Answer:
7161
Step-by-step explanation:
7 + 7(2) + 7(2)² + ... + 7(2)⁹
= ∑₁¹⁰ 7(2)ⁿ⁻¹
= 7 (1 − 2¹⁰) / (1 − 2)
= 7161
Restate the number 4,587,902.453.
Expanded form:
Written form:
Answer:
Expanded form: 4,000,000 + 500,000 + 80,000 + 7,000 + 900 + 2 + 0.4 + 0.05 + 0.003
Word form: Four million, five hundred eighty-seven thousand, nine hundred two and four hundred fifty-three thousandths.
Whats 18x^3 divided by 7x?????
Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?
Answer:
The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 100[/tex]
The percent of people who write this exam obtain scores between 350 and 650
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]
[tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]
[tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]
From the z-table [tex]P(Z < -1.5 ) = 0.066807[/tex]
and [tex]P(Z < 1.5 ) = 0.93319[/tex]
=> [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]
=> [tex]P(350 < X 650 ) = 0.866[/tex]
Therefore the percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
What is the value of s?
Answer:
s = 8
Step-by-step explanation:
2s = s + 8
2s - s = 8
s = 8
The table above shows some values of the functions f
and g. What is the value of f(g(1)) ?
A) 2
B) 3
C) 4
D) 5
Answer:
a
Step-by-step explanation:
g(1)=5
f(g(1))=f(5)
f(5)=2
Figure out if the figure is volume or surface area.
(and the cut out cm is 4cm)
Answer:
Surface area of the box = 168 cm²
Step-by-step explanation:
Amount of cardboard needed = Surface area of the box
Since the given box is in the shape of a triangular prism,
Surface area of the prism = 2(surface area of the triangular bases) + Area of the three rectangular lateral sides
Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]
= [tex]\frac{1}{2}(6)(4)[/tex]
= 12 cm²
Surface area of the rectangular side with the dimensions of (6cm × 9cm),
= Length × width
= 6 × 9
= 54 cm²
Area of the rectangle with the dimensions (9cm × 5cm),
= 9 × 5
= 45 cm²
Area of the rectangle with the dimensions (9cm × 5cm),
= 9 × 5
= 45 cm²
Surface area of the prism = 2(12) + 54 + 45 + 45
= 24 + 54 + 90
= 168 cm²
Please help. I’ll mark you as brainliest if correct!
Answer:
Children = 150
Students = 98
Adults = 75
Step-by-step explanation:
C + S + A = 323
5C + 7S + 12A = 2336
A = 1/2C
C = 150
S = 98
A = 75
Two sides of a triangle are equal length. The length of the third side exceeds the length of one of the other sides by 3 centimeters. The perimeter of the triangle is 93 centimeters. Find the length of each of the shorter sides of the triangle
Answer:
30 cm
Step-by-step explanation:
let x be the lenght of the two sides of equal lenghts, so the other is x+3
and the perimeter is x+x +x +3
P=3x+3
P=3(x+1)
93=3(x+1)
31=x+1
x=30
so the shorter sides are of 30 centimeters and the longest is 33
Evaluate 3h(2) + 2k(3) =
Answer:
6h + 6kStep-by-step explanation:
[tex]3h\left(2\right)+2k\left(3\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=3h\times \:2+2k\times \:3\\\\\mathrm{Multiply\:the\:numbers:}\:3\times \:2=6\\\\=6h+2\times \:3k\\\\\mathrm{Multiply\:the\:numbers:}\:2\times \:3=6\\\\=6h+6k[/tex]
Answer:
Answers for E-dge-nuityyy
Step-by-step explanation:
(h + k)(2) = 5
(h – k)(3) = 9
Evaluate 3h(2) + 2k(3) = 17
Click on the picture for the answer
Answer:
the answer is 1/14
hope this helps you
9514 1404 393
Answer:
(a) 1/14
Step-by-step explanation:
Fractions are multiplied by multiplying numerators and denominators. They are reduced by cancelling common factors. When a product has an even number of minus signs, it is positive.
[tex]\left(-\dfrac{3}{7}\right)\cdot\left(-\dfrac{1}{6}\right)=\dfrac{(-3)(-1)}{7\cdot6}=\dfrac{3}{7\cdot2\cdot3}=\dfrac{1}{7\cdot2}=\boxed{\dfrac{1}{14}}[/tex]
Read the following scenario, which is represented by a polynomial expression. Then answer the questions to interpret the parts of the expression in terms of the given context.
The volunteers at a high school football team’s concession stand are trying to decide on the price of the hot dogs they are selling. When they charge $2 for a hot dog, they sell an average of 70 hot dogs per game. With every $1 increase in the price, the number of hot dogs sold per game decreases by 8.
The volunteers can calculate the revenue earned from selling the hot dogs at each game using the expression -8x2 + 54x + 140, where x is the number of $1 increases in price.
Part A
What is the constant term in the polynomial expression, and what does it represent?
Answer:
x is the number of $1 increase in the price.
If there is no increase, then the total money earned is
2 × 70 = 140
If there is $1 increase, then the total money earned is
(2 + 1) × [70 - 8(1)]
If there is $2 increase, then the total money earned is
(2 + 2) × [70 - 8(2)]
If we continue the pattern, for x times $1 increase, total money earned is
(2 + x)(70 - 8x) = -8x^{2} +54x+140−8x2+54x+140
If we substitute x = 0 in the above equation, we will get
the total money earned = $140.
It means if there is no increase, then the total money earned = 140.
Hence, 140 is the constant term and it represents that there is no increase in price.
Which points are on the graph of a linear function? Select all that apply.
(-1, 7), (0,5), (1,3)
(-1, 1), (0, 0), (1, 1)
(0,5), (2,5), (3, 14)
(0, -3), (2, 5), (4, 13)
Answer:
Step-by-step explanation:
(-1,7), (0,5), (1,3)
and
(0,-3), (2,5), (4,13)
After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth
$213,022?
Provide your answer below:
9514 1404 393
Answer:
19 years
Step-by-step explanation:
The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
Solving for t, we get ...
t = log(A/P)/(n·log(1 +r/n))
Using the given values, we find t to be ...
t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000
The investment will be worth $213,022 after 19 years.
inveres laplace transform (3s-14)/s^2-4s+8
Complete the square in the denominator.
[tex]s^2 - 4s + 8 = (s^2 - 4s + 4) + 4 = (s-2)^2 + 4[/tex]
Rewrite the given transform as
[tex]\dfrac{3s-14}{s^2-4s+8} = \dfrac{3(s-2) - 8}{(s-2)^2+4} = 3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}[/tex]
Now take the inverse transform:
[tex]L^{-1}_t\left\{3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3L^{-1}_t\left\{\dfrac{s-2}{(s-2)^2+2^2}\right\} - 4L^{-1}_t\left\{\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3e^{2t} L^{-1}_t\left\{\dfrac s{s^2+2^2}\right\} - 4e^{2t} L^{-1}_t\left\{\dfrac{2}{s^2+2^2}\right\} \\\\ \boxed{3e^{2t} \cos(2t) - 4e^{2t} \sin(2t)}[/tex]
A player at a fair pays Rs. 100 to roll a dice. The player receives Rs. 50 if the number of dots facing up is equal to 5, Rs. 200 if the number is 6, but nothing otherwise. Find the expected value of the reward Y. What is the expected value of the gain? Find out the standard deviation of Y.
Answer:
The dice has 6 options:
if the outcome is 5, player wins 50
if the outcome is 6, player wins 200
if the outcome is another number, the player does not win anything.
Now, remember that the expected value can be written as:
E = ∑xₙpₙ
where xₙ is the event n, and pₙ is the probability of that event.
for a dice, the probabilty for each number is 1/6
The expected value is:
E = (1/6)*(0 + 0 + 0 + 0 + 50 + 200) = 41.66
The expected gain will be E - 100 (because the player pays 100 in order to play)
Then the expected gain is:
G = 41.66 - 100 = -58.33
The standard deviation can be written as:
s = √( ∑(x - x)^2/n)
where x is the mean, in this case the mean is:
(200 + 50 + 4*0)/6 = 41.66 and n = 6.
s = √( (1/6)*(4*(0 - 41.66)^2 + (50 - 41.66)^2 + (200 - 41.66)^2) ) = 73
So we have a lot of standard deviation on Y.
Solve x2 + 9x + 8 = 0 by completing the square. What are the solutions?
O (1.-8)
O (1.8)
O (-1-8)
Rabi Sahu fixed the marked price of his radio to make a profit of 30 %. Allowing 15 % discount on the marked price, the radio was sold. What percent profit did he make?
