The probability that an athlete used steroids, given that they tested positive, is approximately 0.5025%.
In order to calculate the probability that an athlete used steroids given the information provided, we need to know the probability that they tested positive. To do this, we can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, we are trying to find the probability that an athlete used steroids (A) given that they tested positive (B). We know that the probability of A is 1% and the probability of B is 0.5%, so we can calculate P(A and B) by multiplying these two probabilities together:
P(A and B) = 1% * 0.5% = 0.005%
Next, we need to calculate P(B), which is the probability that the athlete tested positive. Since we know the false positive rate and the true positive rate of the test, we can use these to calculate P(B) using the formula:
P(B) = P(A and B) + P(not A and B)
P(B) = P(A|B) * P(B) + P(not A|B) * P(B)
P(B) = 0.99 * 0.005% + 0.005 * (1 - 0.005%)
P(B) = 0.00495% + 0.005 * 0.999
P(B) = 0.0099495%
Now that we have P(A and B) and P(B), we can plug these values into the formula for conditional probability to calculate the probability that an athlete used steroids, given that they tested positive:
P(A|B) = P(A and B) / P(B)
P(A|B) = 0.005% / 0.0099495%
P(A|B) = 0.5025%
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Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x=98.13, y=100.6, r=0.904, P-value=0.000, ŷ=14.68+0.88x, where x represents the IQ score of the twin born first. Find the best predicted value of ModifyingAbove y with caret given that the twin born first has an IQ of 104? Use a significance level of 0.05.
The best-predicted value of Modifying Above y with caret given that the twin born first has an IQ of 104 is 106.2.
The dependent variable's predicted value in basic linear regression is given by the equation = b0 + b1x.
In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. (the error is the difference between the predicted value and the actual value of y).
Use regression equation
ŷ=14.68+0.88x
plug in IQ, which is x
y = 14.68 + 0.88(104)
= 106.2
Hence, the answer is 106.2
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A body moving at an initial velocity of 30m|s and accelerates at 60m|s in 12s & then is uniformly decelerated to rest if the total time taken is 16s find the distance in metres during acceleration
Using equation of motion to calculate the distance covered during acceleration is 540m
What is DistanceDistance is the total length between two points, while displacement is the length between two points, but it also takes into account the direction of the motion. Distance is a scalar quantity, while displacement is a vector quantity.
In this problem, we can either draw a velocity - time graph or proceed to solve using equations of motions.
We are required to calculate the distance covered during the period of acceleration.
Data;
Initial velocity (U) = 30 m /sFinal velocity (V) = 60 m/sTime = 12sa = v - u / t
a = acceleration
a = (60 - 30) / 12
a = 30 / 12
a = 2.5 m/s²
But we have another equation as
v² = u² + 2as
s = distance
60² = 30² + 2*2.5*s
x = 540
The distance covered is 540m
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what is the relationship between the variance and the standard deviation? a) variance is twice the standard deviation. b) variance is the square root of the standard deviation. c) there is no constant relationship between the variance and the standard deviation. d) variance is the square of the standard deviation.
The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.
What is variance?The variance of a random variable from its true population or sample mean is expected in probability theory and statistics. The term "variance" refers to a measurement of how widely apart a group of numbers are from one another.
Here,
Variance and standard deviation are both measures of spread. They calculate the deviation of each data point from the mean. The range of data increases with increasing variation. Using the original unit of measurement, the standard deviation measures the same thing as the variance (whereas variance is the original unit squared).
Therefore ,The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.
