Answer:
Step-by-step explanation:
If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards. The general vertex form of a parabola of this type is
[tex]y=a(x-h)^2+k[/tex]
We have the x, y, h, and k. We will plug all those in and solve for a. That looks like this:
[tex]-5=a(6-4)^2-13[/tex] which simplifies to
-5 = 4a - 13 and
8 = 4a so
a = 2
That means that the paraobola in vertex form is
[tex]y=2(x-4)^2-13[/tex]
1.) Which domain restrictions apply to the rational expression? 14x-2x / x^2-7x
2.) Sara has 85% so far in math. She wants to increase her grade. So far there have been 1,000 points possible in her class. The expression below represents the percent she’ll have if she earns 100% on her final exam, which is worth x points:
(Picture down below)
3.) Solve for x.
3 / x+2 – 1 / x = 1 / 5x
Answer:
3. [tex]\displaystyle 1\frac{1}{3} = x[/tex]
2C. [tex]\displaystyle III.[/tex]
2B. [tex]\displaystyle I.[/tex]
2A. [tex]\displaystyle II.[/tex]
1. [tex]\displaystyle Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]
Step-by-step explanation:
3. See above.
2C. The keyword is ratio, which signifies division, so you would choose "III.".
2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".
2A. The keyword is total, which signifies addition, so you would choose "II.".
1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:
[tex]\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]
I am joyous to assist you anytime.
We found the domain restrictions of a rational expression by checking the values that make the denominator zero. A formula was suggested to calculate Sara's future percentage score. To solve the third equation, a common denominator was found and used to simplify the expression.
Explanation:1. The domain restrictions for the rational expression 14x-2x/x^2-7x are all real numbers except for the numbers which make the denominator zero. Solving the equation x^2-7x=0, we get x=0 or x=7. Therefore, the domain restrictions are x≠0 and x≠7.
2. There is no picture provided but generally, to calculate the future percentage score given the current percentage score, total points possible, and future total points, you would use the formula (current score/current total points) * 100% + (future score/future total points) * 100%.
3. To solve for x in the equation 3 / (x+2) - 1 / x = 1 / (5x), we first need to find a common denominator. In this case, it would be 5x^2 + 10x. Multiplying each term by the common denominator and simplifying would then give the value of x.
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You have family traveling from far away to come to your house for Thanksgiving. If they travel 324 miles and arrive to your house in 6 hours, how fast were they traveling?
Answer: 54 mph
Step-by-step explanation:
Speed x Time = Distance
So, Speed = Distance/Time
Speed = 324 miles/6hrs = 54 mph
A simple random sample of 1200 adult Americans is selected, and each person is asked the following question: "In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?" Only 39% of those responding answered "Yes." This survey ____.
a. is reasonable accurate since it used a large simple random sample.
b. needs to be larger since only about 24 people were drawn from each state.
c. probably understates the percent of people who favor a system of national health insurance.
d. is very inaccurate but neither understates nor overstates the percent of people who favor a system of national health insurance. Because simple random sampling was used, it is unbiased.
e. probably overstates the percent of people who favor a system of national health insurance.
Answer:
c. probably understates the percent of people who favor a system of national health insurance.
Find the yy-intercept of each line defined below and compare their values.
Answer:
y-intercept: when x = 0
For Line A:
y = 0 + 7 = 7
For line B:
when x = 0, the value is -5
7 > -5, so y-intercept of line A is greater than line B's.
A museum employee surveys a random sample of 350 visitors to the museum. If those visitors, 266 stopped at the gift shop. Based on these results, about how many people out of 3200 visitors to the museum would be expected to stop at the gift shop?
Answer: 2432 visitors
Step-by-step explanation:
An employee of a museum surveyed a random sample of 350 visitors that came to the museum. Of the visitors that were surveyed, 266 stopped at the gift shop.
Since 266 out of 350 stopped at the gist shop, we find the fraction or decimal of people who stopped at the gift shop. This will give 266/350 = 19/25 or 0.76.
If 3200 visitors come to the museum, the expected number of people to stop at the gift shop are:
= 0.76 × 3200
= 2432
2432 visitors are expected to stop at the gift shop out of 3200 visitors.
