Can you check if all these answers are correct?
Question 1: The side length c of the triangle is equal to: c 2 =a 2 +b 2 −2abcosC where a and b are the other two side lengths of the triangle, and C is the angle opposite side c. To solve for c, you can plug in the values of a, b, and C into the formula and solve for c. For example, if a=3, b=4, and C=60 ∘ , then you would plug in these values into the formula and solve for c as follows: c 2 =3 2 +4 2 −2⋅3⋅4cos60 ∘ c 2 =25 c= 25 ​ =5 Therefore, the side length c of the triangle is equal to 5. Question 2: The angle C of the triangle is equal to: cosC= 2ab a 2 +b 2 −c 2 ​ where a, b, and c are the other two side lengths of the triangle. To solve for C, you can plug in the values of a, b, and c into the formula and solve for C. For example, if a=3, b=4, and c=5, then you would plug these values into the formula and solve for C as follows: cosC= 2⋅3⋅4 3 2 +4 2 −5 2 ​ =− 4 1 ​ C=cos −1 (− 4 1 ​ )≈109.47 ∘ Therefore, the angle C of the triangle is approximately 109.47 degrees. Question 3: The area of the triangle is equal to A= 2 1 ​ absinC where a and b are the other two side lengths of the triangle, and C is the angle opposite side c. To solve for A, you can plug in the values of a, b, and C into the formula and solve for A. For example, if a=3, b=4, and C=60 ∘ , then you would plug in these values into the formula and solve for A as follows: A= 2 1 ​ ⋅3⋅4sin60 ∘ =6 3 ​ Therefore, the area of the triangle is equal to 6 3 ​ . Question 4: The perimeter of the triangle is equal to: P=a+b+c where a, b, and c are the three side lengths of the triangle. To solve for P, you can simply add up the values of a, b, and c. For example, if a=3, b=4, and c=5, then you would add up these values to get P=12. Therefore, the perimeter of the triangle is equal to 12. Question 5: The centroid of the triangle is located at a point that is: One-third of the way from each vertex to the opposite side. Equidistant from all three vertices. On the medians of the triangle. To find the centroid of the triangle, you can use the following formula: G=( 3 a+b+c ​ , 3 a+b+c ​ , 3 a+b+c ​ ) where (a,b,c) are the coordinates of the three vertices of the triangle.

Answer:

5 cases

10 additional units

Step-by-step explanation:

Given that:

Total number of units needed = 60 units

Total number of units per case = 14

Hence, the total number of cases required will

be: Number of units needed / number of units per

case

Number of cases required = 60/14 = 4.285 (this be up to 60 units)

means that 5 cases are required as 4 cases won't

With 5 cases, we have exceeded the required units needed:

Additional units will be: (145)-60

Additional units = 70 - 60 = 10 units

Step-by-step explanation:

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The observation table in Annexure A records the minimum and maximum temperature in a community for 30 days.

To collect data on the observation table in Annexure A for 30 days of minimum and maximum temperature in your community, follow these steps:
Obtain a reliable source for temperature data: You can use local weather stations, online weather platforms, or mobile apps that provide accurate and up-to-date temperature information for your community.
Prepare the observation table:

Create a table in Annexure A with columns for Date, Minimum Temperature, and Maximum Temperature.

Make sure there are 30 rows for each day of observation.
Record daily temperatures:

For each day, note down the date and the minimum and maximum temperatures in their respective columns.

Be consistent with the time of day you record these temperatures, ideally early morning for the minimum and late afternoon for the maximum.

Repeat the process:

Continue recording daily temperatures for a total of 30 days.
Review and analyze the data:

Once the 30-day period is complete, you can analyze the data to observe trends or patterns in temperature variation.
Remember to be consistent in your data collection to ensure accurate and reliable results.

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Answer:

false ,true ,true

Step-by-step explanation:

The amount that was loaned are $15,500 at 4% annual interest and $4000 at 14% annual interest.

Given that,

A bank loaned out $19,500.

Amount loaned at 4% annual interest = x

Amount loaned at 14% annual interest = 19,500 - x

Total interest earned for both loans = $1,180

0.04x + 0.14 (19,500 - x) = 1180

0.04x + 2730 - 0.14x = 1180

-0.1x = -1550

x = 15,500

Amount loaned at 4% annual interest = x = $15,500

Amount loaned at 14% annual interest = 19,500 - x = $4000

Hence the loaned amount are $15,500 and $4000.

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Answer:

840, 14

Step-by-step explanation:

(a.) In order to solve a, we first need to solve b since we're essentially dealing with proportions.

(b.) Our proportion to solve for miles per gallon is 350 miles / 25 gallons = x miles / 1 gallon where we solve for x:

[tex]\frac{350}{25}=\frac{x}{1}\\ \\ 25x=350\\\\x=14[/tex]

Thus, the gas mileage is 14 miles per gallon

(a.) Now, we can solve for part a. using the proportion x miles / 60 gallons = 14 miles / 1 gallon:

[tex]\frac{x}{60}=\frac{14}{1}\\ \\ x=840[/tex]

Answer: 12 hours (noon)

Step-by-step explanation:

**For simplicity's sake, we'll use military time (Zulu time).**

- It is 00:00 in North America.

- If one full rotation means a day has passed, or more specifically, that 24 hours have passed, then that means the Earth has rotated 360°.

- So if 360° = 24 hrs, then 180°, being 360/2, or half a rotation, will be 24/2 hrs, or 12 hours.

- So the time is now 12:00, or noon.

Answer:

Step-by-step explanation

The first step is to add up all of the numbers to get the total budget.

Total Budget = 858 + 429 + 924 + 198 + 363 + 528 =3,300

Then to find the percentage for a certain category it is:

[tex]\frac{Budget Category}{Budget Total} times 100%[/tex]

So, 429 / 3300 x 100% = 0.13 x 100% = 13% Car Expense

Answer:

Step-by-step explanation

The first step is to add up all of the numbers to get the total budget.

Total Budget = 858 + 429 + 924 + 198 + 363 + 528 =3,300

Then to find the percentage for a certain category it is:

[tex]\frac{Budget Category}{Budget Total} times 100%[/tex]

So, 429 / 3300 x 100% = 0.13 x 100% = 13% Car Expense

The equation of the line that passes through  (3,-2) and is (a) parallel to the line is y = 3x - 11 and (b) perpendicular to the line is y = - 1 / 3 x - 2.

The equation of a line can be represented in different form such as slope intercept form.

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Hence, let's find the equation of a line passing through (3, -2) and is parallel to the line shown.

Parallel line have the same slope.

Hence,

m = -4 + 1 / 1 - 2

m = -3 / -1

m = 3

Therefore,

y = 3x + b

-2 = 3(3) + b

b = -2 - 9

b = -11

The equation is y = 3x - 11

Hence, let's find the equation of a line passing through (3, -2) and is perpendicular to the line shown.

The slopes of perpendicular lines are negative reciprocals of one another.

hence,

m = - 1 / 3

Therefore,

y = - 1 / 3 x + b

-2 = - 1 / 3(3) + b

b = -2 + 1

b = -2

Therefore, the equation is y = - 1 / 3 x - 2.

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Step-by-step explanation:

30 % of 25 is

                 .30  *  25 = ~ 8 left handed   ( rounded)

Answer:

Step-by-step explanation:

in question no. 17

base=x

perpendicular=9

hipotanus=15

by applying pythagorus

(x)² + (9)² = (15)²

x=√(15)²-(9)²

x= √225-81

x=√144 = 12

now area of triangle = 1/2 ×base×height

= 1/2 × 12 × 9 = 54

area of figure 17 = 54 × 2 = 108

Answer:

12 minutes

Step-by-step explanation:

200/17

= 11.7

round up

12 minutes

People who made more money generally completed more years of college than those who made less money . So correct option is D.

A graph is a visual representation of data or information that uses a set of points or nodes, connected by lines or curves, to convey relationships or patterns. Graphs can be used to illustrate data in a way that is easy to understand and analyze.

There are several types of graphs, each with its own strengths and weaknesses depending on the type of data being presented. Some common types of graphs include:

Line graph: A line graph displays data as a series of points connected by a line, and is commonly used to show trends or changes over time.

Bar graph: A bar graph displays data using rectangular bars, with the length or height of each bar representing the quantity of data being measured. Bar graphs are useful for comparing different values or categories.

Pie chart: A pie chart shows data as a circular graph, with each slice representing a portion of the whole. Pie charts are commonly used to show proportions or percentages.

Scatter plot: A scatter plot displays data as a set of points on a two-dimensional plane, with each point representing the values of two variables. Scatter plots are useful for identifying patterns or trends in the relationship between two variables.

Histogram: A histogram displays data as a set of bars, with the height of each bar representing the frequency or number of occurrences of data within a certain range or interval.

