help me please FIJDJSHEHE

The most reasonable unit of measurement for 3) is option (C): \(m^2\), 4) is option (B): \(km^2\), 5) is \(in^2\).

3) The most reasonable unit for the measurement of the baseball field is \(m^2\) because the baseball field covers a large distance which is not accurately measured by small units  \(cm^2\) or \(mm^2\)  where it is not that big to be measured in large units like \(km^2\). So option C is the correct option.

4) The most reasonable unit for the measurement of a lake is \(km^2\) because lakes are generally very large water bodies that cover a large distance and are not accurately measured by small units like \(cm^2\) , \(mm^2\) , and \(m^2\). So option B is the correct option.

5) The most reasonable unit for the measurement of the area of a door is \(in^2\) because doors are relatively small compared to the other options and are often measured in square inches or square feet. So option B is the correct option.

Therefore the correct answers question-wise are:

3) \(m^2\)

4) \(km^2\)

5) \(in^2\)

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Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

Answer:

Step-by-step explanation:

In triangle ΔABC,

<C=90° (Given angle is a right angle).

m∠A=65° (Also given).

The sum of angles of a triangle is 180°.

We can set an equation for angles A, B and C.

<A+<B+<C=180°.

Now we are plugging values of <A and <C in the equation above.

90°+<B+65°=180°

<B+155=180.

Subtract 155 from both sides.

<B+155-155=180-155.

<B=25°.

Therefore, <B=25°.

Now, in triangle ΔCBD.

<D=90°. (Give CD is perpendicular to AB. A perpendicular line subtands an 90° angle.)

<B=25° (We found above).

Now, the sum of the angles of triangle ΔCBD is also 180°.

We can set up another equation,

<B + <D + < BCD = 180 °.

Plugging values of B and D in the equation above.

25+90+<BCD=180.

115+<BCD=180.

Subtract 115 from both sides.

115+<BCD-115=180-115.

<BCD=65°.

Now, in triangle ΔCAD.

<D = 90°.

<A = 65°

We need to find <ACD.

Now, the sum of the angles of triangle ΔCAD is also 180 degrees.

We can set up another equation,

<A+<D+<ACD=180°.

65+90+<ACD=180.

155+<ACD=180.

Subtract 155 from both sides.

<ACD+155-155=180-155.

<ACD=25°.

Therefore, <ACD=25°, <BCD=65°, <D=90°, <B=25°.

The given information can be used to determine the measures of the required angles, so that:

i. the measure of all angles in ΔCBD are:

m<BCD = \(65^{o}\)

m<CDB = \(90^{o}\)

m<B = \(25^{o}\)

ii. the measure of angles in ΔCAD are:

m<A = 65°

m<ACD = \(25^{o}\)

m<ADC = \(90^{o}\)

From ΔABC, given that m∠A = 65° and <C = \(90^{o}\) then;

m<A + m<B + m<C = \(180^{o}\)

65° + m<B + \(90^{o}\) = \(180^{o}\)

m<B = \(180^{o}\) - \(155^{o}\)

       = \(25^{o}\)

m<B = \(25^{o}\)

a. CD is perpendicular to AB, so that:

m<ADC = m<BDC = \(90^{o}\)

Thus,

m<A + m<ACD + m<ADC = \(180^{o}\)

65° + m<ACD + \(90^{o}\)  = \(180^{o}\)

m<ADC = \(180^{o}\) - \(155^{o}\)

        = \(25^{o}\)

m<ACD = \(25^{o}\)

Also,

m<BCD + m<CDB + m<B = \(180^{o}\)

m<BCD + \(90^{o}\) + \(25^{o}\) = \(180^{o}\)

m<BCD = \(180^{o}\) - \(115^{o}\)

             = \(65^{o}\)

m<BCD = \(65^{o}\)

Therefore;

i. the measure of all angles in ΔCBD are:

m<BCD = \(65^{o}\)

m<CDB = \(90^{o}\)

m<B = \(25^{o}\)

ii. the measure of angles in ΔCAD are:

m<A = 65°

m<ACD = \(25^{o}\)

m<ADC = \(90^{o}\)

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Answer:

-0.33333333333 in other word it o.3 with line over 3

Step-by-step explanation:

Step-by-step explanation:

Integers are a subset of Rational Numbers because all Integers are Rational Numbers.

