Based on the system of equations, the cost of using 19 HCF of water is $35.43
What is an equation?An equation is a mathematical statement that two or more values are equivalent.
Equations are stated to show that two mathematical expressions are equal using the equation sign (=).
Cost of using 17 HCF of water = $32.13
Cost of using 35 HCF of water = $61.83
Total cost of 17 HCF water = 17x + a
17x + a = 32.13 ... equation 1
Total cost of 35 HCF water = 35x + a
35x + a = 61.83 ... equation 2
Subtract equation 1 from equation 2:35x + a = 61.83
-17x + a = 32.13
18x = 29.70
18x = 29.7
x = 29.7/18
x = 1.65
Find a:17x + a = 32.13 ... equation 1
17(1.65) + a = 32.13
28.05 + a = 32.13
a = 4.08 (32.13 - 28.05)
The cost of 19 HCF of water:= 19(1.65) + 4.08
= $35.43
Thus, using the equations above, we can conclude that 19 HCF of water costs $35.43.
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write the following in the form a+bi (2+5) - (-6 +bi)
The complex expression (2+5) - (-6 +bi) in the form a + bi is 13 - bi
How to evaluate the expression?The expression is given as
(2+5) - (-6 +bi)
The above expression is a complex expression
So, we have the following expression
(2+5) - (-6 +bi)
Remove the brackets in the above expression
So, we have the following expression
(2+5) - (-6 +bi) = 2 + 5 + 6 - bi
Evaluate the like terms in the above equation
So, we have the following expression
(2+5) - (-6 +bi) = 13 - bi
Hence, the solution to the complex expression is 13 - bi
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15
A principal needs to order 1,437 T-shirts for students at her school. She rounds to the nearest hundred
to estimate the number of T-shirts to order. Will there be enough T-shirts for all the students? Explain.
There will not be enough T-shirts for all the students
How to determine if the T-shirts will be enough?From the question, the given parameters are:
Number of T-shirt = 1437
From the question, we understand that the principal approximates the number of T-shirts to the nearest hundred
When the number of T-shirts is approximated to the nearest hundred, we have
Approximation = 1400
By comparison, 1400 is less than 1437
This means that the T-shirts will not be enough
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How do I solve this?
Answer: F
Step-by-step explanation:
[tex]\sin(x+y)=\sin x \cos y+\cos x \sin y[/tex]
[tex]\tan x=2 \implies \sin x=\frac{2}{\sqrt{5}}, \cos x=\frac{1}{\sqrt{5}}\\\\\sin y=\frac{8}{17} \implies \cos y=-\frac{15}{17}\\\\\sin (x+y)=\left(\frac{2}{\sqrt{5}} \right) \left(-\frac{15}{17} \right)+\left(\frac{1}{\sqrt{5}} \right) \left(\frac{8}{17} \right)\\\\=-\frac{30}{17\sqrt{5}}+\frac{8}{17\sqrt{5}}\\\\=-\frac{22}{17\sqrt{5}}\\\\=-\frac{22\sqrt{5}}{85}[/tex]
help please
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample 50 of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.
5 9 10 2 2 2 2 7 7 7 7 6 7
8 9 9 2 10 2 7 6 9 8 10 9 2
7 5 7 2 2 7 7 6 2 10 8 2 6
6 9 5 2 10 7 10 2 2 6 6
Develop a confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.
Using the t-distribution, the 95% confidence interval estimate of the population mean rating for Miami is of:
(4.29, 7.71).
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the meaning of the parameters are:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.Using a calculator from the 50 observations given in this problem, the values of the parameters are as follows:
[tex]\overline{x} = 6, s = 2.86, n = 50[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.
Hence the lower bound of the interval is given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6 - 2.0096\frac{6}{\sqrt{50}} = 4.29[/tex]
The upper bound of the interval is given by:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6 + 2.0096\frac{6}{\sqrt{50}} = 7.71[/tex]
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A cricket pitch measures $1$ chain by $10$ feet. What is the area of a cricket pitch in square feet?
(Useful information: there are $3$ feet in a yard, and there are $22$ yards in a chain.)
Area of the cricket pitch is 660 square feet
Given
1 chain is equal to 10 feet
There are 3 feet in a yard
And 22 yards in a chain
Hence it is evident that
One chain is equal to 22 x 3
1 chain = 66 Feet
Area of a rectangle is Length x Width
Length = 66
Width = 10
Hence Area = 66 x 10
Area = 660 Square feet
Hence area of the cricket pitch is 660 square feet.
