Answer:
The son is 10, and the father is 50.
Step-by-step explanation:
10 times 5 would be 50, and 50+10 is 60.
Answer:
Father: 50
Son: 10
Step-by-step explanation:
Son's age: S
Father's age: F
F=5S
F+S=60.
Substitute.
5S+S=60
6S=60
S=10
F=50. As a check, 10+50=60 and 50/5=10.
Hope this was helpful.
~cloud
F is a function that describes a sequence and is therefore defined over the positive
integers. Find the first four terms of the sequence.
f(n) = 100(-0.1)n-1
f(0) = -1000, f(1) = 100, f (2) = -10, f(3) = 1
f(1) = -10, f (2) = 1, f (3) = -0.1, f (4) = 0.01
f(1) = 100, f (2) = 10 f(3) = 1, f (4) = 0.1
f(1) = 100, f (2) = -10, f(3) = 1, f (4) = -0.1
Answer:
Suppose we add up alternate Fibonacci numbers, Fn-1 + Fn+1; that is, what do ... L(1)=1 and L(3)= 4 so their sum is 5 whereas F(2)=1; L(2)=3 and L(4)= 7 so their ... What is the relationship between F(n-2), and F(n+2)? You should be able to find a ... Fib(N); K (an EVEN number!), Lucas(K) and Fib(K) in each expression like ...
Step-by-step explanation:
Serena and Visala had a combined total of $180. Serena then gave Visala $20, and then Visala gave
Serena a quarter of the money Visala had. After this, they each had the same amount. How much
money did Serena start with?
Serena started with approximately $173.33 money.
Let's denote the initial amount of money Serena had as S and the initial amount of money Visala had as V.
According to the problem, their combined total was $180, so we have the equation S + V = 180.
After Serena gave Visala $20, Serena's remaining amount became S - 20, and Visala's amount became V + 20.
Visala then gave Serena a quarter of the money she had, which is (V + 20)/4. After this transaction, Serena's total amount became S - 20 + (V + 20)/4, and Visala's total amount became V + 20 - (V + 20)/4.
It is given that after these transactions, they each had the same amount. Therefore, we can set up the equation:
S - 20 + (V + 20)/4 = V + 20 - (V + 20)/4.
Let's simplify and solve for S:
4S - 80 + V + 20 = 4V + 80 - V - 20.
Combining like terms:
4S + V = 3V + 160.
Substituting the value of S + V = 180 from the first equation:
4S + V = 3(180) + 160,
4S + V = 540 + 160,
4S + V = 700.
Now, we have two equations:
S + V = 180,
4S + V = 700.
Subtracting the first equation from the second equation:
4S + V - (S + V) = 700 - 180,
3S = 520,
S = 520/3 ≈ 173.33.
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Maria needs 0.7 meters of fabric to make a flag. How many flags can she make from 7.42 meters of fabric?
Answer:
10 flags
Step-by-step explanation:
7.42/0.7
Round down since you cant "round up" when talking about physical objects.
Answer:
10 Flags
Step-by-step explanation:
Fifty students in an Italian class were surveyed about how they listen to music. Of those asked:
34 listen to Spotify (S)
30 listen to Pandora (P)
18 listen to the radio (R)
22 listen to Spotify and Pandora
13 listen to Spotify and the radio
4 listen to Pandora and the radio
o 2 listen to Spotify, Pandora, and the radio
(a) Represent this information in a Venn diagram:
(b) How many liked none of these types of music?
(c) How many students liked exactly two of these types of music?
(d) How many liked at least two of these types of music?
In the Italian class survey, 50 students were asked about how they listen to music. A Venn diagram was used to represent the information. Five students liked none of the types of music, 37 students liked exactly two types of music, and 39 students liked at least two types of music.
(a) The information can be represented in a Venn diagram as follows:
In the diagram, S represents the number of students who listen to Spotify, P represents the number of students who listen to Pandora, and R represents the number of students who listen to the radio. The overlapping regions show the number of students who listen to multiple platforms.
___________
| |
| S |
|___________|
| |
R | SP | P
|___________|
| |
| RP |
|___________|
(b) To determine the number of students who liked none of these types of music, we need to find the students who did not fall into any of the three categories. This can be calculated by subtracting the total number of students who liked at least one type of music from the total number of students surveyed.
Total number of students surveyed = 50
Students who liked at least one type of music = S + P + R - (SP + SR + PR) + SPR
Substituting the given values:
Students who liked at least one type of music = 34 + 30 + 18 - (22 + 13 + 4) + 2 = 45
Students who liked none of these types of music = Total number of students surveyed - Students who liked at least one type of music
Students who liked none of these types of music = 50 - 45 = 5
Therefore, 5 students liked none of these types of music.