Graphs can be an effective way to communicate complex information in a simple and easy-to-understand way. They are commonly used in fields such as science, economics, and social sciences, as well as in everyday life to display data and make comparisons.

People who made more money generally completed more years of college than those who made less money .

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The probability that  a random sample of 400 registered voters from this town will have a Maureen Webster under the age of 49 is about 0.0951, or about 9.51%.

Probability is simply how likely something is to happen. When we are uncertain about the outcome of an event, we can talk about the probability of certain outcomes—how likely they are.

We can use the binomial normal approximation to solve this problem because we have a large sample (400) and the probability (p) of preferring Maureen Webster is not too close to 0 or 1.  First, we need to find the mean and standard deviation of the sample proportion, which is given by:

mean = p = 0.53

standard deviation = square (p*(1-p)/n) = square (0.53*0.47/400) = 0.0305

Next, we need to find the z-score corresponding to the sample proportion of 0.49 (which is the "less than 49 percent" threshold). It is given by:

z = (x - mean) / standard deviation = (0.49 - 0.53) / 0.0305 = -1.31

We can now use a standard normal distribution table or calculator to determine the probability that the standard normal variable is less than -1.31. This probability is approximately 0.0951.

Therefore,  we can use the binomial normal approximation to solve this problem because we have a large sample (400) and the probability (p) of preferring Maureen Webster is not too close to 0 or 1.

First, we need to find the mean and standard deviation of the sample proportion, which is given by:

mean = p = 0.53

standard deviation = square (p*(1-p)/n) = square (0.53*0.47/400) = 0.0305

Next, we need to find the z-score corresponding to the sample proportion of 0.49 (which is the "less than 49 percent" threshold). It is given by:

z = (x - mean) / standard deviation = (0.49 - 0.53) / 0.0305 = -1.31

We can now use a standard normal distribution table or calculator to determine the probability that the standard normal variable is less than -1.31. This probability is approximately 0.0951.

Therefore, the probability that  a random sample of 400 registered voters from this town is under the age of 49 Maureen Webster is about 0.0951, or about 9.51%.

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Answer:

In Mathematics, a pattern is a repeated arrangement of numbers, shapes, colours and so on. The Pattern can be related to any type of event or object. If the set of numbers are related to each other in a specific rule, then the rule or manner is called a pattern. Sometimes, patterns are also known as a sequence.

Answer:

  A.  The system has a single solution. The solution set is (x, y) = (-3, 2).

Step-by-step explanation:

You want the solution to the system of equations ...

These standard form equations are different, so they will have one solution.

That solution can be found by adding the equations, eliminating the y-variable.

  (x +y) +(x -y) = (-1) +(-5)

  2x = -6

  x = -3

  y = x +5 = -3 +5 = 2 . . . . . . from the second equation

The solution is (x, y) = (-3, 2).

The null hypothesis states that there is no distinction between the mean shelf life of the rechargeable batteries marketed by Power+ and Electro. Whereas, the alternative suggestion maintains that the mean duration of the batteries sold by Power+ stands greater than that of Electro.

The test statistic is 2.24

Utilizing a t-distribution with degrees of freedom akin to the entire sample size minus two (df = n1 + n2 - 2 = 104) alongside the derived test statistic, the p-value can be accessed via calculator or software as 0.014.

As the figure procured from the p-value is lower than the significance level α = 0.05, we invalidate the null positing. The evidence warrants corroborating the allegation that the rechargeable batteries proffered by Power+ remain usable for longer than those provided by Electro.

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n = 2, in which case D2 is just the cyclic group of order 2, which is commutative.

n is a multiple of 4, in which case Dn is a product of two cyclic groups of order n/2, which are commutative.

A cyclic group is a mathematical group that is generated by a single element, which is called a generator. In other words, a cyclic group is a group in which all elements can be obtained by repeatedly applying the group operation to a single element.

Formally, a cyclic group is defined as a group G that has an element g such that every element of G can be written as a power of g. That is, for every element x in G, there exists an integer n such that x = gⁿ, where gⁿ denotes the product of g with itself n times.

The Dihedral group, denoted by Dn, is a group of symmetries of a regular n-gon. It has 2n elements and is not commutative in general, except for some special cases.

Group Dn has a presentation:

Dn = ⟨r, s | rⁿ = s² = (sr)² = e⟩

where r represents a clockwise rotation of 2π/n radians and s represents a reflection about a line through the center of the n-gon.

If n is odd, then the group Dn is not commutative, because rs is not equal to sr. This can be seen by considering the effect of the two operations on the vertices of the n-gon.

However, if n is even, then the group Dn is commutative in certain cases. Specifically, Dn is commutative if and only if the two generators r and s commute, i.e., if rs = sr. This happens when either:

n = 2, in which case D2 is just the cyclic group of order 2, which is commutative.

n is a multiple of 4, in which case Dn is a product of two cyclic groups of order n/2, which are commutative.

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No, Savannah is incorrect. Doubling the length, width, and height of a right rectangular prism will not double its surface area.

Surface area is the total area of an object's exposed faces, including any external surface area. It is a measure of the size of a surface and is usually expressed in square units such as square meters or square centimeters. Surface area is a two-dimensional measurement, since it only takes into account the area of a surface, and not its thickness or volume.

The surface area of a right rectangular prism is calculated by multiplying the length by the width and then multiplying that number by two and adding the two products together.

For example, the surface area of a right rectangular prism with a length of 15 cm, a width of 10 cm, and a height of 5 cm is calculated as follows:

Surface area = (15 cm * 10 cm) + (15 cm * 5 cm) = 150 cm2 + 75 cm2 = 225 cm2

Doubling the length, width, and height of this right rectangular prism would give us a prism with a length of 30 cm, a width of 20 cm, and a height of 10 cm. The surface area of this new prism would be calculated as follows:

Surface area = (30 cm * 20 cm) + (30 cm * 10 cm) = 600 cm2 + 300 cm2 = 900 cm2

As you can see, doubling the length, width, and height of the right rectangular prism does not double its surface area - the surface area has increased by four times (900 cm2/225 cm2 = 4).

In conclusion, doubling the length, width, and height of a right rectangular prism does not double its surface area; rather, it increases the surface area by a factor of four.

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No, Savannah is incorrect. Doubling the length, width, and height of a right rectangular prism will not double its surface area.

Surface area is the total area of an object's exposed faces, including any external surface area. It is a measure of the size of a surface and is usually expressed in square units such as square meters or square centimeters. Surface area is a two-dimensional measurement, since it only takes into account the area of a surface, and not its thickness or volume.

The surface area of a right rectangular prism is calculated by multiplying the length by the width and then multiplying that number by two and adding the two products together.

For example, the surface area of a right rectangular prism with a length of 15 cm, a width of 10 cm, and a height of 5 cm is calculated as follows:

Surface area = (15 cm * 10 cm) + (15 cm * 5 cm) = 150 cm2 + 75 cm2 = 225 cm2

Doubling the length, width, and height of this right rectangular prism would give us a prism with a length of 30 cm, a width of 20 cm, and a height of 10 cm. The surface area of this new prism would be calculated as follows:

Surface area = (30 cm * 20 cm) + (30 cm * 10 cm) = 600 cm2 + 300 cm2 = 900 cm2

As you can see, doubling the length, width, and height of the right rectangular prism does not double its surface area - the surface area has increased by four times (900 cm2/225 cm2 = 4).

In conclusion, doubling the length, width, and height of a right rectangular prism does not double its surface area; rather, it increases the surface area by a factor of four.

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The correct answer is "not enough information to prove any parallel lines."

If two lines in a two-dimensional plane are parallel, then the corresponding angles formed by a transversal (a line that intersects both lines) are congruent (i.e., they have the same measure).

Additionally, the alternate interior angles (angles that are on opposite sides of the transversal and inside the pair of parallel lines), as well as the corresponding angles (angles that are in the same position relative to the transversal on the two parallel lines), are also congruent.

In the given diagram, line k is parallel to m, while line a is also parallel to line b but forming a transverse line to line k and line m. Also line k and line m form a transverse line to lines a and b.

So we can conclude that not enough information to prove any parallel lines.

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The actual distance between the two cities is equal to 288 miles.

In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the side lengths of the image by the side lengths of the pre-image:

Scale factor = length of image (new figure)/length of pre-image (actual figure).

Scale:

0.25 inch = 24 miles

0.25/24 = New distance/Actual distance

0.25/24 = 3/Actual distance

Actual distance = (24 × 3)/0.25

Actual distance = 288 miles.

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Therefore, the value of k could be either 6 or 24 if the distance between the line x+y-5 and 3x+3y-k=0 is √18.

An equation is a statement that two mathematical expressions are equal. It contains an equal sign and can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to solve problems, find unknown values, and model real-world situations.

Here,

To find the distance between the line x+y-5 and 3x+3y-k=0, we need to find the perpendicular distance between them.

The line x+y-5 can be written in slope-intercept form as y = -x + 5, and its slope is -1.

The line 3x+3y-k=0 can be rewritten as y = -x + k/3, and its slope is also -1.

Since the slopes of the two lines are the same, they are parallel. Therefore, the perpendicular distance between them is the distance between any point on one line and the other line.

Let's choose a point on the line x+y-5. We can choose (1,4) since it lies on the line. The distance between this point and the line 3x+3y-k=0 is:

|3(1) + 3(4) - k|/√(3²+3²)

Simplifying this, we get:

|15 - k|/3√2 = √18

Multiplying both sides by 3√2, we get:

|15 - k| = 3√2 * √18

= 9

This gives us two possible values for k:

15 - k = 9, which gives k = 6

or

k - 15 = 9, which gives k = 24

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Answer:

Pull terms out from under the radical, assuming positive real numbers.

0

Step-by-step explanation:

Step-by-step explanation:

so, overall, 63% will grow.

that means, every seed has a 63% chance to grow. in other words, the probabilty to grow is 0.63 (as 63% means 63 out of 100 = 0.63).

and a chance of

1 - 0.63 = 0.37

to not grow.

fewer than 8 out of 9 seeds means not 8 and not 9.

it is

1 - P(8) - P(9)

with P(x) means the probability that exactly x seeds out of the 9 grow/germinate.

the chance for a group of exactly 8 out of 9 seeds to grow is then the probabilty for 8 to grow and 1 not to grow :

0.63⁸ × 0.37 = 0.009181764...

but these are 8 seeds out of 9.

and we calculated the probability for only one possible grouping.

how many groups of 8 can we build out of 9 ?

as the sequence does not matter, and we cannot have repetitions (every seed can only count as 1), we have combinations

C(9, 8) = 9! / (8! × (9-8)!) = 9!/8! = 9

so, the total probability P(8) for exactly 8 seeds out of 9 to grow/germinate is

9 × 0.63⁸ × 0.37 = 9 × 0.009181764... = 0.082635875... ≈

≈ 0.083

now, the chance for a group of exactly 9 out of 9 seeds to grow is then the probabilty P(9) for all 9 to grow :

0.63⁹ = 0.015633814... ≈ 0.016

the probabilty that fewer than 8 out of the 9 will grow/germinate is

1 - 0.082635875... - 0.015633814... = 0.901730311... ≈

≈ 0.902

If the graph of f(x) is changed to [tex]f(x) = 4(\frac{5}{7} )^{x}-2[/tex], the graph of f(x) would be translated down by 2 units.

An equation of the new horizontal asymptote is y = -2.

In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In this scenario, we can logically deduce that the graph of the parent function f(x) was translated or shifted downward (vertically) by 2 units.

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Answer:

Step-by-step explanation:

Applying the Pythagorean theorem, the exact values of x are:

1. x = 13      2. x = 4      3. x = 6     4. x = 8   5. x = 15    6. x = √7

If a and b are smaller sides (legs) of a right triangle, and c is the longest side (hypotenuse), the Pythagorean theorem states that:

c = √(a² + b²).

Apply the Pythagorean theorem to find the exact value of x:

1. x = √(12² + 5²)

x = 13

2. x = √(5² - 3²)

x = 4

3. x = √(10² - 8²)

x = 6

4. x = √(17² - 15²)

x = 8

5. x = √(12² + 9²)

x = 15

6. x = √(4² - 3²)

x = √7

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The value of the variable x for the arc angle CD and DE is -1and the arc angle FCE = 230°. Also x = 5 for the arc angles RS, ST, TU, and UR, and the arc angle RS = 70°.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

Thus:

17). 2[(x + 131) + (x + 51)]° = 360°

2x + 182° = 180°

2x = 180° - 182°

2x = -2

x = -1

arc angle CD = -1 + 51 = 50°

arc angle DE = -1 + 131 = 130°

arc angle FCE = 2CD + DE

arc angle FCE = 2(50) + 130 = 230°

18). 92 + 27x + (11x + 8) + 15x - 5 = 360°

53x + 95° = 360°

53x = 360° - 95°

53x = 265

x = 5

arc angle RS = 15(5) - 5 = 70°

Therefore, the value of the variable x for the arc angle CD and DE is -1and the arc angle FCE = 230°. Also x = 5 for the arc angles RS, ST, TU, and UR, and the arc angle RS = 70°.

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