PLEASE HELP ,,,,1. If AMNP is an equilateral triangle, find the values of x
and y.

Answer: -(-3)2-(9(-3)-3(-4))

6+27-12

Step-by-step explanation:

Two negatives make a positive and a negative times a positive is negative

The board should be 28 inches long.

What is an expression?

An expression or mathematical expression in mathematics is a finite combination of symbols that is well-formed in accordance with context-dependent principles.

Let's call the length of the first part "x". Then, the length of the second part would be x + 6 inches. The total length of both parts is 50 inches, so we can set up an equation to solve for x:

x + (x + 6) = 50

Expanding and solving for x:

2x + 6 = 50

2x = 44

x = 22

So, the first part should be 22 inches long, and the second part should be 22 + 6 = 28 inches long.

The board should be 28 inches long

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f(x)

(2, 0) and (3, 2)

m = y - y1

x - x1

m = 2 - 0

3 - 2

m = 2

y - y1 = m(x - x1)

y - 0 = 2(x - 2)

y = 2x - 4

f(x) = 2x - 4

g(x)

(2/3, 0) and (1, 2)

m = y - y1

x - x1

m = 2 - 0

1 - 2/3

m = 6

y - y1 = m(x - x1)

y - 2 = 6(x - 1)

y = 6x - 4

g(x) = 6x - 4

since both equations are linear that means the graphs will be straight lines with y-intercept being -4 for both of the graphs.

if,

g(x) = f(k*x)

f(x) = 2x - 4

f(k*x) = 2k*x - 4

6x - 4 = 2k*x - 4

6x = 2kx

6 = 2k

k = 3.

I hope the answer is correct. All the best!

Toni had 17 points, Effie had 25 points and Linda had 18 points.

The question is asking to find the number of points each girl had in a girl's basketball game. To find out how many points Effie had, you must multiply Toni's points by 3, subtract 8, and then multiply the difference by 2. To find out how many points Linda had, you must add 9 to Toni's points and divide the sum by 3. The given information is that Effie scored 9 more than Toni and Linda combined.

Formula and Calculation:

Toni's Points = x

Effie's Points = 3x-8

Linda's Points = (x+9)/3

Effie scored 9 more than Toni and Linda combined, so:

3x-8 = x+9/3 + 9

2x-8 = x+9

x = 17

Therefore, Toni had 17 points, Effie had 25 points and Linda had 18 points.

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Answer:

(1). \(h(t)=-4(t-1)^2+36\)

(2). 1 minute

Step-by-step explanation:

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer:

Point A(5, -1) is mapped to A'(1, 5)

The rule is:

This is 90° anticlockwise rotation

Point B(-4, 6) will map to:

The calculated surface area of the figure is 152 square feet

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

The triangular prism

The surface  area is calculated as

SA = hp + 2B

Where

h = height

p = perimeter of base

B = base area

From the figure, we have

B = 1/2 * 6 * 4 = 12

p = 5 + 5 + 6 = 16

h = 8

So, we have

SA = 8 * 16 + 2 * 12

Evaluate

SA = 152

Hence, the surface area is 152 square feet

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Answer:

x<-2, x>-7

Step-by-step explanation:

1st one

add 7 to 3 =10

-5 divide by 10 = -2

2nd one

add 7 to -42 = -35

-35 divided by 5 = -7

The absolute maximum value of the function f(x) = x² - x - 4 on the interval [0, 4] is 8, and the absolute minimum value is -17/4.

What is Absolute Value?

"It is the distance of a number from zero, without considering direction."

"It is always positive."

To find the absolute maximum and minimum values of the function f(x) = x² - x - 4 on the interval [0, 4], we can follow these steps:

Step 1: Find the critical points by taking the derivative of the function.

f'(x) = 2x - 1

To find the critical points, we set f'(x) = 0 and solve for x:

2x - 1 = 0

2x = 1

x = 1/2

Step 2: Check the endpoints of the interval.

We need to evaluate the function at the endpoints of the interval [0, 4], which are x = 0 and x = 4.

Step 3: Evaluate the function at the critical points and endpoints.

f(0) = (0)² - 0 - 4 = -4

f(1/2) = (1/2)² - (1/2) - 4 = -17/4

f(4) = (4)²- 4 - 4 = 8

Step 4: Determine the absolute maximum and minimum values.

