The solution is, The population would reach 111 million in next 7 years
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
given that,
The initial population of Mexico was 100 million
The growth rate of the population is 1.53 %per year
Then the future population of Mexico is given by
P = P_0(1+r)^t
Where P = future population after t years
P_0= initial population
t = time period in years
Substituting the given vales in above equation we get
(1+ 0.0153)^t = 1.11
Taking log on both sides we get
t* log (1.0153) = log(1.11)
solving we get,
t = 6.87
≈ 7 years
The population would reach 111 million in next 7 years.
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After the reflection of about X-axis,if the image of a point P is P’(-x,-y), in which quadrant does P lie and what is its coordinates?
The original coordinates are P(-x, y), and it is on the second quadrant.
In which quadrant does P lie and what is its coordinates?Remember that for a general point (a, b), a reflection about the x-axis changes the sign of the y-component, so we will get the image (a, -b)
Here we know that the image after the refection is P' = (-x, -y), then the coordinates of point P are (-x, y)
If we assume both x and y to be positive, then point P would be on the second quadrant.
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Keith needs to buy some pencils. Brand A has a pack of 24 pencils for $8.77. Brand B has a pack of 26 pencils for $9.84.
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
Round your answers to the nearest cent.
Unit price for the Brand A pencils:
Unit price for the Brand B pencils:
The better buy:
O Brand A
O Brand B
for each pencil
$for each pencil
Neither (They have the same unit price)
The brand that is the better buy based on their unit price is; Brand A
How to find the Unit Price?A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint, which can be used to compare the same type of goods sold in varying weights and amounts.
It is also referred to as a product's average price which is the result of dividing the product's total sales revenue by the total units sold.
Thus;
Unit price of Brand A = 8.77/24 =$0.365 per pencil
Unit price of Brand B = 9.84/26 = $0.378 per pencil
The cheaper one is the better buy which is Brand A.
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Solve for x
Plea help me
Answer:
x ≈ 73.4°
Step-by-step explanation:
using the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{23}{24}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{23}{24}[/tex] ) ≈ 73.4° ( to the nearest tenth )
Find the missing angle measurement.
?
OA) 3 degrees
OB) 13 degrees
OC) 23 degrees
OD) 90 degrees
67°
Answer:
23 degrees
Step-by-step explanation:
Sum of interior angles in a triangle = 180°
∴Sum of interior angles in the right- angled triangle in the question:
67° + 90° + ? = 180°
= ? = 180° - 90° - 67°
∴ ? = Missing angle measurement = 23°
= 23 degrees
Create a large coordinate graph on graph paper
and graph the triangle at right. Multiply the
y-coordinate of each point by 4. Then graph the
new shape. Make sure you connect your points.
List the points for the new shape. Are the two
figures similar? Why or why not?
The two figures (i.e. triangles) are similar triangles
How to determine if the triangles are trianglesLet's create a triangle with the following coordinates:
A = (0, 0)
B = (3, 0)
C = (0, 4)
To get the new coordinates, we need to multiply the y-coordinate of each point by 4:
A' = (0, 0 * 4)
B' = (3, 0 * 4)
C' = (0, 4 * 4)
So the new points are:
A' = (0, 0)
B' = (3, 0)
C' = (0, 16)
To determine if the two figures are similar, we need to check if they have the same shape but different sizes.
Specifically, the new triangle is four times larger in the vertical direction but has the same shape and angles as the original triangle.
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Carol buys a house for £2349000
she pays a 10% deposit
work out the amount of deposit paid by carol
Carol pays a 10% deposit, it means the amount of deposit she pays is £234,900.
To work out the amount of deposit paid by Carol, we need to find 10% of the house price. We can do this by multiplying the house price by 10/100 or 0.10.
Here are the steps to find the amount of deposit paid by Carol:
1. Start with the house price: £2349000
2. Multiply by 0.10 to find 10% of the house price: £2,349,000 x 0.10 = £234,900
3. The amount of deposit paid by Carol is £234,900.
So, the answer is £234,900.
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Please help I can’t do this
The four consecutive numbers which adds to give 130, are 31, 32, 33, 34
What are consecutive numbers?Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.
Given that, there are four consecutive numbers which adds to give 130,
According to the definition of consecutive numbers, we add 1 to each previous integer to get the successive integer,
Therefore, let us consider x, x+1, x+2, x+3 be the four consecutive numbers,
Therefore,
x+x+1+x+2+x+3 = 130
4x + 6 = 130
4x = 124
x = 31
Therefore, the required consecutive integers are, 31, 32, 33, 34
Hence, the four consecutive numbers which adds to give 130, are 31, 32, 33, 34
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5. y=-2² + 12x - 15
a=-2
b=12
11
·2
NO NEED FOR HELP ON QUESTION 5 and 7
The axis of symmetry, vertex, domain, and range of each of the quadratic function are as follows;
Axis of symmetry = 3.
Vertex = (3, 3).
Domain = {-∞, ∞}.
Range = {-∞, 3}.
Axis of symmetry = 4.
Vertex = (4, -2).
Domain = {-∞, ∞}.
Range = {-2, ∞}.
How to calculate the axis of symmetry of a quadratic function?Mathematically, the axis of symmetry (vertex) of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry (vertex), Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
Note: The domain of a quadratic function (parabola) is always all real numbers on the x-axis of a cartesian coordinate.
For the given quadratic function y = -2x² + 12x - 15, we have:
Axis of symmetry (vertex), Xmax = -b/2a
Axis of symmetry (vertex), Xmax = -12/2(-2)
Axis of symmetry (vertex), Xmax = -12/-4 = 3.
Vertex (h, k) = (3, 3).
Domain = {-∞, ∞} or x ∈ R.
Range = {-∞, 3}.
x y
1 2
1 4
3 3
For the given quadratic function y = 2x² - 16x + 30, we have:
Axis of symmetry (vertex), Xmax = -b/2a
Axis of symmetry (vertex), Xmax = -(-16)/2(2)
Axis of symmetry (vertex), Xmax = 16/4 = 4.
Vertex (h, k) = (4, -2).
Domain = {-∞, ∞} or x ∈ R.
Range = {-2, ∞}.
x y
3 0
5 0
4 -2
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Which angle is formed by a secant and tangent line?ANGA) GSEB) EGSC) NGL
In the image line segment SE is the tangent. The secant line making an angle with tangent line SE is NS. So the angle is ∠GSE. So option B is the correct answer.
Tangent is a line which intersect with only a single point on the curve. The point where the line meets is the point of tangency. Tangent line is always perpendicular to the radius drawn to the point of tangency. Here the tangent line is SE, point of tangency is S.
Secant lines are the lines which passes through two points of a curve. A chord drawn to the circle is a secant line. Here there are two secant lines NS and NA. Here only NS makes an angle with the tangent line.
So the angle made by a tangent and secant line is ∠GSE.
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The image for the question is attached below.
When a 7-ohm resistor is connected in a parallel circuit with a resistance of
x ohms, the total resistance R (in ohms) is given by:
R = 7/7/2
7+1
Find the resistance x (in ohms) that results in a total resistance of 6 ohms.
You may complete the work on your student work document. Type the final answer in the space below.
You must show work to receive full credit.
on solving the provided question we can say that for parallel combination, the equation will be 1/R = 1/R1 + 1/R2.
What is equation?A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.
we have,
Total Resistance (R) = 1.403 kilo-ohm.
R1 = 2.0 Kilo-ohm.
1.403 kilo-ohm = 1403 ohm.
for parallel combination, the equation will be
1/R = 1/R1 + 1/R2
[tex]1/1403 = 1/2000 + 1/ R2\\.1/1043 - 1/2000 = R2\\2000 - 1403 / 1403 x 2000 = 1/R2\\597/ 1403 x 2000 = 1/R2\\R2 = 1403 x 2000 / 597 = 2806000 / 597 = 4700.16\\R2 = 4700.16 ohm[/tex]
103 ohm = 1 kilo-ohm => 4700 ohm = 4.7 kilo-ohm
so, R2 = 4.7 kilo-ohm.
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Solve the L.P.P graphically- Maximize z=y-2x subject to x-y >=2 ,x + y<=4 , x>=0 ,y>=0
Answer: 8y=2h
Step-by-step explanation: you have to subtract the first 2 numbers then add the others and then add letters and boom
A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
We are are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.242895 in first simulation and between 0.1948 and 0.2732 in second simulation.
A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
A 95% confidence interval gives us a range of values that we are 95% confident contains the true proportion of wins that the new game strategy will produce in the long run. To construct the confidence interval for each simulation, we can use the following formula:
CI = p ± 1.96 * sqrt(p * (1 - p) / n)
where p is the sample proportion of wins, n is the number of trials, and 1.96 is the z-score corresponding to a 95% confidence level.
For the first simulation, p = 212 / 1000 = 0.212 and n = 1000, so the confidence interval is:
CI = 0.212 ± 1.96 * sqrt(0.212 * (1 - 0.212) / 1000)
CI = (0.1812, 0.2428)
This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.2428.
For the second simulation, p = 235 / 1000 = 0.235 and n = 1000, so the confidence interval is:
CI = 0.235 ± 1.96 * sqrt(0.235 * (1 - 0.235) / 1000)
CI = (0.1948, 0.2732)
This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1948 and 0.2732.
In general, larger sample sizes lead to narrower confidence intervals. In this case, both confidence intervals overlap, indicating that the two simulations are consistent with each other. This gives us additional confidence in the estimated proportion of wins using the new strategy.
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Answer:
the confidence interval for the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.
Step-by-step explanation:
got it right on the test :)
What is the doubling time formula?
The doubling time formula is used to calculate the time required for a quantity to double in size at a constant growth rate. The formula is: doubling time = ln(2) / r
Where ln(2) is the natural logarithm of 2, and r is the annual growth rate expressed as a decimal. The doubling time represents the number of time units it takes for the quantity to double, such as years, months, or days, depending on the time unit used for the growth rate. This formula is commonly used in many fields, such as finance, biology, and demography, to estimate the future growth of a quantity based on its current growth rate.
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Question 2 (2 points)
If (63, x, 105) form a Pythagorean Triple, what is the value of x?
If (63, x, 105) generate a Pythagorean Triple, the value of x is 84.
Before starting to solve this problem we must know that the Pythagorean theorem is a theorem that realizes the sides of a right triangle and has many applications for it.
A Pythagorean Triple is a set of three integers that satisfy the Pythagorean Theorem, [tex]a^2 + b^2 = c^2[/tex]. In this case, 63 and 105 are two sides of a right triangle, and x is the third side. We can plug in the values and solve for x:
63² + x² = 105²
3969 + x² = 11025
x² = 7056
x = √7056
x = 84
Therefore, the value of x is 84, and the Pythagorean Triple is (63, 84, 105).
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Hello can someone please help HHHHHHHEEEEELLLLLPPPPP
The value of m∠J in the triangle is 65°
How to find the value of m∠J in the triangle?
Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
We have triangle HIJ and m∠H = (4x + 1)°, m∠I = (2x-6)° and m∠J = (6x-7)°.
Since the sum of angle in a triangle is 180°. We can say:
m∠H + m∠I + m∠J = 180°
(4x + 1)° + (2x-6)° + (6x-7)° = 180°
4x + 1 + 2x-6 + 6x-7 = 180
12x - 12 = 180
12x = 180 + 12
12x = 192
x = 192/12
x = 16
To find m∠J = (6x-7)°, put x = 12 into m∠J = (6x-7)°. That:
m∠J = 6(12) - 7
m∠J = 72 - 7
m∠J = 65°
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Help me please!! T^T
The length of line FG is 16 units
How to find length of FGThe length of FG is equal to length GH that is to say
line FG = line GH
From the problem, we have that
FG = x + 11
GH = 3x + 1
Equation both lines
x + 11 = 3x + 1
collecting like terms
11 - 1 = 3x - 1
10 = 2x
rearranging and isolating x
2x = 10
x = 5
The line FG = x + 11 = 5 + 11 = 16 units
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There were 65 tickets sold for the school play the total cost of the tickets was $390 how much did each ticket cost
Answer: $6
Step-by-step explanation:
Divide $390 by 65 to find $6 per ticket.
Answer:
$6
Step-by-step explanation:
$390/65=6
Bella works at a popular clothing store. Last winter, her manager asked her to track the
store's sweater sales. This box plot shows the results.
Price of sweaters sold ($)
30
40
50
60
What fraction of the sweaters cost $50 or less?
80
Answer:
Answer is 1/2. Box plot is split into quarters. So 1/4 + 1/4 = 1/2
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the most accurate rate of speed Morris is traveling?
1 mile = 5,280 feet
45 miles per hour
46 miles per hour
47 miles per hour
48 miles per hour
Answer:
Step-by-step explanation:
The best estimate of the speed Morris is traveling will be 48 miles per hour.
What is conversion?
Conversion means to convert the same thing into different units.
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha.
We know that 1 mile = 5,280 feet.
Then convert the feet per second to miles per hour. Then the speed of the Morries will be
⇒ 3 feet / 1 second
⇒ (3 / 5285) miles / (1 / 3600) hour
⇒ (3 / 5285) x (3600)
⇒ 2 miles per hour
Then the best estimate of the speed Morris is traveling will be
⇒ 50 - 2
⇒ 48 miles per hour
The best estimate of the speed Morris is traveling will be 48 miles per hour.
How do I find the length of a curve?
Answer:
Step-by-step explanation:
The length of a curve can refer to the arc length of a function, or the distance along a curved path between two points.
Arc Length of a Function:
For a continuous and differentiable function y = f(x) defined over an interval [a, b], the arc length of the curve between x = a and x = b can be found using the following definite integral:
L = ∫_a^b √(1 + (dy/dx)^2) dx
Where L is the arc length, dy/dx is the derivative of the function with respect to x, and the integral is taken from x = a to x = b.
Length of a Curved Path:
For a curved path defined by a continuous and differentiable function y = f(x), the length of the path between two points (x1, y1) and (x2, y2) can be found using the same definite integral formula as the arc length of a function:
L = ∫_(x1)^(x2) √(1 + (dy/dx)^2) dx
Where L is the length of the path and the integral is taken from x = x1 to x = x2.
Note that finding the exact length of a curve can sometimes be difficult and may require numerical methods such as numerical integration or approximation techniques like Simpson's rule.
Mark collects Pokémon cards. He recently bought 24 cards to add to his collection. He decided to give of all of his cards to his little brother. If he gave a total of 15 cards to his brother, which equation best represents the situation?
A- 1/6c + 15 = 24
B- 1/6 + 24c=15
C- 1/6 (c + 24) = 15
D- 1/6c + 24=15
The required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.
How to use the concept of the equation model?The concept of the equation model is a fundamental part of mathematics, and it is used in a wide range of applications. Here are some ways in which the equation model is used,
1. Solving equations 2. Modeling real-world situations 3.Understanding relationships between variables.
here,
According to the question let the Pokémon cards Mark intially had be c,
So as per the given condition, Mark has c + 24 card and he gives 1/6 of his card to his little brother, which is 15 cards
The equation model of the situation is given as,
1/6(c + 24) = 15
Thus, the required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.
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A
65°
Reflex Angle B =
degrees.
The measure of angle B is given as follows:
<B = 295º.
How to obtain the measure of angle B?Angles A and B in the context of this problem are reflex angles, meaning that the sum of their measures is of 360º.
The measures are given as follows:
<A = 65º.<B is unknown.Hence the measure of angle B is obtained as follows:
65 + <B = 360
<B = 360 - 65
<B = 295º.
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my math question is "Jon buys 3 shirts for $20. write this as a rate" and the same thing for "Brenda records 76 songs on 4 albums, write this as a rate"
Answer: For Jon, buying 3 shirts for $20 can be written as a rate as follows:
The number of shirts Jon buys per dollar spent = 3 shirts / $20 = 3/20 shirts/dollar
For Brenda, recording 76 songs on 4 albums can be written as a rate as follows:
The number of songs Brenda records per album = 76 songs / 4 albums = 19 songs/album
So, the rate of songs Brenda records per album can be written as 19 songs/album.
Step-by-step explanation:
select all of the options below that represent a continuous relationship
A. answers the number of problems in each of your homework assignments
B. The speed of an airplane during the flight from Los Angeles to New York
C. The temperature of an apple pie during the time it spends in the oven.
D. The number of pumpkins your family carves every year for Halloween.
E. is the first graph
F. is the second graph
The temperature of an apple pie during the time it spends in the oven shows the continuous relationship.
What is continuous function?In mathematics, a continuous function is a function that does not have discontinuities that means any unexpected changes in value. A function is continuous if we can ensure arbitrarily small changes by restricting enough minor changes in its input.
A function f(x) is said to be a continuous function in calculus at a point x = a if the curve of the function does NOT break at the point x = a.
A continuous function, on the other hand, is a function that can take on any number within a certain interval. For example, if at one point, a continuous function is 1 and 2 at another point, then this continuous function will definitely be 1.5 at yet another point.
Therefore, option C and E are the correct answers.
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Complete the table for this triangle
Answer:
[tex]\sin A=\frac{a}{b}[/tex]
[tex]\cos A=\frac{c}{b}[/tex]
[tex]\tan A=\frac{a}{c}[/tex]
[tex]\csc A=\frac{b}{a}[/tex]
[tex]\sec A=\frac{b}{c}[/tex]
[tex]\cot A=\frac{c}{a}[/tex]
Step-by-step explanation:
Here are the definitions of the trig functions listed in the picture
[tex]\sin x=\frac{O}{H}[/tex]
[tex]\cos x=\frac{A}{H}[/tex]
[tex]\tan x=\frac{O}{A}[/tex]
[tex]\csc x=\frac{H}{O}[/tex]
[tex]\sec x=\frac{H}{A}[/tex]
[tex]\cot x=\frac{A}{O}[/tex]
Note:
[tex]A[/tex] = side adjacent to angle
[tex]O[/tex] = side opposite to angle
[tex]H[/tex] = hypotenuse
All 6 questions are about angle A.
The side adjacent to angle A is side c.
The side opposite to angle A is side a.
The hypotenuse is side b.
Therefore we can write
[tex]A=c\\O=a\\H=b[/tex]
Knowing that we can fill out the table.
[tex]\sin A=\frac{a}{b}[/tex]
[tex]\cos A=\frac{c}{b}[/tex]
[tex]\tan A=\frac{a}{c}[/tex]
[tex]\csc A=\frac{b}{a}[/tex]
[tex]\sec A=\frac{b}{c}[/tex]
[tex]\cot A=\frac{c}{a}[/tex]
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Find the sum of interior angles for the polygon below:
Answer:
The polygon has 8 sides, so the sum of its interior angles is 1080 degrees. Each interior angle is equal to 135 degrees
the interior angle of a regular polygon is equal to the total number of its sides minus two, multiplied by 180 degrees divided by the number of sides. For example, in a regular polygon with 8 sides, one interior angle would equal 1080 degrees (8 - 2) x 180/8 = 1080.
Click to show whether each function is linear or non-linear.
The required solution is given as,
f(x) = 22 + x = Linear
f(x) = x²+1 = Non-linear
f(x) = x³ +2x+1 = Non-linear
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Linear functions are functions that can be represented by a straight line on a graph. These functions have a constant rate of change and can be written in form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.
Non-linear functions are functions that do not have a constant rate of change and cannot be represented by a straight line on a graph.
Thus, the required solution is given as,
f(x) = 22 + x = Linear
f(x) = x²+1 = Non-linear
f(x) = x³ +2x+1 = Non-linear
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composite figure is shown. Which of the following represents the total area of the figure?
The total area of the composite figure can be found to be 24. 52 cm ²
How to find the total area ?First, find the area of the first triangle :
= 1 / 2 x base x height
= 1 / 2 x 3 x 2. 7
= 4. 05 cm ²
The area of the second triangle :
= 1 / 2 x 3 . 4 x ( 6. 8 - 2 . 7 )
= 6. 97 cm ²
Then the area of the rectangle :
= 5 x 2. 7
= 13. 5 cm ²
The total area of the composite shape is :
= 13.5 + 6.97 + 4. 05
= 24. 52 cm ²
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b. Write an equation relating the the number of individual songs s and the number
of albums a Jada can download. ax+by=c
Jada can get 4 albums or she can get 80 individual songs for $20. The equation will be written as 0.25s + 5a = 20.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that It costs $0.25 to download an individual song and $5 to download an album. Jada has $20 to spend downloading music.
The equation will be written as,
0.25s + 5a = $20
The number of individual songs will be,
0.25s = 20
s = 20 / 0.25
s = 80
The number of albums,
5a = 20
a = 20 / 5
a = 4
The complete question is given below.
It costs $0.25 to download an individual song and $5 to download an album. Jada has $20 to spend downloading music.
a. Make a table showing three ways Jada can spend $20 downloading individual songs and albums. (s the being number of individual songs and a being the number of albums.)
b. Write an equation relating the number of individual songs (s) and the number of albums(a) in standard form.
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PLEASE ANSWER
!!!!!!!!
The measure of angle X is given as follows:
40º.
How to obtain the value of x?We have two secants in this problem, and point C is the intersection of the two secants, hence the angle measure of x is half the difference between the angle measure of the largest arc by the angle measure of the smallest arc.
The arc angles are given as follows:
125º and 45º.
Hence the value of x is given as follows:
X = 0.5 x (125 - 45)
x = 40º.
More can be learned about angle measures at brainly.com/question/30820033
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