Given that h(x) = -2x + 5, g(x) =
2x – 7; compute g(h(x))

For finding a 95% confidence interval:

a) The sample mean is x = 16.13.

The sample standard deviation is s = 6.948.

The degrees of freedom are df = 10.

The critical value of t for a 95% confidence interval is t = 2.228.

The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.

The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).

b) The 95% confidence interval is (11.867, 20.393).

This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.

c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.

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The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Answer:

8

Step-by-step explanation:

The probability that all three murders were committed with a gun is: 0.252.

The probability that one murder was committed with a gun is:

P(Gun) = (6368 + 364 + 200 + 3326)/13927 = 0.632

Therefore, the probability that all three murders were committed with a gun is:

P(3 Guns) = P(Gun) * P(Gun) * P(Gun) = \(0.632^3\) = 0.252

The probability that a murder was committed with a handgun given that a gun was used is:

P(Handgun | Gun) = P(Handgun and Gun) / P(Gun)

We need to find P(Handgun and Gun). From the table, we see that 6368 murders were committed with a handgun and 6368 + 364 + 200 = 6932 murders were committed with a gun. Therefore:

P(Handgun and Gun) = 6368/13927

And:

P(Handgun | Gun) = (6368/13927) / (6368 + 364 + 200 + 3326)/13927 = 0.542

The probability that two murders involved a gun and two involved a cutting instrument is:

P(2 Guns and 2 Cutting instruments) = (C(4,2) * C(6932,2) * C(1476,2)) / C(13927,4)

Where C(n,r) is the number of combinations of n things taken r at a time.

Thus, calculating this gives: P(2 Guns and 2 Cutting instruments) = 0.150

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Answer: El índice de refracción del vidrio flint es mayor que el del aire. Cuando la luz pasa de un medio con un índice de refracción menor (como el aire) a un medio con un índice de refracción mayor (como el vidrio), experimenta un cambio de dirección. Este fenómeno se conoce como refracción.

Cuando observamos el bloque de vidrio flint desde arriba, la luz que proviene del bloque sufre refracción al pasar del vidrio al aire. Debido a la refracción, los rayos de luz se desvían y parecen venir de una posición más alta dentro del vidrio de lo que realmente están. Esto crea una ilusión óptica que hace que el espesor aparente del bloque de vidrio se vea más delgado de lo que realmente es.

La cantidad exacta de adelgazamiento aparente depende del ángulo de incidencia de la luz y de los índices de refracción del vidrio y el aire. Sin más información, no es posible determinar el espesor aparente específico del bloque de vidrio flint cuando se ve desde arriba.

Step-by-step explanation:

We know 1 day = 24 hours

Let's convert 5 days to hours:

Now, we have the ratio:

22 hours to 120 hours

We can write it as a fraction:

This is not in its lowest terms. We can divide numerator and denominator by "2", to get:

Thus, final answer is:

11/60

or

Answer:

Step-by-step explanation:

45+8x+21+90=180 degree(sum of interior angles of a triangle)

156+8x=180

8x=180-156

8x=24

x=24/8

x=3

The type of relationship that is indicated by the residual plot is given as follows:

Non-linear relationship.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

For this problem, we have an alternative pattern, where the function neither multiplied nor added/subtracted by a constant value when the input is increased by one, hence we merely classify the relationship as a non-linear relationship.

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Answer:

Step-by-step explanation:

x^3 + 3x^2 - 10x

~Factor

x(x - 2)(x + 5)

Solve for the zero.

x(x - 2)(x + 5) = 0

We know that; x = 0, x - 2 = 0, and x + 5 = 0

x = 0

x - 2 = 0

x = 2

x + 5 = 0

x = -5

Best of Luck!

Here we are provided with an polynomial of degree 3 and we have to factorise it first and then we have to compute it's zeroes.

Given Polynomial:

Taking common x from all the 3 terms,

➝ x(x² + 3x - 10)

Factorising through Middle term factorisation,

➝ x(x² + 5x - 2x - 10)

➝ x{x(x + 5) - 2(x + 5)}

➝ x(x - 2)(x + 5)

Hence, Factorised !!

Now equating to 0 to find the zeroes of the poly.

➝ x(x - 2)(x + 5) = 0

That means,

So, the zeroes of the polynomial is 0, 2 or -5

And we are done....

Carry On Learning \(!\)

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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The length of v to the nearest 10th of an inch is 2.0 inches.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

We can use the Law of Sines,

Which states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle opposite the angles A, B, and C.

Now,

a = UV = u = 3.4 inches

A = ∠TUV

  = 180° - m∠U - m∠V

  = 180° - 144° - 35°

  = 1°

B = ∠UTV

   = m∠U

   = 144°

C = ∠TVU

  = m∠V

  = 35°

Using the Law of Sines,

v/sin(C) = u/sin(B)

Substituting in the values.

v/sin(35°) = 3.4/sin(144°)

Solving for v.

v = (3.4 × sin(35°)) / sin(144°)

v = 1.97 inches

Therefore,

The length of v to the nearest 10th of an inch is 2.0 inches.

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Answer:

135 minutes

Step-by-step explanation:

Answer:

135 minutes

Step-by-step explanation:

1 hour= 60 minutes

2hours=60x2=120 minutes

120+15=135 minutes

plz mark me as brainliest.

If g(t) is cut in half, then t is doubled. Halving the growth factor halves the rate of growth, reducing the time required for a generation to develop to full size.

Growth factor refers to a mathematical expression or a metric that measures the rate of increase or growth of a quantity over time. It is used in many fields such as biology, economics, finance, and others to quantify the increase in size, population, revenue, or any other variable of interest. The growth factor can be represented as a ratio, percentage, or an exponential function and is used to predict future growth based on past trends.

3 potential points

Three tries are permitted.

If g(t) is divided in half, t is also divided in half. This is because the growth factor is a measure of the rate of growth, and halving it equals halves the rate of growth. As a result, the time required for a generation to develop to full size is cut in half.

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The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.

To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.

Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π

The length of the 45° arc is approximately 3.14 miles.

Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.

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Answer:

after 2 seconds

0=40-10t-5t^2

t^2+2t-8=0

(t+4)(t-2)=0

t=-4 or t=2

I think this is correct

Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

The graph represents a functional relationship between two variables X and Y. We get y=3 for the value x=2

Domain is defined as the set of values of independent variables.

In the question, all x coordinates are domain.

In a function, for each domain we get a possible output from the dependent variables which is termed as range. In this graph, the y coordinates are range because y value is dependent on x value.

The graph shows five points are plotted on XY coordinate system that represents a relationship between independent variable X and dependent variable Y.

hence, this graph is plotted from a function.

from the graph we get the domain as {-4, -2, 0, 2, 4}

the ranges are = {-3, -2, -1, 1, 3}

we get, y=3 for the value of x= 2  

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Answer:

x = y = 26 cm; z = 13 cm

Step-by-step explanation:

We can calculate the dimensions of the square base as

∛(2·8788) = 26 cm

the height of the box will be half of 26/2 which is 13 cm.

x = y = 26 cm; z = 13 cm

then the minimum area for the given volume can be calculated using what we call Lagrange multipliers, this makes it easier

area = xy +2(xz +yz)

But we were given the volume as 8788

Now we will make the partial derivatives of L to be in respect to the cordinates x, y, z, as well as λ to be equal to zero, then

L = xy +2(xz +yz) +λ(xyz -8788)

For x: we have

y+2z +λyz=0

For y we have

y: x +2z +λxz=0

For z we have 2x+2y +λxy=0............eqn(*)

For we have xyz -8788=0

If we simplify the partial derivative equation of y and x above then we have

λ = (y +2z)/(yz).

= 1/z +2/y............eqn(1)

λ = (x +2z)/(xz)

= 1/z +2/x.............eqn(2)

Set eqn(1 and 2) to equate we have

1/z +2/y = 1/z +2/x

x = y

From eqn(*) we can get z

λ = (2x +2y)/(xy) = 2/y +2/x

If we simplify we have

1/z +2y = 2/x +2/y

Then z = x/2

26/2 =13

Therefore,

x = y = 2z = ∛(2·8788)

X= 26

y = 26 cm

z = 13 cm

Answer:

29%

Step-by-step explanation:

You add the 18 and 53 then subtract by 100 to receive your answer

Answer:

29%

Step-by-step explanation:

You add the percentages of the other categories (18 - children, 53 - adult fiction) then subtract from 100.

Answer:

it's a yes

Step-by-step explanation:

X/6 ≤ 30

to find the value of X we have to move the numerical to the other side

in this case the number is 1/6

X * 1/6 ≤ 30

so to balance the both side and get rid of the number on the left side we multiple with 6.

1/6*6 = 1 on the left side

30*6 = 180 on the right side

so the full equation will be

X * 1/6 * 6 ≤ 30 * 6

X * 1 ≤ 180

X ≤ 180

Given that the probability that Joe burns dinner is:

You need to use the following Binomial Distribution Formula, in order to solve the exercise:

Where "n" is the sample size, "x" is the number of successes desired, and "p" is the probability of getting a success in a trial.

(a) You must find the probability that in the next 7 dinners Joe prepares, 4 of them will burn. Therefore, for this case:

Then, you can substitute values into the formula and evaluate:

(b) You must find the probability that in the next 7 dinners Joe prepares, at least 5 of them will burn. Therefore, since "at least" indicates greater than or equal to 5, you need to set up this Sum for:

Then:

Evaluating, you get:

(c) You must find the probability that in the next 7 dinners Joe prepares, less than 3 of them will burn. Therefore, you need to set up a Sum for:

As follows:

Evaluating, you get:

Hence, the answers are:

(a)

(b)

(c)

answer:

Max =$131,250

Sherry=$140,000

Duane=$78,750

Step-by-step explanation:

Max will receive 3/8 ×$350,000=$131,250

Sherry will receive 2/5 × $350,000=$140,000

Duane will receive $350,000-$(131,250+140,000)

$350,000-$271,250=$78,750.

Answer:

Answer is explained in the explanation section

Step-by-step explanation:

Solution:

Converse of the pythagorean theorem helps us to check whether a triangle is a right triangle or not. Converse of the pythagorean theorem is simply the opposite of the pythagoren theorem. Pythagorean theorem states that, if triangle is right triangle, then \(a^{2} + b^{2} = c^{2}\). On the other hand, Converse of the Pythagorean theorem states that, if  \(a^{2} + b^{2} = c^{2}\), then triangle is a right triangle.

Pythagorean theorem = \(c^{2} = a^{2} + b^{2}\)

Converse of the pythagorean theorem = \(a^{2} + b^{2} ? c^{2}\)

First of all let's check the first triangle is right triangle or not.

a = 12

b= 16

c= 20

So,

\(a^{2} + b^{2} = c^{2}\).

144 + 256 = 400

400 = 400

Yes, 1st triangle is no doubt a right triangle. On the other hand, we are given that 2nd triangle = right triangle as we are given the 90 degree angle already. Here, we know that triangle is a right triangle

hence, \(a^{2} + b^{2} = c^{2}\). will surely be there.

Now, we have find out the side opposite to the 90 degrees angle, which is c.

we also know that, right triangles sides follow the pattern of 3x,4x and 5x

Since, c is the longest side.

Hence, c= 5x

Answer:

Answer:

$260,000

Step-by-step explanation:

Explanation:

Given the problem above, we solve for original value

Hence, in this case, we are given

percentage (35%) and the New Value ($351,000).

We can substitute this into the formula and solve for X

Let X be the original price, Hence, X = 100%

Therefore, $351000 = 135%

Divide both sides by 135

351000÷ 135 = 135÷135

2600 = 1%

Multiply both sides by 100

2600 * 100 = 1% * 100

$260000 = 100% = X

Hence, final answer is $260000

Answer:

1/3a - 8

Step-by-step explanation:

Distribute negative sign:

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

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

2/3a + -5 + -1/3a + -3

Combine like terms:

2/3a + -5 + -1/3a + -3

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

= 1/3a - 8

Answer:

Time taken by kangaroo to travel 5 km = 4.27 minutes.

Step-by-step explanation:

Speed of kangaroo is 44 mph.

Speed of kangaroo = 44 mph = 44 x 1.6 = 70.4 kmph = 19.5 m/s

We need to find how much time it takes to travel 5 km

Distance traveled = 5 km = 5000 m

We have

          Distance traveled =  Speed x Time taken

          5000 = 19.5 x Time taken

          Time taken = 256.41 seconds

           Time taken = 4.27 minutes.

Answer:7.5

Step-by-step explanation:

Answer:

It's   -8

Step-by-step explanation:

DISTRIBUTE :

4x + 2( x - 2 ) = 4x + x - 12

4x + 2x - 4 = 4x + x - 12

COMBINE LIKE TERMS :

4x + 2x - 4 = 4x + x - 12

6x - 4 = 4x + x - 12

COMBINE LIKE TERMS :

6x - 4 = 4x + x - 12

6x - 4 = 5x - 12

ADD 4 TO BOTH SIDES :

6x - 4 = 5x - 12

6x - 4 + 4 = 5x - 12 + 4

ADD THE NUMBERS/ SIMPLIFY :

6x = 5x - 8

SUBTRACT 5x FROM BOTH SIDES :

6x = 5x - 8

6x - 5x = 5x - 8 - 5x

SIMPLIFY :

x = -8

Answer:

Please help im on that 2dd

Step-by-step explanation:

dddd