Answers
Answer:
b = -1
Step-by-step explanation:
5 ^ ( 3b-1) = 5 ^ ( b-3)
since the bases are the same, the exponents are the same
3b-1 = b-3
Subtract b from each side
3b-1-b = b-3-b
2b -1 = -3
Add 1 to each side3
2b-1+1 = -3+1
2b = -2
Divide by 2
2b/2 = -2/2
b =-1
Answer:
b = -1.
Step-by-step explanation:
Since the bases are the same (they are both 5), you can set 3b - 1 equal to b - 3.
3b - 1 = b - 3
3b - b = -3 + 1
2b = -2
b = -1
To make sure you are correct...
5^(3 * -1 - 1) = 5^(-1 - 3)
5^(-3 - 1) = 5^(-4)
5^(-4) = 5^(-4)
Since it matches up, you know that b = -1.
Hope this helps!
Related Questions
Trina uses 1/2 of the cup of sugar and 3/4 cup of flour of recipe. How many cups of sugar would she need if she uses 3 cups of flour?
Answers
Answer:
you need 2 cups of sugar
Step-by-step explanation:
1/2 cups of sugar = 3/4 cup of flour
x = 3 cups of flour
1/2*3 = 3/4x
3/2 = 3/4x
x =3/2 ÷ 3/4
x =2
which of the following box plots best represents the set of data below?
Answers
Answer:
not sure
Step-by-step explanation:
Answer:
answer B
Step-by-step explanation:
to set up whisker plots you have to find the 1st 2nd and 3rd quartile.
hopes this helps
Alex records the running time—the number of minutes a movie lasts from start to finish—of 50 popular movies. The distribution of times, in minutes, is shown in the histogram below. Which of these intervals contains the most movies? 80–90 minutes 90–100 minutes 100–110 minutes 110–120 minutes
Answers
Answer:
Check Explanation
The histogram for the question isn't attached. But from the options provided for this question (80–90 minutes 90–100 minutes 100–110 minutes 110–120 minutes), it is evident that the bars and intervals for the question have the same width. So, the interval with the most movies will be the interval whose bar is the tallest.
Pick the interval whos bar has the highest height.
Step-by-step explanation:
The histogram for this question is missing. I couldnt get the histogram online, so, I will use a random histogram example to explain how to pick the interval with the highest frequency.
A histogram is a chart representation that uses bars to describe numerical data. It divides the entire distribution into Intervals and the number of variables in each interval (the frequency) corresponds to the area of each bar. This is the major difference between a bar chart and a histogram; the bars can be unequal for a histogram unlike that of bar charts.
If the bars are of equal widths, then the frequency of each interval is simply the height of the interval's bar.
In the attached histogram example for this question, the histogram shows the monthly salaries of workers and the frequency of workers receiving whichever salary. The intervals for these salaries for this histograms are in steps of $25. The bars start from $800 to $825, $825 to $850 and so on.
Since all the intervals have the same width, the interval with the most workers receiving the salary in that interval is the $900 to $925 interval with the tallest bar with frequency of 150.
If the bars weren't of the same width, the area of each bar is computed and the bar with the highest area has the highest frequency.
From the options provided for the question asked (80–90 minutes 90–100 minutes 100–110 minutes 110–120 minutes), it is evident that the bars and intervals for the question have the same width. So, the interval with the most movies will be the interval whose bar is the tallest.
Hope this Helps!!!
Answer:
maybe A
Step-by-step explanation:
Can someone please help me find the answer and help me solve.
Answers
Answer:
sure
Step-by-step explanation:
Answer:
The answer is answer
Step-by-step explanation:
No need for it
A line passes through the points (7, 10) and (7, 20) which statement is true about the line.
Answers
Answer:
You didn't give any statements so I'll tell you that it's a vertical line.
Step-by-step explanation:
Answer:
the answer is C on edge
Step-by-step explanation:
How are periodic phenomena relatively easy to model using trig functions? What makes them difficult to model this way?
Answers
Answer:
Periodic phenomena means that the phenomena has a (almost) constant time period or space period.
As you know, the trigonometric functions cos(x) and sin(x) also have a constant period of 2*pi, so these functions are really useful to model periodic phenomena.
Now, the problem may be that the trigonometric functions may be useful to describe the "periodic" part, but not to describe the actual phenomena.
An example of this can be a square alternating current.