The percent profit that Rabi made will be 10.5%
Let's assume that the price of the house is $100.
Since he fixed the marked price of the good to make a profit of 30%, then the price will be:
= $100 + (30% × $100)
= $100 + $30
= $130
Now, there is a discount of 15%, then the selling price of the good will be:
= $130 - (15% × $130)
= $130 - (0.15 × $130)
= $130 - $19.50
= $110.50
Then, the percentage of profit made will be:
= [($110.50 - $100) / $100] × 100%
= $10.50/$100 × 100%
= 10.5%
In conclusion, the percent profit that he makes is 10.5%.
Read related link on:
https://brainly.com/question/16306955
Which is a factor of: 2x2+10x+8 ?
Answer:
2 ( x+4) ( x+1)
Step-by-step explanation:
2x^2+10x+8
Factor out 2
2 ( x^2 +5x+4)
What two numbers multiply to 4 and add to 5
4*1 = 4
4+1 = 5
2 ( x+4) ( x+1)
[tex] \large{ \underline{ \underline{ \bf{ \pink{To \: factorise}}}}}[/tex]
2x² + 10x + 8Factorisation:By middle term factorisation,
⇛ 2x² + 2x + 8x + 8
⇛ 2x(x + 1) + 8(x + 1)
⇛ (2x + 8)(x + 1)
⇛ 2(x + 4)(x + 1)
☃️ Now you can break it down and check which are the factors of the polynomial according to options.
━━━━━━━━━━━━━━━━━━━━
Need the help thanks guys
Answer:
Option D is the correct answer.
Step-by-step explanation:
The equation of the function is in vertex form. Thus, we can analyze the equation to determine the x and y values of the vertex. We know that the template format of a vertex form equation is as follows:
f(x) = a(x – h)2 + k . The only constants we need are h and k, where 'h' is the x-value of our vertex and 'k' is the y-value of our vertex.
The value of 'k' can be found quite simply by looking at the equation: -9.
The value of 'h' is a little trickier, as we must take into account the 'subtract' sign of the template equation, meaning that the '+7' in the given equation actually means that we are subtracting negative seven. Thus, the value of 'h' is -7.
Thus, the vertex of this graph is (-7,-9).
This means that option D is correct.
Answer:
The vertex is at ( -7, -9)
Step-by-step explanation:
y = (x+7)^2 -9
This is written in vertex form
y = a( x-h)^2 +k where ( h,k) is the vertex
y = ( x - -7)^2 + -9
The vertex is at ( -7, -9)
Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x
Answer:
[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]
Step-by-step explanation:
Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:
1) [tex]t = 2-x[/tex] Given
2) [tex]y = 5\cdot x +11[/tex] Given
3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties
4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property
5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property
6) [tex]y = -5\cdot (-x)+11[/tex] [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]
7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property
8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse
9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties
10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property
11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]
12) [tex]y = (-5)\cdot t +21[/tex] By 1)
13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result
14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition
15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition
16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property
17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property
18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result
In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].
Pls help!!
An educator hypothesizes that the median of the number of students enrolled in cyber schools in school districts in southwestern Pennsylvania is 25. At a = 0.05, is there enough evidence to reject the educator’s claim? The data are shown here. What benefit would this information provide to the school board of a local school district? 12 41 26 14 4 38 27 27 9 11 17 11 66 5 14 8 35 16 25 17
Answer:
nbbhhghhhjjjjjjjjjkjjjjnnmmmmmmmmbv b b j
graph the linear equation using the slope and y-intercept y=1/9x+5
Answer:
Slope= 1/9
Y-Intercept= 5
Solve for x: −3x + 3 −1 b. x −3
Answer:
2/3
Step-by-step explanation:
Your −3x + 3 −1 is not an equation and thus has no solution.
If, on the other hand, you meant
−3x + 3 = 1
then -3x = -2, and x = 2/3
-3x=6x + 2 solve for x
Answer:
Step-by-step explanation:
6x+3x= -2
9x= -2
x= -2/9
Answer:
-3x=6x+2
⇒-9x=2
⇒x=-2/9
Step-by-step explanation:
The Rogers family and the Brooks family each used their sprinklers last summer. The Rogers family's sprinkler was used for 30 hours. The Brooks family's sprinkler was used for 25 hours. There was a combined total output of 1775 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65 L per hour?
Step-by-step explanation:
what happens if there is excess or deficit of proteins in our body
Given the number of trials and the probability of success, determine the probability indicated: a. n = 15, p = 0.4, find P(4 successes) b. n = 12, p = 0.2, find P(2 failures) c. n = 20, p = 0.05, find P(at least 3 successes)
Answer:
A)0.126775 B)0.000004325376 C) 0.07548
Step-by-step explanation:
Given the following :
A.) a. n = 15, p = 0.4, find P(4 successes)
a = number of trials p=probability of success
P(4 successes) = P(x = 4)
USING:
nCx * p^x * (1-p)^(n-x)
15C4 * 0.4^4 * (1-0.4)^(15-4)
1365 * 0.0256 * 0.00362797056
= 0.126775
B)
b. n = 12, p = 0.2, find P(2 failures),
P(2 failures) = P(12 - 2) = p(10 success)
USING:
nCx * p^x * (1-p)^(n-x)
12C10 * 0.2^10 * (1-0.2)^(12-10)
66 * 0.0000001024 * 0.64
= 0.000004325376
C) n = 20, p = 0.05, find P(at least 3 successes)
P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)
To avoid complicated calculations, we can use the online binomial probability distribution calculator :
P(X≥ 3) = 0.07548
Find the solution set of the inequality and what is the number? 16x − 7 ≤ − 71 A. C. ≤ D. ≥ E. =
x ≤ − 4
Step-by-step explanation:
Answer:
x ≤ -4
Step-by-step explanation:
16x − 7 ≤ − 71
Add 7 to both sides.
16x ≤ -64
Divide both sides by 16.
x ≤ -4
A circle's circumference is approximately 76 cm. Estimate the radius, diameter, and area of the circle by using 3 for pi.
Step-by-step explanation:
Circumference = 76cm
Circumference = 2(π)(r)
r -> radius
=> 2(π)(r) = 76
=> (π)(r) = 76/2
=> (π)(r) = 38
=> 3r = 38
=> r = 38/3
=> r = 13cm (Approx.)
Diameter = 2r = 2(13) = 26cm
Area = π(r)^2
= 3(13)^2
= 3(169)
= 507 cm^2
Answer
d=25.34cm
a=160.53cm
cf=12.67cm
Step-by-step explanation:
circumference=cf
diameter=d
radius=r
area=a
d=2r
=2×12.67cm
=25.34cm
cf=2πr
76cm=2(3)r
76cm=3r
2
38cm=r
3
r=12.66^cm
r=12.67cm
find the area
a=πr^2
a=12.67×12.67πcm
a=160.53πcm(it is near to this)
what are the steps required to determine the equation of a quadratic function given its zeros and a point?
Answer:
Below
Step-by-step explanation:
The quadratic equations form is:
● ax^2+bx+c
Using the zeroes, we can write a factored form.
● a (x-x') (x-x")
x and x' are the zeroes
■■■■■■■■■■■■■■■■■■■■■■■■■■
●y = a (x-x') (x-x")
x' and x" are khown but a is not.
We are given a point so replace x and y with its coordinates to find a.
So the steps are:
● 1) Write the factored form of the quadratic equation
● 2) replace x' and x" with their values.
● 3) replace x and y with the coordinates of a khwon point.
● 4) solve the equation for a.
The steps are write the factored form of the quadratic equation then, replace x' and x" with their values. To replace x and y with the coordinates of a known point. To solve the equation for a.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Using the zeroes, we can write a factored form;
a (x-x') (x-x")
x and x' are the zeroes
y = a (x-x') (x-x")
x' and x" are known but a is not.
We are given a point so replace x and y with their coordinates to find a.
So the steps are:
1) Write the factored form of the quadratic equation
2) To replace x' and x" with their values.
3) To replace x and y with the coordinates of a known point.
4) To solve the equation for a.
Learn more about quadratic equations;
brainly.com/question/13197897
#SPJ2
PLS HELP ASAP Solve the inequality and enter your solution as an inequality in the box below 8>4-x>6
Answer:
−4<x<−2
Step-by-step explanation:
8 > 4 − x > 6
8 > −x + 4 > 6
8 + −4 > −x + 4 + −4 > 6 + −4
4 > −x > 2
Since x is negative we need to divide everything by -1 which gives us...
−4 < x < −2