a = amount invested at 8%
how much is 8% of "a"? (8/100) * "a", namely 0.08a.
b = amount invested at 6%
how much is 6% of "b"? (6/100) * "b", namely 0.06b.
we know the total amount invested is 210000, so whatever "a" and "b" might be, we know that a + b = 210000.
we also know that the yielded amount in interest is the same for both, so whatever 0.08a and 0.06b are, we know they're the same.
[tex]\begin{cases} a+b=210000\\\\ 0.08a=0.06b \end{cases}\hspace{5em}a+b=210000\implies b=210000-a \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.08a~~ = ~~0.06(210000-a)}\implies 0.08a=12600-0.06a\implies 0.14a=12600 \\\\\\ a=\cfrac{12600}{0.14}\implies \boxed{a=90000}\hspace{9em}\boxed{\stackrel{210000~~ - ~~90000}{b=120000}}[/tex]
Enter an expression that represents the following statement, and then solve the expression.
3 less than the product of 6 and −4.
The expression is .
The value of the expression is
Answer:
-27
Step-by-step explanation:
6 * (-4) -3 =
= -24 - 3 =
= -27
the time it takes a woman to travel from her apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes. if she leaves home at 9:05 a.m., what is the probability that she will get to the station between 9:25 and 9:30 a.m.?
The probability that she will get the station between 9:25 and 9:30 is 1/2.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given: The time it takes a woman to travel from her apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes.
She leaves home at 9:05 a.m.
Let x be the random variable denoting that travel time of a women from apartment to bus stop.
Here x ≈ U (20, 30)
⇒ F(x) = (x - 20) / (30 - 20)
To find, she leaves home at 9:25 at reach bus stop at 9:25 to 9:30
⇔ P(20 < x < 25)
= (25 - 20) / (30 - 20)
= 5 / 20
= 1/2
Hence, the probability is 1/2.
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A recipe for whole grain bread calls for 1 oz of rye flour for every 4 oz of whole wheat flour. How many ounces of each kind of flour should be used to make a loaf of bread weighing 22 oz?
In the making of 22 oz of bread rye flour and whole wheat requirements are 4.4 0z and 17.6 oz.
What is the different method of writing a ratio?A ratio is a comparison between two quantities in simplest form.
A ratio of the from a : b can be written as a/(a + b) and b/(a + b).
Given, A recipe for whole grain bread calls for 1 oz of rye flour for every 4 oz of whole wheat flour.
∴ In the making of 22 oz of bread rye flour needed is 1/(1 + 4)×22
= (1/5)×22.
= 4.4 oz.
In the making of 22 oz of bread whole wheat needed is 4/(1 + 4)×22.
= (4/5)×22.
= 17.6 oz.
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assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis? group of answer choices increase the sample variance decrease the sample size none of the other 3 options would increase the likelihood. increase the sample mean difference
Assuming that other factors are held constant, the sample means difference Increases. (option C)
The null hypothesis and the alternative hypothesis are the two types of hypotheses for a test.
Step 1: The null hypothesis is based on the assumption that there is no difference between the true mean (µ) and the compare value ([tex]m_{o}[/tex]). The alternative hypothesis is based on this assumption.
Step 2: Increasing the sample mean difference would probably make it more likely that the null hypothesis will be rejected, as long as other factors stay the same.
As a result, option C is the right one.
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(Complete question)
Assuming that other factors are held constant, which approach would tend to increase the likelihood of rejecting the null hypothesis?
a. Decrease the sample mean difference.
b. Increase the sample variance.
c. Increase the sample mean difference.
d. Decrease the sample size.
what is the y-intercept of the line given by the equation below?
y=4x-6
A. (4, 0)
B. (0, 4)
C. (-6, 0)
D. (0, -6)
Answer:
D: (0,-6)
Step-by-step explanation:
the y intercept in an equation is the "b" value in y=mx+b
Answer:
(0,-6)
Step-by-step explanation:
you can look at the last term in the equation which is -6
Or you can set x to 0
y=4(0)-6
y=-6
Hopes this helps please mark brainliest
PLEASEEEE HELP 100 POINTS AND I WILL MARK BRAINLIEST PLEASE
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C(t) = −2t^2 + 8t, where the time, t, is hours after injection.
