Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning

The null hypothesis population proportion for this test is 33%. The test is used to determine if the proportion of only children in the special program is significantly different from the proportion for the school district, at an alpha level of 0.05.

Step 1: Define the parameters:

Population proportion (p): 33%

Significance level (α): 0.05

Step 2: Calculate the test statistic:

Sample proportion (p-hat): 130/345 = 0.37

Step 3: Calculate the critical value:

Critical value (α): 0.05

Step 4: Compare the test statistic to the critical value:

Test statistic (p-hat) > Critical value (α): 0.37 > 0.05

The test statistic is greater than the critical value, so the null hypothesis is rejected. Therefore, the proportion of only children in the special program is significantly different from the proportion for the school district.

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The builder will need a total of 372 square feet of countertop.

First, let's convert all dimensions to feet:

The 15' countertops are 15 * 12 = 180 inches long.

The 24" deep countertops are 24 / 12 = 2 feet deep.

The 48" x 36" island countertop is 48 / 12 = 4 feet wide and 36 / 12 = 3 feet deep.

Next, we can calculate the square footage of each countertop:

The 15' countertops are 180 inches long and 2 feet deep, so the square footage is 180 * 2 = 360 square feet.

The island countertop is 4 feet wide and 3 feet deep, so the square footage is 4 * 3 = 12 square feet.

Finally, we can add the square footage of each countertop to find the total square footage:

360 square feet + 12 square feet = 372 square feet

Therefore, The builder will need a total of 372 square feet of countertop.

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The equation is x² - 7x+11 is in form of quadratic equation ax²+bx+c where a = x² , b = -7 and c = 11 .

Option B is correct.

Quadratic equations are second-degree algebraic expressions with the form ax² + bx + c = 0. The word "quadratic" comes from the word "quad," which means square. To put it another way, an "equation of degree 2" is a quadratic equation. Numerous situations call for the use of a quadratic equation.

Factoring  x²-7x+11

The first term is,  x²  its coefficient is  1 .

The middle term is,  -7x  its coefficient is  -7 .

The last term, "the constant", is  11

                                                    x² - 7x  + 11  = 0

When two things are multiplied together and both depend on the same variable, quadratic equations are frequently used. A quadratic equation is used, for instance, when working with area when both dimensions are written in terms of the same variable.

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The equation of the line whose x and y -intercepts are -5/3 and 3/5 respectively is  [tex]9x - 25y + 15 = 0\\[/tex] .

Given,

           The x-intercept of a line = -5/3

            The y-intercept of a line = 3/5

   by substituting values in the intercept form of a line:

                         [tex]-\frac{3x}{5} + \frac{5y}{3} = 1\\[/tex]

     On multiplying the equation by 15 both L.H.S. & R.H.S.

                          [tex]-9x + 25y = 15[/tex]

                      ⇒ [tex]9x - 25y + 15 = 0\\[/tex]

Therefore, the Equation of line is   [tex]9x - 25y + 15 = 0\\[/tex] .

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The total time of homework is represented by T = 2x + 20.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Vlad spent 20 minutes on his history homework and then completely solved X math problems that took two minutes to complete.

The expression can be written as:-

T = 2x + 20 minutes

Here, T is the total time, and x is the number of math problems.

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Los valores de las expresiones polinomicas son:

10*(1/2)^2 - 4*(1/2) = 1/2

(2/3)*(-3/4) - (1/2)*(-3/4)^2 = -25/32

En este problema queremos encontrar los valores de dos expresiones polinomicas.

La primera es:

10*(1/2)^2 - 4*(1/2)

Primero resolvemos el cuadrado del primer termino, esto da:

10*(1/4) - 4*1/2

10/4 - 4/2

Ahora queremos tener el mismo denominador en ambas fracciones, asi reescribimos la primear como:

5/2 - 4/2

1/2

Ese es el valor numerico.

La segunda expression es:

(2/3)*(-3/4) - (1/2)*(-3/4)^2

Primero resolvemos el cuadrado, recordar que esto cancela el signo negativo:

(2/3)*(-3/4) - (1/2)*(9/16)

Ahora tomamos los productos entre fracciones:

(2/3)*(-3/4) - (1/2)*(9/16)

-6/12 - 9/32

Simplificamos ambas fracciones:

-1/2 - 9/32

Escribimos ambas fracciones con el mismo denominador:

-16/32 - 9/32 = -25/32

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y=7 is One of line M's potential equations.

Let L and M be two lines that are perpendicular to each other. Slope of line is given by m=x 2 −x 1/ y 2​ −y 1

If the denominator is zero, or if the value of the x-coordinate is the same at all points, the value of m is undefined. Every point lying on L has the same value of the x-coordinate because L has an undefined slope.

L is a vertical line because it is parallel to the Y-axis.

Lines that are vertical and horizontal are perpendicular to one another.

∴ Line M will be parallel to the X-axis since it is perpendicular to line L.

Every point located on M will have a constant y-coordinate.

∴ m=0 for M.

Thus, y=7 is one of line M's potential equations.

​

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​

When the sum of two numbers is 22, and their difference is 12, the lesser of the two numbers is 5.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

Let numbers be a and b.

a+b=22

a=22-b

b-a=12

b-(22-b)=12

2b-22=12

2b=34

b=17

a=5

The lesser of the two numbers is 5 when the sum of two numbers is 22, and their difference is 12.

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(a) It will take approx 10.2 years to double your principal at 7% interest.

(b) The required rate of interest to double our income in 2 years is approx 44%

(a)    Given,

                  Annual rate of interest = 7%

                    Let the principal be [tex]x[/tex].

         Formulae for compound interest :

                    [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Substituting the value of   [tex]P , r , n[/tex] in above formulae.

                  [tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{0.07}{1})^{1t}\\\\2 = 1.07^{t} \\\\t=\frac{ln(2)}{ln(1.07)\\}\\\\t = 10.244768[/tex]

Therefore, it took approx. 10.2 years to double your principal at 7% interest.

(b) Given,

                  The annual rate of interest = [tex]r[/tex]%

                    Let the principal be [tex]x[/tex].

         Formulae for compound interest :

                         [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

we want our money to double in 2 years

                         [tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{r}{1})^{2}\\\\2 = (1+r)^{2} \\\\\sqrt{2} = 1 + r\\\\r=0.44[/tex]

Therefore, the required Rate of interest is approx 44%.

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The measure of angle 2 is given as follows:

115º.

When two parallel lines are cut by a transversal, the consecutive angles relative to the same vertex are linear pairs, which are supplementary angles.

When two angles are supplementary, the sum of their measures is of 180º, meaning that the equation for this problem is given as follows:

m < 1 + m < 2 = 180º.

Since m < 1 = 65º, the measure of angle 2 is obtained as follows:

m < 2 = 180 - 65

m < 2 = 115º.

The figure giving context to the problem, without scaling, is given at the end of the answer.

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Answer:

B

Step-by-step explanation:

If both signs are the same (++,--), then you subtract.

If the two signs are different(+-,-+), then you add.

As a result, there is an 11/16 chance that there will be at least as many heads as tails.

The branch of mathematics concerned with probability is known as probability theory. Although there are several different interpretations of probability, probability theory treats the concept rigorously mathematically by expressing it through a set of axioms. The probability is a measure of the likelihood that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the likelihood or chance that a specific event will occur. Probabilities can be expressed as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The likelihood that there will be more tails, more heads, or equal numbers of each is 5/16, 5/16, and 6/16, respectively. Therefore, the probability that there will be at least as many heads as tails is 11/16.

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Complete Question:

Harold tosses a nickel four times. The probability that he gets at least as many heads as tails is:

The statement b(14) = 170 is interpreted using the function 1850 - 120w = b to be:

When w is 14 b is equal to 170

The function 1850 - 120w = b  as in the problem is a linear function.

A linear function is one which all the parameters has exponents of one. In the linear function parameters are defined below

b = the output value

w = the input value

120 = slope

1850 = the y intercept

The statement b(14) = 170 means that at input of 14 the out put is 170. this is shown mathematically

1850 - 120w = b

1850 - 120 * 14 = b

1850 - 120w = 170 = b

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The impedance of the circuit in this problem is given as follows:

Z = (26 + 39i)/11.

The impedance of a circuit of Voltage V and Current I is given by the equation presented as follows:

Z = V/I.

The parameters for this problem are given as follows:

Hence the impedance is given as follows:

Z = (12 + 5i)/(3 - 2i).

Removing the complex number from the denominator, we have that:

Z = (12 + 5i)/(3 - 2i) x (3 + 2i)/(3 + 2i)

Z = [(12 + 5i)(3 + 2i)]/11

11 because (3 - 2i)(3 + 2i) = 9 - 2i² = 9 + 2 = 11, as i² = -1.

Hence:

Z = (36 + 39i - 10)/11

Z = (26 + 39i)/11.

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The limit of the function is 2 as x approaches 1.

in mathematics, the limit of a function is the value that the function approaches as the input (or independent variable) gets closer to a certain value. The limit of a function is a fundamental concept in calculus, and is used to study the behavior of a function as the input gets arbitrarily close to a certain value, but not necessarily equal to it. The limit is usually denoted by the symbol "lim" and it is read as "the limit of f(x) as x approaches a is L" where f(x) is the function, a is the value that x approaches and L is the limit.

so we need to find

[tex]\lim_{x \to \ 1}\frac{x^2-1}{x-1}[/tex]  ---(i)

we will observer that the function reduces to [tex]\frac{0}{0}[/tex] form at x=1

factorisation of x² -1 = (x+1)*(x-1)

substituting the value of x² -1 in equation (i) we get

[tex]\lim_{x \to \ 1} x+1[/tex]

=> 2

so the value of [tex]\lim_{x \to \ 1}\frac{x^2-1}{x-1}[/tex] =2

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Complete question:

Find the limit of the function as x approaches 1 .

f(x) = [tex]\frac{x^2-1}{x-1}[/tex]

Part 1

Angles of a quadrilateral add to 360 degrees.

[tex]7x+65+85+105=360\\\\7x+255=360\\\\7x=105\\\\x=15[/tex]

Part 2

If [tex]x=15[/tex], then [tex]7x=105^{\circ}[/tex]. Thus, the angles measuring [tex]7x[/tex] and [tex]105^{\circ}[/tex] are opposite angles since opposite angles of a kite are congruent.

This means the remaining angles, which are the angles measuring [tex]65^{\circ}[/tex] and [tex]85^{\circ}[/tex], are also opposite using the process of elimination.

The end behaviour of the graph shows that the range of the graph ranges from 0 to ∞.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

In the given image the graph is showing a parabola symmetric about the y-axis. The range of the graph is varying from 0 to ∞. The graph's end behaviour indicates that the graph's range is from 0 to.

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Answer:

x = 20

Step-by-step explanation:

Sum of 12, 8, 6, 4 and x is:

S = 12 + 8 + 6 + 4 + x = 30 + x

[tex]\dfrac{2}{5}S = \dfrac{2}{5}\cdot 30 + \dfrac{2}{5}x\\\\=12 + \dfrac{2}{5}x\\\\\\\textrm{But left side is nothing but x}\\\\\textrm{So we get }x = 12 + \dfrac{2}{5}x\\\\\rm{Subtract $\dfrac{2}{5}x$ from both sides}\\\\x - \dfrac{2}{5}x = 12\\\\\dfrac{3}{5}x = 12\\\\x = \dfrac{12 \cdot 5}{3} \\\\x = 20\\\\[/tex]

Verify

12 + 8 + 6 + 4 + 20 = 50

(2/5) x 50 = 20

When given the point-slope form of a line, we first must identify the point and the slope in order to create a graph of the line.

The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept). In order to emphasise the slope and y-intercept of the same line, we can rewrite an equation in point-slope form to be in slope-intercept form, y=mx+b.

Plug the slope and the (x, y) point values into y = mx + b, then solve for b using the substitution method.Point-slope form is represented as y y 1 = m (x x 1), where (x 1, y 1) is the supplied point and m is the given slope.

Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). A graph is usually simple to make.

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The given points can be written in point-slope form as y - 6 = -6(x - 4) and slope intercept form as y  = -6x + 30.

The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept). In order to emphasise the slope and y-intercept of the same line, we can rewrite an equation in point-slope form to be in slope-intercept form, y=mx+b.

Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). A graph is usually simple to make.

Given, x intercept = 5

which means when y = 0, x = 5 i.e. (5, 0)

And given a point (4, 6)

using the two points in slope formula

[tex]$\mathrm{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

[tex]$\mathrm{m = \frac{6- 0}{4 - 5}}[/tex]

m = 6/-1

m = -6

Now, as we have slope, put the data in point-slope form

y-y₁ = m(x -x₁)

y - 6 = -6(x - 4)   ⇒  point-slope form

y - 6 = -6x + 24

y  = -6x + 24 + 6

y  = -6x + 30    ⇒ slope intercept form

Thus, the given points can be written in point-slope form as y - 6 = -6(x - 4) and slope intercept form as y  = -6x + 30.

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Approximately 43.3% of the respondents rated overall television quality with a rating of 50 or below. The closest answer choice is D. 40

What is the range of the data?

The range is the spread of your data from the lowest to the highest value in the distribution. It is a commonly used measure of variability. Along with measures of central tendency, measures of variability give you descriptive statistics for summarizing your data set

The stem-and-leaf display shows that the data ranges from 0 to 100.

The leaves on the stem for the number "5" are 0, 0, 1, 2, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9.

This means that 13 of the respondents rated overall television quality with a rating of 50 or below.

To find the percentage of respondents who rated television quality 50 or below, we need to divide the number of respondents who rated television quality 50 or below (13) by the total number of respondents and multiply by 100.

13/30 * 100 = 43.333...

Hence, approximately 43.3% of the respondents rated overall television quality with a rating of 50 or below. The closest answer choice is D. 40%.

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Answer:

3.725

Step-by-step explanation:

10-6.275

4-0.275

3.725

Answer:

4000-x

Step-by-step explanation:

both accounts - account x = account y

(x+y) - x = y

It’s cAnswer:

Step-by-step explanation:

it’s right

The graph that represents the situation is added as an attachment

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

This means that the graph would be represented using a distance/time graph

Such that the distance would be on the y-axis and the time would be on the x-axis

See attachment for the graph

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The constant change rate will be straight according to the solution.

When the ratio of something like the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope is another name for the constant change rate. For linear functions, the rate of change will be constant.

The change rate (slope) is constant for straight lines (always the same). The rate of change for such lines is constant. With the aid of the resources on this page, you may learn how to calculate slope and change rate as well as the rate of change formula.

Age                        Height

9                                  54

10                                 56

11                                  58

12                                 60

The constant rate of change will be straight. because the given data will form a straight line on the graph.  the rate of change (slope) is constant (always the same). For such lines, the rate of change is constant.

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Answer:

*50

Step-by-step explanation:

Sum of the interior angle

(n - 2) 180

From the question n is 3.

=(3 - 2) 180

=(1) 180

=180

The value of x

x + (x + 5) + (x + 25) 180

=x + x + x + 5 + 25 = 180

=3x + 30 = 180

=3x = 180 - 30

=3x = 150

=3x/3 = 150/3

x = 50

Therefore the value of x is 50.

This accuracy is comparable to shooting an arrow at a target fifty feet away and missing the exact center by the distance;  0.000001 miles

Proportion word problems are simply ways of expressing proportion problems in words. For example we share oranges among three people each receiving 2, 3 and 4 respectively and as such the ratio of the proportion is 2:3:4.

Now, we are told that  after a journey of 300 million miles, the rover Spirit landed on Mars and began sending back information to Earth. It landed only six miles from its target. This is comparable  to shooting an arrow at a target fifty feet away and missing the exact center.

Thus, if the comparable distance missed is x, then we can say that;

x/50 = 6/300000000

x = (6 * 50)/300000000

x = 3/3000000

x = 0.000001

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The equation that represents the town's population is p = 78,000 x 0.97^5.

The equation that represents the town's population is an exponential equation. The general form of exponential equation is f(x) = [tex]e^{x}[/tex]

Where:

The form o f the equation is:

Future population = present population x (1 - rate of decline/100)^number of years

p = 78,000 x (1 - 3/100)^5

p = 78,000x (1 - 0.03)^5

p = 78,000 x (0.97^5)

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Chemical A's rate law may be zero order and is unaffected by the ratio of reactant to product concentrations.

For the zero order reaction, [tex]$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$[/tex]

Rate equation is : Rate [tex]$=\mathrm{k}[\mathrm{A}]^0[\mathrm{~B}]^0$[/tex]

As a result, the pace of the reaction is unaffected by the amounts of reactant and product present.

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In 1 week, Toby and his sister will each have saved $40.

The first step is to form a linear equation that represents the equation in the question. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of a linear equation that represents the amount saved by the siblings is:

Total amount saved = amount they have already saved + (number of weeks x amount saved per week)

Amount saved by Toby = $26 + ($14 x w)

$26 + $14w

Amount saved by his sister = $28 + ($12 x w)

$28 + $12w

When the siblings have saved the same amount of money, the two above linear functions would be equal:

$26 + 14w = $28 + $12w

In order to determine the value of w, take the following steps:

Combine and add similar terms:

$14w - $12w = $28 - $26

2w = 2

Divide both sides of the equation by 2

w = 2 / 2

w = 1 week

Total amount that would have been saved = $28 + $12(1)

$28 + 12 = $40.

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