Answer:
y=-5/2x-1
Step-by-step explanation:
first find the gradient whereas since the two lines are parallel they hav the same gradient. y=mx+c whereas m is the gradient. 5x+2y=12
2y=-5x+12
y=-5/2x+12(so the gradient is -5/2x..... gradient=-5/2
y-4=-5/2
x+2
y-4=-5/2(x+2)
y-4=-5/2x-5
y=-5/2x-5+4
y=-5/2x-1
The equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4) is y = -5/2 x - 1.
What is the Equation of line in Slope Intercept form?Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.
Given that the equation of the line is,
5x + 2y = 12
2y = -5x + 12
y = -5/2 x + 6
This is in the slope intercept form, where the slope = -5/2.
Slopes of two parallel lines are equal.
So any line parallel to the given line will be of the form y = -5/2 x + c
Given line passes through (-2, 4).
Substituting (-2, 4) in y = -5/2 x + c, we get,
(-5/2) (-2) + c = 4
c = -1
So the equation is, y = -5/2 x - 1
Hence the required equation is y = -5/2 x - 1.
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Can you help me with this one don’t get it
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].
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Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives
Answer:
0.2946
Step-by-step explanation:
Number of tosses, n = 200
P(obtaining a 5), p = 1/6
q = 1 - p = 5/6
Normal approximation for binomial distribution
P(X < A) = P(Z < (A - mean)/standard deviation)
Mean = np
= 200 x 1/6
= 33.33
Standard deviation = √npq
= √(200(1/6)(5/6) )
= 5.27
P(at most 30 fives) = P(X ≤ 30)
= P(Z < (30.5 - 33.33)/5.27) (continuity correction of 0.5 is added to 30)
= P(Z < -0.54)
= 0.2946
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
Which graph represents this equation y-4= -3(x+5)
Answer:
Graph B
Step-by-step explanation:
Simplify.
y - 4 = -3x - 15 Distribute
y = -3x - 11 Add 4 on both sides
The y-intercept should be negative, and option B has a negative y-intercept.
The graph of the given function will be represented by graph B so the correct answer is option B.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph of the function is attached with the answer below.
Simplify.
y - 4 = -3x - 15 Distribute
y = -3x - 11 Add 4 on both sides
The y-intercept should be negative, and option B has a negative y-intercept.
Therefore the graph of the given function will be represented by graph B so the correct answer is option B.
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What is the solution set of the quadratic inequality x2+x-2
Answer:
The solution set is x = 1 and x = -2
Step-by-step explanation:
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.
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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
Please help. I’ll mark you as brainliest if correct
Answer:
12 + -6i
a=12
b=-6
Step-by-step explanation:
( -4 + 3i ) ( -3 - 2i )
-4 * -3 = 12
3i * -2i= -6i
12 + -6i
Which of the following best forms the figure shown
Answer:
2 rays that meet at an endpoint
Step-by-step explanation: A ray starts with a dot, or point and continues on forever with an arrow. There are two rays in that drawing that start at the same endpoint.
Answer:
2 rays that meet at an endpoint.
Step-by-step explanation:
A ray is straight but has one endpoint and the other end go on infinitely.
A line is straight and goes on infinitely.
A line segment is straight and has two endpoints.
The picture shows two rays meeting at an endpoint.
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]
Solve 4x+5≥-23. show your work
Answer:
x≥-7
Step-by-step explanation:
4x+5≥-23
Subtract 5 from each side
4x+5-5≥-23-5
4x≥-28
Divide each side by 4
4x/4≥-28/4
x≥-7
Answer:
X≥-7
Step-by-step explanation:
Step 1: Subtract 5 from both sides.
4x+5-5≥-23-5
4x ≥-28
Step 2: Divide both sides by 4.
4x/4 ≥-28/4
X ≥-7
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.
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
"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
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]
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]
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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]
The lengths of nails produced in a factory are normally distributed with a mean of 5.02 centimeters and a standard deviation of 0.05 centimeters. Find the two lengths that separate the top 6% and the bottom 6%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
The length that separates the top 6% is 5.1 centimeters.
The length that separates the bottom 6% is 4.94 centimeters.
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
[tex]\mu = 5.02, \sigma = 0.05[/tex]
Find the two lengths that separate the top 6% and the bottom 6%.
Top 6%:
The 100-6 = 94th percentile, which is X when Z has a pvalue of 0.94. So X when Z = 1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.555 = \frac{X - 5.02}{0.05}[/tex]
[tex]X - 5.02 = 1.555*0.05[/tex]
[tex]X = 5.1[/tex]
So the length that separates the top 6% is 5.1 centimeters.
Bottom 6%:
The 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.555 = \frac{X - 5.02}{0.05}[/tex]
[tex]X - 5.02 = -1.555*0.05[/tex]
[tex]X = 4.94[/tex]
The length that separates the bottom 6% is 4.94 centimeters.
What are the terms in the algebraic expression
102 + 10 +
3b
Answer:
102, 10, and, 3b
Step-by-step explanation:
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
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)
Find the range of the set of numbers shown by the box-and-whisker plot.
6
6
7
8
9
10
11
12
13
14
16
16
17
18
19
20
21
22
Answer:
16
Step-by-step explanation:
The range is the difference between the highest and lowest number of a data set. 22-6=16
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.
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.
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
60 is what percent of 400
Answer:
15%
Step-by-step explanation:
Is means equals and of means multiply
60 = P * 400
Divide each side by 400
60/400 = P
.15 = P
Change to percent form
15% is the percent
Answer:
the answer to the question you've asked is 15
Choose the following which is COMPLETELY correct:
Answer:
D
Step-by-step explanation:
Mean = (4+4+5+8+9) / 5
30 / 5
6
Median = put them in order and the one in the middle is the median.
4, 4, 5, 8, 9
Mode = the most common
4, 4, 5, 8, 9
What is 40% of 160?
Answer:
40% of 160 is 64
Step-by-step explanation:
You can easily find the answer in one step, just multiplying the whole (160) by the percentage (40) divided by 100.
So, 40% of 160 = 160 × 0.4 = 64.
Answer:
64
Step-by-step explanation:
You first have to subtract 40% from 160 and then you subtract that amount with is 96 from 160 and you get your answer 64
Given that d is the midpoint of line segment ab and k is the midpoint of line segment bc, which statement must be true? (May give brainliest)
Answer:
B is the midpoint of line segment AC
