Final answer:
The wallet contains a total of $55, given that there are 8 $5 bills and 15 $1 bills.
Explanation:
The student's question involves determining the total amount of money in a wallet given a specific mix of $1 bills and $5 bills. According to the information provided, there are 23 bills in total, with 7 more $1 bills than $5 bills.
Let's denote the number of $5 bills as x. Therefore, there are x + 7 $1 bills. The total number of bills is the sum of the number of $1 bills and the number of $5 bills, which gives us the equation:
x + (x + 7) = 23
Solving the equation for x will give us the number of $5 bills:
2x + 7 = 23
2x = 23 - 7
2x = 16
x = 8
Now, since there are 8 $5 bills, and 7 more $1 bills than $5 bills, we have:
Number of $1 bills = 8 + 7 = 15
Thus, the total amount of money in the wallet is:
($5 × 8) + ($1 × 15) = $40 + $15 = $55
Therefore, the wallet contains $55.
Greatest common factor
N an algebra classroom, a teacher has created an estimation game using a jar of pennies. six students remain in the contest. each student makes one guess and their guesses are as follows: 62, 52, 59, 42, 49, 65. one guess is 12 away from the exact number of pennies in the jar while the other guesses are 1, 4, 6, 9, and 11 pennies away. determine exactly how many pennies are in the guessing jar.
how do u do that 2*2/2*2
If a and b are positive numbers, find the maximum value of f(x) = xa(7 â x)b on the interval 0 ⤠x ⤠7.
Final Answer:
The maximum value of f(x) = xa(7 - x)b on the interval 0 ≤ x ≤ 7 occurs when x = 7/2 for a > 0 and b > 0.
Explanation:
To find the maximum value of f(x) on the interval 0 ≤ x ≤ 7, we'll use calculus. First, take the derivative of f(x) with respect to x.
f'(x) = a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a
Setting f'(x) = 0 to find critical points:
a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a = 0
Solving for x gives x = 7/2. To determine if this point is a maximum, minimum, or inflection point, we'll use the second derivative test.
f''(x) = a * (7 - x)^(b-1) * x^(a-2) * ((a - 1) * x - 7) - b * a * (7 - x)^(b-2) * x^(a-1) * ((b - 1) * x - 7)
When x = 7/2, f''(7/2) > 0, indicating a concave-up shape and confirming it as a local minimum. Therefore, the maximum value of f(x) occurs at the endpoints of the interval, x = 0 and x = 7, or potentially at x = 7/2 if it surpasses these values.
For a > 0 and b > 0, plugging in x = 7/2 into f(x) = xa(7 - x)b yields the maximum value of the function within the given interval.
Understanding the critical points through derivatives helps identify where the maximum or minimum points occur in the function. In this case, x = 7/2 stands as the point of maximum value within the interval 0 ≤ x ≤ 7 when a and b are both positive.
Find the next two numbers in the sequence 1, 5, 17, 53, 161, _____, _____
The required missing term of the given sequence is given as 485 and 1457.
What is a sequence?The sequence is a pattern of placing the values in a specified manner.
here,
5 = 1 + 4
Since, [tex]b_0 = 4[/tex] and [tex]a_0 = 1[/tex]
17 = 5 + 12
So, the general term is given as
[tex]a_n = a_{n-1} + b_{n}[/tex]
Where, [tex]b_n = 3b_{n-1}[/tex]
For 6 th term
6 the term = 161 + 3(108)
6 the term = 485
For the 7th term
7th term = 485 + 3(324)
7th term = 1457
Thus, the required missing term of the given sequence is given as 485 and 1457.
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The larger of two supplementary angles measures 20° less than four times the measures of the smaller angle .find the degree measure of each angle
We want to create a system of equations that allows us to find the values of two supplementary angles.
We will find that the larger angle measures 140° and the smaller one measures 40°.
------------------------
Two angles A and B are supplementary if their measures add up to 180°, so we have:
A + B = 180°.
Let's assume that B is the larger one, we also do know that:
"The larger is 20° less than 4 times the smaller"
Then we can write:
B = 4*A - 20°.
Then our system of equations is:
A + B = 180°.
B = 4*A - 20°.
To solve it we need to isolate one variable in one of the equations and replace it on the other equation. Here we can see that B is already isolated on the second equation, so we can replace it in the first one to get:
A + B = 180°.
