Answer: Dimension = 27 inches by 39.75 inches
Concept:
A perimeter is a path that encompasses/surrounds/outlines a shape.
Perimeter (rectangle) = 2 (l + w)
l = length
w = width
Solve:
l = 2w - 14.25
w = w
P = 133.5
Given equation
P = 2 (l + w)
Substitute values into the equation
133.5 = 2 (2w - 14.25 + w)
Combine like terms
133.5 = 2 (3w - 14.25)
Distributive property
133.5 = 6w - 28.5
Add 28.5 on both sides
133.5 + 28.5 = 6w - 28.5 + 28.5
162 = 6w
Divide 6 on both sides
162 / 6 = 6w / 6
w = 27 in
l = 2w - 14.25 = 2 (27) - 14.25 = 39.75 in
Hope this helps!! :)
Please let me know if you have any questions
One ingot contains 10 kg of pure silver and 2 kg of league. What quantity of silver, whose grade is 0.700; is it necessary to melt to obtain silver with a grade of 0.750?
a) 20
b) 22
c) 16
d) 24
e) 19
Answer:
a) 20
Step-by-step explanation:
If x is the kg of 0.700 grade silver, then:
Silver in ingot + silver in 0.700 alloy = silver in 0.750 alloy
10 + 0.7x = 0.75(x + 12)
10 + 0.7x = 0.75x + 9
1 = 0.05x
x = 20
A bookstore sells books at a profit of at least 15% of the final selling price. The store buys a certain book at a cost of £17. If the store gives students a 20% discount, what should the selling price of the book before the discount be?
The Selling Price of The Book before discount will be 20
(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.
v⃗ =
(b) Show that the point (−1,−1,1) lies on both planes. Then find a vector parametric equation for the line of intersection.
r⃗ (t)=
Find the intersection of the two planes. Do this by solving for z in terms of x and y ; then solve for y in terms of x ; then again for z but only in terms of x.
-4x + 2y - z = 1 ==> z = -4x + 2y - 1
3x - 2y + 2z = 1 ==> z = (1 - 3x + 2y)/2
==> -4x + 2y - 1 = (1 - 3x + 2y)/2
==> -8x + 4y - 2 = 1 - 3x + 2y
==> -5x + 2y = 3
==> y = (3 + 5x)/2
==> z = -4x + 2 (3 + 5x)/2 - 1 = x + 2
So if we take x = t, the line of intersection is parameterized by
r(t) = ⟨t, (3 + 5t )/2, 2 + t⟩
Just to not have to work with fractions, scale this by a factor of 2, so that
r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩
(a) The tangent vector to r(t) is parallel to this line, so you can use
v = dr/dt = d/dt ⟨2t, 3 + 5t, 4 + 2t⟩ = ⟨2, 5, 2⟩
or any scalar multiple of this.
(b) (-1, -1, 1) indeed lies in both planes. Plug in x = -1, y = 1, and z = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,
r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩
Suppose 232subjects are treated with a drug that is used to treat pain and 50of them developed nausea. Use a 0.01significance level to test the claim that more than 20%of users develop nausea. Identify the null and alternative hypotheses for this test.
A. Upper H0?: p equals 0.20
Upper H1?: p not equals 0.20
B. Upper H0?: p equals 0.20
Upper H1?: p greater than 0.20
C. Upper H0?: p greater than 0.20
Upper H1?: p equals 0.20
D. Upper H0?: p equals 0.20
Upper H1?: p less than 0.20
Identify the test statistic for this hypothesis test. Identify the P-value for this hypothesis test.
Identify the conclusion for this hypothesis test.
