The function that could be used to represent the total cost of the shoes by applying the $15 coupon first and the 20% member discount second for original cost, using proportions, is of:
C(x) = 0.8(x - 15).
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially division and multiplication, to find the desired amounts in whichever context of the problem.
The value of shoe is given as follows:
x.
The discounts are given as follows:
$15 off coupon: x - 15.20% member discount: 0.8(x - 15) -> as the discount of 20% means that 80% of the original price will be paid.Hence the function that gives the total cost paid is presented as follows:
C(x) = 0.8(x - 15).
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Assume that a simple random sample has been selected from a normally distributed
population. Find the test statistic t.
A local newspaper reported that for the adult population of a town, the mean annual salary is $30,000.
Test the claim that for the adult population of this town, the mean annual salary is greater than
$30,000. Sample data are summarized as n = 17, sample mean = $22,298, and s = $14,200. Use a
significance level of alpha = 0.05.
Find the test statistic t.
a) -2.24
b) -1.57
c) 1.57
d) 2.24
e) 0.05
The test statistic when the a simple random sample has been selected from a normally distributed population is a) -2.24
What is test statistic?The test statistic is a number derived from a statistical test that is used to determine whether your data could have occurred under the null hypothesis.
u = 30000
x = 22298
s = 14200
n = 17
Test statistic = = (x - u) / s / ✓n
x = mean
u = theoretical value
s = standard deviation
{n} = variable set size
= (x - u) / s / ✓n
= (22298 - 30000) / 14200 / ✓17
= -2.24
Test statistic = -2.24
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A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 1700 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
Let (7, -4) be a point on the terminal side of 0. Find the exact values of sin0, escO, and cott.
The exact values of the trigonometric functions of the ordered pair are listed below:
sin θ = - 4√65 / 65 sec θ = √65 / 7 cot θ = - 7 / 4What are the exact values of three trigonometric functions associated with an ordered pair?In this problem we find an ordered pair in rectangular form (x, y) that the represents the terminal side of angle θ and from which we must determine the exact values of the sine, secant and cotangent. The definitions for each of the three functions are:
sin θ = y / √(x² + y²)
sec θ = √(x² + y²) / x
cot θ = x / y
If we know that x = 7 and y = - 4, then the exact values of the trigonometric functions are, respectively:
sin θ = (- 4) / √[7² + (- 4)²]
sin θ = - 4√65 / 65
sec θ = √[7² + (- 4)²] / 7
sec θ = √65 / 7
cot θ = 7 / (- 4)
cot θ = - 7 / 4
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Big Drop is twice as long as Little Drop. How long is Little Drop?
Answer:
Half as big as little drop?
Step-by-step explanation:
if you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long, how much string do you still have?
If you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long, Then 16.875 is the remaining string.
What is Fraction?A fraction represents a part of a whole.
1 foot =12 inches
2 foot=24 inches.
Given,
if you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long.
Then how much string do you still have
We have to subtract the used strings from 24 inches string.
4 3/4 inches=19/4
2 3/8 inches=19/8
Now we have to subtract 19/4 and 19/8 from 24 inches.
24-19/4-19/8
24-4.75-2.375
16.875
Hence 16.875 is the string left with us.
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Find the value of x.
f(x)= (1/3)x + 5
Has the output value of -15
Answer:
-60
Step-by-step explanation:
-15 = 1/3x + 5 Multiply all the way through by 3
-45 = x + 15 Subtract 15 from both sides of the equation
-60 = x
Answer: -60 = x
Step-by-step explanation:
If the output value is -15, we need to do this equation.
-15 = (1/3)x + 5.
-5 -5
-20 = (1/3)x
x3 x 3
-60 = x.
Now, let's double-check our answer.
f(60) = (1/3)(-60) + 5
f(-60) = -20 + 5
f(-60) = -15.
This means that x = -60 is our correct answer.
What is the image point of (2, −6) after the transformation R270° ○ D1/2?
The image point of (2, −6) after the transformation R270° is (4,3).
