____ < √97 < ____ integers to complete the following inequality.

Answer:

The smaller number is 24

The larger number is 45

Step-by-step explanation:

smaller number  = x

Larger: 2x - 3

Smaller + larger = 69

x + 2x - 3 = 69                        Combine left

3x - 3 = 69                              add 3 to both sides

3x - 3+3 = 69+ 3                     Combine

3x = 72                                    Divide by 3

3x/3 = 72/3                        

x = 24

Larger number = 2*24 - 3

Larger number = 45

Take into account the following property:

Then, for the given expression you have:

Hence, the answer is approximately 3.322

Answer:

2201.8348 ; 3 ; x / (1 + 0.01)

Step-by-step explanation:

1)

Final amount (A) = 2400 ; rate (r) = 6% = 0.06, time, t = 1.5 years

Sum = principal = p

Using the relation :

A = p(1 + rt)

2400 = p(1 + 0.06(1.5))

2400 = p(1 + 0.09)

2400 = p(1.09)

p = 2400 / 1.09

p = 2201.8348

2.)

12000 amount to 15600 at 10% simple interest

A = p(1 + rt)

15600 = 12000(1 + 0.1t)

15600 = 12000 + 1200t

15600 - 12000 = 1200t

3600 = 1200t

t = 3600 / 1200

t = 3 years

3.)

A = p(1 + rt)

x = p(1 + x/100 * 1/x)

x = p(1 + x /100x)

x = p(1 + 1 / 100)

x = p(1 + 0.01)

x = p(1.01)

x / 1.01 = p

x / (1 + 0.01)

Answer:

2201.8348 ; 3 ; x / (1 + 0.01)

Step-by-step explanation:

Hope this helps! (:

The new coordinated after reflection over the y axis are

C' (-4, 2)

A' (-3, -1)

J' (-4, -3)

T' (-5, -2)

In geometry, reflection refers to a transformation that flips a figure across a line, known as the line of reflection.

When a figure is reflected, it is essentially mirrored across the line of reflection, so that each point on the original figure is transformed to a corresponding point on the reflected figure that is equidistant from the line of reflection.

The transformation rule for reflection over the y axis is

(x, y) → (−x, y)

The preimage coordinates are

C (4, 2)

A (3, -1)

J (4, -3)

T (5, -2)

Applying the rule results to an image with coordinates

C (4, 2)  →  C' (-4, 2)

A (3, -1)  →  A' (-3, -1)

J (4, -3)  →  J' (-4, -3)

T (5, -2)  →  T' (-5, -2)

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a = 12 (cos(π/3) + i sin(π/3))

b = 3 (cos(π/4) + i sin(π/4))

a • b = 36 (cos(π/3) cos(π/4) + i cos(π/3) sin(π/4) + i cos(π/4) sin(π/3) + i ² sin(π/3) sin(π/4))

… = 36 (cos(π/3 + π/4) + i sin(π/3 + π/4))

… = 36 (cos(7π/12) + i sin(7π/12))

… ≈ -9.32 + i 34.8

The relationship between the linear correlation coefficient r and the slope b of a regression line is that the value of r will always have the same sign as the value of b. So, the correct option is B.

This means that if the slope is positive, indicating a positive relationship between the variables, the correlation coefficient will also be positive. Similarly, if the slope is negative, indicating a negative relationship between the variables, the correlation coefficient will also be negative. It is important to note that the magnitude of r and the magnitude of b may not necessarily be the same. Therefore, option B is the correct answer.

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Answer:

A

-by-step explanation:

i have that exact question

H0:μ1≥μ2; Ha:μ1<μ2 are the null and alternative hypotheses for the scenario in question.

The alternative hypothesis is one of the offered propositions in statistical hypothesis testing.

An assertion used in statistical inference experiments is known as the alternative hypothesis.

It is indicated by Hₐ or H₁ and runs counter to the null hypothesis.

Another way to put it is that it is only a different option from the null.

An alternative theory in hypothesis testing is a claim that the researcher is testing.

So, the null and alternative hypotheses in the given situation:

The mean durability of running shoes 1 must be comparable to the mean durability of running shoes in order for them to be as durable as running shoes 2.

Since the null hypothesis must be equal in some way, Ha is equal to μ1≠μ2, and H0 is equal to μ1=μ2.

Therefore, H0:μ1≥μ2; Ha:μ1<μ2 are the null and alternative hypotheses for the scenario in question.

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Complete question:

Identify the null and alternative hypotheses in the following scenario:

To determine if running shoes 1 have the same durability as running shoes 2, the mean durability, in miles, of the two competing running shoes is compared. Fourteen runners are randomly assigned to test each type of shoe. Both populations have normal distributions with known standard deviations.

The brownies will not taste differently if you add the ingredients in different orders, due to the mixing and the fact that the proportions of each substance are the same.

A proportion is obtained as the division of the desired amounts by an amount that represents the total amount.

For this problem, no matter the order in which you insert the substances, the total amounts will be the same, hence the proportions are also going to be the same, and thus the brownies are going to have an equal taste.

