Triangle $ABC$ has vertices $A(0, 8)$, $B(2, 0)$, $C(8, 0)$. A line through $B$ cuts the area of $\triangle ABC$ in half; find the sum of the slope and $y$-intercept of this line.

840  ways can we form a subcommittee with 3 republicans and 2 democrats

Given that

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical. (It is not important how each set's members are arranged.) If there are n elements in the set, then C kn is the number of k-combinations.

a senate committee has 8 republicans and 6 democrats.

now, we need to find how many ways can we form a subcommittee with 3 republicans and 2 democrats

= 8[tex]C_{3}[/tex] × 6[tex]C_{2}[/tex]

=[tex]\frac{8!}{5!3!}[/tex] × [tex]\frac{6!}{4!2!}[/tex]

=56 × 15

=840

840  ways can we form a subcommittee with 3 republicans and 2 democrats

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The equation of a line is 3y+x+10 = 0 when it passes through the point (-5,5).

What is Equation of Straight line ?

Equation of Straight line as follows , y = mx+b

where m is slope of the line.

Given ,

The equation of line k is y+10=3(x+3).

Perpendicular to line k is line , which passes through the point (5,–5)

So, the given equation could be,

y = 3x+9-10

y = 3x-1

m = 3

So, the slope of the another line = -1/3

So, the equation could be ,

when it passes through the point (5,-5) is

y - (-5) = -1/3  ( x - 5 )

y+ 5 = -1/3  ( x-5)

3 (y+5) = -1 (x-5)

3y+15 = -x + 5

3y+x+15-5 = 0

3y+x+10 = 0

Hence, The equation of a line is 3y+x+10 = 0 when it passes through the point (-5,5).

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The union of two or more events is a single event that represents all the outcomes that belong to at least one of the original events.

16) It is often represented using the symbol "U" or "∪". For example, if event A is "rolling a 3 on a die" and event B is "rolling a 4 on a die", the union of A and B would be "rolling a 3 or a 4 on a die".

17)  The intersection of two or more events is a single event that represents all the outcomes that belong to all of the original events. It is often represented using the symbol "∩". For example, if event A is "rolling an even number on a die" and event B is "rolling a number greater than 3 on a die", the intersection of A and B would be "rolling a 4 on a die".

18)  The union of two or more events represents all the outcomes that belong to at least one of the original events, while the intersection of two or more events represents all the outcomes that belong to all of the original events. The union is a "larger" event that includes all outcomes from the original events, while the intersection is a "smaller" event that only includes outcomes that belong to all of the original events.

For example, if event A is "rolling an odd number on a die" and event B is "rolling a number less than 4 on a die", the union of A and B would be "rolling a 1,3, or a 2 on a die" while the intersection of A and B would be "rolling a 1 or a 3 on a die".

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a). 115.26 is the upper bound of a 98% band (b). 93.36 to 116.63 is the 98% confidence interval (c). We have 98% confidence that the collected sample data will include the true worth of the population parameter.

By multiplying the total number of numbers by amount of all the numbers, one can approximate the average. A mean can be established by the average of such probabilities in a survey of data. In other words, an average is also known as the arithmetic mean. The average is referred to as having a mean.

[tex]\begin{aligned}& \mu=105 \\& \sigma_x=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{9}}=5\end{aligned}[/tex]

(a). The maximum 98% interval

[tex]=\mu+Z_{0.02} * S D=105+2.0537 * 5=115.2685[/tex]

(b). 98 percent confidence band

[tex]\begin{aligned}& \left(\mu-Z_{\frac{0.02}{2}} * S D, \mu+Z_{\frac{0.02}{2}} * S D\right) \\& (105-2.3263 * 5,105+2.3263 * 5)=(93.3685,116.6315)\end{aligned}[/tex]

(c). We have 98% confidence that the collected random sample would also include the true value of said population parameter.

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The complete question is-

Suppose you administer a certain aptitude test to a simple random sample of 9 students in your school, and that the average score is 105 . From past experience, scores on such a test among students like those at your school follow a Normal distribution. We want to determine the mean score [tex]$\mu$[/tex] of the population. Assume a standard deviation of [tex]$\sigma=15$[/tex] for the test.

(a). What is the upper critical value for a 98% confidence interval? (Show the key numbers in the sketch of the distribution.)

(b). Construct and interpret a 98% confidence interval for the mean score [tex]$\mu$[/tex]. Follow the Inference Toolbox.

(c). Explain the meaning of 98 % confident.

