In a class of 42 students, 25 take biology,15 take history,and 18 take biology but not history.i.Draw a Venn diagram to show the informationii.find how many students take niether history nor biology
Answers
In the class, there is a total of 42 students.
25 take biology.
15 take history.
18 take biology but not history.
There are four situations that you have to include in the Venn diagram:
"The students take only biology"
"The students take only history"
"The students take biology and history"
"The students take neither classes"
To draw the Venn diagram, you have to make one circle for each subject, i.e. one circle for biology and one for history, and label them.
Then you have to enter the similarities between both subjects, this means, where the circles overlap, you will find the students that take both subjects.
Finally, outside the circles, you will find the students that take neither subject:
Now, you have to determine how many students are included in each part of the Venn Diagram.
1) You know that 25 students take biology and that 18 take biology but not history, to determine the number of students that take both subjects, you have to calculate the difference between both values:
[tex]25-18=7[/tex]7 students take biology and history.
2) 15 students take history out of these you know that 7 take also biology. To determine the number of students that take only history, you have to calculate the difference between both values:
[tex]15-7=8[/tex]8 students take history but not biology.
3) To determine the number of students that take neither class, you have to subtract to the total number of students, those who take only biology plus those who take only history plus those who take both classes:
[tex]\begin{gathered} \text{Neither}=\text{Total-(only biology + only history + both)} \\ \text{Neither}=42-(18+7+8) \\ \text{Neither}=42-33 \\ \text{Neither}=9 \end{gathered}[/tex]9 Students of the class take neither class.
Finally, you can write each value in the corresponding part of the Venn diagram:
• Inside the green circle, you have to include the 18 students that take only biology.
,• Inside the blue circle, you have to include the 8 students that take only history.
,• Where both circles overlap, you have to include the 7 students that take both classes.
,• Outside the circles, you have to include the students that take neither.
Related Questions
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 8 times t squared plus 56 times t end quantity over the quantity t squared plus 3 times t plus 2 end quantity comma where the time, t, is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
Answers
(a). The domain of the function C(t) based on the context of the problem is t≥0
(b). The greatest concentration of the medication that a patient will have in their body is 7mg/L
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
(a). C(t) = (-8t² +50t)/(t² + 3t +2 )
The domain of the function :
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is: t≥0
(b).From the graph, the maximum y-value is 7.
Hence, the greatest concentration of the medication is 7mg/L
(a). The domain of the function C(t) based on the context of the problem is t≥0
(b). The greatest concentration of the medication that a patient will have in their body is 7mg/L
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If f(x) = x^5 + 4x - 5, then what is the remainder when f(x) is divided by
x - 3?
Answers
If f(x) = x^5 + 4x - 5, is divided by x - 3 the remainder is 220.
What is a remainder ?
In mathematics, the term "remnant" refers to the amount that is "left over" after performing a calculation. In mathematics, the integer that is left over after dividing two integers to produce an integer quotient is known as the residual (integer division). In algebra of polynomials, the "remainder" is the polynomial that is left over after dividing one polynomial by another. The operation that yields such a remainder when a dividend and a divisor are both present is the modulo operation.
How are functions divided?
Simply multiply or divide the numbers at each point where it makes sense to multiply or divide a function. If the functions are specified by formulas, you can simply multiply or divide the formulas (inserting numbers before or after is irrelevant).
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Write brackets in this statement to make each statement correct
Answers
Answer:
a. 4 x (5 + 3) = 32
b. 3 + 4 x (5 + 6) = 47
c. (2 + 7) x (5 + 3) =72
Step-by-step explanation:
Find the slope of the line that passes through the pair of points.
(5, −1)
and
(−1, −7)
Answers
Answer:
The slope is 1.Step-by-step explanation:
Slope:
[tex]\Rightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
y2=(-7)
y1=(-1)
x2=(-1)
x1=5
[tex]\sf{\dfrac{-7-\left(-1\right)}{-1-5}}[/tex]
Solve.
