Triangle ABC is defined by the points A(3,8), B(7,5), and C(2,3).

Create an equation for a line passing through point A and perpendicular to BC.

Best-fit values

Slope

Y-intercept

X-intercept

1/Slope

0.6000 ± 0.1155

4.000 ± 0.6633

-6.667

1.667

95% Confidence Intervals

Slope

Y-intercept

X-intercept

0.2326 to 0.9674

1.889 to 6.111

-25.31 to -2.028

Goodness of Fit

R square

Sy.x

0.9000

0.7303

Is slope significantly non-zero?

F

DFn,DFd

P Value

Deviation from horizontal?

27.00

1,3

0.0138

Significant

Data

Number of XY pairs

Equation

5

Y = 0.6000*X + 4.000

Step-by-step explanation:

graph till you find the answer

B

Answer:

length of rope=34.56

Step-by-step explanation:

1) find the circumference of the circle (its the full circle just separated into 2 halves)

c=2[tex]\pi[/tex]r

c=2[tex]\pi[/tex]4

c=25.13

2) find the circumference of the smaller circle

c=2[tex]\pi[/tex]r

c=2[tex]\pi[/tex]3

c=18.85

divide this answer by 2 because its a semi-circle

c=9.43

3) add the 2 values together

length of rope=34.56

Answer:

1). If the algae doubles every day, it will take 15 days for it to cover half the lake. This means it would happen on January 15.

2). Your friend may be skeptical because they may not believe that the algae can grow so quickly and cover the entire lake in just 30 days. Alternatively, they may not believe that you have accurate information about the situation.

3). Removing most of the algae on January 29 would significantly reduce the amount of algae in the lake and would likely help prevent the lake from becoming completely covered. However, if 1% of the surface is still covered with algae on February 1, it is possible that the problem has not been fully solved and the algae could continue to grow and potentially become a problem again in the future. It would be best to continue monitoring the lake and taking action to prevent the algae from growing.

If we roll a dice three times and we can stop in the first time only when it come 6. The expected payoff is 4.557.

According to the question:

The number of times you can get 06 are:

(i). If the third toss rolls a 6:  6

In this case her first two digits can be any of the five numbers. No. The number of cases is 5 × 5 = 25.

(ii). If you get a 6 on the second throw. The number of cases is -5 (no third throw in this case)

(iii). If the first roll rolls a 6. The number of cases is -1.

2. Number of times you can get 5 Are-

(i). If there is only one 5 in 3 rolls . The number of cases will simply be

3 × 4 × 4

(Because there are 5 possibilities in 3 places and 4 in the remaining places.)

(ii). If there are two 5s, the number of cases is 3×4. (Because there are 3 places where 5 cannot exist, and the places are filled with 4 possibilities.)

(iii). If there are three 5s, the number of possibilities is -1.

Similarly, for 4,3,2,1, the number of possibilities is (3*3*3 + 3*3 + 1), (3*2*2 + 3*2 + 1), (3 × 1×1 + 3×1 + 1), 1 each.

So the number of possibilities for 1,2,3,4,5,6 are 1,7,19,37,61,31 respectively .

You can now get the expected profit by taking the weighted average of the numbers with the possible outcome odds.

So the result is (6*31 + 5*61 + 4*37 + 3*19 + 2*7 + 1)/(31+61+37+19+7+1)

which is 711/ 156 = 4.557

Therefore, the expected payout is 4.557.

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Answer: B.83

Step-by-step explanation:

Answer: B.83

Step-by-step explanation:

The number 2,158 is called the numerator or dividend, and the number 26 is called the denominator or divisor.

The quotient of 2,158 and 26, the ratio of 2,158 and 26, as well as the fraction of 2,158 and 26 all mean (almost) the same:

2,158 divided by 26, often written as 2158/26. 2,158 divided by 26 = 83

The result of 2158/26 is an integer, which is a number that can be written without decimal places.

   2158 divided by 26 in decimal = 83

   2158 divided by 26 in fraction = 2158/26

   2158 divided by 26 in percentage = 8300%

Question

The two lines graphed below are not parallel. How many solutions are there to

the system of equations?

•A. Infinitely many

•B. Two

•C. Zero

•D. One

D: One is the answer

Answer:

(-7, -5)

Step-by-step explanation:

y = x + 2

2x - 3y = 1

2x - 3(x + 2) = 1

2x - 3x - 6 = 1

-x - 6 = 1

    +6  +6

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

-x = 7

÷-1  ÷-1

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

x = -7

y = x + 2

y = -7 + 2

y = -5

I hope this helps!

The probability that Mia is on time to exactly one of the classes is 0.5

Given that

probability of she is late for the art class (x)= 0.5

probability of she is late for the calculus class(y) = 0.4

the probability of she is not late for the art class (z)= 1 - x = 1 - 0.5 =0.5

the probability of she is not late for the calculus class(p)= 1 - y = 1 - 0.4 = 0.6

the probability that Mia is on time to exactly one of the classes =

Probability of arriving (late for Calculus and on time for Art)) or (late for Calculus and on time for Art)

= (x × p) + (y × z)

=(0.5 × 0.6) +(0.4 × 0.5)

=0.3+0.2

= 0.5

The probability that mia is on time to exactly one of the classes = 0.5

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The smallest perfect number is 6.

Any positive integer whose sum is equal to its divisors is known as a perfect number. A point to be noted is that the number itself is not included here.

If we go serially,

1 cannot be included as its only divisor is the number itself.

2's divisor is 1, and we can clearly see they are not equal.

3's divisor is 1 again. Hence not a perfect number.

4's divisor is 1 and 2.  1 + 2 = 3, which again is not 4.

5's divisor is 1.

6's divisors are 1, 2 and 3.

We can see that 1 + 2 + 3

= 6

Hence, the smallest perfect number is 6.

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6 is the smallest or first perfect number in a mathematics.

Any positive integer in which whose sum is equal to its divisors is known as a perfect number. A point is to be noted that should not be a number itself is not included here as required so the number should be deterministic .

1  is  a number  cannot be included as its only divisor is the number to  itself.

2's divisor is 1, and we can clearly see that  they are not equal.

3's divisor is 1 again. Hence the number 1 is not a perfect number.

4's divisor is 1 and 2.  1 + 2 = 3, which again is not 4.

5's divisor is 1.

6's divisors are 1, 2 and 3.

We can see that 1 + 2 + 3 = 6

Hence, the smallest perfect number is 6.

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Applying the sine ratio, the value of x is calculated as: x = 6.

The sine ratio is part of the trigonometric ratios that is used to solve a right triangle, which is expressed as:

sin ∅ = opposite side length / hypotenuse length

Given the following:

Apply the sine ratio to find the value of x:

sin 45 = 6√2/x

Multiply both sides by x

sin 45 × x = 6√2

Divide both sides by sin 45:

sin 45 × x / sin 45 = 6√2/sin 45

x = 6√2 / √2/2

x = 6√2 × 2/√2

x = 12/2

x = 6

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For Function 3(5/4)³ , 3 is inital value , 5/4 is base with (-∞, ∞) as Domain

An exponential function is one with the mathematical formula f (x) = ax, where "x" is a variable and "a" is a constant that serves as the function's base and must be greater than 0.

An exponential function f(x) = abˣ,

According to the question,

The given exponential function : f(x) =3(5/4)³

Here, 3 is the Inital value

The base of the function is 5/4

As the function is real, Domain = (-∞, ∞)

The function given only has one value. That is the entirety of its range: [3(5/4)^3, 3(5/4)^3]

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The location of the circumcenter, of the obtuse triangle, which is the center of the circle that inscribes the triangle is at a point lower than the base of the triangle, and therefore, outside the triangle, because the angle of the arc formed by the base at the center is larger than 180°, which is the angle formed by the diameter/ The correct option is option c.

c. Outside the triangle

The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle.

The location of the circumcenter can be inside the triangle, outside the triangle, or on the triangle.

The circumcenter is located on the inside of an acute triangle, while it is located on the hypotenuse side of a right triangle.

The circumcenter is the location of the center of the circle that circumscribe the triangle, such that in an acute triangle, the angle at the center (twice the angle at the circumference), is always less than 180°, which is the angle made by the diameter, which keeps the diameter line and the circumcenter, passing inside the triangle.

However, in an obtuse triangle, the angle at the center, is larger than 180°, such that the line joining the base of the triangle, inscribed in the circle is located above the diameter, and therefore, located above the circumcenter.

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Answer:

A. 0°

Step-by-step explanation:

Answer:

Option A is correct.

Solution for the given equation is,

Step-by-step explanation:

Given that :

Let

then our equation become;

A quadratic equation is of the form:

.....[2] where a, b and c are coefficient and the solution is given by;

Comparing equation [1] and [2] we get;

a = 2 b = -1 and c =-1

then;

Simplify:

Simplify:

y = 1 and

Substitute y = cos x we have;

⇒

and

⇒

The solution set:  

Therefore, the solution for the given equation   is,

When the area of a figure is enlarged by a scale factor of 3, then the area of the figure will be three times of the original area of the figure.

Here, the area of the figure is enlarged by a scale factor of 3

The scale factor is defined as the ratio between the scales of the original object or measurement and the new measurement or object

When the scale factor is greater than 1 the size of the new figure will increase and if the scale factor is less than 1 size of the new figure decreases

Here scale factor is 3, so the area of the figure is increased by three times

Therefore, the the area of the new figure will enlarged by three time

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The polar equation for the curve is x = √3cosФ and y = √3 sinФ.

Here we have to find the polar equation of the curve.

Data given:

The equation is:

x² + y² = 3

This is an equation of a circle.

Its radius is √3 and its √center is (0,0)

To find the polar equation of a circle we use the following formula:

x = h + rcosФ

y = k + r sinФ

where (h,k) is the center of the circle which in this case is (0,0) and by substituting we get:

x = √3 cosФ

y = √3 sinФ

Therefore the polar equation is x =√3cosФ and y = √3sinФ.

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The integer representing the entrance of the cave is 14.

An integer is a whole number from the set of negative, non-negative, and positive numbers. An integer is a number with no decimal or fractional part, and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes: Positive Numbers: A number is positive if it is greater than zero. or we can say an integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z o

Given that, The entrance of a cave is at an elevation of 14 meters. the lowest part of the cave is at an elevation of -86 meters.

We know that, the integer numbers or simply integers are sets of numerical signs that contain the natural numbers (positive numbers), the zero number "0" and the opposite numbers corresponding to the negative numbers of the natural numbers. The integer numbers have no decimal part, are not fractional, nor have imaginary part.

The entrance is at 14 meter, that means the entrance is represented by the integer 14.

Hence, The integer representing the entrance of the cave is 14.

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Part A) If the original price of the model car was $40, and it was sold on the third day, with a daily discount of 5%, the sales amount is $34.30.

Part B) The percentage discount from the original price is 14%.

The percentage discount is the total discount divided by the original price multiplied by 100.

In this instance, we compute the total discount as $5.70, then express this value as a numerator with $40 as the denominator.  The quotient is multiplied by 100.

Original price of the model car = $40

Daily discount = 5%

The date the car sells = the third day

The sales price on the third day = $34.30 ($40 x 95% x 95% x 95%)

Total discounts = $5.70 ($40 - $34.30)

Percentage discount for three days =14.25% ($5.70/$40 x 100)

= 14%

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Answer:

$5.25

Step-by-step explanation:

3 + .75(3)

3 + 2.25

5.25

If p1, p2 and p3 are probabilities of surviving for years 1, 2 and 3 respectively, then the cumulative probability of surviving for 3 years is p1 + p2 + p3

The probability of surviving for 1 year = p1

The probability of surviving for 2 year = p2

The probability of surviving for 3 year = p3

The probability is the ratio of the number of favorable outcomes to the total number of outcomes.

The cumulative probability is defined as the probability distribution of random variables

The cumulative probability = p1 + p2 + p3

Therefore, the cumulative probability of surviving for 3 years is  p1 + p2 + p3

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Which equation has no solution

A 4(x+2)=4(x-3)

B -2(x+1)=3x-2-5x

C 4 (x+1)-7x=-3(x-1)+1

D -5(x-7)=2(2x+3)+x+7

Answer: The answer to this quesiton is A.

B-all real numbers.

C- all real numbers.

D- x=11/5

A= no solution.

so the answer would be A i hope this helps✅

Answer:

In an exponential equation, both sides can be written as power of the same base when the base is the same on both sides of the equation. For example, the equation "2^x = 8" can be rewritten as "2^x = 2^3" because the base, 2, is the same on both sides of the equation.

To solve an exponential equation where both sides can be written as powers of the same base, you can set the exponents equal to each other and solve for the variable. In the example above, setting the exponents equal to each other would give us "x = 3", so the solution is x = 3.

On the other hand, in an exponential equation where both sides can not be written as powers of the same base, you cannot simply set the exponents equal to each other. Instead, you need to use a different method to solve the equation. One way to do this is to use the property of exponents that states that "a^x * a^y = a^(x+y)" to rewrite the equation so that both sides have the same base. For example, the equation "2^x * 3^y = 6" can be rewritten as "2^x * 2^(log3(6)) = 2^(x + log3(6))", where "log3" represents the logarithm with base 3. This allows us to set the exponents equal to each other, giving us "x + log3(6) = 1", and we can solve for x to find the solution.

Answer:

33.33%

Step-by-step explanation:

Calculate percentage change from

V1 = 9 to V2 = 12

(V2-V1)|V1|×100

=(12−9)|9|×100

=3/9×100

=0.333333×100

=33.33%

By using trigonometry, it can be calculated that-

Distance from the top of the tree to the tip of the shadow is 15.46 feet

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions

[tex]sin \theta, cos \theta, tan \theta, cot \theta, sec \theta, cosec \theta[/tex]

[tex]sin \theta = \frac{Perpendicular}{Hypotenuse}\\\\cos \theta = \frac{Base}{Hypotenuse} \\\\tan \theta = \frac{Perpendicular}{Base} \\\\cot \theta = \frac{Base}{Perpendicular} \\\\sec \theta = \frac{Hypotenuse}{Base} \\\\cosec \theta = \frac{Hypotenuse}{Perpendicular} \\\\[/tex]

Let the angle of elevation be [tex]\theta[/tex] and distance from the top of the tree to the tip of the shadow be d feet

Here the tree represents the perpendicular, shadow represents the base and distance from the top of the tree to the tip of the shadow represents the hypotenuse

A tree that is 15 feet tall casts a shadow that is 4 feet long

[tex]tan\theta = \frac{15}{4}\\\theta = tan^{-1}( \frac{15}{4})\\\theta = 75.1^{\circ}[/tex]

Now,

[tex]sin75.1^{\circ} = \frac{15}{d}[/tex]

[tex]0.97 = \frac{15}{d}\\d = \frac{15}{0.97}\\d = 15.46 \ feet[/tex]

Distance from the top of the tree to the tip of the shadow is 15.46 feet

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0.060819 inches per second is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches

Given that

A large helium balloon is being inflated at the rate of 110 cubic inches per second

radius = 12

volume = [tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]

            = 4/3 [tex]\pi[/tex] [tex](12)^{3}[/tex]

            =7234.55

V = 4/3 πr³

dV/dt = 4/3 (3πr² dr/dt) = 4πr² dr/dt

dr/dt = dV/dt / (4πr²)

dr/dt = dV/dt / (4πr²)

= 110/(4[tex]\pi[/tex]×([tex]12^{2}[/tex]))

= 0.060819 inches per second

0.060819 inches per second is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches

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The solution of the given inequality -3/2(y/6 + 4) < -2x will be 8x - y < 24.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

-3/2(y/6 + 4) < -2x

-3y/12 - 6 < -2x

2x - 3y/12 < 6

24x - 3y < 72

8x - y < 24

Hence "The given inequality -3/2(y/6 + 4) -2x has an answer of 8x - y 24.".

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The point H is at 2.5 on the number line

Here we know that point F is at 4 and point G is at -2.

The distance between these 2 points is

4 - (-2)

= 4 + 2 units

= 6 units.

Now let the point H be at x on the number line.

Now it is given that

FH:GH = 3:9

or, FH/GH = 3/9

or, (4 - x) / (x - (-2)) = 3/9

or, (4 - x)/(x + 2) = 1 /3

or, 12 - 3x = x + 2

or, 4x = 10

or, x = 2.5

Hence point H is at 2.5

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Complete Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point F is at 4, and point G is at -2. Point H lies between point F and point G. If the ratio of FH to HG is 3:9, where does point H lie on the number line? Point H is at the number line.

A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.

Using sample data, hypothesis testing is used to determine a hypothesis's credibility. It is represented as H0, and it is sometimes referred to as the "null."

Given; The average thickness and standard deviation of a sample of 50 eyeglass lens samples are 3.05 millimeters and.34 millimeters, respectively.

Such lenses should have a true average thickness of 3.20 mm. Utilizing a =.05

False hypothesis H0: Alternative hypothesis: mu1= mu2 HA: 'mu1' and 'ne'

Sample Size 50 Sample Mean 3.05 Sample Standard Deviation 0.34 Intermediate Calculations Standard Error of the Mean 0.0481 Degrees of Freedom 49 t Test Statistic -3.1196 Two-Tail Test Lower Critical Value -2.0096 Upper Critical Value 2.0096 p-Value 0.0030 Reject the null hypothesis

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