Jenny wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (in ) versus the length (in ).
Find the range and the domain of the function shown.

Area
()
y12345678910x1234567890
Length ()
Write your answers as inequalities, using or as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
look at picture

[tex]\sqrt{252} ~~ \begin{cases} 252=&2\cdot 2\cdot 3\cdot 3\cdot 7\\ &2^2\cdot 3^2\cdot 7\\ &(2\cdot 3)^2\cdot 7\\ &6^2\cdot 7 \end{cases}\implies \sqrt{6^2\cdot 7}\implies 6\sqrt{7}[/tex]

Answer:

We want to test the null hypothesis that the proportion of children aged 8-12 who have cell phones is 0.58, against the alternative hypothesis that the proportion is less than 0.58.

The sample proportion is:

p = 460/822 = 0.559

The sample size is n = 822.

Under the null hypothesis, the test statistic follows a standard normal distribution. The test statistic is:

z = (p - P0)/sqrt(P0(1 - P0)/n)

where P0 is the hypothesized proportion under the null hypothesis.

Substituting the values we obtained, we get:

z = (0.559 - 0.58)/sqrt(0.58(1 - 0.58)/822) = -1.691

The critical value for a one-tailed test with a significance level of 0.10 and 821 degrees of freedom is -1.282. Since the test statistic (-1.691) is less than the critical value (-1.282), we reject the null hypothesis.

Therefore, we can conclude that there is sufficient evidence to support the claim that less than 58% of children aged 8-12 have cell phones.

Hope that is what you are looking for :).

The diameter of the wheel is approximately 45 cm.

To find the diameter of the wheel, we need to determine the circumference of the wheel using the number of revolutions and the distance traveled. The formula for the circumference of a wheel is given by:

Circumference = 2πr

where r is the radius of the wheel. Since we need to find the diameter, we can substitute r with d/2, where d is the diameter. The formula becomes:

Circumference = πd

We are given that the wheel completes 25 revolutions and travels about 35.325 meters. The distance traveled in one revolution is equal to the circumference of the wheel. Let's calculate the circumference of the wheel first:

Circumference = 35.325 m / 25 = 1.413 m

Now we can equate this to πd and solve for d:

1.413 = πd

To find the diameter, we divide both sides of the equation by π:

d = 1.413 / π ≈ 0.449 m

Finally, to convert the diameter to centimeters, we multiply by 100:

d ≈ 0.449 m * 100 ≈ 44.9 cm

Rounding this value to the nearest centimeter, the diameter of the wheel is approximately 45 cm.

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The combination is evaluated to give 20

From the information given, we have the expression as;

⁵C₁

The formula for calculating combination is expressed as;

ⁿCᵣ = n! / (r!(n-r)!)

Such that the parameters of the formula are expressed as;

Now, substitute the values into the formula, we have;

⁵C₁ = 5! / (1!(5-1)!)

= 5! / (1! × 4!)

Find the permutation, we have;

= (5 × 4 × 3 ×2 × 1) / (1 × (4 × 3 × 2 × 1))

Divide the values, we get;

= 20 / 1

Find the value

= 20

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Answer: Given as (x, y) in order from top to bottom: (16, 4); (8, 2); (36, 9)

Step-by-step explanation:

   Since we need to solve for x, we will solve this equation for x first.

Given:

   y = [tex]\frac{x}{4}[/tex]

Multiply both sides of the equation by 4:

   4y = x

   Next, for each given y-value, we will substitute into the given rule we transformed and solve.

   4y = x

   4(4) = 16

   4y = x

   4(2) = 8

   4y = x

   4(9) = 36

Answer:

16

8

36

Step-by-step explanation:

move the /4 to H other side and you get y*4=x,

now put the number on the table and multiply by 4 to get X, for each value,

10.8

.......................................

1. Green Party: Political party prioritizing environmental issues, sustainability, and social justice.

2. The National Environmental Education Act promotes environmental education and awareness.

3.  Urban conditions impact species by habitat loss and fragmentation.

4. Developed countries prioritize environmental conservation; undeveloped countries focus on development.

1.  A green party is a political party that prioritizes environmental issues, sustainability, and social justice. One example of a green party is the Green Party of Germany (Bündnis 90/Die Grünen).

Founded in 1980, they advocate for renewable energy, climate protection, social equality, and grassroots democracy.

They have been part of coalition governments in Germany and have influenced national and European environmental policies.

2. The National Environmental Education Act is a United States federal law that was enacted in 1990 to promote environmental education and awareness among students and the general public.

The Act established the Office of Environmental Education within the Environmental Protection Agency (EPA) to provide funding for environmental education programs and to develop and disseminate environmental education materials.

3. Urban areas can have various negative impacts on species that live in the area. One example is the loss of natural habitat due to urban development.

When forests or wetlands are cleared to make way for buildings or roads, it disrupts the habitat of many species, leading to population declines and biodiversity loss.

4. Societal attitudes in developed countries often prioritize environmental conservation, sustainability, and environmental regulations.

There is generally greater awareness and concern for issues such as climate change, pollution, and resource depletion. In contrast, societal attitudes in undeveloped countries may vary, with more immediate concerns such as poverty and economic development taking precedence over environmental concerns.

5. The global aspect of environmental issues can have both positive and negative impacts on local environmental issues. Positively, global awareness and collaboration can lead to knowledge sharing, resources, and support for local initiatives.

Negatively, global demands and policies may prioritize economic growth, leading to environmental degradation and challenges for local communities.

Regarding the issue with banned questions, I apologize for any inconvenience caused.

The moderation system is in place to ensure compliance with community guidelines and prevent misuse of the platform. It's possible that certain questions may trigger filters due to sensitive topics, inappropriate content, or excessive repetition.

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The solution to the given logarithmic expression is: x = 111.63

The logarithmic form of expression is written as [tex]log_{a} c = b[/tex]. This is simply a rearrangement of the specific exponential form, aᵇ = c. Thus, we can say that exponential equation could be written as a logarithm.

We want to solve the logarithmic expression given as:

log x = [tex]\frac{log 27}{log 5}[/tex]

log x = [tex]\frac{log 3^3}{log 5}[/tex]

log x = [tex]\frac{3 log 3}{log 5}[/tex]

log x = 2.0478

x = [tex]10^{2.0478}[/tex]

x = 111.63

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The x-intercept of the given line is (-10, 0). The y-intercept is determined as (0, -45).

The y-intercept is the point at which the line crosses the y-axis. Geometrically, it speaks to the esteem of the subordinate variable (as a rule signified as y) when the autonomous variable (more often than not indicated as x) is rise to to zero.

On the other hand, the value of x when y is equal to zero, is referred to as the x-intercept of the line.

The x-intercept of the line shown in the image above is (-10, 0), while the y-intercept is (0, -45).

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Answer:

He owns about 4.17% or 4% so the others own about 95.83% or 96% but sense it rounds to the nearest tenth your answer would be 95.8%

Step-by-step explanation:

You can figure this out by doing 11,919 divided by 285,763 in order to figure out the percentage of the company he owns and then just do 100 - your answer.

Step-by-step explanation:

First, we need to find out how much money the three other individuals invested in the company. To do that, we'll subtract Fred's investment from the total investment:

Total investment = 285,763

Fred's investment = 11,919

Investment from the three other individuals = Total investment – Fred's investment

Investment from the three other individuals = 285,763 – 11,919

Investment from the three other individuals = 273,844

Now, to calculate the percentage of ownership for the three individuals, we'll divide their combined investment by the total investment and multiply by 100:

Percentage of ownership = (Investment from the three other individuals / Total investment) * 100

Percentage of ownership = (273,844 / 285,763) * 100

Percentage of ownership ≈ 95.8%

So, the three other individuals own approximately 95.8% of the company. Since the question asks to round to the nearest tenth, the answer is 95.8%.

The measure of angle m∠XKZ is 218°.

An angle is formed when two straight lines or rays meet at a common endpoint.

The six types of angles are,

To find the measure of angle m∠XKZ, we use the formula below

Formula:

From the question,

Given:

Substitute these values into equation 1 and solve for x

Hence, m∠XKZ = [(15×15)-7] = 218°

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Marking the intersection points on the blueprint with yellow points:

To solve for the intersection points of three lines.

Equation 1: Y = -2X + 14

Equation 2: Y = 3X - 7

Equation 3: Y = 0.5X + 2

To find the intersection point of Equations 1 and 2, use the substitution method.

Substituting Equation 1 into Equation 2:

-2X + 14 = 3X - 7

Adding 2X and subtracting 14 from both sides:

-2X + 2X + 14 = 3X + 2X - 7 - 14

14 = 5X - 21

Adding 21 to both sides:

14 + 21 = 5X

35 = 5X

Dividing both sides by 5:

X = 7

Now substitute X = 7 back into Equation 1 to find the corresponding Y value:

Y = -2(7) + 14

Y = -14 + 14

Y = 0

Therefore, the intersection point of Equations 1 and 2 is (7, 0).

To find the intersection point of Equations 1 and 3, use the same substitution method.

Substituting Equation 1 into Equation 3:

-2X + 14 = 0.5X + 2

Adding 2X and subtracting 14 from both sides:

-2X + 2X + 14 = 0.5X + 2X - 14

14 = 2.5X - 14

Adding 14 to both sides:

14 + 14 = 2.5X

28 = 2.5X

Dividing both sides by 2.5:

X = 11.2

Now substitute X = 11.2 back into Equation 1 to find the corresponding Y value:

Y = -2(11.2) + 14

Y = -22.4 + 14

Y = -8.4

Therefore, the intersection point of Equations 1 and 3 is (11.2, -8.4).

To find the intersection point of Equations 2 and 3, substituting Equation 2 into Equation 3:

3X - 7 = 0.5X + 2

Subtracting 0.5X and adding 7 to both sides:

3X - 0.5X = 0.5X + 2 + 7

2.5X = 9

Dividing both sides by 2.5:

X = 3.6

Now substitute X = 3.6 back into Equation 2 to find the corresponding Y value:

Y = 3(3.6) - 7

Y = 10.8 - 7

Y = 3.8

Therefore, the intersection point of Equations 2 and 3 is (3.6, 3.8).

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Step-by-step explanation:

Area = 12 ft x 12 ft = 144 ft^2

Cost =  144 ft^2  *  $ 4/ ft^2 = $ 576

The y-intercept of the line [tex]y = -5x \ is \ 0[/tex].

The equation of a line in slope-intercept form is given by [tex]$y = mx + b$[/tex], where [tex]$m$[/tex] represents the slope and [tex]$b$[/tex] represents the y-intercept. In the equation [tex]$y = -5x$[/tex], the coefficient of [tex]x \ \ is \ -5[/tex], which represents the slope of the line.

To find the y-intercept, we set [tex]$x$[/tex] equal to [tex]$0$[/tex] and solve for [tex]$y$[/tex]. Substituting [tex]$x = 0$[/tex] into the equation gives us [tex]$y = -5(0) = 0$[/tex].

Hence, the y-intercept of the line [tex]y = -5x \ is \ 0[/tex]. In the graph, the line passes through the origin [tex]$(0,0)$[/tex], indicating that it intersects the y-axis at [tex]$y = 0$[/tex]. This means the line passes through the point [tex]$(0, 0)$[/tex] on the coordinate plane. The y-intercept is the point at which the line crosses the y-axis.

The y-intercept is a crucial point on a line as it helps determine its starting position on the y-axis. In the graph, you can visually observe that the line passes through the origin, confirming the y-intercept of [tex]$0$[/tex].

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Answer:(-4,0) (2,0)

Step-by-step explanation:

the points will be (-4,0) & (2,0) while the parabola is concave up

The research question is whether there is a significant relationship between GPA and the four variables, and the assumption of normality is tested by creating a descriptive statistics table with skewness and kurtosis values to determine if the variables follow a normal distribution.

Research question: Is there a significant relationship between GPA and the four variables (variable names not provided)?

Null hypothesis (H0): There is no significant relationship between GPA and the four variables.

Alternative hypothesis (Ha): There is a significant relationship between GPA and the four variables.

Step 2: Testing Assumptions - Normality

Research question: Is the assumption of normality violated for the four variables?

Null hypothesis (H0): The distribution of the four variables follows a normal distribution.

Alternative hypothesis (Ha): The distribution of the four variables does not follow a normal distribution

Next, you are instructed to create a descriptive statistics table in statistical software to assess normality. The table should include the four variables, along with their skewness and kurtosis values. Once you have created the table, you should paste it into the DAA Template.

After pasting the table, you will interpret the skewness and kurtosis values. Skewness measures the symmetry of the distribution, where a skewness value of 0 indicates perfect symmetry.

Positive skewness indicates a right-skewed distribution, while negative skewness indicates a left-skewed distribution. Kurtosis measures the peakedness or flatness of the distribution, with a kurtosis value of 3 indicating a normal distribution.

Positive kurtosis indicates a more peaked distribution (leptokurtic), while negative kurtosis indicates a flatter distribution (platykurtic).

Based on the skewness and kurtosis values, you will determine whether the assumption of normality is violated or not violated for the four variables.

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The radical expression [tex]\sqrt[4]{x^5}[/tex] written as an expression with a rational exponent include the following: A. [tex]\sqrt{x^{\frac{5}{4} }}[/tex]

In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.

Mathematically, an exponent can be represented or modeled by this mathematical expression;

bⁿ

Where:

By applying the law of exponents for powers to the given radical expression [tex]\sqrt[4]{x^5}[/tex], we would have the following simplified expression:

[tex]\sqrt[4]{x^5}=\sqrt{x^{5 \times \frac{1}{4}}}\\\\\sqrt{x^{5 \times \frac{1}{4} }}}=\sqrt{x^{\frac{5}{4} }}}[/tex]

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[tex]\large \maltese \:{ \underline { \underline{ \pmb{ \sf{SolutioN }}}}} : -[/tex]

we have given ,

★ According to Angle sum property of triangle, the sum of interior angles of a triangle is 180°.

