There are 120 children at a school assembly. 15 are 3rd graders; 45 are 4th graders; and 60 are 5th graders. Each student has entered their name in a drawing for a prize.
What is the probability that the winner will be a 3rd grade student?
Answer:
1/8 for a third grader to win
Step-by-step explanation:
15/120=1/8
Write the equation in standard form for the circle passing through (12,0) centered at the origin
SOLUTION
From the question, we are told that the circle pass through (12, 0) and centered at origin. So this means to find the radius, the diagram below would be helpful
From the diagram above, we have that
\(\begin{gathered} r^2=x^2+y^2 \\ r^2=12^2+0^2 \\ r^2=144 \\ r=\sqrt{144} \\ r=12 \end{gathered}\)Equation of a circle is given as
\(\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ We\text{ are told that the center is at the origin, so} \\ (h,k)=(0,0) \\ equation\text{ becomes } \\ (x-0)^2+(y-0)^2=12^2 \\ x^2+y^2=12^2 \end{gathered}\)Hence the answer is
\(x^2+y^2=12^2\)
60% of a number is 90 what is the number?
Answer:
150
Step-by-step explanation:
60% of X = 90
or,60/100 × X = 90
or,3x/5 =90
or,X = 90×5 /3
or,X =150
Answer:
The number is 150
Step-by-step explanation:
Is means equals and of means multiply
60 % * N = 90
.60 N = 90
Divide each side by .6
N = 90/.6
N =150
Please see my question in the attachment, thanks
As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.
In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;
As x → -1⁻, f(x) → ∞.
Read more on vertical asymptotes and functions here: brainly.com/question/28184937
#SPJ1
June has 72 gallons of punch for a party. June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
If June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60 gallons
The bigger cooler is five times as large as the smaller cooler
Consider the capacity of smaller cooler as x
The capacity of bigger cooler=5x
June has 72 gallons of punch for a party
Then the linear equation will be
x+5x=72
6x=72
x=12
Then the capacity of bigger cooler=5x
=5×12
=60
Hence, if June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60 gallons
Learn more about linear equation here
brainly.com/question/11897796
#SPJ1
Write 3 1/2 cups as a multiplication expression using the unit, 1 cup, as a factor.
I ABSOLUTELY NEED HELP BY TOMORROW!!! I AM GIVING 100 POINTS
3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.
How to Write 3 1/2 cups as a multiplication expression using the unit, 1 cup, as a factor.To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:
3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup
Since there are 1 cup in each term, we can rewrite it as:
3 cups + (1/2) cup
Now, we can express each term as a multiplication expression:
3 cups = 3 * 1 cup = 3
(1/2) cup = (1/2) * 1 cup = 1/2
Putting it all together, the multiplication expression is:
3 * 1 cup + (1/2) * 1 cup = 3 + 1/2
Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.
Learn more about expression at https://brainly.com/question/1859113
#SPJ1
Angle θ is in standard position and ( 4 , 4 ) is a point on the terminal side of θ. What is the exact value of sec θ sec 0 in simplest form with a rational denominator?
Answer:
\(\sqrt{2}\)
Step-by-step explanation:
Angle θ is in standard position and (4,4) is a point on the terminal side of θ.
\(\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\$Using Pythagoras Theorem\\Hypotenuse^2=$Opposite^2$+Adjacent^2\\$Hypotenuse^2=4^2+4^2\\$Hypotenuse^2$=32\\Hypotenuse=\sqrt{32}=4\sqrt{2}\)
Now, secant is the inverse of cosine.
Therefore:
\(\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}\)
please help me quick
All the reasoning of the statement is given below.
CA ≅ CB, by the congruent triangles.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given:
CD bisects AB at D.
CD⊥AB
To prove: CA ≅ CB:
Statement 2:
AD ≅ BD
Reason 2:
Definition of segment bisector.
Statement 3:
CD ⊥ AB
Reason 3:
Given.
Statement 6:
CD ≅ CD.
Reason 6:
Reflexive property of congruence.
Statement 7:
ΔCAB ≅ ΔCBD
Reason 7:
Congruent by the criterion SAS.
Therefore, CA ≅ CB.
To learn more about the congruent;
https://brainly.com/question/12413243
#SPJ1
Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys?My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?
Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.
But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.
So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.
To know more about probability,
https://brainly.com/question/11234923
#SPJ4
What are the outputs of the function below?
-6, -3, 1, 5
-6, -3, 4, 6
-8, 2, 4, 6
-8, 2, 1, 5
Answer:
\(5 { \times 54}^{2} \)
To change a mixed number to an improper fraction, you do the following
W(d)+n
d
True or False.
True
False
Answer:
true
Step-by-step explanation:
Please help me ...............,..
Answer:
Angle A and H are Alternate exterior angles and they are congruent.
The first sequence rule is multiply by 3 starting from 5. The second sequence rule is add 9 starting from 18. What is the first number that appears in both sequences?
27
45
72
135
what is the answer
Considering the sequences given, the first number that appears in both sequences is given by: 45.
What numbers appear in the first sequence?The rule is multiply by 3 starting from 5, hence the numbers are:
(5, 15, 45, 135, ...).
