f(x)=4x-9 find point of intersection
Olive buy clothe at a tore with a total bill of $54. 50. She ha a 20% off coupon and pay 7. 5% ale tax. She calculate the total cot of the clothe, uing the expreion: (54. 50÷1. 20)(1. 075). Explain the error in Olive' reaoning. Determine the correct expreion and explain your reaoning
Total bill that should be paid by Olive is $46.61. Olive's calculation is incorrect because she is applying the discount and tax to the original price of the clothes rather than to the discounted price.
A total bill is the final amount of money that is due for payment, usually for goods or services that have been provided. It is the sum of all charges, fees, taxes, and other expenses that have been incurred. The total bill may be presented as a single amount or as a breakdown of the various charges that make up the total.
The correct expression to calculate the total cost of the clothes would be:
Total cost = (Original price * (1 - Discount rate)) * (1 + Tax rate)
In this case, the original price is $54.50, the discount rate is 20%, and the tax rate is 7.5%. Plugging these values into the above expression gives us:
Total cost = (54.50 * (1 - 0.20)) * (1 + 0.075)
Total cost = (54.50 * 0.80) * 1.075
Total cost = $43.60 * 1.075
Total cost = $46.61
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Can someone please help me I’ll mark as brainlist
Answer:
u=14, v=2
Step-by-step explanation:
Here's my attempt:
Proving triangle congruency:
We need to prove that the two triangles are congruent.
First, we need to see which sides/angles correspond (basically how the two triangles overlap each other).
Well, we can see that m∠F = 90° and that m∠D = 90°, so we know that ∠F and ∠D are congruent, and so they correspond.
So, if you drag ΔHFG over to ΔCDE, then sides DC and FH would be right on top of each other. (try drawing this to make it clearer)
Solving for v:
So if sides DC and FH are congruent, then their values are also equal.
DC = 17v and FH = v+32
So if DC=FH, then 17v=v+32
Then, we simplify this:
17v=v+32 [original equation]
16v=32 [subtract v from both sides]
v=2 [divide both sides by 16 to isolate v]
So, we have our value for v: v=2
Solving for u:
Now, it's time to find u: (also, it doesn't matter if you found v first or u first in this problem)
When we overlapped ΔHFG and ΔCDE, we saw that EC = GH
So, using the same method as we used to find v, we can say that
EC=7u and GH = 10u-42
If EC=GH, then 7u=10u-42
Then, we simplify:
7u=10u-42 [original equation]
-3u=-42 [subtract 10u from both sides to get u on just one side]
u=14 [subtract both sides by -3 to isolate u]
Finally, we have our value for u: u=14
But we're not done yet: let's check our work:
Firstly, let's plug our answer for v into our equation for v:
17v=v+32
17(2)=(2)+32
34=34 It works!
Next, we'll plug in our answer for u into our equation for u:
7u=10u-42
7(14)=10(14)-42
98=140-42
98=98 It works!
I hope you read through my explanation and that it helped! :D
Dagne meaure and find that he can do a vertical jump that i 27. 5% of her height. If Dagne can jump 13. 2 inche, how tall, in inche, i he?
The total height of Dange after calculation from the given data is 48 inches.
Let x be the Dange's height ,
then,
27.5% of x = 13.2
x = 13.2*100 / 27.5
x = 48 in
Therefore , he is 48 inch tall.
A value or ratio that can be expressed as a simple fraction of 100 is known as a percentage.
To obtain a percentage we just need to divide it by 100 and then multiply the obtained result by 100.
As a result, the proportion refers to a component per 100. Percentage is denoted as a portion of 100 of something.
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Design your own questionnaire to test this hypothesis. 'Most students in Year 9 sleep at least 10 hours on a school night.'
Answer:
To test the hypothesis that most students in Year 9 sleep at least 10 hours on a school night, a questionnaire could be designed with the following questions:
1) How many hours of sleep do you typically get on a school night?
2) On a scale of 1 to 10, with 1 being "not at all" and 10 being "extremely", how well-rested do you feel when you wake up in the morning?
3) Do you have any difficulties falling asleep at night?
4) Do you have any daytime sleepiness or fatigue?
5) Do you regularly engage in activities that interfere with your sleep, such as using electronic devices before bed or consuming caffeine late in the day?
The questionnaire should also include space for respondents to provide their age and grade level, as well as any additional comments or observations they may have about their sleep habits. By collecting and analyzing this data, it should be possible to determine whether the hypothesis is supported or not.
a fair coin is tossed 29 times. what is the probability that at most 27 heads occur? a) 0.00000006 b) 0.00000081 c) 0.00000076 d) 0.99999994 e) 0.99999919 f) none of the above.
Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.
Given that,
A fair coin is tossed 29 times.
We have to find what is the probability that at most 27 heads occur.
We know that,
A fair coin is tossed 29 times.
n=29
Probability of heads p=1/2
q= 1-p
q=1-1/2=1/2
We get
P (X=x) = ⁿCₓ qⁿ⁻ˣ pˣ
Now, the probability that at most 27 heads occurs is
P(X<27)
=1-[P(X=28)+ P(X=29)]
=1-[²⁹C₂₈(1/2)²⁹⁻²⁸(1/2)²⁸- ²⁹C₂₉(1/2)²⁹⁻²⁹(1/2)²⁹]
=1-[²⁹C₂₈(1/2)²⁹- ²⁹C₂₉(1/2)²⁹]
=1-[28+1](1/2)²⁹
=1-29×0.00000000186
=0.999999945
Therefore, Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.
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there are 15 rooms in a hotel and no more than 5 people can stay in each room. What is the difference between the largest and smallest amount of guests can the hotel accommodate
Answer:
The difference is 60.
Step-by-step explanation:
Since no more than 5 people can stay in each of the 15 rooms, we can multiply these numbers to get the largest amount of guests.
5 x 15 = 75
We assume the smallest amount can be 1 person in each of the 15 rooms.
1 x 15 = 15
We then subtract the smallest from the largest to find the difference.
75 - 15 = 60
a cosine function has a period of 3, a maximum value of 20, and a minimum value of 0. the function is a reflection of its parent function over the x-axis. which function could be the function described? responses f(x)
The description of the cosine function is [tex]\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}[/tex].
A cosine function's general form is given by:
[tex]\mathrm{f(x) = A \times cos(Bx + C)) + D}[/tex]
where:
A stand for amplitude, or the ratio of the maximum to the minimum value.
B = 2π / period
C stands for horizontal phase shift.
(Midpoint between the Maximum and Minimum Values) D = Vertical Shift
We can determine the parameters for the specified function given the information given:
Period = 3 (This means B = 2π / 3)
Maximum value = 20
This means the amplitude A is half of this, so A = 20 / 2 = 10
Minimum value = 0
This means the vertical shift D is half of the difference between the maximum and minimum.
So, D = (20 - 0) / 2
= 10
The amplitude is negative because the function is a mirror of its parent function over the x-axis, hence A = -10.
Putting it all together, the function is:
[tex]\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}[/tex]
Hence the final expression after the transformation is [tex]\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}[/tex].
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What is x?
100^(2x)=1000^(x+6)
Answer:
x = 18
Step-by-step explanation:
You apply the exponent rules
4x = 3 (x + 6)
Then you solve 4x =3 (x + 6)
Which gives you 18
Find the slope of the line that passes through (10, 4) and (2, 13).
Answer:
The slope is -9/8.
Step-by-step explanation:
[tex]m = \frac{13 - 4}{2 - 10} = \frac{9}{ - 8} = - \frac{9}{8} [/tex]
A spherical water tank holds 9000ft ^3 of water. What is the diameter of the tank? (Hint: V = 1/6d^3 3.14)
Set up? :
9000 = 1/6 d ^3 x 3.14
The diameter of the spherical tank that holds 9000ft³ of water is 25.81 ft.
What is diameter?A diameter is a line that divides a circle into two equal parts.
To calculate the diameter of the tank, we use the formula below.
Formula:
V = d³π/6............ Equation 1Making d the subject of the equation,
d = ∛(6V/π).................. Equation 2Where:
V = Volume of the spherical water tankd = Diameter of the tankFrom the question,
Given:
V = 9000 ft³π = 3.14Substitute these values into equation 2
d = ∛(6×9000/3.14)d = 25.81 ftHence, the diameter of the tank is 25.81 ft.
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pleaseee help me lol
12. suppose that n and n+1 represent two consecutive integers
(a) represent their sum in terms of n in simplest form.
(b) explain why this sum must always be odd.
The expression for the sum is 2n + 1 and the sum must be an odd number because it will leave 1 as remainder when divided by 2.
What is Euclid division lemma?The Euclid division lemma states that when two positive integers a and b are divided then their are other two integers q and r that represent quotient and remainder. The equation for the lemma can be written as a = bq + r where r < b.
(a) The given consecutive integers are n and n + 1 respectively.
The expression for their sum can be written as,
n + n + 1
⇒ 2n + 1
(b) The general expression for the sum is 2n + 1.
Now, as per the Euclid's division lemma, the number when divide by 2 will leave remainder as 1.
Which implies the number will be an odd number.
Hence, the expression for the sum is 2n + 1 and it will be an odd number.
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i need the answer to this math problem what's the answer to g(4) =
Step-by-step explanation:
Incomplete problem...