Given:
(2,-6) and R270° and (1,2)
Let (x,y) be the point
First translation (1,2)
(x,y) → (x+1,y+2)
Translation of R270° for translated coordinates
(x+1,y+2) → (-(y+2),x+1)
substitute (2,-6)
= (-(-6+2),2+1)
= (-(-4),3)
= (4,3)
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Order these numbers from least to greatest 5.96 5 2/9 5.961 21/4
The numbers from least to greatest is arranged as 5 2/9 < 21/4 < 5.96 < 5.961
Arranging the Number in Ascending OrderTo solve this problem, we have to arrange the numbers in an ascending order from the least to the greatest. To do this, we can convert all numbers to whole numbers or fractions to decimal form to make it easier.
convert 5 2/9 to decimal = 5.222
convert 21/4 = 5.25
Let's arrange the number in ascending order
5.22 < 5. 25 < 5.96 < 5.961
The numbers can be arranged from least to greatest using a number line.
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The wholesale price for a pair of shoes is $4.50. A certain department store marks up the wholesale price by 50%. Find the price of the pair of shoes in the
department store.
Round your answer to the nearest cent, as necessary.
The price of the pair of shoes in the department store is $7.
The wholesale price for a pair of shoes is $4.50. A certain department store marks up the wholesale price by 50%.
To find out the price of the pair of shoes in the department store:
The price of the pair of shoes in the department store: $7
Given the wholesale price of pair of shoes is $4.50
Department store of wholesale price is 50%
Than whole sale = 1.5 times the whole sale
Price in department store = 1.5*4.5
= $6.75
Rounded to the nearest cent = $7
Hence the answer is the price of the pair of shoes in the department store is $7.
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solve and graph X + 6 > -1
Answer: x > -7, see attached
Step-by-step explanation:
Given:
x + 6 > -1
Subtract 6 from both sides of the equation:
x > -7
Graph, see attached. We will graph x = -7, and shade to the right.
PLEASE HELP ASAP! 2 QUESTIONS
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 80.4° is added to the data, how does the range change?
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 60° is added to the data, how does the median change?
If a value of 80.4° is added to the data, the range does not change.
The range is 48.
If a value of 60° is added to the data, the median change.
The median was 79.5.
The change median is 77.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
The range formula = Highest value - Lowest value
Now,
Highest value = 105
Lowest value = 57
Range = 105 - 57 = 48.
Now,
If the value of 80.4 is added the range remains the same because the range is dependent only on the value of the highest and the lowest value.
We have,
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
The median is the mid value of the given set of data after arranging in ascending order.
Arranging the set in ascending order.
57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
There are 12 elements in the set.
Median = (77 + 82) / 2 = 79.5
If 60 is added we get 13 elements in the set.
The arrangement becomes,
57, 58, 60, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
Median = 77
Thus,
If a value of 80.4° is added to the data, the range does not change.
The range is 48.
If a value of 60° is added to the data, the median change.
The median was 79.5.
The change median is 77.
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Think about
A model of a house was built using the scale 5 in:25 ft. If a window in the
model is 1.5 in. wide, how wide is the actual window?
If a window in the model is 1.5 in. wide, then the actual window is 7.5 feet wide.
What is meant by unit ratio?A two-term ratio expressed with a second term of one is referred to as a unit ratio. A unit ratio can be created from any ratio. Example. An illustration of a set of marbles is shown below. The set has eight blue marbles and two red marbles.
Having a denominator of 1, a unit rate is a ratio between two separate units. Divide the numerator by the denominator to obtain the unit rate. The unit rate is the decimal number that results. The price of a good or service is the numerator of a ratio called the unit price, and the quantity is the denominator.
Given,
The scale of the Model =5 in: 25 ft.
Dividing both sides by 5 we get,
[tex]\frac{5in}{5}[/tex] :[tex]\frac{25ft}{5}[/tex]
1 inch:5 feet
If a window on the model is 1.5 inch wide, then from the unit ratio we get,
1 inch × 1.5 : 5 feet × 1.5 feet
1.5 Inch : 7.5 feet
As a result, a window that is 1.5 inches wide in the model will actually be 7.5 feet wide.
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what is the solution of the following system?
-3x-2y=-12
9x+6y=-9
(2,1)
no solution
(-2,-1)
infinitely many solution
Answer:
no solution
Step-by-step explanation:
If A=(x | x is an even integer), B=(x | x is an odd integer), C=(2, 3, 4, 5), and D=(13, 14, 15, 16), list the element(s) of the following set.
←
A ∩ D
A ∩ D= (Use a comma to separate elements in the set.)
Answer:
A ∩ D = { 14; 16 }======================
A ∩ D means intersection of the two sets or the common elements of A and D.
We observe that:
Set A has all even integers,Set B has even integers 14 and 16.It means the common elements of the two sets are 14 and 16:
A ∩ D = { 14; 16 }Answer:
A ∩ D = {14, 16}
Step-by-step explanation:
Given sets are,
→ A = {x | x is an even integer}
→ D = {13, 14, 15, 16}
Now we have to,
→ find required set of A ∩ D.
Then the answer will be,
→ A ∩ D = {2, 4, 6, 8, ... n} ∩ {13, 14, 15, 16}
→ A ∩ D = {14, 16}
Hence, the required set is {14, 16}.
Killer whale weight 16200 and calf weighs 1130 how many pounds greater is the mothers weight than the calf.
Answer: 15,070
Step-by-step explanation: subtraction 16200-1130=15,070
Alisha and Emily are making t-shirts for the Math team. they need a total of 21 shirts. Alisha has made 13 shirts and Emily made p shirts . Write a formula to model this
The formula to model the given situation is 13 + p = 21 .
In the question ,
it is given that ,
Alisha and Emily are making T- Shirts for the Math's team .
total number of T- Shirts required = 21 shirts .
number of shirts made by Alisha = 13 shirts
number of shirts made by Emily = p shirts
So , the equation that represents the given situation is
13 + p = 21
Solving further , we get
p = 21 - 13
p = 8
So , Emily made 8 T - Shirts .
Therefore , The formula to model the given situation is 13 + p = 21 .
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how many times smaller is 4 than 400?( Hint -4 does not have any zeros, 2-0=2.
Answer:
396
Step-by-step explanation:
400-4=396
Answer:
396
Step-by-step explanation:
The Old Farmer’s Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.
The probability that the mean of the sample is between 120 and 126 gallons is 0.4176
How to determine the probability that the mean is between 120 and 126 gallons?The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation
Given: population mean (µ) = 123, standard deviation(σ) =21 and number of sample (n) = 15
Let X represent the gallons of water: We want to find:
P(120 ≤ X ≤ 126)
Z-score(Z) = (X-µ) / (σ/√n)
Z₁ = (120-123)/ (21/√15) = -0.55
Z₂ = 126-123/ (21/√15)= 0.55
P(-0.55≤ Z ≤ 0.55) = = 0.7088 - 0.2912 = 0.4176
(Check the image of the table attached)
Therefore, the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons is 0.4176
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Given that M > N determine whether the inequality M/N > N/M always, sometimes, or never true.
if M > N then the inequality M/N > N/M will be always true
What is Linear Inequality?
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.
As in the question M is always greater N
So, is M is divided by a number that is less than M the answer will always be greater than 1
but on the other hand, if N is divided by a number greater than N then the answer will always be less than 1
Therefore, M/N > N/M will always be True
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Complete the statements below with the process used to achieve steps 1-4. Select the correct answer from each drop-down menu. Consider the equation below. -2(5x+8)=14+6x The equation was solved using the following steps.
The complete statements for solving the equation in the steps are:
1. Distribute -2 to 5x and 8
2. Subtract both sides by 6x
3. Add both sides by 16
4. Divide both sides by -16
How to Solve an Equation?Solving an equation involves finding the value of the variable in the equation that would make the it true. This is done by isolating the variable to one side of the expression to determine its value.
Given the equation, -2(5x + 8) = 14 + 6x, the following steps are taken to find the value of x in the expression:
Step 1: Distribute -2 to 5x and 8
10x + 16 = 14 + 6x
Step 2: Subtract both sides by 6x
-16x + 16 = 14
Step 3: Add both sides by 16
-16x = 30
Step 4: Divide both sides by -16
x = 30/-16
Simplify
x = -15/8
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A burst pipe fills a basement with 37 in. of water. A pump empties the water at a rate of 1.5 in./hr. The water level h, in inches, after t hours is represented by h = 37 - 1.5t. How long until the water is drained from the basement?
