The solution to given system of equations is x = 2 and y = -5
Solution:
Given the system of equations are:
4x + y = 3 ---------- eqn 1
-2x + 3y = -19 ---------- eqn 2
We have to find the solution to above system of equations
We can solve the system by substitution method
From eqn 1,
4x + y = 3
Isolate y to one side
y = 3 - 4x ----------- eqn 3
Substitute eqn 3 in eqn 2
-2x + 3(3 - 4x) = -19
-2x + 9 - 12x = -19
Combine the like terms
-14x = -19 - 9
-14x = -28
Divide both sides of equation by -14
x = 2Substitute x = 2 in eqn 3
y = 3 - 4(2)
y = 3 - 8
y = -5Thus the solution is x = 2 and y = -5
HELP!Please solve! this!!
Answer:
Recursive formula for geometric sequence
[tex]a_{n}=a_{n-1}\times r[/tex]
is [tex]a_{n}=a_{n-1}\times 6[/tex]
and explicit formula for geometric sequence [tex]a_{n}=a_{1}^{r-1}[/tex] is
[tex]a_{n}=(\frac{1}{2})^{6-1}[/tex]
Step-by-step explanation:
Given sequence is [tex]\frac{1}{2},3,18,108,648,...[/tex]
To find the recursive and explicit formula for this sequence:
Let [tex]a_{1}=\frac{1}{2},a_{2}=3,a_{3}=18,a_{4}=108,a_{5}=648,...[/tex]
To find the common ratio r:
[tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]=\frac{3}{\frac{1}{2}}[/tex]
[tex]=3\times 2[/tex]
[tex]=6[/tex]
Therefore r=6
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]=\frac{18}{3}[/tex]
[tex]=6[/tex]
Therefore r=6
Therefore the common ration r=6
Therefore the given sequence is geometric sequence
Recursive formula for geometric sequence is [tex]a_{n}=a_{n-1}\times r[/tex]
[tex]a_{n}=a_{n-1}\times 6[/tex]
and explicit formula is [tex]a_{n}=a_{1}^{r-1}[/tex]
[tex]a_{n}=(\frac{1}{2})^{6-1}[/tex]
[tex]=(\frac{1}{2})^{5}[/tex]
[tex]=\frac{1}{32}[/tex]
Therefore [tex]a_{n}=\frac{1}{32}[/tex]
Answer:
Recursive: a(n) = 6a(n-1)
Explicit: a(n) = (6^n)/12
Step-by-step explanation:
3 = 6 × ½
18 = 6 × 3
.
.
.
Recursive formula:
a(n) = 6a(n-1)
Explicit:
a(n) = a × r^(n-1)
a(n) = ½ × 6^(n-1)
a(n) = (6^n)/12
Select the graph of the solution set that would represent the following expression. 2 ( x + 1 ) > 3 x − 2
Answer:
B
Step-by-step explanation:
x>4
Answer:
None of the options are right. The correct answer is x < 4
Step-by-step explanation:
2(x + 1) > 3x - 2
2x + 2 > 3x - 2
2 > x - 2
4 > x
x < 4
Find the area of the sector of a circle with radius 4 inches formed by a central angle of [tex]\frac{5\pi}{4}[/tex] radians. Give your answer correct to 3 decimal places.
Answer:
10in²
Step-by-step explanation:
5π/4 is 62.5% of a circle if you look at the unit circle.
So just find the area of a circle and take 62.5% of it.
A = πr²
A = π(4)²
A = 16π
16π(.625) = 10
The distance between Quebec City and New York City is 520 miles. If Kate leaves Quebec and will leaves New York at 9 am and the drive towards each other at 55 mph and 75 mph respectively at what time will they meet
Answer:they would meet at 1 pm
Step-by-step explanation:
The distance between Quebec City and New York City is 520 miles.
At the point where Kate and Will meet, they would have travelled 520 miles.
Let t represent the time it takes Kate to travel a certain distance before they met.
