Answer:
p
=
2
(
4
x
+
3
)
+
2
(
2
x
−
6
)
or simplified
p
=
12
x
−
9
Explanation:
By definition the perimeter of an object is the length of all its sides.
Also by definition, for a rectangle the 2 sides of the width are equal and the 2 sides of the length are equal.
Therefore the equation for the perimeter of a rectangle can be written as:
p
=
2
⋅
l
+
2
⋅
w
where
p
is the perimeter,
l
is the length and
w
is the width.
Substituting what was given about the length and width gives the equation:
p
=
2
(
4
x
+
3
)
+
2
(
2
x
−
6
)
Simplifying this equation gives:
p
=
8
x
+
3
+
4
x
−
12
p
=
8
x
+
4
x
+
3
−
12
p
=
12
x
−
9
Step-by-step explanation:
A 35-kg trunk is dragged 10 m up a ramp inclined at an angle of 12 degrees to the horizontal by a force of 90 N applied at an angle of 20 degrees to the ramp. At the top of the ramp, the trunk is dragged horizontally another 15 m by the same force. Find the total work done.
Answer:
The total work done is approximately 2,114.308 J
Step-by-step explanation:
The mass of the trunk = 35 kg
The height to which the trunk is dragged, d₁ = 10 m
The inclination of the plane on which the trunk is dragged = 12°
The applied force F = 90 N
The angle of inclination of the force to the ramp = 20°
The distance the trunk is dragged horizontally at the top of the ramp, d₂ = 15 m
Work = Force × Distance
The work done along the inclined plane, W₁ = 90 N × cos(20°) × 10 m ≈ 845.723 J
The work done along the horizontal, W₂ = 90 N × cos(20°) × 15 m ≈ 1,268.585 J
The total work done, W = W₁ + W₂
∴ W = 845.723 J + 1,268.585 J = 2,114.308 J
Suppose that the width of a certain rectangle is 1 inch more than one-fourth of its length. The perimeter of the rectangle is 72 inches. Find the length and width of the rectangle.
Answer:
Length = 28 inches
Width = 8 inches
Step-by-step explanation:
Let length be L
Let Width be W
Given : W = 1 + (1/4)L
Perimeter = 2 x ( L + W)
[tex]72 = 2 (L + (1 + \frac{1}{4} L))\\\\36 = L + 1 + \frac{1}{4} L\\\\36 - 1 = \frac{5}{4} L\\\\35 = \frac{5}{4} L\\\\5L = 35 \times 4\\\\L = \frac{140}{5} = 28 \ in[/tex]
[tex]W = 1 + (\frac{1}{4} \times 28) = 1 + 7 = 8 \ in[/tex]
Which of the following is the converse of the statement "If it is my birthday,
then it is September"?
A. If it is not September, then it is my birthday.
B. If it is not September, then it is not my birthday.
O
C. If it is September, then it is not my birthday.
D. If it is September, then it is my birthday.
SUBMIT
Help
Answer:
D
Step-by-step explanation:
If it is September, then it is my birthday
The converse of the statement "If it is my birthday, then it is September" is If it is September, then it is my birthday option (D) is correct.
What is the converse of a statement?A conditional statement with the antecedent and effect reversed is known as a converse statement.
We have a statement:
"If it is my birthday, then it is September"
As per definition, the converse of the statement says antecedent and effect reversed is known as a converse statement.
We can converse the given statement as follows:
If it is September, then it is my birthday.
Thus, the converse of the statement "If it is my birthday, then it is September" is If it is September, then it is my birthday option (D) is correct.
Learn more about the converse of a statement here:
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I think of a number subtract 5 and then multiply by 2 my awnser is 80 what is my number
Answer:
45
Step-by-step explanation:
45-5= 40
40*2= 80
What statement is NOT true about the pattern shown below? 2/3, 4/6, 8/12, 16/24 Choices: Each fraction is greater than the previous fraction. Each fraction is equal to the previous fraction in the pattern multiplied by 2/2 Each fraction is equivalent to 2/3 The next fraction in the pattern is 32/48. Plsss help me out I need the answer like, rn. (That means SAY THE ANSWER RIGHT NOW!)
Answer: Each fraction is greater than the previous fraction.