[tex]\sf{\dfrac{-7-\left(-1\right)}{-1-5}=\dfrac{-6}{-6}=\boxed{\sf{1}}}[/tex]
Therefore, the slope is 1, which is our answer.
I hope this helps, let me know if you have any questions.
Calculate the work done when a load of 50N is lifted through a distance of 6m.
Answers
The amount of work done when a load of 50 newton is lifted through a distance of 6m is 300 joules.
What is the amount of work done in lifting the load?Work done is simply the energy transfer that takes place when an object is either pushed or pulled over a distance by an external force.
It is expressed as;
Work done = force × distance
Given the data in the question;
Force applied = 50N = 50kgm/s²Distance covered = 6mWork done = ?To determine the work done, plug the given values into the above formula and solve W.
Work done = force × distance
Work done = 50kgm/s² × 6m
Work done = 50kgm²/s² × 6
Work done = 300kgm²/s²
Work done = 300J
Therefore, 300 joules is the work done in lifting the load.
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The graph of the derivative of a function f crosses the x-axis 3 times. What does this tell you about the graph of f ?
Answers
Answer:
D. The function f has 3 horizontal tangent lines
Step-by-step explanation:
Well whenever any function crosses the x-axis, it means that the y-value is equal to zero.
In this case when the derivative passes the x-axis it indicates the tangent line corresponding to that x-value has a slope of zero, which when plotted is a horizontal line.
This means that the graph f has 3 horizontal tangent lines.
Answer:
D. The function f has 3 horizontal tangent lines
Step-by-step explanation:
i got 100%
Seven times the sum of a number and 9
is 5
Answers
Seven times the sum of a number and 9 is 5 then the number is -58/7 .
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
We have been given that
Seven times the sum of a number and 9 is 5
Let the number is n.
let's write "the sum of a number and 9"
n + 9 .
Then, "seven times" the sum can be written as:
7 (n + 9)
This "is 5" or "is equal to 5" and can be written as:
7 (n + 9) = 5
To solve, first expand the term in parenthesis on the left side of the equation by multiplying each term in the parenthesis by
(7×n) + (7×9) = 5
7n + 63 = 5
Next, subtract 63 from each side of the equation to isolate the n term while keeping the equation balanced:
7n + 63 - 63 = 5 - 63
7n = -58
Now, divide each side of the equation by 7 to solve for n while keeping the equation balanced:
7n / 7 = -58 / 7
n = -58/7
The number is −58/7.
Hence , the number is -58/7 when a number is seven times its sum and 9 is 5.
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There are 3 consecutive integers that add up to 33. What are the integers?
Answers
Answer:
-33, -12, -11, -10Step-by-step explanation:
The three consecutive integers whose sum is -33 are -12, -11 and -10
Brainlist maybe :)?
Rewrite the following statement using a number in scientific notation.
My new music player has a capacity of 300 gigabytes. (Recall that giga means billion.)
Answers
Answer: My new music player has a capacity of 3 * 10^11 bytes.
Step-by-step explanation: giga=billion=10^9. 300 in scientific notation is 3*10^2. Since 3 is between 1 and 10. So 10^2 * 10^9=10^11.
1*2 + 2*3 + 3*4 + . . . + n(n + 1) = [ (n)(n + 1)(n + 2) ] / 3 whenever n is a positive integer. What is the next term in the sequence for the equation on the left?
Answers
P(k + 1) follows, and it is likewise true.
As a result, after demonstrating that P(k) is true for any chosen value of k, we also demonstrated that P(k + 1) is true. According to the induction hypothesis, P(n) is true for all n ∈ Z+
What is mathematical induction ?To demonstrate that the mathematical proposition P(n) holds for all natural integers n = 1, 2, 3, 4,..., one uses the mathematical induction technique. It is frequently referred to as the induction principle in mathematics. We establish that P(1) holds in order to demonstrate a result P(n) using the mathematical induction technique. If P(1) is valid, we can assume that P(k) holds for some natural number k and use this assumption to demonstrate that P(k+1) is valid. The assertion P(n) applies to all natural numbers if and only if P(k+1) holds true.
