Answer:
[tex]\large\boxed{x=\dfrac{1}{a}}[/tex]
Step-by-step explanation:
[tex]2-4(ax-3)=10\qquad\text{subtract 2 from both sides}\\\\-4(ax-3)=8\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4(ax-3)}{-4}=\dfrac{8}{-4}\\\\ax-3=-2\qquad\text{add 3 to both sides}\\\\ax-3+3=-2+3\\\\ax=1\qquad\text{divide both sides by}\ a\neq0\\\\x=\dfrac{1}{a}[/tex]
15pts awarded and brainliest will be chosen!!!!!
The ideal length of a particular metal rod is 30.5 cm. The measured length may vary from the ideal length by at most 0.015 cm. What is the range of acceptable lengths for the rod?
Answer: OPTION B
Step-by-step explanation:
Let be "x" the acceptable lengths for the rod.
You know that the ideal length of the metal rod is 30.5 centimeters and the measured length may vary from the ideal length by at most 0.015 centimeters.
Therefore, knowing this, you can say that the acceptable lengths must be:
[tex]30.5cm-0.015cm\leq x\\\\30.485\leq x[/tex]
[tex]x \leq 30.5cm+0.015cm\\\\x\leq 30.515[/tex]
Therefore, the range of acceptable lengths for the rod is the following:
[tex]30.485\leq x\leq 30.515[/tex]
This range matches with the one shown in the option B.
Tom opened a lemonade stand to earn money to buy a new bike for $200. He sells a cup of lemonade for $1.00. On the first day he sold 8 cups of lemonade, on the second day he sold 16 cups and on the third day he sol 32 cups. If Tom keeps selling cups of lemonade this way on what day will he have a total of $200.
1 - 8
2 - 16
3 - 32
x - +200
Each lemonade has a profit of $1, so the number of cups of lemonade he sells is the same as the amount of dollars he has. You just need to add each previous day's total to the next day's, doubling the amount of cups from the previous day's for each new day.
4 - (32 x 2 = ) 64
8 + 16 + 32 + 64 = 120. We need at least $80 dollars more, so we continue.
5 - (64 x 2 = ) 128
120 + 128 = $248.00 That's more than enough, so Tom will have enough money for his bike after the fifth day of selling lemonade.
What does it mean when a scatter plot has a good or bad fit? And how can you tell if it has a good or bad fit?
Snake wnemwmammwmenkk ju jxi I I i I jus uo I j i I i I i I i I i i izj
A scatter plot has a good fit when data points cluster near the line of best fit and show a clear positive or negative correlation, suggesting a strong relationship between variables. A bad fit is characterized by scattered data points with no apparent pattern and large residuals between the points and the line, indicating a weak or no correlation.
When a scatter plot has a good fit, it means that the line of best fit accurately represents the trend in the data. This line minimizes the distances, or residuals, between itself and all the points on the graph. You can tell if a scatter plot has a good fit if the data points form a pattern that closely follows the line of best fit, indicating that the variables have a strong correlation. Conversely, a bad fit is evident when the data points are widely scattered and do not follow a distinct pattern, suggesting a weak or no correlation between the variables.
Signs of a Good Fit in Scatter Plots
Data points cluster near the line of best fit.Residuals (distances between data points and the line) are generally small.The pattern is either a clear positive or negative correlation.Signs of a Bad Fit in Scatter Plots
Data points are spread out with no discernible trend.Residuals are large, indicating significant variance from the line.No apparent correlation, positive or negative, is observable.Whether the X and Y variables in a scatter plot are good candidates for linear regression depends on the aforementioned signs. If there is a clear positive or negative correlation and data points approximate a linear trend, they are good candidates for linear regression.
The ordered pair (-2,-1) is a solution to which of the following equations?
The equation that has (-2, -1) as a solution is, C. 4x - y = -7.
How to Find the Ordered Pair That is a Solution to an Equation?To determine if an ordered pair is a solution to an equation, plug in the values of the coordinates of the pair into the equation to check if it will make it true
If it makes it true, it is a solution, otherwise, it is not if it does not make the equation true.
