Answer:
75
Step-by-step explanation:
15 + 2 × 30
Answer:
1320 seats.
Step-by-step explanation:
The given scenario can be modeled as an arithmetic series.
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
The first term is the number of seats in the front row.
Given that the number of seats in a row increases by 2 with each successive row, the common difference is 2.
The nth term is 30 since there are 30 rows in the theater.
Therefore:
a = 15d = 2n = 30Substitute the values into the arithmetic series formula and solve:
[tex]\implies S_{30}=\dfrac{1}{2}(30)[2(15)+(30-1)2][/tex]
[tex]\implies S_{30}=15[30+(29)2][/tex]
[tex]\implies S_{30}=15[30+58][/tex]
[tex]\implies S_{30}=15[88][/tex]
[tex]\implies S_{30}=1320[/tex]
Therefore, the total seating capacity of the theater is 1320 seats.
Find the volume of a cone with radius 8 and height 4.
The volume of the cone is:
[tex]85.33\pi[/tex]Explanation:The volume of a cone is given by the formula:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Given radius, r = 8, and height, h = 4, we have:
[tex]\begin{gathered} V=\frac{1}{3}\pi(8^2)(4) \\ \\ =\frac{256}{3}\pi \\ \\ =85.33\pi \end{gathered}[/tex](6x10^2)/(3x10^-5) standard form
Answer:
2×10^7
Step-by-step explanation:
cuz 3:6 is 2 and 10^2÷10^-5 equals 10⁷
Answer:
2×10^7
Step-by-step explanation:
6×10²/3×10^5
6/3×10²-10^-5
2×10²-^(-5)
2×10²+^5
2×10^7
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of all postsecondary degrees awarded in the united states, including master's and doctorate degrees, 21% are associate's degrees, 58% are earned by people whose race is white, and 12% are associate's degrees earned by whites. what is the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree? give your answer to three decimal places.
The conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree, is 0.571.
The percentage of associate's degrees is 21%.
The percentage of degrees earned by people whose race is white is 58%.
The percentage of associate's degrees out of all degrees earned by people whose race is white is 12%.
Let the probability of earning an associate's degree be P(A).
P(A) = 0.21
Let the probability of earning a degree by the people whose race is white be P(B).
P(B) = 0.58
Let the probability of earning an associate's degree by the people whose race is white be P(C).
P(C) = 0.12
P(C) = P(A∩B)
We need to find the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree.
P(B/A) = P(A∩B)/P(A)
P(B/A) = 0.12/0.21
P(B/A) = 0.571
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if f(3)=6, what is the value of f^-1(6)?
If the function f(3) has a value of 6, then the value of f⁻¹(6) is 3
How to determine the composite function?From the question, the definition of the function is given as
f(x)
Such that
The value of f(3) is 6
This is represented as
f(3) = 6
Also, the function can be represented as
y = f(x)
In f(3) = 6, we have
x = 3 and y = 6
When the inverse function is calculated, we have
f⁻¹(y) = x
This means that
f⁻¹(6) = 3
Express as an inverse function
f⁻¹(6) = 3
Hence, the inverse function f⁻¹(6) has a value of 3
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a $25$ foot ladder is resting against a wall so that the bottom of the ladder is $7$ feet from the wall. the bottom of the ladder starts slipping away from the wall at a rate of $1$ foot per second. how many feet per second is the top of the ladder sliding down the wall when it is $15$ feet above the ground?
The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. When the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.
Given that,
The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. A feet per second of the ladder's bottom begins to slide away from the wall.
We have to find when the ladder is 15 feet above the ground, how many feet per second is the top of the ladder falling down the wall.
Let us take x = height where the ladder hits the building
7 squared + x squared=25 squared
49+x squared=625
x squared=576
x=24 feet
Now,
If it slips 15 feet that 24-15=9 feet
Let x = distance from wall:
x² + 9² = 25²
x² + 81= 625
x² = 544
x = 23.3 feet
Therefore, when the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.
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How do I get n from 2n C n =70?
After evaluating the expression, the value of n is √(70/2C).
