Answer:
m = -4
Step-by-step explanation:
The given expression is :
[tex](17)^{3}\cdot(289)^{-6}=(17)^{2m-1}[/tex]
We need to find the value of m
We know that, 17² = 289
So,
[tex](17)^{3}\cdot(17^2)^{-6}=(17)^{2m-1}\\\\(17)^{3}\cdot(17)^{-12}=(17)^{2m-1}[/tex]
Also,[tex]x^ax^b=x^{a+b}[/tex]
So,
[tex]17^{3-12}=17^{2m-1}\\\\17^{-9}=17^{2m-1}\\\\\implies -9=2m-1\\\\-9+1=2m\\\\-8=2m\\\\m=-4[/tex]
So, the value of m is equal to -4.
In January, the average temperature t hours after midnight in Mumbai, India, is given by:
T(t)=24.5-5.5sin((2pi(t+1))/24)
What is the coldest time of day in Mumbai? give an exact answer
The coldest time of day in Mumbai is 5 hours after midnight.
Since the average temperature t hours after midnight in Mumbai, India, is given by:
T(t)=24.5-5.5sin((2pi(t+1))/24)
We have that
T(t) = 24.5 - 5.5sin((2π(t+1))/24)
The coldest time of day is when T(t) is minimum.
T(t) is minimum when 5.5sin((2π(t+1))/24) is minimum where t is the coldest time of day at minimum temperature, T(t).
Since for a sine function, -1 ≤ sinФ ≤ 1, the minimum value of sinФ = -1.
So, T(t) = 24.5 - 5.5sin((2π(t+1))/24) is minimum when
5.5sin((2π(t+1))/24) is minimum.
Also, -5.5sin((2π(t+1))/24) = 5.5 × -1 at minimum temperature T(t)
So, 5.5 × -1 = 5.5 × -sin((2π(t+1))/24)
So, -sin((2π(t+1))/24) = -1
sin((2π(t+1))/24) = 1
Taking inverse sine of both sides, we have
sin⁻¹sin((2π(t+1))/24) = sin⁻¹(1)
((2π(t+1))/24) = π/2
Multiplying both sides by 24, we have
(2π(t+1))/24 × 24 = π/2 × 24
(2π(t+1)) = 12π
Dividing both sides by 2π, we have
2π(t+1)/2π = 12π/2π
t + 1 = 6
t = 6 - 1
t = 5 hours
So, the coldest time of day in Mumbai is 5 hours after midnight.
Learn more about average temperature here:
https://brainly.com/question/19388300
super easy question, will mark brainliest if the answer is correct
a water container is 1/8 full. 35 litres if water are now poured into the container. The container is now 3/4 full.
When the container is full, how much water does it hold?
Answer:
56 litres
Step-by-step explanation:
let x be the amount when the container is full.
1/8x + 35 = 3/4x
-5/8x = -35
x = 56
Simplify the expression:
4 + 4f2 + 6f - 6f
Answer:
4f^2 +4
Step-by-step explanation:
4 + 4f^2 + 6f - 6f
Combine like terms
4f^2 +4
A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost F(m) is a function of the number of miles M that the car is driven.
Plan A: f(m) = 0.12 + 75
Plan B: f(m) = 0.35m
I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven.
II. For each function, determine how the rate of change will affect the total cost of a car rental.
III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective?
Answer:
Plan B
Step-by-step explanation:
plz plz solve this.
Step-by-step explanation:
Disclaimer: When writing this on the paper use the theta symbol, I'm using x since I'm on mobile.
2.
i).
[tex] \sin(x) \tan(x) \sec(x) = \tan {}^{2} (x) [/tex]
[tex] \sin(x) \sec(x) \tan(x) = \tan {}^{2} (x) [/tex]
[tex] \sin(x) \frac{1}{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]
[tex] \frac{ \sin(x) }{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]
[tex] \tan( x) ) \tan(x) = \tan {}^{2} (x) [/tex]
[tex] \tan {}^{2} (x) = \tan {}^{2} (x) [/tex]
iii).
[tex] \sec {}^{2} (x) (1 - \sin {}^{2} ( x ) ) = 1[/tex]
[tex] \sec {}^{2} (x) ( \cos {}^{2} (x) ) = 1[/tex]
[tex] \frac{1}{ \cos {}^{2} (x) } \cos {}^{2} (x) = 1[/tex]
[tex]1 = 1[/tex]
v).
