Consider points A(1,3) , B(4,-2) , and C(5,2). Let D be the midpoint of AB. How can you prove that C lies on the perpendicular bisector of AB? Complete each statement.

If triangle abc is an isosceles triangle with side lengths of 25, 25 and 48 centimeters, the area of triangle ABC is 600√(3) square centimeters.

To find the area of an isosceles triangle, we need to first determine the length of the altitude or height that is perpendicular to the base of the triangle.

In an isosceles triangle, the altitude divides the base into two equal parts, creating two right triangles. Using the Pythagorean theorem, we can find the length of the altitude.

Let x be the length of the altitude. Then, we have:

(25/2)^2 + x^2 = 25^2

625/4 + x^2 = 625

x^2 = 625 - 625/4

x^2 = 468.75

x = √(468.75)

x = 5√(75)

Now that we know the length of the altitude, we can find the area of the triangle using the formula:

Area = (1/2) x base x height

In this case, the base of the triangle is 48 cm and the height is 5sqrt(75) cm. Therefore, we have:

Area = (1/2) x 48 x 5√(75)

Area = 120√(75)

Area = 120 x 5√(3)

Area = 600√(3) cm^2

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Answer:

x=6

Step-by-step explanation:

Because the angles will be equal we set the equations to be equal to each other

4x+19=6x+7

12=2x

x=6

Answer: Beth Blauer

Step-by-step explanation:

In response to the stated question, we may state that According to the inequality facts provided, the only choice that must be true is B, because g must be bigger than 1.5. As a result, the solution is: B. g > 1.5

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.

We know that h > 3 and h - 2g = 0.

When we plug h = 2g into the first inequality, we get:

2g > 3

g > 1.5

As a result, we know that g must be bigger than 1.5, ruling out alternatives C and D.

Option A is not certainly true since we don't know if the value of g is bigger than 2.5.

Option E is also not certainly true, because we only know that g is more than 1.5, but not if it is bigger than 2.

According to the facts provided, the only choice that must be true is B, because g must be bigger than 1.5. As a result, the solution is:

B. g > 1.5

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The height of the building in the scale drawing will be 5 inches.

The scale ratio must be used to determine the height of the building in the scale drawing.

The scale ratio is:

1 inch = 170 feet

We can devise a ratio:

1 inch / 170 feet = x inches / 850 feet

In the scale drawing, x represents the height of the building in inches.

To find x, we can cross-multiply and simplify:

1 inch * 850 feet = 170 feet * x inches

850 inches = 170 feet * x

Dividing both sides by 170 yields:

x = 850 inches / 170 = 5 inches

As a result, the building's height will be 5 inches in the scale drawing.

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The required value of TV is 2 units.

A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.

We have given that;

TW = y²

WV = 2y − 1

We know that in parallelogram

TW = WV

y² = 2y − 1

y² - 2y + 1 = 0

y² - y - y + 1 =0

y(y - 1)-1(y - 1) = 0

(y - 1)(y - 1) = 0

(y - 1)² = 0

y - 1 = 0

y = 1

So;

TV = TW + WV

TV = y² + 2y − 1

TV = 1² + 2(1) - 1

TV = 1 + 2 - 1

TV = 2 units

Thus, required value of TV is 2 units.

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In linear equation, 65.625% of the pupils travel by bus.

What is  linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

A) 1800 * 0.55 * 0.3 = 297 Girls.

B)  1800 * 0.45 * 0.7 = 567 boys

C)  Girl

      297/864 * 100%  = 34.375%

  boy -

       567 ÷ (297 + 567 ) * 100%  = 65.625%

         864 = 297 + 567

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In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.

Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.

Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:

P(accurate order) = 1246 / 1300 = 0.958 for McDonald's

P(accurate order) = 1020 / 1100 = 0.927 Taco Bell

P(accurate order) = 708 / 800 = 0.885 for Burger King

P(accurate order) = 940 / 1000 = 0.94 for Wendy's

P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929

As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

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So,

120% is the same as 1.2 or 6/5.  80% is the same as 0.8 or 4/5.

