The probability that exactly 6 of 8 adult use their smartphones in meetings or classes is 0.147 or 14.7% .
The complete question is
Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.
What is Probability ?Probability is the measure of likeliness of an event to happen.
The probability given is
p = 54% = 0.54
n =8
r = 6
The binomial Probability is given by
[tex]\rm P(x) = ^n C_r p^r q^{n-r}[/tex]
The probability that exactly 6 people use smartphones in a class of 8 student is given by
[tex]P(x) = \dfrac{n!}{r! (n-r)!} p^r q^{n-r}[/tex]
Here q represents the complement
q = 1 -p
q = 1-0.54 = 0.46
[tex]P(6) = \dfrac{8!}{6! (2)!} 0.54^6 0.46^{2}\\\\\P(6) = \dfrac{8 * 7}{ 2} 0.54^6 0.46^{2}\\\P(6) = 0.147[/tex]
Therefore The probability that exactly 6 of 8 adult use their smartphones in meetings or classes is 0.147 or 14.7% .
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D is the midpoint of AB and E is the midpoint of BC. If AC=48, what is the length of DE ?
Answer:
24 is the answer for the following
Step-by-step explanation:
please mark me as brainlest
Work out the bearing of Y from W.
(Not drawn accurately)
Answer:
206°
Step-by-step explanation:
The bearing of y from w is the angle y makes with w moving from the north pole in clockwise direction.
So from the north pole, move in clockwise direction and stop at the line joining w and y
the angles there are 90+116= 206°
Therefore the bearing of Y from W is 206°
Please help answer needed asap
Answer:
A
Step-by-step explanation:
a = 3n-30 solve for 'n'
a + 30 = 3n
n = (a+30)/3
n(a) = (a+30)/3
Charlie is installing new carpet in his rectangular living room, which is 5 feet longer than it is wide. He has received quotes for the total
installation costs from two different contractors for the same style of carpet.
Contractor A charges an installation fee of $125 plus $2 per square foot for the carpet.
Contractor B charges an installation fee of $75 plus $2.50 per square foot for the carpet.
Based on this information, which system of equations could be used to determine the width of the living room, x, in feet, at which the
quote for the installation costs, y, is the same for both companies?
Considering the area of a rectangle, the equation that could be used to determine the width for which the costs are the same is:
125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:
A = lw
In this problem, the dimensions are given as follows:
w = x, l = x + 5.
Hence the area in square feet is:
A = x(x + 5) = x² + 5x.
Then the costs are given as follows:
A(x) = 125 + 2(x² + 5x).B(x) = 75 + 2.5(x² + 5x).The costs will be equal when:
A(x) = B(x)
125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
can someone please help and explain these problems ??
Answer:
AAA
Step-by-step explanation:
yesss
2) You translate an object point 3 units to the right and 2 units down. Explain (with the aid of an equation) how you would find the coordinates of the image point. (4 marks)
Answer: By adding 2 to y and subtracting x by 3.
Step-by-step explanation: Let’s use the equation y = x since it’s simple. In order to translate an equation anywhere to the right, you have to subtract x by a unit. Since it’s 3 units, the equation is now y = x - 3. To translate an equation down, you have to add a unit to y. Since the questions asks for two units, add 2 to y. The equation should now be y + 2 = x - 3.
4(p+q) /p-q x q+p/8(p+q)
Answer:
[tex]\frac{q+p}{2(p-q)}[/tex]
Step-by-step explanation:
[tex]\frac{4(p+q)}{p-q} *\frac{q+p}{8(p+q)}[/tex]
We will cancel out like terms.
[tex]\frac{4}{p-q} *\frac{q+p}{8}\\=\frac{4(q+p)}{8(p-q)} \\=\frac{q+p}{2(p-q)}[/tex]
when 7 is subtracted from 3 times a certain number , the result is 28. What is the number
The number will be equal to 11.67.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The expression will be formed from the given data. Let the number be x so the expression will be:-
3x - 7 = 28
3x = 35
x = 35 / 3
x = 11.67
Therefore the number will be equal to 11.67.
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Find the value of x. Round the length to the nearest tenth.
Answer:
6 m
Step-by-step explanation:
[tex]sin22 = x/16\\x = 16sin22\\x = 6[/tex]
Consider an investment of $6000 that earns 4.5% interest
What is the value of the investment after
15 years if the interest is compounded
annually?
Answer:
$11,611.69
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $6,000r = 4.5% = 0.045n = 1 (annually)t = 15 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=6000\left(1+\frac{0.045}{1}\right)^{(1 \times 15)}[/tex]
[tex]\implies \sf A=6000(1.045)^{15}[/tex]
[tex]\implies \sf A=11611.69466...[/tex]
Therefore, the value of the investment after 15 years will be $11,611.69 to the nearest cent.
