Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:
[tex]H_0: \mu = 16[/tex]
At the alternative hypothesis, it is tested if the mean is different, hence:
[tex]H_1: \mu \neq 16[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are:
[tex]\overline{x} = 15.75, \mu = 16, \sigma = 1.46, n = 150[/tex].
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{15.75 - 16}{\frac{1.46}{\sqrt{150}}}[/tex]
z = -2.1
What is the p-value and the conclusion?Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.
Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.
More can be learned about the z-distribution at https://brainly.com/question/16313918
#SPJ1
Neil emptied his change jar and noticed he only had pennies, nickels, and quarters. He had coins for a total of . He had fewer quarters than nickels. How many pennies did Neil have? The solution is
Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.
Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)
Hence:
0.1x + 0.05y + 0.25z = 4.6 (1)
Also:
x = 3y (2)
And:
z = y + 4 (3)
From the equations:
x = 18, y = 6, z = 10
Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
The formula =MID("ABCDEFGHI",3,4) would yield the result
If the formula, =MID("ABCDEFGHI",3,4) is used, the result yielded would be CDEF.
What would =MID("ABCDEFGHI",3,4) yield?When using the =MID function on a spreadsheet, the number after the text in the formula would show the position of the text from the left that the function would begin to count from.
The text in the third position from the left as shown in ABCDEFGHI is C so we need to start counting from letter C.
The second number in the function would then show the number of texts that needs to be counted and selected from the row of letters. That number is 4.
So from the letter C, you'll count 4 letters including the letter C itself.
The result you get would therefore be C, D, E, F which are the four letters from C.
In conclusion, the formula =MID("ABCDEFGHI",3,4) would yield the result, "C, D, E, F,."
Find out more on spreadsheet functions at https://brainly.com/question/23883174
#SPJ1
Given the vertex of a quadratic function, find the axis of symmetry.
(i) The equation of the axis of symmetry is x = - 5.
(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.
How to analyze and interpret quadratic functions
In this question we must find and infer characteristics from three cases of quadratic equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.
(ii) We need to transform the quadratic equation into its vertex form to determine the coordinates of the vertex by algebraic handling:
y = x² - 8 · x - 2
y + 18 = x² - 8 · x + 16
y + 18 = (x - 4)²
In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) Now here we must apply a procedure similar to what was in used in part (ii):
y = - 2 · (x² - 4 · x + 2)
y - 4 = - 2 · (x² - 4 · x + 2) - 4
y - 4 = - 2 · (x² - 4 · x + 4)
y - 4 = - 2 · (x - 2)²
According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.
To learn more on quadratic equations: https://brainly.com/question/1863222
#SPJ1
Fertiliser is applied at the rate of a grams per square metre. It
takes b kilograms to cover a field of area c square metres. Find a
formula for b in terms of a and c.
Step-by-step explanation:
1 kilogram (kg) = 1000 grams (g)
as "kilo" means 1000.
b = a × c / 1000
it is simple : we have "c" square meters. as we need to apply "a" grams per square meter, we need to multiply both numbers to know how many grams we need for that many square meters. hence a × c.
and to get kg, we need to divide this number of grams by 1000.
that's it.
a storage room measures 20 feet by 15 feet. the floor is covered by tiles that cost $7.50 per square foot. what will be the cost of the entire floor with tiles?
Answer: $2250
Step-by-step explanation:
Given information
Dimension of the room = 20 feet × 15 feet
Cost of tiles = $7.50 / ft²
Derived formula from the given information
Total cost = Floor area × Cost of tiles
Substitute values into the formula
Total cost = Floor area × Cost of tiles
Total cost = (20 × 15) × (7.5)
Simplify by multiplication
Total cost = 300 × (7.5)
[tex]\Large\boxed{Total~cost~=~2250~Dollars}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Se tiene 10 fichas, las 5 primeras de color
azul numeradas del 1 al 5 y las 5 restantes
blancas también numeradas del 1 al 5. Se
colocan en una caja sacando una ficha y
posteriormente otra más, entonces la
probabilidad de que ambas estén
numeradas con el valor 1, es:
Usando la distribución hipergeométrica, la probabilidad de que ambas estén numeradas con el valor 1, es: 0.0222 = 2.22%.
¿Qué es la fórmula de distribución hipergeométrica?
La fórmula es:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
x es el número de éxitos.N es el tamaño de la población.n es el tamaño de la muestra.k es el número total de resultados deseados.Los valores de los parámetros son:
N = 10, k = 2, n = 2.
La probabilidad de que ambas estén numeradas con el valor 1, es P(X = 2), entonces:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,10,2,2) = \frac{C_{2,2}C_{8,0}}{C_{10,2}} = 0.0222[/tex]
Puede-se aprender más a cerca de la distribución hipergeométrica en https://brainly.com/question/24826394
#SPJ1
Establish the identity.
(2 cos 0-6 sin 0)² + (6 cos 0+2 sin 0)2 = 40
Rewriting the left-hand side as follows,
[tex](2\cos\theta-6\sin \theta)^2 +(6\cos \theta+2\sin \theta)^2\\\\=4\cos^2 \theta-24\cos \theta \sin \theta+36 \sin^2 \theta+36 \cos^2 \theta+24 \cos \theta \sin \theta+4 \sin^2 \theta\\\\=40\cos^2 \theta+40 \sin^2 \theta\\\\=40(\cos^2 \theta+\sin^2 \theta)\\\\=40[/tex]
Heyy i just need some help with questions 21and 25 if anyone could help me and show the work that would be amazing thank you!!
Step-by-step explanation:
21) f(x)=1/x-6. g(x)=7/x+6
f(g(x))=f(7/x+6)=1÷7/x+6 - 6=x+6/7 - 6
g(f(x))=g(1/x-6)=7÷1/x-6 - 6 =7(x-6) - 6
simplify forward
25)f(x)=|x| g(x)=5x+1
f(g(x))=f(5x+1)=|5x+1|=5x+1=g(x)
g(f(x))=g(|x|)=5|x|+1=5x+1=g(x)
please I need help in these exercises and I tried to solve them but I can't, crown to the best answer <'3
(a) The result of the long division is a - b + c.
(b) The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).
How to find an algebraic expression by long division
Long division is an algebraic procedure with which we can find the result of a division of two polynomials. Now we proceed to present the entire procedure explained:
(a) a² - b² + 2 · b · c - c² divided by a + b - c.
1) Multiply a + b - c by a and subtract it from a² - b² + 2 · b · c - c²: Result: a / Remainder: - b² - a · b + 2 · b · c + a · c - c²
2) Multiply a + b - c by - b and subtract it from the result of 1): Result: a - b / Remainder: b · c + a · c - c²
3) Multiply a + b - c by c and subtract it from the result of 2): Result: a - b + c / Remainder: 0
The result of the long division is a - b + c.
(b) 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4 divided by m⁴ - 3 · m² + 4.
1) Multiply m⁴ - 3 · m² + 4 by 3 · m³ and subtract it from 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4: Result: 3 · m³ / Remainder: 2 · m⁵ + m⁴ + 6 · m³ - 8 · m + 3 · m² + 4.
2) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 1): Result: 3 · m³ + 2 · m / Remainder: m⁴ + 12 · m³ - 16 · m + 3 · m² + 4.
3) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 2): Result: 3 · m² + 2 · m + 1 / Remainder: 12 · m³ - 16 · m + 6 · m².
The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).
To learn more on long divisions: https://brainly.com/question/12342242
#SPJ1
Find the cube root of 1+¡^5
need help please...
Answer:
[tex]\sf 28 \frac{1}{3} \:ft=28.3\:ft\:(nearest\:tenth)[/tex]
Step-by-step explanation:
Given information:
It takes Mr Kelly 6 strides to walk 20 ft.It takes Mr Kelly 8.5 strides to walk the other side of his house.Let x be the unknown length of the other side of Mr Kelly's house.
To solve, set up a ratio with the given information and the defined unknown, then solve for x:
[tex]\textsf{20 ft : 6 strides = x ft : 8.5 strides}[/tex]
[tex]\implies \sf 20:6 = x:8.5[/tex]
[tex]\implies \sf \dfrac{20}{6}=\dfrac{x}{8.5}[/tex]
[tex]\implies \sf x=\dfrac{20 \cdot 8.5}{6}[/tex]
[tex]\implies \sf x=\dfrac{170}{6}[/tex]
[tex]\implies \sf x=28 \frac{1}{3} \:ft[/tex]
[tex]\implies \sf x=28.3\:ft\:(nearest\:tenth)[/tex]
Therefore, the length of the other side of Mr Kelly's house that takes him 8.5 strides to walk is 28.3 ft (nearest tenth).
Let that be x
20:x=6:8.520/x=6/8.520/x=12/1712x=17(20)12x=340x=340/12x=28.3ft5 + 4 ⋅ ( 8 − 6 ) ^2
[tex]\boldsymbol{\sf{5+4\cdot(8-6)^{2} \ \ \longmapsto \ \ [Subtract \ 6 \ from \ 8.] }}[/tex]
[tex]\boldsymbol{\sf{5+4\cdot2^{2} }}[/tex]
Calculates 2 to the power of 2 and gets 4.
[tex]\boldsymbol{\sf{5+4\cdot4 \ \ \longmapsto \ \ [Multiply] }}[/tex]
[tex]\boldsymbol{\sf{5+16 \ \ \longmapsto \ \ [Add]}}[/tex]
[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ 21}}}}[/tex]
Answer:
5+16x
Step-by-step explanation:
5+4x(8−6)
2
Subtract 6 from 8 to get 2.
5+4x×2
2
Calculate 2 to the power of 2 and get 4.
5+4x×4
Multiply 4 and 4 to get 16.
5+16x
Question: You can work 40 hours per pay period while attending school earning $12.50 an hour. There are two pay periods per month. NOW Assume you have deductions for health care of $25 per pay period and 401K deduction of $50 per pay period. These deductions are pretax.
Gross Pay per pay period: $
Taxable Income per pay period:
You pay 11% in federal taxes. Federal tax withholding per pay period: $
___
Use the state tax rates below and calculate State tax withholding per pay period: $
(round to two decimals)
_____
From the image:
Calculate FICA withholding per pay period: $
Calculate Medicare withholding per pay period: $
(round to two decimals)
What is your Net pay per pay period: $
(round to two decimals)
1) Based on the information, the following taxation calculations can be made:
a) Gross Pay per pay period: $500
b) Taxable Income per pay period: $425
c) Since you pay 11% in federal taxes, the Federal tax withholding per pay period is $46.75.
2) The State tax withholding per pay period is $20.
3) The calculation of FICA, Medicare, and the Net Pay per pay period is as follows:
FICA withholding per pay period: $25.50
Medicare withholding per pay period: $6.16
Net Pay per pay period = $326.59
Data and Calculations:Total hours worked per pay period = 40 hours
Rate per hour = $12.50
Pay periods per month = 2
Gross pay per pay period = $500 (40 x $12.50)
Deductions per pay period:Health care = $25
401K deduction = $50
Total deductions per pay period = $75
Taxable income per pay period = $425 ($500 - $75)
Federal taxes = 11%
Federal tax withholding per pay period: $46.75 ($425 x 11%)
Annual taxable income = $10,200 ($425 x 24)
State withholding tax (annual) = $480 {$120 + ($10,200 - $5,000) x 5%}
State withholding tax per pay period = $20 ($480/24)
FICA withholding per pay period: $25.50 ($425 x 6.2%)
Medicare withholding per pay period: $6.16 ($425 x 1.45%)
Net Pay per pay period:Gross Pay $500
Total deductions $75
Taxable income = $425
Federal Withholding = $46.75
State Withholding = $20
]FICA Withholding = $25.50
Medicare Withholding = $6.16
Net Pay per pay period = $326.59
Learn more about computing the net pay at https://brainly.com/question/15858747
#SPJ1
HELP NEED ANSWERS QIUCKLY! WILL GIVE BRAINLEST!
1. What is the difference between arithmetic and geometric?
2. Which formulas are used for each? Explain ratio and difference.
3. Given 4, 8, 16, 32 identify the next term and if its a ratio or difference
4. Explain the steps in using the sigma notation.
Answer:
Arithmetic => each new term differs from the previous term by a fixed amount
an = a1 + d (n − 1)
Geometric => each element after the first is obtained by multiplying the previous number by a constant factor
an = a1 (r)^(n − 1)
4,8,16,32 the difference is not fixed so it is a geometric so it is ratio
the ratio is 2 and n is 5 so 4*(2)^4 =4*16=64
To generate the terms of a series given in sigma notation, replace the index of summation with consecutive integers from the first value to the last value of the index.
if you also want the sum of them
arithmetic -> (n/2)(a1+an)
geometric -> (a1*(1-r^n))/(1-r) or
when the sequence is infinite you can use a1/(1-r)
Step-by-step explanation:
Arithmetic => 1,3,5,7,9,11,13,15....
