Answers
The slope of the line y = 1/2 x - 3 is equal to 1/2.
What is the slope-intercept form?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept.Next, we would use an online graphing calculator to plot the given equation in slope-intercept form. By critically observing the graph (see attachment), we can logically deduce that the y-intercept is equal to -3 while the slope's line is equal to 1/2.
In conclusion, the linear function does not represent a proportional relationship because the line didn't pass through the origin (0, 0).
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Related Questions
pls help due tomorrow!!!!!!!
Answers
All the possible values of each expression is given as an inequality as;
1 < a/b < 5
How to solve Linear Inequalities?We are given the inequalities of the domain and range as;
2 < a < 5
1 < b < 2
Thus, we can say that the maximum value of a/b will be the division of the maximum value of a by the minimum value of b to give;
(a/b)max = 5/1
(a/b)max = 5
Similarly, minimum value of a/b will be the division of the minimum value of a divide by the maximum value of b to give;
(a/b)min = 2/2
(a/b)min = 1
Thus, all possible values would be expressed as;
1 < a/b < 5
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Find the foci of the ellipse with the equation x^2/49 + y^2/64=1
Answers
Using the provided equation of the ellipse as [tex]\frac {x^2}{49} + \frac {y^2}{64} = 1[/tex] and comparing with the general form, The answer is (0,+- 3.87)
What do you mean by ellipse?An ellipse is a geometric shape that is defined as the set of all points such that the sum of the distances from two fixed points (called the foci) is constant. It is a closed curve that is similar to a circle, but with a different shape. An ellipse can be defined by its semi-major and semi-minor axes, and its center. It is often used in mathematics and physics to describe the orbits of planets, moons, and other celestial bodies. The semi-major axis is the distance from the center of the ellipse to the longest point on the ellipse, and the semi-minor axis is the distance from the center of the ellipse to the shortest point on the ellipse.
What are the parameters of ellipse?The standard equation of an ellipse can be written as:
(x - h)^2/a^2 + (y - k)^2/b^2 = 1
where (h, k) is the center of the ellipse, and a and b are the semi-major and semi-minor axes, respectively. The semi-major axis is the distance from the center of the ellipse to the longest point on the ellipse, and the semi-minor axis is the distance from the center of the ellipse to the shortest point on the ellipse. The foci (plural of focus) of an ellipse are two points located inside the ellipse that are used to define its shape.
equation provided,
[tex]\frac {x^2}{49} + \frac {y^2}{64} = 1[/tex]
[tex]64x^2+49y^2-3136 = 0[/tex] is the general form.
foci = (0,+- 3.87)
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Answer:
foci (0 +- sqrt 15)
Step-by-step explanation:
This standard form is given. We are given [tex]a^{2}[/tex] = 64 and [tex]b^{2}[/tex] = 49. We need to figure out [tex]c^{2} =a^{2} -b^{2}[/tex]. Substitute 64 for a, and 49 for b.
[tex]c^{2} =64-49[/tex]
[tex]c^{2} =15[/tex]
Take the square root of both sides to get [tex]\sqrt{c^{2} } =\sqrt{15}[/tex].
[tex]c=\sqrt{15}[/tex]
This is a horizontal ellipse, so the x-values will be 0 for each focal point.
The foci are (0, ±[tex]\sqrt{15}[/tex])
Mrs. Wicklund sets a lawn sprinkler to cover part of a circular region. The central angle and radius for the covered part
are shown.
130⁰
square feet
25 ft-
To the nearest 10 square feet, what is the area of the 130° part covered by the sprinkler? Enter your answer in the box.
Answers
Multiply the central angle by the radius squared, and divide by 2: Sector Area = r² × α / 2.
To the nearest 10 square feet, what is the area of the 130° part covered by the sprinkler?
