The ticket price that maximizes revenue is $8.50.
What ticket price maximizes revenue for the baseball team?Let x be the ticket price in dollars
Let y be the attendance.
We are given two points: (12, 20000) and (11, 24000).
Using the point-slope formula, we can find the equation of the line:
y - 20000 = (24000 - 20000)/(11 - 12) * (x - 12)
y = -4000x + 68000.
Revenue R is equal to the product of price and attendance: R = xy.
Substituting y = -4000x + 68000, we get:
R = x(-4000x + 68000)
R = -4000x^2 + 68000x.
Using [tex]x = -b/(2a)[/tex] where a and b are the coefficients from the form ax2 + bx + c]
= - 68000/(2*-4000)
= 8.5.
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In questions have a pair of similar three-dimensional objects. Find the surface area indicated. 2cm is the length of shape (the small shape) -surface area= =3.1 cm². the second shape has length of 6cm and surface area of b.
find b
The surface area of the second shape, denoted as b, is 9.3 cm².
To find the surface area of the second shape, we need to determine the relationship between the lengths and surface areas of the two shapes. Since the shapes are similar, the ratio of their surface areas will be equal to the square of the ratio of their lengths.
Let's denote the surface area of the second shape as B and the length of the second shape as L. We can set up the following proportion based on the given information:
(Surface area of the first shape)/(Surface area of the second shape) = (Length of the first shape)/(Length of the second shape)
Substituting the given values:
3.1 cm²/B = 2 cm/L
To find B, we can rearrange the equation:
B = (L * 3.1 cm²) / 2 cm
Now, we're given that the length of the second shape is 6 cm. Substituting this value:
B = (6 cm * 3.1 cm²) / 2 cm
Calculating:
B = (18.6 cm³) / 2 cm
B = 9.3 cm²
Therefore, the surface area of the second shape, denoted as b, is 9.3 cm².
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
A) x² + (y - 3)² = 36
E) x² + (y + 8)² = 36
Step-by-step explanation:
The formula for the equation of a circle is:
[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]
where:
(h, k) is the center of the circle.r is the radius of the circle.The diameter of a circle is twice its radius.
Therefore, if the diameter of the circle is 12 units, its radius is r = 6.
If the center of the circle lies on the y-axis, the x-value of the center is zero. Therefore, h = 0.
Substituting this information into the formula for the equation of the circle gives:
[tex](x-0)^2+(y-h)^2=6^2[/tex]
[tex]x^2+(y-h)^2=36[/tex]
Therefore, the two equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
x² + (y - 3)² = 36 x² + (y + 8)² = 36A ball is thrown vertically in the air with a velocity of 100ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in seconds, the ball is at a height of 150ft. Round your answer(s) to the nearest tenth of a second.
The times are 2.5 sec and 3.75 sec
* Lets explain the projectile formula
- The ball thrown vertically in the air with initial velocity 100 ft/sec
- the projectile formula is h = -16 t² + vo t, where h is the height of the
ball after thrown it in t seconds and vo is the initial velocity
∵ The initial velocity is 100 ft/sec
- substitute vo by 100
∴ The projectile formula is h = -16 t² + 100 t
- To find the time that the ball is at a height of 150 ft substitute
h by 150 in the projectile formula
∵ h = - 16 t² + 100 t
∵ h = 150 ft
∴ 150 = -16 t² + 100 t
- Subtract 150 from both sides
∴ 0 = -16 t² + 100 t - 150
- Multiply the both sides by -1
∴ 16 t² - 100 t + 150 = 0
* Lets factorize it to find the value of t
∵ 16 t² = 4t × 4t ⇒ first terms in the 2 bracket
∵ 150 = 15 × 10 ⇒ second terms in the two brackets
∵ 4t × 15 = 60 t ⇒ nears
∵ 4t × 10 = 40 t ⇒ extremes
∵ 6t + 40 t = 100 t ⇒ middle term
∴ 16 t² - 100 t + 150 = (4t - 15)(4t - 10)
∵ 16 t² - 100 t + 150 = 0
∴ (4t - 15)(4t - 10) = 0
- Equate each bracket by 0
∴ 4t - 15 = 0 ⇒ add 15 to both sides
∴ 4t = 15 ⇒ divide both sides by 4
∴ t = 3.75
- OR
∴ 4t - 10= 0 ⇒ add 10 to both sides
∴ 4t = 10 ⇒ divide both sides by 4
∴ t = 2.5
- The ball will be at height 150 ft in 2.5 seconds we the ball goes up
and again ate 3.75 seconds when the ball goes down after it
reached its maximum height
* The times are 2.5 sec and 3.75 sec.
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What information would you need to conclude this using the SSS Congruence Theorem?
convert 4 5/7 to improper fraction
Answer:
33/7
Step-by-step explanation:
7x4=28
28+5=33
Factorize:
+1/3+2
x² +
+2 +6x +
a (2 − ²1 ) ( 2 + 6)
a.
-
X
6
I
1
b. (2 + ²/² ) ( 2 + ² + + 6)
x
X
1
= (x + ²) (² + + 7 +
C.
x
2
8)
6)
1
a (x + 1) ² ( x + = + 0)
x² + 2 + 6x: The quadratic expression can be factorized as (x + 2)(x + 3).
How to solveThe factorization of the given expressions is as follows:
+1/3 + 2: This is a simple addition and cannot be factorized.
x² + 2 + 6x: The quadratic expression can be factorized as (x + 2)(x + 3).
a(2 − ¹)(2 + 6)/(a - x/6)(x - 1): This expression cannot be factorized further due to the presence of variables in the denominator.
(2 + √2)(2 + √6)/x: This expression cannot be factorized further due to the presence of variables in the denominator.
(x + 1)² (x + 6): This expression is already fully factorized.
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The complete question
a) Factorize the expression: x² + 6x + 8
b) Factorize the expression: x² - 1
c) Factorize the equation: x² + 2x - 3 = 0
Seven villages A, B, C, D E, F and G are situated as follows:
E is 2 km to the west of B
F is 2 km to the north of A
C is 1 km to the west of A
D is 2 km to the south of G
G is 2 km to the east of C
D is exactly in the middle of B and E.
Which two villages are the farthest from one another?
The two villages farthest from one another are E and F.
To determine which two villages are the farthest from one another, we need to analyze the given information and calculate the distances between all possible pairs of villages.
Let's start by visualizing the locations of the villages based on the given information:
B ---- F
/ |
/ |
A |
| C ---- D
| |
| |
E -------------- G
Using the information provided, we can calculate the distances between the villages:
Distance between E and F: Since E is 2 km to the west of B and F is 2 km to the north of B, we can calculate the distance between E and F using the Pythagorean theorem. The distance is approximately √(2^2 + 2^2) = √8 ≈ 2.83 km.
Distance between E and C: E is exactly in the middle of B and E, which means the distance between E and C is half the distance between B and C. Using the Pythagorean theorem, the distance between B and C is √(2^2 + 1^2) = √5 ≈ 2.24 km. Therefore, the distance between E and C is 2.24 km / 2 = 1.12 km.
Distance between E and D: Since D is 2 km to the south of A, and A is the same as E, the distance between E and D is the same as the distance between A and D, which is 2 km.
Distance between E and G: Since G is 2 km to the east of C, the distance between E and G is the same as the distance between C and G, which is 2 km.
Now, let's compare the distances between all possible pairs of villages:
E and F: 2.83 km
E and C: 1.12 km
E and D: 2 km
E and G: 2 km
From the above calculations, we can see that the farthest distance is between E and F, which is approximately 2.83 km.
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Find the value of k such that 156k is a perfect square
Answer:To find the value of k such that 156k is a perfect square, we need to determine the factors of 156 and look for a common factor that can be squared to obtain a perfect square.
The prime factorization of 156 is [tex]2^2[/tex] * 3 * 13. A perfect square must have an even exponent for each prime factor in its prime factorization. Thus, for 156k to be a perfect square, k must have an even exponent for each prime factor in the prime factorization of 156.
Analyzing the prime factorization, we can see that the exponent of 2 in 156 is 2, the exponent of 3 is 1, and the exponent of 13 is 1. To make each exponent even, we need to multiply 156 by another 2. Therefore, k should be equal to 2.
Let's verify this by calculating 156 * [tex]2^2:[/tex]
156 * [tex]2^2[/tex] = 156 * 4 = 624
624 is a perfect square since it can be expressed as [tex]24^2.[/tex] Hence, the value of k that makes 156k a perfect square is 2.
In summary, the value of k that makes 156k a perfect square is 2.
Step-by-step explanation:
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dy/dx=(4x^2 + 3y^2)/2xy
In the figure, QN¯¯¯¯¯¯¯¯ is the perpendicular bisector of LM¯¯¯¯¯¯¯¯¯ . A triangle L M P with a perpendicular bisector Q N passing through point P. Which of the following can be used to prove that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯? Responses First, state that PL¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯ by the definition of a perpendicular bisector. Second, state that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯ because of the definition of congruence. First, state that line segment cap p liters is congruent to line segment cap p cap m by the definition of a perpendicular bisector. Second, state that point P is equidistant from the endpoints of line segment cap l cap m because of the definition of congruence. First, state that PL¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯ because corresponding parts of congruent triangles are congruent. Second, state that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯ because of the definition of congruence. First, state that line segment cap p liters is congruent to line segment cap p cap m because corresponding parts of congruent triangles are congruent. Second, state that point P is equidistant from the endpoints of line segment cap l cap m because of the definition of congruence. First, prove that △LNP≅△MNP by the side-side-side theorem. Second, prove that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯ by showing that PL¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯ because corresponding parts of congruent triangles are congruent. First, prove that △LNP≅△MNP by the side-side-side theorem. Second, prove that point P is equidistant from the endpoints of line segment cap l cap m by showing that line segment cap p liters is congruent to line segment cap p cap m because corresponding parts of congruent triangles are congruent. First, prove that △LNP≅△MNP by the side-angle-side theorem. Second, prove that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯ by showing that PL¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯ because corresponding parts of congruent triangles are congruent. First, prove th
Jacquie used an app to simulate a coin flip 40 times. It lands on heads 20 times.
Based on her results, Jacquie predicts the expected number of times the coin will land on heads in 1,000 trials is 500 times.
Do you think that Jacquie's results are correct?
Jacquie's prediction of 500 heads in 1,000 trials is actually correct based on the assumption of a fair coin.
Jacquie used an app to simulate a coin flip 40 times, and it landed on heads 20 times. From these results, Jacquie predicts that the expected number of times the coin will land on heads in 1,000 trials is 500 times.
Jacquie's prediction is not correct. The expected number of times the coin will land on heads in 1,000 trials can be estimated using the concept of probability. For a fair coin, the probability of landing on heads in a single flip is 0.5 (assuming the coin is unbiased).
In a large number of trials, the expected number of heads can be calculated by multiplying the probability of heads by the total number of trials. Therefore, the expected number of heads in 1,000 trials would be:
Expected number of heads = Probability of heads × Total number of trials
Expected number of heads = 0.5 × 1000
Expected number of heads = 500
Thus, Jacquie's prediction of 500 heads in 1,000 trials is actually correct based on the assumption of a fair coin. However, we cannot conclude the fairness of the coin based on her previous 40 flips, as this sample size is too small to accurately represent the expected outcome. The Law of Large Numbers suggests that as the number of trials increases, the observed results should converge towards the expected probabilities. Therefore, it would require a larger number of trials to validate the fairness of the coin and provide a more accurate estimation of the expected number of heads.
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Myron records the number of chirps per minute (x) that crickets make at
different temperatures (v) in degrees Fahrenheit.
He determines that the association is linear and that the line of best fit is
y=+50.
What is the interpretation of the slope and y-intercept of this equation?
A. The slope predicts a temperature increase of about 50° for every
increase of 1 chirp per minute. The y-intercept shows that when
the crickets are not chirping (x = 0), the temperature is 0°.
B. The slope predicts a temperature increase of about 6* for every
increase of 50 chirps per minute. The y-intercept shows that when
the crickets are not chirping (x= 0), the temperature is
OC. The slope predicts a temperature increase of about for every
increase of 1 chirp per minute. The y-intercept shows that when
the crickets are not chirping (x = 0), the temperature is 50°.
D. The chirping increases as the temperature goes down.
The correct interpretation of the slope and y-intercept of the equation
y = 50 is:
A. The slope predicts a temperature increase of about 50° for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x = 0), the temperature is 0°.
In the given equation y = 50, the slope of 50 indicates that for every increase of 1 chirp per minute (x), the temperature (y) increases by approximately 50° Fahrenheit.