What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases.So, 2nCn = 70:
Now, solve for n as follows:
2nCn =702Cn² = 70n² = 70/2Cn = √(70/2C)Therefore, after evaluating the expression, the value of n is √(70/2C).
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Does this graph represent a function? Why or why not
robert has 30 socks in his sock drawer. 16 of the socks are white, 6 are black, 2 are red, and 6 are yellow.what is the prbability that he randomly pulls out a black sock
The Probability that Robert randomly pulls out a black sock is 1/5 .
In the question ,
it is given that
Total number of socks in sock drawer = 30 socks
number of white socks in the drawer = 16 socks
number of black socks in the drawer = 6 socks
number of red socks in the drawer = 2 socks
number of yellow socks in the drawer = 6 socks
So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )
= 6 / 30
= 1/5
Therefore , The Probability that Robert randomly pulls out a black sock is 1/5 .
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Which logical argument could you use to prove that triangle ABC is congruent to triangle DEF?
A. SSS Postulate
B. HL Theorem
C. SAS Postulate
D. ASA Postulate
tell me if the way I did it includes what's in this equation like if its commutative, associative, distributive or combined like terms
On the first line the distributive property was used. This property says that the product of a constant with a sum of two numbers is equal to the sum of the products.
On the third line the "associative" property was used. This property says that if you have the sum of three numbers the order at which you sum them doesn't affect the results.
Pls let me see the work!!
The recipe for the waffles presented using rational numbers are as follows;
1. The recipe for 2 waffles is as follows;
[tex] \displaystyle \frac{3}{5} [/tex] cups of flour
[tex] \displaystyle \frac{2}{15} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{5} [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{7}{20} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{15} [/tex] Cup of butter
2. The recipe for 5 waffles is as follows;
[tex] \displaystyle 1\frac{1}{2} [/tex] cups of flour
[tex] \displaystyle \frac{1}{3} [/tex] teaspoon of salt
[tex] \displaystyle 2 [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{7}{8} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{6} [/tex] Cup of butter
3. The recipe for 300 waffles is as follows;
900 cups of flour
200 teaspoon of salt
1200 teaspoons of baking powder
525 Cups of milk
100 Cup of butter
4. The required number of waffle irons is 50
5. It would take approximately 6 servers
It would take 34 trips
What is a rational number?A rational number is one that can be expressed as a fraction.
From the given table, we have;
The recipe for 10 waffles includes;
3 cups of flour
[tex] \displaystyle \frac{2}{3} [/tex] teaspoon of salt
4 teaspoons of baking powder
[tex] \displaystyle 1\frac{3}{4} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{3} [/tex] Cup of butter
1. To make 2 waffles, we have;
[tex] \displaystyle 2 = \frac{10}{5} [/tex]
Dividing each of the quantities required to make 10 waffles by 5 gives;
[tex] \displaystyle \frac{3}{5} [/tex] cups of flour
[tex] \displaystyle \frac{2}{3 \times 5} = \frac{2}{15} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{5} [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{1\frac{3}{4}}{5} = \frac{7}{20} [/tex] Cups of milk
[tex] \displaystyle \frac{\frac{1}{3}}{5} = \frac{1}{15} [/tex] Cup of butter
2. If each person gets 1 waffle, we have;
Number of waffles = 1 + 4 = 5
[tex] \displaystyle 5 = \frac{10}{2} [/tex]
Dividing the recipe for 10 waffles by 2 gives;
[tex] \displaystyle \frac{3}{2} = 1\frac{1}{2} [/tex] cups of flour
[tex] \displaystyle \frac{2}{3 \times 2} = \frac{1}{3} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{2} = 2 [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{1\frac{3}{4}}{2} = \frac{7}{8} [/tex] Cups of milk
[tex] \displaystyle \frac{\frac{1}{3}}{2} = \frac{1}{6} [/tex] Cup of butter
3. When each of 300 people can have one, the number of waffles is 300, which gives;
30 × 10 = 300
Multiplying the quantity of each ingredients required to make 10 waffles by 300 gives;
300× 3 = 900 cups of flour
[tex] \displaystyle 300 \times \frac{2}{3} = 200 [/tex] teaspoon of salt
300 × 4 = 1200 teaspoons of baking powder
[tex] \displaystyle 300 \times 1\frac{3}{4} = 525 [/tex] Cups of milk
[tex] \displaystyle 300 \times \frac{1}{3} = 100 [/tex] Cup of butter
4. Time it takes to cook a waffle = 10 minutes
Number of waffles required = 300
Time allowed = 1 hour = 60 minutes
The number of waffle iron is therefore;
[tex] \displaystyle {n = \frac{300 \times 10}{60} = 50} [/tex]
The number of waffle irons required is 50 waffle irons
5. Number of waffles each server can deliver = 9 waffles
The time it takes each server per trip = 10 minutes
Number of waffles to be delivered = 300
Time in which to deliver the 300 waffles = 1 hour
The number of servers is therefore;
[tex] \displaystyle {n = \frac{300}{9 \times 6} = 5. \overline 5 \approx 6} [/tex]
The number of trips is therefore;
5 servers will deliver 5×9×6 = 270
The sixth server will deliver the remaining 300 - 270 = 30 waffles in 30 ÷ 9 = 3.3 ≈ 4
The number of trips all together is therefore; 5×6 + 4 = 34 trips
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Isabella is making bread. She has 7/2 cups of flour. each loaf uses 3/4 cup of flour. How many whole loaves of bread can Isabella make? will she have flour left over?
A. 5 loaves with flour left over.
B. 5 loaves with no flour left over.
C. 4 loaves with flour left over.
D. 4 loaves with no flour left over.
Please help
Answer: C. Four loaves, with flour left over.
Step-by-step explanation:
7/2 simplifies to 3 1/2
Do the math,
3/4 + 3/4 = 1 1/2 2 loaves
1 1/2 + 3/4 = 2 1/4 3 loaves
2 1/4 + 3/4 = 3 4 loaves
Now when we add 3/4 to 3, we get more than 3 1/2. Which means we do not have enough flour for another loaf of bread. So, we can make four loaves and still have some four left over. The answer is C.
Which answer seems the most reasonable answer to the problem below? *
(-5.6) (3.4) =
-20
18
-15
12
Answer:
-20
Step-by-step explanation:
1- each of the two numbers are inside parenthesis and are beside each other which means they should be multiplied like this: -5.6 * 3.4
2- because 5.6 is negative, the rule in multiplying different signs would result to a negative number
3- and when you accurately multiply them, the answer is 19.04, and the options here are estimated so you should estimate the 19.04 too
4- 1 after it is 9 and nine is a great number, 1 turns to 2 and 9 turns into 0, which equals to 20, and DO NOT forget to add the sign, which is negative as i said previously
Please help I need answers right now plsssss. The angle of elevation to a nearby tree from a point on the ground is measured to be 54 degrees . How tall is the tree if the point on the ground is 52 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.
Using the angle of elevation, the height of the tree is 71.57 feet.
How to find the height of the tree using angle of elevation?The angles of elevation to a nearby tree from a point on the ground is measured to be 54 degrees.
The distance from the tree to the point on the ground is 52 feet.
The height of the tree can be found as follows:
The situation can be modelled to a right triangle.
Therefore, the height of the tree is the opposite side of the right triangle formed.
Hence,
tan ∅ = opposite / adjacent
where
∅ = angle of elevation
tan 54 = h / 52
cross multiply
h = 52 tan 54
h = 52 × 1.37638192047
h = 71.5718598645
Therefore,
height of the tree = 71.57 feet.
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A segment is m units long. Find the distance between the midpoints of the first and last parts if the segment is divided into 5 equal parts.
The midpoints of the first and last parts are 4/5m units apart
How to determine the distance between the midpoints?The length of the line segment is given as
Length = m units
From the question, the number of partitions is given as
Partition = 5
So, the length of each partition is
Each partition = Length/Partition
This gives
Each partition = m/5
The midpoint of a partition is
Partition midpoint = m/5 x 1/2
Evaluate
Partition midpoint = m/10
The distance between the midpoints of the first and last segments is then calculated as
Distance = Length - 2 x Partition midpoint
So, we have
Distance = m - 2 x m/10
Evaluate
Distance = m - m/5
This gives
Distance = 4/5m
Hence, the distance is 4/5m units
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the difference between the are of arc length and area of a sector please include the formulas for both in your answer
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a cyber hacker is trying to identify the mean age of customers that make frequent purchases on the online retail platform. the hacker does not have access to the raw data, however, the hacker had guessed that the age of customers is normally distributed with a standard deviation of 5 years. in addition to the above, the hacker knows that 70% of the time the age of the customers does not exceed 30 years old. calculate the mean age of customers, relying on the above information.
The mean age of customers is 27.35 years.
It is well known that age has a normal distribution with a 5-year standard deviation. Additionally, 30% of the time, customers are under the age of 30.
Mathematically,
P (age ≤ 30) = 0.70
Let μ be the mean age of the customer.
P [z ≤ (30 - μ) / σ] = 0.70
The equivalent of "age" in a conventional normal distribution is the z-score or z. It is evident from the usual normal distribution table that when z=0.53, 0.70 probability is reached.
Thus,
z = (30 - μ) / σ
⇒ 0.53 = (30 - μ) / 5
⇒ μ = 27.35
As a result, the average consumer is 27.35 years old.
The probability at each z-score in a standard normal table is represented by the associated z-score. We will look for the number 0.70 in the table, then the row value of 0.5 and the associated column value of 0.03 will be examined. They add up to 0.53 when combined.
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Tara makes two batches of purple food coloring. The table show the number of drops of red and blue coloring she uses for each batch. Do the two batches use the same number of drops of red per drop of blue.
Given data:
The number of red drops for first batch are r=100.
The number of blue drops for first batch are b=20.
The number of red drops for second batch are r'=75.
The number of blue drops for second batch are b'=15.
The expression for the red per blue drop for first batch is,
n=r/b
Substitute the given values in the above expression.
n=100/20
=5
The expression for the red drop per blue drop of the second batch is,
n'=r'/b'
Substitute the given values in the above expression.
n'=75/15
=5
Thus, yes the ratio of red to the blue drop is same for both batches.
Find the value of each variable
Answer:
y=9
Step-by-step explanation:
16y and 18y-18 are vertical angles. The definition of Vertical Angles states that both of the measures of the angles are equal to each other. Therefore,
18y-18=16y
2y-18=0
2y=18
y=9
Select the correct answer from each drop-down menu.
AABC is translated 6 units up and 3 units left to create AABC
If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at
Reset
V
and vertex B is at
Next
From the translation described, If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at (-4, 8). See the justification for the same below.
What is a vertex?A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect. Angles, polygons, polyhedra, and graphs are the most typical places to find vertices. Nodes are another name for graph vertices.
The explanation of the translation is given as follows:
According to the translation rule for translating a point h units left is given as:- (x, y) → (x-h, k)
The translation rule for translating point k units up is given as:
(x,y) → (x, y+k).
Since ∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5).
Then,
The vertex A' =
A (-1, 2) → (-1 -3, 2+6)
= (-4, 8)
Therefore, the vertex A' is at (-4,8).
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From the translation described, the vertex A' is at the point (-4,8).
What is a vertex?A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect.
Angles, polygons, and graphs are the most typical places to locate the vertices.
The explanation of the translation will be:
Based on the translation rule for translating a point h units left is follows as
(x, y) → (x-h, k)
The translation rule for point k units up is follows as:
(x,y) → (x, y+k).
Since ∆ABC is translated to the 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at; (1, 5).
The vertex A' ;
A (-1, 2)
(-1 -3, 2+6)
= (-4, 8)
Therefore, the vertex A' is at the point (-4,8).
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Amy has a piece of wood that measures 42 inches. The model shows the length remaining after she cut a piece from the 42-inch piece of wood. About how many inches did Amy cut from the 42-inch piece of wood? 2 3 4 5 6 7 8 10 12 inches
Given data
Ammy has a piece of wood that measures 42 inches
Ammy cut from the 42-inch piece of wood is calculated as
[tex]42-9=33\text{ inches}[/tex]Thus, Amy cut from the 42-inch piece of wood is 33 inches
Can someone help me with this
Answer:
1st one- 4
2nd one- 1
3rd one- 5
4th one-6
5th one-3
6th one-2
1/2 - 9/4x = -2/3 solve for x and simplify your answer as much as possible
Answer: 14/27
Step-by-step explanation:
The sum of two consecutive integers is 97. What is the smaller integer?
Answer: 48 is the smaller integer
Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.
The formula written in symbols as T =UN. Solve the formula for U.
The formula written in symbols as T =UN. Solve the formula for U.
we have
T=U*N
solve for U
so
isolate the variable U
step 1
divide by N both sides
T/N=U*N/N
T/N=U
therefore
U=T/Nsin(40 + 2°) csc(30 + 5°) = 1
sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.
Given,
sin(40 + 2°) cosec(30 + 5°) = 1
To prove the trigonometry function equal to 1.
Now, According to the question:
We know that
Sin 42° = 0.66913061
Cosec 35° = 1.7434468
sin(40 + 2°) cosec(30 + 5°) = 1
sin 42° × cosec 35° = 1
Plug the values of sin and cosec in above function:
0.66913061 × 1.7434468
= 1.16659
But we take the before decimal value i.e., 1
Hence, sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.
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2. Mr V bought 2 pajama sets for christmas for $25. He realized that he needed 2 more pajama sets. So now he bought 4 pajama sets for $50. Part A: Is this relationship proportional? Explain. *
We will have that the relationship is proportional because each time he bought more sets they had the same cost, and the total cost added to the sum of the independent cost. And we have the following relationship for the 2 sets and 4 sets:
2 sets:
[tex]\frac{25}{2}=12.5[/tex]So, each individual set is $12.5.
4 sets:
[tex]\frac{50}{4}=12.5[/tex]So, each individual set is $12.5.
So, each individual set for each relationship has the same cost, therefore the relationship is proportional.
One fourth the sum of r and ten is identical to r minus 4.
⇒Mathematically this means
[tex]\frac{1}{4} (r+10)= r-4\\\frac{r}{4} +\frac{10}{4} =r-4\\\frac{r}{4}(4) +\frac{10}{4} (4)=r(4)-4(4)\\r+10=4r-16\\r-4r=-16-10\\-3r=-26\\\frac{-3r}{-3} =\frac{-26}{-3} \\r=\frac{26}{3}[/tex]
Attached is the solution.
Any body know the answer to this question?
The curves are intersecting at (1, 1) and (-10, -4)
Nonlinear functions are the functions where the equations are not linear or the highest degree is more than 1. The following are some examples where the functions are not linear or non-linear. Ex. [tex]x^{2}[/tex] + 4x -1
In the above question, a graphical representation of non-linear system of equations is given
We need to find the solution of this non-linear system of equations based on the graphical representation
We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations
We can clearly see that, the curves are intersecting at
(1, 1) and (-10, -4)
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The curves are intersecting at (1, 1) and (-10, -4)
Nonlinear functions are the functions where the equations are not linear or the highest degree is more than 1. The following are some examples where the functions are not linear or non-linear. Ex. [tex]x^{2}[/tex] + 4x -1
In the above question, a graphical representation of non-linear system of equations is given
We need to find the solution of this non-linear system of equations based on the graphical representation
We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations
We can clearly see that, the curves are intersecting at
(1, 1) and (-10, -4)
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Which equations pass through the points (1, 3) and (7 9)?
Answer:
f(x)=x+2 Passes through
x-y=2 DOES NOT pass through
Step-by-step explanation:
Method- plug in x and see if the y matches the points. (1,3) (7,9)
f(x)=x+2
f(1)=1+2=3
f(7)=7+2=9
Matches!
x-y=2
1-y=2 --> y=-1
Does not match