Answer
P(A∩B) = 0.021
Step-by-step explanation:
For independent events P(A∩B) is the same as P(A)*P(B) so for this 0.42*0.05 = 0.021
Type the correct answer in each box. Use numerals instead of words.
If x>0, what values of c and d make the equations true?
Equation A √448 x⁽=8 x³ √7 x
Equation B ∛576 xᵃ=4 x ∛9 x²
In equation A, c is
In equation B, d is
The value of c in the equation A is 7 and the value of d in the equation B is 5
The first equation is
[tex]\sqrt{448x^c}=8x^3 \sqrt{7x}[/tex]
Move the term 8x^3 inside the square root
[tex]\sqrt{448x^c}=\sqrt{7x(8x^3)^2}[/tex]
Multiply the terms in the equation
[tex]\sqrt{448x^c}=\sqrt{448x^7}[/tex]
Here the both terms are equal. Therefore the value of x^c and the x^7 will be equal.
Then the value of c = 7
Part 2
The second equation is
[tex]\sqrt[3]{576x^d}=4x\sqrt[3]{9x^2}[/tex]
Move the term 4x inside the square root
[tex]\sqrt[3]{576x^d}=\sqrt[3]{9x^2(4x)^3}[/tex]
Multiply the terms in the equation
[tex]\sqrt[3]{576x^d}=\sqrt[3]{576x^3}[/tex]
Here the both terms are equal. Therefore the value of x^d and the x^5 will be equal
Then the value of d = 5
Therefore, the value of c = 7 and the value of d = 5
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Select the correct answer.
Solve the following.
√50 x 3√2 = ?
6√13
10
30
6
30 is the correct answer.
The square root of 50 is 5x sqrt of 2 and the multiplied by 3 becomes 15 times 2 = 30 because the two square roots of 2 multiplied together become 2.
5 x 3 x 2 = 30
WILL MARK BRAINLIEST
Your friend Samir very excitedly tells you about opening his new checking account. “I’m so glad they only had a minimum opening amount of $50! I will leave my money in there so it can grow!” What is some advice you might give to Samir? Responses A checking account isn’t very safe, so you should hide your money in your mattress instead A checking account isn’t very safe, so you should hide your money in your mattress instead A checking account is the best place to leave your money because of the high interest rates A checking account is the best place to leave your money because of the high interest rates A checking account won't grow your money much because of low interest rates and fees A checking account won't grow your money much because of low interest rates and fees A checking account won’t be good because it will be difficult to get your money into and out of A checking account won’t be good because it will be difficult to get your money into and out of
Answer:
A checking account is the best place to leave your money because of the high interest rates.
Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C.F(x,y) = (e^x -3 y)i + (e^y + 6x)jC: r = 2 cos thetaThe answer is 9 pi.
the work done by the force F on a particle moving counterclockwise around the closed path C is 9π by integral.
Green's Theorem states that:
∮C F · dr = ∫∫D (∂Q/∂x - ∂P/∂y) dA
Where C is the boundary of the region D, P and Q are the components of the vector field F, and dr is the vector differential along the boundary C.
In this case, the region D is a circle with radius 2, so we can express the boundary C as r = 2 cos θ. We also need to calculate the components of the vector field F. These are P = e^x - 3y and Q = e^y + 6x.
Plugging these values into Green's Theorem, we get integral:
∮C F · dr = ∫∫D (∂Q/∂x - ∂P/∂y) dA
= ∫∫D (e^y + 6 - (-3)) dA
= ∫∫D (e^y + 9) dA
= ∫ 0 2π ∫ 0 2 (e^2 cosθ
+ 9) (2 dθ)
= 4π ∫ 0 2 (e^2 cosθ + 9) dθ
= 9π
Therefore, the work done by the force F on a particle moving counterclockwise around the closed path C is 9π.
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For this philosopher, the existence of human beings is not reduced to the realization of an essence thought by God; man exists to the extent that he is carried out, it is the set of his acts and nothing else.
The philosopher who thought that the existence of human beings is not reduced to the realization of an essence thought by God has been Jean-Paul Sartre.
¿Who was Jean-Paul Sartre?This character was a Frenchman who had several professions and stood out in different branches, Jean-Paul Sartre was:
PhilosopherWriterNovelistPlaywrightPolitical activistBiographerLiterary criticJean-Paul Sartre is recognized for being an exponent of existentialism and humanist Marxism, among his thoughts, he himself thought that man exists to the extent that he is realized.
¡Hope this helped!
Solve for x, (7x-4) (73)
Answer:
x = 11
Step-by-step explanation:
Angles EIC and DJH are alternate exterior angles, which means they're congruent and equal.
Therefore, we can find x by setting the two angles equal to each other:
[tex]7x-4=73\\7x=77\\x=11[/tex]
Cash 25 selects 6 numbers between 1 and 25.where repetition isn’t allowed but order doesn’t matter?
organic chemists often purify organic compounds by a method known as fractional crystallization. an experimenter wanted to prepare and purify 4.85 g of aniline. ten 4.85-gram specimens of aniline were prepared and purified to produce acetanilide. the following dry yields were obtained: 3.85, 3.88, 3.90, 3.62, 3.72, 3.80, 3.85, 3.36, 4.01, 3.82 construct a 95% confidence interval for the mean number of grams of acetanilide that can be recovered from 4.85 grams of aniline. assume that the obtained dry yields of acetanilide are i.i.d. and approximately normally distributed with an unknown mean and variance.
As calculated from the given data the confidence interval for μ is (3.65, 3.91).
Let X_1,..,X_nX 1 ,..,X n are n observations
from population with mean μ.
Than sample mean
= n1i=1/n∑X i
Sample variance is defined by,
s = 1/( n-1 )∑(X i - mean) ²
n = sample size = 10
c = 95%
therefore ,
mean = 37.82/10
=3.782
variance = 0.29556/9
=0.03
Data points' variance from the mean is a measure of how they vary. A variance, according to Layman, is a measurement of how widely apart a set of data (numbers) are from their mean (average) value.
Finding the expected difference of deviation from the actual number is what is meant by variance. As a result, variance is influenced by the data set's standard deviation.
Data is more dispersed from its mean the higher the variance value, and less dispersed from mean if the variance value is low or minimal. As a result, it is referred to as a measure of data spread from mean.
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if an exponentiated logistic regression coefficient, i.e. exp(b), is greater than one, when its associated x-variable increases, predicted odds will decrease, holding other x-variables constant.
For the exponential logistic regression coefficient Exp(b) is greater than one it represents the associated x-variable increases and the corresponds to predicted odds will decrease and holding other variables constant is false statement.
As given in the question,
Exponential logistic regression coefficient Exp(b) or given odds ratio, is the predicted change value in odds for a unit value increase in the predictor.The Exp represents the exponential value of b. When Exp(b) is less than 1, and increases values of the x- variable correspond to the decreasing odds of the occurring event's .Here exp(b) is greater than 1 which represents all the all other coefficients should lies between 0 and 1 or less than one.Therefore, the exponential logistic regression coefficient Exp(b) is greater than one it represents the associated x-variable increases is a false statement.
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PLEASE HELP WILL MARK BRAINLIEST
Answer: C. [tex]y=2(x+4z)[/tex]
Step-by-step explanation:
[tex]m=\frac{0-8z}{-4z-0}=2\\\\\therefore y=2x+8z=2(x+4z)[/tex]
What is the value of s?
10
units
The value of s is 17.
What is the Pythagorean theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given
AB = 5, BD = 15
We have to find AD.
By applying the Pythagorean Theorem, we get
AB² + BD² = AD²
5² +15² = AD²
AD² = 289
AD = 17
Hence, the value of s is 17.
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7.) Bart is required to pass out 80 flyers for an upcoming event. He passes out an average of 10 flyers per minute. The situation can be represented using the function f(x)=80-10x where x represents time in minutes.
a.) Create a graph of the situation
After finding the point from the given function, we draw the graph. The graph of the given function is given below:
In the given question, Bart is required to pass out 80 flyers for an upcoming event. He passes out an average of 10 flyers per minute.
The situation can be represented using the function f(x)=80-10x
where x represents time in minutes.
We have to create a graph of the situation.
To create the graph we firstly find the value of f(x) for x=0,1,2,3,..............
The given function is f(x) = 80-10x
Now put x = 0
So f(0) = 80-10(0)
f(0) = 80-0
f(0) = 80
Now put x = 1
So f(1) = 80-10(1)
f(1) = 80-10
f(1) = 70
Now put x = 2
So f(2) = 80-10(2)
f(2) = 80-20
f(2) = 60
Now put x = 3
So f(3) = 80-10(3)
f(3) = 80-30
f(3) = 50
Now put x = 4
So f(4) = 80-10(4)
f(4) = 80-40
f(4) = 40
Now the table is
x 0 1 2 3 4
f(x) 80 70 60 50 40
Firstly we denote the point in the graph then we connect the all point to form a graph.
The graph of the given function is given below:
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What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?
As x→-co, Y→- and as x→∞o, y →→∞
As x→-co Y→- and as x→∞ Y→∞
As x→-co, Y→∞ and as x→∞o, y →-co
As x→-co, y →∞and as x→∞o, y →∞
The end behavior of the graph of the polynomial function (x)=3x⁶+ 30x⁵ + 75x⁴ is x→±∞, y→∞.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial function is f(x)=3x⁶+ 30x⁵ + 75x⁴
y=f(x)=3x⁴(x+5)²≥0
The zeros are 0, 0, 0,0,-5 and -5.
x-intercept ( y = 0 ): x = -5.
Local mini/max turning points ( y' = 0 ): 0 0, 0, -10/3 and -5.-,
As x→±∞, y→∞.
Hence, the end behavior of the graph of the polynomial function (x)=3x⁶+ 30x⁵ + 75x⁴ is x→±∞, y→∞.
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Answer:
the 4th option
Step-by-step explanation:
ed2023
7. suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. use the 68-95-99.7 rule to find the percentage of buyers who paid: a. between $147,700 and $152,300 if the standard deviation is $2300. b. more than $154,800 if the standard deviation is $2400.
a. 68 % between $147,700 and $152,300 if the standard deviation is $2300
b. 2.5 % more than $154,800 if the standard deviation is $2400
Given that:
Prices of a certain model of a new home are normally distributed with a mean of $150,000.
Using the 68-95-99.7 rule , find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.
Let X = prices of a certain model of a new home
SO, X ~ Normal ( μ = 150,000 , σ = 2,300 )
z score probability distribution for normal distribution
Z = X - μ / σ
where μ population mean price = $150,000
σ standard deviation = $2,300
According to 68-95-99.7 rule;
Around 68% of the values in a normal distribution lies between μ - σ and μ +σ .
Around 95% of the values occur between μ - 2σ and μ + 2σ .
Around 99.7% of the values occur between μ - 3σ and μ + 3σ.
Find the z scores for both given values
Z = X - μ / σ
= [tex]\frac{147,700 - 150,000}{2,300}\\ \\ \\[/tex]
= -1
Z = X - μ / σ
= [tex]\frac{152,300 - 150,000}{2,300}[/tex]
= -1
The z score indicates that the category of between μ - σ and μ +σ .
Therefore , this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.
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The table of values represents a proportional relationship.
What is the constant of proportionality in the relationship, written as an improper fraction (fraction greater than one)?
X Y
2 3
6 9
The constant of proportionality in the relationship is 3/2
How to determine the constant of proportionality in the relationshipFrom the question, we have the following parameters that can be used in our computation:
X Y
2 3
6 9
The above represents the table of values
Since the data on the table of values represents a proportional relationship, then the constant of proportionality is
Constant of proportionality = Y/X
So, we have
Constant of proportionality = 3/2
Hence, the constant of proportionality is 3/2
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Use the given conditions.
tan(u) = -3/4, 3π/2 < u < 2π
(a) Determine the quadrant in which u/2 lies.
O Quadrant I
O Quadrant II
O Quadrant III
O Quadrant IV
(b) Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas.
sin(u/2) =
=
cos(u/2) =
tan(u/2)
Submit Answer
The quadrant in which u/2 lies is II quadrant.
What is Quadrant?
Quadrant is a business intelligence tool that helps companies extract, analyze, and visualize data from multiple sources in real-time. It enables users to create actionable insights to improve decision-making, optimize operations, and increase profitability. Quadrant provides an intuitive platform for teams to uncover hidden trends and correlations in data, develop predictive models, and generate reports. It also allows users to customize dashboards and create interactive visualizations. Quadrant simplifies data analysis and helps teams make more informed decisions.
a) tan(u) = -3/4, 3π/2 < u < 2π
[tex]\frac{3\pi }{2} < u < 2\pi \\\\270^{o} < u < 360^{o}\\\\Dividing\ both\ side\ by\ 2\\\\135^{o} < \frac{u}{2} < 180^{o}[/tex]
u/2 lies in II quadrant.
b) We have half angle formula's,
[tex]sin(\frac{u}{2} )= \sqrt[]{\frac{(1-cos\\ u)}{2} } \\[/tex]
[tex]sin \frac{u}{2} = \frac{3}{5}[/tex]
[tex]cos(\frac{u}{2} )= \sqrt[]{\frac{(1+cos\ u)}{2} } \\[/tex]
[tex]cos\frac{u}{2} =\frac{4}{5}[/tex]
[tex]tan(\frac{u}{2} )= \sqrt[]{\frac{(1-cos\ u)}{sin \ u} } \\[/tex]
[tex]tan(\frac{u}{2} )= \frac{3}{4}[/tex]
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sage measured her rectangular house is 15.24m long and 9.1m wide. using her calculator she multiply the length by the width
Therefore, the area of rectangular house is 138.684 [tex]m^{2}[/tex].
Specify the area.The size of a region on a planar or curved surface can be expressed mathematically using the idea of area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas the term "plane area" refers to the area of a shape or planar lamina.
Here,
Given :
the length of the rectangular house =15.24 m
the width of the rectangular house = 9.1 m
thus, we find the area of rectangular house
Using formula,
=> Area= length * width
=> Area = 15.24 * 9.1
=> Area = 138.684 [tex]m^{2}[/tex]
Therefore, the area of rectangular house is 138.684 [tex]m^{2}[/tex].
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which of the following statements are true regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable? select all that apply. multiple answers: multiple answers are accepted for this question select one or more answers and submit. for keyboard navigation...show more a f(x)
The likelihood that a random cumulative variable will fall within a specific range of values rather than taking on a single value is specified by the Probability Density Function.
The probability density function (PDF), also known as the density of a continuous random variable, is a function whose value at any specific sample (or point) in the data point (the range of potential values for the random variable) can be understood as having given a relative likelihood that the value of something similar to the random variable would be closer to that sample.
There is no absolute probability that a random variable will take on any specific value because there are an unlimited number of alternative values to begin with. However, the PDF value at two samples can be used to estimate how much more likely it is for the random variable to have that particular value in any given draw.
The Cantor distribution, which although having no discrete component, does not assign positive probabilities to any specific locations, and discrete random variable probability distributions do not all have a density function.
A distribution has a density function if and only if the cumulative distribution function F(x) is fully continuous. In this case, F is typically always differentiable, and its derivative can be used to symbolize the probability density.
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Bob bought a sofa on sale for $134.40. This price was 68% less than the original price. What was the original price?
Answer:
$420
Step-by-step explanation:
To find the original price, we need to determine how much the sale price was discounted, and then add that amount back to the sale price. Since the sale price was 68% less than the original price, the discount was 100% - 68% = 32% of the original price.
To find the amount of the discount, we multiply the original price by the discount percentage: 32% * original price = $134.40
Dividing both sides of the equation by the discount percentage gives us the original price: original price = $134.40 / (32% * 1) = $134.40 / 32% = $420.
Therefore, the original price of the sofa was $420.
The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). 50 points!!!
The value of the area of the shaded region in the circle is 4π - 8.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The longest line which can be drawn inside the circle will be the diameter.
As per the given circle,
By Pythagoras' theorem,
LN = √(4² + 4²) = √32
Radius r = LN/2 = √32/2
Area of shaded region = area of the semicircle - the area of right angle triangle.
A = π(√32/2)²/2 - (1/2) × 4 × 4
A = (32π)/8 - 8
A = 4π - 8
Hence, "The circle's shaded region's area has a value of 4 to 8".
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Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.6
hours per week. The standard deviation of the sample was 2.3. Estimate the mean of the population with 99% confidence.
Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final
answers to one decimal place.
0
6
Answer:
The mean of the population with 99% confidence is between 43.1 and 46.1
Step-by-step explanation:
The mean of the population with 99% confidence and The standard deviation of the sample was 2.3, which is between 43.07 to 46.13.
What is mean?Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Given:
A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.6 hours per week, X = 44.6
The standard deviation of the sample was, n = 2.3,
The confidence = 99%,
1 - α = 99%
α = 1 - 0.99
α = 0.01
Calculate the margin of the error as shown below,
[tex]E = Z_{\alpha /2} \ Mean / standard\ deviation[/tex]
E = 2.576 × 2.3 / √15
E = 1.5298
Calculate the mean as shown below,
X - E < Mean < X + E
44.6 - 1.5298 < Mean < 44.6 + 1.5298
43.07 < Mean < 46.13
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[tex]f(x)= 5\sqrt{x^2}[/tex]
The values of f(x) for x = 1, 2, 3, 4, 5, ,,,, are 5, 10, 15, 20, 25, 30, , , ,
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
f(x) = 5 √x²
√x² = x
f(x) = 5x
For x = 1, 2, 3, 4, 5, ,,,,,,
f(1) = 5
f(2) = 10
f(3) = 15
f(4) = 20
f(5) = 25
Thus,
The final expression is f(x) = 5x.
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To do a case insensitive compare which of the following could be used to test the equality of two strings, str1 and str2?
The following can be used to test the equality of two strings str1 and str2
.(str1.equalsIgnoreCase(str2))
.(str1.compareToIgnoreCase(str2)==0)
what is string?A string is a series of character in computer programming,either as a literal constant or some sort of variables.it must be enclosed in quotation for it to be recognized as a string.It is used for sorting text or character.The term string can also refer to more general arrays or other sequence data type and structures.
what is string compare?The string = compare two strings and is true if they are same (corresponding character are identical) but is false if they are not same.
The function equal calls string =if applied to two string.The string () compare two string character by character.if string are equal the function return to zero.
Therefore, the given test can be used to find the equality and compare of the string.
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PLEASE QUICK I NEED IT NOW URGENT!!
c) For the high jump, each competitor receives multiple opportunities to clear the bar at each height. On average, Shane completes 3 out of 3 jumps on the lowest bar, 5 out of 6 jumps on the middle bar, and 3 out of 4 jumps on the highest bar. What is
Shane’s overall average number of jumps completed? (2 points)
d) If Shane’s average number of jumps completed is greater than one-half, then the eighth graders earn 50 points. Which grade should be awarded 50 points**? (1 point)
Answer:
c) To find Shane's overall average number of jumps completed, we need to add up the total number of jumps he completed at each height and divide by the total number of jumps he attempted.
At the lowest height, Shane completed 3 out of 3 jumps, for a total of 3 completed jumps.
At the middle height, Shane completed 5 out of 6 jumps, for a total of 5 completed jumps.
At the highest height, Shane completed 3 out of 4 jumps, for a total of 3 completed jumps.
In total, Shane completed 3 + 5 + 3 = 11 jumps out of a total of 3 + 6 + 4 = 13 jumps attempted.
His overall average number of jumps completed is 11 / 13, or approximately 0.85 jumps.
d) Since Shane's average number of jumps completed is greater than one-half (0.5), the eighth graders should be awarded 50 points
Step-by-step explanation:
For your other question A and B for A Correct! To find the total distance thrown by Claire and Grace, you first converted the mixed numbers 5/8 and 3/5 to fractions with a common denominator (in this case, 40), then added those fractions together to find the total distance in fraction form. Finally, you converted the fraction 49/40 back to a mixed number and added it to the whole number distances thrown by Claire and Grace to find their total distance.
The total distance thrown by Claire and Grace is 82 feet 9/40 inches, or approximately 82.225 feet. For B also Correct! Since the total distance thrown by Claire and Grace is not greater than 83.7 feet, the eighth graders should be awarded 50 points.
PLEASE HELP WILL MARK BARINLIEST
The length of the side AB of the triangle ACB will be equal to 12.72.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices.
Triangles can be divided into a variety of categories according to their sides and angles.
As per the given information in the question,
As we can see, the triangle ACB in the figure,
AC = 9 cm
Angle = 45°
cos θ = B/H
cos 45° = 9/H
1/√2 = 9/H
H = 12.72 cm
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the folllowing is a trues statement ab out safety stock: safety stock only applies to independent demand invenstory
Yes, this is true. Safety stock is an inventory strategy used to ensure that a company has enough of a particular item in stock to meet customer demand.
It is typically used to protect against unexpected changes in demand and/or supply, and is most applicable to independent demand inventory.
Safety stock is an inventory strategy used to ensure that a company has enough of a particular item in stock to meet customer demand. It is typically used to protect against unexpected changes in demand and/or supply. These changes can include anything such as supplier delays, unexpected customer orders, or seasonal fluctuations. Safety stock is most applicable to independent demand inventory, which is inventory that is driven by customer demand and not production requirements. Therefore, the statement that safety stock only applies to independent demand inventory is true.
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Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
.
Answer:
The answer is 6 days
Step-by-step explanation:
$30 - $18 = $12
$12 / $1.99 = 6.03015075377= 6 days
A bag contains 100 marbles which are red, green, and blue. suppose a student randomly selects a marble without looking, record's the color,and then places the marble back in the bag the student has recorded 7 red marbles, 2 green marbles and 11 blue marbles. predict how many green marbles are in the bag
Answer: 10 marbles
Step-by-step explanation:
First, arrange all the numbers of marbles that the student picked in a ratio
red:green:blue
7:2:11
When adding all the coloured marbles that the student picked together, you get 20 marbles or "parts" as you would usually say in ratio.
Then, it would be helpful to rewrite the ratios as fractions, with 20 as the denominator:
[tex]\frac{7}{20}:\frac{2}{20}:\frac{11}{20}[/tex]
However, the bag contains 100 marbles so we should have 100 as the denominator instead of 20. 20 is a fifth of 100, so in this case, we would multiply everything (the numerator and the denominator) by 5:
[tex]\frac{7*5}{20*5} :\frac{2*5}{20*5} :\frac{11*5}{20*5}[/tex]
[tex]\frac{35}{100}:\frac{10}{100}:\frac{55}{100}[/tex]
Therefore, you could predict you would get 35 red marbles, 10 green marbles, and 55 blue marbles.
Which of the following functions represent the graph g(x) above?
Answer:
The first one, G(x)=| x+4 |
Step-by-step explanation:
find the nth maclaurin polynomial for the function f (x )space equals space sin space x comma space space n space equals space 5. the coefficient of x to the power of 5 is
The nth maclaurin polynomial for the function sinx= x -[tex]\frac{x^{3} }{3!}[/tex]+[tex]\frac{x^{5} }{5!}[/tex]-[tex]\frac{x^{7} }{7!}[/tex]+[tex]\frac{x^{9} }{9!}[/tex]
we can find this by using maclaurin series.
what is expansion of function?A relation in which involving one or more variables.It represent partial function as sum of power in one variables or by sum of power of other function.
what is maclaurin series used for?It can be used to approximate function ,find the antiderivative of complicated function or compute on otherwise uncomputable sums.It is a type of series expansion in which all terms are non-negative integer power of the variables.
Now given a function is
f(x)=sinx n=5
Using x=0 the given equation becomes
f(0)= sin(0) = 0
Now taking derivative of given function and using x=0
Then we have
[tex]f_{1}[/tex](x)= cosx [tex]f_{1}[/tex](0)=cos(0)=1
[tex]f_{2}[/tex](x)=-sinx [tex]f_{2}[/tex](0)=sin(0)=0
[tex]f_{3}[/tex](x)= - cosx [tex]f_{3}[/tex](0)= - cos(0)= -1
[tex]f_{4}[/tex](x)= sinx [tex]f_{4}[/tex](0)= sin(0) = 0
[tex]f_{5}[/tex](x)=cosx [tex]f_{5}[/tex](0)= cos(0)= 1
and so on.
Now using maclaurin polynomial series
f(x)=f(0)+x[tex]f_{1}[/tex](0)+[tex]\frac{x^{2} }{2!}[/tex][tex]f_{2}[/tex](0)+ [tex]\frac{x^{3} }{3!}[/tex][tex]f_{3}[/tex](0)+[tex]\frac{x^{4} }{4!}[/tex][tex]f_{4}[/tex](0)..............
by putting the value in the above series
sinx=0+x(1)+[tex]\frac{x^{2} }{2!}[/tex](0) +[tex]\frac{x^{3} }{3!}[/tex](-1)+[tex]\frac{x^{4} }{4!}[/tex](0)........
sinx=x -[tex]\frac{x^{3} }{3!}[/tex]+[tex]\frac{x^{5} }{5!}[/tex]-[tex]\frac{x^{7} }{7!}[/tex]...
Hence this is the 5th term maclaurin series.
To learn more maclaurin polynomial visit the link;
https://brainly.com/question/24188694
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