Answers
Answer:
t = 1.322
Step-by-step explanation:
4×(2^t) = 10
2^t = 10/4 = 2.5
t = log2(2.5)
now, the logarithm to the base 2 of 2.5 must be larger than 1, as 2.5 is larger than 2.
so, it can be only the 4th answer option.
now, to actually calculate it :
log2(2.5) = log10(2.5) / log10(2) = 1.321928095... ≈
≈ 1.322
we were correct.
Answer:
t = 1.322
Step-by-step explanation:
Given equation:
[tex]4(2^t)=10[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4(2^t)}{4}=\dfrac{10}{4}[/tex]
[tex]\implies 2^t=2.5[/tex]
Method 1Take natural logs of both sides:
[tex]\implies \ln 2^t = \ln 2.5[/tex]
[tex]\textsf{Apply the natural log power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies t \ln 2 = \ln 2.5[/tex]
Divide both sides by ln 2:
[tex]\implies \dfrac{t \ln 2}{\ln 2} = \dfrac{\ln 2.5}{\ln 2}[/tex]
[tex]\implies t= \dfrac{\ln 2.5}{\ln 2}[/tex]
[tex]\implies t=1.321928095...[/tex]
Method 2[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies \log 2 (2.5)=t[/tex]
[tex]\implies t=1.321928095...[/tex]
SolutionTherefore, the solution that is nearest to the exact solution is t = 1.322
Related Questions
Marvin used the Quantitative Reasoning Process to build a budget while he is going to college. He worked hard over the summer and saved $2,595.9 to live on during the next two semesters of school. Marvin will receive a scholarship each semester for $958.35. If he plans to use up all of his savings while at school, how much money can Marvin spend each month, on average, for things like groceries, entertainment, and miscellaneous items?
Assume two semesters equals 8 months total. Also assume Marvin has no other expenses than what he has listed here.
Scholarship for each Semester: $958.35
Tuition & Books Cost per Semester: $2,000
Housing Cost for a two-semester Contract: $1,000
If he has money left, what is the average monthly amount Marvin can afford to spend each month?
If he has overspent, what is the average monthly amount Marvin would be in debt each month?
(Indicate this amount with a negative sign)
Answers
For Marvin used the Quantitative Reasoning Process to build a budget while he is going to college. He worked hard over the summer and saved $2,595.9 to live on during the next two semesters of school. Marvin will receive a scholarship each semester for $958.35 money can Marvin spend each month, on average, for things like groceries, entertainment, and miscellaneous items is mathematically given as
$4512.6
How much money can Marvin spend each month, on average, for things like groceries, entertainment, and miscellaneous items?Savings with Marvin = $2,595.9
Scholarship amount = $958.35
Total Scholarship amount received in 2 semesters = $958.35 X 2 = $ 1916.7
Now total money that Paolo have = (Savings with Marvin) + (Total Scholarship amount received in both semesters) = $2,595.9 + $1916.7 = $ 4512.6
Tuition & books cost = $2000
Tuition & books cost for 2 semesters = $2000 X 2 = $4000
Housing cost for 2 semester contract =$1,000
Total expenses in books and housing = $4000+ $1000 = $5000
Money left with Marvin after Total expenses in books and housing = $ 4512.6 - $5000 = −487.4
This means he has overspent.
as no. of months in 2 semesters = 8
Amount that Marvin would be in debt each month = −487.4/8 = −$60.925
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A grocery store sells a bag of 8 oranges for $4.40. How much would it cost for 9 oranges?
Answers
To solve this exercise, we apply the rule of three:
Oranges......................Price
8.................................$4.40
9.......................................x
We solve as follows:
[tex]\boldsymbol{\sf{x=\dfrac{9\times4.40}{8}=\dfrac{39.6 }{8}=4.9 }}[/tex]
Therefore, 9 oranges would cost $4.9.
{ Pisces04 }The required cost of the amount of 4.95 dollars would be for 9 oranges.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have been given that a grocery store sells a bag of 8 oranges for $4.40.
We have to determine the cost for 9 oranges.
Let's assume x dollars would it cost for 9 oranges.
