Answer:
5. 94 square units.
6. 159 square units.
Step-by-step explanation:
By using Heron's Formula: [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
5.
Using the values c = 17, b = 13, and a = 15,
Calculate the semi-perimeter of the triangle as:
s =[tex]\frac{a+b+c}{2}[/tex]
s =[tex]\frac{15 + 13 + 17}{2}=22.5[/tex]
Using Heron's formula, the area of the triangle is:
A = [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
A = [tex]\sqrt{22.5(22.5-15)(22.5-13)(22.5-17)}=93.90[/tex] ≈94 approximately
Therefore, the area of triangle ABC is approximately 94 square units.
6.
Using the values, a = 23, b = 25, and c = 14,
we can calculate the semi-perimeter of the triangle as:
s =[tex]\frac{a+b+c}{2}[/tex]
s =[tex]\frac{ 23 + 25 + 14}{2}[/tex]
s = 31
Using Heron's formula, the area of the triangle is:
A = [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
A = [tex]\sqrt{31(31-23)(31-25)(31-14)}=159.05[/tex]≈159 approximately
Therefore, the area of triangle ABC is approximately 159 square units.
Answer:
5) 93.90 square units (2 d.p.)
6) 159.05 square units (2 d.p.)
Step-by-step explanation:
To find the area of a triangle given its side lengths, use Heron's formula.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
[tex]\hrulefill[/tex]
Question 5Given side lengths of triangle ABC:
a = 15b = 13c = 17To find the half perimeter, s, half the sum of the 3 side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{15+13+17}{2}=22.5[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{22.5(22.5-15)(22.5-13)(22.5-17)}\\&=\sqrt{22.5(7.5)(9.5)(5.5)}\\&=\sqrt{8817.1875}\\&=93.89988019...\\&=93.90\; \sf units^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of triangle ABC is 93.90 square units, to two decimal places.
[tex]\hrulefill[/tex]
Question 6Given side lengths of triangle ABC:
a = 23b = 25c = 14To find the half perimeter, s, half the sum of the 3 side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{23+25+14}{2}=31[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{31(31-23)(31-25)(31-14)}\\&=\sqrt{31(8)(6)(17)}\\&=\sqrt{25296}\\&=159.0471628...\\&=159.05\; \sf units^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of triangle ABC is 159.05 square units, to two decimal places.
Pretty sure x is 75 but what do i write for the reason?
Thank uu
Answer:
Step-by-step explanation:
Interior angle sum = 180
2x - 45 + x = 180
3x - 45 = 180
x - 15 = 60
x = 75
HELP Plsssssssssssss
Answer:
[tex]9^{\frac{1}{8}x }[/tex]
Step-by-step explanation:
The function in the question
[tex]\sqrt[4]{9} ^{\frac{1}{2}x }[/tex]
is equivalent to
[tex]9^{(\frac{1}{4})(\frac{1}{2} x) }[/tex]
where you multiply the powers and get the final answer
[tex]9^{\frac{1}{8}x }[/tex]
For positive acute angles A and B, it is known that SinA= 11/61 and tan B=4/3. Find the value of Cos(A-B) in simplest form.
For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.
We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).
First, we need to find the value of cosA and sinB:
Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:
cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61
Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:
hypotenuse = √(4² + 3²) = 5
sinB = opposite/hypotenuse = 4/5
Now we can substitute these values into the formula:
cos(A-B) = cosA cosB + sinA sinB
= (60/61)(3/5) + (11/61)(4/5)
= 180/305 + 44/305
= 224/305
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The owner of a computer store estimates profits using
the equation P = 4x² - 15x - 20 where P is the profit, in
dollars, and x is the number of
computers sold.
What is the estimated profit when 60 computers are
sold?
$26,400
$15,320
O $14,400
$13,520
$13,480
Answer:
(e) $13,480
Step-by-step explanation:
You want the estimated profit from selling 60 computers, if the profit from selling x computers is P = 4x² -15x -20.
ProfitPut 60 where x is in the profit equation and do the arithmetic.
The result is an estimated profit of $13,480.
__
Additional comment
To simplify evaluation, the polynomial can be written in "Horner form:"
P = (4x -15)x -20
Evaluating it this way takes fewer math operations and generally involves smaller numbers.
<95141404393>
PLEASE HELP ME!!!!! The cost that a carpet cleaning company charges is directly proportional to the number of rooms cleaned. The cost is $22 for each room.
(a) Write a direct variation equation to represent the cost.
(b) How many rooms can a hotel pay the company to clean for $200? Write and solve an equation.
(c) Suppose the hotel plans to tip the carpet cleaners $40, how many rooms can the hotel get cleaned for $200 now? Write and solve an equation.
Answer:
Step-by-step explanation:
A submarine dives to a depth of 3775 m. It then climbs to a depth of 1395 m before descending one more time to a depth of 2890 m. How many meters in total has the submarine dived? What is the total distance (up and down) it has travelled? (Include the first descent in your calculations).
Step-by-step explanation:
3775 + 2890-1395 = total diving meters = 5270 m
Total movement = 3775 + ( 3775 - 1395 ) + (2890 - 1395 ) = 7650 m
HELP!
To keep fish in an aquarium healthy, the aquarium must maintain an average water temperature of 67°F. For 14 hours of the day, no hearing is required as the aquarium is naturally at 69°F. However, if left unheated for the remaining hours the temperature would drop to 50°F. How many degrees (during heating hours) should the tank temperature increase to maintain the average temperature?
Answer:
Step-by-step explanation:
To find out how many degrees the tank temperature should increase during the heating hours to maintain the average temperature, we need to calculate the temperature difference between the target average temperature of 67°F and the temperature during the unheated hours (50°F).
The difference in temperature is:
67°F - 50°F = 17°F
Since the heating hours account for the remaining hours of the day, which is 24 hours minus the 14 hours when no heating is required, we have:
24 hours - 14 hours = 10 hours
To maintain the average temperature of 67°F, the tank temperature should increase by 17°F during the 10 hours of heating.
To find the increase per hour, we divide the total temperature increase by the number of heating hours:
17°F / 10 hours = 1.7°F
Therefore, the tank temperature should increase by 1.7°F per hour during the heating hours to maintain the average temperature of 67°F.
here is a rhombus.A strait line joining the midpoints of two of its sides are work out the size of angle a
The size of angle can be expressed as 130 degrees
How can the side of the angle be worked out?Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees.
Considering the given figure, if we look at the right top triangle we can deduced that it is an isosceles, then the supplementary angle of angle α can be calculated as
(180 - 80)/2
= 50 degrees.
Hence, α = 180 - 50
= 130 degrees.
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Safiya needs to find a number that can be multiplied by 3√18
to result in a rational product.Which values could she use?
Safiya can use either ∛12 or ∛(1/6) to find a rational product when multiplied by ∛18. So, correct options are e and f.
The cube root of 18 is an irrational number because it cannot be expressed as a fraction of two integers. Safiya needs to find a rational number that, when multiplied by ∛18, results in a rational product. To do this, she needs to look for cube roots of numbers that are perfect cubes of integers.
Option a) ∛4 is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option b) ∛18 is the given number and is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option c) ∛3 is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option d) ∛(1/18) is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option e) ∛12 is a rational number and it can be expressed as ∛(2³ × 3). Therefore, it is a valid choice.
Option f) ∛(1/6) is a rational number and can be expressed as ∛(1/216). Therefore, it is a valid choice.
So, correct options are e and f.
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what is √5^9 written without using any radicals?
Step-by-step explanation:
the square root of 5 can be written as 5 ^ (1/2).
We can then multiply the exponents, so it's 9/2.
So the answer could be written as 5 ^ (9/2).
The domain of this emath equation is
Answer:
x ≥ 5
Step-by-step explanation:
You want the domain of the equation y = √(x -5) -1.
DomainThe domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...
x -5 ≥ 0
x ≥ 5 . . . . . . the domain of this function
__
Additional comment
The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.
<95141404393>
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
The required sample size for the confidence interval and given margin of error is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
[tex]\pi = 0.5[/tex]
Then the sample size for M = 0.04 is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]
n = 1037.
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I am struggling bad Can I get help finding the Domain and Range thank you everyone
The domain and the range of the graph seen in the figure are X = {- 5, - 4, - 1, 3} (or x ∈ [- 5, 3]) and Y = {- 2, 0, 2, 4} (or y ∈ [- 2, 4]).
How to determine the domain and the range of the graph
Herein we find a graph generated by four points of the form (x, y) set on Cartesian plane. The domain of the graph consists in the set of all x-coordinates of the graph, whereas range is for the set of all y-coordinates.
Domain
X = {- 5, - 4, - 1, 3}
(Interval notation)
x ∈ [- 5, 3]
Range
Y = {- 2, 0, 2, 4}
(Interval notation)
y ∈ [- 2, 4]
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For what values of x does 5x^2+4x-4= 0
The values of x that satisfy the equation are x = (-4 + 2√6) / 5 and x = (-4 - 2√6) / 5
What values of x satisfy the given equation?The values of x that satisfy the equation 5x² + 4x - 4 = 0 can be determined using the quadratic formula given below:
x = (-b ± √(b² - 4ac)) / (2a)
From the equation:
a = 5, b = 4, and c = -4.
Substituting these values into the quadratic formula:
x = (-(4) ± √((4)² - 4(5)(-4))) / (2(5))
Simplifying to solve for values of x
x = (-4 ± √(16 + 80)) / 10
x = (-4 ± √96) / 10
x = (-4 ± 4√6) / 10
x = (-4 ± 2√6) / 5
Hence, x = (-4 + 2√6) / 5 or x = (-4 - 2√6)
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What is true about the triangles shown in the diagram? Select all that apply.
Answers:
Choice A) Segment AC = 2*sqrt(17)
Choice B) Segment BD is 32 units long
Choice F) Segment AB is approximately 33 units long.
==========================================================
Explanation:
The triangles are similar, so we can form this proportion
CD/DA = DA/BD
2/8 = 8/x
2x = 8*8
2x = 64
x = 64/2
x = 32
BD is 32 units long
This means one of the answers is choice B. It rules out choice D.
--------------
The legs of right triangle ABD are
AD = 8BD = 32Use the pythagorean theorem to find hypotenuse AB.
a^2 + b^2 = c^2
(AD)^2 + (BD)^2 = (AB)^2
8^2 + 32^2 = (AB)^2
(AB)^2 = 64 + 1024
(AB)^2 = 1088
AB = sqrt(1088)
AB = sqrt(64*17)
AB = sqrt(64)*sqrt(17)
AB = 8*sqrt(17)
AB = 32.984845
Segment AB is approximately 33 units long.
This tells us another answer is choice F. Choice C is false because 4*sqrt(5) = 8.94427
--------------
BC = BD + DC
BC = 32 + 2
BC = 34
BC is the hypotenuse of triangle ABC
Use the pythagorean theorem to determine AC.
a^2 + b^2 = c^2
(AB)^2 + (AC)^2 = (BC)^2
(sqrt(1088))^2 + (AC)^2 = (34)^2
1088 + (AC)^2 = 1156
(AC)^2 = 1156 - 1088
(AC)^2 = 68
AC = sqrt(68)
AC = sqrt(4*17)
AC = sqrt(4)*sqrt(17)
AC = 2*sqrt(17)
Another answer is Choice A. It rules out choice E because 2*sqrt(17) = 8.2462 approximately.
Given the arithmetic sequence an with a1=−10 and d=−2, find a3.
The value of a3 in the Arithmetic sequence with a1 = -10 and d = -2 is -14.
The value of a3 in the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1) * d
Where:
- an is the nth term in the sequence
- a1 is the first term of the sequence
- d is the common difference between consecutive terms
- n is the position of the term we want to find
In this case, we are given that a1 = -10 and d = -2. We want to find the value of a3, which corresponds to the third term in the sequence (n = 3).
Plugging in the values into the formula, we have:
a3 = a1 + (3 - 1) * d
= -10 + 2 * (-2)
= -10 - 4
= -14
Therefore, the value of a3 in the arithmetic sequence with a1 = -10 and d = -2 is -14.
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Hii please answer i would appreciate it thankssss
Reason of congruency for each of the triangle are :
(a) SAS rule
(b) Triangles are not congruent.
Given are some triangles where some of the angles and sides are given to be equal.
We have to find the reason of congruency.
(a) Given two sides are equal.
One of the triangle has an included angle of 110°.
Find the included angle of the other one.
Included angle = 180 - (40 + 30) = 110°
So two sides and included angle of one is equal to the corresponding sides and angle.
So congruency is SAS rule.
(b) Length of the hypotenuse of first triangle = √(2² + 4²) = √20 cm
Length of hypotenuse of other triangle = 4 cm
The lengths are not equal.
So they are not congruent.
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Can someone answer this question
Answer: x+2
Step-by-step explanation:
It is not factorable through grouping method. You can test for factors if you divide the factor and it goes in evenly (no remainder) then, it is a factor.
I will use synthetic division to test:
X-8:
8 | 1 -14 56 -64
| 8 -48 64
1 -6 8 0 =>no remainder so yes this is a factor
X+2:
-2 | 1 -14 56 -64
| -2 32 -176
1 -16 88 -240 => remainder so NOT factor
X-2:
2 | 1 -14 56 -64
| 2 -24 64
1 -12 32 0 =>no remainder so yes this is a factor
X-4:
4 | 1 -14 56 -64
| 4 -40 64
1 -10 16 0 =>no remainder so yes this is a factor
Mrs. Sarfo is now three times as old as his daughter Joyce. If the sum of their ages 8 years ago was 48, find the girls present age
If the sum of their ages 8 years ago was 48 then the present age of girl is 16 years.
Mrs. Sarfo is three times as old as her daughter, so her present age would be 3J years.
8 years ago, Joyce's age would have been J - 8, and Mrs. Sarfo's age would have been 3J - 8.
The sum of their ages 8 years ago was 48:
(J - 8) + (3J - 8) = 48
Simplifying the equation:
4J - 16 = 48
Adding 16 to both sides:
4J = 64
Dividing both sides by 4:
J = 16
Therefore, the present age of Joyce is 16 years.
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Hellooo i’m pretty sure x is 30 but can someone tell me what im meant to write for the reason. Thank youuu
Answer:
2x and 180 - 5x are complementary angles.
2x + 180 - 5x = 90
-3x + 180 = 90
-3x = -90
x = 30
please answer all 3 and show work
The equation of the Damari's investment is B(x) = 30000 * 1.03ˣ
Sky's family should take the offer of $5000 for the boatThe rule of the function is f(x) = 8 * 0.6ˣCalculating the equations of the functionsDamari's investment
Given that
Initial value, a = 30000
B(3) = 32306.72
The function is calculated as
B(x) = a * bˣ
Using B(3), we have
30000 * b³ = 32306.72
So, we have
b³ = 1.077
Take the cube root of both sides
b = 1.03
So, we have
B(x) = 30000 * 1.03ˣ
So, the function is B(x) = 30000 * 1.03ˣ
The boat of Sky's family
Here, we have
Initial value = 6000
Rate of depreciation = 6%
So, the function is
f(x) = 6000 * (1 - 6%)ˣ
So, we have
f(x) = 6000 * (0.94)ˣ
In 2024, we have
x = 2024 - 2021
x = 3
So, we have
f(3) = 6000 * (0.94)³
Evaluate
f(3) = 4983.50
This value is less than the offered value of $5000
This means that Sky's family should take the offer
The rule of the function
Here, we have the graph
From the graph, we have
Initial value, a = 8
Rate, b = 4.8/8
So, we have
Rate, b = 0.6
So, the function is
f(x) = 8 * 0.6ˣ
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Help pleaseeeeeeeeee
16800 cubic inches of concrete is needed to make the stairs
How many cubic inches of concrete is needed to make the stairs?Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.
The given stairs can be divided into 3 rectangular prisms as shown in the image attached.
Volume of a concrete needed = Volume of A + Volume of B + Volume of C
Volume of a rectangular prism = l × w × h
where l is the length, w is the width and h is the height
For A:
l = 40, w = 10 in and h = 7 + 7 + 7 = 21 in
For B:
l = 40, w = 10 in and h = 7 + 7 = 14 in
For C:
l = 40, w = 10 in and h = 7 in
Volume of a concrete needed = (40 * 10 * 21) * (40 * 10 * 14) + (40 * 10 * 7)
Volume of a concrete needed = 8400 + 5600 + 2800
Volume of a concrete needed = 16800 in³
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At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
Answer:
Step-by-step explanation:
5/12 pounds more
Which point would NOT be a solution to the system of linear inequalities shown below
The point (4, - 1) will not be a solution to the system of linear inequalities shown.