While it has a constant period like a trigonometric function, the trigonometric functions can not really model the "square" part of this current (you know that the sinusoidal functions actually are curves and continuous)
Here comes something called the Fourier Series, that are series of the form:
F(x) = a₀ + ∑(aₙ*cos(nx) + bₙ*sin(nx))
That can be used to model almost any periodic phenomena, but the actual Fourier Series may be hard to construct.
if f(x) = - 5^x - 4 and g (x) = - 3 x - 2 find (f - g) (x)
O A. ( f - g )(x) = 5^x - 3x + 2
O B. ( f - g )(x) = -5^x - 3x - 6
O C. ( f - g )(x) = - 2x -2
O D. ( f - g )(x) = -5^x + 3x - 2
Answers
Answer:
answer D
Step-by-step explanation:
hello,
[tex]f(x)=-5^x-4 \ and \ g(x)=-3x-2\\(f-g)(x)=f(x)-g(x)=-5^x-4+3x+2=-5^x+3x-2[/tex]
hope this helps
The value of function (f - g) (x) is,
⇒ 5ˣ + 3x - 2
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Functions are,
⇒ f (x) = - 5ˣ - 4
⇒ g (x) = - 3x - 2
Hence, We get;
The value of function (f - g) (x) is,
⇒ (f - g) (x)
⇒ f (x) - g(x)
⇒ (5ˣ - 4) - (- 3x - 2)
⇒ 5ˣ - 4 + 3x + 2
⇒ 5ˣ + 3x - 2
Thus, The value of function (f - g) (x) is,
⇒ 5ˣ + 3x - 2
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
Erica's collection has 3 times as many action figures in it as Ricardo's collection. They have 68 action figures together. How many action figures does Erica have? How many action figures does Ricardo have
Answers
Answer:
Erica has 51 action figures and Ricardo has 17 action figures.
Step-by-step explanation:
First, label your variables.
x=the number of action figures Erica has
y=the number of action figures Ricardo has
You know that they have 68 total action figures so x+y=68.
Erica has 3 times as many as Ricardo so 3y=x. Then solve for x and y.
x+y=68 3y=x (Substitue 3y for x)
3y+y=68 (Then combine like terms)
4y=68 (Divide each side by 4)
y= 17
Now that you know that Ricardo has 17 action figures, you can plug 17 in for y in either equation to find x.
3(17)=x
x=51
To check your answers, you can plug them back into the original equations.
Answer:
Erica:51 action figures; Ricardo: 17 action figures
Reason:
68/4=17
17*3=51<- this is the amount of action figures that Erica has.
17 <-this is the amount of action figures that Ricardo has.
17 (Ricardo) + 51 (Erica) = 68 (total amount)
Which ordered pair is a solution of the equation? 2x+4y=6x-y OPTION A: Only (4,5) OPTION B: Only (5,4) OPTION C Both A and B OPTION D None
Answers
Answer:
option b
Step-by-step explanation:
replace x and y with the x and y of the ordered pair
option a: 2(4)+4(5)=6(4)-5
solve
8+20=24-5
28=19 not true
option b:2(5)+4(4)=6(5)-4
solve
10+16=30-4
26=26 true
g Random digits are integers selected from among {0,1,2,3,4,5,6,7,8,9} one at a time in such a way that at each stage in the selection process the integer chosen is just as likely to be one digit as any other. In simulation experiments it is often necessary to generate a series of random digits by using a random number generator. In generating such a serie, let X denote the number of trials needed to obtain the first zero. a) What is the functional form of the pmf? b) Find the P(X=3). c) Find P(X<=5). d) What is the mean of X? e) What is the Var(X)?
Answers
Answer:
a) P(X=x) = p× (1-p)^(x-1)
b) P(X=3) = 0.081
c) P(X≤5) = 0.40951
d) Mean of X= 10
e) Var(X)= 90
Step-by-step explanation:
This is a question on geometric distribution.
In geometric distribution, we have two possible outcomes for each trial (success or failure) for independent number of binomials series trial. Also the probability of success is constant for each trial.
This discrete probability distribution is represented by the probability density function: f(x) = p× (1-p)^(x-1)
For a random variable with a geometric distribution, we do not know the number of trials we will have = {1, 2, 3, ...}
We stop the trials when we get a success.
From the question, there are 10 numbers
The probability of success = p = 1/10
For the solutions of the question from (a-e), See attachment below.
f(x) = P(X= x)
Where P(X= x) is the probability of X taking on a value x
Pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeee help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 4 * f(6)−6*g(5)=
Answers
Answer:
6(4f - 5g)
Step-by-step explanation:
4f × 6 - 6g × 5 = 24f - 6g × 5
24f - 30g → 6 (4f - 5g)
Hope this helped! :)
Answer:
f(6)−6*g(5)= 6f - 30g
Step-by-step explanation:
Hope this helped you!
