In one day, 500 people played a fairground game.
The relative frequency of winning the game was
0.38
How many times was the game won that day?

Answer:

\(x=-\frac{4}{5}\)

Step-by-step explanation:

\(6=\frac{3}{4}(10x+16)\\\mathrm{or,\ }6\times 4=3(10x+16)\\\\\mathrm{or,\ }24=30x+48\\\\\mathrm{or,\ }-24=30x\\\\\mathrm{\therefore}\ x=-\frac{4}{5}\)

Answer:

155°

Step-by-step explanation:

<O=24

<P=2x+9

<N=180-(3x-28) (It’s the supplement of 3x-28)

Add them together to equal 180. (180 is the sum of the 3 interior angles of a triangle.)

24+2x+9+180-(3x-28)=180

24+2x+9+180-3x+28=180

-1x+241=180

-1x=-61

x=61

Now that we’ve solved for x, plug it back into <MNO

<MNO=3x-28=3(61)-28=183-28=155°

9514 1404 393

Answer:

  90°

Step-by-step explanation:

On a standard 12-hour analog clock, the minute hand will be at the 12, and the hour hand will be at the 3 at 3:00. The smaller angle between the two hands is 90°. Of course, the larger angle is 360° -90° = 270°.

The expansion will be 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

We can expand (2d+3)^6 using the binomial theorem, which states that:

(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn-1 * a^1 * b^(n-1) + nCn * a^0 * b^n

where nCk is the binomial coefficient, given by:

nCk = n! / (k! * (n-k)!)

Expanding (2d+3)^6 using this formula, we get:

(2d+3)^6 = 6C0 * (2d)^6 * 3^0 + 6C1 * (2d)^5 * 3^1 + 6C2 * (2d)^4 * 3^2 + 6C3 * (2d)^3 * 3^3 + 6C4 * (2d)^2 * 3^4 + 6C5 * (2d)^1 * 3^5 + 6C6 * (2d)^0 * 3^6

Simplifying each term using the binomial coefficient formula, we get:

(2d+3)^6 = 1 * 64d^6 * 1 + 6 * 32d^5 * 3 + 15 * 16d^4 * 9 + 20 * 8d^3 * 27 + 15 * 4d^2 * 81 + 6 * 2d * 243 + 1 * 1 * 729

Simplifying each term further, we get:

(2d+3)^6 = 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

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Answer:

A diagonal

Step-by-step explanation:

Answer + Step-by-step explanation:

At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Step-by-step explanation:

7! = 5040 ways

The calculation of this can be done by first determining the future value of the monthly payments of $327.50

The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,

which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.

The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35

This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.

Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.

 for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).

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Answer:

A

Step-by-step explanation:

10^0 = 1

so 1*10^0 = 1*1 = 1m

B = 10m which is too long for a human stride

Answer:

1/13

Step-by-step explanation:

y is proportional to x ⇒ y = kx

Plug in (26,2) and solve for k:

2 = k·26

k = 2/26 = 1/13

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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The value of x is 10°.

What is a measure of an angle?

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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The value of x is 10°.

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

1.75a+8b

Step-by-step explanation:

Question = 0.75a + 10b + a - 2b

First collect like terms 0.75a + a + 10b - 2b

= 1.75a + 8b

what are like terms : they are terms with the same variable and the same exponent. example: 9xy and -6xy etc.......

If it's helpful ❤❤❤

THANK YOU

Answer:

B

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Older drivers tended to have fewer accidents per 100 drivers

Answer:

Step-by-step explanation:

Please leave a rating if this helped :)

Answer:

Step-by-step explanation:

Total Females = 3 + 4 + 6 + 3  = 16

Number of female seniors = 3

P ( Female | senior )  

number of female seniors / total female  = \(\frac{3}{16}\)

In percent,

\(\frac{3}{16}\) · 100 = 0.1875 · 100 = 18.75%

18.75% rounded to nearest whole percent is 19%

The solution is : 40%, is the probability the student is a senior given that it's female.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Probability that student is a male Given that it's a senior ::

Recall :

P(A | B) = (AnB) / B

Hence, we have ;

P(male | Senior) = number of (Male n Senior) / total Senoirs

From the table :

Total seniors = 2 + 3 = 5

Male n Seniors = 2

P(male | Senior) = 2 / 5 = 0.4 = 40%

Hence, The solution is : 40%, is the probability the student is a senior given that it's female.

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The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

An equation for a transformed cosine wave with the following properties can be written in the form:

y = A× cos(B(x - C)) + D

Where:

A = amplitude (positive value)

C = phase shift (horizontal shift of the wave)

D = vertical shift (shift of the wave up or down)

Here we have

Amplitude = 3

Period = π

Horizontal shift = None

Vertical shift  = 4 units  up  

As we know Period P = 2π/B

From the data => 2π/B = π

=> B = 2  

Hence,

Equation for a transformed cosine wave, y = 3 × cos(2(x - 0)) + 4

=> y = 3 × cos(2(x )) + 4

=> y = 3cos2x + 4  

Therefore,

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

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Answer:

The company lost 3 dollars

9-6= (-3)

Step-by-step explanation:

Answer:

54 + 42 = 6 (9 + 7)

Sorry if this answer is not correct, if it is or is not, please tell me in the comments!

Step-by-step explanation:

The equation already gives the 7 in the parenthesis, so we know that 7 x 6 = 42.

The 6 will be on the outside of the equation since we will be using Distributive Property to multiply the 6 and 7.

Since we already know the 6 is on the outside, your new equation is:

6 x (what number) = 54

54 divided by 6 = 9

Answer

Explanation

Given:

Factor z out in the right hand side of the equation

Divide both sides by w - c⁵

Elements of following sets are

A = {1}

B = {-1, 1}

C = Q ∩ [0, 1]

Sets

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set. A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Given that

A = {n ∈ N : cos(nπ) greater than or equal to 0}

B = {cos(nπ) : n ∈ N}

C = {q + r : q, r ∈ Q ∩ [0, 1]}

Therefore elements of

A = {1}

as cos 2\(\pi\), cos 4\(\pi\), cos 6\(\pi\), cos 8\(\pi\) and so on is equal to 1.

B = {-1, 1}

as cos \(\pi\) , cos 2\(\pi\), cos 3\(\pi\), cos 4\(\pi\), cos 5\(\pi\) and so on is equal to -1 and 1.

C = Q ∩ [0, 1]

as q and r both belongs to Q ∩ [0, 1] and their sum will be also equal to Q ∩ [0, 1].

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Answer:

4x + 6 = 38

Step-by-step explanation:

Substitute x in for x and see which equation is true

2x + 3 = 13

2*8+3 = 16+3 = 19  this is not 13 so it is false

4x + 6 = 38

4*8+6 = 32+6 = 38

This is true

3x - 5 = 29

3*8 -5 = 24-5 = 19

False

5x - 8 = 48

5*8-8 = 40-8 = 32

False​

Answer:

4 seconds

Step-by-step explanation:

6000/1500=4

Hi there!

~

\(1500 \div 6000 = 4\)

Hope this helped you!

Answer:

Pattern:

\({x}^{2} + 3 \\ \)

Next Number:

\({7}^{2} + 3 \\ 49 + 3 \\ 52\)

If the next number you want to calculate is the 8th number then you substitute 8 in x's place

Answer:

The point lies on (-5, 1).

Step-by-step explanation:

1. Graph the point.

2. Translate (move) the point 5 units to the left (a negative direction).

3. Translate down 1 unit (another negative direction).

4. The final point rests on (-5, 1).

HOPE THIS HELPED!!!

Answer:

1. E. Reject H0 if t > 1.721

2. B. 1.679

Step-by-step explanation:

This would be a hypothesis test for the difference between two means. In the way that the alternative hypothesis.

The critical value depends on the significance level, the test type (one-tail or two-tailed) and the degrees of freedom.

This is a t-test type, so the statistic is t and not z. In the way that the alternative hypothesis, where only matter if the mean A is significantly bigger than mean B, this is a one-tail test.

The degrees of freedom can be calculated as:

\(df=n_1+n_2-2=13+10-2=21\)

Then, for a one-tail t-test, with significance level of 0.05 and 21 degrees of freedom, the critical value is t=1.721.

The standard deviation of the difference between the two means can be calculated as:

\(s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{5^2}{13}+\dfrac{3^2}{10}}\\\\\\s_{M_d}=\sqrt{1.923+0.9}=\sqrt{2.823}=1.6802\)

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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