in the diagram below A, B, C are points in the same horizontal plane with AC =BC=22.3 meters.AD is a vertical tower which is anchored at B and C.The angle of elevation of D from B is 25.4. BDC=58.6 and ACB= 50.8.​

The solution for x in the equation (x – 7)^2 = 36 are x = 13 and x = 1

We can solve for x by taking the square root of both sides of the equation:

(x – 7)^2 = 36

Taking the square root of both sides:

x - 7 = ±6

Adding 7 to both sides:

x = 7 ± 6

Therefore, the values of x are:

x = 7 + 6 = 13

x = 7 - 6 = 1

So the correct answers are x = 13 and x = 1. The values x = -29 and x = 42 are not solutions to the equation.

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The values received after utilizing confidence interval are (0.614, 0.674)

Poll = n = 918

X = 592

Calculating the value of p -

p = x/n

= 592/918

= 0.644

The mean of an estimate plus and minus the range of that estimate constitutes a confidence interval. inside a specific degree of confidence, this is the range of values that anticipates the estimate to fall inside if the test is repeated.

Using the formula of confidence interval -

[tex]CI = p + z\sqrt{} p ( 1-p/n)[/tex]

Substituting the values -

[tex]CI = 0.644 + 1.645 \sqrt{} ( 0.644 ( 1 - 0.644) / 918)[/tex]

= 0.644 ± 0.030

Thus, the interval values are -

= 0.644 + 0.030 = 0.674

= 0.644 - 0.030 = 0.614

With 90% certainty that this range represents the true percentage of the population who feel vulnerable to identity theft.

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The rise and run of the line is shown in the image below, where: slope of the line (m) = -3/4.

The slope refers to how steep a line is. To find the slope of a line on coordinate plane, find the rise and the run of the line, then find their ratio.

Slope of a line (m) = change in y / change in x = rise / run

The red line in the image below represents the rise of the line while the blue line represents the run of the line.

The rise = 3 units

The run = 4 units

Therefore, we have:

Slope (m) = rise/run = -3 units / 4 units

Slope (m) = -3/4.

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12 - 2^2 x 2

---Remember: PEMDAS

---In this case exponents are first, then multiplication, then subtraction

12 - 4 x 2

12 - 8

4

Answer: 4

Hope this helps!

There is a local maximum at the point (-1,6), therefore, for x = -1

option D is correct

A local maximum point on a function is  described as a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).

We see  that the function adopts values smaller than 6 to the left of x = -1, and to the right of it:

(-3, -2), (-2, 0) to the left of x = -1 where the function's value is 6

and (0, 0), and (1, -2) to the right of x = -1

Therefore, we can say that the pints  (-1, 6) is a maximum, that is for x = -1, where the function renders a value of 6.

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The Length of the arc in the circle shown is calculated to one decimal place, in terms of pi, as approximately 3.6π cm.

The length of an arc in a given circle can be calculated by applying the formula as expressed below:

Length of arc (s) = ∅/360 * 2πr, where:

Reference angle = ∅

Radius of the circle = r.

Given the parameters:

Radius (r) = 16 cm

Reference angle (∅) = 40 degrees.

Plug in the values:

Length of the arc (s) = 40/360 * 2 * π * 16

Length of the arc (s) = 3.6π cm

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Answer:

To calculate the length of the minor arc AB in terms of pi, you need to know the measure of the central angle that intercepts the arc and the radius of the circle. Do you have that information?

Step-by-step explanation:

Piston movement compresses air in Small compressors type of air compressor

Piston movement compresses air in small compressors. Small compressors, also known as portable compressors, are commonly used for home improvement projects, powering tools, and inflating tires or other objects. The piston moves back and forth inside a cylinder, compressing air and increasing its pressure. The compressed air is then stored in a tank until it is needed to power a tool or inflate an object.

Small compressors are generally less powerful than medium or industrial compressors, but they are more affordable, portable, and easier to use for smaller tasks. They can be powered by electricity or gasoline, and they come in a range of sizes and capacities to meet different needs. Overall, piston-driven small compressors are an efficient and cost-effective way to compress air for various applications.

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Answer:

its prime

Step-by-step explanation:

it can not be factored using foil

Answer:

Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.

Step-by-step explanation:

My apologies for the confusion. Let's analyze how Elin arrived at her answer.

According to the given information, car A travels 221.5 km at a given time. Elin interpreted the statement "car B travels 1.2 times the distance car A travels at the same time" to mean that the distance traveled by car B is 1.2 times the distance traveled by car A.

To calculate the distance traveled by car B, Elin multiplied the distance of car A (221.5 km) by 1.2:

Distance of Car B = 1.2 * Distance of Car A

Distance of Car B = 1.2 * 221.5 km

Distance of Car B = 265.8 km

Therefore, Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.

The actions that have more than 4 possible outcomes are:

- Selecting an 8 or 9 card of any color (each set has 2 cards for a total of 8 possible outcomes)

- Selecting a yellow card greater than 4² (there are 7 yellow cards that meet this criteria)

- Selecting a blue card that is a multiple of 3 (there are 5 blue cards that meet this criteria)

Therefore, only three of the given actions have more than 4 possible outcomes.

The probability that a randomly selected point within the red-shaded square is 0.16

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

The areas of the above shapes are

Red square = 6 * 6 = 36

White square = 15^2 = 225

The probability is then calculated as

P = Red square /White square

So, we have

P = 36/225

Evaluate

P = 0.16

Hence, the calculated value of the probability that the point falls in the red square is 0.16

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Answer: y = (9/5)x + 5.

Step-by-step explanation:

The slope of the given line is -5/9. The slope of a line perpendicular to it would be the negative reciprocal of -5/9, which is 9/5. Using the point-slope form of a line, we can write the equation of the line as y - (-4) = (9/5)(x - (-5)). Simplifying this equation gives y + 4 = (9/5)x + 9. Solving for y, we get y = (9/5)x + 5. This is the equation of the line in slope-intercept form.

In summary, the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) is y = (9/5)x + 5.

assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

The mean of the sample proportion distribution is given by:

μp(hat) = p = 0.22

The standard deviation of the sample proportion distribution is given by:

σp(hat) = sqrt((p*(1-p))/n) = sqrt((0.22*0.78)/50) = 0.0802

To find the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night, we need to find the z-score corresponding to this value:

z = (0.20 - 0.22) / 0.0802 = -0.2494

Using a standard normal table or calculator, we find that the probability of obtaining a z-score of -0.2494 or less is 0.4019. Therefore, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night,

Hence assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.

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The value of x in the polygon is 5 centimetres.

A polygon is a two-dimensional geometric figure that has a particular number of sides.

Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio .

Therefore, using the ratio of the similar polygon, let's find the value of x as follows:

35 / x = 42 / 6

cross multiply

35 × 6 = 42x

210 = 42x

divide both sides of the equation by 42

x = 210 / 42

x = 5 cm

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Answer:

Step-by-step explanation:

14+12 = 26+8 = 34 + 6 is 40

the answer is 40.

Answer:

[tex]2\sqrt{10[/tex]

Step-by-step explanation:

Add all the numbers together on your calculator

Answer: 76

Step-by-step explanation:

The surface area is all of the area faces added together

The blue is 5*4  but I have 2 of those faces so I multiply by 2

(5*4*2)=40

The red is 4*2  but I have 2 of those faces so I multiply by 2

(4*2*2)=16

The green is 5*2  but I have 2 of those faces so I multiply by 2

(5*2*2)=20

Add those together

A=40+16+20=76

Answer:3

Step-by-step explanation: 1/2 X 6 = 3

Answer:

6 x 1/2 = 3 full bottles

Step-by-step explanation:

Answer:

-------------------------

Convert the given equation as below:

Let's substitute x² - 9x - 1 = t, then the equation is:

Comparing both sides, we see that x = t, so:

Solving this quadratic equation we get:

The equation x⁴/y = 7 represents a relationship of direct proportionality between x and y, where x⁴ and y are inversely proportional to each other.

The equation x⁴/y = 7 represents a relationship between the variables x and y. Specifically, it shows that the fourth power of x divided by y is equal to 7.

This equation can be rewritten as x⁴ = 7y, which means that if we know the value of y, we can determine the corresponding value of x that satisfies the equation. For example, if y = 1, then x⁴ = 7, and taking the fourth root of both sides of the equation gives us x = ± √7.

Conversely, if we know the value of x, we can solve for y by rearranging the equation as y = x⁴/7. This shows that y is directly proportional to x raised to the fourth power, meaning that as x increases, y will also increase, but at a faster rate due to the exponent of 4.

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Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.

B = 1/4 * S

S = 2/3 * P

B + S + P = 23.75 - 4.50

Emma spent 23.75 - 4.50 = $19.25 on the brush, sketchbook, and paint set.

Now we have the equation:

B + S + P = 19.25

Substitute the expressions from relationships 1 and 2 into the equation:

(1/4 * S) + S + (3/2 * S) = 19.25

Now combine the terms:

(1/4 * S) + (4/4 * S) + (6/4 * S) = 19.25

(11/4 * S) = 19.25

Now, to solve for S, multiply both sides of the equation by the reciprocal of the fraction (4/11):

S = (4/11) * 19.25

S = 7

The sketchbook cost $7. Now we can find the costs of the brush and the paint set using relationships 1 and 2:

B = 1/4 * S = 1/4 * 7 = 1.75

P = 3/2 * S = 3/2 * 7 = 10.5

Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.

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Complete question

Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items. What is the total cost for each item

The size of matrix cM is given as follows:

9 x 10.

When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.

The parameters for this problem are given as follows:

Hence the size of matrix cM is given as follows:

9 x 10.

(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).

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The graph of the piecewise function is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

All the three definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.

The definitions are given as follows:

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Answer: The coordinates of F' are (14, 21).

Step-by-step explanation:

       Since we are rotating -90° clockwise about the origin (or 90° counterclockwise), we will apply (x, y) becoming (-y,x). I have also graphed this, see attached.

               (21, -14) ➜ (14, 21)

               The coordinates of F' are (14, 21).

There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

To test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.

Let p be the true proportion of mathematics research published by U.S. authors.

The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).

sample proportion, x/n = 62/130 = 0.477

The test statistic for a two-tailed test is given by:

z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)

= 2.41

Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.

Since  0.016 < 0.05

, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

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Using a linear equation, the minutes it would take both pipes to drain the swimming pool that holds 450,000 liters is 90 minutes.

A linear equation is an equation of a straight line written in the form of y = mx +b, where m is the slope.

The quantity of water the swimming pool holds = 450,000 liters

The drainage time of Pipe A working alone = 150 minutes

Drainage rate of Pipe A = 3,000 liters per minute (450,000 ÷ 150)

The drainage time of Pipe B working alone = 225 minutes

Drainage rate of Pipe B = 2,000 liters per minute (450,000 ÷ 225)

The drainage rate of the combined pipes = 5,000 liters per minute (3,000 + 2,000)

Let the number of minutes for both pipes to drain the pool = x

Therefore, the linear equation is 5,000x = 450,000

x = 90 minutes (450,000 ÷ 5,000)

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