Answer:
7.1
Step-by-step explanation:
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }570
a=starting value = 570
r=\text{rate = }26.9\% = 0.269
r=rate = 26.9%=0.269
\text{Exponential Decay:}
Exponential Decay:
b=1-r=1-0.269=0.731
b=1−r=1−0.269=0.731
\text{Write Exponential Function:}
Write Exponential Function:
y=570(0.731)^x
y=570(0.731)
x
Put it all together
\text{Plug in time for x:}
Plug in time for x:
y=570(0.731)^{14}
y=570(0.731)
14
y= 7.091174
y=7.091174
Evaluate
y\approx 7.1
y≈7.1
round
To calculate the remaining amount of an element undergoing exponential decay, use the formula A = A0 * (1 - r)^t, where A is the remaining amount, A0 is the initial amount, r is the decay rate per minute, and t is the time in minutes. In this case, approximately 12.3 grams of the element is remaining after 14 minutes.
Explanation:
To calculate the amount of the element remaining after 14 minutes, we need to use the formula for exponential decay, which is A = A0 * (1 - r)t, where A is the remaining amount, A0 is the initial amount, r is the decay rate per minute (in decimal form), and t is the time in minutes.
In this case, the initial amount is 570 grams, the decay rate is 26.9% or 0.269 per minute, and the time is 14 minutes.
Plugging these values into the formula, we get:
A = 570 * (1 - 0.269)14 = 570 * (0.731)14 = 570 * 0.0221 = 12.27 grams.
Therefore, approximately 12.3 grams of the element is remaining after 14 minutes.
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How do you interpret the statement that F(60)=86?
Answer:
Step-by-step explanation:
"F" is the name of a function. If we choose "60" as the input to this function, the resulting output vaue is 86. The function F maps 60 (input) onto 86 (output).
check the superb reply above, however to the risk of sounding redundant.
[tex]\bf f(\stackrel{\stackrel{in put}{x}}{60})=\stackrel{\stackrel{ou tput}{f(x)}}{86}~\hspace{8em} \stackrel{x}{in put}\textit{ of 60, will yield an }\stackrel{f(x)}{out put}\textit{ of 86}[/tex]
PLEZ HELP ASAP
Complete the sentence by selecting the correct word from each drop-down menu. The middle value of a data set that is ordered from least to greatest is called the (a)____ . This value is a measure of (b)____.
(a): mean, median , and range
(b): center, range, variations
Answer:
a median
b center
Step-by-step explanation:
The middle value of a set of numbers is the median
The mean is the average value and the range is the largest minus the smallest.
This value is a measure of the center ( or a measure of the middle)
The range is a measure of the spread
Answer:
(a) is median and (b) is center.
Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x^2 - 21 = 0
The value of X from the given equation above would be =1.526
How to calculate the missing value in the given equation?To determine the missing value in the equation above, the following steps needs to be considered as follows:
The equation ;
9x² - 21 = 0
9x² = 21
make x² the subject of formula;
x² = 21/9
= 2.33
X = √2.33
= 1.526
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Jayden has already jarred 1 liter of jam and will jar an additional 6 liters of jam every day. Write an equation that shows the relationship between the days d and the jam made j.
Write your answer as an equation with j first, followed by an equals sign
please help
Answer:
[tex]j=1+6d[/tex]
Step-by-step explanation:
Jayden jars jams at a rate of 6 liters per day which can be represented by the variable [tex]6d[/tex]. In other words, the amount of jam Jayden will have made in the end (j) is 6 liters multiplied by the number of days (d) he spent jarring jam.
However, Jayden has already jarred 1 liter of jam which has to be factored into the end total (j). To factor this liter in, you can add 1 (liter) to 6d.
Henry has 2 3/4 cups flour. He uses 1 1/2 cups of the flour to bake muffins. How much flour does Henry have left?
Answer:
1 1/4
Step-by-step explanation:
subtract 1 1/2 from 2 3/4
After using part of his flour, Henry subtracts the amount used from the initial amount to find that he has 1 cup of flour left.
The question asks about subtracting fractions in order to determine how much flour is left after some is used. We start with Henry's initial amount of flour, which is 2 3/4 cups, and subtract the amount he used to bake muffins, which is 1 1/2 cups. To perform this subtraction, we first need to have the fractions with a common denominator. Since 4 is the least common multiple of 4 and 2, we convert 1 1/2 to 3/4. Now, we have 2 3/4 cups - 1 3/4 cups, which can be simplified step-by-step:
Subtract the whole numbers: 2 - 1 = 1.Subtract the fractions: 3/4 - 3/4 = 0.Combine the whole number and the fraction: 1 + 0 = 1.Therefore, Henry has 1 cup of flour left after making muffins.
To provide another example, if we were to reference a cooking equation like the one for biscuits, where 2 cups of flour make 12 biscuits, we could determine how much product we can make with a given amount of reactants (flour). Similarly, with the given measurements in the question, we are finding the remainder of the reactant (flour) after it's been partially used.
1. What is the value of H? (1 point)
A. 4
B. 8√3
C. 16
D. 8√2
Answer:
D
Step-by-step explanation:
Using the sine ratio in the right triangle
noting that sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] ← exact value
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{h}[/tex]
Multiply both sides by h, then
h ×[tex]\frac{1}{\sqrt{2} }[/tex] = 8
Multiply both sides by [tex]\sqrt{2}[/tex]
h = 8[tex]\sqrt{2}[/tex] → D
Answer:
In the event that this is the practice, these are the correct answers.
1.d
2. c
3. a
4.a
5.c
6.b
Step-by-step explanation:
WORTH 20 POINTS PLEASE HURRY !!!!!!!
Solve the System of Equations using Elimination/Combinations
- 2x - y = - 4
x = 2y = 5
Answer:
Step-by-step explanation:
Okay so solve this this is how you do it
[tex]-2x-y=-4[/tex] and [tex]x+2y=5[/tex]
To cancel out the X we have to make x into 2 x
[tex]1(-2x-y=-4)\\2(x+2y=5)\\\\[/tex]
[tex]-2x-y=-4\\2x+4y=10[/tex]
we can cancel out -2x and 2x now leaving us with
[tex]-y=-4\\4y=10[/tex]
add them both and solve for y
[tex]3y=6\\y=\frac{6}{3}\\y=2[/tex]
Now just substitute 2 for y
[tex]-2x-2=-4\\-2x=-4+2\\-2x=-2\\x=\frac{-2}{-2} \\x= 1[/tex]
Or
[tex]x+2(2)=5\\x+4=5\\x=5-4\\x=1[/tex]
In both the equations your answer will be the same
Hope this helps :)
If you have an doubt or need further help just reply :)
The figure is made up of 2 cones and a cylinder. The
cones and cylinder have a 4 cm diameter.
3 cm 17
cm 4 cm
What is the exact volume of this figure?
57 cm
127 cm
207 cm
367 cm
The exact volume of the figure made up of two cones and a cylinder with a 4 cm diameter is [tex]\(76 \pi \, \text{cm}^3\)[/tex], which is approximately 238.64.
1. Volume of the Cylinder:
[tex]\[ V_{\text{cylinder}} = \pi \times (2 \, \text{cm})^2 \times 17 \, \text{cm} \][/tex]
[tex]\[ V_{\text{cylinder}} = \pi \times 4 \, \text{cm}^2 \times 17 \, \text{cm} \][/tex]
[tex]\[ V_{\text{cylinder}} = 68 \pi \, \text{cm}^3 \][/tex]
2. **Volume of each Cone:**
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \times (2 \, \text{cm})^2 \times 3 \, \text{cm} \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \times 4 \, \text{cm}^2 \times 3 \, \text{cm} \][/tex]
[tex]\[ V_{\text{cone}} = 4 \pi \, \text{cm}^3 \][/tex]
Since there are two cones, the total volume for the cones is [tex]\(2 \times V_{\text{cone}} = 8 \pi \, \text{cm}^3\)[/tex].
3. Total Volume:
[tex]\[ V_{\text{total}} = V_{\text{cylinder}} + 2 \times V_{\text{cone}} \][/tex]
[tex]\[ V_{\text{total}} = 68 \pi + 8 \pi \, \text{cm}^3 \][/tex]
[tex]\[ V_{\text{total}} = 76 \pi \, \text{cm}^3 \][/tex]
Now, the exact volume is [tex]\(76 \pi \, \text{cm}^3\)[/tex]. To find the numerical approximation, you can use the value of [tex]\(\pi\)[/tex], which is approximately 3.14.
[tex]\[ V_{\text{total}} \approx 76 \times 3.14 \, \text{cm}^3 \approx 238.64 \, \text{cm}^3 \][/tex]
what property is shown in the equation below
Answer:
A
Step-by-step explanation:
Zero property of multiplication states that anything multiplied by 0 is 0.
A relay race covers 1 1/2 kilometers, and each runner on a team will run 1/4 of a kilometer. How many runners are in a team?
Answer:
6 runners
Step-by-step explanation:
the total divided by the distance each runner will run
1.5/0.25=6
please help with question 6 with reasoning first person will get brainliest
Answer:
I think it's $216
Step-by-step explanation:
0.3 times 720
A bag contains 5 red balls, 3 green balls, and 2 yellow balls. Find the sum of the probability of drawing a red ball, replacing it, drawing a green ball, replacing it and drawing a yellow ball.
Red - 5/10
Green - 3/10
Yellow 2/10
Easyyy
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ You replace the balls, so the type of probability is independent.
First of all, the probability of getting a red ball is:
5/10 or 1/2
As you can see, the probability of getting a green ball is:
3/10
Lastly, the probability of getting a yellow ball is:
2/10 or 1/5
The sum of all of them added together is always:
10/10, or 1
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬TROLLER (don't worry i didn't troll you)
100 points and brainliest
We can use the vertical line test to check if each graph is a function. If the line passes through two points, it is not a function. If it only passes through one point then it is a function.
Graph 1:
It is a function because the line doesn't pass through more than one point. (yellow)
Graph 2:
It is not a function because the line does pass through more than one point. (orange)
Graph 3:
Horizontal lines are not functions. (orange)
Graph 4:
It is a function because the line doesn't pass through more than one point. (yellow)
Best of Luck!
Answer:
Graph 1:
It is a function because line don't pass more than one point. (yellow)
Graph 2:
It is not a function because line does pass through more than one point. (orange)
Graph 3:
Horizontal lines are not functions. (orange)
Graph 4:
It is a function because the line doesn't pass through more than one point. (yellow)
Step-by-step explanation:
please mark as brainliest
The table shows the outputs, y, for different inputs, x: Input (x) 6 12 15 25 Output (y) 14 15 15 16 Part A: Do the data in this table represent a function? Justify your answer. (3 points) Part B: Compare the data in the table with the relation f(x) = 7x − 15. Which relation has a greater value when x = 6? (2 points) Part C: Using the relation in Part B, what is the value of x if f(x) = 6? (5 points) (10 points
Answer:
Part A: No it is not a function
Part B: The equation
Part C: x = 3
Step-by-step explanation:
Part A - The table:
Input (x) Output (y)
6 14
12 15
15 15
25 16
This is a function because it has no repeating inputs values which have alternate outputs. Each input is assigned exactly one output.
Part B - The relation y = 7x - 15 has the value y = 27 when x = 6. You can find it by substituting into the equation.
y = 7(6) -15
y = 42 - 15
y = 27
The value of the relation in the table when x = 6 is y = 14. The equation has the greater value.
Part C: To find when y = 6, set it equal to 6 and solve for x.
6 = 7x - 15
21 = 7x
3 = x
Answer:
Part A: No it is not a function
Part B: The equation
Part C: x = 3
Step-by-step explanation:
Rachel can type 450 words in 6 minutes
How many words can Rachel type in 1 minuet
450/6 = X/1
75 = X
Rachel can type 75 words in a minute!
Which of the following statements about cubes is false? Fast please!
Answer:
B and D
Step-by-step explanation:
The surface area is the area of each face of the cube. The volume is the amount that will fill the cube. These are two separate processes which cannot give you the same measurement by calculating one part of the surface area. B is false.
Doubling the sides of the cube will not double the surface area. It will quadruple it. D is false too.
Tyler simplified the expression. His procedure is shown below.
Answer:
Step-by-step explanation:
1
Tyler correctly rewrote x^(-3) as ------- , but
x³
1
he incorrectly wrote y^(-9) as ---------
y^(-9)
Both x^9 and y^9 should be in the denominator. This corresponds to the 2nd given possible answer.
Answer:
B:Both powers should be in the denominator with positive exponents.
Step-by-step explanation:
We are given that Tyler simplified an expression
[tex]x^{-3}y^{-9}[/tex]
We have to find an error which Tyler makes in her simplification
Step 1: [tex]x^{-3}y^{-9}[/tex]
Step 2:[tex]\frac{1}{x^3}\cdot y^{-9}[/tex]
Step 3:[tex]\frac{1}{x^3y^9}[/tex]
Hence, Tyler's error is both exponents should be denominator with positive exponents.
Answer:B:Both powers should be in the denominator with positive exponents.
Find the sum of the first 10 terms
Answer: 265
Step-by-step explanation: In order to find the sum of the first 10 terms in the series you need to first identify what the series is. The numbers are being reduced by 3 for each number, so the the first 10 terms would be 40, 37, 34, 31, 28, 25, 22, 19, 16, 13
The sum means the total of them all added together, which is 265.
The answer to this question is 265
Micah drew a map of his neighborhood. The actual distance from his house to the school is 5.75 miles. What is the actual distance from the library to the park
Answer:
2.875 mi
Step-by-step explanation:
A scale factor (SF) is the ratio of two corresponding lengths in similar figures.
SF = actual distance/map distance = 5.75 mi/2 in
or 1 in = 2.875 mi
On the map, the distance from the library to the park is 1 in, so the actual distance is 2.875 mi.
A model's scale ratio is the proportionate ratio of a linear dimension. The actual distance from the library to the park is 2.875 miles.
What is the scale ratio?A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.
Given that the actual distance from Micah's house to school is 5.75 miles, while the same distance on the map is represented by 2 inches. Therefore, the scale ratio can be written as,
Scale Ratio = Distance on Map/ Distance in real
= 2 inches / 5.75 miles
Now, the distance between the library and the park is given 1 inch on the map. Therefore, using the scale ratio, the actual distance from the library to the park is,
Scale Ratio = Distance on Map/ Distance in real
2inches /5.75 miles = 1 inch/ Distance in real
Distance in real = (5.75 miles×1 inch)/2 inches
Distance in real = 2.875 miles
Hence, the actual distance from the library to the park is 2.875 miles.
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At the zoo, there are 3 fewer ferrets than twice the number of tigers. If there are 21 ferrets, what's an equation for the number of tigers at the zoo?
What is the number of ferrets?
12x2-3=21
this would be your equation because there are 12 tigers
Please Help! Given parallelogram ABCD with the measures shown, what is the Measure of 5?
Answer:
[tex]m\angle 5=76\degree[/tex].
Step-by-step explanation:
In the given parallelogram, line AC is a transversal.
Using the alternate interior angles theorem,
[tex]m\angle 5=76\degree[/tex].
You can observe this by tracing a Z-pattern.
You will then observe that m<5 and the [tex]76\degree[/tex] angles are alternate interior angles.
Find the value of each variable. X and y. 26 30
Answer:
x = 13 and y = 13√3
Step-by-step explanation:
Recall that sin Ф = opposite side / hypotenuse, and that
cos Ф = adjacent sice / hypotenuse.
if we recognize that the angle Ф is 30° here, then we know that:
x = opposite side = hypotenuse * sin 30° = 26*(1/2) = 13.
and....
y = adjacent side = hypotenuse*cos 30° = 26*√3/2 = 13√3
In summary, x = 13 and y = 13√3
Consider f(x)=-(x+7)^2+4. Which of the following are true for f(x)?Check all that apply.
Answer:
A, D, F
Step-by-step explanation:
A. True, because [tex]f(x)=-(x+7)^2+4[/tex] represents quadratic function (the greatest power of x is 2)
B. False, because this function is quadratic, so cannot be linear
C. False. The vertex of the parabola is at point (-7,4) (see diagram)
D. True. The axes of symmetry is the line x=-7 that passes through the vertex.
E. False. The y-intercept is at point x=0 and [tex]y=-(0+7)^2+4=-49+4=-45.[/tex]
F. True. The graph has the maximum at vertex, where [tex]y_{max}=4.[/tex]
G. False. The graph of the parabola intersects the x-axis at two points (-9,0) and (-5,0), so x=-9 and x=-5 are two real solutions of the equation f(x)=0.
How many solutions are there to 3x-10(x+2) =13-7x
This is the following way to solve this problem:
3x-10(x+2)=13-7x
3x-10x-20=13-7x (multiply 10 times what's in the parentheses)
-7x-20=13-7x ( subtract 3x from -10x)
-7x-20-13=-7x ( since the 13 is positive, when we move it to the other
side, we change it's sign, so now we subtract 13 from 20
-7x-7=-7x
-7=-7x+7x ( we do the same thing we did above, now with the -7x)
-7=x
x=-7
Answer: x = -7
--- --- --- --- --- --- ---
: )
Expanded expression of -12(4x+8)
-48x - 96 (multiply -12 by both numbers separately)
Answer:
-12×4x + -12×8
-48 + -96
Step-by-step explanation:
Mark noticed that his bus is late to school 5% of the time. He wants to design a spinner he can use to simulate the situation and determine the probability that the bus will be late three times next week.
How should Mark divide his spinner to best simulate the situation?
Answer:
D. 20 equal-sized sections
Step-by-step explanation:
The average distance of all data values from the mean of the data is called the
Answer:
mean absolute deviation
Step-by-step explanation:
The mean absolute deviation of a data set is the average distance between each data point and the mean. It gives us an idea about the variability in a data set since it is a measure of dispersion
Final answer:
The average distance of all data values from the mean of the data is called the 'standard deviation'. It measures how data points vary from the mean and indicates the data's spread. Standard deviation is calculated by finding the square root of the average squared deviations from the mean.
Explanation:
The Average Distance of Data Values from the Mean
The average distance of all data values from the mean of the data is referred to as the standard deviation. This statistical measure expresses the extent to which data points in a data set diverge from the average, or mean, value. When the standard deviation is small, it indicates that the data points are clustered closely around the mean, showing little variation. Conversely, a large standard deviation suggests that the data points are spread out over a wider range, signifying greater dispersion in the data set.
The calculation of the standard deviation starts with computing the variance, which is the average of the squared deviations from the mean. The formula for variance is s² = Σ(Yi - Y)² / (n - 1), where s² is the variance, Yi represents each data point, Y is the mean of the data, and n is the sample size. After calculating the variance, the standard deviation is found by taking the square root of the variance.
Plant’s height this month: 20cm, Plant’s height last month: 15cm what is the percent of increase?
*EASY* WILL MARK BRAINEST! Find the slope of the line in the image below!
Answer:
5/4
Step-by-step explanation:
We have two points so we can use the formula for slope
(-3,-2) (1,3)
m = (y2-y1)/(x2-x1)
= (3--2)/(1--3)
= (3+2)/(1+3)
=5/4
The slope is 5/4
5/4 is the slope
Count the rise over run and you will get the slope
The box on the left is 8 inches wide and 8 inches tall what is the surface area of the box
Answer:
384 inches
Step-by-step explanation:
8 x 8 = 64
one face of the box is 64
6 faces of the box would be 384