Yesterday, Raina had 129 baseball cards. Today she got c more. Using c, write an expression for the total number of baseball cards she has now.

Answer:

the acorn is 32 feet from the base of the tree.

Answer:

The acorn is 32 feet from the base of the tree.

Step-by-step explanation:

This is an problem where the Pythagorean Theroem.

The formula is \(a^2+b^2=c^2\) where a & b are the legs and c is the hypotenuse.

In this problem, we are given the height, which is a and the hypotenuse, which the flying squirrel glides, which is c.

We can substitute the values and solve for b which is the distance from the base to the acorn.

The new equation would be \(60^2+b^2=68^2\)

We can simplify the exponents and we get: \(3600+b^2=4624\).

Now, we have to solve for b.

1. Subtract 3600 on both sides: \(b^2=1024\)

2. Take the square root of both sides: \(\sqrt{b^2} =\sqrt{1024}\)

3. Since the exponent and the radical cancel each other, we are left with just b. The square root fo 1024 is 32, which is the value of b.

So the distance from the acorn to the base of the tree is 32 feet.

a) To find the value of k such that the lines and are perpendicular, we need to find the dot product of their direction vectors and set it equal to zero.

The direction vector of the first line is (3, -1, k), and the direction vector of the second line is (2, -2, 5). Taking their dot product, we have:

(3, -1, k) · (2, -2, 5) = 3*2 + (-1)*(-2) + k*5 = 6 + 2 + 5k = 8 + 5k

For the lines to be perpendicular, the dot product must be zero. Therefore, we have:

8 + 5k = 0

Solving this equation, we find:

5k = -8

k = -8/5

So the value of k that makes the lines perpendicular is k = -8/5.

b) To determine parametric equations for the plane through the points A(2, 1, 1), B(0, 1, 3), and C(1, 3, −2), we first need to find two vectors in the plane. We can take the vectors AB and AC. The vector AB is obtained by subtracting the coordinates of point A from those of point B: AB = (0-2, 1-1, 3-1) = (-2, 0, 2). Similarly, the vector AC is obtained by subtracting the coordinates of point A from those of point C: AC = (1-2, 3-1, -2-1) = (-1, 2, -3).

Now, we can express any point (x, y, z) in the plane as a linear combination of these vectors:

(x, y, z) = (2, 1, 1) + s(-2, 0, 2) + t(-1, 2, -3)

where s and t are parameters. These equations represent the parametric equations for the plane through the points A, B, and C.

c) To determine a vector equation for the plane that is parallel to the xy-plane and passes through the point (4, 1, 3), we can use the fact that the normal vector of the xy-plane is (0, 0, 1). Since the plane we are looking for is parallel to the xy-plane, its normal vector will be the same.

Using the point-normal form of a plane equation, the vector equation for the plane is:

(r - r0) · n = 0

where r is a position vector in the plane, r0 is a known point in the plane, and n is the normal vector. Plugging in the values, we have:

(r - (4, 1, 3)) · (0, 0, 1) = 0

Simplifying, we get:

(0, 0, 1) · (x - 4, y - 1, z - 3) = 0

0*(x - 4) + 0*(y - 1) + 1*(z - 3) = 0

z - 3 = 0

Therefore, the vector equation for the plane that is parallel to the xy-plane and passes through the point (4, 1, 3) is z - 3 = 0.

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a. The standard error of the mean for n = 25 is 3 cm

b.  The standard error of the mean for n = 100 is 1.5 cm.

Agronomist measured the height of n corn plants. If the mean height is 220 cm and the standard deviation is 15 cm, then we can calculate the standard error of the mean for n = 25 and n = 100 as shown below -

(a) For n = 25:

    If n = 25, then the formula for calculating the standard error of the mean is as follows -

    Standard Error of the Mean = (Standard Deviation / √n)

    Given,

    Standard deviation (σ) = 15 cm

    Number of samples (n) = 25 cm

    We can calculate the standard error of the mean as follows -

    Standard Error of the Mean = (Standard Deviation / √n)

                                                   = (15 / √25)

                                                   = 3

    Hence, the standard error of the mean for n = 25 is 3 cm.