Distance = speed × time
If Kate drives at 55mph, the distance covered would be
55 × t = 55t.will drives at 75 mph
Since Will left same that that Kate left, distance travelled by Will in t hours would be
75 × t = 75t
Since the total distance covered is 520 miles, it means that
55t +75t = 520
130t = 520
t = 520/130 = 4
9 am + 4 hours = 1 pm
Answer:
1 pm
Step-by-step explanation:
Their combined speed is 55 + 75 = 130 miles per hour. That is the rate at which the distance between them is decreasing. The time it takes for the distance between them to become zero is found from the relation ...
time = distance/speed
time = (520 mi)/(130 mi/h) = 4 h
4 hours after 9 am, Kate and Will will meet. That time is 1 pm.
A bag contains 5 red marbles, 10 blue marbles, and 14 yellow marbles. If Jen selects a marble from the bag without looking, what is the probability that she will not pull a red marble
Answer:
The answer to your question is 0.83 or 83%
Step-by-step explanation:
Data
5 red marbles
10 blue marbles
14 yellow marbles
Process
1.- Calculate the total amount of marbles
Total amount = 5 red + 10 blue + 14 yellow
Total amount = 29 marbles
2.- Calculate the amount of marbles that are not red
No red marbles = 10 + 14
= 24 marbles
3.- Calculate the probability
Probability of not pulling a red marble = [tex]\frac{no red marble}{total amount of marbles}[/tex]
Probability of not pulling a red marble = [tex]\frac{24}{29} = 0.83 or 83%[/tex]
While performing intravenous drug injections, it is necessary to decrease the angle of the needle once a flashback is seen in the intravenous catheter to?
Answer: avoid passing through the vein.
Step-by-step explanation:
Calculate the following derivatives. Assume y is a function of t . Use Y for the derivative of y . (a) d dt y7= Incorrect: Your answer is incorrect. (b) d dt y3e4t= Incorrect: Your answer is incorrect. (c) d dt t7 cos(y6)=
Answer:
(a) d dt y7=7Y^6
(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}
(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5
Step-by-step explanation:
We calculate the following derivatives. Since these are complex derivatives, we also calculate the formula for complex derivatives. We use Y for the derivative of y . Therefore, we calculate and we get
(a) d dt y7=7Y^6
(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}
(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5
Select all that apply.
Which of the following are important properties of circles?
Radius
Midpoint
Origin
Center
Final answer:
The important properties of circles from the given options are the radius and the center. Midpoint and origin are not inherent properties of all circles. Properties such as radial and centripetal nature, and the uniqueness of the circle's foci at the center, are paramount.
Explanation:
The important properties of circles that apply from the options given are:
Radius: The distance from the center of the circle to any point on the circumference.
Center: The point that is equidistant from all points on the circumference of the circle.
While midpoint and origin can be related to circles, they are not properties intrinsic to all circles. The origin is more generally associated with a coordinate system, whereas the midpoint refers to the middle point of a segment and does not describe the circle itself unless referring to the midpoint of a diameter, which would be the circle's center.
Furthermore, properties of circles such as being boundary-curves and equidistant-curves are vital. The radial nature of the radius and the centripetal force that acts towards the center of a circular path are central to understanding movement along the circle. Importantly, the foci of a circle, unlike an ellipse, are located at the same point as the center.
Each person in a group of twenty people at a hotel orders one meal chosen from oatmeal, eggs, or pancakes and one hot beverage chosen from coffee or tea. One person will be selected at random from the twenty people. What is the sample space for the meal and beverage for the person selected?
1. {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)}2. {(oatmeal, pancakes), (oatmeal, eggs), (eggs, pancakes), (coffee, tea)}3. {(coffee, tea, oatmeal), (coffee, tea, eggs), (coffee, tea, pancakes)}4. {oatmeal, coffee, pancakes, eggs, tea}5. {(oatmeal, eggs, pancakes), (coffee, tea)}
Answer:
{(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)
Step-by-step explanation:
Sample space is the set of all possible outcomes of an experiment.
