Portus has four 1-cent stamps, three 5-cent stamps, and three 25-cent stamps. 79 different postage amount of at least one cent can postbus make.
We can get the sums of 1 cent, 2 cents, 3 cents and 4 cents by combining one 1-cent coin, two 1-cent coins, three 1-cent coins and four 1-cent coins, respectively. i.e., 4 different sums.
We can get three sums of 5 cents, 10 cents, and 15 cents by combining mean five-cent coins., i.e. 3 different sums.
we can get three sums of 25 cents, 50 cents, and 75 cents by combining means twenty-five-cent coins. i.e,3 different sums.
Now,
4*3 = 12 different sums by combining 4 one-cent coins with 3 five-cent coins.
Again,
4*3 = 12 different sums by combining 4 one-cent coins with 3 twenty-five-cent coins. 3*3 = 9 different sums by combining 3 five-cent coins with 3 twenty-five-cent coins.4*3*3 = 36 different sums by combining 3 five-cent coins with 3 five-cent coins and 3 twenty-five-cent coins.Now,
add all these combinations:
4 + 3 + 3 + 12 + 12 + 9 + 36 = 79.
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A botanist is studying the growth of the sequoia tree. He selects one sequoia tree and records it’s hight each year. What is the equation of the line in slope-intercept form? Define your variables. Show your work
Answer: h= 4/5yr+ 5
Step-by-step explanation: by looking at the graph the slope is 4/5 and it intercepts the graph at 5 so y=4/5x + 5, then I plugged in the variables on the graph to get yr for year and h for height
The results of a confidence interval and significance test should agree as long as:
the significance test is two-sided
both are conducted on the same data set
we are making inferences about means
we are making inferences about proportions
The right answer involves doing both studies with the identical data set, drawing conclusions regarding means, and using a two-sided significance test.
What exactly are ratios?An algorithm which it sets two ratios to the same value is called a fraction. You might, for instance, write its ratio as follows: 1: 3 in the case of 1 male & Three girls (for every one boy there are 3 girls) There are 3 out of 4 females and 1 out of 4 guys. 0,25 are men (by dividing 1 by 4)
What's an illustration of proportion?A ratio that connects a part to yet another is a percentage. For instance, there are 100 students in the class containing 20 men or 80 women. The percentage of males is 20/100, or 20%. 80 out of 100, or 80%, are women.
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our water polo team has 15 members. i want to choose a starting team consisting of 7 players, one of whom will be the goalie (the other six positions are interchangeable, so the order in which they are chosen doesn't matter). in how many ways can i choose my starting team?
you can choose my starting team in equation of 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7 x 5 x 4 x 3 x 2 = 2520 ways.
7 x 6 (choose 7 players from 15) x 5 x 4 x 3 x 2 x 1 (7 players in any order) = 7 x 5 x 4 x 3 x 2 (7 players in any order, ignoring the goalie)
= 2520 ways.
In order to figure out how many ways I can choose my starting team, I can use a combination equation. Start by taking the number of players (15) and subtracting the number of players I need for the starting team (7). This gives me 8 players who will not be chosen. Now, I can calculate the number of ways I can choose the 7 players from the 15 available players. This is equal to 15 x 14 x 13 x 12 x 11 x 10 x 9. This is the same as 7 x 6. Now, I need to account for the order in which I choose the players. Since the 6 players other than the goalie can be interchangeable, I can use the equation 7 x 6 x 5 x 4 x 3 x 2 x 1. This gives me 2520 ways to choose my starting team. To simplify this, I can factor out the 7 and the 1, leaving me with 7 x 5 x 4 x 3 x 2, which is still equal to 2520. Therefore, I can choose my starting team in 2520 ways.
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a roast removed from an oven has an internal temperature of 160f and it is left to sit at room temperature, which is 72f. after 8 minutes the internal temperature of the roast has dropped to 155f. the roast is ready to eat when its temperature has dropped 150f. how long does the roast need to sit before it is ready to be eaten?
The roast needs to sit 116 minutes before it is ready to be eaten.
Let T(t) = temperature after t minutes
By Newton's Law of Cooling, T(t) = 75 + (185-75)e^kt = 75 + 110e^kt
Newton's law of cooling states that the rate of change of temperature of an object is directly proportional to the difference in temperature between the object and its surroundings. Mathematically, it can be expressed as:
dT/dt = k(T - T0)
Where:
dT/dt is the rate of change of temperature (in degrees per time unit, such as degrees per second)
k is the cooling constant (in units of 1/time), which is a measure of how quickly an object cools down and depends on the properties of the object and its surroundings
T is the current temperature of the object (in degrees)
(a). T(30) = 75 + 110e^30k = 150
⇒110e^30k = 75
⇒e^30k = 0.681818
⇒30k = ln(0.681818)
⇒k = -0.0127664
We know, T(t) = 75 + 110e^-0.0127664t
So, T(45) = 75 + 110e^-0.0127664(45) ≈ 137°
(b). T(t) = 100 when 75 + 110e^-0.0127664t = 100
⇒ e^-0.0127664t = 0.2272727
⇒-0.0127664t = ln(0.2272727)
⇒t ≈ 116 minutes
Therefore, The roast needs to sit 116 minutes before it is ready to be eaten.
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37) Kelly opened a bank account that earns 1.2% simple interest each year. After 7 years, Kelly will earn $126 in
interest. How much did Kelly deposit when she opened the account? _
Answer:
13.4 dollars
Step-by-step explanation:
13.4 dollars is how much kelly deposit
please answer my revision q xx
Answer:
k - 2n = x
Step-by-step explanation:
4^n = 2 ^ 2n
2^k/2^2n = 2^(k-2n) = 2^x
k - 2n = x
Thanks
Answer:
x = k - 2n
Step-by-step explanation:
The main exponent properties
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex] ........ (1)
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] ........ (2)
[tex](a^{m} )^{n}[/tex] = [tex]a^{m*n}[/tex] = [tex]a^{mn}[/tex] ........ (3)
~~~~~~~~~~~~~~~~~~
[tex]\frac{2^{k} }{4^{n} }[/tex] = [tex]2^{x}[/tex]
Let apply (3) and (2) exponent properties
L.H. = [tex]\frac{2^{k} }{(2^2 )^{n} }[/tex] = [tex]\frac{2^{k} }{2^{2n} }[/tex] = [tex]2^{k-2n}[/tex]
[tex]2^{k-2n}[/tex] = [tex]2^{x}[/tex] ⇒ x = k - 2n
A 9-kilogram bag of rice costs $12.96. What is the unit price?
Answer:
$1.44
Step-by-step explanation:
9kg costs $12.96
1kg costs ($12.96*1kg)÷9kg
=$1.44
-2(3n+6) = 3(-n+12)
Solve for n
Please explain each step
Answer: n = -16
Step-by-step explanation:
1) Distribute
—2(3n +6) = 3(-n + 12)
—6n - 12 =3(-n + 12)
2) Distribute
—6n - 12 = 3(-n + 12)
—6n — 12 = —3n +36
3) Add 12 to both sides
—6n — 12 = -3n +36
-6n = 12+ 12 = - 3n + 36 + 12
4) Simplify
----Add the numbers
—6n = -3n +48
5) Add 3n to both sides
—6n = -3n +48
—6n + 3n = —3n + 48 + 3n
6) Simplify
- Combine like terms
—3n = 48
7) Divide both sides by the same factor
—3n = 48
-3n ÷ -3 = 48 ÷ -3
8) Simplify
- Cancel terms that are in both the numerator and denominator
- Divide the numbers
n = —16
Please give brainliest
Which function includes the data set {(2,4), (6,6) (12,9)}?
The function that includes the data-set {(2,4), (6,6) (12,9)} is given as follows:
D. y = x/2 + 3.
How to obtain the points of the data-set?The points of the data-set follow the format given as follows:
(x,y).
Hence the meaning of each point is given as follows:
(2,4): when x = 2, y = 4.(6,6): when x = 6, y = 6.(12,9): when x = 12, y = 9.Then the correct option is given by option D, that is:
y = x/2 + 3.
As we obtain the numeric values of y for the input x as follows:
x = 2: y = 2/2 + 3 = 1 + 3 = 4.x = 6: y = 6/2 + 3 = 3 + 3 = 6.x = 12: y = 12/2 + 3 = 6 + 3 = 9.Which are the three points that compose the data-set.
Missing InformationThe options are given by the image presented at the end of the answer.
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olve the differential equation by variation of parameters. Y" + y = sin?(x) y(x) =
The provided statement indicates that the differential equation's solution will be y = c₁ + c₂ e⁻ˣ - 1/2 cos x
With examples, define differential equation:Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variable x and y are related because y is an unidentified function of x. The component of y is also on the equation's left-hand side.
The analytical solution is, given that.
⇒ y'' + y = sin x
Now,
The system of equations as follows:
The difference between these two is,
⇒ y'' + y = sin x
Find its auxiliary equation as;
⇒ m² + m = 0
⇒ m (m + 1) = 0
⇒ m = 0 or m = - 1
Therefore, the auxiliary equation is c1 e0 + c2 ex.
= c₁ + c₂ e⁻ˣ
And, Particular integral = 1/(D² + D) (sin x)
= 1/2D (sin x)
= 1/2 (- cos x)
= - 1/2 cos x
Consequently, the differential equation's solution will be;
⇒ y = A.E + P.I
⇒ y = c1 + c2 e x - cos x / 2
As a result, the differential equation's solution is;
⇒ y = c1 + c2 e x - cos x / 2
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The complete question is-
Solve the differential equation by variation of parameters.
y'' + y = sin x
if a regression model is estimated using observations on each of these variables, what are the degrees of freedom (df) for the regression sum of squares, error sum of squares, and total sum of squares?
The degrees of freedom for the regression sum of squares in a regression model is determined by the number of variables that are being used to make predictions. For example, if you have three independent variables in your model, the degrees of freedom for the regression sum of squares would be 3.
The degrees of freedom for the error sum of squares is the total number of observations in your dataset, minus the number of independent variables used in the model.
The total sum of squares is the sum of the squared differences between each observation and the overall mean of the variable being predicted. This has the same number of degree of freedom as the error sum of squares, which is total number of observations -1.
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sarah can bicycle a loop around the north part of lake washington in 2 hours and 40 minutes. if she could increase her average speed by 1 km/hr, it would reduce her time around the loop by 6 minutes. how many kilometers long is the loop? (round your answer to two decimal places.)
The loop is 4112.16 kilometers long.
To solve this problem, we can set up the following equation:
distance = speed x time
We know that Sarah's current speed is s km/hr, and that the loop is d kilometers long. We also know that her current time is 2 hours and 40 minutes, or 160 minutes.
From the information given, we know that if Sarah increases her speed by 1 km/hr, her time around the loop would be reduced by 6 minutes. Therefore, we can set up the following equation:
d = (s + 1)(160 - 6) = (s + 1)154
We also know that Sarah's current speed is s km/hr, and that the loop is d kilometers long and the time she takes is 160 minutes. Therefore, we can set up the following equation:
d = s * 160
We can now solve for s by substituting the first equation into the second equation:
d = s * 160
d = (s+1)154
s160 = (s+1)*154
We can now solve for s
s = 154/6 = 25.66 km/hr
Now we can plug in s into the first equation we have:
d = s * 160
d = 25.66 * 160
d = 4112.16 km
The loop is 4112.16 kilometers long.
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This pentagonal right pyramid has a base area of 30 m. 5 m 7 m 8 m What is the volume of the figure?
The volume of the pentagonal right pyramid with base area 30 square metres and height 5 metre is 50 m³.
Therefore the answer is 50 m³.
To find the volume of a pentagonal pyramid, we can use the formula:
V = (Bh)/3
where V is the volume, B is the area of the base and h is the height.
Area of the base is given, B = 30 m². From figure it is evident that the height of the pentagonal right pyramid is 5m. Therefore the volume of the figure is
V = 30 × 5/ 3
V = 50 m³
--The question is incomplete, answering to the question below--
"This pentagonal right pyramid has a base area of 30 m². What is the volume of the figure?"
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the radius of a wheel rolling on the ground is 80 centimeters. if the wheel rotates through an angle of 60, how many centimeters does it move? express your answer in terms of pand then round to two decimal places.
The radius of a wheel rolling on the ground is 80 centimeters. if the wheel rotates through an angle of 60. Therefore, It move to 84 cm.
Circumference Of Circle:
The total length of the circle boundary. The circumference of a circle is the product of the constant π and the diameter of the circle. A person walking across a circular park or a circular table needs this measure of circumference. The circumference is a length value and its units are the same as the length units. A circle is a round closed figure with all endpoints equidistant from a fixed point called the center.
The formula for the circumference of a circle is expressed using the values of the circle's radius 'r' and 'pi'. It is represented by the equation of circumference = 2πr. Using this perimeter formula, if you don't have a value for the radius, you can use the diameter to find it. To calculate the circumference is to use the formula circumference = π × diameter.
If you need to calculate the radius or diameter, consider the circumference of a circle and use the following formula:
Radius = circumference/2π
Now,
According to the Question:
If the radius is 80cm
and, the circumference is 2×π×80cm.
If the wheel rotates by 60° then a fraction 60/360 (= 1/6) of the circumference moves over the ground.
Therefore, the distance moved is
[tex]\frac{2*\pi*80 }{6}[/tex]
= 83.77580
≈ 84 cm.
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work out the area of this shape
Answer:
80
Step-by-step explanation:
96-16
M109) solve
cos²x + 2 cosx + 1 = 0
Answer:
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \: \: \huge \color{green}{ \fbox \colorbox{black}{ \fbox{ \green {Answer} \: }}}[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + 2 \cos(x) + 1} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + \cos(x) + \cos(x) + 1} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{} (x) ( \cos(x) + 1)+ 1(\cos(x) + 1} )= 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( \cos(x) + 1)(\cos(x) + 1} )= 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{2} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos(x) {}^{} }= - 1[/tex]
[tex]\longrightarrow \sf \color{teal}{ x{}^{} }= \cos {}^{ - 1}( - 1)[/tex]
[tex]\longrightarrow \sf \color{teal}{ x = (2n + 1) \pi \: \: \: \: rad}[/tex]
where, [tex]{ n \in \{whole \:\; number\}} [/tex]
Principle value -
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \cos {}^{ - 1} ( - 1) [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2n + 1) \pi \: \: \: \: rad \: [/tex]
put n = 0
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2(0) + 1) \pi \: \: \: \: rad \: [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (0 + 1) \pi \: \: \: \: rad \: [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \pi \: \: \: \: rad \: = 180 \degree[/tex]
1) Pastor and Mrs. Gentle visited ten more church members this week than the number they visited last week divided by four. If they visited sixteen members this week, how many did they visit last week?
Answer:
24
Step-by-step explanation:
Let the number of members they visit last week be x.
Then, they visit x/4 + 10 this week
x/4 + 10 = 16
x = 4 x 6
x = 24
Pls mark as brainliest if possible. Don't know why i need it, but i do. Cheers
What is a 1-factor graph theory?
A 1-factor graph is a graph that can be decomposed into one or more 1-factors. In other words, a 1-factor graph is a graph that can be partitioned into disjoint perfect matchings.
In graph theory, a 1-factor is a subgraph of a graph that forms a perfect matching, or 1-factorization. A perfect matching is a set of edges in a graph such that each vertex is incident to exactly one edge in the set. A 1-factorization of a graph is a collection of perfect matchings such that every vertex is included in exactly one perfect matching.
The study of 1-factors and 1-factorizations is an important area of graph theory because of its connections to other areas of mathematics such as algebra, combinatorics, and statistical physics. It has various applications including coding theory, scheduling, and transportation networks.
1-factor graph theory is the study of graphs that can be decomposed into 1-factors and the properties of such graphs. This field of study helps to understand the conditions under which a graph can be decomposed into 1-factors and the properties of such graphs.
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CLASS 10 CBSE
PLS ANSWER ASAP
from a solid cylinder whose height is 15 cm and the diameter is 16 cm a conical cavity of the same height and same diameter is hollowed ou
t find the total surface area of remaining solid
The total surface area of the remaining solid is 443.14cm2
What drives your use of surface area?A three-dimensional object's surface area is the sum of all of its faces. Real- world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.
Here,
Given:
h = 15, r = 8cm
Slant height of cone
1 = r2+h2 = (8)2 + (15)2 = 17
Total Surface Area = Curved Surface area of Cylinder + Curved Surface area of Conical Part + Area of Circular
=2arh+arl+πr2
=2(3.14)(8) (1.5) + (3.14) (8) (17) + (3.14)(17)2 =443.14cm2
Therefore , the solution of the given problem of surface area comes out to be 443.14cm2.
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What is an equation of the line that passes through the point (1, 7) and is parallel to the line 32 -y= 1?
The general form of a linear Equation in two variables is ax + by + c = 0.
32-y=1
0.x+y+32 = 0
Hence Proved.
we have 4 women and 5 men and want to create a committee with 2 women and 2 men. in how many ways we can do this?
126 number of ways we can arrange the men, women in order to committee with 2 women and 2 men ,the combination is explained below as
We can use the combination formula to find out the number of ways to choose 2 women and 2 men from a group of 4 women and 5 men.
as we know the formula for combination as :
C(n ,k) = n! / (k!(n-k)!)
where n is the total number of people, k is the number of people we want to choose, and ! denotes factorial to find the number of combinations (i.e. the product of all integers up to that number, e.g. 4! = 432*1 = 24).
In this case, to choose the number of individuals as = 4 + 5 = 9 and k = 2 + 2 = 4. So, the number of ways to choose the committee is:
C(9,4) = 9! / (4!(9-4)!) = 126 ways
Hence the number of ways to choose committee is 126 ways.
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Find the lengths of AC and BC in cm to the nearest hundredth
Answer:
Step-by-step explanation:
Flavia bought a pair of roller blades. the regular price was 129.50. they were bought for 40% off and the sales tax was 15%. determine each of these amounts:
On solving the provided question, we can say that equation of cost of the roller blades is $ 89.66
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Let the total cost = A
initial cost = $ 129.50
he discount percentage = 40 %
So , the equation will be
= 129.50 - ( 40/100 ) x 129.50
= 129.50 - 51.8
= $ 77.7
sales tax percentage = 15 %
So , the equation will be
= 77.7 + ( 15/100 ) x 77.7
= 77.7 + 11.655
= $ 89.655
final cost is A = $ 89.66
final cost of the roller blades is $ 89.66
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One of the solutions to the equation 5x^2+bx+12=0 is -4/5. Find the value of b.
Answer:
19
Step-by-step explanation:
Substitute x = -4/5 and solve for b.
5x² + bx + 12 = 0
5(-4/5)² + b(-4/5) + 12 = 0
16/5 − 4/5 b + 12 = 0
16 − 4b + 60 = 0
4b = 76
b = 19
Answer:
Step-by-step explanation:
the length of the three sides of a a triangke is 2.92 meters, 7.67 meters and 8.82 meters what is the cosine
Answer: The cosine of angle C is -0.0168.
Step-by-step explanation: To find the cosine of the angle opposite the side of length 2.92 meters, you can use the cosine law which states that:
c^2 = a^2 + b^2 - 2ab * cos(C)
where c is the length of the hypotenuse (the longest side), a and b are the lengths of the other two sides, and C is the angle opposite side c.
So in this case,
c = 8.82 m
a = 2.92 m
b = 7.67 m
then we can substitute the values into the equation and solve for cos(C):
(8.82)^2 = (2.92)^2 + (7.67)^2 - 2(2.92)(7.67) * cos(C)
cos(C) = (a^2 + b^2 - c^2) / (-2ab)
cos(C) = (2.92^2 + 7.67^2 - 8.82^2) / (-22.927.67)
cos(C) = -0.0168
a curve passes through the point (4,2) and has the property that the slope of the curve at every point p is three times the y-coordinate p. what is the equation of the curve?:
The slope of the curve at a point (x,y) is given as 3y. This means that the equation of the curve is in the form of y = mx + b, where m is the slope of the curve and b is the y-intercept.
Since the curve passes through the point (4,2), we can use this point to find the value of b:
y = mx + b
2 = 3(4) + b
b = -10
So the curve's equation is: y = 3x - 10
You can confirm this by plugging in the point (4,2) into the equation.
2 = 3(4) - 10
2 = 12 - 10
2 = 2
How many integers fall between $\sqrt5$ and $\sqrt{50}$ on a number line?
Answer:
We can start solving this problem by finding the two numbers that bound the range of integers we're looking for.
First, we can approximate $\sqrt{5}$ to the nearest integer by finding the square root of 5. We know that 2^2 = 4 and 3^2 = 9, so 2 < $\sqrt{5}$ < 3. Therefore, $\sqrt{5}$ is a little bit more than 2 and a little bit less than 3.
Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.
Step-by-step explanation:
Similarly, we can approximate $\sqrt{50}$ to the nearest integer by finding the square root of 50. We know that 7^2 = 49 and 8^2 = 64, so 7 < $\sqrt{50}$ < 8. Therefore, $\sqrt{50}$ is a little bit more than 7 and a little bit less than 8.
Now we know that the range of integers we are looking for is between 2 and 7, inclusive. There are 7-2+1 = 6 integers between 2 and 7: 2, 3, 4, 5, 6, 7.
Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
5. Find the distance between (-1, -1) and (1, 1). Round to the nearest tenth if needed.
A. 6
B. 2.9
C. 2.8
D. 31
Answer: C. [tex]2.8[/tex]
Step-by-step explanation:
Using the distance formula, [tex]\sqrt{(-1-1)^2 +(-1-1)^2} \approx 2.8[/tex].
You purchae a computer for $1999. 99 plu 7% ale tax. The electronic tore offer an intallment loan that allow you to pay for the computer by making 12 equal monthly payment of $203. 30. What i the cot of credit, in dollar, for thi loan?
The cost of credit, in dollars, for this loan is 299.6107 dollars.
Let's recall the total cost of the computer with tax C. Then,
C = 1999.99 + 0.07 × 1999.99 = 1999.99 + 139.9993 = 2139.9893.
Since the loan allows you to pay for the computer in 12 equal payments of $203.30, the total cost of the loan is 12 × 203.30 = 2439.60.
The cost of credit is then the difference between the total cost of the computer with tax and the total cost of the loan: 2439.60 - 2139.9893 = 299.6107.
So the cost of credit is 299.6103 dollars.
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