Geometric => 1,2,4,8,16,32,64....
The hypotenuse of an isosceles right triangle is 14 centimeters longer than either of its legs. Find the exact length of each side. (Hint: An isosceles right triangle is a right triangle whose legs are the same length.)
The Pythagorean theorem states that:
[tex]a^2+b^2=c^2[/tex]
a and b are two legs of a right trianglec is the hypotenuseThe Quadratic Formula[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Solving the QuestionLet a represent the length of one leg.
Because the hypotenuse is 14 cm longer than a leg, we can say that the hypotenuse's length is 14 + a.
Plug these into the Pythagorean theorem:
[tex]a^2+b^2=c^2\\a^2+a^2=(14+a)^2\\2a^2=14^2+2(14)a+a^2\\2a^2=196+28a+a^2\\a^2=196+28a\\a^2-196-28a=0\\a^2-28a-196=0[/tex]
Factor using the quadratic formula:
[tex]a=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]a=\dfrac{-(-28)\pm \sqrt{(-28)^2-4(1)(-196)}}{2(1)}\\\\a=14\pm14\sqrt{2}\\\\a=14+14\sqrt{2}[/tex]
We know that it's plus because subtracting results in a negative value, and length cannot be negative.
This is the length of each side.
Because the hypotenuse is 14 cm longer, we can say that the hypotenuse is [tex]28+14\sqrt{2}[/tex].
AnswerLeg length = [tex]14+14\sqrt{2}[/tex]
Hypotenuse length = [tex]28+14\sqrt{2}[/tex]
Please help! Help Will Give 100 PTS
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
Square Root 3x+12 = 9
Answer:
x = 23; not extraneous
Step-by-step explanation:
A solution is extraneous if it does not satisfy the original equation. Extraneous solutions can sometimes be introduced in the process of solving radical and rational function equations.
SolutionSquaring both sides of the given equation, we get ...
√(3x +12) = 9
3x +12 = 81 . . . . . . square both sides
x +4 = 27 . . . . . . . divide by 3
x = 23 . . . . . . . . . . subtract 4
CheckThere is only one solution, and it satisfies the equation:
√(3×23 +12) = √81 = 9
The solution x = 23 is not extraneous.
Answer: x = 23; not extraneous
Step-by-step explanation:
Solve this system of linear equations. Separate the x- and y-values with a comma. 8x + 10y = 10 5x + 4y = -14
Answer
{-10, 9}
Step-by-step explanation:
The above are Simultaneous equations
What are simultaneous equations?These are two or more equations that share same variables.
8X + 10Y = 10--------(1)
5X + 4Y = -14-------(2)
Multiply equation (1) by 5 and equation (2) by 840X + 50Y = 50 ---------(3)
40X + 32Y = - 112--------(4)
Subtract equation (4) from (3)18Y = 162
Divide bothsides by 18[tex] \frac{18y}{18} = \frac{162}{18} \\ y = 9[/tex]
Substitute y = 9 into equation (3)40X + 50Y = 50
40X + 50(9) = 50
40X + 450 = 50
40X = 50 - 450
40X = - 400
[tex]Dividing \: bothsides \: by \: 40 \\ \frac{40x}{40} = \frac{ - 400}{40} \\ \\ x = - 10 \\ therefore \: the \: values \: are \: -10, \: 9[/tex]{-10, 9}
Instructions: Identify the vertices of the feasible region for the given linear programming constraints.
Optimization Equation:
z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Fill in the vertices of the feasible region:
(0, )
(−3, )
(3, )
The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
How to identify the vertices of the feasible region for the given linear programming constraints?The optimization equation is given as
z=−3x+5y
The constraints are given as:
x+y≥−2
3x−y≤2
x−y≥−4
Next, we plot the constraints on a graph and determine the points of intersections
See attachment for the graph
From the attached graph, the points of intersections are
(-3, 1), (3, 7) and (0, -2)
So, we have:
(0, -2)
(-3, 1)
(3, 7)
Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
So, the complete parameters are:
Optimization Equation:
z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Vertices of the feasible region
(0, -2)
(-3, 1)
(3, 7)
Read more about feasible region at
https://brainly.com/question/14381991
#SPJ1
From the diagram below, if the tree is 34 ft. tall, and the angle of elevation from point B to the top of the tree is 26 °, find the distance that the tree is from point B. (Round to the nearest whole foot.)
Given the height of the tree and the angle of elevation from point B, the distance between the tree is from point B is approximately 70ft.
What is the distance between the tree and point B?
Given the data in the question;
Height of tree opposite angle of elevation = 34ftAngle of elevation θ = 26°Distance between tree and point B| Adjacent = ?Since the scenario form a right angle triangle, we use trig ratio.
tanθ = Opposite / Adjacent
tan( 26° ) = 34ft / x
We solve for x
x = 34ft / tan( 26° )
x = 34ft / 0.4877
x = 70ft
Given the height of the tree and the angle of elevation from point B, the distance between the tree is from point B is approximately 70ft.
Learn more about trigonometric ratio here: https://brainly.com/question/28038732
#SPJ1
A company reports cost of goods manufactured of $918,700 and cost of goods sold of $955,448. Compute the average manufacturing cost per unit assuming 18,374 units were produced.
If the cost of goods manufactured of $918,700 and cost of goods sold is $955,448. The average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.
Average manufacturing cost per unitUsing this formula to determine the average manufacturing cost per unit
Average manufacturing cost per unit= Total cost/Number of units produced
Where:
Total cost=$918,700+$955,448=$1,874,148
Number of units produced=18,374 units
Let plug in the formula
Average manufacturing cost per unit=$918,700+$955,448/18,374
Average manufacturing cost per unit=$1,874,148/18,374
Average manufacturing cost per unit=$102 per unit
Therefore the average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.
Learn more about Average manufacturing cost per unit here:https://brainly.com/question/25056982
#SPJ1
Number #2 please, I don’t know how to solve it.
Answer:
See below
Step-by-step explanation:
Here is HOW to solve this problem:
b = pounds of blue candy then r = 11-b = pounds of red candy
.79b = cost of blue candy 1.29 (11-b) = cost of red candy
these two costs sum to 11.19
.79b + 1.29 ( 11-b) = 11.19 Now you can solve for 'b' the 'r' = 11-b
Answer:
Red candy =5
Blue candy = 6
Step-by-step explanation:
Let the pounds of red candy be x and blue candy y. Then y=11-x
Also 1.29x + 0.79y=11.19
1.29x+0.79(11-x)=11.19
0.5x=11.19–8.69
0.5x=2.5
X=5
Red candy =5
Blue candy = 6
can someone answer this?
Step-by-step explanation:
f(x)=-3x+4
f(a)= -3a +4
So,
2f(a)= f(a) + f(a)
=(-3a +4) +(-3a + 4)
=-3a + 4 -3a - 4
=-6a
f(2a)=2(-3a + 4)
=-6a +8
f(a+2)=(-3a + 4) + 2
= -3a +4 +2
= -3a + 6
f(a) + f(2)= -3a +1+5
because, f(2)= -3(2)+1
=-6+1
=5
and f(a)= -3a+1
4x-12y=-20 substitution method
If we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.
Given two equations x-2y=5 and 4x+12y=-20.
We are required to find the value of x and y through substitution method.
Equation is like a relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Equation can be a linear equation,quadratic equation, cubic equation or many more depending on the power of variable.
They can be solved as under:
x-2y=5---------------1
4x+12y=-20--------2
Finding value of variable x from equation 1.
x=5+2y--------------3
Use the value of variable x in equation 2.
4x+12y=-20
4(5+2y)+12y=-20
20+8y+12y=-20
20y=-20-20
20y=-40
y=-40/20
y=-2
Use the value of variable y in equation 3.
x=5+2y
x=5+2*(-2)
x=5-4
x=1
Hence if we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.
Question is incomplete as it should include one more equation x-2y=5.
Learn more about equations at https://brainly.com/question/2972832
#SPJ1
If a square root parent function is vertically stretched by a factor of 6, what is
the equation of the new function, G(x)?