The time until the water is drained from the basement is 24.67 hours.
How to calculate the time?From the information, it was stated that the burst pipe fills a basement with 37 in. of water and a pump empties the water at a rate of 1.5 in./hr.
Also, the water level h, in inches, after t hours is represented by h = 37 - 1.5t. In this case, for the water to be drained, it'll be at zero. This will be illustrated as:
37 - 1.5t = 0
1.5t = -37
Divide.
t = 37 / 1.5
t = 24.67 hours.
The time is 24.67 hours.
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Jack has 32 quarters on his desk and Molly has q quarters in her purse
Answer:
32+q
Step-by-step explanation:
it doesn't ask for money
Use the Distributive property to express 18+24
The distributive property allows the expression 18 + 24 to be expressed as 6(3 + 4).
What is a distributive property?Most algebraic structures that include two operations, addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields, are defined in terms of this fundamental feature of numbers. The distributive property of binary operations generalizes the equality-proclaiming distributive law in mathematics. One of the axioms for rings and fields is that of the distributive laws. Boolean algebras like the algebra of sets or the switching algebra are examples of structures with two operations that are each distributive over the other.
We do the following to express using the distributive property:
Find the biggest common factor between the numbers 18 and 24.
18 = 1, 2, 3, 6, 9, 18
24 = 1, 2, 3, 4, 6, 8, 12, 24
6 is the most common value between the numbers 18 and 24, making it the most common factor
The values should be divided by 6 and expressed in the form a(b + c):
b = 18 /6 = 3
c = 24 / 6 = 4
6(3 + 4)
Consequently, the necessary expression is 6(3 + 4).
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Watch help video
What is the discriminant of the quadratic equation-2a2- 5x+7=0?
0-81
O 81
0-31
O 31
Submit Answer
The discriminant of the quadratic equation -2x²-5x+7=0 is 81 units when formula of discriminant is (b²-4ac).
What is the discriminant of the quadratic equation?Keeping in mind that a, b, and c are the coefficients of your quadratic in standard form, the discriminant is calculated using the formula b squared minus 4ac. It reveals how many possible answers there are to a quadratic equation. There are two solutions if the discriminant is greater than zero. The square root's argument (i.e., its contents), which is the expression b²-4ac, is known as the "discriminant" because using its value, you can "discriminate" between (i.e., be able to distinguish between) the different solution types.
Here,
-2x²-5x+7=0
discriminant=(b²-4ac)
=(-5)²-(4*-2*7)
=25+56
=81 units
When the discriminant formula is (b²-4ac), the discriminant of the quadratic equation (-2x²-5x+7=0) is 81 units.
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The size P of a certain insect population at time t (in days) obeys the function P(t) = 700e^0.04t
(a) Determine the number of insects at t = 0 days.
(b) What is the growth rate of the insect population?
(c) Graph the function using a graphing utility.
(d) What is the population after 10 days?
(e) When will the insect population reach 1190?
(f) When will the insect population double?
The number of insects at t=0 is 700, the growth rate is 28e^0.04, population of insects after 10 days is 1044, and the graph of the function is attached.
What is function?
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
a) Number of insects at time (t) = 0 days,
Putting t = 0 in given function:
P(t) = 700e^0.04(0) = 700e^0 = 700
Hence, the number of insects at t = 0 days is 700.
b) Growth rate of insect population,
In order to find growth we need to differentiate the given function with respect to t.
So, dP(t)/dt = 700(0.04)e^0.04(0)
= 28e^0.04
Hence, the growth rate is 28e^0.04.
c) Graph the function is attached in the question.
d) The population of the insects after 10 days,
putting t = 10,
= 700e^0.04(10) = 1044
Hence, population of insects after 10 days is 1044.
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Vocabulary How does a flow proof show
logical steps in the proof of a conditional
statement
Starting with the provided assertions, a flow proof arranges statements in a logical order.
Define the term flow proof?A mathematically formatted proof known as a "flow proof" uses logic to back up a truth assertion.
A proof will always be a series of assertions that ultimately to a conclusion in mathematics. One or more supplied statements are presented to start a proof. Until the intended conclusion is reached, the given statement is followed by subsequent statements. A chain of statements needs to be logically substantiated for each statement. The statements are verified by comparison to mathematical definitions, properties, and theorems.Thus, opening with the provided assertions, a flow proof arranges statements in a logical order. Arrows are being used to show the sequence of the assertions, and each assertion has its justification stated beneath it.
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Let y = tan(3x + 8). Find the differential dy when x = 4 and dx = 0.1 cbc homepage Find the differential dy when x = 4 and dx = 0.2
The value of differential dy when x = 4 and dx = 0.2 is 0.68 .
In the question ,
it is given that ,
the equation is y = tan(3x + 8) ,
we need to find the differential dy , when x = 4 and dx = 0.2
So , differentiating y = tan(3x + 8) with respect to "x" ,
we get
dy/dx = sec²(3x + 8) *3
dy/dx = 3*sec²(3x + 8)
Substituting the values of x = 4 and dx = 0.2 ,
we get ,
dy/(0.2) = 3*sec²(3(4) + 8)
dy/0.2 = 3*sec²(20)
dy/0.2 = 3*1.1324
dy/0.2 = 3.3972
dy = 0.2 * 3.3972
dy = 0.67944
dy ≈ 0.68
Therefore , The value of differential dy when x = 4 and dx = 0.2 is 0.68 .
The given question is incomplete , the complete question is
Let y = tan(3x + 8). Find the differential dy when x = 4 and dx = 0.2 ?
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[tex]\sqrt{2x+3} = 5\\[/tex]
x= 11.
Step-by-step explanation:1. Write the expression.[tex]\sqrt{2x+3}=5[/tex]
2. Square both sides of the equation.[tex]\sqrt{2x+3} ^{2} =5^{2} \\ \\2x+3=25[/tex]
3. Subtract 3 from both sides of the equation.[tex]2x+3-3=25-3\\ \\2x=22[/tex]
4. Divide both sides by 2.[tex]\frac{2x}{2} =\frac{22}{2} \\ \\x=11[/tex]
5. Verify your answer.[tex]\sqrt{2(11)+3}=5\\ \\\sqrt{22+3}=5\\ \\\sqrt{25}=5\\ \\5=5.[/tex]
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Which of the following statements is true for the quadratic equation x² – 16x + 64 = 0?
It's impossible to determine how many solutions the equation has.
The equation has no solutions.
The equation has two solutions.
The equation has one solution.
Since the discriminant of the quadratic equation Δ is equals to 0, the given quadratic equation has one solution. Thus, the fourth option is correct.
We know that for a quadratic equation [tex]ax^{2} +bx+c =0[/tex], there exists a discriminant, Δ = [tex]b^{2}-4ac[/tex]. This discriminant gives us the nature of roots that a quadratic equation can have.
If Δ > 0, the quadratic equation has two real rootsIf Δ = 0, the quadratic equation has single solution as two double rootsIf Δ < 0, the quadratic equation has no real rootsHere, we have the given quadratic equation as -
[tex]x^{2} -16x+64=0[/tex]
Comparing this to the general expression of a quadratic equation, we have
a = 1
b = -16
c = 64
So, now we have to find the discriminant of the given quadratic equation.
Δ = [tex]b^{2}-4ac[/tex]
[tex]= (-16)^{2} -4*1*64\\= 256-256 = 0[/tex]
We see that the discriminant, Δ = 0. This implies that the given quadratic equation has one solution. Thus, the fourth option is correct.
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Solve one sixth times quantity x plus 24 end quantity equals negative 6.
The value of one sixth times quantity x plus 24 end quantity equals negative 6 is -180.
Whet is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, the expression given will be illustrated as:
1/6x + 24 = -6
Collect like terms
x / 6 = -6 - 24
x/6 = -30
Cross multiply
x = -30 × 6
x = -180
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Answer:
Answer: (D) x= 12
Step-by-step explanation:
First you would distribute 1/6 into everything. 1/6 is equal to .16, so you can do that if you would like. you would get .16x + 4
Next, divide .16 on both sides. It should look like this
.16x/.16 + 4/.16.
Your answer should be x+ 25 = -6, or x = 12.
I hope this helps, as I could be wrong. Good luck!
P.S. The guy above me just put the question into AI and just copy pasted it. Not worrying if it was right or not.