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Spontaneous dental hydroplosion is a disease makes your teeth spontaneously turn into liquid. To investigate whether a new drug can prevent the onset of this disease, Jim Halpert decided to perform a study in which half of the fourteen employees at Dunder Mifflin Scranton received the drug and the other half received a placebo. Neither Jim nor the employees were told who received which treatment, and the number of times a subjectâs teeth turned into liquid was recorded. This is an example of (A) A double-blind experiment. (B) A matched-paired experiment. (C) An experiment, but neither double-blind or matched-pair. (D) An observational study. In order to make thorough conclusions, the most important condition for statistical inference is usually that (A) the population distribution follows a Normal distribution exactly. (B) the data does not contain outliers. (C) the data follows the asymmetric, single-peaked distribution. (D) the data can be treated as a random sample from the population of interest. A study was taken at the large senior living retirement community, The Senior Living Community, found that the average age of residents is 73 years with a standard deviation of 6.1 years. A simple random sample of 100 residents is selected and the sample mean age !Ì("x-bar") of these residents is calculated. you know that the random variable X has approximately a normal distribution because of (A) the central limit theorem. (B) the 68-95-99.7 rule. (C) the population that youâve sampled from does not have a Normal distribution. (D) the law of large numbers.
For the study for investing the result of drugs in a particular diseases,
(1)This is an example of double blind experiment. So,correct option is option A
(2) The Correct option is option (C) i.e. the data can be treated as a random sample from the population of interest.
(3) The random variable X has approximately a normal distribution because of Central Limit Theorem i.e the Correct option is option (A).
Here , Spontaneous hydrostatic collapse is a disease in which teeth spontaneously turn into fluid. Jim Halpert decided to perform a study to find out if new drugs can prevent the development of this disease.
1. Since, neither researcher nor the employees were told who received which treatment, this is an example of a double-blind experiment.
2. In order to make thorough conclusions, the most important condition for statistical inference is usually that data can be treated as a random sample from the population of interest.
3. The sample mean age, X-bar of these residents has approximately a normal distribution because of the central limit theorem. Hence, we get all required answers for asking questions.
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in triangle ABC, AB = 5, BC = 6, and AC= 7 , the the nearest degree, what is the measurment of angle ABC
how can i find it
Answer:
∠ ABC ≈ 78°
Step-by-step explanation:
using the Cosine rule in Δ ABC
cos ABC = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]
where a is the side opposite ∠ A , b is the side opposite ∠ B and c the side opposite ∠ C
here a = BC = 6 , b = AC = 7 and c = AB = 5 , then
cos ABC = [tex]\frac{6^2+5^2-7^2}{2(6)(5)}[/tex] = [tex]\frac{36+25-49}{60}[/tex] = [tex]\frac{12}{60}[/tex] , then
∠ ABC = [tex]cos^{-1}[/tex] ( [tex]\frac{12}{60}[/tex] ) ≈ 78° ( to the nearest degree )
PLEASE HELP ASAP
1. bisect an angle
2.copy an angle
3.construct a perpencicular line to a point not on the line
4. copy a segment
Answer:Bisect an angle :)
Step-by-step explanation:
select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x 5)4 2x2 5 = 0 6(2x 4)2 = (2x 4) 2 6x4 = -x2 5 8x4 2x2 – 4x = 0
An equation is quadratic if the greatest power of the coefficients is 2. Hence, for the given equations, only 6(2x + 4)2 = (2x + 4) + 2 is quadratic in nature.
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation with one variable that goes like this: x ax2 + bx + c = 0. with a ≠ 0 .
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. The answer could be simple or complicated.
Why it is called quadratic equation?
In mathematics, a quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring."
This vocabulary is based on the fact that a square's area is equal to the product of its side length and itself. The Latin word quadratum, which means square, is where the word "quadratic" derives.
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The complete question is -
Select all of the following equation(s) that are quadratic in form.
x4 – 6x2 – 27 = 0
3x4 = 2x
2(x + 5)4 + 2x2 + 5 = 0
6(2x + 4)2 = (2x + 4) + 2
6x4 = -x2 + 5
8x4 + 2x2 – 4x = 0
Which of the following is NOT valid for proving that triangles are congruent? (A) AAA, (B) ASA (C) SAS, (D) HL
Answer:
A) AAA
Step-by-step explanation:
This proved similarity, but not necessarily congruency. If the angles are the same in a triangle, they could be smaller and larger versions of themselves. They will have the same shape, but not necessary the same size. The side lengths will be proportional. If the scale factor between the two triangles is 1 , then the triangles would be congruent, but they could have any scale factor greater or less than 1 too.
