Chris and Jim must replace a total quantity of 17 tyres.
What is the minimum number of tyres to be replaced?
In this problem we must use an inequality of the form f(x) ≥ a, where f(x) is the difference between the number of tyres replaced by Jim and the number of tyres replaced by Chris:
(25/20) · x - x ≥ 3
(5/20) · x ≥ 3
x ≥ 12
Then, the minimum number of tyres to be replaced is n = 15 + 12 = 17 tyres.
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calculate the area of the shaded part to the nearest whole unit. (show your work)
The area of the shaded part in figure A and B are 2m² and 49 m² respectively.
Area of the shaded partTo determine the area, we must know the shape of the shaded part.
After identifying the shape, we move further to know the formula for such shape
From the figures given in A, we can see that the shaded region is in form of a triangle
a. The area of a right angle is given as;
The base multiplied by the half the height and vice versa
It is written mathematically as;
Area = 1/ 2 × base × height
Where
base = 2m
height = 2m
Substitute into the formula
Area = 1/ 2 × 2 × 2
Area = 2m²
For figure B, the shaded part is a rectangle
The formula for area of a rectangle is given as;
the width multiplied by the length
Area = width × length
Where width = 7m
length = 7m
Area = 7 × 7
Area = 49m ²
Thus, the area of the shaded part in figure A and B are 2m² and 49 m² respectively.
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Vinny worked 8 hours and was paid a total of $66. At this rate, how long
would it take Vinny to earn $165?
a. 40.5 hours
b. 20 hours
c. 15 hours
d. 2½ hours
Answer:
b, 20 hours
Step-by-step explanation:
First, find out how many times 66 (what Vinny made) goes into 165. (what Vinny wants to make) the answer is 2.5. Then, multiply 8 by 2.5 as well. You get 20. The answer is b, 20.
I hope this helps!
PLEASE HELP ASAP
List these numbers from SMALLEST TO LARGEST
29.94
28.15
27.068
28.08
28.3
Answer:
Step-by-step explanation:
27.068
28.08
28.15
29.94
A rectangular gate measures 1.2 m by 2.3 m with a 2.4 m diagonal. Is the gate
square? If not, should the diagonal be longer or shorter?
10 Points + BRANIEST
Answer:
Step-by-step explanation:
So, we’re probably looking at a n9-m0 cusp, since adding 0 to a number gives a sum lower than adding 9 to a slightly smaller number, something that isn’t true elsewhere in the cycle.
We need a n9 where the sum n+9 is divisible by 3. 9 is divisible by 3 already, so n must be divisible by 3 as well. So, it’s 0, 3, 6, or 9.
Taking as the most likely 3 (because a 39 year old is more likely than a 9 year old, 69 year old, or 99 year old to have a child who doesn’t already know their father’s age) we’ll try 39, 40. 3+9=12, 4+0=4, 12/3=4, this is a possible solution.
Do the others work?
0+9=9, 1+0=1, 9/4=/=1
6+9=15, 7+0=7, 15/4=/=7
9+9=18, 1+0+0=1, 18/4=/=1
1+2+9=12, 1+3+0=4, 12/3=4
there are at least two possibles. the father was correct, the father cannot determine his age from what she has been told, she must guess. From what she knows of him, is it more likely that he’s 39, or 129, or even older?
David invested $230 in a savings account that offers a 3% return on the investment. the value of david's investment will be at least $415 after a
period of years.
hint: use the formula a = a1 + ', where a is the amount after tyears, pis the amount invested, r is the rate of interest, and is the time period.
use a calculator to compute the answer, and round it off to the nearest year.
20 years is the answer.
A= R(1+r)^ t
A-415
R=230
r=3%
415=230 (1+3%)^ t
t=log1.03 315/230
t=19.89 (use calculator)
David will invest at least 20 years.
An investment is a dedication of an asset to achieve an increase in value over a period of time. Investing requires the sacrifice of current assets such as time, money and effort. In finance, the purpose of an investment is to generate a profit on the invested asset
The most common example of an investment type. Investment is generally what you want to use in the future with the aim of generating regular cash flow or increasing the value of something over time so that you can sell it at a higher price than you purchased.
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What is the circumference of a circle (to the nearest whole number) whose radius is 5?
Answer:
31
Step-by-step explanation:
C= 2πr We will used 3.14 for pi and the radius is 5
C = 2(3.14)(5)
C =31.4 Then round to the nearest whole number which would be 31. 31.4 is closer to 31 than 32
Which of the following are identities? I. y=x II. 4=3x2+2 III. x=x−−√ A. II and III B. I and III C. all D. none
None of the expressions is an identity
How to determine the identities?The expressions are given as:
I. y=x
II. 4 = 3x^2 + 2
III. x=x
In algebra, there are three identities; and they are
(x+y)^2 = x^2 + y^2 + 2xy(x-y)^2 = x^2 + y^2 – 2xyx^2 – y^2 = (x+y) (x-y)None of the given expression take the above forms
Hence, none of the expressions is an identity
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Find the slope of the line that passes through the points (7 , 4) and (-9 , 4).
Answer:
0
Step-by-step explanation:
The y values are the same so this line is a straight line with a slop of 0
To check:
To find the slope we use y1-y2/x1-x2
Plug in the numbers: 4-4/-9-7 = 0/-16 = 0
which of the following statements would be most similar to an electiral current passing through a metal wire
The correct option is A. hot water moving through a pipe.
Electrical current passing through a metal wire is similar to hot water moving through a pipe.
What is Electrical current?Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent current. The ampere, denoted by the letter A, is the common unit.
The method of flowing of electrical current in metal wire is-
Faraday's Law established that when spinning magnets are close to a coil of wire, a voltage results. With the help of that voltage, you can force electrons through wires, and the moving electrons will travel to their intended locations and do useful tasks. In essence, that is how the electrical grid functions.Comparison of flow of electricity with flow of water in pipe-
Electrical charge (a current) flowing through a wire is comparable to water flowing through a conduit without any bubbles or leaks. The flow of charge is resisted by a resistor, just as the flow of water is resisted by a constriction in a pipe. A circuit's voltage can be compared to a pipe's pressure.To know more about Electric current, here
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The complete question is-
which of the following situations would be mist similar to an electrical current passing through a metal wire in a closed circuit?
A. hot water moving through a pipe
B. an automobile traveling through a tunnel
C. an airplane flying through clouds
D. a flying pan heating up on a hot plate
E. a bird building a nest
i need help in expanded form and simplify the problem
Answer:
[tex]\frac{1}{7w^{2} }[/tex]
Step-by-step explanation:
The expression can be simplified only if you take the same quantity out of both the top and bottom.
You can simplify the numbers by taking a factor of 3 out of the expression.
The numerator changes to 1 (because 3 / 3 = 1) and the denominator changes to 7 (because 21 / 3 = 7).
The variables can be eliminated through subtraction. The numerator variable is completely removed because you can subtract w³ from w⁵. This makes the denominator w² (because w⁵ - w³ = w²).
Schwiesow corporation has provided the following information: cost per unit cost per period direct materials $ 7.40 direct labor $ 3.80 variable manufacturing overhead $ 1.80 fixed manufacturing overhead $ 16,000 sales commissions $ 1.00 variable administrative expense $ 0.50 fixed selling and administrative expense $ 5,600 if 7,500 units are produced, the total amount of manufacturing overhead cost is closest to:
The total amount of manufacturing overhead cost is closest to $ 29,500.
In business, overhead or overhead rate refers to an ongoing fee for working in a commercial enterprise. Overheads are the expenditure that can not be quite simply traced to or recognized with any unique revenue unit, not like running fees which include uncooked cloth and exertions.
Overhead fees, frequently referred to as overhead or working prices, confer with those expenses associated with running a commercial enterprise that cannot be connected to creating or producing a product or service. they're the prices the business incurs to live in the enterprise, irrespective of its success degree.
Examples of overhead encompass hire, administrative expenses, or worker salaries. Overhead fees may be observed on a business enterprise's income assertion, wherein they are subtracted from its profits to reach at the internet profits discern.
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Which equation is equivalent to the given equation?
−4x = x² + 3
x² - 4x +3=0
x² - 4x - 3=0
x² + 4x - 3=0
x² + 4x +3=0
Answer: x² + 4x +3=0
Step-by-step explanation:
Add 4x to both sides.