Step-by-step explanation:
The fractions given are:
2/3, 4/6, 8/12, 16/24
Note that
2/3 = 4/6 = 8/12 = 16/32
The Fractions are all equal. Each fraction is equivalent to 2/3
The pattern used here is:
2/3 × 2/2 = 4/6
4/6 × 2/2 = 8/12
8/12 × 2/2 = 16/24
16/24 × 2/2 = 32/48
Each fraction is equal to the previous fraction in the pattern multiplied by 2/2
Also, the next fraction in the pattern is 32/48.
The statement that "Each fraction is greater than the previous fraction" is incorrect. The fractions are all equal.
Factor the common factor out of each expression: 18u^2v^5-27uv^5+54uv^4
Answer:
9uv⁴
Step-by-step explanation:
9uv⁴(2v-3v+6)
Answer:
Factor out 9uv^4 from the expression
9uv^4(2uv - 3v + 6)
If you need more steps just ask :)
PLZZZZ BRAINILEST IM FAILINGGGG
Answer:
Base = 7
Height = 10
Area = 35
Step-by-step explanation:
Area is 35.
7 * 10 = 70
70/2 = 35
Base = 7 (Given)
Height = 10 (Given)
Answer:
base: 7 (yd)
height: 10 (yd)
area: 35 (yd²)
Step-by-step explanation:
To find the area of a triangle, multiply the base and height, then, divide the product by 2. The quotient is the area of the triangle.
[tex]7*10=70.[/tex]
[tex]70/2=35.[/tex]
I, therefore, believe the area of this triangle is 35 yd.
Simplify the expression. 4^0
be careful i think this is a trick question
Answer:
1
Step-by-step explanation:
4^0
Any number raised to the 0 power is 1.
Answer:
1
Step-by-step explanation:
Anything raised to 0 is 1.
a study is planned to compare the proportion of men who dislike anchovies with the proportion of women who dislike anchovies. the study seeks to determine if the proportions of men and women who dislike anchovies are different. a sample of 41 men was taken and the p^ estimate for the true proportion of men who dislike anchovies was determined to be 0.67. a sample of 56 women was also taken and the p^ estimate for the true proportion of women who dislike anchovies was determined to be 0.84. are the requirements satisfied to perform this hypothesis test
Answer:
d. No because n·(1 - [tex]\hat p[/tex]) = 8.96 is less than 10
Step-by-step explanation:
Question options;
a. Yes because the sample sizes of both groups are greater than 5
b. Yes, because in both cases n·[tex]\hat p[/tex] > 10
c. Yes, because we know that the population is evenly distributed
d. No, because the n·(1 - [tex]\hat p[/tex]) is less than 10
Explanation;
The given data are;
The number of men in the sample of men, n₁ = 41
The proportion of men who dislike anchovies, [tex]\hat p_1[/tex] = 0.67
The number of women in the sample of women, n₂ = 56
The proportion of men who dislike anchovies, [tex]\hat p_2[/tex] = 0.84
The assumptions for an analysis of the difference between means using a T-test are;
1) The data should be from a random sample of the population
2) The variables should be approximately normal (n·[tex]\hat p[/tex] ≥ 10, and n·(1 - [tex]\hat p[/tex]) ≥ 10)
3) The scale of the data is a continuous ordinance scale
4) The sample size should be large
5) The sample standard deviations should be approximately equal
From the requirement for normality, we have;
For the sample of men, n₁·[tex]\hat p[/tex]₁ = 41 × 0.67 = 24.47 > 10
n₁·(1 - [tex]\hat p[/tex]₁) = 41 × (1 - 0.67) = 13.53 > 10
For the sample of women, n₂·[tex]\hat p[/tex]₂ = 56 × 0.84 = 47.04 > 10
n₂·(1 - [tex]\hat p[/tex]₂) = 56 × (1 - 0.84) = 8.96 < 10
Therefore, the for n₂·(1 - [tex]\hat p[/tex]₂), the sample does not meet the requirement for normality
The correct option is d. No because n₂·(1 - [tex]\hat p[/tex]₂) = 8.96 is less than 10
What is the measure of KPN?