A + (4*A - 20°) = 180°
Now we can solve this for A:
A + (4*A - 20°) = 180°
5*A - 20° = 180°
5*A = 180° + 20° = 200°
A = 200°/5 = 40°
Now that we know the value of A we can get the value of B:
B = 4*A - 20° = 4*40° - 20° = 140°
Then the larger angle measures 140° and the smaller measures 40°
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you place a 3 3/8 pound weight on the left side of a balance scale and a 1 1/5 pound weight on the right side of a balance. How much weight do you need to add right side to balance the scale?
Answer:
[tex]2\frac{7}{40}[/tex] pounds
Step-by-step explanation:
Given information:
Weight on the left side = [tex]3\frac{3}{8}[/tex] pounds
Weight on the right side = [tex]1\frac{1}{5}[/tex] pounds
We need to balance both sides.
Let x be the weight which is added to the right side to balance the scale.
[tex]3\frac{3}{8}=1\frac{1}{5}+x[/tex]
[tex]\frac{24+3}{8}=\frac{5+1}{5}+x[/tex]
[tex]\frac{27}{8}=\frac{6}{5}+x[/tex]
Subtract 6/5 from both sides.
[tex]\frac{27}{8}-\frac{6}{5}=x[/tex]
[tex]\frac{135-48}{40}=x[/tex]
[tex]\frac{87}{40}=x[/tex]
[tex]2\frac{7}{40}=x[/tex]
Therefore, [tex]2\frac{7}{40}[/tex] pounds weight is added to the right side to balance the scale.
Help me Solve this and explain to me the steps thank you
POINTS POINTS POINTS POINTS POINTS! harder question!
45(34- 2)
Answer:
answer is 1440,ok
Step-by-step explanation:
A bag contains 44 red balls and 55 blue balls. 22 balls are selected at random. find the probability of selecting 22 red balls.
The probability of selecting 22 red balls is [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
A bag contains 44 red balls and 55 blue balls
The total number of balls=44+55=99
22 balls are selected at random from bag.
We need to find the probability of selecting 22 red balls.
The probability of selecting 22 red balls from 44 balls
[tex]^{44} C_{22}[/tex]
2,104,098,963,720
and [tex]^{99} C_{22}[/tex] is 5.7190121704386E+21
So probability of selecting 22 red balls is
[tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
Hence, the probability of selecting 22 red balls is [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
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Write an inequality that represents the verbal expression. All real numbers greater than or equal to 74
Solve.
2x + 6 - 7x = 21
Take a look at the figure. What is the value of y?
A. y = 32 B. y = 64 C. y = 14 D. y = 16
What is the definition to an equation?
You are to construct a€cylindrical can out of tin that encloses a volume of exactly 100 cubic inches. to three significant figures, which dimensions (r and h) will give you the tin can that requires the least amount of metal?
The formula for volume of cylinder is:
V = π r^2 h
since volume is 100 cubic inches, so:
100 = π r^2 h
Rewriting in terms of h:
h = 100 / π r^2
The least amount of metal means least amount of surface area needed. The surface area of cylinder is:
A = 2 π r h + 2 π r^2
insert the value of h in terms of r:
A = 2 π r (100 / π r^2) + 2 π r^2
A = 200 r-1 + 2 π r^2
Take the 1st derivate and set to 0, dA/dr = 0:
dA/dr = - 200 r-2 + 4 π r
0 = - 200 r-2 + 4 π r
200 / r^2 = 4 π r
r^3 = 50 / π
r = 2.52 inches
So height h is:
h = 100 / π r^2
h = 100 / π (2.52)^2
h = 5.01 inches
Answers:
r = 2.52 inches
h = 5.01 inches
1/2 divided by 5=1 over blank I need to know the blank number
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y= x/3−1 ?
Belinda keeps a record of her expenses for the week as shown: Bus fare $8.70 Lunch out $7.35 Hair cut $16 Movie rental $5.95 What is the total of Belinda’s expenses for the week? a. $22.16 b. $23.60 c. $37.90 d. $38.00 Please select the best answer from the choices provided A B C D
Final answer:
Belinda's total expenses for the week are the sum of her bus fare, lunch out, hair cut, and movie rental, which adds up to d. $38.00.
Explanation:
To calculate the total of Belinda's expenses for the week, we should add up each of the expenses mentioned. This includes the bus fare, lunch out, hair cut, and movie rental. Here's how we do it step-by-step:
Bus fare: $8.70Lunch out: $7.35Hair cut: $16.00Movie rental: $5.95Now, let's add them up:
$8.70 (Bus fare) + $7.35 (Lunch out) + $16.00 (Hair cut) + $5.95 (Movie rental)
When we sum these amounts, we get $8.70 + $7.35 + $16.00 + $5.95 = $38.00.
Therefore, the total of Belinda's expenses for the week is $38.00, which corresponds to option D.
