(a) The concentration of the solution in the tank will be changing over time.
(b) The amount of salt in the tank after 3.5 hours is 63.292 kg.
(c) When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.
(a) To find the concentration of the solution in the tank initially, we can use the formula:
concentration = mass of salt / volume of solution
The mass of salt in the tank initially is 60 kg, and the volume of solution is 2000 liters.
Therefore, the initial concentration is:
concentration = 60 kg / 2000 L
concentration = 0.03 kg/L
However, we know that a solution with a concentration of 0.015 kg/L is entering the tank at a rate of 9 L/min.
Therefore, the concentration of the solution in the tank will be changing over time.
(b) To find the amount of salt in the tank after 3.5 hours, we can use the formula:
amount of salt = initial amount of salt + (concentration of incoming solution - concentration of solution in tank) x rate x time
The initial amount of salt is 60 kg, and the concentration of the incoming solution is 0.015 kg/L.
We need to find the concentration of the solution in the tank after 3.5 hours.
The rate of flow is 9 L/min, so the total volume of solution that has entered the tank after 3.5 hours is:
volume of solution = rate x time
volume of solution = 9 L/min x 210 min
volume of solution = 1890 L
The total volume of solution in the tank after 3.5 hours is:
total volume = initial volume + volume of incoming solution - volume of drained solution
total volume = 2000 L + 9 L/min x 210 min - 9 L/min x 210 min
total volume = 2000 L
Therefore, the concentration of salt in the tank after 3.5 hours is:
amount of salt = 60 kg + (0.015 kg/L - concentration of solution in tank) x 9 L/min x 210 min
amount of salt - 60 kg = (0.015 kg/L - concentration of solution in tank) x 1890 L
concentration of solution in tank = 0.015 kg/L - (amount of salt - 60 kg) / 1890 L
Now we can substitute the concentration of the solution in the tank into the formula and solve for the amount of salt:
amount of salt = 60 kg + (0.015 kg/L - (0.015 kg/L - (amount of salt - 60 kg) / 1890 L)) x 9 L/min x 210 min
amount of salt = 63.292 kg
Therefore, the amount of salt in the tank after 3.5 hours is 63.292 kg.
(c) To find the concentration of salt in the solution in the tank as time approaches infinity, we need to find the concentration that the solution will reach when the inflow and outflow rates of solution are equal.
At this point, the amount of salt in the tank will remain constant.
Let's denote the concentration of salt in the solution in the tank as c.
We know that the volume of solution in the tank remains constant at 2000 L, and that the inflow and outflow rates are both 9 L/min. Therefore, the amount of salt that enters the tank per minute is 0.015 kg/L x 9 L/min = 0.135 kg/min, and the amount of salt that leaves the tank per minute is c x 9 L/min.
When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.
Therefore, we can set the rate of inflow equal to the rate of outflow and solve for c:
0.015 kg/L x 9.
For similar question on concentration.
https://brainly.com/question/30677144
#SPJ11
call a positive integer kinda-prime if it has a prime number of positive integer divisors. if there are $168$ prime numbers less than $1000$, how many kinda-prime positive integers are there less than $1000$?
There are 173 kinda-prime positive integer less than 1000.
To find the number of kinda-prime positive integer less than 1000, we'll follow these steps:
1. Understand the definition of a kinda-prime number: A positive integer is kinda-prime if it has a prime number of positive integer divisors.
2. Determine the number of prime numbers less than 1000: There are 168 prime numbers less than 1000, as given.
3. Determine the possible prime number of divisors: Since 168 is not too large, we only need to consider 2 and 3 as possible prime numbers of divisors for a kinda-prime number.
4. Analyze the cases:
Case 1: Kinda-prime numbers with 2 divisors (prime numbers)
All prime numbers have exactly 2 divisors (1 and itself). Thus, all 168 prime numbers less than 1000 are kinda-prime.
Case 2: Kinda-prime numbers with 3 divisors
Let N be a kinda-prime number with 3 divisors. Then, N = p^2 for some prime number p. To find the suitable prime numbers p, we need[tex]p^2 < 1000[/tex]. The prime numbers that meet this condition are 2, 3, 5, 7, and 11 (since 13^2 = 169 > 1000). Therefore, there are 5 additional kinda-prime numbers ([tex]2^2, 3^2, 5^2, 7^2, and 11^2[/tex]).
