Answer: The points (9,-) and (9,3) Both have the same (y) coordinate.
Step-by-step explanation:
What is the y value of the y-intercept of the line that contains the points (-8,-5)
and (10, 67)?
We will see that the linear equation that passes through the two given points is:
y = 4x + 28
So the y-intercept is y = 28.
How to find the y-intercept of the line?First, we need to find the linear equation that passes through the two given points. Remember that for a line that passes through two points (x₁, y₁) and (x₂, y₂), the slope is:
m = (y₂ - y₁)/(x₂ - x₁)
Here our line passes through (-8,-5) and (10, 67), then the slope is:
m = (67 + 5)/(10 + 8) = 4
So we can write:
y = 4*x + b
To find the value of b we can use the point (-8,-5), replacing these values we get:
-5 = 4*-8 + b
-4 + 4*8 = b
28 = b
So the y-intercept is 28.
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What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
1/4
Step-by-step explanation:
The points (-4, 5) and (0, 6) lie on the line. Substituting into the slope formula,
[tex]\frac{6-5}{0-(-4)}=\frac{1}{4}[/tex]
Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters. She stands 23.1 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter. -28.15 m (Diagram is not to scale.) T 1.85 m 23.1 m-
The height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
What is the similarity law for triangles?It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
It is given that:
Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
D = 39.75 m
d = 34.9 m
H:h = D:d
H/1.85 = 39.75/34.9
H = 2.11 m
Thus, the height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
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Evaluate the inverse when y=4. Show all of your work.
The inverse of the function y = 4ˣ is f⁻¹(x) = ㏑x / ㏑4.
What is termed as the inverse of the function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function "f" takes x to y, then its inverse will take y to x. The inverse function is signified by f-1 or F-1 if the function is signified by 'f' or 'F'. Here, (-1) should not be confused with exponent or reciprocal.For the given question;
The function is given as;
y=4ˣ
Interchange the variables of the function.
x = 4∧y
Taking log both side.
㏑ x = ㏑(4∧y)
Using the power rule of log function.
㏑ x = y㏑(4)
y = ㏑ x/㏑(4)
Now, replace y with f⁻¹(x).
f⁻¹(x) = ㏑ x/㏑(4)
Thus, the inverse of the function y = 4ˣ is found to be f⁻¹(x) = ㏑x / ㏑4.
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The correct question is-
Evaluate the inverse when y=4ˣ. Show all of your work.
URGENT HELP!!
Approximate the correlation of the data shown below?
The approximate correlation of the data shown on the diagram above is: C. -0.5.
The question says we should approximate the correlation using the given scatter plot. Below shows a detailed explanation on how to do a rough estimation of the possible value of the correlation.
What is the Approximate Correlation of a Data?
Correlation Coefficient, r, is a numerical value of -1 to 1, which tells how strongly related two variables are. If the points on a scatter plot form a trendline that slopes upwards, it is a positive correlation. If it slopes downwards, it is a negative correlation.
The magnitude of the correlation coefficient is dependent on how father apart the points are from each other along a trend line. If they are much farther apart from each other, the correlation coefficient would far from 1 and -1, and close to zero. If they are closer, it would be close to 1 or -1, and far from 0.
The scatter plot shows the data points are moderately spaced from each other and the trendline slopes downwards. Therefore, the best estimate for the correlation is: C. -0.5.
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a lecture hall at nc state has 220 seats with fold-down writing pedestals, 25 of which are designed for left-handers. an intro. to economics class with 215 students meets in this lecture hall. assume that 13% of the general population is left-handed. question 1. what is the probability that at least one right-handed student in this class is forced to use a seat designed for a left-hander? (use 4 decimal places.) question 2. what is the probability that at least one left-handed student in this class is forced to use a seat designed for a right-hander? (use 3 decimal places.)
1) There exists a 3.82% probability that at least one right-handed student in this class is forced to utilize a seat designed for a left-hander.
2) There exists a 68.35% probability that at least one left-handed student in this class is forced to use a seat designed for a right-hander.
What is meant by Binomial probability distribution?The binomial probability exists the probability of exactly x successes on n repeated trials, and X can only contain two outcomes.
[tex]$P(X=x)=C_{n, x} \cdot \pi^x .(1-\pi)^{n-x}$$[/tex]
In which [tex]$C_{n, x}$[/tex] exists the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]$C_{n, x}=\frac{n !}{x !(n-x) !}[/tex]
And π exists the probability of X happening.
Given: 13 % of the students are left-handed and 100 - 13 = 87 % are right handed.
There are 220 sets. Of them, 25 exists designed for left handers and 220-25 = 195 for right handers.
There are 215 students, so n = 215.
In this case, a success is a student being right-handed. So [tex]$\pi=0.87$[/tex].
There are 195 seats for right handed students. If there are 196 or more right handed students, they will have to use a seat designed for a left hander. We have to find [tex]$P(X \geq 196)$[/tex]. Utilizing a binomial probability calculator, we find that [tex]$P(X \geq 196)=0.0382$[/tex]
So, there is a 3.82 % probability that at least one right-handed student in this class exists forced to utilize a seat designed for a left-hander.
There are 25 seats for left-handed students. If there exists 26 , or more, at least one exists going to be forced to utilize a seat designed for a right-hander.
In this case, a success is a student being left-handed. So [tex]$\pi=0.13$[/tex].
We have to find [tex]$P(X \geq 26)$[/tex].
Using a binomial probability calculator, we have that [tex]$P(X \geq 26)=0.6835$[/tex]
There exists a 68.35 % probability that at least one left-handed student in this class is forced to utilize a seat designed for a right-hander.
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The first equation should be multiplied by 7 and the second equation by -6.
Answer:
Step-by-step explanation:
a and b agree to try to meet between 12 and 1pm for lunch. assuming that the arrival times and of a and b are uniform between 12 and 1pm, independently. if whoever comes first waits 15 minutes and then leaves, what is the probability that they actually meet for lunch?
What is the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3? Responses y−1=3(x+2) y plus 1 equals 3 open parenthesis x minus 2 close parenthesis y−2=3(x+1) y minus 2 equals 3 open parenthesis x plus 1 close parenthesis y+1=3(x−2) y plus 1 equals 3 open parenthesis x minus 2 close parenthesis y+2=3(x−1)
The equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5
We need to find the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3
The point slope form of a equation of a line is
y - y₁ = m(x - x₁)
y - (-2) = 3 (x - 1)
y + 2 = 3x - 3
y = 3x - 3 - 2
y = 3x - 5
Therefore the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5.
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consider a normal distribution with mean 20 and standard deviation 9. what is the probability a value selected at random from this distribution is greater than 20? (round your answer to two decimal places.)
The probability that a value selected at random from this distribution is greater than 20 is 0.5.
What is a probability with normal distribution?
The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean. The probabilities for values that are farther from the mean taper off equally in both directions.
Here,
Let us assume that X follows a normal distribution.
If X follows a normal distribution, then
z = (X−μ) /σ, follows a standard normal distribution.
The probability of a value selected at random from this distribution is greater than 20:
P (X > 20) = 1 − P (X ≤ 20)
P ((X − μ) / σ > 20) = 1−P((X − μ) / σ ≤ 20)
P (z > (20 − 20) /5) = 1 − P (z ≤ (20−20 / 5))
P (z > 0) = 1 − P (z ≤ 0)
The value of probability is obtained from the standard normal table as:
P (z > 0) = 1 − P (z ≤ 0)
= 1 - 0.5
= 0.5
Hence, the probability that a value selected at random from this distribution is greater than 20 is 0.5.
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(No need to graph unless want to)Determine the period and asymptotes please grade 12 trig
SOLUTION:
The parent function is;
[tex]f(x)=sec(x)[/tex]The transformation applied is;
[tex]y=-2f(\frac{1}{4}x-\pi)+2[/tex]Graphing this, we have;
The period is the time to complete a cycle .
From the graph, the period is;
[tex]8\pi[/tex]The asymptotes are those lines for which sec x is undefined. those are lines where;
[tex][/tex]1. Priya's favorite kind of dark chocolate comes in a package shaped like a triangular. If the package can hold 144 cm of chocolate and the triangular faces have a base of 3 cm and a height of 4 cm, how tall is the entire package?
ok
Measures base = 3cm
height = 4cm
tall = x
volume = 144 cm^3
Volume = Area of the base * tall
Area of the base = (3 * 4) / 2 = 12/2 = 6 cm^2
144 = 6*x
x = 144/6
x = 24 cm
Result: The chocolate is 24 cm tall.
Someone please help with this math problem?
Both equations' solutions are found at the point (-2, 2). When point (-1,4), the 2x-y=-6 yields the correct point. The second equation is as a result. The point (2, 14) is the answer to the first equation because it provides the answer to the first equation but not the second.