[tex] \cot {}^{2} (a) - \cos {}^{2} (a) = \cot {}^{2} (a) \cos {}^{2} (a) [/tex]
[tex] \frac{ \cos{}^{2} (x) }{ \sin {}^{2} (x) ) } - \cos {}^{2} (x) [/tex]
Factor out cosine
[tex] \cos {}^{2} (x) ( \frac{1}{ \sin {}^{2} (x) } - 1) [/tex]
Simplify
[tex] \cos {}^{2} (x) ( \frac{1 - \sin {}^{2} (x) }{ \sin(x) } [/tex]
[tex] \cos {}^{2} (x( \frac{ \cos {}^{2} (x) }{ \sin {}^{2} (x) } ) = [/tex]
[tex]( \cos {}^{2} ( x ) ( \cot {}^{2} (x) )[/tex]
PLEASE HELP!!! The length, width, and height of a right rectangular prism are doubled. What will be the effect on the volume of the prism?
Answer:
The volume is multiplied by 8.
Step by step explanation:
Let the length equal l, the width equal w, and the height equal h for the original rectangular prism.
The volume of a right rectangular prism with length l, width w, and height h is V=lwh.
Therefore, the volume of the original prism is lwh.
The new rectangular prism has dimensions that are twice those of the original rectangular prism: the length equals 2l, the width equals 2w, and the height equals 2h.
To calculate the volume of the rectangular prism, substitute the doubled values into the formula for the volume of a rectangular prism.
V=2l·2w·2h
Simplify.
V=8lwh
The new volume is 8lwh.
If the length, width, and height of a right rectangular prism are doubled, the volume is multiplied by 8.
Therefore, the new volume is the original volume multiplied by 8.
On a piece of paper, graph y= see pic
Answer:
a
Step-by-step explanation:
assuming theyre asking you to graph y = (x-2)(x+3) -cant see the signs in your photo
the x-intercepts would be 2 and -3 , so option a!
I need help ASAP!! PLEASE EXPLAIN YOUR ANSWER
Answer:
Step-by-step explanation:
Given h ( x ) = 2 x − 1 h(x)=2x−1, find h ( − 1 ) h(−1).
Answer:
-3
Step-by-step explanation:
for this function you have to replace -1 were there's x in the function h(x)=2x-1
h(-1)=2(-1)-1
=-2-1
=-3
hope this helps
Find the indicated side of the
right triangle.
45°
y
6
45
Х
y = [?] /
Answer:
hello dear...
see first of all there's a thm type thing
'' sides opposite to equal angles are equal ''
so here 45 degrees in both sides are equal which leads us that opposite sides are equal as well
so x = 6
now we got value of 2 sides, both are 6 and now applying pythogarus as it is right angle
6^2 + 6^2 = y^2
36+36 = y^2
72 = y^2
y = √72
y = √36*2
y = 6√2
brainliest plssss <33
The circumference of a circle is 17pi ft. what is the area, in square feet?
Answer:
72.25 pi ft^2
Step-by-step explanation:
The circumference of a circle is
C = 2*pi*r
17 pi = 2*pi*r
Divide each side by 2pi
17 pi / 2pi = 2 pi r / 2pi
17/2 = r
We want to find the area
A = pi r^2
A = pi ( 17/2) ^2
A =289/4 pi ft^2
A = 72.25 pi ft^2
The table below shows the estimated number of customers that are subscribed to a streaming service between 2013 and 2017. The equation y=95,000(1.2)x describes the curve of best fit for the subscribed customers (y). Let x represent the number of years since 2013.
Year Subscribed Customers
2013 95,000
2014 114,000
2015 136,800
2016 164,160
2017 196,992
Using this equation, what is the approximate predicted number of subscribed customers in the year 2025?
A
236,390
B
847,030
C
1,016,435
D
1,368,000
Answer:
B847,030
Step-by-step explanation:
y=95,000(1.2)^x
2025 - 2013 = 12
y=95,000(1.2)^12
y=847029.54258
When you calculate (ln) 7, you would be finding the value of which of the following expressions?
log_e 7
log_7 10
log_10 7
log_7 e
Answer:
log_e (7)
Step-by-step explanation:
(ln) 7,
ln stands for natural log, which is log base e
log_e (7)
In a right triangle ∠A = 32° with an adjacent side of 44 what is the length of the opposite side, x?
Answer: About 27.49
Step-by-step explanation:
You use the laws of tangent within a triangle to find x:
[tex]tan(32)=\frac{opposite}{adjacent}= \frac{x}{44}\\ \\x=44*tan(32)=27.49425...[/tex]
3x + 5 = x - 3
What is the solution to this equation? Show all the steps you used to solve this equation.
Answer:
x = -4
Step-by-step explanation:
3x + 5 = x - 3
Subtract x from each side
3x+5-x = x-3-x
2x+5 = -3
Subtract 5 from each side
2x+5-5 = -3-5
2x = -8
Divide each side by 2
2x/2 = -8/2
x = -4
One angle of a rhombus measures 108°, and the shorter diagonal is 9 inches long. Approximately how long is the side of the rhombus?
