Shayla is 3 years older than Todd. If t represents Todd’s age, which expression represents Shayla’s age?

Using the z-distribution, it is found that a sample size of 3,385 is required.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.

We have no prior estimate, hence [tex]\pi = 0.5[/tex] is used, which is when the largest sample size is needed. To find the sample size, we solve the margin of error expression for n when M = 0.02, hence:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.02\sqrt{n} = 2.327 \times 0.5[/tex]

[tex]\sqrt{n} = \left(\frac{2.327 \times 0.5}{0.02}\right)[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.327 \times 0.5}{0.02}\right)^2[/tex]

n = 3,385.

A sample size of 3,385 is required.

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Answer:

13.5 litres

Step-by-step explanation:

the ratios are 2 : 3 : 4 = 2x : 3x : 4x ( x is a multiplier )

given Henrietta produced 1.5 litres more than Gladys , then

4x = 3x + 1.5 ( subtract 3x from both sides )

x = 1.5

then total milk produced by the 3 cows is

total = 2x + 3x + 4x = 9x = 9 × 1.5 = 13.5 litres

See below for the complete table and graph of y = x + 4

The function is given as:

y = x +4

Where x = -2, 0, 2, 6 and 8

So, we have

y = -2 +4 = 2

y = 0 +4 = 4

y = 2 +4 = 6

y = 6 +4 = 10

y = 8 +4 = 12

The above computation implies that the complete table is

Input x        x + 4        Output, y        (x, y)

-2               -2  + 4          2                  (-2,2)

0                 0  + 4          4                  (0,4)

2                 2  + 4          6                  (2,6)

6                 6  + 4          10                 (6,10)

8                 8  + 4          12                  (8,12)

See attachment for the graph of y = -x + 4

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The word problem that depicts this algebraic equation is;

The sum of the weight of my son and my daughter is 9 kg but the product of their weights is 14. Find the weights of each person.

We want to write a word problem with the equation;

x(9 - x) = 14

The word problem that depicts this algebraic equation is;

The sum of the weight of my son and my daughter is 9 kg but the product of their weights is 14. Find the weights of each person.

Now, the word problem above is correct because if we assume their weights are x and y, then we can say that;

x + y = 9

xy = 14

Now, y = 9 - x

Thus, equation 2 is;

x(9 - x) = 14

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Answer:

Step-by-step explanation:

It would be point B. Since y-intercept is when the x is at 0, the answer would be point B.

The line PQ is altitude of the triangle. This can be obtained by understanding what an altitude is.

Properties of altitude of a triangle:

In the given triangle,

it is clear that angle Q is 90° and therefore PQ is a perpendicular line from the point P.

Since the perpendicular line, which is PQ, is drawn from the vertex, which is P  of the triangle to the opposite side, which is SR.

Thus PQ is the altitude of the triangle.

Hence in the given figure, the line PQ is the altitude of the triangle.

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The way to convert counts into relative frequencies in a Two Way Relative Frequency Table is to divide the count by the total number of items

This refers to the depiction of the number of times in which an event occurs in the form of a table.

Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.

Please note that your question is incomplete as you did not provide the frequency table needed and also the trends and generalizations to find, so a general overview was given.

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Answer:

The relative frequency table shows a trend that a majority of people prefer coffee over tea: the ratio in the total row for coffee is 0.65 and just 0.35 for tea. Similarly, more people are night owls than early birds: the total column for night owl is 0.6, but the early bird column is only 0.4.

Answer:

Step-by-step explanation:

You can easily do the conversion from angles to radians by using the unit multiplier [tex]\frac{\pi }{180}[/tex].

210°×[tex]\frac{\pi }{180}[/tex]

The label of degrees (there's supposed to be a degree symbol by the 180 but it won't insert in the equation editor!) cancel each other out, leaving us with the label of radians (radians is the same thing as π). Then reduce between the 210 and the 180. Both are divisible by 30, so the simplification of

[tex]\frac{210\pi }{180}=\frac{7\pi }{6}[/tex]

Do the same with the 315 angle:

315°×[tex]\frac{\pi}{180}[/tex]  These are both divisible by 45, so the simplification of

[tex]\frac{315\pi}{180}=\frac{7\pi}{4}[/tex]

The two radian measures exists [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].