Let
P(n): 1×2 + 2×3+3×4+........+n(n+1)=[tex]\frac{n(n+1)(n+2)}{3}[/tex]
Putting n =1 we get
P(1):1×2 =2
and
[tex]\frac{1(1+1)(1+2)}{3}=\frac{1(2)(3)}{3} =2[/tex]
Therefore P(1) is true.
Let P(K) is true
So,
P(k): 1×2 + 2×3+3×4+........+k(k+1)=[tex]\frac{k(k+1)(k+2)}{3}[/tex]
Now we have to show that P(k +1 )is also true.
P(k+1): 1×2 + 2×3+3×4+........+k(k+1)+(k+1)(k+2)=[tex]\frac{k(k+1)(k+2)}{3}+ (k+1)(k+2)[/tex]
= (k+1)(k+2)[[tex]\frac{k}{3}+1[/tex]]
=[tex]\frac{(k+1)(k+2)(k+3)}{3}[/tex]
P(k + 1) follows, and it is likewise true.
As a result, after demonstrating that P(k) is true for any chosen value of k, we also demonstrated that P(k + 1) is true. According to the induction hypothesis, P(n) is true for all n ∈ Z+.
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Tom says, "If you square a number the answer is always bigger". Show Tom is in correct using two different example.
answer
Answers
Answer:
Tom is correct.
Step-by-step explanation:
Squaring is equivalent to multiplying a number by itself, ie:
2 squared = 2x2 = 4
6 squared = 6x6 = 36
3/11 x 4/9 answered in a fraction form
Answers
Answer:
4/33
Hopes this helps!
Have a good day :)
Mark wants to hang for rectangular pictures in a row on a wall so that the horizontal space between each picture is always the same each picture has a length of 8 inches,the wall has a length of 74 inches.if he wants to have 12 inches of horizontal wall space before the first picture and after the fourth picture how much space should he leave between pictures.help with this please
Answers
18 inches space should he leave between pictures of the wall with length 74 inches
What is Addition?Addition: Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum.
Mark wants to hang for rectangular pictures in a row on a wall so that the horizontal space between each picture is always the same
Length of each picture is =8 inches
Length of the wall=74 inches
The horizontal wall space before the first picture and after the fourth picture = 12 inches
we are asked to find the space between pictures
12+12+8+8+8+8+x=74
x+56=74
x=18
the distance between the picture is 18 inches
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which example are polynomials select each correct answer
Answers
Step-by-step explanation:
The bottom two expressions are polynomials.
During a search and rescue process after an earthquake, a team rescued 15 people in 5 hours. At this rate, what is the total number of people that the team can rescue in another 2 hours?
Answers
Based on the rate that the team is rescuing people per hour, the total number of people that the team can rescue in another two hours is 6 people.
How to find the number of people?First, find the rate at which people are being rescued by the search and rescue team per hour.
The rate of people rescued is:
= Number of people rescued / Number of hours
= 15 / 5
= 3 people per hour
The number of people rescued in 2 hours is:
= Number of hours x People rescued per hour
= 2 x 3
= 6 people
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Write down equation of lines l and m
Answers
ATTACHED IS THE SOLUTION
An elliptical-shaped path surrounds a garden, modeled by quantity x minus 22 end quantity squared over 225 plus quantity y minus 26 end quantity squared over 324 equals 1 comma where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent?
Answers
The ellipse has 2 axis, the minor and the major axis,
The major axis is denoted in blue color and the minor axis in purple color. By comparing our equation with the general equation of the ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]where the lenght of the major axis is given by
[tex]\text{lenght major axis=2b}[/tex]Fron the given equation, we can note that
[tex]b=\sqrt[]{324}=18[/tex]Therefore, the lenght of the major axis is 36 feet. Therefore, the maximum distance between any two persons is 36 feet corresponding to the major axis, which is option 3 from top to bottom
Find the distance between (5, 10) and (8, 10)?
Answers
Answer:
3 units
Step-by-step explanation:
1. Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bucket of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.
