[tex]b. \: \frac{8}{27} [/tex]
Which functions is an exponential growth function?
Answer:
OPTION A
Step-by-step explanation:
The exponential growth functions has the following form:
[tex]y=a(b)^x[/tex]
Where "a" is the principal coefficient and "b" is the base greater than 1.
To know which of the functions shown has exponential growth, identify which one has a base greater than 1.
[tex]\frac{4}{3}=1.33>1[/tex]
Therefore, the exponential growth function is the function shown in the option A.
The answer is:
The correct answer is:
A) [tex]y=(\frac{4}{3})^{x}[/tex]
Why?To identify which of the given functions is an exponential growth function, we need to remember the form of the exponenial growth or decay functions.
We can define the exponential growth or decay function by the following way:
[tex]P(x)=y=StartValue*(rate)^{x}[/tex]
Where,
P(x) or y, is the function
Start value is the starting amount or value
Rate, is the growth or decay rate
x, is the variable (time)
Now, we can identify if the function is a exponential growth or decay function by the following way:
If [tex]rate>1[/tex] the function is an exponential growth function.
If [tex]rate<1[/tex] the function is an exponential decay function.
Now, we are given the function first function, A)
[tex]y=(\frac{4}{3})^{x}[/tex]
Where,
[tex]rate=\frac{4}{3}=1.33[/tex]
and we have that:
[tex]rate>1\\1.33>1[/tex]
So, the function is an exponential growth function.
Hence, the correct answer is:
A) [tex]y=(\frac{4}{3})^{x}[/tex]
Have a nice day!
Which answer is the best estimate of the correlation coefficient for the variables in the scatter plot.
-0.82
-0.52
0.32
0.77
Answer: -0.52
Step-by-step explanation:
From the given scatter plot, it can be seen that there is a moderate negative correlation between the variables as variable X increases variable Y decreases.
i.e. the value of correlation coefficient must be negative.
Also, the value of weak correlation coefficient r, lies between the absolute value of 0.40 to 0.59.
From all the given options -0.52 is the value which is contained in interval 0.40 to 0.59 .
Therefore, the best estimate of the correlation coefficient for the variables in the scatter plot = -0.52
An airplane flies 3344 miles with a constant speed of 760 mph and another 2244.7 miles with a constant speed of 740 mph. What is it’s average speed for the total trip?
The answer is:
The average speed for the total trip is 753.19 mph.
Why?To calculate the average speed for the total trip, we need to calculate the time of travel for both distances according to their speeds.
So, calculating we have:
- First distance and speed: 3334 miles at 760 mph
Let's use the following formula:
[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]
Then, substituting we have:
[tex]time=\frac{3334miles}{760mph=4.39hours}[/tex]
Therefore, we have that the first distance was covered in 4.39 hours.
- Second distance and speed: 2244.7 miles at 740mph
Let's use the following formula:
[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]
Then, substituting we have:
[tex]time=\frac{2244.7miles}{740mph=3.03hours}[/tex]
Therefore, we have that the second distance was covered in 3.03 hours.
Now, calculating the average speed, we have:
[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]
Substuting we have:
[tex]AverageSpeed=\frac{3344miles+2244.7miles}{4.39hours+3.03hours}[/tex]
[tex]AverageSpeed=\frac{5588.7miles}{7.42hours}=753.19mph[/tex]
Hence, we have that the average speed for the total trip is 753.19 mph.
Have a nice day!
Center: (-2,5), radius:7
Answer:
(x + 2)² + (y - 5)² = 7²
Step-by-step explanation:
Incomplete question. I believe you meant, "write the equation of the circle with center at (-2, 5) and radius 7.
That would be:
(x + 2)² + (y - 5)² = 7²
The equation of the circle with center (-2,5) and radius 7 is (x+2)² + (y-5)² = 49.
Explanation:The question is asking for the equation of a circle with center at (-2,5) and radius 7. The general equation for a circle is (x-h)² + (y-k)² = r², with (h,k) as the center and r as the radius. In this case, h = -2, k = 5, and r = 7, so substituting these into the equation gives us the solution:
(x-(-2))² + (y-5)² = 7², which simplifies to (x+2)² + (y-5)² = 49.
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Which number is the additive inverse of –5?
+5 is the additive inverse of (-5)
it is so as. -5 +5 =0
Hope it helps...
Regards,
Leukonov.
The additive inverse of a number is what you need to add to the given number to equal 0. This would be the opposite of the given number.
The opposite of -5 would be positive 5.
-5 + 5 = 0
The answer is 5
ALGEBRA 1 PLEASE HELP
Tammy is choosing between two exercise routines. In routine #1, she burns 20 calories walking. she then runs at a rate that burns 18.5 calories per mimute. In routine #2, she burns 37 calories walking, she then runs at a rate that burns 14.25 calories per minute. For what amounts of time spent running will routine #1 burn fewer than routine #2? Use t for the number of minutes spent running. (Write an inequality to represent the scenario.
Answer:
Step-by-step explanation:
45 Mins
Y=x+4 y=-2x-2 explain the awnser plz
Answer:
x = -2 and y = 2
Step-by-step explanation:
We have the following system of linear equations;
y=x+4
y=-2x-2
To solve the above system, we shall be equating the right hand sides of the two equations since we have y's on the left hand side of both equations;
x + 4 = -2x - 2
add 2x on both sides of the equation;
x + 4 + 2x = -2x - 2 + 2x
3x + 4 = -2
subtract 4 on both sides of the equation;
3x + 4 - 4 = -2 - 4
3x = -6
x = -2
We can use the first equation y=x+4 to determine the value of y;
y = -2 + 4
y = 2
The solution to the system of linear equations is thus;
x = -2 and y = 2
Find the number of gallons of sulfuric acid in 50 gallons of solution in a tank, if the percent of sulfuric acid is 50%.
Answer:
25 gallons
Step-by-step explanation:
Given:
total no. of gallons= 50
Percentage of sulfuric acid= 50%
Number of gallons of sulfuric acid= total no. of gallons x Percentage of sulfuric acid
Putting values in above equation:
Number of gallons of sulfuric acid= 50 x 50/100
= 50 x 1/2
= 25 !
To find the number of gallons of sulfuric acid in a 50-gallon solution with a 50% concentration, multiply the volume of the solution by the concentration.
Explanation:To find the number of gallons of sulfuric acid in a 50-gallon solution with a 50% concentration, you can use a simple calculation. The percent concentration represents the fraction of sulfuric acid in the solution, so you can calculate the amount of sulfuric acid by multiplying the volume of the solution by the concentration:
Volume of sulfuric acid = Volume of solution * Percent concentration
Volume of sulfuric acid = 50 gallons * 0.50 = 25 gallons
Therefore, there are 25 gallons of sulfuric acid in the 50-gallon solution.
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A student calculates that the circumference of a tire with a rim diameter of 15 inches and a sidewall width of 4.6 inches is 61.8 inches by doing the following calculation:(15+4.6)xpi. Explain the error. (Show problem set up. Provide appropriate units)
Answer:
The error was on the diameter. The tire diameter was supposed to be;
4.6+15+4.6=24.2
The student only includes one sidewall width
Step-by-step explanation:
The question is on circumerence of a tire
Here we apply the formulae for circumference of a circle
C=2 [tex]\pi[/tex]×r or [tex]\pi[/tex] × d where r is the radius of the tire and d is the diameter
Finding d= diameter of rim + sidewall to the right +sidewall to the left
d= 15+4.6+4.6=24.2 inches
r=d/2= 12.1
C=2 ×[tex]\pi[/tex]×r
C=2×3.14×12.1 =75.99 Inches
Which point is a solution to the linear inequality y < -1/2 x + 2?
y < -1/2 x + 2
I will try the first-two points. You can then finish.
Let x = 2 and y = 3.
3 < (-1/2)(2) + 2
3 < -1 + 2
3 < 1
False statement. Choice A is not the answer.
Let x = 2 and y = 1
1 < (-1/2)(2) + 2
1 < -1 + 2
1 < 1
False statement. Choice B is not the answer.
Do the same thing with the remaining points. One of the points will make the given inequality a true statement.
The point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)
How to determine the points?The inequality is given as:
y < 1/2x + 2
Next, we test the options
A. (2, 3)
3 < 1/2 * 2 + 2
3 < 3 ---- false
B. (2, 1)
1 < 1/2 * 2 + 2
1 < 3 ---- true
Hence, the point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)
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Solve the formula for the indicated variable.
A = 4πr² for r when r > 0
r =
Answer:
√(A/4π) = r
Step-by-step explanation:
A = 4πr²
r² = A/4π
r = √(A/4π)
Answer:
r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]
Step-by-step explanation:
Given
A = 4πr² ( isolate r² by dividing both sides by 4π )
r² = [tex]\frac{A}{4\pi }[/tex]
Take the square root of both sides
r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
~plz help~
Answer:
x = 56.7°
Step-by-step explanation:
Sin (x) = Oppo. / Hypo.
Sin (x) = 66/79
Sin (x) = 0.8354
x = 56.7°
Answer:
x ≈ 56.7
Step-by-step explanation:
In the right triangle with hypotenuse 79 use the sine ratio to find x
sinx° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{66}{79}[/tex], hence
x = [tex]sin^{-1}[/tex] ([tex]\frac{66}{79}[/tex] ) ≈ 56.7
Simplify 512^1/9 in rational form
Answer:
2
Step-by-step explanation:
512^(1/9)
Write 512 as power of 2:
(2^9)^(1/9)
Multiply the exponents:
2^(9 × 1/9)
2^1
2
Answer:
2
Step-by-step explanation:
The graph of g(x) is a translation of y = 3/x
Which equation represents g(x)?
O g(x) = 3/x-4
O g(x) = 3/x+4
O g(x) = 3/x + 1.5
O g(x) = 3/x-1.5
Answer:
d
Step-by-step explanation:
independent and dependent
Hello There!
First, let me just explain briefly what is an independent variable and a dependent variable.
An independent variable is the variable that changes during an experiment to see if it has an effect on another variable.
A dependent variable is what is being measured in the experiment. It’s also known as outcome or effect.
In this case, the dependent variable is the number of liters of water your drink because that’s what your measuring.
The independent variable is the number of times you drink all the water in your bottle because that changes during the experiment.
what is the graph of 3y-5x<-6?
Answer:
look at the calculator.
ANSWER
EXPLANATION
We want to graph the inequality:
[tex]3y - 5x \: < \: - 6[/tex]
To this inequality, we must first of all graph the corresponding linear equation:
[tex]3y - 5x = - 6[/tex]
When x=0, we have
[tex]3y - 5(0) = - 6[/tex]
[tex]3y = - 6[/tex]
y=-2
We plot the point (0,-2)
When y=0,
[tex]3(0) - 5x = - 6[/tex]
[tex]x = \frac{6}{5} [/tex]
[tex]( \frac{6}{5} ,0)[/tex]
We plot the points and draw a dashed straight line through them.
We test for (0,0).
[tex]3(0)- 5(0)\: < \: - 6[/tex]
[tex]0 < \: - 6[/tex]
This is false hence we shade the lower half plane. See attachment.
A and B are independent events. P(A) = 0.40 and P(B) = 0.20. What is
PA and B)?
Answer:
The value of P( A and B ) is 0.08.
Step-by-step explanation:
When two events are independent then the probability of both occurring is equal to the product of probabilities of both events individually,
That is, If X and Y are independent events,
Then, P(X∩Y) = P(X) × P(Y),
or P(X and Y) = P(X) × P(Y),
Here, P(A) = 0.40 and P(B) = 0.20,
Hence, P(A∩B) = P(A) × P(B)
= 0.40 × 0.20
= 0.08
The value of [tex]\( P(A \text{ and } B) \)[/tex] is 0.08. So option(a) is correct.
To determine[tex]\( P(A \text{ and } B) \)[/tex] for two independent events ( A ) and ( B ) with given probabilities ( P(A) = 0.40 ) and ( P(B) = 0.20 ), follow these steps:
Step 1: Understand the Concept of Independence
For independent events, the probability of both events occurring together (the intersection of A and B, denoted as [tex]\( P(A \cap B) \))[/tex] is the product of their individual probabilities.
Step 2: Apply the Independent Event Formula
Since (A ) and (B ) are self-contained,
[tex]P(A) \times P(B) = P(A \cap B)[/tex]
Step 3: Substitute the Given Probabilities
Insert the given probabilities [tex]\( P(A) = 0.40 \)[/tex] and [tex]\( P(B) = 0.20 \)[/tex] into the formula:
[tex]\[ P(A \cap B) = 0.40 \times 0.20 \][/tex]
Step 4: Perform the Multiplication
Calculate the product of 0.40 and 0.20:
[tex]\[ P(A \cap B) = 0.40 \times 0.20 = 0.08 \][/tex]
Step 5: Interpret the Result
The probability that both events ( A ) and ( B ) occur is 0.08.
