Write the following as an algebraic expression. Then simplify.
The total amount of money (in cents) in x nickles, (x+3) quarters, and 3x dimes. (Hint: The value of a nickel is 5 cents, the value of a quarter is 25 cents, and the value of a dime is 10 cents.)
The total amount of money is ___ cents.
(Simplify your answer. Do not factor.)
Answers
Answer:
[tex]60x+75[/tex]
Step-by-step explanation:
We want to find the total amount of money (in cents) of the expression:
[tex]\text{$x$ nickels, $(x+3)$ quarters, and $3x$ dimes}[/tex]
Since each nickel is worth five cents, each quarter 25 cents, and each dime ten cents, we can write that:
[tex]\displaystyle \text{Total}=5(x)+25(x+3)+10(3x)[/tex]
Simplify. Distribute:
[tex]T=5x+25x+75+30x[/tex]
Combine like terms. Therefore, the total amount of money (in cents) is represented by:
[tex]T=60x+75[/tex]
Related Questions
From 22 potential women jurors and 25 potential men jurors, a jury of 12 is chosen at random. Let X be the number of women selected. Find the probability mass function of X.
Answers
Answer:
The probability mass function is:
[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]
Step-by-step explanation:
The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability mass of the hypergeometric probability distribution is given by:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
22 + 25 = 47 jurors, so [tex]N = 47[/tex]
22 are women, which means that [tex]k = 22[/tex]
Jury of 12, which means that [tex]n = 12[/tex].
Thus
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]
Which is the probability mass function.
Express in simplest radical form.
V9
Answers
Answer:
3
Step-by-step explanation:
[tex]\sqrt{9}=\sqrt{3*3} = 3[/tex]
please helpppp!!! it’s timed!!!! thank u for helping!!!!!
Answers
Answer:
10π in.
Step-by-step explanation:
circumference of a circle = 2πr
=2*π*5
=10π in.
The measures of the angles of the triangle are 32°, 53º,
950. Based on the side lengths, what are the measures
of each angle?
m2A = 95°, mZB = 53º, mZC = 32°
MZA= 32º, mzB = 53º, mZC = 95°
MZA= 43º, mZB = 32°, m2C = 95°
OmZA= 53º, m B = 95°, m2C = 32°
Answers
Answer:
m∠A = 32°
Step-by-step explanation:
8^2 = 12^2 + 15^2 - 2*12*15*cosA
Answer:
B
Step-by-step explanation:
did it on edge
Ivan is saving money to buy a game. So far he has saved 8, which is one-fourth of the total cost of the game. How much does the game cost?
Answers
Answer:
[tex]\$32[/tex]
Step-by-step explanation:
Let the cost of the game be [tex]x[/tex]. Since one-fourth of the cost of the game is equal to 8 dollars, we have the following equation:
[tex]\frac{1}{4}x=8[/tex]
Multiply both sides by 4 to isolate and solve for [tex]x[/tex]:
[tex]x=8\cdot 4=\boxed{\$32}[/tex]
I’ve been stuck on this problem I can’t seem to get 7 9/4 into the ABC form
Answers
Answer:
7 square root 9^4
Step-by-step explanation:
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
Calculate the value of this investment at the end of the 5 years.
Answers
Answer:
The value of this investment at the end of the 5 years is of $662.5.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
This means that [tex]P = 600, t = 5, r = 0.02, n = 1[/tex]. Thus
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 600(1 + \frac{0.02}{1})^{t}[/tex]
[tex]A(t) = 600(1.02)^t[/tex]
Calculate the value of this investment at the end of the 5 years.
This is A(5). So
[tex]A(5) = 600(1.02)^5 = 662.5[/tex]
The value of this investment at the end of the 5 years is of $662.5.
Find the Value of x
Answers
Answer:
42
Step-by-step explanation:
(adjacent straight angles sum up to 180)
3x+54=180
x=42
plz answer this very important
Answers
Answer:
16
Step-by-step explanation:
From the question given above, the following data were obtained:
1 = 1
2 = 4
3 = 9
4 =?
Observing the data, we can see that the numbers on the right side are simple the squares of the numbers on the left side. This is illustrated below:
1 = 1² = 1
2 = 2² = 4
3 = 3² = 9
Thus, we shall use the same logic to obtain that of 4. This is illustrated below:
4 = 4² = 16
Thus the answer to the question is 16.
A rectangle has vertices (−5, 6), (−1, 6), (−1, 3), and (−5, 3). It is first dilated by the rule (x, y)→(7x, 7y) and then translated 10 units down. What are the coordinates of the image?
A(−35, 32), (−7, 32), (−7, 11), (−35, 11)
B(−45, 42), (−17, 42), (−17, 21), (−45, 21)
C(−105, 42), (−77, 42), (−77, 21), (−105, 21)
D(−35,−28), (−7,−28), (−7,−49), (−35,−49)
Answers
Right angle Trigonometry, please help me solve and explain!
Answers
Answer:
theta = arctan 8/5 = 58 degrees
Step-by-step explanation:
The tangent function relates the angle theta to the two side lengths 5 and 8:
tan theta = 8/5 We need to find the angle, theta.
Using a calculator with the inverse tangent funtion built-in, we find that the angle theta is
theta = arctan 8/5 = 58 degrees.
Please help is for now :(
Answers
Answer:
d
Step-by-step explanation:
d part it is. this is the answer
Solve for x. Round to the nearest hundredth.
A. 0.02
B. 25.17
C. 0.03
B. 12.27
Answers
Work Shown:
cos(angle) = adjacent/hypotenuse
cos(64) = x/28
x/28 = cos(64)
x = 28*cos(64)
x = 12.2743921100941
x = 12.27
what is a case control study
Answers
Answer:
A study that compares two groups of people: those with the disease or condition under study (cases) and a very similar group of people who do not have the disease or condition (controls). Researchers study the medical and lifestyle histories of the people in each group to learn what factors may be associated with the disease or condition. For example, one group may have been exposed to a particular substance that the other was not. Also called retrospective study.
Step-by-step explanation:
Answer:
A case-control study is designed to help determine if an exposure is associated with an outcome (i.e., disease or condition of interest).
Step-by-step explanation:
please help i need the explanation to go look back at for similar questions in the future. last word is Bold.
Answers
Answer:
50
Step-by-step explanation:
The given angles in the triangle are vertically opposite angles. Hence;
9x - 4 = 8 + 7x
Collect the like terms
9x - 7x = 8 + 4
2x = 12
x = 12/2
x = 6
Get the bolded angle
Bolded angle= 8 + 7x
Blded angle = 8 + 7(6)
Bolded angle = 8 + 42
Bolded angle = 50
Passion wants to rent a car to take a trip and has a budget of $75. There is a fixed rental fee of $25 and a daily fee of $10. Write ab inequality that would be used to solve for the maximum number of days for which passion can rent the car on her budget
Answers
Answer:
5 days
Step-by-step explanation:
75 = 10d +25
-25 -25
50 = 10d
/ /
10 10
5 = d
The sound pressure P for a given sound is given by:
P= 10 log W/ Wo
Its units are decibels (dB). W is the size of a variable energy source (called the sound power), measured in Watts. Wo is the lowest threshold of sound that humans can typically hear. It is a constant given by:
Wo=10^-12 W/m2
a) Find the rate of change of the sound pressure P with respect to time if W=7.2 and dW/dt = 0.5 at some given time t.
b) If the variable sound power W is given by W = t2 +t +1, find the rate of change of the sound pressure P, at time t = 3s.
c) If W = cos 0.2t, find the rate of change of the sound pressure P, at time t = 15 (calculators in radians)
Answers
Answer:
a. 0.302 dB/s
b. 2.34 dB/s
c. 1.24 dB/s
Step-by-step explanation:
a) Find the rate of change of the sound pressure P with respect to time if W=7.2 and dW/dt = 0.5 at some given time t.
Since P = 10log(W/W₀), its rate of change with respect to time is
dP/dt = dP/dW × dW/dt
dP/dW = d[10logW - 10logW₀]/dt
dP/dW = d[10lnW/2.303 - 10logW₀]/dt
= 10/2.303W - 0
= 10/(2.303W)
dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × dW/dt
Since dW/dt = 0.5 when W = 7.2, then
dP/dt = 10/(2.303 × 7.2) × 0.5
dP/dt = 10/16.5816 × 0.5
dP/dt = 0.603 × 0.5
dP/dt = 0.302 dB/s
b) If the variable sound power W is given by W = t² + t + 1, find the rate of change of the sound pressure P, at time t = 3s.
Since P = 10log(W/W₀), its rate of change with respect to time is
dP/dt = dP/dW × dW/dt
dP/dW = d[10logW - 10logW₀]/dt
dP/dW = d[10lnW/2.303 - 10logW₀]/dt
= 10/2.303W - 0
= 10/(2.303W)
and dW/dt = d(t² + t + 1)/dt = 2t + 1
So, dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × (2t + 1)
dP/dt = 10(2t + 1)/(2.303W)
dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]
we then substitute t = 3 into the equation
dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]
dP/dt = 10(2(3) + 1)/[2.303((3)² + 3 + 1)]
dP/dt = 10(6 + 1)/[2.303(9 + 3 + 1)]
dP/dt = 10(7)/[2.303(13)]
dP/dt = 70/29.939
dP/dt = 2.34 dB/s
c) If W = cos 0.2t, find the rate of change of the sound pressure P, at time t = 15 (calculators in radians)
Since dP/dt = dP/dW × dW/dt and dP/dW = 10/(2.303W) and W = cos(0.2t), dW/dt = -0.2sin(0.2t)
So, dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × -0.2sin(0.2t)
dP/dt = -20sin(0.2t)/(2.303W)
dP/dt = -20sin(0.2t)/(2.303cos(0.2t))
dP/dt = -20tan(0.2t)/2.303
when t = 15, we have
dP/dt = -20tan(0.2 × 15)/2.303
dP/dt = -20tan3/2.303
dP/dt = -20 × -0.1425/2.303
dP/dt = 2.8509/2.303
dP/dt = 1.238
dP/dt ≅ 1.24 dB/s
A positive real number is 4 less than another. if the sum of the squares of the two numbers is 72, then find the numbers
Answers
Answer:
x+4=72
x=72-4
x=68
Step-by-step explanation:
let x be one number and 4 be anothe number then sum of the two number be x and 4
Any help? Algebra I
Answers
9514 1404 393
Answer:
2p +3d = 18.25; 4p +2d = 27.50popcorn: $5.75; drink: $2.25Step-by-step explanation:
a) Let p and d represent the prices of a bag of popcorn and a drink, respectively.
Mohamed's purchase is ...
2p +3d = 18.25
Miguel's purchase is ...
4p +2d = 27.50
__
b) We can subtract half the second equation from the first to get an equation for the cost of a drink.
(2p +3d) -1/2(4p +2d) = (18.25) -1/2(27.50)
2d = 4.50 . . . . . . simplify
d = 2.25 . . . . . . divide by 2
4p +2(2.25) = 27.50 . . . . substitute for d in the second equation
4p = 23.00 . . . . . . . . . subtract 4.50
p = 5.75 . . . . . . . . . divide by 4
The cost of a bag of popcorn is $5.75; the cost of a drink is $2.25.
Help please!!!!! I don't really get this, help asap.
Answers
42/6 = 7 boxes
Answer:
7 boxes
Step-by-step explanation:
We can use ratios to solve
12 bars 42 bars
---------- = ---------------
2 boxes x boxes
Using cross products
12x = 2 *42
12x = 84
Divide by 12
12x/12 = 84/12
x = 7
What is the scale factor of this dilation?
Answers
Answer:
1.333333333333
Step-by-step explanation:
Distribution of Sample Proportions
Susan really loves the lemon-flavored Fruity Tooty candies, but there always seems to be a lot of grape-flavored candies in each bag. To determine whether this is because grape candies are so popular or because each bag contains fewer lemon candies, Susan randomly picks a Fruity Tooty candy from her bag, records its flavor, and places it back in the bag. Each bag contains a mixture of cherry, grape, apple, lemon, and orange flavors. Which statement about Susan's distribution of sample proportions is true?
a) The distribution of the count of picking a cherry candy cannot be modeled as approximately normal if Susan picks candies over 200 times.
b) The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times.
c) The sample proportion of drawing an orange candy is not a binomial distribution.
d) The distribution of lemon candy can be modeled as normal if Susan picks candies 10 times.
Answers
Answer:
Option B, The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times
Step-by-step explanation:
The distribution of apple candies can be represented as normal curve and hence the sample proportion for this is true and can be drawn.
The rest other cases do not represent a normal distribution and hence it will not be easy to plot curve for these samples.
hence, option B is correct
What is the formula of a palindrome?
Answers
Answer:
For example, 6(1001) + 3(110) = 6006 + 330 = 6336 is a palindrome. Since 11 is a factor of both 1001 and 110, we conclude that all four digit palindromes are divisible by 11.
help please show work
Answers
1/2 • 4.7 x 8 = 18.8
8.) 40.96 square miles
6.4^2 = 40.96
9.) 7 square meters
1/2 • 4 • 3.5 = 7
10.) 36.4 square centimeters
(2.6 + 7.8) ÷ 2 x 7
11.) 22.8 square yards
6 • 3.8 = 22.8
12.) 30.6 square centimeters
5.1 • 6 = 30.6
Explanation:
FORMULAS FOR AREAS OF:
Triangle: 1/2 • base • height
Square: side^2
Parallelogram: base • height
Rectangle: Length • width
Trapezoid: (a + b) ÷ 2 x height
(a & b are the two bases)
hope this helps!
Find the equation (in terms of x ) of the line through the points (-2,5) and (3,4)
y=
Answers
Answer:
y = (-1/5)x + 23/5
Step-by-step explanation:
Given:
Two points;
(-2,5) and (3,4)
Find:
Equation of slope
Computation:
y = mx + b
5 = m(-2) + b
5 = -2m + b .......... Eq1
4 = m(3) + b
4 = 3m + b .......... Eq2
Eq2 - Eq1
-1 = 5m
m = -1/5
5 = -2m + b
5 = -2(-1/5) + b
5 = 2/5 + b
b = 23/5
y = mx + b
y = (-1/5)x + 23/5
What is it quadratic, radical, rational?
Answers
Answer:
quadratic formula is ur answer for letter B
Pls help I really need help beg you you
Answers
Answer:0,5
Step-by-step explanation:
what is the value of x?
Answers
Answer:
46
ayo how r u doin siahsvsgshsgsgsgsg
Which expression is equivalent to (6x2 + 4)(x + 5) ?
A 6x2 + 20
B 6x2 + 16x + 20
C 603 + 30x2 + 4x + 20
D) 6x3 + 11x2 + 3x + 20
Answers
Answer: [tex]6x^3 +30x^2 +4x+20[/tex]
Step-by-step explanation:
[tex](6x^2 +4)(x+5)\\\\ =6x^3 +30x^2 +4x+20[/tex]
(Y = 179x
(Y = 105x + 2046
Graph pls
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
A graphing calculator does a nice job of graphing these equations.
__
The very steep slope suggests the graph will need somewhat different vertical and horizontal scales in order to show anything useful.