Answers
Answer: Do you know the answer to this yet??
Step-by-step explanation:
The equation is 4x + 2y = 45 and The y-intercept is the point (0,22.5) and The x-intercept is the point (11.25, 0)
Given,
Kevin took $45 with him to spend on snack
and, The price for each bucket of popcorn was $4.
To plot the graph
Now, According to the question:
Sketch the graph that represents the situation and label the intercepts
Let,
x ------> the number of bags of popcorn
y -----> the number of drinks.
we know that
The price for each bag of popcorn was $4
The price of each drink was half the price of a bag of popcorn
So, The price of each drink was (1/2)$4 = $2
The total bags of popcorn multiplied by $4 plus the number of drinks multiplied by $2 must be equal $45
The equation that represent this situation is :
4x + 2y = 45 -----(1)
Now, Find the y - intercept form:
The y-intercept is the value of y when the value of x is equal to zero
For, x = 0 put the value of x in equation(1)
4(0) + 2y = 45
2y = 45
y = 22.5
The y-intercept is the point (0,22.5)
That means -----> The number of drinks that Kevin can buy when the number of bags of popcorn is equal to zero
For, y = 0 put the value of x in equation(1)
4x + 2(0) = 45
4x = 45
x = 11.25
The x-intercept is the point (11.25, 0)
That means -----> The number of drinks that Kevin can buy when the number of bags of popcorn is equal to zero
Hence, The equation is 4x + 2y = 45 and The y-intercept is the point (0,22.5) and The x-intercept is the point (11.25, 0)
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5. CONSTRUCT ARGUMENTS Isabel wrote the expression 6 + 3 x 5 - 6+8+2 and asked Tamara to evaluate it. When Tamara evaluated it, she got a value of 19. Isabel told Tamara that her value was incorrect and said that the value should have been 38.
Who is correct? Justify your argument.
Answers
Answer:
none is correct
Step-by-step explanation:
6+3×5-6+8+2
6+15-6+8+2
6+9+10
=25
Last year, Elsa invested her money in two purchases. She purchased a certificate of deposit for $7000 that paid 3% interest per year and purchased $9000 in corporate bonds paying 11% interest per year.
Answer the questions below. Do not do any rounding.
Answers
Elsa used her money to make two purchases last year. The Total interest earned by the end of the year is 1200.
Given that,
Elsa used her money to make two purchases last year. She spent $7,000 on a certificate of deposit paying 3% interest annually and $9,000 on corporate bonds paying 11% interest annually.
We have to find the Total interest earned by the end of the year.
We know,
Total interest=adding the interest annually payment
Total interest=0.03×7000+0.11×9000
Total interest=1200
Therefore, The Total interest earned by the end of the year is 1200.
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Out of 350 applicants for a job, 163 are male and 56 are male and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they are male? Express your answer as a fraction or a decimal rounded to four decimal places.
Answers
Probability of a randomly chosen male applicant that has a graduate degree is 28/175.
Total number of applicants for a job= 350
Number of male applicants having a graduate degree = 56
We have to calculate the probability of a randomly chosen applicant that has a graduate degree, given that they are male.
We know ,
Probability = ( Total Number of favorable outcomes) / (Total Outcomes)
probability of a randomly chosen applicant that has a graduate degree, given that they are male = (Number of male applicants having a graduate degree)/ (Total number of applicants for a job) = 56/350 = 28/175
So, the probability of a randomly chosen applicant that has a graduate degree, that has a graduate degree, given that they are male is 28/175.
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Write the equation of the line in slope-intercept form. The coefficients in the equation are b=4 and m=-5
Answers
Answer:
y = -5x + 4
Step-by-step explanation:
Slope-intercept form of the equation is:
y = mx + b
In the question, we are given m = -5 and b = 4.
Fill in the numbers for m and b.
The m tells you how steep the line is (the slope) And b tells you where the line crosses the y-axis (y-intercept).
For what values of x is the inequality (x-4)² > 0 true?
Answers
The values of x must be greater than 4 for the inequality (x-4)² > 0 to be true.
