Answer:
Number of chores done by Janie are 5.
Step-by-step explanation:
Janie's allowance per week is $3.
For each chore she earns $2.
Now we assume that number of chores in a week she does = c
Then total earning from chore = $2 × c
So for the purchase of CD total earning this week inequality will be
⇒ 3 + 2c [tex]\geq[/tex]13
⇒ 2c [tex]\geq[/tex] 13-3
⇒ c [tex]\geq[/tex] 10÷2
⇒ c [tex]\geq[/tex] 5
What is the answer a factory adds three red drops an two blue drops of coloring to white paint to make each pint of purple paint the factory will make 50 gallons of this purple paint how many drops of red and blue coloring will the factory need the 50 gallon batch of purple paint
Answer:
Red = 30 drops
Blue = 20 drops
Step-by-step explanation:
The ratio red to blue is 3 : 2
Sum of ratios = 3 + 2 = 5
Required purple paint = 50 gallons
So,
[tex]Multiplier = \frac{50}{5} = 10[/tex]
Now, Red drops = 3×10 = 30
Blue drops = 2×10 = 20
Answer:
Step-by-step
Colby and Danielle clean pools for extra money over the summer. Colby's income is determined by f(x) = 3x + 12, where x is the number of hours. Danielle's income is g(x) = 5x + 10. If Colby and Danielle were to combine their efforts, their income would be h(x) = f(x) + g(x). Create the new function h(x). If Colby works 4 hours and Danielle works 4 hours, and if they each get half of the money when they work together, will Colby make more money working alone or by teaming with Danielle?
Answer:
Colby makes more money by teaming with Danielle
Step-by-step explanation:
Colby's income =f(x) = 3x+12
and Danielle's income = g(x) = 5x+10
If they combine their efforts the combined income would be
h(x) = 3x+12+5x+10 = 8x +22
If shared equally between them
Colby would get 1/2(8x+22) = 4x+11 and
Danielle would get 1/2(8x+22) = 4x+11
Since given they worked each for 4 hours
Colby income = Danielle income= 4(4) +11 = 27
If not combined, then
Colby income 3(4) + 12=24 and
Danielle income= 5(4) +10 = 30
Because of combining Colby makes more money by teaming with Danielle.
The difference is 3 for 4 hours work.
Answer:
B
Step-by-step explanation:
team with Danielle , h(x)=8x+22
Let us have four distinct collinear points $a,$ $b,$ $c,$ and $d$ on the cartesian plane. the point $c$ is such that $\dfrac{ab}{cb} = \dfrac{1}{2}$ and the point $d$ is such that $\dfrac{da}{ba} = 3$ and $\dfrac{db}{ba} = 2.$ if $c = (0, 4),$ $d = (4, 0),$ and $a = (x, y),$ what is the value of $2x + y$?
Start with a line segment connecting two points, A and B. [tex]\dfrac{DA}{BA}=3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.
But with [tex]\dfrac{DB}{BA}=2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.
Finally, [tex]\dfrac{AB}{CB}=\dfrac12[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.
Now let [tex]d[/tex] be the length of AB. Then the length of CD in terms of [tex]d[/tex] is [tex]4d[/tex]. We have the coordinates of C and D, and the distance between them is [tex]\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2[/tex]. So
[tex]4d=4\sqrt2\implies d=\sqrt2[/tex]
The slope of the line through C and D is
[tex]\dfrac{0-4}{4-0}=-1[/tex]
and so the equation of the line through these points is
[tex]y-4=-(x-0)\implies x+y=4[/tex]
So the coordinates of A are [tex](x,y)=(x,4-x)[/tex]. The distance between C and A is [tex]d=\sqrt2[/tex], so we have
[tex]\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1[/tex]
Since A falls to the right of C (in the [tex]x,y[/tex] plane, not just in the sketch), we know to take the positive value [tex]x=1[/tex]. Then the [tex]y[/tex] coordinate is [tex]y=4-1=3[/tex].
All this to say that A is the point (1, 3), so
[tex]2x+y=2+3=5[/tex]
The value 2x + y of is 5.
Start with a line segment connecting two points, A and B. [tex]\frac{DA}{BA} =3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.
But with [tex]\frac{DB}{BA} =2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.
