The length of Ryan's room was shortened by 7ft. The original length was 29ft. What is the percent decrease

Answer:

30°

Step-by-step explanation:

We know that the angles in triangles always add up to 180°. There is also a right angle in this triangle, which is 90°.

Using this policy, we can assume that:

(3x - 30) + x + 90 = 180

First, we need to combine like terms. We can combine the 3x and the x, and the -30 and the 90.

4x + 60 = 180

Subtract 60 from both sides.

4x = 120

Divide by 4 on both sides.

x = 30

Answer:

C

Step-by-step explanation:

I think so

\(\displaystyle\bf 1\frac{1}{3} -3\frac{5}{6} +5\frac{1}{9} =5+1-3+\frac{1^{/6}}{3} +\frac{1^{/2}}{9} -\frac{5^{/3}}{6}\\\\\\\ =3+\frac{6+2-15}{18} =3-\frac{7}{18}=\boxed{2\frac{11}{18} }\)

All of the given questions(#65 to #70) are AP(s).

Formula to be used: a(n) = a(1) + (n - 1)d

Pronounced as:

nth term = 1st term + (n - 1)d, where d is the common difference.

*d = difference of any two consecutive terms.

65):

1st term = 2, d = 6 - 2 = 4

Therefore,

11th term = 2 + (11 - 1)4 = 42

66):

1st term = 5, d = 15 - 5 = 10

Therefore,

16th term = 5 + (16 - 1)10 = 155

67):

1st term = 19, d = 39 - 19 = 20

Therefore,

21st term = 19 + (21 - 1)20 = 419

68):

1st term = 8, d = 38 - 8 = 30

Therefore,

36th term = 8 + (36 - 1)30 = 1058

69):

1st term = 1/2, d = 1 - 1/2 = 1/2

Therefore,

101st term = 1/2 + (101 - 1)1/2 = 101/2

70):

1st term = 0.75, d = 1.50 - 0.75 = 0.75

Therefore,

151st term = 0.75 + (151 - 1)(0.75) = 113.25

All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.

In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.

By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.

(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:

L = π(7)(13) ≈ 285.7 ft²

Rounding to the nearest tenth, the answer is 285.7 ft².

(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:

B = (24)² = 576 cm²

The perimeter of the base is 4 times the base length, so we have:

P = 4(24) = 96 cm

Now we can use the formula to find the surface area:

A = 576 + (1/2)(96)(16) = 1056 cm²

Therefore, the surface area of the square pyramid is 1056 cm².

(3) The volume of a rectangular prism can be calculated using the formula V = lwh,

where

l is the length

w is the base

h is the height

V is the volume.

Substituting the given values, we have:

V = (5)(7)(3) = 105 mm³

Therefore, the volume of the rectangular prism is 105 mm³.

(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:

B = (9)² = 81 cm²

Now we can use the formula to find the volume:

V = (1/3)(81)(4) = 108 cm³

Therefore, the volume of the square pyramid is 108 cm³.

(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:

V = (1/3)π(10)²(6) ≈ 628.3 mm³

Rounding to the nearest whole number, the answer is 628 mm³.

Therefore, the volume of the cone is 628 mm³.

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The correctanswer is-the percentage of the pieces that will meet the length specs is 98.78%.

The given data may be a random variable that takes after the normal distribution with mean μ=64 and standard deviation σ=0.1

The required value is to discover the rate of the pieces that will meet the length specs which is between 63.76 and 64.24 inches.

To find the required percentage, standardize the given limits as follows: Lower Limit: (63.76 - μ) / σ= (63.76 - 64) / 0.1 = -2.4

Upper Limit: (64.24 - μ) / σ= (64.24 - 64) / 0.1 = 2.4

Using the Standard Normal Distribution Table, the probability that the value will fall between -2.4 and 2.4 is found to be 0.9878.

The required percentage is then found by multiplying the probability by 100, which is: Percentage = 0.9878 x 100% = 98.78%

Therefore, the percentage of the pieces that will meet the length specs is 98.78%.

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The limit of (ln\(x^{5}\))/(x-1) is equal to 20 as x approaches 1.

A limit is defined as a value that a function approaches the output for the given input values. Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity.

we can use L'Hopital's rule to estimate this limit:

lim x approaches 1 (ln\(x^{5}\))/(x-1)

= lim x approaches 1 (5lnx × \(x^{4\))/(1)

= 5 lim x approaches 1 (lnx × \(x^{4}\) )

∴ we can use L'Hopital's rule again:

= 5 lim x approaches 1 [(1/x) × 4x³ ln(x) × 4x³]

= 5 lim x approaches 1 [4x² ln(x) × 12x²]

= 5 [4 ln (1) × 12]

= 20

So, the limit of (ln\(x^{5}\))/(x-1) is equal to 20 as x approaches 1.

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​

Answer:

-5

Step-by-step explanation:

2x-8=7-5x

collect like terms

2x-5x=7+8

-3x=15

x=15/-3

x=-5

Answer: The value of x is -5.

Step-by-step explanation:

As we know that LHS = RHS,

By bringing the constants to one side and variables to one side,the question can be solved.

Given in the question

2x-8 = 7+5x

on bringing variables to LHS,

2x-5x = 8+7

-3x = 15

x=(-15)/3 = -5

Hence the value of x is -5.

Answer:

10 miles

Step-by-step explanation:

her house to school= 3+5=8 then I added two extra miles because 8+2=10

Answer:

32 degrees

Step-by-step explanation:

114° - 82° = r°

=> r = 32°

Step-by-step explanation:

=bc

3x + 1 = 223x+1=22

x = 7x=7

ad = cd = 4(7) = 28ad=cd=4(7)=28

The integral ∫(2e^(π/3) to 1) ∫(2/3t) to ∛t ∫(tan(s)) to π ∫(sin(u)) to e ds du dt evaluates to a specific numerical value that can be calculated by substituting the limits of integration into the integrated expression and performing the necessary calculations.

The given integral is ∫(2e^(π/3) to 1) ∫(2/3t) to ∛t ∫(tan(s)) to π ∫(sin(u)) to e ds du dt.

To evaluate this integral, we need to perform the integration in a step-by-step manner. First, we integrate with respect to s, where we have the integral of tan(s) with respect to s, which results in -ln|cos(s)|. Next, we integrate with respect to u, where we have the integral of -ln|cos(s)| with respect to u. The limits of integration for u are sin(u) to e. After integrating, we obtain -e*ln|cos(sin(u))| + sin(u)*ln|cos(sin(u))|.

Next, we integrate with respect to t, where we have the integral of -e*ln|cos(sin(u))| + sin(u)ln|cos(sin(u))| with respect to t. The limits of integration for t are 2/3t to ∛t. After integrating, we have [-eln|cos(sin(u))| + sin(u)*ln|cos(sin(u))|]∛t - [-eln|cos(sin(u))| + sin(u)ln|cos(sin(u))|](2/3t).

Finally, we evaluate the resulting expression at the limits of integration, which are 2e^(π/3) to 1. Substituting these values, we can find the numerical value of the integral.

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Answer:

165

Step-by-step explanation:

x² + 8x + 12 =

= (9)² + 8(9) + 12

= 81 + 72 + 12

= 153 + 12

= 165

Answer:

-165

Step-by-step explanation:

(-9)2+8×-9+12

-81-72+12

-81-84

-165 answer.

Answer:

P=(A-2B)/H

Step-by-step explanation:

A=PH+2B
takeaway 2b from both sides
A-2b=ph
divide both sides by h
(A-2B)/H=P

Answer:

32

Step-by-step explanation:

simplify

8 [-4 (3-2)]

multiply

8 [-4 (1)]

take absolute value: four becomes positive

8 [-4]

solve

8*4

32

Answer:

i believe its -32

Step-by-step explanation:

Well you start in the parentheses and you get 1 and then you multiply -4 x 1 and you get -4 and then multiply that by 8 and get -32

hope this helps

Answer:

\(\large \boxed{\sf \ \ \ p=-11 \ \ \ }\)

Step-by-step explanation:

Hello,

\(\alpha \text{ and } \beta \text{ are the roots of the following equation}\)

   \(2x^2+6x-7=p\)

It means that

   \(2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\\)

And we know that

\(\alpha= 2\cdot \beta\)

So we got two equations

   \(2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\<=>8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\<=>6\beta^2+6\beta =0\\\\<=>\beta(\beta+1)=0\\\\<=> \beta =0 \ or \ \beta=-1\)

For \(\beta =0, \ \ \alpha =0, \ \ p = -7\)

For \(\beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11\)

I assume that we are after two different roots so the solution for p is p=-11

b) \(\alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1\)

So a quadratic equation with the expected roots  is

\(x(x-1)=x^2-x\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

11

Step-by-step explanation:

A=8x+8

B=8x-4

A+B=180 degrees

therefore,

8x+8+8x-4=180

16x+4=180

16x=176

x=176/16=11

Hope it helps

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If the estimate of the population standard deviation is 8, the sample size is 62

In this question, you want to estimate the population mean with 95% confidence with a margin of error of 2.

if the estimate of the population standard deviation is 8, we need to find the sample size.

here, α = (1 - 0.95)/2

         α = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1 - α

so, z = 1.96

Now, to find the margin of error M we have formula

M = z * σ/√n

2 = 1.96 * 8/√n

√n = 1.96 * 4

√n = 7.84

n = 61.47

n ≈ 62

Therefore,  if the estimate of the population standard deviation is 8, the sample size is 62

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Answer:

If each of the dimensions was enlarged by 3 units then the new length would be 5 and the new width would be 6. To find the area of the triangle we use the formula: A = L x W ÷ 2.


6 x 5 = 30ft2
30 ÷ 2 = 15ft2


Therefore the new area of the triangle would be 15ft2.

Step-by-step explanation:

Have a great rest of your day
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Answer:

A. 900 un³

Step-by-step explanation:

Volume = Area triangle x height

Area triangle = 1/2 (15 x 8) = 1/2(120) = 60

60 x 15 = 600 + 300 = 900 un³

If my answer is incorrect, pls correct me!

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Answer:

   26

Step-by-step explanation:

The length of the midsegment is the average of the lengths of the parallel bases:

  XY = (TR +PA)/2 = (12 +40)/2 = 52/2

  XY = 26

Answer:

that's because it's impossible to add fractions that have a different number of parts

Answer:

first one is 18 second one is 45

Step-by-step explanation:

add 18 and 45 to get 63

area is 63

Answer:

Step-by-step explanation:

first i would combine like terms so 1/4a + 1/3a is equal to 7/12 then the equation would be 7/12a+8=22 simplify the isolate the variable so i think it A=24

Answer:

Hey there!

Step-by-step explanation:

Equation: 1/4a + 1/a + 8 = 22

(The answer is 24)

(You have to do 3 steps in order to solve this question! The steps are below!)

~1. First you have to simplify both sides of the equation.

=> (1/4a + 1/3a) + (8) = 22

=> 7/12a + 8 = 22

~2. Next, subtract 8 from both of the sides.

After you do that you will get, 14

7/12a=14

~3. Lastly, you just multiply both sides by 12/7.

(12/7) x (7/12a)

(12/7) x (14)

~Therefore, A would equal to 24.

A=24

~Hope this helps!

~Good luck! :)

~If you still don’t understand, ask for help! (I would be glad to answer any questions you have! :D )

At the beginning of the proof, it would be assumed that x is an even integer.

Intefers are positive numbers, negative numbers, and zero. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.

At the beginning of the direct proof, we would assume that x is an even integer. An even integer can be represented as x = 2n, where n is an integer. Using this assumption, we will proceed with the proof to show that x² + 3x + 19 is indeed an odd integer.

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Binary integer variables are variables whose values consist of two values, 0 and 1.

Correct answer will be :- b. Variables with values 0 and 1.

These values are also known as bits, which are represented as 0 and 1 in computers. Binary integer variables are used in computing as a way to represent numbers, characters, and instructions. Binary integer variables are used to represent information in digital systems, because they can be used to represent any value with a single bit.

For example, a single bit can represent a number, letter, or instruction. Binary integer variables are also used in computer programming, as they can be used to represent boolean values, such as true and false. Additionally, they can be used to represent various types of data, such as numbers, characters, and images.

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Answer:

B

Step-by-step explanation:

g(2)=-7 because -(2)-5=-7

f(-7)=-18 because 2(-7)-4=-18

Answer:

CA = 32

Step-by-step explanation:

By intersecting chords theorem:

\(12(4x + 1) = 14(3 + 3x) \\ \\ 48x + 12 = 42 + 42x \\ \\ 48x - 42x = 42 - 12 \\ \\ 6x = 30 \\ \\ x = \frac{30}{6} \\ \\ x = 5\)

CA = 14 + ( 3 + 3x)

CA = 14 + ( 3 + 3*5)

CA = 14 + ( 3 + 15)

CA = 14 + 18

CA = 32

Answer:

from my point of view the solution should be 36

Answer:

b > -9

Step-by-step explanation: