Delia and Kari have the same size bathroom. It takes Delia 3 hours longer to finish tiling her bathroom than Kari. If they work together it takes them 2 hours to lay the tiles per bathroom. How long does it take Kari to lay the tiles in her bathroom by herself? How long does it take Delia to finish her bathroom if she works alone? Show your work

The value of x is  10.05 meters .

To find the value of x, we need to consider that the rectangular piece of land has been subdivided into small squares. We can use the given dimensions of the rectangle to determine the number of small squares that will fit along each dimension.

The number of squares along the 9.8km side will be:

Number of squares = length of side / length of each square

Number of squares = 9.8km / x

Similarly, the number of squares along the 7.2km side will be:

Number of squares = width of side / length of each square

Number of squares = 7.2km / x

Since the rectangular piece of land has been subdivided into small squares, the total number of squares can also be calculated as the product of the number of squares along each dimension:

Total number of squares = (9.8km / x) * (7.2km / x)

We can simplify this expression by multiplying the terms in the brackets and simplifying:

Total number of squares = 70.56 / \(x^2\)

We know that the total number of squares is equal to the number of squares that fit in the rectangular piece of land, which is given by:

Total number of squares = (9.8km * 7.2km) / \(x^2\)

We can equate the two expressions for the total number of squares and solve for x:

70.56 / \(x^2\) = (9.8km * 7.2km) / \(x^2\)

\(x^2\) = (9.8km * 7.2km) / 70.56

\(x^2\)= 101.04

x = 10.05 m (rounded to two decimal places)

Therefore, each small square has a side length of approximately 10.05 meters

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Antonella have a number of coins of quaters and nickels whose total value is 250.

The number of coins of nickel is 10 and the number of coins of quarters is 7.

Nickel and quarters are the coin based form of currency in the United States. The value of one nickel is 5 cents, while that of one quarter is 25 cents. We have given that

Antonella has 3 more quaters than nickles.

Let she has "x" number of quaters and "y" be number of nickels .

According to question,

y = 3+ x ---(1)

Combined value of all is 225 cents .

i.e 25 × x + y× 5 = 225 cents

plug the value of y from equation (1) to equation(2) we get,

25 x + 5(3+x) = 225

solve the equation

=> 25x + 15 + 5x = 225

=> 30x = 210

=> x = 7

put the value of x in equation (1)

y = x + 3 = 10

Hence, the number of nickels coins is 10 and numbers of quaters are 7.

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Answer:

distance = 2.6 miles

Step-by-step explanation:

using the Pythagorean theorem:

1²+2.4² = distance²

distance² = 6.76

distance = 2.6 miles

Answer:

13x = 39

x=3

y=10

The leap pattern of the frog is up 2 steps then back 1 step. To reach 10th step she have to take 9 leaps up.

Let represent leaps up with positive number and leaps back with negative number.

Hence, the movement of the little green frog can be written as:

2 - 1 + 2 - 1 + 2 - 1 + ....

Notice, that every 4 leaps (both up and back) she reaches 2 steps.

2 - 1 + 2 - 1  = 2

Hence, after 4 x 4 = 16 leaps she will reach the 8th steps. The last leap in this instant is leap back. Hence, the next leap will be leaps up 2 steps, and she reaches the 10th steps.

In every 4 leaps there are 2 leaps up.

Therefore, she have to leaps up 2 x 4 + 1 = 9 leaps up.

You can also write all her leaps to reach the 10th steps:

2 - 1 + 2 - 1 +    2 - 1 + 2 - 1  +    2 - 1 + 2 - 1  +   2 - 1 + 2 - 1   + 2

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The required line representing the equation part of the constraint is go through (0, 4) and (7,0).

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.

The line representing the equation 7x1 + 4x2 = 28 is a boundary line that separates the feasible solutions from the infeasible solutions in a linear programming problem.

The line passes through two points, which can be determined by substituting the x1 and x2 values into the equation. By substituting the values (4,0) and (7,0) into the equation, we can see that both points satisfy the constraint.

This means that any point on the line also satisfies the constraint, and any point above or to the right of the line would be infeasible as they would not meet the requirement of the constraint.

Understanding the position and shape of the constraint lines is important in solving linear programming problems and finding the optimal solution.

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(a) Volume of the solid generated by revolving the region bounded by the graph is 12.422 cubic units.

(b)

(i) The work done in stretching the spring from its natural length to a length of 10 in. is 54 lb.-in.

(ii) The work done in stretching the spring from a length of 7 in. to a length of 9 in. is approximately 13.5 lb.-in.

(a) To find the volume of the solid generated by revolving the region bounded by the graph\(x^2=y-2\) and 2y-x-2=0 for 0≤x≤1 about y=3, we can use the method of cylindrical shells:

First, we need to find the limits of integration for the radius of the shells. Since we are revolving around y=3, the distance between y=3 and the curve x^2=y-2 will give us the radius of the shell.

Solving for y in \(x^2=y-2\), we get\(y=x^2+2.\) Substituting this into 2y-x-2=0, we get \(x=2y-2y^2-2.\) So the limits of integration for the radius will be from \(3-(x^2+2) to 3-(2y-2y^2-2).\)

Next, we need to find the height of the shells. This is simply the length of the interval of integration for x, which is 0 to 1.

So the volume of the solid is given by the integral:

\(V = \int (3-(x^2+2)) - (3-(2y-2y^2-2)) dx\) from x=0 to x=1

Simplifying and evaluating the integral, we get:

V ≈ 12.422 cubic units.

Therefore, the volume of the solid generated by revolving the region bounded by the graph \(x^2=y-2\) and \(2y-x-2=0\) for 0≤x≤1 about y=3 is approximately 12.422 cubic units.

(b) (i) The work done in stretching the spring from its natural length of 6 in. to a length of 10 in. can be found using the formula:

W =\((1/2)k(d2^2 - d1^2)\)

where k is the spring constant, d1 is the initial length, and d2 is the final length.

Given that the force required to stretch the spring from its natural length of 6 in. to a length of 8 in. is 9 lb., we can find the spring constant as follows:

k = F/(d2 - d1) = 9/(8-6) = 4.5 lb/in

So the work done in stretching the spring from its natural length of 6 in. to a length of 10 in. is:

W = \((1/2)(4.5)(10^2 - 6^2)\)= 54 lb.-in.

Therefore, the work done in stretching the spring from its natural length to a length of 10 in. is 54 lb.-in.

(ii) To find the work done in stretching the spring from a length of 7 in. to a length of 9 in., we can use the same formula:

W =\((1/2)k(d2^2 - d1^2)\)

Using the same spring constant of 4.5 lb/in, the work done is:

W = \((1/2)(4.5)(9^2 - 7^2)\)≈ 13.5 lb.-in.

Therefore, the work done in stretching the spring from a length of 7 in. to a length of 9 in. is approximately 13.5 lb.-in.

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Answer:

We need a picture

The coordinates of point O on the line MN are (-1, 6).

When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula. Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:

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

Given that, point O lies on MN such that MO:NO is 2:3. Graph O.

Coordinates of M(-3, 8) and N(2, 3)

Here, m:n =2:3

Coordinates of O are [((2×2+3×(-3))/(2+3), (2×3+3×8)/(2+3)]

O(x, y)=[-5/5, 30/5]

O(x, y)=(-1, 6)

Therefore, the coordinates of O are (-1, 6).

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Answer:

a. A Estela le entregaron (100 + 30 + 3) tejuelones = 133 tejuelones y aún necesita (138 - 133) tejuelones = 5 tejuelones para que reciba todo el pedido. b.  Don Antonio llevó (150 + 60 + 7) tejuelones = 217 tejuelones.

Step-by-step explanation:

¿Cuántos tejuelones le entregaron a Estela? ¿Cuántos tejuelones es la diferencia para que Estela reciba todo el pedido realizado?

Datos

Pedido de Estela:

138 tejuelones.

Le entregaron:

Dos (2) Paquetes de 50 tejuelones.

Dos (2) Paquetes de 15 tejuelones.

Tres (3) Sueltos.

Operación

Para determinar cuántos tejuelones le entregaron a Estela, efectuamos las siguientes operaciones para determinar el número de tejuelones que le entregaron:

Dos (2) Paquetes de 50 tejuelones

2 * 50 tejuelones = 100 tejuelones

Dos (2) Paquetes de 15 tejuelones

2 * 15 tejuelones = 30 tejuelones

Es decir, multiplicamos el número de paquetes por la cantidad de tejuelones que trae cada uno.

Ahora sumamos el total de ambas cantidades y le adicionamos los tres (3) tejuelones sueltos:

(100 + 30 + 3) tejuelones = 133 tejuelones.

Pero Estela pidió 138 tejuelones, así que aún necesita:

(138 - 133) tejuelones = 5 tejuelones para que reciba todo el pedido realizado.

Respuestas

¿Cuántos tejuelones le entregaron a Estela?

A Estela le entregaron (100 + 30 + 3) tejuelones = 133 tejuelones.

¿Cuántos tejuelones es la diferencia para que Estela reciba todo el pedido realizado?

Estela aún necesita (138 - 133) tejuelones = 5 tejuelones para que reciba todo el pedido.

¿Cuántos tejuelones llevó Don Antonio?

Datos

Pedido de Don Antonio

Tres (3) paquetes de 50 tejuelones.

Cuatro (4) paquetes de 15 tejuelones.

Siete (7) tejuelones sueltos.

Operaciones

Para determinar cuántos tejuelones le entregaron a Don Antonio, debemos multiplicar el número de paquetes por la cantidad de cada uno y sumar los siete (7) tejuelones sueltos, es decir, seguimos el mismo procedimiento de la pregunta anterior.

Tres (3) paquetes de 50 tejuelones

3 * 50 tejuelones = 150 tejuelones.

Cuatro (4) paquetes de 15 tejuelones

4 * 15 tejuelones = 60 tejuelones.

Ahora sumamos estas cantidades y le adicionamos los siete (7) tejuelones sueltos:

(150 + 60 + 7) tejuelones = 217 tejuelones.

Respuesta

¿Cuántos tejuelones llevó Don Antonio?

Entonces, considerando los resultados anteriores, tenemos que Don Antonio llevó (150 + 60 + 7) tejuelones = 217 tejuelones.

Answer:

11

Step-by-step explanation:

11

since it asks the absolute value of -11 it

will be 11 because in absolute value-for negatives it always positive.

Answer:

see attached

Step-by-step explanation:

9514 1404 393

Answer:

  145

Step-by-step explanation:

In this geometry, the central angle (x°) and the external angle (35°) are supplementary.

  x° = 180° -35°

  x = 145

-243

Step-by-step explanation:

số dương nhân -3 thì đc số âm, số âm nhân với -3 để đc số dương.

vd: 1. -3 = -3 ;   -3 .-3= 9 ;..... 81 . -3= -243

Answer:

all once will product the term by mines 3

so the final will bt -3 *81 = -243

The largest scale among the given representative fractions is 1:24,000.A representative scale remains correct even if the map is enlarged or reduced when reproduced. At times, latitudes higher than 66.5 degrees can have 24 hours or more of continuous darkness.

A map scale represents the relationship between the distances on a map and the corresponding distances in the real world. It is expressed as a representative fraction, where the numerator represents the map distance and the denominator represents the equivalent distance on the ground. A smaller denominator indicates a larger scale, meaning that objects on the map are depicted in greater detail.

In the given options, 1:24,000 has the smallest denominator, making it the largest scale. This means that objects on a map with a scale of 1:24,000 are depicted in greater detail compared to the other representative fractions provided.

Representative scales, also known as ratio scales or graphic scales, are designed to maintain their accuracy regardless of the size at which the map is reproduced. These scales are often represented as a linear scale bar, where distances on the map are visually depicted in proportion to the real-world distances they represent.

Unlike verbal scales, which express the relationship between map distances and ground distances through words or ratios, representative scales are visually depicted on the map itself. This allows users to directly measure distances on the map using a ruler or by referencing the scale bar, regardless of the size at which the map is reproduced.

Representative scales are especially useful in situations where maps need to be reproduced at different sizes or scales, such as in printing or digital mapping applications. They ensure that the map's accuracy and proportional relationships are maintained, allowing users to make accurate measurements and calculations based on the map.

Latitudes higher than 66.5 degrees refer to the Arctic and Antarctic regions, also known as the polar regions. These regions experience a natural phenomenon called the polar night, where the sun remains below the horizon for an extended period of time. As a result, these latitudes can have periods of 24 hours or more of continuous darkness during certain times of the year.

The polar night occurs because of the tilt of the Earth's axis. During the winter solstice in the respective hemisphere, the tilt causes the sun's rays to be unable to reach the areas within the Arctic and Antarctic Circles. This results in the prolonged darkness experienced in these regions.

The duration and intensity of the polar night vary depending on the specific latitude. The closer one gets to the poles, the longer the period of continuous darkness becomes. At the North Pole (90 degrees latitude), for example, there can be several months of complete darkness during the winter season.

The polar night has significant implications for the ecosystems and human populations in these regions. Adaptations are necessary to survive and thrive in the extreme conditions of prolonged darkness, such as changes in behavior, migration patterns, and reliance on artificial light sources.

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Answer:

10 is the distance

Step-by-step explanation:

d = square root (x2-x1)^2 + (y2-y1)^2

(5-5)^2 = 0

(2-(-8))^2 = 100

0 + 100 = 100

square root 100 = 10

More specifically, these two triangles are congruent by the SAS congruence theorem. SAS stands for Side Angle Side.

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Answer:

Gross pay per week = $234

Federal income tax = $421.2

Social security = $174.96

Medicare =$40.71

net pay per week = $181

Total gross pay = $2,808

Total net pay = $2172

Step-by-step explanation:

Hi, to answer this question, first, we have to calculate Angela gross income per week:

18 hours per week x $13 per hour = $234 per week (gross)

234 x 12 =2,808

Amount taken ; multiply weekly gross pay by each percentage discount in decimal form (divided by 100)

Federal income tax = 234 x (15/100) = $35.1  (in 12 weeks = 35.1 x 12 = $421.2)

Social security = 234 x (6.2/100)= $14.508 (in 12 weeks = 14.5 x 12 = $174.96)

Medicare = 234 x (1.45/100)=$3.393  (in 12 weeks = 3.39x 12 = $40.71)

Total amount taken (per week)= 35.1+14.508+3.393=$53.001

Net pay per week = 234-53 = $181

For the total gross pay we have to multiply the weekly gross pay by the number of weeks (12)

Total gross pay = 234 x 12 =$2,808

Total net pay = 181 x 12 = 181 per week x 12 = $2172

According to the given data we have the following:

Shift the function f(x)=x^2 to the right 2, vertical stretch by 4, and a shift

up 1 unit.*

If we Shift the function f(x)=x^2 to the right 2, hence the right option would be:

f(x)=4(x+2)^2+1

Hence, the right option would be option 1.

Answer: Area= \(\frac{bh_{b} }{2}\)

Example:

Let the base be 3 and the height(\(h_{b\\}\)) 4

So,

Area= \(\frac{3*4}{2\\}\)-->\(\frac{12}{2}\)=6

The correct answer is 95.44%, representing the confidence level within 2 standard deviations above and below the mean in the standard normal distribution.

In the standard normal distribution, also known as the z-distribution, the mean is 0 and the standard deviation is 1. The Empirical Rule, also known as the 68-95-99.7 rule, states that within 1 standard deviation of the mean, approximately 68% of the data falls. Within 2 standard deviations, approximately 95% of the data falls, and within 3 standard deviations, approximately 99.7% of the data falls.

Thus, within 2 standard deviations above and below the mean of the standard normal distribution, we have approximately 95% of the data. This means that we can be confident about 95.44% of the data falling within this range.

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The amount of cinnamon more than nutmeg that was used is 3/4.

A fraction is a non-whole number that has a numerator and a denominator. In order to determine how much more cinnamon was used, find the difference of the fractions.

How much more cinnamon was used

= \(\frac{11}{12} - \frac{1}{6}\)

=\(\frac{11 - 2}{12}\)

=\(\frac{9}{12}\)= \(\frac{3}{4}\)

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The missing sides and angles of the triangles are:

1) ∠L = 53°

LA = 23.145 ft

AB = 18.9 ft

2) ∠S = 57.31°

SA = 98.57 cm

SW = 69.12 cm

3) B = 30.71°

C = 99.29°

The law of cosine formula is expressed as:

c² = a² + b² - 2ab cos C

The Law of sines is expressed as:

a/sin A = b/sin B = c/sin C

Thus:

1) ∠L = 180 - (102 + 25)

∠L = 53°

LA/sin 102 = 10/sin 25

LA = 23.145 ft

AB = 10 * sin 53/sin 25

AB = 18.9 ft

2) ∠S = 180 - (79 + 43.69)

∠S = 57.31°

84.5/sin 57.3 = SA/sin 79

SA = 98.57 cm

SW/sin 43.69 = 84.5/sin 57.3

SW = 69.12 cm

3) 15/sin 50 = 10/sin B

sin B = (10 sin 50)/15

sin B = 0.5107

B = sin⁻¹0.5107

B = 30.71°

C = 180 - (50 + 30.71)

C = 99.29°

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Answer:

Step-by-step explanation:

The distance formula for a number line is very simple:

\(l=|b-a|\)  The absolute value signs make unimportant which value you choose for a and which one you choose for b. Let's let A = -8 and B = 8 as posted on the number line. The distance between them, using the formula, is

\(l=|8-(-8)|\\l=|16|\\l=16\)

Answer: D

Step-by-step explanation: because I got the same question and got it right

The next crow observed will be black is not supported by the premises in any meaningful way. The premises do not guarantee the outcome of the next observation.  Argument B is the stronger argument.

Argument A is an example of an inductive argument, as it generalizes from a limited sample to make a broader claim about the entire population. This argument form is called induction and can be evaluated on its strength.

Argument B is a deductive argument, as it uses a conditional premise to reach a definite conclusion. In this form of argument, the conclusion necessarily follows from the premises. The strength of a deductive argument depends on the logical structure of the premises and conclusion.

The better argument of the two is argument B. Because in deductive arguments, the conclusion necessarily follows from the premises if the premises are true.

And this argument, the premises state that if 90% of observed crows are black, then the next crow observed will be black.

Additionally, it is also claimed that 90% of observed crows are black. Therefore, it can be logically deduced that the next crow observed will be black

The argument in A, however, is an inductive argument, where the conclusion is not necessarily true even if the premises are true. Even if 90% of observed crows are black, it does not necessarily follow that 90% of all crows are black.

argument B is the stronger argument.

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Answer:

(-2, -5)

(-1, -3)

(0, -1)

(1, -1)

(2, 3)

Step-by-step explanation:

To do this you simply put in an input for x and then solve and you will get your y.

We'll use

x= -2 for this input

y=2(-2)-1

y=-4-1

y=-5

(-2, -5) Is one ordered pair

We'll use

x= -1 for this input

y=2(-1)-1

y=-2-1

y=-3

(-1, -3) Is another ordered pair

We'll use

x= 0 for this input

y=2(0)-1

y=0-1

y=-1

(0, -1) is another ordered pair

We'll use

x= 1 for this input

y=2(1)-1

y=2-1

y=1

(1, -1) is another ordered pair

We'll use

x= 2 for this input

y=2(2)-1

y=4-1

y=3

(2, 3) is the last pair I'll use today.

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!