Problem Statement
We are told a store offers 15% discount on the sale of a stereo originally costing $400. After the sale, the new price is marked up by 15%.
We are asked to find what percentage of the original price is the new marked up price.
Method
T
Write the quadratic function in vertex form. Then identify the vertex.
g(x)=x^2+12x+37
The vertex form is y= (x+ 6)²+1.
What is Vertex form?The vertex form of a quadratic equation is y = a (x- h)² + k as opposed to the regular quadratic form, which is an x² + bx + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.
a=1
b=12
c=37
Consider the vertex form of a parabola.
a(x+ d)²+e
Now, d= b/2a
d=12/ 2
d=6
and, e= c-b²-4a
e= 37 - (12)²/4x1
e= 37 - 36
e= 1
Then, the vertex form is
y = a(x+ d)²+e
y= 1(x+ 6)²+1
y= (x+ 6)²+1
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What value of x makes this equation true?x+7------7A. 6B. 8C. 35 D. 42
We have
[tex]\begin{gathered} \frac{x+7}{7}=6 \\ x+7=6\times7 \\ x+7=42 \\ x=42-7 \\ x=35 \end{gathered}[/tex]Option C
a=460 rounded to the nearest 10 b=11.9 rounded to 1 dp find the minimum (to 2 dp) of a / b
The minimum result (to 2 dp) of a / b is 38.66
What is rounding decimals?The term "rounding decimals" refers to the accurate rounding of decimal figures. When rounding a decimal number, certain principles must be followed. Simply put, if the last digit is less than 5, round down the previous digit. However, if it is 5 or greater, round the previous digit up.Given:
a=460 rounded to the nearest 10
b=11.9
Now, substitute the values of a and b in a/b,
a/b = 460/11.9
Multiply the same integer(10) by both the numerator and denominator,
a/b = 4600/119
Round the number obtained
a/b ≅ 38.66
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A circle has a diameter of 24 centimeters. Central angle FOG is drawn, determining an arc FG. The radian measure of angle FOG is 3/4 What is the length of arc FG in centimeters?16 cm9 cm32 cm18 cm
Answer:
9 cm
Explanation:
We are given the following information:
Diameter = 24 cm
Angle FOG = 3/4 rad
The formula for calculating arc length is written below:
[tex]\begin{gathered} L=\theta\times r \\ where\colon \\ \theta=central\text{ angle of }arc,\text{ in }rad \\ r=radius \\ r=\frac{\text{Diameter}}{2}=\frac{24}{2}=12cm \\ \theta=\frac{3}{4}rad \\ \text{Substitute these into the formula, we have:} \\ L=\frac{3}{4}\times12 \\ L=\frac{3\times12}{4} \\ L=9cm \\ \\ \therefore L=9cm \end{gathered}[/tex]Therefore, the arc length is 9 cm
Describe the shape, orientation, and vertex of
each parabola relative to the graph of y=x².
Sketch each graph.
a) y=-0.5x² + 2
c) y = -0.1x² - 6
e) y=-3x²-5
g)y=8x²+4
b) y = 2x²
d)y=x²+4
f) y=0,1x² +2
h) y=-0.7x²-3
The parabola y = - 0.5x² + 2 opens downwards and the vertex is at (0,2) .
A parabola is a mirror-symmetric planar curve with a rough U-shape. It can be defined by many seemingly unrelated mathematical descriptions that all relate to the same curves.
One way to interpret a parabola is with a line and a point (the focus) (the directrix). The directrix is less significant. The parabola lies between the directrix or the focus and the endpoints in this plane that are uniformly spaced apart.
a) y=-0.5x² + 2 vertex is at (0,2)
c) y = -0.1x² - 6 vertex at (0,6)
d)y=x²+4 vertex at (0,-4)
e) y=-3x²-5 vertex at (0,5)
g)y=8x²+4 vertex at (0,-4)
h) y=-0.7x²-3 vertex at (0,3)
A parabola can also be thought of as a conic section formed by joining a right circular conical area with a plane perpendicular to another axis.
The graph of the parabola is attached below.
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Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
The given inequality has the following solution set
9.52 ≤ x ≤ 22.22
If we express this as an interval, we get [9.52, 22.22].
Here is the inequality which is Kali's earning potential
200 ≤ 15.75x + 50 ≤ 400
To solve the inequality, we must isolate the variable in the center; if we remove 50 from each of the three sides, we get:
200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 - 50
150 ≤ 15.75x ≤ 350
Now we must divide both totals by 15.75, yielding:
150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75
9.52 ≤ x ≤ 22.22
This is the inequality's solution; the solution set expressed as an interval will be [9.52, 22] or 9.52 ≤ x ≤ 22.22
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Find the largest of three consecutive odd integers whose sum is 111.
The largest of three consecutive odd integers whose sum is 111 is 39
What is an integer?Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.
Odd integers that follow each other grow (or shrink) by a factor of 2. Consider the numbers 1, 3, and 5. Add two to the preceding number to move from one to the following. You don't know where to begin, and that is the issue here. In actuality, you are searching for the least of the three integers, therefore this is your unknown.
x + (x + 2) + (x + 4) = 111
x + x + 2 + x + 4 = 111
3x + 6 = 111
3x = 105
x =[tex]\frac{105}{3}[/tex]
x = 35
35 ,37,39
The largest of three consecutive odd integers whose sum is 111 is 39
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Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(x) = x−1⁄3 (x − 12)
The critical value of the given function is = -11/2
The x values for which f'(x) = 0 are the crucial values of a function f(x).
The function in this quandary is:
h(x) = x−1⁄3 (x − 12)
The derivative is discovered using the quotient rule as follows:
[tex]h(x) = \frac{x - 1}{3(x - 12)} \\\\h'(x) = \frac{ (x-1) (3x - 36)' - (x - 1)'(3x - 36)}{(3x - 36)^{2} }\\\\h'(x) = \frac{ (x-1) (3) - (-1)(3x - 36)}{(3x - 36)^{2} }\\\\On equating it to 0\\\\\frac{ (x-1) (3) + 1(3x - 36)}{(3x - 36)^{2} } = 0\\\\3x - 3 + 3x + 36 = 0\\\\6x + 33 = 0\\\\x = \frac{-11}{2}[/tex]
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what is the slope of the line that passes through the points (-7,-8) and (-5,-6)? Write your answer in simplest form.
Answer:
m=1
Step-by-step explanation:
12+212+25,432*5,000+
Answer:
127160224
or use a calculator
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that
each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 18 couples.
Find the expected number of girls in groups of 18 births
Answer:
since the method is deemed to have no effect
which means probability of having a girl child is same as having a boy child which is 0.5
Total births = 18
Therefore, expected number of girls in groups should be equal to = 0.5 × 18 = 9
I hope this is helpful
(2tanθ-3cosθ) Expand
Point P(-3, 4) is a point on the terminal side of 0 in standard form. Find the exact value ofsine, cosine, and tangent for 0.
Solution
Step 1
The terminal side, containing point (-3, 4) is located in Quadrant 2.
sine is positive
cosine and tangent are both negative.
Step 2
Draw a diagram to illustrate the information
Step 3
[tex]\begin{gathered} Find\text{ d using the Pythagoras theorem} \\ d^2\text{ = 3}^2+\text{ 4}^2 \\ d^2\text{ = 9 + 16} \\ d^2\text{ = 25} \\ d\text{ = }\sqrt{25} \\ \text{d = 5} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} sine\text{ = }\frac{Opposite}{Hypotenuse} \\ Sin\theta\text{ = }\frac{4}{5} \end{gathered}[/tex][tex]\begin{gathered} Cosine\text{ = }\frac{Adjacent}{Hypotenuse}\text{ = }\frac{x}{d} \\ Cos\theta\text{ = }\frac{-3}{5} \end{gathered}[/tex][tex]\begin{gathered} tangent\text{ = }\frac{Opposite}{Adjacent}\text{ = }\frac{y}{x} \\ tan\theta\text{ = }\frac{-4}{3} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} sin\theta\text{ = }\frac{4}{5} \\ cos\theta\text{ = }\frac{-3}{5} \\ tan\theta=\frac{-4}{3} \end{gathered}[/tex]How long do people typically spend traveling to work? The answer may depend on where they live. Here are the travel times in minutes of 20 randomly chosen workers in New York state
Based on the information given, the standard deviation for the observation is: 23.802698 or approximately 24.
The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
The formula for Standard deviation is given as:
σ[tex]= \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} .[/tex]
Where
σ = population standard deviation
[tex]\bar x[/tex] = mean
x = each value of the population
n = number of observation
Note that mean ([tex]\bar x[/tex]) = [tex]\( \frac{1}{n} \sum_{i=i}^{n} x_{i} \),[/tex]
[tex]\bar x[/tex] = (5+10+10+10+10+12+15+20+20+25+30+30+40+40+60+60+65+70+70+70)/20
= 33.6
Hence the standard deviation for travel times for these 20 New York workers is:
Standard Deviation = [tex]\sqrt{\frac{\sum(x_{1} - {\bar x})^{2} }{n-1} }[/tex]
= √ [(5-33.6)²+ (10 - 33.6)² + .... + (70 - 33.6)²]/(20-1)]
Standard Deviation = √(10764.8)/(20-1)
SD = √(10764.8/19)
SD = √566.56842
SD = 23.802698
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Full Question:
How long do people spend traveling to work? The answer may depend on where they live here are the travel times in minutes for 20 workers in New York chosen at random by the census bureau:
5 10 10 10 10 12 15 20 20 25 30 30 40 40 60 60 65 70 70 70
What is the standard deviation for travel time for these 20 New York state workers?
Need help with absolute value please
Answer:
let's say you need to find the absolute value of -5 the answer would be 5.
Step-by-step explanation:
Since the distance between -5 and 0 in a number line is 5. This would also be applied If you you were trying to find the absolute value of 5. it would also be 5.
When in math, I figured out negative number's absolute value will always be positive. absolute value numbers of positive numbers will stay the same.
Brittany has 34,011 in a savings account that earns 6% annually. the interest is not compounded. How much interest will she earn in 4 years? use the formula I = PRT, where I is the interest earned, p is the principal, r as the interest rate expressed as a decimal, and T is the time in years.
Notice that we are dealing with simple interest, and therefore given by the formula:
I = P * R * T
where P = $34,011
R = 6% in "decimal" form (0.06)
T = 4 (for 4 years)
Then, we have:
I = 34011 * 0.06 * 4 = $8162.64
This is the interest Brittany earned in 4 years.
11. Algebra The total cost of the Fatigato
family's two cars was $71,482. The cost of
one car was $38,295. Write an equation
using a variable to represent the cost of
the family's other car.
Answer:
$33,187
Step-by-step explanation:
Our total is 71,482 so let's set our equation to 71482=_________
Now we have $38,295 for one car, and we will subtract it from the total to find the other car, as there are 2 cars.
Equation:
71482-38295=x OR 71482=38295+x
X is the cost of the second car.
If one of the flights is randomly selected find the probability that the flight silicon Rosa United Airlines flight given that it was on time.
Total of flights on time: 22 + 53 = 75
probability that the flight selected was silicon Rosa United Airlines:
53/75 = 0.71 = 71%
Two trains leave the same station at the same time, one traveling west at a constant speed of 60 miles per hour, the other traveling south at a constant speed of 80 miles per hour. After how long are the two trains exactly 300 miles apart?
After 2.14 hours the trains are exactly 300 miles apart.
How to find the time the trains travel 300 miles apart?Two trains leave the same station at the same time, one traveling west at a constant speed of 60 miles per hour, the other traveling south at a constant speed of 80 miles per hour.
The time both of them will travel 300 miles can be calculated as follows:
Therefore,
speed = distance / time
distance = speed × time
The train that travel west:
let
t = time of the train that travel west
distance = 60t
The train that travel south:
distance = 80t
Therefore,
total distance = 60t + 80t
300 = 140t
t = 300 / 140
t = 2.14285714286
t = 2.14 hours
Therefore,
time taken = 2.14 hours
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In the diagram below, the circle has a radius of 25 inches. the area of the unshaded is 500pi in^2Determine and state the degree measure of angle Q, the central angle of the shaded sect
1) In this question, we are going to make use of the formula for the area of that sector, to find the central angle.
2) So, let's write it out an expression involving the area of a circle, the unshaded area, and the shaded one and then plug into that the given data:
[tex]\begin{gathered} A=\frac{\alpha}{360^{\circ}}\times\pi r^2 \\ A_{Unshaded}+A_{shaded}=A_{Circle} \\ 500\pi+\frac{\alpha}{360}\times\pi r^2=\pi r^2 \\ \\ 500\pi+\frac{α}{360}\pi25^2=25^2\pi \\ \\ 500\pi+\frac{125\piα}{72}=625\pi \\ \\ 500\pi +\frac{125\pi α}{72}-500\pi =625\pi -500\pi \\ \\ \frac{125\pi α}{72}=125\pi \\ \\ \frac{72\times \:125\pi α}{72}=72\times \:125\pi \\ \\ \frac{125\pi α}{125\pi }=\frac{9000\pi }{125\pi } \\ \\ α=72^{\circ} \\ \\ \end{gathered}[/tex]Thus, the centra angle of that shaded area is 72º
please help me solve. I have the answer in yellow, but it's not correct.
Remember that
27=(3)(3)(3)=3^3
so
[tex]\sqrt[]{3\cdot}\sqrt[\square]{27}=\sqrt[]{3\cdot}\sqrt[\square]{3^3}=\sqrt[]{3^4}=3^2=9[/tex]answer is 9
so
9 NA
blank 1 ------> 9
blank 2 ------> NA
what is the value of a in the equation 5a – 10b = 45, when b =3?a)3b)15c)21d)39
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]5a-10b=45[/tex]STEP 2: Substitute 3 for b in the equation
[tex]5a-10(3)=45[/tex]STEP 3: Simplify the equation to solve for a
[tex]\begin{gathered} 5a-30=45 \\ 5a=45+30 \\ 5a=75 \\ a=\frac{75}{5} \\ a=15 \end{gathered}[/tex]Hence, the value of a is 15
Evaluate the expression below using the properties of operations. -36 ÷ 1/4 • (-1/8) • (-3) ÷ 6
Answer:
-9
Step-by-step explanation:
We are working with multiplications and divisions, which have no precedence over each other. So we can do the operations in order. It is important to remind that in these operations, if two numbers have different signals, the result of the operation is negative, otherwise, positive.
-36 ÷ 1/4
Different signals, so the result will be negative
[tex]\frac{-36}{\frac{1}{4}}=-36\ast\frac{4}{1}=-36\ast4=-144[/tex]-36 ÷ 1/4 • (-1/8) = -144 * (-1/8)
Same signal, so positive
[tex]-144\ast(-\frac{1}{8})=\frac{144}{8}=18[/tex]-36 ÷ 1/4 • (-1/8) • (-3) = 18 * (-3) = -54
-36 ÷ 1/4 • (-1/8) • (-3) ÷ 6 = -54 ÷ 6 = -9
How many solutions does this system of equations have?
y = x2 + x + 3
y = -2x - 5
Answer: (x, y) = (-8/5, -9/5)
Assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $1500. In a random sample of 300 familles, how many pay morethan $6440 annually for day care per child?Of the 300 families, approximately pay more than 56440 annually for day care per child(Round to the nearest whole number as needed.)
Let's begin by listing out the information given to us:
Mean = $8,000, SD = $1,500
In a sample of 300, how many pay more than $6440?
Find X. Circumscribed Angles
The value of of angle x of the circumscribing circle is x° = 140°
In the above question, the following figure is given, where
The angle inside the circle made by the intersection of two line segments is = 40°
We need to find the angle x made by the angle made by the tangents outside the circle
A line that touches a curve or a circle at one point is said to be tangent.
The point of tangency is the intersection of the tangent line and the curve.
We'll find the value of of angle x using the theorems of the circumscribing circle.
The sum of opposite angles of a circumscribing quadrilateral is always 180°
Using this property we can write,
40° + x° = 180°
x° = 180° - 40°
x° = 140°
Hence, the value of of angle x using the theorems of the circumscribing circle is x° = 140°
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8. A car costs $10,500, and you're offered a loan that requires $800 down and a monthly payment of $187.53 for 60 months, how much will you pay in interest? Round your answer to the nearest dollar.$
The Solution:
Given that a car that cost $10500 was offered as a loan with a down payment of $800.
This means the loan balance will now be:
[tex]\text{Loan baleance=10500-800= \$9700}[/tex]The loan payment plan is a monthly payment of $187.53 for 60 months.
[tex]\text{Total Payment=187.53}\times60=\text{ \$11251.80}[/tex]We are required to find how much was paid in interest.
We shall take the difference between the total payment and the loan balance.
[tex]\begin{gathered} \text{Interest paid=Total payment-Loan balance} \\ \text{Interest paid=11251.80-9700= \$1551.80}\approx\text{ \$1552} \end{gathered}[/tex]Therefore, the correct answer is $1552
Find
d93 /dx93 *(cos x)
by taking the first few derivatives and observing the pattern that occurs.
d93 /dx93 *(cos x) = - sin x
Now,
d/dx (cos x ) = -Sin x
d2/dx2 (cos x) = - cos x
d3/dx3 (cos x) = sin x
d4/dx4 (cos x) = cos x
d5/dx5 (cos x) = - sin x
d6/dx6 (cos x) = -cos x
The same pattern will repeat for every 6th derivative so ,
Now,
93 = (4 x 23) + 1
Therefore,
d93 /dx93 *(cos x) = - sin x
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Which expression is equivalent to (sin 2θ)(sec2θ)? 2sin θ sin θ tan θ 2tan θ
Answer:
Explanation:
Here, we want to get the expression that is equivalent to the given expression
We have this as follows:
[tex]\begin{gathered} \text{ sec 2}\theta=\text{ }\frac{\sec^2\theta}{2-\sec^2\theta} \\ \\ \sin 2\theta\text{ = 2sin}\theta\cos \theta \end{gathered}[/tex]Now, we can rewrite the overall expression as:
[tex]undefined[/tex]2(y−1)+6y = −10 please help fastest answer gets 37 points