5. Add the total number of kinda-prime numbers from both cases: 168 + 5 = 173.
Learn more about integer here:
https://brainly.com/question/17118150
#SPJ11
[tex]$(\pi(1000)-1)+11=\boxed{177}$[/tex] "kind a-prime" positive integers less than $1000$.
Let [tex]$n$[/tex] be a positive integer with[tex]$k$[/tex] positive integer divisors.
If [tex]$k$[/tex] is prime, then.
[tex]$n$[/tex] is a "kind a-prime" integer.
[tex]$k$[/tex] must be of the form.
[tex]$k=p$[/tex] or [tex]$k=p^2$[/tex] for some prime [tex]$p$[/tex].
If [tex]$k=p$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p-1}$[/tex] for some prime [tex]$p$[/tex]. Since [tex]$p < 1000$[/tex], there are.
[tex]$\pi(1000)$[/tex]possible values of [tex]$p$[/tex].
[tex]$p=2$[/tex] gives [tex]$2^1$[/tex], which is not prime, so we have to subtract.
[tex]$1$[/tex] from [tex]$\pi(1000)$[/tex] to get the number of possible.
[tex]$p$[/tex].
[tex]$\pi(1000)-1$[/tex] values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
If [tex]$k=p^2$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p^2-1}$[/tex] for some prime[tex]$p$[/tex].
There are.
[tex]$\pi(31)=11$[/tex] primes less than [tex]$31$[/tex], and each of them gives a different "kind a-prime" integer of this form.
Since [tex]$31^5 > 1000$[/tex], no primes larger than [tex]$31$[/tex]can be used to form a "kind a-prime" integer of this form.
[tex]$11$[/tex] possible values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
For similar questions on Positive Integer
https://brainly.com/question/16952898
#SPJ11
Monique claims the surface area of the cylinder is about 1001.66 square feet explain Monique's error find the correct surface area.
Answer: Monique's error is likely due to rounding the surface area to two decimal places, which led to an inaccurate result.
The formula for the surface area of a cylinder is:
S = 2πr^2 + 2πrh
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately 3.14.
To find the correct surface area, we need to know the values of r and h. Without this information, we cannot calculate the exact surface area.
However, we can use Monique's estimate to estimate the values of r and h.
1001.66 = 2πr^2 + 2πrh
Dividing both sides by 2π, we get:
500.83 = r^2 + rh
We don't know the exact values of r and h, but we know that the surface area should be greater than 1001.66 square feet. Therefore, we can assume that the radius and height must be greater than a certain value.
For example, if we assume that the radius is at least 5 feet, we can solve for the minimum value of h:
500.83 = 5^2 + 5h
495.83 = 5h
h = 99.166
So if the radius is 5 feet and the height is 99.166 feet, the surface area would be:
S = 2π(5^2) + 2π(5)(99.166)
S = 1570.8 square feet
This is greater than Monique's estimate of 1001.66 square feet, indicating that her estimate was too low due to rounding.
Step-by-step explanation:
What is the slope of the line?
-2
-1
1
2
Answer: positive 2
Step-by-step explanation:
Show that cosh2x−sinh2x=1 � � � ℎ 2 � − � � � ℎ 2 � = 1 Differentiate with respect to x � e3xx2+1 � 3 � � 2 + 1 y=secx � = sec � y=tanx2 � = tan � 2 Differentiate with respect to x � y=ln(x+sinx) � = ln ( � + sin � ) y=cosxx2 � = cos � � 2 Find dydx � � � � given siny+x2y3−cosx=2y sin � + � 2 � 3 − cos � = 2 � Differentiate from first principles y=cosx � = cos � x3+2x2+3x+4 � 3 + 2 � 2 + 3 � + 4 Find d2ydx2 � 2 � � � 2 Given 3x3−6x2+2x−1 3 � 3 − 6 � 2 + 2 � − 1
We can conclude that cosh2x−sinh2x=1.
What is equation?An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.
