The ratio of the books in the sample above is representative of the books in a bookcase in the library. If there are 35 yellow books in the bookcase, then how many green books are in the bookcase?

Answer:

Step-by-step explanation:

We want to reduce the radical. In order to do that, we want to find the factors of 96 that are square numbers

The factors of 96 are:

\(1, 96, 2, 48, 3, 32, 4, 24, 6, 16...\)

16 is a square number, so we can rewrite

\(\sqrt{96} = \sqrt{16*6} = \sqrt{16} * \sqrt{6} = 4\sqrt{6}\)

Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

*ANSWER:*

I think the answer is Option (B)

Step-by-step explanation:

..........

Answer:

x = 5 ± \(\sqrt{44}\)

Step-by-step explanation:

Given

x² - 10x - 2 = 17 ( add 2 to both sides )

x² - 10x = 19

To complete the square

add ( half the coefficient 0f the x- term )² to both sides

x² + 2(- 5)x + 25 = 19 + 25

(x - 5)² = 44  ( take the square root of both sides )

x - 5 = ± \(\sqrt{44\) ( add 5 to both sides )

x = 5 ± \(\sqrt{44}\)

Then solutions are

x = 5 - \(\sqrt{44}\) , x = 5 + \(\sqrt{44}\)

Answer:

C

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 3, 1) ← 2 points on the line

m = \(\frac{1-0}{-3-0}\) = - \(\frac{1}{3}\)

y = - \(\frac{1}{3}\) x ← equation of line

Answer:

g(-2)=0

g(-1)=3

g(0)=1

g(1):=3

g(2): DNE

Step-by-step explanation:

Answer:

G(- 2) = 0

G(- 1) = 3

G(0) = 1

G(1) = 3

G(2) = 1

Step-by-step explanation:

the point of intersection between the given plane and the line perpendicular to the plane and passing through the point (4, 5, 9) is (4, 5, 9).

To find the point of intersection between the given plane and the line that is perpendicular to the plane and passes through the point (4, 5, 9), we need to determine the equations for both the plane and the line.

Let's assume the equation of the plane is of the form Ax + By + Cz + D = 0, where A, B, C, and D are constants.

Given that the plane is perpendicular to the line passing through the point (4, 5, 9), we know that the direction vector of the line is orthogonal to the normal vector of the plane.

To find the normal vector of the plane, we can consider the coefficients A, B, and C in the plane's equation. Since the coefficients represent the direction ratios of the normal vector, we have the normal vector N = (A, B, C).

Next, we can use the dot product to find the scalar product between the normal vector of the plane and the direction vector of the line. For the dot product to be zero, the vectors must be orthogonal:

N · (x - 4, y - 5, z - 9) = 0

Expanding this equation, we get:

A(x - 4) + B(y - 5) + C(z - 9) = 0

Now, let's substitute the coefficients of the normal vector for A, B, and C:

Ax - 4A + By - 5B + Cz - 9C = 0

Rearranging terms, we have:

Ax + By + Cz = 4A + 5B + 9C        (Equation 1)

This equation represents the plane that is perpendicular to the line passing through (4, 5, 9).

To find the equation of the line passing through the point (4, 5, 9), we can use the parametric form of a line:

x = x₀ + at

y = y₀ + bt

z = z₀ + ct

Since the line is perpendicular to the plane, the direction vector of the line is parallel to the normal vector of the plane. Therefore, the direction vector of the line is given by the coefficients of A, B, and C in Equation 1:

Direction vector of the line = (A, B, C)

Let's assume a parameter t, and substitute the values x₀ = 4, y₀ = 5, z₀ = 9 into the equations:

x = 4 + At

y = 5 + Bt

z = 9 + Ct

Now, we have both the equation of the plane (Equation 1) and the parametric equation of the line.

