Yes, Ms. Ouzts will have enough to purchase the purse as $125 is greater than the total cost of the purse including tax, which is $108.50.
The sales tax in South Carolina is 8.5%, which means that the total cost of the purse including tax will be
= Cost of purse + Sales tax
Substitute the values in the equation
= $100 + (8.5% of $100) = $100 + $8.50 = $108.50
If Ms. Ouzts has $125 to spend on the purse, then she will have enough to purchase it because $125 is greater than $108.50.
In fact, she will have $125 - $108.50 = $16.50 left over after buying the purse.
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ruby is using the quadratic formula to solve a quadratic equation. which of the following is the next step for simplifying x=−6±85√2 responses
x=−3±8√5
x=−3±√5
x=−3±4√5
this is fully simplified.
(1 point) a spherical balloon is inflated so that its volume is increasing at the rate of 2.8 ft3/min . how rapidly is the diameter of the balloon increasing when the diameter is 1.5 feet?
The diameter of the balloon is increasing at a rate of approximately 0.79 ft/min when the diameter is 1.5 feet.
We can use the formula for the volume of a sphere to relate the rate of change of volume with the rate of change of diameter
V = (4/3)πr^3 = (1/6)πd^3,
where V is the volume, r is the radius, and d is the diameter.
Taking the derivative with respect to time t, we get
dV/dt = (1/2)πd^2 (dd/dt),
where dd/dt is the rate of change of diameter.
We are given that dV/dt = 2.8 ft^3/min and d = 1.5 ft, so we can solve for dd/dt
dd/dt = (2dV/dt)/(πd^2) = (2(2.8))/(π(1.5)^2) ≈ 0.79 ft/min.
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The ratio of cars to people in one country is 300 to 1,000. Write a fraction to represent this ratio in simplest form
Answer:
3/10
Step-by-step explanation:
In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About how many times greater was the intensity of the Chilean earthquake? a. 2.5 b. 25 c. 150 d. 316
In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About 316 times greater was the intensity of the Chilean earthquake.
Hence, the correct option is D.
The Richter scale is a logarithmic scale that measures the magnitude of an earthquake. Each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves.
To find out how many times greater the intensity of the Chilean earthquake was compared to the Haitian earthquake, we will have to find the difference in magnitude between the two earthquakes.
9.5 - 7.0 = 2.5
Since each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves, a 2.5 increase represents
10^(2.5) = 316.2
Hence, the intensity of the Chilean earthquake was about 316 times greater than the intensity of the Haitian earthquake.
Hence, the correct option is D.
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Answer:d
Step-by-step explanation:
its d
the _____ (if any) are determined by the values of x that make f(x)=0. to find them, solve the quadratic equation:
The roots (if any) are determined by the values of x that make f(x) = 0. To find them, we solve the quadratic equation associated with the function.
A quadratic equation is an equation of the form:
ax² + bx + c = 0
where a, b, and c are constants. For a quadratic function of the form:
f(x) = ax² + bx + c
the roots are the values of x that satisfy the equation f(x) = 0. To find the roots, we set f(x) equal to zero and solve for x using the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
If the discriminant (b² - 4ac) is negative, then the quadratic equation has no real roots, and the function f(x) does not intersect the x-axis. If the discriminant is zero, then the quadratic equation has one real root, and the function f(x) touches the x-axis at that point. If the discriminant is positive, then the quadratic equation has two real roots, and the function f(x) intersects the x-axis at those points.
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on the coordinate plane, triangle PQR is rotated 180* clockwise about the origin O
we get the coordinates of Q' as (2,3) after rotation of the triangle.
What is rotation of axis?
Rotation of axes is a transformation in which the coordinate axes are rotated by a certain angle with respect to the original axes. This transformation can be used to simplify the equations of curves and to make it easier to solve problems involving them. The rotation is usually done by finding the angle of rotation, which is the angle between the original x-axis and the new x-axis. The formulae for converting coordinates from the old system to the new system can then be applied.
In the given problem, we are given that triangle PQR is located in the xy-plane with coordinates of Q being (2,-3). The task is to find the coordinates of Q' when triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R'.
To start, we apply the 180 degree clockwise rotation about the origin transformation rule to the coordinates of Q (2,-3) which gives us (-2,3).
Next, we reflect the point (-2,3) across the y-axis. Reflecting across the y-axis involves changing the sign of the x-coordinate while leaving the y-coordinate unchanged. Applying this rule,
Hence, we get the coordinates of Q' as (2,3) after rotation of the triangle.
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The center of a circle is at (−2, −7) and its radius is 6.
What is the equation of the circle?
Responses
(x+2)2+(y+7)2=3
open parenthesis x plus 2 close parenthesis squared plus open parenthesis y plus 7 close parenthesis squared equals 3
(x+2)2+(y+7)2=36
open parenthesis x plus 2 close parenthesis squared plus open parenthesis y plus 7 close parenthesis squared equals 36
(x−2)2+(y−7)2=3
open parenthesis x minus 2 close parenthesis squared plus open parenthesis y minus 7 close parenthesis squared equals 3
(x−2)2+(y−7)2=36
option B is correct: [tex](x+2)^2+(y+7)^2=36[/tex]
The general equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where,
(h, k) is the center of the circle and r is the radius of the circle.
As per the statement:
The center of a circle is at (−2, −7) and its radius is 6.
[tex]\implies (h, k) = (-2, -7)[/tex] and [tex]r = 6[/tex] units
Substitute these we have:
[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]
[tex]\implies(x+2)^2+(y+7)^2=36[/tex]
Therefore, the equation of circle is, [tex]\bold{(x+2)^2+(y+7)^2=36}[/tex]
On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. What is the probability that the appliance will work at least six years without requiring repairs?
The probability that the appliance will work at least six years without requiring repairs is 0.2231 or 22.31%.
To find the probability that the appliance will work at least six years without requiring repairs, we need to consider the exponential distribution and the given average repair time. Given that the appliance requires repairs once every four years on average, the rate parameter (λ) for the exponential distribution is 1/4, or 0.25.
Here we want to find the probability that the appliance will work at least six years without requiring repairs, which can be represented as [tex]P(X ≥ 6)[/tex], where X is the time between repairs. Using the complementary probability, we can rewrite this as [tex]P(X ≥ 6) = 1 - P(X < 6)[/tex]
The cumulative distribution function (CDF) of the exponential distribution is given by
[tex]F(x) = 1 - e^{(-λx)}[/tex]
Now, we can plug in the values:
[tex]P(X ≥ 6) = 1 - F(6) \\ P(X ≥ 6) = 1 - (1 - e^{(-0.25 \times 6)}) \\ P(X ≥ 6) = 1 - (1 - e^{(-1.5)}) \\ P(X ≥ 6) = e^{(-1.5)}[/tex]
Therefore, the probability that the appliance will work at least six years without requiring repairs is approximately 0.2231 or 22.31%.
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A credit card starts new customers at a $2,000 limit when they are approved for a card. The company adds $500 annually to this limit for customers who pay their bill on time. Choose the equation below that gives the credit limit, Ln, of customers who have payed on time every year, and who are in their nth year of having the card. Then, use this equation to find the credit limit of a customer in their 10th year of having the card.
On solving the provided question we can say that As a result, the credit equation limit of a client who has paid on time every year for the past ten years is $7,000.
What is equation?A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions. The equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14, for instance.
The relationship between the two sentences that are located on opposite sides of a letter is explained by a mathematical formula. Frequently, the symbol and the single variable are identical. like in 2x - 4 = 2, for example.
The following equation determines the credit limit, Ln, of customers who have made on-time payments each year and are in the nth year of card ownership:
Ln = $2,000 + $500n
where Ln stands for the credit limit in the nth year and n is the number of years the cardholder has had it.
In the equation above, we substitute n=10 to get a customer's credit limit after ten years of card use:
L10 = $2,000 + $500(10)
L10 = $2,000 + $5,000
L10 = $7,000
As a result, a client with a ten-year history of on-time payments has a credit limit of $7,000.
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What is the name corresponding to the metric symbol mL?
838
Discovering Solids Quiz
Geometry B (SP23) 3 / Area
1. How many faces, vertices, and edges are in the figure below?
faces= 6, vertices = 5, edges = 9
Ofaces= 5, vertices = 6, edges = 10
Ofaces = 7, vertices = 7, edges = 12
faces = 8, vertices = 8, edges = 8.
A hexagonal pyramid has seven vertices.
A hexagonal pyramid contains 12 edges.
A hexagonal pyramid has seven faces.
What is a hexagonal pyramid?A hexagonal pyramid is a type of pyramid that exists. A hexagonal pyramid has a hexagonal foundation and isosceles triangles as the faces that join the pyramid together at the top.
A hexagonal pyramid is a 3D pyramid with a hexagonal foundation and sides or faces in the shape of isosceles triangles that form the hexagonal pyramid at the apex or top of the pyramid. A hexagonal pyramid has six sides and six isosceles triangular lateral faces. Heptahedron is another name for a hexagonal pyramid. A hexagonal pyramid has seven faces, twelve edges, and seven vertices. For your convenience, an image of a hexagonal pyramid is provided below.
A hexagonal pyramid has seven vertices in toa
\x linking the triangle edges to the primary vertex and six base edges.
A hexagonal pyramid has seven faces, one for each side of the triangle, and one base.
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Use the figure shown below to complete the sentence? The area of the figure is blank square units
Bret bought his family lunch. Before tax, the bill came to $42. The sales tax was 6% and Bret tipped the waitress 20% before tax was added. How much money did Bret spend?
Answer: Bret spent $52.92 on the lunch, including tax and tip.
Step-by-step explanation:
Given:
The bill before tax = $42
Sales tax = 6%
Tip = 20% before tax
To find:The total amount of money Bret spent
Solution: Calculate the sales tax:
Sales tax = 0.06 * $42 = $2.52
Calculate the total bill, including tax:
Total bill = $42 + $2.52 = $44.52
Calculate the bill before tax, based on which the tip is calculated:
Bill before tax = $44.52 - $2.52 = $42
Calculate the tip amount:
Tip = 0.2 * $42 = $8.40
Calculate the total amount spent by Bret:
Total spent = $44.52 + $8.40 = $52.92
Therefore, Bret spent $52.92 on the lunch, including tax and tip.
Right answer gets brainliest and 25 points‼️‼️‼️‼️
Answer: d
Step-by-step explanation:
Answer:
B: Range of round 1 were higher than the range of Round-2.
Step-by-step explanation:
Please give me Brainliest.
HELP!! I am soooo lost!! And Ineed quick help! 20 points!
From the knowledge of vertical angle theorem, angle TXS is equal to angle RXU which is equal to
62 degreesWhat is vertical angle?Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.
When two lines intersect at a point, they form four angles around that point, and the vertical angles are the pair of opposite angles, which are across from each other and not adjacent.
Vertical angel theorem have it that Vertical angles are congruent, which means that they have the same measure or size. This theorem helps us in providing a correct answer for the problem
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Solve the quadratic equation x² +9x = 0 by
factoring the GCF.
Answer: x=0 and x=-9
Step-by-step explanation:
System analysts define an object's attributes during the systems design process. true or false?
The statement "System analysts define an object's attributes during the systems design process" is true because defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.
In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.
For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.
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show that,for all value for x
(2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2
Answer:
Therefore, the answer is: (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2
Step-by-step explanation:
To prove that (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2 for all values of x, we can simply expand the left-hand side of the equation and simplify it to match the right-hand side.
Expanding the left-hand side using the distributive property, we get:
(2x-1)(x+2)(3x-1) = (2x^2+3x-2)(3x-1)
= 6x^3 + 7x^2 - 9x + 2
This matches the right-hand side of the equation, so we have proven that (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2 for all values of x.
pls help fast with this question
Hence, it will take 2.6 hours for the two trains to be 520 miles apart.
What is the distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
What is the speed ?In everyday use and in kinematics, the speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity..
The two trains are moving away from each other,
so we can add their speeds to get their relative speed:
relative speed = 95 mph + 105 mph = 200 mph
Now ,we determine the time it takes for the trains to be 520 miles apart,
so we can use the formula:
distance = speed × time
let t be the time it takes for the trains to be 520 miles apart.
Then we get,
520 = 200 × t
Solving for t, we get:
t = [tex]\frac{520}{200}[/tex]
t = 2.6 hours
Therefore, it will take 2.6 hours for the two trains to be 520 miles apart.
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Consider the equation: x² + 10x + 22 = 13 1) Rewrite the equation by completing the square. Your equation should look like (x + c)2 = dor (x - c)² = d. 2) What are the solutions to the equation? Choose 1 answer: A x=5±4 x = -5±4 x = 5±16 x = -5±16
The solutions to the equation x² + 10x + 22 = 13 are: x = -5 ± 4
Solving the equation by completing the squareTo rewrite the equation by completing the square, we need to isolate the constant term on one side and group the x-terms together. Starting with:
x² + 10x + 22 = 13
Subtracting 13 from both sides:
x² + 10x + 9 = 0
Next, we add and subtract the square of half of the coefficient of x (which is 5 in this case) to complete the square:
x² + 10x + 25 - 25 + 9 = 0
x² + 10x + 25 - 16 = 0
Factor the perfect square trinomial:
(x + 5)² - 16 = 0
Now that we have rewritten the equation in the form (x + c)² = d, we can solve for x by taking the square root of both sides:
(x + 5)² - 16 = 0
Taking the square root of both sides and solving for x, we get:
x + 5 = ±4
So, we have
x = -5 ± 4
So the solutions to the equation are:
x = -5 + 4 = -1
x = -5 - 4 = -9
Therefore, the answer is x = -5 ± 4.
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solve for x
khan academy solve similar triangles advanced
Value of side CD = x=3
What is similarity of two triangle ?When two triangles are are referred to as similar figures when they share the same shape but different in size.
given that CB and ED are perpendicular to AD,
in triangle ABC and ADE
∠A=∠A (common angle )
∠B=∠D (both are 90 degree)
ΔABC≈ ΔADE by angle-angle similarity .
and we know that when two triangle are similar then their corresponding sides are with in the same ratio or proportional.
so ,here we proved that triangle ABC and ADE are similar,
then ,
[tex]\frac{BC}{ED}=\frac{AB}{AD}[/tex]
[tex]\frac{x}{5}=\frac{9}{9+6}[/tex]
[tex]\frac{x}{5} =\frac{9}{15}\\ X=3[/tex]
x=3
from above result ,value of side CB =x=3
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A plane rises from take-off and flies at an angle of 3 degrees with the horizontal runway. When it has gained 850 feet, find the distance, to the nearest foot, the plane has flown.
How many feet the the plane approximately fly?
By Tangent function, to the nearest foot, the plane has flown approximately 28,333 feet.
Describe Tangent?A closed, two-dimensional shape, a circle is also a curve. The radius of the circle or the line connecting the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying figure.
We are aware of our side and degree. We must determine how far the aircraft has traveled.
To determine how far the plane has traveled, we can utilize the sine function. Keep in mind that the sine function's definition is
tan(θ) = opposite/adjacent = height/distance.
tan(3) = 850/d
Solving for d, we get:
d = 850/tan(3)
d ≈ 28,333 feet
Tangent figure given below:
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Question 10(Multiple Choice Worth 2 points)
(11.01 LC)
What is the range of this data set?
The range of this data set include the following: D. 6.
What is a range?In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph (dot plot) shown in the image attached above, we can reasonably and logically deduce the following range:
Range = {18, 19, 20, 21, 22, 24} = 6.
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a lot is in the shape of a right triangle. the shorter leg measures 150 m. the hypotenuse is 50 m longer than the length of the longer leg. how long is the longer leg?
Answer:
Starting with the 3-4-5 right triangle, multiply all lengths by 50, obtaining 150, 200, and 250. So the length of the longer leg is 200 meters.
Mona loves making beaded necklaces. Today, she has a string that is 20 centimeters long. She leaves 2 centimeters on each end. Then, she fills the rest of the string with little beads that are 4 millimeters wide. How many little beads will she need?
Answer:
40 beads
Step-by-step explanation:
First, let's find the length of string that the beads will be on.
The string is originally 20 cm, but 2 cm is taken off each side.
So, the string that the beads will be on is only 16 cm now.
Each bead is 4 mm wide, so we have to convert the bead width to centimeters.
4/10=0.4
So each bead is 0.4 cm.
Now to find how many beads will fit, we have to divide the length by the width of the bead.
16/0.4=40
So, Mona will need 40 beads. Hope this helps ;)
Solve the following quadratic equation for all values of x in simplest form. 2 ( x+ 8 ) ^2 + 9 =29
Answer:
x = -8 + sqrt(10) and x = -8 - sqrt(10)
Step-by-step explanation:
The quadratic equation to be solved is:
2(x + 8)² + 9 = 29
First, we need to simplify the left-hand side of the equation by expanding the squared term:
2(x + 8)(x + 8) + 9 = 29
Simplifying further, we get:
2(x² + 16x + 64) + 9 = 29
Distributing the 2, we get:
2x² + 32x + 128 + 9 = 29
Combining like terms, we get:
2x² + 32x + 137 = 29
Subtracting 29 from both sides, we get:
2x² + 32x + 108 = 0
Dividing both sides by 2, we get:
x² + 16x + 54 = 0
We can solve this quadratic equation by factoring or by using the quadratic formula :
The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).
You start driving west for 3 miles, turn right, and drive north for another 11 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
we randomly select 100 pell grant recipients from two states. state a is a relatively small state with approximately 4,000 pell grant recipients. state b is a large state with approximately 200,000 pell grant recipients. suppose that the mean and standard deviation in individual pell grants is approximately the same for both states: and . for which state is the sample mean for our 100 pell grant recipients most likely to be within $80 of $2,600? group of answer choices state a because the sample represents a larger segment of this small population. state b because there is less variability in larger populations so estimates from samples are more accurate. equally likely because for both states.
Answer: The answer is state B because there is less variability in larger populations so estimates from samples are more accurate. The standard error of the mean is proportional to the standard deviation of the population and inversely proportional to the square root of the sample size. Since state B has a much larger population, it is more likely that our sample mean will be within $80 of $2,600 for state B than for state A.
Step-by-step explanation:
The radius of a circle is 9 millimeters. What is the circle's circumference?
Use 3.14 for л.
Answer:
56.55
Step-by-step explanation:
C=2πr=2·π·9≈56.54867
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Answer:
The vertex is option C: (-6, -2)
Step-by-step explanation:
The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)
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