Classify the system of equations

Anazlysing the conditions given in the question we can  conclude that there is a statistically significant increase in the consensus estimate of economists.

Financial analysts often use the whisper number, which is a late-breaking estimate of a key economic indicator, to make predictions about the stock market and inform their investment decisions. They may use it to identify potential opportunities for buying or selling stocks based on whether the whisper number is higher or lower than expected.

While the whisper number can provide insight into the current economic conditions, it is not a foolproof way to predict the stock market. It is just an estimate based on a sample of economists' predictions and can be affected by various unpredictable factors. Therefore, it's important to take other economic indicators and market conditions into account when making investment decisions.

To conduct a hypothesis test, we need to first define the null hypothesis and alternative hypothesis.

Null Hypothesis: The whisper number (sample mean) is equal to the consensus estimate (population mean)

H0: μ = 250,000

Alternative Hypothesis: The whisper number (sample mean) is greater than the consensus estimate (population mean)

H1: μ > 250,000

The next step is to calculate the test statistic and p-value. We can use a one-tailed t-test since the sample size is less than 30 and we don't know the population standard deviation.

Test statistic:

t = (266,000 - 250,000) / (24,000 / sqrt(20))

P-value:

Using the t-distribution table with 19 degrees of freedom, the p-value is less than 0.01, which is the significance level we set.

Since the p-value is less than the significance level (0.01), we can reject the null hypothesis and conclude that there is a statistically significant increase in the consensus estimate of economists.

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We know that Nevaeh initially deposited $2,100, and now she has $2,131.50 in her account. The interest earned is $2,131.50 - $2,100 = $31.50. To find out how many months has she been investing her money, we can use the following formula:

Time (in months) = (Interest / Principal) x (12 / Interest Rate)

Where Principal is the initial deposit amount, Interest Rate is the annual interest rate, and Interest is the amount of interest earned.

Plugging in the given values, we get:

Time (in months) = ($31.50 / $2,100) x (12 / 0.06)

Time (in months) = 0.0149 x 200

Time (in months) = 2.98

Since time cannot be in fraction of months, it has to be rounded off. So, Nevaeh has been investing her money for approximately 3 months.

The observed time cycles of five given elements are 2.1, 1.01, 3.4, 4.1, 1.5 respectively

To determine the observed time (OT),

The observed time (OT) of each cycles will be added together for each element. and divided by total number of cycles for each element.

This is done in the following ways

1) (1.2+2.0+2.2+2.1+2.1)/5 = 10.5/5 = 2.1

2) (1.1+1.0+1.2) = 3.3/3 = 1.1

3) (3.4+3.5+3.3+3.5+3.4+3.3)/6 = 20.1/6 = 3.4

4) 4.0+4.2)/2 = 8.2/2 = 4.1

5) (1.4+1.4+1.5+1.5+1.5+1.4)/6 = 8.7/6 = 1.5

therefore each elements total cycle OT is added and then it is divided with each elements relevant number of cycles and this as a result provides the answer to the question

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The alternate interior angles are the angles that are formed inside the two parallel lines, when it is intersected by a transversal, and are equal to its alternate pairs.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.

Alternate angles are shaped by the two parallel lines crossed by a transversal. Consider the given figure, EF and GH are the two parallel lines. If two parallel lines are cut by a transversal, then the alternate angles are equal.

In order to understand alternate interior angles, one must first picture a set of parallel lines, and then a line intersecting them. The intersecting line is called a transversal, and all the angles formed between the parallel lines are the interior angles.

At the point of intersection of transversal and two lines we have:

∠3 + ∠4 = 180 .........(1)

∠6 + ∠8 = 180 ...........(2)

We know that angle 4 and angle 8 are equal:

Thus, using 1 and 2 we have:

∠3 = ∠6

Hence, ∠3 and ∠6 are congruent.

Now, using the alternate interior angle we know that:

∠3 = ∠6

Also, we have:

∠5 + ∠6 = 180 (Straight line)

Substituting the value of ∠6 = ∠3 we have:

∠5 + ∠3 = 180

Thus, the two angles are supplementary.

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The daily cost to heat a building at 10 degrees celsius is  $82.72

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

f(x)=6(1.3)^-x

Then, we have

x = 10

This implies that

f(-10) = 6(1.3)^-(-10)

Evaluate the expression

f(-10) = 82.72

This means that the cost to heat is $82.72

Also, the domain is all set of real numbers and the range is y > 0

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Complete question

During the winter if the low temperature outside is x Celsius,the daily cost to heat a building can be determined using the function f(x)=6(1.3)^-x.find and interpret the given function values and determine an appropriate domain for the function

f(10)

Answer:

don't

Step-by-step explanation:

get that one wrong don't spend to much time on it

Answer:

B. point; vertices; point

Step-by-step explanation:

A pyramid is a 3-dimensional geometric shape that has a base, which is typically a polygon, and a number of triangular faces that all meet at a single point called the vertex. The pyramid has vertices at the corners of the base and all other points where the triangular faces meet.

Answer:

>4

Step-by-step explanation:

the answer of the question is >4

Side AC in the triangle is 3.6 and side BC in the triangle is 1.7

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side AC :

4/sin90 = AC / sin64.3

AC × sin90 = sin 64.3 × 4

AC = 0.9 ×4

AC = 3.6 ( nearest tenth)

To find side BC:

using Pythagoras theorem

4² = 3.6² + (BC)²

16 = 12.96 +(BC)²

(BC)² = 16 - 12.96

(BC)² = 3.04

BC = √ 3.04

BC = 1.7( nearest tenth)

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The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer:

[tex]\boxed{-2 < x\le1}[/tex]

Representation on number line is in attached image.

Notice that -2 has an unfilled circle and 1 has a filled circle. Important

Step-by-step explanation:

The given inequality is

[tex]2 < 4x+10\le14[/tex]

Subtract 10 throughout:

[tex]2-10 < 4x+10-10\le14-10\\\[/tex]

[tex]-8 < 4x\le4[/tex]

Divide throughout by 4:

[tex]-2 < x\le1[/tex]

Answer:    [tex]\boxed{-2 < x\le1}[/tex]

This is represented on the number line as follows: Notice the use of the

The solution for the expression 112 ÷ 0.16 is 700.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

112 ÷ 0.16

This can be written as,

= 112/0.16

= 700

Thus,

The solution is 700

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Answer: The interest rates charged in both formulas are different.

Step-by-step explanation:

To begin with, the simple interest = PRT/100

In this, the interest is the same as the number of years.

For example, P=10,000 R=10% T=2yrs

SI = PRT/100

    = 10,000*10*2/100

    = 2000

This rupee 2000 is the same interest for two years.

compound interest = A= P(1+r/100)^n

In this, the interest changes every year up to the period of time.

For example, P= 10,000 R=10% N=2yrs

A= 10,000(1+10/100)^2

  = 10,000*11/10*11/10

   = 12100

I= A-P

 =12100-10000

 = 2100

This interest varies for 2 years.

Answer:

Step-by-step explanation:

You want to know the amounts invested at each rate if twice as much is invested at 4.5% as at 3.5%, and the total earnings are $1875.

Let x represent the amount invested at 3.5%. Then 2x is the amount invested at 4.5%, and the total earnings are ...

  0.035x +0.045(2x) = 1875

  0.125x = 1875 . . . . . . . . . collect terms

  x = 15000 . . . . . . . . . divide by 0.125

  2x = 30000 . . . . . . . find the other value invested

The amount deposited at 3.5% is $15,000; the amount deposited at 4.5% is $30,000.

The firm needs to sample 138.297 products to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%.

Generally, To determine the sample size needed to achieve a ±5% accuracy at a 95% confidence level, with a maximum expected proportion of defects of 10%, you can use the formula for sample size for a proportion. The formula is:

n = (z^2 * p * (1-p)) / E^2

Where:

Plugging in the given values, we get:

n = (1.96^2 * 0.10 * (1-0.10)) / 0.05^2

n =138.297

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Answer:

  170,483

Step-by-step explanation:

You have N varying jointly with P1 and P2, such that N=109,000 for P1=74000 and P2=189000. You want to know N for P1=125000 and P2=175000.

The relation "N varies jointly with P1 and P2" can be described by the equation ...

  N = k·P1·P2

The value of k can be found as ...

  k = N/(P1·P2)

  k = 109000/(74000·189000) ≈ 7.793508×10^-6

Then the number of calls given the populations P1=125000 and P2=175000 is predicted to be ...

  N = (7.793508×10^-6)(125000)(175000) ≈ 170482.982...

  N ≈ 170483

About 170,483 calls are expected between cities with populations of 125 and 175 thousand.

If the number of phone calls between two nearby cities during a given time period. The number of calls  that are made between two cities with population 125,000 and 175,000 is: 170,482,987,500.

Calls  made between two cities with populations 74,000 and 189,000,

Call = 109,000/(74000 × 189000)

Call = 109,000 / 13,986,000,000

Call = 7.793508

Calls made between two cities with populations 125,000 and 175,000?

Calls =  7.793508 × 125000 ×175000

Calls =170,482,987,500

Therefore the calls made is 170,482,987,500.

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Answer: 49.5

Step-by-step explanation:

Let Thomas' age be [tex]T[/tex]. Then, Hulian's age is [tex]T+14[/tex].

[tex]T+T+14=113\\\\2T+14=113\\\\2T=99\\\\T=49.5[/tex]

Answer:

43%

Step-by-step explanation:

28 questions - 16 wrongs = 12 correct

(12/28) × 100= 42.857.....%

To the nearest percent=43%

The relationship between a young person's height and the recommended wheel diameter is a function, as each input is associated to a single output.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The input and output variables for this problem are given as follows:

As for each height, there is only one recommended wheel diameter, we have that each input is mapped to a single output, and thus the relationship between a young person's height and the recommended wheel diameter is a function.

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Step-by-step explanation:

as always with % calculations :

first find what is 100% or 1%. everything else can be calculated from that.

in our case, we got 100% = 18.

therefore, 1% = 100%/100 = 18/100 = 0.18

how many % are 4 students ?

as many as the times 1% (0.18) fits into 4 :

4 / 0.18 = 22.22222222... %

so,

22.22222222... %

of the students passed.

therefore,

100 - 22.22222222... = 77.77777777... %

of the students did not pass.

Answer:no

Step-by-step explanation:

The graph of the given piecewise function is as attached below.

Piecewise function is a function consisted of pieces of different functions over different intervals.

From the case we have:

f(x) = 3x - 5 if x ≤ -1

f(x) = -2x + 3 if -1 < x < 4

f(x) = 2 if x ≥4

To construct the piecewise function, we can try to find the base points of each functions.

f(x) = 3x - 5; if x ≤ -1

We will take x = -1 to approximate the line position

f(-1) = 3(-1) - 5

f(-1) = -3 - 5 = -8

f(x) = -2x + 3; if -1 < x < 4

(x = -1)

f(-1) = -2 (-1) + 3

f(-1) = 2 + 3 = 5

(x = 4)

f(4) = -2 (4) + 3

f(4) = -8 + 3 = -5

f(x) = 2; if x ≥ 4

(x = 4)

f(4) = 2

We can put each points on the graph and try to construct the piecewise function.

Please refer to the attached graph below for the piecewise function graph

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The constants A and B for the differential equation are given as follows:

The solutions to the differential equation are given as follows:

This means that the roots of the characteristic equation are given as follows:

r = -8 and r = 8.

Considering that the leading coefficient is of 1, as 1 multiplies y'', the characteristic equation is given as follows:

(r + 8)(r - 8) = r² - 64.

Hence the differential equation is given as follows:

y'' - 64y = 0.

Hence the constants are given as follows:

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3/17

Both 3 and 17 are prime numbers, therefore they cannot be simplified by any number expect 1 and itself.

The midpoint of f(x) over the interval [1, 2] is 4.8655

Generally, The point that represents the precise midway point between an interval's beginning and ending points is known as the midpoint of the interval. It may be determined by calculating the average of the two values that serve as endpoints.

For instance, the value 5 would represent the point that is exactly in the middle of the interval [3,7].

The midpoint of the interval [1, 2] is

(1 + 2) / 2

= 1.5.

To calculate the value of f(x) at x = 1.5, we need to substitute 1.5 for x in the function:

f(1.5) = 6 * ln(1.5^2)

= 6 * ln(2.25)

= 6 * 0.83

= 4.8655

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a. The explanatory variable is the new blood clot medication, and the confounding variable is the time period of 12 hours after the stroke begins.

b. The explanatory variable is the new software program, and the confounding variable is the 1-hour period after school

The confounding variable may invalidate the conclusions of the study because it is possible that the higher rate of total recovery is not due to the new medication, but rather due to the fact that the patients are being treated within the crucial 12-hour period after the stroke begins. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where patients are randomly assigned to receive either the new medication or a placebo, and both groups are treated within the 12-hour period after the stroke begins.

In (b) the explanatory variable is the new software program, and the confounding variable is the 1-hour period after school. The confounding variable may invalidate the conclusions of the study because it is possible that the higher scores are not due to the software, but rather due to the fact that the students using the software were given more time to study and practice. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where students are randomly assigned to use the software or not, and both groups are given the same amount of time to study and practice.

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Answer:

[tex] - 2 \sqrt{5} [/tex]

Step-by-step explanation:

[tex] \sqrt{20} - \sqrt{80} [/tex]

[tex]2 \sqrt{5} - 4 \sqrt{5} [/tex]

[tex](2 - 4) \sqrt{5} [/tex]

[tex] - 2 \sqrt{5} [/tex]

[tex]35 cm ^{3}[/tex] is the volume of the prism displayed. The triangular cross section is 1.25 cm tall.

length , l = 7 cm , width w = 4 cm , height , h= 1.25 ,diagonal ,   d=8.15858444 cm , total surface area, [tex]$S_{\text {tot }}=83.5 \mathrm{~m}^2$[/tex] , lateral surface area , [tex]$S_{\text {lat }}=27.5 \mathrm{~m}^2$[/tex] , top surface area , [tex]$S_{\text {top }}=28 \mathrm{~m}^2$[/tex] , bottom surface area , [tex]$S_{\text {bot }}=28 m^2$[/tex] , volume [tex]$V=35 \mathrm{~m}^3$[/tex] .

To calculate the height of a prism, divide its volume by its area at the base. Let's say that the prism has a volume of 600 cubic inches to wrap up this scenario. The height is determined by multiplying 600 cubic inches by 100 square inches.

A prism's volume is calculated using the formula V=Bh, where B denotes the base area and h the height. A rectangular area makes up the prism's base. The rectangle's dimensions are 9 cm long by 7 cm wide. The formula V=Bh, where V stands for volume, B for the prism's area at its base, and h for its height, can be used to determine a prism's volume. B should be replaced with the area of a rectangle formula because this is a rectangular prism.

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a) The perimeter of a rectangle is the sum of all four sides. So to find the perimeter we can add these two sides together, and then double the result.

The simplified expression for the perimeter of the rectangle would be:

2(2n - 3 + 4)

This can also be written as:

2(2n + 1)

This expression represents the mathematical operation where the sum of 2n - 3 and 4 is calculated, then multiplied by 2 to find the perimeter of the rectangle.

b) If the perimeter of the rectangle is 26, we can use the expression for the perimeter that we found earlier to solve for the value of n.

The perimeter of the rectangle is:

2(2n + 1) = 26

So if we divide both sides of the equation by 2, we get:

2n + 1 = 13

then if we subtract 1 from both sides

2n = 12

then if we divide by 2

n = 6

So the value of n is 6.

I hope this helps :)

Answer:

a. [tex]P = 4n + 2[/tex]

b. [tex]n = 6[/tex]

Step-by-step explanation:

a. The formula for the perimeter of a rectangle was:

[tex]P = 2L + 2W[/tex]

Given that the length was 2n-3 and the width was 4, substitute the values its formula:

[tex]P = 2L + 2W\\P = 2(2n-3) + 2(4)\\P = 4n - 6 + 8\\P = 4n + 2[/tex]

b. Since the perimeter of the rectangle was already indicated, we will just sunstitute it to the expression that we get from a.

[tex]P = 4n + 2\\26 = 4n + 2\\26 - 2 = 4n\\24 = 4n\\6 = n[/tex]