Answer:
The quotient of 241 ÷ 5 is 48.
Step-by-step explanation:
Division is splitting into equal parts or groups.
The quotient is the answer after we divide one number by another.
To find the quotient 241 ÷ 5 you must:
Write the problem in long division format
[tex]5\overline{|\smallspace241}[/tex]
Divide 24 by 5 to get 4
Multiply the quotient digit 4 by the divisor 5
Subtract 20 from 24
Bring down the next number of the dividend
Divide 41 by 5 to get 8
Multiply the quotient digit 8 by the divisor 5
Subtract 40 from 41
[tex]\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{241}{5}\:\mathrm{is}\:48\:\mathrm{with\:remainder\:of}\:1\\\\48\quad \mathrm{Remainder}\quad \:1[/tex]
Answer for (12x+5)x-7x+2
Answer:
(12x2-2x+2)
Step-by-step explanation:
(12x)(x)+(5)(x)+-7x+2
12x2+5x+-7x+2
(12x2)+(5x+-7x)+(2)
12x2+-2x+2
I run 200m in 32 seconds, how long will it take to run 5000m
Answer:
It will take 800seconds to you to run 5000m
Step-by-step explanation:
Let time taken to run 5000m is x
Using ratio and proportion
200:32=5000:x
200/32=5000/x
200*x=5000*32
200x=160000
x=800seconds
The energy, E, of a body of mass m moving with speed v is given by the formula below. The speed is nonnegative and less than the speed of light, c which is constant. Use lower case letters here. E = mc^2 (1/Squareroot1 - v^2/c^2 - 1)
(a) Find E/m = c^2Squareroot1 - v^2/c^2 - c^2/1 - v^2/c^2 what is the sign of this partial? Positive negative
(b) Find E/v =?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]\frac{\delta E}{\delta m}= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
b
[tex]\frac{\delta E}{\delta V} = \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Step-by-step explanation:
From the question we are given
[tex]E = mc^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } }- 1 ][/tex]
So we are asked to find [tex]\frac{\delta E}{\delta m}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta m} = \frac{\delta }{\delta m} [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 )][/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2 } } } -1 ] \frac{\delta m}{\delta m}[/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
Also we are asked to find [tex]\frac{\delta E}{\delta V}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta V} = \frac{\delta }{\delta v } [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } - 1 )][/tex]
[tex]\frac{\delta E}{\delta V} = mc^2 [\frac{\delta }{\delta v} (\frac{c}{\sqrt{c^2 -v^2} } - 1 )][/tex]
[tex]= mc^2 [c* [\frac{\delta }{\delta v} (c^2 - v^2 )^{-\frac{1}{2} }] - 0][/tex]
[tex]= mc^3 [- \frac{1}{2} (c^2 - v^2 )^{-\frac{3}{2} } * (-2v)][/tex]
[tex]= \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Find the constant of variation for the relation and use it to write and solve the equation.
if y varies directly as x and as the square of z, and y=25/9 when x=5 and z=1, find y when x=1 and z=4
Answer:
When x = 1 and z = 4, [tex]y=\frac{80}{9}[/tex]
Step-by-step explanation:
The variation described in the problem can be written using a constant of proportionality "b" as:
[tex]y=b\,\,x\,\,z^2[/tex]
The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":
[tex]y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}[/tex]
Knowing this constant, we can find the value of y when x=1 and z=4 as:
[tex]y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}[/tex]
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.
Answer:
f(g(x))=12x+1
Step-by-step explanation:
f(g(x)) = -2(-6x+3)+7
f(g(x))= 12x-6+7
f(g(x))=12x+1
Domain: All real numbers
Halle is enteros cuyo producto sea 253 y uno de los enteros debe ser uno más que el doble del otro.
Answer:
11 y 23
Step-by-step explanation:
Nombrando los números como [tex]x[/tex] y [tex]y[/tex],
Planteamos las siguientes ecuaciones:
[tex]xy=253[/tex] (el producto de los numeros es 253)
[tex]x=2y+1[/tex] (uno de los enteros debe ser uno más que el doble del otro).
