Answer:
x=12
Step-by-step explanation:
8-(2x-+9)=17-24
8-2x=17-24-9
8-2x=-7+-9
8-2x=-16
-2x=-16-8
-2x=-24
x=-24/-2
x=12
Suppose 30% of a population possess a given characteristic. If a random sample of size 1200 is drawn from the population, then the probability that less than 348 possess that characteristic is
Answer:
The probability that less than 348 possess that characteristic is 0.2148 = 21.48%.
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this question, we have that:
[tex]n = 1200, p = 0.3[/tex]
So
[tex]\mu = E(X) = np = 1200*0.3 = 360[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1200*0.3*0.7} = 15.8745[/tex]
The probability that less than 348 possess that characteristic is
Using continuity correction, this is P(X < 348 - 0.5) = P(X < 347.5), which is the pvalue of Z when X = 347.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{347.5 - 360}{15.8745}[/tex]
[tex]Z = -0.79[/tex]
[tex]Z = -0.79[/tex] has a pvalue of 0.2148.
The probability that less than 348 possess that characteristic is 0.2148 = 21.48%.
The population follows a normal distribution.
The probability that less than 348 possess that characteristic is 0.2248
The given parameters are:
[tex]\mathbf{n = 1200}[/tex]
[tex]\mathbf{p = 30\%}[/tex]
Start by calculating the mean:
[tex]\mathbf{\mu =np}[/tex]
[tex]\mathbf{\mu =1200 \times 30\%}[/tex]
[tex]\mathbf{\mu =360}[/tex]
Calculate the standard deviation
[tex]\mathbf{\sigma = \sqrt{np(1 - p)}}[/tex]
[tex]\mathbf{\sigma = \sqrt{360(1 - 30\%)}}[/tex]
[tex]\mathbf{\sigma = \sqrt{252}}[/tex]
[tex]\mathbf{\sigma = 15.87}[/tex]
Calculate the z-score
[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]
Where:
x = 348
So, we have:
[tex]\mathbf{z = \frac{348 - 360}{15.87}}[/tex]
[tex]\mathbf{z = -\frac{12}{15.87}}[/tex]
[tex]\mathbf{z = -0.7561}[/tex]
So, the probability is represented as:
[tex]\mathbf{P(x < 348) = P(z < -0.7561)}[/tex]
From the z-table of probabilities, we have:
[tex]\mathbf{P(x < 348) = 0.2248}[/tex]
Hence, the probability that less than 348 possess that characteristic is 0.2248
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Jenna wants to wrap a shipping box shaped like a rectangular prism. The box is 29 inches tall and has a square base with sides that each measure 5 inches. How much paper will she use?
Answer:
she will use 420 inches of paper with 69 left over
Step-by-step explanation:
It is what it is
Answer:
She would use 330 inches of paper
The height of a trapezoid is 16in. The bases are 32in and 24in. What is the area of the trapezoid.
Answer:
448in^2
Step-by-step explanation:
The area of a trapezoid is the bases added divided by two times the height.
(32+24)/2*16=28*16=448 in^2
Natalie has $250 in savings. At the end of 6 months, she has $450 in savings. What is the percent increase in the amount of her savings?
80 percent. 80 percent of 250 is 200 and 250 increased by a total of 200 therefore 80%
Answer: 80%
Step-by-step explanation:
Rule of 3.
Let's put the money on the left side and the percents on the right side.
[tex]\frac{250}{450}=\frac{100}{x}[/tex]
Solve for x:
[tex]x=\frac{450*100}{250}[/tex]
[tex]x=180[/tex]
Subtract 100 from 180
180-100=80
Determine the intercepts of the line.
Y+1=3(x - 4)
X-intercept:
y-intercept:
Answer:
x-intercept: (13/3, 0)
y-intercept: (0, -13)
Step-by-step explanation:
y+1 = 3x-12
y= 3x-13
For y-intercept:
y= 3(0) -13
y=-13
For x-intercept:
0=3x-13
3x=13
x=13/3
The intercepts of the line will be,
x-intercept: (13/3, 0)
y-intercept: (0, -13)
What is an intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
Given that y+1=3(x - 4). The x-intercept and y-intercept will be calculated as,
y+1 = 3x-12
y= 3x-13
For y-intercept:
y= 3(0) -13
y=-13
For x-intercept:
0=3x-13
3x=13
x=13/3
Therefore, the x-intercept is (13/3, 0) and the y-intercept is (0, -13).
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What term must we add to complete the square on x^2 + 12x
Answer:
Step-by-step explanation:
You need to first find what x equals before you can solve the equation.
Answer:
36
Step-by-step explanation:
x^2+2xy+y^2
12x/2x=6=y
y^2=36
Which student wrote an equation with a solution of x = -8
Jenna: -3 ( x - 9 ) = -3
Archer: 4 ( 2x - 16 ) = 16
both
neither
jenna
archer
Answer:
Neither
Step-by-step explanation:
Both equations are x=10
Please help, it would be greatly appreciated!
Answer:
A
Step-by-step explanation:
6 times 9 times 3 = 162
Oline is solving the equation 0 = x2 – 5x – 4 using the quadratic formula. Which value is the negative real number solution to her quadratic equation? Round to the nearest tenth if necessary. Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction
Answer:
The solution to the equation are [tex]5+\frac{\sqrt{42} }{2\\} \ and \ 5-\frac{\sqrt{42} }{2\\}\\[/tex]
Both of his values are positive real numbers
Step-by-step explanation:
The general formula of a quadratic equation is expressed as [tex]ax^{2}+bx+c = 0\ where;\\x = -b\±\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
Given the expression 0 = x² – 5x – 4 which can be rewritten as shown below;
x² – 5x – 4 = 0
Comparing this to the general equation; a = 1, b = -5, c= -4
To get the solution to the quadratic equation, we will use the general formula above;
[tex]x = -b\±\frac{\sqrt{b^{2}-4ac } }{2a}\\x = -(-5)\±\frac{\sqrt{(-5)^{2}-4(1)(-4) } }{2(1)}\\\\x = 5\±\frac{\sqrt{25+16 } }{2}\\x =5\±\frac{\sqrt{41} }{2}\\x = 5+\frac{\sqrt{42} }{2}\ and \ 5-\sqrt{42} /2\\[/tex]
Both of his values are positive real numbers
Answer: D.–0.7
Step-by-step explanation: hope this helps :)
The frame of the given window is made
of a rectangle with semi-circular top.
Find its perimeter and area.
2.1 m
1.4 m
Answer:
3.7096902=area
Step-by-step explanation:
2.1x1.4=2.94m^2
2.94+(.5pi(.7^2))
What are they?
Equal Lines?
Parallel Lines?
perpendicular Lines?
None of the above?
Answer:
Equal lines
Step-by-step explanation:
-5x-y = -4
Multiply by 3
-15x -3y = -12
This is the same as the second equation
That means the lines are the same
They are equal lines
A baker has 88 muffins. He fills large boxes that hold 9 muffins each.Then, he puts the leftover muffins in a small box. How many muffins are in the small box.
Answer:
7
Step-by-step explanation:
Solve the equation.
29= p x 20
p= __
Answer:
1.45
Step-by-step explanation:
1. divide both sides of the equation by 20 to get rid of the 2o on the right side
[tex]\frac{29}{20}[/tex]= p x [tex]\frac{20}{20}[/tex]
now u end up with 1.45=p
hope it helped
Which equation is not written in slope-intercept form?
Answer:
B) 2x - 5 = 2y + 14
Step-by-step explanation:
slope intercept form: y = mx + b
B) 2x - 5 = 2y + 14 is the only answer choice that does not isolate y, and place all other terms on the other side; therefore, is your answer.
~
Answer:
B
Step-by-step explanation:
slope intercept is a formula of y=mx+b all other answers proposed give a form of slope intercept, but with Choice B you have to do math to convert it to slope intercept.
Suppose compact fluorescent light bulbs last, on average, 11,500 hours. The distribution is normal and the standard deviation is 400 hours. What percent of light bulbs burn out within 12,300 hours?
Answer:
2.275%
Step-by-step explanation:
The first thing to do here is to calculate the z-score
Mathematically;
z-score = (x-mean)/SD
from the question, x = 12,300 hours , mean = 11,500 hours while Standard deviation(SD) = 400 hours
Plugging the values we have;
z-score = (12,300-11,500)/400 = 800/400 = 2
Now, we want to calculate P(z ≤ 2)
This is so because we are calculating within a particular value
To calculate this, we use the z-score table.