A. Reject Upper H 0. There is sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
B. Fail to reject Upper H 0. There is sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
C. Reject Upper H 0. There is not sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
D. Fail to reject Upper H 0. There is not sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
Answer:
A
The correct option is B
B
[tex]t = 0.6093[/tex]
C
[tex]p-value = 0.27116[/tex]
D
The correct option is D
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 232[/tex]
The number that developed nausea is X = 50
The population proportion is p = 0.20
The null hypothesis is [tex]H_o : p = 0.20[/tex]
The alternative hypothesis is [tex]H_a : p > 0.20[/tex]
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{50}{232}[/tex]
[tex]\r p = 0.216[/tex]
Generally the test statistics is mathematically represented as
=> [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p )}{n} } }[/tex]
=> [tex]t = \frac{ 0.216 - 0.20 }{ \sqrt{ \frac{ 0.20 (1- 0.20 )}{ 232} } }[/tex]
=> [tex]t = 0.6093[/tex]
The p-value obtained from the z-table is
[tex]p-value = P(Z > 0.6093) = 0.27116[/tex]
Given that the [tex]p-value > \alpha[/tex] then we fail to reject the null hypothesis
Given that
[tex] log(3) f = a[/tex]
and
[tex] log(3) g = b[/tex]
express
[tex] log(9) ( \frac{ \sqrt{f} }{g})[/tex]
in terms of a and b.
Answer:
(a-2b)/4
Step-by-step explanation:
log 9 (sqrt(f)/g) = 0.5*log 9 (f(x)) - log 9 (g(x))= 0.5*0.5*log 3 f(x) - 0.5*log 3 g(x) = a/4 - b/2=(a-2b)/4
Complete the equation describing how
x and y are related.
X
0
1
2
3
5
6
у
5
6
7
8
9
10
y = x + [?]
Enter the answer that belongs in ?).
Answer:
y= x + 5
Step-by-step explanation:
it is clearly shown
What two rational expressions sum to [tex]\frac{4x+2}{x^{2}-9+8 }[/tex] Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.
Answer:
[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]
Required
Fill in the gaps
Going by the given parameters, we have that
[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]
[tex]x^2 - 9x + 8[/tex], when factorized is [tex](x-1)(x-8)[/tex]
Hence; the expression becomes
[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}[/tex]
Combine Fractions
[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}[/tex]
Simplify the denominators
[tex]4x + 2 = A + B[/tex]
By direct comparison
[tex]A = 4x[/tex]
[tex]B = 2[/tex]
Hence, the complete expression is
[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]
Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)
Cho X là đại lượng ngẫu nhiên có hàm mật độ dạng
fx=k(x-1)(4-x) nếu x∈0;4.
Tìm k, F, EX, P0
which of the following not between -10 and -8
-17/2
-7
-9
-8.5
Answer:
-7Step-by-step explanation:
This is best read on the number line.
Look at the picture.
[tex]-\dfrac{17}{2}=-8\dfrac{1}{2}=-8.5[/tex]
Write in a shorter form:7m -7 +7m +7
Answer:
14m
Step-by-step explanation:
[tex]7m-7+7m-7\\[/tex]
First, we need to eliminate the like term and collect the like term.
[tex]-7+-7=0[/tex]
Now, we have 7m +7m, sum them up and you will get the answer.[tex]7m+7m=14m[/tex]
So, the answer is 14m.
Answer:
14m
Step-by-step explanation:
7m -7 +7m +7
7m + 7m - 7 + 7
14m
4x + 1 -5x =2x +4(x-5)
Answer:
x = 3
Step-by-step explanation:
To answer for x first distribute the 4 in the parenthesis
4x + 1 - 5x = 2x +4x - 20
Next add or subtract the x's
-x + 1 = 6x - 20
Now subtract 6x and 1 on both sides to get x on the left and the rest on the right
-7x = -21
Lastly, divide -7 on both sides
x = 3
PLS SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
10 is -5
Step-by-step explanation:
16.50 and pays 20.00 in cash the change due is
Answer:
Change due is 3.50
Step-by-step explanation:
20.00-16.50 is 3.50
Answer: $3.50
Step-by-step explanation:
You subtract 20 from 16.50.
For what value of x does (x + 3)^2-5=0
Answer:
x = -3±sqrt( 5)
Step-by-step explanation:
(x + 3)^2-5=0
Add 5 to each side
(x + 3)^2-5+5=0+5
(x + 3)^2 = 5
Take the square root of each side
sqrt((x + 3)^2 )=±sqrt( 5)
x+3 = ±sqrt( 5)
Subtract 3 from each side
x+3-3 = -3±sqrt( 5)
x = -3±sqrt( 5)
Which equations has no solution?
Answer: I think it is C
Step-by-step explanation:
There is no answer because A can be many solutions, B is x = -25, you just cannot solve C, and D is y = 7/6
PLEASE HELP ASAP! - 14 POINTS
Answer:
False
Step-by-step explanation:
the answer is false because
year 1 to 2 is $18
year 2 to 3 is $17
year 3 to 4 is $18
year 4 to 5 is $17
false because simple interest always has the same money not a pattern
Jean Paul is an interior designer who is working with a difficult client. Part of his design requires that he put 11 colored vases in a row on a shelf. He has 3 identical blue vases, 2 identical green vases, 4 identical red vases, a purple vase and a yellow vase. He has put up 4 different arrangements of the vases that his client complained about. As he begins to put up the fifth arrangement, he wonders how many different arrangements he might have to go through before his client complains about all of them. How many different arrangements could Jean Paul make
Answer:
138600 arrangements
Step-by-step explanation:
Let n = 11
The different arrangements Jean Paul can make = n!/(4!)(3!)(2!)
Hence, 11!/(4!)(3!)(2!) = 1663200/12 = 138600
6. Find x and y plz help
Answer:
x=6 square root 3 y=9
Step-by-step explanation:
x= 3 square root 3 * 2
y=3 square root 3 times square root 3
Х
30°
Calculate the size of angle x.
angle x =
I
If one Angle is = 30
And the other two angles are equal
Given: x = l
ATQ
⇒30+x+l= 180
⇒x + x = 180-30
⇒2x = 150
⇒x = 150/2
⇒x = 75
Therefore x = 75
And the angles are 30, 75 and 75
Must click thanks and mark brainliest
Write the equation of the line described:
18. Slope 2, y-intercept is -4
(Show answer in slope-intercept form.)
The Masim family’s monthly budget is shown in the circle graph provided in the image. The family has a current monthly income of $5,000. How much money do they spend on food each month? A. $250 B. $500 C. $750 D. 1,100 Please show ALL work! <3
Answer:
C. $750
Step-by-step explanation:
The amount of money to be spent monthly on food = percentage covered by food in the circle ÷ 100% × total monthly income
= [tex] \frac{15}{100}*5000 [/tex]
[tex] = \frac{15}{1}*50 [/tex]
[tex] 15*50 = 750 [/tex]
Amount of money spent each month by the Masims is $750.
What is the ratio of 1:6 and 3:8
1:6 is the same as 1/6
3:8 is the same as 3/8
f(x)=6x+2 and g(x)=-9x-5 Find the product of f and g.
The product of the functions f(x) and g(x) will be negative 2 times (27x² + 24x + 5).
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = 6x + 2 and g(x) = -9x - 5
The product of the functions f(x) and g(x), then we have
⇒ f(x) × g(x)
⇒ (6x + 2) × (-9x - 5)
Simplify the expression, then we have
⇒ (6x + 2) × (-9x - 5)
⇒ 6x(-9x - 5) + 2(-9x - 5)
⇒ -54x² - 30x - 18x - 10
⇒ -(54x² + 48x + 10)
⇒ -2(27x² + 24x + 5)
The product of the functions f(x) and g(x) will be negative 2 times (27x² + 24x + 5).
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
A) Which of triangle A, B, C and D is congruent to triangle E.? B) Which other two triangles (from A, B, C and D) are congruent to each other? Please help!
Answer:
c is congruent to e congruent means to be the same
Step-by-step explanation:
Finding the perimeter or area of a rectangle given one of th
The length of a rectangle six times its width.
If the area of the rectangle is 150 cm”, find its perimeter.
Answer:
The answer is 70cmStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
Area of a rectangle = l × w
where
l is the length
w is the width
From the question
The length of a rectangle six times its width which is written as
l = 6w
Area = 150cm²
Substitute these values into the formula for finding the area
That's
150 = 6w²
Divide both sides by 6
w² = 25
Find the square root of both sides
width = 5cm
Substitute this value into l = 6w
That's
l = 6(5)
length = 30cm
So the perimeter of the rectangle is
2(30) + 2(5)
= 60 + 10
= 70cmHope this helps you
-x + 3y = 3
x - 3y = 3
Does this system have a solution?
Answer:
No solution
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write out systems of equations
-x + 3y = 3
x - 3y = 3
Step 2: Rewrite equations into slope-intercept form
3y = 3 + x
y = 1 + x/3
-3y = 3 - x
y = -1 + x/3
Step 3: Rewrite systems of equations
y = x/3 + 1
y = x/3 - 1
Since we have the same slope for both equations but different y-intercepts, we know that both lines are parallel. If that is the case, they will never touch or intersect each other. Therefore, we have no solution.
HELPPPPP ASAPPPP
Select the correct answer.
A volleyball player sets a volleyball straight up into the air. The height of the volleyball, h(t), is modeled by this equation, where e represents the
time, in seconds, after that ball was set.
= -16t2 + 20t + 6
The volleyball reaches its maximum height after 0.625 seconds. What is the maximum height of the volleyball
A. 11.625 feet
B. 12.25 feet
C. 8.5 feet
D. 1.625 feet
Answer:
The maximum height of the volleyball is 12.25 feet.
Step-by-step explanation:
The height of the volleyball, h(t), is modeled by this equation, where t represents the time, in seconds, after that ball was set :
[tex]h(t)=-16t^2+20t+6[/tex] ....(1)
The volleyball reaches its maximum height after 0.625 seconds.
For maximum height,
Put [tex]\dfrac{dh}{dt}=0[/tex]
Now put t = 0.625 in equation (1)
[tex]h(t)=-16(0.625)^2+20(0.625)+6\\\\h(t)=12.25\ \text{feet}[/tex]
So, the maximum height of the volleyball is 12.25 feet.
Answer:
The correct answer is B. 12.25 feet.
Step-by-step explanation:
I got it right on the Edmentum test.
Is -1 rational or irrational
and is √3 + -1 Rational or irrational
explain if u can pls
Answer:
-1: rational
√3 + -1: irration
Step-by-step explanation:
A rational number is negative, if its numerator and denominator are of the opposite signs.
Hope this helps <3
Help meee I’ll give 10 pts and brainliest!!!
Step-by-step explanation:
i) [tex]\overline{AB} = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}[/tex]
[tex]\:\:\:\:\:\:\:=\sqrt{(2)^2 + (12)^2} = 12.3[/tex]
ii) [tex]m = \dfrac{y_A - y_B}{x_A - x_B} = \dfrac{-12}{2} = -6[/tex]
iii) [tex](\overline{x},\:\overline{y}) = \left(\dfrac{x_A + x_B}{2},\:\dfrac{y_A + y_B}{2}\right)[/tex]
[tex]\:\:\:\:\:\:\:=(3,\:-2)[/tex]
Write an inequality for the shaded region shown in the figure.
Answer:
the equation of the circle is x^2 + y^2 < 36
NOT LESS OR EQUAL cause of the dotted lines
and the theory behind this is because the square root of 36 is +-6 so when the equation is less than +-6 the shade cannot go outside these point, if you know what i mean
hope that answers your question :)