The dress is originally 160$, but we take 30% off which is that same as .3 .
To find 30% or .3 of 160 we multiply 160 by .3 which gets us 48.
48 is 30% of 160 so to find the new price of the dress we need to subtract
160 - 48 = 112. The new price of the dress is 112$.
Since Claire's aunt works at the store Claire will get an additional 10% off from the "new" price which is 112$. 10% is also .1, so we will multiply 112 by .1 which equals 11.20.
As 10% of 112 is 11.20 so we will subtract 11 dollars and 20 cents from the price. 112 - 11.20 = 100.80$.
For sales tax we will do the same thing, multiply 100.80 by .075 which equals 7.56. This time since we are ADDING sales tax, we will add 100.80 and 7.56 rather than subtract. 100.80 + 7.56 = 108.36.
Claire will be paying 108.36$ for the prom dress.
Answer:
c
Step-by-step explanation:
At the Many Chips Cookie Company, they are serious about the number of chocolate chips in their cookies. They claim that each cookie has c chips. If their claim is true, there will be 200 chips in 10 cookies. Write an equation to describe this situation.
Answer:
c=20
Step-by-step explanation:
200=10c
200/10=c
20=c
Factor completely:
Please help me.
Answer:
3x(3x-2)(12x-5) D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
This is a game in which you figure out what the terms of the expression have in common. Clearly, x is a common factor, as 108x³ = x(108x²), -117x² = x(117x) and 30x = x(30). Factoring out x, we get:
x(108x² - 117x + 30).
Next, note that 3 is a factor common to 108, 117 and 30, so now we have:
x(108x² - 117x + 30) → 3x(36x² - 27x + 10). Knowing this enables us to eliminate answers A and B, because neither has that factor 3 in it.
Now take a look at D. This is the only answer choice that produces a '10,' which stems from multiplying -2 and -5. So the only possible answer choice is D.
What does it mean to be "certain" to occur?
What does it mean for an event to be "impossible" to occur?
Certain means the event will happen.
Impossible means the event would never happen.
To be "certain" to occur means the event will definitely happen without any doubt.
For an event to be "impossible" to occur means that there is no chance whatsoever that the event will happen.
When we say an event is "certain" to occur, we mean that the event will definitely happen. In terms of probability, if an event has a probability of (1) (or 100%), it is certain to occur. For example, if you flip a fair coin, the probability of it landing either heads or tails is (1), meaning it's certain to land on one of the two sides.
On the other hand, when we say an event is "impossible" to occur, we mean that the event will definitely not happen. In terms of probability, if an event has a probability of (0) (or (0%), it is impossible to occur. For example, if you roll a six-sided die and ask for a result that is not within the range of 1 to 6, the probability of that happening is (0), so it's impossible for the die to show that result.
These concepts are fundamental to understanding the certainty or impossibility of events in probability theory and are essential for making predictions and decisions based on probabilistic models.
What is the average rate of change from x = −3 to x = −4?
Answer:
-2
Step-by-step explanation:
Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue. We have the work form of a positive upwards-opening parabola as
[tex]y=a(x-h)^2+k[/tex]
where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex. We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1). Now we will fill in the work form equation and solve for a:
[tex]-1=a(-2-(-3))^2-3[/tex]
which simplifies a bit to
[tex]-1=a(1)^2-3[/tex]
and
-1 = a(1) - 3. Therefore, a = 2 and our parabola is
[tex]y=2(x+3)^2-3[/tex]
Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4. Do this by subbing in the values of x one at a time to find y. When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3). When x = -4, y = -1 so the coordinate of that point is (-4, -1). The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:
[tex]m=\frac{-1-(-3)}{-4-(-3)} =\frac{2}{-1}=-2[/tex]
And there you have it! I'm very surprised that this question sat unanswered for so very long! I'm sorry I didn't see it earlier!
Tony is standing at sea level. From his location, the angle of elevation of the top of Blue Mountain is 23°. Staying at sea level, he walks 210 yards toward the mountain. The angle of elevation of the top is now 28°. Find the height of Blue Mountain. Round intermediate results to 3 decimal places and the final answer to 1 decimal place.
