An estimate for the number of pet dogs and cats in the United States based on a recent survey, written as a single digit times an integer power of 10 is 2 x 10⁸.
What is an estimate?An estimate is a rough calculation or judgment arrived at when the details are not required or available.
We can apply number approximation, rounding, and scientific notations in estimation, as above.
First, the number, 183,900,000, can be approximated to 200 million pet dogs as an estimate.
Then, 200,000,000 can be written in a standard form or scientific notation by using an integer that indicates the place value in the power of 10.
Thus, 183,900,000 pet dogs can be estimated as 2 x 10⁸.
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The table shows the linear relationship between the amount of water being pumped
out of a pool over time.
Based on the table, what was the rate of change of the amount of water being
pumped out of the pool over time?
The rate of change of water being pumped out of the pool over time is (C) -2.
What is a linear relationship?A straight-line relationship between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.So, the linear relationship is:
x = 1, y = 8x = 2, y = 6x = 3, y = 4x = 4, y = 2Look at the values of y: 8, 6, 4, 2
The pattern is 8 - 2 = 6; 6 - 2 = 4; 4 - 2 = 2So, the rate of change will be -2.
Therefore, the rate of change of water being pumped out of the pool over time is (C) -2.
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The complete question is given below:
The table shows the linear relationship between the amount of water being pumped out of a pool over time. Based on the table, what was the rate of change in the amount of water being pumped out of the pool over time?
(A) 2
(B) 10
(C) -2
(D) -10
[tex] \rm\sum_{n=2}^\infty \frac{(-1)^n}{n^2(n^2-1)} \binom{2n}{n}^{ - 1}\\ [/tex]
[tex]\:\:\:\:\:\:\:[/tex]
Let
[tex]\displaystyle f(x) = \sum_{n=2}^\infty \frac{x^n}{n^2(n^2-1) \binom{2n}n}[/tex]
Differentiate and multiply by [tex]x[/tex].
[tex]\displaystyle xf'(x) = \sum_{n=2}^\infty \frac{x^n}{n(n^2-1) \binom{2n}n}[/tex]
Now differentiate twice.
[tex]\displaystyle x f''(x) + f'(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{(n^2-1)\binom{2n}n}[/tex]
[tex]\displaystyle xf'''(x) + 2f''(x) = \sum_{n=2}^\infty \frac{x^{n-2}}{(n+1)\binom{2n}n}[/tex]
Multiply by [tex]x^3[/tex].
[tex]\displaystyle x^4 f'''(x) + 2x^3 f''(x) = \sum_{n=2}^\infty \frac{x^{n+1}}{(n+1)\binom{2n}n}[/tex]
Differentiate one last time and multiply by [tex]\frac1x[/tex].
[tex]\displaystyle x^3 f^{(4)}(x) + 6x^2 f'''(x) + 6x f''(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{\binom{2n}n}[/tex]
Now integrate with the fundamental theorem of calculus, noting that [tex]f(0)=f'(0)=0[/tex] follows from our series definition. We do this twice and make use of the recurrence
[tex]I_n = \displaystyle \int_0^x y^n f^{(n+1)}(y) \, dy = x^n f^{(n)}(x) - n I_{n-1}[/tex]
Integrating once yields
[tex]\displaystyle x^3 f'''(x) + 3x^2 f''(x) = \sum_{n=2}^\infty \frac{x^n}{n \binom{2n}n}[/tex]
Multiply by [tex]\frac1x[/tex].
[tex]\displaystyle x^2 f'''(x) + 3x f''(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{n \binom{2n}n}[/tex]
Integrating once more yields the ordinary differential equation
[tex]\displaystyle x^2 f''(x) + x f'(x) - f(x) = \sum_{n=2}^\infty \frac{x^n}{n^2 \binom{2n}n}[/tex]
and we recognize the right side as the series
[tex]\displaystyle \sum_{n=2}^\infty \frac{x^n}{n^2 \binom{2n}n} = 2\arcsin^2\left(\frac{\sqrt x}2\right) - \frac x2[/tex]
Solving the differential equation is quite doable with the variation of parameters method; we ultimately find
[tex]\displaystyle f(x) = \frac12 + \frac{7x}8 - \left(\frac1x+\frac12\right) \sqrt x \sqrt{4-x} \, \arcsin\left(\frac{\sqrt x}2\right) + 2 \left(\frac1x-1\right) \arcsin^2\left(\frac{\sqrt x}2\right)[/tex]
Recover the sum we want by letting [tex]x=-1[/tex]. Recall that
[tex]\arcsin(iz) = i \,\mathrm{arsinh}(z) = i\ln(z + \sqrt{1+z^2})[/tex]
Then we have the following equivalent results involving our old friend [tex]\phi[/tex].
[tex]\displaystyle f(-1) = -\frac38 - \frac{\sqrt5}2\, \mathrm{arsinh}\left(\frac12\right) + 4 \,\mathrm{arsinh}^2\left(\frac12\right) \\\\ f(-1) = -\frac38 - \frac{\sqrt5}2 \ln\left(\frac{1+\sqrt5}2\right) + 4 \ln^2\left(\frac{1+\sqrt5}2\right) \\\\ f(-1) = \boxed{-\frac38 - \left(\frac12 - \phi\right) \ln(\phi) + 4 \ln^2(\phi)}[/tex]
Help me with this question -_-
Answer: u≤29
Hope this helps! :)
In one year a factory produced 11,650 gallons of lemonade 4,950 fewer gallons of ice tea than lemonade anf 3,500 fewer gallon of root beer than iced tea. How many gallons were produced in all
In a single year, factories create a total of 21550 gallons.
In both imperial and US customary units, the gallon is a unit of volume.A gallon is a unit of measurement for liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.
We have been given that
Lemonade = 11,650 gallons
Ice tea = 4,950 fewer than lemonade
Root beer = 3,500 fewer than Ice tea.
After calculating
Ice tea = 11,650 - 4,950
Ice tea = 6700 gallons
Root beer = 6700 - 3,500
Root beer = 3200 gallons
Total factory produced in one year
= 11,650 + 6700 + 3200
Hence , 21550 gallons are total factory produced in one year.
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To find the actual discount, multiply the discount rate by the original amount 'x'. To find the sale price, subtract the actual discount from the original amount 'x' and equate this to given sale price. Solve the equation and find the original amount 'x'.
If the original price =$50
If we take $20 off, we have: $50-20 =$30
Next, taking 25% off of $30, we have:
Final Price = (100%-25%) of $30
=0.75 x 30
Final Price Final 0Price=$22.5
9
If we take $20 off, we have: $90-20 =$70
Next, taking 25% off of $70, we have:
Final Price = (100%-25%) of $70
=0.75 x 70
Final Price =$52.50
pls help this is the last question and i have to get correct
The correct statements regarding sum and subtraction with negative numbers are given as follows:
The inequality p + q < 0 is possible because -5 + (-5) = -10.The inequality p - q > 0 is possible because -4 - (-5) = 1.The inequality p - q < 0 is possible because -5 - (-4) = -1.How to add two negative numbers?When two negative numbers are added, the result is negative, as we keep the signal and then add the absolute amounts of each value, for example:
-5 + (-5) = -(5 + 5) = -10.
Hence the fourth statement is correct, while the first and the third are not.
How to subtract two negative numbers?When we subtract two negative numbers, we first transform the second number to positive, meaning that the result can be either positive or negative, as the result will take the signal of the higher value and their absolute amounts are subtracted.
Hence:
-4 - (-5) = -4 + 5 = (5 - 4) = 1.-5 - (-4) = -5 + 4 = -(5 - 4) = -1.Hence the fifth and the sixth statements are correct.
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Solve the application involving geometry. If necessary, refer to the geometry formulas listed in the inside back cover of the text.
The measure of one angle is 11 times the measure of another. If the two angles are supplementary, find the measures of the angles.