To find the point of intersection, we can substitute the parametric equations of x, y, and z into Equation 1:

A(4 + At) + B(5 + Bt) + C(9 + Ct) = 4A + 5B + 9C

Expanding and collecting terms, we have:

4A + AtA + 5B + BtB + 9C + CtC = 4A + 5B + 9C

Simplifying, we get:

AtA + BtB + CtC = 0

Since this equation represents the sum of squares, it can only be true if each term is zero:

AtA = 0

BtB = 0

CtC = 0

Solving these equations, we find t = 0.

Now, substituting t = 0 into the parametric equations, we have:

x = 4 + 0 = 4

y = 5 + 0 = 5

z = 9 + 0 = 9

Therefore, the point of intersection between the given plane and the line perpendicular to the plane and passing through the point (4, 5, 9) is (4, 5, 9).

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Answer:

Therefore, the area of trapezoid UVWX is 132 square units.

Step-by-step explanation:

To find the area of trapezoid UVWX, we need to use the formula:

Area = (1/2) x Height x (Base 1 + Base 2)

First, we need to find the height of the trapezoid. From the diagram, we can see that the height is the vertical line connecting the two parallel bases, and it has a length of 12 units.

Next, we need to find the lengths of the two bases. Base 1 is the top base, and we can see that it has a length of 8 units. Base 2 is the bottom base, and we can see that it has a length of 14 units.

Now we can plug these values into the formula to find the area:

Area = (1/2) x 12 x (8 + 14)

Area = (1/2) x 12 x 22

Area = 132 square units

a. The domain of this function is all real numbers, or (-∞, ∞).

b. To find the open intervals on which the curve is smooth, we need to find the derivative of r(t), which is r'(t) = Vi + 0j = Vi.

c. The path traced out by this function is a straight line with a slope of V/p in the xy-plane.

d. Other events that can cause a curve to fail to be smooth at a point in time include abrupt changes in direction, such as a sharp turn or a cusp, or a discontinuity in the function, such as a jump or a hole.

The domain of r' is also (-∞, ∞), since it is a constant function. The curve is smooth on the entire domain, since the derivative is constant and therefore there are no points at which the curve changes direction abruptly.

To find the open intervals on which the curve is smooth, we need to find the derivative of r(t), which is r'(t) = Vi + 0j = Vi.

The domain of r' is also (-∞, ∞), since it is a constant function. The curve is smooth on the entire domain, since the derivative is constant and therefore there are no points at which the curve changes direction abruptly.

The path will not be smooth at any point, since the derivative is constant and there are no abrupt changes in direction. The curve will look like a straight line with a slope of V/p.

These events can occur even though the vector-valued function tracing the curve is defined for the value of t at which the curve is not smooth.

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Answer:(-27, -123)

Step-by-step explanation:

Answer: -27,-123

Step-by-step explanation:

Isaac Newton discovered how gravity affects other bodies, but he never discovered where gravity comes from. In fact, Einstein discovered the source of gravity in his theory of relativity.

The plane can be used to symbolize both space and time, according to Einstein's Theory of Relativity. Now, any mass maintained on this plane causes the plane to flex. To make it easier, place a metal ball on a piece of cellophane paper. The cellophane paper will bend as a result. The more mass a body has, the more time and space are bent.

Take a cellophane sheet once more, and place a metal ball on it. Cellophane paper sways slightly. Let's now place a smaller metal close to the larger one. Due to the cellophane paper's curve, you can see the tiny ball travelling towards the larger one. It certainly appears to be gravity. That is gravity in the space-time continuum! The smaller ball will now spin if we throw it in a specific direction around the larger one.

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Answer:

Step-by-step explanation:

The pentagon has been split into 5 congruent triangles.

Each triangle has area of:

The area of the room is:

Answer:

C. 25

Step-by-step explanation:

4*4=16

5*5=25

24 is found in the middle of 16 and 25.

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Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

Therefore, after 10 payments, Jeff owes $1160.

Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.

A mathematical equation, such as 6 x 4 = 12 x 2, can be used to compare two amounts or values. a significant noun. An equation is employed when it's required to integrate two or more elements in order to understand or fully explain a situation.

To determine whose furniture costs more, we need to compare the amounts owed by Jeff and Ella for the same number of payments.

Jeff's equation is y = -108x + 2240, which gives the amount owed after x payments.

Ella's graph does not have an equation provided, but we can see that after 10 payments, she owes approximately $2200.

To compare the amounts owed after 10 payments, we can substitute x = 10 into Jeff's equation:

y = -108(10) + 2240

y = -1080 + 2240

y = 1160

Therefore, after 10 payments, Jeff owes $1160.

Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.

Answer: Ella's furniture costs more than Jeff's.

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The answer is (i) The statement is False, (ii) The statement is false, (iii) The statement is true, (iv) The statement is true.

(i) Let A = {2, 3, 4, 5} and B = {3, 6}

    Now A∩B

    = {2, 3, 4, 5} ∩ {3, 6} = {3}

    Hence, A and B are not disjoint. So the statement is false.

(ii) Let A = {a, e, i, o, u} and B = {a, b, c, d}

    Now A∩B

    = {a, e, i, o, u} ∩ {a, b, c, d}= {a}

    Hence, A and B are not disjoint. So the statement is false.

(iii) Let A = {2, 6, 10, 14} and B = {3, 7, 11, 15}

     Now, A∩B

     = {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ

     Hence, A and B are disjoint sets. So the statement is true.

(iv) Let A = {2, 6, 10} and B = {3, 7, 11}

     Now A∩B  

     = {2, 6, 10} ∩ {3, 7, 11} = Φ

     Hence, A and B are disjoint sets. So the statement is true.

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The lateral surface area is the area of the side thing, not the 2 circles.

If we imagine to stretch the side out, we can get a rectangle with base the circumference to the base circle, and height of 9 inches.

Therefore this area is pi*8*9=72π

Answer:

A= 2

B= 3

D=2

maka

A x B ÷C

2 x 3 ÷ 2

=6 ÷ 2

=3

Answer:

A= 2

B= 3

D=2

maka

A x B ÷C

2 x 3 ÷ 2

=6 ÷ 2

=3

Range = 74.8

IQR = 16.8

Median = 63.95.

To calculate the range, we subtract the smallest value from the largest value:

Range = 88.9 - 14.1 = 74.8

To calculate the median, we find the middle value of the data set. Since there are 40 numbers in the set, the median is the average of the 20th and 21st numbers:

Median = (63.0 + 64.3)/2 = 63.65

To calculate the IQR, we first need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the first half of the data set, and Q3 is the median of the second half of the data set. Since there are an even number of data points, we need to include the median in both halves. Thus, Q1 is the median of the first 20 numbers, and Q3 is the median of the last 20 numbers:

Q1 = (54.2 + 54.7)/2 = 54.45

Q3 = (75.3 + 75.9)/2 = 75.6

IQR = Q3 - Q1 = 75.6 - 54.45 = 21.15

Therefore, the range is 74.8, the median is 63.65, and the IQR is 21.15.

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Answer:

720

Step-by-step explanation:

60×12=720 so the monthly yearly coast would be 720

The correct options are 2,3,4,5, according to given question.

What do you mean by equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

According to data in the given question,

We have the given information:

P = 18

w= l/2

Perimeter of a rectangle equals to twice the sum of length and width:

P= 2(l+w)

If we assume width = x, then:

l = 2x

2(x+2x) = 18 or

2x + 4x = 18

If we assume length = x, then:

w = 1/2x

2(x + 1/2x) = 18 or

2x + x = 18

Therefore, the correct options are below:

x + one-half x = 18   === incorrect                        

2 x + x = 18               === correct

2 (x) + 2 (2 x) = 18     === correct

x + one-half x + x + one-half x = 18 === correct, same as second option

2 (x + one-half x) = 18    === correct, same as second option

2 x + one-half x = 18     === incorrect

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Table B correctly represents the ratio of students to adult

Ratio is an ordered pair of numbers x and y, which can written in form x/ y where y is not 0.

For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 :6 Similarly, the ratio of lemons to oranges is 6:8

ratio 48:6= 48/6

= 8

this means that 8 student to 1 adult

in table B all ratio of student to adult is 8:1

therefore only table 2 obeys this ratio

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Answer:

14x+14=14(x+1)

Answer:

y=13

Step-by-step explanation:

Because m=slope=

13 − 13/11 - 13 = 0

therefore we use y=13 because the y value is always the same, and the two point have the same y value.

​

The null hypothesis to test the faculty member's claim that the improvement is no more than 3% at the 5% significance level is that the true mean score improvement on the outcomes assessment test is equal to or less than 3%.

The null hypothesis is a statement that assumes there is no significant difference or relationship between two variables in a population, or that any observed difference or relationship is due to chance or sampling error. It is usually denoted by "H0" and is used in statistical hypothesis testing to determine whether there is evidence to support an alternative hypothesis.

In the given question,

The null hypothesis to test the faculty member's claim that the improvement is no more than 3% at the 5% significance level would be:

H0: The true mean score improvement on the outcomes assessment test is equal to or less than 3%.

This hypothesis assumes that there is no significant improvement in the mean score on the outcomes assessment test as a result of the review course. The alternative hypothesis would be:

Ha: The true mean score improvement on the outcomes assessment test is greater than 3%.

This hypothesis assumes that there is a significant improvement in the mean score on the outcomes assessment test as a result of the review course.

To test these hypotheses, we would use a one-tailed t-test with a significance level of 0.05 and calculate the t-value and p-value based on the sample data. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that there is evidence of a significant improvement in the mean score on the outcomes assessment test as a result of the review course. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is no evidence of a significant improvement in the mean score on the outcomes assessment test as a result of the review course.

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Therefore, when Savannah is 42 feet above the ferris wheel's horizontal diameter, her angle of rotation is approximately 68.6 degrees.

Given by the question.

Let's first draw a diagram to visualize the situation.

      *

    *    *

  *        * <-- Ferris wheel at 3 o'clock position

 *          *

*            * <-- Highest point

*______________*______

      62 ft

The Ferris wheel is a circle with radius 62 feet, and Savannah is sitting in a bucket that moves along the circle. When she is at the highest point, she is 62 feet away from the center of the circle, and when she is on the horizontal diameter, she is 62 feet - 42 feet = 20 feet away from the center of the circle.

To find Savannah's angle of rotation, we can use the cosine function.

cos(theta) = adjacent / hypotenuse

In this case, the adjacent side is 20 feet, and the hypotenuse is 62 feet.

cos(theta) = 20/62

To solve for theta, we need to take the inverse cosine of both sides.

theta = cos^-1(20/62)

Using a calculator, we get:

theta = 68.6 degrees

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If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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Answer:

-3/2 which is a

Step-by-step explanation: finding the exact value

The value (-15/8 + 1.5) ÷ (15 - \(14\frac{3}{4}\))  = -3/2,

Hence, Option A is correct.

The given expression is,

(-15/8 + 1.5) ÷ (15 - \(14\frac{3}{4}\))

Since we know,

Dividing two fractions is equivalent to multiplying the first fraction by its reciprocal. The first step in splitting fractions is to get the reciprocal of the second fraction (reverse the numerator and denominator). Then, multiply the numerators.

Here we have to find the value of the given expression is,

We can write it as,

⇒  (-15/8 + 1.5) ÷ (15 - 59/4)

⇒  (-15 + 12)/8  ÷ (60-59)/4

⇒  -3/8 ÷ 1/4

⇒  -3/8 x 4/1

⇒  -3/2

Hence,

(-15/8 + 1.5) ÷ (15 - \(14\frac{3}{4}\))  = -3/2

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