To show that cosh2x−sinh2x=1, we can use the identities for cosh2x and sinh2x. The identity for cosh2x is cosh2x=2cosh2x−1 and the identity for sinh2x is sinh2x=2sinh2x−1.
Substituting these identities into the equation cosh2x−sinh2x=1 yields 2cosh2x−1−2sinh2x−1=1. Simplifying this equation yields cosh2x−sinh2x=1, as required. Thus, we can conclude that cosh2x−sinh2x=1.
To know more about equation click-
http://brainly.com/question/2972832
#SPJ1
Simplifying this equation yields [tex]\cosh^2x-sinh^2x=1[/tex], as required. Thus, we can conclude that [tex]\cosh^2x-sinh^2x=1[/tex].
What is equation?An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.
We will show that [tex]\cosh^2x-sinh^2x=1[/tex].
Let us consider the expression [tex]\cosh^2x-sinh^2x.[/tex]
Then, [tex]\cosh^2x=(e^2x+e^{-2}x)/2[/tex] and [tex]sinh^2x=(e^2x+e^{-2}x)/2[/tex]
Substituting, we get [tex]\cosh^2x -\sinh^2x=(e^2x+e^{-2}x)/2\ -(e^2x+e^{-2}x)/2[/tex]
Simplifying, we have [tex]\cosh^2x -\sinh^2x=e^2x+e^{-2}x-e^2x+e^{-2}x[/tex]
[tex]=2e^{-2}x\\\\=2(e^{-2}x)\\\\=2[/tex]
Hence, [tex]cosh^2x-sinh^2x=1[/tex]
Therefore, we have shown that [tex]cosh^2x-sinh^2x=1[/tex]
To know more about equation click-
brainly.com/question/2972832
#SPJ1
The correct form of question is Show that cosh2x−sinh2x=1 .
Keyana puts beads at the ends of her braids. On a single braid, she places 7 beads that are
each 1.03 centimeters long. Then she adds a final bead that is 0.9 centimeter long. The
expression below can be used to find the total length of the beads on one of Keyana's braids.
7 x 1.03 +0.9
What is the total length of the beads on one braid?
A 7.3 centimeters
B.8.11 centimeters
C.9.19 centimeters
D: 10.0 centimeters
The total length of the beads on one braid is 8.11 centimeters
What is the length?Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.
To find the total length of the beads on one braid, we need to evaluate the expression:
7 x 1.03 + 0.9
Multiplying 7 by 1.03 gives us:
7 x 1.03 = 7.21
Then, adding 0.9 gives us:
7.21 + 0.9 = 8.11
Therefore, the total length of the beads on one braid is 8.11 centimeters.
So, the correct answer is B.8.11 centimeters.
To know more about length here:
https://brainly.com/question/28108430
#SPJ1
6) Practice: Using Visual Cues Label each part of the diagram. Then use your labels to complete the sentences. Square Root Notation √6 1. The expression √ means "the of b". 2. The exponent 1 symbol (√) stands for the 3. The number or expression under the radical symbol is called the
1. The expression √b means "the square root of b".
2. The radical symbol (√) stands for the exponent 1/2.
3. The number or expression under the radical symbol is called the radicand.
What is radicand?A radicand is the number or expression underneath a radical symbol (√). It is the number or expression that is being operated on by the root. The square root of the radicand is the result of the operation.
The expression √6 represents the square root of 6. This is the value of x that, when multiplied with itself, results in 6.
The square root of 6 is equal to 2.44948974, which is the positive solution to the equation x² = 6.
The radical symbol (√) indicates that the expression is a root and the number or expression under the radical symbol is called the radicand, which is 6 in this case.
The exponent of the radical symbol is 1/2, which implies that the expression is a square root.
For more questions related to expression
https://brainly.com/question/395066
#SPJ1
which expressions are equivalent to 8 13 ?
The next four equivalent fractions of 8/13 are:
16/2624/3932/5240/65What are some equivalent fractions of 8/13?Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.
In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.
Read more about equivalent expression
brainly.com/question/15775046
#SPJ1
fuel efficiency of manual and automatic cars, part i. each year the us environmental protection agency (epa)releases fuel economy data on cars manufactured in that year. below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions. do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? assume that conditions for inference are satisfied.
