Minja is three years older than her sister June. Minja's brother is eight years younger
than their sister June. The sum of all of their ages is 55 years.
x+3-8x=55.
3x 8x + x 55.
(x+3-8)+x=55
(x+3)+(x-8)+x=55
-

Answer:

a. 54 = 2 * 3³

b. 108 = 2² * 3³

c. 360 = 2² * 3² * 5

etc.

Step-by-step explanation:

So, you need to have a list of primes handy:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, ...

Now, take your number and try to divide it by the first prime, 2.

54 = 27 * 2

That worked. Note down the 2 and repeat with the result. You find 27 cannot be divided by 2 again, but it can be divided by 3 (the next prime in the list):

27 = 9 * 3

Note down the 3 and repeat:

9 = 3 * 3

Note down a 3 again.

So you have

54 = 2*3*3*3 = 2 * 3³

You can continue this until the result is a prime number itself. Then you are done.

Answer:

213 ft^2

Step-by-step explanation:

In this problem, we can create a larger rectangle that engulfs this image with a few missing pieces on the corners. The area of that rectangle would be 18ft * 17 ft = 306 ft^2. The sum of the missing pieces is 2ft * 7ft + 5ft * 6 ft + 7ft * 7ft  = (14 + 30 + 49)ft^2 = 93 ft^2. So, the area of this figure is 306 - 93 = 213 ft^2

ANSWER: S=173ft^2

_._._._._._._._._._._._.

Answer:

4 more laps to reach the goal of 14.4 km.

Step-by-step explanation:

First, let's find the total distance covered so far: 720 m x 16 laps = 11,520 m.

Next, let's convert the goal distance to meters: 14.4 km x 1000 m/km = 14,400 m.

Finally, let's subtract the total distance covered from the goal distance to find the remaining distance: 14,400 m - 11,520 m = 2,880 m.

Since a lap is 720 m long, the remaining distance can be divided by 720 m to find the number of laps left: 2,880 m ÷ 720 m = 4 laps.

Therefore, the runner needs to run 4 more laps to reach the goal of 14.4 km.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

A sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.

To determine the required sample size for a 90% confidence interval with a margin of error of at most 0.04, we can use the formula:

[tex]n = \left(\frac{z \cdot \sigma}{E}\right)^2[/tex]

where:

n is the sample size

z is the z-score associated with the desired confidence level (90% confidence level corresponds to z = 1.645)

σ is the standard deviation of the population (unknown, so we use 0.5 as a conservative estimate, since the proportion of students who would patronize the nightclub is unknown and assumed to be 0.5 for maximum variability)

E is the maximum desired margin of error (0.04)

Plugging in the values, we get:

n = (1.645 * 0.5 / 0.04)²

n ≈ 424

Therefore, a sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.

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Answer:

OD 52020 cubic inches

Step-by-step explanation:

15.0×24.0=360

=360×8.5=3060

3060 inches×17 boxes=52020 inches

Therefore;52020 cubic inches storage space is needed for the crayons

The statement that correctly compares the two functions is

They have the same x-intercept and the same end behavior as x approaches ∞.

A function's final behaviour is represented by the value of f(x) as x approaches infinity. Both functions in this scenario have the same final behaviour because they both have unbounded growth, or they both go to positive infinity.

To find y-intercept of a function we have to put x= 0

So, The y-intercept of f(x) is y = -3.

and, The y-intercept of g(x) is y = -4.

To  find x -intercept of a function put y = 0

So, The x-intercept of f(x) is x = 1.

and, The x-intercept of g(x) is x = 1.

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Answer:

Step-by-step explanation:

i have no idea sorry

Answer:

Ac = 0.833334.

Step-by-step explanation:

SINCE THE QUESTION IS PYTHAGORAS THEOREM.

THE FORMULA IS

[tex] tan = \frac{ |bc| }{ac} [/tex]

From the question tan = 18°

bc = 15

ac= ?

making ac = x

therefore

[tex] tan = \frac{ |bc| }{ |ac| } \\ tan 18 = \frac{15}{x} \\ tan18(x) = x \times \frac{15}{x} \\ tan18x = 15 \\ = \frac{tan18x}{18} = \frac{15}{18} \\ x = 0.8333334[/tex]

therefore x = 0.8333334.

After solving the given inequality question, we will get  x < -9.

A mathematical sign for comparing two values or expressions is an inequality symbol. Inequality symbols include: (less than), > (greater than), (less than or equal to), and (greater than or equal to). Inequalities can be used to represent connections between two or more variables, for as 5 10 indicating that 5 is less than 10. Inequalities can also be used to define mathematical equations or to describe connections between variables. The equation x + 2 7 can, for example, be used to represent the relationship between x and 7, or to communicate that the value of x must be less than 5 for the equation to be true.

In the given question,

2/3x + 2y < -1/3x + 1

⇒ 2/3x + 2y - (-1/3x + 1) < 0

⇒ 5/3x + 3 < 0

⇒ 5/3x < -3

⇒ x < -9

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If the angle of depression to the buoy is 250, then the buoy is approximately 47.2 meters from the base of the lighthouse.

What is angle of depression ?

The angle of depression is the angle between a horizontal line of sight and the line of sight from an observer to a point or object that is lower than the observer. It is commonly used in trigonometry and geometry problems that involve the height or depth of an object relative to an observer or the ground.

We can start by drawing a diagram to visualize the situation.

In the diagram, A represents the location of the lighthouse, B represents the location of the buoy, and x represents the distance from the base of the lighthouse to the buoy that we want to find.

Since the angle of depression from the lighthouse to the buoy is 25 degrees, we know that angle ABx is also 25 degrees. We also know that the height of the lighthouse above sea level is 22 meters.

We can use the tangent function to find the value of x:

tan(25°) = opposite / adjacent

tan(25°) = 22 / x

Solving for x, we get:

x = 22 / tan(25°)

x ≈ 47.2 meters

Therefore, the buoy is approximately 47.2 meters from the base of the lighthouse.

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a) Number of kgs independent variable, the amount charged by the company is the dependent variable.

b) The equation is y= 400+ 0.04x.

c) The equation is used to calculate a table of values with four sets of values to show the moving costs for 0 – 25,000 kg.

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.

It is given that a moving company charges $400 plus 0.04 per kg to move a family from Toronto to Windsor.

a) The number of kgs is the independent variable and the amount charged by the company is the dependent variable because it depends on the number of kgs the family is willing to move.

b) The equation that represents the given data is y= 400+ 0.04x

where y is the total amount charged by the company, and x is the number of kgs.

c) For 4 different values of x between 0 - 25,000 we will find values of y.

x                      y= 400+ 0.04x

6250               650

12500             900

18750              1150

25000             1400

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The probability that the ninth woman to appear is in position 17 is about 5.59%

We can approach this problem by using the binomial probability distribution. Let X be the number of women among the first 16 people in the line. Then X follows a binomial distribution with parameters n = 16 and p, the probability that any given person among the first 16 is a woman. We want to find the probability that X = 8, since this means that the ninth woman to appear is in position 17.

The probability of any given person being a woman is not specified in the problem, but we can assume that it is 0.5 for simplicity. Therefore, p = 0.5, and we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. In this case, it gives the number of ways to choose k women from the first 16 people in the line.

Using this formula with n = 16 and k = 8, we get:

P(X = 8) = (16 choose 8) * 0.5^8 * 0.5^8

= 12870 * 0.00390625

= 50.27

This means that the probability of exactly 8 women appearing among the first 16 people in the line is about 50.27%.

Given that there are 8 women among the first 16 people, the probability that the ninth woman appears in position 17 is 1/9, since there are 9 possible positions for the ninth woman to appear, and they are all equally likely.

Therefore, the overall probability that the ninth woman to appear is in position 17 is:

P(X = 8) * (1/9) = 50.27% * (1/9) = 5.59%

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Answer:

Step-by-step explanation:

I probalby am not reading the question correctly, but it seems be be asking the distance between Myrna's fingertip (18 feet above the ground!) and the top of the 27' foot flagploe.  We are not told where Myrna is standing, nor how she got her fingertip 18 feet high.  Since we are asked for a diagram, I did the best I could, not knowing much about Myrna other than she must be tall.  On her behalf, I assumed Myrna was directly under the flagpoe.  As shown in the attached diagram, her fingertip is 9 feet below the top of the flagpole.  

If the 24 foot wire is stretched all the way (i.e., it takes 24 feet to reach Myrna's fingertip), then she is not standing directly below the flagpole.   But this isn't clear in the problem.  In any event, if the question is how far she is from the very top of the flagpole from where she is standing, it would be the 24 foot lenght of the wire connecting her to the top of the flagpole.  If the question just wants the vertical distance, then it is 9 feet.

If she is standing away from the flagpole, then a diagram would appear roughly as follows:

 x

 x      s

 x 27'        s   24'

 x                       s

 x  ----------z--------------   y

 x                                   y

 x                                   y 18'

 x   ----------z--------------  y                  

flagpole                       Myrna

The distance z is calculated using the Pythagorean Theorem in the top triangle.  The left side is (27'-18') or 9'.  The hypotenuse is 24'.

  z^2 + 9^2 = 24^2

z = 22.2 feet.

Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.

Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.

Measures of variability include the range, variance, and standard deviation, and they give us a sense of how spread out the scores in a distribution are. These measures help us understand the variability or dispersion of the data and how far the individual scores in a distribution deviate from the mean or other measures of central tendency.

Measures of central tendency, such as the mean, median, and mode, describe the central or typical value of a set of scores. They provide a summary of the data and a single value that represents the center of the distribution.

The decisions regarding graph size, shape, and style are usually based on the type of data being presented and the message being conveyed. A histogram, for example, may be used to visually display the distribution of a set of scores, and the size, shape, and style of the graph can be adjusted to highlight important features of the data.

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Answer:

C. Addition Property of Equality

Step-by-step explanation:

From step 4 to step 5, 20 is added to both sides.

Answer: Addition Property of Equality

We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade.  So, there are 299 eighth graders in the school.

We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade. To find the number of eighth graders, we can use the fact that the total number of students is the sum of the number of students in each grade level:

Total number of students = Number of sixth graders + Number of seventh graders + Number of eighth graders

Substituting the given values, we get:

800 = 226 + 275 + Number of eighth graders

Simplifying and solving for the number of eighth graders, we get:

800 = 501 + Number of eighth graders

Number of eighth graders = 800 - 501

Number of eighth graders = 299

Therefore, there are 299 eighth graders in the school.

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The angle m∠B of the quadrilateral has a measure of 72°

The complete question is added as an attachment

For any quadrilateral, the sum of its four interior angles is equal to 360°,

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

17x + 5 + 13x + 7 + 118° + 80° = 360°

Evaluate the like terms

So, we have

30x + 210° = 360°

Subtract 210° from both sides

30x = 150°

So, we have

x = 5

Given that

B = 13x + 7

We have

B = 13 * 5 + 7

Evaluate

B = 72

Therefore, the measure for the angle m∠B is 72°

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Answer: et's call the amount of strawberries Gill uses "x" grams. We know that the ratio of strawberries to bananas is 7:3, so we can set up an equation:

x/144 = 7/3

To solve for x, we'll multiply both sides of the equation by 144:

x = 7/3 * 144

x = 7 * 48

x = 336

So Gill uses 336 grams of strawberries in the smoothie.

Step-by-step explanation:

Answer:

linear

Step-by-step explanation:

when you graph x/2 it is a straight line, therefore it is linear

Answer:

2.0333

Step-by-step explanation:

log 108

Express 108 in terms of 2 & 3.

108 = 2 * 2 * 3 * 3 * 3 = 2² * 3³

log 108 = log 2² * 3³ = log 2² + log 3³ [Using Product Law]

= 2log 2 + 3log 3 [Using Power Law]

Now put the values of log 2 & log 3:

2log 2 + 3log 3

= 2*0.3010 + 3*0.4771

= 0.6020 + 1.4313

= 2.0333

Answer:

  about 2.43 seconds

Step-by-step explanation:

You want the time when the height described by h = -16t² +36t +7 is equal to zero.

The quadratic equation ...

  -16t² +36t +7 = 0

can be solved using the quadratic formula. It tells you the solution to ...

  ax² +bx +c = 0 is ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Then the solutions to the given quadratic are ...

  [tex]x = \dfrac{-36\pm\sqrt{36^2-4(-16)(7)}}{2(-16)}=\dfrac{9\pm\sqrt{109}}{8}\approx\{-0.180,2.430\}[/tex]

The ball will hit the ground after about 2.43 seconds.

In the context of John's baking, the vertex with the maximum profit represents the point where John can maximize his profit. The vertex of a parabola represents the point at which the function reaches its maximum or minimum value.

The profit function is often modeled as a quadratic equation, where the vertex represents the maximum point of the parabola. In this case, the profit function may be a function of the number of cakes or pastries sold, the price at which they are sold, and the cost of producing them. When the profit is maximized at the vertex, it means that John is producing and selling the optimal number of cakes and pastries at the optimal price to maximize his profit. The vertex represents the sweet spot for John's baking business, where he can earn the most profit with the least amount of costs. Therefore, understanding the meaning of the vertex with the maximum profit is important for John to make informed decisions about his business, including the optimal number of cakes and pastries to produce, the price to sell them, and how to allocate his resources to maximize his profits.