What is equation?The word equation and its cognates in other languages may have slightly different meanings; for example, in French an equation is defined as containing one or more variables, while in English any well-formed formula consisting of two expressions related with an equals sign is an equation. An equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.
3x-y=-8
2x-y=-6
given points are (-1,4), (2,14), (-2,2)
On solving the equation,
3x-y=-8
-(2x-y=-6)
x=-2
y=2
The point (-2,2) is the solution to both equations.
The point (-1,4) on putting in the 3x-y=-8 will not give solution but when put in the 2x-y=-6, it gives the result. so it the solution to second equation.
The point (2,14) is the solution to the first equation as it gives the answer to first but not to the second equation.
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assuming that the population size is 1,000 people, the prevalence of smoking in epiland is 60% and the percentage of people drinking water with a high concentration of heavy metals is 30%, calculate the total number of cases of cancer x that could be prevented if each one of the exposures were eliminated. what would be your suggestion to the public health agencies if they asked you which one of the exposures would have a greater impact on reducing the prevalence of the disease if it was eliminated?
1. The total number of cases of cancer x that could be prevented if each one of the exposures were eliminated is 900.
2. The suggestion to the public health agencies if they requested the one exposure that would have a greater impact on reducing the prevalence of cancer x if eliminated is smoking.
What is the prevalence rate?The prevalence rate refers to the proportion of the population who have a particular disease or attribute or can be exposed to risks at a specified time or over a specified period.
The assumed population size in Epiland = 1,000
Prevalence of smoking in Epiland = 60%
The number of Epiland smokers = 600 persons (1,000 x 60%)
Percentage of people drinking water with a high concentration of heavy metals = 30%
The number of people drinking the water = 300 (1,000 x 30%)
The total number of people exposed to cancer x = 900 (600 + 300).
Thus, 90% of the population in Epiland is exposed to cancer x based on the prevalence rate of smoking and the high concentration of heavy metals in their drinking water.
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t - 2 < 21 solve the inequality for t simplify your answer as much as possible
Answer:
t < 23
Step-by-step explanation:
t - 2 < 21
Step 1 : Add 2 on both sides.
t - 2 + 2 < 21 + 2
t < 23
Write the recurring decimal 0.45....... as a fraction.
Given the following question:
We are given the repeating decimal of 0.45
We will use the formula:
[tex]\begin{gathered} \frac{(d\times10^r)-n}{10^r-1} \\ \frac{0.45\times10^2)-0}{10^2-1} \\ \text{ Simplify} \\ \frac{0.45\times2\cdot10^2}{10^2-1}=\frac{45}{99} \\ \text{ Simplify once more} \\ \frac{45}{99}\div9=\frac{5}{11} \\ =\frac{5}{11} \end{gathered}[/tex]Amy has a piece of wood that measures 42 inches. The model shows the length remaining after she cut a piece from the 42-inch piece of wood. About how many inches did Amy cut from the 42-inch piece of wood? 2 3 4 5 6 7 8 10 12 inches
Given data
Ammy has a piece of wood that measures 42 inches
Ammy cut from the 42-inch piece of wood is calculated as
[tex]42-9=33\text{ inches}[/tex]Thus, Amy cut from the 42-inch piece of wood is 33 inches
1+2 |x-1| less than or equal to 9
SOLUTION
The question is
[tex]1+2|x-1|\leq9[/tex]Now let's solve. This becomes
[tex]\begin{gathered} 1+2|x-1|\leq9 \\ 2|x-1|\leq9-1 \\ 2|x-1|\leq8 \\ \\ \text{dividing both sides by x we have} \\ \\ |x-1|\leq4 \end{gathered}[/tex]This becomes
[tex]\begin{gathered} x-1\leq4 \\ or \\ x-1\ge4 \end{gathered}[/tex]So we have our x as
[tex]undefined[/tex]Finding Slope
Help mee
Answer: The slope is [tex]\frac{2}{3}[/tex].
Step-by-step explanation:
[tex]Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } =\frac{-8-(-6)}{-2-1} =\frac{-2}{-3} =\frac{2}{3}[/tex]
36. THOUGHT PROVOKING
Describe a function in which the inputs and/or the
outputs are not numbers. Identify the independent
and dependent variables. Then find the domain and
range of the function.
Answer:
A function is a relation where each input value is assigned to only one output value. The domain of a function is the set of all input values, or x-values, for which the function is defined. The range of a function is the set of all output values, or y-values, for which the function is defined. To write the equation y = ax + b in function notation, substitute f(x) for y.
Step-by-step explanation:
Brainlest, Please!
A 46 gram sample of a substance that's a by product of fireworks has a k-value of 0.1394. Find the substance's half-life in days. Round your answer to the nearest tenth.
N=N0e^-kt
The half life obtained to the nearest tenth is 5.0 days.
What is the half life?The half life is the time taken for only half of the initial amount of the radioactive substance to remain. We know that we have to use the formula;
N=N0e^-kt
N = amount present at time t
No = Amount initially present
k = The constant
t = The half life
We now have that;
HALF LIFE = O.693/k
We have to recall that the term k is the decay constant for the process as shown.
Half life = O.693/0.1394
Half life = 5.0 days
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I need help with my Pre-Calculus homework, the image of the problem is attached!
Answer:
Question 4
Answer: Alternative C - 0
Step-by-step explanation:
Since x→∞, we can substitute the values of x for values as 10, 100, 1000 and see the tendency of the function when the values are getting higher (closer to ∞):
For x = 10
f(10) = 0.5*10^(-3/4)
f(10) = 0.089
For x = 100
f(10) = 0.5*100^(-3/4)
f(10) = 0.016
For x = 1000
f(10) = 0.5*1000^(-3/4)
f(10) = 0.003
As we can see, when the x-values are getting closer to infinite, the y-values tends to zero. Thus, alternative C is correct.
at the annual dog show, chantel noticed that there were three more scotties than schnauzers. she also realized that the number of wirehaired terriers was five less than twice the number of schnauzers. if there were dogs in all (counting schnauzers, scotties, and wirehaired terriers), how many schnauzers were there? write and solve an equation.
The no. of schnauzers in the annual dog show are 20.
Assume that there are x Schnauzers at the annual dog show.
Scotties entered in the yearly dog show: x + 3
There are 2x - 5 Wirehaired Terriers entered in the annual dog show.
There are 78 dogs in all competing in the yearly dog show.
Consequently, the equation becomes
x + x + 3 + 2x - 5 = 78.
4x - 2 = 78
4x = 78 + 2
4x = 80
x = 80/4
= 20
In the yearly dog show, there are 20 Schnauzers. I hope you can understand the process without too much trouble. It is crucial to thoroughly study the equation so that you can easily solve the issue.
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Find the slope between these two points:
(12, -18), (-15, -18)
Answer:
The slope is 0.
Step-by-step explanation:
Using the slope formula which is m= y2 - y1 / x2 - x1, plug in the x values and y values of the two points. (12,-18) is x1 and y1. (-15,-18) is x2 and y2.
When plugging it in we get -18 - (-18)/ -15 - 12. You cannot subtract a negative so it turns from subtraction to addition. So, -18 + 18 / -15 - 12 which equals 0/-27. 0 divided by any number is 0. So the slope is 0, m=0.
Hope this helps :)
What is the image of ( − 8 , − 4 ) after a dilation by a scale factor of 1 4 4 1 centered at the origin?
The image of the point after the dilation is (-2, -1)
What is dilation?Dilation is the process of altering the side length of a shape or a function
How to determine the image of the points?From the question, the given parameters are:
Point = (-8, -4)
The scale factor of dilation is given as
Scale factor = 1/4
Mathematically, this transformation can be represented as
(x, y) = k(x, y)
Where k = 1/4 i.e. the scale factor
So, we have
(x, y) = (kx, ky)
This gives
(x, y) = (1/4x, 1/4y)
When represented as an equation, we have
Image = 1/4 * Point
Substitute the equation Point = (-8, -4) in the equation Image = 1/4 * Point
So, we have the following equation
Image = 1/4 * (-8, -4)
Evaluate the product
Image = (-2, -1)
Hence, the image is (-2, -1)
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Tell which of the following is a linear equation in one variable:
a) x² - 4x + 3 = 0
b) 6x - 2y = 7
c) 3x - 1 = -2x
d) pq - 3 = p
e) 3x + 2 = 4 ( x +7 ) + 9
For 100 Points
Answer:
c and e
Step-by-step explanation:
(a)
x² - 4x + 3 = 0 ← is a quadratic and not linear
(b)
6x - 2y = 7 ← is a linear equation in 2 variables, x and y
(c)
3x - 1 = - 2x ( add 2x to both sides )
5x - 1 = 0 ← is a linear equation in 1 variable
(d)
pq - 3 = p ← is a linear equation in 2 variables , p and q
(e)
3x + 2 = 4(x + 7) + 9 ← is a linear equation in 1 variable
Valeria created a triangular pyramid as part of her science fair project. The triangular base has a height of 8 cm and a length of 6 cm. The height of the pyramid is 12 cm. Determine the volume of Valeria's pyramid.A. 192 cm B. 288 cmC. 96 cmD. 576 cm
Given:
Height of triangular base = 8 cm
Length of traingular base = 6cm
Height of pyramid = 12 cm
Let's determine the volume of Valeria's pyramid.
To find the volume of the triangular pyramid, apply the formula:
[tex]V=\frac{1}{3}(A\ast h)[/tex]Where A is the area of the triangular base and h is the height of the pyramid
To find the area of the triangular base, apply the area of a triangle formula:
[tex]\begin{gathered} A=\frac{b\ast h}{2} \\ \\ A=\frac{6\ast8^{}}{2}=\frac{48}{2}=24cm^2 \end{gathered}[/tex]To find the volume of the pyramid, substitute 24 for A and 12 for h in the formula above.
Thus, we have:
[tex]\begin{gathered} V=\frac{1}{3}(A\ast h) \\ \\ V=\frac{1}{3}(24\ast12) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} V=\frac{1}{3}(288) \\ \\ V=\frac{288}{3} \\ \\ \text{ V = 96 cm}^3 \end{gathered}[/tex]Therefore, the volume of Valeria's pyramid is 96 cubic centimeters.
ANSWER:
[tex]\text{ C. 96 cm}^3[/tex]Simple Interest QuizIf $3,000 is loaned for 48 months at a 4.5% annual rate, how much is the ending balance?
Given:
Principal (p) =$3,000
Time (T) = 48 months = 4 years
Interest rate = 4.5%
Required :
Ending balance = ?
The simple interest :
[tex]\begin{gathered} SI\text{ = PRT} \\ =\text{ 3000 }\times\text{ 0.045 }\times\text{ 4} \\ =\text{ \$ 540} \end{gathered}[/tex]Ending balance :
[tex]\begin{gathered} \text{Ending balance = Principal + SI} \\ =\text{ \$ 3000 + \$ 540} \\ =\text{ \$ 3540} \end{gathered}[/tex]Ending balance = $ 3540
vehicle speed on a particular bridge in china can be modeled as normally distributed. (a) if 5% of all vehicles travel less than 39.18 m/h and 10% travel more than 73.27 m/h, what are the mean and standard deviation of vehicle speed? (round your answers to three decimal places.) mean standard deviation
The mean and standard deviation of the vehicle speed are 58.33 and 11.64 respectively.
The vehicle speed on a particular bridge in china has normal distribution.
5% represents the 5th percentile which is here, 39.18 m/h.
Since 10% travels more than 73.27 m/h, 90% travels less than 73.27 m/h.
So here the 90th percentile is 73.27 m/h.
Also the z-score, z = (x-μ)/σ, where μ is the mean of normal distribution and σ, the standard deviation.
So 39.18 corresponds to the z with p-value 0.05, i.e., z = -1.645 [from the normal tables]
Hence, z = (x-μ)/σ
⇒ -1.645 = (39.18 - μ)/σ
⇒ -1.645σ = 39.18 - μ
⇒ μ = 39.18 + 1.645σ ----------(1)
Also 73.27 corresponds to the z with p-value 0.9,i.e., z = 1.28.
Hence , z = (x-μ)/σ
⇒ 1.28 = (73.27 - μ)/σ
⇒ 1.28σ = 73.27 - μ
⇒ μ = 73.27 - 1.28σ ----------(2)
Equating (1) and (2), we get,
39.18 + 1.645σ = 73.27 - 1.28σ
2.925σ = 34.05
σ = 11.64
hence μ = 39.18 +1.645 x 11.64
⇒ μ = 58.33
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Which list shows the absolute values in order from greatest to least select each correct answer.
A: | 11 7/10 |, | 11 3/5 |, | 10 3/10 |
B: | -3 1/3 |, | -3 2/3 |, | 2 2/3 |
C: | -1 5/6 |, | 1 7/12 |, | 1 5/12 |
D: | -6 5/7 |, | -6 3/7 |, | 5 2/7 |
Please help I will give 100!
Step-by-step explanation:
A./11.7/,/22.6/,10.3/
11.7<22.6>10.3
B./-10.3/,/-10.7/,/7.3/
10.3<10.7>7.3
C./-2.5/,/1.42/,/1.25/
2.5>1.42>1.25
D./-9.3/,/-9/,/7.43/
9.3>9>7.43
therefore the answer is C and D