Sustituimos la segunda ecuación en la primera:
[tex](2y+1)(y)=253[/tex]
resolvemos para encontrar y:
[tex]2y^2+y=253\\2y^2+y-253=0[/tex]
usando la formula general para resolver la ecuación cuadrática:
[tex]y=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
donde
[tex]a=2,b=1,c=-253[/tex]
Sustituyendo los valores:
[tex]y=\frac{-1+-\sqrt{1-4(2)(-253)} }{2(2)} \\\\y=\frac{-1+-\sqrt{2025} }{4}\\ \\y=\frac{-1+-45}{4} \\[/tex]
usando el signo mas obtenemos que y es:
[tex]y=\frac{-1+45}{4} \\y=\frac{44}{4}\\ y=11[/tex]
(no usamos el signo menos, debido a que obtendriamos fracciones y buscamos numeros enteros)
con este valor de y, podemos encontrar x usando:
[tex]x=2y+1[/tex]
sustituimos [tex]y=11[/tex]
[tex]x=2(11)+1\\x=22+1\\x=23[/tex]
y comprobamos que el producto sea 253:
[tex]xy=253[/tex]
[tex](23)(11)=253[/tex]
Simplify the following expression and then write down the coefficient of x²: x² + x² + x² + x²
Answer:
The expression is 4x² and coefficient is 4.
Step-by-step explanation:
All have the same variables, x², so you add up together :
[tex] 1{x}^{2} + 1{x}^{2} + 1{x}^{2} + 1{x}^{2} [/tex]
[tex] = 4 {x}^{2} [/tex]
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2013?
Answer: The population will be 408,000 people.
Step-by-step explanation:
So in 2000 there were 200,000 people and it started to grow 8% every year so up to 2013.
so find 8% of 200,000 and then multiply it by the the number of years.
8% * 200,000 = 16,000
Find the difference between the years.
2013 - 2000 = 13 years
13 * 16000 = 208000 This is the amount of new people from 2000 to 2013 so add it to the original population.
208,000 + 200,000 = 408,000
Solve the inequality 2(4x-3)>-3(3x)+5
Answer:
48x>+2
Step-by-step explanation:
A battery with 20 percent of its full capacity is connected to a charger. Every minute that passes, an additional 5% , percent of its capacity is charged.
Answer:
y = 5x + 20
Step-by-step explanation:
The initial percent is 20.
Every minute, the percent goes up 5%, so the slope is 5.
So the equation of the line is y = 5x + 20.
Which transformations could be performed to show that
AABC is similar to AA"B"C"?
10
8
B
4
VX
2
A
-10 -3 -6 -4 -21 14
B"
4
8 10
X
O a reflection over the x-axis, then a dilation by a scale
factor of 3
O a reflection over the x-axis, then a dilation by a scale
factor of
O a 180° rotation about the origin, then a dilation by a
scale factor of 3
O a 180° rotation about the origin, then a dilation by a
scale factor of
6
8
-10
Save and Exit
Next
Submit
Mark this and return
Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
What is mean by Transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Given that;
Triangle ABC is similar to A"B"C".
Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)
Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
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A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.
1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.
2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.
Which statement is correct?
-Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.
-Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.
-Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
-Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
The correct answer is C. Mark’s method is correct because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Explanation:
To begin Mark should determine the rate of delivery (number of houses the carrier can deliver in 1 minute). This can be found by dividing the houses by the minutes (36 / 30 = 1.2 houses per minute). This means the 1.2 rate found by Mark is correct; also, in this case, it is important to clarify, the carrier will not deliver to 1.2 houses at the same time, but this is the delivery rate or number used to understand the relationship between the number of houses, and the time.
Moreover, you can use this rate, and multiply it by 7.5 and this will show you how many houses the carrier can deliver in this time (7.5 (minutes) x 1.2 (delivery rate) = 9 houses). Thus, the method is correct, and in it, 1.2 represents the unit rate, this is why even when it is not possible to deliver to 1.2 houses all the process is correct.
Answer:
c
Step-by-step explanation:
i took the test
16. Convert 55° to radians.
Answer:
0.96 radians
Step-by-step explanation:
Formula
1° = [tex]\frac{\pi }{180}[/tex] radians
Multiplying both sides by 55, It becomes
55° = [tex](\frac{\pi }{180} )*55[/tex]
55° = [tex]\frac{55\pi }{180}[/tex]
= 172.8/180
= 0.96 radians
A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group (drawing 4 slips without replacement from among 24).
(a) How many selections result in all 4 workers coming from the day shift? What is the probability that all 4 selected workers will be from the day shift? (Round your answer to four decimal places.)
(b) What is the probability that all 4 selected workers will be from the same shift? (Round your answer to four decimal places.)
(c) What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.)
(d) What is the probability that at least one of the shifts will be unrepresented in the sample of workers? (Round your answer to four decimal places.)
The probability that all 4 selected workers will be from the day shift is, = 0.0198
The probability that all 4 selected workers will be from the same shift is = 0.0278
The probability that at least two different shifts will be represented among the selected workers is = 0.9722
The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257
To solve this question properly, we will need to make use of the concept of combination along with set theory.
What is Combination?In mathematical concept, Combination is the grouping of subsets from a set without taking the order of selection into consideration.
The formula for calculating combination can be expressed as:
[tex]\mathbf{(^n _r) =\dfrac{n!}{r!(n-r)! }}[/tex]
From the parameters given:
Workers employed on the day shift = 10Workers on swing shift = 8Workers on graveyard shift = 6A quality control consultant is to select 4 of these workers for in-depth interviews:
Using the expression for calculating combination:
(a)
The number of selections results in all 4 workers coming from the day shift is :
[tex]\mathbf{(^n _r) = (^{10} _4)}[/tex]
[tex]\mathbf{=\dfrac{(10!)}{4!(10-4)!}}[/tex]
= 210
The probability that all 5 selected workers will be from the day shift is,
[tex]\begin{array}{c}\\P\left( {{\rm{all \ 4 \ selected \ workers\ will \ be \ from \ the \ day \ shift}}} \right) = \dfrac{{\left( \begin{array}{l}\\10\\\\4\\\end{array} \right)}}{{\left( \begin{array}{l}\\24\\\\4\\\end{array} \right)}}\\\end{array}[/tex]
[tex]\mathbf{= \dfrac{210}{10626}} \\ \\ \\ \mathbf{= 0.0198}[/tex]
(b) The probability that all 4 selected workers will be from the same shift is calculated as follows:
P( all 4 selected workers will be) [tex]\mathbf{= \dfrac{ \Big(^{10}_4\Big) }{\Big(^{24}_4\Big)}+\dfrac{ \Big(^{8}_4\Big) }{\Big(^{24}_4\Big)} + \dfrac{ \Big(^{6}_4\Big) }{\Big(^{24}_4\Big)}}[/tex]
where;
[tex]\mathbf{\Big(^{8}_4\Big) = \dfrac{8!}{4!(8-4)!} = 70}[/tex]
[tex]\mathbf{\Big(^{6}_4\Big) = \dfrac{6!}{4!(6-4)!} = 15}[/tex]
P( all 4 selected workers is:)
[tex]\mathbf{=\dfrac{210+70+15}{10626}}[/tex]
The probability that all 4 selected workers will be from the same shift is = 0.0278
(c)
The probability that at least two different shifts will be represented among the selected workers can be computed as:
[tex]= 1-\dfrac{ (^{10}_4) }{(^{24}_4)}+\dfrac{ (^{8}_4) }{(^{24}_4)} + \dfrac{ (^{6}_4) }{(^{24}_4)}[/tex]
[tex]=1 - \dfrac{210+70+15}{10626}[/tex]
= 1 - 0.0278
= 0.9722
The probability that at least two different shifts will be represented among the selected workers is = 0.9722
(d)
The probability that at least one of the shifts will be unrepresented in the sample of workers is:
[tex]P(AUBUC) = \dfrac{(^{6+8}_4)}{(^{24}_4)}+ \dfrac{(^{10+6}_4)}{(^{24}_4)}+ \dfrac{(^{10+8}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]
[tex]P(AUBUC) = \dfrac{(^{14}_4)}{(^{24}_4)}+ \dfrac{(^{16}_4)}{(^{24}_4)}+ \dfrac{(^{18}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]
[tex]P(AUBUC) = \dfrac{1001}{10626}+ \dfrac{1820}{10626}+ \dfrac{3060}{10626}-\dfrac{15}{10626}-\dfrac{70}{10626}-\dfrac{210}{10626} +0[/tex]
The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257
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Calculate simple interest
Question
Carolyn makes a deposit of $2,800 into a savings account. The bank calculates simple interest annually at a rate of 7.5%.
Interest is added every year on the anniversary of the initial deposit. How many years must Carolyn wait before her
investment exceeds $3,500? Give your answer in years. Do not include units in your answer.
Provide your answer below:
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Answer:
4
Step-by-step explanation:
A=P0(1+rt).
We know that A=$3,500,P0=$2,800 and r=7.5%=0.075, so we can rearrange the formula for A to get an explicit expression for t:
A=P0(1+rt)⟹t=A−P0P0r,
and substituting the known quantities gives
r=$3,500−$2,800$2,800×0.075=3.33,
which means, since the interest is paid annually, that she must wait four years for the total investment to exceed $3,500.
Please answer this correctly
Answer:
24.99
Step-by-step explanation:
If the area of the quarter circle is 38.465, then the equation to find this would be
3.14*r^2 / 4 = 38.465. we solve for r, the radius, and get two solutions. 7 and -7. Obviously the length of the radius can't be -7, so we know the radius is 7.
Now we must solve for the perimeter. The perimeter is equal to 2r + (2*3.14*r)/4
Plugging 7 in as the radius, r, we get 24.99 as our final answer.
A mountain bike is priced at $413. If the sales tax is 6.5 percent, what is the cost to purchase the mountain bike? Round to the
nearest cent if necessary.
$26.85
$28.91
$437.78
$439.85
answer: D) 439.85
Step-by-step explanation:
we are given the price of the bike which is $413.
we are also given the sales tax which is 6.5%.
sales tax is added to the original price to give us our total. so in order to find the total cost we need to find what the 6.5% sales tax is and add it to our original price. to find the sales tax number in dollars we need to set up our formula. The easiest formula is to use a proportion. X is out of 413 = 6.5% is out of 100%. X/413=6.5/100. We can then cross multiply then divide. 6.5 times 413=2,684.5. then divide 2684.5÷100= 26.845.
we need to round up to the nearest cent since we are working with dollars and cents 26.85. 26.85 is 6.5% of the price of the bike which is 413. Now we just simply add the tax to the original price and we get the cost. 413+26.85=439.85
Answer: The answer is D) 439.85
Step-by-step explanation:
A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 1100 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?
Answer:
Length = 550 m
Width = 275 m
Area = 151,250 m2
Step-by-step explanation:
One side of the farmland is bounded by the river, so the perimeter we will need to enclose is:
[tex]Perimeter = Length + 2*Width = 1100\ m[/tex]
And the area of the farmland is given by:
[tex]Area = Length * Width[/tex]
From the Perimeter equation, we have that:
[tex]Length = 1100 - 2*Width[/tex]
Using this in the area equation, we have:
[tex]Area = (1100 - 2*Width) * Width[/tex]
[tex]Area = 1100*Width - 2*Width^2[/tex]
Now, to find the largest area, we need to find the vertex of this quadratic equation, and we can do that using the formula:
[tex]Width = -b/2a[/tex]
[tex]Width = -1100/(-4)[/tex]
[tex]Width = 275\ m[/tex]
This width will give the maximum area of the farmland. Now, finding the length and the maximum area:
[tex]Length = 1100 - 2*Width = 1100 - 550 = 550\ m[/tex]
[tex]Area = Length * Width = 550 * 275 = 151250\ m2[/tex]
the terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis. Describe how to find the measure of the angle in both degree and radian
Measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
What is the terminal side of an angle?The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.
The terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis.
