(i) Express x2−6x+11 in the form (x−p)2+q. (ii) Use the result from part (a)(i) to show that the equation x2−6x+11=0 has no real solutions. (2) (b) A curve has equation y=x2−6x+11. (i) Find the coordinates of the vertex of the curve. (ii) Sketch the curve, indicating the value of y where the curve crosses the y saxis. (iii) Describe the geometrical transformation that maps the curve with equation y=x2−6x+11 onto the curve with equation y=x2. (3) (3)

The no. of ways in which the doctor visits her patients during morning rounds = 5!

That means we can only find the number of ways if we n+1 factorial the number of rounds. In this case, the factorial is 1x2x3x4x5= 120

The product of all positive integers less than or equal to n in mathematics is known as the factorial of a non-negative integer, indicated by the symbol n! Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1.

In addition to highlighting the connections between variables, it also enables the isolation and individual analysis of the impacts of changing a single variable. The primary drawback is how challenging it is to explore with more than two parameters or several levels.

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Answer:

the answer is not b

Step-by-step explanation:

The random sampling used is stratified random sampling

The most accurate type of probability sampling is random sampling. Each person in a population has an equal probability of getting selected for the sample thanks to this method of sampling.

This kind of sampling is perfect for highly controlled investigations where it is unacceptable to have human bias in the selection of the sample.

Each sampling unit in a population has an equal probability of being included in the sample when using simple random sampling (SRS). As a result, each potential sample has an equal probability of being chosen.

Given data ,

Mark used a stratified random sampling method by dividing the list of students into boys and girls and drawing from each group in proportion to their numbers in the population. This method helps ensure that the sample is representative of the population in terms of gender.

Hence , the sample is likely to represent the population. Answer: C. Yes, stratified random sampling.

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Answer:

\(in \: the \: triangles \: abc \: and \: bdc\)

\(c.60\)

I hope this helps

Answer:

I belive the answer would be 4ajjdbnmsfnksfnbdnsdbcs,mdv bn,zdb xzvndzsmbznx,vsdanvbf.  : ) ahaha

24600 feet per second would equal around 4.66 miles per second and be equivalent to 16772.727 miles per hour

Step-by-step explanation:

Let say the unknown number we dont know is x

2x+4=6

2x=6-4

2x=2

x=2/2

x=1

So the unknown number is 1

Answer:

The correct answer is 672.

Step-by-step explanation:

Plz mark as brainliest ! :D

Answer:

Marking braily:)

Step-by-step explanation:

Answer:

i just wanted to say god bless yall and im sry for not answerinng the question

Step-by-step explanation:

The measure of Angle ∠A is 93

The given parameters are

Angle ∠A = 2x + 19

Angle ∠B = 3x - 18

The angles are vertical angles

So, we have

Angle ∠A = Angle ∠B

This gives

3x - 18 =2x + 19

Collect the like terms

3x - 2x = 18 + 19

Evaluate the like terms

x= 37

Substitute x= 37 in Angle ∠A = 2x + 19

Angle ∠A = 2 x 37 + 19

Evaluate

Angle ∠A = 93

Hence, the measure of Angle ∠A is 93

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To find the standard error (se) in this context, we need to calculate the standard deviation of the residuals. The residuals are the differences between the observed values of annual sales (yi) and the predicted values based on the regression model.

The formula to calculate the standard error is:

se = sqrt[(SSR / (n - 2))]

where SSR is the sum of squared residuals.

To calculate SSR, we need to find the predicted values of annual sales (yi) based on the regression model. The regression model is given by:

yi = b0 + b1xi

where b0 and b1 are the coefficients estimated from the regression analysis.

First, let's calculate the coefficients b0 and b1 using the given summary measures:

b1 = Σ(xi - x)(yi - y) / Σ(xi - x)²

b0 = y - b1x

where x and y are the sample means of sales experience and annual sales, respectively.

Using the given summary measures, we can calculate:

x= Σxi / n = 70 / 7 = 10

y = Σyi / n = 70 / 7 = 10

Σ(xi - x)(yi - y) = Σxiyi - n(x)(y) = 816 - 7(10)(10) = 816 - 700 = 116

Σ(xi - x)² = Σxi² - n(x)² = 896 - 7(10)² = 896 - 700 = 196

Now we can calculate the coefficients:

b1 = 116 / 196 = 0.5918

b0 = 10 - 0.5918(10) = 10 - 5.918 = 4.082

Next, we calculate the predicted values of annual sales (ŷi) using the regression model:

yi = 4.082 + 0.5918xi

Now we calculate the residuals:

ei = yi - yi

Finally, we calculate SSR, the sum of squared residuals:

SSR = Σ(ei)²

Once we have SSR, we can calculate the standard error using the formula mentioned earlier:

se = sqrt[(SSR / (n - 2))]

By substituting the values into the formula, we can find the standard error.

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78 sit ups in 2 minutes

so

= 78 : 2 sits in 1 minute = 39 sits up per minute

x 5 = 195 sit ups in 5 minutes

Answer:  39 situps per time

Step-by-step explanation:

The ratio of sides of the triangle is found as 1/15 : 1/6 : 1/5.

For the given question.

The ratios of the altitude of triangle are given as; 2:5:6 = 2x:5x:6x.

From the drawn figure.

The area of the triangle will be same.

Thus,

1/2*BC*AD = 1/2*AB*FC = 1/2*AC*BE

Or, BC*AD = AB*FC = AC*BE

Put the value of altitude in the ratios.

BC*5x = AB*2x = AD*6x

Taking the LCM of (2, 5, 6).

Thus,

BC/6 = AB/15 = AD/5

Ratio becomes;

1/15 : 1/6 : 1/5

Thus, the ratio of the sides of the triangle is found as 1/15 : 1/6 : 1/5.

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Answer:

X=2

Step-by-step explanation:

I'm sure it's the result.. Jdjdj

If observations of y tend to increase as observations of x increase, the relationship between these two variables will be best describe as positive correlation.

Correlation refers to a pattern or relationship between the values of two variables. If correlation exist between two variables, a pattern can be observed as variables are plotted on a scatter plot. A pattern approximated by a line is called a linear correlation otherwise it is a non-linear correlation. There are three ways to define a correlation or a relationship between variables: positive correlation, negative correlation, and no correlation. A positive correlation demonstrates that as one variable increases it causes the other variable to increase as well. A negative correlation shows that as one variable increases it causes the other variable to decrease. A no correlation exists when one variable increases the other variable remains constant.

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The rate at which the distance from the plane to the station is increasing when it has a total distance of 4 miles away from the station is 317.5 mi/h.

A rate in which a certain number of units of the first quantity are compared to one unit of the second quantity is not the same as a unit rate. In other words, we may state that the comparison's second amount is always 1.

Thus, P denotes the plane's location, R denotes the radar's location, and V denotes the point that is vertical to the radar and at the plane's height.

Assume that h is the height of the plane, s is the separation from the radar, and x is the separation from point V.

The plane travels at 480 miles per hour and has a 3 mile height. Ds-480 miles per hour.

dt By Pythagorean theorem,

x² = h² + s²

x² = 3²+s²

x² = 9 + s²

Differentiate implicitly with respect to t.

2x dx/dt = 2s ds/dt + 0

x dx/dt = s ds/dt

Use (1)

dx/dt = \(\frac{dx}{dt} =\frac{\sqrt{x^2-9} }{x}\)

= √7/4 x 480

= 120√7

≈ 317.49

Hence, the distance increasing at the rate of dx/dt is 317.5 mi/h.

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Answer:

52, 60, 68, 76..

Step-by-step explanation:

SOLUTION

The triangle in the picture has two sides to be equal. This means that the triangle is an isosceles triangle.

The base angles of an isosceles triangle are equal.

This implies that angle C = B = 49 degrees

So both angles B and C are 49 degrees each.

Now let's find angle A

A + B + C = 180 degrees (sum of angles in a triangle)

Then

The line bisects angle A into two equal triangles, that is angle y and the angle at the other side

This means that

Now let's find x.

Angles x, y, and B make up a triangle. This means that

Therefore, x = 90, and y = 41

Step-by-step explanation:

y = 200  - 3 *x  has slope = -3   this is downward sloping from L to R

Answer:downward sloping

Step-by-step explanation:

negative slope

Answer:

Place compass point on the vertex of the angle (point B), Stretch the compass to any length that will stay ON the angle, Swing an arc so the pencil crosses both sides (rays) of the given angle, Place the compass point on one of these new intersection points on the sides of the angle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.

Step 1:

Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches.

Step 2:

Substitute the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.

Step 3:

Combine like terms: (18 + 24) squared = 30 squared.

Step 4:

Evaluate each side: 1764 not-equals 900.

Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?

The triangle is actually a right triangle. In step 2, Chelsea incorrectly substituted the values into the Pythagorean theorem.

The triangle is not a right triangle, but in step 2 Chelsea incorrectly substituted the values into the Pythagorean theorem.

The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.

The triangle is not a right triangle, but in step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.

Answer:

\(\frac{3}{5} *5\) or \(5*\frac{3}{5}\)

Step-by-step explanation:

Each circle has 3/5 shaded, and there are 5 circles.

So our multiplication equation is:

\(\frac{3}{5} *5\) or \(5*\frac{3}{5}\) (they mean the same thing)

\(\frac{3}{5} *5=3\)

Hope this helps!

Answer:

b is the correct answer

To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The normal distribution appears as a "bell curve" on a graph.

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Answer:

Step-by-step explanation:

there u go!!

Step-by-step explanation:

strange, you solved much more complicated questions. this here is just to calculate a formula with the given parameters.

the only tricky thing, maybe : the % are to be used as decimal (4.5% = 0.045).

so, the balance after 15 years (compounded quarterly, so n = 4) is

3500×(1 + 0.045/4)^(4×15) = 3500×(1.01125)⁶⁰ =

= 3500 × 1.956645179... = 6,848.258127... ≈

≈ $6,848.26

In the triangle the value οf x is D) 27.

A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.

Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.

Here in the given triangle, using ratiο then

=> \(\frac{x+8}{10}=\frac{2x-5}{14}\)

=> \(14\times(x+8)=10(2x-5)\)

=> 14x+112=20x-50

=> 20x-14x=112+50

=> 6x = 162

=> x =\(\frac{162}{6}\)

=> x = 27

Hence the cοrrect οption is D)27.

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Answer:

Step-by-step explanation:

This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:

\(y=a(x-h)^2+k\) and this will allow us to solve for the value of a:

\(6=a(6-4)^2+5\) and

\(6=a(2)^2+5\) and

6 = 4a + 5 and

1 = 4a so

\(a=\frac{1}{4}\) and the equation is

\(y=\frac{1}{4}(x-4)^2+5\)