Answer:

b

Step-by-step explanation:

sr =

[tex] \sqrt[10]{3} [/tex]

On solving the provided question we can say that by unitary method number of extra copies made by machine 2 = 192 – 180 = 12

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen.

In 8 minutes, Machine 1 produces 240 copies. In 5 minutes, machine 2 produces 240 copies. The rates of operation for each machine are constant.

machine 1 makes 240 = 8 mins

[tex]1 min = 240/8 = 30\\6 min = 3 X 6 = 180[/tex]

In 5 minutes, machine 2 produces 240 copies.

[tex]1 min = 240/5 = 48\\4 min = 192[/tex]

number of extra copies made by machine 2

[tex]= 192 – 180\\ = 12[/tex]

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The final distance from U to T is 112 miles.

Since U and T are the midpoints of SR and ST respectively, we know that SU and RT are congruent and have the same length.

We need to find the overall displacement of U&T.

Also, we know that the distance between S and R is 56 miles.

Therefore, the distance from U to T is equal to twice the distance from S to U which is 2 * (distance from S to R) = 2 * 56 = 112 miles.

Therefore, The final distance from U to T is 112 miles.

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a)

b) The slope-intercept definition of the linear function is given as follows:

y = 3x + 3.50.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points on the linear function in this problem are given as follows:

(2, 9.50) and (5, 18.50).

The slope is given by the division of the change in y by the change in x, hence:

m = (18.50 - 9.5)/(5 - 2)

m = 9/3

m = 3.

Representing the hourly charge.

Hence:

y = 3x + b.

When x = 2, y = 9.50, hence the intercept b, representing the rental fee, is given as follows:

9.5 = 3(2) + b

b = 3.50.

Meaning that the function is defined as follows:

y = 3x + 3.5.

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The number of ways for the four beasts to wear these hats so each beast is wearing a different hat, and no one is wearing a hat marked with the first letter of their name is given as follows:

8.

Winnie is wearing a hat that does not have any letter, while the letters on the other helmets are G, L and A, meaning that Winnie can wear four helmets.

For Grogg, Lizzie, and Alex, they can't wear the helmet with their own letters.

Hence the possible combinations, considering only them, are listed as follows:

As Winnie can wear any of the four helmets, and Grogg/Lizzie/Alex can also wear the red helmet, the number of outcomes is given as follows:

4 x 2 = 8.

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On solving the provided question, we can say that here, in equation the greatest distance the ball is from the ground is -y = -4.9 + 9.8 +2 = 6.9

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the equation y=-4.9x^2+9.8x+2

where y = the distance the ball is from the ground in meters

x = the elapsed time in seconds

the greatest distance the ball is from the ground is -

[tex]y=-4.9x^2+9.8x+2[/tex]

x = 1

y = -4.9 + 9.8 +2 = 6.9

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Answer:

V÷ 2

Step-by-step explanation:

Get peevious number and divide by half.

Answer:

34

Step-by-step explanation:

They gave us -3+5i.

The conjugate of -3+5i is

-3 - 5i

You use the same numbers -3 and 5i, but with a minus sign instead of a plus.

Then multiply them together.

(-3 + 5i)(-3 - 5i)

-3•-3 + 15i - 15i - 25i^2

= 9 - 25i^2

Remember i^2 is -1.

= 9 - 25(-1)

= 9 + 25

= 34

Shortcut version:

When you multiply a complex number and its conjugate, square both numbers and add them together.

3^2 + 5^2

= 9 + 25

= 34

The area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is given by

Area = ∬R dA where R is the region we're trying to find the area of.

We can find the area of the region by subtracting the area of the smaller circle from the area of the larger circle.

The area of the larger circle is:

Area = ∬R dA = ∬((x − 2)^2 + y^2 <= 4) dA = π*4 = 4π

The area of the smaller circle is:

Area = ∬((x^2 + y^2) <= 4) dA = π*4 = 4π

Therefore, the area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is

Area = 4π - 4π = 0

The area of the region is 0 square units.

Answer:

I agree with kiddobreeze08

The slope of the line parallel to BC is 18/7 * (x + 0) is 18/7 y. the orthocenter is where concurrency occurs.

Hana fastens tiny wood strips perpendicular to the opposing edge from each vertex. As a result, the orthocenter is where concurrency occurs.

Given: Hana fastens small wood strips perpendicular to the opposing edge from each vertex.

As a result, the orthocenter is where concurrency occurs.

Think of the ABC triangle with coordinates.

A(0, 0) B(0, 58), C(36, 44) (36, 44)

first determine the angles of the triangle's two sides.

Formula for slope: (y 2 - y 1)/(x 2 - x 1)

slope of the AB& A(0, 0) matrix side matrix, Slope of BC side B(0,58), B(0, 58) = (58 + 0)/(0 + 0) = 0 C(36,44) = (44 - 58)/(36 + 0) = - 14/36 = - 7/18

Use Equation of the altitude perpendicular to AB's point slope form after that.

The vertex in opposition to AB is point C.

A line perpendicular to AB has a slope of zero.

y-y 1 = m(x-x 1) y-44 = 0(x-36) y = 44

Altitude Equation Perpendicular to BC

The vertex opposite BC is Point A. A line perpendicular to BC has a slope of 18/7.

y + 0 = 18/7 * (x + 0)

y = 18/7 * x

Change the value of y in the equation above. y = 18/7 * x 44 = 18/7 * x

x = 17.11 The slope of the line parallel to BC is 18/7 * (x + 0) = 18/7 y.

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Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.

What is compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is different from simple interest, which is calculated only on the initial principal.

To find out how much Caleb needs to invest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal or initial investment

r = the annual interest rate (expressed as a decimal)

n = the number of times per year that interest is compounded

t = the number of years the investment will be held

We know that Caleb wants the future value of the investment to be $1,900 in 5 years and interest is compounded daily with an annual rate of 6%. So we can set up the equation as:

A = P(1 + r/n)^(nt)

1900 = P(1 + 0.06/365)^(365*5)

To solve for P, we can use a calculator to get the result:

P = $1,764.69

Hence, Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.

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The Medicine Concentration drops 70 % each hour .

What is a graph ?

graph can be defined as a visual indicator in which we can represent the data.

Given,

A certain medicine is injected, its concentration in the bloodstream changes exponentially over time as shown in graph

Concentration of medicine when it was injected

=> at t = 0

Hence 100  mg/l  was concentration when medicine was injected

Nt  = No [tex]e^{-kt}[/tex]

N₀  - initial Quantity = 100 mg/l

at  t = 1  Concentration is 70 mg/l

=>  70 = 100   [tex]e^{-kt}[/tex]

=> k =  0.3567

Decay Constant = 0.3567

T = Half life period

50 = 100  [tex]e^{-kt}[/tex]

=> -0.693 = -kT

=>  1.943 hr

Hence , Medicine Concentration drops 70 % each hour .

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There are different tables used in mathematics i.e. logarithmic tables, semi-logarithmic tables, exponential tables, trigonometric function tables, etc.

The tables are provided with data that is needed for the calculations. For example: if the value of Sin 45° needs to be found then we have to move to the table of Sin Θ and then follow the rows of angles where the value of Sin 45° can be obtained. Similarly, the values of other functions can be found in this way. However, the trigonometric table also provides the relation between two functions like Tan Θ= [tex]\frac{SinΘ}{CosΘ}[/tex].

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Step-by-step explanation:

your teacher gave you even the formula. so, what is still not clear ?

in regular words, the slope of a line is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

so, we have here (-2, 1) and (3, 2).

x changes by +5 (from -2 to 3).

y changes by +1 (from 1 to 2).

so, the slope is +1/+5 = 1/5

In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass. thus it is the correct option.

Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

The response variable (or the dependent variable) always belongs on the y-axis (represented as the second column of the table).

Since the explanatory variable (or the independent variable) always belongs on the x-axis (represented as the first column of the table).

According to the table of values showing the mass of a radioactive isotope over time.

Based on explanation above the correct choice is C which could be In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass.

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Factors of polynomial x²+5x+6 are -2,-3.

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

The expression is categorised as monomial based on how many terms are included in it:

An expression with just one term is referred to as a monomial. A monomial expression must have a single term that is not zero in order to qualify. A Monomial examples include 5x and 3.

Binomial:-

An expression of a polynomial with exactly two terms is called a binomial.  Examples of binomials are:

– 5x+3, 6a^4 + 17x.

Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:

– 8a^4+2x+7, 4x^2 + 9x + 7.

Now Given polynomial is x^2+5x+6

To find factors put it equal to zero

x^2+3x+2x+6=0

x(x+3)+2(x+3)=0

x+3=0, x+2=0

x=-2,-3

Hence, The factors of the given polynomial are -2,-3.

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Using Euclid's theorem for the right triangle AD  is ≈ 2.67

DB = 4 and DC = 6 , We need to find AD

Using Euclid's theorem for the right triangle

∴ DB² = AD * DC

∴ 4² = AD * 6

∴ 6 AD = 16

∴ AD = 16/6 = 8/3 ≈ 2.67

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Answer: If 7 men can paint 42 square feet in a day, then we can say that each man paints 42/7 = 6 square feet per day.

If 20 men paint, then they would paint 20 * 6 = 120 square feet per day.

Step-by-step explanation:

Answer:

WXUV

Step-by-step explanation:

Well, you see, think of it as a reflection.

Answer:

see photo attached

Step-by-step explanation:

The two possible sets of four numbers are (9,-27,81, -243) and (-18,-54,-162,-486).

A geometric progression is a special type of progression where the successive terms bear a constant ratio known as a common ratio. It is also commonly referred to as GP. The GP is generally represented in form a, ar, ar2.... where 'a' is the first term and 'r' is the common ratio of the progression. The common ratio can have both negative as well as positive values. To find the terms of a geometric series, we only need the first term and the constant ratio. Finite geometric progression contains a finite number of terms. It is the progression where the last term is defined. Infinite geometric progression contains an infinite number of terms. It is the progression where the last term is not defined.

Let the first term of the geometric progression be a and the common ratio be r.

The second term is less than the first by 36.

∴ a - ar = 36

⇒ a(1-r) = 36 --- (1)

The third term is greater than the fourth term by 324.

∴ ar² - ar³ = 324

⇒ ar²(1-r) = 324  --- (2)

Divide equation (2) by equation (1):

∴ r² = 9

⇒ r = ±3

Put r in the first equation:

⇒ a - ar = 36

⇒ a(1 - (±3) = 36

⇒ a = 36/4 or 36/-2

∴ a = 9 or -18

Similarly finding the other three terms:

ar = 9× -3 or -18×3  = -27 or -54

ar² = -27×-3 or -54×3 = -81 or -162

ar³ = -81×-3 or -162×3 = 243 or -486

Thus, the two possible sets of four numbers are (9,-27,81, -243) and (-18,-54,-162,-486).

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Answer: 150 miles

Step-by-step explanation: the car goes 30 miles every half hours, therefore, in five half hours it goes 150 miles.

The expression 5+4*2+6-2*2-1 has a value of 14 using order of operations

The order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved. A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation

Parenthesis            (  )

Exponent                a⁷

Multiplication          x

Division                   ÷

Addition                  +

Subtraction             -

Let's use PEMDAS:

Remember, multiplication comes before addition and subtraction, thus, we have:  

5+4×2+6-2×2-1 = 5 + (4×2) + 6 - (2×2) - 1

                        =  5 + 8 + 6 - 4 - 1

                        =  14

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For the given line segments 12cm ,7cm and 5cm , a triangle cannot be constructed as the sum of two sides is not greater than third side .

What is a Triangle ?

a Triangle is closed figure joined by three line segments .

The condition for the sides to form a triangle , is :

the sum of any two sides of triangle should be greater than the third side of the triangle :

the given side lengths are : 12cm ,7cm and 5cm ;

on adding the two sides of triangle ,

we get ;

⇒ 12+7 = 19 > 5 ; True

⇒ 12+5 = 17 > 5 ; True

⇒ 7+5 = 12 > 12 ; False

The third condition is not met .

Therefore , the line segments 12 , 7 and 5 do not form a triangle .

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An Equation of the tangent line to the curve is 18y=x+81

Given equation

y²=x

This is an equation of a parabola. graph{y^² = x [-10, 10, -5, 5]}

For finding the tangent to the equation, we first differentiate it.

The goal here is to find the value of dy/dx which will give the slope of the tangent to the parabola.

So,

[tex]\frac{d}{dy}(y^2)=\frac{dx}{dy} \\\\2y=\frac{dx}{dy} \\\\\frac{1}{2y} =\frac{dx}{dy} \\\\[/tex]

Now, we want to evaluate the slope at the given point. So substituting y we get,

[tex]\frac{1}{18} =\frac{dx}{dy}[/tex]

This is the slope of the tangent.

It passes through (81,9) [as per in the question]

The general equation of a line is y=mx+c

m is the slope of the line.

For the line/tangent that we got

[tex]m=\frac{dy}{dx}[/tex]

[tex]y=\frac{x}{18} +C[/tex]

The point should satisfy the equation of the line/ tangent. So,

[tex]9=\frac{x}{18} +C[/tex]

So, c=9/2

Finally, substitute the value in our equation of the line/tangent:

[tex]y=\frac{x}{18} +\frac{9}{2}[/tex]

18y=x+81

Therefore, the equation of the tangent line to the curve at the given point, y =√ x, (81, 9) is 18y=x+81

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B-The two distributions for number of cars in line are both skewed right.

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