Here a person should choose one meal and a hot drink. Hence, each element in the set includes one meal and one beverage, which eliminates 2,because it indicates person choses oatmeal and pancakes which has no beverage. Sets should have elements in pairs so ,We should eliminate 3 ,4,5.
As a result person can choose
oatmeal as meal and coffee as drink
oatmeal as meal and tea for drink
eggs for meal tea for drink
eggs for meal coffee for drink
pancakes for meal tea for drink finally
pancakes for meal and coffee for drink
The sample space of a distribution is the list of possible options.
The sample space for the meal and the beverage is (a) {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)
From the question, the meals are:
Meals: Oatmeal, Eggs, Pancakes
And the beverages are:
Beverages: Coffee, Tea
This means that, the available selections are:
Oatmeal and CoffeeOatmeal and TeaEggs and CoffeeEggs and TeaPancakes and CoffeePancakes and TeaHence, the sample space is (a)
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Mr. Mole left his burrow and started digging his way down. AAA represents Mr. Mole's altitude relative to the ground (in meters) after ttt minutes. A=-2.3t-7A=−2.3t−7A, equals, minus, 2, point, 3, t, minus, 7 How far below the ground does Mr. Mole's burrow lie? Meters below the ground
Answer:
Mr. Mole's burrow lie 7 meters below the ground.Explanation:
The information given can be summarized as:
Mr Mole's altitude relative to the ground, in meters: A = - 2.3t - 7Time, since Mr. Mole started digging, in minutes: tInterpetration of the terms in the model A = -2.3t - 7
The equation A = -2.3t - 7 is a linear function, which consists of two terms:
The term -2.3t indicates that the altitude of Mr Mole decreases by 2.3 meters every minute. This is, -2.3 is the slope of the line in the graph that represents the altitude.The constant term - 7 is the altitude at t = 0, because at t = 0 A = -2.3(0) - 7 = 0 - 7 = 0. This is, -7 is the intercept with the vertical axis in the graph that represents the altitude.Thus, altitude at which Mr. Mole's burrow lie is the initial value given by the function, this is the altitude at t = 0, or the vertical intercept of the line; which, as just said is - 7. The negative sign tells that the value is below the ground (ground level is 0 meters). Then, Mr. Mole's burrow lie 7 meters below the ground.
Mr. Mole's burrow lies 7 meters below the ground which is represented by the equation A = -2.3t - 7.
Given that:
The altitude of Mr. Mole's burrow can be calculated by determining the equation A = -2.3t - 7, where A represents the altitude in meters and t represents time in minutes.
The coefficient of t is -2.3, which shows that the altitude is decreased by 2.3 meters for every minute that passes. At t = 0, the constant term is -7, which represents an initial altitude of -7 meters.
Since Mr. Mole is digging downward and wants to find how far below the ground his burrow lies, we will consider the absolute value of the altitude.
The absolute value of the altitude, which is the distance below the ground, is: |A| = 2.3t + 7
The distance below the ground increases by 2.3 meters for every minute that passes and there's an initial distance of 7 meters below the ground.
Therefore, Mr. Mole's burrow lies 7 meters below the ground.
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Identify the type of sampling used. A statistics student is trying to determine the proportion of all people who own cell phones. He interviews everyone in his apartment building to determine who owns a cell phone. What sampling technique was used?
Answer:
Convenience Sampling
Step-by-step explanation:
The given situation indicates the non-probability sampling because the sampling units are not selected at random and every unit in population has unequal chance of being selected. Convenience sampling is a type of non-probability sampling in which the sampling unit close to interviewer are selected. In the situation statistics student interviews the individual that resides in his building, so it is a convenience sampling.
Final answer:
The statistics student used convenience sampling, a non-probability method, by interviewing individuals in his apartment building to determine cell phone ownership. This method is subject to sampling bias and does not provide generalizable results.
Explanation:
The type of sampling used in the scenario where a statistics student interviews everyone in his apartment building to determine who owns a cell phone is called convenience sampling. This non-probability sampling method involves choosing participants because they are convenient to the researcher, not because they are randomly selected or necessarily representative of the larger population. Therefore, while it is easy and cost-effective, the results of convenience sampling cannot be reliably generalized to the wider population due to potential sampling bias.
The next one will be my last! Will someone please make sure to explain it in depth so I understand 100% how to do these! Thanks
Step-by-step explanation:
Before we start, let's look at what we're trying to prove: that two triangles are congruent. There are a few ways we can do that: SSS, SAS, ASA, or AAS. Whichever we choose, we'll need to show that at least one pair of sides is congruent. We can do that, since we know that H is the midpoint of LM. So we'll either use ASA or AAS.
1. LG || JM, H is the midpoint of LM
Given
2. LH ≅ HM
Definition of midpoint
3. ∠GLH ≅ ∠JMH
Alternate interior angles theorem
(∠GLH and ∠JMH are alternate interior angles. Since LG and JM are parallel, the alternate interior angles are congruent.)
4. ∠LHG ≅ ∠MHJ
Vertical angles theorem
(∠LHG and ∠MHJ are vertical angles, which are always congruent.)
5. ΔLGH ≅ ΔMJH
ASA
(We have two pairs of congruent angles, and a pair of congruent sides between them.)
Now, I chose to use ASA. However, you could use AAS. Instead of using vertical angles in step 4, we could have used alternate interior angles theorem to show that ∠LGH ≅ ∠MJH.
40 points!! What is the limit of the infinite series?
As n goes onto infinity, the expression [tex]\frac{3n^5}{4n^5+1}[/tex] will approach [tex]\frac{3}{4}[/tex]. Note the 3 and 4 come from the leading coefficients of the numerator and denominator respectively. This only works because the degrees for the numerator and denominator are both the same (both are 5).
Since [tex]\frac{3n^5}{4n^5+1}[/tex] is not approaching 0 when n gets really large, adding on successive terms of these values will have the infinite sum diverge. After some very large n, we are effectively adding on 3/4 each time and that just makes the overall sum keep growing forever.
Answer: The sum divergesFinal answer:
The limit of an infinite series depends on whether it converges or diverges. If it converges, the limit is the value the series approaches as the number of terms approaches infinity. If it diverges, it does not have a finite limit.
Explanation:
The limit of the infinite series depends on the specific series being referred to. To find the limit of an infinite series, you need to determine if it converges or diverges. If the series converges, then the limit is the value that the series approaches as the number of terms goes to infinity. If the series diverges, then it does not have a finite limit.
For example, consider the series 1/2 + 1/4 + 1/8 + ... This is a geometric series with a common ratio of 1/2. It converges to the value of 1, so the limit of this series is 1.
Some various tests and properties can be used to determine if a series converges or diverges. Some common ones include the ratio test, the root test, and the comparison test.
The Cookie Monster stole 4 cookies before getting caught by grandma Cookie Monster.He continues stealing cookies when he gets caught. If he steals no less than 10 cookie how many more cookies does he need to steal?
Answer:
Cookie monster needs to steal at least 6 cookies more.
Step-by-step explanation:
Given:
Number of cookies already stole = 4
Total number of cookies he wants to steal [tex]\geq 10[/tex]
We need to find how many cookie he needs to steal more.
Solution:
Let number of cookies he needs to steal more be 'x'.
Now we can say that;
Number of cookies already stole plus number of cookies he needs to steal more should be greater than or equal to Total number of cookies he wants to steal
framing in equation form we get;
[tex]4+x\geq 10[/tex]
Now using Subtraction property of Inequality we will subtract both side by 4 we get;
[tex]4+x-4\geq 10-4\\\\x\geq 6[/tex]
Hence Cookie monster needs to steal at least 6 cookies more.
The Cookie Monster needs to steal at least 6 more cookies after getting caught.
Explanation:The Cookie Monster stole 4 cookies initially before getting caught. If he steals no less than 10 cookies each time, we need to determine how many more cookies he needs to steal. Let's represent the number of cookies he needs to steal as x. The equation to represent this situation is: x >= 10 - 4.
Simplifying the equation, we have x >= 6. Therefore, the Cookie Monster needs to steal at least 6 more cookies after getting caught.
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Tiny marine organisms reproduce at different rates. Phytoplankton doubles in population twice a day, but foraminifera doubles every five days. If the two populations are initially the same size and grow exponentially, how long does it take for (a) The phytoplankton population to be double the foraminifera population. (b) The phytoplankton population to be 1000 times the foraminifera population.
The phytoplankton population will be double the foraminifera population at the end of the first day. It'll take approximately 6.44 days for the phytoplankton population to be 1000 times the foraminifera population.
Explanation:To solve this problem, we'll need to figure out the exponential growth rate for each organism. As per the question, phytoplankton doubles its population twice a day and the foraminifera doubles every five days.
To find when phytoplankton's population is double, consider that they both start at the same population size. On the first day, the phytoplankton's population will double twice, becoming 4 times its original size, whereas the foraminifera's population will stay the same. Thus, it already exceeds two times the foraminifera's population on the first day.To find when phytoplankton's population is 1000 times more than the foraminifera's population let's calculate it. Think of day zero as being the time when both populations are equal. Now, every day the phytoplankton population multiplies by 4 whereas the foraminifera multiplies by 1 every day until the fifth day. Then it doubles. So, if N is the number of days, we need to find smallest N where 4^N > 1000*(2^(N/5)). We can do this manually or by using a computational tool and we will find out that it takes roughly 6.44 days for the phytoplankton population to be 1000 times the foraminifera population.Learn more about Exponential Growth
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Final answer:
To find when the phytoplankton population is double that of the foraminifera, we solve the equation 2^(t/5) = 2^(2t-1), yielding approximately 1.67 days. To find when the phytoplankton population is 1000 times the foraminifera population, we solve 1000 × 2^(t/5) = 2^(2t), resulting in approximately 5.95 days.
Explanation:
To solve this problem, we use the formula for exponential growth: N(t) = N_0 × 2^(t/T), where N(t) is the population at time t, N_0 is the initial population, and T is the doubling time. For phytoplankton with a doubling time of 0.5 days, we have N_p(t) = N_0 × 2^(2t), because they double twice a day. For foraminifera, which double every 5 days, we have N_f(t) = N_0 × 2^(t/5).
Part A
To find when the phytoplankton population is double the foraminifera population, we set 2N_f(t) = N_p(t) and solve for t. This gives us 2 × N_0 × 2^(t/5) = N_0 × 2^(2t). Canceling N_0 and dividing by 2, we get 2^(t/5) = 2^(2t-1), thus t/5 = 2t-1. Solving for t gives us t = 5/3 days, or approximately 1.67 days.
Part B
To determine when the phytoplankton population is 1000 times the foraminifera population, we set 1000N_f(t) = N_p(t). Solving for t in 1000 × N_0 × 2^(t/5) = N_0 × 2^(2t) and simplifying, we find that t = 5 × log2(1000)/3, which is about 5.95 days.
Which expressions are equivalent to 8 (negative 10 x + 3.5 y minus 7)? Select two options. Negative 80 x + 24.5 y minus 56 Negative 80 x + 28 y minus 56 80 x + 28 y + 56 4 (negative 20 x + 7 y minus 14) Negative 4 (negative 20 x + 7 y minus 14)
Answer:
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
This is equivalent to -80x + 28y - 56
Step-by-step explanation:
Let's find out the options that are equivalent to:
8 (negative 10 x + 3.5 y minus 7)
8 ( - 10x + 3.5y - 7) =
-80x + 28y - 56
Options:
A. Negative 80 x + 24.5 y minus 56
This is not equivalent.
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
-80x + 28y - 56
This is equivalent to -80x + 28y - 56
D. Negative 4 (negative 20 x + 7 y minus 14)
80x - 28y + 56
This is not equivalent.
Answer:
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
Step-by-step explanation:
I need help with this!!!!
Options are,
A: 1/3
B: 3/1
C: 1/4
D: 2/4
Answer:
D: 2/4
Step-by-step explanation:
Usually when we talk about a point partitioning a segment, we are interested in the ratio of the first segment to the second:
BC : CD = 2 : 2 = 1 : 1
Since this is not an answer choice, we need to "reverse engineer" the answer list to see if we can find an answer that corresponds to a reasonable interpretation of the question.
__
None of the segments is 3 units long, so neither of answer choices A or B makes any sense.
While segment BD is 4 units long, there is no segment that is 1 unit long, so answer choice C makes no sense, either.
There are segments that are 2 units long and a segment that is 4 units long, so if we interpret the question to be "what is the ratio of BC to BD?" then answer choice D is appropriate.
Help please! 10 pts
Find the missing side length in the right triangle below. Show your work.
Answer:
i think it is 18 or something
Step-by-step explanation:
Answer:
Side length B is 17.
Step-by-step explanation:
Use the Pythagorean Theorem a^2 + b^2 = c^2. if one of the legs is 8, and another is 15, the hypotenuse will be 17.
need help ASAP
Solve the equation by factoring x^2+6x-27=0
a. {-3,9}
b. {-9,3}
c. {3,9}
d. {-3,-9}
Answer:
b. {-9, 3}.
Step-by-step explanation:
x^2 + 6x - 27 = 0
We need 2 numbers whose product is -27 and whose sum is + 6.
These are + 9 and - 3. So the factors are:
(x - 3)(x + 9) = 0
(x - 3) = 0 or (x + 9) = 0
x = 3 or -9.
Answer: option b is the correct answer.
Step-by-step explanation:
The given quadratic equation is expressed as
x^2+6x-27=0
In order to solve the equation by factorization, the first step is to find two numbers such that their sum or difference is 6x and their product is
- 27x^2. The two numbers are 9x and - 3x. Therefore,
x^2 + 9x - 3x - 27 = 0
x(x + 9) - 3(x + 9) = 0
x - 3 = 0 or x + 9 = 0
x = 3 or x = - 9
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the equation or formula for the indicated variable. T= 2 r π h + 2 π r ^2; for h
For this case we have the following equation:
[tex]T = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
We must solve the equation for the variable "h":
We subtract [tex]2 \pi * r ^ 2[/tex] from both sides of the equation:
[tex]T-2 \pi * r ^ 2 = 2 \pi * r * h[/tex]
We divide by [tex]2 \pi * r[/tex] on both sides of the equation:
[tex]\frac {T-2 \pi * r ^ 2} {2 \pi * r} = h\\h = \frac {T} {2 \pi * r} - \frac {2 \pi * r ^ 2} {2 \pi * r}\\h = \frac {T} {2 \pi * r} -r[/tex]
Answer:
[tex]h = \frac {T} {2 \pi * r} -r[/tex]
Francis invested $20,000. Some was invested in bonds that made a 4% profit, and the rest was put into stocks that made an 8% profit. How much did Francis invest in bonds if his total profit on both types of investments was $1,120?
Answer:he invested $12000 in bonds and $8000 in stocks.
Step-by-step explanation:
Let x represent the amount that was invested in the bond that made 4% profit.
Let y represent the amount that was invested in the stock that made 8% profit.
Francis invested $20,000. Some was invested in bonds that made a 4% profit, and the rest was put into stocks that made an 8% profit. This means that
x + y = 20000
Profit made from the amount invested in the bond is
4/100 × x = 0.04x
Profit made from the amount invested in stock is
8/100 × y = 0.08y
if his total profit on both types of investments was $1,120, it means that
0.04x + 0.08y = 1120 - - - - - - - - - - 1
Substituting x = 20000 - y, it becomes
0.04(20000 - y) + 0.08y = 1120
800 - 0.04y + 0.08y = 1120
- 0.04y + 0.08y = 1120 - 800
0.04y = 320
y = 320/0.04 = 8000
x = 20000 - y = 20000 - 8000
x = $12000
Francis invested $12,000 in bonds.
Let's denote the amount invested in bonds as B and the amount invested in stocks as S.
We can set up a system of equations based on the given conditions:
1. B + S = 20,000 (Equation 1) - Total investment amount
2. 0.04B + 0.08S = 1,120 (Equation 2) - Total profit
We can solve this system of equations to find the amount invested in bonds B.
From Equation 1, we can express S in terms of B:
S = 20,000 - B
Now, substitute this expression for S into Equation 2:
0.04B + 0.08(20,000 - B) = 1,120
Let's solve for B:
0.04B + 1,600 - 0.08B = 1,120
-0.04B = 1,120 - 1,600
-0.04B = -480
Now, divide both sides by -0.04:
[tex]\[B = \frac{-480}{-0.04} \][/tex]
B = 12,000
So, Francis invested $12,000 in bonds.
The duck pond games at the carnival has a pool with 75 toy ducks twenty five of these ducks are marked underneath as winners. To play you pick up a duck do not replace it then pick up another what is the probability that both ducks picked are winners?
Answer:
50?
Step-by-step explanation:
Answer:
Step-by-step explanation:
D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2 and less than 9} The number 4 is D ∩ (E ∩ F).
1. True
2. False
Answer: 1. True
Step-by-step explanation:
Given : D = {x|x is a whole number} = { 0, 1 , 2, 3, 4, 5, ..................}
E = {x|x is a perfect square between 1 and 9} = {4 }
F = {x|x is an even number greater than or equal to 2 and less than 9} ={4 , 6 , 8}
Since intersection of sets contains all the values they have common.
Then, E ∩ F= {4}
Now , D∩ (E ∩ F) = { 0, 1 , 2, 3, 4, 5, ..................} ∩ {4} = {4}
Hence , The number 4 is D ∩ (E ∩ F).
Thus , the given statement is 1 . true.
Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on one day a week for a given year on one day a week for a given year, and the average (mean) value is 144.3 volts. Choose the correct answer below. A. The given value is a parameter parameter for the year year because the data collected represent a population population. B. The given value is a parameter parameter for the year year because the data collected represent a sample sample. C. The given value is a statistic statistic for the year year because the data collected represent a sample sample. D. The given value is a statistic statistic for the year year because the data collected represent a population population.
Answer:
C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.
Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
Step-by-step explanation:
The sample mean obtained was :
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}= 144.3[/tex]
A. The given value is a parameter parameter for the year year because the data collected represent a population population.
False. The data colected represent a sample of the population of interest, so for this case is not a parameter because we don't have the information about all the population of interest.
B. The given value is a parameter parameter for the year year because the data collected represent a sample sample.
False. First the sample average is not a parameter, and second the population mean is not equal to the sample mean most of the times.
C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.
Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
D. The given value is a statistic statistic for the year year because the data collected represent a population.
False. If is an statistic can't represent the population, since the parameter represent the population not the statistic.
In this exercise we have to use the knowledge of statistics to be able to identify the correct statement, so I can say that it is:
The letter C
So knowing the statistics topics we can recognize the true alternative:
A. False. The information in visible form colected show a sample of the inhabitants of a place of interest, so for this case exist not a limit cause we forbiddance bear the facts about all the inhabitants of a place of interest.
B. False. First the sample average exist not a limit, and second the inhabitants of a place mean happen inadequate the average value most of the opportunity.
C. Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
D. False. If exist an detail of action can't represent the inhabitants of a place, because the limit represent the inhabitants of a place not the detail of action.
See more about statistics at brainly.com/question/10951564
Use the three steps to solve the problem.
One number is five more than another and their sum is three less than three times the smaller. Find the numbers.
List your answers in numerical order, separated by a comma.
Answer:
The answers in numerical order are 4, 9.
Step-by-step explanation:
i)Let the two required numbers be x, y .
ii) It is given that x = y + 5
iii) it is also given that x + y = 3y - 3.
iv) substituting the value of x from ii) in equation iii) we get
(y + 5) + y = 3y - 3 ⇒ 2y = 8 ∴ y = 4
v) Substituting the value of y from equation iv) in equation ii) we get
x = 4 + 5 = 9
vi) The answers in numerical order are 4, 9.
What is an equation of the line that passes through (0, 8) and (4, 0)?
y = 2 x + 8
y = 2 x + 4
y = -2 x + 4
y = -2 x + 8
Step-by-step explanation:
Say y=ax+b. It goes through (0,8) and (4,0). Therefor we can say 8=a(0)+b which gives us b=8. Then we fill in (4,0) which results in 0=a(4)+8. Given that, a=-2. so y=-2+8
Final answer:
The equation of the line that passes through points (0, 8) and (4, 0) is y = -2x + 8. The slope is calculated as -2 and the y-intercept is 8.
Explanation:
To find the equation of a line passing through two points, we can use the formula y = mx + b where m is the slope of the line and b is the y-intercept. The slope m is calculated by the change in y over the change in x, also known as rise over run. For the points (0, 8) and (4, 0), the slope is calculated as (0 - 8)/(4 - 0) which simplifies to -2. Thus, the slope m is -2.
Since the line passes through the point (0, 8), we already know the y-intercept b; it is 8. Now, we can write the equation of the line using the slope we found and the y-intercept: y = -2x + 8.
Raymond has $10.00 in a savings account that's earns 10% interest per year. The interest is not compounded. How much interest will in the earned in 2 years?
Final answer:
Raymond will earn a total of $2.00 in interest over 2 years on his $10.00 savings account with a non-compounding 10% annual interest rate, as he receives the same amount of interest each year.
Explanation:
To calculate the interest Raymond earns in 2 years on his $10.00 savings at a 10% annual interest rate, where the interest is not compounded, we can follow these steps:
In 2 years, he will earn $1.00 (year 1) + $1.00 (year 2), which equals $2.00 in interest.
In conclusion, Raymond will earn $2.00 in interest over 2 years on his $10.00 savings account with a 10% annual interest rate.
Traviling upstream on the Mississippi River, a barge travels 56 mi in 7 h. Downstream, it travels the same distance in 4 h. Find the rate of the barge in still water and the rate of the current
Answer:the speed of the barge in still water is 11 mph
the speed of the current is 3 mph
Step-by-step explanation:
Let x represent the speed of the barge in still water.
Let y represent the speed of the current.
Traveling upstream on the Mississippi River, the barge travels 56 mi in 7 h. This is against the water current. It means that the total speed of the barge would be
x - y mph
Distance = speed × time
Therefore,
56 = 7(x - y)
8 = x - y - - - - - - - - - - - -1
Downstream, it travels the same distance in 4 h. This is in the same direction with the water current. It means that the total speed of the barge would be
x + y mph
Therefore,
56 = 4(x + y)
14 = x + y - - - - - - - - - - - -2
Adding equation 1 and equation 2, it becomes
22 = 2x
x = 22/2 = 11
Substituting x = 11 into equation 2, it becomes
14 = 11 + y
y = 14 - 11 = 3
Find the value of x. Round to the nearest degree.
Answer:
The answer to your question is 32.64°
Step-by-step explanation:
Data
hypotenuse = 19
adjacent side = 16
x = ?
Process
1.- To solve this problem use trigonometric functions.
The function that relates the adjacent side and the hypotenuse is cosine.
cos x = [tex]\frac{adjacent side}{hypotenuse}[/tex]
2.- Substitution
cos x = [tex]\frac{16}{19}[/tex]
3.- cos x = 0.842
4.- cos ⁻¹x = x = 32.64°
In 12 games last season the school baseball team scored 5, 11, 2, 0, 4, 8, 9, 6, 7, 4, 1, and 2 runs. What is the average number of runs scored per game? Round to the nearest tenth.
Answer:
For Plato users the Answer is C
Step-by-step explanation: