A triangular garden is to be split so that the angle at vertex B is bisected. This diagram was supplied by the landscape architect, but you do not have a way to measure the angles at B. You do have the given side lengths, so what is the length of side that will allow the angle at B to be bisected?

A diagram shows a triangle ABC. BD is a line drawn to the base AC. The length of AB is 5 m, BC is 7 m, AD is x m, DC is 4 m, and AC is 12 m.

The zeroes of the function g(x) = x² +3x -4 as given in the task content is; x = -4 and x = 1.

It follows from the task content that the function g(x) given in the task content is; g(x) = x² +3x -4.

On this note, it follows that the zeroes of the function can be determined by solving the quadratic function as follows;

x² +4x -x -4 = 0

(x+4) (x-1) = 0

Ultimately, it can be concluded that the values of x which represents the zeroes of the function are; x = -4 and x = 1.

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The area of the rhombus is 100 mm². The correct answer is D.

A rhombus is one type of parallelogram and has 4 sides and 4 vertices.

Every side is equal in length and opposite angles are equal.

Given:

A rhombus with horizontal diagonal length 25 millimeters,

and vertical diagonal length 8 millimeters.

Let d₁ = 25 mm and, d₂ = 8 mm.

Let A be the area of rhombus.

To find the area of rhomus:

Using diagonals,

A = (1/2) × d₁× d₂.

Substituting the values of diagonals,

A = 1/2 x 25 x 8

A = 200/2

A = 100 mm².

Therefore, 100 mm² is the area of the rhombus.

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logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x

What is logarithmic equation?

The given logarithmic equation is;

[tex]log x = 4[/tex]

Since, log with base 10 is written as [tex]log x[/tex]  simply, therefore, we have:

[tex]log_{10} x[/tex] = 4

Using the definition of logarithm, we get;

[tex]x = 10^{4}[/tex]

Equivalently, [tex]10^{4} = x[/tex]

Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x

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The complete question is -

Which exponential equation is equivalent to this logarithmic equation?

log x = 4

0.9544 = 95.44% of scores lie between 220 and 380 points.

Normal distribution problems can be solved using the Z-score formula.

With a set of means and standard deviations, the Z-score for measure X is given by: After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is less than X. H. Percentile of X. Subtract 1 from the p-value to get the probability that the value of the measure is greater than X.

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

We are given mean 300, standard deviation 40.

This means that µ= 300, σ = 40

What proportion of scores lie between 220 and 380 points?

This is the p-value of Z when X = 380 subtracted by the p-value of Z when X = 220.

X = 380

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

Z= (380-300)/40

Z= 2

Z=2 has a p-value of 0.9772.

X=300

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

Z= (220-380)/40

Z=-2

Z=-2 has a p-value of 0.9772.

0,9772 - 0,0228 = 0,9544

0.9544 = 95.44% of scores lie between 220 and 380 points.

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The total pay for hours worked is $980.013

The method with which a daily worker's wage is being paid is by calculating the total hours worked and multiplying it with the fixed hourly pay.

From the information given:

In hours, we have:

= (38 + 0.9667) hours

= 38.9667 hours

If a fixed hourly pay of $25.15 is being paid, we have:

= $(38.9667 × 25.15)

= $980.012505

= $980.013 to the nearest hundredth.

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Answer:

Power Bars are cheaper!

Step-by-step explanation:

FG: $18/12 Bars = $1.50 per bar

PB: $21.75/15 Bars = $1.45 per bar

Answer:

Super Power bars

Step-by-step explanation:

In order to find the best price, we want to calculate the unit rate, or the price for each bar. Let's start with the Fee Great energy bars. Since they are $18 for 12 bars, we divide 18 by 12 to figure out how much each bar costs. We get 1.5, or $1.50 per bar. Next lets claculate the unit rate for the Super Power bars. Since its $21.75 for 15 bars, we divide 21.75 by 15. We get 1.45, or $1.45 per bar. Since the price for one bar is cheaper for the Super Power bars as $1.45 is less than $1.50, the Super Power bars are the best price for each bar.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

A mean is also referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both players A and B is given by:

Distance = Mean of player B - Mean of player A

Distance = 10 - 6

Distance = 4.

The mean absolute deviation (MAD) for player A is given by:

MAD A = 1/11[2(3 - 6) + 2(4 - 6) + (5 - 6) + (6 - 6) + (7 - 6) + 2(8 - 6) + 2(9 - 6)]

MAD A = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]

MAD A = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]

MAD A = 1/11 × [22]

MAD A = 22/11

MAD A = 2.

Also, the mean absolute deviation (MAD) for player B is given by:

MAD B = 1/11[2(7 - 10) + 2(8 - 10) + (9 - 10) + (10 - 10) + (11 - 10) + 2(12 - 10) + 2(13 - 10)]

MAD B = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]

MAD B = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]

MAD B = 1/11 × [22]

MAD B = 22/11

MAD B = 2.

