Ella can type faster than Andrew because the rate at which she types is faster than Andrew's rate by 0.5 text per second.
What is rate of change?In Mathematics, rate of change can be defined as a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.
In this scenario, we would determine the rate of change with respect to the amount of words that Andrew and Ella can type per second as a ratio. For the amount of words that Andrew can type per second, we have:
Andrew = 7/21 = 28/84 = 1/3 or 1:3.
For the amount of words that Ella can type per second, we have:
Ella = 4/14 = 16/56 = 1/3.5 or 1:3.5
Difference = 3.5 - 3
Therefore, we can logically conclude that Ella can type faster.
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Ali is collecting signatures for a petition. He currently has 520 signatures. He has 6 more weeks to collect the remaining signatures he needs. He needs a total of at least 1,000 signatures before he can submit the petition. Ali wants to collect the same number of signatures each week. Write and solve the inequality for the situation
An inequality that represents the number of signatures Ali needs to collect in each of the remaining weeks so that he will have enough signatures to submit the petition: 520 + 6m ≥ 1000
and the minimum number of signatures he needs to collect = 80
Given that Ali wants to collect the same number of signatures each week.
Assume that Ali collects m number of signatures each week.
He has 6 weeks to collect the remaining signatures he needs.
So, by unitary method in 6 weeks the number of signatures he would collect:
6 × m
He currently has 520 signatures and he needs a total of at least 1,000 signatures before he can submit the petition.
so, we get an inequality.
520 + 6m ≥ 1000
We solve above inequality.
6m ≥ 1000 - 520
m ≥ 480/6
m ≥ 80
Ali needs to collect at least 80 signatures, so that he will have enough signatures to submit the petition.
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6) Set up and solve an equation to
find x PLEASE SHOW WORK AND ALSO TELL ANSWER I NEED HELP also it is NOT 37.5
Answer:
is not 37.5
it's 25
Step-by-step explanation:
25+25+15+115=180
50+130=180
180=180
Answer:
25°
Step-by-step explanation:
25 + x + 15 = 3x – 10 ( Sum of two opposite interior angles is equal to the exterior angle)
40 + x = 3x - 10
40 + 10 = 3x - x
50 = 2x
[tex]x = \frac{50}{2} [/tex]
x = 25°
Please help I have a learning disablity
Find the value of x that makes a true statement.
24 + x = 24
x =
Answer:
24 + x + 24
X is 0
Answer: substract 24 from both sides
then x = 0
Step-by-step explanation:
The residents of downtown neighborhood designed a triangular-shaped park as part of a city beautification program. The park is bound by streets on all sides. The second angle of the triangle is 5 degrees more than the first. The third angle is 5 degrees less than four times the first. Find the measures of the angle
The triangular park has three angles: 60°, at its base, 55° at its top, and 65° at its base.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
As part of a civic beautification initiative, residents in a downtown neighbourhood created a park with a triangle shape.
Let's say that the initial angle is x°.
Accordingly, the second angle is (x + 5)° and the third angle is (5x - 5)° from the information provided.
The inner angles of a triangle are known to add up to 180 degrees.
∴ x + (x + 5) + (x - 5) = 180°
3x = 180°
x = 180°/3
x =60 °.
Hence, the triangular park has three angles: The triangular park has three angles: 60°, at its base, 55° at its top, and 65° at its base.
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What are the values of sin cos and tan?
Step-by-step explanation:
bhshshssf just use some time and fouries and fouries and I don't have a car but who wants the French
The sum of three consecutive integers is 27. Find the value of the greatest of the three.
Answer: The greatest of the three is 10.
Step-by-step explanation:
27/3=9 so the numbers will be around nine.
8+9+10=27
Answer:
Let x represent the value of the smallest of the three consecutive integers.
Then, the value of the middle integer is x+1, and the value of the greatest integer is x+2.
Since the sum of the three integers is 27, we have:
x + (x+1) + (x+2) = 27
Combining like terms, we have:
3x + 3 = 27
Subtracting 3 from both sides, we have:
3x = 24
Dividing both sides by 3, we have:
x = 8
Therefore, the value of the smallest integer is 8, the value of the middle integer is 8+1 = 9, and the value of the greatest integer is 8+2 = 10.
Thus, the value of the greatest integer is 10.
Step-by-step explanation:
What is the probability that andre olivia and zack all win gift cards that are at least $25
The probability that Andre, Olivia, and zack all win gift cards that are at least $25 is 1/4. Hence option C is the correct option.
What is an event?
An event is a collection of experiment results (a subset of the sample space) to which a probability is ascribed in probability theory.
The wheel consists of 8 equal sections. Each section contains the price of a gift card. 4 sections contain a $5 gift card, 2 sections contain a $5 gift card, one section contains a $25 gift card, one section contains a $50 gift card.
To win at least $5, they have to get either $25 or $50.
Thus the number of outcomes of favorable event is 2.
Total number of outcomes is 8.
The probability to win at least $25 is 2/8
Divide denominator and numerator by 2:
2/8 = 1/4
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7•e^.1t =47 express the solution as a logarithmic in base e
Answer:
The value of t is 19.04
Step-by-step explanation:
[tex]7e^{0.1t} = 47\\[/tex]
[tex]e^{0.1t} = \frac{47}{7}[/tex]
take log both sides :
[tex]ln(e^{0.1t}) = ln(\frac{47}{7}) \\0.1t = 1.9042\\t = \frac{1.9042}{0.1}\\t = 19.04[/tex]
A small business makes bottles of
temonade. Today, they have 528 ounces
of lemonade to bottle. Each bottle holds
24 ounces of lemonade. They sell each
bottle for $2.
Write two equations with variables that
can be used to find how many dollars
the business will receive by selling all of
the bottles.
The amount of money that the business will receipt is $44.
given:
Small business makes bottles of lemonade today they have 528 oz of lemonade to the bottle each bottle holds 24 oz of lemonade they sell each bottle for $2 how much money will the business receipt
From the above question:
24oz of Lemonade = 1 bottle
528 oz of Lemonade = x
Cross Multiply
24 × x = 528
x = 528/24
x = 22 bottles
We are told that: they sell each bottle for $2
Hence:
1 bottle = $2
22 bottles = y
Cross Multiply
y = 22 × $2
y = $44
Therefore, the amount of money that the business will receipt = $44
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Tom is adding soil to his raised garden bed. The depth of the soil is currently 8 inches, and for each bag of soil he adds, the depth will increase by 1/2 of an inch. You can use a function to describe the depth of the soil in the garden bed after Tom adds x bags of soil.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x.
The function that describes the depth of the soil is h(x) = -(1/2)x + 8.
Where x is the number of bags of soil.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Depth of the soil = 8 inches
One bag of soil increases by 1/2 of an inch.
Now,
The function denotes the depth of the soil.
h(x) = -(1/2)x + 8
Where x is the number of bags of soil
Thus,
The function is h(x) = -(1/2)x + 8.
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A new disease has been observed, and experts believe that 1% of the population have it. A test is developed that has 95% true positive rate (it identifies 95% of people with the disease as "positive") and 1% false positive rate (it misidenfies 1% of people without the disease as "positive"). If Alice tests positive and the experts are right on the population prevalence, what is the probability that Alice has the disease (up to 2 decimal places)?
If Alice tests positive and the experts are right on the population prevalence, the probability that Alice has the disease is 0.489.
In the given question, a new disease has been observed, and experts believe that 1% of the population have it.
A test is developed that has 95% true positive rate and 1% false positive rate.
From the given data,
Let E be the event that a patient has a disease and F be the event that a patient has tested positive.
Then according to Bayes' theorem we have,
P(E/F) = P(E)P(E/F)}/(P(E)P(E/F)+P(E')P(F/E')
P(E/F) = (1*95)/(1*95)*(99*1)
P(E/F) = 95/194
P(E/F) = 0.489 (approx.)
Hence, the probability that Alice has the disease 0.489.
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Left Riemann sum approximation Question...
The left Riemman sum approximation for f(x) = x^5, between x = 0 and x = 5, considering 5 intervals, is given as follows:
5.3248.