The number of people who enter a drugstore in a given hour is a Poisson random variable with parameter λ = 10 . Compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour. What assumptions have you made?
To calculate the conditional probability of at most 3 men entering the drugstore given that 10 women entered using Poisson Distribution. The gender doesn't influence the probability, therefore the events are treated as independent. Assumption made is that occurrences are independent and happen at a known average rate.
Explanation:To compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour, we would apply Poisson Distribution. Poisson Distribution is used to find the probability of a number of events in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event.
However, in this case, the number of men entering is independent of the number of women entering. Therefore, the fact that we know 10 women entered does not affect the probability regarding the number of men. The gender of the individuals entering the drugstore is irrelevant, and we can consider them as independent events. The result is the same if we simply asked: What is the probability that at most 3 people entered the drugstore?
To calculate this, we would use the formula for Poisson Distribution, summing up the probabilities of 0, 1, 2 and 3 events happening. The assumption made here is that the occurrences are independent of each other and occur with a known average rate, λ, which is 10 in this question.
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A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at , the average attendance had been 27,000. When ticket prices were lowered to , the average attendance rose to 33,000. (a) Find the demand function, assuming that it is linear. (b) How should ticket prices be set to maximize revenue?
Answer:
$9.50
Step-by-step explanation:
Solution is in the attachment . You can see it.
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?
a) 6
b) 9
c) 12
d) 27
e) 48
Answer:
b) 9
Step-by-step explanation:
Given: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in [tex]36[/tex] hours.
To Find: If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled.
Solution:
Let the time taken by one machine to fill a certain production alone be[tex]=\text{x}[/tex]
Time taken when three machine operate independently and simultaneously
[tex]\frac{1}{\text{x}}+\frac{1}{\text{x}}+\frac{1}{\text{x}}=\frac{1}{36}[/tex]
[tex]\frac{3}{\text{x}}=\frac{1}{36}[/tex]
[tex]\text{x}=108[/tex] [tex]\text{hours}[/tex]
Let time taken when one additional machine is used [tex]=\text{y}[/tex]
Time when when one additional machine is used
[tex]\frac{1}{108}+\frac{1}{108}+\frac{1}{108}+\frac{1}{108}=\frac{1}{\text{y}}[/tex]
[tex]\frac{4}{108}=\frac{1}{\text{y}}[/tex]
[tex]\text{y}=27[/tex] [tex]\text{hours}[/tex]
it takes [tex]27[/tex] [tex]\text{hours}[/tex] when one additional machine is used
Now,
fewer hours taken when one additional machine is used
[tex]=\text{number of hours taken when three machines are used}-[/tex][tex]\text{number of hours taken when one additional machine is used}[/tex]
[tex]36-27[/tex]
[tex]9[/tex] [tex]\text{hours}[/tex]
in [tex]9[/tex] fewer hours of simultaneous operation the production order can be filled if one additional machine is used
Hence option b) is correct.
A ladder leans against a brick wall. The foot of the ladder is 7 feet from the wall. The ladder reaches a height of 22 feet on the wall. What is the angle the ladder makes with the wall? (to the nearest tenth) A) 15.4° B) 17.7° Eliminate C) 18.6° D) 21.5°
Answer:
the answer is 17.7
Step-by-step explanation:
Apply tanθ =
opposite
adjacent
tanθ =
7
22
θ = tan−1(
7
22
)
θ = 17.7°
The angle the ladder that will make with the wall is 17.7°.
What is tangent of an angle?
Tangent of the angle is the ratio between the opposite side and adjacent side of the angle in the right angle triangle.
So according to the asked question,
the distance between lader foot and the wall is 7feet.
the height of the wall is 22feet.
So in triangle ΔABC ,
the height of the wall =AB=22feet
the distance between lader foot and the wall=BC=7feet
∠ABC=90°
the angle between the ladder and the wall= ∠BAC=θ
So in ΔABC,
tan ∠BAC=tan θ=BC/AB
⇒tan θ=7/22
⇒θ=tan⁻¹(7/22)
⇒θ=17.7⁰
Therefore the angle the ladder that will make with the wall is 17.7°.
