Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
After basketball practice, Courtney spent extra time working on free throws. Overall, she made 3 of her 5 shots. What percent of her total shots did she make?
Answer:
I know the answer
Step-by-step explanation:
Courtney made 60% of her shots
Answer:
she made a 60%
Step-by-step explanation:
first you do this 3÷5
that gives you .60
inorder to get a percent multiply by 100
that gives you an end result of 60
add the percent sing and your done 60%
hope i helped
Select the graph that correctly represents f(x) = –(x + 1)^2 – 3.
Answer:
Hey there!
The third graph, with a maximum at (-1, -3) is the correct choice.
Let me know if this helps :)
Answer:
see below
Step-by-step explanation:
f(x) = –(x + 1)^2 – 3
We know that this is a parabola in the form
y = a( x-h)^2 +k
where ( h,k) is the vertex
y = -1( x- -1)^2 + -3
a is negative so the parabola opens downward
( -1,-3) is the vertex
Given that f(x) = x + 4 and g(x) = x + 7, find (g - 4(x).
Answer: The value of [tex](g - f)(x)=4 .[/tex]
Step-by-step explanation:
Given functions : [tex]f(x) = x + 4[/tex] and [tex]g(x) = x + 7[/tex]
To find : [tex](g - f)(x)[/tex]
Difference between two functions: [tex](u-v)(x)=u(x)-v(x)[/tex]
Then, [tex](g-f)(x)=g(x)-f(x)[/tex]
[tex]=(x+7)-(x+4)=x+7-x-4\\\\=7-4=3[/tex]
Hence, the value of [tex](g - f)(x)=4 .[/tex]
For the equation ax+c =bx +d where a≠b and c≠d , what is x expressed in terms of a,b,c, and d?
Answer:
x = (d - c) / (a - b)
Step-by-step explanation:
Let's simply isolate and solve for the variable x.
ax + c = bx + d
ax - bx + c = d
x (a - b) = d - c
x = (d - c) / (a - b)
Thus, we have expressed x in terms of a,b,c, and d.
Cheers.
:)
The value of x in terms of a,b,c, and d will be x = (d - c) / (a - b).
What is an arithmetic operation?It is described as the process through which we add, subtract, multiply, and divide numerical values. It has the fundamental operators +, -, ×, and ÷.
The order in which arithmetic operations must be performed in an equation is referred to as PEMDAS. This rule states that operations must be performed as follows: parentheses, exponents, multiplication, or division, followed by addition or subtraction.
It is given that,
ax+c =bx +d
a≠b and c≠d
Rearrange the equation and solve it for the x in the following steps,
ax - bx + c = d
x (a - b) = d - c
x = (d - c) / (a - b)
Thus,the value of x in terms of a,b,c, and d will be x = (d - c) / (a - b).
Learn more about the arithmetic operation here:
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What is 45x62 Please help.
Answer:
45
62x
______
90
2700+
_________
2790
Step-by-step explanation:
Convert the decimal 0.984 to a fraction.
984/100
984/1000
984/99
984/999
Answer:
[tex]\boxed{\frac{984}{1000}}[/tex]
Step-by-step explanation:
Hey there!
Well .984 is 984 over 1000 so .984 as a fraction is 984/1000.
We can check this by doing 984 / 1000 which is .984.
Hope this helps :)
The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100, and the standard deviation is 2. You wish to test H0: μ = 100 versus H1: μ ≠ 100 with a sample of n = 9 specimens.
A. If the acceptance region is defined as 98.5 le x- 101.5, find the type I error probability alpha.
B. Find beta for the case where the true mean heat evolved is 103.
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?
Answer:
A.the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]
B. β = 0.0122
C. β = 0.0000
Step-by-step explanation:
Given that:
Mean = 100
standard deviation = 2
sample size = 9
The null and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o: \mu = 100}[/tex]
[tex]\mathtt{H_1: \mu \neq 100}[/tex]
A. If the acceptance region is defined as [tex]98.5 < \overline x > 101.5[/tex] , find the type I error probability [tex]\alpha[/tex] .
Assuming the critical region lies within [tex]\overline x < 98.5[/tex] or [tex]\overline x > 101.5[/tex], for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is [tex]\mu = 100[/tex]
∴
[tex]\mathtt{\alpha = P( type \ 1 \ error ) = P( reject \ H_o)}[/tex]
[tex]\mathtt{\alpha = P( \overline x < 98.5 ) + P( \overline x > 101.5 )}[/tex]
when [tex]\mu = 100[/tex]
[tex]\mathtt{\alpha = P \begin {pmatrix} \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline 98.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} + \begin {pmatrix}P(\dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{101.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} }[/tex]
[tex]\mathtt{\alpha = P ( Z < \dfrac{-1.5}{\dfrac{2}{3}} ) + P(Z > \dfrac{1.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\alpha = P ( Z <-2.25 ) + P(Z > 2.25) }[/tex]
[tex]\mathtt{\alpha = P ( Z <-2.25 ) +( 1- P(Z < 2.25) })[/tex]
From the standard normal distribution tables
[tex]\mathtt{\alpha = 0.0122+( 1- 0.9878) })[/tex]
[tex]\mathtt{\alpha = 0.0122+( 0.0122) })[/tex]
[tex]\mathbf{\alpha = 0.0244 }[/tex]
Thus, the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]
B. Find beta for the case where the true mean heat evolved is 103.
The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis [tex]\mathtt{H_o}[/tex]
Thus;
β = P( type II error) - P( fail to reject [tex]\mathtt{H_o}[/tex] )
∴
[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]
Given that [tex]\mu = 103[/tex]
[tex]\mathtt{\beta = P( \dfrac{98.5 -103}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-103}{\dfrac{2}{\sqrt{9}}}) }[/tex]
[tex]\mathtt{\beta = P( \dfrac{-4.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-1.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\beta = P(-6.75 \leq Z \leq -2.25) }[/tex]
[tex]\mathtt{\beta = P(z< -2.25) - P(z < -6.75 )}[/tex]
From standard normal distribution table
β = 0.0122 - 0.0000
β = 0.0122
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?
[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]
Given that [tex]\mu = 105[/tex]
[tex]\mathtt{\beta = P( \dfrac{98.5 -105}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-105}{\dfrac{2}{\sqrt{9}}}) }[/tex]
[tex]\mathtt{\beta = P( \dfrac{-6.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-3.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\beta = P(-9.75 \leq Z \leq -5.25) }[/tex]
[tex]\mathtt{\beta = P(z< -5.25) - P(z < -9.75 )}[/tex]
From standard normal distribution table
β = 0.0000 - 0.0000
β = 0.0000
The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.
PLEASE HELP!! (1/5) -50 POINTS-
Answer:
[tex]X=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]
Step-by-step explanation:
We are given the following matrix equation, from which we have to isolate X and simplify this value.
[tex]\begin{bmatrix}2&4\\ \:\:\:5&4\end{bmatrix}X\:+\:\begin{bmatrix}-8&-8\\ \:\:\:12&1\end{bmatrix}=\:\begin{bmatrix}-10&6\\ \:\:\:25&24\end{bmatrix}[/tex]
To isolate X, let us first subtract the second matrix, as demonstrated below, from either side. Further simplifying this equation we can multiply either side by the inverse of the matrix being the co - efficient of X, isolating it in the doing.
[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}[/tex] (Simplify second side of equation)
[tex]\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}=\begin{bmatrix}\left(-10\right)-\left(-8\right)&6-\left(-8\right)\\ 25-12&24-1\end{bmatrix}=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] ,
[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] (Multiply either side by inverse of matrix 1)
[tex]X=\begin{bmatrix}2&4\\ 5&4\end{bmatrix}^{-1}\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]
Our solution is hence option c
6(x + 2) = 30Solve the following linear equation
Answer:
[tex]\huge \boxed{x=3}[/tex]
Step-by-step explanation:
[tex]6(x+2)=30[/tex]
[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]
[tex]x+2=5[/tex]
[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]
[tex]x=3[/tex]
Answer:
3
Step-by-step explanation:
30 = 6(x+2)
30/6 = 5
5 = x+2
5-2 = 3
3=x
This is a pretty simple question and I tried to make it as simple as possible when explaining it.