Given the above prompt on hypothesis testing, we can state that specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.
What is the explanation for the above response?
To determine if there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage, we can conduct a two-sample t-test assuming unequal variances. The null hypothesis is that there is no difference in the average city mileage between the two types of transmissions, and the alternative hypothesis is that there is a difference.
The t-test statistic is calculated as follows:
t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Plugging in the values from the given statistics, we get:
t = (16.12 - 19.85) / sqrt((3.85^2/26) + (4.51^2/26))
t = -3.31
Using a significance level of 0.05 and 50 degrees of freedom (approximated by n1+n2-2), the critical t-value is ±2.01.
Since the calculated t-value (-3.31) is less than the critical t-value, we can reject the null hypothesis and conclude that there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage.
Specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.
Learn more about hypothesis testing at:
https://brainly.com/question/30588452
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
The volume of a cylinder is given by the formula v - pi^h, where r is the radius of the cylinder and h is the height.
Which expression represents the volume of this cylinder?
The expression that represents the volume of the cylinder is:
V = π[tex]r^{2}[/tex]h
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases. The cylinder can be thought of as a tube or a can. The lateral surface of the cylinder is formed by "unrolling" a rectangular shape along the circumference of the base.
There appears to be a typographical error in the given formula for the volume of a cylinder. The correct formula is:
V = π[tex]r^{2}[/tex]h
where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.
Using this formula, the expression that represents the volume of the cylinder is:
V = π[tex]r^{2}[/tex]h
To learn more about cylinder from the given link:
https://brainly.com/question/16134180
#SPJ1
The data for the height and weight of different people was collected the line of best fit for this date it was determined to be Y equals 0. 9 1X -65. 5 where X is the height in centimeters and why is the weight in kilograms is in the equation predict the height of a person who weighs 63 kg
According to the equation, a person who weighs 63 kg is predicted to be approximately 141 centimeters tall.
The equation given is Y = 0.91X - 65.5, where X represents the height in centimeters and Y represents the weight in kilograms. To predict the height of a person who weighs 63 kg, we need to solve for X, the height in centimeters.
To do this, we can plug in the given weight of 63 kg for Y in the equation and then solve for X. So, we have:
63 = 0.91X - 65.5
Adding 65.5 to both sides, we get:
63 + 65.5 = 0.91X
Simplifying, we have:
128.5 = 0.91X
Finally, to solve for X, we divide both sides by 0.91, giving:
X = 141.21
To know more about equation here
https://brainly.com/question/10413253
#SPJ4
armer abe has a budget of $300 to build a rectangular pen to protect his rambunctious sheep. he decides that three sides of the pen will be constructed with chain-link fence, which costs only $1 per foot. farmer abe decides that the fourth side of the pen will be made with sturdier fence, which costs $5 per foot. find the dimensions of the largest area the pen can enclose.
Let x be the length of the pen and y be the width of the pen.
The total cost of the pen is given by:
Cost = 3x + 5y = 300
3x + 5y = 300
3x = 300 - 5y
x = (300 - 5y)/3
The area of the pen is given by:
Area = xy = (300 - 5y)/3 * y
. imagine you had a research question in which you wanted to compare a sample mean to the mean of a population. under these circumstances you would either do a z-test or a one-sample t-test. what key piece of information would be missing if you needed to do a one-sample t-test?
Sample size and sample standard deviation are the key information needed for a single-sample t-test.
In the event that you need to compare the test cruel with the populace cruel, and you perform a single-sample t-test rather than a z-test, the vital piece of data that will be lost is the populace standard deviation.
Within the z-test, the populace standard deviation is known and the standard mistake of the cruel is calculated utilizing the populace standard deviation.
In a single-sample t-test, the populace standard deviation is obscure, and the standard mistake of the cruel is evaluated from the test standard deviation.
Therefore, sample size and sample standard deviation are the key information needed for a single-sample t-test.
learn more about standard deviation
brainly.com/question/23907081
#SPJ4
Solve x^2 + 6x + 9 = 0 by graphing. Please enter the number part of your answer only.
If your answer has two numbers, enter them like this: x = 6 and -1 should be entered as "6, -1" (no quotes).