➝ ∠ A + ∠ B + ∠ C = 180°

➝ 60° + 60° + ∠ C = 180°

➝ 120° + ∠ C = 180°

➝ ∠ C = 180° - 120°

➝ ∠ C = 60°

Now,

★ Calculating for x :-

↝ ∠ C + x = 180°

↝ 60° + x = 180°

↝ x = 180° - 60°

↝ x = 120°

Hence, The value of x will be 120°.

Answer:

The major of the exterior angle is 120°

Step-by-step explanation:

In given triangle we have to find the value of exterior angle and in interior of the triangle there are two angles 60 degree and second one is also 60 degree and we have to find value of exterior angle which is x.

So, here we apply exterior angle property which is exterior angle is equal to the sum of the two interior opposite angles. Here, there are two opposite interior angles so we have to add these two and we get the value of exterior angle.

Exterior angle property :-

[tex] \implies \sf \angle60 \degree + \angle60 \degree[/tex]

[tex] \implies\angle120 \degree[/tex]

Some important properties :-

Exterior angle property :- An exterior angle of a triangle is equal to the sum of its interior opposite angles.

Angle sum property :- The total measure of the three angles of a triangle is 180°

Answer: {m∠HLI = m∠ILM}

Examining the figure the option that must be true is

D. m< HLI = m< ILM

The knowledge of angle on a straight line which is 180 degrees is used here,

Using the given angles and the concept of adjacent angles we have that

angle GLH = 150 - 60 = 60

Using angles on a straight line being 180 degrees we have that

angle ILJ = 180 - 60 - 60 - 30 - 15 = 15 degrees

Using adjacent angles

angle ILM = 15 + 15 = 30 degrees

hence we can say that m< HLI = m< ILM

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Answer:

942.48 meters

Step-by-step explanation:

The circumference of a circle can be calculated using the formula:

Circumference = π * Diameter

where π (pi) is a mathematical constant approximately equal to 3.14159.

Given a diameter of 300 meters, we can calculate the circumference as follows:

Circumference = 3.14159 * 300

Circumference ≈ 942.48 meters

Therefore, the circumference of a circular amphitheater with a diameter of 300 meters is approximately 942.48 meters.

The length of ribbon that Hannah has is 57 inches.

The length of the ribbon that Hannah has can be determined by adding the length of each ribbon together. Addition is the process of determining the sum of two or more numbers.

Before the addition can be done, feet has to be converted to inches.

1 foot = 12 inches

1 3/4 x 12

= 7/4 x 12 = 21 inches

3 x 12 = 36 inches  

Total length of the ribbons = 21 + 36  =57 inches

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The amount that Za Kingdom charges for each pizza is $8.

To determine the amount charged by Za Kingdom, we first note that the cost of each pizza plus the delivery fee is $21.

Assuming the basic price to be $8 and the delivery fee of $13, we have the sum of $21. So, for 3 pizzas, we will have 8 times 3 = 24 + 13 = 37

Also, the amount for 10 pizzas will be 8 times 10 = 80 + 13 = 93. So, the price of each pizza is $8.

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Answer:

Step-by-step explanation:

hoop 132

The third point so the hypotenuse of the triangle has a length of 13 could be; (-4, 2)

We are given Pythagoras' theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|[tex]AC|^2 = |AB|^2 + |BC|^2[/tex]

we know that 5, 12, 13 is a Pythagorean triple;

[tex]c^2-a^2=b^2[/tex]

[tex]13^2-5^2=b^2[/tex]

[tex]169-25=b^2[/tex]

[tex]144=b^2[/tex]

12=b

The point so the hypotenuse of the triangle has a length of 13 is (-4, 2)

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The conversion of 2553 base 10 to base 7 is 10305 base 7.

We are given that;

The value= 2553 base 10

Now,

To convert 2553 base 10 to base 7, we need to divide 2553 by 7 repeatedly and write down the remainders. The final answer will be the remainders read from bottom to top. Here are the steps:

Divide 2553 by 7. The quotient is 364 and the remainder is 5. Write down 5.

Divide 364 by 7. The quotient is 52 and the remainder is 0. Write down 0 below 5.

Divide 52 by 7. The quotient is 7 and the remainder is 3. Write down 3 below 0.

Divide 7 by 7. The quotient is 1 and the remainder is 0. Write down 0 below 3.

Divide 1 by 7. The quotient is 0 and the remainder is 1. Write down 1 below 0.

Therefore, by conversion the answer will be 10305 base 7.

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