The number of students that are in both the Categories A and B are 16 students.
In the question ,
it is given that ,
the total number of students in category A and category B is 32 students .
which is represented as A union B ,
that is n(AUB) = 32 ,
the number of students in category A = n(A) = 24
the number of students in category B = n(B) = 24
we need to find the number of students that are in both category ,
that is n(A∩B) .
we know that ,
n(AUB) = n(A) + n(B) - n(A∩B)
Substituting the values , we get
n(A∩B) = 24 + 24 - 32
= 48 - 32
= 16
Therefore , The number of students that are in both the Categories are 16 students.
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What is one possible dividend, greater than 1,000, if the quotient is 37 R4
A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomrua in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from "Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomrua in Older Adults," by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min. Does zopiclone appear to be effective?
A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
What is a confidence interval?
A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.
Here,
From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,
98%C.I. = µ ± z * σ / n = 98.90 ± 2.33 * 42.30 / sqrt of 16 = 98.90 ± 24.64 = 74.26 to 125.54
The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.
Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
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Here i a ample data et, 19 39 9 33 15 16 2 33 16 Find the mallet number (Minimum) from the data et Find the firt quartile Q1 Find the median Find the third quartile Q3 Find the larget number (Maximum) from the data et
a) The smallest number is 2
b) The first quartile Q1 is 12
c) The median is 16
d) Third quartile Q3 is 33
e)The largest number is 39
What Is Quartile Formula?
To divide a set of observations into four equal pieces, use the quartile formula. The median and the first term are where the first quartile is located. The median represents the middle quartile. The third quartile represents the midway value that falls between the median and the last term.
Given data set:
19, 39, 9, 33, 15, 16, 2, 33, 16
Arrange the data in ascending order:
2, 9 ,15 ,16 ,16 ,19 ,33 ,33 ,39
a) Smallest number: 2
b) The first quartile Q1 :
number of terms=n=9
Q1= (n+1)/4 th term
Q1= (9+1)/4 = 2.5th terms
This means, Q1=mean of 2nd and 3rd terms= (9+15)/2 = 12
c) Median:
M=(n+1)/2 th term = (9+1)/2 =5th term = 16
d) Third quartile Q3:
Q3= 3[(n+1)/4] th term
Q3= 3[(9+1)/4] = 7.5th terms
This means, Q3=mean of 7th and 8th terms= (33+33)/2 = 33
e) largest number : 39
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Sum and Product of Two Numbers Find two numbers whose sum is 20 and whose product is the maximum possible value. (Hint: Let x be one number. Then 20 - x is the other number. Form a quadratic function by multiplying them, and then find the maximum value of the function.)
Answer:
The numbers are 10 and 10Step-by-step explanation:
As described in the hint:
the numbers are x and 20 - x, their product is maximum possible value.The product is:
x(20 - x) = - x² + 20xThis is a quadratic expression ax² + bx + c with the leading coefficient of a = - 1, b = 20 and c = 0.
It has a maximum and no minimum value since a < 0.
The x-coordinate of the maximum is the vertex which is x = - b/2a.
The x- coordinate of the vertex is:
x = - 20/-2 = 10The maximum value itself is:
- 10² + 20*10 = - 100 + 200 =100Answer:
10 and 10.
[tex]f(x)=-x^2+20x[/tex]
Maximum value of the function is 100.
Step-by-step explanation:
Two numbers whose sum is a positive integer, and whose product is the maximum possible value have to be two positive integers.
Pairs of positive integers whose sum is 20:
1 and 192 and 183 and 174 and 165 and 156 and 147 and 138 and 129 and 1110 and 10The pair of numbers whose product is the maximum possible value is the pair of numbers that are closest to each other.
Therefore the pair of numbers is 10 and 10:
[tex]\implies x = 10[/tex]
[tex]\implies 20 - x = 10[/tex]
Form a quadratic function by multiplying:
[tex]\implies f(x)=x(20-x)[/tex]
[tex]\implies f(x)=20x-x^2[/tex]
[tex]\implies f(x)=-x^2+20x[/tex]
The maximum value of the function is the y-value of its vertex.
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
To convert the function to vertex form, complete the square.
Factor out negative 1:
[tex]\implies f(x)=-(x^2-20x)[/tex]
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=-\left(x^2-20x+\left(\dfrac{-20}{2}\right)^2-\left(\dfrac{-20}{2}\right)^2\right)[/tex]
[tex]\implies f(x)=-(x^2-20x+100-100)[/tex]
[tex]\implies f(x)=-(x^2-20x+100)+100[/tex]
Factor the perfect square trinomial:
[tex]\implies f(x)=-(x-10)^2+100[/tex]
Therefore, the vertex of the function is (10, 100), and so the maximum value of the function is 100.
Write a mathematical sentence that expresses the information given below.