If f(x)=ax+b and f(2)=1 and f(-3)=11, what is the value of A?
Answer:
a = -2
Step-by-step explanation:
f(x)=ax+b
f(2)=1
f(-3)=11
f(2) = 1 means 2a+b =1
f(-3)=11 means -3a + b = 11
Subtracting the two equations
-(-3a +b =11) becomes 3a -b = -11 so we can add
2a+b =1
3a - b = -11
----------------------
5a = -10
Divide by 5
5a/5 = -10/5
a=-2
For a trip, Eli packed 3 shirts, 3 pairs of pants, and 2 pairs of shoes. How many different outfits can Eli make? A. 6 outfits B. 8 outfits C. 9 outfits D. 18 outfits Please include ALL work!
Answer:
18 outfits
Step-by-step explanation:
To determine the number of outfits available
3 shirts * 3 pairs of pants * 2 pairs of shoes
3*3*2
18
If the circumference of a circle is equal to 14, what is the diameter?
Answer:
7
Step-by-step explanation:
What best explains whether a triangle with side links 5 cm 13 cm and 12 cm is a right triangle
Step-by-step explanation:
Pythagoras Theorem
If the sum of the squares of the smaller two sides is equal to the square if the third side then it is a right triangle
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
So, (5)^2 + (12)^2
is 25 + 144 = 169
Which is equal to (13)^2 which is also 169
The sides of the given triangle follows pythagoras theorem, therefore it is a right triangle
Hope it helps:)
Answer:
Pythagorean theorem
Step-by-step explanation:
We can explain it using the Pythagorean theorem. Right triangles always have a hypotenuse which is the longest side. That means 13 must be the hypotenuse of the triangle. The Pythagorean theorem is a^2+b^2=c^2
We already know all the values since every side is given so we just fill it in.
5^2+12^2=13^2
25+144=169
169=169
It is a right triangle
A librarian needs to package up all of the children's books and move them to a different location in the library. There are 625 books, and she can fit 25 books in one box. How many boxes does she need in order to move all of the books? 5 B. 25 C. 125 D. 600 E. 650
Answer: B. 25
Step-by-step explanation:
Given: Total books = 625
Number of books can fit in one box = 25
Now, the number of boxes she need to move all of the books = (Total books) ÷ (Number of books can fit in one box )
= 625÷25
= 25
hence, she requires 25 boxes in order to move all of the books.
So, correct option is B. 25.
The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 12 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Answer:
129 m/s^2
Step-by-step explanation:
The length of a rectangle is increasing at a rate of 9m/s
dL/dt = 9m/s
The width is increasing at a rate of 7m/s
dw/dt= 7m/s
The formular for solving the area of a rectangle is length × width
Therefore, to calculate how fast the rectangle is increasing we will apply the product rule
dA/dt= L × dw/dt + W × dl/dt
= 12×7 + 5×9
= 84+45
= 129m/s^2
Hence the area of the rectangle is increasing at 129m/s^2
The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)
a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14
b) How much will the DVD movies cost?
They will cost $—
Answer:
1 box of 20 and 1 box of 14
They will cost $410
Step-by-step explanation:
1. Find how many boxes of 20 DVD movies can be bought
415 - 240 = 175
1 box of 20 DVD movies can be sold
2. Find how many boxes of 14 DVD movies can be bought from $175
175 - 170 = 5
1 box of 14 DVD movies can be bought
3. Find the cost
240 + 170 = 410
A rotating light is located 16 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
Answer:
a
Step-by-step explanation:
answer is a on edg
Find the value of x.
Answer:
6x + 6 = 32
6x = 32 - 6
6x = 26
divide both sides by 6
6x/6 = 26/6
6x + 6 = 4.35
9x - 9 = 24
9x = 24 + 9
9x = 33
divide both sides by 9
9x/9 = 24/9
9x + 9 = 2.66
9x + 9 = 2.66
Answer: x=3
Step-by-step explanation:
[tex]\frac{32}{24} =\frac{4}{3} \\\\\frac{4}{3}=\frac{6x+6}{9x-9}\\ x=3[/tex]
A circle has a radius of 7 inches. What is the area of the circle?
A. 21.98 in^2
B. 43.96 in^2
C. 153.86 in^2
D. 615.44 in^2
Please include ALL work! <3
Answer:
C. 153.86 in^2[tex]area = \pi {r}^{2} \\ r = 7 \\ a = \frac{22}{7} \times {7}^{2} [/tex]
[tex]a = \frac{22}{7} \times 49 \\ a = 22 \times 7 = 154 {cm}^{2} [/tex]
Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ a \: = 3.14 \times {7}^{2} \\ a \: = 3.14 \times 49 = 153.86 {cm}^{2} [/tex]
Answer:
C. 153.86 in^2
Step-by-step explanation:
The area of a circle can be found using the following formula.
[tex]a=\pi r^2[/tex]
where r is the radius.
We know the radius is 7 inches. Therefore, we can substitute 7 in for r.
[tex]r= 7 in[/tex]
[tex]a=\pi (7 in)^2[/tex]
Evaluate the exponent.
(7 in)^2= 7 in * 7 in= 49 in^2
[tex]a= \pi * 49 in^2[/tex]
Let's use 3.14 for pi.
[tex]a= 3.14 * 49 in^2[/tex]
Multiply 3.14 and 49
3.14 * 49=153.86
[tex]a= 153.86 in^2[/tex]
The area of the circle is 153.86 square inches. Therefore, C is the correct answer.
Which system of linear inequalities has the point (3, –2) in its solution set?
Answer:
see below
Step-by-step explanation:
We want where both inequalities are true
y > -3
-2 >-3 this is true
y ≥ 2/3x -4
-2≥ 2/3*3 -4
-2 ≥ 2 -4
-2≥ -2
This is true
This is is the graph
Answer:
[tex]\boxed{\sf Option \ 3}[/tex]
Step-by-step explanation:
[tex]\sf The \ values \ must \ be \ true \ for \ both \ inequalities.[/tex]
[tex]x = 3\\y = -2[/tex]
[tex]y>-3\\-2>-3\\ \sf True[/tex]
[tex]y\geq \frac{2}{3}x-4 \\ -2\geq \frac{2}{3}(3)-4\\2\geq 2-4\\-2\geq-2 \\ \sf True[/tex]
a shopping center form 300000 square feet to an excess of 1 million square feer that consists mostly of large national chain stores is called a
Answer: Honeymoon2871
Step-by-step explanation:
slope=-3, passing through (-9, -9)
Hey there! I'm happy to help!
We want to find the equation of a line in y-intercept form, which is y=mx+b, where x and y are a point on the line, m is the slope, and b is the y-intercept.
We already know that our slope is -3.
y=-3x+b
We want to solve for b now. We can plug in our point (-9,-9) to solve for it.
-9=-3(-9)+b
-9=27+b
b=-36
So, our equation is y=-3x-36.
I hope that this helps! Have a wonderful day! :D
PLS HELP ASAP:Find all the missing elements:
Answer:
b ≈ 9.5, c ≈ 14.7
Step-by-step explanation:
Using the Sine rule in Δ ABC, that is
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values
[tex]\frac{7}{sin23}[/tex] = [tex]\frac{b}{sin32}[/tex] ( cross- multiply )
b × sin23° = 7 × sin32° ( divide both sides by sin23° )
b = [tex]\frac{7sin32}{sin23}[/tex] ≈ 9.5 ( to the nearest tenth )
Also
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
[tex]\frac{7}{sin23}[/tex] = [tex]\frac{c}{sin125}[/tex] ( cross- multiply )
c × sin23° = 7 × sin125° ( divide both sides by sin23° )
c = [tex]\frac{7sin125}{sin23}[/tex] ≈ 14.7 ( to the nearest tenth )
Johnny and Steven ate a 12-piece pizza. If Johnny ate 3/4 of the pizza, how many pieces did Steven eat? *
Answer:
Steven ate 3 pieces
Step-by-step explanation:
If Johnny ate 3/4 , then Steven at 1 - 3/4 or 1/4
12 * 1/4 = 3
Steven ate 3 pieces
Answer:
3 slices of pizza
Step-by-step explanation:
There are 12 total slices of pizza. In order to find how much Johnny ate, we must multiply 12 by 3/4.
