The probabilities in this problem are given as follows:
A. False - negative: 0.08 = 8%.
B. True - negative: 0.48 = 48%.
C. False-negative given that the result is negative: 0.1429 = 14.29%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which the parameters of the formula are given as follows:
P(B|A) is the probability of event B happening, given that event A happened.[tex]P(A \cap B)[/tex] is the probability of both events A and B happening.P(A) is the probability of event A happening.The probability of a false negative is composed as follows:
20% have the flu.Of those, 40% have negative results.Hence:
P(FN) = 0.2 x 0.4 = 0.08 = 8%.
The probability of a true negative is composed as follows:
80% do not have the flu.Of those, 60% have negative results.Hence:
P(TN) = 0.8 x 0.6 = 0.48 = 48%.
The probability of negative results is:
P(N) = P(FN) + P(TN) = 0.08 + 0.48 = 0.56.
Hence the conditional probability is given by:
P(FN|N) = 0.08/0.56 = 0.1429 = 14.29%.
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A zookeeper is 6 14 feet tall. A young giraffe in his care is 93/8 feet tall. How many times as tall as the zookeeper is the giraffe?
solve for x. 7/13=x/48
Answer:
25.7
Step-by-step explanation:
7/13=x/48. By cross multiplication 13 x=326 = 25.7
The ratio of the area between a small square of land and a large squareof land is 3: 7. Given that the total area of the two squares of land is4,000 m2, find the area of each square of land.
Given:
The ratio of the area between a small square of land and a large square
of land is 3: 7.
Total area of the two squares of land (in sq. meter) is 4000.
Required:
The area of each square of land.
Answer:
We have the ratio of the area between a small square of land and a large square of land is 3: 7.
Let
[tex]x^[/tex]be the area of the square of land.
Then their ratio is given by,
[tex]3x^:7x^[/tex]Also given that the total area of the two squares of land (in sq.meter) is
4,000.
The area of
Therefore,
[tex]\begin{gathered} 3x^+7x^=4000 \\ \Rightarrow10x^=4000 \\ \Rightarrow x^=400 \\ \end{gathered}[/tex]Therefore,the area of small square (in sq. meter) is,
[tex]3x=3(400)=1200[/tex]and the area of large square (in sq. meter) is,
[tex]7x=7(400)=2800[/tex]Final Answer:
The area of small and large square respectively (in sq. meter) is,1200 and 2800.
The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?
If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm
Consider the width of the rectangle as w
The length of a rectangle is 3 cm less than twice the width of the rectangle
The length of the rectangle = 2w-3
Perimeter of the rectangle = 75 cm
Perimeter of the rectangle =2(l+w)
Where l is the length and w is the width of the rectangle
Substitute the values in the equation
2(2w-3+w) = 75
2(3w-3) = 75
6w-6 = 75
6w = 81
w = 13.5 cm
The length of the rectangle = 2(13.5)-3
=24 cm
Hence, If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm
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=
O DECIMALS, PROPORTIONS, PERCENTS
Simplifying a ratio of whole numbers: Problem type 1
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
40 L: 72 L
Answer:
5/9
Step-by-step explanation:
You want the reduced fraction equivalent to the ratio 40L : 72L.
Reduced ratioA ratio is reduced by removing the greatest common factor from all parts of the ratio. Here, that factor is 8L.
40L : 72L = (8L)(5) : (8L)(9) = 5 : 9 = 5/9
The ratio is 5/9.
__
Additional comment
The greatest common factor can be found several ways. The easiest is for you to make use of your knowledge of multiplication tables:
40 = 5·8
72 = 9·8
8 is a common factor. Since 5 and 9 have no common factors, 8 is the greatest common factor of 40 and 72.
13. Making an argument. Your friend claims that a line always represents a function. Is your friend
correct? Explain your reasoning
Based on the given argument, it is concluded that my friend's reasoning was incorrect.
What is a Linear Function?This refers to the type of function that represents one line on a linear plane in cartesian mathematics.
With this in mind and from the claim of my friend that a line always represents a function, my friend is incorrect because If the line was vertical, then it could not pass through and as such, cannot represent a function.
