Answer:
Solution given:
g-¹(-2)=?
we have
g(x)=4-2x
let
g(x)=y
y=4-2x
Interchanging role of x and y
x=4-2y
2y=4-x
dividing both side by 2
2y/2=(4-x)/2
y=(4-x)/2
f-¹(x)=(4-x)/2
now
Substitute value -2 in place of x
f-¹(-2)=(4-(-2))/2=(4+2)/2=6/2=3
the value of g-¹(-2) is 3.
A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line? Question 26 options: a) y = x b) y = –x – 7 c) y = x + 3 d)y = –x + 2
Answer:
sorry my bad bro I have no clue
Which function describes this graph? (CHECK PHOTO FOR GRAPH)
A. y = x^2 + 7x+10
B. y = (x-2)(x-5)
C. y = (x + 5)(x-3)
D.y = x^2+5x+12
Answer:
Option A. y = x² + 7x + 10
Step-by-step explanation:
We'll begin calculating the roots of the equation from the graph.
The roots of the equation on the graph is where the curve passes through the x-axis.
The curve passes through the x-axis at –5 and –2
Next, we shall determine the equation. This can be obtained as follow:
x = –5 or x = –2
x + 5 = 0 or x + 2 = 0
(x + 5)(x + 2) = 0
Expand
x(x + 2) + 5(x + 2) = 0
x² + 2x + 5x + 10 = 0
x² + 7x + 10 = 0
y = x² + 7x + 10
Thus, the function that describes the graph is y = x² + 7x + 10
A quiz consists of 10 multiple-choice questions, each with 4 possible answers, only one of which is correct. A student who does not attend lectures on a regular basis has no clue what the answers are, and therefore uses an independent random guess to answer each of the 10 questions. What is the probability that the student gets at least one question right
Answer:
.943686485
Step-by-step explanation:
1=p(0)+p(1)+p(2)+p(3)+.....p(10)
1-p(0)=P(1)+p(2)+p(3)+....p(10)
or
1-p(0)= p(at least one)
p(0)=
[tex]{10\choose0}*.25^0*.75^{10}=.056313515[/tex]
1-.056313515=.943686485
Find the equation, in slope-intercept form, of the line passing through the point (2,5) and perpendicular to the line 2x + y = 7
Answer:
[tex]y=\displaystyle\frac{1}{2}x+4[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-interceptPerpendicular lines always have slopes that are negative reciprocals (examples: 1/2 and -2, 3/4 and -4/3)1) Determine the slope (m)
[tex]2x + y = 7[/tex]
Reorganize the given equation into slope-intercept form; subtract 2x from both sides to isolate y:
[tex]2x + y-2x = -2x+7\\y= -2x+7[/tex]
Now, we can easily identify the slope of the line to be -2. Because perpendicular lines always have slopes that are negative reciprocals, the slope of a perpendicular line would be [tex]\displaystyle\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\displaystyle\frac{1}{2}x+b[/tex]
Plug in the given point (2,5) and solve for b:
[tex]5=\displaystyle\frac{1}{2}(2)+b\\\\5=1+b[/tex]
Subtract 1 from both sides to isolate b:
[tex]5-1=\displaystyle\frac{1}{2}(2)+b-1\\4=b[/tex]
Therefore, the y-intercept of the line is 4. Plug this back into [tex]y=\displaystyle\frac{1}{2}x+b[/tex]:
[tex]y=\displaystyle\frac{1}{2}x+4[/tex]
I hope this helps!
HELP!!!!!!!!!!! SOMEONE PLEASE HELP!!!
For the graph below, which of the following is a possible function for h?
A) h(x) = 4-x
B) h(x) = 2x
C) h(x) = 5x
D) h(x) = 3x
9514 1404 393
Answer:
C) h(x) = 5^x
Step-by-step explanation:
h(x) is shown on the graph as having the highest rate of growth. That means, relative to the other functions, the base of the exponential is larger. Of the choices offered, the one with the largest growth factor is ...
h(x) = 5^x
_____
The general form of an exponential function is ...
f(x) = (initial value) · (growth factor)^x
Which of the following exponential equations is equivalent to the logarithmic
equation below?
log 970 = x
A.x^10-970
B. 10^x- 970
C. 970^x- 10
D. 970^10- X
Given:
The logarithmic equation is:
[tex]\log 970=x[/tex]
To find:
The exponential equations that is equivalent to the given logarithmic equation.
Solution:
Property of logarithm:
If [tex]\log_b a=x[/tex], then [tex]a=b^x[/tex]
We know that the base log is always 10 if it is not mentioned.
If [tex]\log a=x[/tex], then [tex]a=10^x[/tex]
We have,
[tex]\log 970=x[/tex]
Here, base is 10 and the value of a is 970. By using the properties of exponents, we get
[tex]970=10^x[/tex]
Interchange the sides, we get
[tex]10^x=970[/tex]
Therefore, the correct option is B, i.e., [tex]10^x=970[/tex].
Note: It should be "=" instead of "-" in option B.
what is the solution to the equation?
Answer:
Step-by-step explanation:
log(20x³) - 2logx = 4
log(20x³) -log(x²) = 4
log(20x³/x²) = 4
log(20x) = 4
20x = 10⁴
x = 10⁴/20 = 500
The restrictions for f(x)=2x+3/x^2−4 are ±2
True
False
Answer: True
=========================================================
Explanation:
If you meant to say [tex]f(x) = \frac{2x+3}{x^2-4}[/tex], then we cannot have x^2-4 equal to 0
We can never have 0 in the denominator.
Set the expression equal to 0 and solve for x
x^2 - 4 = 0
(x-2)(x+2) = 0 .... difference of squares rule
x-2 = 0 or x+2 = 0
x = 2 or x = -2
So if either x = 2 or x = -2, then we have x^2-4 equal to zero.
So these are the values we must kick out of the domain to avoid a division by zero error.
In short, the restrictions for x are 2 and -2. That's why the statement is true.
please see the question and solve plz
Answer:
Step-by-step explanation:
sin²β + sin²β×tan²β = tan²β
sin²β( 1 + tan²β ) = tan²β
~~~~~~~~~~~~~~~~
sin²β + cos²β = 1
[tex]\frac{sin^2\beta }{cos^2\beta }[/tex] + [tex]\frac{cos^2\beta }{cos^2\beta }[/tex] = [tex]\frac{1}{cos^2\beta }[/tex] ⇒ tan²β + 1 = sec²β ⇔ 1 + tan²β = sec²β
~~~~~~~~~~~~~~
1 + tan²β = [tex]\frac{1}{cos^2 \beta }[/tex]
L.H. = sin²β ( [tex]\frac{1}{cos^2 \beta }[/tex] ) = tan²β
R.H. = tan²β
Please see attached for the question. The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1400 and the standard deviation is $95.
Answer:
1. 2.1%
2. 47.7%
3. 68.2%
4. 34.1%
5. 49.9%
6. 0.1%
These values may be rounded differently depending on set rounding limits.
I need help understanding how to get the answer.
Answer:
-157.87
Step-by-step explanation:
1) the rules are:
[tex]log_a(bc)=log_ab+log_ac;[/tex]
and
[tex]log_ab^c=c*log_ab.[/tex]
2) according to the rules above:
[tex]log_7(yz^8)=log_7y+8log_7z=-6.19-8*18.96=-157.87.[/tex]
1. Write a variable expression that matches the following situation: Marguerite wants to put a garland around her garden. If the length of the garden is 50 meters and the width of the garden is 2 more than the length, what is the perimeter of the garden?
Answer:
3x2,−23y,√5m, 3 x 2 , − 2 3 y , 5 m
Step-by-step explanation:
that is the answer i think
An inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours. How long will it take both pipes to fill the pool?
Answer:
It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
Step-by-step explanation:
Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:
1/5 + 1/4 = X
0.20 + 0.25 = X
0.45 = X
9/20 = X
9 = 60
2 = X
120/9 = X
13,333 = X
Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
Consider A Triangle ABC. Suppose That A= 119 Degrees, B=53, And C=57. Solve The Traingle
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Answer:
a = 94.8, B = 29.3°, C = 31.7°
Step-by-step explanation:
Side 'a' can be found using the Law of Cosines:
a² = b² +c² -2bc·cos(A)
a = √(2809 +3249 -6042·cos(119°)) ≈ √8987.22 ≈ 94.8
Then one of the other angles can be found from the Law of Sines.
sin(C)/c = sin(A)/a
C = arcsin(c/a·sin(A)) ≈ arcsin(0.525874) ≈ 31.7°
Then the remaining angle can be found to be ...
B = 180° -A -C = 180° -119° -31.7° = 29.3°
__
The solution is a ≈ 94.8, B ≈ 29.3°, C ≈ 31.7°.
6(x+8)=-36 what does x equal
Answer:
Step-by-step explanation:
6(x+8) = -36
divide both sides by 6: x+8 = -6
subtract 8 from both sides: x = -14
Answer:
6(x+8)=-36
6x+48=-36
6x=84
x=14
Which table represents a relation that's a non-function?
Answer:
The table in the attachment is the right option
Step-by-step explanation:
A table that represents a function must have exactly one y-value assigned to every x-value. In other words, a table that is a function cannot have any x-value (input) with two corresponding different y-values (outputs).
The table in the attachment below represents a relation that is non-function because it has two outputs, 5 and 7, that are assigned or corresponding to one input, 7.
What is this can someone help
⏫
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
see this attachment ☝
A teacher claims that over 5% of statistics students have cheated in his classes in the past few years. In a random sample of 350 statistics students, he has caught 25 students cheating in the past few years. Is there enough evidence to support the teacher’s claim?
Answer:
no
Step-by-step explanation:
Factor the trinomial x^2-8x-65
Step-by-step explanation:
here's the answer to your question
Solve the following system of equations
x^2+2y^2=59
2x^2+y^2=43
(x ,y), (x, y) (x, y) (x, y)
Answer:
(-3,5),(-3,-5),(3,5),(3,-5)
Step-by-step explanation:
i changed my answer :)
Can you help me please,
?
Consider the following results for two independent random samples taken from two populations.
Sample 1 Sample 2
n1=50 n2=35
x¯1=13.6 x¯2=11.6
σ1=2.2 σ2=3.0
Required:
a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.
Answer:
a. 2
b. The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
[tex]\mu_1 = 13.6, s_1 = \frac{2.2}{\sqrt{50}} = 0.3111[/tex]
Sample 2:
[tex]\mu_2 = 11.6, s_2 = \frac{3}{\sqrt{35}} = 0.5071[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 13.6 - 11.6 = 2[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.3111^2+0.5071^2} = 0.595[/tex]
a. What is the point estimate of the difference between the two population means?
Sample difference, so [tex]\mu = 2[/tex]
b. Provide a 90% confidence interval for the difference between the two population means.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
The margin of error is:
[tex]M = zs = 1.645(0.595) = 0.98[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 0.98 = 1.02
The upper end of the interval is the sample mean added to M. So it is 2 + 0.98 = 2.98
The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. Provide a 95% confidence interval for the difference between the two population means.
Following the same logic as b., we have that [tex]Z = 1.96[/tex]. So
[tex]M = zs = 1.96(0.595) = 1.17[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 1.17 = 0.83
The upper end of the interval is the sample mean added to M. So it is 2 + 1.17 = 3.17
The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
A group of rowdy teenagers near a wind turbine decide to place a pair of pink shorts on the tip of one blade, they notice the shorts are at its maximum height of 16 meters at a and it’s minimum height of 2 meters at s.
Determine the equation of the sinusoidal function that describes the height of the shorts in terms of time.
Determine the height of the shorts exactly t=10 minutes, to the nearest tenth of a meter
The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9
Question: The likely missing parameters in the question are;
The time at which the shorts are at the maximum height, t₁ = 10 seconds
The time at which the shorts are at the minimum height, t₂ = 25 seconds
The general form of a sinusoidal function is A·sin(B(x - h)) + kWhere;
A = The amplitude
The period, T = 2·π/B
The horizontal shift = h
The vertical shift = k
The parent equation of the sine function = sin(x)
We find the values of the variables, A, B, h, and k as follows;
The given parameters of the sinusoidal function are;
The maximum height = 16 meters at time t₁ = 10 seconds
The minimum height = 2 meters at time t₂ = 25 seconds
The time it takes the shorts to complete a cycle, (maximum height to maximum height), the period, T = 2 × (t₂ - t₁)
∴ T = 2 × (25 - 10) = 30
The amplitude, A = (Maximum height- Minimum height)/2
∴ A = (16 m - 2 m)/2 = 7 m
The amplitude of the motion, A = 7 meters
T = 2·π/B
∴ B = 2·π/T
T = 30 seconds
∴ B = 2·π/30 = π/15
B = π/15
At t = 10, y = Maximum
Therefore;
sin(B(x - h)) = Maximum, which gives; (B(x - h)) = π/2
Plugging in B = π/15, and t = 10, gives;
((π/15)·(10 - h)) = π/2
10 - h = (π/2) × (15/π) = 7.5
h = 10 - 7.5 = 2.5
h = 2.5
The minimum value of a sinusoidal function, having a centerline of which is on the x-axis, and which has an amplitude, A, is -A
Therefore, the minimum value of the motion of the turbine blades before, the vertical shift = -A = -7
The given minimum value = 2
The vertical shift, k = 2 - (-7) = 9
Therefore, k = 9
Therefore;
The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9
More can be learned about sinusoidal functions on Brainly here;
https://brainly.com/question/14850029
Bob's truck averages 23 miles per gallon. If Bob is driving to his mother's house, 72 miles away, how many gallons of gas are needed? Round to the nearest tenth.
Answer:
3.1 gallons
Step-by-step explanation:
To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that
miles of gas / gallons = miles of gas / gallons
23 miles / 1 gallon = 72 miles / gallons needed to go to Bob's mother's house
If we write the gallons needed to go to Bob's mother's house as g, we can say
23 miles / 1 gallon = 72 miles/g
multiply both sides by 1 gallon to remove a denominator
23 miles = 72 miles * 1 gallon /g
multiply both sides by g to remove the other denominator
23 miles * g = 72 miles * 1 gallon
divide both sides by 23 miles to isolate the g
g = 72 miles * 1 gallon/23 miles
= 72 / 23 gallons
≈ 3.1 gallons
I really need help big time thank you
Which number are between 9.23 and 9.25
Answer:
9.24
Step-by-step explanation:
Angles are not necessarily drawn to scale.
X=?
Answer:
x = 76
Step-by-step explanation:
A line has an angle measurement of 180 degrees.
Knowing that, let's first find the angle measurement of DIJ:
180 - 107 = 73
Angle DIJ has an angle measurement of 73
To find the angle measurement of DJI, we have to apply knowledge of angles in a triangle. When you add all the angles in a triangle, they ALWAYS equal to 180 degrees.
Using that knowledge, we can add 73 and 31 and subtract that value from 180:
73 + 31 = 104
180 - 104 = 76
The angle measurement of Angle DJI is 76.
Because vertical angles are ALWAYS going to have the same angle measurement, Angle AJF is going to have an angle measurement of 76 as well.
So x = 76
Hope that helps (●'◡'●)
A recipe calls for 2 1/2 tablespoons of oil and 3/4 tablespoons of vinegar. What is the ratio of oil to vinegar in this recipe?
Answer:
10:3
Step-by-step explanation:
Make 2 1/2 an improper fraction, you will get 5/2. You dont have to do anything to the 3/4.
For you to find the ratio of an fraction, you have to take the numerator but the denominator has to be the same.
So make 5/2 to a 10/4.
Take the numerator 10 & 3.
Your answer will be 10:3
No problem.
Pleas help me in this question Find R
Answer:
R = 25.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos R = adj side / hyp
cos R = 9/10
Taking the inverse cos of each side
cos ^-1 ( cos R) = cos^ -1 ( 9/10)
R=25.84193
Rounding to the nearest tenth
R = 25.8
Answer:
[tex]\boxed {\boxed {\sf D. \ 25.8 \textdegree} }[/tex]
Step-by-step explanation:
We are asked to find the measure of an angle given the triangle with 2 sides. This is a right triangle because of the small square representing a right angle. Therefore, we can use trigonometric functions. The three major functions are:
sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacentWe are solving for angle R, and we have the sides TR (measures 9) and SR (measures 10).
The side TR (9) is adjacent or next to angle R. The side SR (10) is the hypotenuse because it is opposite the right angle.We have the adjacent side and the hypotenuse, so we will use the cosine function.
[tex]cos \theta = \frac {adjacent}{hypotenuse}[/tex]
[tex]cos R = \frac {9}{10}[/tex]
Since we are solving for an angle, we must take the inverse cosine of both sides.
[tex]cos^{-1}(cos R) = cos ^{-1} ( \frac{9}{10})[/tex]
[tex]R = cos ^{-1} ( \frac{9}{10})[/tex]
[tex]R= 25.84193276[/tex]
If we round to the nearest tenth, the 4 in the hundredth place tells us to leave the 8 in the tenths place.
[tex]R \approx 25.8 \textdegree[/tex]
The measure of angle R is approximately 25.8 degrees and choice D is correct.
PLEASE HELP AND BE RIGHT BEFORE ANSWERING
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Since point P is the center of dilation, it doesn't move. (It is "invariant.") The other points on the figure move to 1/4 of their original distance from P. On this diagram, it is convenient that the distances are all multiples of 4 units, so dividing by 4 is made easy.