f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.
Find the required equation:The zeroes or roots of a polynomial function are x values for which f(x) = 0If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
where a is the leading coefficient
Here in the question it is given that,
Polynomial should be with degree 3zeros of f(x) are − 3 , 4 , − 3By using the formula of polynomial function we get,
⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))
⇒ f(x) = 1(x + 3)(x - 4)(x + 3)
⇒ f(x) = (x + 3)(x² - x - 12)
⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36
⇒ f(x) = x³ + 2x² - 15x - 36
Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.
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Example
A soccer league has 60 returning players and 36 new players. Each team will have
the same ratio of returning players to new players as the league has. How many
new players will a team with 10 returning players have?
You can use a double number line to find ratios equivalent to 60: 36.
Number pairs that line up vertically represent equivalent ratios.
Returning Players 0
New Players 0
10
++
6
+6
+
-6
60
36
You can divide each quantity in 60: 36 by 6 to find the equivalent ratio 10:6.
A team with 10 returning players will have 6 new players.
1 Sophia says that you can solve the problem in the Example by multiplying both
quantities in the ratio 60:36 by. Is Sophia correct? Explain.
Answer:
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
urgent help thank you
Answer:
-4
Step-by-step explanation:
7x^3 + 5x^2 - 2
= 7*-1 + 5*1 - 2
= -7 + 5 - 2
= -4
train travelling at a uniform speed covers a distance of 255 km in Find the speed of the train and 3 4/5 1 1/2 the distance covered in hours. hours.
The speed of the train is 150 km/hour.
The distance covered by the train in 3 4/5 hours is 570 km.
The speed of a body is calculated using the formula, speed = distance/time.
The distance covered is calculated using the formula, distance = speed*time.
The time taken by a body is calculated using the formula, time = distance/speed.
In the question, we are asked for the speed of a train, when it covers a distance of 225 km in 1 1/2 hours.
Distance = 225 km.
Time = 1 1/2 hours = 1.5 hours.
Speed = Distance/Time = 225/1.5 km/hour = 150 km/hour.
Now, we are asked to calculate the distance covered by the train in 3 4/5 hours.
Speed = 150 km/hour.
Time = 3 4/5 hours = 3.8 hours.
Distance = Speed*Time = 150*3.8 km = 570 km.
Thus, the speed of the train is 150 km/hour.
The distance covered by the train in 3 4/5 hours is 570 km.
The provided question is incorrect. The correct question is:
"A train at a uniform speed covers a distance of 225 km in 1 1/2 hours. Find the speed of the train and the distance covered in 3 4/5 hours.
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Consider the following figure:
The value of a is
Answer:
125
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation according to this information and that will help us find the value of x:
65 + 60 = x add like terms
125 = x is the answer we are looking for.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{equation:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\huge\textsf{solving:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\large\textsf{60 + 65 = a}[/tex]
[tex]\huge\textsf{simplify it:}[/tex]
[tex]\large\textsf{a = 125}[/tex]
[tex]\huge\textsf{therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{a =} \frak{125}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
P=2(L+W) Solve for W
Answer:
W = (P -2L)/2
Step-by-step explanation:
P = 2(L + W) Distribute the 2
P = 2L + 2W Subtract 2L from both sides
P - 2L = 2W Divide both sides by 2
(P-2L)/2 = W
Find the length of UX
Answer:
[tex]\dfrac{8}{\sin(6^\circ)} \approx 76.53[/tex]
Step-by-step explanation:
[tex]UX \sin(6^\circ) = 8 \Rightarrow \boxed{UX = \dfrac{8}{\sin(6^\circ)} \approx 76.53}[/tex]
Consider the spiral curves given parametrically by: (see picture and answer question)
a. The arc length is given by the integral
[tex]L(r) = \displaystyle \int_3^\infty \sqrt{x'(t)^2 + y'(t)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\left(\frac{t\cos(t) - r\sin(t)}{t^{r+1}}\right)^2 + \left(-\frac{t\sin(t) + r\cos(t)}{t^{r+1}}\right)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\frac{(t^2+r^2)\cos^2(t) + (t^2+r^2)\sin^2(t)}{\left(t^{r+1}\right)^2}} \, dt \\\\ ~~~~~~~~ = \boxed{\int_3^\infty \frac{\sqrt{t^2+r^2}}{t^{r+1}} \, dt}[/tex]
b. The integrand roughly behaves like
[tex]\dfrac t{t^{r+1}} = \dfrac1{t^r}[/tex]
so the arc length integral will converge for [tex]\boxed{r>1}[/tex].
c. When [tex]r=3[/tex], the integral becomes
[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2+9}}{t^4} \, dt[/tex]
Pull out a factor of [tex]t^2[/tex] from under the square root, bearing in mind that [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex].
[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2} \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{|t| \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{t \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{\sqrt{1+\frac9{t^2}}}{t^3} \, dt[/tex]
since for [tex]3\le t<\infty[/tex], we have [tex]|t|=t[/tex].
Now substitute
[tex]s=1+\dfrac9{t^2} \text{ and } ds = -\dfrac{18}{t^3} \, dt[/tex]
Then the integral evaluates to
[tex]L(3) = \displaystyle -\frac1{18} \int_2^1 \sqrt{s} \, ds \\\\ ~~~~~~~~ = \frac1{18} \int_1^2 s^{1/2} \, ds \\\\ ~~~~~~~~ = \frac1{27} s^{3/2} \bigg|_1^2 \\\\ ~~~~~~~~ = \frac{2^{3/2} - 1^{3/2}}{27} = \boxed{\frac{2\sqrt2-1}{27}}[/tex]
a) The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].
b) r > 1 for a spiral with finite length.
c) The length of the spiral when r = 3 is (1 - 2√2) / 9 units.
How to characterize and analyze a group of parametric functions
a) The arc length formula for 2-dimension parametric functions is defined below:
L = ∫ √[(dx / dt)² + (dy / dt)²] dt, for [α, β] (1)
If we know that [tex]\dot x (t) = \frac{t \cdot \cos t - r \cdot \sin t}{t^{r+1}}[/tex], [tex]\dot y(t) = \frac{t\cdot \sin t + r\cdot \cos t}{t^{r + 1}}[/tex], α = 0 and β → + ∞ then their arc length formula is:
[tex]L = \int\limits^{\infty}_{3} {\sqrt{\left(\frac{t\cdot \cos t - r\cdot \sin t}{t^{r + 1}}\right)^{2}+\left(\frac{t\cdot \sin t + r\cdot \cos t}{t^{r+1}}\right)^{2}} } \, dt[/tex]
By algebraic handling and trigonometric formulae (cos ² t + sin² t = 1):
[tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex] (2)
The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].
b) By ratio comparison criterion, we notice that √(t² + r²) is similar to √t² = t and [tex]\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}}[/tex] is similar to [tex]\frac{t}{t^{r +1}} = \frac{1}{t^{r}}[/tex].
The integral found in part a) has a finite length if and only the governing grade of the denominator is greater that the governing grade of the numerator. and according to the ratio comparson criterion, the absolute value of the ratio is greater than 0 and less than 1. Therefore, r > 1 for a spiral with finite length.
c) Now we proceed to integrate the function:
L = ∫ [√(t² + 9) / t⁴] dt, for [3, + ∞].
L = ∫ [t · √(1 + 9 / t²) / t⁴] dt, for [3, + ∞].
By using the algebraic substitutions: u = 1 + 9 / t², du = - (18 / t³) dt → - (1 / 18) du.
L = ∫ √u du, for [3, + ∞].
L = - (1 / 9) · √(u³), for [3, + ∞].
L = - (1 / 9) · [√(1 + 9 / t²)³], for [3, + ∞].
L = - (1 / 9) · [√(2³) - √(1³)]
L = - (1 / 9) · (2√2 - 1)
L = (1 - 2√2) / 9
The length of the spiral when r = 3 is (1 - 2√2) / 9 units.
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Type the correct answer in the box.
Which trigonometric expression can be used to find value of x? Replace a and b with the correct values.
(trigonometry)
Answer:
x = 12cos(35)
Step-by-step explanation:
Well you have hyp and adj, meaning cosine. and u have the angle and need the adjacent, so side(cos(theta)).
12cos(35).
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder over the past 12 months are satisfied with their products. If there are 4 different brands of videocassette recorders made by the company, the best sampling strategy would be to use a
The best sampling strategy would be a stratified sample.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.For this problem, the 4 different brands of the recorders must be considered, hence the buyers should be divided into groups, and a proportion of each group should be sampled, hence a stratified sample should be used.
