Each column of the matrix (blank) represents a vertex of a triangle. If Bella scales the triangle by finding 3T, what are the vertices of the scaled triangle?

The units that each student used, given the measurement that they got and all of them being right was:

The height of a bookshelf is typically measured in inches, feet, or yards .

Student A measured 72 units, which is equal to 6 feet. Student B measured 2 units, which is equal to 24 inches .

Student C measured 6 units, which is equal to 18 yards. All three students are correct, as they all used different units to measure the same height .

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Full question is:

Three students measure the height of a bookshelf. Student A measures 72 units, Student B measures 2 units, and Student C measures 6 units. The teacher says all three students are correct. What units did each student use?

To find the probability that 15 or more instructors choose the book with the better format and illustrations, we can use the binomial distribution formula.

Let's denote the event of an instructor choosing the book with the better format and illustrations as "success" (S), and the event of an instructor choosing the other book as "failure" (F). The probability of success is p = 0.5, and the probability of failure is q = 1 - p = 0.5.

We want to find the probability of 15 or more successes in a sample of 25 instructors. We can calculate this probability by summing the probabilities of exactly 15, 16, 17, ..., 25 successes.

P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)

Using the binomial distribution formula, the probability of exactly k successes in a sample of n trials is:

P(X = k) = C(n, k) * p^k * q^(n-k)

where C(n, k) is the binomial coefficient "n choose k," given by:

C(n, k) = n! / (k! * (n-k)!)

Applying this to our problem, we can calculate the probability as follows:

P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)

= Σ[ k = 15 to 25 ] ( C(25, k) * p^k * q^(25-k) )

Let's calculate this probability using the binomial distribution formula:

P(X ≥ 15) = Σ[ k = 15 to 25 ] ( C(25, k) * (0.5)^k * (0.5)^(25-k) )

Calculating this sum gives us the probability that 15 or more instructors choose the book with the better format and illustrations.

Answer:

see explanation

Step-by-step explanation:

using any of the tangent, sine, cosine ratios in the right triangle.

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{6}[/tex] , then

Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{7}{6}[/tex] ) ≈ 49.40° ( to 2 decimal places )

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

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{6.32}[/tex]

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{6.32}[/tex]

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2}{6}[/tex]

Answer: rental is $415, and the standard deviation is $5.

Step-by-step explanation:

If about 99.7 percent of the monthly rentals fall between 400 and 430, it implies that this range encompasses three standard deviations from the mean.

To calculate the mean, we can find the midpoint of the given range:

Mean = (400 + 430) / 2 = 415

Since the range of three standard deviations covers about 99.7 percent of the data in a normal distribution, we can use this information to estimate the standard deviation (σ).

Standard deviation (σ) = (430 - 415) / 3 = 15 / 3 = 5

Therefore, based on the given information, the mean monthly rental is $415, and the standard deviation is $5.

The reason of discontinuity of the given function is described below.

Since we know that,

A continuous function, as the name implies, is one whose graph is continuous with no breaks or jumps. In other words, if we can draw the curve (graph) of a function without ever raising a pencil, we may claim that the function is continuous. The study of a function's continuity is critical in calculus because a function cannot be differentiable unless it is continuous.

A function is considered continuous if its graph is an uninterrupted curve with no holes, gaps, or breaks.

Now by mathematical definition of continuity

Left hand limit of a function at any point = right hand limit of function at that point = value of function at that point

Now from the graph we can see that,

At point point 3

The left hand limit and right hand limit are not equal and also the curve is discontinuous.

Hence, the given function is discontinuous function.

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To find the length of DE in circle D, we can use the properties of a circle and the given information.

In a circle, if two chords intersect, the product of the segments of one chord is equal to the product of the segments of the other chord. In this case, we have chord EF intersecting chord DE at point D.

Let x represent the length of segment DE, and y represent the length of segment DF. Therefore, the length of segment EF would be (x + y).

According to the chord-chord power theorem:

DE * EF = DF * DF

Substituting the given values:

x * (x + y) = y * y

x^2 + xy = y^2

We are also given that angle EDF measures 70 degrees. According to the angle intercepting chord theorem, the intercepted arc EF is twice the measure of angle EDF. So, the measure of arc EF is 2 * 70 = 140 degrees.

Now, we can use the length of arc EF to find the ratio of the lengths of segments EF and DF.

The ratio of the lengths of the intercepted arcs is equal to the ratio of the lengths of the corresponding chords. Therefore:

EF / DF = arc EF / arc DF

(x + y) / y = 140 / 360 [Using the measure of the intercepted arcs]

Simplifying this equation:

(x + y) / y = 7 / 18

Cross-multiplying:

18(x + y) = 7y

18x + 18y = 7y

18x = 7y - 18y

18x = -11y

Dividing by -11:

x = -11y / 18

We need to find the value of x, which represents the length of segment DE. Since segment lengths cannot be negative, we can disregard the negative sign.

x = 11y / 18

Substituting this value of x in the equation x^2 + xy = y^2:

(11y / 18)^2 + (11y / 18) * y = y^2

Simplifying:

121y^2 / 324 + 11y^2 / 18 = y^2

Multiplying through by 324:

121y^2 + 594y^2 = 324y^2

715y^2 = 324y^2

715y^2 - 324y^2 = 0

391y^2 = 0

y^2 = 0

Since y^2 = 0, it implies that y = 0. This means that segment DF has zero length.

Now, substituting y = 0 into the equation x = 11y / 18:

x = 11 * 0 / 18

x = 0

Therefore, the length of DE is 0.

In conclusion, the length of DE is 0.

I cannot load the image that you have provided this is what the answer is according to the text provided.

The probability that either event A or B will occur is 11/17.

We have,

The Addition Rule for Probability:

P(A U B) = P(A) + P(B) - P(A ∩ B),

where P(A U B) represents the probability of the union of events A and B, P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of the intersection of events A and B.

Now,

P(A) = 9/17

P(B) = 2/17

There is no intersection of Q and B so,

P(A ∩ B) = 0

Now,

P(A U B) = P(A) + P(B) - P(A ∩ B),

Substituting the values.

P(A U B) = The probability that either event A or B will occur.

So,

P(A U B)

= 9/17 + 2/17 - 0

= 11/17

Thus,

The probability that either event A or B will occur is 11/17.

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Answer:

The answer James

Step-by-step explanation:

James=2/5hours

J=2/5×60=2×12=24 minutes

Sandle=4/12×60=4×5=20 minutes

Answer:

[tex]\theta = 60; \theta \approx 83; \theta \approx 277; \theta = 300[/tex]

Note that the approximate value you should calculate properly with the inverse cosine function of your calculator to the number of digits you want.

Step-by-step explanation:

you already have a cosine. You might as well change that sine in a cosine too:

[tex]8(1-cos^2\theta) +6cos\theta-9=0\\8cos^2\theta -6cos\theta+1 =0[/tex]

(note that in the second line I also switched every sign by multiplying by -1 just to have a positive lead coefficient - just a pet peeve of mine. Now replace [tex]x=cos\theta[/tex] and let's solve

[tex]8x^2-6x+1=0\\\frac\Delta4 = 9-8 = 1\\x=\frac {3\pm1}8[/tex]

At this point we're back to the replacement. We have two options

[tex]cos\theta = \frac48 = \frac 12 \implies \theta = 60\°; \theta = 300\°\\cos\theta =\frac 18 \implies \theta \approx 83\°; \theta \approx 277\°[/tex]

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  [tex]x\leq 2[/tex]

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

The minimum y-value of g(x) is -3 and g(x) has the smallest possible y-value.

The function  f(x) = 32 - 3 is a constant function, as there is no variable term involving x. It simplifies to f(x) = 29.

Regardless of the value of x, the function f(x) will always have a y-value of 29.

Therefore, option A is incorrect because there is no minimum y-value for f(x); it is a constant.

g(x) = 7x² - 3 is a quadratic function in the form of ax² + bx + c, where a = 7, b = 0, and c = -3.

The coefficient a (7) is positive, indicating that the parabola opens upward.

Since there is no linear term (bx), the vertex of the parabola is located at the point (0, -3), which corresponds to the minimum y-value of the function.

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Given statement solution is :- 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.

To find the percentage of pupils who passed the final examination, you can use the following formula:

Percentage = (Number of pupils passed / Total number of pupils) * 100

Given that 90 pupils passed the final examination out of a total of 150 pupils, we can substitute these values into the formula:

Percentage = (90 / 150) * 100

Percentage = 0.6 * 100

Percentage = 60%

Therefore, 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.

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Answer:

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

In ΔNOP, we are given:

Use the law of cosines to find side o:

Now, use the law of sines to find ∠N:

So,  ∠N is approximately 10°.

Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

The expressions are simplified to;

a. 4pq

b. t³

Algebraic expressions are defined as expressions that are made up of terms, variables, coefficients, factors and constants.

These algebraic expressions are also made up of mathematical or arithmetic operations, such as;

From the information given, we have that;

The expressions are;

1.  p x q x 4

Multiply the terms, we have that;

4qp

2.t x t x t

Multiply the terms, we get;

t³

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Answer:

15.36

Step-by-step explanation:

192*0.02*4= 15.36

Answer: 70 + 3 + [tex]\frac{9}{100}[/tex]

Step-by-step explanation:

     Firstly, what is expanded form? Expanded form is a sum of a number's digit place values.

     For example, the expanded form of 814 is 800 + 10 + 4.

To find the expanded form of 73.09, we will do the same as the example provided above. However, we have a decimal. This means we will use a fraction. This 9 is in the hundredth place, so we will use the fraction  [tex]\frac{9}{100}[/tex].