Find the value of x. Then find the measure of each labeled angle.
Answer:
x = 70 and the labeled angles are 110 and 70
Step-by-step explanation:
This is a trapezoid, the bases are parallel.
Since the bases are parallel, given two angles are supplementary and their sum is equal to 180:
x + 40 + x = 180 add like terms
2x + 40 = 180 subtract 40 from both sides
2x = 140 divide both sides by 2
x = 70 and the labeled angles are 110 and 70
inequalities i need help question is in picture
Answer:
19-73 19-73 is fine thanks 70-65-46 024 465 8554 48-57
If f(x) = 3x^2 - x, find f(-2).
Answer:
14
Step-by-step explanation:
to find f(value), we plug that x value into the equation
so, if..
f(x)= 3x² -x
f(-2)= 3 · (-2)² - (-2)
f (-2) = 3 · 4 + 2
f (-2) = 12 + 2
f (-2) = 14
Answer:
14
Step-by-step explanation:
f(x) =3x^2-x
here,
f(-2)= 3(-2)^2 -(-2)
=3*4+2
=12+2
=14 Answer.
Which of the following is equivalent to the logarithmic equation below? in x=3
Can line r be parallel to line s and line p be parallel to line q at the same time ? Explain
Yes, the line r is parallel to the line s and the line p is parallel to the line q.
Parallel lines are straight lines that do not intersect at any point.They never meet. They are always in the same distance. But they are not always ways inIf two lines AB and CD are parallel, then it can be represented by AB || CD. Some examples: Cricket stumps, white lines of zebra crossing, opposite boundaries of an rectangular box, etc.Here the given lines are p, q, r, s.
Line p and q are parallel to each other.
and the line p is parallel to the line q.
Therefore, Yes, the line r is parallel to the line s and the line p is parallel to the line q.
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what is the ratio 3:1
Answer:
3:1
Step-by-step explanation:
3 and 1 is not divisible by any number
The sum of three consecutive multiples of 7 is 693. Find the no
Let x be a multiple of 7
The next two consecutive multiples of 7 are x + 7 and x + 7 + 7 (i.e. x + 14)Three consecutive multiples of 7 are
xx + 7x + 14According to the condition[tex] \\ \large\blue\longrightarrow\rm \large \:x \: + \: (x \: + \: 7) + (x \: + \: 14) \: = \: 693[/tex]
[tex] \large\blue\longrightarrow \rm \large \:3x \: + \: 21 \: = \: 693[/tex]
[tex] \large\blue\longrightarrow \rm \large \:3x \: = \: 693 \: - \: 21[/tex]
[tex] \large\blue\longrightarrow \rm \large \:3x \: = \: 672[/tex]
Dividing both sides by 3 , we have
[tex]\large\blue\longrightarrow \rm \large \: \frac{3x}{3} \: = \: \frac{672}{3} \\ [/tex]
[tex]\large\blue\longrightarrow \rm \large \: \ \: \frac{ \cancel3x}{ \cancel3} \: = \: \frac{ \cancel{672} \: \: ^{ \red{224}} }{ \cancel3} \\ [/tex]
[tex]\large\blue\longrightarrow \rm \large \:x \: = \: 224 \\[/tex]
x = 224x + 7 = 224 + 7 = 231x + 14 = 224 + 14 = 238Three consecutive multiples of 7 are
224231238Help please I'll mark you as brainlist if the answer is correct
if (x + q) is a factor of two polynomials x2 + px + q and x2 + mx + n, then prove that a = n-q m-p
If (x + q) is factor of two polynomial [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex] than [tex]a = \frac{n - q}{m- p}[/tex].
x + a is factor of equations [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex]
What is a polynomial equation?Polynomial equation is equation of independent variables.
Putting it in both the equations
[tex]x^2+px+q=0[/tex]
[tex](-a)^2+p(-a)+q=0\\a^2-ap+q=0 ........(1)[/tex]
[tex]x^2+mx=n = 0\\(-a)^2+m(-a)+n=0\\a^2-am+n=0 .....(2)[/tex]
subtracting (2) from (1)
[tex]-am+ap+n-q=0[/tex]
[tex]a=\frac{n-q}{m-p}[/tex]
Thus, the required expression is [tex]a=\frac{n-q}{m-p}[/tex].
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Which point has coordinates (5,-7pi/6)?
Point A
Point B
Point C
Point D
Use properties to evaluate 3/4(1/5÷3/5)(-8).
A. 2
OB. 5
O C. -2
OD. -5
Answer:
C. -2
Step-by-step explanation:
Use A-P-E-X
How I solved it:
3/4(1/5÷3/5)(-8)
3/4(1/5×5/3)(-8)
3/4(1/3)(-8)
1/4(-8)=-2
Hope this helps!
If not, I am sorry.
a television set was priced $1659 after a 30% discount. What original price before the discount?
=======================================================
Work Shown:
x = price before the discount
30% of x = 0.30x = amount saved
x - 0.30x = 0.70x = price after discount = 1659
0.70x = 1659
x = 1659/(0.70)
x = 2370
First we'll have to convert the percent into decimal.
We'll have to divide the value by 100.
[tex]\frac{30}{100}[/tex]
[tex]\bold{=0.30}[/tex]
Now, we can find the original price.
[tex]\large\boxed{\bold{Formula:OP= \frac{price}{1-Discount}}}[/tex]
We have all the necessary values to find the original price.
Let's solve!
Substitute the values according to the formula.
[tex]OP=\frac{1659}{1-0.30}[/tex]
OP= $2370
Therefore, the original price of the television set is $2370
Which best describes why the function is nonlinear? the rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees. the rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
What is a nonlinear function?A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.
The rate of change between 2 and 3 trees is given by:
R₂₃ = (180 - 120)/(3-2)
R₂₃ = 60.
Also, the rate of change between 3 and 5 trees is given by:
R₃₅ = (290 - 180)/(5-3)
R₃₅ = 110/2
R₃₅ = 55.
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Complete Question:
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?
The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
What is a nonlinear function?
A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.
The rate of change between 2 and 3 trees is given by:
R₂₃ = (180 - 120)/(3-2)
R₂₃ = 60.
Also, the rate of change between 3 and 5 trees is given by:
R₃₅ = (290 - 180)/(5-3)
R₃₅ = 110/2
R₃₅ = 55.
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Complete Question:
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?
John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.
Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?
w(w – 2) = 48
w(w + 2) = 48
2w(w – 2) = 48
2w(w + 2) = 48
The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The mosaic to be formed is rectangular in shape.
Area of a rectangle = length x width
The length is longer than the width by 2,
So, length = w+2
Area of a rectangle = (w+2) x w
The correct equation is B: w(w + 2) = 48
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Answer: B
Step-by-step explanation:
A ration of two numbers is equal to 3:8 if the smaller number is 14 find the greatest number
Answer:
34 and ⅔
Step-by-step explanation:
added in the picture
Hi, can someone help please? Thanks! Calculate the correlation coefficient of the following data
Answer:
Option C is correct
Correlation coefficient of the following data is 0.37
Step-by-step explanation:
Correlation coefficient formula :
r = Σ [([tex]x - x_{m}[/tex]) × ([tex]y - y_{m}[/tex])] ÷ √ [Σ [tex](x - x_{m})^{2}[/tex] × Σ [tex](y - y_{m}) ^{2}[/tex]]
x = Data points in Data set x
y = Data points in Data set y
[tex]x_{m}[/tex]= Mean of Data set x
[tex]y_{m}[/tex]= Mean of Data set y
Now put all the values and sumation it as of given in the formula
Mean of Data set x = (1+4+8+6+2)÷5 = 21÷5 = 4.2
Mean of Data set y = (16+20+15+22+9)÷5 = 82÷5 = 16.4
Now put the values in the equation
r = Σ [(x - 4.2) × (y - 16.4)] ÷ √ [Σ [tex](x - 4.2)^{2}[/tex] × Σ [tex](y - 16.4) ^{2}[/tex]]
Now put every single value of x and y and after we will get the required Correlation coefficient.
And that is Correlation coefficient of the following data is 0.37
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a city's monthly precipitation amounts, in inches, for the last two years are recorded in the table. which histogram corresponds to the table?
Based on the given histograms, and the table on the city's monthly precipitation amounts, the histogram that corresponds to the table is Histogram 1.
Which histogram is the appropriate fit?The number of months with 0 - 1.992 inches is 8 months which means that the first bar on the histogram of between 0 to 2 inches should reach the 8 month mark.
6 months had 1.992 - 3.994 inches so the next bar should stop at the 6th month mark. The next bar should stop at the 4 month mark.
The one after that should stop at the 5 month mark. The last bar would stop at the 1 month mark.
The only histogram that has this is histogram 1 which is not shown clearly but it likely the only one with these qualities as the others don't have it.
Rest of the question:
Amount (inches) 0 - 1.992 - 3.99 4 -5.996 - 7.998 - 9.99
Number of Months 8 6 4 5 1
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Golf balls cost $0.90 each at Jerzy’s Club, which has an annual $25 membership fee. At Rick and Tom’s sporting-goods store, the price is $1.35 per ball for the same brand. Where you buy your golf balls depends on how many you wish to buy. Explain, and illustrate your reasoning with a graph.
Answer:
See attached graph.
Step-by-step explanation:
Each situation can be expressed as an equation:
Jerzy: Total Cost (y1) is the $25 membership fee plus $0.80/golf ball (x):
y1 = $25 + $0.90x
Rick and Tom's: Total Cost (y2) is $1.25 per golf ball, x.
y2 = $1.25x
See the attached graphs of these two equations. Jerzy's cost less after 56 balls are purchased.
Use the properties of exponents to rewrite this expression. Then evaluate the rewritten expression for the given values to
complete the statement.
(11j³k²) (³4)
When j = -8and k = 7
The value of the expression for the given values is 1294139
Evaluating an expression
From the question, we are to rewrite the expression
(11j⁻³k²) (j³k⁴)
This can be rewritten as
11 × j⁻³ × k² × j³ × k⁴
11 × j⁻³ × j³ × k² × k⁴
11 × j⁻³⁺³ × k²⁺⁴
11 × j⁰× k⁶
= 11 × 1 × k⁶
= 11k⁶
Now we are to evaluate the expression for when j = -8 and k = 7
The expression is
= 11 × k⁶
= 11 × 7⁶
= 1294139
Hence, the value of the expression for the given values is 1294139
Here is the complete question:
Use the properties of exponents to rewrite this expression. Then evaluate the rewritten expression for the given values to
complete the statement.
(11j⁻³k²) (j³k⁴)
When j = -8 and k = 7
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Answer:
539
Step-by-step explanation:
Calculate the following limit:
[tex]\displaystyle \lim_{x \to \infty}{\dfrac{\log(x^8 - 5)}{x^2}}[/tex]
If we evaluate at infinity, we have:
[tex]\bf{\displaystyle L = \lim_{x \to \infty}{\frac{\log(x^8 - 5)}{x^2}} = \frac{\infty}{\infty} }[/tex]
However, the infinity of the denominator has a higher order. Therefore, we can conclude that [tex]\boldsymbol{L = 0.}[/tex]
However, proving that the limit is 0 without using L'Hopital or the "order" criterion is complicated. To do so, let us denote:
[tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} }[/tex]
To find the limit, we must look for two functions h(x) and g(x) such that h(x)≤ f(x)≤ g(x) and
[tex]\boldsymbol{\displaystyle \lim_{x \to \infty}{h(x)} = 0, \qquad \lim_{x \to \infty}{g(x)} = 0}[/tex]
If we find these functions, then we can conclude that [tex]\bf{\lim_{x \to \infty}{f(x)} = 0.}[/tex]
First, let's note that when x⁸ - 5 > 1, then log(x⁸ - 5) > 0 (and this is true when x is large). Likewise, we have that x² > 0 for x > 0. Therefore, we have:
[tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} \geq 0}[/tex]
when x "is big enough". Thus, we have h(x) = 0 where it is clear that [tex]\bf{\lim_{x \to \infty}{h(x)} = 0.}[/tex]
To find the second function, let's first note that \log is an increasing function, so since x⁸ ≥ x⁸ - 5, then log(x⁸) ≥ log(x⁸ - 5). So we have to
[tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} }[/tex]
now, if we take y = e^y, then we can write
[tex]\boldsymbol{\displaystyle \frac{\log(x^8)}{x^2} = \frac{\log(e^{8y})}{e^{2y}} = \frac{8y}{e^{2y}}}[/tex]
A very important property about the exponential function is
[tex]\boldsymbol{\displaystyle e^x > \frac{x^n}{n!}}[/tex]
For any n [tex]\bf{n \in \mathbb{N}}[/tex] and x > 0. If we take n = 2, then we have
[tex]\boldsymbol{\displaystyle e^{2y} > \frac{(2y)^2}{2!} = \frac{4y^2}{2} = 2y^2}[/tex]
From this it follows that
[tex]\boldsymbol{\displaystyle \frac{1}{e^{2y}} < \frac{1}{2y^2} }[/tex]
Therefore, we have to
[tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} < \frac{8y}{2y^2} = \frac{4}{y} = \frac{4}{\log x} }[/tex]
yes, [tex]\bf{g(x) = 4/\log x}[/tex] where [tex]\bf{\lim_{x \to \infty}{g(x)} = 0}[/tex]. Also, [tex]\bf{h(x) \leq f(x) < g(x)}[/tex]. Therefore, [tex]\bf{\lim_{x \to \infty}{f(x)} = 0}[/tex].
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\sf{\purple{Pisces04}}}}}}}[/tex]
If angle D is an acute angle and its tangent ratio is 1.055, then what is the measure of angle D to the nearest tenth of a degree?
The measure of angle D to the nearest tenth of a degree is 47 degrees
Application of SOH CAH TOAThis theorem is used to determine the measure of sides and angles of a triangle.
According to the theorem
tan theta = opp/adj = 1.055
theta = arctan(1.055)
theta = 46.53 degrees
Hence the measure of angle D to the nearest tenth of a degree is 47 degrees
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