Clare would like to buy a video game that costs at least $130. She has saved $48 so far and plans on saving $5 of her allowance each week. Write an inequality to find out the number of weeks it will take until she has enough money to buy the game.

Answer:

1

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Answer:

4

Step-by-step explanation:

\(\frac{sin 30}{1+cos 30} +\frac{1+cos 30}{sin 30} \\=\frac{sin 30(1-cos30)}{(1+cos30)(1-cos30)} +\frac{1+cos30}{sin 30} \\=\frac{sin30(1-cos30)}{1-cos^230 } +\frac{1+cos30}{sin 30} \\=\frac{sin 30(1-cos30)}{sin^2 30} +\frac{1+cos30}{sin30} \\=\frac{1-cos30}{sin30 } +\frac{1+cos30}{sin30} \\=\frac{1-cos30+1+cos 30}{sin 30} \\=\frac{2}{sin 30} \\=\frac{2}{\frac{1}{2} } \\=4\)

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

-0.0625

Step-by-step explanation:

Answer:

  A.  675 units²

Step-by-step explanation:

The formula for the surface area of a square pyramid is ...

  A = s(s +2h)

where s is the side length of the base, and h is the slant height of a face.

__

The given pyramid has s=15 and h=15, so the surface area is ...

  A = (15)(15 +2×15) = 15(45) = 675 . . . square units

Answer: G. (-6,4), (3,5), (2,2) and (-5,1) just look where the dot plot is and you with know the answer.

Step-by-step explanation: Hope this help :)

Answer:

Step-by-step explanation:

You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.

David's solution is correct up to Step 4.

At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...

  Step 4: (5 -3)x -4 = 2x -4

David's incorrect solution should have been 2x -4.

Answer:

Step-by-step explanation:

The following code is written in Python. It is a function that takes in the number of miles as an argument and returns the number of laps that those miles represents.

def miles_to_laps(miles):

   laps = miles / 0.25

   return laps

===========================================

Explanation:

If Hannah saves 30%, then she pays the remaining 70%, which then converts to the decimal form 0.70

The 15% discount leads to her paying the remaining 85% and that converts to the decimal 0.85

We'll multiply 0.70 and 0.85 to find the net discount

0.70*0.85 = 0.595

After combining both discounts, she pays 59.5% of the original price.

If the original price was $75, then she pays 0.595*75 = 44.625 = 44.63 dollars after applying both discounts.

Answer:

tan (a+b) = 2.27  or (345/152)

Step-by-step explanation:

a and b are in the fourth quadrant

sin a = -12/13             tan a = - 12/5 = - 2.4

cos b = 20/29           tan b = - 21/20 =.1.05

tan (a+b) = (tan a + tan b) / (1 - tan a * tan b)

              = (-2.4 + - 1.05) / ( 1 - (-2.4)*(-1.05))

              = (-3.45) / (-1.52)

              = 2.27

5π/3=5π/3×180/π=300°

300° is the correct answer

Answer:

300 degrees

Step-by-step explanation:

To convert from radians to degrees, multiply by 180/ pi

5 pi /3  * 180/pi

5/3 * 180

5 * 60

300

Answer:

x>-1/4

Step-by-step explanation:

-3x/4<3

x/4>-1

x>-1/4

Answer:

x∠-4

Step-by-step explanation:

Like and give 5 star rating

The word best describes the degree of overlap between the two data sets

O low

The degree of overlap generally refers to the extent to which two or more sets share common elements.

Specifically the degree of overlap can be defined as the number of elements that are contained in more than one of the sets being considered

In the problem the degree of overlap is low, since the data points shared only points 50 and 55

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Answer:

the answer is 12

Step-by-step explanation:

d=2r=2*6.2=12.4

Answer:  Choice C.

The difference between our sample mean and our hypothesized mean was statistically significant.

=========================================================

Explanation:

The null hypothesis is always set up in a way to state the following: "The mean mu is equal to some value"

The mu is a greek letter often used as the population mean symbol. The actual symbol itself looks like this \(\mu\)

When we reject the null, we reject the idea that the mu is whatever stated value we said in the null. So we must go with the alternative hypothesis.

The sample mean we computed (xbar) is different enough from the mu value that we're able to make such a rejection. We consider this statistically significant, which is another way of saying that such a difference is not simply due to random chance.

The given random variable which is the length of life of a washing machine is a discrete random variable because it involves counting, Such variables can only take a certain number of values, unlike continuous variables which can take on any value within a given range.

The length of life of a washing machine is something that can be measured in years, so it can only take on certain values , where discrete random variables can be further classified as either finite or infinite.

Finite discrete random variables are those with a set number of possible outcomes, such as the number of heads that result when a coin is flipped. Infinite discrete random variables, on the other hand, have an infinite number of possible outcomes  such  as the number of cars passing through an intersection in a  given hour

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Answer:

The area of the trapezoid is 238 \(m^2\).

Step-by-step explanation:

The formula to use in order to calculate the area of a trapezoid is \(\frac{h}{2}(b_{1} +b_{2})\) where \(b_{1}\) and \(b_{2}\) are the lengths of the top and bottom bases of the trapezoid, and \(h\) is the height of the trapezoid. In this case, we can rewrite the formula by inserting the corresponding values into the expression. The area of the trapezoid will be \(\frac{14}{2} (15+19)=7*34=238m^2\).

Answer:

238m^2

Step-by-step explanation:

1/2(15+19)*14

1/2(34)*14

17*14

238

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the right trianglea are not given. The general explanation is as follows.

Using Pythagoras Theorem, we have:

a² = b² + c²

Where:

a => hypotenuse

Assume that the opposite and the adjacent sides are given as 3 and 4, respectively.

The hypotension becomes

a² = 3² + 4²

a² = 9 + 16.

a² = 25

Take square roots.

a = 5

If any of the other side lengths is missing; you make that side the subject and then solve.

Answer:

Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.

Step-by-step explanation:

The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.

The equation from the fourth column is:

0.35x + 0.10(1300 - x) = 0.25(1300)

Solving for x, we get:

x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600

The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.

The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.

The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.

Therefore, the probability of the friend being between 10 and 30 minutes late is:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

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The common ratio of the associated geometric sequence is 4

The table of values is given as:

x y

1 9

2 36

3 144

4 576

5 2304

The common ratio is calculated as:

Ratio = y(2)/y(1)

This gives

Ratio = 36/9

Divide

Ratio - 4

Hence, the common ratio is 4

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The length in each circle is:

(a) CD = 19.5 units

(b) UZ = 12.8 units

(a) The Intersecting Secant-Tangent Theorem states that "if two secant lines intersect outside a circle, and a tangent line is drawn from the point of intersection to the circle, then the product of the lengths of the two secant segments is equal to the square of the length of the tangent segment".

Using the theorem, we have:

EC * ED = EG²

6.5 * ED = 13²

6.5ED = 169

ED = 169/6.5

ED = 26 units

ED = EC + CD

26 = 6.5 + CD

CD = 26 - 6.5

CD = 19.5 units

(b) The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

UZ * UW = UX * UY

UZ * 40 = 8 * 64

40UZ = 512

UZ = 512/40

UZ = 12.8 units

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The slope-intercept equation of a linear function f whose graph satisfies the given condition is y = 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is perpendicular to x = 6, which is a vertical line, the other line must be horizontal with a slope of zero (0). Therefore, the required equation is given by:

y - y₁ = m(x - x₁)

y - 5 = 0(x - (-5))

y - 5 = 0(x + 5)

y - 5 = 0

y = 5.

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ok

Original amount = 5600

20 years later = 5600 - 2100 = 3500

Today = 3500 -1050 = 2450

It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?