How to obtain the Riemman sum approximation?First we must obtain the Delta value, which is the difference between the bounds of the integral, divided by the number of integrals, thus:
[tex]\Delta_x = \frac{b - a}{n} = \frac{2 - 0}{5} = 0.4[/tex]
Then the values of x at which the numeric values are calculated are obtained as follows:
[tex]x_i = a + \Delta_x(i - 1)[/tex]
Thus the values of x are of:
[tex]x_1 = 0[/tex].[tex]x_2 = 0.4[/tex][tex]x_3 = 0.8[/tex][tex]x_4 = 1.2[/tex][tex]x_5 = 1.6[/tex]The numeric values are given as follows:
f(0) = 0^5 = 0.f(0.4) = 0.4^5 = 0.01024.f(0.8) = 0.8^5 = 0.32768.f(1.2) = 1.2^5 = 2.48832.f(1.6) = 1.6^5 = 10.48576.Then the Riemann sum approximation for the integral is given as follows:
[tex]\sum_{i = 1}^{n} \Delta_x f(x_i)[/tex]
Thus:
0.4(0 + 0.01024 + 0.32768 + 2.48832 + 10.48576) = 5.3248.
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what is the total cost with sales tax? price 120.00 tax 5%
Answer:
5% of 120 is 6, so you would add that 6 to 120.
120 + 6 = 126.
The total cost will sales tax would be $126.00.
Step-by-step explanation:
Hope it helps! =D
What are the different types of time complexity analysis available?
There are five different types of Time complexity analysis:
Constant Time ComplexityLogarithmic Time Complexity Linear Time Complexity O(n log n) Time ComplexityQuadratic Time ComplexityWhat is Time complexity?
The computational complexity that describes the amount of computer time required to run an algorithm is known as time complexity in computer science. The time complexity of an algorithm is commonly estimated by counting the number of elementary operations performed by the algorithm, assuming that each elementary operation takes a fixed amount of time to perform.
As a result, the time required and the number of elementary operations performed by the algorithm are assumed to be proportional. Because the running time of an algorithm varies among different inputs of the same size, the worst-case time complexity, which is the maximum amount of time required for inputs of a given size, is commonly considered.
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The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by f(p)= -50p2 + 1600p - 11,000, where p is the price per shirt and f (p) is the monthly profit based on that price. (a) Find the price that generates the maximum profit. (b) Find the maximum profit. (c) Find the price(s) that would enable the company to break even. If there is more than one price, use the "and" button. Part 1 of 3 (a) The price that generates the maximum profit is S 16 Part 2 of 3 (b) The maximum profit is $ 1800 Part: 2/3 Part 3 of 3 (c) The price(s) that would enable the company to break even:
The price that maximize the profit is $10 or $22.
What is maximum profit?
In economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit.
Given:
f(p) = -50p^2 + 1600p - 11000
Now to find velocity point
[tex]-\frac{b}{2a} = \frac{-1600}{2(-50)} = \frac{1600}{100} = 16[/tex]
So for the price p = 16 that generates maximum profit.
Now
f(16) = -50(16)^2 + 1600(16) - 11000 = 1800
The maximum profit is 1800.
At breakeven, f(p) = 0
So,
[tex]-50p^2 + 1600p - 11000 = 0\\p = \frac{-1600 + -\sqrt{(1600)^2 - 4(-50)(-11000)} }{2(-50)} \\p = \frac{-1600 + - \sqrt{2560000 - 2200000} }{-100} \\p = \frac{-1600+-\sqrt{360000} }{-100} \\p = \frac{-1600+-600}{100}\\ p = 10, 22[/tex]
So p = $10 or p = $22
Hence, the price that maximize the profit is $10 or $22.
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Explain why the initial value of any function of the form
f(x)= a(b) is equal to a.
Hello there!
Initial value is the y-intercept so x = 0. Then b⁰ = 1 because x⁰ = 1 if x ≠ 0. So the value of function is a * 1 which is equal to a.
Step-by-step explanation: The initial value of any function of the form f(x)= a(b) is equal to a because this type of function is a linear equation, which means that the rate of change (slope) is constant. This means that the output is always equal to the input multiplied by a constant, which is the coefficient a. Therefore, when the input (x) is equal to 0, the output (f(x)) is equal to 0 multiplied by a, which is equal to a.
The age at which small breed dogs are fully housebroken follows a Normal distribution with mean ms = 6 months and standard deviation ss = 2. 5 months. The age at which large breed dogs are fully housebroken follows a Normal distribution with mean mL = 4 months and standard deviation sL = 1. 5 months. Let xS – xL represent the sampling distribution. Be sure show all work and conditions. Let the sample size for both sets be 25 dogs. Should we be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs? Explain your answer
The answer is no, we would not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.
HOUSEBROKEN AGE PROBABILITYThe sampling distribution for the difference in sample means, xS - xL, is also normally distributed with a mean of ms - mL = 6 - 4 = 2 months.The standard deviation of √((ss²/nS) + (sL²/nL)) = √((2.5²/25) + (1.5²/25)) = 0.5 months, where nS and nL are the sample sizes for the small and large breed dogs, respectively.Using a z-score, we can calculate the probability of observing a sample mean difference of at least 3 months between the small and large breed dogs, given that the true difference in population means is 2 months. This probability can be found using the standard normal table or calculator.The z-score formula is (x - mu) / sigma, where x is the observed sample mean difference, mu is the population mean difference, and sigma is the standard deviation of the sampling distribution.z = (3-2) / 0.5 = 2
The probability of observing a z-score of 2 or greater is approximately 0.0228, or 2.28%. This is a small probability, so we would be surprised if the sample mean housebroken age for small breed dogs was at least 3 months more than the sample mean housebroken age for the large breed dogs.So, the answer is no. Not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.Learn more about Probability here:
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For a project in his Geometry class, Elijah uses a mirror on the ground to measure the height of his school building. He walks a distance of 8. 25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0. 8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1. 45 meters. How tall is the school? Round your answer to the nearest hundredth of a meter
The school is 24.63 meters tall.
To calculate the height of the school, Elijah can use the concept of similar triangles. Since the mirror is on the ground and parallel to it, the angle between the ground and the line from his eyes to the mirror is 90 degrees. The angle between the ground and the line from his eyes to the top of the school is also 90 degrees. The triangle formed by these lines and the line from his eyes to the top of the school is similar to the triangle formed by these lines and the line from his eyes to the mirror.
Using the similar triangles, the ratio of the height of the school to the distance from Elijah's eyes to the mirror is equal to the ratio of the distance from Elijah's eyes to the ground to the distance from the mirror to the school.
Therefore
(Height of school) / (Distance from eyes to mirror) = (Distance from eyes to ground) / (Distance from mirror to school)
Plug in the given values:
(Height of school) / 0.8 = 1.45 / (8.25 - 0.8)
Solving for the height of the school:
Height of school = (0.8 * 1.45) / (8.25 - 0.8)
= 1.16 / 7.45
= 0.1562
= 24.63 meters
The school is 24.63 meters tall.
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Circumference question
1. Suppose a bottle of Buckley's has a radius of 2cm. If you created a label for this product. What is the length of this label?
2. Assumes the company uses 22cm x 12cm boxes for delivery to stores. How many vials will be in each box?
suppose the price of each vial is $5.00. What is the cost of a box?
Write four different expressions for the perimeter of a square whose sides are all s 2 2 units long.
Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both.
What are expressions in maths?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.For a square whose side are 2 units long is :
= 2 + 2 x 2 + 2
= ( 2 + 2 ) x 2
= 2 x 4
= 2 x 3 + 2 = 8
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Arlene buys a phone case and charging cord for 15% off. The original cost of the phone case is $18. Her total discount is $4. 20.
Write and solve an equation to find the original price of the charging cord, x
The equation to find the original price of the charging chord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.
Let the price of the phone case is x.
And the price of the charging cord is y.
Discounted price for phone case: 15% of x = 0.15x
Discounted price for charging cord = 0.15y
Now, according to the question, the total discount is $4. 20
⇒0.15x + 0.15y = 4.20
⇒0.15 * 18 + 0.15y = 4.20
⇒2.7 + 0.15y = 4.20
⇒0.15y = 4.2 - 2.7
⇒y = 1.5/0.15
⇒y = $10
Therefore the equation to find the original price of the cord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.
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Find the equation of the line that goes through ( 5, 3 ) and ( − 1, 2 ). Select one: a. x + 6y + 13 = 0 b. x − 6y + 13 = 0 c. 6x + y + 13 = 0 d. 6x − y + 13 = 0
Answer:
C.
Step-by-step explanation:
To find the equation of the line that goes through the points (5, 3) and (-1, 2), we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
To find the slope of the line, we can use the following formula:
m = (y2 - y1)/(x2 - x1)
Plugging in the coordinates of the two points, we get:
m = (2 - 3)/(-1 - 5) = -1/6
Substituting this value of m and the coordinates of one of the points into the point-slope form, we get:
y - 3 = -1/6(x - 5)
This simplifies to:
6x + y - 13 = 0
Therefore, the equation of the line is:
6x + y - 13 = 0
What is the slope of this line? (5 points)
Show all work.
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{3 +4}{4 +2} \implies {\large \begin{array}{llll} \cfrac{7 }{ 6 } \end{array}}[/tex]
How do you check if an inverse is a function?
If a value of y relates only to one value of x, then the function does have an inverse function.
Define the term function and its inverse?A relation between such a collection of inputs and outputs is known as a function.
A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is just the input.If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f does have an inverse (passing from the vertical line test).Thus, if a value of y relates only to one value of x, then the function does have an inverse function.
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What is the slope of this line? (5 points)
Show all work.
Slope of the line AB is 7/6.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the given graph the coordinates of A are (4, 3) and B is (-2, -4)
Slope AB=-4-3/-2-4
=-7/-6
Slope=7/6
Hence, slope of the line AB is 7/6.
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If 27³+27³+27³=27x,what is the value of x?
Answer:
x = 2,187
Step-by-step explanation:
27×27×27+27×27×27+27×27×27 =27x
19,683+19,683+19,683 =27x
59,049 = 27x
divide both sides by the coefficient of x ( 27 )
59,049 / 27 = 27x / 27
x = 2,187
Can you help me with this
The graph of the line y = 4x + 3 is shown below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 4x + 3
When x = 0, y = 3
When x = 1, y = 4 + 3 = 7
When x = 2, y = 11
Similarly for negative x values, we get,
x = -1, y = -4 + 3 = -1
x = -2, y = -8 + 3 = -5
So on......
So we must get the following coordinates:
(-1, -1), (-2, -5), (0, 3), (1, 7), (2, 11),, ........
Thus,
The graph is shown below.
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If 14 more than the product of -3 and a number x
is less than 56, which values could represent x?
Check all that apply. Write and solve the inequality.
-17
-14
■
-21
-2
-9
-15
bring the variable to the left side and bring all the remaining values to the right side.
How do you write a step-by-step inequality?Image search results for Write the inequality and solve it. -17 -14 ■ -21 -2 -9 -15
To fix an inequality, use these steps:
Step 1: Remove fractions by multiplying all terms by the fractions’ least common denominator.
Step 2 Simplify the inequality by merging like words on either side.
Step 3 Subtract or add amounts to get the unknown on one side and the digits on the other.
In algebra, the letter “x” is frequently used to represent an unknown value. It is referred to as a “variable” or “unknown” at times. X is a variable in x + 2 = 7, but we can deal with it.
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What is the mole of o2?
The number of mole O₂ is 2. Since the subscript of oxygen denotes the number of moles.
What is a diatomic element?
Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).
One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.
The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.
The subscript part of a chemical compound represents the number of moe of the chemical compound. The subscipt of O₂ is 2. Thus the number of mole is 2.
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A store marks up a laptop 150% from its original price of $399. There is a sale for 25% off all items in the store. What is the sale price for the computer
Answer:
multiply the original price ($299) by the first markup percentage (150%)
299*1.50= $448.50
that is markup price!
then you have to do the sale % (25%)
so you'll multiply your (25%) by your new price ($448.50)
448.50*.25= $112. 125
then you will subtract the sale price ($112.125) by the upcharged price ($448.50)
448.50-112.125= 336. 375
= $336. 38(round off)