Susie is 13
5
6
years old. Dwight is 1
1
3
years older than Susie and Jane is 1
1
4
years older than Dwight. How old is Jane?

The proof using Bolzano-Weierstrass Theorem is suggestive of the fact that the bounded sequence that is given has a subsequence that is convergent.

The Bolzano-Weierstrass theorem, is a key conclusion regarding convergence in a finite-dimensional Euclidean space in mathematics, notably in real analysis.

According to the theorem above, each bounded sequence in Rⁿ has a convergent subsequence.

***See proof in the attached document.

Hence the given sequence is bounded. It is safe therefore to state that given Bolzano-Weierstrass theorem, the stated real bounded sequence has a convergent subsequence.

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Answer:

Option (4)

Step-by-step explanation:

Each value of x maps onto only one value of y, so it is a function.

Answer:

The Third would be 72

Step-by-step explanation:

The sum of the two is 16+22=38. the third one is 72-38=34

The present value of the nominal rate of the annuity will be $535.

Annuity amount = 20

Number of annuities = 32

APR = 16%

PV of annuities = 357

Number of years to perpetuity = 8

Quarterly perpetuity = 25

PV of perpetuity at 9th year = 625

PV of perpetuity today = 178

Total PV = 357 + 178 = 535

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a) The equation of axis is the middle y-coordinate, which is y = -1.5.

b) The period is the amount of time it takes for the graph to repeat, which is 6.

c) The amplitude is the vertical distance from an extreme point to the midpoint, which is 3.

d) This is a cosine graph since when x=0, y is not equal to 0.

Using the inscribed angle theorem, the value of x is: 9.

Note that an intercepted arc is regarded as part of the circumference of a circle, which is between a chord and a tangent. Thus, based on the inscribed angle theorem, the inscribed angle measure = 1/2(the intercepted arc measure).

So, we would have:

m∠DEF = 1/2(arc DE)

m∠DEF = 4x + 19

arc DE = 360 - (28x - 2) = 360 - 28x + 2

arc DE = 362 - 28x

Plug in the values

4x + 19 = 1/2(362 - 28x)

Solve for x

2(4x + 19) = 362 - 28x

8x + 38 = 362 - 28x

8x + 28x = 362 - 38

36x = 324

x = 324/36

x = 9

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Answer:

3) 194 feet

Step-by-step explanation:

The other house:

"a house that is 33 ft wide and 50 ft long"

area = LW = (33 ft)(50 ft) = 1650 ft²

This house:

LW = A

L × 22 ft = 1650 ft²

L = 75 ft

P = 2(L + W)

P = 2(75 ft + 22 ft)

P = 194 ft

Answer: 3) 194 feet

Answer:

3) P = 194 ft.

Step-by-step explanation:

[tex]A=wl[/tex]

[tex](30)(50)=22l[/tex]

[tex]1650=22l[/tex]

[tex]l=1650/22=75[/tex]

the dimensions of the house are: (22 × 75)

Perimeter:

[tex]p=2(22)+2(75)=44+150=194[/tex]

Hope this helps

The amount of the lease receivable will be $146999.

It should be noted that lease receivables means all the payments under the operative documents in respect of:

(i) the Purchaser Basic Rent,

(ii) the Maximum recourse amount,

(iii) the Purchaser Balance and

(iv) any purchase by the Lessee of the Properly up to the amount of the Capital then outstanding.

In this case, the lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year and the first payment is received on January 1, 2017.

The lease receivable will be:

= PVAD8%,7 × Lease payment

= 5.62288 × 26143

= $146999

In conclusion, the lease receivable is $146999.

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The inequality of the graph is y < -1/2(x - 16)^2 + 32

A quadratic function is represented as:

y = a(x - h)^2 + k

The vertex of the graph is

(h, k) = (16, 32)

So, we have:

y = a(x - 16)^2 + 32

The graph pass through the point

(x, y) = (12, 24)

So, we have:

24 = a(12 - 16)^2 + 32

Evaluate the like terms

-8 = a(-4)^2

This gives

16a = -8

Divide by 16

a = -1/2

Substitute a = -1/2 in y = a(x - 16)^2 + 32

y = -1/2(x - 16)^2 + 32

The graph is a less than graph.

So, we have

y < -1/2(x - 16)^2 + 32

Hence, the inequality of the graph is y < -1/2(x - 16)^2 + 32

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Answer:

D.  -11

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases}2x-3 & \textsf{if }x \leq -4\\x^2 & \textsf{if }-4 < x < 0\\x+5 & \textsf{if }x \geq 0\end{cases}[/tex]

Therefore, the function has three definitions:

[tex]f(x)=2x-3 \quad \textsf{ when x is equal to or less than -4}[/tex]

[tex]f(x)=x^2 \quad \textsf{ when x is greater than -4 or less than zero}[/tex]

[tex]f(x)=x+5 \quad \textsf{ when x is greater than zero}[/tex]

f(-4) means to substitute x = -4 into the function.

As x = -4 satisfies the interval of the first piece of the function, substitute x = -4 into f(x) = 2x - 3:

[tex]\begin{aligned}\implies f(-4) & =2(-4)-3\\& = -8 -3\\& = -11\end{aligned}[/tex]

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Answer is D. -11

Answer:

Solution Given:

f(-4) depends on the condition x≤-4,

so

f(-4)=2*-4-3=-8-3=-11

The ordered pair (2,-1) is a solution the inequality.

Given the inequality is 3x-4y<12.

An inequality is a statement that compares two quantities and claims that one is greater or less than the other (the equation may also be included). These inequalities are linear if the variables are only linear.

By substituting each of the given option in the given inequality we will check which ordered pair satisfy the inequality.

1. (4,0)

Here x=4 and y=0

Substitute this in the inequality 3x-4y<12, we get

3(4)-4(0)<12

12<12

This is not true

2. (0,-3)

Here x=3 and y=-3

Substitute this in the inequality 3x-4y<12, we get

3(0)-4(-3)<12

12<12

This is not true.

3. (2,-1)

Here x=2 and y=-1

Substitute this in the inequality 3x-4y<12, we get

3(2)-4(-1)<12

6+4<12

10<12

This is true.

4. (4,-3)

Here x=4 and y=-3

Substitute this in the inequality 3x-4y<12, we get

3(4)-4(-3)<12

12+12<12

24<12

This is not true.

Hence, the ordered pair that satisfy the given inequality 3x-4y<12 is (2,-1).

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Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

The circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.

The steps involved in inscribing a triangle;

If the line drawn from point B to point P measures 2 inches, then the diameter is

=  2 × 2

= 4 inches.

The formula for calculating the circumference of a circle is given as;

Circumference = 2 π r

Radius = diameter/ 2

Radius = 4/2 = 2 Inches

Substitute the values

Circumference = 2 × 3. 142 × 2

Circumference = 12. 57 inches

Area = π r²

Area = 3. 142 × 2²

Area = 3. 142 × 4

Area = 12. 57 square inches

Thus, the circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.

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The appropriate  journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.

Sheffield corporation entries

Debit Cash $18,870

[$21500-($480+ ($21500×10%))]

Debit Advertising expense $480

Debit Commission expense $2,150

(21,500×10%)

Credit Revenue from consignment sales $21,500

Debit Cost of goods sold $13,888

[($20400+$2000)×62%]

Credit Inventory on consignment $13,888

Therefore  journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.

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The curve will be dotted and upper portion of the graph will be shaded.

Inequality are expressions not separated by an equal sign Given the following inequality

y−x>−x2−1

Equate to zero

y > x^2 + x -1

Since the inequality sign in the given expression is a less than sign, hence the curve will be dotted.

Also, since the inequality sign is a "greater than", hence upper portion of the graph will be shaded.

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Answer:

2x+9=1x-5

2x-1x=-5-9

x=-14

Answer:

At maximum, she can buy 5 tomatoes.

Step-by-step explanation:

If you solve the inequality, as so:

1.2x+1.8 <=7.8

1.2x <= 6

x <= 5

Answer:

B, C

Step-by-step explanation:

Look at the lower blue point.

Its coordinates are (4, 3).

The x-coordinate, 4, stands for minutes.

The y-coordinate, 3, stands for number of boxes.

This is a slope of 3/4, corresponding to 0.75 boxes per minute, or 3 boxes every 4 minutes.

Answer: B, C

Answer:

3 boxes are filled every 4 minutes.

Step-by-step explanation:

Look at the graph; at the bottom of the graph, it is shown that every __ minutes, __ boxes are filled. If you look at the first shown blue point on the left of the graph, it shows that on the fourth minute, three boxes are filled, as from the axis, you go right four and up three.

Answer: C, D

Step-by-step explanation:

[tex]x^2 +10x+18=0\\\\x=\frac{-10 \pm \sqrt{10^2 - 4(1)(18)}}{2}\\\\x=\frac{-10 \pm \sqrt{28}}{2}\\\\x=-5 \pm \sqrt{7}[/tex]

The volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.

To find the volume of the solid generated, we use the shell method since the cross-sections are parallel to the axis of rotation.

So, [tex]V = 2\pi\int\limits^a_b {xy} \, dx[/tex]

Now given that  the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis.

So, we integrate from x = 0 to x = 2.

[tex]V = 2\pi\int\limits^a_b {xy} \, dx\\= 2\pi\int\limits^2_0 {x(x^{2} + x)} \, dx\\= 2\pi\int\limits^2_0 {(x^{3} + x^{2} )} \, dx\\= 2\pi\int\limits^2_0 {x^{3} + 2\pi\int\limits^2_0 x^{2} } \, dx\\= 2\pi[\frac{x^{4} }{4}]_{0}^{2} + 2\pi[\frac{x^{3} }{3}]_{0}^{2} \\= 2\pi[\frac{2^{4} - 0^{4} }{4}}]+ 2\pi[\frac{2^{3} - 0^{3} }{3}]\\= 2\pi[\frac{16 - 0}{4}}]+ 2\pi[\frac{8 - 0}{3}]\\= 2\pi[\frac{16}{4}}]+ 2\pi[\frac{8}{3}]\\= 2\pi (4)+ [\frac{16\pi}{3}]\\= 8\pi + [\frac{16\pi}{3}]\\[/tex]

[tex]= \frac{24\pi + 16\pi}{3} \\= \frac{40\pi}{3}[/tex]

So, the volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.

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Answer:

4

Step-by-step explanation:

both sides are multiplied by 2 which means its the original area*2*2 which means it's the original area*4

The rule for learning the > sign is demonstrating eating with the right hand.

The inequality signs are;

The rule for teaching your students the greater than > sign is by imagining eating with their right hand. The shape of the hand when taking food into the mouth is the greater than sign.

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The margin of sampling error is obtained by multiplying the standard error with the critical value.

The margin of sampling error is a statistic that tells a researcher by how many percentage points the result gotten from the sample value would differ from that of the population. This value is obtained by multiplying the standard error with the critical value.

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[tex]y=9x^2-4\\9x^2=y+4\\x^2=\dfrac{y+4}{9}\\x=\pm\sqrt{\dfrac{y+4}{9}}=\pm\dfrac{\sqrt{y+4}}{3}\\\\\text{inverse: }y=\pm\dfrac{\sqrt{x+4}}{3}[/tex]

The inverse of the function y = 9x² - 4 is y = ±√((x + 4)/9). The correct option is A.

To find the inverse of a function, we need to swap the positions of the input variable (usually x) and the output variable (usually y), and then solve for y. The resulting equation will be the inverse function.

To find the inverse of the function y = 9x² - 4, we need to swap the positions of x and y and then solve for y.

So, starting with y = 9x² - 4:

y = 9x² - 4

x = 9y² - 4 (swapping x and y)

x + 4 = 9y² (adding 4 to both sides)

y² = (x + 4)/9 (dividing both sides by 9)

y = ±√((x + 4)/9) (taking the square root of both sides, plus or minus)

So the inverse of the function y = 9x² - 4 is:

y = ±√((x + 4)/9)

Note that since we have a plus or minus sign in the expression, this means that the inverse is actually two functions: one that gives the positive square root, and one that gives the negative square root.

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The number of agents required in the morning shift 8:00 AM to 12:00 PM is 624.36 agents

Agent required in the morning = (32% of 473) + 473

= (32/100 × 473) + 473

= (0.32 × 473) + 473

= 151.36 + 473

= 624.36 agents

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The effective sizes for parametric tests, non parametric tests and chi square tests are as detailed below.

11) Parametric t-tests are statistical tests that assume the data approximately follows a normal distribution. Now, when trying to check for parametric t-tests, the effective size we use is Cohen's d which is an appropriate effect size for the comparison between two means.

12) Nonparametric t-tests are those statistical tests that don’t assume anything about the distribution followed by the data, and hence are also known as distribution free tests.

In non - parametric t - tests, we calculate effect size by using the formula;

r = z/√N

where;

r is effect size

z is z value

N is Observation number.

13) In the chi-square test, the effect size index (w) is calculated by dividing the chi-square value by the number of scores and taking the square root.

The effective size is considered small if w = 0.10, Considered medium if w = 0.30, and large if w = 0.50.

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For the given inverse functions we have:

a) f⁻¹(5) = 7

b) f(-2) = -3

Remember that if f(x) and g(x) are inverse functions, then:

[tex]f(x) = y\\then\\g(y) = x[/tex]

a) Now we know that:

f(7) = 5

Then if f⁻¹(x) is the inverse, we have:

f⁻¹(5) = 7

b) Now we know that:

f⁻¹(-3) = -2

Again, using the rule for inverse functions, we will have:

f(-2) = -3

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When the coordinate satisfies the original inequality, if a stays the same, b must be greater than its previous value to satisfy the new inequality.

It should be noted that inequality provides an interval to the solution.

This is illustrated graphically. Let's illustrate this with an example, suppose a =1, b = 3

a - b < 0.

1 - 3 < 0

-2 < 0

If a stays the same value, b will be greater than 1.

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The unknown number of the given expression is 8

Let the unknown number be x such that three times the sum of some number plus 3 is equal to 7 times the number minus 23 is expressed as;

3(x + 3) = 7x - 23

Expand

3x + 9= 7x - 23

Collect the like terms

3x-7x = -23 - 9

-4x = -32

x = 8

Hence the unknown number of the given expression is 8

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