One angle's measurement is 11 times that of another. if the two angles supplementary one another. The measure of the angles area one is 165° and other angle is 15°.
Given that,
One angle's measurement is 11 times that of another. if the two angles supplementary one another.
We have to determine the angles' measurements.
The word "supplementary" refers to two angles coming together to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles. If two angles complement one another
It has an acute angle on one side and an obtuse angle on the other.
The angles are both right angles.
So, It follows that A + B = 180°.
Angle A is 11 times angle B means
A=11B
We get,
11B+B=180
12B=180
B=180/12
B=15°
Then angle A is
A=11×15
A=165°
Therefore, The measure of the angles area one is 165° and other angle is 15°.
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Find the circumference of a circle with diameter, d = 2.76m. Give your answer rounded to 2 DP.
The circumference of a circle with diameter 2.76 m is 8.66 m.
What is Circumference?
Circumference of a circle is perimeter of circle.
Given that;
Diameter of a circle = 2.76 m
Since, Circumference of a circle = 2πr
Where, r is radius of circle.
Now, Diameter of a circle = 2.76 m
Then, Radius of a circle = 2.76/2 = 1.38 m
Hence, Circumference of a circle = 2πr
Substitute all the values;
Circumference of a circle = 2 x 3.14 x 1.38
= 8.66 m
Thus, The circumference of a circle with diameter 2.76 m is 8.66 m.
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Probability of distribution: Four children are born, and the number of boys is noted assume an equal chance of a boy or a girl for each birth
The subset's components can be listed in any order when combined.
The former two are both 15/16.
What is the difference between combinations and permutations?A set of elements can be divided into subsets in two different ways: by combination and by permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order. n distinct things permuted (when repetition is not allowed) Repetition when it is acceptable. When the objects are not distinct, permutation (Permutation of multi sets).P(at least one boy) and then P(at least one Girl)
P(at least one boy and one girl)
If we assume P(girl) = P(boy) = 50%
The latter results from the 16 possible combinations.
noting only two of which are single sex.
So 14/16 = 7/8.
Therefore, the former two are both 15/16.
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What is another way to represent an angle in standard position that has a measure of 530º
By finding coterminal angles, we conclude that another way of writing the angle 530° is 170°.
In which other way can we represent the angle?For any angle A, we define the family of coterminal angles B as:
B = A + n*360°.
Where n is an integer different than zero.
In this case we have A = 530°
Then the coterminal angles are:
B = 530° + n*360°
If we define n = -1, then:
B = 530° - 360° = 170°
So 170° is another way of writing 530°.
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The path of a diver is modeled by
f(x) = −
4
9
x2 +
24
9
x + 13
where f(x) is the height (in feet) and x is the horizontal distance (in feet) from the end of the diving board. What is the maximum height of the diver?
Answer:
Here's your answer :)
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5s • 2 to the power of 3 + (h-1)to the power of 2
What is the value of the expression when: h= 4 and s = -1?
A -49
B -31
C 49
D 164
The most appropriate choice for exponent will be given by-
-31 is the required answer. The second option is correct
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2\times 2\times 2\times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times.....\times a[/tex] (m times), a is the base and m is the index.
The laws of index are
[tex]a^m \times a^n = a^{m + n}\\\frac{a^m}{a^n} = a^{m - n}\\a^ 0 =1\\(a^m)^n = a^{mn}\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\a^{-m} = \frac{1}{a^m}[/tex]
Here,
[tex]5s \times 2^3 + (h-1)^2\\h = 4, s = -1\\5(-1) \times 8 + (4 - 1)^2\\-40 + 9\\-31[/tex]
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-3v-7v
What is the answer to this question
Answer:
-10v
Step-by-step explanation:
-3v - 7v
OR
(-3v)+(-7v)
= -10v
Answer:
the answer is -3v-7v= -10
This is math… i swear please do not leave i have had 4 people leave me :(
B
1) To solve this question, we can write out two equations within this expression:
[tex]\begin{gathered} (x)30+(30-x)15=30(20) \\ 30x+450-15x=600 \\ 15x=600-450 \\ 15x=150 \\ \frac{15x}{15}=\frac{150}{15} \\ x=10 \end{gathered}[/tex]So we can do it with 10L of that 30% solution.
2)Let's find the other volume, plugging into that x=10, since the whole volume of this new solution is 30L we can subtract from that 30L that 10L we have just found:
[tex]30-10=20l[/tex]3) So we found 20l of the 15% solution.
Thus the answer is B
12. Evelyn deposited $5,000 into a savings
account that earns an annual simple
interest rate of 0.1%. To the nearest tenth
of a year, how long will it take for the
account to reach $5,750?
It takes 1.5 years for Evelyn to reach $5,750.
In this question, it is clear that principal amount that Evelyn deposited is $5,000. The annual interest rate as per the question is 0.1%. The final amount that Evelyn gets is $5,750.
Lets assume that it will take t years for Evelyn to get a final amount of $5,750.
So,
Principal amount, P = $5,000
annual rate, r = 0.1%
Final amount, A = $5,750
From the formula for simple interest, we have,
A = P( 1 + rt)
Hence, t = (1/r) x { (A/P) -1 }
= 1/0.1 x { (5750/5000) - 1}
= 10 x { 1.15 - 1 }
= 10 x 0.15
=1.5
Therefore it will take 1.5 years for Evelyn to get a total amount of $5,750 provided she deposited an amount of $5,000 at an annual simple interest rate of 0.1%
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PLEASE HELP!!!!!!!!!!
Explanation
Step 1
et
w represents the cost of gift-wrapping.
then
Jessie spent a total of $14
total= 14
the cost for postage=$2.25
the cost of the gift( itself)=9.50
in words, the total is
the total cost is the cost of the gift plus the cost of the postage plus the cost of gift-wrapping
Now,replace
[tex]\begin{gathered} 14=\text{ \$9.50 +\$ 2.25 +w} \\ \text{reordering} \\ \text{ \$9.50 +\$ 2.25 +w=14} \end{gathered}[/tex]The height of the real painting is 24 inches. What is the height of the painting in the scale drawing? (b)In the scale drawing, the length of the painting is 7 centimeters. What is the length of the real painting?
The scale drawing height is 4 cm and the actual drawing length is 42 in
The height of the painting in the scale drawingThe complete question is added as an attachment
From the attachment, we have the ratio to be given as
Scale ratio, 1 cm : 6 in
Rewrite as
Scale measurement : Actual measurement = 1 cm : 6 in
In this question, we have
Actual measurement = 24 inches
This means that
Scale measurement : 24 in = 1 cm : 6 in
Multiply 1 cm : 6 in by 4
Scale measurement : 24 in = 4 cm : 24 in
By comparison, we have
Scale measurement = 4 cm
Hence, the scale drawing height is 4 cm
What is the length of the real painting?Recall that
Scale ratio, 1 cm : 6 in
Rewrite as
Scale measurement : Actual measurement = 1 cm : 6 in
In this question, we have
Scale measurement = 7 cm
This means that
7 cm : Actual measurement = 1 cm : 6 in
Multiply 1 cm : 6 in by 7
7 cm : Actual measurement = 7 cm : 42 in
By comparison, we have
Actual measurement = 42 in
Hence, the actual drawing length is 42 in
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1. Approximate using perfect squares.
<78 <
<√78<
<√78 <
So V78 is between
and
Answer:
8 and 9
Step-by-step explanation:
consider perfect squares either side of 78
64 < 78 < 81 , then
[tex]\sqrt{64}[/tex] < [tex]\sqrt{78}[/tex] < [tex]\sqrt{81}[/tex] , that is
8 < [tex]\sqrt{78}[/tex] < 9
Which expression is equivalent to (4.3x + 4)(-1.8x)?