Answer:
angle KPN=95 degree
Step-by-step explanation:
angle KPN = angle JPO (because they are vertically opposite angles)
Now,
angle JPO+angle LOP=180 degree(being co interior angles)
angle JPO + 85 =180
angle JPO =180-85
angle JPO =95
since angle JPO is equal to KPN ,angle KPN is 95 degree
Pedro y su socia Karina vendieron 520 calendarios en el mes de Diciembre. Pedro vendió 120 calendarios más que su socia. ¿Cuántos calendarios vendió cada uno?
Answer:
Pedro vendió = 320 calendarios
Katrina vendió = 200 calendarios
Step-by-step explanation:
Dejemos que el número de calendarios
Pedro vendió = x
Katrina vendió = y
Pedro y su compañera Karina vendieron 520 calendarios en diciembre.
x + y = 520 .... Ecuación 1
Pedro vendió 120 calendarios más que su socio.
x = y + 120
Sustituimos y + 120 por x
y + 120 + y = 520
2 años = 520 - 120
2 años = 400
y = 400/2
y = 200 calendarios
Resolviendo para x
x = y + 120
x = 200 + 120
x = 320 calendarios
Por lo tanto,
Pedro vendió = 320 calendarios
Katrina vendió = 200 calendarios
solve for x please !URGENT!
Answer:
It is x=908.
Might be wrong tho so dont jump me
Answer: 908
Step-by-step explanation:
x/4 = 89 + 138
x/4 = 227
x = 227 x 4
x = 908
Hello please help asap, thanks!
Answer:
Last image.
Step-by-step explanation:
So, we know that the orginal graph is of [tex]\sqrt[7]{x}[/tex]
We need to find the graph of [tex]-\sqrt[7]{x}-8[/tex]
First off, we see a negative in front of the root.
This means that all the values will be flipped across the x axis.
This removes the first two answer graphs, for they are of the postive root.
Next, we have a -8 following the root.
So, when another number is inside of the root(example: [tex]\sqrt[7]{x-6}[/tex]) You are going to add 6 to the x axis, basically shifting everything to the right(postive). If it was a postive 6 inside the root, we would move it left(negative)
This is not what is being done in our graph, I just wanted to explain this for future graphing.
Now, when a number is outside the root, such as the one above, then it shifts the y axis. In this case we have a -8 outside the root. This means that the graph will be shifted down(negative) by 8.
This eliminates the 3rd graph image, leaving the last graph answer shown below.
Hope this helps!
Use the Distributive Property to expand
the expression:
2 (y + 5x - 3)
It costs $198.00 to buy beef to make 300 meatballs. What will the cost be
to make 120 meatballs?
Answer:$181.81
Step-by-step explanation:300/198
=1.5151515….multiple by 120
=181.818181
There are 5 red, 4 blue, and 3 green marbles in a bag. What are the odds of randomly pulling a blue marble out of the bag and then randomly pulling a green marble out of the bag? The blue marble is NOT replaced.
A - 7/2
B - 12/24
C - 1/12
D - 1/11
What are the vertices of the resulting image A'B'C'D'E' after rotating the figure 90° about the origin? ty A 4 B 2. E D 0 0 N 4
Answer:
A (5,4)
B (5,3)
C (6, 3)
D (2,0)
E (2,1)
Step-by-step explanation:
If the figure is rotated about the origin by 90 degrees, then the values of the co-ordinates of all the vertices will be as follows -
A (5,4)
B (5,3)
C (6, 3)
D (2,0)
E (2,1)
please help me thanks
Answer: A) (-1, 3)
Step-by-step explanation:
When reflecting across the y-axis the y value of the point stays the same and the x values flips to it's opposite.
The point of A on ΔABC is (1, 3)
The x value is 1. The opposite value of 1 is -1 giving us the coordinates (-1, 3)
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+165x+69
Answer:
The rocket hits the gorund after approximately 10.71 seconds.
Step-by-step explanation:
The height of the rocket y in feet x seconds after launch is given by the equation:
[tex]y=-16x^2+165x+69[/tex]
And we want to find the time in which the rocket will hit the ground.
When it hits the ground, its height above ground will be 0. Hence, we can let y = 0 and solve for x:
[tex]0=-16x^2+165x+69[/tex]
We can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = -16, b = 165, and c = 69.
Substitute:
[tex]\displaystyle x=\frac{-165\pm\sqrt{(165)^2-4(-16)(69)}}{2(-16)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{-165\pm\sqrt{31641}}{-32}=\frac{165\pm\sqrt{31641}}{32}[/tex]
Hence, our solutions are:
[tex]\displaystyle x_1=\frac{165+\sqrt{31641}}{32}\approx 10.71\text{ or } x_2=\frac{165-\sqrt{31641}}{32}\approx-0.40[/tex]
Since time cannot be negative, we can ignore the first answer.
So, the rocket hits the gorund after approximately 10.71 seconds.
Answer:
10.71
Step-by-step explanation:
the person below was correct!
Ethan is installing a new tile backsplash in his kitchen. The tile he likes costs $3.50 per square foot. The area he is tiling is 36.5 square feet. How much will Ethan pay for the tile for his backsplash?
Answer:
$127.75
Step-by-step explanation:
Multiply the cost by the area to find the total cost
Escreva os números abaixo em notação científica:
1) 5 000 000 000 000 =
2) 0,000 007 =
3) 58 600 000 000 000 =
4) 0,000 005 874 =
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
╭═══════ღ❦ღ══╮
Os números em notação científica são os seguintes : -
1) 5,000,000,000,000 ⟹ [tex]\boxed{5 × 10^{12}}[/tex]
2) 0,000,007 ⟹ [tex]\boxed{7 × 10^{0}}[/tex]
3) 58,600,000,000,000 ⟹ [tex]\boxed{5.86 × 10^{13}}[/tex]
4) 0,000,005,874 ⟹ [tex]\boxed{5.874 × 10^{3}}[/tex]
╰══ღ❦ღ═══════╯
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# [tex]\large\boxed{RainbowSalt2^{2}2^{2}}[/tex] ღ
3/4x × 12/11 ÷ 3x/22
Answer:
242/48
Step-by-step explanation:
The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs. Click on the datafile logo to reference the data. City Daily Living Cost ($) City Daily Living Cost ($) Bangkok 242.87 Mexico City 212.00 Bogota 260.93 Milan 284.08 Cairo 194.19 Mumbai 139.16 Dublin 260.76 Paris 436.72 Frankfurt 355.36 Rio de Janeiro 240.87 Hong Kong 346.32 Seoul 310.41 Johannesburg 165.37 Tel Aviv 223.73 Lima 250.08 Toronto 181.25 London 326.76 Warsaw 238.20 Madrid 283.56 Washington, D.C. 250.61 a. Compute the sample mean (to 2 decimals). b. Compute the sample standard deviation (to 2 decimals). c. Compute a confidence interval for the population standard deviation (to 2 decimals).
Answer:
[tex]\bar x = 260.1615[/tex]
[tex]\sigma = 70.69[/tex]
The confidence interval of standard deviation is: [tex]53.76[/tex] to [tex]103.25[/tex]
Step-by-step explanation:
Given
[tex]n =20[/tex]
See attachment for the formatted data
Solving (a): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}[/tex]
[tex]\bar x = \frac{5203.23}{20}[/tex]
[tex]\bar x = 260.1615[/tex]
[tex]\bar x = 260.16[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
[tex]\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}[/tex][tex]\sigma = \sqrt{\frac{94938.80}{19}}[/tex]
[tex]\sigma = \sqrt{4996.78}[/tex]
[tex]\sigma = 70.69[/tex] --- approximated
Solving (c): 95% confidence interval of standard deviation
We have:
[tex]c =0.95[/tex]
So:
[tex]\alpha = 1 -c[/tex]
[tex]\alpha = 1 -0.95[/tex]
[tex]\alpha = 0.05[/tex]
Calculate the degree of freedom (df)
[tex]df = n -1[/tex]
[tex]df = 20 -1[/tex]
[tex]df = 19[/tex]
Determine the critical value at row [tex]df = 19[/tex] and columns [tex]\frac{\alpha}{2}[/tex] and [tex]1 -\frac{\alpha}{2}[/tex]
So, we have:
[tex]X^2_{0.025} = 32.852[/tex] ---- at [tex]\frac{\alpha}{2}[/tex]
[tex]X^2_{0.975} = 8.907[/tex] --- at [tex]1 -\frac{\alpha}{2}[/tex]
So, the confidence interval of the standard deviation is:
[tex]\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }[/tex] to [tex]\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }[/tex]
[tex]70.69 * \sqrt{\frac{20 - 1}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{20 - 1}{8.907}[/tex]
[tex]70.69 * \sqrt{\frac{19}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{19}{8.907}[/tex]
[tex]53.76[/tex] to [tex]103.25[/tex]
116,02 LC)
Which of the triangles shown are obtuse triangles? (2 points)
A. Triangle A and Triangle B
B. Triangle B and Triangle D
C. Triangle C
D. Triangle A, Triangle B, and Triangle C
Answer:
Trangle B and D
Step-by-step explanation:
They look more than 90 degrees
Please help!! I keep getting a different answer!!! 14 points!!
