The maximum number of students who studied all subjects is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total students = 40
Number of students who studied maths = 32
Number of students who studied geography = 28
Number of students who studied social science = 26
The maximum number of students who studied all subjects.
= Highest number of students who studied one subject - Least number of students who studied a subject
= 32 - 26
= 6
Thus,
6 is the maximum number of students who studied all subjects.
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Please answer #6a and 6b
The possible values of x for the given triangle ABC are 0.75<x<8.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, m∠A < m∠B < m∠C.
a) From triangle ABC,
BC<AC<AB
2x+3<6x<5x+8
Now, 2x+3<6x
Subtract 2x on both the sides of an inequality, we get
3<4x
Divide 4 on both the sides of an inequality, we get
0.75<x
Here, 6x<5x+8
Subtract 5x on both the sides of an inequality, we get
x<8
So, possible values of x are 0.75<x<8
b) From triangle ABC,
BC<AC<AB
3x+1<4x+8<7x+2
Now, 3x+1<4x+8
Subtract 3x on both the sides of an inequality, we get
1<x+8
Subtract 8 on both the sides of an inequality, we get
-7<x
Here, 4x+8<7x+2
Subtract 4x on both the sides of an inequality, we get
8<3x+2
Subtract 2 on both the sides of an inequality, we get
6<3x
Divide 3 on both the sides of an inequality, we get
2<x
So, possible values of x are -7<x<2
Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.
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A quadrilateral
is a polygon with four sides. Consider
the quadrilateral and the dashed segment. What is the sum
of the measures of the four interior angles of this quadrilateral?
Draw a different quadrilateral. Can you guess the sum
of the measures of its angles? Is it possible to generalize about
the angles of a quadrilateral?
The sum of the measures of the four interior angles of a quadrilateral is always 360°
What is a quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given is, A quadrilateral is a polygon with four sides. Consider the quadrilateral and the dashed segment
If we draw one diagonal to quadrilateral we will get two triangles i.e. △ABC and △ACD and we know that sum of the angles of a triangle is 180°
Sum of angles of quadrilateral ABCD = sum of angles of △ABC + sum of the angles △ACD
= 180° + 180°
= 360°
If we take examples of a square or a rectangle, we know that they are also a quadrilateral and also their each angle is right angle, i.e. 90°
Therefore, the sum of their interior angles will = 90×4 = 360°
Hence, we can say that the sum of the measures of the four interior angles of a quadrilateral is always 360°
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What does FG mean mass?
FG is an abbreviation for "Femtogram," which is a unit of mass equal to one quadrillionth of a gram (10^-15 g).
An exclamation is an emphatic expression of emotion or emphasis. It is often used to express strong feelings such as surprise, joy, excitement, anger, or disbelief. Exclamations are also used to emphasize a point or give an opinion. Exclamations are most commonly used in spoken language, particularly in informal conversations. They can also be used in written language, but they should be used sparingly. Exclamations are often followed by an exclamation point, although they can also be followed by a question mark or an ellipsis. Exclamations can be used to add emphasis or emotion to a statement, making it more powerful and memorable.
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A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.
What are the odds against exactly 5 cars passing over the bridge in that time?
The odds against exactly 5 cars passing over the bridge in that time are given as follows:
5.25:1.
What is the relation between probabilities and odds?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
An odd, conversely, is calculated as the division of the number of desired outcomes by the number of non-desired outcomes.
The probability(in favor) that 5 cars will pass over a small bridge in a 4-minute period is 0.16, hence the odds are given as follows:
0.16 : (1 - 0.16) = 0.16 : 0.84.
To obtain the odds against, we must exchange the desired and the non-desired outcomes, meaning that the odds against is then given as follows:
0:84 : 0.16.
As the quotient of 84 by 16 is of 5.25, the simplified odd is given as follows:
5.25 : 1.
Meaning that it is 5.25 times more likely that exactly 5 cars do not pass over the bridge over that time rather that they do pass.
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Someone please help me !!???? ASAP show steps please
Answer:
To find the answer, use the Pythagorean theorem. It would be the last choice.
Step-by-step explanation:
The formula for the Pythagorean theorem is:
a^2 + b^2 = c^2.
a = 10
b = 15
c = x
Make your equation.
10^2 + 15^2 = x^2.
Hope this helps!
You spin a spinner with 4 sections numbered 1-4and then flip a coin. List all the possible outcomes with a tree diagram.
Answer:
/ heads
1
\ tails
/ heads
2
\ tails
/ heads
3
\ tails
/ heads
4
\ tails
someone helpp me plsss
Answer: 2i+5
Step-by-step explanation: so (-2+14i)-(-7+12i)
Multiply (-1) to 7 and -12
Then: -2+14i+7-12i
Common numbers: (7-2) and 14i-12i
Then you get 2i+5
Is Y =- 3 vertical or horizontal?
According to the following graph, y = -3 makes the horizontal line on graph.
The term graph in math is known as a pictorial representation or a diagram that represents data or values in an organized manner and the points on the graph often represent the relationship between two or more things.
Here we have given the expression y = -3.
Now, we have to plot these on the graph, then we get the graph like the following.
While looking into the given graph, we have identified that y = -3 is a horizontal line, and that passes through y-axis, here at a distance of 3 units on the bottom of the origin and is parallel to x-axis.
Therefore, the expression y = -3 makes the horizontal line which crosses the y -axis at (0,−3).
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What’s is the prime factorization of |-21|
What is the slope of 5x 2y =- 3?
The slope of 5x 2y =- 3 is -5/2.
To find the slope of the equation 5x 2y =- 3, we need to rearrange it into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
We start by rearranging the equation 5x 2y = -3 so that all the terms with y are on one side and all the terms with x are on the other side.
5x -2y = -3
Now, we divide both sides by -2 to isolate y.
-5x/2 = y + 3/2
Finally, we subtract 3/2 from both sides to get the equation in the slope-intercept form.
-5x/2 = y - 3/2
Therefore, the slope of the equation 5x 2y = -3 is -5/2.
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Algebra: For what values of x and y must each figure be a parallelogram?
Need help please, and explanation.
9514 1404 393
Answer:
x = 60
y = 30
Step-by-step explanation:
Adjacent angles in a parallelogram total 180°. This relation can be used to form equations to find x and y.
Right Side Angles
x° +(5x -180)° = 180°
6x = 360 . . . . . . . . . . . divide by °, add 180
x = 60 . . . . . . . . divide by 6
__
Left Side Angles
4y° +2y° = 180°
6y = 180 . . . . . . . . . divide by °
y = 30 . . . . . . . divide by 6
If gas costs $5.09 per gallon, how many whole gallons of gas could you buy with $54.00?
Answer:
10 gallons
Step-by-step explanation:
drag expression into order to show how to find 4 x 3/5
Answer:
4x3 12 12 3/5 0,5 12,32,98/37
PLEASE SOMEONE HELPPPPP
Simplify (36)18
O a
Ob
Oc
Od
33
312
324
3108
Answer:
d. 3^108
Step-by-step explanation:
Just multiply 6 and 18.
how do i solve this?
Answer:
Degree: 4
Number of terms: 4
Leading Coefficient: 4
Constant: -20
Step-by-step explanation:
1) Expand (x+3)(x-4) into x^2 - x - 12
2) Combine like terms; equation becomes 4x^4 + x^2 + 4x - 20
3) Degree is looking for the highest exponent; in this case, it's 4
4) Number of terms is looking for how many terms there are in this equation; there are 4 terms
5) Leading Coefficient is looking for the coefficient of the term with the highest exponent, so the answer is 4
6) Constant is looking for the term without a variable
Hope this helps!
the researcher plans to examine the effects on a groyup of randomly selecred subjects. what is wronhg with this design
In random assignment design the subjects are not randomly assigned to an experimental group and control group.
What is random assignment?Random assignment improves the study's internal validity by ensuring that there are no systematic differences between the participants in each group. This allows you to conclude that the outcomes are due to the independent variable.In most cases, participants are randomly assigned to one of two groups: control or experimental. We can assume that the groups are essentially identical with the exception of the manipulation of the independent variable in the experimental group because participants are randomly assigned to either group.Random assignment is important in experimental research because it ensures that the experimental and control groups are comparable and that any differences between them are due to random chance.The complete question:
"A researcher wishes to examine the effects of a new medical treatment on patients with Alzheimer's disease. The researcher plans to examine the effects on a group of randomly selected subjects. What is wrong with this design?
Select all that apply.
A. Subjects are not randomly assigned to an experimental group and
control group.
B. A control group is not used.
C. Only one researcher is used.
D. An entire population is not used."
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HELP! The diameter of a circle is 12 cm. Find its area in terms of π. (pi)
The area of the given circle in terms of π is 36π cm².
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
Area = πr²
where 'r' is the radius of the circle
Given that the diameter of the circle is 12 cm, we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2
Radius = 12 cm / 2
Radius = 6 cm
Now, we can substitute the radius value into the formula:
Area = π x (6 cm)²
Area = π x 36 cm²
Therefore, the area of the circle in terms of π is 36π cm².
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In a classroom, 1 10 of the students are wearing blue shirts , and 2 5 are wearing white shirts. There are 20 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts
Answer:
10 students are wearing shirts other than blue or white.
Step-by-step explanation:
1 10 of the students in the classroom are wearing blue shirts, which is 1/1020 = <<1/1020=2>>2 students.
2 5 of the students in the classroom are wearing white shirts, which is 2/5*20 = 8 students.
Altogether, 2+8 = <<2+8=10>>10 students are wearing either blue or white shirts.
There are 20 students in the classroom, so 20-10 = <<20-10=10>>10 students are wearing shirts other than blue or white.
100 students were surveyed about which subject they liked best. 41 students said they like math, and 25 students said they liked Science. Of those students surveyed, 19 said they liked both.
How many students is the complement of math?
In 100 students, Science was rated favorably by 25 students, while math received ratings from 41 students. 19 of the students polled indicated that they approved of both. 16 students are the complement of math.
What is complement of a number?The phrase "complement" is typically used to describe a subset of a set that does not include another subset. The entire original set is obtained by adding the complement and its taking. The complement of a set is typically represented by the notations. The complement of a set is the set that includes all the elements of the universal set that are not present in the given set.
The Total number of students were 100
Students who like maths were 41
Students who like science were 25
Students who like both maths and science were 19
Students who does not like maths are 41-25 = 16.
So the students who are the complement of math are 16.
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Gordon rolls a fair dice 162 times.
How many times would Gordon expect to roll a four?
Answer:
27 times
Step-by-step explanation:
A regular dice usually has 6 sides. A fair dice means you have an equally likely chance of landing on any face.
So we would do 162 ÷ 6 to get 27.
what is the solution to the equation 6m = 60
Answer:
m=10
Step-by-step explanation:
divide 6m by 6 and 60 by 6 and you get m=10
Answer:
10
Step-by-step explanation:
divide both sides
6m÷6=60÷6
m=60÷6
m=10
Given f(x) = − x² - 4x – 12, find f(-7)
Answer:
f(-7) = -33
Step-by-step explanation:
f(x) = − x² - 4x – 12
f(-7) = ?
We put -7 in for x and solve
f(-7) = -(-7)^2 -4(-7) - 12
f(-7) = -(49) + 28 - 12
f(-7) = -49 + 28 - 12
f(-7) = -33
only do 18.
A bag contains 36 marbles. If the probability of reaching in and pulling out a blue marble is
how many blue marbles are in the bag? Show your work or Explain. (2points)
The number cube with sides labeled 1 through 6 is rolled.
Which events are likely to occur? Select all that apply. Multiple select question. A) rolling a 1 or a 2 B) rolling an odd number C) rolling an even number D) rolling a a number less than 6 E) rolling a number greater than 2
Answer:
Events D and E are likely to occur.----------------------------------------
The number cube has sides 1 through 6. The probability of each number is same, 1/6.
Given events below, see how likely they are to occur:
A) rolling a 1 or a 2,
this is a 2/6 = 1/3 < 1/2, not likely;B) rolling an odd number,
this is a 3/6 = 1/2, not likely;C) rolling an even number,
this is a 3/6 = 1/2, not likely;D) rolling a a number less than 6,
this is 5/6 > 1/2, likely to occur;E) rolling a number greater than 2,
this is a 4/6 = 2/3 > 1/2, likely to occur.Anybody know the answer to this ?
On solving the provided question, we can say that - the data from graphs represents a curvilinear and straight graph.
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
Here,
in graphs,
as per data we can say that there two types
one is curvilinear and other is straight graph.
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Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)
The answer choice which represents a number line for the intersection of the given intervals is; (-∞, 2).
The answer choice which represents a number line for the union of the given intervals is; (-∞, ∞).
What is the number line representation of the intersection and union of the given intervals?It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.
Since the given intervals are; (-∞, 2) and [0,∞).
It follows that the intersection of both intervals is the interval; (-∞, 2).
Also, the interval which represents the union of both intervals is; (-∞, ∞).
Hence, the image which represents both scenarios is attached.
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help please due monday
Answer:
I think it is D, but I am not sure.
Step-by-step explanation:
Have a nice day!
please help me. I figured out my last question but i really need help!!! please
The area of the figure is 51.63 m²
How determine area of the composite figure?
A composite figure is figure that is made up of two or more different shapes.
The composite figure in the given image is made up of a rectangle, semicircle and a triangle. Therefore, the area of the composite figure will be the sum of the areas of the shape it is made of. Thus:
Area of figure = area if rectangle + area of semicircle + area of triangle
Area of figure = LW + 1/2πr² + 1/2bh
Area of figure = (6 × 5) + (1/2 × 3.14 × 3²) + (1/2 × 3 × 5)
Area of figure = 30 + 14.13 + 7.5
Area of figure = 51.63 m²
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Which mixed number is equal to 35
Answer:
35 [tex]\frac{0}{1}[/tex]
Step-by-step explanation:
What is the x-intercept of the graph of y x2 4x 4?
The x-intercept of the graph of y = x² - 4x + 4 is x = 2.
By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.
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