What is the solution of the linear inequalities?The solution of the linear inequalities is calculated by simplifying the linear inequalities as follows;
The given linear inequalities;
y ≥ -x/4 + 7
y > 4x + 4
Solve the linear inequalities as follows;
4x + 4 ≥ -x/4 + 7
Collect similar terms together;
4x + x/4 ≥ 7 - 4
4x + x/4 ≥ 3
Multiply through by 4;
16x + x ≥ 12
17x ≥ 12
divide through by 17;
x ≥ 12/17
x ≥ 0.7
The value of y is calculated as;
y ≥ -x/4 + 7
y ≥ - (0.25 x 0.7) + 7
y ≥ 6.8
Since y is greater than or equal to 6.8, the point (4, - 1) will not be a solution to the system of linear inequalities shown.
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I need help with this math
Answer:
500 and 4.3
Step-by-step explanation:
A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.
5000 × 0.1 = 500
4300 × 0.001 = 4.3
Thus, the answers [in order] are 500 and 4.3
Hope this helps and feel free to ask any questions.
A 3-D jigsaw puzzle becomes a cube with a volume of 1 cubic foot when it is solved. Mr. Ruiz stores several of these puzzles in a storage nook in his classroom. The nook is shaped like a rectangular prism and has a height of 3 feet. A layer of 8 puzzles will completely cover the floor of the nook. What is the volume of the storage nook?
The volume of the storage nook is 24 cubic feet.
How to find the volume of the storage nookTo find the area of 8 puzzles, we multiply the area of one puzzle by 8:
Area of 8 puzzles = 1 square foot * 8 = 8 square feet
Now, to find the volume of the storage nook, we multiply the area of the floor by its height:
Volume of the nook = Area of the floor * Height
= 8 square feet * 3 feet
= 24 cubic feet
Hence, the volume of the storage nook is 24 cubic feet.
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here are five number cards
2,5,7,8,9
one of the cards is removed and the mean average of the remaining four number cards is 6
which card was removed
show your working
Answer:
7
Step-by-step explanation:
Since one card was removed:
6 = x/4
x = 6 X 4
x = 24
Then you sum the numbers on the five cards and subtract 24 from it
(2 + 5 + 7 + 8 + 9) - 24
= 31 - 24
= 7
Therefore card with number 7 was removed.
Can someone answer this question
The coefficients used to perform the synthetic division are given by the first option in this problem.
How to apply the synthetic division algorithm?In the synthetic division algorithm, the coefficients of a polynomial, which is the dividend, are each divided by a value.This divisor is the goes into the far left box.The standard format of the polynomial in this problem is given as follows:
[tex]6x^4 - 7x^3 + x^2 + 3[/tex]
Considering that x has a coefficient of zero, the order of the coefficients of the polynomial function is given as follows:
6, -7, 1, 0 and 3.
The divisor is of:
x + 4.
Hence the term on the left box is of:
x + 4 = 0 -> x = -4.
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The radius of a circle is 14 yards. What is the circle's circumference?
Use 3.14 for .
pls help
Use technology or a z-score table to answer the question. The odometer readings on a random sample of identical model sports cars are normally distributed with a mean of 120,000 miles and a standard deviation of 30,000 miles. Consider a group of 6000 sports cars. Approximately how many sports cars will have less than 150,000 miles on the odometer? O 300 951 O 5048 O 5700
Approximately 5048 sports cars will have less than 150,000 miles on the odometer
Mean = 120,000
Standard deviation = 30,000
Total group = 6000
Total Miles = 150,0000
An odometer is a device used to gauge how far a wheeled vehicle has driven. The tool might be mechanical, electrical, or a hybrid of the two.
Calculating the Z score -
z = x - u/a
= 15,0000 - 12,0000/30000
= 30000/30000
= 1
Using the standard normal table, to determine the value -
P ( Z<1) = 0.8413
Calculating the total number of cars -
= P value x total group of cars
= 6000 x 0.8413
= 5047.7 or 5048
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