Answer: Yes, I can solve this problem using a system of equations. Let n be the number of nickels and q be the number of quarters. Then we can write two equations:
The total number of coins is 25: n + q = 25.
The total value is $3.85: 0.05n + 0.25q = 3.85
We can solve this system of equations using substitution or elimination. Let's use substitution:
From equation (2), we can solve for n: n = (3.85 - 0.25q)/0.05.
Substitute this expression for n into equation (1): (3.85 - 0.25q)/0.05 + q = 25.
Multiply both sides by 0.05 to clear the denominators: 3.85 - 0.25q + 0.05q = 25 * 0.05.
Simplify the left side: 3.85 = 1.25q.
Divide both sides by 1.25 to solve for q: q = 3.08
Substitute this value for q into equation (1) or the expression for n from step (1) to find n: n = 25 - q = 25 - 3.08 = 21.92
Since n and q represent the number of coins, we round them down to the nearest whole number. So, there are 21 nickels and 3 quarters.
Step-by-step explanation:
Suppose a function f(x) is defined on the domain [-8,4]. If we define a new function g(x) by g(x) = f(-2x), then what is the domain of g(x)? Express your answer in interval notation
The required domain of the function If g(x) = f(-2x) is [-16, 8] in interval notation.
How to find domain of function?The domain of g(x) is the set of all x for which the function g(x) is defined. If g(x) = f(-2x), then the domain of g(x) is the same as the domain of -2x, subject to the restriction that f(x) is defined for the corresponding values of x.
According to question:In interval notation, the domain of -2x is (-∞, ∞).
However, since f(x) is defined only on the interval [-8, 4], the domain of g(x) must be restricted to values of x that correspond to values of -2x within the interval [-8, 4].
To find the corresponding values of x, we need to solve the equation -2x = t for x, where t is a number in the interval [-8, 4].
Solving for x, we get x = -t/2. So, the domain of g(x) is the set of all x such that -t/2 is in the interval [-8, 4], or equivalently, t is in the interval [-16, 8]. In interval notation, this is [-16, 8].
So, the domain of g(x) is [-16, 8] in interval notation.
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angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence.
Angelique needs 3 8/15 hours to completely build the fence.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Angelique builds a fence and she can build 5/8 of the fence in 2 5/6 = 17/6 hours.
We know a number multiplied to its reciprocal is 1.
Therefore, The amount of time Angelique needs to complete the fence is,
(5/8)×(8/5) the complete fence in (17/6)×(8/5) hours.
= 136/30 hours.
= 3 16/30 hours.
= 3 8/15 hours.
Q. Angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence, how much time she needs to complete the fence?
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What is the simplified form of 4 log3x + 6 log3y - 7 log3z?
The simplified form of 6 log₃x - 7 log₃y + 4 log₃z is log₃{(x⁶z⁴)/y⁷}.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.
The simplification of the provided logarithmic expression can be done as follows:-
6 log₃x - 7 log₃y + 4 log₃z,
= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law}
= log₃x⁶ + log₃z⁴ - log₃y⁷
= log₃x⁶z⁴ - log₃y⁷ {Using the Product law}
= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law}.
Hence, the simplified form of 6 log₃x - 7 log₃y + 4 log₃z is log₃{(x⁶z⁴)/y⁷}.
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I'm doing ixl and I don't understand what I need to do in the problem.
Answer:
3C ÷ 21 = 63 C = 21
great question BTW
Please Help I need this ASAP will award Brainliest if correct
The center of dilation is (1, -4).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
From the given graph,
Vertices of RSTV are R(1, -4), S(2, 0), T(1, 2) and V(-2, 1).
Vertices of R'S'T'V' are R'(1, -4), S'(4.5, 2), T'(2, 5) and V'(-2.5, 3.5).
Here, the center of dilation is (1, -4).
The transformation is enlargement by scale factor 1.5
Therefore, the center of dilation is (1, -4).
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What is the value of x?
Answer:
im pretty sure ia 31,61
Step-by-step explanation:
√ always together equals about 15 but as of your value of eggs that could not be possible so establishing the 6 x -5 doesn't make any difference apart from the question being so brought a part the answer would be above 30 it could be 30 to 65 anything but if you equal those balls at the bottom you get to .5 as again does 2.5 x 8 has something that equals a bunch of those 2.5 x 8 is 24.5 making 24.5 but the top one makes it al be 31.5Answer: 10⁰
Step-by-step explanation:
We know that,
the summation of 3 angles of a triangle is 180⁰.
now, (6x-5)⁰+(5x-5)⁰+8x⁰=180
or, 19x-10=180⁰
or, 19x=190⁰
or, x= (190/19)⁰
or, x= 10⁰
Drag and drop the constant of proportionality into the box to match the table. If the table is not proportional, drag and drop "not proportional" into the box.
The value of proportionality is not same.So the it is not proportional.
What is Proportionality?Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
According to question:Let
y ∝ x
y = kx , k is constant
Take x = 2, y = 3
3 = k(2)
k = 3/2 = 1.5
At x= 4, y = 7
7 = k(4)
k = 7/4 = 1.75
The value of proportionality is not same.So the it is not proportional.
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I’m confused please help
Answer:
First option: 4.9 in
Step-by-step explanation:
The area of a circle, given radius = r is computed using the formula
A = πr²
Here we are given the area and asked to find the radius r
A = 75.43 in² = πr²
So
πr² = 75.43
r² = 75.43/π
= 24.01
= 24 rounded to nearest integer
r = √24
= 4.9
The population in a certain town is increasing linearly each year. The population at time t=4 is 1580 and at time t=7 is 2000, where t is the number of years after 1990.
If P(t) is the population at time t, which of these equations correctly represents this situation?
We can use the two points given to find the slope of the line (which represents the population growth) and then use the point-slope form of the equation of a line to write an equation.
The population at time t=4 is 1580, which means P(4) = 1580. The population at time t=7 is 2000, which means P(7) = 2000. We can use these two points to find the slope:
slope = (P(7) - P(4)) / (7 - 4) = (2000 - 1580) / 3 = 140
So the slope of the line representing population growth is 140. Now we can use the point-slope form of the equation of a line to write an equation:
P - 1580 = 140(t - 4)
Simplifying and rearranging, we get:
P = 140t - 380
So the correct equation that represents the situation is:
P(t) = 140t - 380.
A ball thrown upwards hits a roof and returns back to the ground.
The upward movement is modeled by a function s=−t2+3t+4
and the downward movement is modeled by s=−2t2+t+7
, where s is the distance (in metres) from the ground and t
is the time in seconds.
Find the height of the roof from the ground.
Answer: To find the height of the roof, we need to find the point where the ball reaches the maximum height, i.e., the point where the velocity of the ball is equal to 0.
The velocity of the ball can be found by taking the derivative of the function s. The derivative of the function s = −t^2 + 3t + 4 is given by v = ds/dt = 3 − 2t, and the derivative of the function s = −2t^2 + t + 7 is given by v = ds/dt = 1 − 4t.
Setting v = 0, we get 3 − 2t = 0 and t = 3/2 seconds.
Plugging t = 3/2 seconds into the first equation, s = −t^2 + 3t + 4, we get s = −(3/2)^2 + 3(3/2) + 4 = 9/4 + 9/2 + 4 = 7 metres.
Therefore, the height of the roof from the ground is 7 metres.
Step-by-step explanation:
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If a = 6.7 feet and c = 10 feet, what is b? If necessary, round to the nearest tenth.
Answer:
7.4
Step-by-step explanation:
Use Pythagorean Theorem: [tex]a^2+b^2+c^2[/tex]
In this case we have a and c. So let's plug those into the equation:
[tex](6.7)^2+b^2=10^2[/tex]
[tex]44.9+b^2=100[/tex]
[tex]b=\sqrt{55.1}[/tex]
[tex]b=7.4[/tex]
If you want to estimate the mean height of all the .students at a university, which one of the following sampling strategies would be best? Why? Note that none of the methods are true simple random samplesi. Measure the heights of 50 students found in the gym during basketball intramurals ii. Measure the heights of all engineering majors. iii. Measure the heights of the students selected by choosing the first name on each page of the cam pus phone book.
The optimum sampling strategy is (iii), which is listed below.
By selecting a student's initial name from each page of the cam pus phone book, you may measure the heights of the chosen pupils.
What is Sampling?Sampling is a technique for selecting a small group of people or a subset of the population in order to make generalizations and estimate the features of the population. In order to acquire relevant information without studying the entire society, researchers commonly use a variety of sampling approaches in market research.
To ascertain the average height of all students at a certain institution and guarantee that the result is statistically reliable, the sampling process must be applied.
a. Measure the heights of 50 students found in the gym during basketball intramurals.
This approach is not ideal since you would only sample basketball players while leaving all other university students out; hence, your sample would not be representative of all students, simply those who play basketball.
b. Measure the heights of all engineering majors.
This approach is flawed since the sample exclusively includes engineering majors, leaving out students studying other courses.
c. Measure the heights of the students selected by choosing the first name on each page of the campus phone book.
This strategy, which is the finest of the three, allows you to select students independent of the sport or subject they are pursuing. It is more representative of the university student population.
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Sally saved $182 in March. Her father gave her $20 for every
$50 she saved. How much did Sally's father give her?
Answer:
$60
50×3=150
182-150=32
so Sally made 3 $50 so 20+20+20=60
Jewel completed 12 out of 20 of her homework questions last night. What percent did she complete?
Answer:
60%
Step-by-step explanation:
12/20 = 3/5 = 0.6 = 60%
Hey there! To find out how much of her homework Jewel completed, all we need to do is a little math. First, let's divide the number of questions she did by the total number of questions. That's 12 divided by 20 which equals 0.6.
Now, we just need to turn that decimal into a percentage. To do that, we simply multiply 0.6 by 100, which gives us 60. And voila! Jewel completed 60% of her homework.
Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. a. List the sample points.b. Assign probabilities to the sample points.c. Determine the probability of observing each of the following events:A: { Two blue marbles are drawn. }B:{ A red and a blue marble are drawn. }C:{ Two red marbles are drawn. }
The probabilities of all the events related to drawing two marbles without replacement are discussed below.
What is meant by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
Number of blue marbles B = 2
Number of red marbles R = 3
Number of marbles drawn = 2
a) Sample points are different possible combinations.
{ R,R} , {R,B}, {B, R}, {B,B}
b) Probablitiy of { R,R} = 3/5 * 2/4 = 6/20 = 3/10 = 0.3
Probablitiy of {R,B} = 3/5 * 2/4 = 0.3
Probablitiy of {B,R} = 2/5* 3/4 = 0.3
Probablitiy of {B,B} = 2/5 * 1/4 = 0.1
c) A: { Two blue marbles are drawn. }
Probability = 2/5 * 1/4 = 0.1
B:{ A red and a blue marble are drawn. }
Probability = 0.3 ( from above)
C:{ Two red marbles are drawn. }
Probability = 0.3 (from above)
Therefore the different sample points are found and probabilities of different events are also found.
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A scaffold has a diagonal support beam to strengthen it. When the scaffold is 15 feet high and 5 feet wide, how long must the support beam be?
Answer:
15.81 ft
Step-by-step explanation:
Basically it's giving your 2 sides of the right angle triangle & ask you for the long side length.
15²+5²=250
√250 =15.81
what is the missing length of a triangle?
H= 8yd
Area= 63.6 yd
The length of the triangle is given by the equation L = 15.9 yards
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the length of the triangle be represented as L
Now , the equation will be
Let the base of the triangle be represented as W
Now , the value of W = 8 yards
The area of the triangle = 63.6 yards²
Now , Area of the triangle = ( 1/2 ) x Length x Base
Substituting the values in the equation , we get
Area of the triangle A = ( 1/2 ) x 8 x L
4L = 63.6
Divide by 4 on both sides of the equation , we get
L = 15.9 yards
Hence , the length of the triangle is 15.9 yards
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POPULATION A city's population is 358,000 and is decreasing at an annual rate of 0.25%.
Which function represents the estimated population after "t" years?
Answer:
pop'n = 358000*(1-0.25%)^t
Step-by-step explanation:
pop'n = 358000
decreasing rate = 0.25%
after t years
pop'n = 358000*(1-0.25%)^t
Alvin's age is two times Elga's age. The sum of their ages is 27. What is Elga's age?
Answer:
52
Step-by-step explanation:
my boy its 52 she said times it means multiply
need help with pre cal hw
The factors of the quadratic function x² - 2x - 4 is equal to
(x + 1 + √5)(x - 1 + √5)
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, The zeros of the quadratic function x² - 2x - 4 are,
(1 + √5) and (1 - √5). (As they occur in conjugate pairs).
Therefore, The factors of (x + (1 + √5))(x + (x - (1 - √5))
x² - 2x - 4 = (x + 1 + √5)(x - 1 + √5)
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an object is thrown upward at a speed of 156 feet per second by a machine from a height of 19 feet off the ground. the height of the object after seconds can be found using the equation h= -16t^2 +156t +5. When will the height 269feet?. When will the object reach the ground?
Solving the quadratic equation, we found that the object is at a height of 269 feet when t is 1.99s and 8.55s and the object reaches the ground when t = 9.78s.
What is a quadratic equation?
Any equation in algebra that can be written in standard form:
ax² + bx + c =0
where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
The given equation of height h = -16t² + 156t +5
a) The time when the height is 269 feet can be found by substituting this value for h in the above equation.
h = -16t² + 156t +5
169 = -16t² + 156t +5
16t² - 156t + 164 = 0
Solving we get t = 8.55 s, 1.99s
b) The time when the object reaches the ground.
For this, we can take h = 0
-16t² + 156t +5 = 0
t = -0.03, 9.78
The negative value can be ignored.
Therefore solving the quadratic equation, we found that the object is at a height of 269 feet when t is 1.99s and 8.55s and the object reaches the ground when t = 9.78s.
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Simplify.
4x²+2x
x²+x-2
8x² + 4x
3x2 +10x+8
Elizabeth has 10 mangoes
eats 5 and gives
2 to Mary and throws 1 away how many mangoes are left
Answer:
2
Step-by-step explanation:
10-5=5.....the ones she ate
5-2=3 .... the 2 she gave to Mary
3-1 =2.....the one she threw away
2 mangoes!
10 - 5 = 5
5 - 2 = 3
3 - 1 = 2
Rahela's account has an annual interest rate of 6.5% compounded semiannually. What is the annual percentage yield for Rahela's account?
Answer: The annual percentage yield for Rahela's account can be calculated by finding the effective annual interest rate, which takes into account the frequency of compounding. The effective annual interest rate is calculated as follows:
Effective annual interest rate = (1 + (6.5/2))^2 - 1 = 6.6725%
So, the annual percentage yield for Rahela's account is 6.6725%.
Step-by-step explanation:
The table shows the amount of money, A, in a savings account after m months.
The equations that represent the balance A after m months are given as follows:
A - 700 = 100m.A = 700 + 100m.A = 1200 + 100(m - 5).What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the initial amount.For this problem, we have that each month, the balance increases by 100, hence the slope m is given as follows:
m = 100.
Hence:
y = 100x + b.
When x = 5, y = 1200, hence the intercept b is given as follows:
1200 = 500 + b
b = 700.
Hence these following two equations are correct:
A - 700 = 100m.A = 700 + 100m.Taking the fifth month as the initial month, we consider an intercept of 1200, hence the final equation is given as follows:
A = 1200 + 100(m - 5).
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Complete the process of solving the equation.
Fill in the missing term and select the missing description. Simplify any
fractions.
11(u-4)=-11
U-4 =-1
U=
Add 4 to both sides
A rectangular yard measuring
30
by
35ft
is bordered (and surrounded) by a fence. Inside, a walk that is
3ft
wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
Compare A and B in three ways, where A= 51,102 is the number of deaths due to a deadly disease in the United States in 2005 and B= 17,056 is the number of deaths due to the same disease in the United States in 2009.
Answer:
Step-by-step explanation:
Here are three ways to compare A and B, where A= 51,102 is the number of deaths due to a deadly disease in the United States in 2005 and B= 17,056 is the number of deaths due to the same disease in the United States in 2009:
Magnitude: A is approximately three times larger than B. This means that the number of deaths due to the disease was significantly higher in 2005 than in 2009.
Trend: There was a significant decrease in the number of deaths due to the disease between 2005 and 2009. The number of deaths decreased by approximately 67%, from 51,102 in 2005 to 17,056 in 2009.
Impact: Despite the significant decrease in the number of deaths, the disease still caused a significant number of deaths in both 2005 and 2009. This highlights the ongoing importance of disease prevention and treatment efforts to reduce the impact of the disease on public health.
determine if the statements are true or false. an even degree polynomial must be an even function. true false every polynomial of odd degree has at least one zero. true false every rational function that is not a polynomial has a vertical asymptote. a. true b. false
A rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.
An even degree must be an even function is true. This is because a polynomial with an even degree has an even-numbered power, such as f(x)=x^2. This means that the function is symmetrical when its graph is reflected over the y-axis. This means that the graph will look the same if the x-values are reflected over the y-axis. For example, if f(3)=9, then f(-3)=9 as well.
Every polynomial of odd degree has at least one zero is true. This is because a polynomial with an odd degree will always have at least one x-value for which the equation is equal to 0. This is because the highest power of the equation must be odd, and the equation must cross the x-axis at least once. For example, f(x)=x^3 will have at least one x-value, such as x=0, where f(x)=0.
Every rational function that is not a polynomial has a vertical asymptote is false. A rational function that is not a polynomial may have a vertical asymptote, but it is not guaranteed. A vertical asymptote is created when the denominator of a rational equation has a factor that is equal to 0. This means that when this factor is equal to 0, the equation has an undefined value. If a rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.
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please help me with this question thank you
The average rate of change for the given function is -72.
What Is the Average Rate of Change?
To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change. To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.
The rate of the change for the interval [a,b] is given by
[tex]\frac{f(b)-f(a)}{b-a} \\[/tex]
For the given interval [3,11],
[tex]= \frac{f(11)-f(3)}{11-3} \\\\= \frac{-623+47}{8} \\\\= -72[/tex]
So, the required average rate of change is -72.
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