A rectangle is 21 meters long and I1 meters wide

the probability of rolling two 3's is 1/36.Since we are rolling two number cubes, the sample space contains 6x6 = 36 equally likely outcomes, one for each possible pair of numbers that can be rolled.

what is probability  ?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated as the number of ways the event can occur, divided by the total number of possible outcomes.

In the given question,

Since we are rolling two number cubes, the sample space contains 6x6 = 36 equally likely outcomes, one for each possible pair of numbers that can be rolled.

To find the probability of rolling two 3's, we need to count the number of outcomes that result in two 3's, and divide by the total number of possible outcomes.

From the diagram, we can see that there is only one outcome that results in two 3's, namely the outcome where the first cube shows a 3 and the second cube shows a 3. Therefore, the number of favorable outcomes is 1.

The probability of rolling two 3's is therefore:

P(rolling two 3's) = favorable outcomes / total outcomes = 1/36

So the probability of rolling two 3's is 1/36.

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If the figure "WXYZ" is a kite and m∠WXY=13x+24, then the measure of the angle-ZYX is 101.6 degrees.

A "Kite" is defined as quadri-lateral which has two pairs of "adjacent-sides" which are congruent and "one-pair" of "opposite-angles" which are congruent .

We know that the sum of all the vertices of the kite is 360 degree,

So, we add all the vertices of the kite,

We get,

⇒ m∠WXY + m∠WZY + m∠ZWX + m∠ZYX = 360°,

Substituting the values,

We get,

⇒ 13x + 24 + 35 + 13x + 4 + m∠ZYX = 360°,

⇒ 26x + 63 + m∠ZYX = 360°,

⇒ m∠ZYX = 360 - 63 - 26x,

⇒ m∠ZYX = 297 - 26x,      ...equation(1)

We also know that, "two-angles of kite are equal where "unequal-sides" meet".

So, m∠ZWX = m∠ZYX,

Substituting the values,

We get,

⇒ 13x + 4 = m∠ZYX,       ....equation(2),

Equating equation(1) and equation(2),

we get,

⇒ 13x + 4 = 297 - 26x,

⇒ x = 293/39,

Substituting this in equation(2),

We get,

⇒ 13(293/39) + 4 = m∠ZYX,

⇒ 293/3 + 4 = m∠ZYX,

⇒ m∠ZYX ≈ 101.6 degree.

Therefore, the measure of the angle ZYX is 101.6 degrees.

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The given question is incomplete, the complete question is

The figure WXYZ is a kite. If m∠WXY=13x+24, m∠WZY=35, and m∠ZWX=13x+4, find m∠ZYX?

The weight of the plane if it is carrying gallons of fuel is 2336 pounds, under the condition of when carrying 10 gallons, and 45 gallons he airplane weighs 2056  and 2252 pounds.
We can utilize the two given points to create two linear equations

y = mx + b
2056 = 10m + b
2252 = 45m + b

We can find m and b by subtracting the first equation from the second equation:

(45m + b) - (10m + b) = 2252 - 2056
35m = 196
m = 5.6

For finding b by substituting m into one of the original equations:

2056 = 10(5.6) + b
b = 2000

The equation is

y = 5.6x + 2000

To evaluate  how much the airplane weighs when carrying 60 gallons of fuel,  now lets substitute x into the equation

y = 5.6(60) + 2000
y = 336 + 2000
y = 2336

The weight of the plane if it is carrying gallons of fuel is 2336 pounds, under the condition of when carrying 10 gallons, and 45 gallons he airplane weighs 2056  and 2252 pounds.

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The complete question is
Suppose that the weight (in pounds) of an airplane is a linear... Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 10 gallons of fuel, the airplane weighs 2056 pounds. When carrying 45 gallons of fuel, it weighs 2252 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?

Answer:

b. 8/17

Step-by-step explanation:

hope this helps ;)

If a circle graph were created using the findings, A. Kayaking would be the lake activity with a central angle of 54°.

A central angle is one having endpoints on the perimeter and a vertex in the centre of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle.

Lake Activity             Number              Degrees

                             of Campers

Kayaking                     15                         (15/100 x 360°) = 54°

Wakeboarding            11                        (11/100 x 360°) =  40°

Windsurfing                 7                        (7/100 x 360°) = 25°

Waterskiing                13                        (13/100 x 360°) = 47°

Paddleboarding        54                         (54/100 x 360°) = 194°

Total number             100

Thus, Kayaking hence has a 54° central degree when viewed proportionately.

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The number of coins that are mistakes in 20 days are 12000000

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

Mistake on 3% of the coins

Rate = 20000000 coins a day,

This means that

Mistakes = 3% * 20000000 * days

For the coins that are mistakes in 20 days, we have

Mistakes = 3% * 20000000 * 20

Evaluate

Mistakes = 12000000

Hence, the coins are mistakes in 20 days are 12000000

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The equation of the tangent line at the point of inflection is y = -3x + 1, which corresponds to option (b).

To find the equation of the tangent line at the point of inflection for the given function [tex]y = x^3 + 3x^2 + 2,[/tex] we first need to determine the point of inflection. A point of inflection occurs where the second derivative changes sign.

First, let's find the first and second derivatives of the given function:
[tex]y' = 3x^2 + 6x[/tex] (first derivative)
[tex]y'' = 6x + 6[/tex] (second derivative)

To find the point of inflection, set the second derivative equal to zero and solve for x:
[tex]6x + 6 = 0 x = -1[/tex]

Now, plug x = -1 back into the original function to find the corresponding y-coordinate:
[tex]y = (-1)^3 + 3(-1)^2 + 2\\y = -1 + 3 + 2\\y = 4[/tex]

The point of inflection is (-1, 4). Next, find the slope of the tangent line at this point using the first derivative:
[tex]y'(-1) = 3(-1)^2 + 6(-1)\\y'(-1) = 3 - 6\\y'(-1) = -3[/tex]

Now, use the point-slope form of the equation of a line to find the tangent line:
y - y1 = m(x - x1)
y - 4 = -3(x - (-1))
y - 4 = -3(x + 1)

Simplify the equation to get the answer:
y = -3x - 3 + 4
y = -3x + 1

The equation of the tangent line at the point of inflection is y = -3x + 1, which corresponds to option (b).

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The scale factor used to create the image include the following: C. 2.

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).

Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:

Scale factor = side length of image/side length of pre-image

By substituting the given side lengths or dimensions into the formula for scale factor, we have the following;

Scale factor = 2/1

Scale factor = 2.

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To determine how fast the height of the pineapple juice is increasing in a cylindrical can with radius 1 inch and filling rate of [tex](2)^{\frac{3}{s} }[/tex], we can use the formula for the volume of a cylinder and then differentiate it with respect to time.

The formula for the volume of a cylinder is [tex]V = πr^2h[/tex], where V is the volume, r is the radius, and h is the height. In this case, r = 1 inch.

Now, we are given [tex]\frac{dV}{dt}= (2)^{\frac{3}{s} }[/tex], which is the rate at which the volume of pineapple juice is increasing.

1. Plug in the radius value into the volume formula: [tex]V=π(1)^{2h}=πh[/tex].
2. Differentiate both sides of the equation with respect to time: [tex]\frac{dV}{dt} = π(\frac{dh}{dt})[/tex].
3. Plug in the given value of [tex]\frac{dV}{dt} :2 =  π \frac{dh}{dt}[/tex].
4. Solve for [tex]\frac{dh}{dt} : \frac{dh}{dt} = \frac{2}{π}[/tex].

So, the height of the pineapple juice is increasing at a rate of [tex]\frac{2}{π}[/tex]  inches per second.

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The angle x subtended by the arc of the circle between the two tangents is 130 degrees.

In trigonometry, the tangent (often abbreviated as tan) is a mathematical function that describes the ratio of the length of the side opposite to an angle in a right-angled triangle to the length of the adjacent side.

The formula 50=180-x represents the fact that the angle between two tangents drawn to a circle from an external point is equal to the difference of the angles subtended by the tangents in the opposite segment of the circle.

Using this formula, we can solve for x as follows:

50 = 180 - x (given)

x = 180 - 50 (subtracting 50 from both sides)

x = 130 (simplifying)

Therefore, the angle x subtended by the arc of the circle between the two tangents is 130 degrees.

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The domain is all real numbers, range is all positive real numbers. As x decreases, h(x) will decrease. As x increases, h(x) will increase.

The domain of the exponential function h(x) = 125x is all real numbers, as x can take on any value.

The range of the function is all positive real numbers, as the base (125) raised to any power (x) will always be positive.

As x decreases, h(x) will decrease. This is because when the base of an exponential function is greater than 1, as is the case here with 125, the function increases as the exponent increases, and decreases as the exponent decreases. So, as x becomes more negative, h(x) becomes smaller.

As x increases, h(x) will increase. This is because, as mentioned above, when the base of an exponential function is greater than 1, the function increases as the exponent increases. So, as x becomes more positive, h(x) becomes larger.

Overall, the function h(x) = 125x is an increasing function with a domain of all real numbers and a range of all positive real numbers.

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Answer:

on what

Step-by-step explanation:

The requried surface area of the regular pyramid is 147.6 cubic meters.

The surface area of the regular pyramid is given as:

Surface area = base area + 1/2 [perimeter×slant height]
Surface area = 1/2 × base × height + 1/2 [perimeter×slant height]
Surface area =1/2 × 8 × 6.9 + 1/2 [3×8 × 10]
Surface area =147.6 cubic meters

Thus, the requried surface area of the regular pyramid is 147.6 cubic meters.

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The total area of the given figure is 85.2m² respectively.

The quantity of unit squares that cover a closed figure's surface is its area.

Square units like cm² and m² are used to measure area.

A shape's area is a two-dimensional measurement.

The space inside the perimeter or limit of a closed shape is referred to as the "area".

Area of rectangle one:

= l*b

= 4*11.4

= 45.6m²

Area of rectangle second:

= l*b

= 4*8.4

= 33.6m²

Area of the triangle:
= 1/2*b*h

= 1/2*4*(11.4-8.4)

= 1/2*4*3

= 2*3

= 6m²

Total area of the figure: 45.6 + 33.6 + 6 = 85.2m²

Therefore, the total area of the given figure is 85.2m² respectively.

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Statements I, II, and III are partially correct, but statement II needs to be corrected to indicate that stem plots are better for small to moderate-sized datasets.

We might choose to display data with a stem plot rather than a boxplot because:

Reveals the shape of the distribution.

Is better for small to moderate-sized datasets.

Displays the actual data.

A stem plot is a type of graph that shows the distribution of data by grouping the observations into stems and leaves.

It allows for the display of the actual data values, which is not possible in a boxplot.

Additionally, stem plots are particularly useful for small to moderate-sized datasets as they provide a detailed view of the distribution, allowing for the identification of patterns such as skewness, multimodality, and outliers.

On the other hand, boxplots are better for large datasets as they provide a more concise summary of the distribution, including information about the median, quartiles, and outliers, while still conveying information about the spread and shape of the distribution.

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The function that models the total amount of money Julia has after x weeks is f(x) = 27x + 254

An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.

Let f(x) represent the total amount of money Julia has after x weeks.

Julia has $254 and saves $27 each week, hence:

f(x) = 27x + 254

The function is f(x) = 27x + 254

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Answer:

156

Step-by-step explanation:

Use the system of PEMDAS.
6*3 = 18
6*4 = 24
6*5 = 30
6*8 = 48
2[3*4+1/2(3*4)] = 36
Add all.
18+24+30+48+36 = 156

Answer: Ashley hit the softball farther.

Step-by-step explanation: Ashley hit the softball farther, since her distance of 65 meters is greater than Nicole's distance of 6,700 centimeters.To compare these distances, we need to convert Nicole's distance from centimeters to meters, since Ashley's distance is given in meters.To do this, we can divide Nicole's distance by 100, since there are 100 centimeters in a meter:6700 cm / 100 cm/m = 67 mTherefore, Ashley hit the softball 65 meters, which is less than the 67 meters that Nicole hit it. This means that Ashley hit the softball farther.

Answer: The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.

Step-by-step explanation: You can find the mean, or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

Therefore , the solution of the given problem of unitary method comes out to be the athletes completed a total of 12 laps.

Finish the project using the tried-and-true basic methodology, the actual variables, and any pertinent knowledge you gain from the broad and specific questions. In response, customers might be given another opportunity to sample expression the products. We'll miss out on important breakthroughs in programming comprehension if these changes don't take place.

Here,

In accordance with the information provided, for each sprint around the track, the runners jogged three times. So, three times as many laps are jogged around the track.

Furthermore, it is known that the runners jogged six more laps than they ran. Therefore, we can construct the following equation:

Jogging laps equals sprinting laps plus six.

=> 3x = x + 6

=> 3x - x = 6

=> 2x = 6

=> x = 6/2

=> x = 3

Total laps equal 3x + x = 4x times the amount of jogged and sprinting laps.

By changing the value of x, we obtain:

Laps completed = 4 (3) = 12

As a result, the athletes completed a total of 12 laps.

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Answer:

There are a total of 4 + 6 + 10 = 20 CDs in the case. Eric has a 10/20 = 1/2 chance of picking a pop CD since there are 10 pop CDs in the case.

Therefore, the answer is D) 1/2.

Answer:

Step-by-step explanation:

Eric has a total of 4 + 6 + 10 = 20 CDs in the case.

The probability of picking a pop CD is the number of pop CDs divided by the total number of CDs:

P(pick a pop CD) = 10/20 = 1/2 = 0.5

Therefore, the probability of Eric picking a pop CD is 0.5 or 50%.

The inequality to represent the possible number of hours Kat can afford to book the DJ is 80x + 225 ≤ 970 and one possible length Kat can afford to book the DJ is 9 hours.

(a) Let x be the number of hours that Kat can book the DJ. Then, the total cost of the DJ is 80x, and the total cost of the party is 80x + 225.

Since Kat has $410 saved and will earn another $560, the total amount she can spend on the party is $410 + $560 = $970.

Therefore, we can write the following inequality to represent the possible number of hours Kat can afford to book the DJ:

80x + 225 ≤ 970

b) To solve for x, we can start by subtracting 225 from both sides of the inequality:

80x ≤ 745

Then, we can divide both sides by 80:

x ≤ 9.3125

Since Kat can only book the DJ in whole hours, the largest integer less than or equal to 9.3125 is 9. Therefore, one possible length Kat can afford to book the DJ is 9 hours.

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The technique being described is random sampling without replacement, which is option a.

This technique is called "sampling without replacement."

However, you've also mentioned convenience sampling, which is a different method.

Let me briefly explain both concepts.

Sampling without replacement is a method in which each item, score, event, or participant is chosen from the population and is not returned to the pool for further selections.

This ensures that each element can only be selected once, eliminating the chance of duplication in the sample.

This method is often used in surveys, experiments, and research to maintain the independence of observations and provide a more accurate representation of the population.
Select an item, score, event, or participant from the population.
Record the selected item and remove it from the population.

Repeat steps 1-2 until the desired sample size is obtained.
Convenience sampling, on the other hand, is a non-probability sampling method where researchers select participants based on their accessibility and ease of recruitment.

This approach may introduce bias and limit the generalizability of the study results, as it does not ensure that the sample is representative of the population.
Identify the target population.
Recruit participants who are easily accessible and willing to participate.
Collect data from the selected participants.
In summary, sampling without replacement is a technique that prevents the same item from being selected more than once, while convenience sampling is an approach that focuses on selecting participants based on their accessibility. Both methods serve different purposes in research and should be chosen based on the study's objectives and available resources.

Option a is correct.

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The y-intercept of the tangent line is b. -1

The y-intercept of a line is the value of y at which the line crosses the y axis

To determine the value of y-intercept of a line with the given slope -3 that is a tangent line to the curve y = -x² - 5x -5.

We proceed as follows

First we differentiate the equation of the curve.

So,  y = -x² - 5x -5.

dy/dx = d(-x² - 5x -5)/dx

=  d-x²/dx - d5x/dx - d5/dx

= -2x - 5 - 0

= -2x - 5

Since the derivative of the curve equals the value of the tangent at the point, we have that

dy/dx = -3

-3 = -2x - 5

-3 + 5 = -2x

2 = -2x

x = 2/-2

x = -1

So, substituting x = -1 into the equation for y to find the y intercept, we have that

y = -x² - 5x -5.

y = -(-1)² - 5(-1) -5

= -1 + 5 - 5

= -1 + 0

= -1

So, the y-intercept is b. -1

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After  converting 2.340 x 10⁴ to decimal format we will be getting 0.000234. So, the correct answer choice is options (C) which is  0.000234.

In order to convert the given epression i.e. 2.340 x 10⁴ to decimal format, we are required to move the decimal point four places to the left since the exponent is negative.

In order to find the correct decimal format, starting with 2.340, we move the decimal point four places to the left, then the value we will be getting is equal to 0.000234

Therefore, from the above calculation we can draw the inference that the correct answer is option C) i.e 0.000234.

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The final expression that gives us the cost of x skirts and y hats in pounds is 24x + 15y.

In this case, our variables are x and y, which represent the number of skirts and hats, respectively. Our constants are 24 and 15, which represent the cost of one skirt and one hat, respectively. And our operations are multiplication and addition.

The cost of x skirts is simply the cost of one skirt (which is 24) multiplied by the number of skirts (which is x). So, the expression for the cost of x skirts would be:

24x

Similarly, the cost of y hats is the cost of one hat (which is 15) multiplied by the number of hats (which is y). So, the expression for the cost of y hats would be:

15y

To find the total cost of x skirts and y hats, we simply add the two expressions together. Thus, the expression for the cost in pounds of x skirts and y hats is:

24x + 15y

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The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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the area of the rhombus is approximately 74.60 square units.

How to solve the question?

To find the area of a rhombus using decomposition, we first need to draw its diagonal lines. Let's label the points where the diagonals intersect as points A and B.

Now we can decompose the rhombus into two congruent triangles, ABC and ABD, where AB is the diagonal and AD and BD are half of the diagonals.

We can find the length of AD and BD using the Pythagorean theorem. Since x=4 units and y=6 units, we have:

AD²= (x/2)² + h²

AD² = (4/2)²+ 5²

AD²= 4² + 5²

AD² = 41

AD = sqrt(41)

Similarly, we can find the length of BD:

BD²= (y/2)² + h²

BD²= (6/2)² + 5²

BD²= 3²+ 5²

BD²= 34

BD = √(34)

Now we can find the area of each triangle:

Area of ABC = (AB * BD) / 2

Area of ABC = (2 * √(41) * √(34)) / 2

Area of ABC = √(1394)

Since the rhombus is made up of two congruent triangles, its total area is twice the area of one triangle:

Area of rhombus = 2 * Area of ABC

Area of rhombus = 2 * √(1394)

Area of rhombus ≈ 74.60 square units

Therefore, the area of the rhombus is approximately 74.60 square units.

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