Find the measure of angle 1 in a triangle if angle 2 and angle 3 both have a measure of 75⁰.

The required expression for

[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.

Given,

In the question:

The expression is given as:

Log subscript 5 baseline (startfraction x over 4 endfraction) squared

To find the which expression is equivalent?

Now, According to the question:

The expression is given as:

[tex]log_5(\frac{x}{4} )^2[/tex].

We know that from the properties of logarithm, the following identities

[tex]log m^n = n log m...(1)\\\\log\frac{m}{n} = log m - log n .....(2)[/tex]

Now,  [tex]log_5(\frac{x}{4} )^2[/tex] = 2 log [tex]\frac{x}{4}[/tex] (using 1 identity)

Again, Using (2) identity we get,

[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.

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The correct option is A. The formula for the mean absolute deviation over a range of forecasted values is  MAD t 1 t 1.

Forecasting is the method of creating predictions primarily based on past and gift information. Later these can be compared (resolved) against what occurs. for example, a company would possibly estimate their sales in the next yr, then examine it in opposition to the real results. Prediction is similar, but the more preferred time period. Forecasting would possibly confer with particular formal statistical methods using time series, pass-sectional or longitudinal information, or as an alternative to less formal judgmental strategies or the manner of prediction and resolution itself. utilization can range among regions of application:  

for example, in hydrology, the phrases "forecast" and "forecasting" are sometimes reserved for estimates of values at sure unique future instances, at the same time as the term "prediction" is used for extra widespread estimates, consisting of the wide variety of times floods will arise over an extended duration.

chance and uncertainty are vital to forecasting and prediction; it's miles generally taken into consideration as an excellent practice to indicate the diploma of uncertainty attached to forecasts. in any case, the information ought to be updated in order for the forecast to be as accurate as possible. In a few instances, the information used to are expecting the variable of the hobby is itself forecast

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The total of 4 players left after 5 rounds.

Given information,

Given that a neighborhood tennis club holds a fundraising competition every year. A total of 128 players are permitted to enter. In each round, half the participants are eliminated.

The function will be written as,

[tex]F(x) = 128e^x[/tex]

To know how many players left after 5 rounds,

Round 1 ⇒ 128/2 = 64

Round 2 ⇒ 64/2 = 32

Round 3 ⇒ 32/2 = 16

Round 4 ⇒ 16/2 = 8

Round 5 ⇒ 8/2 = 4

Hence, 4 players will be left after 5 rounds.

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The value of x will be;

⇒ x = 3

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now,

All the sides are given in figure.

By definition of proportionality, we get;

⇒ 3 / (6x - 2 - 10) = (3 + 5) / (6x - 2)

Solve for x as;

⇒ 3 / (6x - 12) = 8 / (6x - 2)

⇒ 3 (6x - 2) = 8 (6x - 12)

⇒ 18x - 6 = 48x - 96

⇒ 96 - 6 = 48x - 18x

⇒ 90 = 30x

⇒ 30x = 90

⇒ x = 90/30

⇒ x = 3

Thus, The value of x will be;

⇒ x = 3

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The car travels 183 miles distance in 3 hours.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Distance travelled by car in 4/5 hour = 48⁴/₅ miles  or 244/5 miles.

To find distance travelled by car in 3 hours, use ratio property,

4/5 hours = 244/5 miles

⇒1 hour = 61 miles

⇒3 hours = 61×3 = 183 miles

The distance covered by car in 3 hours is 183 miles.

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The probability of contracting an illness is 0.0475.

According to our question-

D: The patient has the illness

ND: the individual without the disease

TD: The results of the test show the patient has the illness.

P(D) will therefore equal 0.001 since only 0.001 of the population is affected by the disease.

P(ND) = 0.991

Because the test successfully identifies a patient with the condition 99% of the time, P(TD/D) = 0.99.

P(TD/ND) = 0.02 because the test indicates that a healthy person contracts the disease 2% of the time.

We are seeking for P(D|TD) and P(ND|TD), respectively.

According to the Bayes formula, 0.00099/0.00099+0.01982 = 0.00099/0.02081 = 0.0475 = (0.99*0.001)/(0.99*0.001)+(0.02*0.991)

And, \s = 1 - \s = 1 - 0.0475 \s = 0.9525

Therefore,

The likelihood of having an illness is 0.0475.

The likelihood of not having any sick people is 0.9525.

