Mia is three years older than twice her sister Brooke's age. The sum of their ages is less than 30.
What is the greatest age Brooke could be?

a.) 7
b.) 8
c.) 9
d.) 10

The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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Answer:

Step-by-step explanation:

To the 4th power means that all the items in the parenthesis is mulitplied 4 times

(9m)⁴

=9*9*9*9*m*m*m*m*m  or

= (9m)(9m)(9m)(9m)

The distance between the two planes is decreasing is approximately 323.6 mi/h and the traffic controller has approximately 9.7 min to get planes on different flight path before distance between becomes zero.

a) The rate at which the distance between the two planes is decreasing can be found by taking the derivative of the distance equation with respect to time:

\(s^2 = (149^2 + x^2) + (190^2 + x^2) - 2(149)(190)cos(90°) = 44961 + 2x^2\)

Taking the derivative with respect to time, we get:

\(2s(ds/dt) = 4x(dx/dt)\)

Solving for ds/dt, we get:

\(ds/dt = 2x(dx/dt) / s\)

\(x^2 = 149^2 + 190^2\) = 62081

x = sqrt(62081) = 249 mi

Thus, the rate at which the distance between the two planes is decreasing is:

\(ds/dt = 2(249)(489) / sqrt(44961 + 2(249^2))\) ≈ 323.6 mi/h.

Therefore, the distance between the planes is decreasing at a rate of approximately 323.6 mi/h.

b) Setting s = 0 in the equation derived above and solving for x, we get:

x = sqrt(22480.5)

Since x is decreasing at a rate of 489 mi/h, the time it takes for x to reach 0 is:

t = sqrt(22480.5) / 489 ≈ 9.7 min.

Therefore, the traffic controller has approximately 9.7 min to get one of the planes on a different flight path.

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Answer:

70

Step-by-step explanation:

using the Pythagorean theorem we see that the side length is 29, meaning the perimeter is 70

Taking into account the definition of a system of linear equations, the length and width of the rectangle is 22.5 cm and 19.5 cm respectively.

Systems of linear equations are groupings of first degree equations with the same unknowns, of which a common solution must be found.

In the systems of equations, the values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

2x + 2y= 84

x= y + 3

The substitution method is a way to solve systems of equations. To use the substitution method, you choose an equation and find an expression for one of the variables in terms of the other variable. Then substitute that expression for the variable in the other equation.

In this case, substituting the second equation in the first one you get:

2×(y+3) + 2y= 84

Solving:

2y+ 2×3 + 2y= 84

2y+ 6 + 2y= 84

2y + 2y= 84 - 6

4y= 78

y= 78÷4

y= 19.5

Replacing this value in the second equation, you get:

x= 19.5 + 3

x= 22.5

Finally, the length of the rectangle is 22.5 cm and the width of the rectangle is 19.5 cm.

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Answer:

C bˆ is unbiased.

Step-by-step explanation:

In statistics, the sampling distribution showcases the distribution of obtained values by the statistics in all possible sample sizes of the same population. A statistic that estimates a population parameter is termed to be an unbiased estimator if the mean of such distribution appears to be equal to the true value of the estimated parameter.

Thus, from the aforementioned, the property exhibited by b- is unbiased.

d is biased

Step-by-step explanation:

The expected value of d is not D

The property where the expected value of d is D is called unbaisedness, hence d is biased

Answer:

380

Step-by-step explanation:

i plugged in g(x) = 20 to the given equation and plugged it in my algebraic calculator; 20^2-20 and got 380

(L3) Circumcenters and centroids involve midpoint.   Circumcenters and centroids are important points in a triangle that are determined by the location of the vertices and midpoints of the sides.

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect, while the centroid is the point where the medians of a triangle intersect. Both of these points involve the midpoint of the sides of the triangle. The circumcenter involves the midpoint of the perpendicular bisectors of the sides, while the centroid involves the midpoint of the sides themselves. The location of these points can provide valuable information about the geometry of the triangle, such as its center of mass or the location of its circumcircle.

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Answer:

\( \frac{ {x}^{ - 2} {y}^{ \frac{1}{2} } }{ \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{ {x}^{2} \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{6 {x}^{2}y \sqrt{x} } = \frac{1}{6 {x}^{ \frac{5}{2} } {y}^{ \frac{1}{2} } } = \frac{1}{6} {x}^{ - \frac{5}{2} } {y}^{ - \frac{1}{2} } \)

\( \frac{1}{6} \times - \frac{5}{2} \times - \frac{1}{2} = \frac{5}{24} \)

Answer:

Step-by-step explanation:

\( - 1 | \frac{2}{3} - 4| \div \frac{5}{6} \\ - 1 | \frac{2}{3} - \frac{4 \times 3}{1 \times 3} | \div \frac{5}{6} \\ - 1 | \frac{2 - 12}{3} | \div \frac{5}{6} \\ - 1 | \frac{ - 10}{3} | \div \frac{5}{6} \\ \frac{10}{3} \div \frac{5}{6} \\ \frac{10}{3} \times \frac{6}{5} \\ \frac{2}{1} \times \frac{2}{1} = 4 \)

We are given three set of system of equations

3x + 2y + z = 8

x + y + 2z = 4

4x + y + z = 7

We have three equations with three unknowns (x, y, and z)

Firstly, we need to eliminate of the variables, so that we can solve the remaining equation simultaneously.

Firstly., we will be eliminating z

Let us combine equation 1 and 2 together

3x + 2y + z = 8 ------ equation 1

x + y + 2z = 4 --------- equation 2

To eliminate z, multiply equation 1 by 2 and equation 2 by 1

3x * 2 + 2y*2 + 2*z = 2 * 8

x *1 + y * 1 + 1 * 2z = 1 * 4

6x + 4y + 2z = 16 ------ equation 4

x + y + 2z = 4 ----------- equation 5

Substract equation 5 from 4

6x - x + 4y - y + 2z - 2z = 16 - 4

5x + 3y + 0 = 12

5x + 3y = 12 -------------- equation 6

Secondly, combine equation 2 and 3 together

x + y + 2z = 4

4x + y + z = 7

To eliminate z, multiply equation 1 by 1 and equation 2 by 2

x * 1 + y * 1 + 2z * 1= 4*1

4x *2 + 2 * y + 2*z = 2 * 7

x + y + 2z = 4 ----------- equation 7

8x + 2y + 2z = 14 -------- equation 8

Substract equation 8 from 7

x - 8x + y - 2y + 2z - 2z = 4 - 14

-7x - y + 0 = -10

-7x - y = -10 -------------- equation 9

Solve equation 6 and equation 9 simultaneously to get the values of x and y

5x + 3y = 12

-7x - y = -10

Let us eliminate y

To eliminate y, multiply equation 6 by 1 and equation 9 by 3

5x * 1 + 3y*1 = 12*1

-7x * 3 - y*3 = -10*3

5x + 3y = 12 ------ equation 10

-21x - 3y = -30----- equation 11

Add equation 11 and 10 together

5x + (-21x) + 3y + (-3y) = 12 + (-30)

5x - 21x + 3y - 3y = 12 -30

-16x + 0 = -18

-16x = -18

Divide both sides by -16

-16x/-16 = -18/-16

x = 18/16

x = 8/9

To find y, put the value of x in equation 9

-7x - y = -10

-7(8/9) - y = -10

-72/9 - y = -10

Collect the like terms

-y = -10 + 72/9

-y = -10 *9 / 1 + 72 x 9 / 9 / 9

-y = -90 + 72 / 9

-y = -18/9

-y = -2

Divide both sides by -1

-y/-1 =- -2/-1

y = 2

To find the value of z, substitute the values of x and y into equation 2

x + y + 2z = 4

Make 2z the subject of the formula

2z= 4 - x - y

2z = 4 -8/9 - 2

2z = 4 x 9 - 8 - 2*9 /9

2z = 36 - 8 - 18 / 9

2z = 10/9

Divide both sides by 2

2z / 2 = 10/9 / 2

z = 10/18

z = 5/9

The solutions are x = 8/9, y = 2 and z = 5/9

On solving the provided question we can say that the slope is - m = (y2 y1)/(x2-x1) Using (0,-5) and (3,-3): m = (-3-(-5))/(3-0) = 2/3

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasized in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

The table gives you three points

that are on the line:

(-5, -7), (0, -5), (3, -3)

the slope is -

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

Using (0,-5) and (3,-3):

m = (-3-(-5))/(3-0) = 2/3

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The correct question is -

How do I write a slope-intercept form equation from a table?

If I have the table,

x         y

-5      -7

0       -5

3       -3

There are 12,376 different groups of six passengers that can be selected from the plane flight of 17 passengers.

To calculate the number of different groups of six passengers that can be selected from a plane flight with 17 passengers, we can use the concept of combinations.

The number of ways to choose a subset of k items from a set of n items is given by the combination formula:

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

In this case, we need to select 6 passengers from a group of 17. Thus, we can calculate the number of different groups using the combination formula:

C(17, 6) = 17! / (6!(17-6)!)

        = 17! / (6!11!)

        = (17 * 16 * 15 * 14 * 13 * 12) / (6 * 5 * 4 * 3 * 2 * 1)

        = 12376

Therefore, there are 12,376 different groups of six passengers that can be selected from the plane flight of 17 passengers.

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Answer:

Amount after 22 year = $484.80 (Approx.)

Step-by-step explanation:

Given:

Amount deposit in bank = $150

Double in year = 13 year

Find:

Amount after 22 year

Computation:

A = P[1+r]ⁿ

Amount after 13 year = 2 x 150

Amount after 13 year = $300

300 = 150[1+r]¹³

2 = [1+r]¹³

Rate of interest = 5.477%

Amount after 22 year

A = P[1+r]ⁿ

Amount after 22 year = 150[1+5.477%]²²

Amount after 22 year = $484.80 (Approx.)

Answer:

m= -3

b= 4

Step-by-step explanation:

whatever number has x next to it is always slope, that is how you find slope in a equation. To find y-intercept (b) you can just use the other number that doesn't have x to it.

Hope this helps!!!

Answer:

I think the answer would be 17 inches wide!

Step-by-step explanation:

If you subtract 15 (which is the new height) from 4 (which was the original height) you would get 11. So then you would take 6 and add 11 to it to get the new answer of 17 if I'm doing my math right.

The area of the base of the panter is approximately 28.5 square inches.

To find the area of the base of the panter, we need to know the dimensions of the base. Since the panter is shaped like a rectangular prism, we know that the base is a rectangle.

Let's use the formula for the volume of a rectangular prism to find the dimensions of the base:

Volume = Length x Width x Height

We know the height is 9.5 inches and the volume is 769.5 cubic inches. So we can rearrange the formula to solve for the area of the base:

Area of Base = Volume / (Length x Width)

Substituting in the values we know:

Area of Base = 769.5 / (Length x Width)

We need to find the values of Length and Width that satisfy this equation. We know that the base is a rectangle, so we can use the formula for the area of a rectangle to find another equation:

Area of Base = Length x Width

Substituting this equation into the previous one:

Area of Base = 769.5 / (Area of Base / Width)

Multiplying both sides by (Area of Base / Width):

Area of Base^2 = 769.5 x Width

Solving for Width:

Width = Area of Base^2 / 769.5

Now we can substitute this value back into the equation for the area of the base:

Area of Base = 769.5 / Width

Area of Base = 769.5 / (Area of Base^2 / 769.5)

Area of Base = 769.5 / (Area of Base^2 / 769.5)

Area of Base = 769.5 x 769.5 / Area of Base^2

Multiplying both sides by Area of Base^2:

Area of Base^3 = 769.5 x 769.5

Taking the cube root of both sides:

Area of Base = (769.5 x 769.5)^(1/3)

Area of Base = 28.5 inches^2 (rounded to one decimal place)

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a) It takes the shirt 2.23 seconds to reach the maximum height

b) The maximum height reached by the T-shirt is approximately 78.85 feet.

c) 90 feet is the range of the function.

We can use the kinematic equations of motion to find the answers to the given questions.

The equation that relates the height (h) of an object to its initial velocity (v0), time (t), and acceleration due to gravity (g) is:

h = v0t - 1/2g*t^2

where g is approximately 32.2ft/s^2 and the upward velocity is considered as positive.

a) To find the time it takes for the T-shirt to reach its maximum height, we need to find the time at which the vertical velocity becomes zero. We know that the initial velocity is 72 ft/s, and the acceleration due to gravity is -32.2 ft/s^2 (since it acts in the opposite direction to the initial velocity).

At maximum height, the vertical velocity (v) is zero:

v = v0 - gt

0 = 72 - 32.2t

t = 2.23 seconds (rounded to two decimal places)

Therefore, it takes the T-shirt 2.23 seconds to reach its maximum height.

b) To find the maximum height, we substitute the time found above into the equation for height:

h = v0t - 1/2gt^2

h = 722.23 - 1/232.2(2.23)^2

h = 78.85 feet (rounded to two decimal places)

Therefore, the maximum height reached by the T-shirt is approximately 78.85 feet.

c) Assuming no air resistance, the height of the T-shirt over time can be modeled using the following equation of motion:

h(t) = -16t^2 + v0t + h0

where h(t) is the height of the T-shirt at time t, v0 is the initial upward velocity of the T-shirt, and h0 is the initial height of the T-shirt. The factor of -16 is due to the acceleration due to gravity.

Substituting the given values into the equation, we get:

h(t) = -16t^2 + 72t + 6

To find the range of the function, we need to determine the maximum height reached by the T-shirt and the time it takes to reach that height. The maximum height is achieved when the T-shirt reaches the highest point in its trajectory, at which its vertical velocity is zero. We can find this height and time by setting the derivative of h(t) with respect to t equal to zero:

dh/dt = -32t + 72 = 0

t = 2.25 seconds

Substituting this time back into the equation for h(t), we get:

h(2.25) = -16(2.25)^2 + 72(2.25) + 6

h(2.25) = 90 feet

Therefore, the range of the function is from the initial height of 6 feet to the maximum height of 90 feet.

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Answer:

3.5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

4c is 50a/c % of the expression 2a

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

Expression = 2a

Percentage = 4c

Represent the percentage expression with x

So, we have the following equation

x% * Percentage  = Expression

Substitute the known values in the above equation, so, we have the following representation

x% * 4c = 2a

Evaluate

x = 50a/c %

Express as percentage

Hence, the percentage is 50a/c %

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Answer:

d > -2

Step-by-step explanation:

-2d-2 < 3d+8

3d+8 > -2d-2

3d + 2d > -2 -8

5d > -10

d > -2

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it's x with the line and less than sign

Answer:

usas la sustitución para resolver esto

Step-by-step explanation:

Restar y

de ambos lados de la ecuación.

x = 7 − y

x − y = 1

Reemplazar todas las apariciones de x

en x − y = 1 con 7 − y

.

x = 7 − y

(7 − y) −y = 1

Restar y

de −y

.

x = 7 − y

7−2y = 1

Resuelve por y

en la segunda ecuación

x = 7 − y

y = 3

Reemplazar todas las ocurrencias de y

en x = 7 − y con 3

.

x = 7− (3)

y = 3

Simplifica 7− (3)

x = 4

y = 3

La solución al sistema de ecuaciones se puede representar como un punto.

(4,3)

El resultado se puede mostrar en múltiples formas.

Forma de punto:

(4,3)

Formulario de ecuación:

x = 4, y = 3

espero que esto ayude :)

Answer:

48 degrees

Step-by-step explanation:

1) Solve for x

Complementary angles add up to 90 degrees. Therefore, m<A + m<B is equal to 90:

\(A+B=90\\(2x+20)+(3x)=90\)

Open up the parentheses

\(2x+20+3x=90\\5x+20=90\)

Subtract 20 from both sides

\(5x+20-20=90-20\\5x=70\)

Divide both sides by 5

\(\frac{5x}{5} =\frac{70}{5} \\x=14\)

Therefore, x is equal to 14.

2) Determine angle A

\(A=2x+20\)

Substitute x with 14

\(A=2(14)+20\\A=28+20\\A=48\)

Therefore, the measure of angle A in degrees is 48 degrees.

I hope this helps!

The standard deviation for the number of people with the genetic mutation in such groups of 100 is 1.4

From the information given,

About 2% of the population has a particular genetic mutation, and 100 people are randomly selected.

The standard deviation for the number of people with the genetic mutation in such groups of 100 is obtained below;

The required standard deviation is,

p = 0.02 and n = 100;

1 - p = 1 - 0.02

       = 0.98

σ = \(\sqrt{n*(1-p)*p}\)

σ = \(\sqrt{100*0.02*0.98}\)

σ = 1.4

The standard deviation for the number of people with the genetic mutation in such groups of 100 is 1.4

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Answer:

Step-by-step explanation:

it is 2x

-300 degrees in radians is equivalent to - 5/3 \(\pi\) rad in negative degrees rad.by dividing it by \(\pi\)/180°.

a unit of plane angular measurement equal to the angle at the center of a circle covered by an arc with the same radius as length. 180/PI radians are equal to one radian, and 180/PI is equal to one degree. Thus, to convert a given number of degrees to radians, multiply the degrees by PI/180 (for instance, 90 degrees = 90 x PI/180 radians = PI/2).

here calculation

radians = degrees * \(\pi\)/180°.

radians = -300 *  \(\pi\)/180°.

= - 5/3  \(\pi\) rad.

-300 degrees in radians is equivalent to - 5/3 \(\pi\) rad in negative degrees rad.by dividing it by \(\pi\)/180°.

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Answer:

7

Step-by-step explanation:

8+x=15    subtract 8 both sides

x = 7