The solo plans Debra offers her clients are plan A and plan B. Each client can only do one plan .
According to the question the plan only ran on wednesday and thursday.
Wednesday = plan A has 5 client and plan B has 3 clients.
Thursday = plan A has 7 client and plan B has 9 clients.
On wednesday she trained her client for 6 hours.
On thursday she trained her client for 12 hours.
let
x = hour of plan A workout for each client
y = hour of plan B workout for each client
[tex]\begin{gathered} 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}\mathrm{}(i) \\ 7x\text{ + 9y = 12}\ldots\ldots\ldots\text{.(2)} \\ 3y\text{ = 6 - 5x} \\ y\text{ = }\frac{6}{3}\text{ - }\frac{5}{3}x \\ y\text{ = 2 - }\frac{5}{3}x \\ 7x\text{ + 9(2 - }\frac{5}{3}x\text{) = 12} \\ 7x\text{ + 18 - }\frac{45}{3}x\text{ = 12} \\ 7x\text{ + 18 - }15x\text{ = 12} \\ -8x\text{ = 12 - 18} \\ -8x\text{ = - 6} \\ x\text{ = }\frac{6}{8} \\ x\text{ = }\frac{3}{4} \\ 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}(i) \\ 5(\frac{3}{4})\text{ + 3y = 6} \\ \frac{15}{4}\text{ + 3y = 6} \\ 3y\text{ = 6 - }\frac{15}{4} \\ 3y\text{ = }\frac{24-15}{4} \\ 3y\text{ = }\frac{9}{4} \\ y\text{ = }\frac{9}{4}\text{ }\times\text{ }\frac{1}{3} \\ y\text{ = }\frac{9}{12} \\ y\text{ = }\frac{3}{4} \end{gathered}[/tex]on wednesday plan A lasted for 5 * 3/4 = 15/4 hrs and plan B lasted for 3 * 3/4 = 9/4 hrs
On thursday plan A lasted for 7* 3/4 = 21/4 hrs and plan B lasted for 9 * 3/4 = 27/4 hrs
Each of the work out lasted for 3/4 hrs = 0.75 hrs
an 8-foot ladder leaning against a wall makes an angle of elevation of 70 degrees with the ground how far up the wall is the ladder to the nearest Foot
The length of the ladder is L = 8 foot.
The angle of ladder with ground is 70 degree.
The ladder lean on the wall can be expressed as,
Determine height on the wall to which ladder is up on the wall.
[tex]\begin{gathered} \sin 70=\frac{h}{8} \\ h=0.9397\cdot8 \\ =7.51 \\ \approx8 \end{gathered}[/tex]So up the wall is the ladder is 8 foot.
Carolina wants to find out how many different ways can she arrange the apps on her Iphone on the first row. The first row has space for 4 apps, and she has 12 apps to choose from
ANSWER
495 ways
EXPLANATION
Carolina has 12 apps to choose from and she only has space for 4 apps.
To find out how many ways she can do it, we will need to use combination.
That is:
[tex]^{12}C_4[/tex]Note: we use combination because the order of the apps is not a factor
So, we have that:
[tex]\begin{gathered} ^{12}C_4\text{ = }\frac{12!}{(12\text{ - 4)! 4!}}\text{ = }\frac{12!}{8!\text{ 4!}} \\ =\text{ 495 ways} \end{gathered}[/tex]She can arrange them in 495 ways.
Solve p3 = −512.
p = ±8
p = −8
p = ±23
p = −23
Answer:
B. p = −8
Step-by-step explanation:
Hope this helps you on whatever your doing. :))
if its incorrect, please let me know.
The solution is, the value is, p = −8.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
p^3 = −512.
so, we know, p^3 = p*p*p
and, 512 = 8*8*8
now, we get,
p^3 = - 8*8*8
so, solving we get,
p = -8
Hence, The solution is, the value is, p = −8.
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Find the x-intercept and y-intercept of the line.
5x-9y=-12
The x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
What is termed as the x and y intercepts?An intercept is a y-axis point that the slope of a line passes. It is the y-coordinate of the a point on the y-axis where a straight line or even a curve intersects. This is represented by the equation for a straight line, y = mx+c, where m is the slope and c seems to be the y-intercept. There are two types of intercepts: x-intercept and y-intercept.For the given question,
The equation of the line is 5x-9y=-12.
For the x intercept, Put y = 0.
5x-9×0=-12.
x = 12/5
x intercept = (12/5, 0)
For y intercept, put x = 0.
5×0-9y=-12
y = -12/9
y = -4/3
y intercept = (0, -4/3)
Thus, the x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
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Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared
Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared
we have that
F=m*a
we have
m=30 kg
F=60 N
substitute in the formula
60=30*a
solve for a
a=60/30
a=2 m/s^2
therefore
the answer is 2 meters per second squaredSolve the quadratic equation using any algebraic method.
X²-11x+30=0
Answer:
5, 6
Step-by-step explanation:
using Vieta's formulas:
x₁ + x₂ = 11
x₁*x₂ = 30
x₁ = 5
x₂ = 6
What interest will be earned if $11,000.00 is invested for 3 years at 11% compounded semi-annual?You would earn $ in interest. (Round to 2 decimal places.)
Answer:
$4,167.27
Explanation:
The amount, A(n) in an account for a Principal invested at compound interest is calculated using the formula:
[tex]\begin{gathered} A(n)=P(1+\frac{r}{k})^{nk}\text{ }where=\begin{cases}P=Prin\text{cipal} \\ r=\text{Annual Interest Rate} \\ k=\text{Compounding Period}\end{cases} \\ n=nu\text{mber of years} \end{gathered}[/tex]In the given problem:
• P = $11,000.00
,• r=11% = 0.11
,• n= 3 years
,• k=2 (semi-annual)
Substitute these into the formula:
[tex]\begin{gathered} A(n)=11,000(1+\frac{0.11}{2})^{2\times3} \\ =11,000(1+0.055)^6 \\ =11,000(1.055)^6 \\ =\$15,167.27 \end{gathered}[/tex]Next, we find the interest earned.
[tex]\begin{gathered} \text{Interest}=\text{Amount}-\text{Prncipal} \\ =15167.27-11000 \\ =\$4,167.27 \end{gathered}[/tex]You would earn $4,167.27 in interest (rounded to 2 decimal places).
Enter the correct answeach column.5. Bellatrix Lestrange keeps her money in GringottsWizarding Bank. She decided to take $100,000out of her vault and split it among three differentaccounts. She placed part in a savings accountpaying 3% per year, twice as much in Wizard bondspaying 5.5%, and the rest in a mutual fund thatreturned 4%. Her income from these investmentsafter one year was $4,480. How much did Bellatrixplace in each account?11223334.44HOW MUCH DID BELLATRIX PLACE IN THEMUTUAL FUND?556670N (0088
Assum,e that she put x in the account of 3%
So in wizard bonds, she put twice so it is 2x
The rest in the account of 4%
The rest is 100,000 - x - 2x = 100,000 - 3x
The rule of the investment is :
[tex]I=\text{prt}[/tex]I is the interest, P is the money she invested, r is the rate and t is the time
We will make equation for each account
[tex]\begin{gathered} I_1=x(\frac{3}{100})(1)=0.03x_{} \\ I_2=(2x)(\frac{5.5}{100})(1)=0.11x \end{gathered}[/tex][tex]I_3=(100,000-3x)(\frac{4}{100})(1)=4000-0.12x[/tex]The sum of the interest is 4,480, so add them and equate the sum by 4,480 to find the value of x
0.03x + 0.11x + 4000 - 0.12x = 4,480
Add like terms in the left side
0.02x + 4000 = 4,480
Subtract 4000 from both sides
0.02x + 4000 - 4000 = 4,480 - 4000
0.02x = 480
Divide both sides by 0.02
x = 24,000
The value in the mutual fund is 100,000 - 3x, so substitute s by 24,000
The mutual fund = 100,000 - 3(24,000) = 100,000 - 72,000 = 28,000
The mutual fund = $28,000
Help 40 points please (show ur work)
The trail map having a trail length of 7 1/2 in has an actual distance of 3 miles
The amount Kepler paid for the tool not including tax is $120
34% of 850 is 289
How to find the actual length of if 7 1/2 inch in drawingGiven that
5 in ⇒ 2 miles
7 1/2 in ⇒ ?
The question is about scaling a map, the scale is 2miles is represented by 5 inches. This information is used to calculate the actual length when a measure of 7 1/2 inch is taken from the drawing
5 * ? = 7 1/2 * 2
? = 7 1/2 * 2 / 5
? = 3 miles
Hence 7 1/2 inch in the drawing represent an actual distance of 3 miles
How to find the amount Mr Kepler paid for the tool, not including taxGiven that:
with a discount of 40% off the regular price
The regular price was $200
A discount of 40% is given to Mr Kepler. Discount represents amount less the total amount. At a 40% discount Mr Kepler paid 60%
40% = 0.4
40% discount = 1 - 0.4 = 0.6 (equivalent to 60%)
The amount Kepler paid
= 0.6 * 200
= $120
Knowledge of percentage is used here and the amount Mr Kepler paid is $120 not including tax
34% of 850
The statement 34% of 850 means 34 divided by 100 multiplied by 850. The division by hundred takes care of the percent, then "of" means multiplication
34% = 0.34
0.34 * 850 = 289
Hence, we conclude that the concept of percentage and division is used to solve 34% of 850 to get 289
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New Orleans is 2 feet below sea level. Salton City has an elevation that is lower than New Orleans. What is a possible elevation, in feet, of Salton City?
Answer:
-4 feet (4 feet below sea level)
Salton City's potential elevation is determined to be 3 feet below sea level by using a number line and the elevation of New Orleans, which is 2 feet below sea level.
What is meant by number line?A number line is a mathematical visual representation of numbers on a straight line. On a number line, the numbers are arranged in order at regular intervals along its length.It often appears horizontally and could extend indefinitely in either direction. A number line is a horizontal line with consistently spaced numerical increments.How the number on the line can be answered depends on the numbers that are present. Given, the elevation indicates that New Orleans is 2 feet below (lower than) sea level.The elevation of Salton City is lower than that of New Orleans. Required; potential rise of Salton CitySalton City's elevation can be calculated using the information below on a number line: We have;& |t; |-3 |-2 |0 > if SL stands for sea level, N for New Orleans, and S for Salton City. On the number line above, a S. N. SLA point to the right of the -2 mark denotes an elevation that is higher than New Orleans, and a point to the left of -2 denotes an elevation that is lower than New Orleans.Therefore,
Salton City should be located to the left of -2, which is a point, at a distance of x -2 feet.
Salton City's elevation, which is determined by the set x -2 feet, is less than 2 feet above sea level.
Since -3 feet is less than -2 feet, Salton City's elevation might be as low as x = 3 feet below sea level, which is less than () 2 feet below sea level.
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I need help A. -3 B. 3 C. -2D. -10
The average rate of change can be calculated as the division of the output of the function on the interest interval by the size of the interval. To do that we have to find the value of "y" at the end of the interval and subtract it by the value of "y" at the beggining. This is shown as an expression below:
[tex]\text{average rate of change=}\frac{y_{\text{ final}}-y_{\text{ initial}}}{x_{\text{ final}}-x_{\text{ initial}}}[/tex]For this function the values of x are:
[tex]\begin{gathered} x_{\text{ initial}}=0 \\ x_{\text{ initial}}=3 \end{gathered}[/tex]The values for y are:
[tex]\begin{gathered} y_{\text{ initial}}=10 \\ y_{\text{ final}}=1 \end{gathered}[/tex]Using these values we can calculate the average rate of change:
[tex]\text{average rate of change=}\frac{1-10}{3-0}=\frac{-9}{3}=-3[/tex]The average rate of change for this function is approximately -3 for the given interval. The correct answer is A.
STATEMENTREASON1. DBC - RST1. Given2. ZABC - ZDBC+ ABD2. Angle addition therom3.3. Ifa=b+cand c>0,thena > b4. ABC > RST4. SubstitutionWhich of the following statements would complete the proof in line 3?O ZABC> ZABDO LABC> DBCO ZDBC> ZABD
Answer
Option B is correct.
Angle ABC > Angle DBC
Explanation
Since it's been proven that
Angle ABC = Angle ABD + Angle DBC
Since Angle ABD > 0,
Angle ABC > Angle DBC is the part that completes the proof that
Angle ABC > Angle RST
Hope this Helps!!!
Find the perimeter and area for each figure.
10.
6 in.
P =
A =
3 in.
6 in.
2 in.
5 in.
11.
7 in.
P =
A =
6 in.
(each side is 6 in.)
The perimeter and the area of a rectangle of dimensions 15 cm and 8 cm is given as follows:
Perimeter: 46 cm.Area: 120 cm².What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter are given, respectively, by these following equations:
Area: A = lw.Perimeter: = 2(l + w).In the context of this problem, the dimensions are given/supposed as follows:
l = 15 cm, w = 8 cm.
Applying the rule, the area, in cm², as the variables are multiplied, is given as follows:
A = 15 x 8 = 120 cm².
The perimeter, in cm, as the measures are added, is given as follows:
P = 2 x (15 + 8) = 2 x 23 = 46 cm.
Missing informationThis problem is incomplete and could not be found on any search engine, hence we suppose that it is a rectangle of dimensions 15 cm and 8 cm.
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The triangles formed by two ladders leaning against a wall are similar. How long is the shorter ladder?
To solve this problem we must use proportions
[tex]\begin{gathered} \text{ }\frac{x}{8}\text{ = }\frac{42}{24} \\ \text{ x = }\frac{8\text{ x 42}}{24} \\ \text{ x = }\frac{336}{24} \\ \text{ x = 14} \end{gathered}[/tex]The length of the shortest ladder is 14.
letter B is the correct answer.
Not sure how to approach this question whether to use the factor theorem or to use the synthetic division
EXPLANATION
If x+2 is a factor, we need to equal the factor to zero, isolate x and substitute the value into the function:
[tex]x+2=0\text{ --> x=-2}[/tex]Plugging in x=-2 into the function:
[tex]P(-2)=(-2)^4-2(-2)^2+3m(-2)+64[/tex]Computing the powers:
[tex]P(-2)=16-2*4-6m+64[/tex]Multiplying numbers:
[tex]P(-2)=16-8-6m+64[/tex]Adding numbers:
[tex]P(-2)=72-6m=0[/tex]Adding +6m to both sides:
[tex]72=6m[/tex]Dividing both sides by 6:
[tex]\frac{72}{6}=m[/tex]Simplifying:
[tex]12=m[/tex]In conclusion, the value of m is 12
If the correlation coefficient r is equal to 0.755, find the coefficient of determination and the coefficient of nondetermination.Question 10 options: The coefficient of determination is 0.430 and the coefficient of nondetermination is 0.570 The coefficient of determination is 0.869 and the coefficient of nondetermination is 0.131 The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430 The coefficient of determination is 0.131 and the coefficient of nondetermination is 0.869
Given the word problem, we can deduce the following information:
The correlation coefficient r is equal to 0.755.
To determine the coefficient of determination and the coefficient of nondetermination, we use the formulas below:
[tex]Coefficient\text{ }of\text{ }Determination=r^2[/tex][tex]Coefficient\text{ }of\text{ N}ondetermination=1-r^2[/tex]Now, we first plug in r=0.755 to get the coefficient of determination:
[tex]Coeff\imaginaryI c\imaginaryI ent\text{ o}f\text{ D}eterm\imaginaryI nat\imaginaryI on=r^2=(0.755)^2=0.57[/tex]Next, we get the coefficient of nondetermination:
[tex]\begin{gathered} Coeff\imaginaryI c\imaginaryI ent\text{ o}f\text{ N}ondeterm\imaginaryI nat\imaginaryI on=1-r^2=1-0.57=0.43 \\ \end{gathered}[/tex]Therefore, the answer is:
The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430
25. Brett wants to sound proof his studio, which is in the shape of a box. He will cover all 4 walls, the floor and the ceiling with the sound proof padding material. If the floor's dimensions are 15ft x 20ft and the height of the room is 10ft tall, how much will Brett spend on padding that costs $2.50 per square foot?
We have that the floor's dimensions are 15ft x 20ft and the height of the room is 10ft tall. This is
if we extended it we would have:
We want to find how many square foot Brett needs to cover. We just find the area of each side of the studio.
We find it just by multiplying both of its sides (they all are rectangles):
Wall 1
area = 10ft x 15 ft
area = 150 ft²
Wall 2
area = 10ft x 20 ft
area = 200 ft²
Wall 3
area = 10ft x 15 ft
area = 150 ft²
Wall 4
area = 10ft x 20 ft
area = 200 ft²
Floor
area = 15ft x 20 ft
area = 300 ft²
Ceiling
area = 15ft x 20 ft
area = 300 ft²
A condensed way....
TOTAL AREA
Now, we add all the areas found, this will be the total area Brett must cover:
Wall 1 + wall 2 + Wall 3 + Wall 4 + ceiling + floor = total area
150 ft² + 200 ft² + 150 ft² + 200 ft² + 300 ft² + 300 ft² = 1300 ft²
COST
Since the padding costs $2.50 per square foot, and there are 1300 square foot to cover. Brett will spend
$2.50 x 1300 = $3250
Answer: Brett spend on padding $3250
How do you solve this?
Answer: I thought you already asked this question.
Step-by-step explanation:
NO LINKS!! Please help me with this probability question
Answer: B) 46.67% approximately
=================================================
Work Shown:
A = it will be cloudy tomorrow
B = it will be rainy tomorrow
P(A) = 0.30
P(B) = 0.15
P(A and B) = 0.14
Apply the conditional probability formula.
P(B given A) = P(A and B)/P(A)
P(B given A) = 0.14/0.30
P(B given A) = 0.4667 approximately
P(B given A) = 46.67% approximately
Answer:
b) About 46.67%.
Step-by-step explanation:
Let event A = being cloudy.
Let even B = being rainy.
Given probabilities:
Probability of being cloudy = 30%.Probability of being rainy = 15%.Probability of being cloudy and rainy = 14%.Therefore:
P(A) = 0.3P(B) = 0.15P(A ∩ B) = 0.14Conditional Probability Formula
[tex]\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}[/tex]
The probability of being rainy given it is cloudy = P(B | A).
Substitute the given values into the formula:
[tex]\implies \sf P(B|A)=\dfrac{0.14}{0.3}=0.46666...=46.67\%\;(2\;d.p.)[/tex]
Therefore, the probability of it being rainy if you know it will be cloudy is about 46.67%.
Look at this graph: у 10 9 8 7 6 5 3 2 1 0 1 2 3 4 5 6 7 8 9 10 What is the slope?
EXPLANATION
As we can see in the graph, we can calculate the slope with the following equation:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Let's consider any ordered pair, as (x1,y1)=(1,7) and (x2,y2)=(5,8), replacing this in the equation will give us:
[tex]\text{Slope}=\frac{(8-7)_{}}{(5-1)}=\frac{1}{4}[/tex]Answer: the slope is equal to 1/4.
I have 4 questions I need help with This is first question number 2
We have the next function that models the Australian GDP since 1960 :
[tex]G(i)=1806x(1.037)^t[/tex]Where t is the number of years since 1960.
a)If we are in the year 1960, it means t=0
Therefore:
[tex]G(t)=1806x(1.037)^1[/tex][tex]G(0)=1806x(1.037)^0[/tex][tex]G(0)=1806[/tex]b)Now, we need to find the Australia capita in 1963.
This means t=3
Therefore:
[tex]G(t)=1806x(1.037)^t[/tex][tex]G(3)=1806x(1.037)^3[/tex][tex]G(3)=2013.974721[/tex]c) We need to find when the function is equal to 100,000.
Therefore we equal the function G(t)=100,000.
Then:
[tex]1806x(1.037)^t=1000000[/tex]Solve for t:
Divide both sides by 1806:
[tex]\frac{1806x(1.037)^t}{1806}=\frac{100000}{1806}[/tex][tex](1.037)^t=\frac{50000}{903}[/tex]Add Ln for each side:
[tex]\ln (1.037)^t=in(\frac{50000}{903})[/tex][tex]t\ln (1.037)=in(\frac{50000}{903})[/tex]Then:
[tex]t=\frac{in(\frac{50000}{903})}{\ln (1.037)}[/tex][tex]t=110.48286[/tex]Rounded to the nearest year:
[tex]t=110[/tex]Therefore: 1960 +110 = 2070
On 2070 the Austranlian GDP reaches 100,000 USD
I don’t understand how to explain this question
The segments cannot be set equal since the constant terms 15 is greater than two. The variable x remains like a constant term in both sides of the point B. we say that 15x > 2x
What is inequality?In mathematics, the signs used inequality calculations are
greater thanless thangreater than or equal toless than or equal toUsing the picture as evidence the mark represented by B is not the midpoint hence the equality sign will not be used here. The sign to be used is the inequality sign.
In addition, the constants 15 and 2 shows that 15 is greater than 2. and there is no other addition to the variable x to help check the effect of the greatness of 15
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What is the value of 10 1
10
10x1=10
Hope this helps
The rate of growth of a particular population is given by dP/dt=50t^2-100t^3/2, where P is population size and t is fine and years. Assume the initial population is 25,000. a) determine the population function, P(t)b) estimate to the nearest year how long it will take for the population to reach 50,000
SOLUTION
Step1: write out the giving equation
[tex]\frac{dp}{dt}=50t^2-100t^{\frac{3}{2}}[/tex]Step2: Integrate both sides of the equation above
[tex]\int \frac{dp}{dt}=\int 50t^2dt-\int 100t^{\frac{3}{2}}dt[/tex]Then simplify by integrating both sides
[tex]p(t)=\frac{50t^{2+1}}{2+1}-\frac{100t^{\frac{3}{2}+1}}{\frac{3}{2}+1}+c[/tex][tex]p(t)=\frac{50}{3}t^3-40t^{\frac{5}{2}}+c[/tex]since the initial value is 25,000, then
the Population function is
[tex]\begin{gathered} p(t)=\frac{50}{3}t^3-40t^{\frac{5}{2}}+25000\ldots\ldots..\ldots\text{.. is the population function} \\ \text{where t=time in years} \end{gathered}[/tex]b). For the population to reach 50,000 the time will be
[tex]\begin{gathered} 50000=\frac{50}{3}t^3-40t^{\frac{5}{2}}+2500 \\ 50000-25000=\frac{50}{3}t^3-40t^{\frac{5}{2}} \\ 25000=\frac{50}{3}t^3-40t^{\frac{5}{2}} \\ \text{Then} \\ \frac{50}{3}t^3-40t^{\frac{5}{2}}-25000=0 \\ \end{gathered}[/tex]Multiply the equation by 3, we have
[tex]\begin{gathered} 50t^3-120t^{\frac{5}{2}}-75000=0 \\ \end{gathered}[/tex]To solve this we rewrite the function as
[tex]14400t^5=\mleft(-50t^3+75000\mright)^2[/tex]The value of t becomes
[tex]\begin{gathered} t\approx\: 15.628,\: t\approx\: 9.443 \\ t=15.625\text{ satisfy the equation above } \end{gathered}[/tex]Then it will take approximately
[tex]16\text{years}[/tex]
PLEASEEEE HELPPPPAdd. 3+(-7)=
The problem is asking as to perform an addition of signed numbers.
The firs one to add is 3 and the other one is -7.
We can understand the meaning of this type of addition by using the number line forst, and then have a very simple "short cut" every time we fce problems like this.
The number line approach:
locate yourself at the mark "3" on the number line, and then add the number "-7" whichmeans go to the left (as the negative indicates) 7 units. You will see that you move through zero, and then land on the number "-4".
Mr. Herman had $125, and Mr.Chandra had $80. After each of them had paid for a concert ticket, Mr. Herman had 6 times as much money as Mr. Chandra. how much money did Mr. Chandra have left?
We have
Let x = cost of the ticket
After paying for the tickets, Mr. Herman had 125 - x
and Mr Chandra had 80 - x
Then, the equation is:
[tex]125-x=6(80-x)[/tex]So, solve for x:
[tex]\begin{gathered} 125-x=480-6x \\ 125-x+6x=480-6x+6x \\ 125+5x=480 \\ 125+5x-125=480-125 \\ 5x=355 \\ \frac{5x}{5}=\frac{355}{5} \\ x=71 \end{gathered}[/tex]The concert ticket cost is $71
Therefore, Mr. Chandra have left:
[tex]80-71=9[/tex]Answer: $9
A sample has a sample proportion of 0.3. Which sample size will produce the widest 95% confidence interval when estimating the population parameter?A. 36B. 56C. 68D. 46
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sample proportion = 0.3
widest 95% confidence interval
sample = ?
Step 02:
p = 0.3
1 - α = 0.95 =>> z α/2 = 1.96
We must check each value to find the solution.
A. sample = 36
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3-0.1499 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3+0.1499 \end{gathered}[/tex]confidence interval (0.1501 , 0.4499)
difference = 0.2998
B. sample = 56
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=0.3\text{ - }0.120 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=\text{ 0.3 + }0.120 \end{gathered}[/tex]confidence interval (0.18 , 0.42)
difference = 0.24
Analyzing these two values, we can conclude that the widest confidence interval will be for the smallest sample.
The answer is:
Sample = 36
Which of the following is NOT an equation?1. 5(2x+1)=10x+52. 4x-13. 5+3=104. x/2+1=7
By definition, an equation is a statement that two mathematical expressions are equal.
Equations always contain the equal sign "="
Out of the 4 expressions listed, number 2. does not contain the equal sign, which means that this expression is not an equation.
All other expressions contain the equal sign, they can be considered equations.
Which equation is set up for direct use of the zero-factor property? A. 3x2 - 19x - 14 = 0 C.X2 + x = 42 B. (7x + 9)2 = 3 D. (3x - 2)(- 2) = 0
Explanation:
The zero-factor property states that if ab=0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more factors is zero.
From these options only B and D have factors, but B equals to 3. In D we have that (3x-2) = 0 or the other factor is zero (or both)
Answer:
The correct answer is option D
2x -1/4y = 1 Solve the equation for y.
Given:
Given the equation
[tex]2x-\frac{1}{4}y=1[/tex]Required: Solve for y.
Explanation:
Subtract 2x on both sides.
[tex]\begin{gathered} 2x-\frac{1}{4}y-2x=1-2x \\ -\frac{1}{4}y=1-2x \end{gathered}[/tex]Multiply both sides by -4.
[tex]\begin{gathered} y=-4(1-2x) \\ =4(2x-1) \end{gathered}[/tex]Final Answer: y = 4(2x - 1)