y-(-4) =m(x-(-5)) solve for m
Answer:
m = [tex]\frac{y+4}{x+5}[/tex]
Step-by-step explanation:
y-(-4) = m(x-(-5))
Simplify, distribute the negative sign outside of the parenthesis, remember negative times negative equals positive
y + 4 = m (x + 5)
Inverse operations, divide the equation by the value inside of the parenthesis
[tex]\frac{y+4}{x+5}[/tex] = m
Answer:
m=y+4x/x+5 your welcome !!
CAN YOU PLS HELP ME WITH THIS I NEED THIS NOW!! I WILL GIVE BRAINLY TO BEST ANSWER THANK YOU!!
A rental car agency has 2 car rental plans. When will Plan A cost more than Plan B?
Plan A: $35 a day plus a fee of $32
Plan B: $25 a day plus a fee of $68
Write an inequality that expresses this real-world scenario.
Answer:
35d+ 32 > 25d+68
Step-by-step explanation:
Plan A: $35 a day plus a fee of $32
35d+ 32
Plan B: $25 a day plus a fee of $68
25d+68
We want to know when A costs more than B
35d+ 32 > 25d+68
From a stick 2y metres long, I cut a piece of length 4y centimetres. What fraction of the original stick remains?
Answer: [tex]\dfrac{49}{50}[/tex]
Step-by-step explanation:
Given
Length of the stick is [tex]2y\ m[/tex]
A piece of [tex]4y\ cm[/tex] is cut
We know, 1 m=100 cm
So, [tex]2y\ m[/tex] in cm is [tex]200y\ cm[/tex]
Remaining length after cut is
[tex]\Rightarrow 200y-4y=196y[/tex]
Fraction of length that is left after the cut is
[tex]\Rightarrow \dfrac{196y}{200y}\\\\\Rightarrow \dfrac{49}{50}[/tex]
Thus, [tex]\frac{49}{50}[/tex] fraction of original stick remains after cut
The amount of ice cream dispensed from a machine at an ice cream shop is normally
distributed. If the machine is used 800 times in a day, how many times did the
machine dispense an amount that falls within three standard deviations from the
mean amount?
A 798
B 760
C 544
D 267
Let z be inversely proportional to the cube root of y. When y =.064, z =3
a) Find the constant of proportionality k.
b) Find the value of z when y = 0.125.
Given:
z be inversely proportional to the cube root of y.
When y =0.064, then z =3.
To find:
a) The constant of proportionality k.
b) The value of z when y = 0.125.
Solution:
a) It is given that, z be inversely proportional to the cube root of y.
[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]
[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, z=3 when y=0.064. Putting these values in (i), we get
[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]
[tex]3=k\dfrac{1}{0.4}[/tex]
[tex]3\times 0.4=k[/tex]
[tex]1.2=k[/tex]
Therefore, the constant of proportionality is [tex]k=1.2[/tex].
b) From part (a), we have [tex]k=1.2[/tex].
Substituting [tex]k=1.2[/tex] in (i), we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]
We need to find the value of z when y = 0.125. Putting y=0.125, we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]
[tex]z=\dfrac{1.2}{0.5}[/tex]
[tex]z=2.4[/tex]
Therefore, the value of z when y = 0.125 is 2.4.
Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n}[/tex]
or
[tex]n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For the given case, it is given that:
[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]
Let the constant of proportionality be k, then we have:
[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]
It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:
[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]
Thus, the constant of proportionality k is 1.2. And the relation between z and y is:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]
Putting value y = 0.0125, we get:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]
Thus, for the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4Learn more about proportionality here:
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