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Answer:

Step-by-step explanation:

200 rimwjh hdwqheywgygwuivug

The expression equivalent to  -2x +3+ 7y + 4x -5 is 2x+7y-2.

What exactly are expressions?

Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.

Now,

Given expression is   -2x +3+ 7y + 4x -5

writing same terms together

=4x-2x+7y+3-5

=2x+7y-2

hence,

             The expression equivalent to  -2x +3+ 7y + 4x -5 is 2x+7y-2.

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Answer:

JGK = 29 degrees

Step-by-step explanation:

i hope this helped :)

The polynomial (x-a)(x-b)(x-c)....(x-z) has a coefficient of -351 for the x²⁵ term. Since there are 26 variables, the sum of all coefficients is 2²⁵, or 33554432.

The polynomial (x-a)(x-b)(x-c)....(x-z) can be written as

x²⁶ - (a+b+c+...+z)x²⁶ + (sum of products of pairs)x²⁴ - ... - abc...xyz

The coefficient of x²⁵ is the negative sum of the constants, which is -(a+b+c+...+z). Since there are 26 variables in total, the sum of the constants is just the sum of the first 26 letters of the alphabet, which is

(a+b+c+...+z) = 1 + 2 + 3 + ... + 26 = 351

So the coefficient of x²⁵ is -351.

To find the sum of all the coefficients, we can simply evaluate the polynomial when x = 1. At x = 1, each term in the polynomial is just the product of some combination of (1-a), (1-b), (1-c), ..., and (1-z). Since each variable is a letter from the alphabet, each term is either 0 or 1, depending on whether the corresponding letter is equal to 1 or not.

The sum of all the coefficients is therefore just the number of terms in the polynomial that are equal to 1.

Since there are 26 variables, there are 2²⁶ possible combinations of (1-a), (1-b), (1-c), ..., and (1-z), and exactly half of them are equal to 1 (since each variable is either 0 or 1 with equal probability). Therefore, the sum of all the coefficients is

2²⁵ = 33554432

So the sum of the coefficients of the polynomial (x-a)(x-b)(x-c)....(x-z) is 33554432.

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The graplh shows that it will take 3.33 weeks to pay up the money borrowed

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = money borrowed from your parents =  $50.00

m = you are paid $15 per week to walk the dog for 20 minutes each weekday = $15

x = number of weeks

y = amount remaining

The equation is

y = 15x - 50

From the graph the pay will be completed at x = 3.33 (3.33, 0)

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Answer:

8/25

Step-by-step explanation:

5+8+12=25
8/25

Answer: 8/25

Step-by-step explanation:

Find probability with item/total.

total is 25

there are 8 chocolate chip cookies

8/25 is your answer

HOPE THIS HELPS _ MM

Melissa earned [tex]$152.84\\[/tex] this week. This means that she earned a total of [tex]$174.49[/tex] over the two week period.

To determine how much Melissa earned last week, we can subtract the [tex]$21.65[/tex] that she earned more this week from the total amount earned over the two week period. Therefore, Melissa earned [tex]$152.84[/tex] this week, and [tex]$21.65[/tex] more than she earned last week. Subtracting [tex]$21.65[/tex]from [tex]$174.49[/tex] gives us [tex]$152.84[/tex], which is the amount Melissa earned last week. This means that Melissa earned [tex]$152.84[/tex] last week .To summarize, Melissa earned $152.84 this week, which was[tex]$21.65[/tex] more than she earned last week. This means that Melissa earned a total of [tex]$174.49[/tex]over the two week period, and by subtracting [tex]$21.65[/tex] from the total amount earned over the two week period, we can determine that Melissa earned[tex]$152.84[/tex] last week.

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The value of x is given as follows:

x = 131º.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Considering the above text, the measure of the top angle of the bottom triangle is given as follows:

a = 180 - 98

a = 82.

The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence:

2b + 82 = 180

2b = 98

b = 49.

(the sum of the measures of the internal angles of a triangle is of 180º).

Considering the vertical angles, the base angles of the top triangle are given as follows:

b = 49.

Hence the value of x is given as follows:

x = 180 - 49

x = 131º.

(as the top triangle is also isosceles, and the angle measure x is the exterior angle of an interior angle with measure of 49º).

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