(c) To find the number of students who liked exactly two types of music, we need to calculate the sum of the students in the overlapping regions of the Venn diagram.
Students who liked exactly two types of music = SP + SR + PR - (SPR)
Substituting the given values:
Students who liked exactly two types of music = 22 + 13 + 4 - 2 = 37
Therefore, 37 students liked exactly two types of music.
(d) To determine the number of students who liked at least two types of music, we need to add the students who liked exactly two types of music to the number of students who liked all three types of music.
Students who liked at least two types of music = Students who liked exactly two types of music + Students who liked all three types of music
Students who liked at least two types of music = 37 + 2 = 39
Therefore, 39 students liked at least two types of music.
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Explain how g is 62 degrees using angle theorem. Ex supplementary angle theorem, ASTT. Etc
Answer:
The exterior angle is 35° + 62° = 97°
And 97° > 35°
And 97° > 62°
Step-by-step explanation:
Answer:
pppop-
That’s what u get
Step-by-step explanation:
HELPPP!!
Find the value of x in the parallelogram!
Answer:
x = 17
Step-by-step explanation:
Area of a parallelogram:
A = bh
Given:
A = 153
b = 9
Work:
A = bh
h = A/b
h = 153/9
h = 17
Evaluate the expression 6 + 5 × 32 - 8.
43
11
6
91
Answer:
158
Step-by-step explanation:
All i know is that these answer choices cannot be found in the calculator
Answer:
158.....
PEMDAS
you multiply first 6+160-8
then you add or subtract
158
The point P is on the unit circle. Find P(x, y) from the given information.
The x-coordinate of P is positive, and the y-coordinate of P is
-(square root 10)/10.
The coordinates satisfy the equation x^2 + y^2 = 1. In this specific problem, we found that P(x, y) = (3 * sqrt(10)) / 10 , - (sqrt(10)) / 10.
To solve this problem, we need to recall some basic trigonometry concepts related to the unit circle. The unit circle is a circle of radius 1 centered at the origin of a coordinate plane. Any point on the unit circle can be represented by its coordinates (x, y), where x and y are the horizontal and vertical distances from the origin, respectively.
Since the given problem tells us that the x-coordinate of P is positive, we know that x > 0. Additionally, we are given that the y-coordinate of P is -(square root 10)/10. We can use this information to solve for x.
From the Pythagorean theorem, we know that for any point (x, y) on the unit circle, x^2 + y^2 = 1. Substituting y = -(square root 10)/10, we get:
x^2 + ((-sqrt(10))/10)^2 = 1
Simplifying this expression, we get:
x^2 + 10/100 = 1
x^2 = 90/100
x = sqrt(90)/10
Since we know that x is positive, we can simplify this expression further by factoring out a square root:
x = (sqrt(9) * sqrt(10)) / 10
x = (3 * sqrt(10)) / 10
Therefore, the coordinates of point P are:
P(x, y) = (3 * sqrt(10)) / 10 , - (sqrt(10)) / 10
We can check our answer by verifying that these coordinates satisfy the equation x^2 + y^2 = 1:
(3 * sqrt(10) / 10)^2 + (-sqrt(10) / 10)^2 = 9/100 + 10/100 = 1/10
Simplifying this expression, we get:
1/10 = 1/10
This confirms that our answer is correct and that P lies on the unit circle.
In summary, to find the coordinates of a point P on the unit circle given its y-coordinate and the fact that its x-coordinate is positive, we can use the Pythagorean theorem to solve for the x-coordinate. We then check our answer by verifying that the coordinates satisfy the equation x^2 + y^2 = 1. In this specific problem, we found that P(x, y) = (3 * sqrt(10)) / 10 , - (sqrt(10)) / 10.
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On the highway, the gas mileage of Jesse’s motorcy- cle is twice that of his car. If his car gets 28 mpg on the highway, what is the gas mileage of his motor- cycle on the highway?
Based on the ratios of gas mileage of Jesse's motorcycle to that of his car, 2x and x respectively, we have found out that the gas mileage of Jesse’s motorcycle on the highway is 56 mpg.
To solve the problem of finding out the gas mileage of Jesse’s motorcycle on the highway, it is necessary to use ratios. The first ratio is based on the gas mileage of Jesse’s car on the highway which is 28 mpg, then the ratio for his motorcycle is set as 2x, where x is the mileage per gallon of Jesse’s car, 28.
Therefore, the second ratio is 2x. Then we can equate these ratios in order to solve the problem. This can be done as follows: 2x/28 = y/1, where y represents the gas mileage of Jesse’s motorcycle on the highway.
Solving for y yields the following:
2x/28 = y/1
2x * 1 = 28 * y
2x = 28y
2x/2 = 28y/2
x = 14y
So the gas mileage of Jesse’s motorcycle on the highway is 14 times the mileage of his car. Therefore, to find out the gas mileage of his motorcycle on the highway, we need to multiply 28 by 2 and then divide the result by 1 which is equal to 56. Therefore, the gas mileage of Jesse’s motorcycle on the highway is 56 mpg.
In conclusion, based on the ratios of gas mileage of Jesse's motorcycle to that of his car, 2x and x respectively, we have found out that the gas mileage of Jesse’s motorcycle on the highway is 56 mpg. This has been calculated using the equation 2x/28 = y/1, where y is the gas mileage of Jesse’s motorcycle on the highway.
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Find the area of the shaded region.
Answer:
area = 3.44 in²
Step-by-step explanation:
area of square = 4 x 4 = 16 cm²
area of circle = (3.14)(2²) = 12.56 cm²
area = 16 - 12.56 = 3.44 in²
A set of data may have more than one mode.
(1 Point)
True
False
he manager of a book store believes that 33% of the store's customers have read at least one book from the Henry Pottar series. A simple random sample of 100 customers was selected. Using the manager's belief, determine:
1. The standard error for the sampling distribution of proportion. (4 decimal places)
2. The probability that between 26% and 35% of the customers have read at least one book from the Henry Pottar series . (4 decimal places)
1. The standard error for the sampling distribution of proportion is approximately 0.0478.
The standard error for the sampling distribution of proportion can be calculated using the formula:
SE = sqrt((p * (1 - p)) / n)
where p is the population proportion and n is the sample size. In this case, p = 0.33 and n = 100.
Plugging in the values, we have:
SE = sqrt((0.33 * (1 - 0.33)) / 100) ≈ 0.0478
Therefore, the standard error for the sampling distribution of proportion is approximately 0.0478.
2. The probability that between 26% and 35% of the customers have read at least one book from the Henry Potter series is approximately 0.7789.
To calculate the probability, we need to find the z-scores corresponding to the percentages 26% and 35% and then find the area between these two z-scores under the standard normal distribution curve.
First, we calculate the z-scores using the formula:
z = (x - p) / sqrt((p * (1 - p)) / n)
where x is the given percentage, p is the population proportion, and n is the sample size.
For x = 26%:
z = (0.26 - 0.33) / sqrt((0.33 * (1 - 0.33)) / 100) ≈ -1.232
For x = 35%:
z = (0.35 - 0.33) / sqrt((0.33 * (1 - 0.33)) / 100) ≈ 0.522
Using a standard normal distribution table or calculator, we can find the area between -1.232 and 0.522, which is the probability that between 26% and 35% of the customers have read at least one book from the Henry Potter series. The approximate probability is 0.7789.
Therefore, the probability that between 26% and 35% of the customers have read at least one book from the Henry Potter series is approximately 0.7789.
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draw a hypothetical demand curve for tickets to a particular rock concert. use the drop box to upload an image or file containing your demand curve.
The hypothetical demand curve for tickets to a particular rock concert is given in the image attached.
What is the hypothetical demand curve
According to Samuelson: theory, the law of demand states that people buy more at lower prices and less at higher prices when other things remain constant.
Note that by using the image,
Prices of ticket (cent) Demand by consumer
5 35
4 30
3 70
2 80
1 95
Therefore, "Demands curves show how much people will buy the ticket at different prices over time." The Curve shows consumer purchases at different prices.
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If x≠-4, which answer choice represents the following in simplified form (question attached)
A. X+3
B. X-4
C. 2x+6
D. X-3
Answer:
[tex]A) x+3[/tex]
Step-by-step explanation:
[tex]\frac{2x^{2}+14x+24 }{2x+8}[/tex]
[tex]=\frac{2(x^{2}+7x+12)}{2(x+4)}[/tex]
[tex]=\frac{x^{2} +7x+12}{x+4}[/tex]
[tex]=\frac{(x+4)(x+3)}{x+4}[/tex]
[tex]=x+3[/tex]
The copy machine runs for 20 seconds and then jams. About how many copies were made before the jam occurred? Round your answer to the nearest tenth
Answer:
10.7
Step-by-step explanation:
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!
Answer:
3 times greater
Step-by-step explanation:
6.7 x 10 to the 6 = 6700000
2x 10 to the 7 = 20000000
20000000/6700000 = 2.98507462687
Rounded - 3
Write the Mayan numeral as a Hindu Arabic numeral 10:03
The Hindu Arabic numeral for the Mayan numeral is 103.
The given Mayan numeral needs to be converted to Hindu Arabic numeral.
The Hindu Arabic numeral system includes ten digits from 0 to 9. This numeral system is used to represent numbers in almost all the countries in the world.
10:03 in Mayan Numeral System is as shown below:MAYAN_NUMERALS: 10:03 = 10.|. 0. | 3. ||||||. |||..........||||||... ||.......... |||||||||||||||||||||||||||||||10.|.0.|.3.|. = 103The above given Mayan Numeral system converted to Hindu Arabic Numeral is 103.
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A solid wooden cone of a diameter 14 cm and vertical length 24 cm is vertically cut into two equal halves. One half is to be covered by colourful paper at the rate of Rs. 7 per sq. cm, find the total cost of the paper required.
(The answer must come Rs. 5950)
plz anyone ASAP help.
Answer:
The answer given is incorrect
The correct answer is Rs. 3640
The total cost of the paper required to cover one-half of the wooden cone is Rs. 3846.5.
What is the surface area of a cone?The surface area of a cone is given by the formula:
surface area = π x r x s
where r is the radius of the base of the cone and s is the slant height of the cone. The slant height of the cone is the distance from the apex of the cone to the base, measured along the surface of the cone.
In this case, the diameter of the base of the cone is 14 cm, so the radius is half the diameter or 14 cm / 2 = 7 cm.
The vertical length of the cone is 24 cm, so the slant height of the cone is the square root of the vertical length squared plus the radius squared:
s = √(24² + 7²)
s = √(576 + 49)
s = √(625)
Which simplifies to:
s = 25 cm
Now that we have the radius and slant height of the cone, we can use the formula for the surface area of a cone to find the surface area of one-half of the cone:
surface area = π x 7 cm x 25 cm = 175π cm²
To find the total cost of the paper required, we need to multiply the surface area by the cost per square centimeter:
total cost = 175 x 3.14 cm² x Rs.7/cm² = Rs. 3846.5
Therefore, the cost of the paper needed to cover one-half of the wooden cone is Rs. 3846.5.
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please whats the answer?
Answer:
=93
Step-by-step explanation:
[tex]7 \frac{5}{6} + 5 \frac{1}{9} [/tex]Then mutiply 6 x7 with will give you 42 then add 5 which will equal =47SALE
80% OFF!
What is the sale price of a basketball jersey originally priced at $40?
Answer:
20
Step-by-step explanation:
Solve the system by substitution.
x – 4y = -8
5у – 1 = x
Submit Answer
Answer:
y = -7 and x = -36
Step-by-step explanation:
x - 4y = -8
5y - 1 = x
→ Substitute 5y - 1 into x - 4y = -8
5y - 1 - 4y = -8
→ Simplify
y - 1 = -8
→ Add 1 to both sides
y = -7
→ Substitute y = -7 into 5y - 1
( 5 × -7 ) - 1 = -36
Answer:
The solution is (-36, -7)
Step-by-step explanation:
Since 5y - 1 = x, we can replace x in the first equation by 5y - 1:
5y - 1 - 4y = -8
Collecting like terms, we get:
y = -7
If y = 7, then by the second equation x = 5(-7) - 1 = -36
The solution is (-36, -7)
what is a profit margin
Can somebody help me
Answer:
25
Step-by-step explanation:
If it has 25 miles across from the 1 hour it means that it goes 25 miles per hour.
find the corresponding point to the function
Answer:
If you begin with the graph for f(x) and then substituted x+3 for x, the effect on the graph will be to move the whole graph 3 units to the left.
Given that (-9,-1) is on the graph of f(x), and that we are to move the entire graph 3 units to the left, then the coordinate -9 becomes -9-3, or -12: (-12,-1).
Step-by-step explanation:
Change die exponential statement to an equivalent statement involving a logarithm. 9 = 3^2 The equivalent logarithmic statement is. (Type an equation.)
The equivalent logarithmic statement is log base 3 of 9 = 2 for the equation 9 = 3².
To convert the exponential statement 9 = 3² into an equivalent logarithmic statement, we can use the logarithm with base 3.
Step 1: Identify the base and exponent in the exponential statement.
In our case, the base is 3 and the exponent is 2.
Step 2: Write the equivalent logarithmic statement.
Using the base 3 logarithm, we have:
log₃(9) = 2
This logarithmic statement can be read as "the logarithm base 3 of 9 is equal to 2."
The logarithm function gives us the exponent or power that the base needs to be raised to in order to obtain the given number. In this case, log₃(9) tells us that 3 raised to the power of 2 equals 9.
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Victoria earns a gross annual income of $124,482 and is buying a home for $225,500. She is making a 20% down payment and financing the rest with a 30-year loan at 4.5% interest.
(a) What is the mortgage amount she will borrow?
(b) Can she afford this mortgage?
(c) What will her monthly mortgage payment be?
(d) What will her total payment for the house be?
(e) What is the amount of interest she will pay?
Answer:
(a) The mortgage amount she will borrow is $180,400
(b) Yes she can
(c) Her monthly payment will be approximately $914.06
(d) Her total repayment is approximately $329,061.6
(e) The amount of interest is approximately $148,661.6
Step-by-step explanation:
The details of the transactions are;
The gross annual income Victoria earns = $124,482
The cost price of the home she is buying, C = $225,500
The amount she is making as down payment = 20%
The duration the loan she id financing the rest with, t = 30-years
The interest rate on the loan, r = 4.5%
(a) The mortgage amount she will borrow, 'P', is the cost of the home less the down payment
The down payment = 20% of the cost of the home
∴ The down payment = (20/100) × $225,500 = $45,100
∴ P = $225,500 - $45,100 = $180,400
The mortgage amount she will borrow, P = $180,400
(b) Using the 2× to 2.5× gross income rule, we have;
2 × her annual income = 2 × 124,482 = 248,964
∴ 2 × her annual income > The mortgage = 180,400
She can afford the mortgage
(c) The monthly fixed payment for the mortgage is given as follows;
[tex]M = P \times \dfrac{r}{n} \times \dfrac{\left(1+ \dfrac{r}{n} \right)^{n \cdot t}}{\left[\left(1 + \dfrac{r}{n} \right)^{n\cdot t} - 1\right]}[/tex]
Where;
n = The number of periods per year = 12 monthly periods per year
180,400*0.045*(1 + 0.045)^(30)/((1 + 0.045)^(30) - 1)
[tex]M = 180,400 \times \dfrac{0.045 }{12} \times \dfrac{\left(1+\dfrac{0.045 }{12}\right)^{30 \times 12}}{\left[\left(1 + \dfrac{0.045 }{12}\right)^{30 \times 12} - 1\right]} \approx 914.060298926[/tex]
Her monthly payment will be M ≈ $914.06
(d) The total repayment is given as follows;
n × t × M
∴ 12 × 30 × 914.06 = 329061.6
The total payment for the house = $329,061.6
(e) The amount of interest = The total payment - The principal loan amount
∴ The amount of interest = $329061.6 - $180,400 = $148,661.6
HELP ME ASAP!!!!!!!!!!!!
See picture attached.
Please friend request me if you get it right.
Thanks xx
Answer:
Number of cubes = 8 large and 32 small, or 40 total
Step-by-step explanation:
each layer = 2 large and 8 small cuboids.
each layer = 128 cm³
512/128 = 4 layers
so:
4 x 2 = 8 large cuboids
4 x 8 = 32 small cuboids
What is the other measure of the other acute angle? Pls explain how you got your answer !
Answer:
[tex]65^{o}[/tex]
Step-by-step explanation:
Angles in a triangle add up to 180
An acute angle is any angle smaller than 90
Since it is a right angle triangle, one of the angles is a right angle and therefore 90
So 180 - 90 - 25 = 65
i need help with this questionnnn
1. Consider a damped spring-mass system with m = 1kg, = 2
kg/s^2 and c = 3 kg/s. Find the general solution. And solve the
initial value problem if y(0) = 1 and y′(0) = 0.
The general solution of the damped spring-mass system with the given parameters is y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)]. By applying the initial conditions y(0) = 1 and y'(0) = 0, the specific solution can be obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t).
The equation for the damped spring-mass system can be expressed as my'' + cy' + ky = 0, where m is the mass, c is the damping coefficient, and k is the spring constant. In this case, m = 1 kg, c = 3 kg/s, and k = 2 kg/[tex]s^2[/tex].
To find the general solution, we assume a solution of the form y(t) = e^(rt). By substituting this into the equation and solving for r, we get [tex]r^2[/tex] + 3r + 2 = 0. Solving this quadratic equation gives us the roots r1 = -2 and r2 = -1.
The general solution is then given by y(t) = c1e^(-2t) + c2e^(-t). However, since we have a damped system, the general solution can be rewritten as y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)], where √7/2 = √(3/4).
By applying the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the coefficients c1 and c2. The specific solution is obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t). This satisfies the given initial value problem.
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