State the relationship between the congruent angles
Answer:
1. Alternate exterior angles
2. Vertically opposite angles
3. Alternate interior angles
4. Corresponding angles
sales at a fast-food restaurant average $6,000 per day. the restaurant decided to introduce an advertising campaign to increase daily sales. to determine the effectiveness of the advertising campaign, a sample of 49 days of sales were taken. they found that the average daily sales were $6,300 per day. from past history, the restaurant knew that its population standard deviation is about $1,000. the restaurant wishes to test whether sales have increased as a result of the advertising campaign. if the level of significance is 0.05, what is the decision?
Answer: The null and alternative hypothesis 6000 > 6000 This is an one tailed test Test statistic 6300 = 1000 n= 49 Thus , test statistic is = 2.1 Q1. At 0.025 le
Step-by-step explanation:
Thomas increased the amount of water she gives her plants from 2 cups to 2 1/2 cups. By what percentage did Thomas increase the amount of water?
find f(2), f(3), f(4), and f(5) if f is defined recursively by f(0) = f(1) = 1 and for n = 1, 2, …
As a set of inputs with one output for each, a function is defined as a relationship between them.
What is meant by functions?An equation, rule, or law in mathematics that establishes the link between the independent variable and the dependent variable (the dependent variable). Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.
We have given, f(0) = 3 for all parts.
a) f(n+1) = -2 f(n)
For f(1) put f(n) = f(0), f(0+1) = -2 f(0)
f(1) = -2(3) = -6
For f(2) put f(n = 1), f(1+1) = -2 f(1)
f(2) = -2(-6) = 12
For f(3) put f(n) = f(2), f(2+1) = -2 f(2)
f(3) = -2(12) = -24
For f(4) put n = 3, f(3+1) = -2 f(3)
f(4) = -2(-24) = 48
For f(5) put n = 4, f(4+1) = -2 f(4)
f(5) = -2(48) = -96
b) f(n+1) = 3, f(n) + 7
For f(1) put n = 0, f(0+1) = 3 f(0)+7
f(1) = 3(3)+7 = 16
For f(2) put n = 1, f(1+1) = 3 f(1)+7
f(2) = 3(16)+7 = 55
For f(3) put f{n}=f{2}, f(2+1)=3 f(2)+7
f(3) = 3(55) + 7 = 172
For f(4) put n = 3, f(3+1) = 3 f(3)+7
f(4) = 3(172)+7 = 523
For f(5) put n = 4, f(4+1) = 3 f(4)+7
f(5) = 3(523)+7 = 1576
c) f(n+1) = f(n)²-2 f(n)-2
For f(1) put n = 0, f(0+1) = f(0)²-2 f(0)-2
f(1) = 3²-2(3)-2 = 1
For f(2) put n = 1, f(1+1) = f(1)²-2 f(1)-2
f(2) = 1²-2(1)-2 = -3
For f(3) put n = 2, f(2+1) = f(2)² - 2 f(2) - 2
f(3) = -3² - 2(-3) - 2 = 13
For f(4) put n = 3, f(3+1) = f(3)² - 2 f(3) - 2
f(4) = 13² - 2(13) - 2 = 141
For f(5) put n=4, f(4+1) = f(4)² - 2 f(4) - 2
f(5) = 141² - 2(141) - 2 = 19597
d) f(n+1)[tex]=3^{\frac{f(n)}{3}}$[/tex]
For f(1) put n = 0, f(0+1) [tex]$=3^{\frac{f(0)}{3}}$[/tex]
f(1) = [tex]3^{\frac{3}{3}}[/tex] = 3
For f(2) put n = 1, f(1+1) [tex]=3^{\frac{f(1)}{3}}$[/tex]
f(2) [tex]=3^{\frac{3}{3}}[/tex] = 3
For f(3) put n = 2, f(2+1) [tex]=3^{\frac{f(2)}{3}}$[/tex]
f(3) [tex]=3^{\frac{3}{3}}[/tex] = 3
For f(4) put n = 3, f(3+1) [tex]$=3^{\frac{f(3)}{3}}$[/tex]
[tex]$f(3)=3^{\frac{3}{3}}=3$[/tex]
For f(4) put n = 3, f(3+1) = [tex]$3^{\frac{f(3)}{3}}$[/tex]
f(4) [tex]$=3^{\frac{3}{3}}[/tex] = 3
