Answer:
[tex]a. \: 30 + a = 40 \\ a = 40 - 30 \\ a = 10 \\ b. \: 500 + b = 200 \\ b = 200 - 500 \\ b = - 300 \\ c. \: - 1 + c = - 2 \\ c = - 2 + 1 \\ c = - 1 \\ d. \: d +3.567=0 \\ d = 0 - 3.567 \\ d = - 3.567[/tex]
hope it helps:)
The administrator of a county's museum is considering increasing the price of an annual pass by 1% from $25 to $25.25. At the current price, the museum sells 2500 annual passes and the point of elasticity is 0.73. What effect would the increase in price have on the museum's annual pass revenue?
Answer: the increase in price from $25 to $25.25 would result in a small increase in annual pass revenue of $178.50 or about 0.3%.
Step-by-step explanation: we can calculate the modern yearly pass income by increasing the modern amount requested by the unused cost of $25.25:
Unused yearly pass income = Modern cost x Modern amount requested
Unused yearly pass income = $25.25 x 2482 = $62,678.50
We as of now know that the ancient yearly pass income is $62,500 (since 2500 passes were sold at $25 each), so ready to calculate the alter in yearly pass income:
Alter in yearly pass income = Unused yearly pass income - Ancient yearly pass income
Alter in yearly pass income = $62,678.50 - $62,500 = $178.50
Please help !!!!!!!!!
100 Points! Algebra question. Please show as much work as possible. Photo attached. Thank you!
The value of the constant term k in the exponential model of the bacteria population is k ≈ 0.0972
What is an exponential function?An exponential function is one in which the input variable is part of the exponent of the expression for the function.
The function for the population of the bacteria indicates;
[tex]P(t) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\cdot t)}}[/tex]
The population of the bacteria after t = 1 hour is P(1) = 10,532
Therefore;
[tex]P(1) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\times 1)}} = 10,532[/tex]
[tex]1 + 1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532}[/tex]
[tex]1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532} - 1[/tex]
[tex]e^{(-k\times 1)} = \frac{\frac{22,000}{10,532} - 1}{1.2}[/tex]
Taking the natural logarithm of both sides, we get;
[tex]\ln (e^{(-k\times 1)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]
[tex]\ln (e^{(-k)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]
[tex]\ln (e^{(-k)}) = -k = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex] ≈ -0.0972 (rounded to 4 decimal places)
-k ≈ -0.0972
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Determine the line of Reflection. A(-3,3) B(-3,6) C(1,6) D(1,3) E(-1,1); A'(-5,3), B(-5,6), C(-9,6), D(-9,3) E(-7,1)
The line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).
What is line of reflection?A line of reflection is a line that acts as a mirror, reflecting a figure across it. Each point on the original figure is reflected over the line and the resulting image is the same size and shape as the original, but appears to be "flipped" or "mirrored" across the line of reflection. The line of reflection is the perpendicular bisector of the segment connecting each point on the original figure to its corresponding point on the reflected image.
In the given question,
To determine the line of reflection, we need to find the perpendicular bisector of each line segment between the point and its image.
First, we find the midpoint of the line segment between A and A': (A + A')/2 = (-3 + (-5))/2, (3 + 3)/2 = (-4, 3)
The perpendicular bisector of the line segment AA' is a vertical line passing through (-4, 3).
Similarly, we find the midpoints and perpendicular bisectors of the line segments BB', CC', DD', and EE'.
The perpendicular bisectors of the line segments BB', CC', DD', and EE' are also vertical lines passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1), respectively.
Therefore, the line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).
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How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%? a previous study indicates that the proportion is 21%
Using the data given such as the margin of error, sample size and z-score, the maximum sample size required is 499
How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%?To solve this problem, we need to know the minimum sample size required. The formula for this is given as;
n = (z² * p(1 - p))/ E²
n = sample sizeE = Maximum margin of errorp = estimated proportion from the given previous studyz = z-scoreSubstituting the values into the formula;
n = (1.645² * 0.21(1 - 0.21))/ 0.03²
n = 498.8
The sample size should be at least approximately 499
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A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, what is the strength of the drug?
In a case whereby A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, the strength of the drug can be expressed as 41%.
How can the strength of the drug be calculated?From the question, the total mass =400 g
The solvent mass = 236 g
Then the mass of the drug = 400-236
= 164
Then the mass percentage of the drug can be calculated as 164/400 * 100
= 41%
Therefore, the strenght of the drug can be expressed as 41%
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wing Lines Parallel
Solve for x to make A||B.
B
3x
A
X = = [?]
7x
Enter
If line A is parallel to line B then the value of x is 18.
Given that a line A is parallel to line B
We have to find the value of x
3x+7x=180
Combine the like terms
10x=180
Divide both sides by 10
value x=18
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help pls i dont understand this
The equation that can be used to determine the cost of each admission ticket is 4x + $25.00 = $175.00.
The cost in dollars of the admission ticket is $ 37.50.
How to find the cost of the tickets ?Let x be the cost, in dollars, of each admission ticket, including tax.
The total cost of 4 admission tickets can be expressed as 4x, since the cost of each ticket is the same.
The total cost of 4 admission tickets and parking is given as $175.00, so we can write:
4x + $25.00 = $175.00
Simplifying the equation, we can solve for x:
4x = $175.00 - $25.00
4x = $150.00
x = $37.50
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−9⋅(5j+k)
Apply the distributive property to create an equivalent expression.
Answer:
-45j - 9k
Step-by-step explanation:
-9(5j + k)
-9(5j) + -9(k)
-45j - 9k
Helping in the name of Jesus.
The equation y = 10x + 15 models the amount of money y, in dollars, that Jack earns shoveling snow for x hours. How many hours does Jack need to work to earn $55?
A Petri dish is filled with 250 bacterial cultures. The number of bacteria in the dish triples every hour.
a. Write a recursive and an explicit formula to represent the sequence that models the scenario.
Explicit formula:
Recursive formula:
b. Predict the number of bacterial cultures in the dish after 8 hours. Explain your reasoning.
c. Does this sequence represent a function? Explain your reasoning.
Answer:
a. Let's denote the number of bacterial cultures after n hours by B_n. We know that the number of bacteria triples every hour, so we can write:
- Recursive formula: B_n = 3*B_(n-1) with initial condition B_0 = 250.
- Explicit formula: B_n = 250 * 3^n.
b. To predict the number of bacterial cultures after 8 hours, we can use the explicit formula and substitute n=8:
B_8 = 250 * 3^8 = 250 * 6561 = 1,640,250
Therefore, there will be 1,640,250 bacterial cultures in the dish after 8 hours.
c. Yes, this sequence represents a function. For each input value (number of hours), there is a unique output value (number of bacterial cultures). The explicit formula gives a direct way of computing the output for any input, so it satisfies the definition of a function.
Please see the attached
HELP ME PLEASEEEE The matrix below represents a system of equations.
Which matrix represents the solution to this system of equations?
The matrix that represents the solution to this system of equations is
1 0 0 2
0 1 0 -4
0 0 1 3
Therefore option B is correct.
What is a matrix in mathematics?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
We solve a matrix by Arranging the elements of equations in matrices and find the coefficient matrix, variable matrix, and constant matrix.
We then go ahead to write the equations in AX = B form.
we then take the inverse of A by finding the adjoint and determinant of A. Multiply the inverse of A to matrix B, thereby finding the value of variable matrix X.
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What are the domain and range of the function f(x) x^2 +8x+7 over x+1
Answer: The function given is f(x) = (x^2 + 8x + 7)/(x + 1).
The domain of a function is the set of all possible input values for which the function is defined. In this case, the function f(x) is defined for all real numbers except for x = -1, because division by zero is undefined in mathematics. Therefore, the domain of f(x) is all real numbers except x = -1, or in interval notation: (-∞, -1) ∪ (-1, ∞).
The range of a function is the set of all possible output values that the function can produce. For this rational function, the range depends on the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function f(x) approaches 0, because the highest power of x in the numerator (x^2) and the highest power of x in the denominator (x) have the same degree, and their coefficients (1 in the numerator and 1 in the denominator) are equal. Therefore, the range of f(x) is all real numbers except 0, or in interval notation: (-∞, 0) ∪ (0, ∞). Note that f(x) never actually equals 0, because the function is defined for all real numbers except x = -1. However, it can arbitrarily approach 0 as x approaches positive or negative infinity. So, 0 is excluded from the range. Therefore, the correct answer is: Range = (-∞, 0) ∪ (0, ∞). Note that the range is expressed in interval notation, which uses parentheses to indicate open intervals (excluding the endpoints) and the union symbol (∪) to indicate the combination of two or more sets. In this case, the range consists of all real numbers except 0, expressed as two separate open intervals. The domain is also expressed in interval notation, with the union symbol (∪) used to indicate the combination of two disjoint sets. In this case, the domain consists of all real numbers except -1, expressed as the union of two separate intervals. So, the final answer is: Domain = (-∞, -1) ∪ (-1, ∞) and Range = (-∞, 0) ∪ (0, ∞). I hope this helps! Let me know if you have any further questions. I am here to help! Keep in mind that if you need to use the function f(x) in a real-world context, you should also consider any additional restrictions or conditions that may apply. It's always important to carefully analyze the properties of a function in the context of the problem you are trying to solve.
Step-by-step explanation:
the cost of a luna bar is 2 dollars at harmons. what is the cost of 30 luna bars
Answer:
60
Step-by-step explanation:
2$ times 30 luna bars at harmons is $60
It’s due tomorrow I really need help
Answer:
B.
Step-by-step explanation:
As the steps imply,
Step 1 is to first convert the 3.5% (0.035) and then multiply it by 16 to find out by how many grams the amount should decrease (0.035 * 16 = 0.56). Step 2 is to subtract this amount from 16 to find the amount remaining after one hour (16 - 0.56 = 15.44). Step 3 is to convert 4.25% to a decimal (0.0425) and multiply it by the amount remaining at the end of one hour to find out by how many grams this amount should decrease after two hours (0.0425 * 15.44 = 0.6562)Step 4 finally is to subtract this amount from 15.44 to find the amount remaining after two hours (15.44 - 0.6562 = 14.7838)a) Close the following accounts. 9
K. Emmanuel
$
2020
$
640
360
2020
800
Feb. 10 Bank Cash
25
200
Feb. 1 15
Sales Sales
J. Amaze
$
$
2020
2020
260 1090
1350
Mar. 12
Returns inwards
Mar4
Sales
18
Bank
Z. Ventour
2020
$
2020
$
May 13
Cash
518
May 10
Purchases
518
FSampath
2020
$
2020
July 14 22
Returns outwards
Bank
$
220
July 3
Purchases Purchases
8
25
Bank
800
1500
830
350
Answer:
I dont know the answer I dont know what it is I just needed points bye
Step-by-step explanation:
Cheryl and her sister Diane walk to school along the same route. Cheryl walks at an average of
80 steps per min while Diane walks at an average of 90 steps per min. Cheryl takes steps
of 81 cm each. She takes 12 min to walk to school.
A) If each of Diane's steps in 72 cm, how long does Diane take to walk to school?
Answer: Let's first convert Cheryl's walking speed to meters per minute. Since she takes 80 steps per minute and each step is 81 cm, her walking speed is:
80 steps/min x 81 cm/step = 6480 cm/min
To convert this to meters per minute, we can divide by 100:
6480 cm/min ÷ 100 cm/m = 64.8 m/min
Now, let's find out the distance Cheryl walks to school. Since she walks for 12 minutes at a speed of 64.8 m/min, the distance she covers is:
distance = speed x time = 64.8 m/min x 12 min = 777.6 m
Next, let's find out how many steps Diane takes per minute on average:
90 steps/min
Since each of Diane's steps is 72 cm long, her walking speed is:
90 steps/min x 72 cm/step = 6480 cm/min
To convert this to meters per minute, we can divide by 100:
6480 cm/min ÷ 100 cm/m = 64.8 m/min
So Diane's walking speed is the same as Cheryl's. To find out how long it takes Diane to walk to school, we can use the formula:
distance = speed x time
Since Diane and Cheryl walked the same distance, we can use the distance we found for Cheryl:
777.6 m = 64.8 m/min x time
Simplifying this equation, we get:
time = 12 minutes
Therefore, Diane takes 12 minutes to walk to school.
Answer:
12 min
Step-by-step explanation:
You want to know how long it takes Diane to walk to school if she takes 90 steps of 72 cm per minute, while Cherly takes 80 steps of 81 cm per minute and traverses the distance in 12 minutes.
SpeedThe speed of each girl is the product of the number of steps per minute and the length of the step:
Cheryl: (80 step/min)(81 cm) = 6480 cm/min
Diane: (90 step/min)(72 cm) = 6480 cm/min
Both girls travel at the same speed, so will take the same amount of time to get to school. It takes Diane 12 minutes to walk to school.
Find m/_U. Write your answer as an integer or as a decimal rounded to the nearest tenth.
The measure of angle U = 41.83 degree.
In the given right angle triangle
VW = 6
UV = 9
Since sinΘ = (opposite side)/(hypotenuse)
Therefore,
sin U = VW/UV
= 6/9
= 0.667
Take inverse of sin both sides
∠U = arcsin(0.667)
= 41.83
Hence ∠U = 41.83 degree
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The probability that Rosie goes to the beach after school is 6 11 If she does go to the beach, then the probability that she does her homework is ) If she does not go to the beach, then the probability that she does her homework is 3 4 Work out the probability that Rosie does her homework. Give your answer as a fraction in its simplest form.
The probability that Rosie does her homework is: 27/44
How to find the conditional probability?Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
Thus, we can solve this probability as:
(6/11 * 1/2) + ((1 - (6/11) * 3/4)
= (3/11) + (5/11 * 3/4)
= (3/11) + 15/44
= 27/44
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Can someone help me with this pls
if my circular garden requires 2 cups of water per 10 square feet, how many cups of water do i need when the radius is 3 feet
Find the volume of the composite solid. Round your answer to the nearest hundredth.
To the nearest hundredth, the volume of composite solid, giving us 904.600 cubic metres.
specify the solid volume?How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many unit cubes are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.
For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:
V = l × w ×h
The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and two hemispheres. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.
Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.
V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.
We arrive at a total volume of 792 cubic meters by adding these volumes together.
To the nearest hundredth=904.600 cubic meters.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
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3. How many different numbers can be created by selecting 4 of the digits from the number 8712395?
840 different numbers can be created selecting 4 of the digits from the number
How many different numbers can be created selecting 4 of the digits from the numberFrom the question, we have the following parameters that can be used in our computation:
Number = 8712395
Digits = 4
The count of digits in the number is 7
Using the above as a guide, we have the following:
First digit = any of the 7second digit = any of the remaining 6Third digit = any of the remaining 5Fourth digit = any of the remaining 4So, we have
Numbers = 7 * 6 * 5 * 4
Evaluate
Numbers = 840
Hence, 840 numbers can be formed
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Enter the endpoints as ordered pairs (x, y).
Provide your answer below:
The endpoints of the latus rectum are and
(y + 3)² = (x - 2)
The endpoints of the latus rectum of the parabola are (3, -2) and (3, -4)
Given data ,
Let the equation of the parabola be (y + 3)² = (x - 2)
Now , y² + 6y + 9 = x - 2
y² + 6y = x - 11
Now we can see that the vertex of the parabola is (2, -3), and the axis of symmetry is parallel to the y-axis. This means that the focus and directrix will also be parallel to the y-axis.
x = h - p
where (h, k) is the vertex and "p" is the distance between the vertex and the focus. In this case, (h, k) = (2, -3) and p = 1, so
x = 2 - 1
x = 1
Therefore, the equation of the directrix is x = 1
And , the axis of symmetry of the parabola is parallel to the y-axis, the latus rectum will be parallel to the directrix, and its endpoints will be equidistant from the focus and the directrix
The distance between the focus and the directrix is 1 unit, so the distance between the endpoints of the latus rectum will also be 1 unit
Therefore, the endpoints of the latus rectum will be at the points where the perpendiculars drawn from the focus to the directrix intersect the parabola
To find the points of intersection between this line and the parabola, we can substitute x = 3 into the equation of the parabola and solve for y
(y + 3)² = (x - 2)
(y + 3)² = (3 - 2)
(y + 3)² = 1
y + 3 = ±1
y = -2 or y = -4
Hence , the points of intersection between the perpendicular and the parabola are (3, -2) and (3, -4)
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CAN SOMEONE HELP WITH THIS QUESTION?
The total cost for the first 25 units is given as follows:
$140.
How to obtain the total cost?The marginal cost function is defined as follows:
[tex]c(x) = \frac{14}{\sqrt{x}} = 14x^{-\frac{1}{2}}[/tex]
The total cost function is the integral of the marginal cost function, hence it is given as follows:
[tex]t(x) = \int c(x) dx[/tex]
[tex]t(x) = 28\sqrt{x}[/tex]
Applying the Fundamental Theorem of Calculus, the total cost from x = 0 to x = 25 is given as follows:
t(25) - t(0).
Thus:
t(25) = 28 x 5 = 140.t(0) = 28 x 0 = 0.Hence:
140 - 0 = $140.
(Applying the Fundamental Theorem of Calculus, we subtract the numeric values at each endpoint of the integral).
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20x^2-7x-6=0 by factoring
Answer:
x = -2/5
x = 3/4
Step-by-step explanation:
Factoring:
20x²-7x-6=0
20x²+8x - 15x - 6 = 0
4x * (5x + 2) - 3 * (5x + 2) = 0
(5x + 2) * (4x - 3) = 0
Cases:
5x + 2 = 0
4x - 3 = 0
x = -2/5
x = 3/4
Answer:
20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120
Step-by-step explanation:
now,
20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)
5x(4x-3) +2(4x-3)=0
(5x+2) (4x-3)=0
Either 5x=-2
X=-2/5
Or
4x=3
X=3/4
In the diagram, AB, BC and CD are three sides of a regular polygon F
A
a) Work out the size of angle y.
square polygon P
B
D
square
regular 12-sided polygon
y z
b) Work out the size of angle z.
c) What is the name of polygon P?
Answer:
Step-by-step explanation:
The size of each interior angle of the polygon is 4x+28 °
The value of x is 34 degree and y is 56 degree.
What is a Tangent?Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.
here, we have,
We have, BOA is an isosceles triangle.
< CBO = 90°
So, < DBO = 90 - 56
<DBO = 34
and, <ODB = 34°
Now, let the angle ODB be x
As, from the figure < EBD is also 90°
So, <y = 180 - (90+34) (Angle sum property)
<y = 56
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complete question:
Work out the size of angle x and work out the size of angle y
Justin mowed 45% of her garden in 18 minutes.how many minutes will it take him to mow all of his garden at this rate? Explain
If Justin mowed 45% of her garden in 18 minutes, then we can set up a proportion to find how long it would take him to mow 100% of the garden:
45/100 = 18/x
where "x" is the unknown number of minutes it would take to mow 100% of the garden.
To solve for "x," we can use cross-multiplication:
45x = 100 * 18
Simplifying the right-hand side:
45x = 1800
Dividing both sides by 45:
x = 40
Therefore, it would take Justin 40 minutes to mow all of his garden at the same rate of 45% in 18 minutes.
To explain this, we used the fact that the amount of work done (mowing a certain percentage of the garden) is directly proportional to the time it takes to do that work. This means that if Justin mowed 45% of the garden in 18 minutes, he would take proportionally longer to mow the entire garden. The proportion we set up allows us to find the unknown amount of time it would take to mow the entire garden. Solving the proportion, we found that it would take Justin 40 minutes to mow all of his garden at the same rate he mowed the 45%.