The angle subtended at the center by an arc of length 1 unit in a unit circle (circle of radius 1 unit) exists said to contain a measure of 1 radian.

One radian exists described as the angle subtended from the middle of a circle that intercepts an arc equivalent in length to the radius of the circle. When no symbol exists utilized, radians exist supposed. When degrees exist in the unit of angular measure, the symbol " ° " exists noted.

Degree to radian [tex]$=D \times \frac{\pi}{180}$[/tex]

Substitute the values and simplifying the above equation, we get

For [tex]$210^{\circ}=210 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{6}$[/tex]

For, [tex]$315^{\circ}=315 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{4}$[/tex]

So the missing measures are [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex]

Therefore, the correct answer is [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].

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Answer: 6435

Step-by-step explanation:

[tex]\binom{15}{8}=6435[/tex]

Answer:

Absolute value parent function

Explanation:

What is an Absolute value function?

It is a function in Algebra in where the variable is inside the absolute value bars (| |)

f(x)=|x|

y=x on the right side and y=-x on the left side of the graph

Hope it helps!

As the person that is in charge of public relations the steps that you would take to deal with the issue on ground would be:

This is the term that is concerned with the part of management that is concerned with the maintenance of a positive image for an organization.

The director has to take proactive steps in order to take care of the issue in a timely and good manner.

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The approximate percentage of daily phone calls numbering between 36 and 56 by the receptionists is 95.44%.

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 46 and a standard deviation of 5.

Hence, Mean,μ=46 and Standard deviation,σ=5.

To find the probability of daily phone calls numbering between 36 and 56,

P(36≤X≤56)

To convert the X score to Z score, use the formula, Z=(X-μ)/σ

Then we get,

P((36-46)/5 ≤ Z ≤ (56-46)/5) = P(-2 ≤ Z ≤ 2)

By using the property of the normal bell curve, we get

P(-2 ≤ Z ≤ 2) = P(2 ≤ Z) - P(-2 ≤ Z)

As per the normal distribution table,

P(2 ≤ Z) - P(-2 ≤ Z) = 0.9772-0.0228

∴ P(36≤X≤56) = 0.9544

Hence, the approximate percentage of daily phone calls numbering between 36 and 56 by the receptionists is 95.44%.

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Graph 3

Because

The graph is like the first graph

When x approaches+oo y approaches+oo

But when x is negative the reverse thing happens

Hence Graph C is correct

Answer:

Graph 3

Step-by-step explanation:

Given function:

[tex]f(x)=\sqrt[3]{-x}[/tex]

Therefore, the parent function is:

[tex]f(x)=\sqrt[3]{x}[/tex]

(The graph of the parent function is the first graph in the answer options).

The transformation that takes the parent function to the given function is:

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Therefore, the graph of the given function is the third graph in the given answer options (see attached).

Answer: I am pretty sure you are correct from my standpoint

Step-by-step explanation:

If you look closely he is pretty close to the answer or it is the answer or this is just answer on my point or if its wrong try b

Answer:

Division property of inequality

Step-by-step explanation:

24<4x

24/4<4x/4

6<x

(1/4)×24 < (1/4) ×4x

6 < x

Answer:

4/91

Step-by-step explanation:

There are a total of 15 marbles.  In the first selection there are 15 marbles and 6 are blue.  That would be 6/15.

Since we are not replacing marbles, we now have 14 marbles and we want to select one of the 5 white marbles.  That would be 5/14.

Lastly we now only have 13 marbles and of those we want to select one of the 4 red ones.  That would be 4/13.

Now we take these 3 fractions and multiply them together.

6/15(5/14)(4/13).  I am going to try to make this a little easier and see if I can find any factors that any top number shares with any bottom number.

I see 5 on the top shares a common factor with 15 on the bottom.  I will divide these numbers by 3, so now I have

6/3(1/14)(4/14).  I think that I can do better than that.  I see that 6 on the top and 3 on the bottom share a common factor of 3.  I will divide both of these numbers by 3.  Which will give me:

2/1(1/14)(4/13) I see a 4 on top and a 14 on the bottom.  Those are both divisible by 2 so, I will divided them both by 2 and that leaves me with

2/1(1/7)(2/13)  That is a lot easier, now I will just multiple the top numbers and multiply the bottom numbers to get

4/91

Using the corresponding angles postulate:

m∠3 = 150°

m∠5 = 150°

According to the corresponding angles postulate, corresponding angles, ∠3 and ∠5 are congruent to each other.

Thus, we would have the following equation:

m∠3 = m∠5

Plug in the values

50x - 100 = 25x + 25

50x - 25x = 100 + 25

25x = 125

x = 125/25

x = 5

m∠3 = 50x − 100 = 50(5) − 100 = 150°

m∠5 = 25x + 25 = 25(5) + 25 = 150°

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Answer:

A

Step-by-step explanation:

The pattern is quadrilateral (4-gon), pentagon (5-gon), and hexagon (6-gon). Therefore the next figure would be a heptagon (7-gon).

Using the commutative property for (-5) * 8, we can say that;  (-5) * 8 = 8 * (-5)

The commutative property of algebraic multiplication states that changing the order of factors does not change the product. For example:

4 × 3 = 3 × 4

Similarly, 5 * 6 = 6 * 5

Now, we want to use commutative property to use (-5) * 8. Thus, we can say that;  (-5) * 8 = 8 * (-5)

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Answer:

what do you need person jjff

Given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i

The given complex number is z = -1 - i

[tex]z^3[/tex] means to raise z to the power of 3

[tex]z^3=(-1-i)^3[/tex]

Expand and simplify the expression:

[tex]z^3=(-1)^3+3(-1)^2(-i)+3(-1)(-i)^2+(-i)^3\\\\z^3=-1-3i-3i^2-i^3[/tex]

Note that:

[tex]i^2=-1\\\\i^3=-i[/tex]

Substitute these into the resulting expression

[tex]z^3=-1-3i-3(-1)-(-i)\\\\z^3=-1+3-3i+i\\\\z^3=2-2i[/tex]

Therefore, given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i

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Answer: 12

Step-by-step explanation:

22

bc I know that is 22 so just put that

Answer:

[tex]x \approx 1.16[/tex]

Step-by-step explanation:

a.

To find the values of m and n, we have to first expand  [tex](x + m)^2 + n[/tex] :

[tex](x + m)^2 + n[/tex]

⇒ [tex]x^2 + 2mx + m^2 + n[/tex]

[tex]f(x) = x^2 + 4x - 6[/tex]

Now  compare the coefficients of the x-terms:

• [tex]2mx = 4x[/tex]

⇒ [tex]\bf m = 2[/tex]

• [tex]m^2 + n = -6[/tex]

⇒  [tex]2^2 + n = -6[/tex]

⇒ [tex]n = -10[/tex]

b.

[tex]x^2 + 4x - 6 = 0[/tex]

∴ [tex](x + 2)^2 - 10 = 0[/tex]

⇒ [tex](x + 2)^2 = 10[/tex]

⇒ [tex]x + 2 = \sqrt{10}[/tex]

⇒ [tex]x = \sqrt{10} -2[/tex]

⇒ [tex]x \approx 1.16[/tex]

The value of CE = 18.3

According to the statement

Here we have given the value of tangents AE = 8 and BC = 3

we have to find the value of CE and

It is given that AE is the tangent to the circle.

Now we make a equation to find the CE then

(8)^2 = 3(x+3)

In this equation the value of AE is 8. and

In this x is the value of CE and BC have value 3.

And the total value of BE becomes the 3(x+3) and 3 is the parts by which  BE is formed.

Then solve the equation

64= 3x +9

3x = 64-9

x = 18.3

So, The value of CE = 18.3

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The solution of the differential equation y(3)=29/9.

Given a differential equation y'+(y/x)=x for y(1)=1.

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

We will solve this differential equation by using the integrating factor method.

Firstly, we will find the integrating factors by using the formula, we get

[tex]I.F=e^{\int Pdx}[/tex]

Here P=1/x and substitute this in the formula, we get

[tex]\begin{aligned}I.F.&=e^{\int \frac{1}{x}dx}\\ &=e^{\log x}\\ &=x\end[/tex]

Now, we will substitute the values in the formula

[tex]y\times I.F.=\int Q\times I.F.dx[/tex]

Here Q=x an substitute this in the above formula, we get

[tex]\begin{aligned}y\times x&=\int x\times xdx\\ yx&=\int x^{2} dx\\ yx&=\frac{x^3}{3}+C\end[/tex]

Further, we will divide both sides with x, we get

y=(x²/3)+(C/x)                       ......(1)

Given that y(1)=1 means when x=1 then y=1 so substitute this in equation (1) to find the value of C, we get

1=(1/3)+C

1-(1/3)=C

2/3=C

Substitute the value of C in equation (1), we get

y=(x²/3)+(2/(3x))

Now find the value of y when x=3, we get

y=(9/3)+(2/9)

y=3+(2/9)

y=29/9

Hence, in the differential equation y'+(y/x)=x for y(1)=1 then y(3) is 29/9.

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a) The resultant force on the particle is equal to - 225 · x, where x is measured in meters.

b) The particle moves with simple harmonic motion.

c) The motion has a period of approximately 1.257 seconds.

d) The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.

e) The equation for the position of the particle is x(t) = 0.5 · cos 25t, where t is in seconds.

In this case we have a system with a particle under periodic motion due to two reactive forces from two springs. a) The system is represented by the following formula based on Newton's laws:

∑F = - k₁ · x - k₂ · x = m · a      (1)

Where:

If we know that k₁ = k₂ = 112.5 N/m, then the resultant force on the particle is equal to - 225 · x, where x is measured in meters.

b) The particle is under simple harmonic motion has a differential equation of the form:

x'' + ω² · x = 0       (2)

Where:

By some algebraic handling on (1), we find the following differential equation:

x'' + [(k₁ + k₂) / m] · x = 0     (3)

Thus, the particle moves with simple harmonic motion.

c) The period of the motion (T), in seconds, is determined by T = 2π / ω. Then, the period is described by the following expression:

T = 2π · √[m / (k₁ + k₂)]

T = 2π · √(9 kg / 225 N /m)

T ≈ 1.257 s

The motion has a period of approximately 1.257 seconds.

d) The speed of the particle (v), in metres per second, can be found by the principle of energy conservation:

(1 / 2) · k · A² = (1 / 2) · k · x² + (1 / 2) · m · v²      (4)

v = √[k · (A² - x²) / m]

Where:

If we know that k = 225 N / m, A = 0.5 m, x = 0.05 m and m = 9 kg, then the speed of the particle is:

v = √[(225 N / m) · [(0.5 m)² - (0.05 m)²] / (9 kg)]

v ≈ ± 2.488 m / s

The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.

e) The function position for a particle under simple harmonic motion:

x(t) = A · cos ω · t      (5)

If we know that A = 0.5 m and ω = 25 rad / s, then the equation for the position of the particle is:

x(t) = 0.5 · cos 25t

The equation for the position of the particle is x(t) = 0.5 · cos 25t.

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The value of the house 2 years from now is $276,480.

Option (C) is correct.

According to the question,

Cost of house last year = $  160000

Cost of house at present = $ 192000

The increase in the price of the house is calculated by finding the difference between the prices in two consecutive years.

Increment in cost = $ (192000-160000) =$ 32000

The rate of increment can be calculated by dividing the increment by the original price and then multiplying it by 100%.

Rate of increment = 32000/160000 * 100 =20%

Thus, the value of the house 2 years from now is calculated as:

=192000(1+20/100)(1+20/100)

=192000*120/100*120/100

= $ 276480

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Answer:

Step-by-step explanation:

Reflecting across the x-axis means (x,y) maps onto (x,-y).

So, A' has coordinates (-2,0), B' has coordinates (-6,-5), and C' has coordinates (-3, -4).