Only 46 students like vanilla ice cream.
What is union and interaction?
Union of Disjoint Sets:
If A and B are two finite sets and if A ∩ B = ∅, then
n(A ∪ B) = n(A) + n(B)
In simple words if A and B are finite sets and these sets are disjoint then the cardinal number of Union of sets A and B is equal to the sum of the cardinal number of set A and set B.
Given,
total number of students = 97
students who like chocolate and vanilla flavors = 25
students who like strawberry and vanilla flavors = 16
students who like chocolate and strawberry flavors = 17
students who like all three flavors = 9
students who do not like ice cream = 5
Let C,S,V represent the chocolate, strawberry, vanila
therefore,
n(C∪S∪V) = n(C) + n(S) + n(V) - n(C∩V) - n(V∩S) - n(C∩S) + n(C∩V∩S)
97 = n(C)+n(S)+n(S)-25-27-9-5
141 = n(C) +2n(S)
141 = 3n(C)
n(C)=48
n(S) = n(V) =n(C)-2
=46
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Please help will mark Brainly
Your answer is -5.
Hope this helps.
PLEASEEEEEEE HELP DUE NOWWWWWWWWW
Alright! I have two more questions! Please give an explanation of how to get x ,y, and z! Thanks!
Using the definition of isosceles and equilateral triangles:
12. x = 77°; y = 58°; z = 122°
13. x = 60°; y = 120°; z = 60°
What are Equilateral and Isosceles Triangles?All three sides and angles of an equilateral triangle are equal in measure. On the other hand, two sides and two base angles of an isosceles triangle are equal to each other.
12. x = 1/2(180 - 26) [based on the definition of isosceles triangle]
x = 1/2(154)
x = 77°
y = 1/2(180 - (90 - 26)) [based on the definition of isosceles triangle]
y = 1/2(180 - 64)
y = 1/2(116)
y = 58°
z = 180 - 58 [base angles of isosceles triangle are equal]
z = 122°
13. Each interior angle of an equilateral triangle is equal to 60 degrees.
Therefore, x = the measure of one interior angle
x = 60°
y = 180 - 60 [linear pair]
y = 120°
The base angles of the triangle that has two equal sides would be 60° [180 - 120]
Therefore:
z = 180 - 2(60)
z = 60°
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A certain store is selling packages of 10 pencils and 4 pens for back to school. The store manager wants to make a larger package in the same ratio. If the large package has 10 pens, how many pencils are in the large package?
The number of pencils that will be in the large package, given the ratio of the pencils to pens in the package, is 25 pencils
How to find the number of pencils?In the original package, the ratio was such that there was 4 pens for every 10 pencils. This means that the number of pencils per pen was:
= 10 / 4
= 2. 5 pencils per pen
If there is a larger package with the same ratio and the number of pens in the package is 10 pens, then the number of pencils would be:
= Number of pens x Pencils per pen
= 10 x 2.5
= 25 pencils
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3.13.R Question:
Which of the following are exponential functions? (select all that apply)
The functions representing exponential growth or decay are f(x) = 3²ˣ⁺¹, f(x) = 0.8ˣ⁻⁰, f(x) = π⁴ˣ, f(x) = (4/9)ˣ, f(x) = -(3)ˣ, f(x) = (-3)ˣ
Exponential FunctionAn exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form f(x) = aˣ
Where a>0 and a is not equal to 1, and x is any real number.
If the variable is negative, the function is undefined for -1 < x < 1.
Here,
“x” is a variable“a” is a constant, which is the base of the function.An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.
In the question, the functions that are exponential are
f(x) = 3²ˣ⁺¹, f(x) = 0.8ˣ⁻⁰, f(x) = π⁴ˣ, f(x) = (4/9)ˣ, f(x) = -(3)ˣ, f(x) = (-3)ˣ
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Andrea can type 15 words per minute. If she types for 7 minutes, how many
words did she type?
Answer: 105 words
Step-by-step explanation:
15x7=105
The half-life of Radium-226 is 1590 years. If a sample contains 200 mg}, how many mg will remain after 1000 years?
_________mg
Give your answer accurate to at least 2 decimal places.
Answer:
137.11 mg
Step-by-step explanation:
divide 200 mg by 2 = 100 mg
divide 100 by 1590 = 0.0628930818
multiply this by 1000 = 62.8930818
subtract 62.8930818 from 200 = 137.1069182
137.1069182 rounded to 2 decimal places is 137.11 mg
therefore, the answer is 137.11 mg
The first angle in a triangle is three times that of a second angle. The second angle is two times that of the third angle. Find the ratio of the angles in the triangle.
The first angle in a triangle is three times that of a second angle. The second angle is two times that of the third angle. The ratio of the angles in the triangle is 1:2:3.
Define angle.When two rays are joined at one point, they produce the geometric shape known as an angle. The vertex is the shared point between the two rays, which are known as the arms or sides of the angle. When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolised by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees.
Given,
A first angle of let x
2x = 2nd angle
3x = 3rd angle
Angle sum = 180
x + 2x + 3x = 180
6x = 180
Dividing,
x = 30°
2x = 2(30)
2nd angle = 60
3x = 3(30)
3rd angle = 90
30°, 60°, and 90° are the three angles.
Ratio 1:2:3
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POLIGONOS: si tengo de informacion que 360 entre n es igual a 72 como puedo saber cual es el angulo interno la suma de angulos interno y el nombre del poligono?
El polígono regular tiene las características de un pentágono, cuya medida de ángulo central es 72° y la suma de todos los ángulos centrales es igual a 360°.
¿Qué polígono tiene un ángulo central de 72 grados?
En este problema debemos determinar que polígono regular tiene un ángulo central con medida de 72°, la suma de todos los ángulos centrales de un polígono es igual a 360°. El número de lados del polígono se puede determinar mediante la siguiente operación:
n = 360° / θ
Donde θ es la medida del ángulo central, en grados.
Si sabemos que θ = 72°, entonces el número de lados del polígono:
n = 360° / 72°
n = 5
El polígono regular es un pentágono.
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express 1-tan(a) as a product
The given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).
The given trigonometric expression is 1-tan(a).
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
We know that, tanθ=sinθ/cosθ
Now, 1-tan(a) =1-sin(a)/cos(a)
= (cos(a)-sin(a))/cos(a)
Therefore, the given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).
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Hotdogs are sold for a dollar and hamburgers are sold for $1.50. 175 hotdogs and hamburgers were sold in $235 was collected. How many hotdogs were sold?
Answer:
55 Hot dogs were sold
Step-by-step explanation:
Let d = hot dogs
Let h = hamburgers
d + h = 175
d + 1.50h = 235
Re-write
d + h = 175 for d and then substitute this into the second equation
d = 175 - h
d + 1.5 h = 235
175 - h + 1.50h = 235 Combine like terms
175 + .5h = 235 Subtract 175 from both sides
.5 h = 60 Divide both sides by .5
h = 120
120 Hamburgers were sold.
Plug in 120 for h to solve for hot does
d + h = 175
d + 120 = 175 Subtract 120 from both sides
d = 55
Check
d + 1.5h = 235
55 + 1.5(120) = 235
55 + 180 = 235
235=235
For every 10 children 4 wore glasses. There were 30 children. How many did not wear glasses?
Answer:
18
Step-by-step explanation:
If 4 out of 10 wore glasses, then 6 out of 10 did not wear classes. This would be 60% or .6
.6x30 = 18
A steel beam can be cut to different lengths for a project. Assuming the weight of a steel beam is proportional to
its length, what information would you need to know to write an equation that represents this relationship?
Answer:
You can write a statement of proportionality without any additional information:
... weight = k × length . . . . . . . . for some constant k
If you need to know the specific weight of a specific length, then you need to know the constant of proportionality (the value of k).
Step-by-step explanation:
Determine a series of transformations that would map Figure I onto Figure J.
A blank followed by a blank
The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.
What is a transformation of a shape?
A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.
From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
If the geometry is rotated, then there is no change in angles.
The translation does not change the shape and size of the geometry. But changes the location.
The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.
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Disclaimer
The question given by you is incomplete, so a similar question have been solved here and the image is attached.
Determine a series of transformations that would map Figure M onto Figure N.
Evaluate the exponential function f(x)=(1/8)^-x
The exponential function f(x)=(1/8)^-x can be evaluated to give us:
f(2)= 64f(-3)= 1/512f(-3)= [tex]\frac{1}{\sqrt{\frac{1}{8} } }[/tex]What is exponential function?An exponential function serves as Mathematical function in the form f (x) = ax hving “x” as variable,the conceptis the concept of exponential function.
The given function is f(x)=(1/8)^-x
Then f(2)=(1/8)^-2 = 1/(1/8)^2 =1/(1/64) =64
f(-3)=(1/8)^-(-3) = 1/512
f(-3)=(1/8)^-(1/2) =[tex]\frac{1}{\sqrt{\frac{1}{8} } }[/tex]
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What number of inches is equivalent to 848
not defined because 848 has no unit
Astorepays£98foramicroscope.Thestoremarksupthepriceby50%.Whatistheamountofthemark-up
Using percentage formula, the mark up price on the microscope is £49
Percentage
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Markup shows how much more a company's selling price is than the amount the item costs the company. In general, the higher the markup, the more revenue a company makes. Markup is the retail price for a product minus its cost, but the margin percentage is calculated differently.
Actual price = £98Markup percent = 50%Let's find 50% of £98
50 / 100 = x / 98
0.5 = x / 98
x = 0.5 * 98
x = 49
The mark up price is £49
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Two cones are similar. The volume of the larger cone is 27 cm³ and the volume of the smaller cone is 8 cm³. The height of th
smaller cone is 2 cm.
What is the height of the larger cone?
Enter your answer in the box.
cm
If two cones are similar, then the height of the larger cone will be equal to 3 cm.
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the data provided in the question,
For volume, the scale factor is,
k³ = 27/8
For length, the scale factor is,
k = ∛27/8
k = 3/2
Then the height of the larger will be,
h = 3/2 × 2
h = 3 cm.
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answer the 4 questions attached below ⬇️
The area and perimeter of the composite figures are as follows;
Figure 1;
Perimeter = 70 km
Area = 200 km²
Figure 2
Perimeter = 28 cm
Area = 24 cm²
Figure 3
Perimeter = 40 m
Area = 88 m²
Figure 4
Perimeter = 64 m
Area = 96 m²
What is the area of a composite figure?The area of a composite figure is the sum of the areas of the parts or simple figures that make up the figure.
Figure 1
The perimeter = 10 + 10 + 5 + 20 + 5 + 10 + 10 = 70
The perimeter of the figure is 70 kilometersThe area = 10 × (10 + 5) + 10 × 5 = 200
The area of the figure is 200 km²Figure 2
The perimeter of the figure is; 6 cm + 5 cm + 2 cm + 3 cm + 2 cm + 3 cm + 2 cm + 5 cm = 28 cmArea of the figure is 5 cm × 2 cm + 2 cm × 2 cm + 5 cm × 2 cm = 24 cm²Figure 3
The perimeter of the figure is 12 m + 6 m + 4 m + 2 m + 8 m + 8 m = 40 mThe area of the figure is 6 m × 12 m + 8 m × 2 m = 88 m²Figure 4
Perimeter of the figure is 12 m + 12 m + 2 m + 8 m + 4 m + 8 m + 4 m + 8 m + 2 m + 4 m = 64 mArea of the figure is 12 m × 2 m + 4 m × 4 m + 4 m × 12 m + 4 m × 2 m = 96 m²Learn more about finding the area and perimeter of composite figures here:
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(03.02 MC)
a
R
Which set of transformations would prove AQRS-AUTS?
Reflect AUTS over y = 2, and dilate AUT'S' by a scale factor of 2 from point S.
Reflect AUTS over y = 2, and translate AU'T'S' by the rule (x - 2, y + 0).
Translate AUTS by the rule (x + 0, y + 6), and reflect AUT'S' over y = 6.
Translate AUTS by the rule (x-2, y + 0), and reflect AU'T'S' over y = 2.
solve ((-3) x (10 + (-7))) to the power of 2 /n3 - (-9) to the power of 2)
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
[-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
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1/8 of the pupils at jake's school walked to school. 3/8 came by bus. waht fraction either walked or came by bus
By adding the two given fractions we will see that 1/2 of the students either walked or came by bus
What fraction either walked or came by bus?Let's say that there are N students in total. We know that a fraction of 1/8 of these N students walk to school.
And a fraction of 3/8 of the students go by bus to the school.
Then the fraction that either walks or came by bus to school is given by the addition between the two fractions above, then we just need to solve.
f = 3/8 + 1/8
We can see that we have the same denominator in both fractions, so we can directly add the numerators:
f = (3 + 1)/8 = 4/8
Now we can simplify the fraction to get:
f = 1/2
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Which function has a greater y-intercept? f(x)=1/3x+1/2
Answer:
f(x)
Step-by-step explanation:
the function g(x) has y-interception in point (0;0), the function f(x) has y-interception in point (0; 1/3). For more details see the attachment.
Find the volume of the solid generated by revolving the region bounded by y = x
and y = x²-3x about the x axis
The volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis will be x³/3-3x²/2+c.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
y = x²-3x
The volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis is obtained as,
[tex]=\int\:x^2-3x \ dx \\\\ = \int \:x^2dx-\int \:3xdx \\\\ =\frac{x^3}{3}-\frac{3x^2}{2} \\\\ =\frac{x^3}{3}-\frac{3x^2}{2}+C[/tex]
Thus, the volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis will be x³/3-3x²/2+c.
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Find all values of n for which the equation has two complex (non-real solutions)
6r² = 8r+ (n + 4)
Answer:
When n < - 6 2/3 the given equation has two complex solutions------------------------------
Given is a quadratic equation:
6r² = 8r+ (n + 4) ⇒ 6r² - 8r - (n + 4) = 0A quadratic equation has no real solutions if its discriminant is negative.
The discriminant of ax² + bx + c is:
D = b² - 4acApply to given equation:
D = (-8)² - 4*6*( - (n + 4)) = 64 + 24(n + 4) = 64 + 24n + 96 = 24n + 160Find the value of n when D < 0:
24n + 160 < 024n < - 160n < - 160/24 n < - 20/3 n < - 6 2/3In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Answer:
22/27
Step-by-step explanation:
5 play nothing.
27 - 5 = 22
22 play basketball only or baseball only or both.
p(plays baseball or basketball) = 22/27
See question in screenshot below:
The cos, tan, sec, csc and cot of the angle θ in quadrant IV are 3/5, -4/3, 5/3, -5/4 and -3/4 respectively
How to find the trigonometric ratio of the angle?
Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Given that: sin(θ) = -4/5 and θ is in quadrant 4.
Using this information, we can sketch the location of the angle θ in the quadrant (See the attached image). Therefore:
(a) cos(θ) = 3/5 (adj/hyp)
(b) tan(θ) = -4/3 (opp/adj)
(c) sec(θ) = 1/cos(θ) = 5/3
(d) csc(θ) = 1/sin(θ) = -5/4
(e) cot(θ) = 1/tan(θ) = -3/4
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Match each equation with the inverse operation you should use (on both sides of the equation) to solve for x.
x + 2 = 10 _____
x - 2 = 10 ____
2x = 10 ____
x/2 = 10 ____
x + 2 = 10
x + 2 - 2 = 10 - 2
x = 8
x - 2 = 10
x - 2 + 2 = 10 + 2
x = 12
2x = 10
2x/2 = 10/2
x = 5
x/2 = 10
x/2 × 2 = 10 × 2
x = 20
I HOPE IT HELPS EVEN THOUGH YOUR ANSWER TO MY QUESTION IS JUST A NONSENSE.A theatre contains 414 seats and the ticket prices for a recent play were $47 for adults and $22 for children. If the total proceeds were $12,983 for a sold-out matinee, how many of each type of ticket were sold?
The system of linear equations shows that the adult tickets was 155 and children ticket was 259
System of Linear EquationIn algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."
To solve this problem, we can set up two equations for this
Let;
adult ticket = xchildren ticket = yx + y = 414 ...eq(i)
47x + 22y = 12983 ...eq(ii)
Solving both equations; the values of x and y are 155 and 259 respectively
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subtract 9t*3-3t+8 and t*2-8t+4 from the sum of 12t+8 and t*2 - 10t +3.
⇒Find the sum of 12t+8 and [tex]t^{2} -10t+3[/tex]
⇒For sum we add:
[tex]=(12t+8)+(t^{2} -10t+3)\\=12t-10t+8+3+t^{2} \\=2t+11+t^{2}[/tex]
⇒The next step is to subtract [tex]9t^{3} -3t+8[/tex] and [tex]t^{2} -8t+4[/tex] from the answer we got above.
[tex]=(2t+11+t^{2} )-(9t^{3} -3t+8)-(t^{2} -8t+4)\\=2t+11+t^{2} -9t^{3} +3t-8-t^{2} +8t-4\\=2t+3t+8t+11-8-4+t^{2} -t^{2} -9t^{3} \\=13t-1-9t^{3} \\[/tex]
⇒The answer is shown above.