Part A: What are the domain and range of the function C(t) based on the context of the problem? Show all necessary calculations.
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.
Answer:
See below
Step-by-step explanation:
First, graph the function to see that the domain ( the values of x the function can have in this context goes from 0 to 4 hours ( after four hours the concentration goes negative.....can't happen in the real world)
and the range is 0 to max of 8 mg/L
Here is the graph :
someone pls help me. i dont understand this at all :c
A professor has 125 students in her classes at the beginning of the semester, but 16 students withdraw from her classes before Test #3. If she has 1 classes in total and each class has an equal number of students, how many students are in each class? Round your answer to the nearest ones (i.e., one student).
Answer:
Students in her classes At the beginning of the semester, but 13 students withdraw from her classes before Test three. So now she has 150 students. If she has one classes in total, in each class has an equal number of students. How many students are in each class round your answer to the nearest ones? Well, first of all, if she only has one class, then there's 150 students in that class is or class, this is the middle school math teacher signing out.
lazyuser30
(3xy^(2))^(3)*(-(2)/(3)x^(2)y^(3))^(4)
Answer:
its B!!
Step-by-step explanation:
I took the test and got it wrong but the review said it was B
Riley walked 6 players in 3
innings. How many players is
he likely to walk in 5 innings?
m -10
-------- = 0
-2
What is the answer
An artist charges $980 for a portrait but gives 5% discount for cash. Calculate the cash Price of the portrait
Answer: $49
Step-by-step explanation: 5% of 980 = 0.05 × 980 = 49
Answer:
$931
Step-by-step explanation:
Discount = less money paid
100% - 5% = 95%
95% = 0.95
980 * 0.95 = 931
What is 52 increased by 18
52 increased by 18 is basically 52 + 18 = 70
I hope this helps!
Round to the nearest 10th
Answer:
30
Step-by-step explanation:
Well I hope this helps Have a good day! :)
The figure shows lines r, n, and p intersecting to form angles 1, 2, 3, 4, 5, and 6. All 3 lines lie in the same plane. Based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line p ? Select all that apply. M∠4 + M∠5 = 60° M∠3 = M∠6 M∠6 = 90° M∠1 + M∠6 = 90° M∠5 + M∠4 = 90° M∠2 = 90°
The individual statements which would provide enough information to conclude that line r is perpendicular to line p are m∠3 = m∠6, m∠6 = 90°, and m∠5 + m∠4 = 90°. Option B, option C, and option E are correct.
First, let us understand the angle formed by intersecting lines:
The types of angles formed by intersecting lines are adjacent angles, vertical angles, etc.
We are given;
The figure shows lines r, n, and p intersecting to form angles 1, 2, 3, 4, 5, and 6.
All 3 lines lie in the same plane.
If line r is perpendicular to line p, then;
m∠1 + m∠2 = m∠5 + m∠4 = 90° (Vertical angles)
m∠3 = m∠6 = 90° (Vertical angles)
Thus, the individual statements which would provide enough information to conclude that line r is perpendicular to line p are m∠3 = m∠6, m∠6 = 90°, and m∠5 + m∠4 = 90°. Option B, option C, and option E are correct.
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Xavier earns $20 each time he walks someone's dog. He walks his neighbor's dog each day. He also earned an additional $10 for running with the dog one day.
Part B: Write an algebraic expression from your written description used in Part A. Let d stand for the number of days.
The numbers i am using is $20 and $10 so just use those numbers and do the rest please because i don't know.
54 people can unload a ship in 5 hours. 54 people started unloading at 3pm. After 2 hours, 36 people had to leave. The remaining people kept working to finish unloading the ship. How many hours after 8pm did the remaining people each have to work?
Answer: 6 hours
to be honest i got 7 hours but i typed in 6 and it was correct so i cant really tell you how i got it right :/
The distribution of annual profit at a chain of stores was approximately normal with mean μ = $ 66 , 000 μ=$66,000mu, equals, dollar sign, 66, comma, 000 and standard deviation σ = $ 22 , 000 σ=$22,000sigma, equals, dollar sign, 22, comma, 000. The stores with profits in the top 5 % 5%5, percent each had a reward party for the employees to celebrate. What is closest to the minimum annual profit for a store that had a reward party?.
From the given mean and standard deviation the closest minimum annual profit, for a store that had a reward party is equal to $102,300.
As given in the question,
Given distribution of annual profit :
Approximately normal with mean μ = $66,000
Standard deviation σ = $22,000
Profits in the top 5 percent
Apply z-score formula :
z = ( x - μ) / σ
Top 5% mean 95% and more.
Using normal distribution table,
z -score corresponding to 95% or 0.95 is equal to 1.65.
Substitute all value in the formula we get,
1.65 = ( x - 66,000 ) / 22,000
⇒ x - 66,000 = 1.65 × 22,000
⇒ x = 36,300 + 66,000
⇒ x = 102,300
Therefore, from the given mean and standard deviation the closest minimum annual profit, for a store that had a reward party is equal to $102,300.
The complete question is :
The distribution of annual profit at a chain of stores was approximately normal with mean μ = $66,000, standard deviation σ = $22,000. The stores with profits in the top 5 percent each had a reward party for the employees to celebrate.
What is closest to the minimum annual profit for a store that had a reward party?
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consider the following problem: a farmer with 750 ft of fenc- ing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. what is the largest possible total area of the four pens?
The largest possible total area of the four pens is 14,062.5 ft.²
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
Diagrams illustrating the situation can be formed adjusting the width of the included diagram illustrating the general situation.
The expression for the total area is A=( 150- (2Y)/5 ) Y
Reasons:
The given parameter are;
Length of fencing available = 750 ft.
Area to be enclosed = Rectangular
Number of included pens with parallel fencing = Four
Let Y represent the width of the area and let X represent the breadth
Therefore, we have;
2·Y + 5·X = 750
Which gives;
X=(750/5)-(2Y/5)=150-(2Y/5)
The area is therefore;
A=Y [150-(2Y/5)] = 150Y-(2Y²/5)
Differentiate with respect to Y and equate to zero
dA/dY = 150- (4Y/5)=0
Y=(150*5)/4 = 187.5
The width of the maximum area, Y = 187.5 ft.
Which gives;
X=150- (2*187.5)/5 = 75
The breadth of the area, X = 75 ft.
The maximum area, = Y × X, which gives;
= 187.5 ft. × 75 ft. = 14,062.5 ft.²
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How do you remove the vertical asymptote from the domain in pre calc
Answer:
Step-by-step explanation:
..................
write a linear function f with f(5)=-1 and f(0)=-5
f(x)= ?
to get the equation of any straight line, we simply need two points off of it, let's use the provided ones
[tex]f(5)=-1\implies \underline{(\stackrel{x}{5}~~,~~\stackrel{y}{-1})}\hspace{5em}f(0)=-5\implies \underline{(\stackrel{x}{0}~~,~~\stackrel{y}{-5})} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{5}}} \implies \cfrac{-5 +1}{-5} \implies \cfrac{ -4 }{ -5 } \implies \cfrac{4 }{ 5 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{4 }{ 5 }}(x-\stackrel{x_1}{5}) \implies y +1 = \cfrac{4 }{ 5 } ( x -5) \\\\\\ y-1=\cfrac{4 }{ 5 }x-4\implies {\Large \begin{array}{llll} y=\cfrac{4 }{ 5 }x-3 \end{array}}[/tex]
The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the the domain of the inverse function.
The given descriptions "The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the domain of the inverse function." is stated about the logarithmic function.
First, let us understand the logarithmic function:
The inverses of exponential functions are logarithmic functions, and any exponential function could be represented in logarithmic form.
The given description fully stated about the logarithmic function.
Thus, the given description "The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the domain of the inverse function." is stated about the logarithmic function.
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Question 6
Write an equation in point-slope form for the line that passes through the given points.
(4,-6), (6,-4)
[tex]-6=-3x^{2}-3x\\[/tex]
Given the following formula, solve for a.
8 = a+b+c
O A.
a
OB. a
OC. a = s- bzc
OD.
28 b + c
-
28 b - c
-
a = s - btc
2
Answer:
a = -b - c + 8
Step-by-step explanation:
8 = a + b + c. Solve for a.
Subtract b from both sides
8 - b = a + c
Subtract c from both sides
8 - b - c = a
It is customary to rearrange so that the variable we solved for is on the left side
a = -b - c + 8
Rochelle had 3/4 yard of twine each party favor requires 3/8 yard howmany party favors can Rochelle make
Rochelle can make 2 party favors with 3/4 yards of wine.
According to the question,
We have the following information:
Rochelle had 3/4 yard of wine. Each party favor requires 3/8 yard.
Now, we will find how many parts of a party can 1 yard of wine favor using division.
So, we have the following expression:
1 party = 3/8 yards
1 yard = 8/3 party
Now, Rochelle has 3/4 yards of wine in total. So, we can find the number of party favors using multiplication.
3/4 yards = (3/4)*8/3
3/4 yards = 2 parties
Hence, Rochelle can make 2 party favors with 3/4 yards of wine.
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The area of the triangle below is 8.64 square inches. What is the length of the base?
Answer: The base is 4.8 sq inches.
Step-by-step explanation: The formula for a triangle is (B x H) x 1/2. Knowing this, we can double 8.64 to nullify the 1/2. This gives us 17.28. 17.28 divided by 3.6 gives us 4.8
Answer:
4.8
Step-by-step explanation:
The area of a triangle is half the base times the height.
[tex]0.5*b*3.6=8.64 \\ b = \frac{8.64}{0.5*3.6}[/tex]
1. an ecologist studying starfish populations collects the following data on randomly-selected 1-meter by 1-meter plots on a rocky coastline. --the number of starfish in the plot. --the total weight of starfish in the plot. --the percentage of area in the plot that is covered by barnacles (a popular food for starfish). --whether or not the plot is underwater midway between high and low tide. how many of these measurements can be treated as continuous random variables and how many as discrete random variables? a) three continuous, one discrete. b) two continuous, two discrete. c) one continuous, three discrete. d) two continuous, one discrete, and a fourth that cannot be treated as a random variable. e) one continuous, two discrete, and a fourth that cannot be treated as a random variable.
2 measurements can be treated as continuous random variables. 1 discrete random variable, and a fourth that cannot be treated as a random variable. (option d)
There are a few ways that a continuous random variable differs from a discrete variable: Due to the fact that it can contain an infinite number of values within a given interval, continuous random variables are typically uncountable. Measurements like height, weight, distance, and a plethora of other decimal values are examples of these variables. On the other hand, discrete random variables have values that can be counted, and the values of successive values are typically whole numbers.
In the above scenario, The number of starfish is a discrete variable, whereas the starfish's weight and percentage of the plot's area are continuous variables.
It is not a random variable whether the plot is in progress or halfway between high tide and low tide.
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Ue the factor Theorem to determine if
the given binomial i a factor of f(x)
f(x)=2x^3x^2-9x-6;x-1
By using factor theorem it is obtained that,
x - 1 is not a factor f(x) =[tex]2x^5-9x-6[/tex]
What is factor theorem?
At first, it is important to know about remainder theorem
Remainder theorem states that if f(x) is divided by (x - a), then the remainder is f(a)
If the remainder is zero, then f(a) is a factor of f(x)
Factor theorem states that if f(a) = 0, then (x - a) is a factor of f(x).
Here,
[tex]f(x)=2x^5-9x-6[/tex]
Divisor = x - 1
x - 1 = 0
x = 1
By remainder theorem,
Remainder = f(1)
f(1) =
[tex]2(1)^5 - 9(1) - 6\\2 - 9 -6\\-13[/tex]
Which is not equal to zero
x - 1 is not a factor f(x) [By factor theorem]
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Model with math Katrina and Becca exchanged 270 text messages in 45 minutes. An equal number of texts was sent each minute. The girls can send 90 more text messages before they are charged additional fees. Complete the double-number line diagram . At this rate for how many more minutes can the girls exchange texts before they are charged extra
At this rate 15 more minutes the girls can exchange texts before they are charged extra.
Given that,
Katrina and Becca exchanged 270 text messages in 45 minutes. An equal number of texts was sent each minute. The girls can send 90 more text messages before they are charged additional fees.
Here,
Total message sent = 270
in time = 45 minutes
Rate = 270 / 45 = 6 messages per minute
Time for the exchange of 90 messages = 90 / 6 = 15 minutes
Thus, At this rate 15 more minutes the girls can exchange texts before they are charged extra.
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