Multiplying polynomials (8v - 5)(v + 7)

In the figure, applying  perpendicular bisector theorem for chords in a circle, the value of JN = 9 1/2

The perpendicular bisector theorem for chords in a circle states that if a radius of a circle is perpendicular to a chord, then it bisects the chord.

In other words, the radius divides the chord into two equal segments.

This theorem is a direct consequence of the properties of perpendicular lines and congruent triangles.

applying this to the figure

JN = JK/2

JN = 19/2

JN = 9 1/2

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Answer:

m<A = 66.2°

Step-by-step explanation:

m<A + m<B = 180°

m<B = 113.8°

m<A + 113.8° = 180°

m<A = 180° - 113.8°

m<A = 66.2°

(a) The area of the office is 53.55 meters square.

(b) The area of the Carpet would be 52.6656 meters square.

(c) The area of the surrounding is 0.8844 meters square.

Area of the office floor= Length × Breadth

                                     = 8.5 meters × 6.3 meters

                                     = 53.55 meters square

Area of the Carpet = Length × Breadth

                               = (8.5-0.06) meters × (6.3-0.06) meters

Since, 60 cm = 0.06 meters

Because 1 meter = 100 cm

                                = 52.6656 meters square

Area of surrounding = Area of Office floor - Area of Carpet

                                  = 53.55 meters square - 52.6656 meters square

                                  = 0.8844 meters square

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5. The minimum value of g(x) is -8.

The maximum value of g(x) is 17.

6. The average rate of change of the function g(x) over the interval [-2, 3] is 5.

By critically observing the table representing the function g(x), we can logically deduce the following minimum value and maximum value over the interval [-2, 3];

When x = -2, the minimum value of g(x) is equal to -8.

When x = 0, the maximum value of g(x) is equal to 17.

Question 6.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function g(x) over the interval [-2, 3]:

a = -2; f(a) = -8

b = 3; f(b) = 17

Average rate of change = (17 + 8)/(3 + 2)

Average rate of change = 25/5

Average rate of change = 5

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Answer: 17 months

Step-by-step explanation:

Total cost of the bike = $1,867

Down payment = $320

so $1,867 - $320 = $1,547

$91 * 17 = 1,547

(17 = months) so $91 * 17 months = 1,547

The simplified exponential expression in the context of this problem is given as follows:

[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]

The exponential expression in the context of the problem is defined as follows:

[tex](6m^5g^5)^2[/tex]

The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.

Applying the exponent of 2, we have that:

Hence the simplified exponential expression in the context of this problem is given as follows:

[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]

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The measures of angle T and angle V are T = 90 and V = 90

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

The circle

The point T and V are at the tangent of the circle

By definition, the tangent is perpendicular to the radius of the circle, with which it intersects.

This means that the angle T and angle V are right angled

Using the above as a guide, we have the following:

T = 90 and V = 90

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Answer:

∫(1 - 25x²) dx

Step-by-step explanation:

The y-intercept of f(x + 4) + 8 is given as follows:

10.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function for this problem is given as follows:

[tex]f(x) = \log_2{x}[/tex]

The translated function is then given as follows:

[tex]g(x) = \log_2{x + 4} + 8[/tex]

The y-intercept of the function is the numeric value at x = 0, hence:

[tex]g(0) = \log_2{0 + 4} + 8[/tex]

g(0) = 2 + 8 = 10.

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Answer:

Step-by-step explanation: you are sped that is the answer black n

a. The image is attached below.

b. Length of the equator is 24,000 miles.

c. The image is attached below.

d. No, it is not possible for a satellite to see 50% of the Earth's equator.

Satellite B will see more of the Earth's equator than Satellite A. This is because the viewing angle of Satellite B is larger than the viewing angle of Satellite A. The viewing angle of Satellite B is 60 degrees, while the viewing angle of Satellite A is 45 degrees.

The length of the equator in view of Satellite B is 24,000 miles. This can be calculated using the following formula:

length of the equator = 2 * [tex]\Pi[/tex] * radius * sin(m/2)

Use a third color to draw the viewing angle from Satellite C. Label the points of tangency J and K. If m/C=45", find the mJK and mJZK

This is because the Earth is a sphere, and a sphere has no flat surfaces. A satellite can only see a portion of the Earth's surface, and the portion that it sees will always be less than 50% of the total surface area.

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Here are two significant advantages of a 401(k) over an IRA:

Higher Contribution Limits: 401(k) plans allow for higher annual contributions compared to IRAs. The contribution limit for a 401(k) is $19,500 (or $26,000 for individuals aged 50 and older), while the limit for an IRA is $6,000 (or $7,000 for individuals aged 50 and older).

Employer Contributions and Matching: 401(k) plans often offer employer contributions and matching programs. Employers may contribute to an employee's 401(k) account, adding to their retirement savings without any direct cost to the employee.

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Explanation:

The horizontal component is found using cos fxn

80 x cos 20 =  75.2 pounds

Appling the tangent of circle properties, the length of RS is solved to be

C. 13 in

To find the length of the tangent named RS, we applied the tangent of a circle property which says that the length of tangents to a particular point are equal

This leads to the mathematical equation represented below

SR = 7 in + 6 in

SR = 13 in

thus we can say that length of the tangent SR = 13 in

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The sound emitted from the jet plane has a sound intensity of approximately 149.13 decibels.

Using the formula:

D = 10 * log(I/I0),

where D represents the sound intensity in decibels, I is the given sound intensity, and I0 is the reference intensity of 10^-12 watts per square meter.

Substituting the given values:

D = 10 * log(8.2*10^2 / 10^-12).

To simplify the calculation, we can rewrite the division as multiplication by the reciprocal:

D = 10 * log(8.2*10^2 * 10^12).

Using the logarithm property log(a * b) = log(a) + log(b):

D = 10 * (log(8.2) + log(10^2) + log(10^12)).

Using the logarithm property log(a^b) = b * log(a):

D = 10 * (log(8.2) + 2 * log(10) + 12 * log(10)).

Since log(10) = 1:

D = 10 * (log(8.2) + 2 + 12).

D = 10 * (log(8.2) + 14).

Using a calculator or logarithm table, we can find log(8.2) ≈ 0.913.

D = 10 * (0.913 + 14).

D = 10 * 14.913.

D ≈ 149.13.

Therefore, the sound emitted from the jet plane has a sound intensity of approximately 149.13 decibels.

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Answer:

  x = 2

Step-by-step explanation:

You want the value of x that satisfies x|x| = 4.

The absolute value function splits the domain of the equation into two parts.

For x < 0, the equation is ...

  x(-x) = 4

  x² = -4

There are no real solutions in this domain.

For x ≥ 0, the equation is ...

  x² = 4

  x = √4 = 2

The only solution is x = 2.

__

Additional comment

In the attachment, we have rewritten the equation to ...

  x|x| -4 = 0

The graphing calculator readily identifies x-intercepts, so this is a convenient way to find the solution. You will notice that for x < 0, the graph is of -x²-4, which is never zero.

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The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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Answer:

What the other guy said

Step-by-step explanation:

The statements that are true regarding the expression with the exponents -1, -3, and 1 are;

An exponent is a quantity or power to which a value, expression or number is to be raised.

The specified expression can be presented as follows;

8⁻¹ × 8⁻³ × 8

Therefore; 8⁻¹ × 8⁻³ × 8 = 8⁽⁻¹ ⁺ ⁻³ ⁺ ¹⁾ = 8⁻³ = 1/8³

1/8³ = 1/512

Similarly, we get; 8⁷ × 8⁻¹⁰ = 8⁽⁷ ⁻ ¹⁰⁾ = 8⁻³ = 1/8³

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The probability of accepting the whole shipment is 0.9093. Therefore, almost all such shipments will be accepted.

The probability that the whole shipment will be accepted is calculated as follows;

First, we calculate the probability of having at most 3 batteries that do not meet specifications out of the 40 randomly tested batteries.

Assuming:

We can use the binomial probability formula to calculate the probability:

[tex]P(X \leq k) = \sum (from\: i = 0 \:to\: k) [(nCi) * p^{i} * q^{(n-i)}][/tex]

P(X ≤ 3) = [(⁴⁰C₀) * (0.03⁰) * (0.97⁴⁰] + [(⁴⁰C₁) * (0.03¹) * (0.97³⁹)] + [(⁴⁰C₂) * (0.03²) * (0.97³⁸)] + [(⁴⁰C₃) * (0.03³) * (0.97³)]

P(X ≤ 3) = 0.9093.

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The correct option is the second one, the order is:

g(x), f(x), h(x).

To find the rate of change for a function f(x) on an interval [a, b] we need to get:

R = (f(b) - f(a))/(b - a)

Here the interval is [-1, 3]

The first function is:

f(x)=  (x + 3)² - 2

Evaluating we get:

f(-1) = (-1 + 3)² - 2

f(-1) = 2² - 2 = 4 -2 = 2

and f(3) = (3 + 3)² - 2 = 34

Then the rate is:

R = (34 - 2)/(3 + 1) = 8

For g(x) we can use the graph, we have:

R = (0 + 2)/4 = 1/2

For the last function we need to use the table, then we will get:

R = (62 - 14)/(3 + 1) = 12

Then the order, from least to greatest is:

g(x), f(x), h(x).

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Answer:

x = 10.5

y =5.25

Step-by-step explanation:

sin60° = 21√3/x

√3/2 = 21√3/x

=> x = 21√3/√3/2 = 10.5

cos60° = y/x

1/2 = y/10.5

y = 10.5/2 = 5.25

The missing angles are m ∠1 = 53° and m ∠k = 12°.

Given that are two circles we need to find the missing measures,

Using the concept of intersecting chords angles,

When two chords intersect inside a circle, the angle between the chords is half the sum of the intercepted arcs.

And,

When two chords intersect outside a circle, the angle between the chords is half the difference of the intercepted arcs.

So,

a) m ∠1 = 1/2 [arc LP + arc RQ]

m ∠1 = 1/2 [50°+56°]

m ∠1 = 1/2 × 106°

m ∠1 = 53°

b) m ∠k = 1/2 [arc MJ - arc LR]

arc LR = 360° - [72° + 100° + 140°]

arc LR = 48°

So,

m ∠k = 1/2 [72° - 48°]

m ∠k = 12°

Hence the missing angles are m ∠1 = 53° and m ∠k = 12°.

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Answer:

The figure is omitted--please sketch it to confirm my answer.

[tex]\pi {(5 \sqrt{2}) }^{2} - {10}^{2} [/tex]

[tex]50\pi - 100 = 50(\pi - 2) = 57.08[/tex]

The area inside the square and outside the circle is about 57.08 cm^2.

The probability that the next customer will pay with something other than cash, rounded to the nearest Whole number, is approximately 12%.

The probability that the next customer will pay with something other than cash, we need to consider the total number of customers who paid with something other than cash and divide it by the total number of customers in the last week.

In the given information, it is stated that 69 customers paid with cash, 2 customers used a debit card, and 7 customers used a credit card. To find the total number of customers who paid with something other than cash, we add the number of customers who used a debit card and the number of customers who used a credit card:

Total number of customers who paid with something other than cash = Number of customers who used a debit card + Number of customers who used a credit card

= 2 + 7

= 9

Now, to calculate the probability, we divide the number of customers who paid with something other than cash by the total number of customers:

Probability = Number of customers who paid with something other than cash / Total number of customers

= 9 / (69 + 2 + 7)

= 9 / 78

= 0.1154 (rounded to four decimal places)

To express the probability as a percentage, we multiply the probability by 100:

Probability as a percent = 0.1154 * 100

≈ 11.54

Therefore, the probability that the next customer will pay with something other than cash, rounded to the nearest whole number, is approximately 12%.

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Answer:

They would stop jumping rope at 12:46

Step-by-step explanation:

I'd probably say P.M considering the fact that I don't think kids would be having recess at midnight

Based on the information given about the geometry, the value of CF will b A. 6cm.

Since OE and OF are both 4 cm, then OEF is an equilateral triangle. This means that EOF is 60 degrees.

Since AB is 12 cm, then AB is twice the length of OE. This means that ABE is a 30-60-90 triangle.

In a 30-60-90 triangle, the hypotenuse is twice the length of the side opposite the 30 degree angle. This means that CF is 6 cm.

In conclusion, the correct option is A.

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There is 90% confidence that the population standard deviation is between 5.094 weeks and 19.803 weeks.

The correct option is C.

To construct a confidence interval for the population standard deviation, we can use the chi-square distribution.

Given data:

Sample size (n) = 12

Sample standard deviation (s) = 9.904 weeks

The chi-square distribution is right-tailed and at 90% confidence level, the significance level is 0.1 on each tail.

Degrees of freedom (df) = n - 1

Degrees of freedom (df) = 12 - 1

Degrees of freedom (df) = 11

From the chi-square distribution table, the critical values for a 90% confidence level with 11 degrees of freedom are 3.816 and 22.362.

Therefore, the 90% confidence interval for the population standard deviation is:

Lower bound = √(n-1) * s² / χ² upper)

Lower bound = √(11 * 9.904²) / 22.362)

Lower bound = 5.094

Upper bound = √(n-1) * s² / χ² lower)

Upper bound = √(11 * 9.904²) / 3.816)

Upper bound = 19.803

Therefore, there is 90% confidence that the population standard deviation of the age at which babies first crawl is between approximately 5.094 weeks and 19.803 weeks.

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The value of p² is approximately 0.999999528.

To find the value of oe (the standard error of estimate) and p² (the coefficient of determination), we can use the given population data set information.

The formula for the standard error of estimate (oe) is:

oe = √((Σy² - (Σy)² / N) / (N - 2))

Substituting the given values, we have:

oe = √((135675 - (1456)² / 250) / (250 - 2))

oe = √((135675 - 2124736 / 250) / 248)

oe = √(541.96)

oe ≈ 23.27

Therefore, the value of oe is approximately 23.27.

The coefficient of determination (p²) can be calculated using the formula:

p² = 1 - (Σxy - (Σx × Σy) / N) / ((Σx² - (Σx)² / N) × (Σy² - (Σy)² / N))

Substituting the given values:

p² = 1 - (85080 - (9880 × 1456) / 250) / ((485870 - (9880)² / 250) × (135675 - (1456)² / 250))

p² = 1 - (85080 - 14358080 / 250) / ((485870 - 968144 / 250) × (135675 - 2124736 / 250))

p² = 1 - (85080 - 57432.32) / (478352.56 × 123346.74)

p² = 1 - (27647.68) / (59022875580.02)

p² ≈ 0.999999528

Therefore, the value of p² is approximately 0.999999528.

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