40 students (the total) represents 100%
To find what percentage represents 3 students (number of students with bedtime but no curfew), we can use the next proportion:
[tex]\frac{40\text{ students}}{3\text{ students}}=\frac{100\text{ \%}}{x\text{ \%}}[/tex]Solving for x,
[tex]\begin{gathered} 40\cdot x=100\cdot3 \\ x=\frac{300}{40} \\ x=7.5\text{ \%} \end{gathered}[/tex]Test scores are normally distributed with a mean of 86 and a standard devotion of 2.2 what percent scored between 83.8 and 92.6? What percent scored below 83.8?
Z- Score formula is:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z\text{ is the z-score (Standard score)} \\ X\text{ is the value to be standardized} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]Here, the mean is 86, while the standard deviation is 2.2
Percent between 83.8 and 92.6 is;
[tex]P(\frac{83.8-86}{2.2}The percent between 83.8 and 92.6 = 0.83999[tex]P(Z<-1)=\text{ 0.15866}[/tex]Percent score below 83.8 is 0.15866
Approximate the intervals where each function is increasing and decreasing.
1)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-1.2,2)\cup(1.2,\infty) \\ \text{Decreasing:} \\ D\colon(-\infty,-1.2)\cup(2,1.2) \end{gathered}[/tex]2)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-3,0.5) \\ \text{Decreasing:} \\ D\colon(-\infty,-3)\cup(-0.5,\infty) \end{gathered}[/tex]3)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(3,\infty) \\ \text{Decreasing:} \\ D\colon(-\infty,3) \end{gathered}[/tex]4)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-\infty,4) \\ \text{Decreasing:} \\ D\colon(4,\infty) \end{gathered}[/tex]How do I get my answer?
Answer:
[tex] \frac{2}{9 {d}^{14} } [/tex]
Step-by-step explanation:
[tex] \frac{ {4d}^{ - 5} }{18 {d}^{9} } = \frac{4}{18} \times \frac{ {d}^{ - 5} }{ {d}^{9} } = \frac{2}{9} {d}^{ - 14} = \frac{2}{ {9d}^{14} } [/tex]
triangle QRS is shown below using the information given determine the measure of r
Consider the circle x ^ 2 + y ^ 2 = 100 and the line x + 3y = 10 and their points of intersection (10, 0) and B = (- 8, 6) . Find coordinates for a point C on the circle that makes chords AB and AC have equal length . Be sure to justify your answer.
The equation of circle is given by,
[tex]x^2+y^2=100\text{ ---(1)}[/tex]The equation of line is given by,
[tex]x+3y=10\text{ ---(2)}[/tex]The points of intersection of the circle and line is,
A=(Xa, Ya)=(10, 0)
B=(Xb, Yb)=(-8, 6)
The length of chord AB can be calculated using distance formula as,
[tex]\begin{gathered} AB=\sqrt[]{(X_b-X_a)^2+(Y_b-Y_a)^2} \\ =\sqrt[]{(-8-10)^2+(6-0)^2} \\ =\sqrt[]{(-18)^2+6^2} \\ =\sqrt[]{324+36} \\ =\sqrt[]{360} \\ =6\sqrt[]{10} \end{gathered}[/tex]Let (Xc, Yc) be the coordinates of point C on the circle. Hence, using equation (1), we can write
[tex]X^2_c+Y^2_c=100\text{ ---(3)}[/tex]Using distance formula, the expression for the length of chord AC is given by,
[tex]AC=\sqrt[]{(X_c^{}-X_a)^2+(Y_c-Y_a)^2_{}}[/tex]Since (Xa, Ya)=(10, 0),
[tex]\begin{gathered} AC=\sqrt[]{(X^{}_c-10_{})^2+(Y_c-0_{})^2_{}} \\ AC=\sqrt[]{(X^{}_c-10_{})^2+Y^2_c} \end{gathered}[/tex]It is given that chords AB and AC have equal length. Hence, we can write
[tex]\begin{gathered} AB=AC \\ 6\sqrt[]{10}=\sqrt[]{(X^{}_c-10_{})^2+Y^2_c} \end{gathered}[/tex]Squaring both sides of above equation,
[tex]\begin{gathered} 360=(X^{}_c-10_{})^2+Y^2_c\text{ } \\ (X^{}_c-10_{})^2+Y^2_c=360\text{ ----(4)} \end{gathered}[/tex]Subtract equation (4) from (3) and solve for Xc.
[tex]\begin{gathered} (X^{}_c-10_{})^2-X^2_c=360-100 \\ X^2_c-2\times X_c\times10+100-X^2_c=260 \\ -20X_c=260-100 \\ -20X_c=160 \\ X_c=\frac{160}{-20} \\ X_c=-8 \end{gathered}[/tex]Put Xc=-8 in equation (3) to find Yc.
[tex]\begin{gathered} (-8)^2+Y^2_c=100 \\ 64+Y^2_c=100 \\ Y^2_c=100-64 \\ Y^2_c=36 \\ Y^{}_c=\pm6 \\ Y^{}_c=6\text{ or }Y_c=-6 \end{gathered}[/tex]So, the coordinates of point C can be (Xc, Yc)=(-8, 6) or (Xc, Yc)=(-8, -6).
Since (-8, 6) are the coordinates of point B, the coordinates of point C can be chosen as (-8, -6).
Therefore, the coordinates of point C is (-8, -6) if chords AB and AC have equal length.
One pump can empty a pool in 7 days, whereas a second pump can empty the pool in 14 days. How long will it take the two pumps, working together, to empty the pool? (Fractional answers are OK.)The first pump's rate is_____per day.The second pump's rate is____per day.The combined pumps rate is____per day.It will take the two pumps_____per day.
The first step is to define the daily rates of each pump
From the information given,
First pump can empty the pool in 7 days. This means that
Daily rate of first pump = 1/7
The first pump's rate is 1/7 per day
Second pump can empty the pool in 14 days. This means that
Daily rate of second pump = 1/14
The second pump's rate is 1/14 per day
Let t be the number of days it will take both pumps, working together to empty the pool. Thus,
combined daily rate of both pumps = 1/t
The rates are additive. It means that
1/7 + 1/14 = 1/t
Simplifying the left side, we have
3/14 = 1/t
The combined pumps rate is 3/14 per day
By taking reciprocal of both sides,
t = 14/3 = 4.67
It will take the two pumps 4.67 days to empty the pool together
how do I find the correct answer? (answers in the dropbox below)
A rhombus have 4 sides and angles
it first must be proven to have 4 sides, or 4 angles
thats a definition for Quadrilateral
then correct option is D
A statement of Chandler's biweekly earnings is given below. What is Chandler's gross pay?
SOLUTION:
Step 1:
In this question, we are asked to calculate Chandler's gross pay from the statement of bi-weekly earnings.
Step 2:
To get the Gross pay, we need to do the following:
[tex]\text{Gross pay - Total Deductions = Net Pay}[/tex]Now, we need to calculate Total Deductions:
[tex]\text{ \$ 105.00 + \$ 52.14 + \$ 10.62 + \$ 26. 15 = \$ 193.91}[/tex]Now, we have that the Net Pay = $ 780. 63
Then,
[tex]\begin{gathered} \text{Gross Pay - \$ 193. 91 = \$ 7}80.\text{ 63} \\ \text{Gross pay = \$ 780.63 + \$ 193.91} \\ \text{Gross Pay = \$ 974. 54} \end{gathered}[/tex]CONCLUSION:
Chandler's Gross Pay = $ 974. 54
200 lottery tickets are sold for $6 each. The person with the single winning ticket will get $71. What is the expected value for a ticket in this lottery?
Given:
200 lottery tickets are sold for $6 each.
The person with the single winning ticket will get $71.
So, The probability of winning = 1/200
The probability of losing =
[tex]undefined[/tex]
Answer: the expected value is. aroud 1-2
Step-by-step explanation:
What is the value of the expression below when z6?9z + 8
Hello!
Let's solve your expression:
[tex]9z+8[/tex]Let's replace where's z by 6, look:
[tex]\begin{gathered} (9\cdot z)+18 \\ (9\cdot6)+18 \\ 54+18 \\ =72 \end{gathered}[/tex]So the value of this expression when z=6 is 72.
the fraction 1-2 equals?
The given fraction is 1/2.
IF we divide, we have
[tex]\frac{1}{2}=0.5[/tex]Therefore, the answer is 0.5.what is the solution to the system 3x-y+5=02x+3y-4=0A. X= -1, Y= -2B. X= -1, Y= 2C. X= 2, Y= -1D. X= 2, Y= 1
To find the solution to the system of equation
we will use the elimination method
3x - y = - 5 ----------------------------(1)
2x + 3y = 4 -------------------------------(2)
We will eliminate y and solve for x
multiply equation (1) through by 3
9x - 3y = - 15 ------------------------------------(3)
add equation (2) and equation (3)
11x = -11
divide both-side of the equation by 11
x = -1
substitute x = -1 in equation (1) and solve for y
3x - y = - 5
3(-1) - y = -5
-3 - y = -5
add 3 to both-side of the equation
- y = -5 +3
-y = -2
multiply through byb -1
y = 2
Hence, the correct option is B
Find the principal which amounts to #5,000 at simple interestin 5 years at 2% per annum
To answer this we have to apply the simple interest formula:
I =P x r x t
Where:
I= interest
P= Principal
R= Interest rate ( in decimal form)
t = time (years)
Replacing with the values given:
Interest= I
Principal = ?
Interest rate = 2/100 =0.02
time= 5 years
I = P x 0.02 x 5
I= 0.1P
Amount= P+I
A = P+0.1P
5,000= P+0.1P
5,000= 1.1P
5,000/1.1 =P
4,545.45 =P
Open the most convenient method to graft the following line
You have the following expression:
3x + 2y = 12
the best method to graph the previous expression is by intercepts.
In this case, you make one of the variables zero and solve for the other one. Next, repeat the procedure wi
In shop, you make a table. The sides of the table measure 36" and 18". If the diagonal of the table measures 43", is the table "square"? (In construction, the term "square" just means the table has right angles at the corners.)
We are given the following information:
Table sides = 36 inches & 18 inches
Diagonal of table = 43 inches
We are to find out if the table is "square" (that is if the table follows the Pythagoras theorem). We will check this below:
[tex]\begin{gathered} \text{The Pythagoras Theorem is given by:} \\ c^2=a^2+b^2 \\ c=43in,b=36in,a=18in \\ \text{Substituting we have:} \\ 43^2=18^2+36^2 \\ 1849=324+1296 \\ 1849=1620 \\ \Rightarrow1849\ne1620 \\ \\ \therefore\text{ The table is not ''square''} \end{gathered}[/tex]Therefore, the table is not "square" (it does not have right angles at the corners)
Robin Sparkles invests $3,760 in a savingsaccount at her local bank which gives 1.8%simple annual interest. She also invests$2,400 in an online savings account whichgives 5.3% simple annual interest. After fiveyears, which one will have earned moreinterest, and how much more interest will ithave earned, to the nearest dollar?
The formula for determining simple interest is expressed as
I = PRT/100
where
I = interest
P = principal or amount invested
T = time in years
R = interest rate
Considering the amount invested in her local bank,
P = 3760
R = 1.8
T = 5
I = (3760 x 1.8 x 5)/100 = 338.4
Considering the amount invested in online savings,
P = 2400
R = 5.3
T = 5
I = (2400 x 5.3 x 5)/100 = 636
After 5 years, the investment in the online savings account earned more interest.
The difference in interest earned is
636 - 338.4 = $298 to the nearest dollar
It has earned $298 more than the local bank's interest
Which expression simplifies to 5. A. 27/3 - 14. B. 27/3+4. C. -27/3-4. D. -27/3+14
Which of the following is a valid application of the distributive property?
A. 5.2+3=5 (2+3)
B. 5 2+3=5 (2) +5. (3)
ONeither A nor B
OB only
O A only
O Both A and B
5 2+3=5 (2) +5. (3) is a valid application of the distributive property.
What is a distributive property?
According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given that,
A. 5.2+3=5 (2+3)
B. 5 2+3=5 (2) +5. (3)
Distributive property
a*(b+c) = a*b+a*c
In option A the RHS part is not correct.
In option B both part is correct.
5*(2+3)= 5*2+5*3
5*5 = 10+15
25 = 25
LHS = RHS
Hence, Option B is correct.
To learn more about distributive property from the given link:
https://brainly.com/question/2807928
#SPJ13
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!
Answer:
A. reflection over the y-axis
B. translation 3 units right
C. translation 4 down
D. reflection over the x-axis
Given the function [tex]y=(m^2-1)x^2+2(m-1)x+2[/tex] , find the values of parameter m for which the function is always positive.
Answer: [tex](-\infty, -1) \cup (1, \infty)[/tex]
Step-by-step explanation:
The function is always positive when it has a positive leading coefficient (since that means the graph will open up), and when the discriminant is negative (meaning the graph will never cross the x-axis).
Condition I. Leading coefficient is positive
[tex]m^2 -1 > 0 \implies m < -1 \text{ or } m > 1[/tex]
Condition II. Discriminant is negative
[tex](2(m-1))^2 -4(m^2 -1)(2) < 0\\\\4(m^2 -2m+1)-8(m^2 -1) < 0\\\\4m^2 -8m+4-8m^2 +8 < 0\\\\-4m^2 -8m+12 < 0\\\\m^2 +2m-3 > 0\\\\(m+3)(m-1) > 0\\\\m < -3 \text{ or } m > 1[/tex]
Taking the intersection of these intervals, we get [tex]m < -1[/tex] or [tex]m > 1[/tex].
I'll send in pictures of the question questions 2 goes with number 1
Since the equation is y=3/8x and x is equal to 44/3, we have
[tex]\begin{gathered} y=\frac{3}{8}\cdot\frac{44}{3}=\frac{132}{24} \\ \frac{132}{24}=\frac{66}{12}=\frac{33}{6}\text{ Simplifying} \\ \frac{33}{6}=5.5\text{ Dividing} \\ \text{Answer is: }y=5.5 \end{gathered}[/tex]ur answer as a polynomial in standard form.=f(x) = 5x + 1g(x) = x2 – 3x + 12=Find: (fog)(x)
(fog)(x) = 5x² - 15x + 61
Explanation:The given functions are:
f(x) = 5x + 1
g(x) = x² - 3x + 12
(fog)(x) = f(g(x))
This means that we are substituting g(x) into f(x)
(fog)(x) = 5(x² - 3x + 12) + 1
(fog)(x) = 5x² - 15x + 60 + 1
This can be further simplified as:
(fog)(x) = 5x² - 15x + 61
Identify the measurement that cannot be taken directly if you were constructing a two-
dimensional visual representation of the fish tank.
The measurement that cannot be taken directly in 2-D is depth
What do you mean by measurement?
Measurement is the quantification of an object's or event's properties for comparison with other objects or occurrences. Measurement, in other terms, is the act of establishing how large or little a physical amount is in comparison to a fundamental reference quantity of the same sort. The scope and use of measurement are context and discipline dependent. Measurements do not apply to nominal qualities of things or events in natural sciences and engineering, which is compatible with the recommendations of the International Bureau of Weights and Measures' International lexicon of metrology. However, measures in other domains, such as statistics and the social and behavioral sciences, can have numerous levels.
The measurement that cannot be taken directly in 2-D is depth
To know more about measurements, click on the link
https://brainly.com/question/27233632
#SPJ9
Use Descartes Rules of signs to complete the chart with possibilities for the nature of the roots of the following equations:A) x^3 - x^2 + 4x - 6 = 0B) x^5 - x^3 + x + 1 = 0
Given:
[tex]\begin{gathered} x^3-x^2+4x-6=0 \\ x^5-x^3+x+1 \end{gathered}[/tex]Required:
To determine the possibilities for the nature of the roots of the given equation.
Explanation:
(A)
Point-Slope Form: y + 2 = -7(x − 4)Rewrite the equation in slope-intercept form
Given the equation of a line in Point-Slope Form:
[tex]y+2=-7(x-4)[/tex]You need to rewrite it in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, you have to solve for "y":
1. Apply the Distributive Property on the right side of the equation. Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]Then:
[tex]y+2=(-7)(x)+(-7)(-4)[/tex][tex]y+2=-7x+28[/tex]2. Apply the Subtraction Property of Equality by subtracting 2 from both sides of the equation:
[tex]y+2-(2)=-7x+28-(2)[/tex][tex]y=-7x+26[/tex]Hence, the answer is:
[tex]y=-7x+26[/tex]Do you know how to solve? I got 3.99 for the mean (it was correct)For the sample standard deviation I got 1.1285 ( but it was wrong)
Explanation
Given the sample below, we are asked to find the mean and the standard deviation.
Part A
We can find the mean below using the formula
[tex]\begin{gathered} \text{Mean}=\frac{\sum ^{}_{}x}{n} \\ \text{where x is the sample value and n is the sample size} \end{gathered}[/tex]Therefore,
[tex]\text{Mean }=\frac{79.8}{20}=3.99[/tex]Answer =3.99
Part B
The standard deviation of the sample size can be found using the formula below;
[tex]\begin{gathered} S.D=\sqrt[]{\sum ^{}_{}\frac{(x-\bar{x})^2}{N-1}} \\ =\sqrt[]{\frac{20.938}{19}} \\ =\sqrt[]{1.102} \\ =1.05 \\ \end{gathered}[/tex]Answer: 1.05
Can you evaluate 3 + (a + 4)(8- b ) when a= 5 and b=6
The expression to evaluate is:
[tex]3+a+4\mleft(8-b\mright)[/tex]When
a = 5 and b = 6
We simply plug in the values of 5 and 6, into a and b respectivly. And do algebra to get our answer. The process is shown below:
[tex]\begin{gathered} 3+a+4\mleft(8-b\mright) \\ 3+5+4\mleft(8-6\mright) \\ 3+5+4(2) \\ 3+5+8 \\ 16 \end{gathered}[/tex]The answer is 16.
Use the parabola tool to graph the quadratic function f(1) = 2x^2+16x+30Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
vertex(-4,-2)
focus(-4,-15/8)
Axis of symmetry,x=-4
directrix, y=-17/8
x y
-6 6
-5 0
-4 -2
-3 0
-2 6
an athlete eats 46 g of protein per day while training. how much protein will she eat during 23 days of training?
ANSWER
1058 grams
EXPLANATION
Each day she eats 46 grams of protein. In 23 days of training, she will eat 23 times that amount,
[tex]46g\times23=1058g[/tex]Hence, in 23 days she will eat 1058 g of protein.
Jim baked 48 cookies with 4 scoops of flour. How many scoops of flour does Jim need in orderto bake 96 cookies? Assume the relationship is directly proportional.
Given:
Jim baked 48 cookies with 4 scoops of flour.
So, the unit rate will be = 48/4 = 12 cookies/scoop of flour
So, for 96 cookies, the number of scoops of flour will be =
96/12 = 8
So, the answer will be 8 scoops of flour