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A coin has 2 sides: heads (H) and tails (T). A bag has 3 balls: 1 red (R), 1 green (G), and 1 blue (B). You toss a coin and randomly pick a ball. What is the sample space?
The space sample is the total quantity of possible results
for each toss there are 3 possible results
so the total results are 2x 3 = 6
The only option with 6 elements is B
so the answer is B.
A tank truck holds 35.3 kiloliters of oil. How many gallons does it hold?
The truck holds approximately _____ gallons of oil.
round to the nearest hundredth as needed
Full in the spaces to complete the equality:
The measure of USV is ________ degrees.The solution is _________________
Since ∠VST measures 90°, the measure of ∠RSV must also be 90° because the two angles are linear pair.
Since m∠RSU=51°, then the measure of ∠USV is as follows:
[tex]\begin{gathered} m\angle USV=m\angle RSV-m\angle RSU \\ m\angle USV=90\degree-51\degree \\ m\angle USV=39\degree \end{gathered}[/tex]What number would you add to both sides of x2 + 7x = 4 to complete the square?2²0 72이를즐이
To complete the square, we want a number such that:
[tex]\begin{gathered} 2\sqrt{a}=7 \\ a=(\frac{7}{2})^2 \end{gathered}[/tex]because in this way we can writte the square as follows:
[tex]\begin{gathered} x^2+7x+(\frac{7}{2})^2=4+(\frac{7}{2})^2 \\ (x+\frac{7}{2})^2=4+(\frac{7}{2})^2 \end{gathered}[/tex]Hence the answer is the last option:
[tex](\frac{7}{2})^2[/tex]help meeeeeee pleaseee !!!!
The linear function that passes through the points (-3, 18) and (2, -7) is defined by the rule:
y = -5*x + 3
How to find the linear function?We can find a general linear function in the slope-intercept form as:
y = m*x + k
Where m is the slope and k is the intercept of the y-axis.
If we know that the line passes through the points (a, b) and (c, d) then the slope of the function is:
m = (d - b)/(c - a)
In this case the line passes through the points (-3, 18) and (2, -7), then the slope is:
m = (-7 - 18)/(2 + 3) = -5
So the line is something like:
y = -5*x + k
To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:
-7 = -5*2 + k
-7 = -10 + k
-7 + 10 = k
3 = k
So the linear function is:
y = -5*x + 3
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I really don't know where to start on this problem and I would like it if some could help me please.
We can draw the following picture:
Since we have a right triangle with hypotenuse equal to 28ft, we can use the trigonometric function. That is, we can write the following relationships:
[tex]\begin{gathered} \sin 30=\frac{RG}{28} \\ \text{and } \\ \cos 60=\frac{RG}{28} \end{gathered}[/tex]both give the same result.
If we use the first one, we have
[tex]\begin{gathered} RG=28\cdot\sin 30 \\ \end{gathered}[/tex]since sin30=0.5, we have
[tex]\begin{gathered} RG=28\cdot(0.5) \\ RG=14 \end{gathered}[/tex]that is, RG = 14 ft, which corresponds to the first option
Calculate the missing information. Round dollars to the nearest cent and percents to the nearest tenth of a percent.
Item
Bar of soap
Cost
$1.17
Amount of
Markup
$0.79
Selling Price (in $)
$1.96
Percent
Markup
Based on
Cost
X%
Percent
Markup
Based on
Selling Price
%
MY N
The markup indicates the difference between the selling price and the item's cost to the business.In general, a corporation generates more money the higher the markup.The retail price of a product less its cost is known as markup, although the margin percentage is determined in a different way.
Calculate percentage on markup based on cost ?
The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.The markup percentage, which is computed as (12 - 8) / 8, is 50% for an item that costs the business $8 to produce but is priced at $12.Selling price = cost + markup
= 1.17+0.78
=1.96
percentage markup based on cost = markup/cost*100
0.78/1.17*100
= 66.66
percentage on selling = percentage on markup cost/100+percentage on cost
= 66.66/100%+66.66
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Multiply. Write your answer in scientific notation.
2.(4 × 10³)
À La Mode Ice Cream Parlor uses the function f(x) to calculate its profits. When the parlor sells x cones, it makes f(x) dollars in profit.
What does f(50)=85 tell you?
Help please
Answer: When the Ice Cream Parlor sells 50 ice cream cones, they make $85 dollars in profit.
Step-by-step explanation:
x = cones
the function f tells us the profit for whatever x
Identify the coefficient and the exponent for each term of 8x² - 2x.
The coefficients are 4 and 1. The exponents are 8 and -2.
The coefficients are 8 and -2. The exponents are 4 and 0.
The coefficients are 8 and 2. The exponents are 4 and 0.