Write down the equation of the straight line which passes through (0, -3) and parallel to the straight line y = -2x+1
Answer:
y = -2x - 3
Step-by-step explanation:
Equation of line:Parallel lines have same slope.
y = -2x + 1
Compare with the equation of line in slope intercept form y = mx + b
Here m is the slope and b is the y -intercept
m = -2
m = -2 ; line passes through (0 , -3)
Equation of line in slope intercept form:
[tex]\sf \boxed{\bf y - y_1=m(x-x_1)}[/tex]
y - [-3] = -2(x - 0)
y +3 = -2x
y = -2x - 3
A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three-topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni.
The probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni is 1/560 given that there are 16 toppings to choose from. This can be obtained by finding the total number of all possible three-topping pizzas (3 distinct toppings) using combination formula and finding the probability.
What is the required probability?Given that there are 16 toppings,
the total number of all possible three-topping pizzas,
ⁿCₓ = [tex]\frac{n!}{x!(n-x)!}[/tex] = 16!/[3!(16-3)!] = 16!/[3!(13)!] = 14×15×16/3×2 =560
Probability of choosing pizza topped with ham, artichoke hearts, and pepperoni,
P(ham, artichoke hearts, pepperoni) = 1/560
Hence the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni is 1/560 given that there are 16 toppings to choose from.
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Which expression is equivalent to (q^6)^2
which of the following expresses the possible number of positive real solutions for the polynomial equation shown below
The polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.
In the question, we are asked for the number of positive real solutions for the polynomial equation, x³ - 4x² - 7x + 28 = 0.
To find the solutions, we do as follows:
x³ - 4x² - 7x + 28 = 0,
or, (x³ - 7x) - (4x² + 28) = 0 {Grouping},
or, x(x² - 7) - 4(x² - 7) = 0 {Taking common},
or, (x - 4)(x² - 7) = 0 {Grouping},
or, (x - 4)(x + √7)(x - √7) = 0 {Using the formula: [tex]a^2 - b^2 = (a+b)(a-b)[/tex]}.
By the zero-product rule, the solutions are:
x - 4 = 0, or, x = 4,
x + √7 = 0, or, x = -√7,
x - √7 = 0, or, x = √7.
Thus, the positive real solutions are 4, and √7. Hence, there are two positive real solutions.
Thus, the polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.
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The complete question is:
"Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
x³-4x²-7x+28=0
a. two or zero
b. three or one
c. one
d. two"
Answer:
Two or zero.
Step-by-step explanation:
Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown:
Two right triangles ABC and EDC have a common vertex C. Angle ABC and EDC are right angles. AB is labeled 12 feet, AC is labeled 14 feet, EC is labeled 10 feet, and ED is labeled 7 feet.
What is the approximate distance, in feet, between the two poles?
7.14 feet
7.21 feet
14.35 feet
15.59 feet
Answer:
14.35 ft
Step-by-step explanation:
We can use the pythagorean theorem to find the distance between the poles since both triangles are right triangles.
a^2 + b^2 = c^2
a^2 + 12^2 = 14^2
a^2 + 144 = 196
a^2 = 52
a = 7.21 ft
a^2 + b^2 = c^2
a^2 + 7^2 = 10^2
a^2 + 49 = 100
a^2 = 51
a = 7.14 ft
7.21 + 7.14 = 14.35 ft
Brainliest, please :)
Answer: c; 14.35
Step-by-step explanation: I need help on this and i saw this guy asked for brainlist and i think two people need to anser so please give him brainlist.
The roots of the equation (p+2)x^2-2px=5-p are complex; find the range of values of p
Range of values of the variable p is [tex]0\leq p\leq \frac{10}{3}[/tex]
Step-by-step explanation:
From general quadratic equation [tex]ax^{2} +bx+c[/tex], for imaginary case-
[tex]D\leq 0\\b^2-4ac\leq 0[/tex]
In given question, [tex]a= p+2[/tex], [tex]b=2p[/tex], [tex]c= 5-p[/tex]
using above condition-
[tex]b^2-4ac = 4p^2-4(2p)(5-p)\leq 0\\4p^2 - 40p+8p^2\leq 0\\12p^2-40p\leq 0\\4p(3p-10)\leq 0[/tex]
Here, [tex]4p\leq 0, p\leq 0[/tex]
and
[tex]3p-10\leq 0\\p\leq \frac{10}{3}[/tex]
Therefore, range of values of the variable p is [tex]0\leq p\leq \frac{10}{3}[/tex].
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A house is octagon-shaped, and each side measures 22 feet long. How many lineal feet of exterior wall does this house have
Length of each side is 176 feet ² .
What is octagon ?A polygon of eight angles and eight sides.It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° ( radians). The central angle is 45° ( radians).each side of house = 22 feet long
Perimeter of octagon = 8 × sides
Length of each side of house = 8 × 22 ⇒ 176 feet²
Therefore, length of each side is 176 feet ² .
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Problem
Solve for x in the image below.
18
Solution
We can start with the pythagorean theorem:
(leg 1)² + (leg 2)² = (hypotenuse)²
Answer:
20.1246118
Step-by-step explanation:
hypotenus^2 - (leg1)^2 = (leg2) ^2
27^2-18^2 = (leg2)^2
729-324 = (leg2)^2
405 = (leg2)^2
20.1246118 = leg 2
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3
The linear inequality of the given graph is: D. y < -2x + 3.
How to Determine the Linear Inequality of a Graph?First, using two points on the line, (0, 3) and (1.5, 0), find the slope (m).
Slope (m) = change in y / change in x = (3 - 0) / (0 - 1.5)
Slope (m) = 3/-1.5 = -2.
Next, substitute (x, y) = (0, 3) and m = -2 into y = mx + b to find the value of b.
3 = -2(0) + b
3 = 0 + b
b = 3
Substitute m = -2 and b = 3 into y < mx + b (the shaded part is at the left, so we use the "<" sign)
y < -2x + 3
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Given: mAngleTRV = 60°
mAngleTRS = (4x)°
Prove: x = 30
3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees.
What is the missing reason in step 3?
A 2-column table with 6 rows is shown. Column 1 is labeled Statements with entries measure of angle T R V = 60 degrees and measure of angle T R X = (4 x) degrees, angle T R S and angle T R V are a linear pair, measure of angle T R S + measure of angle T R V = 180, 60 + 4 x + 180, 4 x =120, x = 30. Column 2 is labeled Reasons with entries given, definition of a linear pair, question mark, substitution property of equality, subtraction property of equality, division property of equality.
substitution property of equality
angle addition postulate
subtraction property of equality
addition property of equality
Mark this and return
https://brainly.com/question/68367When two lines intersect at a point, angles are formed. Some of these angles formed are vertically opposite and thus are equal.
Therefore, the required proof and answer to the question are stated below:
a) m< TRV = 60° (given)
m<TRS = 4x° (given)
Thus, it can be concluded from the diagram that:
<TRV ≅ m<BRW (vertically opposite angle property)
Also,
m<TRS ≅ m<VRW (vertically opposite angle property)
But,
m<VRW = m<VRZ + m<ZRW
Thus,
m<TRV ≅ m<BRW = 60°
m<TRV + m<BRW + m<TRS + m<VRW = [tex]360^{o}[/tex]
60° + 60° + m<TRS + m<VRW = [tex]360^{o}[/tex]
m<TRS + m<VRW = [tex]360^{o}[/tex] - [tex]120^{o}[/tex]
= [tex]240^{o}[/tex]
2m<TRS = [tex]240^{o}[/tex] (since m<TRB = m<VRW )
m<TRS = 120
4x = 120
x = [tex]\frac{120}{4}[/tex]
= [tex]30^{o}[/tex]
Thus, x = [tex]30^{o}[/tex]
b) The missing reason in step 3 is the angle addition postulate.
jhgvbiluhliuhnhl
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Anna and Damien are doing inventory at their pet store. Anna has counted 3 cages with 3 rabbits in each. Damien counted 4 cages with 2 rabbits in each. Which expression will help Anna and Damien count the rabbits at their store?