Given the ordered pair, (-2, -1) substitute the values to check which will be true:
-4(-2) - (-1) = 7
9 = 7 [not true].
4x + y = -7
4(-2) + (-1) = -7
-9 = -7 [not true]
4x - y = -7
4(-2) - (-1) = -7
-7 = -7
Therefore, the equation is: C. 4x - y = -7.
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Complete Question:
The ordered pair (-2,-1) is a solution to which
of the following equations?
A.-4x - y = 7
B. 4x+y=-7
C. 4x - y = -7
D. -4x + y = -7
Will mark as brainliest!!
Lorenz wants to build a bigger flower box for his home. The current box has dimensions of 18“ x 12“ x 36“. What happens to the volume of the box if you double each dimension
Answer:
The answer is 62208
Step-by-step explanation:
The reason is because 18*2=36 12*2=24 and 36*2=72
36*24*72=62208
Can I get brainliest
The test to detect the presence of respiratory syncytial virus is 97% accurate for a person who has the virus and 99% accurate for a person who does not have the virus. In a given population, 0.55% of the people are infected. The probability that a randomly chosen person gets an incorrect result is .
[tex]\textrm{97 percent accurate for individual with the virus}[/tex]
[tex]\text{3 percent inaccurate}[/tex]
[tex]\textrm{99 percent accurate for an individual}[/tex]
[tex]\textrm{1 percent inaccurate probability}[/tex]
[tex]\textrm{Probability of infected:}[/tex]
[tex].0055[/tex]
[tex]\textrm{Probability of not being infected}[/tex]
[tex]1 - .0055 = .9945[/tex]
[tex]\textrm{Combine it all together}[/tex]
[tex]0.0055 * 0.03 + 0.9945 * 0.01 = 0.01011[/tex]
[tex]\textrm{The probability that a randomly chosen person gets an incorrect result is 0.01011}[/tex]
[tex]\textbf{Answer}[/tex]
[tex]\textrm{0.01011}[/tex]
The probability of an incorrect result for the test to detect respiratory syncytial virus is calculated by considering the test's sensitivity and specificity, along with the prevalence of the virus in the population.
Explanation:In order to calculate the probability that a randomly chosen person gets an incorrect result, we first need to understand how test accuracy works. Sensitivity refers to how often the test correctly identifies the presence of a disease when it is indeed there, while specificity refers to how often it correctly identifies the absence of a disease when it isn't there. In this case, the sensitivity is 97%, meaning it correctly identifies the virus in 97% of individuals who have the virus; the specificity is 99%, meaning it correctly identifies no virus in 99% of individuals who do not have the virus.
For the given population, 0.55% are infected. Hence, the probability of an incorrect result for a person with a virus is 3% (100% - 97%), and for a person without the virus is 1% (100% - 99%). Therefore, the total probability of getting an incorrect result is (0.55%/100 * 3%) + [(1 - 0.55%/100) * 1%].
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Thom's restaurant bill is $45, and he leaves a 20 percent tip. What is the total cost for Thom's meal?
Multiply the price before the tip by .20
[tex]45 * .20 = 9[/tex]
Add 9 to the total:
[tex]45 + 9 = $54[/tex]
So, the total cost for Thom's meal is $54
The total cost for Thom's meal is $54.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.
Given
Thom's restaurant bill is $45
20 percent tip = 20 % of 45 = 20/100*45 = 9
Total cost = Thom's restaurant bill + 20 percent tip
= 45+ 9 = 54
Therefore, The total cost for Thom's meal is $54.
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What is the degree of the polynomial p(x) = [tex]17x^{4}-12x^3+51x^2-137x+2[/tex]
The degree of a polynomial is the highest exponent.
The highest exponent in this equation is 17x^4
The degree is 4.
What is the formula for the sum of the interior angles of a polygon
Answer:
Sum of the interior angles = (n-2) x 180°
where
n is the number of sides of the polygon
Step-by-step explanation:
The formula for the sum of the interior angles of a polygon is:
[tex]sum=(n-2)*180[/tex]
where
[tex]sum[/tex] is the sum of the interior angle of the polygon
[tex]n[/tex] is the number of polygons
Let's check the formula using an example:
We want to find the sum of the interior angles of a square, we know that a square has 4 sides, so [tex]n=4[/tex].
Replacing values
[tex]sum=(4-2)*180[/tex]
[tex]sum=(2)*180[/tex]
[tex]sum=360[/tex]
We can apply the same procedure to any convex polygon with n sides.
Answer:
The fomula for the sum of the interior angles of a polygon is:Sum of the interior angles = (n - 2) × 180°.
Where n is the number of sides of the polygon.
Explanation:
The formula (n - 2) × 180° is valid for any convex polygon.
A convex polygon is one whose interior angles (every interior angle) measure less than 180°.
You can prove and remember that formula following this reasoning:
If you pick one vertex of the polygon you can build (n - 2) diagonals, and so split the figure into n - 2 triangles.Since, the sum of the interior angles of any trianle is 180°, the sum of the total angles is (n - 2) × 180°. And this is the formula for the sum of the interior angles of a polygon.For example, for a pentagon, a polygon with 5 sides, you can can draw 5 - 2 = 3 diagonals from one vertex, and so obtain 3 triangles. Then the sum of the interior angles shall be (n - 2) × 180° = (5 - 2) × 180° = 3 × 180° = 540°.
A rectangle has length (x+4) cm and width (x-3) cm. Its area is 30 square centimeters. Write a quadratic equation and solve it to find the length of the rectangle.
(x+4)(x-3)=30
x^2 +x -12 =30
x^2 +x =42
x^2 +x -42 =0
(i solved it by factorising: _x^2 × -42)
x^2 -6x +7x -42 =0
x(x-6) +7(x-6) 0
(x-6)(x+7)=0
x=6; x=-7
since it's a length, x can't be a negative number, so it must be 6
20 pts awarded and brainliest marked, plz help ASAP!!!!!!
Mark all the statements that are true.
- The equation of this line is x=3.
- And I think it's also, This graph is a function of whose range is set at {3}.
Answer:
D. The equation of this line is x=3
E. This graph is not a function because the value x=3 is assigned to mre than one y-value.
Step-by-step explanation:
The range is all real numbers.
The domain of this graph is x=3, but it is not a function
The graph is a vertical line whose equation is x=3 because the graph passes through (3,y).
This graph cannot represent a function because it will not pass the vertical line test.
In other words, the x-value of 3 is assigned to more than one y-value.
Therefore the correct answers are:
Option D and E
PLEASE HELP ASAP 60 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
x(x-3)(x+2)
Step-by-step explanation:
x^3-x^2-6x
First subsitute out x:
x(x^2-x-6)
Find the multiples of the x's:
x(x-3)(x+2)
Answer:
x(x-3)(x+2)
Step-by-step explanation:
x^3-x^2-6x
First subsitute out x:
x(x^2-x-6)
Find the multiples of the x's:
x(x-3)(x+2)
Step-by-step explanation:
Why is (6, –2) not a solution to the system of equations given below?
{2x-3y=18
5x=3y=3
A.
It satisfies the top equation but not the bottom equation.
B.
It satisfies the bottom equation but not the top equation.
C.
It doesn’t satisfy either the top or the bottom equations.
D.
It satisfies both the top and the bottom equations.
ANSWER
A.
It satisfies the top equation but not the bottom equation.
EXPLANATION
The given equations are;
2x-3y=18
5x+3y=3
When we substitute x=6 and y=-2 into the top equation we get,
2(6)-3(-2)=18
12+6=18
18=18
This is true. Hence the point satisfy the top equation.
But when we substitute x=6 and y=-2 into the bottom equation we get,
5(6)+3(-2)=3
30-6=3
24=3
Hence the bottom equation is not satisfied.
The first choice is correct.
Tax returns filled manually have a 20% chance of containing errors while tax returns filled electronically have a .05% chance of containing the same if 2.7 million tax returns are filed each way how many more erroneous manually filed returns will there be than erroneous electronically filed returns
Answer:
538,650
Step-by-step explanation:
We must first find how many errors there will be if filed manually and if filed electronically
Manually: 2,700,000*20% or 2,700,000*.2
Answer: 540,000 errors
Electronically: 2,700,000*.05% or 2,700,000*.0005
Answer: 1,350 errors
We must then find the difference; 540,000-1,350=538,650
Answer:
538,650.
Step-by-step explanation:
Number of erroneous manual returns = 20% of 2.7 million
= 0.20 * 2,700,00 = 540,000.
Number for electronically returned = 2,700,000 * 0.0005 = 1350.
Difference = 540,00 - 1350 = 538,650.
Find the number of positive three-digit integers whose digits are among 9, 8, 7, 5, 3, and 1.
18
216
729
Answer:
216
Step-by-step explanation:
Each of the three digit positions can have any of 6 values, so there are ...
6^3 = 216
possible numbers that can be formed.
Match the rectangles formed by the sets of points to their corresponding areas. A(-9, 8), B(-5, 5), C(1, 13), D(-3, 16) 50 square units E(30, 20), F(39, 29), G(49, 19), H(40, 10) 300 square units I(-6, 2), J(2, 2), K(2, -8), L(-6, -8) 100 square units M(5, 5), N(11, 5), O(11, -5), P(5, -5) 80 square units Q(10, 0), R(15, 5), S(25, -5), T(20, -10) U(0, 5), V(15, 20), W(25, 10), X(10, -5) arrowBoth arrowBoth arrowBoth arrowBoth
Answer:
The area of ABCD is 50 units²
The area IJKL is 80 units²
The area of QRST is 100 units²
The area of UVWX is 300 units²
Step-by-step explanation:
* Lets revise the area of the rectangle
- The area of any rectangle = its length × its width
- To solve the problem find the lengths of two adjacent sides and
consider that one of them is the length and the other is the width
- Use the rule of the distance between two points (x1 , y1) and (x2 , y2)
the distance = √[(x2 - x1)² + (y2 - y1)²]
# In rectangle ABCD
∵ A = (-9 , 8) , B = (-5 , 5) , C = (1 , 13)
∴ AB = √[(-5 - -9)² + (5 - 8)²] = √[(4)² + (-3)²] = √[16 + 9] = √25 = 5 units
∴ BC = √[(1 - -5)² + (13 - 5)²] = √[(6)² + (8)²] = √[36 + 64] = √100 = 10 units
∴ The area of ABCD = 5 × 10 = 50 units²
# In rectangle EFGH
∵ E = (30 , 20) , F = (39 , 29) , G (49 , 19)
∴ EF = √[(39 - 30)² + (29 - 20)²] = √[9² + 9²] = √[81 + 81] = √162 unit
∴ FG = √[(49 - 39)² + (19 - 29)²] = √10² + (-10)²] = √[100 + 100] = √200 units
∴ The area of EFGH = √162 × √200 = 180 units²
# In rectangle IJKL
∵ I = (-6 , 2) , J = (2 , 2) , K = (2 , -8)
∴ IJ = √[(2 - -6)² + (2 - 2)²] = √[8² + 0²] = √8² = 8 units
∴ JK = √[(2 - 2)² + (-8 - 2)²] = √[0² + (-10)²] = √10² = 10 units
∴ The area IJKL = 8 × 10 = 80 units²
# In rectangle MNOP
∵ M = (5 , 5) , N = (11 , 5) , O = (11 , -5)
∴ MN = √[(11 - 5)² + (5 - 5)²] = √[6² + 0²] = √6² = 6 units
∴ NO = √[(11 - 11)² + (-5 - 5)²] = √[0² + (-10)²] = √10² = 10 units
∴ The area of MNOP = 6 × 10 = 60 units²
# In rectangle QRST
∵ Q = (10 , 0) , R = (15 , 5) , S = (25 , -5)
∴ QR = √[(15 - 10)² + (5 - 0)²] = √[5² + 5²] = √[25 + 25] = √50 units
∴ RS = √[(25 - 15)² + (-5 - 5)²] = √[10² + (-10)²] = √[100 + 100] = √200 units
∴ The area of QRST = √50 × √200 = 100 units²
# In rectangle UVWX
∵ U = (0 , 5) , V = (15 , 20) , W = (25 , 10)
∴ UV = √[(15 - 0)² + (20 - 5)²] = √[15² + 15²] = √[225 + 225] = √450 units
∴ VW = √[(25 - 15)² + (10 - 20)²] = √[10² + (-10)²] = √100 + 100 = √200 units
∴ The area of UVWX = √450 × √200 = 300 units²
Please help me out with this
Answer:
x = 17
Step-by-step explanation:
For the parallelogram to be a rhombus then then the diagonal must bisect the given angle, thus
3x - 11 = x + 23 ( subtract x from both sides )
2x - 11 = 23 ( add 1 to both sides )
2x = 34 ( divide both sides by 2 )
x = 17
Help with this question, please!! I don't understand!
Answer:
(0, 1)
Step-by-step explanation:
all of the points are the same number away: 2√5
Answer:
(0, 1)
Step-by-step explanation:
A, B, and C are points on a circle. You are being asked to find the center of the circle. You can do that any of several ways.
I find it useful to plot the points on a graph. Doing so reveals that AB is perpendicular to BC, so ABC is a right triangle, and the center you want is the midpoint of the hypotenuse (AC).
(A+C)/2 = ((2, -3) +(-2, 5))/2 = (2-2, -3+5)/2 = (0, 1) . . . . . coordinates of center
___
From a construction point of view, the center of the circle is the point of intersection of the perpendicular bisectors of the chords. In the attached, we have used a geometry program to draw the perpendicular bisectors of AB and BC. They meet at (0, 1).
___
From an algebra point of view, the points on the circle with center (h, k) and radius r satisfy the equation ...
(x -h)^2 +(y -k)^2 = r^2
Filling in the point values, you get three equations in the three unknowns (h, k, r):
(2-h)^2 +(-3-k)^2 = r^2(4-h)^2 +(3-k)^2 = r^2(-2-h)^2 +(5-k)^2 = r^2Finding the difference between any two pairs of these will result in two linear equations in h and k, so are easily solved.
First - second: (4 -4h +h^2) +(9 +6k +k^2) -(16 -8h +h^2) -(9 -6k +k^2) = r^2 -r^2
-12 +4h +12k = 0 . . . simplify
h +3k = 3 . . . . . . . . . put in standard form
Second -third: (16 -8h +h^2) +(9 -6k +k^2) -(4 +4h +h^2) -(25 -10k +k^2) = r^2 -r^2
-4 -12h +4k = 0 . . . . simplify
3h -k = -1 . . . . . . . . . put in standard form
Now, we can add 3 times the second of these equations to the first to find h:
(h +3k) +3(3h -k) = (3) +3(-1)
10h = 0
h = 0
Then either of the equations can be used to find k = 1.
The center is (h, k) = (0, 1).
A weather forecast predicts a 25% probability of thunderstorms for tomorrow and a 10% probability of thunderstorms and hail. What is the probability that there is hail tomorrow given that there are thunderstorms?
Answer:
[tex]P(B | A)=0.4=40\%[/tex]
Step-by-step explanation:
Call A to the event in which there are electrical storms.
Call B the event in which there is hail.
Then, by definition.
The Probability of B given A is:
[tex]P(B | A)=\frac{P(B\ and\ A)}{P(A)}[/tex]
We know that:
[tex]P(B\ and\ A)= 10\%=0.1\\\\P(A) = 25\%=0.25[/tex]
Therefore
[tex]P(B | A)=\frac{0.1}{0.25}[/tex]
[tex]P(B | A)=0.4=40\%[/tex]
The conditional probability of hail given thunderstorms is calculated using the formula P(Hail | Thunderstorms) = P(Thunderstorms and Hail) / P(Thunderstorms). Given the probabilities of 10% for thunderstorms with hail and 25% for thunderstorms, the result is a 40% probability of hail when thunderstorms are present.
Explanation:The student is asking to find the conditional probability of hail occurring, given that thunderstorms are already happening. This is a probability question that involves understanding and applying the concept of conditional probability.
The probability of thunderstorms is given as 25% (or 0.25 in decimal form), and the probability of thunderstorms with hail is given as 10% (or 0.10 in decimal form). To find the probability of hail given thunderstorms, you use the formula for conditional probability which is P(Hail | Thunderstorms) = P(Thunderstorms and Hail) / P(Thunderstorms). The 'given' part is represented by the condition after the vertical bar '|', and the numerator is the probability of both thunderstorms and hail occurring.
Substituting the given values into the formula, we get P(Hail | Thunderstorms) = 0.10 / 0.25 = 0.40 or 40%. Therefore, if thunderstorms are occurring, there is a 40% probability that there is also hail.
The clothes is having a 60% off sale for shorts. Ben paid $14 for the shorts. What is the original price
Answer:
$35
Step-by-step explanation:
since it is 60% off, $14 is 40% of original price.
1% of original price (original price is 100%)
= $14 ÷ 40
= $0.35
original price
= $0.35 × 100
= $35
PLS HELP!!!!
Drag a statement or reason to each box to complete this proof.
If x−24=2, then x=10.
Statement Reason
1. x−24=2 Given
2. 4(x−24)=4∙2 ?
3. ? Simplifying
4. x−2+2=8+2
5. ? ?
______________________________________________________________
simplifying multiplication property of equality
addition property of equality x=10 x-2=8
Answer:
2. simplifying multiplication property of equality
3. x - 2 = 8
5. x = 10 , addition property of equality
Step-by-step explanation:
* Lets explain how to solve the problem
- The equation is [tex]\frac{x-2}{4}=2[/tex]
- The value of x is 10
- We want to a statement reason to each step to complete the proof
* Lets write each step with statement reason
1. [tex]\frac{x-2}{4}=2[/tex] ⇒ Given
2. [tex]4(\frac{x-2}{4})=4*2[/tex] ⇒ simplifying multiplication property of equality
3. x - 2 = 8 ⇒ Simplifying
4. x - 2 + 2 = 8 + 2
5. x = 10 ⇒ addition property of equality
- In step 2 we multiply both sides by 4 to cancel the denominator of
the left hand side (simplifying multiplication property of equality)
- Then we simplify the two sides to get (x - 2 = 8)
- Then we add two to both sides to cancel -2 in the left hand side
- Then after adding we find (x = 10) , (addition property of equality)
* The answer is:
2. simplifying multiplication property of equality
3. x - 2 = 8
5. x = 10 , addition property of equality
Suppose the function g(x) = 7x + 6 is translated down 9 units to become a new function, h(x). What's the equation of the new function?
Answer:
g(x)=7x-3
Step-by-step explanation:
the y axis becomes -3 because 6-9=-3
Please help me out please
Answer:
110.9 sq ft
Step-by-step explanation:
split the equilateral triangle into two right triangles. use pythagorean theorem to discover that the height is about 13.86 ft. use the area formula, A= (1/2)bh
A=(1/2)(8)(13.86)= 110.9
Answer:
A = 64√2 ft² = approx. 90.5 ft²
Step-by-step explanation:
Because this is an equilateral triangle, the interior angles are also equal and are 60° each. We'll use the area-of-a-triangle formula, A = (1/2)(b)(h), to find the area of this particular triangle. We see from the diagram that the base is 16 ft.
Drawing an imaginary line representing the height of this triangle, and letting h represent this height, we get
sin 60° = opp / hyp = h / (16 ft) = 1/√2, so that
h 1
----- = -----
16 √2 16
and so √2*h = 16, and h = -------
√2
1 16 16
Then the area of this blue triangle is A = (1/2)(b)(h) = ---- * ----- * -------
2 1 √2
128 128√2
or A = ------- = ------------ = 64√2 ft² = approx. 90.5 ft²
√2 2
Generalize the pattern by finding the nth term. 6, 10, 14, 18, 22, ... options: A. 4n B. 4n + 2 C. 4n + 10 D. 6n + 4
ANSWER
B.