OA. G(x) = -6√√x
O B. G(x)=√x
OC. G(x) = √6x
O D. G(x) = 6-√x
Parent function = √x
On stretching vertically by factor of 6
New function G(x) = 6√x
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
a. Central angle: Angle BAC
b. Major arc: Arc BEC
c. Minor arc: Arc BC
d. m(BEC) = 260°
e. m(BC) = 100°
What is a Major Arc?A major arc can be defined as an arc that has a measure that is greater than a semicircle (half a circle) or greater than 180 degrees.
What is a Minor Arc?A minor arc can be defined as an arc that has a measure that is less than a semicircle (half a circle) or less than 180 degrees.
What is a Central Angle?An angle whose vertex is at the center of a circle and has two radii of as its sides is called a central angle of a circle.
a. Central angle in the image given is: Angle BAC
b. Major arc of the circle is: Arc BEC
c. Arc BC is a minor arc.
d. m(BEC) = 360 - 100 [based on the central angle theorem]
m(BEC) = 260°
e. angle BAC = 100°
m(BC) = angle BAC [based on the central angle theorem]
m(BC) = 100°
Learn more about major and minor arcs on:
https://brainly.com/question/228276
#SPJ1
Which expression has a value of -24 when a = -2 and b = 3?
A. a√16 + b - 10
B. a(√16 + b) -10
C. a√16 + (b - 10)
D. (a√16) + b - 10
The option B is correct, The second expression gives the correct value -24.
According to the statement
we have given that the some expression and a = -2 and b = 3 and we have to which expression gives a output of answer -24 after put the values in the expressions.
So, For this purpose
First expression:
[tex]a\sqrt{16} + b - 10[/tex]
Put a = -2 and b = 3
then
[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]
Second expression:
[tex]a(\sqrt{16} + b) -10[/tex]
Put a = -2 and b = 3
then
[tex]a(\sqrt{16} + b) -10\\-2(4 +3) -10\\-14-10\\-24[/tex]
Now,
Third expression:
[tex]a\sqrt{16} + (b - 10)[/tex]
Put a = -2 and b = 3
then
[tex]a\sqrt{16} + (b - 10)-2*4 + (-7)\\-8-7\\-15[/tex]
Now,
Fourth expression and first expression are same,
So,
Fourth expression:
[tex]a\sqrt{16} + b - 10[/tex]
Put a = -2 and b = 3
then
[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]
The second expression gives the correct value -24.
So, The option B is correct, The second expression gives the correct value -24.
Learn more about Expressions here
https://brainly.com/question/4344214
#SPJ1
A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the Empirical Rule to estimate the proportion.
Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.140 = 110 + 2 x 15.These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
More can be learned about the Empirical Rule at brainly.com/question/24537145
#SPJ1
Find the difference between 0.84 and 17.1. (a) Give your answer as a mixed number in its simplest form. (b) Divide your answer by 9 and give your answer correct to 2 decimal places.
Answer:
in case you don't understand feel free to ask bye.
(3x+1)^2-2(3x+1)(3x+5)^2+(3x+5)^2
Answer:
soln,
write the question
=9x^2+1-6x-2×9x^2+25+9x^2+25
=9x^2+1-6x-18x^2+25+9x^2+25
=9x^2-18x^2+9x^2+1+25+25-6x
=51-6x
if(3x+1)^2 mean that (3x+1)has power of 2 and u don't have to use the formula this is the answer
Step-by-step explanation:
it's just BODMAS method
The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). Stops Price (dollars) 333 6.506.506, point, 50 777 12.5012.5012, point, 50 111111 18.5018.5018, point, 50 What is the fee per stop?
Based on the task content given; the initial fee and the fee per stop is $2 and $1.5 respectively.
Equationlet
Initial fee = xFee per stop = yx + 3y = 6.50
x + 7y = 12.50
Subtract both equation to eliminate x7y - 3y = 12.50 - 6.50
4y = 6
y = 6/4
y = 1.5
Substitute y = 1.5 intox + 3y = 6.50
x + 3(1.5) = 6.50
x + 4.5 = 6.50
x = 6.50 - 4.5
x = 2
Therefore, the initial fee and the fee per stop is $2 and $1.5 respectively.
Learn more about equation:
https://brainly.com/question/11418438
#SPJ1