12/1 × 3/4 OR 12 × 0.75 = 9
Johnny ate 9 slices of pizza.
Then, we have to subtract 9 from 12 to determine how many slices Steven ate.
12 - 9 = 3
Steven ate 3 slices of pizza.
I need help with this math problem
Answer:
1). [tex]\frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}[/tex]
2). [tex]\frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}[/tex]
Step-by-step explanation:
In this question we have to write the fractions in the factored form.
Rational expressions are [tex]\frac{2}{x^{2}-x-12 }[/tex] and [tex]\frac{1}{x^{2}-16 }[/tex].
1). [tex]\frac{2}{x^{2}-x-12 }[/tex]
Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12
= x(x - 4) + 3(x - 4)
= (x + 3)(x - 4)
Therefore. [tex]\frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}[/tex]
2). [tex]\frac{1}{x^{2}-16 }[/tex]
Factored form of the denominator (x² - 16) = (x - 4)(x + 4)
[Since (a²- b²) = (a - b)(a + b)]
Therefore, [tex]\frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}[/tex]
Hellllppp!!!! Please!Match the numbers with the correct label.
Answer:
(a = 1/7 (b = .2 (c = 3/9
Step-by-step explanation:
1/7 = .14
1/4 = .25
3/9 = .33
a & b are lower than 1/4 and c is higher
Please help!!! A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.What is the line of best fit?A.y = –0.984x + 13.5B.y = –2.9x + 13.5C.–0.984 = –2.9x + 13.5D.y = 13.5x – 2.9
Answer:
B.y = –2.9x + 13.5 i think dont word me for it
Step-by-step explanation:
Equation of line is y = –2.9x + 13.5 which is correct option(B).
What is linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
Let y = a + bx, where a is the y-intercept and b is the slope.
[tex]\sum{x} = 1 + 2 + 3 + 4 + 5 = 15[/tex]
[tex]\sum{y} = 11 + 8 + 4+ 1 + 0 = 24[/tex]
[tex]\sum {xy} = 11 + 16 + 12 + 4 + 0 = 43[/tex]
[tex]\sum{x^2} = 1 + 4 + 9 + 16 + 25 = 55[/tex]
[tex]n = 5[/tex]
[tex]b= \dfrac{n\sum{xy}-\sum{x}\sum{y}}{n{\sum{x^2}-(\sum{x}})^2}[/tex]
[tex]b= \dfrac{ 5 (43) - (15) . (24)}{{5 (55) - (15})^2}[/tex]
[tex]b= -2.9[/tex]
[tex]a = \dfrac{25}{5} - (-2.9)\dfrac{15}{5}[/tex]
[tex]a=13.5[/tex]
Hence, equation of line is y = –2.9x + 13.5
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Help us plazz this is mathematics IGCSE fast as you can
Answer:
Step-by-step explanation:
y varies direcrtly with √(x+5) wich can be expressed mathematically as:
● y = k*√(x+5)
Let's calculate k khowing that y=4 and x=-1
● 4 = k*√(-1+5)
● 4 = k*√(4)
● 4 = k * 2
● k = 4/2
● k = 2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's calculate y khowing that x = 11
● y = k*√(x+5)
● y = 2×√(11+5)
● y = 2× √(16)
● y = 2× 4
● y = 8
Answer:
The value of y is 8.
Step-by-step explanation:
Given that y is directly proportional to √(x+5) so the equation is y = k√(x+5) where k is constant. First, you have to find the value of k with given values :
[tex]y = k \sqrt{x + 5} [/tex]
[tex]let \: x = - 1,y = 4[/tex]
[tex]4 = k \sqrt{ - 1 + 5} [/tex]
[tex]4 = k \sqrt{4} [/tex]
[tex]4 = k(2)[/tex]
[tex]4 \div 2 = k[/tex]
[tex]k = 2[/tex]
So the equation is y = 2√(x+5). In order to find the value of y, you have to substitute x = 11 into the equation :
[tex]y = 2 \sqrt{x + 5} [/tex]
[tex]let \: x = 11[/tex]
[tex]y = 2 \sqrt{11 + 5} [/tex]
[tex]y = 2 \sqrt{16} [/tex]
[tex]y = 2(4)[/tex]
[tex]y = 8[/tex]
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
It is possible to measure 2 kilograms or 2000 grams in 8 cups, it is not possible to measure in three weighs.
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
What is percentage?The percentage is defined as the ratio expressed as a fraction of 100.The percentage is denoted by sign of %.For example, if XYZ scored 46% marks in his test, it means that he scored 46 marks out of 100. It is written as 46/100 in the fraction form and 46:100 in terms of ratio.
Given data as :
9kg of oats and cup scales that gears of 50g and 200g.
Total oats need to measure = 9kg
Since, 1 kg contains 1000 grams.
1 kg = 1000 grams
2kg = 2000 grams
9kg = 9000 grams
Cup scales that gears as 50g and 200g
The number of one cup contains in gram = 200 + 50 = 250
The number of cups, considering that each cup weighs 250 grams.
The number of cups = 2000/250
The number of cups = 8
Hence, while it is possible to measure 2 kilograms or 2000 grams in 8 cups, it is not possible to measure in three weighs.
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Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?
A)Right
B)Obtuse
C)Can't be determined
D) Acute
Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
A)0.33 feet
B)3.75 feet
C)3 feet
D)5 feet
Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?
A)Acute
B)Right
C)Can't be determined
D)Obtuse
Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
A)21.34 ft.
B)21.93 ft.
C)27.73 ft.
D)19.21 ft.
Answer:
Question 1 = D) Acute
Question 2 = C)3 feet
Question 3 = D) Obtuse
Question 4 = C)27.73 ft.
Step-by-step explanation:
Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?
In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem
Where:
If a² + b² = c² = Right angle triangle
If a² +b² > c² = Acute triangle.
If a² +b² < c² = Obtuse triangle.
It is important to note that the length ‘‘c′′ is always the longest.
Therefore, for the above question, we have lengths
5 = a, 6 = b and c = 7
a² + b² = c²
5² + 6² = 7²
25 + 36 = 49
61 = 49
61 ≠ 49, Hence 61 > 49
Therefore, this is an Acute Triangle
Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
This is question that deals with proportion.
The formula to solve for this:
Height of the statue/ Length of the shadow of the person = Height of the person/ Length of the shadow of the person
Height of the statue = 15 feet
Length of the shadow of the person = 20 feet
Height of the person = unknown
Length of the shadow of the person = 4
15/ 20 = Height of the person/4
Cross Multiply
15 × 4 = 20 × Height of the person
Height of the person = 15 × 4/20
= 60/20
Height of the person = 3 feet
Therefore, the person is 3 feet tall.
Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?
In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem
Where:
If a² + b² = c² = Right angle triangle
If a² +b² > c² = Acute triangle.
If a² +b² < c² = Obtuse triangle.
It is important to note that the length ‘‘c′′ is always the longest.
Therefore, for the above question, we have lengths 17, 12, 9
9 = a, 12 = b and c = 17
a² + b² = c²
9² + 12² = 17²
81 + 144 = 289
225 = 289
225 ≠ 289
225 < 289
Hence, This is an Obtuse Triangle.
Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
To calculate how far apart the two friends are we use the formula
Distance = √ ( Length² + Breadth²)
We are given dimensions: 12ft by 25ft
Length = 12ft
Breadth = 25ft
Distance = √(12ft)² + (25ft)²
Distance = √144ft²+ 625ft²
Distance = √769ft²
Distance = 27.730849248ft
Approximately ≈27.73ft
Therefore, the friends are 27.73ft apart.