Therefore, the correct answer is (a) 0.08.
Complete Question:
A and B are independent events. P(A)=0.40 and P(B)=0.20 . What is P(A and B) ?
A. 0.08
B. 0.60
C. 0
D. 0.80
Cheryl recorded the number of bees on two different fruit trees during different times of the day. The tables show the data from these observations.
Which statement is true about the data Cheryl collected?
There was no difference in the number of bees observed in both trees at each time of the day.
The greatest number of bees observed on both trees occurred at 12:00 p.m.
More bees were observed on both trees from 12:00 p.m. to 6:00 p.m. than from 6:00 p.m. to 9:00 p.m.
The total number of bees observed on the apple tree was higher than the total number on the cherry tree.
Answer: More bees were observed on both trees from 12:00 p.m. to 6:00 p.m. than from 6:00 p.m. to 9:00 p.m.
Step-by-step explanation:
12:00 p.m. to 6:00 p.m: 135 bees
6:00 p.m to 9:00 p.m: 28 bees
The gum you like to buy is on sale. It is
regularly priced at $1.59.
Write an equation that will help you determine
how much you'll save if you buy the pack
today.
Let's let
S = sale price per pack
C = cost savings
Answer:
c=$1.59-s
Step-by-step explanation:
Let
s ----> the sale price per pack
c ---> cost savings
we know that
The equation that represent this situation is
c=$1.59-s
-6- -54/(-9) -5+-3
Please help. I just can’t figure it out, I’ve tries multiple answers!
Answer:
-20
Step-by-step explanation:
-Follow PEMDAS.
-2 negatives equal a positive.
-6 + 54/(-9) - 5 - 3
-6 + (-6) - 5 - 3
-12 - 5 - 3
-20
-20
Use PEMDAS
-6- -54/(-9) -5+-3
-6+54/(-9) -5+-3
-6+-6-5-3
-12-5-3
-17-3
-20
The covered part of this figure is a semicircle. What is the best approximation for the area of this figure?
Answer:
94.18
Step-by-step explanation:
Given in the question a semi circle and a right angle triangle
Step 1
Find the diameter of the semi circle
To find the diameter we will use pythagorus theorem
hypotenuse² = height² + base²here,
hypotenuse will be diameter of semicircle
height = 9
base = 4
Plug values in the formula above
diameter = √(9²+4²)
diameter = √97
Step 2
Find radius
radius = diameter / 2Step 3
Area
π(r)²π(√97/2)²
= 76.18
Step 4
Total surface area = area of circle + area of right angle triangle
= 76.18 + 1/2(9)(4)
= 94.18
what is the volume of the pyramid? round to the nearest tenth.
Check the picture below.
[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{8.4\times 8.4}{70.56}\\ h\approx& 8.6 \end{cases}\implies V=\cfrac{1}{3}(70.56)(8.6) \\\\\\ V=202.272\implies \stackrel{\textit{rounded up}}{V=202.3}[/tex]
HI I NEEEEEEEEEEEED HELP
Answer:
Step-by-step explanation:
Givens
a = 10b = 11h = 10Formula
V = (a * b)/2 * h
Solution
V = (10 * 11)/2 * 10
V = 110/2 * 10
V = 55 * 10
V = 550
For this case we have that by definition, the volume of the prism shown is given by:
[tex]V = A_ {b} * h[/tex]
Where:
[tex]A_ {b}:[/tex] It is the area of the base
h: It's the height
[tex]A_ {b} = \frac {b * h} {2}[/tex]
Where:
b: It is the base of the triangle
h: It's the height of the triangle
Substituting the values:
[tex]A_ {b} = \frac {10 * 11} {2}\\A_ {b} = 55 \ cm ^ 2[/tex]
Then, the volume is:
[tex]V = 55 * 10\\V = 550 \ cm ^ 3[/tex]
ANswer:
550
Marcus is treating his family to ice cream he buys 4 Sundaes and 3 cones for the total of $26 Brian also buy ice cream for his family his total is 29 for purchasing 2 cones and 5 Sundaes determined the system of equation that can be used to find the cost of one Sundaes, S, and the cost of one cone, c
Answer:
Required system of equation is
4s+3c=26 and 5s+2c=29.
Step-by-step explanation:
Let cost of 1 sundaes = s
Let cost of 1 cone = c
Then statement "Marcus is treating his family to ice cream he buys 4 Sundaes and 3 cones for the total of $26", gives equation:
4s+3c=26...(i)
And statement "Brian also buy ice cream for his family his total is 29 for purchasing 2 cones and 5 Sundaes " gives equation:
5s+2c=29...(ii)
Hence required system of equation is
4s+3c=26 and 5s+2c=29.
Answer:
4s+3c=26
5s+2c=29.
Step-by-step explanation:
I need both really bad please and thank you
b and c is the answer .
Number 7 - Second answer
Number 8 - Third answer
I WILL MARK BRAINLIEST
PLEASE SHOW WORK
Answer:
V =91.125 in ^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V= 4.5 ^ 3
V =91.125 in ^3
Given : Length of side of a cube = 4.5 inches.
We know that,
Volume of cube = (side)³ cu. units
= (4.5)³ inches³
= 91.125 inches³
Hence,
Volume of a cube = 91.125 inches³
If f(x) = x and g(x) = 2, what is (f*g)(x)
a:2x
b:2
c:x+2
d:x/2
Answer: Option a:
[tex](f * g) (x) = 2x[/tex]
Step-by-step explanation:
The expression [tex](f * g) (x)[/tex] refers to the multiplication of two functions f and g.
In this case we know that the functions are:
[tex]f (x) = x\\\\g (x) = 2[/tex]
Then you must multiply the two functions we get.
[tex](f * g) (x) = f (x) * g (x)\\\\(f * g) (x) = 2 * x\\\\(f * g) (x) = 2x[/tex]
The correct answer is option a.
Use complete sentences to describe why it is necessary to do the same thing to both sides of an equation to perform valid operations
It is important to do the same thing to both sides of an equation because in the end, both sides will be equivalent, or equal, therefor making the problem true. If you didn't do the same thing on both sides of an equation, one side would be incorrect and not equal to the other side. Hope this helps! Please mark brainliest. Thank you v much! :)
It's necessary to do the same thing to both sides of an equation to maintain balance and allow valid operations. This basic principle is crucial for solving and simplifying equations in mathematics.
Explanation:In mathematics, it is necessary to do the same thing to both sides of an equation to perform valid operations. An equation represents a balance; what is done to one side must also be done to the other to maintain this balance. For instance, if you add, subtract, multiply, or divide a value from/to one side of an equation, you have to do the same to the other side. This principle is essential for solving and simplifying equations. For example, in the equation 5x + 3 = 18, to solve for x, you would subtract 3 from both sides, establishing the new equation 5x = 15, maintaining the balance.
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Mr. Kelly's company manufactures a cylindrical soup can that has a diameter of 6 inches and a volume of 226 cubic inches. If the diameter stays the same and the height is doubled, what will happen to the can's volume?
The volume of a cylinder is given by
[tex]V = A_bh[/tex]
Where [tex]A_b[/tex] is the base area and h is the height.
So, if we call [tex]V_1,\ V_2[/tex] the volumes with the original and the doubled area, we have
[tex]V_1 = A_bh,\quad V_2 = A_b(2h)[/tex]
Since the height was doubled. We deduce that
[tex]\dfrac{V_2}{V_1}=\dfrac{2A_bh}{A_bh}=2[/tex]
So, if the height is doubled, the volume will double as well.
Need help with this two step equation
well, do a payments table of values, just like before for each mont hmm let's see
1st month.......................3500 + p(1)
2nd month....................3500 + p(2)
3rd month.....................3500 + p(3)
4th month.....................3500 + p(4)
5th month.....................3500 + p(5)
36th month..................3500 + p(36)
[tex]\bf \stackrel{\textit{total value}}{17900}=\stackrel{\textit{down payment}}{3500}+\stackrel{\stackrel{\textit{payments for}}{\textit{36 months}}}{36p} \\\\\\ 14400=36p\implies \cfrac{14400}{36}=p\implies 400=p[/tex]