Chase answers 3/4 of his math questions correctly. There were 40 questions on the test.

a. How many did he get right?

b. How many did he miss?

Answer: Our required probability is 0.34.

Step-by-step explanation:

Since we have given that

Number of seventh grade student s= 21

Number of eight grade students = 14

Number of ninth grade students = 7

Total number of boys and girls = 42

Probability of an eigthth grader winning the competition would be

[tex]\dfrac{14}{42}\\\\=\dfra{1}{3}\\\\=0.3333333..................\\\\\approx 0.34[/tex]

Hence, our required probability is 0.34.

Answer:  The values are

[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]

Step-by-step explanation:  For an angle [tex]\theta[/tex],

[tex]\sin \theta=-\dfrac{\sqrt3}{2},~\pi<\theta<\dfrac{3\pi}{2}.[/tex]

We are given to find the values of [tex]\cos\theta[/tex] and [tex]\tan \theta[/tex].

Given that

[tex]\pi<\theta<\dfrac{3\pi}{2}\\\\\\\Rightarrow \theta~\textup{lies in Quadrant III}.[/tex]

We will be using the following trigonometric properties:

[tex](i)~\cos \theta=\pm\sqrt{1-\sin^2\theta},\\\\(ii)~\tan\theta=\dfrac{\sin\theta}{\cos\theta}.[/tex]

The calculations are as follows:

We have

[tex]\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(-\dfrac{\sqrt3}{2}\right)^2}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{\left(\dfrac{1}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\dfrac{1}{2}.[/tex]

Since [tex]\theta[/tex] is in Quadrant III, and the value of cosine is negative in that quadrant, so

[tex]\cos\theta=-\dfrac{1}{2}.[/tex]

Now, we have

[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac{\sqrt3}{2}}{-\frac{1}{2}}=\sqrt3.[/tex]

Thus, the values are

[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]

Since the given theta lies in third quadrant, then you can use the fact that only tangent and cotangent are positive in third quadrant, rest are negative.

The value of cos and tan for given theta is:

[tex]cos(\theta) = -\dfrac{1}{2}\\\\ tan( \theta) = \sqrt{3}[/tex]

If angle lies between 0 to half of pi, then it is int first quadrant.

If angle lies between half of pi to a pi, then it is in second quadrant.

When the angle lies between [tex]\pi[/tex] and [tex]\dfrac{3\pi}{2}[/tex], then that angle lies in 3rd quadrant.

And when it lies from [tex]\dfrac{3\pi}{2}[/tex] and 0 degrees, then the angle is in fourth quadrant.

Only tangent function and cotangent functions.

In first quadrant, all six trigonometric functions are positive.

In second quadrant, only sin and cosec are positive.
In fourth, only cos and sec are positive.

We can continue as follows:

[tex]sin(\theta) = -\dfrac{\sqrt{3}}{2}\\ sin(\theta) = sin(\pi + 60^\circ)\\ \theta = \pi + 60^\circ[/tex]

Thus, evaluating cos and tan at obtained theta:

[tex]cos(\pi + 60^\circ) = -cos(60) = -\dfrac{1}{2}\\ tan( \pi + 60^\circ) = tan(60) = \sqrt{3}[/tex]

Learn more about trigonometric functions and quadrants here;

https://brainly.com/question/25952919

To subtract the mixed numbers 9 1/4 and 6 2/3, first convert them to improper fractions, find a common denominator, and then perform the subtraction. The result is expressed as the mixed number 2 7/12 with the fractional part in lowest terms.

Subtracting Mixed Numbers

The question involves subtracting mixed numbers, specifically 9 1/4 (nine and one quarter) from 6 2/3 (six and two thirds). First, we need to convert these mixed numbers into improper fractions for easier subtraction.

The answer is 2 7/12.

To subtract mixed numbers, find a common denominator. Subtract the fractional part by subtracting the numerators. Subtract the whole numbers as usual. The answer is 8 7/12.

To subtract mixed numbers, we first need to find a common denominator. In this case, the common denominator is 12. Then, we can subtract the fractions by subtracting the numerators and leaving the denominator the same.

For the whole numbers, we simply subtract them as usual.

So, 9 1/4 - 6 2/3 = 8 7/12.

The volume of the cylinder is  1177.5 cubic inches.

Given that the diameter of the cylinder is 10 inches, the radius r is half of that, so [tex]\( r = \frac{10}{2} = 5 \)[/tex] inches.

The height h is three times the radius, so [tex]\( h = 3r = 3 \times 5 = 15 \)[/tex] inches.

Now, we can substitute these values into the formula for the volume of a cylinder:

[tex]\( V = \pi r^2 h \)\\ \( V = 3.14 \times (5)^2 \times 15 \)\\ \( V = 3.14 \times 25 \times 15 \)\\ \( V = 3.14 \times 375 \)\\ \( V = 1177.5 \) cubic inches.[/tex]

Rounded to the nearest tenth.

The simplified form of the given expression is [tex]25 x^{2} y^{20}[/tex].

Simplifying expressions mean rewriting the same algebraic expression with no like terms and in a compact manner.

The different Laws of exponents are:

According to the given question.

We have an expression [tex](5xy^{7} )^{2}(y^{2} )^{3}[/tex]

To simplify the above expression we use the exponent rules.

Therefore,

[tex](5xy^{7} )^{2}(y^{2} )^{3}[/tex]

[tex]= 5^{2}x^{2} y^{7\times2} y^{2\times3}[/tex]

[tex]= 25 x^{2} y^{14} y^{6}[/tex]

[tex]= 25 x^{2} y^{14+6}[/tex]

[tex]= 25 x^{2} y^{20}[/tex]

Therefore, the simplified form of the given expression is [tex]25 x^{2} y^{20}[/tex] .

Find out the more information about the simplified form of the expression and exponent rules here:

https://brainly.com/question/14575743

#SPJ2

Answer:

A ⊆ B

Step-by-step explanation:

To find Ron's age, we set up equations based on their age relations and the total sum of their ages. After solving the system of equations, we determine that Ron is 15 years old.

The question deals with a basic age-related algebra problem. To solve for how old Ron is, we can set up a system of equations based on the information provided:

Let R represent Ron's age.

Let S represent Sam's age.

Let T represent Ted's age.

From the information:

Ron is half as old as Sam, so R = 1/2 * S

Sam is three times as old as Ted, so S = 3 * T

The sum of their ages is 55, so R + S + T = 55

Substituting the expressions for R and S in terms of T into the third equation gives:

1/2 * (3 * T) + 3 * T + T = 55

Simplifying and solving for T, we find that:

1.5T + 3T + T = 55

5.5T = 55

T = 10

Now we can find Sam's age:

S = 3 * 10 = 30

And Ron's age:

R = 1/2 * 30 = 15

Therefore, Ron is 15 years old.

Answer:

Step-by-step explanation:

Given dimensions of original rectangle , length(l)=3 cm and width(w)=2.5 cm

We know that after dilation with scale factor (k), the dimension of new figure = k times the original dimensions.

Thus width of new rectangle=[tex]4\times2.5=10\ cm[/tex]

length of new rectangle=[tex]4\times3=12\ cm[/tex]

∴The dimensions of the new rectangle will be 10 cm by 12 cm.

Now, Perimeter of original rectangle=[tex]2(l+w)=2(3+2.5)=2(5.5)=11\ cm[/tex]

Thus, Perimeter of new rectangle=[tex]2(4l+4w)=2(12+10)=2(22)=44\ cm[/tex]

⇒ Perimeter of new rectangle=44 cm=[tex]4\times11\ cm[/tex]

∴The new perimeter will be 4 times the original perimeter.

Now, Area of original rectangle=[tex]lw=3\times2.5=7.5\ cm^2[/tex]

Thus, Area of new rectangle=[tex]4l\times4w=12\times10=120\ cm^2[/tex]

Area of new rectangle=[tex]16lw=16(lw)[/tex]

⇒The new area will be 16 times the original area.

A loss of 6 yards is represented by -6, and a loss of 5 yards by -5. After losses of 6 and 5 yards, and a gain of 12 yards, the team will be 1 yard past their original starting position, not exactly back to the original position.

A loss of 6 yards can be represented by the number -6, and a loss of 5 yards can be represented by the number -5.

When the football team on the next play gains 12 yards, we add this value to their previous position, which results from adding -6 and -5. To determine if the team returns to their original starting position, we calculate -6 + -5 + 12. The sum of -6 and -5 is -11, then adding 12 gives 1, which means the team advances 1 yard past the original starting position, not just back to it.

Therefore, the team will not be at their original starting position after gaining 12 yards, they will be 1 yard ahead.

it should be 1/6 not 16

there are 6 numbers on a die so to get a number you have a 1/6 probability

 so 1/6 x 1/6 = 1/36

the probability of getting both a 6 and a 3 is 1/36

$4100*(1+0.04/12)^(12*10)

4100*1.490832682=

$6112.41

Answer:

the answer on edge is D) h(3)-h (0)/3

And, the answer to the equation is 156.

180° rotation about the origin change the coordinates from (x,y) to (-x,-y). In this exercise:

A = (-4, 5) -> (4, -5)  

B = (-3, 1) -> (3, -1)

C = (-5, 2) -> (5, -2)

Translation 7 units up change the coordinates from (x, y) to (x, y+7). Continuing with the exercise:

(4, -5) -> (4, 2)

(3, -1) -> (3, 6)

(5, -2) -> (5, 5)

Which are not the coordinates of triangle DEF.

Reflection across the x-axis change the coordinates from (x, y) to (x, -y). In this exercise:

A = (-4, 5) -> (-4, -5)  

B = (-3, 1) -> (-3, -1)

C = (-5, 2) -> (-5, -2)

In 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across  x-axis (x, y) becomes (x, -y).

180° rotation about the origin change the coordinates from (x,y) to (-x,-y). It means if an object having coordinates (3,4) then it will be (-3,-4).

Translation 7 units up change the coordinates from (x, y) to (x, y+7). It means if an object having coordinates (3,4) then it will be (3,4+7).

Reflection across the x-axis change the coordinates from (x, y) to (x, -y). It means if an object having coordinates (3,4) then it will be (3,-4).

Hence we can summarize the above phenomenon as in 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across  x-axis (x, y) becomes (x, -y).

For more details on Reflection, Rotation and Translation follow the link:

https://brainly.com/question/9475847

area = S^2

 side = 12 miles

12^2 = 144

 area = 144 miles

Answer:

x = 2.75

Step-by-step explanation:

5x - 2 = x + 9

5x = x + 11

4x = 11