a line segment is divided so that the lesser part is to the greater part as the greater part is to the whole. if is the ratio of the lesser part to the greater part, then the value of

Solving the statement, we get the equation x=2.5-y

Exponents are a mathematical notation used to represent repeated multiplication of a number by itself. Exponents are written as a superscript to the right of the base number, which is the number being multiplied.

given equation:

3²ˣ × [tex]9^{y}[/tex] = 243

Simplifying the expression on the right-hand side, we get:

3²ˣ × [tex]9^{y}[/tex]  = 3⁵

Using the property of exponents that states that when multiplying powers with the same base, we can add their exponents, we get:

[tex]3^{2x+2y}[/tex] = 3⁵

For the equation to hold, the exponents on both sides must be equal. Therefore:

2x + 2y = 5

Dividing both sides by 2, we get:

x + y = 2.5

x=2.5-y

Hence, solving the statement, we get the equation x=2.5-y

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Using functions,

a) 1. 48

2. 21

3. 75 - 4.5w

b) r = 75 - 4.5w

c) Graph is attached.

d) The restaurant has 30kgs of rice after 10 weeks.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here as per the question,

a)

1. 75 - (4.5 × 6)

= 75 - 27

= 48

2. 75 - (4.5 × 12)

= 75 - 54

= 21

3.  75 - (4.5 × w)

= 75 - 4.5w

b)

r = 75 - 4.5w

c) Image is attached for the graph.

d) 30 = 75 - 4.5w

Subtracting both sides by 30:

⇒ 0 = 75 - 4.5w - 30

Adding both sides by 4.5w:

⇒ 4.5w = 75 - 30

⇒ 4.5w = 45

Dividing both sides by 4.5:

⇒ w = 45/4.5

⇒ w = 10.

Therefore, the restaurant has 30kgs of rice after 10 weeks.

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The complete question is:

b. Use function notation to write a rule

that defines function r.

c. On the coordinate plane, sketch a

graph of function r.

d. Solve the equation r(u) = 30 and

explain what the solution means in

this situation.

To determine when the ball strikes the ground, we need to find the value of t when the height h(t) is 0.

The equation for the ball's height h at time t seconds after launch is:

h(t) = -4.9t^2 + 9.31t + 239.12

Setting h(t) to 0, we get:

0 = -4.9t^2 + 9.31t + 239.12

We can solve this quadratic equation using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -4.9, b = 9.31, and c = 239.12.

Answer: 6.12 seconds

Step-by-step explanation:

To find when the object strikes the ground, we need to find the time t when the height h(t) is equal to 0 (since the ground is at height 0). We have the equation:

h(t) = -4.9t² + 9.31t + 239.12

To find the time when the object strikes the ground, we need to find the value of t when h(t) = 0:

0 = -4.9t² + 9.31t + 239.12

This is a quadratic equation of the form at² + bt + c = 0, where a = -4.9, b = 9.31, and c = 239.12. We can solve this equation for t using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Plugging the values of a, b, and c into the formula, we get:

t = (-(9.31) ± √((9.31)² - 4(-4.9)(239.12))) / (2(-4.9))

t = (-9.31 ± √(86.6161 + 4694.336)) / (-9.8)

t = (-9.31 ± √(4780.9521)) / (-9.8)

t ≈ (-9.31 ± 69.14) / (-9.8)

We will have two possible values for t:

t₁ ≈ (-9.31 + 69.14) / (-9.8) ≈ 6.12 (rounded to two decimal places)

t₂ ≈ (-9.31 - 69.14) / (-9.8) ≈ 8.00 (rounded to two decimal places)

Since the height function describes the motion of the ball from a platform, we can discard the negative solution as it represents an invalid time before the ball is launched. Thus, the object strikes the ground at approximately t ≈ 6.12 seconds.

Answer:

a) 0.128 b) 0.51 c) 7.27

Step-by-step explanation:

a)

Lower Bound: 176

Upper Bound: 99999

μ: 143

σ: 29

= 0.1275….

b)

Lower Bound: 176

Upper Bound: 99999

μ: 143

σ: 29

0.1275… (4) = 0.51

c)

Lower Bound: 176

Upper Bound: 99999

μ: 143

σ: 29

0.1275… (57) = 7.27

The value of x in the given right triangle can be found with help of trigonometric-ratios, given an angle 16° and hypotenuse 37 units is 35.566657. On rounding off to nearest tenths we get 35.6 units.

What are trigonometric-ratios?

In a given right triangle, the ratios of different sides are represented as six trigonometric ratios which are cosine,sine,cosecant,cot,secant and tan.

Sin of an angle=[tex]\frac{side opposite to the angle}{hypotenuse of triangle}[/tex]

Cosine of an angle=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]

tan of an angle= [tex]\frac{side opposite to the angle}{side adjacent to the angle}[/tex]

And cosecant, secant and cot are the reciprocals of sine, cosine & tan respectively.

Here,on naming the given right triangle we can see that

∠A = 16° , AC=37 units and Side AB= x units

Applying cosine of angle  16°, we get

cos A=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]

Cos 16°=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]

Cos  16°= [tex]\frac{AB}{AC}[/tex]

0.961261= [tex]\frac{AB}{AC}[/tex] {Cos  16°=0.961261}

0.961261=[tex]\frac{x}{37}[/tex]    {AB=x and AC=37}

           x = 0.961261 (37)

           x = 35.566657

On rounding off to nearest tenths x=35.6 units

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Refer to the attachment for complete question & naming of triangle.

Answer:

Step-by-step explanation:

Area = length x height
A = 2.4 x 5.6
A = 13.44 in^2

Answer: 2^12

4^6

64^2

the cube root of 4,096

256 times 2

8^6

65,536/4

16 times 16 times 16

256 cubed root of 256

256/16^4

64 times 4 times 2

Step-by-step explanation: All of these expressions are equal to 16 cubed, which is 4,096.

Answer:

4096 have a nice day

Step-by-step explanation:

pl z mark me brianliest :)

The test statistic for this hypothesis test is -0.3886.

In statistical hypothesis testing, a test statistic is a numerical value that is calculated from a sample of data and used to determine whether to accept or reject the null hypothesis.

To calculate the test statistic for this hypothesis test, we need to use the formula for the proportion test

z = (p - P) / sqrt(P(1-P) / n)

Where

p is the proportion of Canadian content in the sample (33/100 = 0.33)

P is the hypothesized proportion (35% = 0.35)

n is the sample size (100)

Substituting the values, we get

z = (0.33 - 0.35) / sqrt(0.35(1-0.35) / 100)

z = -0.02 / 0.0516

z = -0.3886

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In the histogram , the number of students in Ms. Gioia's class took the science test is 27.

What is histogram?

A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.

Here according to the histogram ,

The number of students score between 71-75 = 4

The number of students score between 76-80 = 6

The number of students score between 86-90 =8

The number of students score between 91-95 = 7

The number of student score between 96-100 = 2

Then number of students in Ms. Gioia's class took the science test is,

=> 4+6+8+7+2 = 27

Hence the number of students in Ms. Gioia's class took the science test is 27.

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the equation that relates the time it took James to sort the supplies for b bags is: t = 1.5b

option D.

Sherry sorted enough supplies for 10 bags in 30 minutes (from 10:10 a.m. to 10:40 a.m.). Let's call the rate at which Sherry sorted the supplies "r."

Then, we can write:

r = 10 bags / 30 minutes

r = 1/3 bags per minute

Since James sorted twice as fast as Sherry, his rate is 2r:

2r = 2/3 bags per minute

To find the time it took James to sort b bags, we can use the formula:

time = (amount of work) / (rate of work)

In this case, the "amount of work" is b bags, and the "rate of work" is 2/3 bags per minute. So, we get:

time = b / (2/3)

time = (3/2) b

Therefore, the equation that relates the time it took James to sort the supplies for b bags is:

t = (3/2) b

So, the correct answer is (D) t = 1.5b.

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The values of x and w in the two triangles are w = 50and x = 24

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

two triangles

The sum of angles in a triangle is 180 degrees

This means that

w = 180 - 2 * 65

And we have

x = 180 - 2 * 78

When evaluated, we have

w = 50

x = 24

Hence, the values are w = 50and x = 24

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a) If the true rate of rejection is 10%, then the probability that the production will be suspended based on a sample of 15 bearings is 10%.

b)  The assumptions made in part a are that the sample of 15 bearings is representative of the population of bearings produced, and that each bearing is independent of the others.

To ensure that the production process is producing quality products, samples of 15 bearings are taken periodically and carefully inspected. If more than 2 bearings in a sample of 15 fail to meet the required specifications, production is suspended for necessary adjustments.

a) If the true rate of rejection is 10%, what is the probability that the production will be suspended based on a sample of 15 bearings? To answer this question, we need to use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials. In this case, the number of trials is 15, and the probability of success (i.e., a bearing not meeting the required specifications) is 10%.

b) The assumptions allow us to use the binomial distribution to calculate the probability of having a certain number of bearings fail to meet the required specifications in a sample of 15. Additionally, we assume that the true rate of rejection is 10%, which may not always be the case.

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By the AA similarity theorem, we can conclude that triangles FGH and FPQ are similar.

To prove that triangles FGH and FPQ are similar, we need to show that their corresponding angles are congruent and their corresponding sides are proportional.

Angle F in triangle FGH corresponds to angle F in triangle FPQ

Angle H in triangle FGH corresponds to angle Q in triangle FPQ

Angle G in triangle FGH corresponds to angle P in triangle FPQ

From the problem, we know that angle F = 63 degrees and angle H = 30 degrees. We also know that angle GPQ = 93 degrees, which means angle G + angle P = 93 degrees. Therefore, angle G = 93 degrees - angle P

Using the fact that the sum of angles in a triangle is 180 degrees, we can find angle Q:

Angle FGH: angle F + angle G + angle H = 63 degrees + (93 - angle P) + 30 degrees = 186 - angle P degrees

Triangle FPQ: angle F + angle P + angle Q = 180 degrees

Therefore, angle Q = 180 - angle F - angle P = 117 - angle P degrees

Now, we can compare the corresponding sides:

Side FG in triangle FGH corresponds to side FQ in triangle FPQ

Side GH in triangle FGH corresponds to side PQ in triangle FPQ

Side FH in triangle FGH corresponds to side PQ in triangle FPQ

To show that these sides are proportional, we can use the Angle-Angle (AA) similarity theorem and We already know that angle F in triangle FGH corresponds to angle F in triangle FPQ, and angle G in triangle FGH corresponds to angle P in triangle FPQ. We just showed that angle Q in triangle FPQ corresponds to angle H in triangle FGH. Therefore, we have two pairs of corresponding angles that are congruent.

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Answer: The answer is C, f(x) = 2x^2 + 3.

Step-by-step explanation: Check the graph below.

Answer:

Growth & 36.2%

Step-by-step explanation:

Exponential Growth Formula

A = A0 (1 + r)^t

A is the amount after certain number years

A0 is the initial amount

r is the rate

t is the number of years

Growth models are identified by the number between the parenthesis. If the number is greater than 1, then it represents a growth model. If the number is less than 1, then it represents a decay model.

To find the percentage by which it increases, you would simply convert the decimal. 1.362 becomes 36.2%. You move the decimal point two places to the right and add a percentage symbol next to it.

The reflection that occurred is over the x-axis.

Based on the given coordinates, it can be observed that each point of the pre-image was reflected over the x-axis, resulting in a new image. Therefore, the type of reflection that occurred is a reflection over the x-axis.

To explain this with equations, we can use the transformation formula for a reflection over the x-axis:

(x, y) → (x, -y)

Using this formula, we can find the image coordinates of the pre-image points:

A' = (-1, -8)

B' = (5, 3)

C' = (-5, 1)

As we can see, the y-coordinates of each point have been negated, indicating a reflection over the x-axis. Therefore, the type of reflection that occurred is a reflection over the x-axis.

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a. Mason's error is that he flipped the inequality sign. The correct solution is x > 6.

b. This indicates that any value of x greater than 6 (but not equal to 6) will satisfy the inequality x > 6.

An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to). Inequalities can be used to describe a range of values that a variable can take, rather than just a single value.

a. Mason's error is that he flipped the inequality sign. The correct solution is x > 6.

b. To show the correct solution on the number line, we start by marking 6 on the number line with an open circle (since x is not equal to 6). Then, we shade the area to the right of 6, because x is greater than 6. The graph should look like this:

0 1 2 3 4 5 6o 7 8 9

--------

shaded

This indicates that any value of x greater than 6 (but not equal to 6) will satisfy the inequality x > 6.

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The probability that the manufacturer's claim is valid is 0.0037, or 0.37%.

The student question asks about the probability that the car manufacturer's claim of the hybrid car traveling at speeds more than 60 mpg is valid. The actual mpg is approximately normally distributed with a mean of 52 miles and a standard deviation of three miles.
To calculate the probability, we will use the Z-score formula:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the value we want to find the probability for (in this case, 60 mpg)
μ is the mean (52 miles)
σ is the standard deviation (3 miles)
Plug in the values into the Z-score formula:
Z = (60 - 52) / 3
Calculate the Z-score:
Z = 8 / 3 ≈ 2.67
Now we have the Z-score of 2.67, which tells us how many standard deviations above the mean the value of 60 mpg is. The next step is to use a Z-table (also known as the standard normal table) to find the probability.
Look up the Z-score in the Z-table:
For a Z-score of 2.67, the corresponding probability in the Z-table is 0.9963.

This means that 99.63% of the data falls below 60 mpg.
Find the probability that the claim is valid:
Since we want to find the probability that the car travels at speeds more than 60 mpg, we need to find the area to the right of the Z-score in the normal distribution curve. To do this, we subtract the probability from 1
Probability = 1 - 0.9963 = 0.0037
The probability that the manufacturer's claim is valid is 0.0037, or 0.37%.

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Based on the calculations using z-scores, we can conclude that the Grande Mocha Cappuccino at Ruth's Roast's has less sugar relative to the other drinks at its respective store than the Grande Mocha Cappuccino at Coffee Haven.

What is Coffee Haven?

"Coffee Haven" was used as an example name for one of the coffee shops in a previous question. It is not an actual coffee shop. The name was used to illustrate a point about comparing the sugar content of drinks between different coffee shops.

To compare the sugar content of the Grande Mocha Cappuccino between the two coffee shops, we can use z-scores to standardize the sugar content based on the mean and standard deviation of each shop's drinks.

For the first coffee shop, let's call it Coffee Haven, we know that the mean sugar content is 20g with a standard deviation of 8g. Therefore, the z-score for the Grande Mocha Cappuccino at Coffee Haven is:

z = (13 - 20) / 8 = -0.875

For the second coffee shop, Ruth's Roast's, we know that the mean sugar content is 16g with a standard deviation of 6g. Therefore, the z-score for the Grande Mocha Cappuccino at Ruth's Roast's is:

z = (13 - 16) / 6 = -0.5

Comparing the two z-scores, we see that the z-score for the Grande Mocha Cappuccino at Ruth's Roast's is greater than the z-score for the Grande Mocha Cappuccino at Coffee Haven. This means that the Grande Mocha Cappuccino at Ruth's Roast's has less sugar relative to the other drinks at its respective store than the Grande Mocha Cappuccino at Coffee Haven.

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According to given c represents the initial number οf birds οn the island

A pοlynοmial οf degree twο in οne οr mοre variables is referred tο as a quadratic pοlynοmial. The pοlynοmial functiοn that a quadratic pοlynοmial defines is knοwn as a quadratic functiοn.

functiοn represents a quadratic mοdel fοr the bird pοpulatiοn, we can write it in standard fοrm as:

f(t) = at² + bt + c

where a, b, and c are cοnstants.

Substituting t = 0 in the standard fοrm οf the quadratic functiοn, we get:

f(0) = a(0)² + b(0) + c

f(0) = c

Therefοre, the value οf c in the standard fοrm οf the quadratic functiοn represents the number οf birds present οn the island when cοunting first started.

Sο, the fοrm that reveals the number οf birds present οn the island when cοunting first started is the standard fοrm. f(t) = at²+ bt + c

where c represents the initial number οf birds οn the island.

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We need to find the GCF of 72 and 90 to solve this problem. We can calculate it in the following manner.

To solve this problem, we need to find the greatest number of party bags April can make with no candies left over. This means we need to find the greatest common factor (GCF) of 72 and 90.

The GCF of two numbers is the largest number that divides evenly into both of them. In this case, we need to find the largest number that can divide both 72 and 90 without any remainder.

Once we have found the GCF, we can divide both 72 and 90 by it to find the maximum number of party bags April can make with no candy left over.

Therefore, we need to find the GCF of 72 and 90 to solve this problem.

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Brooklyn have to pay total for the 11 rides is $43 and for r rides she have to pay is $10+$3×r.

If Brooklyn goes on 11 rides, she will have to pay $10 for admission and $3 for each of the 11 rides she goes on. So her total cost would be:

$10 + (11 rides x $3/ride) = $10 + $33 = $43

If she goes on r rides, her total cost would be:

$10 + (r rides x $3/ride) = $10 + $3r

So, for example, if she goes on 15 rides, her total cost would be:

$10 + (15 rides x $3/ride) = $10 + $45 = $55

An arithmetic expression is a combination of numbers, operators (such as +, -, x, ÷), and parentheses that can be evaluated to produce a numerical result.

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Answer:

186 inches

Step-by-step explanation:

8×6=48

5.5×16=88

10×5=50

48+88+50=186

Answer:

Answer: 40j - 16 = 40j + (-16) (Additive inverse property) = 40j + (-1)(16) (Distributive property) = 40j + (-1)(4)2 (FOIL - first, outer, inner, last) = (40j + (-1)4) + (-1)2 (Order of operations - parentheses first) = (40j - 4) + (-1)2 (Distributive property) = 36j - 2

Answer:

8(5j−2)

Step-by-step explanation:

1 / 4

Let's find the greatest common factor of 40

8 is greatest common factor

40j/8 - 16/8

=

8(5j-2)

Answer:

2.5

Step-by-step explanation:

51x - 19.5 + 19.5 = 108 + 19.5

51x = 127.5

x = 127.5/51

= 2.5

The distance between the points (15, -17) and (-20, -5) is 37.

The distance formula is a mathematical formula used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and can be used to find the distance between any two points, whether they are on the same line or on different lines.

We can use the distance formula to find the distance between two points:

[tex]\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Let [tex]\rm (x_1,y_1)[/tex] = (15,-17) and [tex]\rm (x_2, y_2)[/tex] = (-20,-5)

Then, plugging into the formula, we get:

[tex]\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]\rm = \sqrt{(-20-15)^2 + (-5-(-17))^2}[/tex]

[tex]= \sqrt{(-35)^2 + (12)^2}[/tex]

[tex]= \sqrt{1225+144}[/tex]

[tex]= \sqrt{1369}[/tex]

= 37

Therefore, the distance between the points (15, -17) and (-20, -5) is 37.

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Complete question:

Find the distance between point (15,-17) and (-20,-5).

4/3 Gallons of wood sealant are needed to cover the floor of Jose's vacation home.

To determine how many gallons of wood sealant are needed to cover the floor, first, we need to find the relationship

between the surface area of the hemispherical ceiling and the floor.

Calculate the surface area of the hemispherical ceiling.

The surface area of a hemisphere is given by the formula [tex]3πr^2[/tex], where r is the radius.

Calculate the surface area of the floor.

The floor is a circle, so its surface area is given by the formula[tex]πr^2[/tex].

Determine the ratio between the surface areas.

Divide the surface area of the floor by the surface area of the hemispherical ceiling: [tex](πr^2) / (3πr^2).[/tex] The [tex]πr^2[/tex]terms

cancel out, leaving 1/3.

Apply the ratio to the amount of wood sealant used for the ceiling.

Since Jose used 4 gallons of wood sealant for the ceiling, we can multiply this by the ratio to find the amount needed

for the floor: 4 gallons × (1/3) = 4/3 gallons.

Therefore, 4/3 gallons of wood sealant are needed to cover the floor of Jose's vacation home.

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