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(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Answer:

$4280

Step-by-step explanation:

$5x8= $40

107x$40= $4280

Answer:

The value of angle 2 is 114 degrees

Step-by-step explanation:

We start with 180 degrees, since it is a Line.

To fine the other degree, subtract 66 from 180, which is 114

Angle 2 is 114 because of the theory of interior alternate angles are congruent. Angle 1 is 66 degrees because of the same reason.

Answer:

A = 54π Km²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \(\frac{135}{360}\) ( r is the radius )

   = π × 12² × \(\frac{3}{8}\)

   = 144π × \(\frac{3}{8}\) ( cancel 144 and 8 by 8 )

  = 18π × 3

 = 54π Km²

Answer:

36 cm²

Step-by-step explanation:

1/2 × (8.9+5.5) ×5.5

1/2×14.4×5.5

1/2×72

36 cm²

Answer:

EC and CB

DC and AC

Angle DCB and Angle ECA

Step-by-step explanation:

Line EC and Line CB both have the same measure of 32ft.

Line DC and Line AC both have the same measure of 28ft.

The angles are the sum of the same measures.

Answer:

one temp that ice freezes or could exist would be 32°F and at -34°C

Step-by-step explanation:

To prove that Qn(s) = sP1(Qn-1(s)), we can use the definition of the probability generating function (PGF) and the properties of branching processes.

First, let's define the probability generating function P₁(s) as the PGF of the family-size distribution, which represents the number of offspring produced by each individual in the process.

Next, let's consider Qn(s) as the PGF of the total number of individuals in the first n generations of the process, and Zn as the random variable representing the total number of individuals.

Now, let's derive the expression Qn(s) = sP1(Qn-1(s)) using the properties of branching processes.

Base Case (n = 1):

Q₁(s) represents the PGF of the total number of individuals in the first generation. Since P(X₀ = 1) = 1, we have Q₁(s) = s.

Inductive Step (n > 1):

For the inductive step, we assume that Qn(s) = sP1(Qn-1(s)) holds for some n > 1.

Now, let's consider Qn+1(s), which represents the PGF of the total number of individuals in the first n+1 generations.

By definition, Qn+1(s) is the PGF of the sum of the number of offspring produced by each individual in the nth generation, where each individual follows the same distribution represented by P₁.

We can express this as:

Qn+1(s) = P₁(Qn(s))

Now, substituting Qn(s) = sP1(Qn-1(s)) from the inductive assumption, we have:

Qn+1(s) = P₁(sP1(Qn-1(s)))

Simplifying, we get:

Qn+1(s) = sP1(Qn-1(s)) = sP1(Qn(s))

This completes the inductive step.

By induction, we have shown that for n > 2, Qn(s) = sP1(Qn-1(s)).

Therefore, we have proved that for n > 2, Qn(s) = sP1(Qn-1(s)).

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Answer: 227

Step-by-step explanation:

To find the 46th term of the sequence, we need to first determine the pattern of the sequence. We can see that the sequence increases by 5 between each consecutive term. Therefore, the common difference of the sequence is 5.

Using this information, we can find the \(n\)th term of the sequence using the formula:

\(\Large \boxed{an = a1 + d(n-1)}\)

where

Using the given terms, we have:

To find the 46th term, we substitute \(n = 46\) into the formula:

Therefore, the 46th term of the sequence is 227.

________________________________________________________

To find the pattern in the sequence, we can observe that each term is obtained by adding 5 to the previous term. Therefore, we can write the recursive formula for the sequence as:

\(\large a_1 = 2\)

\(\large a_n = a_{n-1} + 5\)

To find the 46th term, we can use the recursive formula to generate each term until we reach the desired term:

\(\large a_1 = 2\)

\(\large a_2 = a_1 + 5 = 2 + 5 = 7\)

\(\large a_3 = a_2 + 5 = 7 + 5 = 12\)

\(\large a_4 = a_3 + 5 = 12 + 5 = 17\)

\(\vdots\)

\(\large a_{46} = a_{45} + 5 \approx \boxed{227}\)

\(\therefore\) The 46th term of the sequence is approximately 227.

We can also write the explicit formula for the sequence as:

\(\large a_n = 5n - 3\)

To verify that this formula generates the same sequence as the recursive formula, we can substitute the value of n = 1, 2, 3, etc. and compare the results.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Step-by-step explanation:

9 is the answer

26+ (-30) + 13 =

26-30 +13 =

-4 + 13 = 9

hope it's helpful to you

Answer:

1. BC≅DC ; AC≅EC

2. ∠BCD≅∠ACE and ∠BCA≅∠DCE

3. SAS (side angle side)

Step-by-step explanation:

Total cost in dollars of the meal, tax and tips is $18.75

Tips are bonus or extra payment that a customer wants to pay to the counter of restaurant or to certain workers to express the gratitude toward their hospitality. How much money will be paid is determined by the customer himself.

given, cost of meal = $15 before tax and tip

After that $7% tax and $18% tip are included upon the cost of meal

Now, cost for tax = $ (7/100 × 15) = $1.05

cost for tip = $ (18/100 × 15) =$2.7

Total cost for meal, tax and tips = cost for meal + cost for tax + cost for tip

 Total cost = $18.75

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Answer:

Step-by-step explanation:

answer is $100.00 is original price

40% of 100 = $90

Answer:

29 degrees

Step-by-step explanation:

Both angles are the same.

Answer: D i think lol

Step-by-step explanation:

Answer:

welp

Step-by-step explanation:

Let ABC be triangle and I its incenter. we have proved that angle IDB is equal to angle IEA. Angle IAE = 180 degrees - angle BAI - angle ABI.

To prove that angle IDB is equal to angle IEA, we will use the properties of the incenter and the midpoint of an arc in a triangle. Here's a step-by-step proof:

Step 1: Draw the triangle ABC with its incenter I, the midpoint D of BC, and the midpoint E of arc BC.

Step 2: Draw lines AI and BI.

Step 3: Since I is the incenter, it lies on the angle bisector of angle BAC. Therefore, angle BAI = angle IAC.

Step 4: Similarly, angle ABI = angle IBC.

Step 5: Since D is the midpoint of BC, we have BD = CD.

Step 6: Since E is the midpoint of arc BC, we have AE = EC.

Step 7: Now consider triangles AIB and CIB. By the Angle Bisector Theorem, we know that AB/BC = AI/IC. Therefore, AB/BD = AI/IC.

Step 8: By the Midpoint Theorem, we know that BD/DC = AB/AC. Combining this with the previous result, we have AB/AC = AI/IC = AB/BD.

Step 9: This implies that AC = BD, which means triangle BCD is isosceles.

Step 10: Since triangle BCD is isosceles, we have angle IBD = angle ICD.

Step 11: Similarly, since AE = EC, triangle AEC is isosceles. Therefore, angle IAE = angle ICE.

Step 12: Now consider the quadrilateral IDCE. Since it is a cyclic quadrilateral (opposite angles add up to 180 degrees), we have angle ICD + angle ICE = 180 degrees.

Step 13: Combining this result with Step 10 and Step 11, we get angle IBD + angle IAE = 180 degrees.

Step 14: Rearranging the equation from Step 13, we have angle IBD = 180 degrees - angle IAE.

Step 15: Since angles in a triangle sum up to 180 degrees, we have angle BAI + angle ABI + angle IAE = 180 degrees.

Step 16: By rearranging the equation from Step 15, we get

angle IAE = 180 degrees - angle BAI - angle ABI.

Step 17: Comparing the equations from Step 14 and Step 16, we see that angle IBD = angle IAE.

Therefore,we have proved that angle IDB is equal to angle IEA.

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a. The appropriate hypothesis test for this situation can be formulated as follows: Null Hypothesis (H₀) and Alternative Hypothesis (H₁)

b. To test the hypothesis, we can use the z-test for proportions.

c. We can find the p-value associated with z = 5.1493.

d. Conclusion:

If the p-value is less than α, we reject the null hypothesis.

If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

A hypothesis known as the null hypothesis states that sample observations are the result of chance.

(a) Hypothesis Test:

The appropriate hypothesis test for this situation can be formulated as follows:

Null Hypothesis (H₀): The proportion of children with autism is equal to 5% (p = 0.05).

Alternative Hypothesis (H₁): The proportion of children with autism is different from 5% (p ≠ 0.05).

(b) Test Procedure:

To test the hypothesis, we can use the z-test for proportions. The steps for this test procedure are as follows:

1. Formulate the null and alternative hypotheses as stated in part (a).

2. Set the significance level (α) to determine the threshold for rejecting the null hypothesis.

3. Collect a random sample of children and record the number of children showing signs of autism.

4. Calculate the sample proportion (\(\bar p\)) of children with autism.

5. Calculate the standard error of the proportion (SE):

  SE = √((p₀ * (1 - p₀)) / n),

  where p₀ is the hypothesized proportion (0.05 in this case) and n is the sample size.

6. Calculate the test statistic (z):

  z = (\(\bar p\) - p₀) / SE

7. Calculate the p-value associated with the test statistic using a standard normal distribution table or a statistical software.

8. Compare the p-value with the significance level (α).

  - If the p-value is less than α, reject the null hypothesis.

  - If the p-value is greater than or equal to α, fail to reject the null hypothesis.

(c) Perform the Test and Calculate the p-value:

In this case, the sample size is 384, and the number of children showing signs of autism is 46.

\(\bar p\) = 46/384 = 0.1198

SE = √((0.05 * (1 - 0.05)) / 384) ≈ 0.0134

z = (0.1198 - 0.05) / 0.0134 ≈ 5.1493

Using a standard normal distribution table or a statistical software, we can find the p-value associated with z = 5.1493. The p-value represents the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the assumption that the null hypothesis is true.

(d) Conclusion:

Based on the calculated p-value and the chosen significance level (α), we can draw a conclusion:

If the p-value is less than α, we reject the null hypothesis.

If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

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Answer:

-33

Step-by-step explanation: