symmetry axis, is where it is symmetric.At the origin, marking the minimal turning point, y has its minimum value. It is sometimes referred to as the parabola's vertex.The parabola's arms are infinitely long.Thus, from the given graph the value are obtained as:
the axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .Know more about parabolic function
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The Laurier Company’s brand has a market share of 30%. Suppose that 1,000 consumers of the product are asked in a survey which brand they prefer. What is the probability that more than 32% of the respondents say they prefer the Laurier brand?
Answers
Answer:
The probability is
\(P(Z>1.3793 ) = 0.083901\)
Step-by-step explanation:
From the question we are told that
The proportion proportion is \(p = 0.30\)
The sample size is \(n = 1000\)
The sample proportion \(\r p = 0.32\)
Generally the standard error is mathematically represented as
\(SE = \sqrt{\frac{p (1 - p)}{ n} }\)
\(SE = \sqrt{\frac{ 0.30 (1 - 0.30 )}{ 1000} }\)
\(SE = 0.0145\)
The probability that more than 32% of the respondents say they prefer the Laurier brand is mathematically represented as
\(P(X > 0.32 ) = P( \frac{X - p }{ SE} > \frac{\r p - p }{ SE} )\)
Here \(\frac{X - p }{SE} = Z (the \ standardized \ value \ of \ X)\)
\(P(X > 0.32 ) = P(Z>1.3793 )\)
From the z -table \(P(X > 0.32 ) = P(Z>1.3793 ) = 0.083901\)
\(P(Z>1.3793 ) = 0.083901\)
Using the normal distribution and the central limit theorem, it is found that there is a 0.0838 = 8.38% probability that more than 32% of the respondents say they prefer the Laurier brand.
In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample proportions of a proportion p in a sample of size n has mean \(\mu = p\) and standard error \(s = \sqrt{\frac{p(1 - p)}{n}}\).In this problem:
The Laurier Company’s brand has a market share of 30%, hence \(p = 0.3\)1,000 consumers are asked, hence \(n = 1000\).Then, the mean and the standard error are given by:
\(\mu = p = 0.3\)
\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.3(0.7)}{1000}} = 0.0145\)
The probability that more than 32% of the respondents say they prefer the Laurier brand is 1 subtracted by the p-value of Z when X = 0.32, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.32 - 0.3}{0.0145}\)
\(Z = 1.38\)
\(Z = 1.38\) has a p-value of 0.9162.
1 - 0.9162 = 0.0838
0.0838 = 8.38% probability that more than 32% of the respondents say they prefer the Laurier brand.
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Based on an indication that mean daily car rental rates may be higher for Boston than for Dallas, a survey of eight car rental companies in Boston is taken and the sample mean car rental rate is $47, with a standard deviation of $3. Further, suppose a survey of nine car rental companies in Dallas results in a sample mean of $44 and a standard deviation of $3. Use alpha = 0.05 to test to determine whether the average daily car rental rates in Boston are significantly higher than those in Dallas. Assume car rental rates are normally distributed and the population variances are equal. The null hypothesis for this problem is ______.
a) μ1 - μ2 < 0
b) μ1 - μ2 > 0
c) μ1 - μ2 = 1
d) μ1 - μ2 ≠ 0
e) μ1 - μ2 = 0
Answers
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean daily car rental rates for Boston and μ2 be the mean daily car rental rates for Dallas.
The random variable is μ1 - μ2 = difference in the mean daily car rental rates for Boston and the mean daily car rental rates for Dallas
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 0
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
μ1 = 47
μ2 = 44
s1 = 3
s2 = 3
n1 = 8
n2 = 9
t = (47 - 44)/√(3²/8 + 3²/9)
t = 1.41
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [3²/8 + 3²/9]²/[(1/8 - 1)(3²/8)² + (1/9 - 1)(3²/9)²] = 4.515625/0.28571428571
df = 16
We would determine the probability value from the t test calculator. It becomes
p value = 0.09
Since alpha, 0.05 < than the p value, 0.09, then we would fail to reject the null hypothesis.
A sample of 36 observations is selected from a normal population. The sample mean is 49, and the population standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level.
H0: ? = 50
H1: ? = 50
What is the value of the test statistic?
What is the p-value?
A recent national survey found that high school students watched an average (mean) of 6.5 DVDs per month with a population standard deviation of 0.60 hour. The distribution of DVDs watched per month follows the normal distribution. A random sample of 33 college students revealed that the mean number of DVDs watched last month was 5.80. At the 0.05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?
What is the p-value?
Answers
Answer:
A) p = 0.230139
B) p = 0 .00001
There is not enough evidence to show that fewer DVDs a month than high school students
Step-by-step explanation:
A) The correct hypothesis are;
Null hypothesis;H0: μ = 50
Alternative hypothesis;H1: μ ≠ 50
We are given;
Sample mean; x' = 49
Standard deviation; σ = 5
Sample size;n = 36
Formula for the test statistic is given by;
z = (x' - μ)/(σ/√n)
z = (49 - 50)/(5/√36)
z = -1.2
So, from online p-value calculator from z-values as attached, using z-score of -1.2, significance level of 0.05, two tailed, we have;
p = 0.230139
B) we are given ;
x = 5.80
μ = 6.5
n = 33
Standard deviation;σ = 0.6
Significance level = 0.05
Hypotheses are;
Null hypothesis;H0: μ = 6.5
Alternative hypothesis; μ < 6.5
So, formula for the test statistic again;
z = (x' - μ)/(σ/√n)
z = (5.8 - 6.5)/(0.6/√33)
z = -6.7
from online p-value calculator z-values as attached, using z-score of -6.7, significance level of 0.05, one tailed tailed, we have;
p = 0 .00001
This is less than the significance level of 0.05, thus we will reject the null hypothesis and conclude that there is no evidence to show that fewer DVDs a month than high school students
-2x (-3x²y)(2y) = _______.
Answers
Answer:
12x³y²
Step-by-step explanation:
You want the product -2x (-3x²y)(2y).
ExponentAn exponent is a means of telling the number of times the base is a factor in a product. For example, the exponent 2 means the base is a factor twice in the product:
x² = x·x
ApplicationWhen the same factor appears a number of times in a product, an exponent can be used to represent that number.
(-2x)(-3x²y)(2y) = (-2)(-3)(2)(x·x²)(y·y)
The factor x appears 3 times in the product, and the factor y appears twice. The numerical product can be simplified, so the result is ...
12x³y²
find a polynomial function with the leading coefficient one or negative 1 that has the given zeros multiplicity and degrees 01 multiplicity to 03 multiplicity to degree 4
Answers
The function is negative for since the leading coefficient is positive and the highest degree is odd (9) (-inf, -6).
Find a polynomial function ?The function is negative for since the leading coefficient is positive and the highest degree is odd (9) (-inf, -6).
It then crosses the -6 root to turn positive until it again crosses the -2 root.
(It crosses because the odd multiplicity of both roots)
The function remains negative from -2 until root 4, where it crosses into the positive, where it does not cross since there is an even multiplicity.
In light of the aforementioned, only the first option makes sense. because the leading coefficient is positive and the highest degree is odd (9) the function is negative for (-inf, -6).
Then it crosses the -6 root to become positive until it crosses again the root -2.
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Samantha has a shelf that is 95 over 4 inches wide. How many books can Samantha arrange on the shelf if each book is 5 over 4 inches thick? Work it out.
Answers
Answer:
19 books
Step-by-step explanation:
95/4÷5/4=19bks
Solve the inequality 2x+3 < 7
Answers
Answer:
x < 2
Step-by-step explanation:
2x + 3 < 7
2x < 4
x < 2
Answer:
x<2
Step-by-step explanation:
2x<7−3
2x<4
x<4/2
x<2
a tree measured 12 1/2 feet tall. over the next 5 1/2 years it grew to be 51 feet left. During 5 1/2 years, what was the average yearly growth rate of the tree?
Answers
Answer:
7 feet per yearStep-by-step explanation:
Average growth rate is the difference in growth over the period of the time:
(51 - 12 1/2) ÷ 5 1/2 = (102 - 25)/2 ÷ 11/2 = 77/2 × 2/11 = 7 feet / yearfind the area of a rectangle with a length of 10 inches and a width of 4 inches
Answers
Answer:
40 in²---------------------
Formula for area of a rectangle with dimensions l and w is:
A = lwSubstitute 10 for l and 4 for w:
A = 10*4A = 40 in²9. CONSTRUCT AN ARGUMENT Determine
if the following statement is true or false.
Construct an argument to defend your
response.
Proportions can only be used to solve
problems where the smaller values are
known and a larger value is unknown.
Answers
Answer:
Step-by-step explanation:
The correct answer is true. If you know that the relationship between quantities is proportional, you can use proportions to find missing quantities.
100 points please help
Factor 36x2 + 60x + 25.
(6 x + 5) 2
(12 x + 5)(3 x + 5)
(6 x + 5)(6 x - 5)
Answers
SOMEONE PLEASE ANSER THIS QUESTION ASAP!!!
Answers
Answer: 28
Step-by-step explanation:
Complete the table for the given rule.
Rule: y is 1 less than 2 times x
Answers
According to the rule, the table is:
x|y
2|3
3|5
4|7
The translation of the rule to a math expression is:
\(y = 2x - 1\)
Then, for x = 2:
\(y = 2(2) - 1 = 4 - 1 = 3\)
For x = 3:
\(y = 2(3) - 1 = 6 - 1 = 5\)
For x = 4:
\(y = 2(4) - 1 = 8 - 1 = 7\)
Thus, the table is:
x|y
2|3
3|5
4|7
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Selling Price = $ 504 and Gain % = 12%
Answers
Answer:
Step-by-step explanation:
sp = 504
gain = 12%
in this case
sp =100%+12%=504
112%=504
1%=504/112 =4.5
100%=450
so cost =$450
Hope im correct, if i am im glad to be of service.
What is the value of 8.3 x 10^4
Answers
Answer:
B) 83,000 or eighty-three thousand
Step-by-step explanation:
First of all, 10^4 is the same as 10 × 10 × 10 × 10, which equals 10,000. So now 8.3 × 10,000 = 83,000 .
Hope this helps :)
The probability line shows the probability of 5 chance events (A, B, C, D, and E) occurring. Which THREE statements BEST describe the likelihood of the event occurring?
A) Event A is certain to occur.
B) Event E is certain to occur.
C) Event D is certain to occur.
D) Event B is not likely to occur.
E) Event C has an even chance of either occurring or not occurring.
Answers
Answer:
The answer is:
B) Event E is certain to occur.
D) Event B is not likely to occur.
E) Event C has an even chance of either
Step-by-step explanation:
Event E is certain to occur. Event B is not likely to occur and Event C has an even chance of either occurring or not occurring so options (B),(D), and (E) are correct.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin, the probability of coming head and tail is nothing but the chance that either head will appear.
As per the given probability line.
The probability of event E = 1 so it will be certain to occur.
The probability of event B is very close to zero so it will not likely occur.
The probability of event C is 0.5 so it has an equal chance to occur or not.
Hence "Event E will definitely happen. Event C has an equal chance of happening or not, but Event B is not likely to happen".
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The full question below,
A skating rink charges a group rate of $8 plus a fee to rent each pair of skates. A family rents 5 pairs of skates and pays a total of $28.
Answers
Answer:
the fee for the skates is 4$ ea
Step-by-step explanation:
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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salesperson earns $345 for selling $2300 in merchendice find the commison rate
Answers
Answer:
The commission rate is 15%
Step-by-step explanation:
commission = commission rate x sales
where the commission rate is expressed as a decimal.
In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:
345 = commission rate x 2300
To solve for the commission rate, we can divide both sides by 2300:
commission rate = 345/2300
Simplifying this expression, we get:
commission rate = 0.15
So, the commission rate is 15%
On a test that has a normal distribution, a score of 29 falls three standard deviations above the mean, and a score of 23 falls one standard deviation above the mean. Determine the mean of this test.
Answers
The mean of the test is 20.
To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.
Let's denote the mean of the test as μ, and the standard deviation as σ.
We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:
29 = μ + 3σ
Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:
23 = μ + σ
Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.
From the second equation, we can isolate μ:
μ = 23 - σ
Substituting this value into the first equation, we have:
29 = (23 - σ) + 3σ
Simplifying the equation, we get:
29 = 23 + 2σ
2σ = 29 - 23
2σ = 6
σ = 3
Substituting the value of σ back into the second equation, we find:
μ = 23 - 3
μ = 20
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help huryyyyyyyyyyyyy
Answers
Answer: 4
Step-by-step explanation:
Because %s can be expressed as fractions over 100, because 90 is 70% of x, 70% is 70% of 100. Thus, 90/x = 70/100.
Hope it helps <3
Answer:
4
Step-by-step explanation:
90 is 70% of x.
90 = 70% × x
90 = 70/100x
Divide both sides by x.
90/x = 70/100
Simplify using the order of operations. 2+6*8=
Answers
Answer:
The answer is 50.
Step-by-step explanation:
Use MDAS
Multiplication, Division, Addition and Subtraction
2 + 6 * 8 =
Multiply first then add
2 + 6*8 = ?
= 2 + 48
= 50
PLS HELP WITH BOTH ASAP WILL GIVE BRAINLIEST
Answers
Answer:
13) 25 and 17
14) cupcakes = $5
brownies = $3
Step-by-step explanation:
13) you can set this up as equations
so x + y = 42
x-y = 8
solve simultaneously by subtracting from each other
2y = 34
y= 17
if y = 17
42 - 17 = 25 = x
14) set up as equations again
Ben 7c + 10b = 65
franklin 7c +7b = 56
subtract from eachother
3b = 9
b = $3
7c + 10(3) = 65
7c = 35
c = $5
Answer:
First question = 2&8
Second question = Cupcakes 6.5 Brownies 8
Step-by-step explanation:
There are 9 players on a youth baseball team. To create the lineup, the coach chooses three players to play pitcher, catcher, and first base. How many ways can the coach choose these three positions?
Answers
Step-by-step explanation:
how many ways can the coach make out the batting order? 9! = 9 · 8 · 7 · 6 · 5 ·4 · 3 · 2 · 1 = 362,880 .