Determine whether the statement is true or false.
limx→3 (2x/x-3 – 6/x-3) = limx→3 2x/x-3 - limx→3 6/x-3.

The result of testing the given claim is; c) H₀: p = .5, Hₐ: p≠ .5; z = 0.8; Fail to reject H₀ at the 1% significance level

We are given;

Sample size; n = 100

Sample proportion; p' = 54/100 = 0.54

In general, population proportion is; p = 0.5

Thus;

The null hypothesis is, H₀: p = 0.5

Alternative hypothesis is; Hₐ: p ≠ 0.5

z-test statistic is defined as:

z = √[(p' - p)/(p(1 - p)/n)]

Plugging in the relevant values gives;

z = √[(0.54 - 0.5)/(0.5(1 - 0.5)/100)]

z = 0.8

From p-value from z-score calculator, we have;

p-value = 0.4237

The P-value is greater than the 1% level of significance. We fail to reject the null hypothesis at the 1% level of significance.

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As a result, 4/9 participants choose vanilla ice cream with hot fudge topping.

A fraction is a number that symbolises a portion of a whole. It is written as two integers: the numerator, which is written above a line, and the denominator, which is written below the line. The denominator is the total number of equal parts in the whole, while the numerator is the number of equal parts that are being taken into account.

given

The chart indicates that a total of 20 partygoers selected ice cream and toppings. We must examine the intersection of the row for vanilla ice cream and the column for hot fudge topping in order to determine the percentage of persons who selected it. Four persons choose vanilla ice cream with hot fudge topping, according to the table.

The percentage of those who choose vanilla ice cream with hot fudge topping is as follows:

4 (consumers who selected vanilla ice cream with hot fudge topping) / 9 (consumers who did not) = 4/9

As a result, 4/9 participants choose vanilla ice cream with hot fudge topping.

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1/8 is in it 3/2 if that is it

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

5

Step-by-step explanation:

A proportional relation has the following equation:

y = kx

where k = constant of proportionality.

Plug in any given ordered pair into x and y and solve for k.

Let's us (7, 35).

35 = k * 7

k = 35/7 = 5

Answer: The constant of proportionality is 5.

Answer:

y=3

Step-by-step explanation:

Answer:

\(x^{2} + 19x + 90\)

Step-by-step explanation:

I’ve attached my work!

Hope it helps :)

If you have any questions or anymore help lmk, happy to help with any school work!!

Have a nice day, you’ll got this :D

Answer:

36 cm

Step-by-step explanation:

8cm=1km

4.5km=?

We know,

4.5km=8×4.5

4.5km=36

Answer: High quality services cause customers to return for additional meals.

Step-by-step explanation:  The 90% crosses out the first option. Because it's 90% we don't know if all the customers reported their service. The last one just to me wouldn't make sense.

he inverse Laplace transform of f(s) is \(6(t-1)e^{(-6t)\).

The inverse Laplace transform of f(s) = 6 / (s² + 12s + 36) first need to factor the denominator of f(s):

s² + 12s + 36 = (s + 6)²

We can rewrite f(s) as:

f(s) = 6 / [(s + 6)²]

The Laplace transform of the function \(6te^{(-6t)\) has the Laplace transform:

\(L{6te^{(-6t)}\) = 6 / (s + 6)²

The inverse Laplace transform of f(s), we get:

\(L^{-1}{f(s)}\) =\(L^{-1}{6 / [(s + 6)^2]}\)

= \(L^{-1}{6te^{(-6t)}\)

= \(6(t-1)e^{(-6t)\)

The inverse Laplace transform of f(s) is \(6(t-1)e^{(-6t)\).

The denominator of f(s) before we can compute the inverse Laplace transform of f(s) = 6 / (s2 + 12s + 36):

s² + 12s + 36 = (s + 6)²

F(s) may be rewritten as f(s) = 6 / [(s + 6)2].

The function 6te(-6t)'s Laplace transform has the following properties:

\(L{6te^{(-6t)}\)= 6 / (s + 6)²

The inverse Laplace transform to the function f(s) we obtain:

L-1f(s) = L-16 / [(s + 6)²]

= L-16te(-6t)

= 6(t-1)e(-6t).

6(t-1)e(-6t) is the inverse Laplace transform of the function f(s).

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Answer:

B

Step-by-step explanation:

You add 6+6+2+2=16

Answer:

$900

Step-by-step explanation:

I am going ahead with the assumption that the interest is calculated as simple interest and not compound interest since nothing has been mentioned on this aspect.

The interest on a principal P at i% interest rate for t years is given by

I = Prt  where r = interest rate as decimal = i/100

Here r = 4/100 = 0.04

t = 4 years

So I = P · 0.04 · 4 = 0.16P

The total amount at the end of 4 years will be this interest added to the sum so it will be

P + 0.16P = P(1+0.16) = P · 1.16 or 1.16P

We are told that at the end of 4 years the amount becomes 1044

So we equate the terms
1.16P = 1044

P = 1044/1.16 = 900

So the answer is $900  ANSWER

Check

I = 900 x 0.04 x 4 = 144

900 + 144 = 1044

Answer:

77 is the correct answer

Step-by-step explanation:

using pemdas

Answer:

77

Step-by-step explanation:

68−5−(13−27)

=63−(13−27)

=63−(−14)

=77

Without the specific values, we cannot ascertain the true statement. The five-number summary typically includes the minimum, first quartile (Q1), median (second quartile or Q2), third quartile (Q3), and maximum values of a dataset.

Without the specific values provided for the credit hours, it is not possible to determine the true statement. However, I can explain the general interpretation of the five-number summary.

In the first paragraph, we are unable to determine which statement is true without the actual values for the five-number summary of credit hours for the statistics class.

The five-number summary provides a concise summary of the distribution of data. The minimum represents the smallest value, Q1 represents the lower quartile or the value below which 25% of the data falls, the median represents the middle value or the value below which 50% of the data falls, Q3 represents the upper quartile or the value below which 75% of the data falls, and the maximum represents the largest value. By analyzing these summary statistics, we can gain insights into the spread, central tendency, and skewness of the dataset.

To determine which statement is true, we would need the actual values for the five-number summary. For example, if the minimum value is 2, Q1 is 4, the median is 6, Q3 is 8, and the maximum value is 10, we can make statements about the distribution of credit hours based on these values. However, without the specific values, we cannot ascertain the true statement.

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Answer:

Option B is the correct answer

Step-by-step explanation:

B. x2 + y2 = 25

Answer:

y=34x-2

Step-by-step explanation:

The answer is that because everyday he loses 2 dollars and has a 34 gift card

Answer:

What caused the differences in their behavior? The food coloring in cool water remained at the bottom of the container. ... The behavior of the food coloring was caused by the movement of heat through the water and the formation of convection currents. The warmer water is less dense, so it rises to the surface.

Step-by-step explanation:

Answer:

10 - .65r

Step-by-step explanation:

you just have to combine like terms, in this case the whole numbers. 7 + 3 = 10 so yup

Answer:

19 cents

Step-by-step explanation:

2.85/15 = .19

Answer:

6.6 miles

Step-by-step explanation:

$3 + $1.50 = $4.50

30 divided by 4.5 is 6.6

Domain: For sales, x > 0 (positive values); for returns, x < 0 (negative values).

Range: F(x) ≥ 0 (non-negative values).

The given function is defined as follows:

For x > 0 (sale): F(x) = |x| * 0.015

For x < 0 (return): F(x) = |x| * 0.005

The domain of the function is the set of all possible input values, which in this case is all real numbers. However, due to the specific conditions mentioned, the domain is restricted to positive values of x for the "sale" scenario (x > 0) and negative values of x for the "return" scenario (x < 0).

Therefore, the domain of the function F(x) is:

For x > 0 (sale): x ∈ (0, +∞)

For x < 0 (return): x ∈ (-∞, 0)

The range of the function is the set of all possible output values. Since the function involves taking the absolute value of x and multiplying it by a constant, the range will always be non-negative. In other words, the range of the function F(x) is:

For x > 0 (sale): F(x) ∈ [0, +∞)

For x < 0 (return): F(x) ∈ [0, +∞)

In conclusion, the domain of the function F(x) is x ∈ (0, +∞) for sales and x ∈ (-∞, 0) for returns, while the range is F(x) ∈ [0, +∞) for both scenarios.

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The expression that is equivalent to the given expression is \(3\sqrt[6]{z}\)

From the question, we are to determine which of the expressions is equivalent to the given expression

The given expression is

\(6\sqrt{z} \div \sqrt[3]{8z}\)

The expression can be simplified as

\(6\sqrt{z} \div \sqrt[3]{8z}\)

\(\frac{6\sqrt{z}}{\sqrt[3]{8z}}\)

\(= \frac{6 \times \sqrt{z}}{\sqrt[3]{8} \times \sqrt[3]{z}}\)

\(= \frac{6 \times z^{\frac{1}{2} } }{2 \times z^{\frac{1}{3} }}\)

\(= 3\times z^{\frac{1}{2} -\frac{1}{3}}\)

\(= 3\times z^{\frac{1}{6}}\)

\(= 3\times\sqrt[6]{z}\)

\(= 3\sqrt[6]{z}\)

Hence, the expression that is equivalent to the given expression is \(3\sqrt[6]{z}\)

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The correct answer is option C which is the ratio of the numbers is 3:4.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

Given that:-

As we can see that the numbers are more than 20% so suppose the third number is x so the increased number is 1.2x.

Similarly the second condition the increased number is 1.6x.

So the ratio of the numbers will be:-

Ratio = \(\dfrac{1.2x}{1.6x}\)

Ratio = \(\dfrac{3}{4}\)

Therefore the correct answer is option C which is the ratio of the numbers is 3:4.

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The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

see below

Step-by-step explanation:

x < -3  for the first equation

x > 4 for the second equation

The statement "if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s" is false.

A vector set's linear independence is an important attribute. If no vector in a set can be written as a linear combination of the other vectors in the set, the set is said to be linearly independent. The set is said to be linearly dependent if any of the vectors can be represented as a linear combination of the others.

If S is a linearly dependent set, then each vector in S is a linear combination of the others.

This is false.

For example, v₁ = (1,0), v₂ = (2,0), and v₃ = (1,1). Then v₂ = 2v₁ but v₃ is not a linear combination of v₁ and v₂, since it is not a multiple of v₁. But 2v₁ - 1v₂ + 0 v₃ = 0.

If an indexed set of vector S is linear dependent, then it is only necessary that one of the vectors is in the set.

Hence, the correct answer would be option (B).

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Answer:

1/3, 1/2, 3/4

Step-by-step explanation:

The new equilibrium price is $12. The Option B is correct.

To find new equilibrium price, we need to compare the original supply and demand schedules to the new supply schedule after the technological advance.

The new supply schedule can be found by adding 60 units to the original quantity supplied at each price.

Price $10 11 12 13 14 15

Quantity Demanded 100 150 190 220 245 265

Original Quantity Supplied 295 275 250 220 180 135

New Quantity Supplied 355 335 310 280 240 195

The new equilibrium price is where the quantity demanded equals the quantity supplied. Looking at the new schedules, we can see that the new equilibrium price is $12.

Full question" Use the following table to answer the question below. Price $10 11 12 13 14 15 Quantity Supplied Quantity Demanded A) $13. 100 150 190 220 245 265 295 275 250 220 180 135 If a technological advance lowers production costs such that the quantity supplied increases by 60 units of this product at each price, the new equilibrium price would be Price $10 11 12 13 14 15 A) $13. B) $12. C. $14 D. $11

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Answer:

77

Step-by-step explanation:

you can cut them into different shapes then add at the end.

7 x 4 = 28

3 x 14 = 42 (you get the three by 7 - 4 = 3)

1 x 7 = 7

28

42

7

+

77

hope this helps