(b) For n = 100:

    If n = 100, then the formula for calculating the standard error of the mean is as follows -

    Standard Error of the Mean = (Standard Deviation / √n)

    Given,

    Standard deviation (σ) = 15 cm

    Number of samples (n) = 100 cm

    We can calculate the standard error of the mean as follows -

    Standard Error of the Mean = (Standard Deviation / √n)

                                                   = (15 / √100)

                                                   = 1.5

    Hence, the standard error of the mean for n = 100 is 1.5 cm.

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Nathan needs to make 13 visits to make enough points for a movie ticket.

When Nathan joined, he received 40 reward points. This means that out of the 225 points he needs for a movie ticket, he now only needs:

= 225 - 40

= 185 points

He gets 14.5 points for every visit which means that the number of visits he needs to get to 185 points is:

= Number of points remaining / Number of points per visit

= 185 / 14.5

= 12.76 visits

= 13 visits

Nathan therefore needs at least 13 visits to get enough points.

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(2x - 6) - (10x - 7) # Starting expression

-8x - 1 # Combine like terms

Final answer:

-8x - 1

Hope this helps!

Answer:

\(3^{0} =1\)

Step-by-step explanation:

Answer: 1. [-8, 8]

2. [-27, 27]

Step-by-step explanation:

1. |X|≤8

x≤8 or x>=-8

-8<=x<=8 ==> [-8, 8]

2. |X|≤27

x≤27 or x>=-27

-27<=x<=27 ==> [-27, 27]

The area of the shaded region is approximately 18.38 square feet.

To find the area of the shaded region between the larger circle with a radius of 10.2 feet and the smaller circle with a radius of 5.4 feet, we can use the concept of circle sectors.

The area of a circle sector can be calculated by finding the difference between the area of the corresponding triangle and the area of the circular segment.

First, let's calculate the area of the larger circle:

A_large = π(10.2)^2

Next, we calculate the area of the smaller circle:

A_small = π(5.4)^2

To find the area of the shaded region, we need to find the difference between the two circle sectors formed by the radii of the larger and smaller circles.

The angle of the sector formed by the radii can be found using trigonometry. Let's call it θ.

sin(θ) = (10.2 - 5.4) / 10.2

sin(θ) = 0.4706

Using inverse sine, we find θ ≈ 28.15 degrees.

Now we can calculate the area of the shaded region:

Shaded area = (θ / 360°) * A_large - (θ / 360°) * A_small

Shaded area ≈ (28.15 / 360) * π(10.2)^2 - (28.15 / 360) * π(5.4)^2

Shaded area ≈ (0.0782) * π(104.04) - (0.0782) * π(29.16)

Shaded area ≈ 8.1403π - 2.2832π

Shaded area ≈ 5.8571π

Finally, to approximate the value, we use the approximation π ≈ 3.14159:

Shaded area ≈ 5.8571 * 3.14159

Shaded area ≈ 18.38 square feet.

Therefore, the area of the shaded region is approximately 18.38 square feet.

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Answer:

x = -175

Step-by-step explanation:

Given:

⇒ \(-\frac{x}{7}-8=17\)

Solution:

Work:

\(-\frac{x}{7}-8=17\)

\(-\frac{x}{7}-8+8=17+8\)    ⇒ Add 8 to both sides

\(-\frac{x}{7}=25\)

\(7\left(-\frac{x}{7}\right)=25\cdot \:7\) ⇒ Multiply both sides by 7

-x = 175

\(\frac{-x}{-1}=\frac{175}{-1}\) ⇒ Divide both sides by -1

x = -175

Check:

Since, x = -175. We can substitute into the equation to check.

\(-\frac{-175}{7}-8=17\)

\(-\frac{-175}{7}=25\)

\(25-8=17\) ⇒ Statement = True (25 minus 8 is 17.

Hence, x = -175

Lenvy~

Answer:

0.05x + 0.10y = 34.40

x + y = 468

Step-by-step explanation:

Step-by-step explanation:

The The guy above is correct

For a data set, half of the observations are always greater than the median. The median is the middle value in a set of data when it is arranged in order of increasing or decreasing magnitude.

It is a measure of central tendency that is more robust to outliers than the mean. The median splits the data set in half, with half of the observations being greater than it and half being less than it.

The median is a crucial measure of central tendency that helps us understand the distribution of a data set. It represents the value that separates the top half of the data from the bottom half. The median is often used as an alternative to the mean when the data set contains outliers or extreme values that can skew the mean. The median is easy to calculate and provides a clear picture of the middle of a data set. Therefore, it is a useful tool for statisticians, researchers, and analysts who need to summarize and describe data sets accurately.

In summary, the median is the value that divides a data set into two equal halves, with half of the observations being greater than it and half being less than it. It is a robust measure of central tendency that is widely used in statistics to describe the distribution of data sets.

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So, the hose can complete the job alone in approximately 2.62 hours, and the inlet pipe can complete the job alone in approximately 1.62 hours.

Let the time it takes for the hose alone to fill the pond be H hours, and the time it takes for the inlet pipe alone be P hours. According to the given information:

1) P = H - 1 (The inlet pipe alone can complete the job in one hour less time than the hose alone)

2) In one hour, the hose fills 1/H of the pond, and the inlet pipe fills 1/P of the pond. Together, they can fill the pond in one hour, so: (1/H) + (1/P) = 1

Now, substitute the value of P from equation 1 into equation 2:

(1/H) + (1/(H-1)) = 1

To solve for H, first find a common denominator (H*(H-1)):

(H-1) + H = H*(H-1)

Combine the terms on the left:

2H - 1 = H^2 - H

Rearrange to form a quadratic equation:

H^2 - 3H + 1 = 0

Now, solve the quadratic equation using the quadratic formula:

\(H = (3 + sqrt(5))/2 or H = (3 - sqrt(5))/2\)

However, since H > 0, the only valid solution is H = (3 + sqrt(5))/2 ≈ 2.62 hours.

Now, find the time it takes for the inlet pipe alone to complete the job:

P = H - 1 = 2.62 - 1 = 1.62 hours

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Answer:

-6 is the y coordinate

Step-by-step explanation:

Answer:

tx=y

Step-by-step explanation:

For every hour you spend on the computer is t. So if it cost x per customer then you can just simply multiply x and t. It says y is the total cost so that would be what is equalls to.

Example:

x= $5

t=3 hours

Using these sample numbers we can put them into the equation

3·5=y

15=y

15 dollars in total

Answer:

3.5 and -3.5

Step-by-step explanation:

absolute value is the distance from zero to that number so 3.5 and -3.5 should be correct.

Answer:3.5 and -3.5

Step-by-step explanation:

n has absolute value marks, so whatever n is is positive. 3.5 and |-3.5| =3.5

Answer:

3,250g

Step-by-step explanation:

22kg = 22,000g - 18,750g = 3250g

Answer:

there is no picture/screenshot of the table.

Step-by-step explanation:

I could see if I can help but I don't know where the question or the table is.

Answer:

False

Step-by-step explanation:

Keep in mind both the right and left-side limits of a function have to be equal to each other in order for the limit of the function to exist:

Right side limit: \(\lim_{x \to 2^{+}} \frac{1}{3x-6}=\infty\)

Left-side limit: \(\lim_{x \to 2^{-}} \frac{1}{3x-6}=-\infty\)

Because both side limits do not equal \(\infty\), then the limit does not exist, which means that the statement is false.

You can also see this visually on a graph if you'd wish to plug in the function

The coordinates of the point D that partitions the segment in ration 1:2 is D = (4. 3).