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I need help… a lot of it im so confused
[tex] \sqrt[3]{b {}^{2} } = b {}^{ \frac{2}{3} } [/tex]
2)[tex]f(4) = 2(3) {}^{4} = 2 \times 81 = 162[/tex]
3)[tex]f( \frac{1}{2} ) = \frac{1}{3} (9) {}^{ \frac{1}{2} } + 5 = \frac{ \sqrt{9} }{ 3} + 5 = 6[/tex]
4)
[tex]f(5) = - 4(2) {}^{ - 5 + 1} = - 4(2) {}^{ -4} = \frac{2 {}^{2} }{2 {}^{4} } = \frac{1}{2 {}^{2} } = \frac{1}{4} [/tex]
5)[tex]f(10) = 2e {}^{0.15 \times 10} = 2e {}^{1.5} = 8.96[/tex]
6)[tex]y = 10(b) {}^{x} \: \: \\ 10 = 10(b) {}^{0} \: duh \\ 2 = 10b {}^{1} \\ b = \frac{2}{10} = \frac{1}{5} [/tex]
7)[tex]y = a(b) {}^{x} \\ 3 = a(b) {}^{0} \\ a = 3 \\ \\75 = 3(b) {}^{2} \\ b {}^{2} = 25 \\ b = + 5 \: \: \: or \: \: \: \: b = - 5[/tex]
8)[tex]s = 1000(1 + \frac{0.045}{4} ) {}^{4 \times 10} = 1564.38[/tex]
9)[tex]s = 2500.e {}^{0.07 \times 20} = 10138[/tex]
A block exerts a force of 84 Newtons on a table.
The pressure on the table is 30 N/m².
Work out the area of the box that is in contact with the table.
Total for question 5 is 2 marks)
pressure =
force
area
Answer:
2.8m²
Step-by-step explanation:
p = F / A
A = F / p
A = 84 / 30
A = 2.8m²
will give brainliest
The possible rational roots of the given equation are 1 and -3
Solving polynomial equationsFrom the question, we are to determine all the possible rational roots of the given equation
The given equation is
x⁴ -2x³ -6x² +22x -15 = 0
To determine the rational roots, we will test for values that make the equation equal to zero
Test for -1(-1)⁴ -2(-1)³ -6(-1)² +22(-1) -15
1 + 2 - 6 - 22 -15
= -40
∴ -1 is not a root of the equation
Test for 1(1)⁴ -2(1)³ -6(1)² +22(1) -15
1 - 2 - 6 + 22 -15
= 0
∴ 1 is one of the roots of the equation
Test for -2(-2)⁴ -2(-2)³ -6(-2)² +22(-2) -15
16 + 16 - 24 - 44 -15
= -51
∴ -2 is not a root of the equation
Test for 2(2)⁴ -2(2)³ -6(2)² +22(2) -15
16 - 16 - 24 + 44 -15
= 5
∴ 2 is not a root of the equation
Test for -3(-3)⁴ -2(-3)³ -6(-3)² +22(-3) -15
81 + 54 - 54 -66 -15
= 0
∴ -3 is one of the roots of the equation
Test for 3(3)⁴ -2(3)³ -6(3)² +22(3) -15
81 - 54 - 54 + 66 -15
= 24
∴ 3 is not a root of the equation
The other roots of the equation are irrational roots.
Hence, the possible rational roots of the given equation are 1 and -3
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questions c, d, e please!
Answer:
c) 3 units
d) g(x) - f(x) = x² + 2x
e) (-∞, -2] ∪ [0, ∞)
Step-by-step explanation:
Part (c)To calculate the length of FC, first find the coordinates of point C.
The y-value of point C is zero since this is where the function f(x) intercepts the x-axis. Therefore, set f(x) to zero and solve for x:
[tex]\implies 1-x^2=0[/tex]
[tex]\implies x^2=1[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{1}[/tex]
[tex]\implies x= \pm 1[/tex]
As point C has a positive x-value, C = (1, 0).
To find point F, substitute the x-value of point C into g(x):
[tex]\implies g(1)=2(1)+1=3[/tex]
⇒ F = (1, 3).