The height of Blue Mountain is _____ yards.
The height of Blue Mountain is determined by setting up two equations based on the tangent of the observed angles of elevation from two different points and solving for the distance to the mountain. The height is then calculated using this distance and rounded to the nearest tenth.
Explanation:Tony is trying to find the height of Blue Mountain using trigonometry and the angles of elevation observed from two different points. We can solve this problem using right-angled triangles and trigonometric functions (specifically tangent).
Step-by-Step Calculation
First, we use the angle from the first observation point:
tan(23°) = height / distance
Height = distance * tan(23°). We call this height 'h'.
Then, when Tony moves 210 yards closer, the distance from the mountain is 'distance - 210 yards', and we use the angle from this second point:
tan(28°) = height / (distance - 210)
Height = (distance - 210) * tan(28°). We call this height 'h' as well because the height of the mountain doesn't change.
Therefore, we have two equations:
h = distance * tan(23°)
h = (distance - 210) * tan(28°).
By equating the two expressions for 'h', we find the distance 'd':
distance * tan(23°) = (distance - 210) * tan(28°).
We can now solve for 'distance' numerically. After calculating distance, we can use it to find the actual height 'h' using the tangent function with any of the two angles.
Final Result
We round intermediate results to 3 decimal places and the final height to 1 decimal place, giving us the height of Blue Mountain.
A toy rocket is launched straight up into the air with an initial velocity of 60 ft/s from a table 3 ft above the ground. If acceleration due to gravity is –16 ft/s2, approximately how many seconds after the launch will the toy rocket reach the ground?
Answer:
Answer:
t = 3.8 s
option 3
Step-by-step explanation:
For this case we have the following equation:
h (t) = at ^ 2 + v * t + h0
Substituting values we have:
h (t) = - 16 * t ^ 2 + 60 * t + 3
We equate the equation to zero:
-16 * t ^ 2 + 60 * t + 3 = 0
We look for the roots of the polynomial:
t1 = -0.04935053979258153
t2 = 3.7993505397925817
We are left with the positive root and round:
t2 = 3.8 s
Answer:
7,55 seg
Step-by-step explanation:
Initial Velocity = 60 ft/s
High = 3ft
Acceleration = -16 ft/s2
According to the next formula
H = Vi(t) - 1/2 gt2
We got a cuadratic formula which roots are
t1 = -0,04 seg and t2 = 7,55 seg
the time not negative so t= 7,55 seg
Which of the following expressions is equal to sin(-150°)?
A. sin(30°)
B. -sin(-30°)
C. -sin(30°)
D. sin(150°)
Check the picture below.
let's notice that the angle -150° has a reference angle of 30°, so any trigonometric function for either angle will be the same value, however, let's recall that the sine or y-coordinate is negative on the III Quadrant, so sin(-150°) is the same as sin(30°) BUT negative, -sin(30°).
Answer:
C. -sin(30°)
Step-by-step explanation:
180-150=30
-sin(30) = -.5 on calculator j like sin(-150) is
Paul's bathtub is clogged. He has to empty 30 liters of water by hand. If Paul carries two buckets each trip, what combination of sizes allow him to empty the bathtub in exactly 4 trips?
5 liter bucket with the 3 liter bucket twice, and then use the 3 liter bucket and the 4 liter bucket twice.
if 5x^2 + 7x = 6, which statement is correct?
A) x = 2 or x = 3/5
x = -2 or x = 3/5
X=2 or X= -3/5
x=-2 or X =-3/5
Answer:
12x^2=6
Divide by 12
x^2=1/2or.5
square root
x=0.707
Step-by-step explanation:
Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and what is the value of this maximum?
f(x), and the maximum is 3.
g(x), and the maximum is 5.’
f(x), and the maximum is 2.
g(x), and the maximum is 2.
Answer:
Second option
g(x), and the maximum is 5.’
Step-by-step explanation:
In the graph it can easily be seen that the maximum value reached by the function f(x) is y = 3.