Answer:
-3
Step-by-step explanation:
You want the graphical solution to x² +6x +9 = 0.
GraphThe graph of the expression on the left shows it has a value of 0 when x = -3.
The solution is x = -3.
__
Additional comment
A graphing calculator is very helpful when you want a graphical solution.
If you want to graph this by hand, you can rewrite it as ...
(x +3)² = 0
The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.
If you spin the spinner 36 times, what is the best prediction possible for the number of times
it will land on green or blue?
The best prediction possible for the number of times the spinner will land on green or blue is given as follows:
30 spins.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Out of six regions, three are green and two are blue, hence the probability of one spin resulting in green or blue is given as follows:
p = (3 + 2)/6
p = 5/6.
Thus the expected number out of 36 trials of spins resulting in green or blue is given as follows:
E(X) = 5/6 x 36
E(X) = 30 spins.
More can be learned about probability at https://brainly.com/question/24756209
#SPJ1
Lucia has three separate pieces of ribbon. Each piece is 5 yards long. She needs to cut pieces that are 27 inches long to decorate folklorico dance dresses. What is the greatest number of 27-inch pieces that she can cut from three pieces of ribbon?
A 20
B 18
C 7
D 6
The greatest number of 27-inch pieces that she can cut from three pieces of ribbon is found to be 19. So, option B is the correct answer choice.
Each yard is equal to 36 inches, so 5 yards are equal to 180 inches. Therefore, each piece of ribbon is 180 inches long.
To find out how many 27-inch pieces Lucia can cut from each piece of ribbon, we divide 180 by 27.
180/27 = 6.67
Since Lucia can only cut whole pieces, she can cut 6 pieces of ribbon from each piece of ribbon.
Therefore, she can cut a total of 6 x 3 = 18 pieces of ribbon from the three separate pieces of ribbon.
Learn more about Division :
https://brainly.com/question/19871608
#SPJ4
brainliest+100 points
2x + 2y = 4xy is wrong
2x + 2y = 2(x+y) is correct
b.3x+4= 7x wrong
c4x²+5x = 9x² wrong
23x²+3x²+4x = 6x² + 4x = 2x(3x + 2)
3sorry I don't understand this one.....
4-4(3x-5) = -12x + 20
5 120 12 10 4 3 5 26Answer:
120
12 10
4 2 5 2
2 2
please help!
If r=0.5 m, A = ???
(Use the r key.)
The area of a circle of radius of 0.5 meters is 0.785 square meters.
How to find the area of the circle?Remember that for a circle of radius r, the area is:
A = pi*r²
Where pi = 3.14
Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.
A = 3.14*(0.5m)²
A = 3.14*0.25 m²
A = 0.785 m²
That is the area of the circle.
Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?
Learn more about circles in https://brainly.com/question/29142813
#SPJ1
Peter needs to borrow $10,000 to repair his roof. He will take out a 317-loan on April 15th at 4% interest from the bank. He will make a payment of $3,500 on October 12th and a payment of $2,500 on January 11th.
a) What is the due date of the loan?
b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.
c) Calculate the interest due on January 11th and the balance of the loan after the January 11th pa payment.
d) Calculate the final payment (interest + principal) Peter must pay on the due date.
Please only serious answers
Answer:
A. February 26th
B. $3,500 - Balance ≈ $6,697.26
C. $2,500 - Balance ≈ $4,263.46
D. $4,284.81
Step-by-step explanation:
a) What is the due date of the loan?
The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.
April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days
Subtracting 48 days from April 15th, we get:
Due date = February 26th (of the following year)
b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.
First, we need to calculate the number of days between April 15th and October 12th:
April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days
Now, we will calculate the interest for 180 days:
Interest = Principal × Interest Rate × (Days Passed / 365)
Interest = $10,000 × 0.04 × (180 / 365)
Interest ≈ $197.26
Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:
Balance = Principal + Interest - Payment
Balance = $10,000 + $197.26 - $3,500
Balance ≈ $6,697.26
c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.
First, we need to calculate the number of days between October 12th and January 11th:
October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days
Now, we will calculate the interest for 91 days:
Interest = Principal × Interest Rate × (Days Passed / 365)
Interest = $6,697.26 × 0.04 × (91 / 365)
Interest ≈ $66.20
Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:
Balance = Principal + Interest - Payment
Balance = $6,697.26 + $66.20 - $2,500
Balance ≈ $4,263.46
d) Calculate the final payment (interest + principal) Peter must pay on the due date.
First, we need to calculate the number of days between January 11th and February 26th:
January (20 days) + February (26 days) = 46 days
Now, we will calculate the interest for 46 days:
Interest = Principal × Interest Rate × (Days Passed / 365)
Interest = $4,263.46 × 0.04 × (46 / 365)
Interest ≈ $21.35
Finally, we will calculate the final payment Peter must pay on the due date:
Final payment = Principal + Interest
Final payment = $4,263.46 + $21.35
Final payment ≈ $4,284.81
I will be given brainliest!!!!
Answer:2/3
Step-by-step explanation:
its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD
Answer: 2/3
Step-by-step explanation:
The corresponding side of AD is A'D'.
AD = 30
A'D' = 20
Scale factor = 2/3 because AD * 2/3 = A'D'
If I'm wrong, please tell me.
Solve for length of segment d.
= 4 cm
b = 12 cm
c = 6 cm
4. ? =
].d
Enter the segment length tha
belongs in the green box.
If two segments intersect inside
or outside a circle: ab = cd
Answer: Using the given information and the formula ab = cd, we can write:
d = (ab) / c
We are given b = 12 cm and c = 6 cm. To find ab, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a is the unknown length we want to find. Substituting the given values, we get:
a^2 + 12^2 = 6^2
a^2 + 144 = 36
a^2 = -108 (which is not a possible solution)
This means that the given values do not form a valid triangle. Therefore, we cannot find the length of segment d using the given information.
Step-by-step explanation:
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 to describe the relationship.
In the given equation r = 2/5 t "r" is the dependent variable.
Dependent variables:In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.
An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.
A dependent variable is a variable whose value depends on the value of one or more other variables in the equation
Here we have
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups.
She writes the equation r = 2/5 t to describe the relationship.
In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.
Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.
The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.
Therefore,
In the given equation r = 2/5 t "r" is the dependent variable.
Learn more about Variables at
https://brainly.com/question/1479694
#SPJ1
Complete Question:
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.
in a recent basketball game, shenille attempted only three-point shots and two-point shots. she was successful on 20% of her three-point shots and 30% of her two-point shots. shenille attempted 30 shots. how many points did she score?(2013 amc 12a
The probability of a score for a recent basketball game, shenille attempted only three-point shots and two-point shots is 18 points in the game. The answer is Option B.
Let x be the number of three-point shots and y be the number of two-point shots attempted by Shenille.
Then, we have:
x + y = 30 (total number of shots attempted)
Let's solve for one of the variables. For example, we can solve for x by subtracting y from both sides of the equation:
x = 30 - y
Now, we can express Shenille's points in terms of x and y:
Points = 3x + 2y
Substituting x = 30 - y, we get:
Points = 3(30 - y) + 2y
Points = 90 - y
Shenille's success rate for three-point shots is 20%, so the number of successful three-point shots she made is 0.2x. Similarly, the number of successful two-point shots she made is 0.3y.
Total points scored = (0.2x)(3) + (0.3y)(2)
Substituting x = 30 - y, we get:
Total points scored = (0.2(30 - y))(3) + (0.3y)(2
Total points scored = 18 + 0.4y
Now we need to maximize the total points scored by Shenille. Since she attempted 30 shots in total, we have:
y = 30 - x
Substituting this into the equation for total points, we get:
Total points scored = 18 + 0.4(30 - x)
Total points scored = 30 - 0.4x
This is a linear function, which is maximized at its endpoint. The maximum value of this function occurs at x = 0, which means Shenille attempted all two-point shots. In this case, y = 30, and the total points scored would be:
Total points scored = 0 + 0.3(30)(2)
Total points scored = 18
Learn more about probability at
https://brainly.com/question/30034780
#SPJ4
The question is -
In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on 20% of her three-point shots and 30% of her two-point shots. Shenille attempted 30 shots. How many points did she score?