With sales tax, it costs $94.83 to
buy an $87 silver ring. What is the
sales tax percentage?
Answer: 9%
Step-by-step explanation:
First, take 94.83 divided by 87, then times 100% = 109%
Then take 109 -100 = 9%
So the sales tas percentage is 9%
What is the circumference of a circle whose radius is 16 feet leave answer in terms of pi . Please show ur work because I have too!
The circumference of a circle is 32π feet, which is the correct answer would be option (B).
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
We have to determine the circumference of a circle whose radius is 16 feet
As per the question, we have
The radius of the circle r = 16 feet
Circumference of a circle = 2πr
Substitute the value of r in the above formula, and we get
Circumference of a circle = 2π(16)
Circumference of a circle = 32π
Hence, the correct answer would be an option (B).
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In the long run, if the firm decides to keep output at its initial level, what will it likely do?.
False, Stay on SRATC3 but decrease to the point touching LRATC.
What is LRAC curve ?
The LRAC curve is the curve that a company would follow in order to reduce its cost per unit for each specific long-run quantity of output.
One particular level of fixed costs is represented by each of the short-run average cost (SRAC) curves that make up the LRAC curve.
Why is Lrac crucial?
Over a variety of outputs, the effect is a decrease in average costs. A company may gain a competitive edge in a market thanks to these lower expenses, which signify an increase in production efficiency.
Consumer prices may be reduced as a result, and corporate earnings and dividends may increase.
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how much does it cost to buy 1500g of cornflakes
Answer:
£2.94
Step-by-step explanation:
You need two 750g boxes to get 1500g of cornflakes.
Buy one and get 2nd at half price:
1.96 + 1.96/2 = £2.94
Which of the following rational functions is graphed below?
Answer:
A) F(x) = 1/(x-2)(x-2)
Step-by-step explanation:
Below in the picture of how the graph will look like:-
I hope my answer helps you.
Solve for x. Round to the nearest tenth.
The value for x is 25.5 units.
What are the Basic Trigonometry Formulas?
Basic trigonometry formulas are used to find the relationship of trig ratios and the ratio of the corresponding sides of a right-angled triangle. There are basic 6 trigonometric ratios used in trigonometry, also called trigonometric functions- sine, cosine, secant, co-secant, tangent, and co-tangent, written as sin, cos, sec, csc, tan, cot in short.
We have,
Perpendicular side = 18
Hypotenuse side = x
θ = 90/2 = 45°
sinθ = Perpendicular side/Hypotenuse side
sinθ = 18 / x
sin(45°) = 18 / x
1/√2 = 18 / x
x = 18 *√2
x = 25.4558
x = 25.5
Hence, the value for x is 25.5 units.
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FILL IN THE BLANK. a _______ random variable has either a finite or a countable number of values.
A Discrete random variable has either a finite or a countable number of values.
Exploring Discrete Random VariablesA discrete random variable is a random variable that is capable of taking on only a finite or countable number of distinct values. This means that the possible values of the random variable can be listed out, such as 1, 2, 3, 4, and so on.
Discrete random variables are commonly used in statistics to describe situations where the possible outcomes can be counted, such as the number of heads in a series of coin flips, or the number of students in a class.
Discrete random variables can take on either discrete values (such as integers) or continuous values (such as real numbers). They are often used to model a process that is composed of a finite number of distinct steps, such as a multiple choice test with a fixed set of questions and answers.
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Mary plants roses in 1/4 of her garden. She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. What fraction of Mary's garden has tulips?
Help!!! PLEASE!!!!
thx
Answer:
(c) (1/14)xy(x² +8y)
Step-by-step explanation:
You want the greatest common factor factored out of the expression 1/14x³y +8/14xy².
Common factorThe coefficients 1/14 and 8/14 have a common factor of 1/14.
The variable terms x³y and xy² have variables x and y. The exponents of x are 3 and 1, so x¹ = x will be the common factor.
Similarly, the exponents of y are 1 and 2, so y¹ = y will be their common factor.
When we factor out (1/14)(x)(y) from the terms of the given expression, it becomes ...
1/14xy(x² +y)
a researcher is interested in the issue of cheating on college campuses. she conducts an anonymous survey about cheating among college freshmen. one survey group included freshmen who live on campus, and the other survey group included freshmen who live off-campus. the standard error formula for the difference between sample proportions is. calculate the standard error for a survey comparing proportions of cheating of freshmen living on campus to freshmen living off campus, where p1
Standard error for sample proportion = √{[p₁/p₂(1-p₁/p₂)]/2}
What means standard error?
Standard error is a statistical statement that express the accuracy of an estimation resulting from survey study. It indicates how much a sample means is differ from actual population mean.
How to calculate standard error?
We calculate standard error for the two-survey group by using the following formula.