We are given the value of a, which is 12.

6/5 of a, or 1.2 times a, is equal to 4/5 of b, or 4/5 times b.

[tex]\dfrac{6}{5} (12)=\dfrac{4}{5} b[/tex]

Simplify.

[tex]\dfrac{72}{5} =\dfrac{4}{5} b[/tex]

Multiply both sides by 5/4.

[tex]\dfrac{72}{4} \ \text{or} \ 18=b[/tex]

Therefore, the sum of a and b is 12 + 18 = 30.

(a) Mean: 207.7

(b) Median: 207

(c) Mode: None

(d) Range: 198

(e) Variance: 3705.5

(f) Standard deviation: 60.72

(g) Coefficient of variation: 29.34

Answer:

To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.

F1 × F2 can be expanded using the distributive property:

F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3

= 36y^2 + 12y - 54y - 18

= 36y^2 - 42y - 18

Now we can subtract F3 from the result:

F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)

= 36y^2 - 42y - 18 + y + 8

= 36y^2 - 41y - 10

Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.

(please mark my answer as brainliest)

Answer:

Assuming that (gof)(5) means (g(f(5))):

(gof)(5) = g(f(5)) = g(3x + 7) = 5x + 2

Therefore, (gof)(5) = 5(3x + 7) + 2 = 15x + 17.

Answer:

Step-by-step explanation:

gfds5u4wsr5wj6wrs

The probability of one event given the known outcome of a (possibly) related event is known as conditional probability.

Conditional probability is the measure of the probability of an event occurring given that the another event will already occurred. It is denoted by P(A | B), which represents the probability of event A given that event B has occurred. The conditional probability of A given B can be calculated using the formula:

P(A | B)=P(A and B)/P(B)

where P(A and B) represents the probability of both events A and B occurring, and P(B) represents the probability of event B occurring.

For example, consider a deck of 52 playing cards. The probability of drawing a king from the deck is 4/52, or 1/13. If one card is drawn from the deck and it is revealed to be a heart, then the probability of drawing a king from the remaining cards in the deck that are not hearts is:

P(king | heart) = P(king and heart) / P(heart)

P(king and heart) = 1/52 (there is only one king of hearts in the deck)

P(heart) = 13/52 (there are 13 hearts in the deck)

P(king | heart) = (1/52) / (13/52) = 1/13

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Answer:

Step-by-step explanation:

To solve this problem, we will use the properties of the normal distribution and standardize the given value using the formula:

z = (x - μ) / σ

where:

x = 4.6 inches (the given value)

μ = 5 inches (the mean)

σ = 0.5 inches (the standard deviation)

So we have:

z = (4.6 - 5) / 0.5

z = -0.8

Now we need to find the probability that the standardized value is less than -0.8. We can use a standard normal distribution table or a calculator to find this probability.

Using a standard normal distribution table, we can look up the probability for z = -0.8, which is 0.2119.

Therefore, the probability that a randomly chosen item is less than 4.6 inches long is 0.2119 or approximately 21.19%.

The angles for the given parallel lines are estimated.

m(∠DGF ) = 92; m(∠HGF ) = 88; m(∠AGD ) = 88; m(∠BDG ) = 92; m(∠BDC ) = 88; m(∠CDE ) = 92 ; m(∠EDG ) = 88.

A line that cuts over two parallel lines is referred to as a transversal line.

Each pair of internal angles located on the exact side of a transversal that meets two parallel lines is supplementary, or they add up to 180°.

The opposing angles created by the junction of two lines are known as vertical angles but rather vertically opposite angles.

m(∠AGH ) = m(∠BDG ) (corresponding angles)

3x +  2 = 2x + 32

x = 30

m(∠AGH ) = 3(30) +  2 = 92

m(∠BDG ) = 2(30) + 32 = 92

m(∠DGF ) = m(∠AGH ) = 92 (vertically opposite angles)

m(∠HGF ) = 180 - m(∠AGH ) = 180 - 92 = 88 (linear pair).

m(∠AGD ) = m(∠HGF ) = 88 (vertically opposite angles)

m(∠BDG ) = 92 (calculated earlier)

m(∠BDC ) = m(∠AGD ) =  88 (corresponding angles)

m(∠CDE ) = m(∠BDG ) = 92  (vertically opposite angles)

m(∠EDG ) = m(∠BDC ) =  88  (vertically opposite angles).

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The Tip cost for the meal is found as: $8.7975. The total cost of the meal is $67.4475.

'Percent' refers to a number that is 'out of 100. Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

At stores, online, in commercials, and in the media, you can see percentages practically anywhere. Understanding what percentages signify is a crucial skill that could help you save time as well as money and raise your employability.

Original cost of meal = $58.65

Tip cost = 15% of $58.65

Tip cost = 15*58.65 / 100

Tip cost = $8.7975

Total cost = Original cost of meal  + Tip cost

Total cost = $58.65 +  $8.7975

Total cost = $67.4475

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The data consists of 24 rows representing gender, admission status, and department for 4,526 applicants. The admission rate for men was 45%, for women was 30%, and the table of numbers is consistent with the given rates.

The data has a tabular structure with six rows corresponding to the six departments (A-F) and four columns representing the Gender, Admission status, Department, Count

The data is different from other datasets in that it provides information for each gender and admission status for each department separately. The 24 rows in the data set represent the different combinations of gender, admission status, and department.

The admission rate for all applicants is calculated by dividing the number of admitted applicants (1,755) by the total number of applicants (4,526), which gives an overall admission rate of approximately 0.387.

The admission rate for men is calculated by dividing the number of admitted men (1,493) by the total number of male applicants (3,356), which gives a male admission rate of approximately 0.445.

The admission rate for women is calculated by dividing the number of admitted women (1,262) by the total number of female applicants (1,670), which gives a female admission rate of approximately 0.301.

The table below summarizes the number of rejected and admitted applicants for each gender:

Gender Number Rejected    Number Admitted

Male          1863                 1493

Female         557                         1262

The numbers in the table are consistent with the given admission rates for men and women, as the admission rate for men is higher than that for women, and the number of male applicants is greater than the number of female applicants.

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_____The given question is incomplete, the complete question is given below:

Describe the structure of the data. Is it different than data you have examined before? Specifically, there are 24 rows in this data set, but the set provides information about 4,526 observations (the sum of the "count" column). Describe what each row represents. Each of the six departments (A-F) have four rows of data in this set corresponding to each of the following. 1st row Men who were admitted 9 . 2nd row Men who were not admitted . 3rd row Women who were admitted . 4th row Women who were not admitted . of the 4,526 applicants in this data set, 1,755 were admitted for an overall admission rate of approximately 39%. The admission rate for men was 45%, while the admission rate for women was 30%. Complete the following table. Gender Number Rejected Number Admitted 1198 Male 1493 ✓ Female 557 1278 Indicate how your numbers are consistent with these given admission rates for men and women. (Round your answers to four decimal places.)

Answer:

76(/783/)-468

Step-by-step explanation:

In linear equation, 28  pieces of cake did Mrs Devi buy.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.  

                                   Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Cost of M cake = $3.5

For every 3 M cakes she bought 7 B cakes.

Let 1 unit be 3 M cakes and 7 B cakes. 1 unit costs= 3(3.5) + 7(2.5)= $28

She bought $112 / $28 = 4 units of cakes.

Which means 12 M cakes and 28 B cakes.

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a. The slope of AB is  [tex]m = 1[/tex] and slope of BC is [tex]m = -4/7.[/tex]

b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.

c. The mid-point of Diagonal AC is  [tex](0, -1/2)[/tex]

A clοsed shape nοted fοr having sides with variοus widths and lengths is a quadrilateral. It is a clοsed, two-dimensional pοlygοn with fοur sides, fοur angles, and fοur vertices. Quadrilaterals include the trapezium, parallelοgram, rectangle, square, rhοmbus, and kite, amοng οthers.

a.

Slope is given by

[tex]A = (-2, 3) and B = (-5, 0)[/tex]

[tex]m = 1[/tex]

[tex]B = (-5, 0) and C = (2, -4)[/tex]

[tex]m = -4/7[/tex]

Thus, The slope of AB is m = 1 and slope of BC is [tex]m = -4/7[/tex]  .

b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.

c. Midpoint of a segment is given by the 2 divided by of sum x and and sum of y

Thus, Diagonal  [tex]A = (-2, 3)[/tex] and [tex]C = (2, -4)[/tex]

Midpoint  [tex]= ((-2 + 2), (3 + -4))[/tex]

[tex]= ((0), (-1))[/tex]

Now divide them by 2

[tex]= ((0/2), (-1/2))[/tex]

[tex]= (0, -1/2)[/tex]

Therefore, the mid-point of Diagonal [tex]AC is (0, -1/2)[/tex]

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The percentages of the area under curve are 50%, 68%, and 99.7%.

Assuming a standard normal distribution with mean m = 0 and standard deviation s = 1, the percentage of the area under the curve can be determined as follows

To the left of m: This is equivalent to finding the area to the left of the z-score corresponding to m = 0. This is 50%, as the normal distribution is symmetric around the mean.

Between m s and m 1 s: This is equivalent to finding the area between the z-scores corresponding to z = -1 and z = 1. Using a standard normal distribution table or calculator, this is approximately 68% (which is also known as the 68-95-99.7 rule).

Between m 3s and m 1 3s: This is equivalent to finding the area between the z-scores corresponding to z = -3 and z = 3. Using a standard normal distribution table or calculator, this is approximately 99.7% (which is also known as the 68-95-99.7 rule).

Therefore, the percentages of the area under the normal curve are: (a) 50%, (b) 68%, and (c) 99.7%.

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Answer:

60 degrees

Step-by-step explanation:

cos(x)=1/2

cos(x)=0.5

(x)=[tex]cos^-1[/tex] (0.5)

(x)=60

Answer:

[tex](x-4)^2+(y+1)^2=162[/tex]

Step-by-step explanation:

Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):

[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\[/tex]

Hence, the equation of the circle that meets these criteria is[tex](x-4)^2+(y+1)^2=162[/tex]

From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.

A line segment having a single endpoint and an infinite length in one direction is known as a ray. A ray's length cannot be determined.

There are two endpoints to a line segment. Every point on the line connecting these endpoints to one another is also included. The length of a line cannot be measured, but the length of a segment can.

An eternally long and thin line is a group of points that stretches in two opposite directions.

From the given figure we observe that,

1. Two line segments are LA and EP.

2. Two rays are EC and AH.

3. Two lines are b and AP.

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Answer:

Z-0.15Z

Step-by-step explanation:

multiply z by the decimal form of 15, but since it's decreased by z you need to include a way of subtracting the z

The algebraic expression for the given statement is 0.85Z

An algebraic expression is a mathematical expression that consists of variables, numbers and operations.

Given that, Z decreased by 15%, we need to convert it into an algebraic expression

Multiply z by the decimal form of 15, but since it's decreased by z we will  subtract z from that,

So,

= Z - 15% of Z

= Z - 0.15Z

= Z(1-0.15)

= 0.85Z

Hence, the algebraic expression for the given statement is 0.85Z

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The correct answer is (c) 6/7 times 6/7 equals 36/49.

The correct evaluation for the exponential expression 6/7 to the power of 2 is (c) 6/7 times 6/7 equals 36/49.

To evaluate this expression, you need to multiply 6/7 by itself 2 times (since the exponent is 2). This gives you:

(6/7) to the power of 2 = (6/7) x (6/7) = 36/49

Therefore, the correct answer is (c) 6/7 times 6/7 equals 36/49.

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From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.

A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.

The ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.

A line is a collection of points that extends in two opposing directions and is endlessly long and thin.

From the given figure we observe that,

1. Two line segments are LA and EP.

2. Two rays are EC and AH.

3. Two lines are b and AP.

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