A restaurant manager believes that a majority of customers who dine at his restaurant would rate the food as excellent. To investigate this belief, he sends an email survey to a random sample of 50 customers from the large list of customers who have signed up for his frequent diner club. To encourage the customers to complete the survey, he offers a $10 gift card upon completion of the survey. He receives 22 responses, of which 20 rated the food as excellent. He would like to know if these data provide convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent. Are the conditions for inference met

Answer:

[tex] x =\pm \sqrt{26}[/tex]

Step-by-step explanation:

Given :-

And we need to find the potential solutions of it. The given equation is the logarithm of x² - 25 to the base e . e is Euler's Number here. So it can be written as ,

Equation :-

[tex]\implies log_e {(x^2-25)}= 0 [/tex]

In general :-

[tex]\implies log_a b = c [/tex]

Then this can be written as ,

[tex]\implies a^c = b [/tex]

In a similar way we can write the given equation as ,

[tex]\implies e^0 = x^2 - 25 [/tex]

[tex]\implies 1 = x^2 - 25 \\\\\implies x^2 = 25 + 1 \\\\\implies x^2 = 26 \\\\\implies x =\sqrt{26} \\\\\implies x = \pm \sqrt{ 26}[/tex]

Hence the Solution of the given equation is ±√26.

Answer:

4multiply by 10 lolllllllll

Answer:

20 each

Step-by-step explanation:

10 x 4 = 40 40 - 20 = 20

The equation of the line perpendicular to the line 5x-4y=10 and passing through the point (5,12) is y = 4x/5 + 8.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

The line 5x-4y=10.

Simplifying,

y = (-5/4)x + 5/2

Comparing with the slope-intercept form,

y = mx + b,

where m is the slope and b is y-intercept.

The slope is = -5/4

The slope of the perpendicular line,

= negative reciprocal of the slope of the line where the line is perpendicular.

= 4/5

So, the line:

If a line passes through one point (x₁ ,y₁) and have slope m,

then the equation of line is

y - y₁ = m (x - x₁)

y - 12 = (4/5)(x-5)

y = 4x/5 + 8

Therefore, the equation of the line is y = 4x/5 + 8

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b because you are dividing

Answer: D (3:7)

Step-by-step explanation:

You need to simplify the 56:24 until fully simplified (using the highest common factor). Flip this so it is instead surfboards to umbrellas rather than umbrellas to surfboards.

56/8 = 7
24/8 = 3

Statement 1 is correct and Statement 2 is not correct.

As A, B and C represent distinct non-zero digits

For least value of x

Let A=1, B=2, C=3

The possible numbers that can be formed using 1,2,3 are 6 {using permutations}

123, 132, 213, 312, 231, 321

x is the sum of all possible 3-digit numbers formed by A, B and C without repetition so

x= 123+ 132+ 213+ 312+ 231+ 321

x=1332

So statement 1 is correct

statement 2 cannot be correct as least value of x is  4-digit so  greatest value of x cannot be a three digit number.

The 4-digit least value of x is 1332 so Statement 1 is correct and Statement cannot be correct.

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Answer:

  (a)  (5, 9)

Step-by-step explanation:

You want the solution to the system ...

The value of x is already given, so no work is required to find that.

The value of y is found by using that value of x in the equation for y:

  y = 2x -1

  y = 2·5 -1 = 10 -1 = 9

The solution is (x, y) = (5, 9).

Answer:

360 degrees

Step-by-step explanation:

Answer:

360°

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

Answer:

5√2

Step-by-step explanation:

Hello!

To simplify the radical, we can identify perfect square factors in the radicand or the number inside the square root.

We know that 50 is 25 times 2, so we can expand the radical like this...

Now we can simplify each radical:

The simplified form is 5√2.

a: 235 92 U + 1 0 n → 90 36 Kr + 141 56 Ba + 3 1 0 n

b: 239 94 Pu + 1 0 n → 96 38 Sr + 143 55 Ba + 3 1 0 n

c: It is not possible to complete this nuclear fission reaction as it is not a valid input. There is no nuclide with the atomic number 94 and mass number 239.

Nuclear reactions are those that involve the nucleus of an atom. Nuclear fission involves the splitting of an atomic nucleus and the formation of two distinct atomic species.

Nuclear fission is a nuclear reaction in which the nucleus of an atom is split into two or more smaller nuclei, along with the release of a large amount of energy. In the first reaction, an atom of Uranium-235 (U-235) is hit by a neutron, which causes the nucleus to split into Krypton-90 (Kr-90) and Barium-141 (Ba-141) along with 3 neutrons. In the second reaction, an atom of Plutonium-239 (Pu-239) is hit by a neutron, which causes the nucleus to split into Strontium-96 (Sr-96) and Barium-143 (Ba-143) along with 3 neutrons.

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Step-by-step explanation:

215÷3=71

143÷6=23.9

71+23.9+60=154.9

The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse.

To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.

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The measure of length of FG is 105 units.

What is bisection?

To determine the roots of a polynomial problem, utilise the bisection method. It splits and separates the interval in which the equation's root is located. The continuous functions intermediate theorem serves as the method's guiding premise.

From the given diagram, since Line DF bisects angle EDG, then -

EF = FG

Given the following parameters -

EF = 9n - 3

FG = 8n + 9

Equating both expressions -

9n - 3 = 8n + 9

9n - 8n = 9 + 3

n = 12

Get the measure of FG -

FG = 8n + 9

FG = 8(12) + 9

FG = 96 + 9

FG = 105

Hence, the line FG measures as 105 units.

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On solving the provided question, we can say that Probability ( At least one of the students is a senior) = 0.4632 approx

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

P(All four players are senior) = 0.00033 approx

P(There is one each: freshman, sophomore, junior and senior) = 0.0944 approx.

P(There are 2 sophomores and 2 freshman) = 0.0568  approx

P( At least one of the students is a senior) = 0.4632 approx

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Answer:

38

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

(x,y)

if the first cord is 0 its on y

is the second cord is 0 its on x

Answer: True

Since the x-coordinate being 0, the point lies on the y-axis. The y-coordinate =+3 being positive, the point lies on the +ve y-axis.

Step-by-step explanation: Hope this help :D

There is a relationship between the numbers of strawberries gathered and the amount of rainfall that can be found in a model (function).

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.1 is valid based on the provided scatter plot.

Part B:

The independent variable (the explanatory variable) is the cause of the dependent variable in a causal connection.

As a result, you need to identify a plausible factor that can influence the number of strawberries collected.

The week before harvest, I could picture how much it would rain.

Hence, There is a relationship between the number of strawberries gathered and the amount of rainfall that can be found in a model (function).

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Answer:

12?

Step-by-step explanation:

Answer:

Function Domain and Range

g(x)=\sqrt{x} -5

what is the range and domain

To find the range of g(x), we can substitute a few values of x into the expression for g(x) to see what the output is. For example, when x = 0, g(x) = sqrt(0) - 5 = 0 - 5 = -5. When x = 1, g(x) = sqrt(1) - 5 = 1 - 5 = -4. When x = 2, g(x) = sqrt(2) - 5 = 1.4142 - 5 = -3.5858.

As we can see, the output of g(x) is always a negative number for any value of x in the domain. Therefore, the range of g(x) is the set of all negative real numbers, or (-infinity, 0).

So, the domain of g(x) is all real numbers x such that x >= 0, and the range of g(x) is all negative real numbers (-infinity, 0).

Answer:

4

Step-by-step explanation:

→ –36 – ( –40 )

→ –36 + 40

→ 4

[tex] \therefore [/tex] 4 is the required answer.

Answer:

45

Step-by-step explanation:

when a = 6 , b =2

2a^2/ b^3 + b(2a+6)

=2(6)^2/ (2)^3 +(2)[2(6)+6)

=45

No, 12 16 20 is not a right triangle. In order to be a right triangle, one side must be the same as the square root of the sum of the squares of the other two sides. In this case, the hypotenuse (side 20) is not equal to the square root of 12^2 + 16^2 which is 20.

No, 12 16 20 is not a right triangle. To determine whether or not something is a right triangle, we need to use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is side 20, and the other two sides are 12 and 16. When we calculate the square root of 12^2 + 16^2, we get 20, which does not match the length of the hypotenuse. Therefore, 12 16 20 is not a right triangle.

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By using formula and solving, Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t

A collision is an event in which two or more objects come into contact with each other. In physics, a collision is defined as a rapid and forceful interaction between two or more objects that causes a transfer of energy. Collisions can be elastic or inelastic, depending on whether or not the total kinetic energy of the objects is conserved.

Force is a physical quantity that describes the interaction between two or more objects. It is a vector quantity, meaning it has both magnitude and direction. Forces can cause an object to accelerate, change its shape, or change its direction of motion. Forces can be categorized into different types, such as contact forces, which act when two objects are in contact, and non-contact forces, which act at a distance. Some examples of non-contact forces are gravitational force, electric force, and magnetic force.

To calculate the force of impact on the bowling ball and bowling pin during the collision, you can use the formula:

Force of Impact = Change in momentum / Time of collision

The change in momentum is given by the formula:

Change in momentum = Final momentum - Initial momentum

The initial momentum of the 6 kg bowling ball traveling at 2 m/s is:

Initial momentum (ball) = 6 kg * 2 m/s = 12 kg*m/s

The final momentum of the bowling ball can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision. In this case, since the bowling pin is moving after the collision and the bowling ball is not, the final momentum of the bowling ball is zero.

Final momentum (ball) = 0

Change in momentum (ball) = Final momentum (ball) - Initial momentum (ball) = 0 - 12 kgm/s = -12 kgm/s

The force of impact on the bowling ball is:Force of impact (ball) = Change in momentum (ball) / Time of collision = -12 kg*m/s / t (t is the time of collision, assuming it's a short time)

Similarly, the initial momentum of the 1.5 kg bowling pin at rest is:

Initial momentum (pin) = 1.5 kg * 0 m/s = 0 kg*m/s

The final momentum of the bowling pin can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision.

Final momentum (pin) = Initial momentum (ball) = 12 kg*m/s

Change in momentum (pin) = Final momentum (pin) - Initial momentum (pin) = 12 kgm/s - 0 kgm/s = 12 kg*m/s

The force of impact on the bowling pin is:

Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t

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Answer:

[tex]11\pi[/tex]

Step-by-step explanation:

[tex]s = r \times theta[/tex]

where r is the radius.

The radius is 11 and theta(in radians) is pi so

[tex]s = 11\pi[/tex]

Answer:

P(x) = ([tex]\frac{2}{5}[/tex])x(x + 3)(x - 1)²

Step-by-step explanation:

Given - The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=-3. It goes through the point (5,256)

To find - Formula for P(x) ?

Proof -

Given that,

P(x) has a root of multiplicity 2 at x=1

So,

(x - 1)² is a factor.

Now,

Given that, there is roots of multiplicity 1 at x=0 and x=-3

So,

(x - 0) and ( x - (-3) are also factor

So,

P(x) can be written as

P(x) = Ax(x + 3)(x - 1)²           .........(1)

where A is a constant.

Now,

Given that, It goes through the point (5,256)

⇒At x = 5, P(x) = 256

So,

Put the values of x and P(x) in equation (1), we get

P(x) = Ax(x + 3)(x - 1)²

⇒256 = A(5)(5 + 3)(5 - 1)²

⇒256 = 5A(8)(4)²

⇒256 = 40A(16)

⇒256 = 640 A

⇒A = [tex]\frac{256}{640}[/tex] = [tex]\frac{2}{5}[/tex]

∴ we get

P(x) = ([tex]\frac{2}{5}[/tex])x(x + 3)(x - 1)²

Answer:

D.) 12/5

Step-by-step explanation:

tangent is opposite over the adjacent side so the opposite of x is 24 and the adjacent is 10 so 24/10 divided by 2 gets you 12/5

Answer:

7 months

Step-by-step explanation:

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