The expression that help Anna and Damien count the rabbits at their store is (3 * 3) + (4 * 2)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Anna has counted 3 cages with 3 rabbits in each. Damien counted 4 cages with 2 rabbits in each. Hence:
Total rabbits = (3 * 3) + (4 * 2)
The expression that help Anna and Damien count the rabbits at their store is (3 * 3) + (4 * 2)
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Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate z dV E , where E lies above the paraboloid z
The resulted integral is [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].
What is integrals?In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or just an added to the initial, the derivative of which is initial function (indefinite integral).
Computation of the integrals:
Step 1: We employ the equations in cylindrical coordinates.
[tex]x=r \cos \theta, y=r \sin \theta, z=z[/tex]
Thus, in cylindrical coordinate system,
E lies above the paraboloid [tex]z=r^{2}[/tex] and below the plane [tex]z=2 r \sin \theta[/tex] .
Therefore, the top part E is [tex]z=2 r \sin \theta[/tex] is the cross-section between paraboloid and the plane.
Now, at the cross-section use, [tex]r^{2}=2 r \sin \theta[/tex] and [tex]z=2 r \sin \theta[/tex] .
Thus, the limits are given as ;
[tex]r^{2} \leq z \leq 2 r \sin \theta \quad 0 \leq r \leq 2 \sin \theta[/tex]
Apply the limits as compute the integration;
[tex]\begin{aligned}I=\iiint_{E} z d V &=\int_{0}^{\pi} \int_{0}^{2 \sin \theta} \int_{\tau^{2}}^{2 r \sin \theta} z r d r d z d \theta \\&=\int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[\frac{z^{2}}{2}\right]_{r^{2}}^{2 r \sin \theta} r d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{2} \sin ^{2} \theta-r^{4}\right] r d r d \theta\end{aligned}[/tex]
[tex]\begin{aligned}&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{3} \sin ^{2} \theta-r^{5}\right] d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi}\left[r^{4} \sin ^{2} \theta-\frac{r^{6}}{6}\right]_{0}^{2 \sin \theta} d \theta \\&=\frac{8}{3} \int_{0}^{\pi} \sin ^{6} \theta d \theta\end{aligned}[/tex]
Step 2: Now, calculate for the [tex]I_{1}=\int_{0}^{\pi} \sin ^{6} \theta d \theta[/tex].
[tex]\begin{aligned}\sin ^{6} \theta &=\left(\sin ^{2} \theta\right)^{2} \times \sin ^{2} \theta \\&=\left[\frac{1-\cos 2 \theta}{2}\right]^{2} \times\left[\frac{1-\cos 2 \theta}{2}\right] \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\cos ^{2} 2 \theta\right)(1-2 \cos 2 \theta) \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\frac{1+\cos 4 \theta}{2}\right)(1-2 \cos 2 \theta)\end{aligned}[/tex]
[tex]\begin{aligned}&=\frac{1}{16}(3-4 \cos 2 \theta+\cos 4 \theta)(1-2 \cos 2 \theta) \\&=\frac{1}{32}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta)\end{aligned}[/tex]
Further compute the value of
[tex]\begin{aligned}I_{1} &=\int_{0}^{\pi} \sin ^{6} \theta d \theta \\&=\frac{1}{32} \int_{0}^{\pi}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta) d \theta \\&=\frac{1}{32}\left[10 \theta-\frac{15 \sin 2 \theta}{2}+\frac{3 \sin 4 \theta}{2}-\frac{\sin 6 \theta}{6}\right]_{0}^{\pi} \\&=\frac{5 \pi}{16}\end{aligned}[/tex]
Therefore, the obtained integral is [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].
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The complete question is -
Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate ∫∫∫E z dV, where E lies above the paraboloid
z = x² + y²
and below the plane z = 2y. Use either the Table of Integrals or a computer algebra system to evaluate the integral.
On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).
Which statement is true about the graphed function?