Merely divide the area of the room by the number of sprinklers to get the area of coverage for each sprinkler. Shown on the left is a room that meets the spacing requirements of the small room rule—the sprinkler is 9 ft. from one wall and not more than 7.5 f.New fire codes allow a single sprinkler head to protect up to 200 square feet, depending on the design of the fire sprinkler, flammability of the building and the materials within it. The NFPA delineates spacing requirements based on the material hazards, plumbing, and piping systems of the specific construction.Equation: Static pressure – friction loss +/-- change in elevation = psi available to sprinkler.Example: You measure your static pressure at 65 psi and your total flow rate from your spigot at 10 gpm.
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What is the factor of x³ 5x² 2x 24?
Answers
The factor of x3 5x2 2x 24 is (x - 4)(x + 2)(x + 6), which can be expanded as x3 + 2x2 - 4x2 + 6x - 8x - 24.
1. Factor out the greatest common factor (GCF) from the coefficients of the terms.
x3 5x2 2x 24
2. Factor out the GCF from each term:
x3 = x•x•x
5x2 = 5•x•x
2x = 2•x
24 = 24
3. Our factors are now:
x•x•x 5•x•x 2•x 24
4. Group the terms with common factors:
(x•x•x) (5•x•x) (2•x) (24)
5. Factor out the common factor from each group:
x•x (x•5) (2•x) (24)
6. Our factors are now:
x (x•5) (2•x) (24)
7. Factor out the common factor from each group:
x (x•5) (2•x) (24)
8. Our factors are now:
x (x + 2)(x + 6) (24)
9. Our final answer is:
(x - 4)(x + 2)(x + 6)
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How many 4 digit numbers greater than 4000 can be formed?
Answers
The number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition is 192.
We are having digits 2,3,4,5 and 6. Numbers greater than 4000 are to be formed using these digits without repetition.
The number can have 4 digits but greater than 4000 or can have 5 digits.
The total number of 4 digits number greater than 4000 is => 3*4P3 = 3*24 = 72.
Total number of 5 digits numbers = 5P5=5!=120
So, the Total number of required numbers =120+72=192
Hence, The number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition is 192.
Complete question: Find the number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition.
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According to the combination method, the number of formation using the digit 4 is 192
The term combination in math is called as the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
While we looking into the four-digit has 4 digits and the first digit is the thousands place. Then the digits 2 and 3 are less than 4, here we know that they can't take the thousands place. Here we also know that the digit 4, 5, and 6 can take this place.
Here we have the remaining 4 numbers and the remaining three digits can be taken by any of them to form a number greater than 4000.
Then the number of ways is calculated as
=> 3×4×3×2 = 72
Then the number of 5 digit numbers greater than 4000.
Here we have to observe that all five-digit numbers are greater than 4000. And here we have 5 digits and hence the number of five-digit numbers is written as
=> 5×4×3×2×1 = 120
Then the total number of ways is calculated as
=> 72 + 120 = 192
Therefore the number of numbers that are greater than 4000 which can be formed using the digits 2, 3, 4, 5, 6 without repetition is 192.
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20 pts. Find the inverse
Answers
The inverse of the given statement is if x does not equal 4 then 4x - 5 doesn't equal 11. Option C is the correct option.
What is a statement?
A statement in mathematics is a declarative utterance that can only be either true or false. A proposal is another name for a statement. It's important that there be no ambiguity. A sentence can only be true or untrue and not both for it to be a statement.
The given statement is if x equals 4, then 4x - 5 equals 11.
Each of the original statements' inverses is presumptive in the inverse statement.
The inverse statement of the given statement is if x does not equal 4 then 4x - 5 doesn't equal 11.
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Mark fires 500 arrows at a target on 457 occasions. Use this information to estimate the probability that he will hit the target with every shot when he fires:
A. 1 arrow
B. 2 arrows
C. 3 arrows
Answers
The probability that Mark would hit the target with every shot when he fires 1 arrow is 0. 914 arrows.
The probability that Mark would hit the target with every shot when he fires 2 arrows is 1. 8 arrows
The probability that Mark would hit the target with every shot when he fires 3 arrows is 2. 7 arrows
How to find the probability ?To find the probability that Mark is able to hit the target, look at the probability from when 500 arrows were fired :
= 457 / 500
= 0. 914
= 91. 4 %
If Mark fires 1 arrow, the probability that he hits the target is 0. 914 arrows:
If Mark fires 2 arrows, the probability that he will hit the target is 1. 828 arrows:
= 0. 914 x 2
= 1. 828
If Mark fires 3 arrows, the probability that he will hit the target is 2. 7 arrows:
= 0. 914 x 3
= 2. 7 arrows
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in an election, 52496 people voted for ron, 44929 people for jhon and 36824 people for Mike in town. if everyone one voted in the town, what is the total number of voted
Answers
Answer:
Step-by-step explanation:
52496 + 44929 + 35824 = 133,249 people
If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x) as defined in the following table:
x 0 1 2 3 4 5 6 7 8
P(X=x) 0.06528 0.3870 0.03062 0.0968 0.06913 0.0968 0.04846 0.01252 0.1935
Determine the mean and variance of the random variable.
(a) mean
(b) variance
Answers
Mean and Variance of the given table are 3.43672 and 7.837755 respectively.
What is probability ?
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
a)E(x) = ∑ xᵢp(xᵢ)
∑ xᵢp(xᵢ) = 1(0.3870) + 2(0.038062) + 3(0.0968) + 4(0.06913) + 5(0.0968) + 6(0.04846) + 7(0.01252) + 8(0.1935)
∑ xᵢp(xᵢ) = 3.43672
Mean = 3.43672
b) Variance = E(x²) - [E(x)]²
E(x²) = ∑ x²ᵢp(xᵢ)
∑ x²ᵢp(xᵢ) = 1²(0.3870) + 2²(0.038062) + 3²(0.0968) + 4²(0.06913) + 5²(0.0968) + 6²(0.04846) + 7²(0.01252) + 8²(0.1935)
∑ x²ᵢp(xᵢ) = 19.6488
∴ Variance = 19.6488 - (3.43672)² = 7.837755
Hence , Mean and Variance of the given table are 3.43672 and 7.837755 respectively.
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A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of
−0.7
meter per second
(ds/dt = −0.7 m/sec)
. Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 2. (Round your answers to three decimal places.)
Answers
The rate of vertical change is -0.4 m/s and the rate of horizontal change is -0.7 m/s.
THE RATE OF VERTICAL AND HORIZONTAL CHANGETo find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 2, we need to use the chain rule of Calculus.The chain rule states that if we have a function f(g(x)) and we know the derivative of f and the derivative of g, we can find the derivative of f(g(x)) by multiplying the derivative of f by the derivative of g. In this case, y is a function of x and x is a function of t. So we have:dy/dt = dy/dx * dx/dt
To find dx/dt, we can use the fact that the pipe is being pulled in at a rate of -0.7 m/s. So dx/dt = -0.7 m/s.To find dy/dx, we can use the equation for the pipe, which is:y = 12 - √(12² - x²)
Taking the derivative of this equation with respect to x, we get:dy/dx = x/(√(12² - x²))
Now that we have both dx/dt and dy/dx, we can use them in the chain rule to find dy/dt:dy/dt = x/(√(12² - x²)) * (-0.7 m/s)
To find the rate of vertical change, we need to find dy/dt at the point where y = 2. We know that x = sqrt(12² - 2²) = √(144-4) = √(140) = 2√(35). So we can substitute this value of x into the equation for dy/dt and find the rate of vertical change:dy/dt = 2√(35)/√(140) * (-0.7 m/s) = -0.4 m/s
To find the rate of horizontal change, we know that dx/dt = -0.7 m/s, so the rate of horizontal change is:dx/dt = -0.7 m/s
So the rate of vertical change is -0.4 m/s and the rate of horizontal change is -0.7 m/s.Learn more about rate of vertical and horizontal change here:
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Question #1:
y
m=
b=
Line: Solid or Dashed?
Shade: Above or Below?
>
Are these points solution: (0,0)
(3,2)
(4,5)
Answers
Answer:
m = 1/3
b = 1
Dashed
Below
Step-by-step explanation:
171 people used the public swimming pool. The daily prices are 1.50 for children and 2.50 for adults. The receipts for admission totaled 321.50 How many children and how many adults swam at the public pool that day? I need this done fast because I have a big test coming up and this is the only question I'm having trouble with its and i have to send this review in by 12:00 tonight
Answers
Answer:
65 Adults and 106 children
Step-by-step explanation
a= adults
c= children
2.5a+1.5(171-a) =321.5
a=65
now we have the number of adults we minus that by the amount of people (171) to give us for the number of children and we get 106.
On a school trip, a class travels 471.459 kilometers by train and 2.66 kilometers by bus. How far did the class travel?
Answers
Answer:
474.119 kilometers
Step-by-step explanation:
The class traveled 474.119 kilometers in total. You can find this by adding the distance traveled by train (471.459 km) to the distance traveled by bus (2.66 km).
471.459 + 2.66 = 474.119
Which statement correctly compares the values of the digit 4 in the numbers 3,245 and 8,407?
Answers
Statement correctly compares the values of the digit 4 in the numbers 3,245 and 8,407 are number 4 is in 10th place, and number 4 is in the 100th place respectively.
What are numbers?
A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.
In mathematics, the first ten numbers are referred to as the fundamental numbers. These fundamental numbers are listed beginning at 0 and ending at 9. Basic numbers include 0 through 9 are 0, 1, 2, 3, 4, 5, 6, 7, and 8.
The given numbers are 3245 and 8407.
We have to find the place of 4 in the given numbers.
Consider, the number 3245.
In this number 4 is in 10th place.
Consider, the second number 8407.
In this number 4 is in the 100th place.
Hence, statement correctly compares the values of the digit 4 in the numbers 3,245 and 8,407 are number 4 is in 10th place, and number 4 is in the 100th place respectively.
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Really need answer. I have 1 more try
Answers
The correct value of the expression is, 10.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is,
⇒ 5/8 × 16
Now,
Simplify the expression as;
⇒ 5/8 × 16
⇒ 5 × 2
⇒ 10
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3 The length of a mobile phone is twice the width.
There is a border around the screen.
The border is 1.5cm wide at the top and bottom.
The border is 0.25 cm wide at the sides.
The perimeter of the screen is 32 cm.
Let the width of the phone be.xcm.
(a) Form an equation in x.
(b) Hence find the area of the screen in cm².
Answers
On solving the provided question we can say that - the linear equation of .25x + 3y = 1 +3 = 4
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here, x= 4 and = 1
.25x + 3y
= 1 +3
= 4
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go on a 4-day vacation and bring $84 for spending money. You spend $16 each of the first 3 days. Write a linear function that describes the amount of money, a, that you have after d days. On the last day, you want to buy a sweatshirt that costs $38. Do you have enough money to buy the sweatshirt?
Answers
The linear function is a = -16d + 84
You do not have enough money to buy the sweatshirt.
How to write a linear function that describes the amount of money, a, that you have after d days?
The general form of a linear function is y = mx + b
where m is the rate of spending and b is the starting money
Given that: you go on a 4-day vacation and bring $84 for spending money. You spend $16 each of the first 3 days.
m = -16 (negative because spending means decrement), b = 84, y = a (amount of money left) and x = d (days).
Thus, the linear function will be:
a = -16d + 84
On the last day, d = 4. Thus, the amount left will be:
a = -16d + 84
a = -16(4) +84
a = -64 + 84
a = $20
The amount left is $20 (which is less than $38). Therefore, you do not have enough money to buy the sweatshirt.
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someone please help. how would this be graphed??
Answers
Answer:
See picture
Step-by-step explanation:
What is the approximate length of the radius, r? a. 4.5 cm b. 9.0 cm c. 14.2 cm d. 28.3 cm
Answers
The approximate length of the radius, r is 4.51 cm. SO the option 1 is correct.
In the given question we have to find the approximate length of the radius, r.
As given, circle O has a circumference of approximately 28.3 cm.
The calculation of the circle's boundary is referred as the perimeter or circumference of the circle. Although the circumference of the circle determines the space it occupies.
The circumference of a circle is its length when it's actually opened and represented as a single direction. Units like cm or unit m are typically used to measure it.
As we know that the formula of circumference of circle = 2πr
As circumference of circle = 28.3 cm
So 2πr = 28.3 cm
Divide by 2π on both side, we get
r = 14.15/π
π = 3.14
So r = 14.15/3.14
r = 4.51 cm
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The complete question is:
Circle O has a circumference of approximately 28.3 cm.
What is the approximate length of the radius, r?
a. 4.5 cm
b. 9.0 cm
c. 14.2 cm
d. 28.3 cm
The approximate length of the radius, r, is 4.5 cm.
The formula for calculating the radius, r, of a circle is r = C/2π, where C is the circumference of the circle. In order to calculate the approximate length of the radius, we must first calculate the circumference.
Let's assume that the circumference of the circle is 28.3 cm. To calculate the circumference, we can use the formula C = 2πr. We know the circumference and want to solve for the radius, so we can rearrange the formula to solve for r: r = C/2π.
Plugging in our values, we can calculate the approximate length of the radius: r = 28.3 cm/2π = 4.5 cm. Therefore, the approximate length of the radius, r, is 4.5 cm.
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The endpoints of LF¯¯¯¯¯¯¯ are L(-2, 3) and F(3, 1). The endpoints of JR¯¯¯¯¯¯¯ are J(1, -1) and R(2, -3). What is the approximate difference in the lengths of the two segments?
Answers
The approximate difference in the lengths of the two segments is given as follows:
3.2 units.
How to obtain the distance between two points?The coordinates of the points have the following format:
[tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex]
Hence the distance is given as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The length of a segment is given by the distance between it's two endpoints.
Hence the length of segment LF is given as follows:
[tex]D_{LF} = \sqrt{(3 - (-2))^2+(1 - 3)^2}[/tex]
[tex]D_{LF} = \sqrt{29}[/tex]
[tex]D_{LF} = 5.4[/tex]
The length of segment JR is given as follows:
[tex]D_{JR} = \sqrt{(-3 - (-1))^2+(2 - 1)^2}[/tex]
[tex]D_{JR} = \sqrt{5}[/tex]
[tex]D_{JR} = 2.2[/tex]
Hence the distance is of:
5.4 - 2.2 = 3.2 units.
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y varies directly as x. y=8 when x=12 Find x when y=6
Answers
Answer:
x = 9
Step-by-step explanation:
8 = 12k Divide both sides by 12
k = 2/3
6 = 2/3 x Multiply both sides by 3/2
x = 9
9/10 x 5/7 fraction form
Answers
Answer:
9/
Step-by-step explanation:
As we have to multiply the fraction so we will multiply numerator with numerator and denominator with denominator we get 45/70. As we know both 45 and 70 are divisible by 5 and the simplest form answer we get will be 9/ 14
How many number's between 1 to 1000 are not divisible by 3 or by 5 or by 7?
Answers
There are 719 integers between 1 and 1000 that are not divisible by 3, 5, or 7.
1. 1000/3 = 333.333 (333 integers divisible by 3)
2. 1000/5 = 200 (200 integers divisible by 5)
3. 1000/7 = 142.857 (142 integers divisible by 7)
4. 1000 - (333 + 200 + 142) = 325
5. 1000 - 325 = 675
6. 675 + 333 + 200 + 142 = 1350
7. 1350 - 1000 = 350
8. 350/3 = 116.667 (116 integers divisible by 3 and 5)
9. 350 - 116 = 234
10. 234/7 = 33.429 (33 integers divisible by 7 and 5)
11. 234 - 33 = 201
12. 201/5 = 40.2 (40 integers divisible by 5 and 7)
13. 201 - 40 = 161
14. 161/3 = 53.667 (53 integers divisible by 3 and 7)
15. 161 - 53 = 108
16. 108/7 = 15.429 (15 integers divisible by 3 and 5 and 7)
17. 108 - 15 = 93
18. 1000 - (333 + 200 + 142 + 116 + 33 + 40 + 53 + 15) = 719
19. 719 number's between 1 to 1000 are not divisible by 3 or by 5 or by 7
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What are the slope and y-intercept of the line 4y = -x - 32?
Answers
Answer:
slope = - [tex]\frac{1}{4}[/tex] , y- intercept = - 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4y = - x - 32 ( divide through by 4 )
y = - [tex]\frac{1}{4}[/tex] x - 8 ← in slope- intercept form
with slope m = - [tex]\frac{1}{4}[/tex] and y- intercept c = - 8
jennifer is on a trip and travels a distance of 150 miles. she spends some of her time walking, and some of her time travelling by train. if she spends w hours walking and t hours travelling by train, what is the meaning of 3w in the equation below? 50t 3w
Answers
Answer:
it means 3 weeks and time traveled
What is an equation of the line that passes through the points (3, 3) and
(3, -3)?
Answers
Answer:
X = 3
Step-by-step explanation:
this is a vertical line passing through x = 3.
How much money should you deposit in a bank so that it would accumulate to 100,000 at 1% simple interest for 10 years?
Answers
The principal money that will be deposited to accumulate 100,000 is 1 000 000 at 1% simple interest for 10 years
How to find the principal for the simple interest for 10 yearsThe principal is calculated using the simple interest formula
The formula is stated as
Simple interest = Principal * time * rate / 100
In the problem the give data include
principal = ?
rate= 1%
time = 10 years
plugging in the values
Simple interest = Principal * time * rate / 100
100 000 = P * 10 * 1 / 100
10 000 000 = P * 10
P = 1000 000
The principal is 1 000 000
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A city doubles its size every 41 years. If the population is currently 700,000, what will the population be in 123 years?
Answers
The population in 123 years will be 5600000.
How to calculate the population?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case, the city doubles its size every 41 years. If the population is currently 700,000. After 123 years, it'll have doubled 3 times.
The population will be:
= 700000 × 2³
= 5600000
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Answer: 5600000
Step-by-step explanation: I got it right on my ixl
two payment options to rent a car you can pay $20 a day plus 25 cents a mile (option a) or pay $10 a day plus 50 cents a mile (option b) for what amount of daily miles will option a be the cheaper plan?
Answers
Answer:
Option A will be the cheaper plan for any daily mileage over 80 miles.
Step-by-step explanation:
Owen spent $10 on 4 pieces of toast and 7 pieces of bacon. James spent $4 on 1 piece of toast and 1 piece of bacon. Which systems of equations models the situation given b for bacon and t for toast?
Answers
The system of equations that models the situation and can be used to get the prices is:
4*t + 7*b = $10
t + b = $4
Which system of equations models the situation?We know that the variables that we will be using are:
b = cost of a piece of bacon.t = cost of a piece of toast.First, we know that Owen spent $10 on 4 pieces of toast and 7 pieces of bacon, so we can write the equation:
4*t + 7*b = $10
And James spent $4 on 1 piece of each, then the other equation is:
t + b = $4
Then the system of equations that models this situation is the one we can make with these two equations:
4*t + 7*b = $10
t + b = $4
Learn more about systems of equations:
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