Use p as your variable name. If necessary:
type <= to mean <
or > = to mean 2.
A football team had 52 players at the start of the season, but then some
players left the team. After that, the team had 43 players.
The mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season or p = 52-43.
According to the question,
We have the following information:
A football team had 52 players at the start of the season, but then some players left the team. After that, the team had 43 players.
Now, let's take the number of players who left the team to be p.
So, we have the following expression:
p = 52-43
p = 9
Hence, the mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season.
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A family buys a studio apartment for 150,000. They pay a down payment of $22,500. a)Their down payment is what percent of the purchase price? b) What percent of the purchase price would a $7500 down payment be?
Answer:
15% and 40%
Step-by-step explanation:
22500/150000 is 15/100 or 15%
60000/150000 is 40/100 or 40%
a 14-ounce can of green beans contains two teaspoons of salt. how much sodium is present in 2 teaspoons (11.5 grams) of salt?
The percentage of salt in green beans can is 2.89%.
It is important to know about the percentage first, the percentage is a part of the sample in the population. It can be determined by this formula
A% = x / N . 100%
where A% is the percentage, x is the sample and N is the total population
From the question above, we know that :
x = 11.5 grams
N = 14 ounce = 396.89 grams
By substituting the parameter to the equation, we get
A% = x / N . 100%
A% = 11.5 / 396.89 . 100%
A% = 2.89%
Hence, the total salt in the can is 2.89%
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HELPPPPPPPPPP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
150 plates
Step-by-step explanation:
if 1 stack = 10 plates then
15 stacks =?
15×10 =150
Answer:
150
Step-by-step explanation:
If 1 stack = 10 plates all you have to do is figure out how 1 changes to 15 ( in this case multiply). You tyen multiply 10 by 15 which equals to 150.
Josh has to walk 9/10 of a kilometre to school.He is 1/3 of the way there. How much further will he have to walk?
Find the least common denominator for this pair of algebraic fractions:
p/4 and p/16
The least common denominator for this pair of algebraic fractions: p/4 and p/16 is 16.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In the case, the fraction is illustrated as p/4 and p/16.
It should be noted that the lowest common multiple for 4 and 16 is 16. This is the denominator.
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A sheet of metal 10 inches by 8 inches is to be used to make a open box. Squares of equal sides x are cut out of each corner then the sides are folded to make the box. Find the value of x (correct to 2 decimal places) that makes the volume a maximum.
Answer:
1.81 inches
Step-by-step explanation:
Find the area of the triangle.
A=?in^2
Answer:
A = 7.5 in^2
Step-by-step explanation:
the formula for a triangles area is [(h)(b)]/2
2.5 is the h (height) and 6 is the b (base)
first multiply h and b
2.5 * 6 = 15
now divide by 2
15 / 2 = 7.5
that is your answer
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
2, 8, 14, ...
Find the 42nd term.
The 42nd term of the sequence is 248
What is Arithmetic Progression?
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
The furmula is [tex]a_{n}[/tex]=a + (n - 1 )d
where a = The first form of A.P
n = Number of terms given to find
d = Common difference between each terms
Given,
a = 2
n = 42
d = 6
Now,
[tex]a_{42\\[/tex] = 2 + (42 - 1)6
[tex]a_{42}[/tex] = 2 + (41)6
[tex]a_{42}[/tex] = 2+ 246
Therefore, for 42nd term
[tex]a_{42}[/tex] = 248
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A furniture maker uses the specification 17.9≤w≤18.1 for the width w in inches of a desk drawer. Write the specification as an absolute value inequality.
The specification as an absolute value inequality is l w - 18 l ≤ 0.1.
Given:
A furniture maker uses the specification 17.9≤w≤18.1 for the width w in inches of a desk drawer.
m = 17.9 + 18.1 / 2
= 36/2
= 18
t = 18.1 - 17.9
= 0.2/2
= 0.1
l w - 18 l ≤ 0.1
Therefore The specification as an absolute value inequality is l w - 18 l ≤ 0.1.
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how much of brand A fruit punch (20% fruit juice) must be mixed with 9 L of brand b fruit punch (40% fruit juice) to create a mixture contains 32% fruit juice ?
6 liters of brand A fruit punch must be mixed with 9 L of brand b fruit punch.
Let x=liters of Brand A fruit punch to be mixed with 9 liters of Brand B fruit punch.
x + 9 = liters of mixture.
20%(x) + 9*40% = 32%(x+9)
20/100 x + 9*40/100 = 32/100 (x+9)
0.2x + 360/100 = 0.32x + 9*0.32
0.2x + 3.6 = 0.32x + 2.88
0.12x = 3.6 - 2.88
0.12x = 0.72
divide by 0.12 on both sides
x = 0.72/0.12
= 72/100/12/100
= 72/12
= 6 liters.