(A) 12
(B) 18
(C) 24
(D) 30
(E) 36
Solve for x please
Choices are...
10
5
25
90
Answer:
x = 10
Step-by-step explanation:
Angle form is = 90°
therefore
5x + 25 + x + 5 = 90
6x + 30 = 90
6x = 90-30
6x = 60
6x/6 = 60/6
x = 10
From a horizontal distance of 80.0 m, the angle to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.
1. 24.7 meters
2. 76.1 meters
3. 26.0 meters
4. 25.3 meters
Answer:
The figure is omitted--please sketch it to confirm my answer.
Set your calculator to degree mode.
Let h be the height of the flagpole.
[tex] \tan(18) = \frac{h}{80} [/tex]
[tex]h = 80 \tan(18) = 25.994[/tex]
The height of the flagpole is approximately 26.0 meters. #3 is correct.
Find the solution to the system of equations. Write the solution as an ordered pair. If there are no solutions, write 'no solutions'. If there are infinitely many, write 'infinitely many'.
y = −72
x + 11
7x + 2y = 20
The solution to the system of equations is (23, -72).
How to find system of equations ?The first equation is y = -72, which means that whatever the value of x is, the value of y will always be -72.
Substituting y = -72 in the second equation, we get:
7x + 2(-72) = 20
Simplifying this equation, we get:
7x - 144 = 20
Adding 144 to both sides, we get:
7x = 164
Dividing both sides by 7, we get:
x = 23.428571...
So the solution to the system of equations is the ordered pair (x, y) = (23.428571..., -72).
However, we usually express solutions as ordered pairs of integers, so we can round x to the nearest integer to get:
(x, y) = (23, -72)
Therefore, the solution to the system of equations is (23, -72).
Learn more about system of equations here:https://brainly.com/question/25976025
#SPJ1
Lin plans to swim 12 laps in the pool. She has swum 9.75 laps so far.
How many laps does she have left to swim? Use y
for the number of laps that Lin has left to swim.
Lin plans to swim 12 laps and has already swum 9.75 laps, so the number of laps she has left to swim can be found by subtracting 9.75 from 12:
y = 12 - 9.75
Simplifying the right side:
y = 2.25
Therefore, Lin has 2.25 laps left to swim.
Which statement is true?
Please help
A=P(1+r/n)^nt Find how long it takes for $1400 to double if it is invested at 7% interest compounded monthly. Use the formula A = P to solve the compound interest problem. TE The money will double in value in approximately years. (Do not round until the final answer. Then round to the nearest tenth as needed.)
It will take 10 years to double the amount.
Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,
[tex]A = P(1+r/n)^{nt}[/tex]
[tex]2800 = 1400(1+0.0058)^{12t}[/tex]
[tex]2= (1.0058)^{12t[/tex]
㏒ 2 = 12t ㏒ (1.0058)
0.03 = 12t (0.0025)
12t = 120
t = 10
Hence, it will take 10 years to double the amount.
Learn more about compound interest click;
https://brainly.com/question/14295570
#SPJ1
a kite flying in the air has a 94- string attached to it, and the string is pulled taut. the angle of elevation of the kite is . find the height of the kite. round your answer to the nearest tenth.
The height of the kite is approximately 68.4 ft.
To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:
tan(46°) = height / 94
Solving for height, we get:
height = 94 * tan(46°)
Using a calculator, we get:
height ≈ 68.4 ft
Therefore, the height of the kite is approximately 68.4 ft.
We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.
Learn more about the height
https://brainly.com/question/28122539
#SPJ4
Complete Question:
A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.
A helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram how far is the object from the helicopter to the nearest foot
The distance of the object from the helicopter is 698 ft.
What is distance?Distance is the length between two points.
To calculate how far the object is above the helicopter, we use the formula below.
Formula:
Sin∅ = O/H..................... Equation 1Where:
∅ = AngleO = OppositeH = Hypotenus = Distance of the object from the HelicopterFrom the question,
Given:
O = 250 ft∅ = 21°Substitute these values into equation 1 and solve for H
H = 250/Sin21°H = 697.61 ftH ≈ 698 ftHence, the distance is 698 ft.
Learn more about distance here: https://brainly.com/question/26046491
#SPJ1