Answer:
The range is {4,5,7}
Step-by-step explanation:
The range of a relation is the output values The values are 4,7,5 we normally put them in order from smallest to largest
The range is {4,5,7}
A 45 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1088
Answer:
The substance's half-life is 6.4 days
Step-by-step explanation:
Recall that the half life of a substance is given by the time it takes for the substance to reduce to half of its initial amount. So in this case, where they give you the constant k (0.1088) in the exponential form:
[tex]N=N_0\,e^{-k\,*\,t}[/tex]
we can replace k by its value, and solve for the time "t" needed for the initial amount [tex]N_0[/tex] to reduce to half of its value ([tex]N_0/2[/tex]). Since the unknown resides in the exponent, to solve the equation we need to apply the natural logarithm:
[tex]N=N_0\,e^{-k\,*\,t}\\\frac{N_0}{2} =N_0\,e^{-0.1088\,*\,t}\\\frac{N_0}{2\,*N_0} =e^{-0.1088\,*\,t}\\\frac{1}{2} =e^{-0.1088\,*\,t}\\ln(\frac{1}{2} )=-0.1088\,t\\t=\frac{ln(\frac{1}{2} )}{-0.1088} \\t=6.37\,\,days[/tex]
which rounded to the nearest tenth is: 6.4 days
Answer:
6.4
Step-by-step explanation:
I did it on the same site and got it correct
In 2014, 2.756 billion dollars of e-cigarettes were sold worldwide. Fill in the table with the 2014 sales amount written in millions of dollars.
Answer:
$2756 million
Step-by-step explanation:
2.756×10⁹ = 2756×10⁶
Sales in 2014 were $2756 million.
_____
Comment on the question
In the US, a billion is 1000 million. In some other parts of the world, a billion is a million million. This sort of question can be ambiguous.
What percent of forty-eight is thirty?
Answer:
P = 62.5 %
Step-by-step explanation:
Of means multiply and is means equals
P * 48 = 30
Divide each side by 48
P = 30/48
P = .625
Change to percent form
P = 62.5 %
Answer:
62.5%
Step-by-step explanation:
30 is 62.5% of 48 since:
30÷48=0.625
0.625×100=62.5%
What are the terms in the algebraic expression
102 + 10 +
3b
Answer:
102, 10, and, 3b
Step-by-step explanation:
An engineering consulting firm wantedto evaluate a rivet process by measuring the formed diameter. The following data represent the diameters (in hundredths of an inch) for a random sample of 24 rivet heads:
6.81 - 6.79 - 6.69 - 6.59 - 6.65 - 6.60 - 6.74 - 6.70 - 6.76
6.84 - 6.81 - 6.71 - 6.66 - 6.76 - 6.76 - 6.77 - 6.72 - 6.68
7.71 - 6.79 - 6.72 - 6.72 - 6.72 - 6.79 - 6.83
a) Set up a 95% confidence interval estimate of the average diameter of rivet heads (in hundredths of an inch).
b) Set up a 95% confidence interval estimate of the standard deviation of the diameter of rivet heads (in hundredths of an inch)
Answer:
Step-by-step explanation:
6.81 - 6.79 - 6.69 - 6.59 - 6.65 - 6.60 - 6.74 - 6.70 - 6.76
6.84 - 6.81 - 6.71 - 6.66 - 6.76 - 6.76 - 6.77 - 6.72 - 6.68
7.71 - 6.79 - 6.72 - 6.72 - 6.72 - 6.79 - 6.83
[tex]\bar x =6.77[/tex]
S.D = 0.21
[tex]I=6.77\pmt\times\frac{s}{\sqrt{n} }[/tex]
df = 24
α = 0.05
t = 2.064
[tex]I=6.77\pm2.064\times\frac{0.21}{\sqrt{25} } \\\\=6.77\pm0.087\\\\=[6.683,6.857][/tex]
b)
[tex]\sqrt{\frac{(1-n)s^2}{X^2_{\alpha /2} } < \mu <\sqrt{\frac{(1-n)s^2}{X^2_{1-\alpha/2} } }[/tex]
[tex]\sqrt{\frac{24 \times 0.21^2}{39.364} } < \mu <\sqrt{\frac{24 \times 0.21^2}{12.401} } \\\\=0.1640<\mu<0.2921[/tex]
The following data values represent a population. What is the variance of the
values?
8, 10, 14,4
A. 14
B. 10
C. 9
D. 13
Answer:
D: 13
So first you write down your equation ( its on the picture I posted) Then you need to find the mean which is the sum of all the values over the number of values you have (n) After finding your mean, you subtract it from every value you have. To check if what you have done is correct you add all the values you got after subtracting, if you get 0 your answer is correct. Then you square each of those answers you get after you subtract. You get the total which you then divide by the number of values you have (n)
I hope you understand, I am not that good at explaining. And I am not completely sure with my answer, but I think it's correct.
en una division el 42 es el cociente el divisor 12 y el dividendo 513 ¿Cual es el resto?
Answer:
El resto es 9.
Step-by-step explanation:
En una división el cociente es el resultado que se obtiene, el divisor es el número por el que se divide otro número, el dividendo es el número que va a dividirse entre otro y el resto es lo que queda cuando un número no puede dividirse exactamente entre otro. De acuerdo a esto, la división planteada se encuentra en la imagen adjunta donde al resolverla se encuentra que el número que queda es 9 y este es el resto.
The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning at least 30 times. Group of answer choices Greater than 0.60 Between 0.20 and 0.40 Between 0.01 and 0.20 Between 0.40 and 0.60 Almost 0
Answer:
Between 0.01 and 0.20
Step-by-step explanation:
I am going to use the normal approximation to the binomial 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 problem, we have that:
[tex]n = 500, p = 0.05[/tex]
So
[tex]\mu = E(X) = np = 500*0.05 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734/tex]
Find the probability of winning at least 30 times.
Using continuity correction, this is [tex]P(X \geq 30 - 0.5) = P(X \geq 29.5)[/tex]. So this is 1 subtracted by the pvalue of Z when X = 29.5. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29.5 - 25}{4.8734}[/tex]
[tex]Z = 0.92[/tex]
[tex]Z = 0.92[/tex] has a pvalue of 0.8212
1 - 0.8212 = 0.1788
So the correct option is:
Between 0.01 and 0.20
Serena wants to determinethe area of the lawn the grass part of her front yard using the information given in the diagram below Serena knows that she needs to divide by 9 to change the units from square yards so she writes the expression below to determine the area of grass in square yards
Answer:
The answer is 295 square yards.
Step-by-step explanation:
[48(72-12)-15^2] divide by 9
3456-576-225 divide by 9
Subtract 3456 by 576
2880-255
2655 divide by 9
=295 square yards.
Hope this helped!
The answer is 295 square yards.
What is the area of square space?To find the area of square , take the square of side.
Given expression is [48(72-12)-15^2] divide by 9 .
Let the unknown area is x.
x = {48 * 60 - 15^2 } divide by 9
x = 2880 - 225 divide by 9
x = 2655 divide by 9
x =295 square yards.
Hence, The answer is 295 square yards.
To learn more about the area of square;
https://brainly.com/question/27776258
#SPJ2
Which of the following shows the extraneous solution to the logarithmic equation log Subscript 7 Baseline (3 x cubed + x) minus log Subscript 7 Baseline (x) = 2 x = negative 16 x = negative 4 x = 4 x = 16
Answer:
x = -4Step-by-step explanation:
A graphing calculator shows there is one solution to ...
[tex]\log_7{(3x^2+x)}-\log_7{(x)}=2[/tex]
However, the usual solution method would be to combine the logarithms and take the antilog to get ...
[tex]\log_7{\left(\dfrac{3x^3+x}{x}\right)}=2\\\\\log_7{(3x^2 +1)}=2\\\\3x^2+1=7^2\\\\x^2=\dfrac{49-1}{3}=16\\\\x=\pm 4\qquad\text{take the square root}[/tex]
This gives two solutions. the "solution" x = -4 is extraneous, as it doesn't work in the original equation. "x" must be positive in the log expressions.