[tex] 4n + 2[/tex]
EXPLANATION
The given pattern is:
6, 10, 14, 18, 22, ...
The first term if the pattern is a=6.
The common difference among the terms is
[tex]d = 10 - 6 = 4[/tex]
The general pattern can be found using the formula:
[tex]f(n)=a+d(n-1)[/tex]
We substitute the values to get,
[tex]f(n)=6+4(n-1)[/tex]
Expand to get;
[tex]f(n)=6+4n-4[/tex]
[tex]f(n) = 4n + 2[/tex]
The correct answer is B.
Pleeeeeeeeease help!!!!!!!
Answer:
x = 11
Step-by-step explanation:
If a radius bisects a chord ( as in the lower chord )then it is perpendicular to the chord.
Thus both chords are equidistant from the centre ( both 12 ) and are therefore congruent.
Hence x = 11
A thirty year old man is considering buying a one-year life insurance policy for $500 with a coverage of $150,000. The probability of his living through the year is 0.994. Based ONLY on this information, should the man buy the policy?
Answer:
The man should not buy the policy.
Step-by-step explanation:
A life insurance policy is a contract that pays a sum assured to a policy holder upon death, either immediately or at the end of year of death. The policy holder pays a premium amount in advance to cater for the future benefits (sum assured).
In the scenario presented, the man is 30 years old with a probability of 0.994 of survival with respect to mortality. The high probability of being alive through the year implies that the man is very unlikely to die and thus the probability of receiving the coverage amount is too minimal
Answer: The expected value is $400, so the man should buy the insurance policy.
Step-by-step explanation:
(150,000-500)(.006)-500(.994)=400
What is the value of x? Enter your answer in the box
x = 180° - 67° - 52°
x = 61°
So, the value of x is 61°
Please help me out please
Answer:
x = 30°
Step-by-step explanation:
x° is the other acute angle of the right triangle with 60° as the acute angle at the center of the circle. (The tangent line makes a right angle with the radius at the point of tangency.)
1.) A multiple choice test has 7 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer 3 or more questions correctly?
0.311
0.0156
0.244
0.756
2.) In a survey of 300 college graduates, 63% reported that they entered a profession closely related to their college major. If 9 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 4 or fewer of them entered a profession closely related to their college major?
0.149
0.0512
0.793
0.207
Final answer:
The probability that Judy guesses at least 3 questions correctly in a multiple-choice test is calculated using the binomial probability formula. For the survey question, the hypergeometric distribution is used to find the probability of 4 or fewer out of 9 people entering a profession related to their major. Exact probabilities require mathematical computation.
Explanation:
Probability of Answering Multiple-Choice and Survey Questions Correctly
For question 1, we must calculate the probability that Judy guesses at least 3 questions correctly on a 7-question multiple-choice test, where each question has 4 possible answers. Since only one answer is correct per question, her probability of guessing a question correctly is 1/4. To find the total probability of answering 3 or more questions correctly, we use the binomial probability formula which considers the probability of success (1/4) and the number of trials (7 questions). We sum the probabilities of getting exactly 3, 4, 5, 6, or all 7 questions correct.
For question 2, regarding the survey of 300 college graduates, we use the hypergeometric distribution since the samples are taken without replacement. We need to determine the probability that 4 or fewer of the randomly selected 9 survey subjects entered a profession closely related to their college major. We know that 63% of the entire group, which is 189 individuals, entered a relevant profession. We sum the probabilities of 0, 1, 2, 3, and 4 people from our sample of 9 falling into the group who are working in their field.
The correct probabilities from the provided choices are not directly calculable without doing the necessary computations using the respective formulas for each scenario, which are beyond the scope of this response as we do not have the calculations or the respective formulas provided within the context of this interaction.
Please answer this correctly
Answer:
The missing number is 8
Step-by-step explanation:
Hope this helps (3
it will be 297,088 as the answer