Answer:
6
Step-by-step explanation:
The given function to us is ,
[tex]\rm\implies f(x)= log_a(x) [/tex]
And its value at 7 is 2 , that is ,
[tex]\rm\implies f(x)= log_a(7) =2[/tex]
Taking this ,
[tex]\rm\implies 2= log_a(7) [/tex]
In general we know that ,
[tex]\bf\to log_a b = c ,\ then \ a^c = b [/tex]
Using this , we have ,
[tex]\rm\implies a^2 = 7 [/tex]
Squarerooting both sides ,
[tex]\rm\implies a =\sqrt{ 7 }[/tex]
Therefore , when x is 343 ,
[tex]\rm\implies f(343)= log_{\sqrt7} ( 343) [/tex]
We can write , 343 as 7³ ,
[tex]\rm\implies f(343)= log_{\sqrt7}7^3 [/tex]
[tex]\rm\implies f(343)= log_{7^{\frac{1}{2}}} 7^3 [/tex]
This can be written as ,
[tex]\rm\implies f(343)= \dfrac{ 3}{\frac{1}{2}} [/tex]
[tex]\rm\implies \boxed{\blue{\rm f(343)= 6 }}[/tex]
Hence the required answer is 6.
a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by
Complete Question:
A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.
a. What is his maximum profit per day?
b. How many cans must be sold in order to obtain the maximum profit?
Answer:
a. $450
b. 1500 cans
Step-by-step explanation:
Given the following quadratic function;
P(x) = -0.001x² + 3x - 1800 ......equation 1
a. To find his maximum profit per day;
Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]
Note : the standard form of a quadratic equation is ax² + bx + c = 0 ......equation 2
Comparing eqn 1 and eqn 2, we have;
a = -0.001, b = 3 and c = -1800
Now, we determine the maximum profit;
[tex] x = \frac {-b}{2a} [/tex]
Substituting the values, we have;
[tex] x = \frac {-3}{2*(-0.001)} [/tex]
Cancelling out the negative signs, we have;
[tex] x = \frac {3}{2*0.001} [/tex]
[tex] x = \frac {3}{0.002} [/tex]
x at maximum = 1500
Substituting the value of "x" into equation 1;
P(1500) = -0.001 * 1500² + 3(1500) - 1800
P(1500) = -0.001 * 2250000 + 4500 - 1800
P(1500) = -2250 + 2700
P(1500) = $450
b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.
Not sure how to do this
15
Simplify
a
25
O A. a3
O B. a10
O c. a-10
O D. a-3
Answer:
B is the correct answer of your question.
I HOPE I HELP YOU....
In forming a confidence interval for μ1 - μ2, only two assumptions are required: independent samples and sample sizes of at least 30.
a. True
b. False
If you make $11.25/hour, how many hours will you need to work to earn $416.25? Please explain how you figured this out.
Answer:
37 hours.
Step-by-step explanation:
Since you need $416.25 start with that. Then divide by $11.25 to see how many hours you need to work. 416.25 divided by 11.25 is 37.
The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the diameter is13cm. (Round your answer to three decimal places if required)
Answer:
Step-by-step explanation:
This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.
We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of
[tex]S=4\pi r^2[/tex]
In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that
d = 2r so
[tex]\frac{d}{2}=r[/tex] Now we can have the equation in terms of diameter instead of radius. Rewriting:
[tex]S=4\pi(\frac{d}{2})^2[/tex] which simplifies to
[tex]S=4\pi(\frac{d^2}{4})[/tex] and a bit more to
[tex]S=\pi d^2[/tex] (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.
[tex]\frac{dS}{dt}=\pi*2d\frac{dD}{dt}[/tex] Now let's look at the problem and see what we are given as far as information.
The rate at which the surface area changes is -3.8, and we are looking for [tex]\frac{dD}{dt}[/tex], the rate at which the diameter is changing, when the diameter is 13. Filling in:
[tex]-3.8=\pi(2)(13)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:
[tex]-\frac{3.8}{26\pi}=\frac{dD}{dt}[/tex] and divide to get
[tex]\frac{dD}{dt}=-.459\frac{cm}{min}[/tex] Obviously, the negative means that the diameter is decreasing.
Зу = -2 - 6
3y = 2z - 6
Answer:
y = -8/3, z = -1
f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).
Answer:
4x-5=4x-5
(f+g) (x)=6x³+3Step-by-step explanation:
Purpose: The purpose of this learning activity is to demonstrate the understanding of correlation and regression and how they could be important in your future practice. Instructions: Submit 1 paragraph answering the following questions: • What are the differences between results that demonstrate a correlation between two variables and results where a regression is run using two variables? • Think about your future clinical role and provide a clinical example of variables that you may want a correlation analysis run and explain. • Think about your future clinical role and provide a clinical example of variables that you may want a regression analysis run and explain.
Answer:
A correlation shows strength and regression tells the pattern.
Step-by-step explanation:
• The differences between the results that demonstrate a correlation between two variables and results where a regression is run using two variables are as follows
1) the correlation is the measure of degree to which any two variables may vary together.
2) if both variables tend to increase or decrease together the correlation is said to be direct or positive.
3) the correlation gives the strength of relationship between two quantities
4) The regression gives the relationship in the form of an equation.
5) The regression investigates the dependence of the dependent variable on the independent variable.
6) it shows the relationship whether it is linear or curved or parabolic etc.
• I may record the ages and the blood pressure of the patients and run a correlation analysis which may not be positive as blood pressure does not always increase with age
• I may record the ages and the blood pressure of the patients and may want to run a regression analysis which will show the relationship of the patients suffering from high blood pressure and their ages whether it follows a similar pattern or not.
Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by
The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is
[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]
In this case, we have
x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )
y(t) = 5 - 2t ==> dy/dt = -2
and [a, b] = [0, 2]. The length of the curve is then
[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]
[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]
The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.
[tex]e^2 -\dfrac{1}{e^2 }[/tex]
What is integration?It is the reverse of differentiation.
The parametric equations are given below.
[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]
Then the arc length of the curve will be given as
[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]
Then
[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]
More about the integration link is given below.
https://brainly.com/question/18651211
JK=8x+6 KL=6x+20 find JL
Answer:
14x + 26
Step-by-step explanation:
JL = JK + KL
= 8x + 6 + 6x + 20
= 8x + 6x + 6 + 20
JL = 14x + 26
Find x on this triangle
Answer:
3 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = x/6
6 cos 30 = x
6 ( sqrt(3)/2) = x
3 sqrt(3) =x
Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1
Answer:
d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer
The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3(2x -1/3y)=0.
Now, 6x-1/y=0
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Here, coefficient of y is 1.
Therefore, option B is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
In the picture the exponent says 5/3
Answer:
the answer is B
Step-by-step explanation:
[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]
write -8 form of 2 on up and complete other steps
Combine the expressions below
4x+(-2x)+6+(-9)
=4x-2x=2x
=6-9=-3
=2x-3
can someone help me out with this question???
Answer:
a
Step-by-step explanation:
I need help with this
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Engineering
When p= 3, q. I and r. 2, the
expression 2p² q3 is equal to
Answer:
[tex]{ \tt{2 {p}^{2} {q}^{3} }} \\ = { \tt{ {2(3)}^{2} . {(1)}^{3} }} \\ = 18[/tex]
if p is a acute angle then p is how many degrees
Answer:
Less than 90⁰
Step-by-step explaination:
If p is an acute angle then, p can be equal to any measurement less than 90⁰
It can be upto 89⁰
Answer:
0 < angle < 90
Step-by-step explanation:
Acute angles are between 0 and up to 90 degrees
Right angles are 90 degrees
Obtuse angles are greater than 90 degrees and less than 180 degrees
If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *
Given:
There is a 65% chance you will make a free throw.
To find:
The percent of the time you will miss.
Solution:
If p is the percent of success and q is the percent of failure, then
[tex]p+q=100\%[/tex]
[tex]q=100\%-p[/tex] ...(i)
It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss. It means we have to find the percent of failure.
Substituting p=65% in (i), we get
[tex]q=100\%-65\%[/tex]
[tex]q=35\%[/tex]
Therefore, there is a 35% chance you will miss the free throw.
Mikita is painting a spherical model of a human cell for a science fair. She uses 452.16 square inches of paint to evenly cover the outside of the cell with one coat of paint. What is the diameter of the cell model? (Use 3.14 for the value of π.)
6 in.
12 in.
24 in.
36 in.
Answer:
12
Step-by-step explanation:
Basically you have to divide 3.14 by 452.16 (the formula for area of circle is pi times r squared) and that will get you 144. The square root of 144 is 12 :)
What is the value of the expression 10(6 + 5)² when b = 3?
10(3+5)^2
10(8)^2
10(64)
=640
the length of a rectangle is twice its width the perimeter is 48 cm what are the dimensions of the rectangle
Answer:
The length=16cm and the width=8cm.
Step-by-step explanation:
Given that the length is twice the breadth or width of the rectangle
Let's assume that the breadth of the rectangle is x.
Thus the length is 2x.
Given perimeter=48cm
The formula for the perimeter of a rectangle is 2(l+b) where l is length and b is breadth.
2(x+2x)=48
(3x)=48/2
3x=24
x=8cm
2x=16cm
Step-by-step explanation:
length=2x
width=x
2x+x+2x+x=48
6x=48
6x÷6=48÷6
x=8
length=16
width=8
Josue leans a 26-foot ladder against a wall so that it forms an
angle of 80° with the ground. How high up the wall does the
ladder reach? Round your answer to the nearest hundredth of a
foot if necessary.
Answer:
25.61 feet
Step-by-step explanation:
First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.
Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.
One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have
sin(80°) = opposite / 26 feet
multiply both sides by 26 feet
sin(80°) * 26 feet = opposite
= 25.61 feet as the height of the wall the ladder reaches
The height of the wall does the ladder reach to the nearest hundredth of the foot is 25.61 feet.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
Josue leans a 26 feet ladder against a wall so that it forms an angle of 80° with the ground.
The condition is shown in the diagram.
Then the height of the wall will be
[tex]\rm \dfrac{h }{26 } = sin 80 \\\\h \ \ = 26 \times sin 80\\\\h \ \ = 25.61 \ ft[/tex]
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
The travel time on a section of a Long Island Expressway (LIE) is normally distributed with a mean of 80 seconds and a standard deviation of 6 seconds. What travel time separates the top 2.5% of the travel times from the rest
Answer:
The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 80 seconds and a standard deviation of 6 seconds.
This means that [tex]\mu = 80, \sigma = 6[/tex]
What travel time separates the top 2.5% of the travel times from the rest?
This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 80}{6}[/tex]
[tex]X - 80 = 6*1.96[/tex]
[tex]X = 91.76[/tex]
The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.
What is the value of x in the equation
-%y = 30, when y = 15?
Answer:
x not given
therefore no answer for x
Select the correct answer.
Simplify the following expression. Classify the resulting polynomial.
3x(x − 3) + (2x + 6)(-x − 3)
quadratic monomial
quadratic binomial
quadratic trinomial
linear binomial
Answer:
quadratic trinomial
Step-by-step explanation:
3x(x − 3) + (2x + 6)(-x − 3)
Distribute
3x^2 -9x + (2x + 6)(-x − 3)
FOIL
3x^2 -9x + -2x^2 -6x -6x -18
Combine like terms
x^2-21x-18
This has 3 terms so it is a trinomial
The highest power of x is 2 so it is quadratic
9514 1404 393
Answer:
x² -21x -18quadratic trinomialStep-by-step explanation:
Eliminating parentheses, we get ...
= (3x)(x) -(3x)(3) +(2x)(-x -3) +6(-x -3)
= 3x² -9x +(2x)(-x) +(2x)(-3) +(6)(-x) +(6)(-3)
= 3x² -9x -2x² -6x -6x -18
= x²(3 -2) +x(-9-6-6) -18
= x² -21x -18
The highest power is 2, so this is a quadratic.
There are 3 terms, so this is a trinomial.
Miller's Steakhouse offers 8 side dishes, 5 types of steak, and 4 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 3 different toppings and 3 different side dishes?
Answer:
1120
Step-by-step explanation:
To find the possible number of steak dinners, you would multiply the number of choices for each part of the dinner. You would used combinations instead of permutations since the order of the toppings chosen or side dishes chosen do not matter. There are 5 choose 1 choices for types of steak, which is just 5. There are 8 choose 3 choices for side dishes, which is 56. There are 4 choose 3 choices for toppings, which is 4. 5*56*4 is 1120, so there are 1120 possible steak dinners.
Hii guys if you have time plz help me
Answer:
[tex]5 {x}^{2} + 21 + 5x[/tex]
Step-by-step explanation:
TOTAL AMOUNT earned = Tim money + Melina money
[tex]5 {x}^{2} - 4x + 8 + (9x + 13)[/tex]
[tex] = 5 {x}^{2} - 4x + 8 + 9x + 13[/tex]
[tex] = 5 {x}^{2} + 21 + 5x[/tex]
Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0.
a. Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0.
b. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?
Answer:
[tex](a)\ \frac{dP}{dt} = kP + r[/tex]
[tex](b)\ \frac{dP}{dt} = kP - r[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = kP[/tex]
Solving (a): Differential equation for immigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP + r[/tex]
Solving (b): Differential equation for emigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP - r[/tex]