The positive slope suggests a positive correlation between the number of chirps per minute and temperature.
The y-intercept of 0 in this equation represents the temperature when the crickets are not chirping (x = 0). It implies that when there are no chirps per minute, the temperature is at 0° Fahrenheit.
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Find all real zeros of
f
(
x
)
=
x
3
-
x
2
-
68
x
+
186
.
x
=
(Enter the zeros as a list, e.g.
1
,
2
,
3
. Use exact forms, not decimal approximations.)
The real zeros of the function f(x) = x³ - x² - 68x + 186 are x = 3, x = -1 + 3√7 and x = -1 - 3√7
Finding all real zeros of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x³ - x² - 68x + 186
To find the real zeros of the function, we set the function to 0
Using the above as a guide, we have the following:
x³ - x² - 68x + 186 = 0
Next, we solve by graphing (see attachment for graph)
With the use of a graph, the real zeros of the function are
x = 3, x = -1 + 3√7 and x = -1 - 3√7
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Complete questions
Find all real zeros of f(x)=x3-x2-68x+186.x=(Enter the zeros as a list, e.g. 1,2,3. Use exact forms, not decimal approximations.)
NO LINKS!! URGENT HELP PLEASE!!
Please help me with 1aa and 2aa
Answer:
1) 23.4 km²
2) 403.1 mi²
Step-by-step explanation:
The formula for the area of a regular polygon is half the product of its apothem and perimeter.
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{1}{2}aP$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the apothem.\\ \phantom{ww}$\bullet$ $P$ is the perimeter.\\\end{minipage}}[/tex]
From inspection of the given regular polygons, we have been given the perimeter or side length only. Therefore, we need to calculate the apothem.
The formula for the length of the apothem of a regular polygon is:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Length of apothem}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Question 1The given polygon has 6 sides, and its perimeter is 18 km. Therefore:
n = 6s = 18/6 = 3 kmSubstitute the values of s and n into the apothem formula and solve for a:
[tex]\begin{aligned}\implies a&=\dfrac{3}{2 \tan\left(\dfrac{180^{\circ}}{6}\right)}\\\\&=\dfrac{3}{2 \tan\left(30^{\circ}\right)}\\\\&=\dfrac{3}{\left(\dfrac{2\sqrt{3}}{3}\right)}\\\\&=\dfrac{3\sqrt{3}}{2}\end{aligned}[/tex]
To find the area of the polygon, substitute the found value of a, along with the perimeter, P = 18, into the area formula:
[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \cdot\dfrac{3\sqrt{3}}{2}\cdot 18\\\\&=\dfrac{54\sqrt{3}}{4} \\\\&=23.382685...\\\\&=23.4\; \sf km^2\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the area of the regular polygon is 23.4 km² to the nearest tenth.
[tex]\hrulefill[/tex]
Question 2The given polygon has 12 sides, and the length of one side is 6 miles. Therefore:
n = 12s = 6 milesSubstitute the values of s and n into the apothem formula and solve for a:
[tex]\begin{aligned}\implies a&=\dfrac{6}{2 \tan\left(\dfrac{180^{\circ}}{12}\right)}\\\\&=\dfrac{6}{2 \tan\left(15^{\circ}\right)}\\\\&=\dfrac{3}{\tan\left(15^{\circ}\right)}\\\\&=\dfrac{3}{2-\sqrt{3}}\\\\&=6+3\sqrt{3}\end{aligned}[/tex]
The perimeter of the polygon is n · 2 = 12 · 6 = 72 miles.
To find the area of the polygon, substitute the found value of a, along with the perimeter, P = 72, into the area formula:
[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \cdot (6+3\sqrt{3})\cdot 72\\\\&=36 (6+3\sqrt{3})\\\\&=216+108\sqrt{3}\\\\&=403.061487...\\\\&=403.1\; \sf mi^2\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the area of the regular polygon is 403.1 mi² to the nearest tenth.
Answer:
1.23.38 km^2
2.402.84 mi^2
Step-by-step explanation:
Note:
The area of a polygon can be found using the following formula:
[tex]\boxed{\bold{Area = \frac{Perimeter*apothem}{2}}}[/tex]
where:
Perimeter is the total length of all the sides of the polygon
Apothem is the distance from the center of the polygon to a point on any side
To find , use this formula
[tex]\boxed{\bold{Apothem = \frac{ length\:of\:side }{ 2 *tan(\frac{180}{n})}}}[/tex]
where:
n is the number of sides of the polygon
For question:
1.
