rationalize i)✓2 by✓3
ii)5✓2 by2✓3
iii)15 by ✓5
iv)✓5 by 5✓6
plz solve in notebook​

Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

The correct statements are The manager can improve his estimate by surveying 50 customers instead of 10, The manager can improve his estimate by randomly selecting customers throughout the week. Option B, C.

Let's evaluate each statement regarding the manager's estimation of the percentage of customers who like orange juice:

a) The statement "The manager’s sample is unlikely to be biased because the first 10 customers on Monday morning represent all his customers" is incorrect. The sample of the first 10 customers on Monday morning may not be representative of all the customers who visit the grocery store.

There could be various factors that influence the type of customers who shop at a particular time of day or day of the week, such as work schedules, personal preferences, or other external factors. Therefore, it is not safe to assume that the first 10 customers on Monday morning represent all the customers and the sample may be biased.

b) The statement "The manager can improve his estimate by surveying 50 customers instead of 10" is generally true. Increasing the sample size tends to improve the accuracy of the estimate. With a larger sample, the estimate becomes more reliable and provides a better representation of the overall customer population.

However, it is important to ensure that the sample is still representative and avoids any bias that may arise from the selection process.

c) The statement "The manager can improve his estimate by randomly selecting customers throughout the week" is true.

By randomly selecting customers throughout the week, the manager can reduce the potential bias that may arise from surveying customers during specific times or days. Random selection helps ensure a more representative sample, increasing the likelihood that the estimated percentage reflects the entire customer population.

d) The statement "The only way the manager can estimate the percentage is to ask every customer throughout the week" is incorrect. While surveying every customer throughout the week would provide the most accurate estimate, it is often impractical or not feasible due to time and resource constraints.

Sampling a subset of customers and using statistical techniques allows for reliable estimates without the need to survey every customer. So Option B, C is correct

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Answer:

x = 2

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

Answer:

A.  3 / 1/8

Step-by-step explanation:

You see 3 units on the number line.

Each unit is divided into 8 equal parts.

Answer: A.  3 / 1/8

Step-by-step explanation:

3 ÷ ¹/18 is your answer.....

HCF/GCF 32 and 48

listing factor

32: 1, 2, 4, 8, 16, 32

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

HCF: 16

prime factorization

32: 2 x 2⁴

48: 3 x 2⁴

HCF: 2⁴ = 16

Answer:

The smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.

Step-by-step explanation:

The complete question is:

The mean salary of people living in a certain city is $37,500 with a standard deviation of $2,103. A sample of n people will be selected at random from those living in the city. Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income. Round your answer up to the next largest whole number.

Solution:

The (1 - α)% confidence interval for population mean is:

\(CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

The margin of error for this interval is:

\(MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

The critical value of z for 90% confidence level is:

z = 1.645

Compute the required sample size as follows:

\(MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

      \(n=[\frac{z_{\alpha/2}\cdot\sigma}{MOE}]^{2}\\\\=[\frac{1.645\times 2103}{500}]^{2}\\\\=47.8707620769\\\\\approx 48\)

Thus, the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.

There are no two Real numbers that add up to -2 and multiply to 10.

The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:

Equation 1: x + y = -2

Equation 2: x * y = 10

To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:

1. Solve Equation 1 for x:

  x = -2 - y

2. Substitute the value of x in Equation 2:

  (-2 - y) * y = 10

3. Simplify the equation:

  -2y - y^2 = 10

4. Rearrange the equation to standard form:

  y^2 + 2y + 10 = 0

5. Since the equation is a quadratic equation, we can apply the quadratic formula:

  y = (-b ± √(b^2 - 4ac)) / (2a)

  In this case, a = 1, b = 2, and c = 10.

6. Calculate the discriminant: b^2 - 4ac:

  2^2 - 4(1)(10) = 4 - 40 = -36

7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.

In conclusion, there are no two real numbers that add up to -2 and multiply to 10.

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The Hooke's law is given by:

F = k*x

Where:

F = force

k = constant factor

x = distance

If F = 20 and x = 20

20 = k*20

Solving for k:

20/20 = k

k = 1

So: how far will a 29 pound mass stretch the spring?

29 = 1* x

Solving for x:

29/1 = x

x = 29 in

The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is 27/8 square inches or 3 3/8 square inches

From the question, we are to determine the area of the cross-section of the cone

To determine the area of the cross-section of the cone, we will determine the radius of the cross-section.

Let the radius of the cross-section be x and radius of the base of the be r.

The height of the cone is 8 inches and the height of the cone formed from the cross-section is 3 inches

By similar triangle theorem, we can write that

8/r = 3/x

x = (3r)/8

From the given information,

The area of the base is 24 square inches

Thus,

πr² = 24

Therefore, r² = 24/π

The area of the cross-section will be

A = πx²

But, x = (3r)/8

Thus,

A = π [(3r)/8]²

A = π × 3²/8² × r²

A = π × 9/64 × 24/π

A = 27/8 square inches

Hence, the area is 27/8 square inches or 3 3/8 square inches

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Answer:

yes of course it is a whole number sinse it is a number that would be on a number line

Answer:

yes

Step-by-step

Hope you could understand.

If you have any query, feel free to ask

The value of the expression (a - b)² from the given equations is; 16

We are given the two equations as;

a + b = 10   -----(eq 1)

ab = 21    ------(eq 2)

From eq 1, square both sides;

(a + b)² = 10²

a² + 2ab + b² = 100

a² + b² = 100 - 2ab

We are given ab = 21. Thus;

a² + b² = 100 - 2(21)

a² + b² = 58

Now, we know that (a - b)² = a² - 2ab + b²

Thus;

(a - b)² = 58 - 2(21)

(a - b)² = 16

Complete question is;

If a + b = 10 and ab = 21, then the value of (a - b)² is?

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The point Q that partitions the line segment is Q(2,28)

Given that the directed line segment AB, with endpoints A(20, 6) and B(-16, 50) and divide the segment into a 1:1 ratio.

A line segment is a part of a line bounded by two distinct endpoints and containing all the points of the line segment between its endpoints.

We will find the point Q by using the section formula that is

Q(x,y)=((mx₂+nx₁)/(m+n),(my₂+ny₁)/(m+n))

The given ratio is m:n=1:1 and the points (x₁,y₁)=(20,6) and (x₂,y₂)=(-16,50).

Firstly, we will find the point Q for x-axis, we get

Q(x)=(mx₂+nx₁)/(m+n)

Q(x)=(1×(-16)+1×20)/(1+1)

Q(x)=(-16+20)/2

Q(x)=4/2

Q(x)=2

Now, we will find the point Q for y-axis, we get

Q(y)=(my₂+ny₁)/(m+n)

Q(y)=(1×50+1×6)/(1+1)

Q(y)=(50+6)/2

Q(y)=56/2

Q(y)=28

The point Q that partitions the line segment is Q(x,y)=(2,28)

Hence, point Q partitions this segment into a 1:1 ratio with directed line segment AB, with endpoints A(20, 6) and B(-16, 50) is Q(2,28).

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Mr. Powel, who is our geometry teacher, told us we have a geometry test next week.

A nonrestrictive element is an element of a sentence that is not necessary for understanding the basic meaning of the sentence, but instead provides additional information. Nonrestrictive elements are usually set off with commas, while restrictive elements are not. For example, “My brother, who is an engineer, works in Chicago” is a sentence with a nonrestrictive element. The nonrestrictive element (“who is an engineer”) provides additional information about the brother, but does not provide any information about which brother is being referred to. The restrictive element “My brother who works in Chicago” does provide information about which brother is being referred to.

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The perimeter of the figure with side length of 5 units is 50 units

From the question, we have the following parameters that can be used in our computation:

Shape = rectangle

Smaller shapes = squares

Side lengths = 5 units

The perimeter of the figure is calculated as

Perimeter  = Number of visible sides * Side length of the square shape

In this case, we have

Number of visible sides = 10

Substitute the known values in the above equation, so, we have the following representation

Perimeter  = 10 * 5

Evaluate the products

Perimeter  = 50 units

Hence, the perimeter is 50 units

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Answer:

1/6

Step-by-step explanation:

The common difference of the given sequence is 1/6.

If a sequence has a constant common difference throughout the sequence, then the sequence is called Arithmetic Progression.

Where 'd' is the common difference of the A.P.

Similarly, finding the common difference of the given sequence

Hope this helps, if so please mark brainliest.

\(f(x) = 2x is linear.f(x) = 4^x is exponential.\) This is where at each level, each branch extends into 4 branches.

In the first prompt, the number of boxes in each row is increasing by a constant amount, so the function is linear. In the second prompt, the number of branches is increasing by a factor of 4 with each level, so the function is exponential.

A linear function is defined as one where the output increases by a constant amount for each increase in the input. An exponential function is defined as one where the output increases by a constant factor for each increase in the input. The first prompt corresponds to a linear function, while the second prompt corresponds to an exponential function.

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The complete question is-

Is the function f(x) = 4^x, where x is the number of branches at level x in a tree diagram, linear or exponential? Explain your answer.

Answer:

\(S \: is \: between \: R \: and \: T.\)

Answer:

S is between R and T.

Step-by-step explanation:

9514 1404 393

Answer:

  1/10

Step-by-step explanation:

The product of fractions is the product of the numerators, divided by the product of the denominators.

  \(\dfrac{1}{2}\text{ of }\dfrac{1}{5}=\dfrac{1}{2}\times\dfrac{1}{5}=\dfrac{1\times1}{2\times5}=\boxed{\dfrac{1}{10}}\)

__

Additional comment

When working with fractions and percentages, you will find that "of" often means "times."

The difference between depths in January and July is 14 feets

The depth of a local river averages 16 ft., which is represented as |−16|.

In January,  The depth of a local river measured 4 ft. deep, or |−4|

in July, The depth of a local river  18 ft., or |−18|

The average depth of a local river  is measured as -16 because it is below the ground level and hence measured or plotted on -y axis

the difference between depths in January and July can be measured as

|−18| -  |−4|

This is absolute sign which means every number inside this sign should be treated as positive

18 - 4 = 14

Hence, the difference between depths in January and July is 14 feets

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Answer: a

Step-by-step explanation:

Answer:

Around 8 inches of rain, if you want the exact amount it would be 7.8975. Hope this helps :)

Step-by-step explanation:

If  rain is falling at a rate of 2.43 inches per hour, then 8 inches of rain we can expect after 3.25 hours.

Two or more expressions with an Equal sign is called as Equation.

Given that rain is falling at a rate of 2.43 inches per hour,

We need to find how much rain would you expect after 3.25 hours

Let x be the amount of rain in 3.25 hrs.

Let us formulate a equation

2.43/1=x/3.25

Apply cross multiplication

2.43×3.25=x

7.89=x

8=x

Hence 8 inches of rain we can expect in 3.25 hours.

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Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

Answer:

a = 5

Step-by-step explanation:

For the quadratic equation

ax² + bx + c = 0,

the discriminant is

b² - 4ac

Here we have ax² - x - 3, so we have

a = a

b = -1

c = -3

b² - 4ac = 61

(-1)² - 4(a)(-3) = 61

1 + 12a = 61

12a = 60

a = 5

Answer:

below smallest to greatest:

Step-by-step explanation:

1)  1/4--> 3/8 --> 1/2

b) 4/9 --> 1/2 --> 2/3 -->5/6

c) 1/5--> 7/10 --> 3/4--> 4/5

Answer:

by questioning why you post this that are now answered

x = how many acres

keeping in mind that  one yd² has 9 ft², and that an acre has 4840 yd²

\((300ft)(160ft)\implies 48000ft^2\implies \cfrac{48000}{9}\implies \cfrac{16000}{3}~yd^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} acre&yd^2\\ \cline{1-2} 1 & 4840\\[1em] x&\frac{16000}{3} \end{array} \implies \cfrac{1}{x}~~=~~\cfrac{4840}{ ~~ \frac{16000}{3} ~~ }\implies \cfrac{1}{x}=\cfrac{14520}{16000} \\\\\\ 16000=14520x\implies \cfrac{16000}{14520}=x\implies 1.10\approx x\)

Answer:

Yes, it is a true statement

Step-by-step explanation:

Since two negatives cancel out the equation would be

4 + 10 and that equals 14.

So the statement is true!

Answer:

See below

Step-by-step explanation:

When you see PER think fractions. Miles PER hour is

\( \frac{miles}{hour} \)

We are given miles and told to solve for time. Use your knowledge of fractions to get what you need

The reciprocal of mi/hr would get what we need

\(miles \times \frac{hours}{miles} \)

Miles cancels out here. So that means you can do this

\( \frac{1hour}{50miles} \times 999.9 \: miles\)

In your calculator. Same with the other rate.