Answer:
x = - 4
Step-by-step explanation:
Got it right :)
What is the average rate of change of f over the interval [-1, 4] Give an exact number.
Answer:
1.4
Step-by-step explanation:
The average rate of change is the "rise" divided by the "run".
rise/run = (f(4) -f(-1))/(4 -(-1)) = (0 -(-7))/(4+1)
rise/run = 7/5 = 1.4
The average rate of change on the interval [-1. 4] is 1.4.
We will see that the average rate of change in the given interval is 1.4
How to find the average rate of change?
For a given function f(x), the average rate of change on an interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In this case the interval is [-1, 4], using the graph we can see that:
f(-1) = -7
f(4) = 0
replacing that in the formula we get:
[tex]r = \frac{0 - (-7)}{4 - (-1)} = \frac{7}{5} = 1.4[/tex]
If you want to learn more about rates of change, you can read:
https://brainly.com/question/8728504
Answer 5x + 8 − 3x = −10
Answer:
-9
Step-by-step explanation:
5x+8-3x = -10
Combine like terms
2x+8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
Answer:
-9
Step-by-step explanation:
5x + 8 - 3x = -10
Combine like terms
2x + 8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
A trapezoid is shown. The lengths of the bases are 4 and 8. The height of the altitude is 4. What is the area of the trapezoid?
Answer:
24
Step-by-step explanation:
Formula
The area of a Trapezoid is given as
A = (b1 + b2)*h/2
Givens
b1 = 8
b2 = 4
h = 4
Solution
Area = (8 + 4)*4/2
Area = 12*4/2
Area = 24
The sum of two consecutive odd integers is 156. Which is an equation that can be used to solve for x? Please
Answer:
x+(x+2) = 156
Step-by-step explanation:
Let x = 1st odd integer
x+2 = next odd integer
x+(x+2) = 156
2x+2 =156
Subtract 2
2x= 154
Divide by 2
x = 77
x+2 = 79
"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 33 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 55 feet from the wall?"
Answer:
Step-by-step explanation:
The question has typographical errors. The correct question is:
"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?
Solution:
The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.
Let x represent the distance from the top of the ladder to the ground(opposite side)
Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)
The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,
dy/dt = 3 ft/s
The rate at which x is reducing would be
dx/dt
Applying Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side², it becomes
x² + y² = 12²- - - - - - - -1
Differentiating with respect to time, it becomes
2xdx/dt + 2ydy/dt = 0
2xdx/dt = - 2ydy/dt
Dividing through by 2x, it becomes
dx/dt = - y/x ×dy/dt- - - - - - - - - - 2
Substituting y = 5 into equation 1, it becomes
x² + 5 = 144
x² = 144 - 25 = 119
x = √119 = 10.91
Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes
dx/dt = - 5/10.91 × 3
dx/dt = - 1.37 ft/s
Matt brought $40.50 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1 6 as much as the sketchbook, and the sketchbook cost 3 4 the cost of the paint set. Matt had $3.00 left over after buying these items.
Answer:
idk what you mean
Step-by-step explanation:
idk
Find the population mean or sample mean as indicated.
Sample 17, 13, 5, 12, 13
Answer:
13
Step-by-step explanation:
I think
what function is increasing? will give brainlist !
Answer:
Option B.
Step-by-step explanation:
Option A.
f(x) = [tex](0.5)^{x}[/tex]
Derivative of the given function,
f'(x) = [tex]\frac{d}{dx}(0.5)^x[/tex]
= [tex](0.5)^x[\text{ln}(0.5)][/tex]
= [tex]-(0.693)(0.5)^{x}[/tex]
Since derivative of the function is negative, the given function is decreasing.
Option B. f(x) = [tex]5^x[/tex]
f'(x) = [tex]\frac{d}{dx}(5)^x[/tex]
= [tex](5)^x[\text{ln}(5)][/tex]
= [tex]1.609(5)^x[/tex]
Since derivative is positive, given function is increasing.
Option C. f(x) = [tex](\frac{1}{5})^x[/tex]
f'(x) = [tex]\frac{d}{dx}(\frac{1}{5})^x[/tex]
= [tex]\frac{d}{dx}(5)^{(-x)}[/tex]
= [tex]-5^{-x}.\text{ln}(5)[/tex]
Since derivative is negative, given function is decreasing.
Option D. f(x) = [tex](\frac{1}{15})^x[/tex]
f'(x) = [tex]-15^{-x}[\text{ln}(15)][/tex]
= [tex]-2.708(15)^{-x}[/tex]
Since derivative is negative, given function is decreasing.
Option (B) is the answer.
Please answer this correctly
Answer:
1.2 km
Step-by-step explanation:
The first thing that we should go over is the formula for the area of a trapezoid.
Recall that it is [tex]A= \frac{b_1 +b_2}{2} *h[/tex]
From this image, we have the following information
[tex]b_1=2.5\\\\b_2=1.5\\\\A=2.4[/tex]
Now, we can plug this information into our formula and then solve for h.
[tex]2.4=\frac{2.5+1.5}{2} *h\\\\2.4=\frac{4}{2} *h\\\\2.4=2h\\\\h=1.2[/tex]
Another method that can be employed is to use the pythagorean theorem.
A trapezoid can be be broken into a rectangle and two triangles.
If we look at the difference in the sizes of the bases, the bottom base is 1 km larger. This means that the base of each triangle would be 0.5 km long.
As we have two side lengths of the triangle, we can now use the Pythagorean theorem to find the third side, which is h.
[tex](1.3)^2=h^2+(0.5)^2\\\\h^2=1.69-0.25\\\\h=\sqrt{1.44} \\\\h=1.2[/tex]
Answer:
h=1.2 km
Step-by-step explanation:
This is the formula of a Trapezium
A=[tex]\frac{h(a+b)}{2}[/tex]
[tex]2.4=\frac{(2.5+1.5)h}{2}\\ 2.4=\frac{4h}{2}\\ 2.4*2=4h\\4.8=4h\\h=1.2[/tex]
Whats the answer?
A) 35
B)55
C)70
D)110
Answer:
D
Step-by-step explanation:
If <CAD=35, <KNL=55 because the remaining angle is 90 since it's a right angle. Therefore <KNM=110 because 55+55=110
If someone have all the proofs of this I’ve been trying since yesterday PLEASE
Answer:
Please see steps below
Step-by-step explanation:
Notice the following:
(a) Angles 5 and 1 are alternate angles between parallel lines, and then they must be congruent (equal in measure) [tex]\angle 1 \,=\,\angle 5[/tex]
(b) Angles 6 and 3 are also alternate angles between parallel lines, so they must be congruent (equal measure) [tex]\angle 3 \,=\,\angle 6[/tex]
Therefore, instead of expressing the addition:
[tex]\angle 5\,\,+\,\,\angle 2\,\,+\,\,\angle 6[/tex]
we can write:
[tex]\angle 1\,\,+\,\,\angle 2\,\,+\,\,\angle 3[/tex]
which in fact clearly add to [tex]180^o[/tex]
Find the x- and y-intercepts of the equation 7x + 14y = 28.
Answer: The x-intercept is 4 and the y-intercept is 2.
Step-by-step explanation:
The x is intercept is when y is 0 and the y intercept is when x is 0.So using this information you can put in 0 for x and another 0 for y and solve for the x and y intercepts.
7(0) + 14y = 28
0 + 14y = 28
14y = 28
y = 2
7x + 14(0) = 28
7x + 0 = 28
7x = 28
x = 4
The [tex]x[/tex]-intercept of the given equation is [tex]4[/tex] and the [tex]y[/tex]-intercept is [tex]2[/tex].
Given:
The equation is:
[tex]7x+14y=28[/tex]
To find:
The [tex]x[/tex]-intercept and [tex]y[/tex]-intercept of the given equation.
Explanation:
We have,
[tex]7x+14y=28[/tex] ...(i)
Substitute [tex]x=0[/tex] in (i) to find the [tex]y[/tex]-intercept.
[tex]7(0)+14y=28[/tex]
[tex]14y=28[/tex]
[tex]\dfrac{14y}{14}=\dfrac{28}{14}[/tex]
[tex]y=2[/tex]
Substitute [tex]y=0[/tex] in (i) to find the [tex]x[/tex]-intercept.