A.-4.14x² +0.08x
B.-7.74x2 - 7.2
C.-7.74x² - 7.2x
D.-7.74x² + 7.2x
PLSSS ANSWER QUICK
Step-by-step explanation:
jsjsnsnsnnsnskskskskskskwwkwkkww
Carmen has 4 tomatoes she will eat this week. The first tomato Carmen will eat weighs 2/8 of a pound .which point on the number line represents the first tomato Carmen will eat
The point on the number line which represents the first tomato Carmen will eat is: B. K.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
In Mathematics, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
By critically observing the number line (see attachment) which models the weight of the tomatoes Carmen would eat, we can logically deduce that each of the interval represent 1/8 pound.
First tomato = 2/8
First tomato = 1/8 + 1/8 ≡ 2/8 = point K.
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Complete Question:
Carmen has 4 tomatoes she will eat this week. The first tomato Carmen will eat weighs 2/8 of a pound. Which point on the number line represents the first tomato Carmen will eat?
A. J
B. K
C. L
D. M
someone in a car going past you at the speed of 41 m/s drops a small rock from a height of 1.6 m . How far from the point of the drop will the rock hit the ground? the acceleration due to gravity is 9.8 m/s^2
Answer:
please mark my brain list answer
Answer:
s = ut + 1/2 at²
2.4 = 4.9t²
t = 0.70
distance = speed x time
d = 24 x 0.7
d = 16.8 m
A tank has 500 litres of salt water, which includes 10 kg of salt. At time t = 0, a solution of salt water (concentration 0.01 kg/l) is pumped in the tank at a rate of 10 l/min. At the same time, the tank starts to be emptied at rate of 20 l/min.
Use your knowledge of differential equations to solve an equation of the amount (mass) of salt within the tank at any given time t.
The differential equation used to solve an equation of the amount (mass) of salt within the tank at any given time t is [tex]\frac{ds}{0.04s-0.1} = dt[/tex].
What are differential equations?A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the two.Let the amount of salt any time t is given by s kg then the rate of change of s with respect to t is given by,
[tex]\frac{ds}{dt}[/tex] = (rate of salt out) - (rate of salt in)
Rate of salt in = 0.01 kg/litre × 10 litre/min = 0.1 kg/min
Rate of salt out = s/500 kg/litre × 20 litre/min = (20s/500) kg/min
A differential equation can be made on the concept that the rate of change of salt is the difference between the rate of in and the rate of out.
That gives us when combined,
[tex]\frac{ds}{dt} = 0.04s -0.1[/tex]
Now solving this differential equation,
[tex]\frac{ds}{0.04s-0.1} = dt[/tex]
Integrating both sides,
[tex]\int\ {\frac{ds}{0.04s-0.1} } \, = \int dt[/tex]
[tex]\frac{ln(0.04s -0.1)}{0.04} = t+C_{1}[/tex]
[tex]ln(0.04s - 0.1) = 0.04t +0.04C = 0.04t +C_{2}[/tex]
[tex]0.04s - 0.1 =e^{0.04t + C_{2} } =Ae^{0.04t}[/tex]
Now at t = 0, s = 10 kg
0.04(10) - 0.1 = A
A = 0.3
So the differential equation can be written as,
[tex]0.04s - 0.1 = 0.3e^{0.04t}[/tex]
Now time at which no salt is left which means s = 0 at some time t
[tex]0.1 - 0.04(0) = -0.3e^{-20t}[/tex]
The equation is not further solvable as we can see.
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a) Find the function algebraically. Show yourwork!b) Where is the asymptote on the graph of thisfunction? Give as an equation.c) What is the domain and range of thisfunction?Domain:Range:
(a)
In order to find the function, let's use the ordered pair (-3, 8) in the given exponential function f(x).
So we have:
[tex]\begin{gathered} f(x)=a^x \\ \\ (-3,8)\colon \\ 8=a^{-3} \\ 2^3=(\frac{1}{a})^3 \\ 2=\frac{1}{a} \\ a=\frac{1}{2} \end{gathered}[/tex]So the function is f(x) = (1/2)^x
(b)
The asymptote of this graph is y = 0, that is, the horizontal axis.
(c)
The domain is the values that x can assume, so the domain of this function is all real numbers, that is, (-infinity, infinity)
The range is the values that f(x) can assume, so the range of this function is y>0, that is, all positive numbers: (0, infinity)
The length of a swimming pool is triple the width. The area of the pool is 6627 ft2. Find the length and width of the pool.
For the given statement, the length and width of the pool are 141 feet and 47 feet respectively.
What is meant by the area of the rectangle?The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle. In the aforementioned illustration, a rectangle with dimensions of 4 inches long by 3 inches wide has a surface area of 12 square inches. 4 plus 3 equals 12, so. A rectangle's area is calculated by multiplying its length by its width. Therefore, the product "l w" is the formula for the area, "A," of a rectangle whose length and breadth are "l" and "w," respectively.
Rectangular area is equal to (length breadth) square units.
Given,
length of the pool = 3 (width of the pool)
Let width of the pool = x
Length of the pool = 3x
Area of the pool = Length × Width
6627 = x × 3x
⇒ 3x² = 6627
⇒ x² = 2209
⇒ x = 47
⇒ 3x = 47 × 3
⇒ 141
This implies that the length and width of the pool are 141 feet and 47 feet respectively.
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Find domain and range of this function using h interval motion
Answer:
Domain: [-1, 4)Range: [-5, 4]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Only questions #9,13,17,21,25 please show work
THANK YOU
Simplification of the given expression to single complex number are as follow :
9. -11 +4i
13. 30 - 10i
17.20
21. (3 + 5i)/2
25. -1
As given,
To simplify the following expressions to a single complex number,
9) (- 5 + 3 i) - (6 - i)
= - 5 + 3 i - 6 + i
= - 5 - 6 +3i + i
= - 11 + 4 i
13) (6 - 2 i) 5
= (6 x 5) - (2 x 5) i
= 30 - 10 i
17) (4 - 2 i) (4 + 2 i)
= [tex]4^{2} - (2i)^{2}[/tex]
= 16 - 4 [tex]i^{2}[/tex]
= 16 - 4 (-1)
= 16 + 4
= 20
21) [tex]\frac{-5+3i}{2i} = \frac{i(-5+3i)}{2i^{2}} = \frac{-5i + 3i^{2} }{2(-1)}[/tex]
= [tex]\frac{-5i+3(-1)}{-2} = \frac{3+5i}{2}[/tex]
25) [tex]i^{6} = (i^{2})^{3} = (-1)^{3} = -1[/tex]
Note: To simplify a fraction where denominator has complex component (i) as coefficient, multiply both numerator and denominator by i to eliminate i from denominator (by converting it to real number)
Therefore, simplification of the given expression to single complex number are as follow :
9. -11 +4i
13. 30 - 10i
17.20
21. (3 + 5i)/2
25. -1
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The average price of gas in 1990 was $1.22 per gallon. The average price of gas in 2022 was $4.62 per gallon. What was the percent increase in the price of gas?
PLS HELP GAVE ME THE RIGTH ASWER AND I WILL GIVE LOTS OF POINTS I NEED IT RIGHT CAUSE ITS A GRADE PLS
Describe the transformation that shows Figure A is similar to Figure B. PLEASE HELP!!!
Answer:
C. the dilate with scale of 2
Step-by-step explanation:
when you dilate, a scale bigger than 1 means you enlarge the figure A
no other choices make figure a bigger to 'fit into' or be the same as figure B
so thus, the answer is C.
Answer:
C.
Step-by-step explanation:
as we can clearly see, when going from figure A to figure B every length and coordinate is doubled. that means a constant scale factor of 2 for all of that. but the angles and the general structure of the object remained the same (so, both are similar).
Andy has $310 in his account. Each week, w, he withdraws $30 for his expenses. Which expression could be used if he wanted to find out how much money he had left after 8 weeks?
1) 310-8w
2) 280+30(w-1)
3) 310w-30
4) 280-30(w-1)
Hey you man what are you doing here go to there