Therefore, distance between the means = two (2) times the MAD.

Distance = Means × MAD

4 = 2 × 2.

In conclusion, we can infer and logically deduce that there is some overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.

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The parent function of the function represented in the table is exponential.

If function f was translated down 4 units, the f(x) values would be decreased by 4.

A point on the table for the transformed function would be (4, 87).

The coordinate of P is (A) ( 40, 96).

To find What are the x- and y- coordinates of point p on the directed line segment from K to J:

It can be seen from the figure the coordinates of K and J:

The coordinates of P can be determined as:

[tex]x=\frac{m}{m+n} (x_{2}-x_{1})+x_{1} } \\y=\frac{m}{m+n} (y_{2}-y_{1})+y_{1} } \\[/tex]

So, as the P point divides the line into three-fifths of the length,

Which gives the ratio as 3: 2.

m:n = 3:2

Therefore, the coordinate of P is (A) ( 40, 96).

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The complete question is shown below:

What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J?

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

(A) (40, 96)

(B) (85, 105)

(C) (80, 104)

(D) (96, 72)

Answer:100

Step-by-step explanation: The question asks us to round the given numbers to the nearest hundred. 295 rounded to the nearest hundred is 300 and 198 rounded to the nearest hundred is 200. 300-200 is 100, so they need to sell 100 more tickets for the show to be houseful.

Using proportions, the length of x is of 2.9.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The triangles are similar, that is, they have the same angles, hence the corresponding sides are proportional, by the following rule of three:

x/7 = 5/12

Applying cross multiplication:

12x = 35

x = 35/12

x = 2.9.

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Using a system of equations, it is found that there were 4,000 children tickets sold.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given by:

The attendance at the amusement park is 5,000 attendees, hence:

x + y = 5000 -> y = 5000 - x.

Considering the cost of parking and that the total money earned by the park is $100,000, we have that:

15x + 40y = 100000

Applying the multiplication of the matrices, these equations are the same that the system gives. Replacing the second equation into the first:

15x + 40(5000 - x) = 100000

25x = 100000

x = 100000/25

x = 4000.

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The hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.

The following can be deduced from the information:

x1 = 275

x2 = 170

n1 = 500

n2 = 500

The sample proportion will be:

p1 = 275/500 = 0.55

p2 = 170/500 = 0.34

The pooled proportion will be:

= (275 + 170)/(500 + 500)

= 0.44

The test statistic is 6.681. It should be noted that the test statistics is a number that's calculated by a statistical test. It shows how the observed data are far from the null hypothesis.

The p value in this scenario is extremely small. The p value is a measurement used to validate a hypothesis against the observed data. Therefore, we have to reject the null hypothesis.

In this case, the hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.

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The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

A rectangular prism is a three-dimensional shape, having six faces, where all the faces are rectangles.

The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.

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The factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).

The given expression is 20m²/n²- 30n²/m² +1.

We need to factorise the given expression.

To factor, a trinomial in the form x²+ bx + c, find two integers, r and s, whose product is c and whose sum is b.

Rewrite the trinomial as x²+ rx + sx + c and then use grouping and the distributive property to factor the polynomial. The resulting factors will be (x + r) and (x + s).

Now, we can rewrite 20m²/n² +1 - 30n²/m² as 20m²/n² +25mn/mn- 24mn/mn- 30n²/m².

=(20m²/n² +25mn/mn)- (24mn/mn- 30n²/m²)

=5m/n(4m/n + 5m/n)-6n/m(4m/n+5n/m)

=(4m/n + 5m/n)(5m/n-6n/m)

Therefore, the factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).

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The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = [tex]^{52} C_{2}[/tex]

And, the total number of ways of  getting exactly one face cards

= [tex]^{12} C_{1} \times ^{40} C_{1}[/tex]  + [tex]^{40} C_{1} \times ^{12} C_{1}[/tex]

= 2[tex]^{40} C_{1} \times ^{12} C_{1}[/tex]

Therefore, the probability of getting exactly one face card

= [tex]\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }[/tex]

[tex]= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }[/tex]

[tex]= \frac{2(40\times 12)}{26\times 51}[/tex]

[tex]=\frac{2\times 480}{1326}[/tex]

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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The mean, median, and mode all have the same values in a symmetrical distribution. The mean is frequently chosen as the primary indicator of central tendency in these situations.

The mean, median, and mode frequently occur at the same location in a symmetrical distribution, where the values of variables exist at regular frequencies. The graph's middle can be divided into two sides that mirror one another by drawing a line through it.

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The number has over positive integer divisors. One of them is chosen at random. If each divisor has the same probability, then the likelihood that a random one will be odd is precisely 1/19. This assumes that all divisors have the same probability. This is further explained below.

Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.

In conclusion, The number may be divided into more than positive integers. A selection is made at random from among them. If each divisor has the same probability, then the chance that a random one would be odd is exactly 1/19. This assumes that each divisor has the same probability. This makes the assumption that the probability of each divisor is the same.

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The measure of Arc AU of the given Circle Geometry is; 50°

The circle theorem we will apply to solve for the arc measure states that “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”

We can express the above theorem as;

Angle at the center = 2 × Angle at the circumference

From the attached image below  and from the given statement in the question, we are given that; ∠QUA = 111°

Therefore, applying the circle theorem earlier quoted, we can say that; m∠QDA = 2 × ∠QUA

m∠QDA = 2 × 111° = 222°

Which gives;

∠QOA =  = 360° - 222° = 138°

∠QOA = ∠QOU + ∠UOA (by angle addition property)

Thus;

∠QOA = 138° = 88° + ∠UOA

∠UOA = 138° - 88° = 50°

Thus, the measure of Arc AU is;

Arc AU = ∠UOA = 50°

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Answer: b

Step-by-step explanation:

Answer:

25.0

Step-by-step explanation:

Notice that points A, B, and C form a right triangle. This allows us to use the Pythagorean theorem, a^2 + b^2 = c^2, to find the missing side. AB is the hypotenuse, so substitute 55 for c, and BC is the leg, so substitute 49 into either a or b in the formula.

a^2 + b^2 = c^2

49^2 + b^2 = 55^2

b^2 = 3025 - 2401

b^2 = 624

b = sqrt (624)

b = 24.9799919936

Answer:

A, D, E

Step-by-step explanation:

I got it right.

Answer:

Part A) The system has one solution

Part B) The solution is the point (4,4)

i believe

Answer:

1) (3,1)

2) (4,1)

3) No solution

Step-by-step explanation:

The solution is point where the graphs cross.  It is a little hard to see the pictures, but I think that I have the right ordered pairs.  The ordered pairs are in the order (x,y).  The x tells you how far (in these cases), the point is right of the origin (0,0 the middle of the whole graph).  The y tells us (in these cases) how high the point is from the origin (0,0).

The last answer has no solution because the lines are parallel and they do not cross.

Answer:

either 885 more or 450 more

Step-by-step explanation:

Monday: 1000

Tuesday: 1000*1.3 = 1300

Wednesday:

I'm assuming 45% more from tuesday?

          1300*1.45 = 1885

or if not:

          1000*1.45 = 1450

either 885 more or 450 more

you can also just do 1000*1.3*1.45 = 1000*1.885 = 1885 if thats what the question means

Answer:3 3/4 meters

Step-by-step explanation:

6/(1 3/5)=3.75 meters or 3 3/4 meters

Answer:

31: 98,765 x 9 + 3 = 888,888

32: 12.345 x 9 + 6 = 111,111

33: 3,367 x 15 = 50,505

34: 15,873 x 35 = 555,555

35: 33,334 x 33,334 = 1,111,155,556

36: 11,111 x 11,111 = 123,454,321

You skipped 37-39

40: 3 + 9 + 27 + 81 + 243 = 3(243-1)/2

41: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 1 - 1/32

Step-by-step explanation:

It's just patterns bro

Answer: 2

Step-by-step explanation:

[tex]y=\frac{1}{3}x^2 +2x+5 \longrightarrow \frac{dy}{dx}=\frac{2}{3}x+2[/tex]

Setting this equal to 0 yields [tex]x=-3[/tex].

When [tex]x=-3[/tex], [tex]y=2[/tex]

Answer:

Step-by-step explanation:

Given quadratic equation:

Its leading coefficient is positive, so it has minimum value at vertex.

The x-coordinate of the vertex is:

Substitute the coefficients:

Find the value of y at vertex:

The matching answer choice is A.

Using the hsd test qcrit = 3.65  

HSD testis used to check differences among sample way for significance. The Tukey's HSD assessments all pairwise variations at the same time as controlling the probability of making one or greater type I errors.

A Tukey-Kramer test lets us check the null speculation of no distinction between the population approach for all pairs of businesses. The Tukey-Kramer check (also known as a Tukey sincere importance test, or Tukey HSD), is carried out in R inside the function.

solution

given;

   using HSD test, the degree of freedom = 16

                                                         and α=0. 05

                                                         groups = 3

                         Hence,                    Qcrit = 3.65    {using HSD table}

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Answer:

(-1, 5) and (3, -3)

Step-by-step explanation:

The solutions are all the points where the two functions intersect. Since the lines intersect at two different points, there are two solutions.

The two points at which the functions appear to intersect are (-1, 5) and (3, -3).