In isosceles triangle ABC, AD is altitude .Prove that angle B = angle C

In the Logarithm prompt above, note that the value of In x when In x = e to the power -x is x = 1/e.

The above assertion is right because the definition of the natural logarithm denoted as In x or ln x, is that it is the inverse function of the exponential function, denoted as e to the power x or ex.

This means that if we have an equation of the form In x = ex, then we can find the value of x by simply taking the inverse of both sides of the equation.

So, if we take the inverse of both sides of the equation In x = ex, we get x = In (ex) = In e to the power x = 1/e.

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Answer:

9/10

Step-by-step explanation:

one blue and 9 green  = 10 marbles

P(green) = number of green / total

                 =9/10

The scatter plot that shows correlation with causation is (c)

A scatter plot is a type of graph that displays the relationship between two variables. The position of each point on the plot represents the value of both variables.

If there is a strong positive correlation between two variables, it means that as one variable increases, the other variable also tends to increase.

If there is a strong negative correlation, it means that as one variable increases, the other variable tends to decrease.

The scatter plot with the mst positive or negative correlation is c

This is the scatter plot that shows correlation with causation

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Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

The consumer price index of the raincoat by using the todays and the 1983 costs of raincoat is given by option b 151.

Todays cost of raincoat = $79.25

Cost of raincoat in 1983 = $52.48

Calculate the CPI (Consumer Price Index) in 1983,

Use the formula we have,

CPI = (Cost of the raincoat today / Cost of the raincoat in 1983) x 100

Plugging in the values given in the problem, we get,

⇒ CPI = ($79.25 / $52.48) x 100

⇒ CPI = 1.51009 x 100

⇒ CPI = 151.009

Rounding this to the nearest whole number gives a CPI of $151.

Therefore, the best answer to represent the consumer price index of the raincoat is equals to option  (b) 151.

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Answer:

108

Step-by-step explanation:

240 x 0.45 = 108

In order to find the percentage of something, turn the percentage into a decimal and multiply it by the number. For example 45% becomes 0.45. Then to find the answer you multiply it by 240, finding what 45% of 240 is.

Answer:

108

Step-by-step explanation:

First find 40% of 240 = 96

Then 5% of 240 = 12

Add both of them together

96 + 12 = 108

Answer:

it answer b i think

Step-by-step explanation:

Answer:

\(a_5 = \frac{17}{20}\)

Step-by-step explanation:

Use the general progression formula where

\(d=\frac{3}{20}\\a_n=\frac{1}{4}+\frac{3n-3}{20}\)

Solving this for the 5th term returns the answer

\(a_5=\frac{17}{20}\)

The length of each of the two equal sides of the isosceles triangle is 41.15 meters.

in isosceles triangle, the base angles are given as 34.95 degrees each,  find the third angle by subtracting twice the base angle from 180 degrees (since the sum of angles in a triangle is 180 degrees).

∴ the third angle is 180 - (2 × 34.95) = 110.10 degrees.

Now, we can use the Law of Sines to find the length of the equal sides. According to the Law of Sines, the ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle.

\(\frac{sine of one of the base angles}{length of one of the equal sides}\)       =   \(\frac{sine of the third angle}{length of the base}\)

                              \(\frac{sine 34.95}{x}\) =     \(\frac{sin(110.10)}{57.52}\)

Solving for x, which represents the length of each of the equal sides, we find x ≈ 41.15 meters, rounded to two decimal places.

Therefore, the length of each of the two equal sides of the isosceles triangle is approximately 41.15 meters.

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The equation of line is  5x - y = 1.

What are the types of equation of a line?

Different forms of equations of a straight line

Equations of horizontal and vertical lines.

Point-slope form equation of a line.

Two-point form equation of line.

Slope-intercept form equation of line.

Intercept form.

Normal form.

Given that the slope of the line is 5.

The line pass through the point (2,9).

The equation of line passes through the point (x₁, y₁)  with slope m is

y - y₁ = m (x - x₁).

In the question m = 5, x₁ = 2, y₁ = 9

Putting m = 5, x₁ = 2, y₁ = 9 in y - y₁ = m (x - x₁)

y - 9 = 5 (x - 2)

Applying distributing property:

y - 9 = 5x- 10

5x - 10 - y +9 =0

5x - y -1 = 0

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Answer:

Isosceles triangle

Step-by-step explanation:

Given

Triangle ABC

Required

Reflect across BC and name the triangle according to length of its side

When the triangle is reflected across line BC, the new triangle is ACA (see new attachment)

And the sides of this ACA are:

AC, CA and AA

Such that

AC = CA

and

\(AA = 2 * AB\)

\(AA = 2AB\)

From the description above, we have two sides (AC and CA) of the triangle to be equal.

By classification of sides, when two sides of a triangle are equal; such triangle is an isosceles triangle

Triangle ACA' has two equal sides, based on the side lengths, triangle ACA' can be classified as: an isosceles triangle.

Recall:

Given that triangle ABC is a right triangle, if we reflect it across line BC, we will have  mirror figure of right triangle ABC, forming triangle ACA'.

That is, two right triangles of ABC, which are reflections of each other, will form triangle ACA'. (See image attached).

Thus, this means that:

Therefore,

Also, CA = C'A (congruent sides)

This means that, triangle ACA' has two equal sides that are opposite to each other.

Therefore, based on the side lengths, triangle ACA' can be classified as: an isosceles triangle.

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Answer:

Step-by-step explanation:

     MARKS  

        %    Max   Actual  

Hindi 50%    100 50  

English 75%     140 105  

Math              160 90  

(245/400)

Answer:

K = 15t + 19

E = 9t + 49

After 2 days, Evelyn is farther along.

Step-by-step explanation:

K = page Kayla is on

E = page Evelyn is on

t = number of days

K = 15t + 19

E = 9t + 49

After 2 days, t = 2.

K = 15 × 2 + 19 = 49

E = 9 × 2 + 49 = 67

After 2 days, Evelyn is farther along.

Using the equations written we can conclude that: after 2 days, Evelyn is farther along in the book, as she is on page 67, while Kayla is on page 49.

Let's first write the equations for Kayla and Evelyn's progress in terms of "t" days into the month which represents the situation:

For Kayla:

KK = 19 + 15t

For Evelyn:

EE = 49 + 9t

Now, let's find their progress after 2 days:

For Kayla (t = 2):

KK = 19 + 15 * 2 = 19 + 30 = 49

For Evelyn (t = 2):

EE = 49 + 9 * 2 = 49 + 18 = 67

2 days later, Evelyn has progressed to page 67, which is ahead of Kayla's position at page 49 in the book.

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The null and alternative hypotheses can be described  as shown below:

p1 = p2

p1 ≠ p2

The Null hypothesis has it that there exists no difference in the proportion of undergrad and grad students at UCI that prefer online teaching to in-person teaching.

Therefore p1 = p2

On the other hand, the alternative hypothesis :

says there also exists a difference in the proportion of undergrad and grad students at UCI that  prefer online teaching to in-person teaching.

p1 ≠ p2

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#complete question:

A researcher is interested in understanding if there is a difference in the proportion of undergrad and

grad students at UCI who prefer online teaching to in person teaching, at the α = 0.05 level. They take

2 samples, first, a sample of 300 undergrad students. The second, is a sample of 172 grad students. Of

the undergrads, 186 said they preferred online lectures, and of the graduate students, 104 said that they

prefer online lectures. Let p1 = the proportion of undergrad students who prefer online class and p2 =

the proportion of grad students who prefer online lectures.

(a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret

them in context of the problem).

Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

Answer:

9.5 feets

Step-by-step explanation:

Length of drawing = 8 4/9 inches

Scale : 1/3 inch in drawing = 3/8 actual length

Length of drawing / drawing scale

8 4/9 = 76/9 inches

Number of 1/3 inches in total length of drawing :

76/9 ÷ 1/3

76/9 * 3 / 1

(76*3) /(9*1) = 228 /9 = 9 3/9 = 9 1/3

9 1/3 * 3/8 foot

(228 / 9) * (3 /8)

(228/3) * (1/ 8)

228 / 24

= 9.5 feet

Answer:

3. w = 4

4 . g = 8

5. q = 1

6. m = -3

7. z = -32

8. a = 6

9. h = 4

10. d = -16

11. y = 4

12. n = 4

13. v = 3

14. c = -2

Step-by-step explanation:

3). 3w + 7 = 19

3w = 12

w = 4

4). 2g - 13 = 3

2g = 16

g = 8

5). 11 = 12 - q

q + 11 = 12

q = 1

6). 10 = 7 - m

m + 10 = 7

m = -3

7). -4 * (5) = (z/-4 - 3) * -4

-20 = z + 12

z = -32

8). 3 * (a/3 + 4) = (6) * 3

a + 12 = 18

a = 6

9). 5 * ((h + 6)/5) = (2) * 5

h + 6 = 10

h = 4

10). -2 * ((d - 8)/-2) = (12) * -2

d - 8 = -24

d = -16

11). 8y + 3y = 44

11y = 44

y = 4

12). 36 = 13n - 4n

36 = 9n

n = 4

13). 12v + 10v + 14 = 80

22v + 14 = 80

22v = 66

v = 3

14). 6c - 8 - 2c = -16

4c - 8 = -16

4c = -8

c = -2

Answer:

Step-by-step explanation:

y=1/2-5x

Answer:

Step-by-step explanation:

Using points on the graph to get the equation

Slope intercept form:

From the graph, point (0, -5) we can see y-intercept is b = -5

An calculating the slope using two points (-6, -3) and (6, -7):

So the line is:

The statement provided is actually the opposite of the correct definitions.

In database terminology, a field refers to a single piece of information that is stored in a database table. A field can contain a variety of data types such as text, numbers, dates, and so on. For example, in a database table of customer information, there might be fields for the customer's name, address, phone number, and email.

A record, on the other hand, is a complete set of information about an entity in a database. A record consists of a collection of fields that are all related to each other. For example, in the customer information table mentioned above, a single record might represent a specific customer, and would contain all the fields related to that customer (name, address, phone number, email, etc.).

So to summarize, a field is a single piece of information within a record, while a record is a collection of related fields that together represent a complete set of information about an entity in a database.

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Answer:

the first one and the fith one

Step-by-step explanation:

Answer:

24%

Step-by-step explanation:

we subtract to see how much it increased

62-50=12

Now divide 12 by 50 to get percent

12/50

0.24

0.24x100

24%

Hopes this helps please mark brainliest

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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In parallelogram RSTU with UR = 27, RX = 19, and m∠URS = 46.3°, the length of ST is approximately 20.396 units.



To find the length of ST in parallelogram RSTU, we can use the given information and apply the properties of parallelograms.In a parallelogram, opposite sides are congruent. Therefore, since UR = ST, we can conclude that ST = 27.

Now, let's focus on triangle URS. We know that UR = 27 and RX = 19. Also, m∠URS = 46.3 degrees.

Using the Law of Cosines, we can find the length of US:

US² = UR² + RX² - 2 * UR * RX * cos(m∠URS)

US² = 27² + 19² - 2 * 27 * 19 * cos(46.3)

US² ≈ 729 + 361 - 988.2 * 0.6811

US² ≈ 729 + 361 - 673.45

US² ≈ 416

Taking the square root of both sides, we get:

US ≈ √416

US ≈ 20.396

Since ST is opposite to US in parallelogram RSTU, ST is also approximately 20.396.

Therefore, the length of ST is approximately 20.396 units.

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The probability that the web site has fewer than 5 million visitors in a single day is 0.7293.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 5 million

μ = mean = 4.56 million

σ = standard deviation = 720,000

z-score = (5 million - 4.56 million) / 720,000

z-score = 440,000 / 720,000

z-score = 0.6111

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score =  0.6111

Using interpolation of values,

probability = 0.7293

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Answer:

<C = 54 degrees

b = 123.6

a = 72.6

Step-by-step explanation:

<C = 180 - 90 - 36 = 54 degrees

b = 100/sin54 = 123.6

a = sqrt (123.6^2 - 100^2) = 72.6

The correct option is B• "The LP has multiple optimal solutions". Because  feasible region, intersects with the objective function in multiple points.

The given linear programming (LP) problem consists of two constraints and two decision variables, x1 and x2. The objective function to be minimized is x1 + 2x2.

To determine the nature of the LP problem, we need to analyze its feasible region and objective function.

The first constraint, x1 + x2 ≤ 4, defines a region in the xy-plane that lies below the line x1 + x2 = 4. The second constraint, x1 - x2 ≥ 5, defines a region that lies to the right of the line x1 - x2 = 5. The feasible region is the intersection of these two regions.

By analyzing the feasible region, we can determine the potential optimal solutions. Since the feasible region is a bounded region, there are finite points within it. The objective function, x1 + 2x2, represents a straight line in the xy-plane with a positive slope. As long as this line intersects the feasible region, there will be multiple points of intersection, each representing a potential optimal solution.

Therefore, the LP problem has multiple optimal solutions because there are multiple points of intersection between the objective function and the feasible region.

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