Finally, [tex]\frac{AB}{CB} =\frac{1}{2}[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.
Now let be the length of AB. Then the length of CD in terms of is . We have the coordinates of C and D, and the distance between them is
[tex]\sqrt{(4-0)^2+ (4-0)^2} =4\sqrt{2}[/tex]
So
4d= 4√2 = d= √2
The slope of the line through C and D is
[tex]\frac{0- 4}{4-0} = -1[/tex]
and so the equation of the line through these points is
y- 4 = -(x- 0) =x + y =0
So the coordinates of A are (x, y) = (x,4 -x). The distance between C and A is d= √2, so we have
[tex]\sqrt{(x-0)^2+(4- x - 4)^2} = \sqrt{2x^3} = |x| \sqrt{2} = \sqrt{2} = |x| = 1[/tex]
Since A falls to the right of C (in the x, y plane, not just in the sketch), we know to take the positive value . Then the coordinate is .
All this to say that A is the point (1, 3), so 2x + y= 2+3=5
for such more question on coordinates
https://brainly.com/question/30227780
#SPJ2
Question
Let us have four distinct collinear points a, b, c, and d on the cartesian plane. the point c is such that [tex]\dfrac{ab}{cb} = \dfrac{1}{2}[/tex] and the point d is such that [tex]\dfrac{da}{ba} = 3[/tex] and [tex]\dfrac{db}{ba} = 2[/tex] c = (0, 4), d = (4, 0), and a = (x, y), what is the value of 2x + y?
The sales tax rate is 7.25%. How much tax in dollars is added on an item that costs $56.00?
Hi there! :)
Answer:
$4.06 of taxes is added on an item that costs $56.00 is the sales tax rate is 7.25%.
Step-by-step explanation:
You are looking for 7.25% of $56.00
7.25% is the same thing as 7.25/100, which is the same thing as 7.25 ÷ 100
7.25 ÷ 100 = 0.0725
The word "of" is the same thing as a multiplication sign (×).
SO, 7.25% of $56.00 = 0.0725 × 56
0.0725 × 56 = 4.06 ⇒ YOUR ANSWER
There you go! I really hope this helped, if there's anything just let me know! :)
The tax on that item will be 4.06$.
What is tax?A tax is a necessary fee or financial charge imposed by a government on an individual or an organization in order to raise funds for public works projects that provide the greatest services and infrastructure. The gathered funds are subsequently utilized to finance other government activities.
Given, The sales tax rate is 7.25%. for an item whose cost is 56.00$.
Tax added on that item = 56* 7.25%
Tax added on that item = 4.06$
Therefore, the total tax added on the item whose total value is 56 will be 4.06$.
Learn more about tax here:
https://brainly.com/question/16423331
#SPJ5
Calculate s24 for the arithmetic sequence in which a13=1.9 and the common difference is d=3.7.
Answer:
The correct answer option is 42.6.
Step-by-step explanation:
We know that in a arithmetic sequence, [tex]a_{13}=1.9[/tex] and the common difference is [tex](d)=3.7[/tex].
The standard form of an arithmetic sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]
So we will substitute the given values in this formula to find the value of [tex]a_1[/tex].
[tex]a_{13}=a_1+(13-1)3.7[/tex]
[tex]1.9=a_1+(12)3.7[/tex]
[tex]1.9=a_1+44.4[/tex]
[tex]a_1=-42.5[/tex]
Now finding the 24th term"
[tex]S_{24}=a_1+(n-1)d\\\\S_{24}=-42.5+(24-1)3.7\\\\\\S_{24}=42.6[/tex].
Therefore, the 24th term of the given arithmetic sequence is 42.6.
Answer:
Just took this test the correct answer is 1.2
Samantha is saving to buy a new computer. the first month she saves $100. each of the following months she plans to save 10%more than the previous month. how much money will she have saved after 6 months
She saves $100.She saves 10% more.They want to know how much they will save after 6 months. Multiply 10% by 6months and you get 60%.Then you multiply the answer of .60 (60%) by 100 and you get 60. Lastly, since you wanna know how much you saved,subtract $100-60 and your final answer you get is that she saves $40.Hope that helped!
A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad picks her up and drives her through the remainder of the way at 30 miles per hour. If they arrived at school at 9:00, how far did she walk? Show work
The girl walked a distance of [tex]\boxed{{\mathbf{5 miles}}}[/tex] in her way.
Further explanation:
The time can be calculated as,
[tex]{\text{ time}}=\frac{{{\text{distance}}}}{{{\text{speed}}}}[/tex]
Given:
It is given that a girl stands 20 miles away from the school at [tex]6:50{\text{ am}}[/tex] and she started walking at the rate of [tex]3{\text{ mi/hr}}[/tex] and then after some time her dad pick up and he drives at the rate of [tex]30{\text{ mi/hr}}[/tex] . They reach the school at [tex]9:00{\text{ am}}[/tex] .
Step by step explanation:
Step 1:
Consider [tex]x[/tex] as the distance she walked in her way.
The speed of the girl when she walked is [tex]3{\text{ mi/hr}}[/tex] .
Now use the formula of time to obtain the walk time.
[tex]\begin{gathered}{\text{ walktime}}=\frac{{{\text{distance walked}}}}{{{\text{walking speed}}}}\hfill\\{\text{ walktime}}=\frac{x}{3}\hfill\\\end{gathered}[/tex]
Since the total distance is [tex]20{\text{ miles}}[/tex] .
Then consider [tex]20-x[/tex] as the distance driven by the car.
The driving speed is [tex]30{\text{ mi/hr}}[/tex] .
Now use the formula of time to obtain the drive time.
[tex]\begin{gathered}{\text{drive time}}=\frac{{{\text{distance travelled by car }}}}{{{\text{ speed of car}}}}\hfill\\{\text{drive time}}=\frac{{20-x}}{{30}} \hfill\\\end{gathered}[/tex]
Step 2:
Now we calculate the total time took by girl to reach the school.
[tex]9:00-6:50={\text{2 hrs 10 min}}[/tex]
Now convert the timing into hours as,
[tex]\begin{aligned}2{\text{ hours 10 minutes}}&=2+\frac{{10}}{{60}}\\&=2\frac{1}{6}\\&=\frac{{13}}{6}{\text{ hrs}}\\\end{aligned}[/tex]
Step 3:
Total time is the sum of drive time and walk time.
The total time can be expressed as,
[tex]\frac{x}{3}+\frac{{20-x}}{{30}}=\frac{{13}}{6}[/tex]
Now solve the above equation by cross multiply method.
[tex]\begin{aligned}\frac{x}{3}+\frac{{20-x}}{{30}}&=\frac{{13}}{6}\hfill\\\frac{{10x+20-x}}{{30}}&=\frac{{13}}{6}\hfill\\\frac{{9x+20}}{{30}}&=\frac{{13}}{6}\hfill\\6\left({9x+20}\right)&=13\left({30}\right)\hfill\\\end{aligned}[/tex]
Now simplify the further equation.
[tex]\begin{aligned}6\left({9x+20}\right)&=13\left({30}\right)\hfill\\54x+120&=390\hfill\\54x&=390-120\hfill\\54x&=270\hfill\\\end{aligned}[/tex]
Simplify the further equation.
[tex]\begin{aligned}54x&=270\hfill\\x&=\frac{{270}}{{54}}\hfill\\x&=\frac{{45}}{9}\hfill\\x&=5\hfill\\\end{gathered}[/tex]
Therefore, the girl walked 5 miles.
Learn more:
Learn more about the distance between the points https://brainly.com/question/6278187 Learn more about the equivalent fraction https://brainly.com/question/952259 Learn more about midpoint of the segment https://brainly.com/question/3269852
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Speed, distance and time
Keywords: girl, distance, drive, walk, drive time, dad, speed, travelled, formula, cross multiply, fraction, number, multiply, addition, subtraction, equation, school
Answer:
5 miles
Step-by-step explanation:
A factor adds three red drops and two blue drops of coloring to white paint to make each pint of purple paint. The factory will make 50 gallons of purple paint. Haw many drops of red and blue coloring will the factory need in the 50-gallon batch of purple paint?
There are 8 pints in 1 gallon, so 50×8 = 400 pints in 50 gallons.
400 × 3 red drops = 1200 red drops
400 × 2 blue drops = 800 blue drops
Can someone please please help me?? :(
A driver descends to a location of -50 1/4 meters relative to the surface of the water.
He then descends another 10 1/2 meters. What is the driver’s final location relative to the surface of the water?
Enter your answer as a simplified mixed number in the box.
_________ meter's.
Answer:
-60 3/4m
Step-by-step explanation:
The diver first dives down 50 1/4m, which is represented by the -50 1/4m. He then descends another 10 1/2m down. So -50 1/4m - 10 1/2m.
-50-10=-60
-(1/4)-(1/2)= (1/4)+(1/2)
(1/4+1/2)=(2/8+4/8) you can only add with the same denominators.
=6/8 (simplifies down to 3/4)
The area of the octagon below is 10,391.9 square millimeters. What is the approximate perimeter of the octagon? Round to the nearest whole number. Mm What is the approximate length of one side of the octagon? Round to the nearest whole number. Mm
Answer:
the first one is 371 and the second one is 46
Step-by-step explanation:
Answer:
side of the octagon = 46.38 mm
Perimeter of the octagon = 371.04 mm
Step-by-step explanation:
Area of octagon = 10,391.9 mm²
But, area of octagon is given by the formula = 2(1 + √2)side²
⇒ 2(1 + √2)side² = 10391.9
⇒ 4.83 × side² = 10391.9
⇒ side² = 2151.53
⇒ side of the octagon = 46.38 mm
Perimeter of the octagon = 8 × side
⇒ Perimeter of the octagon = 8 × 46.38
⇒ Perimeter of the octagon = 371.04 mm
A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you? need?
Answer:
[tex]13\frac{1}{3}[/tex] cups
Step-by-step explanation:
We are told that a recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B.
To find the number of cups of ingredient B we will use proportions.
[tex]1\frac{2}{3}=\frac{5}{3}[/tex]
[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{\frac{1}{2}}{\frac{5}{3}}[/tex]
[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]
Now let us substitute our amount of Ingredient A =4 in our proportions.
[tex]\frac{4}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]
[tex]\frac{\text{Number of cups of ingredient B}}{4}=\frac{10}{3}[/tex]
Multiplying both sides of our equation by 4.
[tex]4*\frac{\text{Number of cups of ingredient B}}{4}=4*\frac{10}{3}[/tex]
[tex]\text{Number of cups of ingredient B}=\frac{40}{3}[/tex]
[tex]\text{Number of cups of ingredient B}=13\frac{1}{3}[/tex]
Therefore, we need [tex]13\frac{1}{3}[/tex] cups of ingredient B to make our recipe.
Answer:
Proportion states that the two ratios are equal.
Given statement: A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A.
By using proportion definition to find ingredients B;
[tex]\frac{\frac{1}{2} }{1\frac{2}{3} } = \frac{4}{B}[/tex]
Simplify:
[tex]\frac{\frac{1}{2} }{\frac{5}{3}} = \frac{4}{B}[/tex]
By cross multiply we get;
[tex]B \cdot \frac{1}{2} = 4 \cdot \frac{5}{3}[/tex]
or
[tex]\frac{B}{2} = \frac{20}{3}[/tex]
Multiply both sides by 2 we get;
[tex]B = \frac{20}{3} \times 2 = \frac{40}{3} = 13\frac{1}{3}[/tex]
Therefore, [tex]13\frac{1}{3}[/tex] cups of ingredients B needs.
A biologist is measuring growth of a frog population in a pond. She expects the number of tadpoles to grow every day by a factor of b. On day one, at the start of her experiment, the number of tadpoles is a. Which expression best predicts the number of tadpoles at the start of the nth day?
An3x=2x+1
subtract 2x from both sides
x=1 answer
Step-by-step explanation:
it will only take one day
Answer:
a * b^(n-1)
Step-by-step explanation:
I guessed and got it right :/
Bryan and Seth are both members of the same private social networking site. Bryan’s membership plan can be expressed with the function y = 9.50x + 22, where x is the number of months that he is a member and y is the total cost. Seth’s membership fees are shown in the graph.
If x represents the number of months that they are members of the social networking site, how much will Bryan and Seth each pay after 15 months of membership?
Answer:
After 15 month of membership, Brian will pay $164.5 and Seth will pay $100.
Step-by-step explanation:
Brian
y=9.50(15)+22
y=142.5+22
y=164.5
Seth
(15,100)
Identify the sequence that lists the angles of △JKW in order from largest to smallest. THE ANSWER WITH THE RED ARROW IS WRONG!!
i think that its is w,k,j. i could be wrong though
MATH HELP!!!!! Have no idea what to do!!
Answer:
Step-by-step explanation:
the answer is 26
Answer:
45 units^2
Step-by-step explanation:
Think of this polygon as being the combination of a rectangle and a triangle. The rectangle is at the bottom. It has length 9 and width 2.
The triangle is above it. Its base is also 9 like the rectangle's length. The height of the triangle is the segment from point (2, -1) to (2, 4). The length of the height is 6.
Now use the area formulas for a rectangle and a triangle to find the two areas and add them,
Rectangle: A = LW
Triangle: A = bh/2
Total area = LW + bh/2
Total area = 9 * 2 + 9 * 6/2
Total area = 18 + 54/2
Total area = 18 + 27
Total area = 45 units^2
Please help!!!!
Leonard wants to restrict the domain of the tangent function so that its inverse is a function. Which description best describes how he could restrict the domain?
A) Choose any interval between consecutive asymptotes.
B) Choose any interval that includes two asymptotes.
C) Choose any interval of length 2π radians.
D) Choose any interval of length π radians.
Answer:
Correct choice is A
Step-by-step explanation:
If a function has an inverse, then there is at most one x-value for each y-value.
The tangent function is periodic with period [tex]\pi.[/tex] Hence, at each value for which [tex]f(x)=\tan x[/tex] is defined, [tex]f(x+n\pi )=\tan x[/tex] for each integer n. Therefore, the function [tex]f(x)=\tan x[/tex] does not have an inverse. Since tangent is not a one-to-one function, the domain must be limited. From examining the graph of the tangent function, we see that in each interval of the form
[tex]\left((2k−1)\dfrac{\pi}{2},(2k+1)\dfrac{\pi}{2}\right)[/tex]
where k is an integer, the tangent function assumes every value in its range. Moreover, in each such interval, each y-value is achieved exactly once. Hence, we can create an invertible function by restricting the domain tangent function to one such interval. Such interval is an interval between two consecutive vertical asymptotes [tex]x=(2k−1)\dfrac{\pi}{2}[/tex] and [tex]x=(2k+1)\dfrac{\pi}{2}.[/tex]
please help on this one? :)
Answer:
62 kg: A
Step-by-step explanation:
The black line is called line of best fit. This line shows the points plotted and how they compare to the predicted amounts. The reason why A is the correct answer is because all of the other blue points line up with the line of best fit. Since the point 62kg is NOT on the line of best fit, that is the point where experimental error may have occurred.
Determine which system of equation has (-3,19) and (4,-23) as a solution?
Answer:
y=6x+1
Step-by-step explanation:
First you must find the slope of the two points...
[tex]\frac{4--3}{-23-19}[/tex] which then would equal 6
Then you take the slope and put into point-slope form
(y-y1)=m(x-x1)...take one of the points that is given and plug it into this formula.
so I used (-3,19).
(y-19)=6(x--3)
I would then get y-19=6x+18
Add 19 to both sides and you will get y=6x+1
Identify the value of m. Give your answers in simplest radical form. HELP PLEASE!!!
Answer:
m = 4√2
Step-by-step explanation:
This is a right angled isosceles triangle whose sides are in the ratio 1:1:√2.
So = 8 / √2
= 8 *√2 / 2
= 4√2
Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?
Answer:
The vertex form of the function is [tex]f(x)=(x-1)^2+3[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=4+x^2-2x[/tex]
The vertex form is
[tex]f(x)=(x-h)^2+k[/tex]
Rewrite the given function
[tex]f(x)=(x^2-2x)+4[/tex]
[tex]-\frac{b}{2a}=-\frac{-2}{2(1)}=1[/tex]
Add and Subtract [tex](-\frac{b}{2a})^2[/tex].
[tex]f(x)=(x^2-2x+1)+4-1[/tex]
Use [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]f(x)=(x-1)^2+3[/tex]
Therefore the vertex form of the function is [tex]f(x)=(x-1)^2+3[/tex].
Answer: A on Edge 2020
Step-by-step explanation:
How do the graphs of the function differ from the graph of f(x)=1.5x^3
Answer: p(x) = steeper
q(x) = less steep and reflection
r(x) = reflection
Step-by-step explanation:
The parent graph is: f(x) = 1.5x³
If the absolute value of the coefficient in front of x³ is greater than 1.5, then it is steeper (the graph is stretched).If the absolute value of the coefficient in front of x³ is less than 1.5, then it is less steep (the graph is shrunk/compressed).A negative sign in front of the coefficient represents a reflection over the x-axis.p(x): 2 > 1.5 , so it is stretched (steeper).
p(x): coefficient has a positive sign, so it is NOT a reflection
q(x): 1 < 1.5 , so it is shrunk/compressed (less steep).
q(x): coefficient has a negative sign, so it is a reflection over x-axis
r(x): 1.5 = 1.5 so it is neither a stretch or a shrink
r(x): coefficient has a negative sign, so it is a reflection over x-axis
The graph of the function f(x) = 1.5x^3 has a steep increase or decrease, exhibits symmetry, and passes through the origin.
Explanation:When comparing the graphs of different functions, it's important to analyze their key characteristics. In the case of the function f(x) = 1.5x^3, the graph will be a cubic function. Here are three significant differences between the graph of f(x) = 1.5x^3 and other functions:
The graph will have a steep increase if x > 0 and a steep decrease if x < 0, due to the positive coefficient of the x^3 term.The graph will exhibit symmetry with respect to the y-axis because the power of x is odd.The graph will pass through the origin (0, 0) since there is no constant term in the function.Learn more about Graphs here:https://brainly.com/question/26215563
#SPJ3
the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days what is the probability of randomly selecting a pregnant woman whose length of pregnancy is less than 260 days
a.0.2981
b.0.7019
c.0.8186
d.0.1814
Answer:
a. 0.2981
Step-by-step explanation:
We are told that the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.
Let us find z-score for 260 days.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]x[/tex] = Sample score,
[tex]\mu[/tex] = Mean
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in z-score formula we will get,
[tex]z=\frac{260-268}{15}[/tex]
[tex]z=\frac{-8}{15}[/tex]
[tex]z=-0.53[/tex]
Now we will use normal distribution table to find the area that corresponds to z-score of -0.53.
From normal distribution table we get 0.29806 as our answer. Upon rounding our answer to four decimal places we will get 0.2981 as our answer.
Therefore, probability of selecting the woman whose length of pregnancy is less than 260 days will be 0.2981 and option a is the correct choice.
At the movie theatre 30% of the audience members were children. If the number of children at the movie theatre was 210, what was the total number of people at the movie theatre?
Answer:
The total number of people at the movie theatre is 700.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
At the movie theatre 30% of the audience members were children.
If the number of children at the movie theatre was 210.
Percentage = 30%
Part value = 210
Put in the formula
[tex]30 = \frac{210\times 100}{Total\ value}[/tex]
[tex]Total\ value = \frac{21000}{30}[/tex]
Total value = 700
Therefore the total number of people at the movie theatre is 700.
Use the equation below to answer these questions.
[tex]x+2=\sqrt{3x+10}[/tex]
1.) What is the solution to the equation?
2.) What is the extraneous solution? Why?
3.) In general, what is an extraneous solution?
1) [tex]x+2=\sqrt{3x+10}[/tex]
Square both sides to get
[tex](x+2)^2=(\sqrt{3x+10})^2\implies x^2+4x+4=3x+10\implies x^2+x-6=0[/tex]
Factorize and solve:
[tex]x^2+x-6=(x+3)(x-2)=0\implies x=-3,x=2[/tex]
2) I assume we take [tex]\sqrt x[/tex] to be defined only for [tex]x\ge0[/tex]. Under this condition, a solution would be extraneous if [tex]\sqrt{3x+10}[/tex] is undefined, which happens if [tex]3x+10<0[/tex].
If [tex]x=-3[/tex], then [tex]3x+10=-9+10=1[/tex], so it is not extraneous.
If [tex]x=2[/tex], then [tex]3x+10=6+10=16[/tex], so it is not extraneous.
So there are not extraneous solutions to this equation.
3) Lots of information on this on the web...
The solution for the given equation is x=2. -3 is an extraneous solution caused by the squaring operation and it doesn't satisfy the original equation. An extraneous solution is a solution that does not satisfy the original equation.
Explanation:To find the solution of the equation x+2=√(3x+10), we first square both sides to eliminate the square root: (x+2)2=3x+10.
This simplifies down to x2 + 4x + 4=3x+10. Rearranging terms then gives us x2 + x - 6=0. The solutions of this quadratic equation are x=2 and x=-3.
However, if we substitute x=-3 back into the original equation, it does not hold true. Thus, -3 is an extraneous solution. This extraneous solution arises in this case because we applied the squaring operation, which is not a reversible process. An extraneous solution, generally, is a solution to a transformed equation that does not satisfy the original equation.
Learn more about Extraneous Solution here:https://brainly.com/question/34838129
#SPJ11
you can buy 56 diapers from babies R us for $28 ,and you can buy 112 diapers online for $52 which one is the better deal and how much will you save per diaper
Answer:
From Online Buying is more suitable
The difference between per diaper price is $0.04
Step-by-step explanation:
Given:
56 diapers can be bought for $ 28
and
online 112 diapers for $ 52
TO find:
Better deal = ?
Per diaper save= ?
Solution:
Let the first type be x
Now for x
Price of 56 diapers are $ 28
Price of one diaper = [tex]\frac{28}{56}[/tex]
=$0.5 / diaper
Now for online let it be represented by O
Price of 112 diapers are $52
Price of one diaper = [tex]\frac{52}{112}[/tex]
=$0.46 / diaper
Price of one diaper from online is less then price of one diaper from we bought not online
Difference of per diaper price = 0.5 - 0.46
=$0.04
So buying diapers from online would be suitable
which shows the reflection of the figure over the line
Answer:
The answer is B, I just took the test.
Step-by-step explanation:
Answer:
hello there the answer is b hope this helps
Step-by-step explanation:
The population of the town was 25,000 people.Then 3,200 people moved away.What was the percent of increase?
There was no increase. There was actually a decrease of people in the population. If you are asking for the percent of decrease, the answer is 3200/25000=0.128 0.128*100=12.8%.
what is the factorization of the polynomial below? x^2-x-42
Answer:
(x-7)(x+6)
Step-by-step explanation:
The solution of the equation is -6 and 7 for factorization of the given polynomial [tex]x^{2} - x - 42[/tex].
How to factorize any given polynomial ?Given equation :- [tex]x^{2} - x - 42[/tex]
For finding factors of the equation, we have equate the given polynomial with zero.
∴ [tex]x^{2} - x - 42 = 0[/tex]
Factorizing the above equation,
⇒ [tex]x^{2} - 7x + 6x - 42 = 0[/tex]
⇒ [tex]x (x -7) + 6(x - 7) = 0[/tex]
⇒ [tex](x + 6)(x - 7) = 0[/tex]
∴ Either x + 6 = 0 or x - 7 = 0
∴ x1 = -6 and x2 = 7
Where x1 and x2 are the respective factors of the given polynomial in the question.
Thus, the solution of the equation is -6 and 7 for factorization of the given polynomial [tex]x^{2} - x - 42[/tex].
To learn more about factorization of polynomials, refer -
https://brainly.com/question/25829061
#SPJ2
Jaz was 43 inches tall. Eighteen months later she was 52 inches tall. Find the constant rate of change of jaz's height
Answer:
.5 inches a month
Step-by-step explanation:
52 - 43 = 9 inches
9/18 = .5
Answer:
0.5 inches a month
Step-by-step explanation:
subtract 43 from 52 and divide that answer by 18
52-43=9 9÷18=0.5
please mark me brainliest
Which expression is equivalent to [tex]\frac{4-2}{2^{2}}[/tex]?
A: −16
B: −8
C: 8
D: 16
Answer:
1/2
Step-by-step explanation:
(4-2)
----------
2^2
The numerator is 4-2 = 2
The denominator is 2^2 = 4
2
------
4
1/2