In a recent poll, 230 people were asked if they liked dogs, and 90% said they did. Find the margin of error of this poll, at the 99% confidence level.

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = [tex]a^x[/tex]

Where a>0 and a is not equal to 1.

x is any real number.

If the variable is negative, the function is undefined for -1 < x < 1.

Here,

“x” is a variable

“a” is a constant, which is the base of the function.

The examples of exponential functions are:

f(x) = [tex]2^x[/tex]

f(x) = 1/ [tex]2^x[/tex] = [tex]2^-x[/tex]

f(x) =[tex]2^(x+3)[/tex]

f(x) = [tex]0.5^x[/tex]

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In the lens maker's formula, R1 and R2 represent the radii of curvature

The lens maker's method specifies the association among the focal length, refractive index, and curvature radii of a lens's two surfaces. It's a method that lens makers employ to make lenses with a particular power out of the glass with a particular refractive index.

R1 and R2 in the lens manufacturer's formula stand for the radii of curvature of the two surfaces of a lens. R1 and R2 are the radiuses of the surfaces that face the item being imaged and the surface that faces the image, respectively. A lens's focal length is calculated using a formula based on the lens's surface curvature and the material's refractive index.

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The difference's mathematical equivalent is minus (-). In the subtraction statement, minuend is the initial digit.

Mathematical difference is the outcome of one of the key operations, which is the subtraction of two numbers. It reveals the degree to which one number deviates from the other.

In math, the goal of calculating the difference is to determine how many numbers are present between the two supplied numbers. The difference's mathematical equivalent is minus (-).

In the subtraction statement, minuend is the initial digit. The second number in the subtraction sentence is called subtract, and the outcome is the difference between the two integers.

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Construct a dilate, with scale factor 2, of a triangle using only a ruler and compasses.

The center of dilation—the location from where the picture is shrunk or expanded—is necessary to build a dilation. A scale factor, or the quantity that controls how big or tiny the new picture will be, is also necessary. If the scale factor is more than 1, the new picture will be bigger than the original image, creating an enlargement. We see a decrease if the scale factor is less than 1, as the new picture will be smaller than the original image.

Step-1

Let's dilate triangle PQR by a scale factor of 2 with a center of dilation at point C.

Step-2

First, we will use a straightedge to connect the center of dilation C to each vertex. We are going to extend those lines across the whole page.

Step-3

Next, we'll place the point of the compass on the center of dilation C and the pencil on vertex Q and measure that distance.

Step-4

Now, without changing the size of the compass, we  will move the point of the compass to vertex Q, and make a mark on the line that is extended through Q.

Step-5

Notice that since we measured the distance from C to Q and then used that same distance to mark the line, we have now created a new point that is twice the distance from C that Q was.

We now repeat the process for each of the other vertices of the triangle.

Step-6

These marks represent the vertices of our dilated image. We often use the same letters with an apostrophe to show that it is the corresponding vertex.

Step-7

Finally, we use the straightedge to connect all of the new vertices.

Now,See how triangle P ′ Q ′ R ′  is tw ce the size of the original triangle.

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Joe's hourly rate before his raise is represented by the expression 10.25 - r, where r is the amount of the raise.

Joe's hourly rate before his raise is represented by the expression 10.25 - r, where r is the amount of the raise. The expression 10.25 - r represents the amount of Joe's hourly rate before his raise. This is because when we subtract r from 10.25, we are essentially taking away the raise that Joe received, which leaves us with the amount of his hourly rate before he received the raise. In other words, Joe's hourly rate before his raise is 10.25 minus the amount of the raise. This expression is used to calculate the amount of Joe's hourly rate before his raise.

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A triangle with two equal side lengths is known as an isosceles triangle. The angle of an isosceles triangle is 70 degrees.

A triangle is a three-sided geometry shape with 3 vertices. The internal angle of the triangle, which is 180 degrees, is built. It means that a triangle's internal angles sum to 180 degrees.

A triangle with two equal side lengths is known as an isosceles triangle. The vertex angle is the leftover angle that results from subtracting the two specified angles from 180 degrees. The two angles between it base and equal sides are identical in magnitude.

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Assumption 1: [tex]\triangle ABE \sim \triangle ACD/tex]

[tex]\frac{x}{10}=\frac{3}{15} \implies x=2[/tex]

Assumption 2: [tex]\triangle ABE \sim \triangle ADC[/tex]

[tex]\frac{x}{15}=\frac{3}{10} \implies x=4.5[/tex]

Classifying Triangle by Sides or Angles: Equilateral triangle, Isosceles triangles, Scalene triangle, Right triangle, Obtuse triangle, Acute triangle, Equiangular triangle.

A triangle is said to be equilateral or equiangular if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.

A triangle with two sides that have the same length is said to be isosceles. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

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Answer:

55°

Step-by-step explanation:

so the total should be 360, so if 2 angles are 125 (360-250=110) then the leftover 110 has to be split into 2 angles, which is 55

Answer:

Jon Marc knows the radius of one flower bed is 6.5 feet and the diameter of the other is 30 feet. a. Find the area of each flower bed. Use 3.14 for π.

Step-by-step explanation:

The end behavior of the graph is that it approaches negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

This can be seen by examining the equation of the function. If the leading coefficient is negative, then the graph will be shifted down. As x approaches negative infinity, the term with the highest degree will grow exponentially and dominate the equation, causing the graph to approach negative infinity. Similarly, as x approaches positive infinity, the highest degree term will dominate the equation again, and the graph will approach positive infinity. For example, if the function is f(x) = -2x^4 + 0.5x + 8, the end behavior will be -∞ as x approaches -∞ and +∞ as x approaches +∞. This is because the highest degree term is -2x^4, which has a negative leading coefficient, so the end behavior of the graph will be shifted down. As x approaches negative infinity, the -2x^4 term will dominate the equation, causing the graph to approach negative infinity. Similarly, as x approaches positive infinity, the -2x^4 term will again dominate the equation, causing the graph to approach positive infinity.

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The given quadrilateral ABCD is a rectangle, and the value of x is -2.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. By connecting four non-collinear locations, it is created. Quadrilaterals always have a total internal angle of 360 degrees.

A quadrilateral with parallel sides that are equal to one another, and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Given that ABCD is a rectangle.

In rectangle all the angles are equal, hence equate the two angles as follows:

4x + 8 = 6x + 12

6x - 4x = 8 - 12

2x = -4

x = -2

Hence the value of x is -2.

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Answer:

The mass of Jupiter is about 11.8 times the mass of Venus.

Step-by-step explanation:

Yes, a dilation with a scale factor of 1 /3 a reduction.

What is a scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Here, w

We have to determine if dilation with a scale factor of 1 /3 a reduction.

We concluded that a dilation with a scale factor between 0 and 1 is a reduction because the image will decrease in size.

On the other hand, a dilation with a scale factor greater than 1 is an enlargement, where the image increases in size.

Hence, a dilation with a scale factor of 1 /3 a reduction.

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According to the information of the table, the value of B in the table is 20, So the option is C .

To calculate the value of B in the table we need to analyze the information that is available in the table to understand how to find this value. Once we understand the information we can perform the following mathematical operation calculating the constant of proportionality:

Constant of proportionality = Whole / Part

Constant of proportionality = 40 / 28

Constant of proportionality = 1.4285714

On the other hand, to find the value of B, we must perform the following operation:

Whole = Part × Constant

Whole = 14 × 1.4285714

B = 20

According to the above, the correct answer is the value of B equals 20, so the correct option is C.

Note: This question has the information disorganized and incorrect and is not understood. Below is the information organized for a better understanding:

A three-column table is given.

Part: A C D

Part: 14 28 63

Whole: B 40 90

What is the value of B in the table?

50

36

20

12

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The x coordinate of one of the endpoints of the dilated segment is; x = 8

In the case when a coordinate point (x, y) should be dilated by a scale factor k, it means that the coordinate would be (kx, ky).

Now, since the coordinate point of dilation is given as (4 ,1), it means that if the coordinate is dilated by a factor of 2, then the new coordinate points should be at (2(4), 2(1))

= (8, 2)

Therefore we can conclude that that will be a coordinate of one of the endpoints of the dilated segment and the x-coordinate here is 8

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Answer: A vertical line has an undefined slope, so we cannot use the slope-intercept form (y = mx + b) to write the equation of the line. Instead, we can use the point-slope form (y - y1 = m(x - x1)) where the slope m is undefined and we have a point (x1,y1) on the line.

Since the line goes through the point (8,4), we can use the point (8,4) in the point-slope form:

y - 4 = undefined(x - 8)

We can simplify this equation by dropping the undefined slope and replacing it with a variable:

y = kx + b

Where k is the slope and b is the y-intercept.

The equation of the vertical line that goes through the point (8,4) is x = 8

It's worth noting that the x-coordinate of a vertical line doesn't change, thus it's equal to a constant value and the equation for a vertical line is of the form x=k where k is a constant.

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

The equation of a vertical line is in the form:

x = anumber

You were given the point (8,4) which is in the form (x,y). So x is 8 and y is 4.

x is 8

x = 8

Answer: 7 and 1/2

Step-by-step explanation:

When dividing a fraction by a whole number you could turn the whole number into a fraction:

5 = 5/1

Once you turn the whole number into a fraction you then do the keep, change, flip, method

you would keep 5/1 as it is and change the divide sign to the multiplication sign the flip 2/3 to 3/2:

5/1 x 3/2

then you just multiply across

5/1 x 3/2 = 15/2

and 15/2 could be simplified to 7 and 1/2

15/12 is the right representation of  5 divided by 2/3 as a fraction.

To divide a number by a fraction, you can multiply the number by the reciprocal of the fraction. In this case, to divide 5 by 2/3, you can multiply 5 by the reciprocal of 2/3.

Reciprocal of 2/3 = 3/2

So, 5 divided by 2/3 can be written as:

5 * (3/2)

To simplify this, you multiply the numerators together and the denominators together:

(5 * 3) / (2 * 1) = 15/2

Therefore, 5 divided by 2/3 is equal to 15/2 as a fraction.

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Answer:

Step-by-step explanation:

When doing the calculations it is seen that the ordered pair that would not be a solution would be number 2: (4,9) because if the X is 4 then the Y would be 13 and not 9.

The answers after calculations↓

(0,5)

(4,13)

(-2,1)

(2,9)

The balance of the account with the given data is given as follows:

$1,212.62.

The amount of money earned, in compound interest, after t years, is given by:

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

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

P = 900, r = 0.05, n = 4, t = 6.

Meaning that the balance is given as follows:

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

[tex]A(t) = 900\left(1 + \frac{0.05}{4}\right)^{4 \times 6}[/tex]

A(6) = $1,212.62.

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It is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm because the sum of two sides(2.5 cm and 4.5 cm) are smaller than three sides(8 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 2.5 and 4.5

2.5 + 4.5 < 8

7 < 8

Now we add 2.5 and 8

2.5 + 8 > 4.5

10.5 > 4.5

Now we add 4.5 and 8

4.5 + 8 > 2.5

12.5 > 2.5

It is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm because the sum of two sides(2.5 cm and 4.5 cm) are smaller than three sides(8 cm).

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When the length, breadth, and height are provided as 8 inches, 7.5 inches, and 6 inches, respectively, the rectangular prism's total surface area is 360 inches2.

Surface area is a measure of how much space an object's surface takes up overall. The total area of a three-dimensional shape's surroundings is its surface area. Surface area refers to the total surface area of a three-dimensional shape. You may compute the surface area of a cuboid with six rectangular faces by adding together their individual areas. Alternatively, you can use the following formula to name the box's dimensions: Surface (SA) = 2lh plus 2lw plus 2hw. A three-dimensional shape's surface area is calculated as the total amount of space it occupies (a three-dimensional shape is a shape that has height, width, and depth).

given

rectangle prism has a length of 8 inches and a width of 7.5 inches.

6 inches is the rectangular prism's height.

SA equals two square units of (lh + wh + lw).

A=360 inches2

When the length, breadth, and height are provided as 8 inches, 7.5 inches, and 6 inches, respectively, the rectangular prism's total surface area is 360 inches2.

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We estimate the mean of a population that is normally distributed, has an unknown standard deviation, and small n, because it allows us to make better predictions about the population mean than the standard normal curve.

True, True, True, False, True, True.

The formula for the t-distribution is given by:

t = (x-μ)/(s/√n)

Where x is the mean of the sample, μ is the mean of the population, s is the sample standard deviation, and n is the sample size.

The t-distribution approaches the standard normal distribution as n increases because the denominator, s/√n, gets smaller, making the t-distribution smaller. As n increases, the tails in the t-distribution become "fatter" because the denominator in the formula gets smaller and the resulting t-distribution has a wider range of values.

The shape of the t-distribution depends on its degrees of freedom, which is the number of values in the sample minus one. The more degrees of freedom, the more the t-distribution resembles the standard normal curve.

We use the Student's t-distribution when we estimate the mean of a population that is normally distributed, has an unknown standard deviation, and small n, because it allows us to make better predictions about the population mean than the standard normal curve.

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Answer:

    The x-intercept: The number of minutes it takes for the container to empty

The y-intercept: The number of gallons in the container before the drain is open

Hope this does helps!!

Step-by-step explanation:

The new function's mathematical formula f(x) is 7*.

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Answer: the answer is f(x)=2^(5x)

Step-by-step explanation:

step 1: do the math and divide numbers by more numbers.

Step 2: then add the exponent to another exponent which is a variable.

step 3: then combine the common denominators and you have your answer!

How many crickets did Greta feed Lizzy?

Answer:

56

Step-by-step explanation:

For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Since Gretta fed Draco 77 crickets just do:

77 ÷ 11

= 7

Then:

8 x 7

= 56

You're welcome

The angle m∠7 corresponds to angle m∠3 which is vertically opposite the angle m∠1, and so the measure of the angle m∠7 = 118°

angles m∠1 and m∠3 are vertically opposite angles and are said to be equal so;

m∠1 = m∠3 = 6x - 20

angles m∠3 and m∠7 are corresponding angles and are said to be equal so;

m∠3 = m∠7 = 6x - 20

angles m∠7 and m∠8 lie on a straight line so;

6x - 20 + 4x - 30 = 180°

10x - 50° = 180°

10x = 180° + 50° {collect like terms}

10x = 230°

x = 230°/10 {divide through by 10}

x = 23

Therefore since the value of x is 23, then the measure of the angle m∠7 = 6(23) - 20, which result to 118°

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Answer:

C

Step-by-step explanation:

use 0 and 3 for example:

replace x with 0 give you 2*0=0

add 0 with 3 and you get 3

On solving the provided question, we can say that the equation of the following will be y = x-$25

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the equation will be y = x-$25

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The probabilities for this problem are given as follows:

a) The first free throw that he makes is the fourth shot: 0.0430 = 4.30%.

b) The first is the second or the third: 0.3459 = 34.59%.

c) He misses the first three: 0.0741 = 7.41%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The probability of missing the first three is P(X = 0) when n = 3, hence:

0.42³ = 0.0741 = 7.41%.

For item a, the probability is the above probability multiplied by 0.58 (making the fourth), hence:

0.58 x 0.0741 = 0.0430 = 4.30%.

For the first being the second or the third, the probabilities are given as follows:

Hence:

0.2436 + 0.1023 = 0.3459 = 34.59%.

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