[tex]7x+14(0)=28[/tex]
[tex]7x=28[/tex]
[tex]\dfrac{7x}{7}=\dfrac{28}{7}[/tex]
[tex]x=4[/tex]
Therefore, the [tex]x[/tex]-intercept of the given equation is [tex]4[/tex] and the [tex]y[/tex]-intercept is [tex]2[/tex].
Learn more:
https://brainly.com/question/19669786
A soup can has a diameter of 8 centimeters and a height of 15 centimeters how much soup does the can hold?
Answer:
V = 240 pi
Step-by-step explanation:
We want the volume of a cylinder
V = pi r^2 h
We have the diameter and want the radius
r = d/2 = 8/2 = 4
V = pi ( 4)^2 * 15
V = pi * 16* 15
V = 240 pi
Let pi = 3.14
V =753.6 cm^3
Let pi be the pi button
V =753.9822369 cm^3
Answer:
240 pi
Step-by-step explanation:
found the answer online so now work (don't delete my answer)
marcus has a spinner with 3 red sections, 2blue sections, and 1 purple section match the event of landing on each color to the correct probability
Answer:
see below
Step-by-step explanation:
3 red sections, 2blue sections, and 1 purple section = 6 sections
P( red) = red/total = 3/6 =1/2
P( blue) = blue/total = 2/6 =1/3
P( purple) = purple/total = 1/6
Answer:
This is the answer
Step-by-step explanation:
Help me pleaseeee and thanks
Work Shown:
v - w = ( v ) - ( w )
v - w = ( -3i ) - ( 2-4i)
v - w = ( 0-3i ) - ( 2-4i)
v - w = 0-3i -2+4i
v - w = (0-2) + (-3i+4i)
v - w = -2 + i
during a basketball practice, mai attemoted 40 free throws and was successful on 25% of them how many successful free throws did she make?
Answer:
10 successful throws
Step-by-step explanation:
40 free throws
25% (25)
40 x 0.25 = 10
I NEED HELP PLEASE HELP ME PLEASEEE
Answer:
The answer is 2.5 hours
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Volume of cone = 1/3πr²h
= (1/3)(3.14)(1.5)²(5)
= (1/3)(3.14)(2.25)(5)
= (1/3)(35.3)
= 11.78
≈ 11.8 cubic inches
Calculo el area del búmeran tomando en cuenta que su diámetro es 20 cm
Answer:
50π cm²
Step-by-step explanation:
In this case we have that the area of the boomerang has been the area of the largest semicircle minus the area of the smaller semicircles.
We know that the radius is half the diameter:
r = d / 2 = 20/2
r = 10
Now we have to:
Alargest = π · r²
Alargest = π · (10 cm) ²
Alargest = 100π cm²
Asmaller = π · r²
Asmaller = π · (5 cm) ²
Asmaller = 25π cm²
Finally, the boomerang area has been:
Aboomerang = 100π cm² - 2 · (25π cm²)
Aboomerang = 50π cm²
The lifespan of a car battery averages six years. Suppose the batterylifespan follows an exponential distribution.(a) Find the probability that a randomly selected car battery will lastmore than four years.(b) Find the variance and the 95th percentile of the battery lifespan.(c) Suppose a three-year-old battery is still going strong. (i) Find theprobability the battery will last an additional five years. (ii) Howmuch longer is this battery expected to last
Answer:
Step-by-step explanation:
Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.
Thus , the parameter of the exponential distribution is calculated as,
μ = 6
[tex]\frac{1}{\lambda} =6[/tex]
[tex]\lambda = \frac{1}{6}[/tex]
a) The required probability is
[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]
= 0.513
Hence, the probability that a randomly selected car battery will last more than four years is 0.513
b) The variance of the battery span is calculated as
[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]
The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated
[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]
c)
Let [tex]X_r[/tex] denote the remaining life time of a car battery
i)the probability the battery will last an additional five years is calculated below
[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]
ii) The average time that the battery is expected to last is calculated
[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]