73.09 = 70 + 3 + [tex]\frac{9}{100}[/tex]

1)

The trigonometric functions :

sinA = 5/13 , cosA = 13/12 , tanA = 5/13

Given,

Right angled triangle with:

P = 5

B = 12

H = 13

Then trigonometric ratios,

sinA = P/H

cosA = B/H

tanA = P/B

Hence the ratios can be defined as,

sinA = 5/13

cosA = 12/13

tanA = 5/12

2)

The value x in the radical form 10.77

Given,

Right angled triangle,

Perpendicular = 4

Base = 10

Hypotenuse = x

Apply pythagora's theorem,

P² + B² = H²

4² + 10² = H²

16 + 100 = H²

H = 10.77

Hence the value of x is 10.77 .

3)

The value of x in radical form

Given,

P = 56

B = x

H = 106

Apply pythagora's theorem,

P² + B² = H²

56² + x² = 106²

x = 90

Hence the value of x is 90 .

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Answer:

22 is answer

Step-by-step explanation:

Answer:

лвоалалалоала.сллслала лвлвлвл

The man rotated the window by 45 degrees and covered one of the diagonals, resulting in a smaller square window with sides measuring 1 meter.

The man achieved the transformation of his square window by dividing it into two equal halves and boarding up one of them.

Let's analyze the steps he took to accomplish this:

Initially, the man had a square window with sides measuring 1 meter

This means that the window had an area of 1 square meter (1m x 1m = 1m²).

To reduce the amount of light coming through the window, the man decided to board up half of it.

This implies that he covered one of the equal halves of the square window, while leaving the other half open.

By boarding up half of the window, he effectively blocked off half of the area of the square window.

Since the original window had an area of 1 square meter, boarding up half of it reduces the effective area to 1/2 square meter (1m² ÷ 2 = 1/2m²).

The remaining open half of the window still retains its square shape, with sides equal to 1 meter.

Therefore, the man ends up with a square window that measures 1 meter in height and 1 meter in width, but with an area of only 1/2 square meter.

In summary, the man achieved the transformation by boarding up half of the square window, effectively reducing its area to half of the original size while maintaining the same dimensions for the remaining open half. This manipulation allows him to control the amount of light entering his house while preserving the square shape of the window.

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Answer:

please see answers below

Step-by-step explanation:

i) 5/8  X 320 = 200 people

ii) 0.75 X 200 = 150 (people in farming but also trade). only trade = 320 - 200 = 120.

number of people in trade = 150 + 120 = 270.

b) 0.75 X 5/8 = 3/4 X 5/8 = 15/32 = 150 people (both farm and trade).

c) only farming = 0.25 X 5/8 = 1/4 X 5/8 = 5/32 = 50.

only trade = 320 - 50 (only farm) - 150 (both farm and trade) = 120.

so, only do one activity = 50 + 120 = 170.

d) traders only = 120/320 = 3/8 = 37.5%

e) P(farmer only) = 50/320 = 0.15625

In the ellipse shown below, each point marked with a dot is called a(n)  focus

In an ellipse, the focus (plural: foci) is a pair of special points that play a significant role in defining the shape of the ellipse. The focus points are located inside the ellipse along the major axis, which is the longer axis of the ellipse.

The defining property of an ellipse is that the sum of the distances from any point on the ellipse to the two foci is constant. This property is known as the "focus-directrix property."

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Answer:

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

Given function:

In order to find its inverse, first swap x and y:

Then solve for y:

The inverse function is y= √x.

Answer:

66 inches²

Step-by-step explanation:

Area of 1 triangle = ½ × base × height = ½ × 7 × 4 = 14 in²

Area of 2 triangles = 14 × 2 = 28 in²

Area of outer rectangles = (6 × 2) × 2 = 24 in²

Area of inner rectangle = 2 × 7 = 14 in²

Total surface area = 28+24+14 = 66 in²

[tex]\theta =\cfrac{14}{3}\pi \implies \theta =\cfrac{14\pi }{3}\implies \theta =\cfrac{6\pi +6\pi +2\pi }{3} \\\\\\ \theta =\cfrac{6\pi }{3}+\cfrac{6\pi }{3}+\cfrac{2\pi }{3}\implies \theta =2\pi +2\pi +\cfrac{2\pi }{3}[/tex]

so if we take a look at that, we can say that the angle θ does two revolutions and then it lands on 2π/3, so the terminal point of it is the same as 2π/3's, and if you check your Unit Circle, as you should have one

[tex]\sin(\theta )=\cfrac{\sqrt{3}}{2}\hspace{5em}\cos(\theta )=-\cfrac{1}{2}[/tex]

Answer:

sin∅ = √3/2

cos∅ = -1/2

Step-by-step explanation:

Notice that 14π/3 is just under 3π, so the reference angle made with the negative x-axis is π/3. Since sin(π/3) = √3/2, then sin(14π/3) is also √3/2.

cos(14π/3) works somewhat similarly. Since cos(π/3) = 0.5, and cos(14π/3) would be located in Quadrant II where the negative axis is, then cos(14π/3) = -0.5