For f(5) put n = 4, f(4+1) = [tex]3^{\frac{f(4)}{3}}$[/tex]
f(5) [tex]=3^{\frac{3}{3}}[/tex] = 3
The complete question is:
Find f( 1 ) , f( 2 ) , f( 3 ) , f( 4 ) , and f( 5 ) if f(n) is defined recursively by f( 0 ) = 3 and for n = 0 , 1 , 2 ,... a) f(n + 1 ) = − 2 f(n) . b) f(n + 1 ) = 3 f(n) + 7. c) f(n + 1 ) = f(n) 2 − 2 f(n) − 2. d) f(n + 1 ) = 3 f( slader
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f(2)=4, f(3)=7, f(4)=19, f(5)=40
What is a function?
In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially provided the contemporary concept of function in 1837.
Given, the function is f(n+1) = f(n) + 3f(n-1)
Calculating f(2) by substituting n=1 in the above equation.
f(2) = f(1) + 3f(0)
⇒f(2) = 1 + 3
⇒f(2) = 4
f(3) is calculated by substituting n=2
f(3) = f(2) + 3f(1)
⇒f(3) = 4 + 3
⇒f(3) = 7
f(4) is calculated by substituting n=3
f(4) = f(3) + 3f(2)
⇒f(4) = 7 + 12
⇒f(4) = 19
f(5) is calculated by substituting n=4
f(5) = f(4) + 3f(3)
⇒f(5) = 19 + 21
⇒f(5) = 40
f(2)=4, f(3)=7, f(4)=19, f(5)=40
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(b) Work out the value of 52 + 23
To find the sum of 52 + 23 is the value is worked to be 75
What is addition in math ?Combining things and counting them as one big group is done through addition.
In math, addition is the process of adding two or more integers together.
Addends are the numbers that are added, and the outcome of the operation, or the final response, is referred to as the sum.
How to find the value of 52 + 23In this problem the addends include
52 and23The applying the addition operation
= 52 + 23
= 45
The sum is solved to be 75
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=99(1.04)^4
The percentage rate of increase or decrease of the function y=99(1.04)^4 is 4%
What is an exponential function?This is a type of function that are of 3 main parts
the starting or initial value
base function
the exponents
Considering the given problem, y=99(1.04)^4
the starting = 99
the base = 1.04
the exponents = x
The base is what determines increase or decrease with a base of 1.04 shows a percentage increase is 4%
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Plss help only question 12
Answer:
Step-by-step explanation:
Let's try negative number for n.
n = -3
(n+1)/n
(-3 + 1)/-3 => -2/-3
=> 0.66
Which is less than 1, so therefore the original statement is false
which expression is not equivlent to 8 + ( n - 4)
Answer: The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.
Given :
Expression - 8 + (n - 4)
To simplify the given expression following steps can be used:
Step 1 - Rewrite the given expression.
= (n - 4) + 8
Step 2 - Now, remove the parenthesis in the given expression.
= n - 4 + 8
Step 3 - Now, write 8 as the addition of 4 and 4.
= n - 4 + 4 + 4
Step 4 - Subtract 4 by 4.
= n + 4
5) Consider the equation : y=7x+8
and the linear function represented by the table of values below. Select all of the statements that are correct.
The correct students about the function are;
B: The function represented by the table has a greater rate of change.
C: The function y = 7x + 8 has the greatest y-intercept.
How to Interpret the Function Table?We are looking at the equation;
y = 7x + 8
The general equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, the slope of the given equation is 7 while the y-intercept is 8.
From the table, the rate of change which is also is simply the slope from the formula;
m = (y₂ - y₁)/(x₂ - x₁)
m = (32 - 16)/(4 - 2)
m = 8
Looking at the given options, only options that are correct are Options B and C.
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according to statistics reported on cnbc, a surprising number of motor vehicles are not covered by insurance. sample results, consistent with the cnbc report, showed 46 out of 200 vehicles were not covered by insurance. Develop a 95% confidence interval for the population proportion
The 95% confidence interval for the given population proportion is between 0.1716 to 0.2884.
How to find the confidence interval for a population proportion?The confidence interval for a population proportion is calculated by the formula,
[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]
Where [tex]\bar{p}[/tex] is the sample proportion and α is the level of significance.
Calculation:It is given that,
The statistics reported on CNBC projects, a surprising number of motor vehicles are not covered by insurance. The sample results are
The sample size n = 200;
The number of successes = 46
So, the sample proportion [tex]\bar{p}[/tex] = 46/200 = 0.23
For a 95% confidence interval, the level of significance is
α = 1 - 95/100 = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
Then, the z-score for the value 0.025 is
[tex]z_{\alpha/2}[/tex] = 1.96 (from the table)
Thus, the confidence interval is
[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]
⇒ C.I = 0.23 ± (1.96) × [tex]\sqrt{\frac{0.23(1-0.23)}{200} }[/tex]
⇒ C.I = 0.23 ± 1.96 × 0.0298
⇒ C.I = 0.23 ± 0.0584
So, the upper limit is 0.23 + 0.0584 = 0.2884 and the lower limit is 0.23 - 0.0584 = 0.1716.
Therefore, the 95% confidence interval for the given population proportion lies between 0.1716 to 0.2884.
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Which equation represents a circle with a diameter of 10 units that is centered at (3,-7)
The equation of the given circle is
[tex](x - 3)^2 + (y + 7)^2 = 25[/tex]
What is a circle?
Circle is a two dimensional round figure in which every point on the figure maintains a fixed distance from a point known as the center of the circle.
The fixed distance is called the radius of the circle.
Diameter of circle = 10 units
Radius of the circle = [tex]\frac{10}{2}[/tex] = 5 units
Coordinates of center = (3, -7)
Equation of circle = [tex](x - 3)^2 + (y - (-7))^2 = 5^2[/tex]
[tex](x - 3)^2 + (y + 7)^2 = 25[/tex]
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7. There are 84 people going camping.
a) A bus can take 42 people. How many buses
would be needed?
b) A van can take 12 people. How many vans
would be needed?
c) A car can take 4 people. How many cars
would be needed?
Answer: A) 2 buses B) 7 vans C) 21 cars
Step-by-step explanation:
You divide 84 by the number of people the vehicle can take.
For a. 84/42=2, so you need 2 buses.
For b. 84/12=7, so you need 7 vans
For c. 84/4=21, so you need 21 cars
Solve for x, please help finals are in a day and I have a D in this class(Geometry)
Answer:
x = 2
Step-by-step explanation:
In order to find the value of x, first we need to prove ∆ABC and ∆ADE as similar ∆s.So, let's prove:In ∆ABC and ∆ADE,[tex]\angle ABC \cong \angle ADE....(each \: 90\degree)[/tex][tex]\angle BAC \cong \angle DAE....(common \: \angle s)[/tex][tex]\implies \triangle ABC \sim \triangle ADE[/tex] (By AA postulate)[tex]\implies \frac{AB}{AD}=\frac{BC}{DE}....(csst) [/tex][tex]\implies \frac{2}{2+x}=\frac{1}{2}[/tex][tex]\implies {2+x}=4[/tex][tex]\implies {x}=4-2[/tex][tex]\implies {x}=2[/tex]5x+2y-2z=-57
3x-10y-z=-11
Y=-2
First up is 5x+2y-2z=-57
5x+2y-2z=-57 /You gotta subtract 27 and 2z from both sides
5x+2y-2z- (2y-2z)=-57- (2y-2z) Then simplify-5x =-57-2y+2z
Then divide by both sides:
Answer is: x=-57-2y+2z / over 5
what is the slope of the line whose equation is -3x 8y = -10.