Therefore, the answer to the question is that my friend is incorrect in his claim about lines and functions.
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Perform the given operations on the functions
21) f(x)=x² + 3x, g(x) = 2x + 2,
A. (f+g)(x)
B. (f- g)(x)
Answer:
see explanation
Step-by-step explanation:
A
(f + g)(x)
= f(x) + g(x)
= x² + 3x + 2x + 2 ← collect like terms
= x² + 5x + 2
B
(f - g)(x)
= x² + 3x - (2x + 2)
= x² + 3x - 2x - 2 ← collect like terms
= x² + x - 2
please show all work
The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])
What is coordinate plane ?Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.The following is a definition of a coordinate plane: The intersection of the Y-axis, a vertical line, and the X-axis, a horizontal line, creates a coordinate plane, also referred to as a rectangular coordinate plane grid.
The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])
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Volume is 10x3 + 67x2 + 30x − 72, length is 5x − 4, width is 2x + 3
Answer:
height = x + 6
Step-by-step explanation:
Volume = length x width x height
V = 10x³ + 67x² + 30x − 72
length = 5x - 4 and width = 2x + 3
So length x width = (5x - 4 ) x (2x + 3)
Using the FOIL method:
= (5x)(2x) + (5x)(3) + (-4)(2x) + (-4)(3)
= 10x² + 15x - 8x - 12
= 10x² + 7x -12
So to find height, divide Volume by (length x width)
10x³ + 67x² + 30x − 72 ÷ 10x² + 7x -12
Use polynomial long division. See image ( I did the best I could to capture the process)
The answer is x + 6
To verify
Multiply (5x-4) (2x + 3) (x + 6) = 10x³ + 67x² + 30x − 72
In a standard normal distribution, the range of values of z is from _____.
In a standard normal distribution, the range of values of z is from: D. d. -∞ to ∞.
What is a z-score?A z-score is also known as a standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
What is a normal distribution?A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than the data that are far from the mean.
In conclusion, the range of values of z in a standard normal distribution are all real numbers which typically ranges from negative infinity (-∞) to positive infinity (∞).
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Complete Question:
In a standard normal distribution, the range of values of z is from ______.
a. -3.09 to 3.09
b. -1 to 1
c. 0 to 1
d. -∞ to ∞
Which of the following ordered pairs is either the
x- or y-intercept of the function 3x + 2y = -6?
A. (-3,0)
B.(-2,0)
C.(0,2)
D.(0,3)
The length of a ruler is 12 inches. There are approximately 25.4 millimeters in 1 inch.
The length of the ruler is approximately 304.8 millimeters .
Length is used to measure distance.
According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the metre.The longest dimension of an object is typically understood to be what is meant by length.However, this isn't always the case depending on the object's position.The length of a fixed object is referred to by a number of names, including height, also referred to as vertical length or vertical extension, and width, breadth, or depth.Given that there are approximately 25.4 millimeters in 1 inch.
Therefore the length of the ruler = 25.4 × 12 = 304.8 mm
Hence the length of the ruler is approximately 304.8 millimeters .
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Answer:
304.8
Step-by-step explanation:
12*25.4 = 304.8
I need help with this
Answer:
[tex]\text{ 78 miles per hour}[/tex]Step-by-step explanation:
Given the linear function for the traffic fines:
[tex]f(s)=14(s-60)+40[/tex]If a fine comes to $292, substitute f(s)=292 and solve for "s" to find the speed of the person:
[tex]\begin{gathered} 292=14(s-60)+40 \\ 292=14s-840+40 \\ 14s=292+840-40 \\ 14s=1092 \\ s=\frac{1092}{14} \\ s=78\text{ miles per hour} \end{gathered}[/tex]Determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data.
An elementary school has 92 first graders. Because the first graders are all about the same age, they have heights that are pretty similar to one another.
Would it be best to use the mean, median, or mode to describe the height of the first-graders?
Group of answer choices
Mean
Median
Mo
First graders in an elementary school number 92. We use mode.
Given that,
Determine which statistic would be most appropriate to characterize the middle of the next set of data: the mean, median, or mode.
First graders in an elementary school number 92. The first graders' heights are fairly similar to one another because they are all roughly the same age.
We have to find which statistic—the mean, median, or mode—does the first-graders' height best represent.
First graders in an elementary school number 92.
Depending on which their birthday walls, the first graders might be six, seven and eight on the last day of the second year.
Therefore, We use mode.
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Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function
The definition of the functions implies that the value of x if f(x) = g(x) is 3
The solution for the value of xThe equations of the functions are given as
f(x) = -2x + 4
g(x) = 2x - 8
This means that, we have the following equation
f(x) = g(x)
Substitute the known values in the above equation
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms in the above equation
So, we have
2x + 2x = 8 + 4
Evaluate the like terms in the above equation
So, we have
4x = 12
Divide both sides by 4
x = 3
Hence, the value of x such that the equations are equal is 3
The graph of the functionsThe graph of the functions can be plotted using a graphing tool
See attachment for the graph of the functions
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someone help please, dk what to do
Step-by-step explanation:
equation format: y = mx + b where m is slope and b is the y intercept.
From the points given we find that it is a horizontal line, which means slope or m = 0. So we know so far:
y = 0x + b or y = b
The y-intercept occurs where x = 0. This occurs at y = -7. So the equation for these two points:
EQUATION: y = -7
(Plotted graph attached)
Write an equation in standard form for the line that passes through the given points.
(5,0) and (0,3)
The equation of the line in standard form is
(Type your answer in standard form.)
3x + 5y = 15 is the equation of the line in standard form that passes through the point (5,0) and (0,3).
What is the equation of line that passes through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is the slope and b is the y-intercept.
Given the data in the question;
Point 1 ( 5,0 )
x₁ = 5y₁ = 0Point 2 ( 0,3 )
x₂ = 0y₂ = 3First, we determine the slope of the line.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 3 - 0 )/( 0 - 5 )
Slope m = ( 3 )/( -5 )
Slope m = -3/5
Now, we plug the slope and coordinates of one the point into the equation of line to determine the y-intercept b.
y = mx + b
0 = (-3/5)5 + b
Solve for b
0 = -15/5 + b
0 = -3 + b
b = 3
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-3/5)x + 3
Convert to standard form; Ax + Bx = C
Multiply each term by 5
y = (-3/5)x + 3
5y = 5(-3/5)x + 5(3)
5y = -3x + 15
Reorder the equation
3x + 5y = 15
Therefore, the equation of the line is in standard form is 3x + 5y = 15.
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how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
It should be noted that when the graph of a relationship is a line that passes through the origin, then it is proportional.
How to illustrate the information?A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
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Use the square root property to solve the equation.(x + 8)² = 2Select one:O A. (-8+√√2)OB. √2-√√8O C. (√2+8,-√2+8}O D. (-8± √2)
Answer: D
The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
The part "since ∠ AMC is a right angle, ∠BMC and ∠CMD will be complementary" and "since ∠ BMC is a right angle, ∠BMC and ∠AMB will be complementary" , the paragraph proof is incorrect.
We are given that,
∠ AMC and ∠BMC are right angles.
Since,
∠ AMC = ∠ AMB + ∠ BMC
The paragraph part should have been ∠ AMB and ∠ BMC are complementary angles and,
Since,
∠ BMD = ∠ BMC + ∠ CMD
The paragraph part should have been ∠ CMD and ∠ BMC are complementary angles instead of the part given in the paragraph proof.
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using the path method for multivariable limits, demonstrate that the limit doesn't exist:
[tex]lim_{(x,y) \to (1,1)} \frac{x y - x - y + 1}{x^2 + y^2 - 2 x - 2 y + 2}[/tex]
Demonstrating that the limit doesn't exist
What is Limits?
The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are used to define continuity, derivatives, and integrals.
The limit exists only if the value of the limit along every direction that leads to (1,1) is same.
So by calculating,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line x = 1
Similarly,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line y = 1
And the last limit you calculated is along line y=x.
To answer your question, the calculation of the limit along y=1 would not have been necessary. It is sufficient to demonstrate the absence of a limit by giving just two cases in which it appears to vary along several directions.
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convert 0.43 to a percent
Answer:
43%
Step-by-step explanation:
To convert a decimal to a percent, you have to move the decimal over 2 times to the right.
Shauna calculated the net sales for her company using the following figures: Gross sales = $72,900 Sales discounts = $2,450 Purchase returns and allowances = $3,750 Sales returns and allowances = $2,550 The net sales of Shauna's company are __________.
The net sales of Shauna's company when she calculated the sales for her company using the figures is $66700.
What are net sales?The total of a company's net sales is its gross sales less any returns, allowances, and discounts. Externally, net sales calculations are not always obvious. They can frequently be taken into account when calculating top-line revenues that are shown on the income statement.
The total number of units sold is multiplied by the price per unit for the purpose of calculating gross sales. The term "returns" or "sales returns" refers to products that customers have sent back in exchange for reimbursement.
The nets sales based on the information given will be:
Gross sales = $72900
Less: Retuned sales = $3750
Less Discount = $2450
Net sales = $66700
Therefore, the net sale is $66700.
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Simplify the fraction 112 144 as much as possible.
Answer:
7/9
Step-by-step explanation:
Answer:
7/9
Step-by-step explanation:
I took the quiz
Where do you find a vertical shift in the exponential parent function?
What happens when (x-4) is in the exponent?
What happens when (x+9) is in the exponent?
Where do you find a horizontal shift in the exponential parent function?
What happens when there is a +7 at the end of the exponential parent function?
What happens when there is a -6 at the end of the exponential parent function?
For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
How to work with vertical and horizontal shifts?
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
If N > 0, the shift is upwards.If N < 0, the shift is downwards.For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
If N > 0, the shift is to the left.If N < 0, the shift is to the right.Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
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Please help me with this question
Notice from the graph that data are mostly to the right.
Answer: Option C The distribution is tailed.
I need the answer ASAP
In order to rationalize the denominator of the fraction, we need to multiply the fraction by the conjugate of the expression in the denominator.
The conjugate is the same expression but with the signal between the numbers changed.
So we have:
[tex]\frac{4}{3+\sqrt[]{7}}=\frac{4}{3+\sqrt[]{7}}\cdot\frac{3-\sqrt[]{7}}{3-\sqrt[]{7}}=\frac{4(3-\sqrt[]{7})}{3^2-(\sqrt[]{7})^2}=\frac{12-4\sqrt[]{7}}{9-7}=\frac{12-4\sqrt[]{7}}{2}[/tex]So the new denominator of the fraction is 2, therefore the correct option is D.
3.5 divided by 85
answers:
at least 500/ at least 50/ at least 20/ at least 200
Ive looked up answers to this question in iready but everyone says the answer is 24?
The value of 3.5 divided by 85 will be 0.4118.
What is division?Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.
Division's opposite is multiplication. Dividend Divisor = Quotient + Remainder is a formula for calculating the division of two numbers.
The dividend in this situation refers to the number that is being divided. The divisor is the number that divides the number (dividend) into equal parts.
In this case, 3.5 ÷ 85 = 0.4118. This can be computed through the use of a calculator.
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A pedestrian signal at a crosswalk has the following cycle: "WALK” for 45 seconds, "DON'TSTART" for 30 seconds and "DONT WALK" for 40 seconds. What is the probability the signalwill show "DON'T START" if you arrive at a random time? Write your answer as a percentagerounded to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
The probability is represented by the following equation:
[tex]undefined[/tex]18 is 50% of what????????
Let the unknown value be x.
18 is 50% of ________n can also be written as;
18 = 50% of x
of means multiplication;
18 = 50% * x
18 = 50/100 * x
18 = 50x/100
cross multiply
18 * 100 = 50x
1800 = 50x
Divide both sides by 50
1800/50 = 50x/50
180/5 = x
x = 180/5
x = 36
Hence 18 is 50% of 36