Answer:
8 inches
Step-by-step explanation:
A rhombus is a four sides quadrilateral with the four sides equal in length
A rhombus has 4 equal sides and the diagonal bisect at right angles
Adjacent sides = 9/2 = 4.5
we are to determine the value of the hypotenuse given the adjacent side and angle (108/2) = 54
Cos 54 = adjacent / hypotenuse
0.58778 = 4.5 / hypotenuse
hypotenuse = 4.5 / 0.58778
=7.6559
= 8 inches
Which of the following points lies on the graph of the equation y = 2x +5.
(2, 7)
(4, 9)
(0, 2)
(2, 9)
PLEASE HELP! Simplify 2x^2+4xy+2y^2
Answer:
(x+y)(2x+2y)
Step-by-step explanation:
=2x^2 + 2xy + 2xy + 2y^2
=2x(x+y) + 2y(x+y)
=(x+y)(2x+2y)
Which equation represents a line which is perpendicular to I = 0?
y = 2
-
3
O x = -4y
Submit Answer
2= 5
o
y = -6
PLS HELP ASAP
4x+1+8-x+5x-2=23 linear equations
Step-by-step explanation:
= 4x-x+5x+1+8-2
=8x+7
proved##
Applying a Level of Significance
In this task, you’ll study the data from two experiments. For each data set, you will determine whether the difference of means between the treatment group and the control group is statistically significant and interpret the result in the context of the situation.
Question 1
Researchers want to find a way to increase the growth rate of corn so it can be harvested more often. To test the effectiveness of a new type of spray fertilizer, plants grown from 200 corn seeds were divided equally into two groups: a treatment group and a control group. The treatment group was frequently sprayed with the new type of fertilizer. The growth in centimeters of each corn plant was noted before and after the treatment.
The results showed that the mean change in the growth rate by the treatment group is 8 points more than that of the control group. To test whether the results could be explained by random chance, researchers created a table that summarizes the results of 1,000 re-randomizations of the data with differences of means rounded to the nearest 2 points.
Consider the significance level to be set at 5%, so results less than 5% can be considered statistically significant.
The calculation of the probability and interpretation of the difference in mean and the relation to level of significance between and the treatment and control groups are as follows;
Question 1; Part A
The probability that the treatment group mean is greater than the control group mean by 8 points or more is 3.6%
The completed statement is as follows;
The significance level is set at 5%, and the probability of the result is 3.6%, which is lower than significance level. The result is statistically significant
Part B
The result is statistically significant, which implies that spraying the corn plant with the new type of fertilizer does increase the growth rate
Question 2; Part A
The probability of the treatment group mean is lower than the control group mean by 15 points or more is 7.8%
The completed statement is as follows;
The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is not statistically significant
Part B;
The result is not statistically significant which implies that wearing a watch does not make people manage their time better
The reason for the above solutions is as follows;
Question 1;
The known parameters;
The significance level of the test, α = 5%
The frequencies of the difference in mean between the treatment and control groups given in the table
The number of randomizations, ∑f = 1,000
The required parameter
The probability of the treatment group mean is greater than the control group mean by 8 points or more
The significance of the result
The comparison between the given level of significance and the probability
Method
We find the probability for the required difference in mean from the data given in the table
The probability that the treatment group mean is greater than the control group mean by 8 points or more is given by the following formula;
[tex]\mathbf{P(8 \ or \ more) = \dfrac{\sum f(8 \ or \ more)}{\sum f}}[/tex]
From the table, we have;
∑f(8 or more) = 26 + 8 + 2 = 36
∑f = 1 + 10 + 28 + 58 +...+ 114 + 57 + 28 + 8 + 2 = 1,000
Therefore;
[tex]P(8 \ or \ more) = \dfrac{36}{1,000} = 0.036 = 3.6\%[/tex]
The probability, P(8 or more) 3.6%
Given that the significant level, α = 5% is higher than the probability of 3.6%, the result is statistically significant
Part B
The true statement is that the result is statistically significant, which implies that spraying the corn plant with the new type of fertilizer does increase the growth rate
Question 2;
The known parameters are;
The significance level of the test, α = 5%
The frequencies of the difference in mean between the treatment and control groups given in the table
The number of randomizations, ∑f = 1,000
The required parameter
The probability of the treatment group mean is lower than the control group mean by 15 points or more
The significance of the result
The comparison between the given level of significance and the probability
Method
Using the method from Question 1, we have;
Part A
[tex]\mathbf{P(15 \ or \ more) = \dfrac{\sum f(15 \ or \ less)}{\sum f}}[/tex]
From the table, we have;
∑f(15 or more) = 50 + 18 + 10 = 78
∑f = 10 + 18 + 50 + 127 + 195 + 226 + 180 + 117 + 48 + 17 + 12 = 1,000
Therefore;
[tex]P(15 \ or \ more) = \dfrac{78}{1,000} = 0.078 = 7.8\%[/tex]
The probability, P(15 or more) = 7.8%
Given that the significant level, α = 5% is lower than the probability of 7.8%, the result is not statistically significant
Therefore, we have;
The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is not statistically significant
Part B
The true statement is that the result is not statistically significant which implies that wearing a watch does not make people manage their time better
Learn more about hypothesis testing here;
https://brainly.com/question/4232174
Question 1;
Part A
The significance level is set at 5%, and the probability of the result is 3.6%, which is less than the significance level. The result is statistically significant
Part B
A) The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.
Question 2;
Part A
The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is NOT statistically significant
Part B;
B) The result is not statistically significant, which implies that wearing a watch does not help people manage their time better.
What is the value of r?
Answer:
r = 11
Step-by-step explanation:
Hi there!
This scenario represents a linear relation, given the equation [tex]m=rp+k[/tex].
Linear equations are typically written in the form [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept. As you can see, [tex]y=mx+b[/tex] and the given equation [tex]m=rp+k[/tex] share the same form.
This makes r the slope. This is also stated in the question, as r is the amount of money ($) paid per page.
The ordered pairs in the table represents points on a graph, if we were to graph this. For example, (9, 308) and (12, 341) both fall on the graph of this relation.
To solve for r, we must solve for the slope using the slope equation:
[tex]r=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
We can use any two points from the table in this equation. For example, (9, 308) and (12, 341):
[tex]r=\displaystyle \frac{341-308}{12-9}\\\\r=\displaystyle \frac{33}{3}\\\\r=11[/tex]
Therefore, the value of r is 11.
I hope this helps!
Find the standard deviation for the set of data.
{5,4, 18, 14, 22, 20, 6, 16, 12}
What is the measure of ABC in the figure below?
HELP FAST PLEASE!!! NEED ANSWER IN LESS THAN 10 MINUTES!! WILL GIVE BRAINLIEST!!
1. Compute -2 to the power of -3 × -3 to the power of -2.
2. Compute 2^10 x 2^8 x 2^6 x 2^4 x 2^2 x 2^-1 x 2^-3 x 2^-5 x 2^-7 x 2x-9.
3. Compute 2^16 x 4^-8 x 8^4 x 16^-2
TYSM for your help!!
1. (-(2^(-3)))*(-(3^(-2.)))=0.01388888888
2. -294912
3. 16
Find the sum of all the numbers between 100 and 200 which are divisible by 7.
Answer:
2107
Step-by-step explanation:
In this type of question we have to follow these steps
1) Find the biggest number in interval which is divisible by seven
For this question it is 196
2)Find the smallest number in interval which is divisible by seven
For this question it is 105
3) Then subtract 105 from 196
196-105=91
4) Divide 91 by seven
91:7=13
5)Lastly we have to add 1 to the 13
13+1=14
So we found that we have 14 different numbers that divisible by seven in this interval. So next steps will be about sum of them
To find them sum we have a formula:
(biggest number + smaller number) x number of terms / 2
(196+105) x 14 /2 = 2107
Instructions: Find the missing side of the triangle.
30
х
50
X=
Answer:
x = 40
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 30² = 50²
x² + 900 = 2500 ( subtract 900 from both sides )
x² = 1600 ( take the square root of both sides )
x = [tex]\sqrt{1600}[/tex] = 40
The area of a square field is 1 17/64 m2. What is the perimeter of the square field? Can some1 say this ans fast pls
Answer:
5.41 m
Step-by-step explanation:
First, let's find a side length by taking the square root of the area.
117/64 ^ 1/2 = 1.352...
Next, we need to multiply by 4.
1.352... x 4 = 5.408...
= approximately 5.41
Consider the function below. 74 POINTS!!!!!!!!
Which of the following functions could be the inverse of function f?
Answer:
x -2 3 8 13
f^-1(x) -1 0 1 2
Step-by-step explanation:
The inverse function has the input as the output and the output as the input
x -2 3 8 13
f^-1(x) -1 0 1 2
Answer: C
Step-by-step explanation: In this problem, we're given a function
in the form of a chart and we're asked to find the inverse of the function.
To find the inverse of a function, we simply switch
the x and y values in each point.
In other words, the point (-1, -2) becomes (-2, -1),
the point (0, 3) becomes (3, 0), the point (1, 8) becomes (8, 1),
and the point (2, 13) becomes (13, 2).
A point has
the coordinates (m, 0) and m + 0.
Which reflection of the point will produce an image located at (0, -m)?
• a reflection of the point across the x-axis
O a reflection of the point across the y-axis
O a reflection of the point across the line y = X
a reflection of the point across the line y = -X
Answer:
A reflection of the point across the line y = -x
Step-by-step explanation:
General rule for reflection across line y = -x is
(a,b) -------> (-b , -a)