The total degree in a complete rotation of a side is 360 degrees. The side is rotated 1/6. Thus the angle is rotated is,
[tex]\theta=\dfrac{1}{6}\times360\\\theta=60^o[/tex]
Multiply it with π/180 to find the measure of the angle in radian.
[tex]\theta=60\dfrac{\pi}{180}\\\theta=\dfrac{\pi}{3}\\[/tex]
Hence, the measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
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Which of the options is the response variable?
A. The number of adults.
B. The type of training exercises performed by each participant.
C. The size of the physiological blind spot.
D. The number of times an adult performed training exercises.
Question:
The physiological blind spot refers to a very small zone of functional blindness in the eye where the optic nerve passes through the retina. We do not notice it because our nervous system compensates for it. Can eye training reduce the size of a person's physiological blind spot? Researchers recruited a representative sample of 10 adults with normal vision. Each participant performed training exereises with one eye for three weeks. The size of the physiological blind spot was measured (in degrees of visual angle squared) with a motion detection task both prior to training and again after the training was completed. Which of the options is the response variable?
A) The size of the physiological blind spot
B) The number of adults.
C) The type of training exercises performed by each participant.
D) The size of the physiological blind spot.
E) The number of times an adult performed training exercises.
Answer:
The correct answer is A)
Explanation:
The response variable (when experimenting) is the variable or factor about which the researcher is concerned. It can also be (as the name entails) the variable which respond to changes in the experiment.
The changes in the experiment is the training. The variable which the researcher is concerned about and which may or may not change with the introduction of training is the size of the physiological blind spot.
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Use the 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values. A bell-shaped distribution with mean 1050 and standard deviation 7.
The interval is to:_______.
Answer:
Intervals = (1,064) , (1,036)
Step-by-step explanation:
Given:
Use 95% method
Mean = 1,050
Standard deviation = 7
Find:
Intervals.
Computation:
95% method.
⇒ Intervals = Mean ± 2(Standard deviation)
⇒ Intervals = 1,050 ± 2(7)
⇒Intervals = 1,050 ± 14
⇒ Intervals = (1,050 + 14) , (1,050 - 14)
⇒ Intervals = (1,064) , (1,036)
The Intervals = (1,064) , (1,036)
Given that:
Use 95% methodMean = 1,050Standard deviation = 7Based on the above information, the calculation is as follows:
Intervals = Mean ± 2(Standard deviation)
Intervals = 1,050 ± 2(7)
Intervals = 1,050 ± 14
Intervals = (1,050 + 14) , (1,050 - 14)
Intervals = (1,064) , (1,036)
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An organization will give a prize to a local artist will be randomly chosen from among 6 painters,2 sculptors, and 9 photographers. What is the probability that the artist chosen will be a painter or a sculptor?
Answer: [tex]\bold{\dfrac{8}{17}=47.1\%}[/tex]
Step-by-step explanation:
[tex]\dfrac{\text{painter or sculptor}}{\text{total artists}}=\dfrac{6+2}{6+2+9}=\dfrac{8}{17}[/tex]
Here is rectangle A. Block A. Rectangle B is ¹/₅ longer than A Block B. Rectangle C is ¹/₃ longer than B Block C. The total length of all three rectangles is 133 cm. How much longer is rectangle C than B?
Answer:
Rectangle C is 14 cm longer than B
Step-by-step explanation:
Let x be the length of Rectangle A. Rectangle B is ¹/₅ longer than A Block B,
Therefore the length of rectangle B is:
[tex]x+\frac{1}{5}x[/tex]
Rectangle C is ¹/₃ longer than B, therefore the length of rectangle c is:
[tex]x+\frac{1}{5}x+\frac{1}{3}(x+\frac{1}{5}x) =x+ \frac{1}{5}x+\frac{1}{3}x+\frac{1}{15}x=x+\frac{9}{15}x[/tex]
The total length of all three rectangles is 133 cm.
Length of rectangle A + Length of rectangle B + Length of rectangle C = 133 cm
[tex]x+x+\frac{1}{5}x +x+\frac{9}{15}x=133\\x+x+x+\frac{1}{5}x +\frac{9}{15}x=133\\3x+\frac{12}{15}x=133\\ 45x+12x=1995\\57x=1995\\x=35cm[/tex]
Therefore the length of rectangle A is 35 cm, the length of rectangle B is [tex]35+\frac{1}{5}*35=42\ cm[/tex] and the length of rectangle C is [tex]35+\frac{9}{15}*35=56\ cm[/tex]
Rectangle C is ¹/₃ longer than B, which is 14 cm (42\3) longer than B
What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation.
Answer:
4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-(-2))/(3-1)
m=8/2
m=4
The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the standard deviation is 50. A subject earns a score of 155. How many standard deviations from the mean is the value 155
Answer:
The value 155 is zero standard deviations from the [population] mean, because [tex] \\ x = \mu[/tex], and therefore [tex] \\ z = 0[/tex].
Step-by-step explanation:
The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
z is the z-score.x is the raw score: an observation from the normally distributed data that we want standardize using [1].[tex] \\ \mu[/tex] is the population mean.[tex] \\ \sigma[/tex] is the population standard deviation.Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, [tex] \\ \mu[/tex]. Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.
For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.
These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.
A subject earns a score of 155. How many standard deviations from the mean is the value 155?
From the question, we know that:
x = 155.[tex] \\ \mu = 155[/tex].[tex] \\ \sigma = 50[/tex].Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject earned a score that equals the population mean. Then, using [1]:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{155 - 155}{50}[/tex]
[tex] \\ z = \frac{0}{50}[/tex]
[tex] \\ z = 0[/tex]
As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:
[tex] \\ x = \mu[/tex]
Therefore
[tex] \\ z = 0[/tex]
So, the value 155 is zero standard deviations from the [population] mean.
Homework: Section 1.2 Applications Linear
Score: 0 of 1 pt
8 of 10 (7 complete)
1.2.31
How many quarts of pure antifreeze must be added to 4 quarts of a 10% antifreeze solution to obtain a 20% antifreeze solution?
quart(s) of pure antifreeze must be added.
(Round to the nearest tenth as needed)
Answer:
q = 0.5 quarts of 100% antifreeze
Step-by-step explanation:
q = quarts of pure antifreeze
Set this up as a weighted combination of the mixtures.
(100%)(q) + (10%)(4) = (20%)(q + 4)
100q + 40 = 20(q + 4)
5q + 2 = q + 4
4q = 2
q = 0.5 quarts of 100% antifreeze
A student is interested in becoming an actuary. The student knows that becoming an actuary takes a lot of schooling and will have to take out student loans and wants to make sure the starting salary will be higher than $55,000/year. The student takes a random sample of 30 starting salaries for actuaries and finds a p-value of 0.0392. Use α = 0.05.
a. Choose the correct hypotheses.
H0:μ≠55,000 H1:μ=55,000
H0:μ>55,000 H1:μ≤55,000
H0:μ<55,000 H1:μ≥55,000
H0:μ=55,000 H1:μ>55,000
H0:μ=55,000 H1:μ≠55,000
H0:μ=55,000 H1:μ<55,000
b. Should the student pursue an actuary career?
No, since we can reject the null hypothesis
No, since we can reject the claim
Yes, since we can reject the claim
Yes, since we can can reject the null hypothesis
Answer:
a) H0:μ=55,000 H1:μ>55,000
b) Yes, since we can can reject the null hypothesis
Step-by-step explanation:
a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For this case;
Null hypothesis is that the starting salary will be equal to $55,000/year.
H0:μ=55,000
Alternative hypothesis is that the starting salary will be greater than $55,000/year.
H1:μ>55,000
b) Decision Rule;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
For this case;
P-value = 0.0392
α = 0.05
Since P-value < 0.05, we can reject null hypothesis.
Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.
- Yes, since we can can reject the null hypothesis
Express the following ratio in its simplest form.
4:12
Answer:
1:3
Step-by-step explanation:
divide 4 ...............
.............
ps: idk the explanation
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
Answer:
work is shown and pictured
Answer: x<3
Step-by-step explanation:
Compute 8P2 *
16
O 56
O 28
O
none of these are correct
