Sam rolls a fair dice 150 times.
Work out an estimate for the number of times the dice will land on 4.

The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).

Equation of a circle

A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.

We know that,

Equation of the circle passing through the origin is given by:-

\(x^2+y^2=r^2\)

Where,

r is the radius of the circle, and

(x,y) are the coordinates of each point of the circle.

Hence, we can write,

The radius of the circle will be :-

\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)

Hence, r = 4 units.

Hence, the equation of the circle is given by:-

\(x^2+y^2=16\)

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Answer:

No question.

Step-by-step explanation:

Answer:

-26

Step-by-step explanation:

Hello There!

For this problem all we have to do is plug in -5 into x and calculate the value

so..

-3|-5|+2(-5)-1

so first things first | | means absolute value

The absolute values of -5 is 5 so the equation would be

-3(5) + 2(-5) - 1

-3*5=-15

2*-5=-10

-15-10=-25

-25-1=-26

so the answer would be -26

First, we need to find the total frequency. This is given by adding all the given frequencies. That is,

and the relative frequency is the division of the frequency of the corresponding interval by the total frequency,

Therefore, the answers are:

a) 4/22 but written in simple form:

b)

The equation of line passing through the points (1,1), (2,2), (3,3), and (4,4) is y=x.

The points (1, 1), (2, 2), (3, 3), and (4, 4) all lie on the same line, which means that we can find the equation of the line using any two of these points.

Let's use the first and last points, (1, 1) and (4, 4), respectively. We can find the slope of the line using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (1, 1) and (x2, y2) = (4, 4)

slope = (4 - 1) / (4 - 1) = 1

Now that we know the slope of the line, we can use the point-slope form of the equation of a line to find the equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the points on the line. Let's use the point (1, 1):

y - 1 = 1(x - 1)

y - 1 = x - 1

y = x

So the equation of the line passing through the points is y = x.

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Answer :

94 minutes (movie)

7 minutes (to get to the movie theater)

7 minutes (to get back)

94 + 7 + 7

94 + 14 = 108 minutes

Hope it helped

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Given :

A patient with high blood pressure who weighs 226 pounds is put on a diet to lose 26 pounds in 3 months. The patient loses 8 3/4 pounds the first month and 11 5/8 pounds the second month.

To Find :

How much weight must be lost the third month for the goal to be achieved.

Solution :

Let, weight lose in third month is x.

So, 8 3/4 + 11 5/8 + x = 26

\(\dfrac{32+3}{4}+\dfrac{88+5}{8}+x=26\\\\x = 26 - ( \dfrac{35}{4}+\dfrac{93}{8})\\\\x=5.625\ pounds\)

Therefore, weight lose in third month is 5.625 pounds.

Hence, this is the required solution.

To write a quadratic function from its vertex and another point, we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k. Substitute the coordinates of the vertex and the other point into the vertex form to find the value of a. Then, substitute the value of a back into the vertex form to get the quadratic function.

To write a quadratic function from its vertex and another point, we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k. In this form, (h, k) represents the coordinates of the vertex of the parabola.

Let's say the vertex of the quadratic function is (h, k) and the other point is (x1, y1). We can substitute these values into the vertex form to find the value of a.

Substituting the vertex coordinates, we get:

f(h) = a(h-h)^2 + k

f(h) = k

Substituting the coordinates of the other point, we get:

f(x1) = a(x1-h)^2 + k

Now, we have two equations:

k = a(0)^2 + k

y1 = a(x1-h)^2 + k

From the first equation, we can see that k = k, which is always true. Therefore, we can ignore this equation.

From the second equation, we can solve for a:

y1 - k = a(x1-h)^2

a = (y1 - k) / (x1-h)^2

Now that we have the value of a, we can substitute it back into the vertex form to get the quadratic function:

f(x) = a(x-h)^2 + k

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The amount paid for each lemon if both girls made same profit expressed by 80.25 - 87c and 73.35 - 64c is $0.30.

Therefore, the answer is (A) $0.30.

Girl 1 made a profit of 80.25 - 87c and girl 2 made a profit of 73.35 - 64c. It is given that both girls make same amount of profit. Therefore,

80.25 - 87c = 73.35 - 64c

(87 - 64) × c = 80.25 - 73.35

23c = 6.90

c = 6.90/ 23

c = 0.30

Therefore, the amount of money both of the girls paid for each lemon is $0.30.

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Answer:

Step-by-step explanation:

We need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

What is ASA congruence of triangle?

The two triangles are considered to be congruent according to the ASA rule if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

We are given the following:

1. ∠A ≅ ∠X

2. ∠C ≅ ∠Z

Now, in order to show the triangles as congruent by ASA congruence of triangle, we need the side which is in between both the angles.

The sides in between both the angles are AC and XZ.

Hence, we need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

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Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.

We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:

( 3, 4 ) and ( − 2, 1 )

We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.

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Answer:

in step by step

Step-by-step explanation:

Distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time.

The formula for distance problems is: distance = rate × time or d = r × t.

Things to watch out for:

Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.

It would be helpful to use a table to organize the information for distance problems. A table helps you to think about one number at a time instead being confused by the question.

Distance Problems: Given Total Time

Example:

John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?

Solution:

Step 1: Set up a rtd table.

r

t

d

Case 1

Case 2

Step 2: Fill in the table with information given in the question.

John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?

Let t = time to travel to town.

7 – t = time to return from town.

r

t

d

Case 1

40

t

Case 2

30

7 – t

Step 3: Fill in the values for d using the formula d = rt

r

t

d

Case 1

40

t

40t

Case 2

30

7 – t

30(7 – t)

Step 4: Since the distances traveled in both cases are the same, we get the equation:

40t = 30(7 – t)

Use distributive property

40t = 210 – 30t

Isolate variable t

40t + 30t = 210

70t = 210

210/70

Step 5: The distance traveled by John to town is

40t = 120

The distance traveled by John to go back is also 120

So, the total distance traveled by John is 240

Answer: The distance traveled by John is 240 miles.

Answer:

Option A 26cm3

Step-by-step explanation:

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if a function is differentiable at a point, then it is continuous at that point is True.

If a function is differentiable at a point, it implies that the function is continuous at that point. The reason for this is that differentiability requires the existence of the derivative, which is based on the concept of a limit. And for a function to have a derivative at a point, it must also be continuous at that point. So, differentiability implies continuity.

what is continuity?

Continuity is a fundamental concept in calculus and analysis that describes the smooth and unbroken behavior of a function. A function is said to be continuous at a point if it does not have any abrupt jumps, holes, or vertical asymptotes at that point.

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Answer:

We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

Step-by-step explanation:

The computed confidence interval for a certain statistical parameter gives a range of value represented by a minimum value and a maximum value. The α value upon which the value was calculated represents the probability of the estimated value containing the true value of the parameter in question.

The minimum and maximum values represents the range of possible slope parameters, the true value falls in between two negative values, thus we have a negative slope, depicting a decline in one variable and the as the other increases.

From the options above, the most appropriate option is ;

We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

The output of this code will be the optimal values of the decision variables B, D, E, and S2 that maximize the objective function subject to the given constraints.

To solve this optimization problem using MATLAB, we can use the linprog function from the Optimization Toolbox.

First, we need to rewrite the problem in standard form, which requires converting the objective function to a minimization problem by multiplying it by -1, and expressing all constraints as linear inequalities of the form Ax <= b. In this case, we have:

Minimize: -B - 1.9D - 1.5E - 1.08S2

Subject to:

A + C + D + S0 = 100,000 -> A + C + D + S0 <= 100,000

0.5A + 1.2C + 1.08S0 - B - S1 <= 0

A + 0.5B + 1.08S1 - E - S2 <= 0

A <= 75,000

B <= 75,000

C <= 75,000

We can then use the following MATLAB code to solve the problem:

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% Define the objective function coefficients

f = [-1; -1.9; -1.5; -1.08];

% Define the constraint matrix

A = [1 1 1 1 0 0 0 0 0; 0.5 1.2 0 -1 -1 0 0 1.08 0; 1 0.5 0 -1 0 -1 1.08 0 0; 1 0 0 0 0 0 0 0 0; 0 1 0 0 0 0 0 0 0; 0 0 1 0 0 0 0 0 0; 0 0 0 0 1 0 0 0 0; 0 0 0 0 0 1 0 0 0; 0 0 0 0 0 0 0 0 1];

% Define the constraint RHS vector

b = [100000; 0; 0; 75000; 75000; 75000; 0; 0; 0];

% Define the bounds on the decision variables

lb = zeros(9,1);

ub = [75000; 75000; 75000; Inf; Inf; Inf; Inf; Inf; Inf];

% Solve the linear program

[x, fval, exitflag] = linprog(f, A, b, [], [], lb, ub);

% Print the optimal solution

fprintf('Optimal Solution:\n');

fprintf('B = %.2f\n', -fval);

fprintf('D = %.2f\n', -x(2));

fprintf('E = %.2f\n', -x(3));

fprintf('S2 = %.2f\n', -x(9));

The output of this code will be the optimal values of the decision variables B, D, E, and S2 that maximize the objective function subject to the given constraints.

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Answer:

yes

Step-by-step explanation:

hope this helps

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

slope = 9 y-intercept = -5/2

Step-by-step explanation:

since slope form is y=mx+b we know that m= slope and b=y-intercept. since 9 is in place of the m that shows that 9 is the slope. since 5/2 is in the b place you would think the y-intercept would be 5/2 but since the equation is - 5/2 instead of + 5/2 it would be + (-5/2) making the y-intercept negative. hope this helped. :)

Answer:

C

Step-by-step explanation:

Given

2(5x + 3) + 2 = 10x + 6 ← distribute and simplify left side

10x + 6 + 2 = 10x + 6

10x + 8 = 10x + 6 ( subtract 6 from both sides )

10x + 2 = 10x ( subtract 10x from both sides )

2 = 0 ← not possible

This indicates the equation has no solution

Answer:

no solutions

Step-by-step explanation:

2(5x + 3) + 2 = 10x + 6

* solve for x *

step 1 distribute the 2 to 5x and 3

2 * 5x = 10x

2*3=6

we now have 10x + 6 + 2 = 10x + 6

step 2 combine like terms

6 + 2 = 8

we now have 10x + 8 = 10x + 6

step 3 subtract 10x from each side

10x-10x=0

10x-10x=0

we're left with 8 = 6

8 is not equal to 6 meaning that there are no solutions to the equation

Answer:

C. 13

Step-by-step explanation:

Step-by-step explanation:

Linear function:

\(y=mx+b\\Ax+By=C\\Ax+By+C=0\)

\(y=x\qquad\bold{YES}\\\\y=7\qquad\bold{YES}\\\\2y=x^2\qquad\bold{NO}\ \boxed{x^2}\\\\y=4x^2+3x\qquad\bold{NO}\ \boxed{x^2}\\\\3x+4y=12\qquad\bold{YES}\\\\2x^2+6y=12\qquad\bold{NO}\ \boxed{x^2}\)

Answer:

Equations 3, 4, and 6 are nonlinear equations.  

Step-by-step explanation:

See attachment.

Answer:Each pair of alternate interior angles is congruent, and each pair of alternate exterior angles is congruent.

Step-by-step explanation:

Answer:

Timed test.

Step-by-step explanation:

An operational definition gives exactly what the independent variable means and its mode of measurement. The Independent variable is the variable in a research or experimental study which causes a change in the the measured variable. Hence, the independent variable is the predictor variable. In the study above, the independent variable is the timed test which is used to observe changes in the heart rate of the test taker (test anxiety). The change innheartrate of the test taker is the dependent variable.

Answer:

all together the total amount of money spent was 46$

Step-by-step explanation:

Answer:

C. 118.2°

Step-by-step explanation:

180-61.8=118.2

Answer:

\(y=|x-(-2)|+2\)

Step-by-step explanation:

Hope this is helpful.

The required absolute function is given as y = |x - 2| + 2.

Given that,
From the graph, y = |x - h| + k, values of h and k is to be determined,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the graph and function, h represents the shift on the x-axis, which 2 units left so the value of h is 2, while k is given the shift of the function over the y-axis which 2 units up means that k = 2

Thus, The required absolute function is given as y = |x - 2| + 2.

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Answer:

El número es el 47

Step-by-step explanation: Con los dígitos de los siguientes números se obtiene que su suma es 11

47        4  +  7  =  11

38         3  +  8 =  11

29         2   + 9  = 11

Si se cambia el orden de los dígitos:

47       se convierte en    74        74 - 47  =  27

38                  "    "             83        83 - 38 =  45

29                  "    "             92        92 - 29 = 63

Entonces el número solicitado es el 47