A full pond containing 625 gallons of water begins losing its water at a rate of 20% per week. If the pond now contains 320 gallons of water, how many weeks has it been since the pond was at full capacity?
(Use the digits 0 – 9 to enter a number. Use a decimal point only if necessary.)
Using an exponential function to represent the exponential decay, it will take approximately 4 weeks to reach 320 gallons
Exponential EquationAn exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
To solve this problem, we have to write an exponential equation to calculate the exponential decay.
Data;
A = 320P = 625r = 20% = 0.2t = ?A = P(1 + r)⁻ˣ
320 = 625(1 + 0.2)⁻ˣ
x = 3.67
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Point QQ is located at (3,-1)(3,−1) on the coordinate plane. Point QQ is reflected over the yy-axis to create point Q'Q ′ . What ordered pair describes the location of Q'?Q ′ ?
The ordered pair that describes the location of Q' is (-3, -1)
How to determine the ordered pair that describes the location of Q?From the question, we have the following parameters that can be used in our computation:
Point Q = (3, -1)
This point can be represented as
(x, y) = (3, -1)
Also, from the question, we have the transformation to be:
Point Q is reflected over the y-axis
Mathematically, this can be expressed as
(x, y) = (-x, y)
So, we have the following representation
Point Q' = (-3, -1)
Hence, the image is (-3, -1)
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Suppoe that the concentration of a bacterial ample i 100,000 bacteria per millimeter. If the concentration double every three hour how long will it take for the concentration to reach 350,000 material per millimeter?
The time t = 3.4209 will it take for the concentration to reach 350,000 material per millimeter.
How do you calculate hours and minutes?In an hour, there are 60 minutes. Divide the number of minutes by 60 to convert it to hours. For instance, 120/60=2 means that 2 hours are equal to 120 minutes.
What is millimeter?The millimeter, abbreviated mm in the International System of Units (SI), or millimeter, abbreviated mm in the American spelling, is a unit of length that is one thousandth of a metre long, the SI base unit of length. As a result, a metre is made up of 1000 millimeters.
We are going to use formula
y = a * e ^ (b * t)
a and b are constants and t is for time.
Initially there are 100,000 bacteria, so;
100000 = a * e ^ (b * 0)
100000 = a * 1
a = 100000
given condition is that the concentration doubles every 3 hours so
300000 = a * e ^ (b * 3)
As a equals to 100,000
e ^ (b * 3) = 3
b * 3 = ln 3
b = (ln 3) / 3
b = 0.3662
now we have to find value of the time when concentration of bacteria reaches to 350,000:
350000 = 100000 * (e ^ 0.3662 * t)
3.5 = e ^ 0.3662* t
ln 3.5 = 0.3662* t
t = 1.2527 / 0.3662
t = 3.4209
That is the required value of time
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find a equation line perpendicular to y-8=-2x that passes through the point (8,-5)
Answer:
Step-by-step explanation:
y = -2x + 8
perp.: 1/2
y + 5 = 1/2(x - 8)
y + 5 = 1/2x - 4
y = 1/2x - 9
through (4,-9) perpendicular to 8y=x-16
Answer:
y = -8x + 23
Step-by-step explanation:
8y=x-16
we need to turn this into slope-intercept form by dividing 8 on both sides
y = x/8 - 2
to make a line perpendicular from another, we must make sure the slope is the negative reciprocal of the original line.
Right now, it's the same as the original. To make it a negative reciprocal, switch the places of the denominator and numerator and flip the signs
-8x is the negative reciprocal of x/8
Does it go through (4,-9)? No.
To make sure it goes through 4,-9, we change it's y-intercept.
Plug in the coordinate given (4,-9) in the y = -8x + b ( we removed -2 since it's not the right answer.
y = -8x + b
(-9) = -8(4) + b
-9 = -32 + b
-9 +32= -32 + b +32
23 = b
plug in b and we get our answer
y = -8x + 23
Solve the system of equations using elimination:
-5x + 8y = -6.
-
- 5y = -9 and
Answer:
x=102/25 y=9/5
Step-by-step explanation:
Solve for x . Round to the nearest tenth, if necessary.