What values make an inequality true?A value that makes an inequality true is the solution to the inequality. There may be more than one way to solve an inequality.The solution set is the collection of all inequality solutions.Given inequality is (x - 4)² >0.
To solve the inequality, take square root on both sides
So, (x - 4) > 0
Adding 4 on both sides,
x > 4
The values of x must be greater than 4 for the inequality to be true.
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The cosine function for a specific angle in a triangle is defined by the ratio of the triangle's
A. adjacent side and hypotenuse.
B. adjacent side and opposite angle.
C. opposite side and hypotenuse.
D. opposite side and adjacent side.
Answers
The cosine function for a specific angle in a triangle is defined by the ratio of the triangle's adjacent side and hypotenuse.
This is further explained below.
What is the cosine function?Generally, trigonometric functions are a set of real functions that link the ratios of the lengths of two sides of a right-angled triangle to an angle in the triangle.
They find widespread use in all fields of study that are in some way connected to geometry, including geodesy, solid mechanics, celestial mechanics, navigation, and a great many more.
In conclusion, The ratio of a triangle's adjacent side to its hypotenuse is used to determine the cosine function for a certain angle in the triangle.
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7. Use the quadratic formula to solve for x. a = 2, b = 4 and c = -3
Answers
Answer:
[tex]x=\dfrac{-2 + \sqrt{10}}{2}, \quad x=\dfrac{-2 -\sqrt{10}}{2}[/tex]
Step-by-step explanation:
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Given:
a = 2b = 4c = -3Substitute the given values into the formula and solve for x:
[tex]\implies x=\dfrac{-4 \pm \sqrt{4^2-4(2)(-3)}}{2(2)}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{16-8(-3)}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{16+24}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{40}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{4\cdot 10}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{4}\sqrt{10}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm 2\sqrt{10}}{4}[/tex]
[tex]\implies x=\dfrac{-2 \pm \sqrt{10}}{2}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{-2 + \sqrt{10}}{2}, \quad x=\dfrac{-2 -\sqrt{10}}{2}[/tex]
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Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut butter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn’t think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
Answers
11:28 AM Wed Jun 15roseacademies.owschools.comASSIGNMENTSCOURSESAssignment - 18. Solving Two-order InequalitiesAttempt 1 of 3SECTION 2 OF 2Solve the inequalities by graphing. Identify the graph that shows the following equations.y> Iy<-xOOOOS2C
Answers
The Solution:
GIven:
[tex]\begin{gathered} y>x \\ \\ y<-x \end{gathered}[/tex]We are asked to graph the given inequalities.
Below is the graph of the inequalities:
Thus, the correct answer is [option 1]
Gregoria borrowed $2,450, to be paid back at 3.5% annual simple interest. She repays $3,221.75. How many years was the loan period?
Answers
The loan that was borrowed by Georgina was for a period of 9 years.
How to calculate the value?From the information, Gregoria borrowed $2,450, to be paid back at 3.5% annual simple interest. She repays $3,221.75. The Interest will be:
= $3,221.75 - $2,450
= $771.75
Therefore, the time taken for the loan will be expressed as:
Interest = PRT/100
where P = Principal
R = Rate
T = Time.
Interest = PRT/100
771.75 = (2450 × 3.5 × T) /100
Cross multiply
8575T = 77175
Time = 77175 / 8575
Time = 9
The time is 9 years.
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Mary earns $12 per hour, plus 10% commission on all her sales. Mary worked 10 hours and her sales were $1500. How much money did Mary earn?
Answers
12*10= 120
Mary’s sales were $1500 she earns 10% of 1500*.10=150
Mary earned $270
120+150= 270
Mary earns $12 per/ hr + 10% commission on all her sales.
Mary worked $10 hr
Her sales were $1500
Then,
Mary earns $12*10 = $120 ( working 10 hr)
She got commission 10 % on her sales of $1500
That is, 10% * 1500
= (10/100)* 1500
= $150
Therefore,
Her total earning is = $150 + $120
= $270