Therefore 6 liters of brand A fruit punch must be mixed with 9 L of brand b fruit punch.
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what is an equivelent fraction of 8x^4 * 5x ^3
The equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question as:
8x⁴ × 5x³
We have to determine the equivalent fraction of the given expression.
⇒ 8x⁴ × 5x³
⇒ 8 × 5 × x⁴× x³
Multiply the coefficients in the above expression,
⇒ 40 × x⁴× x³
Add the exponents in the above expression,
⇒ 40 × x⁴⁺³
⇒ 40x⁷
Thus, the equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.
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How do you factor g³ - 343?
Answer:
(g-7)^3
Step-by-step explanation:
(x-y)^3 = x^3 - y^3
In this case you are solving for y, or 343
The cube root of 343 is 7
g^3 - 7^3 = (g-7)^3
(g-7)^3
Step-by-step explanation:
g³-343=0
g³=343
g=³√343
g=7
g³-7³=0
(g-7)^3=0
How do I put 8x=26+14y in standard form
The given equation written in standard form is 8x - 14y = 26
Writing a linear equation in standard formFrom the question, we are to write the given linear equation is standard form.
From the given information, the given linear equation is
8x = 26 + 14y
The standard form of linear equation is given as
Ax + By = C
Where x and y are the variables
A, B, and C are the constants
Now, we will write the given equation in standard form
8x = 26 + 14y
Subtract 14y from both sides of the equation
8x - 14y = 26 + 14y - 14y
8x - 14y = 26
Hence, the equation is 8x - 14y = 26
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Use the GCF and the distributive property to find the sum of 30+45
The sum using the distributive property is 75
How to determine the GCF sum of the expressions?From the question, we have the following expression
30 + 45
Rewrite the given expression as follows
This is represented using
(30 + 45)
Factor out 5 from the expression
So, we have the following representation
30 + 45 = 5(6 + 9)
The above means that 5 is the GCF of the sum expression 30 + 45
This represents the GCF
Solving further, we have
30 + 45 = 5 * 15
Evaluate
30 + 45 = 75
Hence, the sum is 75
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BobbyLou's cell company charges $27 a month for voice service plus $0.43 for each text message. Write the equation that would give you the amount each month, given a certain number of text messages.
The equation that would give the amount each month, given a certain number of text messages is 27 + 0.43t.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of text messages be represented as t.
Since BobbyLou's cell company charges $27 a month for voice service plus $0.43 for each text message. The amount will be:
= 27 + (0.43 × t)
= 27 + 0.43t
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Select all of the roots of x3 + 2x2 – 16x– 32.
–1
–2
–4
1
4
5
Answer:
-4, -2, 4
Step-by-step explanation:
You want the roots of the polynomial x³ +2x² -16x -32.
FactorsThe polynomial can be factored by grouping:
x³ +2x² -16x -32
= (x³ +2x²) -(16x +32) . . . . . . group pairs of terms
= x²(x +2) -16(x +2) . . . . . . . . factor each group
= (x² -16)(x +2) . . . . . . . . . . . . factor out the common factor
Now, the difference of squares can be factored:
= (x -4)(x +4)(x +2)
RootsThe zero product rule tells us the roots are the values of x that make the factors zero:
x -4 = 0 ⇒ x = 4
x +4 = 0 ⇒ x = -4
x +2 = 0 ⇒ x = -2
The roots of the polynomial are {-4, -2, 4}.
__
Additional comment
The factorization of the difference of squares is a special form:
a² -b² = (a +b)(a -b)
Answer:
-2, -4, and 4 are the correct answers on edge
Step-by-step explanation:
2(x-3)^2-12=116 help
Step-by-step explanation:
[tex]2(x - 3) {}^{2} - 12 = 116 \\ [/tex]
[tex]2 \times ( {x}^{2} - 6x + 9) - 12 = 116[/tex]
[tex] {2x}^{2} - 12x + 18 - 12 = 116[/tex]
[tex] {2x}^{2} - 12x - 110 = 0[/tex]
[tex] {x}^{2} - 6x - 55 = 0[/tex]
[tex] {x}^{2} - 11x + 5x - 55 = 0[/tex]
[tex]x(x - 11) + 5(x - 11) = 0[/tex]
[tex](x +5 )(x - 11) = 0[/tex]
Triangle w z y is cut by bisector z x. the lengths of sides z w and z y are congruent. zx bisects ∠wzy. if the measure of ∠yxz is (6m â€" 12)°, what is the value of m? 6 17 90 102
The value of m in the angle (6m - 12)° is m = 17 , the correct option is (b) .
In the question ,
it is given that ,
the triangle WZY is cut by the bisector ZX ,
and also given that ZW and ZY are congruent ,
that means ZW = ZY
Based on the characteristics of the triangle given ,
we can conclude that triangle WYZ is an isosceles triangle ,
that means , triangle WXZ = triangle YXZ
So , ∠YXZ = ∠WXZ = 90°
given that ∠YXZ = (6m - 12)°
So , (6m - 12)° = 90°
6m - 12 = 90
6m = 90 + 12
6m = 102
m = 102/6
m = 17
Therefore , the value of m in the angle (6m - 12)° is m = 17 .
The given question is incomplete , the complete question is
Triangle W Z Y is cut by bisector Z X. The lengths of sides Z W and Z Y are congruent. ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°, what is the value of m?
(a) 6
(b) 17
(c) 90
(d) 102
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Answer:
17
Step-by-step explanation:
i got it right on edge 2022
Choose the graph of y=2|x|+5
Answer:
2nd one
Step-by-step explanation:
You can see that at the end, it is +5. That means it is to the left, NOT the right. So the second one is correct.
Help please <3 end of quarter is soon!
Answer:
x = 2
Step-by-step explanation:
8x - 21 - 5x = - 15 ( collect like terms on left side )
3x - 21 = - 15 ( add 21 to both sides so numeric values on right side )
3x = 6 ( isolate x by dividing both sides by 3 )
x = 2
Dilate the figure by the scale factor. Then enter the new coordinates
K=10
A'(0,20)
B'([?],[])
C'([ ][ ])
The will be A'(0, 20), B'(20, 10) and '(-10, 0). Transformation is the of a point from its to a. Types of transformation are reflection, translation, rotation and dilation.
What is transformation?
When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is obtained. Function transformations are very useful for graphing functions without having to start from scratch because they allow you to move, expand, compress, or reflect the curve. In this article, we will examine the guidelines for function transformations as well as examples of how to transform various function types.
Let ABC be a with coordinates A(0, 2), B(2, 1), C(-1, 0).
The coordinate of points A, B, C will change by below rule
(x, y)↔(10x, 10y)
where 10 is the scale factor.
∴A(0, 2) ↔A'(0, 20)
B(2, 1) ↔B'(20, 10)
C(-1,0) ↔C'(-10, 0)
Hence, will be A'(0, 20) ,B'(20, 10) and C'(-10, 0)
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What is the area of a quadrilateral with vertices at (1, 1), (5, -1),
(1,5), and (5,5)?
The area of the quadrilateral is = 15 square units.
What is area of the quadrilateral ?The quantity of territory contained within a quadrilateral determines its area. Let's review the definition of a quadrilateral. A closed shape with four line segments enclosing it is referred to as a quadrilateral. Both regular and irregular quadrilaterals exist. A quadrilateral with regular sides is one with equal-length sides. An irregular quadrilateral is a quadrilateral that is not regular. There are six different kinds of quadrilaterals.square \srectangle \sparallelogram \strapezoid \srhombus \skite.The area of a quadrilateral is nothing but the region enclosed by the sides of the quadrilateral. It is measured in square units such as m2, in2, cm2, etc.acc to our quesstion-
There are two sets of Y values identical ( 0 and 5 ).There are two sets of identical X values ( -1 and 2)This makes a rectangle.The length is 5-0 = 5The width is 2 - -1 = 3Area = Length x width = 5 x 3 = 15 square units.hence,The area of the quadrilateral is = 15 square units.
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Select each exact root. If the exact roots cannot be found, select the consecutive integers between which the roots are located. If there are no roots, select no real solution.
x2+6x+6=0
Multiple select question.
A) no real solution
B) between −2 and −1
C) between −5 and −4
D) −5
E) −1
F) between 4 and 5
G) between 1 and 2
Answer:
C, B
Step-by-step explanation:
[tex]x^2+6x+6=0 \\ \\ x=\frac{-6 \pm \sqrt{6^2-4(6)}}{2(1)} \\ \\ x=-3 \pm \sqrt{3} \\ \\ \sqrt{3} \approx 1.7 \implies -5<-3-\sqrt{3}<-4, -2<-3+\sqrt{3}<-1[/tex]
Below, the two-way table is given for a class
of students.
Sophomore
Male
Female
Total
Freshmen
4
3
6
4
Juniors
2
6
Seniors Total
2
3
If a female student is selected at random, find the
probability that the student is a senior.
P(Senior | Female ) = [ ? ]%
Round to the nearest whole number.
Answer:
19%
Step-by-step explanation:
You want the probability a student is a senior, given that they are female.
TableThe table indicates that 3 +4 +6 +3 = 16 students are female. Of those, 3 are seniors. The desired probability is ...
P(senior | female) = N(senior & female)/N(senior) = 3/16 = 0.1875
The probability that a female student is a senior is about 19%.
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Convert meters to centimeters. 9.2 m = afers x 1. cm m) cm)