Answer:
The equation of the ellipse is:
(x^2)/16 + (y^2)/4 = 1
Step-by-step explanation:
An ellipse is a set of points on a plane, the sum of whose distances from two fixed points (called foci) is constant. The distance between the foci of an ellipse is denoted by 2c, and the distance between the center of the ellipse and one of its vertices is denoted by a.
In this problem, the foci are located at (2,0) and (-2,0), so the distance between the foci is 2c = 4, which means that c = 2. The major vertices of the ellipse are located at (4,0) and (-4,0), so the distance between the center and one of the vertices is a = 4.
The formula for the equation of an ellipse centered at the origin is:
(x^2)/(a^2) + (y^2)/(b^2) = 1
where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex. Since the center of this ellipse is at the origin and the major axis lies on the x-axis, we know that b = a, so we can substitute a for b in the equation:
(x^2)/(a^2) + (y^2)/(a^2) = 1
To find a, we use the fact that c^2 = a^2 - b^2:
a^2 - b^2 = c^2
a^2 - a^2 = 4
b^2 = 4
b = 2
Now we can substitute a = 4 and b = 2 into the equation:
(x^2)/(16) + (y^2)/(4) = 1
This is the equation of the ellipse.
Cameron wants to buy a coat that costs $220. He has to pay 10% taxes on it.How much will he pay for the coat, including taxes
Cameron will have to pay amount $242 for the coat, including taxes.
If the coat costs amount $220 and there is a 10% tax on it, Cameron will have to pay an additional:
10% of $220 = 0.1 x $220 = $22
So the total cost of the coat including taxes will be:
$220 + $22 = $242
Therefore, Cameron will have to pay $242 for the coat, including taxes.
When purchasing goods or services, it's important to be aware of any additional costs such as taxes. In this scenario, Cameron wants to buy a coat that costs $220. However, there is a 10% tax on it, which means he will have to pay an extra $22 in taxes. The total cost of the coat, including taxes, will be $242. It's important to note that tax rates may vary depending on the location and type of item being purchased. Being aware of these additional costs can help individuals better budget and make informed purchasing decisions.
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Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a 98% confidence level. What does the confidence interval tell about the population of all college students in the state?
3.9, 2.9, 3.9, 4.8, 3.0, 4.2, 3.4, 4.5, 4.5, 4.2, 4.3, 3.9, 3.3, 3.9, 3.7
Answer:
The 98% confidence interval for this data is (3.5, 4.4). This confidence interval tells us that 98% of the time, the average rating of all college students in the state for the course will fall between 3.5 and 4.4.
What is 1. 2 x 10 ^5 in standard form?
Answer: 0.000012
Step-by-step explanation: The exponent is -5, making it 10 to the power of negative 5. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 5 times
1.2 -> 0.000012
Assignment: Waves Math Exploration
What is the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m?
Please answer immediately if able to!
200 m/s is the wave speed of a wave that has a frequency .
What do you name a wave?
There are two different types of waves: longitudinal and transverse. Longitudinal waves are similar to those of sound in that they alternate between compressions and rarefactions in a medium, much like transverse waves in that the surface of the medium rises and falls.
The pattern of disruption brought about by the movement of energy through a medium (such as air, water, or any other liquid or solid matter) as it spreads away from the source of the sound is known as a sound wave.
The wave speed (v) of a wave can be calculated by multiplying its frequency (f) by its wavelength (λ). Mathematically, we can express this as
v = f x λ
Substituting the given values of frequency and wavelength into this formula, we get:
v = 500 Hz x 0.40 m
Multiplying these values, we get:
v = 200 m/s
Therefore, the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m is 200 m/s.
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a wheel whose diameter is 3 feet rolls a distance of 45 feet without slipping. through what radian angle did the wheel rotate?
The wheel having 3feet diameter and travelling a distance of 45 feet is rotated about 30.00 radians.
A circle's circumference is equivalent to π times its diameter.
We can use the circumference formula to determine the circumference of the wheel
C = πd= π(3) = 9.42 feet where d is the diameter.
The wheel has traveled a distance of 45 feet.
We can determine the number of full rotations made by dividing the distance traveled by the circumference of the wheel.