Perimeter(p)=18km
no. of side (n)=6
length of one side= [tex]\frac{p}{n}=\frac{18}{6}=3[/tex] km
Now finding apothem(a),
by substituting value, we get,
[tex]Apothem = \frac{ 3 }{ 2 *tan(\frac{180}{6})}\\Apothem = \frac{ 3 }{ 2 *tan(30)}\\Apothem = \frac{ 3 }{ 2 * \frac{\sqrt{3}}{3}}}\\Apothem =\frac{3\sqrt{3}}{2}} \: or\: 2.598km\\[/tex]
Now, we have
[tex]A=\frac{1}{2}*a*P[/tex]
substituting value:
[tex]A=\frac{1}{2}*2.598*18=23.38 km^2[/tex]
2.
no. of side (n)=12
length of one side(l)=6 mi
Perimeter(p)=n*l=12*6=72 mii
Now finding apothem(a),
by substituting value, we get,
[tex]Apothem = \frac{ 6}{ 2 *tan(\frac{180}{12})}\\Apothem = \frac{ 6 }{ 2 *tan(15)}\\Apothem = \frac{ 3 }{ 2*0.27}}\\Apothem =\frac{6}{0.54}=11.19mi[/tex]
Now, we have
[tex]A=\frac{1}{2}*a*P[/tex]
substituting value:
[tex]A=\frac{1}{2}*11.19*72=402.84 mi^2[/tex]
One valuable decision making tool when it comes to financial choices is the break-even analysis. Use a break even analysis to determine which deductible level the buyer in this example should go with.
Option 1: $250 deductible comes with a $1000 annual premium.
Option 2: $500 deductible comes with a $800 annual premium. Based on the information above, how long would someone have to go without a claim for the higher deductible option to break-even? (calculate as a number of years - so 2.5 if it is 2 1/2 years, which it's not)
The option 1 is a more suitable and preferred option because the deductible is the option2 are more as per the break-even analysis.
Option 1 is preferable if no claims are filed. Let's now think about how long it would take someone to go without a claim for Option 2 to become profitable. The deductible on the option 2 are more as compared to option 1. For each year they don't make a claim, they must save $250 in premiums in order to break even.
The annual premium difference between the two plans is $1000 – $800, or $200. As a result, Option 2 would not become profitable until 1.25 years (or 15 months) in the absence of a claim.
$200 in premium differences divided by $250 in savings from a higher deductible is 1.25 years. So, if the buyer expects to go more than 1.25 years without making a claim, then they should choose Option 2 with the higher deductible.
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After considering the given data we conclude that the most suitable and preferred option will be option 1,in comparison to option 2 due to its deductibility.
Break-even analysis is a imperative tool for making financial decisions. It helps describe how long it would take for a higher deductible option to break-even with a lower deductible option.
For the given case,
$250 deductibility comes with a $1000 annual premium. - Option 1
$500 deductibility comes with a $800 annual premium. - Option 2
To evaluate how long someone would have to go without a claim for the higher deductible option to break-even, we can apply the following formula:
Break-even point = (Higher deductible - Lower deductible) / (Lower premium - Higher premium)
Placing in the values from our example:
Break-even point = (500 - 250) / (1000 - 800)
Break-even point = 250 / 200
Break-even point = 1.25 years
Then, someone would have to go without a claim for 1.25 years for the higher deductible option to break-even with the lower deductible option. Hence Option 1
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The following box plot represents the average heights of the students in Mrs. Hill's sixth grade math class.
Which of the following statements can you determine from the graph?
The student heights were measured in centimeters.
The graph represents the average heights of the girls in Mrs. Hill's class.
The student heights were measured in inches.
The graph represents the average heights of the boys in Mrs. Hill's class.
Answer:
the graph represents the average heights of the girls in mrs.hills class.
Step-by-step explanation:
Please helppppppppp quickkkkk
The measure of the missing arc in this problem is given as follows:
? = 159º
How to obtain the arc measure?We have two secants in this problem, and point C is the intersection of the two secants, hence the angle measure of 50º is half the difference between the angle measure of the unknown far arc by the near arc of 59º.
Hence the measure of the missing arc in this problem is obtained applying the two-secant theorem as follows:
(? - 59)/2 = 50
? - 59 = 100
? = 159º.
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A hotel has $960 to buy new pillows. If the cost of each pillow is $3, how many pillows will the hotel be able to buy?
Answer:
Step-by-step explanation:
The answer is 360.
Explanation: each pillow is $3 and you have $960.
You need to figure out how many times $3 can go into $960 and you do that by dividing.
960 divided by 3 is 360.
The hotel can buy 360 pillows.
a musician borrows 2200 to buy a trumpet the length of the loan is 3 years and the total simple interest owed will be 792
what is the annual rate of interest written as a percent on the musicains loans for the trumpet
To find the annual rate of interest as a percent on the musician's loan for the trumpet, we can use the simple interest formula:
$$\sf\:I = P \cdot r \cdot t \\$$
Where:
- I is the total interest owed (792 in this case)- P is the principal amount (2200 in this case)- r is the annual interest rate (what we need to find)- t is the length of the loan in years (3 in this case)We can rearrange the formula to solve for r :
$$\sf\:r = \frac{I}{P \cdot t} \\$$
Substituting the given values:
$$\sf\:r = \frac{792}{2200 \cdot 3} \\$$
Now, we can calculate the value of r :
$$\sf\:r = \frac{792}{6600} \\$$
Simplifying the fraction:
$$\sf\:r = 0.12 \\$$
To express this as a percentage, we multiply by 100:
$$\sf\:r = 0.12 \times 100 \\$$
Therefore, the annual rate of interest on the musician's loan for the trumpet is 12%.[tex][/tex]
Find the equation of the exponential function represent by the table below:
(i’ll give brainlist !!)
Step-by-step explanation:
y = 4 ^(x+1) by inspection
The points (-5,13) and (-2,r) lie on a line with slope -3. Find the missing coordinate r.
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{13})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{r}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{r}-\stackrel{y1}{13}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{(-5)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -3 }\implies \cfrac{r-13}{-2+5}=-3\implies \cfrac{r-13}{3}=-3 \\\\\\ r-13=-9\implies r=4[/tex]
I will give brainliest and ratings if you get this correct
Using Cramer's rule for first-order condition:
x₁ = -149/444x₂ = -69/222x₃ = 139/444Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.
How to determine 1st and 2nd order condition?(a) Using Cramer's rule for the first-order condition:
To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:
∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]
Setting the gradient equal to zero:
6x₁ - x₂ - 3x₃ - 5 = 0 (1)
-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)
2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)
Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:
|A| =
| 6 -1 -3 |
|-1 12 2 |
|-3 2 -3|
|A| = 444
The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:
|A₁| =
| 5 -1 -3 |
| 0 12 2 |
| 0 2 -3|
|A₁| = -149
The determinant of the matrix obtained by replacing the second column of A with the constants is:
|A₂| =
| 6 5 -3 |
|-1 0 2 |
|-3 0 -3|
|A₂| = -138
The determinant of the matrix obtained by replacing the third column of A with the constants is:
|A₃| =
| 6 -1 5 |
|-1 12 0 |
|-3 2 2|
|A₃| = -278
Therefore, using Cramer's rule:
x₁ = |A₁|/|A| = -149/444
x₂ = |A₂|/|A| = -69/222
x₃ = |A₃|/|A| = 139/444
(b) Using the Hessian for the second-order condition:
To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:
(y) =
| 6 0 -3 |
| 0 12 2 |
|-3 2 8 |
Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):
H(y) =
| 6 0 -3 |
| 0 12 2 |
|-3 2 8 |
The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.
Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.
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Which observation can be made about most United States immigrants?
A. Most groups of immigrants experienced persecution in this
country.
B. Most groups of immigrants came to the United States in order to escape tyrannical governments.
C. Most immigrant groups settled first in rural areas.
D. Most immigrants started in the lowest-paying jobs when they
came to America.