The coefficients are 8 and -2. The exponents are 4 and 1.
The coefficient of the term 8x² is 8 and the exponent is 2 and the coefficient of the term -2x is -2 and the exponent is 1.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = abˣ in mathematics, where x is the independent variable
From the expression, a is the coefficient, x is the exponent, and b is the variable
For the term, y = abˣ, compared with the general equations;
abˣ = 8x²
a = 8 and x = 2
This indicates that the term's coefficient is 8 and its exponent is 2.
Similarly for the second term -2x
So the coefficient of the term -2x is -2 and the exponent is 1
Hence, the coefficient of the term 8x² is 8 and the exponent is 2 and the coefficient of the term -2x is -2 and the exponent is 1.
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Can someone help please
The maximum displacement of this cosine wave function is equal to 8 inches.
The frequency of this cosine wave function is equal to 1/8 Hertz.
The time (t) required for one cycle is equal to 8 seconds.
What is a cosine wave?Mathematically, a cosine wave simply refers to an equation of simple harmonic motion (SHM) and it is modelled by this mathematical expression:
y = asinωt = asin2πft ......equation 1.
Where:
a represents the amplitude or maximum displacement of a cosine wave. f represents the frequency measured in Hertz.ω represents the angular velocity.t represents the time measured in seconds.How to calculate the maximum displacement?From the information provided, the equation for this simple harmonic motion (SHM) is given by:
d = -8cos(π/4)t ......equation 2.
By comparing equation 1 and equation 2, we have the following parameters:
Maximum displacement or amplitude, a = |-8|
Taking the absolute value of a, we have:
Maximum displacement or amplitude, a = 8
For the frequency, we have:
Angular velocity, ω = 2πf
Making frequency (f) the subject of formula, we have:
Frequency (f) = ω/2π
Frequency (f) = (π/4)/2π
Frequency (f) = π/8π
Frequency (f) = 1/8 Hertz.
Finally, we would calculate the amount of time (t) required for one cycle as follows:
Time (t) = 1/f
Time (t) = 1/(1/8)
Time (t) = 8 seconds.
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Complete Question:
An object moves in simple harmonic motion described by the equation d = -8cos(π/4)t, where t is measured in seconds and d in inches. Find the following:
maximum displacement
the frequency
the time required for one cycle.
Eighth grade > T.14 Volume of spheres QX7 What is the volume of this sphere? Use a ~ 3.14 and round your answer to the nearest hundredth. 18 cm cubic centimeters Submit Docs
hello
to solve this question, we need to use the formula for volume of a sphere
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ v=\text{volume} \\ r=\text{radius} \end{gathered}[/tex]from the image above, we can now find the radius of the sphere
[tex]\begin{gathered} radius=\frac{\text{diameter}}{2} \\ d=18\operatorname{cm} \\ r=9\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ v=\frac{4}{3}\times3.14\times9^3 \\ v=3052.08\operatorname{cm}^3 \end{gathered}[/tex]from the calculations above, the volume of the sphere is equal to 3052.08cm^3
ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
Answer:
2^5m^15n^10
Step-by-step explanation:
Answer:
16m^12n^8t^4
Step-by-step explanation:
when raising exponents to another exponent you multiply the exponents
A. 90 degrees clockwiseB. 180 clockwiseC. 90 degrees counter clockwise
1) What we have in the polygon P is at first a
90º Rotation Clockwise because it is in the direction of the clock.
90º Rotation Clockwise
Tracing a line inside the polygon P, we can count approximately 10 units to the right in the translation.
T
a standard number cube number 1 through 6 on east side is rolled 3 times what is the probability of rolling a 2 on all three rolls express your answer as a fraction
the probability of getting a 2 tree times is
[tex]\frac{1}{6}\cdot\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{216}[/tex]PLS HELP!!!
When solving the quadratic-2x² - 9x - 5 = 0, the number of real roots is:
A) 2 real roots.
B) 1 real root.
C) No real roots.
D) None of these choices are correct.
The sum of two whole numbers is 63. The difference between the numbers is less than 10. Find as many solutions
Answer:
hmmph..
(32, 31)
(33,30)
(34, 29)
(35, 28)
(36,27)
(37, 26)
Step-by-step explanation:
That all I got....
According to medical data, the ages at which patients have their first hip replacement
surgery follows a normal distribution. The average age for a first hip replacement is 55
years of age, with a standard deviation of 8 years. Therefore, doctors can expect 95% of
their hip replacement surgery patients to be between what ages?
O 39-71
O 45-65
O 47-63
O 31-79
Question 4
2
95% of the people the doctor expects to have hip replacement surgery will be between the ages of 47 and 63.
What exactly are the mean and standard deviation?
The definition of average is that it is the mean value, which is the ratio of the sum of the values in a particular set to all the values in the set.
The amount of variance from the mean is shown by the standard deviation.
Given that the standard deviation is 8 years and the average age is 55.
x=x0, where x0 and are the mean age and standard deviation, respectively, defines the relationship.
The standard deviation is 8 years, while the mean age is 55 years.
The answer is that 55+8=63 and 55-8=47.
Consequently, the age range is 47 years to 63 years.
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Over the interval [0,2pi), what are the solutions to cos(2x)=cos(x)? Check all that apply.
Answer:
x = 0 and 2pi/3
Explanation
Given the expression
cos(2x)=cos(x)
In trigonometry expression;
cos2x = 2xos^2x - 1
Substituting into the equation given;
cos(2x)=cos(x)
2xos^2x - 1 = cos x
Rearrange
2xos^2x - 1 - cosx - 1 = 0
Let P = cosx
2P^2 - P - 1 = 0
Factorize
2P^2 - 2P+P-1 = 0
2P(P-1)+1(P-1) = 0
2P+1 = 0 and P-1 = 0
P = -1/2 and 1
Recall that P = cosx
-1/2 = cosx
x = cos^-1(-1/2)
x = 120 degrees = 2pi/3
If P = 1
cosx = 1
x = cos^-1(1)
x = 0
Hence the value of x that satisfies the equation is 0 ad 2pi/3
Find the slope of the line that passes through each of the following sets of points (0, 0) and (1, 4)
Answer:
slope would be 4/1
Step-by-step explanation:
its rise over run, so up 4 and out 1
have a good day!
12. In the diagram below, transversal TU intersects PQ and RS at V and W, respectively. If mZTVQ = 5x - 22 and mZTVQ = 3x + 10, for which value of x is PQ parallel to RS? P_ R W A. 6 B. 16 C. 24 D. 28
ANSWER:
The value of x is 16
STEP-BY-STEP EXPLANATION:
With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.
Thanks to this we can make the following equality:
[tex]5x-22=3x+10[/tex]Solving for x:
[tex]\begin{gathered} 5x-3x=22+10 \\ 2x=32 \\ x=\frac{32}{2} \\ x=16 \end{gathered}[/tex]Answer:
16 is the answer
I inserted a image of the question I’m very confused and need help with homework so I do good on test
To find the magnitude of a vector we use the following equation
[tex]\lvert\vec{v}\rvert=\sqrt[]{(v_x)^2+(v_y)^2}[/tex]This comes from taking the value of the hypotenuse by Pythagoras, graphically it can be seen in the following image:
In the case of your exercise, the values would be
[tex]\begin{gathered} v_x=x \\ v_y=y \\ \lvert\vec{v}\rvert=\sqrt[]{(x_{})^2+(y)^2} \end{gathered}[/tex]PLEASE HELP, NO LINKS!
1. What are the key features that can be identified from a linear graph?
2. What is a relation? What makes it different from a function?
3. How can you determine the domain and range from a function?
4. What is Slope and how is it determined from a graph?
5. How do you determine the intercepts from an equation and graph.
6. Provide an example of the different forms linear equations and functions can be written.
Answer:
1 These 5 main features are the title, scale, points, labels, and line.
2. Relations are a group of ordered pairs from one set of objects to another set of objects while functions are relations that connect one set of inputs to another set of outputs. So all functions are relations while all relations are not functions.
3. To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).
4. The slope equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. In other words, Pick two points on the line and determine their coordinates.
5. To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. To find the y-intercept, plug 0 in for 'x' and solve for 'y'.
6. An example of a linear equation is: 2x + y - 3 = 0. It can be written in the standard form, the slope-intercept form, and the point-slope form. Here we mainly used the slope-intercept form y=mx+c y = m x + c . To write linear equations find the slope and y-intercept and then substitute these values into the equation.
Salaries of Business Graduates. Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $45,000 and $60,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation? How large a sample should be taken if the desired margin of error is a. $500? b. $200? c. $100? d. Would you recommend trying to obtain the $100 margin of error? Explain.
3750 is the planning value for the population standard deviation.
In the sampling, one should not recommend trying to obtain the $100 margin of error since the sample size is large.
Firstly, the planning value will be:
= (60000 - 45000) ÷ 4
= 3750
Then the number will be:
= 1.96 × (3750 ÷ 500)²
= 217
Also, for error 200, the desired margin will be:
= 1.96 × (3750 ÷ 100)²
= 5403.
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