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A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of fluid ounces and the sample standard deviation is fluid ounces. Find a 95% two-sided confidence interval on the mean volume of syrup dispensed. Assume the population is approximately normally distributed.
Answer:
You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.
Step-by-step explanation:
Calculation
M = 0.96
Z = 1.96
sM = √(0.96)^2/25) = 0.19
μ = M ± Z(sM)
μ = 0.96 ± 1.96*0.19
μ = 0.96 ± 0.3763
Result
M = 0.96, 95% CI [0.5837, 1.3363].
You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.
Manufacture has been selling 1450 television sets a week at $540 each. A market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
a) Find the function representing price as a function of the demand p(x)p(x), where xx is the number of the television sets sold per week and p(x)p(x) is the corresponding price.
Answer:
[tex]p(x)= -\frac{1}{10}x + 685[/tex]
Step-by-step explanation:
Since, Function of demand is the linear function of quantity.
Let x represents the quantity and p represents the price of each unit.
∵ Manufacture has been selling 1450 television sets a week at $540 each,
i.e. [tex](x_1, p_1) = (1450, 540)[/tex]
Also, for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
i.e. [tex](x_2, p_2) = (1580, 527)[/tex]
Thus, the linear equation of the price,
[tex]p-p_1 = \frac{p_2-p_1}{x_2-x_1}(x-x_1)[/tex]
[tex]p-540 = \frac{527 - 540}{1580-1450}(x-1450)[/tex]
[tex]p-540 = -\frac{13}{130}(x-1450)[/tex]
[tex]p-540 = -\frac{1}{10}(x-1450)[/tex]
[tex]p = -\frac{1}{10}x + 145 + 540[/tex]
[tex]\implies p = -\frac{1}{10}x + 685[/tex]
Hence, the function representing price as a function of the demand is,
[tex]p(x)= -\frac{1}{10}x + 685[/tex]
determine the intervals on which the function is increasing, decreasing and constant
Answer:
increasing: (-∞, 0)decreasing: (0, ∞)Step-by-step explanation:
The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...
increasing from -∞ to 0 (not including 0)
decreasing from 0 to +∞ (not including 0)
_____
At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.
Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. (Assume the car travels the same distance for each one gallon of gas)
The number of miles traveled varies directly with the number of gallons of gas you use.
a. Write an equation that relates miles traveled to gallons of gas used. (Use any variable you like in the equation.
b. How far can you drive with 3.7 gallons of gas? (Make sure to show the calculations you did to determine this answer)
Answer:
Step-by-step explanation:
Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. This means that
1 gallon of gas would be used to drive 392/14 = 28 miles
a) The number of miles traveled varies directly with the number of gallons of gas used.
Let x =number of gallons of gas you use.
Let y = the number of miles travelled.
Since y varies directly with x, we will introduce a constant of proportionality, k. Therefore,
y = kx
If 28 miles will require 1 gallon of gas, it means
28 = 1×k
k = 28
So y = 28x
b) we want to determine how far you can drive with 3.7 gallons of gas.
x = 3.7
y = 28x = 28×3.7
y = 103.6 miles
Please help me out with this!!!!!!!!!!
Answer:
C
Step-by-step explanation:
Rearranging x - y ≤ 2
- y ≤ 2 - x ( multiply through by - 1 )
y ≥ - 2 + x ← change direction of inequality symbol
This region is above the yellow line
y ≥ 0 is above the x- axis
x ≥ 0 is to the right of the y- axis
Thus the solution is the indicated blue region
The inequalities from C satisfy the given graph
Bill and susan buy 16 oranges at a fruit stand. They make orange juice using 3/4 of the oranges. How many oranges do bill and susan use to make orange juice?
they use 12 oranges
4•4=16-4=12 which is 3 of the 4/4
The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, the fraction is the division of the two numbers but the division is not wholly complete.
As per the given,
They make orange juice using 3/4 of the oranges.
3/4 of 16
(3/4)16 = 3 x 4 = 12 oranges
Hence "The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges".
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About 20 different comic books will be distributed to five kids. (a) How many ways are there to distribute the comic books if there are no restrictions on how many go to each kid (other than the fact that all 20 will be given out)?
Answer:
5^20
Step-by-step explanation:
For each comic book, there are five different choices for which kid will receive that comic book. 20 decisions are made, one for each comic book with five different possibilities for each choice. The number of ways to distribute the comic books to the five kids is 5^20.
Final answer:
The formula for distributing 20 comic books among five kids with no restrictions is C(24, 5) = 42,504 ways.
Explanation:
To distribute the 20 comic books to five kids with no restrictions on how many each kid receives, we can use the concept of distributing identical items among distinct groups.
The number of ways to distribute the comic books in this scenario is represented by the formula: C(n+r-1, r) where n is the number of items (in this case, 20 comic books) and r is the number of groups (5 kids).
Therefore, the number of ways to distribute the comic books to the five kids is: C(20+5-1, 5) = C(24, 5) = 42,504 ways.
Given: ∆ABC, AB = 12, AC = 17 Area ∆ABC = 65 Find: BC, m∠A, m∠B, m∠C
Answer:
BC = 10.889m∠A = 39.6°m∠B = 95.8°m∠C = 44.6°Step-by-step explanation:
There are at least a couple of ways you could go at this. Here, we'll use an area formula to find m∠A, then use the law of cosines to find BC. Using BC, we can use the law of sines to find another angle.
Area = (1/2)·AB·AC·sin(∠A)
65·2/(12·17) = sin(∠A) ≈ 65/102
∠A = arccos(65/102) ≈ 39.587°
From the law of cosines, ...
BC² = AB² +AC² -2·AB·AC·cos(∠A)
BC² = 12² +17² -2·12·17·cos(39.587°) ≈ 118.5735
BC ≈ √118.5735 ≈ 10.889
Then ∠C can be found from the law of sines:
sin(∠C)/AB = sin(∠A)/BC
∠C = arcsin(AB/BC·sin(∠A)) ≈ 44.609°
The measure of ∠B will be the angle that makes the total be 180°:
39.587° +∠B +44.609° = 180°
∠B = 95.804°
_____
There is actually another solution, in which ∠A is obtuse. We thought the diagram showed an acute triangle, so we didn't investigate the other alternative. The above calculations show the triangle is obtuse in any event.
See the second attachment for the other solution.
Priya and Han are biking in the same direction on the same path. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many m miles Han has gone after t hours.
m=16t can be used to determine the distance in miles Han has gone after t hours.
Step-by-step explanation:
Speed of Han = 16 miles per hour
Let,
m be the distance covered by Han in miles;
t be the number of hours Han has been biking,
According to formula,
Distance = Speed*Time
[tex]m=16*t\\m=16t[/tex]
m=16t can be used to determine the distance in miles Han has gone after t hours.
Keywords: distance, speed
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Answer:
y = mx + b ( y = 16t + 0
Step-by-step explanation:
Find the slope for each line. And can you show me how you did it.
Answer:
1 : -1
2:2
3:-5
4: 1/2
5: -3
6: -3/2
7: 1/2
8: -1/2
9: 1
10: 1/3
Step-by-step explanation:
well all u have to do is do rise over run, rise/run. find 2 points and go up according to how much it goes up and go left or right based on the graph. AND sometimes the slope will be negative like number 1.
Find all functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).
Answer:
[tex]y=Ae^{-2x}[/tex]
Step-by-step explanation:
Given that the functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).
Let (x,y) be any arbitrary point of contract
The tangent line passes through two points (x,y) and (x+2,0)
Slope of tangent line = f'(x) = change in y/change in x= [tex]\frac{-y}{2}[/tex]
i.e. we have
[tex]\frac{dy}{dx} =\frac{-y}{2}[/tex]
Separate the variables
[tex]\frac{dy}{y} =-2x\\lny =-2x+c[/tex]
Raise to power e
[tex]y=Ae^{-2x}[/tex]
Thus the functions would have the above form for various values of A
The circumference of the outside of a ring is 66 mm and it has an outer diameter of 21 mm so if the circumference of the inside the ring is 50 mm what is the inner diameter of the rain?
Answer: The inner diameter of the ring is 16 mm.
Step-by-step explanation:
As we know that ,
Circumference of a circle = [tex]\pi d[/tex] , where d = diameter of the circle .
We are given that ,
The circumference of the outside of a ring is 66 mm and it has an outer diameter of 21 mm .
Now , if circumference of the inside the ring is 50 mm, then we have
[tex]50 = \pi d[/tex] , where d= diameter of the inner circle .
Then , [tex]d=\dfrac{50}{\pi}=\dfrac{50}{\dfrac{22}{7}}=\dfrac{50\times7}{22}\approx15.909090909\approx16\text{ mm}[/tex]
Hence , the inner diameter of the ring is 16 mm.
The diameter of the inner ring is 15.92mm
Circumference of a circleThe formula for calculating the circumference of a circle is expressed as:
C = πd
d is the diameter
Given the following parameters
C = 50mm
The diameter of the inner ring is given as:
d = C/π
d = 50/3.14
d = 15.92mm
Hence the diameter of the inner ring is 15.92mm
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You formally challenge the classification of information and the classifying agency provides a partial response. What is your responsibility if the classifying agency does not provide a full response within 120 days.
Answer:
I will forward the challenge to the ISCAP.
Step-by-step explanation:
If the classifying agency does not provide a full response within 120 days, then as per my responsibility, I will forward the challenge to the ISCAP.
ISCAP is the Inter agency security classification appeals panel.
ISCAP is a deciding panel that decides on certain classification or declassification issues to its users, with a forum for further review.
A wheelchair ramp is 4.2 m long. It rises 0.7 m. What is it's angle of inclination to the nearest degree?
The inclination angle is 10°
Step-by-step explanation:
The given scenario forms a right angled triangle where the length of ramp is hypotenuse and the rise of ramp is the perpendicular
Given
H = 4.2m
P = 0.7m
We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse
Let x be the angle
then
[tex]sin\ x = \frac{P}{H}\\sin\ x = \frac{0.7}{4.2}\\sin\ x = 0.1666\\x = sin^{-1} (1.666)\\x = 9.59 => 10[/tex]
Hence,
The inclination angle is 10°
Keywords: Trigonometric ratios, Right angled triangle
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The angle of inclination of the wheelchair ramp to the nearest degree is 9 degrees.
[tex]\[ \theta = \arctan\left(\frac{\text{rise}}{\text{run}}\right) \][/tex]
Given the rise of the ramp is 0.7 m and the run (length) is 4.2 m, we can plug these values into the formula:
[tex]\[ \theta = \arctan\left(\frac{0.7}{4.2}\right) \][/tex]
Now, we calculate the value of θ:
[tex]\[ \theta = \arctan\left(\frac{1}{6}\right) \][/tex]
Using a calculator, we find:
[tex]\[ \theta \approx \arctan(0.1667) \] \[ \theta \approx 9.4623 \text{ degrees} \][/tex]
Rounding to the nearest degree, we get:
[tex]\[ \theta \approx 9 \text{ degrees} \][/tex]
Therefore, the angle of inclination of the wheelchair ramp is approximately 9 degrees to the nearest degree.
What solid figure has congruent squares on all six sides
Answer:
Cube.
Step-by-step explanation:
We are asked to find the solid figure, which has congruent squares on all six sides.
We know that a solid, whose length, width, and height are equal in measure is known as cube.
Upon looking at our attached file, we can see that length, width, and height for the solid are equal to x units, which makes its each face a square.
We know that a cube is a three dimensional figure, which contains six equal squares of all six sides.
Therefore, cube has congruent squares on all six sides.
The nutrition information on the box of cereal says that a one third cup serving provides 80 calories and six grams of dietary fiber. At that rate find how many calories and grams of fiber are in a half cup serving
Answer:
120 calories and 9 grams of fiber.
Step-by-step explanation:
We are told that 1/3 cup serving contains 80 calories and 6 grams of fiber.
Let's multiply everything by 3. So,
1 cup serving has 3*80 = 240 calories and 3*6 = 18 grams of fiber.
But, we want to really know about 1/2 cup. So, now we multiply everything by 1/2.
1/2 cup has (1/2) (240) = 40 calories and (1/2) (18 grams) = 9 grams of fiber.
Answer:
240 calories and 9 grams of fiber
Step-by-step explanation:
The birth rate of a population is b(t) = 2300e0.024t people per year and the death rate is d(t)= 1450e0.019t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.)
To calculate the area between the birth rate and death rate curves for a given time interval, find the net growth rate function by subtracting the death rate from the birth rate, and then integrate this function over the time interval. The result reflects the population surge due to the rates of births and deaths.
Explanation:The student's question involves calculating the area between two exponential growth curves, birth rate and death rate, over a given time interval. To find the area between the curves b(t) = 2300e0.024t and d(t) = 1450e0.019t from t = 0 to t = 10, we need to integrate the difference between them with respect to time over the given interval.Step-by-step Solution:
Subtract the death rate from the birth rate to get the net growth rate function: g(t) = b(t) - d(t) = 2300e0.024t - 1450e0.019t.
Integrate the net growth rate function with respect to t from 0 to 10 to find the total area.
Use a calculator or computer software to perform the integration and round the final answer to the nearest integer.
This computation will give the total number of people added to the population over the 10-year period, which reflects the population surge resulting from the different rates of increase in births and deaths.
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A woman has money in two accounts. One account pays 5% annual interest, whereas the other pays 10% annual interest. If she has $800 more invested in 10% than she does at 5% and her total interest for a year is $250, how much does she have in each account?
Answer:
She have $1133.33 in account which pays 5% annual interest and he have $1933.33 in account which pays 10% annual interest
Step-by-step explanation:
Let x be the amount she invested at 5% annual interest
She invested $800 more in 10%
So, she invested x+800 at 10% annual interest
Case 1:
Principal = x
Time = 1 year
Rate of interest = 5%
[tex]Si =\frac{P \times R \times T}{100}[/tex]
[tex]SI=\frac{x \times 5 \times 1}{100}[/tex]
[tex]SI=\frac{5}{100}x[/tex]
Case 2:
Principal = x+800
Time = 1 year
Rate of interest = 10%
[tex]Si =\frac{P \times R \times T}{100}[/tex]
[tex]SI=\frac{(x+800) \times 10 \times 1}{100}[/tex]
[tex]SI=\frac{10}{100}(x+800)[/tex]
Interest = Amount - principal = 880+1.1x-x=880+0.1x
Her total interest for a year is $250
So, [tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]
[tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]
[tex]\frac{5}{100}x+\frac{10}{100}x+80=250[/tex]
[tex]\frac{15}{100}x+80=250[/tex]
[tex]\frac{15}{100}x=250-80[/tex]
[tex]x=170 \times \frac{100}{15}[/tex]
[tex]x=1133.33[/tex]
So the amount she invested at 5% annual interest is $1133.33
She invested at 10% annual interest=x+800=1133.33+800=1933.33
Hence she have $1133.33 in account which pays 5% annual interest and he have $1933.33 in account which pays 10% annual interest
The amount she has in the account that an annual interest of 5% is $3400.
The amount she has in the account that an annual interest of 10% is $4,200.
What is the system of linear equations that represent the question?x - y = $800 equation 1
0.1x + 0.05y = $250 equation 2
Where:
x = amout invested in the account that earns a 10% interesty = amout invested in the account that earns a 5% interestHow much was invested in the account that earns a 5% interest?
Multiply equation 1 by 0.1
0.1x - 0.1y = 80 equation 3
Subtract equation 3 from equation 2
0.05y = 170
Divide both sides by 0.05
y = $3,400
How much was invested in the account that earns a 5% interest?
Substitute for y in equation 1
x - 3400 = 800
x = 3400 + 800
x = $4,200
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
Assume that cans of Coke are filled so that the actual amounts have a mean of 12.00 oz and a standard deviation of 0.11 oz. Find the probability that a single can of Coke has at least 12.19 oz.
Answer:
0.0421
Step-by-step explanation:
Mean(μ) = 12.00 oz
Standard deviation (σ) = 0.11 oz
Z = (x - μ)/σ
Z = (12.19 - 12.00) / 0.11
Z= 0.19/0.11
Z = 1.727
From the normal distribution table, Z = 1.727 = 0.4579
Φ(Z) = 0.4579
Recall that if Z is positive
Pr(x>a) = 0.5 - Φ(Z)
Pr(x > 12.19) = 0.5 - 0.4579
= 0.0421
A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing. What is the largest area that can be enclosed?