Mathematically;
P(z ≤ 2) = 1 - P(z > 2) = 1 - 0.97725 = 0.02275
To percentage = 2.275%
help me pls i dont know what to do
The answer is the last one: k = 5
Hope I helped and good luck!
Is a percent increase for 50 to 70 = to the percent decrease from 70 to50
Answer:
no it is not.
Step-by-step explanation:
%increase = 40% while %loss = about 28.6%
PICK ME!!
How do you use congruence and similarity criteria to prove relationships in geometric figures?
Answer:
Well, as it turns out, when two figures are similar or congruent, they have certain properties, and these properties can be used to prove relationships between the figures. When two figures are similar figures, they have the following properties: Corresponding angles have equal measure.
Step-by-step explanation:
Michelle tried to solve an equation step by step. \begin{aligned} t-\dfrac35&=\dfrac45\\\\ t-\dfrac35+\dfrac35&=\dfrac45+\dfrac35&\green{\text{Step } 1}\\\\ t&=1&\blue{\text{Step } 2} \end{aligned} t− 5 3 t− 5 3 + 5 3 t = 5 4 = 5 4 + 5 3 =1 Step 1 Step 2 Find Michelle's mistake. Choose 1 answer: Choose 1 answer:
Answer:
Step 2
Step-by-step explanation:
Michelle's step in trying to solve the equation is given below:
[tex]\begin{aligned} t-\dfrac35&=\dfrac45\\\\ t-\dfrac35+\dfrac35&=\dfrac45+\dfrac35&\green{\text{Step } 1}\\\\ t&=1&\blue{\text{Step } 2} \end{aligned}[/tex]
Michelle made a mistake in Step 2.
The right hand side of Step 1: [tex]\dfrac45+\dfrac35\neq 1[/tex]
Rather, the correct sum is:
[tex]\dfrac45+\dfrac35=\dfrac75\\\\=1\dfrac25[/tex]
Answer:
Its 1/5
Step-by-step explanation:
Khan
Cross multiplication method, find the value z and y for 3x + 5y = 70 and 7x-3y =60
Answer:
Y=7.05
X= 11.6
Step-by-step explanation:
Equate both equations to zero
3x+5y=70--------equation 1
7x-3y=60---------equation 2
From the equation above
a1=3, b1=5, c1=-70
a2=7, b2= -3, c2=-60
By applying the cross multiplication method
x/b1c2-b2c1= y/a2c1-a1c2= 1/a1b2-a2b1
x/(5)(-60)-(-3)(-70)=y/(7)(-70)-(3)(-60)=1/(3)(-3)-(7)(5)
x/-300-(-210)=y/-490-(-180)=1/-9(-35)
x/-510=y/-310=1/-44
x/-510=1/-44 , y/-310=1/-44
-44x=-510 , -44y= -310
x=11.6 , y=7.05
Thus, the value of x is 11.6 and the value of y is 7.05
The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation I (d B) = 10 log left-bracket StartFraction I Over I Subscript 0 Baseline EndFraction Right-bracket, where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when I = 10 Superscript 32 Baseline (I Subscript 0)?
Answer:
The intensity in decibel is 320 decibelStep-by-step explanation:
Given the intensity, or loudness, of a sound measured in decibels (dB), according to the equation [tex]I (dB)= 10log(\frac{I}{Io} )[/tex] where;
I is the intensity of a given sound and
[tex]Io[/tex] is the threshold of hearing intensity
To get I(dB) when [tex]I=10^{32} Io[/tex]
We will substitute the value of I = [tex]I=10^{32} Io[/tex] into the equation above to have;
[tex]I (dB)= 10log(\frac{10^{32}Io }{Io} )\\I(dB)=10log10^{32}\\ I(dB)=32*10log10\\[/tex]
Since log10 = 1;
[tex]I(dB)=32*10(1)\\I(dB)=320[/tex]
The intensity in decibel is 320 decibel
Answer:
Its D or 80
Step-by-step explanation:
I=10^8 (I subscript 0) can be written as I/I subscript 0, and you can plug that right into the log to get 80.
The boxes below are two similar solids. Find the value of the missing dimensions and support your answer. YOU MUST SELECT 2 ANSWERS
A) b=9
B) b=18
C) h=9
D) h=18
Answer:
b is 9 and h is 18
Step-by-step explanation:
because its times 1.5 for each one so like 5 times 1.5 is 7.5 so we can see that it is times by 1.5
Answer:
A) b = 9
D) h = 18
Step-by-step explanation:
b/6 = 7.5/5 = h/12
b/6 = 1.5
b = 9
1.5 = h/12
h = 18
Someone please help me!!!
Answer: Answer is B
Step-by-step explanation:
Remeber that the shorter a container is doesn't mean it has less mass or volume. the width can mean it holds more. If the radius is twice as big that can mean the contents is more and your getting a better deal. hOpe this will help.
What is the measure of 0 in radians?
Enter an exact expression.
radians
3
7
In the diagram, is a central angle.
Answer:
Θ = π radians
Step-by-step explanation:
The central angle is equal to the arc that subtends it, that is
Θ = π
What is the degree of
6x^5 – 4x^2 + 2x^2 - 3 + x?
A. 3
B. 5
C. 6
D.2
Hello!
Answer:[tex]\boxed{ \bf The~degree~of~the~polynomial~is~B.~5}[/tex]
___________________________________________
Explanation:The term with the greatest exponent determines the degree of the polynomial.
Let's list all the terms:
[tex]6x^{5}[/tex]-4x²2x²-3xOut of all of these terms, the first one has the greatest exponent (5).
the y intercept of G(x) in G(x) = 3x -2 is
Answer:
-2
Step-by-step explanation:
G(x) = 3x -2
Let x = 0 to find the y intercept
G(0) = 3(0)-2
=-2
if an integer from 3 through 14 is chosen at random, what is the probability that the number chosen is not prime
Answer:
Step-by-step explanation:
prime: 3 5 7 11 13
P(notprime) = (12-5)/ 12 = 7/12
Q1: Tyson is taking his basketball team to watch a college basketball game. He bought 8 tickets for $168 $ 168 . One parent bought her son's ticket separately and paid $24 $ 24 . Who had the better deal?
Answer:
Tyson had the better deal
Step-by-step explanation:
We simply want to know who paid less for the ticket.
Tyson bought 8 tickets for the members of his basketball team and it cost it $168 in total.
The cost of each ticket is therefore:
168 / 8 = $21
He paid $21 for each ticket.
The parent bought her son's ticket for $24.
Therefore, Tyson had the better deal because he paid $3 less than the woman.
An angle measures 39.2° less than the measure of its complementary angle. What is the measure of each angle?
Answer: The measures of the angles are 64.6 degrees and 25.4 degrees.
Step-by-step explanation:
Complementary angles add up to 90 degrees.
x can be one angle, and (x-39.2) can be the other
x + (x-39.2) = 90
2x - 39.2 = 90
add 39.2 to both sides
2x = 129.2
divide each side by 2
x = 64.6
find the measure of the other angle
64.6-39.2 = 25.4
The measures of the angles are 64.6 degrees and 25.4 degrees.
Answer:
25.4 and 64.6Step-by-step explanation:
Suppose two complementary angles of measures x And y then
x + y = 90 and y = x - 39.2
if we plug in x - 39.2 instead of y in the equation x + y = 90 we get :
x + (x - 39.2) = 90
then
2x = 90 + 39.2
then
2x = 129.2
then
x = 129.2/2 = 64.6
therefore
y = 64.6 - 39.2
= 25.4
______________________________
:)
A cylinder has a base radius of 4m and a height of 6m. What is its volume in cubic m,
to the nearest tenths place?
Answer:
301.4
Step-by-step explanation:
Volume of a cylinder=pi*[tex]r^{2}[/tex]*h. Assuming you want 3.14 for pi, we can substitue the 4m for r, 6 for h and 3.14 for pi.
V=3.14*[tex]4^{2}[/tex]*6
V=301.44
Since you want to round to nearest tenths, the answer is 301.4
The volume of the cylinder with the given value of radius and height to the nearest tenth place is 301.4 cubic meters.
What is a cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given the data in the question;
Radius r = 4mHeight h = 6mVolume of the cylinder V = ?We substitute our values into the expression above.
V = π × r² × h
V = 3.14 × (4m)² × 6m
V = 3.14 × 16m² × 6m
V = 301.4m³
The volume of the cylinder with the given value of radius and height to the nearest tenth place is 301.4 cubic meters.
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