What numbers appear in the second sequence?The rule is add 9 starting from 18, hence the numbers are:
(18, 27, 36, 45, ...).
45 is the first number that appeared in both sequences.
More can be learned about sequences at https://brainly.com/question/6561461
#SPJ1
7. The exam scores of MBA students are normally distributed with a mean of 950 and a standard deviation of 200. (Also explain all your answers using Graphical work)
a) if your score was 1390 what percentage of students have scored more than you ?
b) What are the minimum and the maximum values of the middle 87.4% of the scores?
c) If there were 165 students who scored above 1432. How many students took the exam?
The percentage of students that have scored more than you is 1.39%
How to illustrate the probability?a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).
Now z= (1390-950)/200
z= 2.2
P(Z<2.2) = 0.9861
So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139
= 1.39 %
Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200
Then % of students between scores of 1100 and 1200 = P2 - P1
Z (X=1100) =0.75 and Z (X=1200) = 1.25
P1 = P(X<1100)= P (Z< 0.75) =0.7734
P2 = P(X<1200)= P (Z< 1.25) =0.8944
Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%
Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.
z value (for P(X<x)= .063) = (-1.53)
But Z= (x-u)/ \sigma from here calculating x, x=644
The minimum value of the middle 87.4% score is 644
The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.
P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.
Z value (for P(X<x)= 1.53
But Z= (x-u)/ \sigma from here calculating x, x=1256
The maximum value of the middle 87.4% score is 1256
Z value for (X=1432)= 2.41
P(Z<2.41) =0.9920
It means that 99.2 % of scores are less than 1432
So only 0.8% of scores are higher than 1432
but , 0.8% = 165
So 100% = 20625
20625 students took SAT
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ1
The drama teacher decreased the length of a play from 90 minutes to 60 minutes. What was the percent decrease in the length of the play?
Please help I need this for a test asapppp and pleased include the solving for this question I need to submit the work
Answer:
It was a 33% decrease
Step-by-step explanation:
90 minutes - 60 minutes = 30 minutes
30/90= .333333333333
The Graduate Management Admission Test (GMAT) is taken by individuals interested in pursuing graduate management education. GMAT scores are used as part of the admissions process for more than 6100 graduate management programs worldwide. The mean sore for all test‑takers is 550 with a standard deviation of 120. A researcher in the Philippines is concerned about the performance of undergraduates in the Philippines on the GMAT. She believes that the mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 550. She has a random sample of 250 college seniors in the Philippines interested in pursuing graduate management education who plan to take the GMAT. Suppose we know that GMAT scores are Normally distributed with standard deviation σ=120. The null and alternative hypotheses are H0:µ=550 versus Ha:µ<550.
Required:
State the null and alternative hypotheses for the study of the performance on the GMAT of college seniors in the Philippines.
Answer:
H₀: μ = 550 vs. Hₐ: μ < 550.
Step-by-step explanation:
A researcher believes that the mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 550.
The mean sore for all test‑takers is μ = 550 with a standard deviation of σ = 120.
A random sample of n = 250 college seniors in the Philippines interested in pursuing graduate management education who plan to take the GMAT were selected.
The null and alternative hypotheses for the study of the performance on the GMAT of college seniors in the Philippines is as follows:
H₀: The mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will not be less than 550, i.e. μ = 550.
Hₐ: The mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 550, i.e. μ < 550.
write the answer in a slope intercept form Y=Mx + b with all fractions written in lowest terms
Recall that two lines are perpendicular if the product of their slopes is equal to -1.
Taking the given equation to its slope-intercept form we get:
\(\begin{gathered} \frac{3y}{3}=\frac{x}{3}+\frac{4}{3}, \\ y=\frac{x}{3}+\frac{4}{3}\text{.} \end{gathered}\)Therefore the slope of the given line is 1/3, therefore, the slope of a perpendicular line to the given line is:
\(-\frac{1}{\frac{1}{3}}=-3.\)Now we will use the following slope-point formula for the equation of a line:
\(y-y_1=s(x-x_1)\text{.}\)Substituting s=-3 and (x₁,y₁)=(-6,8) we get:
\(y-8=-3(x-(-6))\text{.}\)Simplifying the above equation we get:
\(\begin{gathered} y-8=-3(x+6), \\ y-8=-3x-18. \end{gathered}\)Adding 8 to the above equation we get:
\(\begin{gathered} y-8+8=-3x-18+8, \\ y=-3x-10. \end{gathered}\)Answer:
\(y=-3x-10.\)evaluate the expression 3 to the third power multiplied by 12-2 divided by 2 iready
what is the radius for a circles whose equation is x2+y2=36
Answer: R= 6
Step-by-step explanation:
(x−h)2+(y−k)2=r2
(1 1 6 − 7 18 )÷2.8 0.5+ 1 18
Step-by-step explanation:
(116-718) /(2.805+118) [as, there cannot be two decimals in one numbers
=-602/120.805
=0.498
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
Read more about tangent lines at
https://brainly.com/question/21595470
#SPJ1
Use the geometric mean (altitude) theorem. What is the value of m?