Look at ΔABC. Which triangle is congruent to ΔABC by the ASA criterion? triangle 1 triangle 2 triangle 3 triangle 4
Answer:
Triangle 4
Step-by-step explanation:
Congruent triangles are identical in all aspects. They have identical sides and angles.
The ASA the Angle Side Angle criterion.
Congruent triangles should be able to "close up" on each other if one triangle is placed on top of the other. Let's look at the triangle in question.
The triangle ABC is made distinct by the lines on it.
The lines mark the different angles on the triangle.
By looking at the triangle and comparing, Triangle satisfies the ASA criterion
Sam deposited $350 into a savings account that paid 5% in simple interest. When he withdrew his money 8 months later, how much interest did he receive?
What is 435 000 in standardform?
Check my answers please -
The yearly attendance at a local move theatre is 42,000 and grows continuously at a rate of 5.9% each year. what is the approximate attendance at the movie theater in seven years?
A. 43,467
B. 59, 346
C. 63, 476
D. 62, 737 **
The number of customers that visit a local small business is 29,600 and has been continuously declining at a rate of 2.9% each year. what is the approximate number of customers that visit the buisness in 10 years?
A. 22,149 **
B. 21,874
C. 39,558
D. 22,054
I can tell you for sure that the answer to the first one is
C) 63,475
and the second is
A) 22,149
The attendance at the movie theater in seven years will be 63,476. Then option C is correct. And the number of customers that visit the business in 10 years will be 22,149. Then option A is correct.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The yearly participation at a neighborhood movie theater is 42,000 and develops ceaselessly at a pace of 5.9% every year. Then the attendance at the movie theater in seven years will be given as,
[tex]\rm y = 42,000 \times (e)^{0.059\times 7}\\\\y = 42,000 \times (e)^{0.413}[/tex]
Simplify the equation further, then we have
y = 42,000 × 1.5113
y = 63,476
The quantity of clients that visit a neighborhood private venture is 29,600 and has been persistently declining at a pace of 2.9% every year.
Then the number of customers that visit the business in 10 years will be given as,
[tex]\rm y = 29,600\times (e)^{-0.029\times 10}\\\\y = 29,600 \times (e)^{-0.29}\\[/tex]
Simplify the equation further, then we have
y = 29,600 × 0.748
y = 22,149
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How many ways can you split 12 people into 3 groups?
How do you convert 0.45 (45 being repeated) to a fraction?
A bag contains 3 yellow, 1 red, and 2 green beads. Charlene draws a bead, keeps it out, then draws another bead. What’s the probability that Charlene drew the red bead, then a green bead? Write your answer in simplified form.
How many sides does a polygon have if the sum of its interior angles is 2340?
Please help me!!
Solve for B:
C = sqrt(A^2 + B^2)
c^2 = a^2+b^2 now subtract a^2 from both sides
c^2 - a^2 = b^2 Now take the square root of both sides
b = +- sqrt(c^2-a^2)
Final answer:
To solve for B in the equation C = sqrt(A^2 + B^2), you square both sides of the equation, subtract A^2 from both sides, and then take the square root of the result to find B = sqrt(C^2 - A^2).
Explanation:
The equation C = sqrt(A^2 + B^2) is representative of the Pythagorean theorem, which is used in mathematics to relate the sides of a right triangle. To solve for B, we must isolate B on one side of the equation. Here's how you can do it:
Begin with the equation C = sqrt(A^2 + B^2).Square both sides of the equation to eliminate the square root, getting C^2 = A^2 + B^2.Subtract A^2 from both sides to get B^2 = C^2 - A^2.Finally, take the square root of both sides to solve for B, which gives B = sqrt(C^2 - A^2).This gives us the magnitude of B in terms of A and C.
Determine whether the given value is a statistic or a parameter. upper a sample of students is selected and it is found that 25 % own a computer.a sample of students is selected and it is found that 25% own a computer.
The drama club at smith valley middle school is selling cookie dough in order to raise money for costumes. if each tub cookie dough costs $4.75, how many tubs must members sell to make $570.00?
I need a little help please Brainliest
For the first image, the median range would be 88. In order to find the median, you'll place all your numbers in numerical order (smallest to largest). If there are an odd amount of numbers, find the one directly in the middle. If there is an even amount, you'll take the two most central ones and find the mean, that will tell you the median. Therefore, B (88) would be the answer to your first one.
The second one would be C (20.4). It's asking for the mean. In order to find the mean of a set of numbers, you'll simply add up all of the numbers and divide by how many numbers are in your number set. That gives you the mean.