F(x) < 0 over the interval (–∞, –4)
F(x) < 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –4)
The points on the graph of (-4, 0), (-2.5, -12), and (0, -3), gives;
F(x) > 0 over the interval (-∞, -4)Which method can be used to find the true statement?From the description of the graph, we have;
Furthest point left of the graph = (-4, 0)
The furthest point right on the graph = (0, -3) = The maximum point
The minimum point = (-2.5, -12)
F(x) < 0 at the minimum point
The minimum point is to the right of x = -4
The point the graph crosses the y-axis = (0, -3)
Therefore;
The interval of the graph where F(x) is larger than 0 is to the left of (-4, 0), is the interval (-∞, -4)
The true statement is therefore;
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out
Miranda decided to buy a $50,000 term life insurance policy from Palmetto Insurance Company to cover
her until she is 55. She is currently 50 years old and in good health. The probability of death in a given
year is provided by the Social Security Actuarial Life Table.
= Age
50
51
52
53
54
P(Death at a Given Age) 0.0032 0.0035 0.0038 0.0041 0.0044
1. Fill in the expected cost to Palmetto Insurance Company for each year Miranda has the policy.
Age at
Death
Expected
Cost
50
Check
$
Z=
51
$
x
52
$
x
53
$
x
54
$
x
2. The insurance company wants to make a profit of $500. How much would they need to charge for the
policy? $
x
Finish
The expected cost to Palmetto Insurance Company for each year Miranda has the policy is illustrated.
How to illustrate the information?Term policy amount = $50000
x (age) 50 51 52 53 54
p (death) 0.0032 0.0035 0.0038 0.0041 0.0044
1. Expected cost to Palmetto Insurance Company for each year Miranda has the policy
= P(death for a given year)*term policy amount
Thus, when x = 50
Expected cost = P(x) * 50000 = 0.0032*50000 = $160
Thus, when x = 50
Expected cost = P(x) * 50000 = 0.0032*50000 = $160
Thus, when x = 51
Expected cost = P(x) * 50000 = 0.0035*50000 = $175
Thus, when x = 52
Expected cost = P(x) * 50000 = 0.0038*50000 = $190
Thus, when x = 53
Expected cost = P(x) * 50000 = 0.0041*50000 = $205
Thus, when x = 54
Expected cost = P(x) * 50000 = 0.0044*50000 = $220
Thus, the table will become
x (age) 50 51 52 53 54
p (death) 0.0032 0.0035 0.0038 0.0041 0.0044
Expected cost 160 175 190 205 220
2) For company to make $500 profit
They should charge $500 more than their expected cost
= $(500 + 160 + 175 + 190 + 205 + 220)
= $1450
Thus, they need to charge $1450 overall or (1450/5 = $290 per year)
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The sum of two odd numbers is 80 and their difference is 6. work out these numbers.
The two odd numbers are 43 and 37.
What are whole numbers?Whole numbers are positive numbers belonging to the set W ∈ {1, 2,3, 4, ...}
The two odd numbers can be represented as (2m-1) and (2n-1) respectively sum=80 and difference = 6
Let m and n be two whole numbers
Therefore
,[tex]2m-1) + (2n-1)= 80\\(2m-1) - (2n-1)= 6\\\\2(m+n-1)=80\\2(m-n)=6\\\\m+n = 41\\m-n=3\\[/tex]
Adding the two equations
[tex](m+n)+(m-n)=2m=44\\m=22\\n=m-3=19\\[/tex]
so m=22 ad n=19. our two odd numbers are 2m-1 = 43 and 2n-1 = 37
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please help me im stuck on this
Answer:
Step-by-step explanation:
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A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 6.5 inches and standard deviation of 0.5 inches. If a sample of 46 items are chosen at random, what is the probability the sample's mean length is greater than 6.3 inches? Round answer to four decimal places.
The probablity that the sample's mean length is greate than 6.3 inches is0.8446.
Given mean of 6.5 inches,standard deviation of 0.5 inches and sample size of 46.
We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.
Probability is the likeliness of happening an event. It lies between 0 and 1.
Probability is the number of items divided by the total number of items.
We have to use z statistic in this question because the sample size is greater than 30.
μ=6.5
σ=0.5
n=46
z=X-μ/σ
where μ is mean and
σ is standard deviation.
First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.
z=6.3-6.5/0.5
=-0.2/0.5
=-0.4
p value from z table is 0.3446
Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.
Hence the probability that the mean length is greater than 6.3 inches is 0.8446.
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