As per the given condition, we can write the ratio as:
8 oranges : $4.40 = 9 oranges : x dollars
⇒ 8 / 4.40 = 9 / x
Cross multiplication and rearrange the terms of the above equation,
⇒ 8x = 4.40×9
Divide by 8 into both sides of the equation,
⇒ x = (4.40×9)/8
⇒ x = (39.6)/8
⇒ x = 4.95
Therefore, the cost of the amount of 4.95 dollars would for 9 oranges.
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Which of the following is not an example of like terms?
A. 2 and-6
B.2b and-6b
C.2b and 2
D.2b² and 6b²
Answers
Answer:
A. 2 and-6
Step-by-step explanation:
Like terms are terms that contain the same variables raised to the same powers. In other words, they have the same variables with the same exponents.
So in option A, we have the terms 2 and -6. These terms are not like terms because they do not have the same variables.
2 and -6
Subtract -13f^3+9f2+7f-16-(-8 f^3+5f^2+9f-4)
Answers
Answer:
:)\
Step-by-step explanation:
Find the future value if you invest $1200 at 5.25% compounded quarterly for two years.
Answers
In accordance with the compound interest model, the future value if you invest $ 1200 at 5.25 % compounded quarterly for two years is $ 1807.
How to determine the current capital by compound interest model
The compound interest model is based on the assumption that the initial capital obtain gains continuously in time. This model is represented by the following expression:
C' = C · (1 + r/100)ˣ (1)
Where:
C - Initial capitalC' - Current capitalr - Interest ratex - Time, in quartersPlease notice that a year consists in four quarters. If we know that C = 1200, r = 5.25 and x = 8, then the current capital is:
C' = 1200 · (1 + 5.25/100)⁸
C' = 1807
In accordance with the compound interest model, the future value if you invest $ 1200 at 5.25 % compounded quarterly for two years is $ 1807.
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Can it be concluded that AWXY ABCD by SAS? Why or why not?
Ono, because the third corresponding sides must also be given as congruent
Ono, because the corresponding congruent angles listed are not the included angles
Ono, because all corresponding angles must be given as congruent
O yes, because two corresponding sides and a corresponding angle are congruent
Answers
It can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D
What is SAS congruency?SAS congruency states that two triangles are said to be congruent if any two sides or angle between the sides of one triangle are equal to the corresponding two sides and also the angle between the sides of the second triangle.
Thus, it can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D
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Answer:
B. No, because the corresponding congruent angles listed are not the included angles.
Step-by-step explanation:
I need some help please so confused new topic
Answers
what is the surface area of 5 feet and base radius of 8 feet
Answers
Answer:
40 feetI is the correct answer
Please help!! Thank you so much if you do!! Jayla bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 12 cups of soup.
Answers
Answer:
d.) 226.2 cubic inches
Step-by-step explanation:
The soup pot is in the shape of a cylindrical.
And
[tex]\sf Volume \ of \ cylinder= \pi (radius)^2 (height)[/tex]
Here given:
radius: 3 inchheight: 8 inchSo,
[tex]\sf Volume \ of \ pot= \pi (3)^2 (8)[/tex]
[tex]\sf Volume \ of \ pot= 72\pi \ in^3[/tex]
[tex]\sf Volume \ of \ pot= 226.2 \ in^3[/tex]
The selling price of a second hand car is originally N273.000. The dealer reduces the price
in the ratio of 11:13; what is the new selling price of the car?
(a) 273,000 (b) 231,000 (c) 200,000 (d) 50,000
Answers
Answer:
231,000
Step-by-step explanation:
In the ratio of 11:13, if you plug in 13, the corresponding value is 11.
Dividing 11 by 13 shows that if you also multiply 13 by 0.846 (Rounded) it also equals 11.
So multiplying 0.846 by the original price of 273,000, we get 231,000.
The new selling price of the car will be 231,000. Then the correct option is A.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The original selling price of a used automobile is N273,000. The price is dropped by the dealer by a ratio of 11:13.
The new selling price of the car will be given as,
Selling price = 273,000 x 11/13
Selling price = 21,000 x 11
Selling price = 231,000
Thus, the correct option is A.
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Will mark brainiest or whatever its called
Answers
Answer:
5621 years
Step-by-step explanation:
Plug everything in first.
[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]
Round to closest amount of years = 5621 years
prime factorization of 220
Answers
Answer:
The Prime Factorization of 220 is 22 × 51 × 111.
Step-by-step explanation:
Factors of 220 are integers that can be divided evenly into 220. It has total 12 factors of which 220 is the biggest factor and the prime factors of 220 are 2, 5, 11. There for, the Prime Factorization of 220 is 22 × 51 × 111.
A cubic yard of topsoil is to be spread evenly in the garden at Prove It! Math Academy. Thegarden measures 10 feet by 8 feet. How many inches deep will the topsoil be?
Answers
The topsoil will be 4.05 inches deep
Calculating depthFrom the question, we are to determine how many inches deep the topsoil will be
From the given information,
The volume of the topsoil = 1 cubic yard
Convert to cubic feet
1 cubic yard = 27 cubic feet
∴ The volume of the topsoil = 27 cubic feet
Then,
The depth of the topsoil will be = 27/(8 ×10)
Depth of topsoil = 27/80
Depth of topsoil = 0.3375 foot
Now, convert to inches
1 foot = 12 inches
∴ 0.3375 foot = 0.3375×12 inches
= 4.05 inches
Hence, the topsoil will be 4.05 inches deep
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12. Find the slope and y-intercept of the line. y= 1/5x-8
Answers
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want us to find:
slopey-interceptLet's gather the information:
⇒ the information given: y = 1/5 x - 8
⇒ the line is in slope-intercept form
⇒ means:
⇒ coefficient in front of 'x' is the slope
⇒ constant is the y-intercept
slope is 1/5y-intecept is -8Answer:
Slope is 1/5y-intercept is -8Hope that helps!
#LearnwithBrainly
Hi!
The equation that we're working with is provided to us in Slope-Intercept Form:
[tex]\diamondsuit~~~\large\boldsymbol{y=mx+b}[/tex]
In the formula, the letter "m" denotes the slope, and it always comes before x; b is the y-intercept, and it's basically a number that is either added or subtracted from x.
Now let's identify the slope of the line given to us, that is:
[tex]\boldsymbol{\underline{\underline{y=1/5x-8}}}[/tex]
Slope = number before x,
Y-intercept = number added/subtracted from the slope
Therefore,
[tex]\stackrel{\heartsuit}{\boxed{\boxed{\textsc{Answers:}\begin{cases}\bold{Slope:\displaystyle\frac{1}{5}}\\\bold{Y-intercept:-8}\end{cases}}}}[/tex]
I hope it helped! Let me know if you need any explanation or clarification! I'm always happy to help. :D
Alexandria cuts out the net shown and folds it into a number cube. Three faces meet at each corner of the cube. What is the largest sum of three numbers that meet at a corner?
Answers
The largest sum of three numbers that meet at a corner is 15
How to determine the largest sum?The number cube that completes the question is added as an attachment
The largest number in the number cube is 6.
On the number cube, the next largest numbers share the same corner with the number 6
So, the largest set of numbers on the cube are 6, 5, 4
Add the numbers:
Sum = 6 + 5 + 4
Evaluate
Sum = 15
Hence, the largest sum of three numbers that meet at a corner is 15
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Given a normally distributed data set with the mean = 51 and the standard deviation = 12, according to the empirical rule, what percent of the data points are above 27?
Answers
The percentage of data points that are above 27 are; 2.28%
How to use the empirical rule in statistics?We are given;
Mean; μ = 51
Standard deviation; σ = 12
Sample mean; x' = 27
Thus, formula for z-score is;
z = (x' - μ)/σ
z = (27 - 51)/12
z = -2
Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%
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3y−13≥−9 and 3y−13≤−1
Answers
[tex]3y \geqslant 13 - 9[/tex]
[tex]3y \geqslant 4[/tex]
[tex]y \geqslant \frac{4}{3} [/tex]
[tex]3y \leqslant 13 - 1[/tex]
[tex]3y \leqslant 12[/tex]
[tex]y \leqslant 4[/tex]
[tex] \frac{4}{3} \leqslant y \leqslant 4[/tex]
Kareem wrote the expressions shown below.
[3.2] [2.7] [2.9] [4.8]
Which pair is equivalent?
O [2.7] and [3.2]
O [2.9] and [2.7]
O [3.2] and [2.9]
O [4.8] and [3.21]
Answers
The equivalent pair of the given expression is; [4.8] and [3.21]
How to find equivalent pairs?Floor function states that the greatest integer that is less than or equal to x. It is represented by: ⌊ x ⌋.
Ceiling function states that the least integer that is greater than or equal to x. It is represented by ⌈ x ⌉.
