√a +2√y
√a-2√y

Do you know how to rationalize the denominator and simply?

The equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).

A linear equation has the formula y = mx + b, where x and y are variables, m is the angle of the line's slope, and b denotes the y-intercept (the location where the line crosses the y-axis). On a graph, this equation represents a straight line.

The y-intercept of a linear equation, which is determined by the value of b, is first plotted on a graph. The slope is then used to determine further points along the line. How much y changes for each unit of x is indicated by the slope. For instance, if the slope is 2, then y grows by 2 for every unit increase in x.

Given that, a certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute.

Let us suppose number of minutes = x.

Then,

Cost = 0.75 + 0.15(x - 3)

hence, the equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).

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The complete question is:

The 95% confidence interval for the difference between the two proportions is (0.056, 0.164)

Here, we are given that from the sample information for people under 18-

n₁  =  500

x₁ =  180

⇒ p₁  =  180/ 500    

p₁  =  0.36    

then,  

q₁  =  1 -  p₁    

q₁ =  0.64

Similarly, from the sample information for people over 18, we have-

n₂  =  600

x₂  =  150

⇒ p₂  =  150 / 600  

p₂ =  0,25  

then,

q₂  =  1 - p₂  

q₂ =  1 - 0.25  

q₂ = 0,75

Now, we conduct a hypothesis test as follows-

Null hypothesis (H₀) ⇒  p₁  =  p₂

Alternative Hypothesis (Hₐ) ⇒ p₁  ≠  p₂

Confidence interval =  95 %    

⇒ significance level (α) = 5 %  

α  =  0.05  

and α/ 2  =  0.025  

⇒ z at 95% significance level = 1.96 (from z tables)

Now, we calculate z statistic-

z(s)  =  (p₁ - p₂) / EED

EED = √[(p₁*q₁)n₁  +  (p₂*q₂)/n₂]

EED = √[( 0.36*0.64)/500  +  (0.25*0.75)/600]

EED = √[0.00046  +  0.0003125]

EED = 0.028

and (p₁  -  p₂) = 0.36 - 0.25  

= 0.11

Therefore,

z(s)  =  0.11 / 0.028

z(s) = 3.93

we can see that  z(s) > 1.96

⇒ z(s) is in the rejection region for H₀

Thus, we reject H₀. We can´t support the idea of equals means

Now, CI at 95 %  = (p₁ - p₂) ±  z(c) * EED

CI = (0.11 ± 1.96 * 0.028)

CI = (0.11 ± 0.054)

CI =  (0.056, 0.164)

Thus, the 95% confidence interval for the difference between the two proportions is (0.056, 0.164)

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Your question was incomplete. Check for missing content below-

Q1. Let P, represent the proportion under and p, the proportion over the age of 18. The null hypothesis is:_____.

Q2. The 95% confidence interval for the difference between the two proportions is:____.

Answer:

24

Step-by-step explanation:

i dont know if its correct

Answer:

The 14-ounce bottle is the better deal

Step-by-step explanation:

I know this beause inorder to figure out which one is better you have to make them the same price and then see which bottle has more ounces. So I made each price 1$ so there is 1.58-ounces per dollar in the 5-ounce bottle and 1.17 -ounces per dollar in the 14-ounce bottle.

Answer:

4y+8

Step-by-step explanation:

Answer:4y+8

Step-by-step explanation:

To find an equivalent expression you can just simplify this expression by multiplying the numbers in the parentheses by 4. 4y+8

Answer:1897

Step-by-step explanation:

add 74,877 to 21,243 then add 39,643 to get 1897

Using the system of equation and determinant given, the value of k is any real number except -1/3

The determinant is a scalar value that can be computed from the elements of a square matrix. It is a useful tool in linear algebra and is used in many applications, including solving systems of linear equations, finding the inverse of a matrix, and calculating the volume of a parallelepiped.

Given the system of equations 3x + y + 2 = 0, -4x + 2y = k and 3x - y - 3k = 0.

We can write these equations in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix and B is the constant matrix.

A = [3 1 2]

[-4 2 k]

[3 -1 -3k]

X = [x]

[y]

[k]

B = [0]

[0]

[0]

To find the value of k for which the system is consistent, we need to find the determinant of the coefficient matrix.

|A| = (3)(2k) - (1)(-4) + (2)(3) = 6k + 2

For the system of equations to be consistent, the determinant of the coefficient matrix should not be equal to zero.

So, |A| = 6k + 2 ≠ 0

Therefore, the value of k can be any real number except -1/3.

So, the value of k can be any real number except -1/3. The system of equations is consistent for all real numbers except -1/3.

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Answer:

6

Step-by-step explanation:

Answer easy ypu just subtract i am not the best at this so dont take my word for it lol

Answer:

A = 2184 cm²

Step-by-step explanation:

the area (A) of the figure is calculated as

A = \(\frac{1}{2}\) h(b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

here h = 42 , b₁ = 52 , b₂ = 52 , then

A = \(\frac{1}{2}\) × 42 × (52 + 52) = 21 × 104 = 2184 cm²

Answer:

A = 2184 cm2

Step-by-step explanation:

Area of a parallelogram:

\(A = b*h\)

\(b=52,h=42\)

\(A=(42)(52)=2184cm^{2}\)

Hope this helps.

The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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Answer:

Step-by-step explanation:

Arithmetic sequence

First term a = 13

Common difference = 2nd term - first term

                                 = 22 - 13

                             d = 9

\(a_{n}= a + (n-1)d\\\\a_{7}= 13 + 6*9\)

   = 13 + 54

  = 67

Sum of 7 terms = \(\frac{n}{2}(2a + (n-1)d)\\\\\)

                         = \(\frac{7}{2}(2*13+6*9)\\\)

                         =\(\frac{7}{2}(26+54)\\\)

                          = \(\frac{7}{2}*80\\\)

                         = 7 *40

                          = 280

Answer:

280

Step-by-step explanation:

the 7th number is

The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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Answer:

The length of XY is 22.5

Step-by-step explanation:

Since you need to hurry I will not write an explanation

Hope this helps! :)

૮ ・ﻌ・ა

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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Answer:

.62

Step-by-step explanation:

Keep it nice and simple.

Answer:

.62

Step-by-step explanation:

Answer:

I don't know.

What the given experiment demonstrates is; The magnitude of acceleration according tp newton's second law of motion

Newton's second law of motion states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

This law basically establishes a relationship between the net force and the acceleration, which is expressed as;

∑ F = m a

where;

∑F is the sum of the external forces

m the mass of the body

a is the acceleration of the body

The initial situation in the question shows the block and a baking mass. This means that an acceleration is created towards the hanging mass expressed as;

W₁ = M₁ g

F = ma

Thus;

M₁g = m a

a = (M₁g/m)

where;

W₁ is the weight of the body  

M₁ is the mass of the body hanging under the acceleration of gravity.

For the second case, there are two masses, with one on each side, and so we have;

∑ F = W₁ - W₂

∑F = (M₁ - M₂) g

Using Newton's second law of motion gives us;

(M₁ - M₂ )g = ma

a = (M₁ - M₂ )mg

Thus, the acceleration depends on the difference of the hanging masses which proves Newton's second law of motion.

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Answer:

volume

\( = lbh\)

\(31.605 = l \times 3.5 \times 2.1 \\ 31.605 = l \times 7.35\)

divide both side by 7.35

\(l = 4.3\)

Answer:

The Answer is 4.3

Step-by-step explanation:

How i got 4.3 is i multiplied 2.1 and 3.5 and that gave me 7.35

2.1 x 3.5 = 7.35

Then i divided the Volume with 7.35

31.605 ÷ 7.35 = 4.3

So, your answer is 4.3

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Answer:

∠ AEB = 114°

Step-by-step explanation:

the chord- chord angle AEB is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is

∠ AEB = \(\frac{1}{2}\) (AB + CD) = \(\frac{1}{2}\) (140 + 88)° = \(\frac{1}{2}\) × 228° = 114°

Step-by-step explanation:

The amount left is:

A = A₀ (½)^(t/T)

where A₀ is the initial amount,

t is the amount of time,

and T is the half life.

a) A = 100 g (½)^(250 yr / 68.9 yr)

A = 8.09 g

b) 12.5 g = 100 g (½)^(t / 68.9 yr)

0.125 = (½)^(t / 68.9 yr)

3 = t / 68.9 yr

t = 206.7 yr

Given:

a = 13

b = 16.9

A = 26 degrees

Asked: What are the values for angles B and C and side c?

Solution:

To solve this problem, we will be needing the formula for the sine law.

Sine Law Formula:

Now, we will first solve for the angle B.

Now that we have angle B, we can now find angle C by combining all the angles and equate it to 180 degrees.

In order to find side c, we will use again the sine law formula.

ANSWER:

Angle B = 35 degrees

Angle C = 119 degrees

Side c = 25.9

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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Carissa's salary when she sells $2,400 worth of merchandise is $732.

The first step is to determine the base pay and the commission rate.

In order to determine these values, form a system of equations that represent the information in the question:

a + 500b = 390 equation 1

a + 100b = 480 equation 2

Where:

a = base pay

b -= commission rate

Subtract equation 1 from equation 2:

500b = 90

Divide both sides by 500:

b = 90 / 500

b = 0.18

Substitute for b in equation 1:

a + 500(0.18) = 390

a + 90 = 390

a = 390 - 90

a = 300

Salary = 300 + (0.18 x 2400)

Salary = 300 + 432 = $732

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Answer:

f(x)=24578-1345x

$19198

Step-by-step explanation:

Let's suppose "x" years pass.

\(f(x)=24578-1345x\)

When x=4,

\(f(4)=24578-1345*4\\=24578-5380\\=19198\)

The equation is y = $24,578 - $1,345x and value of car after 4 years is

$19,198.

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables.

Given cost of car = $24,578

amount decrease every year = $1,345

let amount after x years be y

where x = time and y = amount

equation is

y = $24,578 - $1,345x

amount after 4 years,

put x = 4

y = $24,578 - $1,345x

y = $24,578 - $1,345(4)

y = $24,578 - $5,380

y = $19,198

Hence equation for amount is y = $24,578 - $1,345x and amount after 4 years is  $19,198.

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Answer:

45 days

Step-by-step explanation:

300 men  = 90 days

the percentage of food consumed by one man

= ( 90 / 300 ) * 100

= 30%  = 0.3

After 40 days

150 men remain to consume at 30%

determine the number of days the remaining food will last ( x )

= x / 150 = 0.3

therefore ; X = 150 * 0.3 = 45 days

Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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\(\\ \rm\longmapsto 6abc^2+6a^2bc\)

\(\\ \rm\longmapsto 6(1)(2)(-3)^2+6(1)^2(2)(-3)\)

\(\\ \rm\longmapsto 12(9)+6(-6)\)

\(\\ \rm\longmapsto 108-36\)

\(\\ \rm\longmapsto 72\)