Answer: 52.5°
Step-by-step explanation:
sin59 = 45/x
sin59(x) = 45
x = 45/sin59 = 52.5°
Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales. Last week, she sold $843 worth of goods. How much was she paid?
The amount that Josephine will be paid is $644.30.
How much was Josephine paid?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this situation, Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales and she sold $843 worth of goods.
The amount she'll be paid will be:
= $560 + (10% × $843)
= $560 + $84.3
= $644.30
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For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
a. stays the same
b. increases
c. decreases
The minimum sample size needed to guarantee a given margin of error increases , the correct option is (b) .
What is Margin Of Error ?
The term margin of error is defined as an estimate of a small sample that is drawn from a relatively large population data.
the margin of error is usually governed by the parameters such as the standard deviation , sample size and desired confidence level.
to find missing term in the given statement , let us consider the values ,
where σ ⇒ Standard deviation for population
and m as "Margin of error" and Z as "Empirical value of Z-score" at a given confidence level .
So , minimum sample size for given confidence level is given by
⇒ (Z×σ)²/m²
from above formula we can conclude that minimum sample size is directly related to population's standard deviation.
Therefore, the minimum sample size required would "increase" with the increase in population "standard deviation" .
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The results of a series of surveys revealed a population with a mean of 15 and a standard deviation of 1.88. If each survey has a sample size of 70, which value falls within the interval where 95% of the sample means occur?
A) 15.66
B) 15.49
C) 14.96
D) 14.34
If each survey has a sample size of 70, a value which falls within the interval where 95% of the sample means occur is: C) 14.96.
What is a confidence interval?In this scenario, the confidence interval at 95% can be represented by this mathematical expression p - E < p < p + E
Based on the parameters provided, we would determine both the lower limit and upper limit for the interval where 95% of the sample means occur as follows;
Lower limit = 15 - 1.88/√70
Lower limit = 15 - 0.23
Lower limit = 14.77
For the upper limit, we have:
Upper limit = 15 + 1.88/√70
Upper limit = 15 + 0.23
Upper limit = 15.23
For 95% of the sample means to occur, the confidence interval is given by;
Confidence interval = (14.77, 15.23)
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question in the image below!!!!!!
Part a: The significance of the piece-wise function is define.
Part b: r(t) be the total amount of snow in cubic ft. is calulated.
Part c: Total volume of the ice is not removed.
Define the term rate of change of volume?The term "rate of change" (ROC) describes the rate which something transforms over time.The indicator that demonstrates how much a volume tendency is developing either in the up or down direction is the volume rate of change.For the given question, the rate function is given as;
f(t) = { 0, 0 ≤ t < 6 ,
125, 6 ≤ t < 7
108, 7 ≤ 9 }
Part a: The significance of the piece-wise function is-
f(t) = { 0, 0 ≤ t < 6 } define the volume of ice per hour accumulated in between 0 to 6 hours is 0 cubic ft/hr.f(t) = {125, 6 ≤ t < 7 } define the volume of ice per hour accumulated in between 6 to 7 hours is 125 cubic ft/hr.f(t) = { 108, 7 ≤ 9} define the volume of ice accumulated per hour in between 7 to 7 hours is 108 cubic ft/hr.
Part b: r(t) be the total amount of snow in cubic ft.
r(t) = { 0, 0 ≤ r < 6 } define the volume of ice accumulated in between 0 to 6 hours is 0 cubic ft: 0 cubic ft.f(t) = {125, 6 ≤ t < 7 } define the volume of ice accumulated in between 6 to 7 hours is 125 cubic ft. is 62.5 cubic ftf(t) = { 108, 7 ≤ 9} define the volume of ice accumulated in between 7 to 7 hours is 108 cubic ft. is 54 cubic ft.Part c: total ice accumulated is;
62.5 ft + 54 ft. = 116.5 cubic ft.
Total volume of the ice accumulated = 367.5 cubic ft.
Thus, no total volume of the ice is not removed.