Given a line with the equation -3x+8y=-10, its slope can be calculated using the slope intercept form of the line that is 3/8.
What is slope?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies). The slope of a line in mathematics indicates how steep a line is. It is also referred to as the gradient. The "change in y" over the "change in x" of a line is referred to as the slope.
Here,
-3x+8y=-10
y=mx+c
where m=slope of line
8y=3x-10
y=3x/8-10/8
slope=3/8
The slope of given line whose equation is -3x+8y=-10 is 3/8 using slope intercept form of line.
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what are the solutions of the equation x4 3x2 2 = 0? use u substitution to solve. and x = ±1 and x = ±i and x = ±i and x = ±1
The solutions of the equation is found for the values of x = ±√2i or x = ±i.
Explain the term imaginary number?A number that produces a negative square root is referred to as an imaginary number. Fundamentally, an imaginary number is indeed the square root of such a negative number does not have a concrete value.An equation x⁴ + 3x² + 2 = 0, has been presented to us.
We are asked to discover the solutions of our supplied equation using substitution.
Our provided equation can be rewritten as: x⁴ + 3x² + 2 = 0
Considering that: u = x²
u² + 3u + 2 = 0
Factorizing the equation;
(u + 2)(u + 1)
or, u = - 2 and u = -1.
When we re-substitute the value of u, we obtain:
x² = -2 or x² = -1
x = ±√-2 or x = ±√-1
x = ±√(-1).2 or x = ±√-1
Now we shall employ imaginary unit i. That is a fact i² = -1.
x = ±√i².2 or x = ±√i²
x = ±√2i or x = ±i
Consequently, the solution obtained for the equation are- x = ±√2i or x = ±i.
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if line segment c b. bisects ∠acd, what additional information could be used to prove δabc ≅ δdbc using sas? select three options.
A) m∠ABC = 125° and AB ≅ DB ; B) ΔACD is isosceles with base AD ; D) CD = 52 cm.
What exactly are triangles?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the three sides' end-to-end connections at a point. The triangle's three angles add up to 180 degrees in total.
Knowing that ACD is isosceles with base AD indicates that AC and DC are congruent. As a result, we have two sides that are at an angle, or SAS.
A congruent relationship exists between AC and CD if we know that CD = 52 cm. As a result, we are left with two sides that include an angle.
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3 workers can load a truck in 8 minutes
The number of extra workers that are needed is 1 extra worker
How many workers are needed?If three workers load the truck in 8 minutes we have that:
3 workers = 8 minutes
We know that if we wanted to reduce the time at, for example, half, we would need to increase the workers in a half. More generally, if we want to reduce the time in 1/X me need to multiply the workers by X.
Here me need to reduce the time in 6/8 as 8*6/8 = 6.
So, we will need:
3*8/6 = 24/6 = 4 workers.
So, we will need 1 more worker as we already have 3.
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Complete question
Three workers can load a truck in 8 minutes. How many workers need to join this team so that they can load that truck in 6 minutes?
He sold a car for 247,250 at a profit of 15%, what was the price of the car?
Answer: Cost Price = 21,50,000
Step-by-step explanation:
He fits all of his boxes exactly into a larger box with a volume of 1,152
cubic inches. How many gift boxes are in the larger box? Explain how you know.
Enter the correct numbers in the boxes to complete the statement and equation.
on solving the provided the question, we got know that - width = 6 in, length = 16 in, and height = 12 in
Waht is factor?Decomposing or decomposing an entity (number, matrix, polynomial, etc.) into another entity or product of coefficients, the multiplication of which yields the original number, matrix, etc. is known in mathematics as factorization or factorization .
A rectangular prism with the dimensions l, w, and h has the following volume:
[tex]V = l * w * h[/tex]
[tex]V = 1152 in^3\\[/tex]
[tex]l = 2w + 4\\h = 18 - w[/tex]
[tex]So,\\ V = l * w * h\\ \\ 1152 = (2w + 4) * w * (18 - w)1152 = (2w^2+ 4w) * (18 - w)\\ 1152 = 36w^2 + 72w - 2 w^3 - 4w^2\\ -2w^3 + 36w^2 - 4w^2 + 72w = 1152\\ -2w^3 + 32w^2 + 72w = 1152\\ -2w^3+ 32w^2 + 72w - 1152 = 0\\ -w^3+ 16w^2 + 36w - 576 = 0\\ w^3 - 16w^2 - 36w + 576 = 0\\ (w^3 - 36w) - (16w^2 - 576) = 0\\[/tex]
[tex]Factor:\\ w * w^2 - w * 36 - (16 * w^2 - 16 * 36) = 0\\ w(w^2 - 36) - 16(w^2 - 36) = 0\\(w - 16)(w^2 - 36) = 0\\(w - 16)(w^2 - 6^2) = 0\\(w - 16)(w - 6)(w + 6) = 0\\[/tex]
So,
w - 16 = 0, or w - 6 = 0, or w + 6 = 0.
w = 16, or w = 6, or w = -6.
Since width cannot be zero, w = –6.
l = 2 * 16 + 4 = 32 + 4 = 36 and h = 18 - 16 = 2 if w = 16
However, because the width must be smaller than the height (h > w), w 16.
l = 2 * 6 + 4 = 12 + 4 = 16 and h = 18 - 6 = 12 if w = 6, respectively.
Consequently, w = 6 in, l = 16 in, and h = 12 in
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every day jo practices her tennis serve by continually serving until she has had a total of 50 successful serves. if each of her serves is, independently of previous ones, successful with probability .4, approximately what is the probability that she will need more than 100 serves to accomplish her goal?
She needs 50 successful serves in the first 100 to attain her target. A 2% chance exists that this will occur.
She therefore has a 98% chance of requiring more than 100 serves to achieve her objective.
What is a probability?The study of probability, which is the potential of any event happening, is a field of mathematics that deals with the occurrence of random events. The probability value is given on a scale from 0 to 1.
How do you find probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
Jo must not complete 50 successful serves in her first 100 attempts in order to need more than 100 serves.
With n=100 and p=0.4, our probability sample of potential outcomes has a binomial distribution.
We will use a normal distribution to approximate n because it is a big enough number. The normal distribution's characteristics are as follows:
To ensure that she receives more than 100 serves, we must determine the likelihood that there will be fewer than 50 successful services. Such is:
We determine X's z value as follows:
Next, we have
That indicates that there is a 98% chance she will require more than 100 serves to accomplish her objective.
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Which of the following is the value of discriminant for √ 2x² − 5x+ √ 2 = 0?
Answer:
The value of the discriminant is 17.
Step-by-step explanation:
⭐What is the discriminant?
[tex]b^2-4ac[/tex]it is the radicand (the value inside of the radical) of the quadratic formulaThus, we have to substitute the values a, b, and c from the quadratic equation we are given into the discriminant formula.
Let's identify what a, b, and c are.
[tex]y = ax^2 + bx + c[/tex]
[tex]y = \sqrt{2}x^2 -5x + \sqrt{2}[/tex]
a = [tex]\sqrt{2}[/tex]
b = -5
c = [tex]\sqrt{2}[/tex]
Now, substitute these values into the discriminant formula.
[tex]b^2 - 4ac =[/tex]
[tex](-5)^2 - 4(\sqrt{2}*\sqrt{2}) =[/tex]
[tex]25 -4(2) =[/tex]
[tex]25-8 =[/tex]
= 17
∴ The value of the discriminant is 17.
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