Answer:4
Step-by-step explanation:
Answer:
Correct answer is c
Step-by-step explanation:
just took the test
In an experimental study
a. 1 variable is measured and 2 groups are compared
b. 2 variables are measured and 2 groups are compared
c. 1 variable is measured and there is only 1 group of participants
d. 2 variables are measured and there is only 1 group of participants
Therefore , the solution of the given problem of variable comes out to be Two groups are contrasted while 1 variable is recorded.
What is variable ?A trait that can be measured and have different values is called a variable. A few instances of variables include height, age, salary, birthplace equation ,province, academic standing, and type of residence.
Here,
A. Two groups are contrasted while 1 variable is recorded.
In an experiment conducted, the researcher controls for unrelated factors while varying a different variables and observing the impact on a dependent variable.
In most studies, there are at least 2 categories: a control groups that is given the experimental modification, and a comparison group that is not. The impact of the change is then assessed by comparing the two groups.
As a result, choice A an is the right response.
To know more about variable , visit
brainly.com/question/29583350
#SPJ4
The sum of three consecutive intgers is 72 find the smallest integer
Step-by-step explanation: 23 is the answer
23+24+25=72
Consider the following function. f(x) = 3x − e x i. Plot the graph of the function f(x) in R and identify the interval that the first positive root lies. Write the command(s) that you use and the result(s).
The interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).
How to find the interval of a function that cannot be solved for x analytically
In this question we have an expression that combines polynomic and exponential expression, whose variable x cannot be cleared by analytical approaches, but by numerical and graphical methods. Herein we decide to find the interval by graphical methods, using a graphing tool:
First, write the function in explicit form (f(x) = 3 · x - eˣ). Second, find the two points such that the function goes through the x-axis (horizontal axis). Third, define the set of possible x-values by interval notation such that y > 0.
Then, the points of the function that are on the x-axis are (x₁, y₁) = (0.6191, 0) and (x₂, y₂) = (1.5121, 0). Then, the interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).
To learn more on functions: https://brainly.com/question/12431044
#SPJ1
please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
Applying the tangent and the circle theorems, we have:
22. x ≈ 9.4; 23. Perimeter of triangle GHI = 168 units
24. m<NSR = 110°; 25. x = 10
How to Find the Missing Measures Using Circle and Tangent Theorems?22. Based on the tangent theorem, the triangle is a right triangle since the line is tangent to the radius of the circle. Therefore, based on the Pythagorean theorem, we have:
x = √[(7.4 + 4.6)² - 7.4²]
x ≈ 9.4
23. JH and HK are tangents, therefore they are equal. Thus:
7x + 4 = 13x - 20
7x - 13x = -4 - 20
-6x = -24
x = 4
Perimeter = GI + GJ + JH + HK + KI
GI = 52
HK = JH = 7x + 4 = 7(4) + 4 = 32
KI = 15
GJ = 52 - 15 = 37
Perimeter of triangle GHI = 52 + 37 + 32 + 32 + 15 = 168 units
24. Based on the angle of intersecting chords theorem, we have:
m<NSR = 1/2(170 + 50)
m<NSR = 110°
25. Based on the inscribed angle theorem, we have:
2(4x - 5) + 290 = 360
Solve for x:
8x - 10 + 290 = 360
8x = 360 - 280
8x = 80
x = 10
Learn more about the tangent theorems on:
https://brainly.com/question/28039126
#SPJ1
What is the y-intercept of the line describe by the equation below? Y=5x-22
Answer:
The y intercept is (0,-22)
Step-by-step explanation:
The y intercept is the value when x =0
Y=5x-22
y = 5*0 -22
y = -22
The y intercept is (0,-22)
problem 4.106 knowing that the allowable stress in section abd is 80 mpa, determine the largest force p that can be applied to the bracket shown
The largest force p that can be applied to the bracket shown - P = 80 MPa × (b × h).
Largest force P that can be applied to the bracket, we need to consider the allowable stress in section ABD, which is given as 80 MPa.
Step 1: Identify the relevant variables
- Allowable stress in section ABD: 80 MPa
Step 2: Determine the cross-sectional area of section ABD
- We need the dimensions of section ABD to calculate the area.
Let's assume the width (b) and height (h) are given.
- Cross-sectional area of section ABD = b × h
Step 3: Apply the stress formula
- Stress = Force / Area
- Allowable stress in section ABD = Force P / Area of section ABD
Step 4: Solve for the largest force P
- 80 MPa = P / (b × h)
- P = 80 MPa × (b × h)
Now that we have a formula for the largest force P, you can plug in the specific dimensions of section ABD (width and height) to find the exact value of P.
For similar question on dimensions.
https://brainly.com/question/11214914
#SPJ11
HELP ME!!!!
ZEARN!!!!!!!!!
A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.
Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.
Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.
Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of
To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).
First, let's convert the fractions 1/5 and 2/3 to fifteenths:
\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)
\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)
Now we can rewrite the expression using the common denominator:
\(3 + \frac{3}{15}+\frac{10}{15}\)
PlZ help pleased I need an answer now
Answer:
1/12
Step-by-step explanation: