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Jenna took a test that had 50 questions in total. She got 62% of them correct. About how many questions were answered

The Pascal's Triangle expansion of (3 x-1)^4 is mathematically given as

\($$\begin{aligned}&1(3 x)^4(-1)^0+4(3 x)^3(-1)^1 +6(3 x)^2(-1)^2+4(3 x)^1(-1)^3 +1(3 x)^0(-1)^4\end{aligned}$$\)

This is further explained below.

Generally,  the equation for the expansion is  mathematically given as

(3 x-1)^4

Pascal's Triangle can be displayed as such:

1

1-1

1-2-1

1-3-3-1

1-4-6-4-1

The triangle can be used to calculate the coefficients of the expansion of (a+b)^n by taking the exponent n and adding 1 .

The coefficients will correspond with line n+1 of the triangle.

For (3 x-1)^4, n=4 so the coefficients of the expansion will correspond with line 5.

The expansion follows the rule

(a+b)^n=c_0 a^n b^0+c_1 a^{n-1} b^1+c_{n-1} a^1 b^{n-1}+c_n a^0 b^n

The values of the coefficients, from the triangle, are $-4-6-4-1.

\($1 a^4 b^0+4 a^3 b+6 a^2 b^2+4 a b^3+1 a^0 b^4$\)

Substitute the actual values of a 3 x and b-1 into the expression.

\($$\begin{aligned}&1(3 x)^4(-1)^0+4(3 x)^3(-1)^1 +6(3 x)^2(-1)^2+4(3 x)^1(-1)^3 +1(3 x)^0(-1)^4\end{aligned}$$\)

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Answer:

Step-by-step explanation:

what is 12/21 + 18/21 + 14/21

(12 + 18 + 14)/21 =

44/21

The critical value (Using FDIST(0.05, 2,9)) = 3.356

Therefore F statistic should be \(\geq 3.356\)

(a) k = number of columns = 5, n = 3,. Therefore N = 15

df1 = k - 1 = 4

df2 = N - k = 15 - 4= 11

The critical value (Using FDIST(0.05, 2,9)) = 3.356

Therefore F statistic should be \(\geq 3.356\)

_________________________________________

(b) k = number of columns = 5, n = 5,. Therefore N = 25

df1 = k - 1 = 4

df2 = N - k = 25 - 4 = 21

The critical value (Using FDIST(0.05, 4,21)) = 2.758

Therefore F statistic should be \(\geq 2.758\)

_________________________________________

(c) k = number of columns = 5, n = 7,. Therefore N = 35

df1 = k - 1 = 4

df2 = N - k = 35 - 4 = 31

The critical value (Using FDIST(0.05, 4,31)) = 2.678

Therefore F statistic should be \(\geq 2.678\)

_________________________________________

(d) Summary:

(i) As the sample size increases, the critical value decreases, and therefore a smaller F statistic is required to reject the null hypothesis.

(ii) Keeping k constant and increasing n, decreases the critical value and

(iii) Keeping n constant and increasing k, will also decrease the critical value.

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Answer:

b or c i think

Step-by-step explanation:

not for sure just a guess

Answer:

(c) is closest to the correct answer

Step-by-step explanation:

The question answers itself: "Mr. Jones's prescription calls for 1.04 tablets PER DAY, thus the amount of tablets Mr. Jones should talk daily are 1.04. Since none of the answers in the answer set have '1.04' in them, we have to use some basic logic:

The list of answers are, a) 1.25. We can rule that one out as it is not 1.04. We can also rule out b) and d) using the same logic. Thus, by process of elimination, we are left with c) 1 O. Not only is 1.0 (or just 1) the closest number to the actual amount (1.04) but it also makes the most sense, as one cannot take .04 (or 4/100ths) of a pill.

Since the Milky Way galaxy has 10x10^10 stars, we have that:

Now we divide the number of stars in the universe by 10^11:

therefore, there are about 10^13 galaxies in the universe

The question is incomplete. The complete question is :

The fuel efficiency for a new helicopter engine is given by the continuous function r(c) where r is measured in gallons per mile and c is measured in miles. What are the units of \($\int_0^7 r(c) \ dc$\)   ?

Solution :

The given continuous function is :

r(c), here c is measured in miles and the unit of r is measured in gallons per mile.

So the unit of  \($\int_0^7 r(c) \ dc$\) is given by :

= gallons per mile x mile

= gallons

So, the final unit is gallons.

Answer:

\(\text{The quotient is}~ x^2 +2x +5 \\\\\text{The remainder is}~ -3\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=1/2=2/4

y=5/4

y=2.5x

10/2.5=4

so x=4

The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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Answer:

183.75 pounds

Step-by-step explanation:

divide 147 by a fourth then add your result onto 147 for your awnser

Answer:

v=2144.66

Step-by-step explanation:

V=4/3πr^3
sub in r which is 8

V=4/3 * π * 8^3
V=4/3 * π * 512

Given:

Culture A contains 8 x10^4 bacteria

Culture B contains 4 x10^6 bacteria

To compare between them we will divide A by B

so,

so, the answer will be:

Culture A contains 1/50 as many bacteria as culture B.​

The answer is option D.

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

The length of side X in simple radical form with a rational denominator is 10/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 2 × 5/√3

Hypotenuse, x = 10/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.

The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.

The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.

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9514 1404 393

Answer:

  (x -4)² +(y +3)³ = 4

Step-by-step explanation:

Each circle is centered on (h, k) = (4, -3). Each circle has a radius 1 unit smaller than the circle just outside of it. The innermost circle shown has a radius of 3, so the next in the pattern of smaller circles will have a radius of 2. The equation for a circle centered at (h, k) with radius r is ...

  (x -h)² +(y -k)² = r²

The next circle in the pattern is centered at (4, -3) and has radius 2, so its equation is ...

  (x -4)² +(y +3)² = 4

The evaluated value of x from the line geometry given is 36.

An angle is the point where two lines meet. From the given diagram, the sum of the angles on the line is 180 degrees.

Take the sum to have

x + 3x + x = 180

Simplify

4x + x = 180

5x = 180

Divide both sides by 5

5x/5 = 180/5

x = 36

Hence the value of x from the diagram is 36

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Answer:

B

Step-by-step explanation:

Answer:

288 donuts

Step-by-step explanation:

Answer:

288 donuts

Step-by-step explanation:

72 divided by 2 is 36 so that means you will make 36 donuts in 1 hour so now we have our unit rate which is 36. so then you multiply 36 by 8 and you get 288. that is your answer

The real-world problem involving perimeter is that the perimeter of a rectangle of length 18 units and width 15 units is 66 units

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

2 x 18 + 2 x 15 = 66

The perimeter of a rectangle can be calculated using

Perimeter = 2 x Length + 2 x Width

Using the above as a guide, we have the following:

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If the slower train travels at a pace of x miles per hour, the faster train will go at x+14 miles per hour.The quicker train travels at 88 miles per hour

Since the two trains are headed in the same direction, their separation is narrowing at a rate equal to their combined speed per hour. Since it will take 4 hours to travel the entire distance between them, we may create the following equation:

4(x + x+14) = 648

By enlarging and condensing, we obtain:

8x + 56 = 648

8x = 592

x = 74

As a result, the quicker train travels at 88 miles per hour, while the slower train moves at 74 miles per hour.

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Answer:

\(\tan{\theta} = \frac{\sqrt{11}}{11}\)

Step-by-step explanation:

Cosecant:

The cosecant is one divided by the sine. Thus:

\(\csc{\theta} = \frac{1}{\sin{\theta}}\)

Tangent is sine divided by cosine, so we first find the sine, then the cosine, to find the tangent.

Sine and cosine:

\(\sin{\theta} = \frac{1}{\csc{\theta}} = \frac{1}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{6}\)

\(\sin^{2}{\theta} + \cos^{2}{\theta} = 1\)

\(\cos^{2}{\theta} = 1 - \sin^{2}{\theta}\)

\(\cos^{2}{\theta} = 1 - (\frac{\sqrt{3}}{6})^2\)

\(\cos^{2}{\theta} = 1 - \frac{3}{36}\)

\(\cos^{2}{\theta} = \frac{33}{36}\)

First quadrant, so the cosine is positive. Then

\(\cos^{2}{\theta} = \sqrt{\frac{33}{36}} = \frac{\sqrt{33}}{6}\)

Tangent:

Sine divided by cosine. So

\(\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{\frac{\sqrt{3}}{6}}{\frac{\sqrt{33}}{6}} = \frac{\sqrt{3}}{\sqrt{33}} = \frac{\sqrt{3}}{\sqrt{3}\sqrt{11}} = \frac{1}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{11}}{11}\)

The answer is:

\(\tan{\theta} = \frac{\sqrt{11}}{11}\)

The inequality that represents the value of x is (b)  x > 80

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

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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The value of a, b and c are found as 6, 10 and 2 respectively.

Values for exponents, commonly referred to as powers, indicate how many often to multiply a quantity by itself.

The given expression is;

\(4x^{8} y^{c} = \frac{24x^{b}y^{-3} }{ax^{2} y^{-5} }\)

Solving expression using the law of indices.

\(x^{8} y^{c} = \frac{6x^{b-2}y^{-3+5} }{a}\)

\(ax^{8} y^{c} = {6x^{b-2}y^{2} }\)

Comparing powers of both sides:

a = 6

8 = b-2 : b = 10

c = 2

Thus, the value of  a, b and c are found as 6, 10 and 2 respectively.

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I think it is greater then  >