50 Points! Multiple choice geometry question. Photo attached. Thank you!

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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Answer: C-Cylinder

Step-by-step explanation:

In this problem, you are rotating the rectangle on the x axis. If you rotate it along this side, the rectangle makes it a cylinder.

Para aquellos que necesitas este respuesta en español: En este problema, estás girando el rectángulo sobre el eje x. Si lo giras a lo largo de este lado, el rectángulo lo convierte en un cilindro.

I hope this helps!

Answer:

The correct answer is (C), cylinder.

Explanation:

When the rectangle is rotated around the axis shown, it will create a three-dimensional shape with two parallel bases that are connected by a curved surface. This shape is called a cylinder.

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

Below are the right probabilities for each scenario;

8. P(red, then green) [tex]\frac{1}{32}[/tex]; P(yellow, then blue) = [tex]\frac{1}{16}[/tex] and P(blue both times) [tex]\frac{1}{4}[/tex]

9. The probability of choosing a boy then rolling a number that is at most 4 is [tex]\frac{5}{14}[/tex]

10. The probability that both flights will be delayed is [tex]\frac{2}{7}[/tex].

11. P(nickel, then quarter) [tex]\frac{1}{20}[/tex];  P(penny, then not a dime) [tex]\frac{1}{10}[/tex]; P(both dimes)[tex]\frac{3}{20}[/tex]; P(both nickels) [tex]\frac{1}{20}[/tex]

For the compounded probability, we can solve them the following way;

8. a) P(red, then green) = P(red) × P(green) = (2/8) × (1/8) = 1/32

b) P(yellow, then blue) = P(yellow) × P(blue) = (1/8) ×(4/8) = 1/16

c) P(blue both times) = P(blue) × P(blue) = (4/8) ×(4/8) = 1/4

9. There are 28 total students and 6 total outcomes on a standard die.

P(boy, then a number at most 4) = (15/28) × (4/6) = 5/14

10. The probability of the first flight being delayed is 6/14, and the probability of the second flight being delayed is 8/12.

P(both flights delayed) = 6/14 × 8/12 = 2/7

11. There are 25 total coins: 4 pennies, 6 nickels, 10 dimes, and 5 quarters.

a) P(nickel, then quarter)  = (6/25) × (5/24) = 1/20

b) P(penny, then not a dime)  = (4/25) × (15/24) = 1/10

c) P(both dimes) = (10/25) × (9/24) = 3/20

d) P(both nickels) = (6/25) × (5/24) = 1/20

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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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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 area of the shaded region is (133π/9) square feet.

Given that the radius (r) is 4 ft, the area of the entire circle is:

A = π(4)² = 16π ft²

To find the area of the sector, we need to calculate the fraction of the circle that the central angle represents.

The fraction is determined by dividing the measure of the central angle (110°) by the total angle in a circle (360°).

Fraction of the circle represented by the sector = 110° / 360° = 11/36

To find the area of the sector, we multiply the fraction by the area of the entire circle:

Area of the sector = (11/36) × (16π)

= (11π/9) ft²

Finally, to find the area of the shaded region, we subtract the area of the sector from the area of the entire circle:

Area of shaded region = Area of entire circle - Area of sector

Area of shaded region = 16π - (11π/9)

= (144π - 11π)/9

= (133π/9) ft²

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Answer:

What the other guy said

Step-by-step explanation:

The ordered pair of W' in trapezoid T'U'V'W' is (7, 2).To reflect a point over the y-axis, we need to change the sign of its x-coordinate while keeping the y-coordinate the same.

In trapezoid TUVW, the ordered pair of W is (-7, 2).

To find the ordered pair of W' in trapezoid T'U'V'W', we need to reflect the x-coordinate of W over the y-axis. Therefore, the x-coordinate of W' will be the opposite of the x-coordinate of W, while the y-coordinate remains the same.

Given that the coordinates of point W are (-7, 2), reflecting it over the y-axis means changing the sign of the x-coordinate, while keeping the y-coordinate the same.

So, when we reflect point W(-7, 2) over the y-axis, the x-coordinate becomes positive and the y-coordinate remains the same. Therefore, the ordered pair of W' is (7, 2).

The x-coordinate of W' will be -(-7) = 7, and the y-coordinate remains 2.

So, the ordered pair of W' is (7, 2).

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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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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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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 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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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:

x=12.124

simplified would be x=12

Step-by-step explanation:

(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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Answer:

length=12ft

width=6ft

Step-by-step explanation:

The volume formula is V=lwh.

Plug the values into the equation like this: 432=(x+6)(x)(6)

Divide both sides of the equation by 6: 72=(x+6)(x)

Distribute the x:  [tex]72=x^{2} +6x[/tex]

Subtract the 72:  [tex]0=x^{2} +6x-72[/tex]

Factor: 0=(x+12)(x-6)

x=-12

x=6

Now, plug in x into the original length and width equations.

length: (6+6)

length=12

width=6

Answer:

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

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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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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Explanation:

The horizontal component is found using cos fxn

80 x cos 20 =  75.2 pounds

Answer:

391 cm²

Step-by-step explanation:

area of the parallelogram,

A = base * height

= 23 * 17

= 391 cm²

Answer:

-8 and 4

Step-by-step explanation:

P= -2

-2+6 = 4

-2-8= -8

Here is your answer!

Answer:

[tex](x - 5)^2 + (y + 2)^2 = 5[/tex]

Step-by-step explanation:

The equation of a circle with a center at (h, k) and radius r is given by:

[tex]\bold{(x - h)^2 + (y - k)^2 = r^2}[/tex]

In this case, the center is at (5, -2) and the point that the circle passes through is (4, 0).

The distance between the center and the point is:

[tex]\sqrt{(5 - 4)^2 + ((-2) - 0)^2} = \sqrt{1 + 4} = \sqrt{5}[/tex]

Therefore, the equation of the circle is:

[tex](x - 5)^2 + (y + 2)^2 = \sqrt{5}^2[/tex]

Simplifying the equation, we get:

[tex]\bold{(x - 5)^2 + (y + 2)^2 = 5}[/tex] is a required equation

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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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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The dimensions of the smaller prism are each multiplied by the factor of 1/3 for length, 1/4 for width, and 1/4 for height to produce the corresponding dimensions of the larger prism.

To determine the factor by which the dimensions of the smaller prism are multiplied to produce the corresponding dimensions of the larger prism, let's consider the relationship between the two prisms.

A prism is a three-dimensional shape with two parallel, congruent bases connected by rectangular faces. Since the problem specifies that the dimensions of the smaller prism are being multiplied to obtain the dimensions of the larger prism, we can infer that the prisms are similar, meaning they have the same shape but possibly different sizes.

Let's denote the dimensions of the smaller prism as length, width, and height, and the corresponding dimensions of the larger prism as L, W, and H.

To find the factor by which the dimensions are multiplied, we need to compare the corresponding sides of the two prisms. Based on the information provided, we can establish the following relationships:

L = 3 × length

W = 4 × width

H = 4 × height

We can rewrite these relationships as:

length = L/3

width = W/4

height = H/4

Now, let's compare the ratios of corresponding sides:

length/L = (L/3)/L = 1/3

width/W = (W/4)/W = 1/4

height/H = (H/4)/H = 1/4

From these ratios, we can observe that each dimension of the smaller prism is one-third (1/3) the size of the corresponding dimension of the larger prism in terms of length, one-fourth (1/4) in terms of width, and one-fourth (1/4) in terms of height.

Therefore, the dimensions of the smaller prism are each multiplied by the factor of 1/3 for length, 1/4 for width, and 1/4 for height to produce the corresponding dimensions of the larger prism.

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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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