The line segment is divided into two pieces by a point, which may or may not be equal. If we know the coordinates of the point, we may calculate the ratio by which the supplied line segment is divided. Also, if we are aware of the ratio that the line segment connecting two places has produced, we may locate the point of division. The two may be accomplished using a section formula from coordinate geometry.

The position of a point that splits a line segment connecting two points into two portions with a length ratio of m:n is found using the section formula.

The coordinates of the point A and B from the given figure is:

A = (1, 3) and B = (10, 3)

The section formula is given as:

(x, y) = (mx2 + nx1 / m+n , my2 + ny1 / m+n)

Substitute the values of m = 1 and n = 2, and the coordinates of the point A and B.

(x, y) = ((1)(10) + (2)(1)/ 3 , (1)(3) + (2)(3) 3)

D(x,y) = (4, 3)

Hence, the coordinates of the point D that partitions the segment in ration 1:2 is D = (4. 3).

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Answer:

30%

Step-by-step explanation:

6/20 = .3

.3 x 100 = 30

After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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Answer:

The function is f(x)=2x

Step-by-step explanation:

Since every single y is 2 times x, it will be 2x. This function just doubles whatever x you put in.

Answer:

Step-by-step explanation:

Those are coordinate points on a line but they are written in table form.

For the first point,  when x=1, y=2  (that's given from the table) but it's a point on the line (1, 2)

The next point (2,4),

(3,6) and so forth.

The format for a line is

y=mx+b (slope-intercept form)

or

\(y-y_{1} = m(x-x_{2})\)   (point-slope form)

They did not give you the y-intercept (that's when x=0) in the chart.  You may have been able to figure it out by looking at the pattern but if not we will use the second formula, point slope form, because we know a point from the chart and we can find slope

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

pick any 2 points from the chart to find slope.  I will pick (1,2) and (2,4)

\(m=\frac{4-2}{2-1 } =\frac{2}{1} =2\)

Now that i know slope m=2  and i will pick (1,2) to plug into formula

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

y-2=2(x-1)       distribute 2

y-2=2x-2          add 2 to both sides

y=2x

The function is increasing at a rate of 2 and the y-intercept is 0.

A rhombus is a quadrilateral that has four sides of equal length. A rhombus also has two diagonals, which are perpendicular bisectors of each other. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

To find the perimeter of a rhombus using diagonals, follow these steps:

Step 1: Obtain the length of each diagonal of the rhombus.

Step 2: Use the length of the diagonals to find the length of each side.

Step 3: Add the length of each side to find the perimeter of the rhombus.

The perimeter is the sum of all the sides of a figure. To get the perimeter of a rhombus using diagonals, the length of each diagonal has to be found first. The formula for finding the length of each side of a rhombus is:  where the diagonal is the measure of the diagonal of the rhombus.

To find the perimeter of a rhombus, add the length of all the sides of the rhombus. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

Therefore, the perimeter of a rhombus using diagonals can be found by following the above procedure and then using the formula to add all the sides of the rhombus.

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Answer:

$ 6,438.51

Step-by-step explanation:

75.36 X 36 = 2,712.96

82.79 X 45 = 3,725.55

2,712.96 + 3,725.55 = 6,438.51

Answer:

Step-by-step explanation:

Two ratios are proportional if their cross products are equal. That is, if we multiply the numerator of one ratio by the denominator of the other ratio, the result should be equal to the product of the denominator of the first ratio with the numerator of the second ratio.

Let's see if this holds true for 1/9 and 6/54:

(1 x 54) = 54

(9 x 6) = 54

Since the cross products are equal, we can say that 1/9 and 6/54 are proportional.

To simplify the ratio, we can divide the numerator and denominator by their greatest common factor (GCF), which is 3.

1/9 ÷ 3/3 = 1/27

6/54 ÷ 3/3 = 2/18 = 1/9

Thus, the simplified ratio of 1/9 and 6/54 is 1/9, and we can see that 1/9 and 6/54 are in fact proportional.