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The function rule for this graph is
Answer:
Step-by-step explanation:
(0, 2) (4, 0)
(0 - 2)/(4 - 0) = -2/4 = -1/2
y - 2 = -1/2(x - 0)
y - 2 = -1/2x + 0
y = -1/2x + 2
Monica has $50 to spend at the video arcade. If each game costs $0.25, which of these graphs shows how much
money she will have after x games?
Answer:
A
Step-by-step explanation:
If Monica has $50 dollars to spend on the video arcade, and each game costs $0.25 then we can use an equation that looks something like this:
total = amount of money × cost of one game
50 × 0.25 = 200
Now look at the graphs.
The graph that best matches this equation is A.
What is the equation for the graph shown?
The linear equation on the graph shown is:
y = (2/3)*x + 4
What is the equation on the graph?
We can see that we have a linear equation on the graph, remember that a general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
On the graph, we can see that the line intercepts the y-axis at y = 4, then the y-intercept is b = 4
y = a*x + 4
To find the slope we can use another point on the line, for example, we can see that (-6, 0) is also on the line, replacing these values in the linear equation above we will get:
0 = a*-6 + 4
6a = 4
a = 4/6 = 2/3
Thus, the line is:
y = (2/3)*x + 4
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∠ABC and ∠KLC form a linear pair with m∠ABC = 74° and m∠KLC = x°.
Answer:
106
Step-by-step explanation:
A linear pair adds to 180
180 - 74 = 106
which is more likely rolling a total of 8 when two dice are rolled or rolling a total of 8 when thre dices are roled
Answer: Two dice
Step-by-step explanation:
For the two dice, there are 5 possible: (6, 2);(5, 3);(4, 4);(3, 5);(2, 6)
So two dice, the probability is 5/36 = 30/216
For three dice, the number of favorable cases is 21
The probability is 21/216
So the two dice are more likely
A regular polygon has its interior angles all equal to 171 Find the number of sides of the polygon.
The measure of the interior angles of a polygon is determined by the formula ((n - 2)180)/n = interior angle
measure
A car wash makes $7 profit p per car, resulting in the equation of the total T; T = 7p. If the car wash made $147, how many cars were washed?
what time will it be in 2 hours 30 minutes . if I went to work at 11:30 am and I clock out in 2 hours 30 minutes but what time will it be in 2 hours 30 minutes
Answer:
I'm pretty sure it would be 3:00
Step-by-step explanation:
I could be wrong tho-
To prove that the triangles are similar by the SAS
similarity theorem, it needs to be shown that
Ozcazc
OC 2G
O AC-H
BC
O AC-BE
HI
It needs to be shown that <W = <H by the SAS congruent theorem
How to determine the additional information?The question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Triangles = IWO, and IHOGiven theorem = SASThe SSS congruent theorem implies that the corresponding sides of the triangles in question and the angles between them are congruent
From the question, we can see that the following corresponding sides on the triangles have the same mark
W O and H O
AO and AO
This implies that these sides are congruent sides
For the triangle to be congruent by SAS, the following sides must also be congruent
Angle W must be congruent to Angle H
Hence, the additional info is <W = <H
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Complete question
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that____
For this function, what is the average rate of change over the interval 3.5 ≤ x ≤ 4?
The average rate of change for 3.5 ≤ x ≤ 4 is 2[f(4) - f(3.5)]
What is Average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
given:
Interval: 3.5 ≤ x ≤ 4
Now, For average rate
= [f(4) - f(3.5)]/(4 - 3.5)
= 2[f(4) - f(3.5)]
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please help need an answer ASAP!!!!!!!!!!!!
Answer:
1/9
Step-by-step explanation:
The y intercept of a line is when x = 0
y = 1/9
Answer:
y = 1/9
Step-by-step explanation:
y = -10x + 1/9
Substitute 0 for x
y = -10 x 0 +1/9
-10 x 0 = 0
y = 1/9
calculate the p-value associated with the null hypothesis that 50% of the students at eastern work more than 10 hours a week.
The p-value associated with the null hypothesis = 0.05
Fail to reject the null hypothesis. The P-value is greater than the level of significance.
Candice should reject the null hypothesis as the 50% confidence interval does not contain 10 hours
Small p-values offer proof that the null hypothesis is false. The stronger the evidence is against the null hypothesis, the smaller (closer to 0) the p-value. The null hypothesis is rejected if the p-value is less than or equal to the chosen significance level; otherwise, it is not.
You have the Hypothesis that "students study less than 10 hours, on average, per week"
Symbolically:
H₀:μ≥10hours
H₁:μ<10hours
The significant level for this case study is 50% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.
The p-value of 0.05 is one of the most often used numbers. When the calculated p-values are less than 0.05, the faulty hypothesis is considered to be fraudulent or invalid (subsequently the name invalid theory). Additionally, the faulty theory is taken into consideration to be clear if the value is greater than 0.05.
The edge for that likelihood in our model is 0.05, and it represents the probability that our results will be similar to the invalid speculation. Therefore, if the calculated p-value is less than 0.05, it actually means that there is a very little likelihood that we would have the same results as the flawed hypothesis. Additionally, if the p-value is greater than 0.05, there is a very strong probability that the results will be similar to the flawed speculation, leading us to conclude that it is legitimate.
Therefore,
Fail to reject the null hypothesis. The P-value is greater than the level of significance.
The p-value associated with the null hypothesis = 0.05
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Solve each system by elimination: 7x+3y=-1 4x+y=3
Using elimination method, the solution to the system of equation is as follows:
x = 2 and y = -5
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's use elimination method to solve the system of equation as follows:
7x + 3y = - 1
4x + y = 3
multiply equation(ii) by 3
Hence,
7x + 3y = - 1
12x + 3y = 9
subtract equation(i) from equation(ii)
5x = 10
x = 10 / 5
x = 2
Let's find y
7x + 3y = - 1
7(2) + 3y = -1
14 + 3y = -1
3y = -15
y = -15 / 3
y = -5
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Two perpendicular lines intersect at K(-2,-5). One line has equation y = -5/3x-25/3. what is the equation of the other line?
Answer:
It is y = 3/5x - 19/5
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes. Thus, the slope is 3/5x. Plug in -2 as x and solve for the intercept. It ii -19/5.
At the Wheatley School, the probability that a student takes Math 8 and Technology is 0.12. The probability the student takes Math 8 is 0.16. Find the probability that the student takes technology given that he is taking Math 8.
The probability that the student takes technology given that he is taking Math 8 is 0.075.
What is conditional probability?
Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Here, we have
Given:
The probability that a student takes Technology and Math 8 is 0.012.
P(Technology and Math 8) = 0.012
The probability that a student takes Math 8 is 0.16.
P(Math 8) = 0.16
We have to find the probability that a student takes Technology given that the student is taking Math 8
we use conditional probability
P(Technology|Math 8) = P(Technology and Math 8)/P(Math 8)
P = 0.012/0.16
P = 0.075
Hence, the probability that the student takes technology given that he is taking Math 8 is 0.075.
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Out of 400 plants sold daily at a nursery, 90% of them have flowers. How many of the plants have flowers?
Answer: 360 plants
Step-by-step explanation:
90% is equivalent to 0.90.
You multiply 0.90 and get your answer of 360.
Min receives an average score of 7 after completing 5 math tests. If she has another test coming up, find what mark she must gain to raise her average to 75.
Min needs to gain 80 marks to raise her average to 75.
What is Average number?Average number is got from sum of all numbers divided by the number of values.
Why we use average value?Average value is used to compare among different quantities of same terms.
given, Min receives an average score 70 from 5 math test.
let she needs to gain X in her 6th test to obtain an average of 75 from the total six test.
she gained average 70 from 5 test
if average is 75 then
75 = (X+ 70)/2
X=80
hence, in the 6th test she needs to gain 80 marks.
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The diagram shows a sector of a circle radius 10 cm.
Find the area of the sector, giving your answer correct to 1 decimal place.
Answer:
[tex]117.8cm ^{2} [/tex]
Step-by-step explanation:
[tex]a = {r}^{2} \theta \: \div 2 \\ = 100 \times 135 \div 2 \\ = 117.8 \: {cm}^{2} [/tex]
what is 6 plues 9 i need it plesae.
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