A line goes through points (0, 3) and (6, 12). What would be the slope of this line's perpendicular bisector?

Answer:

110.0m^2

Step-by-step explanation:

Area = a x b x π

a = 5m, b = 7m so

Area = 35pi which is 110.0m squared to one decimal place

Step-by-step explanation:

(1 − cos x)(1 + cos x)

1 − cos²x

sin²x

Answer:

Step-by-step explanation:

2(5-4g) + 3g - 11 = 5(g-3) - 12 - 3g (remove the parantheses)

10 - 8g + 3g - 11 = 5g - 15 - 12 -3g (Calculate and collect like terms)

-1 - 5g = 2g - 27 (move the terms)

-5g -2g = 27 + 1  (collect like terms and calculate)

-7g = -26 (divide both sides)

so G = 26/7

Answer:

G=27/6

Step-by-step explanation:

2(5−4g)+3g−11=5(g−3)−12−3g

(2)(5)+(2)(−4g)+3g+−11=(5)(g)+(5)(−3)+−12+−3g

10+−8g+3g+−11=5g+−15+−12+−3g

(−8g+3g)+(10+−11)=(5g+−3g)+(−15+−12)

−5g+−1=2g+−27

−5g−1=2g−27

Step 2: Subtract 2g from both sides.

−5g−1−2g=2g−27−2g

−7g−1=−27

Step 3: Add 1 to both sides.

−7g−1+1=−27+1

−7g=−26

Step 4: Divide both sides by -7.

-7g/-7=-26/-7

g=26/7

Answer:

2/3 = \(\frac{10}{15}\)

3/5 = \(\frac{9}{15}\)

Step-by-step explanation:

\(\frac{2}{3} \frac{3}{5}\)

\(\frac{10}{15}\) \(\frac{9}{15}\)

Multiply 2/3 by 5/5 and 3/5 by 3/3.

Hope it helps!

Answer you didnt say what to do

Step-by-step explanation:

After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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First we need the slope which is finding from the following equation.

slope = y(B) - y (A) / x (B) - x(A)

Suppose ;

A = ( 0 , 0 ) & B = ( 10 , 5 )

Thus :

slope = 5 - 0 / 10 - 0

slope = 5 / 10

slope = 1 / 2

__________________________

We have following equation to find the point-slope form of the linear functions.

y - y(0) = s × ( x - x(0) )

__________________________

y(0) & x(0) are the coordinates of the point which line through it like A = ( 0 , 0 ) or B = ( 10 , 5 ).

s = slope

__________________________

I choose point A to put in the equation.

So :

y - ( 0 ) = 1/2 × ( x - ( 0 ) )

y - 0 = 1/2 × x - 1/2 × 0

y = 1/2 × x

y = x/2

Done....

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Answer: x=70 BRAINLY???

Step-by-step explanation:

Since the triangle is isocoles, we can say the other base angle is also "x"

So now with Exterior Angle in triangle theorum,

x + x = 140

2x=140

x=70

The cooking time for Erica's 7-pound roast is 196 minutes.

To determine the cooking time for Erica's 7-pound roast, we can set up a proportion based on the relationship between the weight of the roast and the cooking time.

Let's assume that the cooking time is directly proportional to the weight of the roast. Therefore, the proportion can be set up as follows:

(Weight of 3-pound roast)/(Cooking time for 3-pound roast) = (Weight of 7-pound roast)/(Cooking time for 7-pound roast)

Using the values given in the problem, we can substitute the known values into the proportion:

(3 pounds)/(84 minutes) = (7 pounds)/(x minutes)

To solve for x, we can cross-multiply and then solve for x:

3 * x = 7 * 84

3x = 588

x = 588/3

x = 196

It's important to note that cooking times can vary depending on factors such as the type of oven and desired level of doneness. It is always a good idea to use a meat thermometer to ensure that the roast reaches the desired internal temperature, which is typically around 145°F for medium-rare to 160°F for medium.

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The linear relationship between time and distance can be considered proportional. The constant of proportionality in this case is 4.

In a proportional relationship, the ratio between the two quantities remains constant. Here, as time increases by 2 hours, the distance also increases by 8 miles. Let's calculate the ratio of distance to time for each pair of values:

For the first pair (2 hours, 8 miles):

Ratio = distance / time = 8 miles / 2 hours = 4 miles/hour

For the second pair (4 hours, 16 miles):

Ratio = distance / time = 16 miles / 4 hours = 4 miles/hour

For the third pair (6 hours, 24 miles):

Ratio = distance / time = 24 miles / 6 hours = 4 miles/hour

For the fourth pair (8 hours, 32 miles):

Ratio = distance / time = 32 miles / 8 hours = 4 miles/hour

As we can see, the ratio of distance to time remains constant at 4 miles per hour for all the pairs. This indicates a proportional relationship between time and distance.

Therefore, the linear relationship is also proportional, and the constant of proportionality is 4.

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The inequality that represents the number of hours, h, Mary could work in one weekend is: 8 ≤ h ≤ 14

Let's start by defining some variables:

We know that Mary is paid $12 per hour, so we can write an equation for her earnings based on the number of hours worked:

E = 12h

We also know that Mary's earnings can vary by $36, so we can write an inequality for her average earnings:

132 - 36 ≤ E ≤ 132 + 36

Simplifying this inequality, we get:

96 ≤ E ≤ 168

Substituting the equation for E, we get:

96 ≤ 12h ≤ 168

Dividing all parts of the inequality by 12, we get:

8 ≤ h ≤ 14

Hence, the inequality that represents the number of hours, is: 8 ≤ h ≤ 14

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The probability of selecting a defective bulb is 0.16.

Given: 8 Bulbs are defective out of 50 bulbs. To find the probability that a randomly selected item is defective.

What is probability?

Probability shows the possibility of how likely an event is happening to occur out of all the possibilities.

Let’s solve the problem:

Total number of video recorders: 50

The sample space n(S) = 50

Number of defective bulbs: 8

Let E be the event of selecting a defective bulb.

Then n(E) = 8

Therefore, the probability of selecting a defective bulb: Number of defective bulbs / Total number of bulbs

=> n(E) / n(S)

=> 8 / 50

=> 0.16

Hence the probability of selecting a defective bulb is 0.16.

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Answer:

the third one

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

The other leg is equal to 6.24 units.

Step-by-step explanation:

Using the Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

However we need to find b:

\(c^2-a^2=b^2\)

Substitute:

\(8^2-5^2=b^2\)

\(64-25=b^2\)

\(b^2=39\)

Find the square root:

\(\sqrt{39}=6.24\)

The other leg is equal to 6.24 units.

The repeated measures studies require fewer subjects than matched subjects studies with the same number of outcomes is that repeated measures designs reduce intersubject variability.

In repeated measures studies, each participant is measured multiple times under different conditions or treatments.

Whereas, In a matched-subjects study, each participant in the treatment group is compared to participants in the control group.

Intersubject variability can be large, and differences between treatment and control groups may be attributed to differences in these individual characteristics.

However, in a repeated-measures design, each participant served as its own control, reducing inter-subject variability.

This makes it easier to recognize differences in treatment conditions and can increase effect sizes.

Therefore, a repeated measures study may require fewer subjects to achieve the same statistical power as a matched subjects study with the same number of outcomes.

However, it is important to note that repeated measures designs may have their own limitations:  Potential Order Effect or Practice Effect.

These limitations should be carefully considered when designing a study, and an appropriate design should be chosen based on the research question and the nature of the data.

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Answer:

Square root of 48

Step-by-step explanation:

The cube root of 348 is ~7.03, but the square root of 48 is ~6.9. Making the square root of 48 smaller.

Using the probability, the smallest number of stations required to be at least 99% certain is 4 and the expected number of stations that will detect an enemy plane is 4.55.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a statement being true.

For each station, there are two two possible outcomes. Either they detected the enemy plane, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X=x)=C_{n,x}.p^x.(1-p)^{n-x}\)

In which  is the number of different combinatios of x objects from a set of n elements, given by the following formula.

\(C_{n,x}=\frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

In this problem, we have that:

The probability that a single radar station will detect an enemy plane is

n = 0.65. This means that .

(a) This is the value of n for which , P(X = 0) ≤ 0.02

n = 1.

P(X = 0) = C₁,₀ (0.65)⁰.(0.35)¹ = 0.35

n = 2

P(X = 0) = C₂,₀ (0.65)⁰.(0.35)² = 0.1225

n = 3

P(X = 0) = C₃,₀ (0.65)⁰.(0.35)³ = 0.0429

n = 4

P(X = 0) = C₄,₀ (0.65)⁰.(0.35)⁴ = 0.015

We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

(b) The expected number of successes of a binomial variable is given by:

E(x) = np

So when n = 7

E(x) = 7 x (0.65) = 4.55

If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

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We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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Based on the given probabilities, we can show that P(E ∪ F) ≥ 0.7 and P(E ∩ F) ≥ 0.2.

Let's start by understanding the concepts of union and intersection of events. The union of two events E and F, denoted as E ∪ F, represents the event that either E or F (or both) occur. The intersection of E and F, denoted as E ∩ F, represents the event that both E and F occur simultaneously.

Given that P(E) = 0.7 and P(F) = 0.5, we want to prove that P(E ∪ F) ≥ 0.7 and P(E ∩ F) ≥ 0.2.

To prove P(E ∪ F) ≥ 0.7, we can use the fact that the probability of a union of events is always greater than or equal to the probability of each individual event. Since E ∪ F includes both E and F, the probability of E ∪ F must be at least as large as the probability of each event separately. Therefore, P(E ∪ F) ≥ P(E) = 0.7.

To prove P(E ∩ F) ≥ 0.2, we can again use the fact that the probability of an intersection of events is always less than or equal to the probability of each individual event. Since E ∩ F represents the event where both E and F occur, its probability must be less than or equal to the probability of each event separately. Therefore, P(E ∩ F) ≤ P(E) = 0.7.

However, since P(E) = 0.7 and P(E ∩ F) is a part of E, it follows that P(E ∩ F) ≥ 0.2.

In conclusion, based on the given probabilities, we have shown that P(E ∪ F) ≥ 0.7 and P(E ∩ F) ≥ 0.2, as required.

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Answer:

Complementary angles will add up to 90°. Supplementary angles will add up to 180°. For example, the answer to the first question would be complementary = 70° and supplementary = 160°.

Step-by-step explanation:

To prove the converse of the Vertical Angles Theorem, we need to show that if angles LDBC and LABE are congruent and points D, B, and E are on opposite sides of line AB, then they must be collinear.

Given: ∠LDBC ≅ ∠LABE

To Prove: D, B, and E are collinear

Proof:

1. Assume that points D, B, and E are not collinear.

2. Let BD intersect AE at point X.

3. Since D, B, and E are not collinear, then X is a point on line AB but not on line DE.

4. Consider triangle XDE and triangle XAB.

5. By the Alternate Interior Angles Theorem, ∠XAB ≅ ∠XDE (corresponding angles formed by transversal AB).

6. Since ∠LDBC ≅ ∠LABE (given), we have ∠LDBC ≅ ∠XAB and ∠LABE ≅ ∠XDE.

7. Therefore, ∠LDBC ≅ ∠XAB ≅ ∠XDE ≅ ∠LABE.

8. This implies that ∠XAB and ∠XDE are congruent vertical angles.

9. However, since X is not on line DE, this contradicts the Vertical Angles Theorem, which states that vertical angles are congruent.

10. Therefore, our assumption that D, B, and E are not collinear must be false.

11. Thus, D, B, and E must be collinear. Therefore, the converse of the Vertical Angles Theorem is proven, and we can conclude that if ∠LDBC ≅ ∠LABE and D, B, and E are on opposite sides of line AB, then D, B, and E are collinear.

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The measure of angle EBF is 40 degrees

The complete question is added at the end of this solution

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

EBF = 6x + 4

CBF = 7x - 2

Also from the question, we understand that the measures of angle EBF and the measure of angle CBF are congruent

This can be represented mathematically as follows

EBF = CBF

Substitute the known values in the above equation, so, we have the following representation

6x + 4 = 7x - 2

Multiply through by 1

6x + 4 = 7x - 2

Collect the like terms

7x - 6x = 4 + 2

Evaluate the like terms

x = 6

Recall that

EBF = 6x + 4

Substitute the known values in the above equation, so, we have the following representation

EBF = 6 x 6 + 4

Evaluate

EBF = 40

Hence, the measure is 40 degrees

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Complete question

If the measures of angle EBF and the measure of angle CBF are congruent and EBF = 6x+4 and CBF = 7x-2 find EBF

Number of clients who do not play either the piano or the guitar is 22

To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.

Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments

Substituting the given values, we get

|A ∪ B| = 46 + 58 - 17

|A ∪ B| = 87

Therefore, the number of clients who do not play either instrument is:

109 - 87 = 22

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The type of diagram used to graphically show the relationship between two numerical variables is called a scatter plot.

A scatter plot is a visual representation of data points plotted on a graph, with one variable represented on the x-axis and the other variable represented on the y-axis.

Each data point on the plot corresponds to a pair of values from the two variables being analyzed. The position of each point on the graph indicates the values of both variables, allowing us to examine the relationship between them.

The main purpose of a scatter plot is to visualize the correlation or relationship between the two variables. The pattern formed by the data points on the plot can indicate the direction, strength, and nature of the relationship.

For example, if the points on the scatter plot tend to form a linear pattern, it suggests a linear relationship between the variables. On the other hand, if the points are scattered randomly with no clear pattern, it indicates a weak or no relationship between the variables.

Scatter plots are commonly used in various fields, including statistics, data analysis, and scientific research. They provide a visual way to explore and interpret relationships between variables, identify outliers, detect trends, and assess the strength and direction of associations.

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Answer:

16 cubic units

Step-by-step explanation:

\(\displaystyle V=\int^b_aA(x)\,dx\\\\V=\int^6_2(\sqrt{x})^2\,dx\\\\V=\int^6_2x\,dx\\\\V=\frac{1}{2}x^2\biggr|^6_2\\\\V=\frac{1}{2}(6)^2-\frac{1}{2}(2)^2\\\\V=\frac{1}{2}(36)-\frac{1}{2}(4)\\\\V=18-2\\\\V=16\)

A(x) represents the area of the cross-section, so in this case, we square \(\sqrt{x}-0\) which is just \(\sqrt{x}\)

Answer:

Step-by-step explanation:

z - some integer

then the consecutive integer would be:

z+1,  (or z-1)

the sum is 69 so:

z + z+1 = 96

2z = 68

z = 34

z+1 = 34 + 1 = 35

(or:

z + z-1 = 69

2z = 70

z = 35

z-1 = 35 - 1 = 34)

Answer:

√−100 = 10i

Step-by-step explanation:

The square root of negative 100 can be dissected step by step. The square root of 100 is 10 however there is no such thing as square root of something negative, thus the imaginary notion is applied. square root of -1 is equal to i .Hence the answer to this problem is 10 i.

Answer:

g³ - 24g - 96 = 0

Step-by-step explanation:

g³ = 24(g + 4)

g³ = 24g + 96

g³ - 24g - 96 = 0