From the values obtained in Step 3:

The absolute maximum value is 8, which occurs at x = 4.

The absolute minimum value is -17/4, which occurs at x = 1/2.

Therefore, the absolute maximum value of the function f(x) = x² - x - 4 on the interval [0, 4] is 8, and the absolute minimum value is -17/4.

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Answer:

Geometric Sequence.

Step-by-step explanation:

We are told that the square is split into 4 similar squares. One of the new squares is now split into fourths again and this same sequence is repeated over again.

This means that there is a common ratio which is ¼.

Since there is a common ratio and not common difference, this sequence is said to be a geometric sequence.

Answer:

$1,050

Step-by-step explanation:

Simply multiply the cost per kid ticket and number of kids:

$5.25 x 200 = $1,050

From the information, the equation that represents the sentence will be 3(n - 8).

Let the number be represented as n.

Since the expression is to find the equation that represents the word phrase three times the difference of a number and eight.

This will be:

= 3(n - 8)

Therefore, the correct option is 3(n - 8).

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Answer:

THE ANSWER IS DOWN BELOW :)

Mia is correct. m∠TSU and m∠QSR are congruent because they are vertical angles. ST/SQ is proportional to SU/SR. Therefore  △STU and △SQR are similar by the SAS

In geometry, the term "congruent" means that two figures have the same size and shape. In the statement "m∠TSU and m∠QSR are congruent", the term "congruent" refers to the fact that the two angles have the same measure. This means that the angle formed by the points T, S, and U has the same degree measure as the angle formed by the points Q, S, and R.

The statement "ST/SQ is proportional to SU/SR" can be proven using the properties of parallel lines and transversals.

ST/SQ = 9/4 and  SU/SR = 13.5/6

To show that ST/SQ and SU/SR are proportional;

135/60 = (135 ÷ 15) / (60 ÷ 15) = 9/4

Using the Side-Angle-Side (SAS) similarity criterion, we can conclude that △STU and △SQR are similar.

This is because we have two pairs of corresponding sides that are proportional (ST/SQ and SU/SR) and one pair of corresponding angles that are congruent (m∠TSU and m∠QSR).

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Answer:

A, B, D and F.

Step-by-step explanation:

Volume of A = 1/3 pi r^2h = 1/3 pi 3^2 12

= 36pi unit^3.

B also = 36pi.

C = 1/3 pi 6^2 * 6

=  72 pi.

D. =  4 * pi r^2

= 4*9 pi

= 36pi.

E. v = 1/3 * 12pi * 3

= 12pi.

F. = 3 *4 *3pi

= 36pi.

G. V =  1/2 * 3 *4 * 3pi

= 18pi.

Answer:

y =  3x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, 10 )

m = \(\frac{10-4}{2-0}\) = \(\frac{6}{2}\) = 3

The y- intercept c = 4

y = 3x + 4 ← equation of line

The triangular pyramid has a greater surface area than the square pyramid.

The surface area of a pyramid depends on the shape and dimensions of its base as well as its height and slant height. In this case, the square pyramid has a square base with sides of length 10 cm and four equilateral triangular faces with a height of 8.66 cm. The triangular pyramid has an equilateral triangular base with sides of length 10 cm and three identical equilateral triangular faces, each with a height of 8.66 cm.

To calculate the surface area of the square pyramid, we can first find the slant height of each triangular face using the Pythagorean theorem:

slant height = sqrt(10^2 + (8.66/2)^2) = 10.82 cm

Then, we can calculate the area of each triangular face as:

area = (1/2) * base * height = (1/2) * 10 cm * 8.66 cm = 43.3 cm^2

And finally, the total surface area of the pyramid is:

total surface area = area of base + 4 * area of triangular faces

= 10 cm * 10 cm + 4 * 43.3 cm^2

= 600.8 cm^2

To calculate the surface area of the triangular pyramid, we can use the formula:

surface area = area of base + 1/2 * perimeter * slant height

The area of the equilateral triangular base is:

area = (sqrt(3)/4) * base^2 = (sqrt(3)/4) * 10 cm^2 ≈ 21.65 cm^2

The perimeter of the base is simply 3 times the length of a side, or 30 cm. The slant height of each triangular face is 8.66 cm, so the surface area of the pyramid is:

surface area = 21.65 cm^2 + 1/2 * 30 cm * 8.66 cm

= 21.65 cm^2 + 130.0 cm^2

= 151.65 cm^2

Therefore, the triangular pyramid has a greater surface area than the square pyramid.

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a) The average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. b) The estimated coefficients of REDS and TRAINS in the regression model are 1.3353 (REDS). c) The absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis.

a) To find the average estimated time in minutes for Bill to drive to work when he leaves on time at 6:30 and there are no red lights and no trains at the crossroad to wait, we substitute the values into the regression model:

TIME = -19.9166 + 0.3692(DEPART) + 1.3353(REDS) + 2.7548(TRAINS)

Given:

DEPART = 0 (as he leaves on time at 6:30)

REDS = 0 (no red lights)

TRAINS = 0 (no trains to wait for)

Substituting these values:

TIME = -19.9166 + 0.3692(0) + 1.3353(0) + 2.7548(0)

    = -19.9166

Therefore, the average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. However, it's important to note that negative values in this context may not make practical sense, so we should interpret this as Bill arriving approximately 19.92 minutes early to work.

b) The estimated coefficients of REDS and TRAINS in the regression model are:

1.3353 (REDS)

2.7548 (TRAINS)

Interpreting the coefficients:

- The coefficient of REDS (1.3353) suggests that for each additional red light, the estimated time to drive to work increases by approximately 1.3353 minutes, holding all other factors constant.

- The coefficient of TRAINS (2.7548) suggests that for each additional train Bill has to wait for at the crossing, the estimated time to drive to work increases by approximately 2.7548 minutes, holding all other factors constant.

c) To test the hypothesis that each train delays Bill by 3 minutes, we can conduct a hypothesis test.

Null hypothesis (H0): The coefficient of TRAINS is equal to 3 minutes.

Alternative hypothesis (Ha): The coefficient of TRAINS is not equal to 3 minutes.

We can use the t-test to test this hypothesis. The t-value is calculated as:

t-value = (coefficient of TRAINS - hypothesized value) / standard error of coefficient of TRAINS

Given:

Coefficient of TRAINS = 2.7548

Hypothesized value = 3

Standard error of coefficient of TRAINS = 0.1390

t-value = (2.7548 - 3) / 0.1390

       = -0.2465 / 0.1390

       ≈ -1.7733

Using a significance level of 5% (or alpha = 0.05) and looking up the critical value for a two-tailed test, the critical t-value for 230 degrees of freedom is approximately ±1.9719.

Since the absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that each train delays Bill by 3 minutes.

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One of \(L {tan-'1}\) or \(L {tant}\) exists, yet the other does not because of the differences in the continuity of the two functions. L {tan-'1} exists because it is a continuous function while L {tant} does not exist because it is a discontinuous function.

In mathematical analysis, the set of accumulation points of a sequence, function, or set is known as the limit set. In the study of analysis, there are two types of functions, continuous functions, and discontinuous functions.

\(L {tan-'1}\) exists because it is a continuous function while L {tant} does not exist because it is a discontinuous function.

\(L {tan-'1}\) exists, which implies that it has a limit set because it is a continuous function. It implies that there is a specific point where the function values approach without reaching.

L {tant} does not have a limit set because it is a discontinuous function. The function jumps from one value to another at specific points.

For instance, tan t has a vertical asymptote at \(t= \pi/2.\), where the limit of tan t as t approaches \(\pi/2\) is positive infinity while \(tan-1 t\) does not have vertical asymptotes.

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Answer:

10 is to 1

Step-by-step explanation:

First convert both the distances to the same unit. So,3 km = 3 × 1000 m = 3000 m. Thus,the required ratio, 3 km : 300 m is 3000 : 300 = 10 : 1.

Answer:

option A

Step-by-step explanation:

wkt 1km=1000m

3km=3000m

3000m:300m = 10:1

thus 3km:300m = 10:1

Answer:

Option B

Step-by-step explanation:

The multiplication process of matrices works by multiplying the first row of the  first matrix by the first column of the second matrix. The same goes with the second row of the first matrix by the second column of the other matrix. Below is the solution why option B is the correct answer.

\(A = \left[\begin{array}{ccc}8&11\\13&5\\\end{array}\right]\)              

\(B = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]\)  ← This is the Identity Matrix.

The attached screenshot shows the solution of the multiplication process. In essence, if you multiply any matrix by the identity (Matrix B), you should end up with your original matrix. Thus, multiplying Matrix A by the Identity matrix results in the same values as Matrix A.                                              

Therefore, the correct answer is B.                                    

Answer:

20x-18y

Step-by-step explanation:

26x-2(3x+4y)-10y

26x-6x-8y-10y

20x-18y go doawnload the app photomath its a great tool

Answer:

the circumstance would be 21.99

the area is 38.48

Step-by-step explanation:

radius is half the diameter so your radius is 3.5

The area of a circle is pi times the radius squared (A = π r²) which for you would be A = 3.14 × 3.5²

circumference is found by multiplying 2 times pi times the radius (C = 2πr) which for you would be C = 2 × 3.14 × 3.5

Answer:12

Step-by-step explanation:

Given

Each coin roll can hold 40 quarters

There are a total of 479 quarters

So, no of coin roll \(=\dfrac{\text{Total quarters}}{\text{Holding capacity of each coin roll}}\)

\(\Rightarrow \frac{479}{40}=11.975\)

As no of coin rolls cannot be in decimal

\(\therefore\) there are 12 coin rolls

Answer:

Step-by-step explanation:

(x₁, y₁) = (-10, -10)   & (x₂, y₂) = (-5, -10)

y-intercept = b = -10

There is no change in y- coordinates. So, the line is parallel to x- axis

Slope = 0

Equation: y = b

y = -10

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Both Cov(X,Y) and corr(X,Y) do not depend on the parameter λ.

To compute Cov(X,Y), we first need to compute E(X), E(Y), and E(XY). Since X ∼ Poisson(λ), we have E(X) = λ.

Now, let's compute E(Y). We know that Y represents the number of students on SEF, and each student chooses to follow SEF with probability p.

Therefore, Y follows a binomial distribution with parameters X and p. Hence, E(Y) = X * p.

Next, let's compute E(XY). Since X and Y are independent, we have-

\(E(XY) = E(X) * E(Y)\)

\(= λ * X * p.\)

Now, we can compute Cov(X,Y) using the formula:

\(Cov(X,Y) = E(XY) - E(X) * E(Y).\)

Substituting the values we obtained, we have-

\(Cov(X,Y) = λ * X * p - λ * X * p\)

= 0.

Moving on to compute corr(X,Y), we need to compute Var(X) and Var(Y) first.

Since X ∼ Poisson(λ), we have Var(X) = λ.

For Y, since it follows a binomial distribution with parameters X and p, we have

\(Var(Y) = X * p * (1 - p)\).

Now, we can compute corr(X,Y) using the formula:

\(corr(X,Y) = Cov(X,Y) / sqrt(Var(X) * Var(Y)).\)

Substituting the values we obtained, we have-

\(corr(X,Y) = 0 / sqrt(λ * X * p * X * p * (1 - p))\)

= 0.

Therefore, both Cov(X,Y) and corr(X,Y) do not depend on the parameter λ.

(b) Assuming that the total number of students at UChL is known to be n, we can find the joint distribution of Y, Z, and the number W of students who do not enroll in a degree program in statistical science.

Since each student independently chooses to enroll in a degree program with probability r, the number of students on SEF, Y, follows a binomial distribution with parameters n and r.

Similarly, the number of students on ES, Z, follows a binomial distribution with parameters n and (1 - r).

Hence, the joint distribution of Y and Z is given by P(Y=y, Z=z)

\(= C(n,y) * r^y * (1-r)^(n-y) * C(n-z, z) * (1-r)^z * r^(n-z),\)

Where C(n,y) represents the number of combinations of choosing y items from a set of n items.

To compute corr(X,Y), we can use the relationship that corr(X,Y) = corr(Y + Z, Y)

\(= corr(Y, Y) + corr(Z, Y) + 2 * sqrt(corr(Y, Z) * corr(Y, Y)).\)

Since Y and Z are independent, corr(Y, Z) = 0.

We already computed corr(Y, Y) in part (a), and it is 0.

Hence,

\(corr(X,Y) = corr(Y, Y) + corr(Z, Y) + 2 * sqrt(corr(Y, Z) * corr(Y, Y))\)

= 0 + 0 + 2 * sqrt(0 * 0) = 0.

Therefore, the correlation computed in this part, corr(X,Y), agrees with the correlation computed in part (a), which is also 0.

The correlation between X and Y, corr(X,Y), remains 0 regardless of the parameter values λ and r.

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