The sum of two consecutive ODD integers is -76. Find the integers.​

Answer:

See below

Step-by-step explanation:

\(\cos M=\frac{adjacent}{hypotenuse}=\frac{56}{70}=\frac{4}{5}\\\\\sin L=\frac{opposite}{hypotenuse}=\frac{56}{70}=\frac{4}{5}\)

Hence, both ratios are equal to each other

Step-by-step explanation:

Here

\( \sf \: volume_{(Cylinder)} {\gray{\begin{cases} \sf \rightarrowtail \: \pi {r}^{2}h \\ \sf \rightarrowtail \: 3.14 \times {(2.1)}^{2} \times 6.3 \\ \sf \rightarrowtail \: 3.14 \times 4.41 \times 6.3 \\ \sf \rightarrowtail \: 87.23 \\ \sf \rightarrowtail \: 87.2 {m}^{3} \end{cases}}}\)

Answer:

18

Step-by-step explanation:

Hi there !

2² x 3³ x 4⁵/ 2 x 3 x 4⁵ =

simplify 2 ; 3 ; 4⁵

= 2ₓ3²/1

= 2ₓ9

= 18

Good luck !

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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Answer:

--------------------

Let the original number be n.

We are given that 30% of n is 14.99.

Set up an equation to reflect this relation:

Solve it for n:

The inequality that describes how many movies Parv can buy is: n ≤ 10.025

Let's denote the number of movies Parv wants to buy as n. We are given that each movie costs $3.99. To determine the inequality that describes how many movies Parv can buy, we need to consider the amount of money he has remaining after purchasing the pack of games.

Parv starts with a $50 gift card and spends $9.99 on a pack of games. The remaining amount on the gift card is $50 - $9.99 = $40.01.

Now, let's consider the cost of n movies. Each movie costs $3.99, so the total cost of n movies would be n * $3.99.

Since Parv wants to buy the movies using the remaining amount on his gift card, we can set up the inequality:

n * $3.99 ≤ $40.01

This inequality states that the total cost of n movies, represented by n * $3.99, must be less than or equal to the remaining amount on the gift card, which is $40.01.

Simplifying the inequality further, we have:

3.99n ≤ 40.01

Now, if we want to solve for n, we can divide both sides of the inequality by 3.99:

n ≤ 40.01 / 3.99

Calculating this value, we have:

n ≤ 10.02506265664

Therefore, the inequality that describes how many movies Parv can buy is:

n ≤ 10.025

This means that Parv can buy a maximum of 10 movies, as he cannot purchase a fractional part of a movie.

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Answer:

1st Question: b. x=6.0

2nd Question: a. AA

3rd Question: b.

Step-by-step explanation:

For 1st Question:

Since ΔDEF ≅ ΔJLK

The corresponding side of a congruent triangle is congruent or equal.

So,

DE=JL=4.1

EF=KL=5.3

DF=JK=x=6.0

Therefore, answer is b. x=6.0

\(\hrulefill\)

For 2nd Question:

In ΔHGJ and ΔFIJ

∡H = ∡F Alternate interior angle

∡ I = ∡G Alternate interior angle

∡ J = ∡ J Vertically opposite angle

Therefore, ΔHGJ similar to ΔFIJ by AAA axiom or AA postulate,

So, the answer is a. AA

\(\hrulefill\)

For 3rd Question:

We know that to be a similar triangle the respective side should be proportional.
Let's check a.

4/5.5=8/11

5.5/4= 11/6

Since side of the triangle is not proportional, so it is not a similar triangle.

Let's check b.

4/3=4/3

5.5/4.125=4/3

Since side of the triangle is proportional, so it is similar triangle.

Therefore, the answer is b. having side 3cm.4.125 cm and 4.125cm.

To calculate Nathan's net worth, we need to determine his total liabilities (debt) and subtract that from his total assets. The debt ratio tells us that Nathan's liabilities are 80% of his total net worth.

Total liabilities = Car loan + Mortgage + Student loans = $2,000 + $150,000 + $15,000 = $167,000

Nathan's net worth = Total assets = Total liabilities / Debt ratio = $167,000 / 0.8 = $208,750

So, Nathan's net worth is $208,750.

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Probability of an event is its chance of . The probability that a student not liking mountains doesn't like beach is: Option b: 40.4%

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}}\)

Where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For the given case, from the table (image attached below), we can see that, there are total 94 students who do not like mountains. Now, out of those 94, there are 38 students not liking beach.

Thus, if A = a student not liking beach

B = not liking mountains,

Then ,

P(A|B) = P(A ∩ B)/P(B) = \(\dfrac{38/158}{94/158} = \dfrac{38}{94} \approx 0.404 = 40.4\%\)

Thus, probability of a student not liking beach given that that student doesn't like mountains is 40.4% approx.

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Answer:

40.4%

Step-by-step explanation:

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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Answer and Step-by-step explanation:

The most common (greatest) factor of 120 and 300 is 60.

60 goes into both of them, and it is the greatest number in there list of factors that would go into both of these numbers.

#teamtrees #WAP (Water And Plant)

The proportion of people aged 7 to 18 years gave watching television as their favorite type of leisure activity is 300/2,200

There are 900+1,300=2,200900+1,300=2,200 people aged 7 to 18 years.

200 of those people are aged 7 to 12 years and

100 of those people that are aged 13 to 18 years gave watching television as their favorite leisure activity,

so 200+100=300  200+100=300 of the people aged 7 to 18 years gave watching television as their favorite leisure activity.

Thus the proportion of people aged 7 to 18 years who gave watching television as their favorite leisure activity is 300/2,200

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Answer:

3x² + 7x + 6

Step-by-step explanation:

Big Rectangle:

A = bh

A = (x + 3)(x + 2)

A = x² + 2x + 3x + 6

A = x² + 5x + 6

Small rectangle:

A = bh

A = (x + 1)(2x)

A = 2x² + 2x

Combined:

x² + 5x + 6 + 2x² + 2x

3x² + 7x + 6

The value x in the formula represents the value of each observation of the data-set.

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Answer:

16

Step-by-step explanation:

Add 16

Answer:

16

Step-by-step explanation:

The power series representation of the function f(x) = x^3 / (1 + 3x) centered at x = 0 includes the first five non-zero terms, and its interval of convergence is (-1/3, 1/3).

To find the power series representation centered at x = 0 for the function f(x) = x^3 / (1 + 3x), we can use the geometric series formula:

1 / (1 - r) = 1 + r + r^2 + r^3 + ...

Let's rewrite the function f(x) in a form that resembles the geometric series:

f(x) = x^3 / (1 + 3x)

= x^3 (1 + 3x)^(-1)

Now, we can use the geometric series formula with r = -3x:

f(x) = x^3 (1 - (-3x))^(-1)

= x^3 ∑[n=0,∞] (-3x)^n

Expanding the power series:

f(x) = x^3 (1 - 3x + 9x^2 - 27x^3 + ...)

To find the first five non-zero terms, we can stop the expansion at the term with x^4:

f(x) ≈ x^3 (1 - 3x + 9x^2 - 27x^3 + 81x^4)

The interval of convergence can be determined by considering the radius of convergence. The radius of convergence for this power series can be found using the ratio test. However, since this is a geometric series with a common ratio of -3x, the series will converge as long as the absolute value of -3x is less than 1:

|-3x| < 1

3|x| < 1

|x| < 1/3

Thus, the interval of convergence is (-1/3, 1/3).

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Answer: 1) 36 m and 60 m^2     2) 15π/2 + 10 m and 75π/4 m^2

Step-by-step explanation:

Using the pythagorean theorem in the first question, we get that the slope is 10 m so the perimeter = 10 + 14 + 6 + 6 = 36 m and the area is

(14 + 6)*6/2 = 60 m^2

So in the next question, the arc of the circle has a length of

2π*5*3/4 = 15π/2

So the perimeter is 15π/2 + 5 + 5 = 15π/2 + 10 m

And the area is 3/4*π*5*5=75π/4 m^2

Hope it helps

Answer:

Step-by-step explanation:

speed=75 miles per hour

\(speed=\frac{75 \times 1760 \times 3 }{3600 } =110 ~ft~/ ~s\)

distance covered in 10 seconds=110×10=1100 ft

Answer:

We will use this equation to solve this question: Distance = Speed/Time

Distance = 75 x 5280

                     3600

We are multiplying 75 by 5280 because we want to convert miles to feet. Then, we divide it by 3600, which is equivalent to an hour.

Distance = 396,000

                     3600

              = 110 Feet

Therefore, the car will travel 110 feet in 10 seconds.

Answer:

105, n+5

Step-by-step explanation:

add five to each input

Answer:

each person gets 1/4 of the pizza or .25 of the pizza if it is split equally among the people.

Step-by-step explanation:

Answer:

In order to simplify improper fractions

1. Multiply the denominator and the whole number.

2. Add the numerator to the product.

3. Keep the denominator the same.

4. Easily simplify your solution

Step-by-step explanation:

And for proper fractions, just simplify by finding the GCF and divide Numerator by denominator.

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Have a nice day!

Answer:

-16

Step-by-step explanation:

did the math

Answer:

The answer is 21 units²

Step-by-step explanation:

To find the area of a right triangle you use the formula A=ab/2

So

A=6×7/2 = 21

Answer:

37 inches

Step-by-step explanation:

1369 = l^2

The square root of 1369 is 37.

Answer:

Wdym scientific notations?

Step-by-step explanation:

3.8 x 102 = 387.6

6.4 x 10 = 64

Answer:

21 = k

Step-by-step explanation:

Vertical angles are equal

170 = 6k+44

Subtract 44 from each side

170-44 = 6k+44-44

126 = 6k

Divide each side by 6

126/6 = 6k/6

21 = k

If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

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(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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