A Ferris wheel is 15 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. How many minutes of the ride are spent higher than 15 meters above the ground?
Answers
Answer:
The number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.
Step-by-step explanation:
We will use the sin function for the height of the Ferris wheel.
[tex]y=A\ sin(B(x+C))+D[/tex]
A = amplitude
C = phase shift
D = Vertical shift
2π/B = period
From the provided information:
A = 15/2 = 7.5 m
[tex]Period=2\\\\\frac{2\pi}{B}=2\\\\B=\pi[/tex]
Compute the Vertical shift as follows:
D = A + Distance of wheel from ground
= 7.5 + 1
= 8.5
The equation of height is:
[tex]h(t)=7.5\cdot sin(\pi (t+C))+8.5[/tex]
Now at t = 0 the height is, h (t) = 1 m.
Compute the value of C as follows:
[tex]h(t)=7.5\cdot sin(\pi (t+C))+8.5[/tex]
[tex]1=7.5\cdot sin(\pi (0+C))+8.5\\\\-7.5=7.5\cdot sin\ \pi C\\\\sin\ \pi C=-1\\\\\pi C=sin^{-1}(-1)\\\\\pi C=\frac{3\pi}{2}\\\\C=\frac{3}{2}[/tex]
So, the complete equation of height is:
[tex]h(t)=7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5[/tex]
Compute the number of minutes of the ride that are spent higher than 15 meters above the ground as follows:
h (t) ≥ 15
[tex]h(t)=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))=6.5\\\\sin(\pi (t+\frac{3}{2}))=\frac{6.5}{7.5}\\\\(\pi (t+\frac{3}{2}))=sin^{-1}[\frac{13}{15}]\\\\\pi (t+\frac{3}{2})=60.074\\\\t+\frac{3}{2}=19.122\\\\t=17.622\\\\t\approx 18[/tex]
Thus, the number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.
Ahn, Bill, and Carl are eating a pizza. If Ahn ate 4 slices, Bill ate 3 slices, Carl ate 2 slices, and 1 slice more than half of the slices remain, into how many slices was the original pizza cut ?
Answers
Answer:
20
Step-by-step explanation:
Answer:20
Step-by-step explanation:
Which of the following is an arithmetic sequence that could be modeled by an explicit formula expressed as a linear function? A. −1, −8, −27, −64, −125, … B. −5, −2, 3, 10, 19, … C. −5, −1, 3, 7, 11, … D. 1/2, 1/4, 1/8, 1/16, 1/32, …
Answers
Answer:
C
Step-by-step explanation:
Given
- 5, - 1, 3, 7, 11
There is a common difference d between consecutive terms, that is
11 - 7 = 7 - 3 = 3 - (- 1) = - 1 - (- 5) = 4
This indicates the sequence is arithmetic with explicit formula
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 5 and d = 4 , thus
[tex]a_{n}[/tex] = - 5 + 4(n - 1) = - 5 + 4n - 4 = 4n - 9
What is the quotient? 36 divided by 6 –30 –6 6 30
Answers
[tex]\text{In this question, we're trying to find the quotient}\\\\\text{The quotient is basically the result or answer when you divide a number}\\\\\text{To find the quotient, divide 36 by 6}\\\\36\div6=6\\\\\boxed{\text{Answer: 6}}[/tex]
Answer:
6
Step-by-step explanation:
6x6=36 so, 36÷6=6
Hello! I'm stuck on Pythagorean theorem in geometry. There are some numbers that suppose to have a line on top but I don't know how to put it on top of the number, I just put this `. So, here's the problem: Which side lengths form a right triangle? A. 2,2, v```4``
Answers
Choice A: [tex]2,2, \sqrt{4}[/tex]
Choice B: 9, 40, 41
Choice C: [tex]\sqrt{5}, 10$ and \sqrt{125}[/tex]
Answer:
(B)9, 40, 41
Step-by-step explanation:
To check if the sides form a right triangle, you check to see if they satisfy the Pythagorean theorem.
[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
Note that the longest side length is always the hypotenuse.
Choice A: [tex]2,2, \sqrt{4}[/tex]
Now, [tex]\sqrt{4}=2[/tex]
Therefore:
[tex]2^2\neq 2^2+2^2\\4 \neq 8[/tex]
These side lengths form an equilateral triangle. They do not satisfy the theorem.
Choice B: 9, 40, 41
The longest side length is 41.
[tex]41^2=1681[/tex]
[tex]40^2+9^2=1681[/tex]
Therefore:
[tex]41^2=40^2+9^2[/tex]
These side lengths form a right triangle.
Choice C: [tex]\sqrt{5}, 10$ and \sqrt{125}[/tex]
[tex]\sqrt{5} \approx 2.24 \\ \sqrt{125}\approx11.18[/tex]
Therefore, the longest side length is [tex]\sqrt{125}[/tex]
[tex](\sqrt{125})^2=125\\(\sqrt{5})^2+10^2=5+100=105\\\\(\sqrt{125})^2 \neq (\sqrt{5})^2+10^2[/tex]
These side lengths do not form a right triangle.
Calculate the volume of this cylinder, giving your answer to one decimal place. I will give brainliest
Answers
Answer:
603.2
Step-by-step explanation:
V=πr^2h
V=π(4)^2(12)
V=π(4)^2(12)
V=603.1857895
I need help on this
Answers
Answer:
y = x+5
Step-by-step explanation:
The y intercept is 5 ( where it crosses the y axis)
We need two points to find the slope
(0,5) and (1,6)
The slope is
m = (y2-y1)/(x2-x1)
= (6-5)/(1-0)
= 1/1
=1
The slope intercept is
y = mx+b
y = 1x +5
y = x+5
Answer:
y = x + 5
Step-by-step explanation:
Slope intecept form: y = mx + b
y = x + 5
It is just x because the slope is 1/1 or rise over run. The intercept is 5 because the line crosses the y axis at the point 5.
This figure represents a step in a compass-and-straightedge construction. Identify the construction.
Answers
Answer:
It looks like a DNA strand or an infinity sign
Step-by-step explanation:
Idk if that's the correct answer tho sorry.
Answer: perpendicular bisector
Step-by-step explanation: A line drawn through points C and D will be perpendicular to line segment AB and it will bisect AB
1. What is the lateral surface area of a solid 8 meters high
whose base is the figure at right? Dimensions are in meters.
2. Which inequality corresponds to the graph at right?
Answers
Answer:
Step-by-step explanation:
To calculate the lateral surface of this shape we must divide it into 3 parts :
Part 1 : the half cylinder with the radius r=15We must calculate its perimeter P1 :
P1 = (15*2)*π/2 = 30*π*(1/2)=15π
Part 2 : the half cylinder with the radius r=12-5=7We must calculate its perimeter P2:
P2= (7*2)*π/2=14*π*(1/2)= 7π
Part 3 : the cubeWe won't calculate its perimeter because it has some common sides with the cylinders .
Let P3 be the perimeter of what's remaining from the cube
P3=12+5= 17
Now the total perimeter : Pt
Pt= 15π+7π+17= 22π+17
The lateral surface : Ls
Ls= (22π+29)*8= 784.92 m²
The inequality : -1<x≤4Cathy received a gift of $2,000 to buy a new car when she graduates in a year. She decides to use this money to purchase stock in a new, alternative energy company. Is this a good investment decisions?
A.No, because she will need money a year from now. Generally, stocks are long term investments. It is very unlikely that she will get a return on her investment in a year.
B.Yes, because alternative energy companies guarantee investors a minimum yearly profit.
C.Yes, because the FDIC insures this type of investment.
D.No, she should have invested in technology instead.
Answers
Answer:
a. No, because she will need money a year from now. Generally, stocks are long term investments. It is very unlikely that she will get a return on her investment in a year.
Step-by-step explanation:
Stocks are a riskier investment in comparison to bonds, and may pay higher interest rates, but still require the investment to "sit" for a long period of time. Like a 3 month (APY of about .50%), 6 month (APY of about .30%), 8 month (APY of about .10%), etc. bond, stocks will not grow considerably in a short amount of time.
Which Relation is a Function Please Answer ASAP
Answers
Answer:
A
Step-by-step explanation:
Every input (x value) can have only ONE ouput (y value) to be a function, y- values can be repeated but x- values cannot
Hope that helps
pleasee hellpp pleaseee help
Answers
Answer:
5 cm and 12 cm
Step-by-step explanation:
Calculate the unknown side h using Pythagoras' identity.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
h² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )
h = [tex]\sqrt{25}[/tex] = 5 cm
The perimeter is the sum of the 3 sides, thus
perimeter = 3 + 4 + 5 = 12 cm
Okay HELP i have to questions in one problem.
Question number 1 : Rihannon has a rectangular bedspread that measures 234 inches by 245 inches. She wants to sew a fringe around the edge of the bedspread. What LENGTH of fringe does rihannon need to purchase???
Question number 2 : Rihannon gets a new bedspread that is 33 inches longer. What LENGTH of fringe does Rihannon need for the longer bedspread??? PLEASEEE HELP
Answers
Answer:
1) To calculate length of fringe, we need to find the perimeter
The question does not clearly say how much is length and width
Assuming length = 245 and width = 234 inches
P = 2(length + width)
P = 2 ( 245 + 234)
P = 2 (479)
P = 958 inches
2) To calculate length of fringe, when length is increased by 33 inches
P = 2 ( l + w)
P = 2 (278 + 234)
P = 2 x 512
P = 1024 inches
The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner? (1) Each of the k employees who shared the cost of the dinner paid $19. (2) If the total cost of the dinner had been shared equally by k + 1 of the n employees who attended the dinner, each of the k + 1 employees would have paid $18.
Answers
Answer:
$342
Step-by-step explanation:
Let the total cost of the dinner = C
If it was shared equally by k employees who attended the dinner and each of the k employees who shared the cost of the dinner paid $19.
We have:
[tex]\dfrac{C}{k}=19 \\\\C=19k[/tex]
If the total cost(C) had been shared equally by k + 1 employees who attended the dinner, each of the k + 1 employees would have paid $18.
This written mathematically is:
[tex]\dfrac{C}{k+1}=18 \\\\C=18(k+1)[/tex]
Equating the cost, C from both equations
19k=18(k+1)
19k=18k+18
19k-18k=18
k=18
Therefore, the total cost of the dinner,
C=19k
=19 X 18
=$342
y - 2x + 4
y = 3x - 6
solve using substitution
Answers
Answer:
(10,24)
Step-by-step explanation:
Well first we plug in y = 3x - 6 for y in y = 2x + 4
3x - 6 = 2x + 4
Then we combine like terms and seperate x.
x - 6 = 4
x = 10.
If x is 10 we plug that in
y = 3(10) - 6
y = 30 -6
y = 24
(10,24)
for f(x)=2x+1 and g(x)=x^2-7, find (f+g)(x) A. 2x^2-15 B.X^2+2x-6 C.2x^3-6 D.x^2+2x+8
Answers
Answer:
C
Step-by-step explanation:
(f + g)(x) = f(x) + g(x) , thus
f(x) + g(x)
= 2x + 1 + x² - 7 ← collect like terms
= x² + 2x - 6 → C
insert four irrational numbers between 3 root 2 and 2 root 3
Answers
Answer:
3√2 > √17 > √15 > √14 > √13 > 2√3Step-by-step explanation:
[tex]3\sqrt2=\sqrt{3^2\cdot2}=\sqrt{18}\\\\2\sqrt3=\sqrt{2^2\cdot3}=\sqrt{12}\\\\18>17>15>14>13>12\ \implies\ 3\sqrt2>\sqrt{17}>\sqrt{15}>\sqrt{14}>\sqrt{13}>2\sqrt{3}[/tex]
{√16 = 4 is rational}
What are the total operating expenses? (This is line (c) on the income statement.)
This is a fill in the blank.
Answers
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
In this question some information is missing that's why we explain "operating expenses".
The Operating costs are paid in the business transactions and include property taxes, materials, stock costs, marketing, salary, health coverage, and R&D investments.
For other companies, these expenses are unavoidable and made mandatory. This cost is primarily important because it helps to evaluate the price effectiveness of the company as well as its inventory control. It also shows the costs and requires a consulting company needs to be making to maximize income, which would be a company's main objective.PLEASE! NEED HELP!!!
Answers
Answer:
x² + 2x + 2 = 0Step-by-step explanation:
Formula for finding a quadratic equation when its roots are given is
x² - ( sum of roots)x + product of roots=0
The roots are
- 1 + i
- 1 - i
Sum of roots is = - 1 + i - 1 - i = -2
Product of roots is = ( -1 + i)(- 1 - i)
= 1 + 1 = 2
So the quadratic equation is
x² - (-2)x + 2 = 0
x² + 2x + 2 = 0Hope this helps you
Answer:
x^2+2x+2
Step-by-step explanation:
to find b in the equation :
b^2<4ac when having two complex roots
the required equation is x2 - Sx + P = 0
the sum of the roots :-1-i+-1-i=-2
the product=2
so the equation: x^2-(-2)x+2
x^2+2x+2