√[p(1-p)/n]
p is the proportion of freshmen living on campus to the freshmen living off campus
p = p₁/p₂
According to the given question:
p₁ = freshmen living on campus
p₂= freshmen living off campus
n= number of survey group
n=2
hence, standard error =√{[p₁/p₂(1-p₁/p₂)]/2}
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caitlyn has found that the total fertility rate for montana is 1.73. what other piece of information would caitlyn need to predict how many babies will be born this year in montana?
Caitlyn would need to know the population size of Montana in order to predict how many babies will be born this year in the state.
In order to predict how many babies will be born this year in Montana, Caitlyn needs to have access to the population size of Montana. The total fertility rate for Montana is 1.73, which is the average number of children a woman can expect to have throughout her lifetime. Knowing the population size of Montana will allow Caitlyn to have a better understanding of how many babies are likely to be born this year, as this number is directly correlated to the total fertility rate. By having access to both the population size and the total fertility rate, Caitlyn will be able to make a more informed prediction about the number of babies that will be born this year in Montana.
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Find the measure of each angle indicated
A. 69 degrees
B. 110 degrees
Help!!!
Answer:
It's 111 degrees
Step-by-step explanation:
The unknown angle is alternating with the 111 degrees angle
If m<10 = m<3, then the lines are parallel by the:
alternate exterior angle converse theorem.
alternate interior angle converse theorem.
same-side interior angle converse theorem.
None of these choices are correct.
If m<10 = m<3, then the lines are parallel by the: alternate exterior angle converse theorem.
What is alternate exterior angles?The pair of angles known as alternate external angles are those that are generated on the other side of the transversal from the parallel lines' outer side.
What is alternate exterior angels converse theorem?According to the opposite of the alternative exterior angle theorem, if two lines are cut by a transversal and their alternate exterior angles are congruent, the lines are parallel.
In the figure angel 10 and 3 are alternate exterior angles
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How many solutions does the system of equations below have? 3x - 10y =-7 -17x - 10y = -16
The two lines on the system aren't parallel, thus, the system has only one solution.
How many solutions does the system of equations has?Here we have the following system of equations:
3x - 10y = -7
-17x - 10y = -16
Now, notice that both equations are linear equations, and the equations are not parallel (the coefficients on the left side are different), which means that the two linear equations will intercept at some point (and at only one point)
That is enough to conclude that the system of equations will have only one solution.
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Solve no. 8 and no.9
Answer:
8. 1.5
9 (a) $90
(b) $510
Step-by-step explanation:
8.
[tex]\frac{1}{4} - \frac{2x-7}{8} = \frac {x}{2}[/tex]
Multiply all by 8
[tex]2 - (2x-7) = 4x\\2 - 2x + 7 = 4x\\9 = 4x + 2x\\9 = 6x\\\frac{9}{6} = x\\1.5 = x[/tex]
9. (a)
x = cost of one DVD
Since, a blue-ray disc is equal to 2 DVD minus by 10 dollar, then a blue-ray disc = (2x-$10)
$ 610 = 3x + 2(2x - $10)
$ 610 = 3x + 4x - $ 20
$ 610 + $ 20 = 7x
$ 630 = 7x
Divide both side by 7
x = $ 90
Thus, one DVD cost $ 90.
(b)
Blue-ray disc cost = (2x - $10)
3 Blue-ray disc cost = 3(2x - $10)
= 6x - $30
Replace x with $90, since x = $90
= 6 ($90) - $30
= $ 540 - $30
= $510
3 The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers.
Answer:
The possible pairs of numbers that satisfy the given conditions are (x, y) = (4, 2) and (x, y) = (8, -2).
Step-by-step explanation:
To solve this problem, we can use algebra. Let's call the two numbers x and y. We are given that x + y = 6 and x^2 + y^2 = 28. We can square the equation x + y = 6 to get x^2 + 2xy + y^2 = 36. We can then subtract the equation x^2 + y^2 = 28 from the equation x^2 + 2xy + y^2 = 36 to get 2xy = 8. We can then divide both sides by 2 to get xy = 4.
We can then use the equation x + y = 6 to write x = 6 - y, which we can substitute into the equation xy = to get (6 - y)y = 4. Solving this equation for y yields y = 2 or y = -2.
If y = 2, then x = 6 - y = 6 - 2 = 4, so the two numbers are x = 4 and y = 2. If y = -2, then x = 6 - y = 6 + 2 = 8, so the two numbers are x = 8 and y = -2. Therefore, the possible pairs of numbers that satisfy the given conditions are (x, y) = (4, 2) and (x, y) = (8, -2).
If Lydia has a straight-time pay of $697.20 per Iveek as a dental assistant, how many hours does she work
per week? Use the table from #2 above to help you.