Kareem wrote the expressions;
[3.2] [2.7] [2.9] [4.8]
By definition above;
[3.2] = 4
[2.7] = 2
[2.9] = 3
[4.8] = 4
Thus, the equivalent pair is [4.8] and [3.2]
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Give the digits in the tens place and the tenths place.
83.21?
Answers
Step-by-step explanation:
tens place is 8 because the first number from the back is the unit
the tenth place is 2
The values in the table represent a linear function. How does the value of y change in relation to a change in the value of x?
A) for every change in x by 3, y changes by 2
B) for every change in x by 2, y changes by 3
C) for every change in x by 3, y changes by -2
D) for every change in x by 2, y changes by -3
Answers
if x is changed by 2 , the y changes by +3, Option B is the correct answer.
What is the equation of a Linear Function ?The equation of a Linear Function is given by
y = mx +c
here m is the slope , c is the intercept on the y axis
The data is given in the table
To determine the relation , a function needs to be established between the variables.
m = ( y2 -y1 )/(x2-x1)
m = (-7 +10) /(-2+4)
m = 3 / 2
y = (3/2)x + c
at x = 0 , y= -4
-4 = 0 + c
c = -4
The function is
y = (3/2) x - 4
if x is changed by 2 , the y changes by +3
Therefore Option B is the correct answer.
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If a 6–foot–long ladder leans against a building at an angle of 62 , which of the following triangles accurately represents this situation?
Answers
The triangle formed is a right triangle and the hypotenuse side is 6 ft.
How to represent right triangle?The situation forms a right angle triangle.
A right triangle has one of its angles as 90 degrees.
Therefore, the triangle is represented below
The hypotenuse side of the right triangle is 6 foot, which is the length of the ladder.
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(0, 9)₂
What is the equation of a line that is parallel to y = 6x + 7 and passes through (0,
Enter your equation in the box.
Answers
Answer:
y = 6x+9
Step-by-step explanation:
Equations that are parallel have the same slope
y = 6x+7 is written in slope intercept form where the slope is 6 and the y intercept is 7
The lines will have a slope of 6
The point (0,9) is the y intercept because the x value is 0
We can write the equation in slope intercept form y = mx+b
y = 6x+9
Answer:
Hello! The answer is y = 6x + 9.
Step-by-step explanation:
When lines are parallel, they will have the same slope but a different y-intercept.
The y-intercept, in this case, would be (0, 9) since the x-coordinate equals 0. This leaves us with 9 as the y-intercept.
Our slope-intercept form equation will be written as:
y = 6x + 9
Consider the following figure:
What solid 3D object is produced by rotating the triangle about line m?
Answers
The solid 3D object that is produced by rotating the triangle about line m is a cone.
What is a triangle?It should be noted that a triangle simply means a shape that has three sides and three angles.
In this case, the solid 3D object that is produced by rotating the triangle about line m is a cone.
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What is value of x?
Enter your answer in the box.
Answers
Answer:
[tex]x \ = \ 10[/tex]
Step-by-step explanation:
Let point [tex]D[/tex] be the point where the straight line drawn from point [tex]A[/tex] meets the straight line [tex]BC[/tex], it is evident that [tex]\triangle ABD[/tex] and [tex]\triangle ACD[/tex] is similar given that both triangles share the same angle, [tex]\angle BAD \ = \ \angle DAC[/tex]. Hence, the ratio of the sides of each triangle is the same. Specifically,
[tex]\displaystyle{\frac{x+4}{8} \ = \ \frac{2x+1}{12}}[/tex].
Performing cross multiplication yields
[tex]12\left(x+4\right) \ = \ 8\left(2x+1\right) \\ \\ \rule{0.15cm}{0cm}12x+48 \ = \ 16x+8 \\ \\ \rule{1.1cm}{0cm} 4x \ = \ 40 \\ \\ \rule{1.3cm}{0cm} x \ = \ 10[/tex].
Select the correct answer.
Sterling Company is testing the popularity of two products in the first days following their release. The quantity sold for Product 1,
t days after its initial release, is modeled by the following function.
g(t)= 200(1.36)
The quantity sold for Product 2, t days after its initial release, is shown in the following table.
5
859
t
0
1
2 3 4
f(t) 250 320 410 524 671
Based on this information, which product had the greater average rate of increase in sales after three days?
O Product 1
Both had the same average rate of increase in sales.
This cannot be determined from the given information.
O Product 2
Submit
Answers
Answer:where are the options ???
Step-by-step explanation:
Answer:
Product 1
Step-by-step explanation:
Got it
Let x represent Anna's age. If John's age is Anna's age plus 1 and Tamara is Anna's
decreased by 2, write an expression that represents the sum of Anna's and John's
age, minus Tamara's age?
Answers
Answer:
x + 3
Step-by-step explanation:
x = Anna's age
y = John's age
z = Tamara's age
y = x + 1
z = x - 2
the expression for the sum of Anna's and John's age minus Tamara's age is
x + y - z
and when we use the equations above to simplify that :
x + (x + 1) - (x - 2) = x + x + 1 - x + 2 = x + 3
4 – 15 ÷ (30 – 33) =
Answers
Answer: 9
Step-by-step explanation:
We will use the Order of Operations to solve.
Given:
4 – 15 ÷ (30 – 33)
Subtract 33 from 30:
4 – 15 ÷ (– 3)
Divide -15 by -3:
4 + 5
Add 4 to 5:
9
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{In order for you to solve for this}\\\huge\textbf{equation, you have to do PEMDAS.}\\\\\\\\\huge\textbf{PEMDAS simply means: }[/tex]
[tex]\bullet\large\textbf{ Parentheses}[/tex]
[tex]\bullet\large\textbf{ Exponents}[/tex]
[tex]\bullet\large\textbf{ Multiplication}[/tex]
[tex]\bullet\large\textbf{ Division}[/tex]
[tex]\bullet\large\textbf{ Addition}[/tex]
[tex]\bullet\large\textbf{ Subtraction}[/tex]
[tex]\huge\textbf{Now, let's answer the given equation.}[/tex]
[tex]\mathbf{4 - 15 \div (30 - 33)}[/tex]
[tex]\mathbf{= 4 - 15 \div 3}[/tex]
[tex]\mathbf{= 4 - (-5)}[/tex]
[tex]\mathbf{= 4 + 5}[/tex]
[tex]\mathbf{= 9}[/tex]
[tex]\huge\textbf{We got the \boxed{\bf +} because double negatives}\\\huge\textbf{equal a positive.}[/tex]
[tex]\huge\textbf{We have found the result to the question}[/tex]
[tex]\huge\textbf{Thus, your answer should be: \boxed{\mathsf{9}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Chase makes 2 gallons of soup for a dinner party. He serves 15 cups of soup to his guest. How many cups of soup will he have left over?
Answers
Answer:
17 gallons
Step-by-step explanation:
1 gallon has 16 cups
2 gallons have 32 cups
32-15=17
Answer:
17 cups
Step-by-step explanation:
1 gallon=16 cups
Since he made 2 gallons of soup, multiply 16 x 2 and you will get 32 cups of soup. If he served 15 cups of soup to his guests, he will have 17 cups of soup left over, because 32 - 15 = 17.
I hope i helped!!! :)
Which statement describes a key feature of function g if g(x) = f(x + 4)?
OA y-intercept at (0,4)
OB. x-intercept at (4,0)
OC. horizontal asymptote of y = 0
OD. horizontal asymptote of y = 4
Answers
The statement that describes a key feature of function g if g(x) = f(x + 4) is C. horizontal asymptote of y = 0.
What is a function?It should be noted that a function is an expression that shows the relationship between the variables.
In this case, the statement that describes a key feature of function g if g(x) = f(x + 4) is that the horizontal asymptote of y = 0.
The horizontal asymptote is vital for guiding the variables
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During a cash poker game, a professional gambler bets $6,000 on the cards in his hands. The bet has a 0.81 probability of producing a large profit of $6,500, a 0.08 probability of producing a small profit of $200, and a 0.11 probability of producing a loss of $6,000. If the gambler were to continue making bets with this probability distribution, what would his expected profit be?
Answers
The expected profit for the gambler is $4,621
How to get the expected profit?The possible outcomes are:
Winning $6,500, with a probability of 0.81Winning $200, with a probability of 0.08Lossing $6,000, with a probability of 0.11Then the expected profit is:
P = ($6,500*0.81 + $200*0.08 - $6,000*0.11) = $4,621
The expected profit for the gambler is $4,621
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