Hence, The probability of contracting an illness is 0.0475.

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the answer is -6x and the equation is equivalent

Bisectors are the special segments that pass through the mid point of the lines or line segments.

A bisector is the line, line segment or ray that intercepts and/or divided lines or line segments into two equal line segments and thus passes through the midpoint of the given line segment or line segments.

There can be infinite bisector for one particular line or line segment at multiple angles.

The bisector that intercepts and/or cuts a line in half, passes through the midpoint when it is perpendicular (making an angle of 90°) to the line segment is known as the Perpendicular Bisector.

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In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that B. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, holding x2 constant

Multiple regression is a statistical technique for examining the relationship between a single dependent variable and a number of independent variables. The goal of multiple regression analysis is to use known independent variables to predict the value of a single dependent variable.

Multiple regression predicts the value of one dependent variable by taking into account the values of the available multiple independent variables. For example, suppose a researcher decides to study the performance of students at a school over time.

In this case, the correct option is B.

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Answer:

-1

Step-by-step explanation:

if the input is 4 you just go through the cycles

4 then subtract 7

4-7

-3

Then divide by 3

-3/3

-1

Hopes this helps please mark brainliest

The number of apples that could be in the box is 180

From the question, we have the following parameters that can be used in our computation:

Number of apples = Fewer than 200

Children that can share the apples evenly = 2, 3, 4, 5, or 6 children

This means that the number of apples that could be in the box can be a multiple of 2, 3, 4, 5, or 6

Also, the number must be less than 200

The highest number less than 200 that is a multiple of 2, 3, 4, 5, or 6 is 180

Hence, the possible number of apples is 180

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Answer:

Multiples of 60 under 200!

Step-by-step explanation:

The blackbody surface area cools down the area according to time dependent temperature (t)

Radiation that is incident on an object is partially absorbed and partially reflected. At thermodynamic equilibrium, the rate at which an object absorbs radiation is the same as the rate at which it emits it.

    Therefore, a good absorber of radiation - any object that absorbs radiation, is also a good emitter. A perfect absorber absorbs all electromagnetic radiation incident on it; such an object is called a blackbody.

     The temperature (T) of the object that emits radiation, or the emitter, determines the wavelength at which the radiated energy is at its maximum. For example, the Sun, whose surface temperature is in the range between 5000 K and 6000 K, radiates most strongly in a range of wavelengths about 560 nm in the visible part of the electromagnetic spectrum. The body, when at its normal temperature of about 300 K, radiates most strongly in the infrared part of the spectrum.

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When you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is; Find intersections on the graph of y = 4ˣ and y = 128.

Consider the given equations;

y = 4ˣ and y = 128

Since, the power of 4 equals 128 is unknown.

Thus, draw the graph of equation  y = 128. and y = 4ˣ .

Consider the intersected point from the graph.

Thus, when you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is;

Find intersections on the graph of y = 4ˣ and y = 128.

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Answer:

x>3

Step-by-step explanation:

the answer is x>3 because I took this test in class

2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'

Given,

Triangles ABC and A'B'C' are similar

For ABC;- (x₁, y₁) = (0, 2) and (x₂, y₂) = (2, 2)

For A'B'C' ;- (x₁, y₁) = (-4, -1) and (x₂, y₂) = (1, -1)

We have to find the scale factor of the dilation;

Here,

Find the distance AB and distance A'B' with the formula

Distance, d = [tex]\sqrt{(y_{2} -y_{1})^{2} +(x_{2} -x_{1} )^{2} }[/tex]

Then,

a) Distance of AB

d AB = [tex]\sqrt{(2-2)^{2}+(2-0)^{2} }[/tex]

d AB = [tex]\sqrt{0^{2} +2^{2} }[/tex]

d AB = √4

Distance of AB  = 2 units

b) Distance of A'B'

d A'B' = [tex]\sqrt{(-1+1)^{2} +(1+4)^{2} }[/tex]

d A'B' = [tex]\sqrt{0^{2} +5^{2} }[/tex]

d A'B' = √25

Distance of A'B' = 5 units

Now,

Scale factor;

Scale factor = Distance of AB / Distance of A'B'

Scale factor = 5/2

Scale factor = 2.5

Therefore,

2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'

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if a single card is picked and if it is blue card then the probability is 6 / 19 .

Probability means possibility of happening of event, it varies from 0 to 1.

Generally it helps us in determining odds of this situation. Probability expresses that situation.

Probability is defined as the the number of favourable outcomes to the total number of outcomes.

Red Cards = 1, 2, 3, 4

Blue Cards = 1, 2, 3, 4, 5, 6

Green Cards= 1, 2, 3, 4, 5, 6, 7, 8, 9.

Now,

Total number of cards = 19

P ( Blue card ) =  [tex]\frac{Number of blue cards}{Total number of cards}[/tex]

                        =   6 / 19

Hence, if a single card is picked and if it is blue card then the probability is 6 / 19 .

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The geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.

The word "nilpotent" is missing from the title, rather confusing, since being nilpotent is easily seen to be the only possible obstruction against being diagonalisable for a rank 1 operator. After all, by rank-nullity this implies the nullity equals n−1, and this is (by definition) the dimension of the eigenspace for 0. Also Im(T) is always T-stable, so being of dimension 1 its nonzero vectors are eigenvectors, and if this is for a nonzero eigenvalue λ, then the eigenspaces for 0 and for λ are complementary, and so T is diagonalisable.

So the only thing that can go wrong is that the nonzero vectors of Im(T) are eigenvectors for 0, but then clearly T2=0 so T is nilpotent.

It would have been a bit more fun if instead of T not being nilpotent it had been given that T has nonzero trace. Since 0 is a root of the characteristic polynomial χT with multiplicity at least n−1 (which is its geometric multiplicity), the "final" root of χT equals the sum of all its roots, which is the trace of T. This is also the eigenvalue of nonzero vectors in Im(T), and as we have seen it is zero if and only if T is nilpotent if and only if T is not diagonalisable.

Hence the answer is the geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.

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Answer:7

Step-by-step explanation:

100/20 = 5

35/5 = 7

You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%

Given,

There are three different cars that you could buy. They differ in initial cost, annual operating costs, and life. Your minimum acceptable rate of return is 14%. Use the ROR method to select the best alternative.

Alternative            A             B                 C

Initial Cost          10,000     8,000       5,000

Annual Cost       1,000       1,500        1,500

Life                     8 years    8 years     5 years

Here,

Rate of Return of car A = (10,000 - 1000 x 8) / 100 = 2000/100 = 20%

Rate of Return of car B = (8,000 - 1500 x 8) / 100 = -4000/100 = -40%

Rate of Return of car B = (5,000 - 1500 x 5) / 100 = -2500/100 = -25%

That is,

You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%

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The equation of the  circle , with diameter  DEis (x - 5)² + (y - 7)² = 80

An equation is an expression that appears as the relationship between two or more variables and numbers. since the  standard equation  for a circle  is (x - h)² + (y - k)² = r², where    (h, k)  is the center of the circle and r is the radius. It is given that the diameter of the circle is at D(-3, 3) and E(13, 11). So the coordinate of the center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7) and the  Radius is diameter / 2 = 8√5 ÷ 2 = 4√5.

the equation will be : (x - 5)² + (y - 7)² = (4√5)² => (x - 5)² + (y - 7)² = 80

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Answer:

(x - 5)² + (y - 7)² = 80

Step-by-step explanation:

Answer:

26!

Step-by-step explanation:

let's firstly convert the mixed fraction to improper fraction.

[tex]\stackrel{mixed}{4\frac{1}{3}}\implies \cfrac{4\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{13}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{13}{3}\cdot 6\implies \cfrac{13}{3}\cdot \cfrac{6}{1}\implies \cfrac{13}{1}\cdot \cfrac{6}{3}\implies \cfrac{13}{1}\cdot\cfrac{2}{1}\implies \text{\LARGE 26}[/tex]

The opportunity cost for the Congo to produce additional diamonds is; 4 thousand units of corn.

Opportunity costs are defined as the benefits of an alternative decision when the decision maker is made to reject the alternative.

For example, the opportunity cost of going to college would be the earnings forgone.

The opportunity cost is calculated as the lost benefit when an alternative decision is not followed up.

Fractionally, we can say that the opportunity cost of producing one product A) to another (B) = Units of B/Units of A.

From the attached table, we can deduce the following;

United States opportunity cost to produce diamonds = 60/10 = 6

United States opportunity cost to produce corns = 10/60 = 1/6

Congo's opportunity cost to produce diamonds = 20/5 = 4

Congo's opportunity cost to produce corn = 5/20 = 1/4

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The zeros of the polynomial P(x) = x³ + 7x² - x - 7  is  1 , - 1 , - 7 .

In algebraic expressions, exponents may have rational values. A polynomial, on the other hand, is an algebraic assertion with a whole number exponent on any variable. The places where a polynomial turns 0 are referred to as its zeros.

P(x) = x³ + 7x² - x - 7

Now we have to find one zero of given polynomial.

By hit and trial, we get

P(-7) = (-7)³ + 7 (-7)² - (-7) - 7

        = 0

Hence we get one zero = -7

So, -7 is the roots of the equation.

Now, by factorisation :

   P(x) = x³ + 7x² - x - 7

           = x² ( x+7 ) - 1 ( x+3 )

            = (x² - 1) ( x+7 )

            = ( x-1 )( x+1 )( x+7)

Hence the zeros of the polynomial is 1 , - 1 , - 7.

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All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = x3 + 7x2 − x − 7

The upper sum is 24 and the lower sum is 8 for the given function

f(x) = 6 - x², -2 ≤x≤ 2.

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

Given,

f(x) = 6 - x²

-2 ≤x≤ 2

When n=2, partition of interval -2, 0, 2

When x=-2, f(-2)=6-4

f(-2)=2

x=0, f(0)=6-0

f(0)=6

x=2, f(2)=6-4

f(2)=2

Upper sum= M₁S₁+M₂S₂

=6(2)+6(2)

=24

Lower sum=m₁ s₁+m₂ s₂

=2(2)+2(2)

=8

Therefore, upper sum=24 and lower sum= 8

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Option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].

Here, we are given a polynomial of the form [tex]x^{3}[/tex] + b[tex]x^{2}[/tex] + cx + d

The zeroes of the polynomial are ( -4 + 4i ) and 4

The third root of the cubic equation will be (-4 - 4i) which is the conjugate of (-4 + 4i)

This means that for x = ( -4 + 4i ), ( -4 - 4i ) and 4, the polynomial is equal to 0.

Further, the sum of zeroes of a cubic equation

= -(coefficient of [tex]x^{2}[/tex] )/(coefficient of [tex]x^{3}[/tex])

Thus, -4 + 4i + 4 - 4 - 4i = -b

b = 4

Similarly, the sum of the product of zeroes taken 2 at a time = c

⇒ (-4 + 4i)(-4- 4i) + 4(-4 + 4i) + 4(-4- 4i) = c

c = 16 -16[tex]i^{2}[/tex] - 16 + 16i - 16 - 16i

c = 16 + 16 - 32

c = 0

Further, product of zeroes = -d

-d = (-4 + 4i) (-4- 4i) 4

d = -(16 + 16i - 16i -16[tex]i^{2}[/tex]) 4

d = -(16 + 16)4

d = -128

Thus, we get that option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].

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for point (1,4)

After 1 hour, Evelyn and her friends are 4 miles from shore.

for point (3,12)

After 3 hour, Evelyn and her friends are 12 miles from shore.

A political party is made up of people who band together to run the government, win elections, and shape public policy. Currently, the two major parties in Congress are the Democratic and Republican.

Political parties act as a conduit between the governed and the ruling class. They educate the public, arouse inspiration, and pique interest in and engagement in public affairs. Their main duty is to suggest candidates for elected office.

Self-annuncation, in which a candidate for office only declares their candidacy, is the earliest method of nominating in American politics.

The national chairman, a national committee, the national convention, and two congressional campaign committees make up the party's overall organizational structure. The party is decentralized at the state level, and state legislation generally determines how it is structured.

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Answer:

-19y+20y=-6

Step-by-step explanation:

and means plus so its would be -19y+20y

is=equal sign so -19y+20y=-6

The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.

Given that,

Your subject-matter expert informs you that she believes it will take her 40 hours to finish the work. The project begins on January 20 at 8 a.m. The staff only works throughout the weekdays, eight hours a day.

We have to find when will the assignment be completed.

We know that,

This simple table explains the answer

Thursday, January 20, at 4 p.m. - 8 hours worked

Friday, January 21, at 4 p.m. - 16 hours worked

Monday, January 24, at 4 p.m. - 24 hours worked

Tuesday, January 25, at 4 p.m. - 32 hours worked

Wednesday, January 26, at 4 p.m. - 40 hours worked

Therefore, The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.

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