E. Most immigrants were seeking to escape religious persecution.
Answer:
D. Most immigrants started in the lowest-paying jobs when they came to America.
Which of polygons B,C,D,E and F Are Similar to similar to polygon A? Explain your reasoning
Answer:
do you choose the best
Step-by-step explanation:
To determine which polygons among B, C, D, E, and F are similar to polygon A, we need to examine their corresponding angles and side lengths. Similar polygons have corresponding angles that are congruent and corresponding side lengths that are proportional. Based on this information, we can make comparisons to determine the similar polygons.
Since the options for polygons B, C, D, E, and F are not provided, I cannot provide a direct comparison. However, I can provide you with general guidance on how to determine similarity between polygons:
Angle comparison: Compare the measures of corresponding angles in polygon A and the other polygons. If the corresponding angles are congruent (equal in measure), then the polygons may be similar.
Side length comparison: Compare the lengths of corresponding sides in polygon A and the other polygons. If the corresponding side lengths are proportional (in the same ratio), then the polygons may be similar.
By examining both angle and side length comparisons, you can determine the similarity between polygons. Remember, all corresponding angles must be congruent, and all corresponding side lengths must be proportional for two polygons to be considered similar.
If you provide the specific details or measurements of polygons A and the options (B, C, D, E, F), I can help you determine the similarity relationships between them.
Help please!!!!!!!!!!
Answer:
1. The Answer is a 2. The answer is c and 3. the answer is b
Step-by-step explanation:
Answer:
19 (D)
20(A)
Step-by-step explanation:
you just put those values you given into the expression and punch the calculator for confirmation
Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.
In a case whereby Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo in 1650 feet away.
How can the sound be calculated?In a case whereby you want to hear the echo, the sound will have had to gone out to the wall which will later return , then The sound's speed, in feet/second is:
(750 mi/hour)*(1 hour/3600 seconds)*(5280 feet/mile)
= 1100 ft/sec
However in 3 seconds, the sound will have traveled 3300 feet. Since the sound's movement is a round trip, the canyon wall can be exressed
3300/2
= 1650 feet away.
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measurement assignment swan area
Half of the swans are black, the fraction of the swans are black is 4/8
There are eight swans swimming on a pond and four of those swans are
black.
We have to find the fraction of the swans are black
The fraction of black swans is given by:
4 (number of black swans)
8 (total number of swans)
Simplifying the fraction 4/8 = 1/2
Therefore, half of the swans are black, the fraction of the swans are black is 4/8
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Can yall help me with this pls pls
Measure of angle E is, 25 degree
And, Measure of side FG is,
FG = 10 units
We have to given that;
In parallelogram EFGH,
EF = 3y
EH = 2 (y + 1)
HG = y + 8
Hence, We can formulate;
∠ E = ∠G
⇒ (7x - 15) + (7x - 15) = 90°
⇒ 14x - 30 = 90
⇒ 14x = 60
⇒ x = 30/7
Hence., ∠ E = (7x - 5) = (7 x 30/7 - 5)
= (30 - 5)
= 25
Since, Opposite sides are equal in parallelogram.
Hence, We get;
3y = y + 8
2y = 8
y = 4
Hence, Measure of side FG is,
FG = 2 (y + 1)
FG = 2 (4 + 1)
FG = 10 units
Thus, Measure of angle E is, 25 degree
And, Measure of side FG is,
FG = 10 units
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Line A has a y-intercept of 6 and is perpendicular to the line given by
y = 5x + 1.
What is the equation of line A?
-ive your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.ok
The equation of line A in the form y = mx + c is y = (-1/5)x + 6
We have,
The given line has a slope of 5 since it is in the form y = mx + b where m is the slope.
So a line perpendicular to it will have a slope of -1/5 because the product of the slopes of perpendicular lines is -1.
Since the y-intercept of line A is 6, the equation of line A can be written as:
y = (-1/5)x + 6
Therefore,
The equation of line A in the form y = mx + c is y = (-1/5)x + 6
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sorry if the picture is low quality but can someone answer this please ILL GIVE BRAINLIST (50 points)
The equivalent exponential function is given as follows:
[tex]S(t) = 79(1.25)^t[/tex]
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function for this problem is defined as follows:
[tex]S(t) = 79(2)^{4t}[/tex]
Considering the growth rate as 1 + r = 2 -> r = 1, with a period of n = 4, the equivalent exponential function can be written as follows:
[tex]S(t) = 79(1 + \frac{1}{4})^{t}[/tex]
[tex]S(t) = 79(1.25)^t[/tex]
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