Step-by-step explanation:

3 is integer but it can be written as \frac{3}{1} \ or \ \frac{6}{2},.. etc.

1

3

or

2

6

,..etc. which is rational form. Hence every integer can be express as Rational Number.

Thus the last option is correct.

Further, Integers can be defined as the whole numbers including zero and positive whole numbers. i.e. ......,-3, -2, -1, 0, 1, 2, 3,.....

Example: -546, 87855889, 0, etc.

Rational Number is the number in the form \frac{p}{q}

q

p

, where q≠0.

Example: \frac{2}{9}, \frac{-1}{267}, \frac{875}{2}, 3, etc.

9

2

,

267

−1

,

2

875

,3,etc.

Step-by-step explanation:

The way you can think about volume is that we have some cross sectional area times the height of the solid.

27.

The volume of a square based pyramid is

\(v = {s}^{2} ( \frac{h}{3} )\)

where h is the height of the pyramid

s is the side length of the square base.

S=7

h=12

\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)

28. The volume of a rectangular prism

\(v = l \times w \times h\)

where l is length

w is width

h is height

\(v = 11 \times 11 \times 8 = 968\)

29.

Use the same formula in 27

\(v = 100(3) = 300\)

30.

Volume of a Cylinder is

\(v = \pi {r}^{2} h\)

where r is the radius of the circle

where h is the height

r is half of the diameter

The diameter is 22, thus the radius is 11.

\(v = {11}^{2} (8)(\pi)\)

\(v = 968\pi\)

pi is approximately 3.14

\(v = 3041.06\)

31. Volume of A Sphere

\( \frac{4}{3} \pi {r}^{3} = v\)

The radius is half of diamter, thus r=7

\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)

Answer:

\(a_{61}=-972\)

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

\(a_n=a_1+(n-1)r\)

Where

an = nth term

a1 = first term

r   = common difference

n  = number of the term

We are given the first terms of a sequence:

-12, -28, -44,...

Find the common difference by subtracting consecutive terms:

r = -28 - (-12) = -16

r = -44 - (-28) = -16

The first term is a1 = -12. Now we calculate the term n=61:

\(a_{61}=-12+(61-1)(-16)\)

\(a_{61}=-12-60*16=-12-960\)

\(\mathbf{a_{61}=-972}\)

Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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Check the picture below.

so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".

\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)

Answer:

n₁  > n₂     Sample size of the first sample is bigger

Step-by-step explanation:

CI = 95 %    α = 5 %     α = 0,05

We know the bell shape curve of the normal distribution is symmetrical with respect to the mean, therefore we only need to evaluate one tail of the samples

Then from z-table we find   z(c)  =  1,64

CI   =  (  μ₀ - z(c)*σ /√n   <  X  <   μ₀ + z(c)*σ /√n )

So we must compare the tails of the two CI

Let´s call  n₁    and   n₂   the samples size of two different samples

The CI of the samples begins at

sample 1       μ₀ - z(c)*σ /√n₁        and for sample 2    μ₀ - z(c)*σ /√n₂      

that means   51,7  =  μ₀ - z(c)*σ /√n₁     (1)

and                49,1  =   μ₀ - z(c)*σ /√n₂     (2)

Where   μ₀ ;  z(c) = 1,64 ;  σ  are equal in both equations

Now by simple inspection, we note that the second term on the right side of the second equation should be bigger than the second term on the right side of  the first equation

then    

z(c)*σ /√n₂   >  z(c)*σ /√n₁

Then   n₂    need to be smaller than  n₁

n₁  > n₂

Answer: A: 31

Step-by-step explanation:

2m+9p-11
(plug in m=3, p=4)
2(3)+ 9(4)-11
6+36-11

42-11

31

The number of packs of mini cupcakes ordered by Mary are 15 approximately if she has $200 to spend and the cost of each pack is $12.75 and shipping cost is $14.50.

Total amount, Mary can spend = $200

Cost of one pack = $12.75

Total shipping cost = $14.50

Amount remaining after shipping cost = $200 - $14.50 = $185.50

Total packs Mary can order = $185.50/$12.75 = 14.54

Hence, Mary can order approximately 15 packs of mini cupcakes.

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Answer: 16j^3+2

Step-by-step explanation:

The employee must sell $32,000 worth of merchandise in the month to make a total of $4,000.

Let's first find out how much commission an employee would earn if they sold $x in a month,

where x is the amount of sales over $7,000.

The commission earned would be 8% of x, or 0.08x.

To earn a total of $4,000 for the month, the employee would need to earn a base salary of $2,000 plus an additional $2,000 in commission.

So we can set up the following equation:

0.08x + 2000 = 4000

Subtracting 2000 from both sides, we get:

0.08x = 2000

Dividing both sides by 0.08, we get:

x = 25000

Therefore, the employee must sell $25,000 in a month to make a total of $4,000 for the month. Note that this is the amount of sales over $7,000, so the total sales for the month would be $25,000 + $7,000 = $32,000.

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Answer:

9/4 * 3/4 =  27/16  = 1  \(\frac{9}{16}\)

Step-by-step explanation:

Answer:

(7s-2)+3+(s+3) = 52, or 8s+4 = 52.

Step-by-step explanation:

Since s is the son's age, "two less than seven times" the son's age would be represented by 7s-2. To represent this in 3 years, we would add 3: (7s-2)+3. In 3 years, the son's age, s, would be represented by s+3. We are told that the sum of these ages will be 52; this gives us (7s-2)+3+(s+3) = 52.

To simplify this, combine like terms. 7s+s = 8s; -2+3+3 = 4. This gives us 8s+4=52.

(7s-2)+3+(s+3)=52, or 8s+4 = 52

Answer:Hi

Step-by-step explanation:

Answer:

a+2b-d=1, 3, 5, 7

Step-by-step explanation:

(ax^2+bx+3)(x+d)

ax^3+bx^2+3x+adx^2+bdx+3d

ax^3+bx^2+adx^2+3x+bdx+3d=x^3+6x^2+11x+12

ax^3=x^3, a=1

bx^2+adx^2=6x^2

x^2(b+ad)=6x^2

b+ad=6

b+(1)d=6

b+d=6

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

3x+bdx=11x

x(3+bd)=11x

3+bd=11

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

b=6-d

3+(6-d)d=11

3+6d-d^2=11

3-11+6d-d^2=0

-8+6d-d^2=0

d^2-6d+8=0

factor out,

(d-4)(d-2)=0

zero property,

d-4=0, d-2=0

d=0+4=4,

d=0+2=2

b=6-4=2,

b=6-2=4.

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

a+2b-d=1+2(2)-2=1+4-2=5-2=3

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

a+2(4)-4=1+8-4=9-4=5

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

a+2(2)-4=1+4-4=5-4=1

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

a+2(4)-2=1+8-2=9-2=7

Answer:

\(a+2b-d=1\)

Step-by-step explanation:

We are given that:

\((ax^2+bx+3)(x+d)=x^3+6x^2+11x+12\)

And we want to determine:

\(a+2b-d\)

So, we will determine our unknowns first.

We can distribute our expression:

\(=(ax^2+bx+3)x+(ax^2+bx+3)d\)

Distribute:

\(=ax^3+bx^2+3x+adx^2+bdx+3d\)

Rearranging gives:

\(=(ax^3)+(bx^2+adx^2)+(bdx+3x)+3d\)

Factoring out the variable yields:

\(=(a)x^3+(b+ad)x^2+(bd+3)x+d(3)\)

Since we know that our expression equals:

\(x^3+6x^2+11x+12\)

This means that each of the unknown terms in front of each variable corresponds with the coefficient of the resulting equation. Therefore:

\(\begin{aligned} a&=1\\ b+ad&=6\\bd+3&=11\\3d&=12\end{aligned}\)

Solving the first and fourth equation yields that:

\(a=1\text{ and } d=4\)

Then the second and third equations become:

\(b+(1)(4)=6\text{ and } b(4)+3=11\)

And solving for b now yields that:

\(b=2\stackrel{\checkmark}{=}2\)

Therefore, we know that:

\(a=1, b=2\text{ and } d=4\)

For the equation:

\((x^2+2x+3)(x+4)=x^3+6x^2+11x+ 12\)

Then the expression:

\(a+2b-d\)

Can be evaluated as:

\(=(1)+2(2)-4\)

Evaluate:

\(=1+4-4=1\)

Hence, our final answer is 1.

Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.

The statement that should be true is option A. The average rate of change of f is the same as the average rate of change of g.

It is considered to the mathematical function where x should be the variable and a be the constant that we called as the function-based.

Since Function g is an exponential function passing through the points (3,–53) and (5,-41).

So here the average change rate of f should be similar just like the g.

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We can conclude that the average rates of change of f and g cannot be determined from the given information.

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

We can calculate the average rate of change of function f over the interval (3,5) using the given table:

The average rate of change of f

= (f (5) - f (3)) / (5 - 3)

= (71 - 59) / 2 = 6

To determine the average rate of change of function g over the same interval, we need to find its equation first.

We can use the two given points to set up a system of equations:

-53 = a(3)^b - 41

-53 = a(5)^b - 41

Subtracting the second equation from the first.

0 = a(3^b - 5^b)

Since 3^b ≠ 5^b, we must have a = 0, which means g is not a valid exponential function passing through the given points.

Therefore,

We can conclude that the average rates of change of f and g cannot be determined from the given information.

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Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16

Answer:

The population standard deviation is 1.92.

Step-by-step explanation:

Population mean:

Sum of all values divided by the number of values. Thus:

\(M = \frac{2 + 3 + 5 + 7}{4} = 4.25\)

Population standard deviation:

Square root of the division between the sum of the difference squared of each value and the mean, and the number of values. Thus.

\(S = \sqrt{\frac{(2-4.25)^2 + (3-4.25)^2 + (5-4.25)^2 + (7-4.25)^2}{4}} = 1.92\)

The population standard deviation is 1.92.

we have that

q(x)=7x-1

solve the equation

q(3x)=5q(x)+8

step 1

Find q(3x)

q(3x)=7(3x)-1

q(3x)=21x-1

step 2

substitute in the original expression

21x-1=5(7x-1)+8

21x-1=35x-5+8

21x-1=35x+3

35x-21x=-1-3

14x=-4

x=-4/14

Answer:

0-27

Step-by-step explanation:

The range of a function is representative of the values on the y-axis. In this case, the graph will contain distance on the y-axis at is the dependent variable, while the independent variable is time.

We know that the minimum value of the distance will be 0, given that there can be no negative distance. Moreover, the maximum value is 26.2 miles, since the marathon will then be over. Therefore, a good range for the situation will be 0-27 miles.

I hope this helps. I am sorry if you get this wrong.

The probability density function for U is: f_U(u) = (4/(1+u)^3) * e^-(1+u)/2, u > 0

The joint distribution for the length of life of two different types of components operating in a system is given by f(y_1, y_2) = {(1/8)y_1 e^-(y_1 + y_2)/2, y_1 > 0, y_2 > 0, 0, elsewhere. We are asked to find the probability density function for U = Y_2/Y_1.

To find the probability density function for U, we first need to find the joint distribution of U and Y_1. We can do this by using the change of variables formula:

f_U,Y_1(u, y_1) = f_Y_1,Y_2(y_1, uy_1) * |J|

where J is the Jacobian determinant of the transformation.

The Jacobian determinant is given by:

J = |∂(y_1, uy_1)/∂(u, y_1)| = |y_1|

So, the joint distribution of U and Y_1 is:

f_U,Y_1(u, y_1) = (1/8)y_1 e^-(y_1 + uy_1)/2 * |y_1| = (1/8)y_1^2 e^-(1+u)y_1/2

Next, we need to find the marginal distribution of U by integrating out Y_1:

f_U(u) = ∫f_U,Y_1(u, y_1) dy_1 = (1/8)∫y_1^2 e^-(1+u)y_1/2 dy_1

This integral can be solved using integration by parts. The final result is:

f_U(u) = (4/(1+u)^3) * e^-(1+u)/2

So, the probability density function for U is:

f_U(u) = (4/(1+u)^3) * e^-(1+u)/2, u > 0

This is the final answer.

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Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.

The exact value of the trigonometric relation is given by the equation where sin 2θ = 24/25

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

A = sin 2θ

where the measure of sin θ = 4/5

So , the triangle is represented as ΔABC

where the measure of sin θ = 4/5

And , the measure of cos θ = 3/5

From the trigonometric identities , we get

sin 2θ = 2 sinθ cos θ

On simplifying , we get

sin 2θ = 2 ( 4/5 ) ( 3/5 )

sin 2θ = 24/25

Hence , the equation is sin 2θ = 24/25

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Answer:

- 7

Step-by-step explanation:

Line is passing through the points (2,-11) and (8,-53)

Slope of the line = [-53 - (-11)]/(8 - 2)

= (-53+11)/6

= -42/6

= -7