Then, the function g (x) is:
[tex]g(x) = 3cos(\frac{1}{4}(x + \frac{1}{3}x)) + 2[/tex]
By definition the function
[tex]y = cos(x)[/tex] reaches its maximum value when x = 0, [tex]2\pi[/tex], [tex]4\pi[/tex], ..., [tex]2k\pi[/tex]
So
When [tex](\frac{1}{4}(x + \frac{1}{3}x)) = 0[/tex] entonces [tex]cos((\frac{1}{4}(x + \frac{1}{3}x)) = 1[/tex].
Thus:
[tex]g(0) = 3(1) + 2\\\\g(0) = 5[/tex].
Therefore the function that has the greatest maximum is g(x) when [tex]g(x) = 5[/tex]
The answer is the second option
Please help me asap! In an election, 2/5 of the voters voted for a new school tax. What is the probability that a randomly selected voter did not vote for the tax? Express your answer as a percentage.
a. 40%
b. 6%
c. 60%
d. 4%
Answer:
the answer is c 60%, may i have brainlyiest
Final answer:
To find the probability that a voter did not vote for a new school tax when 2/5 did, subtract 2/5 from 1 to get 3/5, then convert to a percentage to get 60%.
Explanation:
In the given problem, we know that 2/5 of the voters voted for a new school tax. To find the probability that a randomly selected voter did not vote for the tax, we need to calculate the fraction of those who did not vote for the tax. Since the total probability must be 1 (or 100%), those who did not vote for the tax would account for the remaining fraction of 1 - 2/5, which is 3/5. To express this as a percentage, we convert 3/5 into a decimal and then into a percentage.
First, calculate 3/5 as a decimal: 3/5 = 0.6. Then, to convert it to a percentage, multiply by 100: 0.6 × 100 = 60%.
Therefore, the probability that a randomly selected voter did not vote for the new school tax is 60%, which corresponds to answer choice c. 60%.
To ship a 2 pound package, the company will charge $ and to ship a 3.5 pound package, the company will charge $
To determine the shipping cost of a 2-pound package, convert the weight to ounces (32 ounces), account for the initial charge for the first 3 ounces (1.95), and add the cost for the remaining 29 ounces at 0.17 each, totaling 6.88.
Explanation:To calculate the cost of shipping a 2-pound package, we use the given postal rates. Since there are 16 ounces in 1 pound, a 2-pound package equals 32 ounces. The post office charges 1.95 for the first 3 ounces. Every additional ounce costs 0.17. So we subtract the first 3 ounces from the total weight and then calculate the cost for the remaining ounces.
The calculation can be done as follows:
Initial 3 ounces: 1.95Remaining weight in ounces: 32 - 3 = 29 ouncesAdditional cost: 29 ounces x 0.17/ounce = 4.93Total cost: 1.95 + 4.93 = 6.88This approach to calculating postage makes it easy to understand the incremental cost structure of shipping packages.
using the digits, 1,2,3,4,and 5, how many even three digit numbers less than 500 can be formed if each number can be used more than once!
Answer:
Step-by-step explanation:
f(x)= 2 cos π x + sin π x is a sinusoid.
Answer
TRUE
Step-by-step explanation:
We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is a sinusoid.
The function is
f(x) = 2*cos(π*x) + sin(π*x)
Which can be seen in the picture below
We can notice that f(x) is a sinusoid. It has periodic amplitudes, and the function has a period T = 2
The maximum and minimum values are
Max = 2.236
Min = -2.236
What are the amplitude, period, and phase shift of the given function? f(t)=-2/3 cos (3t-3pi)
Answer:
amplitude; [tex]\frac{2}{3}[/tex]
Phase shift; [tex]\pi[/tex] units right
Period;[tex]\frac{2\pi}{3}[/tex]
Step-by-step explanation:
The given function is
[tex]y=-\frac{2}{3}\cos(3t-3\pi)[/tex]
This function is of the form;
[tex]y=A\sin (Bt+C)[/tex]
The period is given by:
[tex]|A|=|-\frac{2}{3}|= \frac{2}{3}[/tex]
The period is given by:
[tex]T=\frac{2\pi}{|B|}= \frac{2\pi}{|3|}=\frac{2\pi}{3}[/tex]
The phase shift is given by;
[tex]\frac{C}{B}=\frac{-\3pi}{3}=- \pi[/tex] or [tex]\pi[/tex] units right.
Please answer fast!!! will give brainliest!!!
given: m arc PIV = 7/2 m arc PKV Find: m∠VPJ
Answer:
The measure of angle VPJ is [tex]140\°[/tex]
Step-by-step explanation:
Let
x-----> the measure of arc PIV
y-----> the measure of arc PKV
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<VPJ=\frac{1}{2}(x)[/tex]
[tex]x=3.5y[/tex] -----> equation A
[tex]x+y=360\°[/tex] -----> equation B
substitute equation A in equation B
[tex]3.5y+y=360\°[/tex]
[tex]4.5y=360\°[/tex]
[tex]y=80\°[/tex]
Find the value of x
[tex]x=3.5(80\°)=280\°[/tex]
Find the measure of angle VPJ
[tex]m<VPJ=\frac{1}{2}(280\°)=140\°[/tex]
The total area of Wisconsin is 65498 square miles. Of that, about 80% is land area. About how many square miles of Wisconsin is not land area?
About 13099.6 square miles of Wisconsin is not land area.
Explanation:To find the amount of square miles of Wisconsin that is not land area, we need to calculate 20% of the total area. First, we find 1% of the total area by dividing it by 100. 65498 square miles / 100 = 654.98 square miles. Then, we multiply this by 20 to find 20%: 654.98 square miles * 20 = 13099.6 square miles. Therefore, about 13099.6 square miles of Wisconsin is not land area.
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Cathy has a nickel, a dime, and a quarter in her purse. She randomly picks a coin, replaces it, and then picks another coin. The probability that the two coins are of different denominations is .
SOMEONE HELP PLEASE THIS IS FOR PLATO.
Hence, the probability that the two coins are of different denomination is:
2/3
Step-by-step explanation:Let N denote nickel, D denotes dime and Q denotes Quarter.
Now when two coins are drawn one after the other with replacement then the outcomes is given by:
(N,N) (N,D) (N,Q)
(D,N) (D,D) (D,Q)
(Q,N) (Q,D) (Q,Q)
This means that there are a total of 9 outcomes.
The outcomes such that both the denominations are different i.e. the number of favorable outcomes are: 6
{ (N,D) (N,Q) (D,N) (D,Q) (Q,N) (Q,D) }
The probability that the two coins are of different denomination is:
6/9=2/3
You and a friend both would like a salad and a small drink. Between the two of you, you have $8.00. A salad costs $2.49 and a small drink is $.99. Can either of you have a second salad or drink? no, you cannot yes, 1 drink yes, 1 salad yes, 1 of each
Answer: yes, 1 of each
You can also get a second salad or drink because of the total as shown below:
$2.49 × 2 + $.99 × 2 = $6.96
What is the amplitude and period of f(t)=2.5 tan t?
Answer:
Option d.
Amplitude: None
Period: π
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached image below, to find more information about the graph
The equation is:
f(t) = 2.5 tan (t)
We can see from the graph that the amplitude goes up to infinity, and the period is equal to π.
Option d.
Amplitude: None
Period: π
The amplitude of the function f(t)=2.5 tan t is 2.5, as it's the coefficient of the tangent function. The period is π, as it's obtained by dividing π by the number multiplying 't', which in this case, is 1.
Explanation:The function given, f(t)=2.5 tan t, is a trigonometric function, which represents a wave. In the context of a wave represented by a trigonometric function such as this, there are several key components. The two most important for this question are:
Amplitude: The amplitude of a wave is the peak value of the wave. In the given equation, the amplitude is the coefficient of the trigonometric function, which is 2.5.Period: The period of a wave is the length of one cycle of the wave. The period of a tan function is (π/b), where 'b' is the number multiplying t. In this case, as 't' doesn't have any multiplier, the period is π. Learn more about Amplitude and Period here:
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What Is The Circumference Of This Circle? Use 3.14 For Pi. There Is A Line Down The Middle Saying "12 cm"
12 is the diameter. We need the circumference which you get by multiplying 12x2 sides which = 24 which is the circumference
What is the 10th term of the geometric sequence 400, 200, 100…?
A. 0.09765625
B. 0.390625
C. 0.78125
D. 1.5625
Answer: The correct option is (C). 0.78125.
Step-by-step explanation: We are given to find the 10th term of the following geometric sequence
400, 200, 100, . . . .
We know that,
the n-th term of a geometric sequence with first term a and common ration r is given by
[tex]a_n=ar^{n-1}.[/tex]
In the given sequence,
first term, a = 400
and
common ration is given by
[tex]r=\dfrac{200}{400}=\dfrac{100}{200}=~.~.~.~=0.5.[/tex]
Therefore, the 10th term of the sequence is
[tex]a_{10}= ar^{10-1}=400\times (0.5)^9=400\times0.001953125=0.78125.[/tex]
Thus, the correct option is (C). 0.78125.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Assume that there are 2 trials.
X = 2 where X represents the number of successes.
Which probability matches the probability histogram?
Round the answer to one decimal place.
Answer: The probability of the histogram is 0.6.
Step-by-step explanation:
Look at the images below for the step-by-step explanation. It's a lot easier to write on docs, rather than on this website. Anyway, I hope you've learned something. Bye!!!
Line CD passes through (0, 1) and is parallel to x + y = 3. Write the standard form of the equation of line CD. x + y = 1 x – y = 1 x + 1 = y x + y = 11
ANSWER
x+y=1
EXPLANATION
We want to find the equation of line CD which passes through (0, 1) and is parallel to x + y = 3.
In slope intercept form, the given line is
y=-x+3
The slope of this line is m=-1
Line CD also has the same slope
The equation is given by:
y=mx+b
The given point (0,1) means the y-intercept;is b=1
Hence the equation is
y=-x+1
In standard form the equation is:
x+y=1
Answer:
The answer is x + y = 1
Step-by-step explanation:
Given: Line CD passes through (0, 1) and is parallel to x + y = 3.
We know that if two line are parallel then they have equal slopes.
Thus, the slope of line = slope of line x + y = 3
x + y = 3 when we compare this to the standard linear equation
= 3 - x
y = m x + c .we get m = -1 .
The slope of CD (m)= -1
Now, the equation of line CD passing through (0,1) is given by :-
( y - 1 ) = m ( x - 0 )
⇒ ( y - 1 ) = ( -1 ) x
⇒ x + y = 1
The equation of line CD = x + y = 1
(8Q) Tell whether the function exhibits damped oscillation. If it does, identify the damping factor and tell whether the damping occurs.
Answer:
Option c.
No damping
Step-by-step explanation:
We can easily solve this question by using a graphing calculator or any plotting tool.
The function is
f(x) = (√11)*cos(3.7x)
Which can be seen in the picture below
We can notice that f(x) is a cosine with maximum amplitude of (√11). Neither this factor nor the multiplication of x by 3.7 serve as a damping factor since they are constants.
f(x) does not present any dampening
Answer:
C) No damping.
Step-by-step explanation:
This is the correct answer on ed-genuity, hope this helps! :)
Solve (x - 2 < 5) U (x + 7 > 6).
A) {x | -1 < x < 7}
B) {all real numbers}
C) Ø
Answer:
A) {x | -1 < x < 7}
Step-by-step explanation:
Given in the question two inequalities,
Inequality 1
(x - 2 < 5)
x < 5 + 2
x < 7
x is smaller than 7
Inequality 2
(x + 7 > 6)
x > 6 - 7
x > -1
x is greater then -1
When (x - 2 < 5) U (x + 7 > 6).
(x < 7) U (x > -1)
-1 < x < 7
When combined, x is greater than -1 but smaller than 7
If A=16°55’ and c=13.7, find a (picture provided)
Answer:
c. 4.0
Step-by-step explanation:
To find a, we'll use the Law of Sines that says:
[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]
And we'll isolate a to get:
[tex]a = \frac{sin(A) * c}{sin(C)}[/tex]
Then we will plug-in the information we already have (changing 16°55' into 16.92)
[tex]a = \frac{sin(16.92) * 13.7}{sin(90)} = 3.99[/tex]
So, let's round it to 4 to match the answer number C.
Answer:
C
Step-by-step explanation:
Use the definition of the sine function:
[tex]\sin \angle A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}.[/tex]
Substitute [tex]\angle A=16^{\circ}55'[/tex] and [tex]c=13.7[/tex] into the previous formula:
[tex]\sin 16^{\circ}55'=\dfrac{a}{c},\\ \\\sin 16^{\circ}55'=\dfrac{a}{13.7},\\ \\a=13.7\cdot \sin16^{\circ}55',\\ \\a\approx 13.7\cdot 0.284\approx 4[/tex]
Please help me..........
Answer:
a = 7
Step-by-step explanation:
45 45 90 right triangle so it's an isosceles triangle (A triangle with two equal sides)
a = 7
What is the solution to the equation below?
[tex]\frac{\sqrt{3-2x} }{\sqrt{4x} } =2[/tex]
A. x = 5/6
B. x = 9/10
C. x = 1/6
D. x = 3/10
Answer: OPTION C
Step-by-step explanation:
Given the equation [tex]\frac{\sqrt{3-2x} }{\sqrt{4x} } =2[/tex], you need to solve for the variable "x".
First, you need to multiply both sides of the equation by [tex]\sqrt{4x}[/tex]:
[tex](\frac{\sqrt{3-2x}}{\sqrt{4x}})(\sqrt{4x} })=2(\sqrt{4x} })\\\\\sqrt{3-2x}=2\sqrt{4x}[/tex]
Now you need to square both sides of the equation:
[tex](\sqrt{3-2x})^2=(2\sqrt{4x})^2\\\\3-2x=4(4x)\\\\3-2x=16x[/tex]
Subtrac 3 and 16x from both sides:
[tex]3-2x-(3)-(16x)=16x-(3)-(16x)\\\\-18x=-3\\[/tex]
Divide both sides by -18:
[tex]\frac{-18x}{-18}=\frac{-3}{-18}\\\\x=\frac{1}{6}[/tex]
If you're any good at inequalities, please help!
The gas tank in Lou’s car holds 13 gallons of gasoline. There are already 7 gallons of gasoline in the tank. He is putting gasoline that costs $2.50 per gallon in his car. Lou spends x dollars putting gasoline in his car. Model a compound inequality for this situation.
Answer:
So the maximum amount of gasoline the tank can contain is 13 gallons and there are already 7 gallons of gasoline in the tank. Therefore, we want to make sure that the amount of gasoline put in the tank doesn't reach any higher than 13 gallon.
The amount of gasoline that Lou bought with x dollars is x/2.50 gallons.
We have the inequality:
x/2.50 + 7 ≤ 13
*If you solve it, x should be smaller or equal to $15.
The math problem can be solved by setting up a compound inequality expressing the range that Lou can spend on gasoline. This factors in the total capacity of his tank, the current amount of gas, and the price per gallon. The result is 0 <= x <= $15.
Explanation:For this problem, Lou needs to fill the remainder of his gas tank, which is 13 gallons total but already has 7 gallons. That means he needs to fill 13 - 7 = 6 gallons more. Gasoline costs $2.50 per gallon, so the total amount of money he spends, represented by x, can be calculated using the inequality $2.50 * number of gallons <= x.
But because Lou can add anywhere from 0 to 6 gallons, we will have a compound inequality. So, the inequality will be: $2.50 * 0 <= x <= $2.50 * 6.
This simplifies to 0 <= x <= $15, meaning Lou can spend anywhere from $0 to $15 on gasoline, depending on how much more he wants to put in his tank.
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