Answer:
Area = 2500 square feet is the largest area enclosed
Step-by-step explanation:
A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing
Let x be the length of each box and y be the width of the box
Perimeter of the box= 3(length ) + 4(width)
[tex]200=3x+4y[/tex]
solve for y
[tex]200=3x+4y[/tex]
[tex]200-3x=4y[/tex]
divide both sides by 4
[tex]y=50-\frac{3x}{4}[/tex]
Area of the rectangle = length times width
[tex]Area = 3x \cdot y[/tex]
[tex]Area = 3x \cdot (50-\frac{3x}{4})[/tex]
[tex]A=150x-\frac{9x^2}{4}[/tex]
Now take derivative
[tex]A'=150-\frac{9x}{2}[/tex]
Set it =0 and solve for x
[tex]0=150-\frac{9x}{2}[/tex]
[tex]150=\frac{9x}{2}[/tex]
multiply both sides by 2/9
[tex]x=\frac{100}{3}[/tex]
[tex]A''=-\frac{9}{2}[/tex]
For any value of x, second derivative is negative
So maximum at x= 100/3
[tex]A=150x-\frac{9x^2}{4}[/tex] , replace the value of x
[tex]A=150(\frac{100}{3})-\frac{9(\frac{100}{3})^2}{4})[/tex]
Area = 2500 square feet is the largest area enclosed
Final answer:
To find the largest enclosed area with 200 feet of fencing divided into 3 plots, solve the equation 2l + 4w = 200 and substitute the value of l into the area formula.
Explanation:
To find the largest area that can be enclosed with 200 feet of fencing and divided into 3 equal plots, we can first find the length of each side of the rectangular piece of land. Let's assume the length of the land is 'l' and the width is 'w'.
Since the land is divided into 3 equal plots, each plot will have a length of l/3 and a width of w.
From the information given, we can form the equation 2l + 4w = 200 (each length side is counted twice and each width side is counted once). We can solve this equation for l and substitute it back into the area formula (A = l * w) to find the largest possible area.
Find an explicit rule for the nth term of the sequence.
7, -7, 7, -7, ... (5 points)
Select one:
a. an = 7 • (-1)n-1
b. an = 7 • (-1)n
c. an = 7 • 1n-1
d. an = 7 • 1n+1
Answer:
(a) The ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7 \times (-1)^{n-1}\\[/tex].
Step-by-step explanation:
Here, the given sequence is 7, -7, 7, -7, ...
The first term = 7, Second term = -7, Third term =-7 and so on..
Now check the given sequence for each given formula, we get:
(1) [tex]a_n = 7 \times (-1)^{n-1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (-1)^{1-1}\\[/tex]
[tex]= 7 \times (-1)^0 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (-1)^{2-1}\\[/tex]
[tex]= 7 \times (-1)^1 = 7 \times (-1) = -7 \implies a_2 = -7[/tex]
Hence, the given formula satisfies the given sequence.
(2) [tex]a_n = 7 \times (-1)^{n}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (-1)^{1}\\[/tex]
[tex]= 7 \times (-1)^1 = 7 \times (-1) = -7 \implies a_1 = -7[/tex]
But, First term = 7
Hence, the given formula DO NOT satisfy the given sequence.
(3) [tex]a_n = 7 \times (1)^{n-1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (1)^{1-1}\\[/tex]
[tex]= 7 \times (1)^0 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (1)^{2-1}\\[/tex]
[tex]= 7 \times (1)^1 = 7 \times (1) = 7 \implies a_2 = 7[/tex]
But, Second term = -7
Hence, the given formula DO NOT satisfy the given sequence.
(4) [tex]a_n = 7 \times (1)^{n+1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (1)^{1+1}\\[/tex]
[tex]= 7 \times (1)^2 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (1)^{2+1}\\[/tex]
[tex]= 7 \times (1)^3 = 7 \times (1) = 7 \implies a_2 = 7[/tex]
But, Second term = -7
Hence, the given formula DO NOT satisfy the given sequence.
So, the ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7 \times (-1)^{n-1}\\[/tex].
Answer:
an=7•(-1)^n-1
Step-by-step explanation: