Juan had 15 quarters. To solve this, we created a system of equations representing the total value of the coins and the relationship between the number of nickels and quarters. Calculations led to the conclusion that there were 15 quarters in total.
The question requires us to solve a system of equations to find out how many quarters Juan had if he had $5.25 in nickels and quarters, with 15 more nickels than quarters. Let's denote the number of quarters as q and the number of nickels as n. Remember, a quarter is worth $0.25 and a nickel is worth $0.05.
Based on the given information, we can establish the following equations:
0.25q + 0.05n = $5.25 (the total value equation)n = q + 15 (the number of coins equation)We can substitute the second equation into the first to find the value of q.
0.25q + 0.05(q + 15) = $5.25
Solving for q:
0.25q + 0.05q + 0.75 = $5.25
0.30q + 0.75 = $5.25
0.30q = $4.50
q = $4.50 / 0.30
q = 15
Therefore, Juan had 15 quarters.
How many ears of corn would equal to 5 pounds?
I NEED UR HELP PLEASE..
Books spontaneously catch on fire in temperatures at or above 451, degree Fahrenheit. Write an inequality that is true only for temperatures (t)(t)left parenthesis, t, right parenthesis at which books spontaneously catch on fire.
Please help :)
Solve the system of equations and choose the correct answer from the list of options.
d + e = 1
−d + e = −5
Label the ordered pair as (d, e). (4 points)
(0, 0)
(3, −2)
(−2, 3)
(−3, 0)
(3, -2)
Given equations are
d+e=1
-d+e=-5
We need to find d and e.
What is system of equations?A system of equations is a set of one or more equations involving a number of variables
The system of equations are
d+e=1....(1)
-d+e=-5....(2)
d=1-e (from 1)
Substitute d in (2)
-(1-e)+e=-5
-1+e+e=-5
-1+2e=-5
2e=-5+1
2e=-4
e=-2
Now substitute value of e in (1)
d-2=1
d=1+2
d=3
Therefore the ordered pair for d + e = 1 and −d + e = −5 is (3, -2)
i.e value of d=3 and e=-2
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There was a sample of 200 milligrams of a radioactive substance to start a study. since then, the sample has decayed by 5.4% each year. let t be the number of years since the start of the study. let y be the mass of the sample in milligrams. write an exponential function showing the relationship between y and t .
The exponential function representing the relationship between the mass y of a radioactive sample in milligrams and t years since the start of the study is y = 200(1 - 0.054)^t.
The student is given a starting mass of a radioactive substance and the percentage of the mass that decays each year. To write an exponential function that models this situation, we consider the initial mass, which is 200 milligrams, and the decay rate, which is 5.4% per year. The relationship between the mass y and the time t in years can be represented by the formula y = 200(1 - 0.054)^t.
Using an exponential decay model, we understand that the amount of substance decreases by a certain percentage each year. To account for this, we raise the base (1 - 0.054) to the power of t, representing the number of years, which gives us the factor by which the original mass has reduced.
What is the domain for the piece of the function represented by f(x) = x + 1?
Answer:
All real numbers
Step-by-step explanation:
The domain of the function represented by f(x) = x + 1 is the all real numbers as there is only addition involved in the function so putting any number as input will not lead the function to infinity.
The equation $1.50p + $5.00 = $14.00 shows the total cost of picking p pounds of blueberries at a local blueberry farm. how many pounds of blueberres were picked/
A cylindrical tank has a radius of 4.5 ft and an altitude of 14 ft. If a gallon of paint will cover 130 ft squared ft2 of surface, how much paint in gallons is needed to put two coats of paint on the entire surface of the tank? Aswer: To put two coats of paint on the entire surface of the tank, ______ full gallons of pain are needed.
What is the 12th term of the sequence?
3, −9, 27, −81, 243, ...
The 12th term of the sequence 3, -9, 27, -81, 243, ... is 177,147.
Explanation:The given sequence is: 3, -9, 27, -81, 243, ...
To find the 12th term, we can observe that the sequence alternates between positive and negative, and each term is obtained by multiplying the previous term by -3. Starting with 3 as the first term, we can find the 12th term using the formula:
an = a1 * (-3)n-1
Substituting the values, we have:
a12 = 3 * (-3)12-1a12 = 3 * (-3)11a12 = 3 * (-32)5a12 = 3 * 95a12 = 3 * 59049a12 = 177,147Final answer:
The 12th term of the geometric sequence is -531441, found by using the formula for the nth term of a geometric series with a first term of 3 and a common ratio of -3.
Explanation:
The sequence given is geometric with each term being multiplied by -3 to obtain the next term. To find the 12th term of the sequence, we can use the formula for the nth term of a geometric sequence: Tn = a * rn-1, where a is the first term, r is the common ratio, and n is the term number.
For the given sequence, the first term a is 3 and the common ratio r is -3. The 12th term is found by placing these values into the formula:
T12 = 3 * (-3)12-1
T12 = 3 * (-3)11
T12 = 3 * (-177147)
T12 = -531441
Therefore, the 12th term of the sequence is -531441.
2. Which of the following is equivalent to 5455 cm3?
(
0.5455 L
5.455 L
54.55 L
5455 L
1. For which angle is secant undefined?
a. 30°
b. 45°
c. 180°
d. 270°
2. Which of the following is csc(-166°) equal to?
a. csc(14°)
b. -csc(14°)
c. -csc(-14°)
d. csc(166°)
1. The secant is defined as the inverse function of co-secant or cos function
Hence when the cosine is 0, the secant is 1/0 which is undefined. So, when cosine is 0, secant is undefined
Cos 30 = [tex] \sqrt{3} /2 [/tex]
Cos 45 = [tex] 1/\sqrt{2} [/tex]
Cos 180 = -1
cos 270 =0
Since cos 270 is 0, secant of 270 is undefined
Answer is d: 270
2. cosec (-x) = - cosec (180 -x)
We have cosec(-166) = - cosec (180-14) = -cosec (14)
Alternatively we can confirm this as csc (-166) = -4.133565 and -csc(14) = -4.133565; Hence, we can reconfirm that the answer arrived at is right
Therefore csc (-166) = -csc(14) (Option B) is the right answer
Pratap Puri rowed 14 miles down a river in 2 hours, but the return trip took him 3 and one half hours. Find the rate Pratap can row in still water and find the rate of the current. Let x equals rate Pratap can row in still water and y equals rate of the current. What is the rate that Pratap rows in still water?
Final answer:
By establishing equations based on Pratap's rowing times upstream and downstream, we find that Pratap's rowing rate in still water is 5.5 miles per hour.
Explanation:
Finding Pratap's Rowing Rate in Still Water and the Current Rate
To calculate Pratap Puri's rowing rate in still water and the rate of the current, we need to set up two equations based on the information provided. We know that Pratap rowed 14 miles down a river in 2 hours and the return trip took 3 and a half hours.
Step-by-Step Solution
Let x be the rate at which Pratap can row in still water, and y be the rate of the current.
The downstream speed (with the current) is x + y, and the upstream speed (against the current) is x - y.
Using the formula distance = rate × time, for the downstream trip we have 14 = (x + y) × 2, and for the upstream trip 14 = (x - y) × 3.5.
Simplifying both equations gives us: 7 = x + y and 4 = x - y.
To find x, add the two equations to eliminate y, yielding 11 = 2x, or x = 5.5.
Therefore, Pratap's rowing rate in still water is 5.5 miles per hour.
Find the area of a trapezoid based on the information given below. H=4√2 b1=5√2 b2=3√2
10 - 3(3x - 40) = -9x A)x = -9 B)no solution C)x = 10 D)all real numbers
Find the first five terms of the sequence: an = 5an – 1 + 2; a1 = 3.
a) {3, 17, 87, 437, 2187}
b) {3, 15, 75, 375, 1875}
c) {3, 12, 17, 22, 27}
d) {3, 11, 27, 59, 123}
What is the equation of the line that passes through (7, 4) and (4, -2)?
a) y = 2x - 10
b) y = -2x - 10
c) y = -2x + 18
d) y = 2x + 18
Solution:
we have been asked to find the equation of the line that passes through (7, 4) and (4, -2).
First we will find the slope of the line using the formula
[tex] m=\frac{y_2-y_1}{x_2-x_1} [/tex]
Plugin the given values we get
[tex] m=\frac{-2-4}{4-7}=\frac{-6}{-3}=2 [/tex]
Now using the point slope form of a straight line
[tex] (y-y_1)=m(x-x_1) [/tex]
Plugin the values
[tex] (y-4)=2(x-7)\\
\\
y=2x-14+4\\
\\
y=2x-10\\ [/tex]
Hence the correct option is a.
A line passes through the points (-6,4) and (-2,2). Which is the equation of the line?
Answer:
The equation of the line is [tex]y=\frac{-1}{2}x+1[/tex]
Step-by-step explanation:
1. The equation of the line that passes through two points can be expresed as:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex] (Eq.1)
where [tex]x_{1}[/tex], [tex]x_{2}[/tex], [tex]y_{1}[/tex] and [tex]y_{2}[/tex] are the given points.
2. Name the points:
[tex]x_{1}[/tex]=-6
[tex]x_{2}[/tex]=-2
[tex]y_{1}[/tex]=4
[tex]y_{2}[/tex]=2
3. Replace the points in the Eq.1:
[tex]\frac{y-4}{x-(-6)}=\frac{2-4}{-2-(-6)}[/tex]
[tex]\frac{y-4}{x+6}=\frac{2-4}{-2+6}[/tex]
[tex]\frac{y-4}{x+6}=\frac{-2}{4}[/tex]
[tex]\frac{4(y-4)}{x+6}=-2[/tex]
[tex]4(y-4)=-2(x+6)[/tex]
[tex]4y-16=-2x-12[/tex]
[tex]4y=-2x-12+16[/tex]
[tex]4y=-2x+4[/tex]
[tex]y=\frac{-2x+4}{4}[/tex]
[tex]y=\frac{-2x}{4}+\frac{4}{4}[/tex]
[tex]y=\frac{-1}{2}x+1[/tex]
Over the past week, 34 baby boys were born at the hospital. this was 54% of all babies born. how many girls were born over the past week? (enter numeric value only. if grounding is necessary, round to the nearest whole number
If the radius of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?
a. 3 7 π inches
b. 7 2 π inches
c. 7 3 π inches
d. 7 6 π inches
The correct answer to this problem C.)7/3
Help on both 13 and 14. Show work please
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
A. y = –x + 1
B. 3x − 4y = −4
C. 4x − 3y = −3
D. y – 2 = –(x – 4)
E. y + 2 = (x + 4)
If the diameter of a sphere is 12cm, what is its volume to the nearest hundredth
Whats the distance between points C(0, 4), T(-6, -3)
a √(37)
b √(85)
c √(109)
What's the diameter of a cirlce eith an area of 615.75?
Randall bought a bond with a face value of $6000 and a coupon rate of 7.25%. the bond will mature in 5 years. how much interest will he receive semiannually?
Answer:
Face value of bond = $ 6000
Rate of interest =7.25 %
The Bond will mature in 5 years.
If the interest is semiannually , the rate of interest will reduce to half.
So, new rate of interest will be [tex]\frac{7.25}{2}=3.625[/tex]
Formula for simple interest
[tex]=\frac{\text{Principal}\times Rate \times time}{100}[/tex]
Interest after 6 months will be
[tex]=\frac{6000 \times 3.625 \times 1}{100}\\\\=60 \times 3.625\\\\=217.5[/tex]
So, interest that Randall will receive after six months = $ 217.50
Base your answer to the question on the diagrams shown below.
What is the probability of drawing a red card and then spinning a 1?
Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
From the given picture, the total number of cards = 5
The number of red card = 2
Thus, the probability of drawing a red card P(red)=[tex]\frac{2}{5}[/tex]
Also, total number of digits on spinner = 8
Number of 1's=4
Thus, the probability of spinning a 1 P( spinning 1)=[tex]\frac{4}{8}=\frac{1}{2}[/tex]
Since both the events of drawing a red card and spinning a 1 are independent events, therefore, the probability of drawing a red card and then spinning a 1=[tex]\text{ P(red)}\times\text{P( spinning 1)}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}[/tex]
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years. Five years after Brian's initial investment, Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar)
Compound interest formula is [tex]A = P(1+r)^t[/tex]
Where P is the principal amount
r is the rate of interest
t is number of years
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years
P = 10,000 , r= 4% = 0.04 , t =10
Plug in all the values
[tex]A = 10000(1+0.04)^{10}[/tex] = 14,802.44
Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.
P = 10,000 , r= 7% = 0.07 , t =5
Plug in all the values
[tex]A = 10000(1+0.07)^5[/tex] = 14,025.52
Brian balance after the interest period = $ 14,802.44
Chris balance after the interest period = $ 14,025.52
Balance in Brian's account is more than Chris account
which graph shows the solution set of the compound inequality 1.5x-1>6.5 or 7x+3<-25
Answer:
It's B
Step-by-step explanation:
What is the best first step in solving the equation 4 + squrt(6x) = 5?