Number of full rotations = distance traveled / circumference of the wheel= 45 / 9.42 = 4.77 full rotations
It is said that the wheel rolled without slipping, therefore the wheel must have turned 4.77 full rotations. The angle in radians through which it rotated is therefore
Angle in radians = number of full rotations x 2π= 4.77 x 2π= 30.00 radians
Therefore, the wheel rotated through a radian angle of 30.00.
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A car travels at a constant speed
It travels a distance of 146.2m, correct to 1 decimal place. This takes 7 seconds,correct to the nearest second
A circle with center � ( 5 , 2 ) O(5,2) contains the point � ( 11 , 10 ) A(11,10)
The point (11,10) lies on the circle with center (5,2).
The equation of the circle with center (5,2) and point (11,10) is given by [tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2.[/tex]
Substitute the coordinates of the center and point in the equation and simplify, we get
[tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2= (x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2= x^2 - 10x + 25 + y^2 - 4y + 4 = x^2 - 22x + 121 + y^2 - 20y + 100= -10x + 25 - 4y + 4 = -22x + 121 - 20y + 100= -10x - 22x = 121 - 25 - 20y + 4y=-32x = 96= x = 3[/tex]
Substitute this value of x in [tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2[/tex] and simplify, we get
[tex](3-5)^2 + (y-2)^2 = (3-11)^2 + (y-10)^2= (-2)^2 + (y-2)^2 = (-8)^2 + (y-10)^2= 4 + y^2 - 4y + 4 = 64 + y^2 - 20y + 100= -4y + 8 = -20y + 96= 16 = 16[/tex]
Hence, the point (11,10) lies on the circle with center (5,2).
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complete question
Explain with formula and calculation how a circle with center (5,2) contains the point (11,10).
a distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. find p81, which is the score separating the bottom 81% from the top 19%.
If the distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. the score separating the bottom 81% from the top 19% is 168.24.
The value of p81, which is the score separating the bottom 81% from the top 19%, can be calculated as follows:
The given, Mean = μ = 93.2
Standard deviation = σ = 87.4
We are supposed to find the score separating the bottom 81% from the top 19% which is nothing but the 81st percentile.
Let X be a random variable with a normal distribution, then the z-score of the 81st percentile is calculated as follows:
z = InvNorm(0.81)
z ≈ 0.8 (by standard normal distribution tables)
The 81st percentile in terms of X is given by:
p81 = μ + zσp81
= 93.2 + 0.8(87.4)p81
p81 = 168.24
Thus, the score separating the bottom 81% from the top 19% is 168.24.
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The attorney does not accept legal cases involving litigation that would result in less than a $45,000 fee. The attorney has the opportunity to represent a client who will pay him $175 per hour plus 25% of the settlement. What is the minimum acceptable settlement on a case on which the attorney spent 110 hours?
Therefore, the minimum acceptable settlement on the case is $103,000.
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100 or 50/100, which is equivalent to the fraction 1/2 or the decimal 0.5.
Percentages are commonly used to express proportions, rates, or changes. They are used in many different fields, such as finance, statistics, science, and everyday life. For instance, we might use percentages to describe the rate of interest on a loan, the percentage of people who have received a vaccine, or the percentage increase or decrease in the stock market.
by the question.
First, we need to calculate the total fee the attorney will earn based on the hourly rate and the percentage of the settlement.
The attorney's fee is the sum of the hourly fee and the percentage of the settlement:
hourly fee = 110 hours x $175 per hour = $19,250
percentage of the settlement = 25% of the settlement
total fee = hourly fee + percentage of the settlement
We know that the total fee must be greater than or equal to $45,000, so we can set up an equation to solve for the minimum acceptable settlement:
$19,250 + 0.25S ≥ $45,000
where S is the settlement amount.
Subtracting $19,250 from both sides, we get:
0.25S ≥ $25,750
Dividing both sides by 0.25, we get:
S ≥ $103,000
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Which can be use to show a decrease in the amount of yogurt in a container?
A. 1/6 B. 1/5 C. Negative 1/3 D. 1/8
The correct answer is option C, Negative 1/3, which means that the container has lost 1/3 of its original yogurt.
When it comes to representing a decrease in the amount of something, the easiest way is to use negative values.
In this case, option C, Negative 1/3 is the correct choice.
The fraction 1/6 means that the container has 1 part of the original 6 parts of the yogurt left.
However, this shows the remaining amount of yogurt in the container, not the decrease.
Therefore, we can say that the fraction 1/6 is not the correct choice in this context.
Similarly, options B and D are not correct choices for the same reason.
The correct answer is option C, Negative 1/3, which means that the container has lost 1/3 of its original yogurt.
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Find the sum of (8a +2b - 4 ) and ( 3b - 5)
The sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9). We can find it in the following manner.
To find the sum of (8a + 2b - 4) and (3b - 5), we can simply add the corresponding coefficients of the variables a and b, as well as any constant terms.
So we have:
(8a + 2b - 4) + (3b - 5)
= 8a + 2b + 3b - 4 - 5 (grouping like terms)
= 8a + 5b - 9
Therefore, the sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9).
We can also explain this process by using the distributive property of addition over subtraction. This property states that the sum of two numbers with the same sign (positive or negative) can be found by adding their absolute values and keeping the common sign.
In this case, we can think of the expression (8a + 2b - 4) as the sum of three terms: 8a, 2b, and -4. Similarly, we can think of the expression (3b - 5) as the sum of two terms: 3b and -5.
Using the distributive property, we can add the terms with the same variable together:
(8a + 2b - 4) + (3b - 5)
= 8a + (2b + 3b) - (4 + 5)
= 8a + 5b - 9
Thus, we obtain the same result.
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Estimate the length of the hypotenuse. y C. 5.7 7 8.1 410
The hypotenuse's length could therefore be between 9.03 and 10.70 units based on these estimates.
Define a right-angled triangle.The term "right triangle" refers to a triangle with an internal angle of 90 degrees. The hypotenuse, the side that faces the right angle and is also the side with the longest side in a right triangle, and the height and base are the two limbs of the right angle.
Based on the information provided, it is reasonable to infer that we have a right-angled triangle with two sides that are y and 7, and we need to determine the length of the hypotenuse.
The hypotenuse's square length is equal to the total of the squares of the lengths of the other two sides, according to the Pythagorean theorem.
The result is:
y² + 7² = hypotenuse²
hypotenuse² = y² + 49
we can determine the length of the hypotenuse by assuming that y is somewhere between 5.7 and 8.1.
If y is 5.7, then:
hypotenuse² = 5.7² + 49
hypotenuse² = 81.49
hypotenuse ≈ 9.03
If y is 8.1, then:
hypotenuse² = 8.1² + 49
hypotenuse² = 114.61
hypotenuse ≈ 10.70
So, based on these estimations, the length of the hypotenuse could be around 9.03 or 10.70 units.
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Complete question
Estimate the length of the hypotenuse, If the length of the two sides is y and 7 respectively
1) If y= 5.7
2) If y= 8.1
In a right-angled triangle, what is the side opposite the right angle called?
Answer:
The hypotenuse.
Step-by-step explanation:
there are six professors teaching the introductory discrete structure class at fiu. the same fnal exam is given by all six professors. if the lowest possible score on the fnal is 0 and the highest possible score is 100, how many students must there be to guaranteethat there are two students with the same professor who earned the same fnal examination score?
607 students must there be to guarantee that there are two students with the same professor who earned the same fnal examination score
We use Pigenhole principle to solve this problem.
We know the Pigenjole principle states that if y number of items are put into z number of containers, with y > z, then it means that that at least one container must definitely contain more than one item.
Here, the possible scores are from 0 to 100 with both inclusive.
So, the number of possible scores = 101.
Now, there are two students with the same professor who earned the same final examination score.
The number of students would be = 101 + 1
= 102
For each student there are 6 professors.
so the possible combination for a score would be = 6
So, the number of students must there be to guarantee that there are two students with the same professor who earned the same fnal examination score: (6 × 101) + 1 = 607
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Harry buys a TV priced at £1200 plus 20% VAT. He pays £300 deposit and the balance in ten equal monthly payments. Calculate each monthly payment.
Answer:
Step-by-step explanation:
Step 1: Find the TV price:
£1200×(100%+20%)= £1440
Step 2: Find the final price Harry have to pay:
since he deposited £300 so the ammout he have to pay is:
£1440 - £300 = £1140
Step 3: Find the monthly payment
in this case he pays equally every month so we take the ammount he has to pay devided by 10 months
£1140÷10=£114
Conclusion: He has to pay £114 every month
There are 1600 students in school. 47. 5% are male. How many are female
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{47.5\% of 1600}}{\left( \cfrac{47.5}{100} \right)1600}\implies 760~\hfill \underset{ females }{\stackrel{1600~~ - ~~760 }{\text{\LARGE 840}}}[/tex]
How do I solve this problem?
QR has a length of 2√3. According to the given question
HOW TO CALCULATE THE SIDE OF THE SQUARE ?
In order to solve for QR, we need to use the information given to us in the problem and apply some basic geometry concepts.
First, we know that the diagonals of a square are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other in half. This tells us that the length of the diagonal is equal to the square root of two times the length of one of the sides of the square, or d = s√2.
Next, we are given that the midpoint of one of the diagonals is point U, and that US has a length of 3. Because U is the midpoint of the diagonal, we know that SU and UR are equal in length. Let's call this length x.
Now we can use the Pythagorean theorem to solve for x:
(US)²+ (UR)² = (SR)²
3²+ x= (s√2)²
9 + x² = 2s²
We also know that SU and UR are each equal to x, so:
2x² = s²
We can substitute 2x² for s² in the previous equation:
9 + x² = 2(2x²)
9 + x²= 4x²
3x² = 9
x² = 3
x = √3
Now we can use x to solve for the length of QR:
QR = 2x = 2√3
Therefore, QR has a length of 2√3.
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Suppose you are working with a data set that is normally distributed, with a mean of 250 and a standard deviation of 44. Determine the value of x from the following information. (Round your answers and z values to 2 decimal places, e. G. 1. 25. ) (a) 70% of the values are greater than x. (b) x is less than 14% of the values. (c) 22% of the values are less than x. (d) x is greater than 57% of the values
(a) 70% of the values are greater than x: x = 233.43
(b) x is less than 14% of the values: x = 313.32
(c) 22% of the values are less than x: x = 287.09
(d) x is greater than 57% of the values: x = 259.26
(a) To calculate x, we need to find the z-score of the 70th percentile. This can be done using the z-score formula: z = (x-mean)/standard deviation. Plugging in our values, this gives us z = (x-250)/44. Solving for x, we get x = 250 + 44z. We can find z by using a z-score table and looking up the 70th percentile, which is 0.84. Plugging this into our equation yields x = 233.43.
(b) Similarly, for x to be less than 14% of the values, we need to find the z-score of the 14th percentile. Looking up the corresponding z-score in a z-score table, we find it to be -0.91. Plugging this into our equation gives us x = 313.32.
(c) To calculate x given that 22% of the values are less than x, we can again use the z-score formula. This time, we need to look up the z-score corresponding to the 22nd percentile, which is -0.52. Plugging this into our equation yields x = 287.09.
(d) Lastly, to calculate x given that it is greater than 57% of the values, we need to find the z-score of the 57th percentile. Looking up the corresponding z-score in a z-score table, we find it to be 0.41. Plugging this into our equation gives us x = 259.26.
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Shen drove 603 miles in 9 hours. At the same rate, how long would it take him to drive 335 miles?
Answer:
5 hours
Step-by-step explanation:
Since Shen drove at the same rate for both distances, we can use a proportion to solve for the time it would take him to drive 335 miles:
[tex]\frac{d_{1} }{t_{1} }=\frac{d_{2} }{t_{2} }[/tex]
where d1 is 603 miles, t1 is 9 hours, d2 is 335, and t2 is the unknown value.
Thus, we can simply plug in everything to the equation and solve for t2:
[tex]\frac{603}{9}=\frac{335}{t_{2} }\\ 67=\frac{335}{t_{2} }\\ 67t_{2}=335\\ t_{2}=5[/tex]
(*Note that 9 divides evenly into 603 and becomes 67, which is why I didn't cross-multiply first with he 603 and t2 and the 335 and 9, although you'd still get the same result for t2)
Thus, it would take Shen 5 hours to drive 335 miles.
You can check by finding the rate for both equations since we know that distance is equal to the product of rate and time (d = rt):
First equation: 603 miles = 9 hours * r mph
67 mph = r
603 = 67 * 9
Second equation: 335 miles = 5 hr * r mph
67 mph = r
335 = 67 * 5
Use regrouping to solve. Make sure your answer is not an
improper fraction.
10-1-1-6-²-2--
69
Noitoont insloviups no son datin
-1
To use regrouping to solve, we need to add and subtract the numbers in the expression, taking care to keep track of any negative signs.
10 - 1 - 1 - 6 - ² - 2
= 10 - (1 + 1) - 6 - ² - 2 [Group the first two numbers together and add them]
= 10 - 2 - 6 - ² - 2 [Simplify the first three terms]
= (10 - 2) - 6 - ² - 2 [Group the first two terms together and subtract them]
= 8 - 6 - ² - 2 [Simplify the first two terms]
= 2 - ² - 2 [Simplify the first two terms]
= -1 [Simplify the expression by subtracting ² and 2 from -1]
Therefore, the final answer is -1.
A concrete pillar has the shape of a cylinder. It has a diameter of 4 meters and a height of 5 meters. If concrete costs $107 per cubic meter, how much did the concrete cost for the pillar?
For your calculations, do not round any intermediate steps, and use the pi button on a calculator. Round your answer to the nearest cent.
The cost of the concrete used to make the cylinder was approximately $6,776.89.
The problem is asking us to find the cost of the concrete used to make a cylindrical pillar, given its dimensions and the cost per cubic meter of concrete. We first need to calculate the volume of the cylinder using the formula for the volume of a cylinder:
[tex]V=pir^2h[/tex]
where V is the volume, r is the radius, h is the height, and π is the constant pi (approximately 3.14159).
In the problem, the diameter of the cylinder is given as 4 meters, which means the radius is half of that, or 2 meters. The height of the cylinder is given as 5 meters.
Substituting these values into the formula, we get:
[tex]V = \pi r^2h = \pi (2)^2(5) = 20\pi cubic meters[/tex]
Next, we need to find the cost of the concrete used to make the cylinder, given that the cost per cubic meter of concrete is $107. We can do this by multiplying the volume of the cylinder by the cost per cubic meter of concrete:
20π × $107 = $6,776.89
Rounding to the nearest cent, we get that the cost of the concrete used to make the cylinder was approximately $6,776.89.
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19. A piece of wire 44 cm long is cut into two parts.
Each part is bent to form a square. Given that
the total area of the two squares is 65 cm², find the
perimeter of each square.
Answer:28 and 16 cams
Step-by-step explanation: let the two parts be x cms and 44 -x cms.
So side of squares will be x/4 and (44-x)/4 resp
Area will be (x/4)^2 and ((44-x)/4)^2 resp
Equation is(x/4)^2 + ((44-x)/4)^2 = 65
(X-28)(x-16) = 0
X =28 or x = 16 cms
WILL GIVE BRAINLIEST, NEED HELP ASAP.
A fisherman on the atchafalaya basin drops a line that lands in the water 1225 ft below, the equation [tex]\frac{d}{25} =t^{2}[/tex] represents the distand in feet, d, the object falls in t seconds. How long does it take to reach the bottom?
Answer:
7 seconds
Step-by-step explanation:
d is 1225, and we need to find t.
plug in 1225 for d:
1225/25 = t^2
49 = t^2
t = 7
Ms. Ibrahim travelled a total of 150 miles for work in 5 days. She traveled the same distance for work each day. Which 3 points lie on the line that represents the total distance in miles y, she traveled for work in x days. Circle three correct points.
Three pοints οn the line are: (0,0), (1,30), and (2,60)
what is slοpe-intercept fοrm?When yοu knοw the slοpe οf the line tο be investigated and the given pοint is alsο the y intercept, yοu can utilise the slοpe intercept fοrmula, y = mx + b. (0, b). The y value οf the y intercept pοint is denοted by the symbοl b in the fοrmula.
Tο sοlve the prοblem, we can start by using the fοrmula fοr the equatiοn οf a line in slοpe-intercept fοrm:
y = mx + b
We can use the given infοrmatiοn tο find the slοpe:
m = tοtal distance / number οf days = 150 miles / 5 days = 30 miles/day
b = 0 miles
Therefοre, the equatiοn οf the line representing the tοtal distance Ms. Ibrahim travels fοr wοrk in x days is:
y = 30x
When x = 0 (i.e., when Ms. Ibrahim dοes nοt wοrk), y = 0.
When x = 1 (i.e., οn the first day), y = 30 miles.
When x = 2 (i.e., οn the secοnd day), y = 60 miles.
Sο, three pοints οn the line are: (0,0), (1,30), and (2,60)
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Using identities evaluate :78x82
Answer:
6436
Step-by-step explanation:
78 x 82
= (80-2) * (80+2)
= (80^2 - 2^2)
= 6436
Mrs. Latham ordered 200 SCVCS business cards and paid $23. She ordered 500 business cards a few moths later and paid $35. Write and solve a linear equation to find out how much Mrs. Latham will spend if she orders 700 business cards.
Thus, to order the 700 business cards, Mrs. Latham will spend the amount of $43.
Define about the linear equation?In a linear equation, a first-degree polynomial is defined as the sum of a group of terms, where each term is the product of a constant as well as the initial power of a variable.
The linear equation using the slope intercept form is -
Y = mX + b,
where, Y - number of cards
X is the cost. m - slope of the line b = the y-intercept (0, b).Slope = (y2 - y1)/(x2 - x1),
y2=500 cards, y1=200 cards, x2=$35, and x1=$23.
m = (500-200)/(35-23) = 300/12
m = 25.
Now, slope m = 25, apply slope-intercept formula to find y when x=0.
Y = mX + b,
25 = (200 - y)/(23-x),
At, x=0,
25 = (200-y)/23
200 - y = 25*23
575 = 200 - y
y = -375 (y - intercept)
The linear equation :
Y = 25X -375.
Y = 700. Find X
700 = 25X - 375
25X = 325
X = $43
Thus, to order the 700 business cards, Mrs. Latham will spend the amount of $43.
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 7
Blue 6
Green 12
Yellow 19
Purple 19
Based on these results, express the probability that the next spin will land on blue as a fraction in simplest form.
Explanation
Add up the frequencies:
7+6+12+19+19 = 63
Out of those 63 total spins, 6 of them landed on blue.
The empirical (aka experimental) probability of landing on blue is therefore 6/63 = 2/21
Given ab and be are diameter of circle P. Diameter whether the arc is a minor arc, a major arc or a semi-circle of circle P. The find the measure of the arc. A. CD b. AE c. BC d. AC e. ADC f.AED g.CE H. BAD
Answer:
a. m(arc) CD = 65°
b. m(arc) AE = 120°
c. m(arc) BC = 55°
d. m(arc) AC = 115°
e. m(arc) ADC = 245°
f. m(arc) AED = 180°
g. m(arc) CE = 125°
h. m(arc) BAD = 240°
Step-by-step explanation:
a.
m<CPD = 180 - 55 - 60 = 65
m(arc) CD = 65°
b.
m<APB = 60°
m<APE = 180° - 60° = 120°
m(arc) AE = 120°
c.
m(arc) BC = 55°
d.
m(arc) AC = 60° + 55° = 115°
e.
m(arc) ADC = 120° + 60° + 65 = 245°
f.
m(arc) AED = 180°
g.
m(arc) CE = 60° + 65° = 125°
h.
m(arc) BAD = 60° + 120° + 60° = 240°
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Therefore, the equation in slope-intercept form that has a y-intercept at (0, -3) and also contains the point (4, 5) is y = 2x - 3.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. An equation is usually written with an equal sign (=) between the two expressions. Equations are used to represent mathematical relationships between quantities, to solve problems, and to model real-world situations. They can be used to find unknown values, to predict outcomes, and to test hypotheses. There are many types of equations, including linear equations, quadratic equations, polynomial equations, trigonometric equations, and differential equations. Each type of equation has its own rules and methods for solving it.
Here,
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given that the y-intercept is (0, -3), so b = -3. To find the slope, we can use the two given points (0, -3) and (4, 5).
slope = (y2 - y1)/(x2 - x1)
= (5 - (-3))/(4 - 0)
= 8/4
= 2
Now that we know the slope and the y-intercept, we can write the equation in slope-intercept form:
y = 2x - 3
To know more about equation,
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
Step-by-step explanation:
Patel could use the Quadratic Formula to solve it
or
he could 'complete the square' to solve it after dividing thru by 8 or he could solve it graphically
{ or he could use factoring to solve it (difficult) }