Length FC is the difference in the y-value of points C and F:
[tex]\begin{aligned} \implies \sf FC& = \sf y_F-y_C\\ & = \sf 3-0\\ & =\sf 3\:units \end{aligned}[/tex]
Part (d)Given functions:
[tex]\begin{cases}f(x)=1-x^2\\ g(x)=2x+1 \end{cases}[/tex]
Therefore:
[tex]\begin{aligned}\implies g(x)-f(x) & = (2x+1) - (1-x^2)\\& = 2x+1-1+x^2\\& = x^2+2x\end{aligned}[/tex]
Part (e)The values of x for which g(x) ≥ f(x) are where the line of g(x) is above the curve of f(x):
point A → ∞point E → -∞Point A is the y-intercept of both functions, therefore the x-value of point A is 0.
To find the x-value of point E, equate the two functions and solve for x:
[tex]\begin{aligned}g(x) & = f(x)\\\implies 2x+1 & = 1-x^2\\x^2+2x & = 0\\x(x+2) & = 0\\\implies x & = 0, -2\end{aligned}[/tex]
As the x-value of point E is negative ⇒ x = -2.
Therefore, the values of x for which g(x) ≥ f(x) are:
Solution: x ≤ -2 or x ≥ 0Interval notation: (-∞, -2] ∪ [0, ∞)Answer:
a)
A = (0, 1)
B = (-1, 0)
C = (1, 0)
D = (-0.5, 0)
b) E = (-2, -3)
c) FC = 3 units
d) x² + 2x
e) x ≤ -2 and x ≥ 0
Explanation:
This question displays one equation of a linear function g(x) = 2x + 1 and a parabolic function f(x) = 1 - x².
a)
A point is where the linear function cuts the y axis.
y = 1 - (0)²
y = 1
A = (0, 1)
B and C point is where the parabolic function cuts the x axis.
1 - x² = 0
-x² = -1
x² = 1
x = ±√1
x = -1, 1
B = (-1, 0), C = (1, 0)
D point is where the linear function cuts x axis.
2x + 1 = 0
2x = -1
x = -1/2 or -0.5
D = (-0.5, 0)
b)
E point is where both equations intersect each other.
y = y
2x + 1 = 1 - x²
x² + 2x = 0
x(x + 2) = 0
x = 0, x = -2
y = 1, y = -3
E = (-2, -3)
c)
C : (1, 0)
To find F point
y = 2(1) + 1
y = 3
F : (1, 3)
[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]\sf d = \sqrt{(1 - 1)^2 + (3 - 0)^2}[/tex]
[tex]\sf d = \sqrt{0 + 3^2}[/tex]
[tex]\sf d = 3[/tex]
FC length = 3 units
d)
g(x) - f(x)
(2x + 1) - (1 - x²)
2x + 1 - 1 + x²
x² + 2x
e)
g(x) ≥ f(x)
2x + 1 ≥ 1 - x²
x² + 2x ≥ 0
x(x + 2) ≥ 0
[tex]\boxed{If \ x \ \geq \ \pm \ a \ then \ -a \ \leq x \ \ and \ x \ \geq \ a }[/tex]
x ≤ -2 and x ≥ 0
Find all the missing values to make the equation true
The missing value in the logarithm are as follows:
log₃ 7 - log₃ 2 = log₃ (7 / 2)log₉ 7 + log₉ 4 = log₉ 28log₆ 1 / 81 = - 4 log₆ 3How to solve logarithm?Using logarithm rule,
logₐ b - logₐ c = logₐ (b / c)
logₐ b + logₐ c = logₐ (b × c)
Therefore,
log₃ 7 - log₃ 2 = log₃ (7 / 2)
log₉ 7 + log₉ 4 = log₉ (7 × 4) = log₉ 28
log₆ 1 / 81 = log₆ 81⁻¹ = log₆ 3⁻⁴ = - 4 log₆ 3
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Which geometric sequence has a common ratio of -9? (only one is correct)
a) {-1, -9, 81, 729, …}
b) {-9; -81; -729; -6,561; …}
c) {1, -9, 81, -729, …}
d) {81; 729; 6,561; 59,049; …}
C
1, -9 , 81 , -729 .....
ratio :-
R1 = -9/1 = -9
R2 = 81/-9 = -9
R3 = -729 / 81 =-9
so ,. R1= R2= R3
find the positive square roots by division method of 151,321
The positive square roots of the number 151,321 according to the task content can be determined by means of division as; 389.
What are the square roots of 151,321 by means of division method?It follows from.the task content above that the number given is; 151,321 whose positive square roots is to be determined.
Upon testing different integers as divisor on the number 151,321; it is concluded that the only positive integer by which 151,321 can be divided to result in a whole is; 389.
Hence, the positive square root of the number 151,321 is; 389.
Consequently, it can be concluded that the positive square root of the number, 151,321 as in the task content is; 389 which is itself a prime number as it is only divisible by 1 and itself.
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please help! will give brainliest to whoever answers
maths functions
Answer:
1. f(x) is reflected across the x-axis
2. f(x) is translated 1 unit up
3. f(x) is vertically scaled by a factor of 2
4. f(x) is reflected across the x-axis AND is vertically scaled by a factor of 2
5. f(x) is vertically scaled by a factor of 3 AND is translated 1 unit down
6. f(x) is vertically scaled by a factor of 1/6 AND is translated 1 unit up
Solving question:
(1) [tex]g(x) = -f(x)[/tex]
This graph has been reflected in the x axis. Equation: [tex]\sf g(x) = -\dfrac{2}{x}[/tex]
(2) [tex]g(x) = f(x) + 1[/tex]
Graph has been translated 1 units up vertically. Equation: [tex]\sf g(x) = \dfrac{2}{x} +1[/tex]
(3) [tex]g(x) = 2f(x)[/tex]
This graph has been stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = \dfrac{4}{x}[/tex]
(4) [tex]g(x) = -2f(x)[/tex]
This graph has been reflected in the x axis and stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = -\dfrac{4}{x}[/tex]
(5) [tex]g(x) = 3f(x) - 1[/tex]
This graph has been stretched vertically by a factor of 3 and translated 1 units down. Equation: [tex]\sf g(x) = \dfrac{6}{x} -1[/tex]
(6) [tex]g(x) = \frac{1}{6} f(x) + 1[/tex]
This graph has been stretched vertically by a factor of 1/6 and translated 1 units up. Equation: [tex]\sf g(x) = \dfrac{1}{3x} +1[/tex]
cual es el valor de x+5=7
Answer: x = 2
Work Shown:
x+5 = 7
x+5-5 = 7-5
x = 2
Subtract 5 from both sides to isolate x. This is to undo the plus 5.
Solve the equation: (1-x)2³ = 8
Answer:
0
Step-by-step explanation:
because 1-0=1*2^3=8
because2^3=8
=
Use the Fundamental Counting Principle to solve.
A television programmer is arranging the order that three movies will be seen between the hours of 6 P.M. and 12
A.M. Two of the movies have a G rating, and they are to be shown in the first two time blocks. One of the movies is
rated NC-17, and it is to be shown in the last of the time blocks, from 10 P.M. until 12 A.M. Given these restrictions,
in how many ways can the three movies be arranged during the indicated time blocks?
The number of different ways the three movies can be arranged during the indicated time blocks is.
(Type a whole number.)
[tex]number \: of \: movies = 3 \\ permutations = 2 \\ \\ c( \gamma ) = 2! \times 1 = 2 \: ways[/tex]
[tex]g(1) \: \: \: \: g(2) \: \: \: \: nc(17) \\ g(2) \: \: \: \: g(1) \: \: \: \: nc(17)[/tex]
Can someone help me with a step by step process of how to solve this? Calculus 2
If you fix a point on the curve in the given interval, and revolve that point about the [tex]x[/tex]-axis, it will trace out a circle with radius given by the function value [tex]y[/tex] for that point [tex]x[/tex]. The perimeter of this circle is then [tex]2\pi(8\sqrt x) = 16\pi \sqrt x[/tex].
The surface in question is essentially what you get by joining infinitely many of these circles at every point in the interval [0, 9].
So, the surface area is given by the definite integral
[tex]\displaystyle \int_0^9 16\pi \sqrt x \, dx = 16\pi\times\frac23 x^{3/2}\bigg|_{x=0}^{x=9} = \frac{32\pi}3 \left(9^{3/2} - 0^{3/2}\right) = \boxed{288\pi}[/tex]
What is The solution to -122 < -3(-2 - 8x) - 8x
A. x<8
B. x<-2
C. x>5
D. x>-8
Answer:
D.
Step-by-step explanation:
We can solve by simply isolating x:
[tex]-122 < -3(-2-8x)-8x\\-122 < 6+24x-8x\\-122 < 6+16x\\-128 < 16x\\-8 < x\\OR\\x > -8[/tex]
You can check by plugging in any value greater than -8
-122<-3(-2-8(-7))-8*-7
-122<-3(-2+56)+56
-122<-3(54)+56
-122<-162+56
-122<-106
what is (4x8) divided by (8+2)
Answer:
3.2
Step-by-step explanation:
4 x 8 / 8 + 2
32/10
=3.2
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
The standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
How to illustrate the information?From the information given, it was stated that the students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury.
Based on the information given, it should be noted that the appropriate thing to do is to find the z score for the 75th percentile.
This will be looked up in the distribution table. In this case, the value is 0.674. Therefore, standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
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1. What is the measure of angle x? O 60° O 90° O 45° O 30°
Answer:
Angle x= 60°
Step-by-step explanation:
For the triangle HIL, you're going to add 30+90=120
Angles in a triangle add up to 180.
So, therefore,
180-120=60 so angle L must equal 60.
HJ is a straight line and angles in a straight line add up to 180.
180-90=90
Angle JIL is equal to 90.
To find y you add 90+45 which equals 135.
Again, angles in a triangle add up to 180.
180-135=45
So,
y = 45
Now we are told that IJK is a right angle and that we are given that IJL is 45. 45 is half of 90 so LJK must be 45.
To find angle JLK we must add angle L and angle y.
60+45=105
Angles in a straight line add up to 180. So,
180-105=75
75 = Angle JLK
75+45=120
Angles in a triangle add up to 180 so,
180-120= 60
Angle x= 60°
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The volume of a packing box is 5 - x cubic feet. The width of the box is x feet and the length is x - 2 feet
Answer:
Step-by-step explanation:
The average of six positive integers starting with a is equal to b. What is the average of five consecutive integers ending with b?
a)a+1
b)a-1
C)a+2
d)a+3
e)a+4
The average of the five consecutive numbers ending with b in discuss when expressed in terms of a is; Choice D; a+3.
What is the average of five consecutive integers ending with b?First, since it was given in the task content that the average of six positive consecutive odd integers starting with a is equal to b, it therefore follows that;
(a+a+2+a+4+a+6+a+8+a+10)/6 = b
6b=6a+30
b=a+5
Also, let the average of the consecutive intergers ending with b be denoted by; x.
(b+b-1+b-2+b-3+b-4)/5 = x
=(5b-10)/5
=b–2
The average, x=b – 2 (where b = a-5)
Ultimately, the value of the required average is; = a+5-2 = a+3.
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(4x + 5) - (2x - 3)
Answer:
2x + 8
Step-by-step explanation:
(4x + 5) - (2x - 3)
4x + 5 - 2x + 3
2x + 8
Answer: 2x+8
Step-by-step explanation:
4x+5-2x+3
=2x+8
Figure ABCD Is a kite. Find x
Answer:
x = 8
Step-by-step explanation:
Diagonals of a kite cross at right angles. That gives us a relation that can be solved for x.
SetupThe measure shown is equal to the angle measure of 90°.
14x -22 = 90
SolutionWe can solve this 2-step linear equation in the usual way.
14x = 112 . . . . . . step 1, add the opposite of the constant to get x alone
x = 112/14 = 8 . . . step 2, divide by the coefficient of x
The value of x is 8.
The net of a pyramid is shown below. 4in 4in 4in 4in 8in. The surface area of the solid is __ square inches.
Answer:
80 in.²
Step-by-step explanation:
The total surface area of the pyramid is the sum of the area of the base and the areas of the 4 triangular sides.
Square: area = s²
Square: side = 4 in.
Triangular side: area = bh/2
Triangular side: base = 4 in.; height = 8 in.
Area of the base: s² = (4 in.)² = 16 in.²
Total area of the 4 triangular sides: 4 × bh/2 = 2bh = 2 × 4 in. × 8 in. = 64 in.²
Surface area = 16 in.² + 64 in.² = 80 in.²
