Solution
We can start with the pythagorean theorem:
(leg 1)² + (leg 2)² = (hypotenuse)²
Substitute the values we know.
15² + x² = 32²
Solve for x.
X =

All exponential functions go through the point (0,1) because the value of x when it equals to 0, in the general form of exponential function f(x) = [tex]a^x[/tex], results in [tex]a^0[/tex] = 1, which is why all exponential functions have the point (0,1) on their graph.

All exponential functions go through the point (0,1) because of the properties of exponential functions. The general form of an exponential function is f(x) = [tex]a^x[/tex], where a is a positive constant. When x = 0, the function evaluates to [tex]a^0[/tex] = 1, which is why all exponential functions have the point (0,1) on their graph.

Another way to understand this is that the exponential function is defined as the function that describes how a quantity grows or decays at a fixed percentage rate over time. The function f(x) = [tex]a^x[/tex], where a is a constant greater than 0 and less than 1, describes the decay of a quantity over time. For example, if the interest rate is 10%, the value of a = 0.1 and the function f(x) = [tex]0.1^x[/tex]. When x = 0, the function evaluates to [tex]0.1^0[/tex] = 1, which means that the initial value of the quantity is 1.

It's important to note that the point (0,1) is called the y-intercept, and it is a special point in the graph of exponential functions, and it's always present in the graph of exponential functions.

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The complete Question is:

Why do all exponential functions go through point(0,1)?

Answer:

B is not true, the other options are correct.

Step-by-step explanation:

B. To subtract powers with the same base, divide the exponents. is not true. The correct operation is to subtract the exponents.

A. To divide powers with the same base, subtract the exponents. is true. When dividing two powers with the same base, you subtract the exponents. For example, (x^3) / (x^2) = x^(3-2) = x^1

C. To multiply powers with the same base, add the exponents. is true. When multiplying two powers with the same base, you add the exponents. For example, (x^3) * (x^2) = x^(3+2) = x^5

D. To raise the power to a power, multiply the exponents. is true. When raising a power to another power, you multiply the exponents. For example, (x^3)^2 = x^(3*2) = x^6

So, B is not true, the other options are correct.

Jamine will earn $193.75.To give us an accurate amount, we round the answer up to the hundredth place, which gives us our final amount of $193.75.

To give us an accurate amount, we round the answer up to the hundredth place, which gives us our final amount of $193.75.

1. Take the hourly rate of $15.50 and multiply it by the number of hours worked, 12.5, to get the total amount earned.

2. $15.50 x 12.5 = $193.75

3. Round the answer up to the hundredth place for a total of $193.75

Jamine charges $15.50 per hour to baby-sit. In one weekend, he baby-sat for 12.5 hours. To calculate how much money he will earn, we take the hourly rate of $15.50 and multiply it by the number of hours worked, 12.5. This gives us a total of $193.75. To give us an accurate amount, we round the answer up to the hundredth place, which gives us our final amount of $193.75.

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Answer:

Adam is currently 4 and Eve is currently 9

Step-by-step explanation:

its right

Answer:

3

Step-by-step explanation:

Dilating a shape will proportionately affect its side lengths.

To find the scale factor between the given triangles, take one side on the larger triangle and divide it by the corresponding side on the smaller triangle. I will divide the triangles' top sides (24 and 8).

[tex]\textrm{scale factor} = \dfrac{24}{8} = 3[/tex]

So, the scale factor used was 3.

Answer:

78 square units

Step-by-step explanation:

Length of the rectangle:

Width of the rectangle:

The area of a rectangle can be calculated by multiplying the length by the width.  Therefore, the equation for the area of the rectangle with the given length and width is:

[tex]\begin{aligned}\implies \textsf{Area}&=\sf length \times width\\& = f(x) \cdot g(x)\\&=(x+3)(6x-5)\\&=6x^2-5x+18x-15\\&=6x^2+13x-15\end{aligned}[/tex]

To find the area of the rectangle if x = 3, substitute x = 3 into the found equation:

[tex]\begin{aligned}\implies \textsf{Area}&=6x^2+13x-15\\&=6(3)^2+13(3)-15\\&=6(9)+13(3)-15\\&=54+39-15\\&=93-15\\&=78\;\; \sf square \; units\end{aligned}[/tex]

Therefore, the area of the rectangle is 78 square units.

First add 15 to 93 which equals 108.
-9h=108

/-9     /-9     divide both sides by -9

h=-12

[tex]-9h-15=93[/tex]

Add 15 to both sides:
[tex]-9h-15+15=93+15[/tex]

[tex]-9h=108[/tex]

Divide both sides by -9:

[tex]\dfrac{-9h}{-9} =\dfrac{108}{-9}[/tex]

[tex]\fbox{h = -12}[/tex]

38/100×350=38/10×35=38/2×7

=266/2=133

Answer: 133

Step-by-step explanation:

38% of 350

You can use is/of=%/100

Plug-in points

is/350=38/100 ----> 133

Remainder Theorem is a method for polynomial division using Euclidean geometry.

Algebraic expressions called polynomials include constants and indeterminates.

Polynomials can be thought of as a type of mathematics.

Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

A specific kind of expression is a polynomial.

A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Hence, Remainder Theorem is a method for polynomial division using Euclidean geometry.

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Option G is the correct one. The table represents the non proportional linear relationship with equation y = 3x - 3.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given values are,

x = 4, then y = 9

x = 5, then y = 12

x = 2, then y = 3

This is clearly not a proportional relation since 4/9 ≠ 5/12

Let y = 3x - 3

If x = 4, then y = (3 × 4) - 3 = 9

If x = 5, then y = (3 × 5) - 3 = 12

If x = 2, then y = (3 × 2) - 3 = 3

This equation holds.

Hence the true statement is option G.

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The amount of yogurt that Karolina used when making 800 ml of salad is 300 ml.

Ratio is  used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another quantity. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.

A salad dressing is made by mixing yoghurt and mayonnaise in the ratio

3:5.

For 800 ml of salad dressing:

Amount of yoghurt = (3 / (3 + 5)) * 800 ml

Amount of yoghurt = 300 ml

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The answer is 300 ml!!!

A polynomial f(x) has a factor (x-a) if and only if f(a) = 0, according to the factor theorem. It's one of the techniques for factoring a polynomial.

Since, the response above already covered the theorem's formulation.

Here, we shall demonstrate the factor theorem formula, which allows us to factor the polynomial.

When the polynomial f(x) is divided by (x-c), f(c) equals 0.

Remainder Theorem demonstrates that f(x)=(x-c)q(x)+f (c)

where the quotient polynomial is q(x) and the target polynomial is f(x).

Because f(c) = 0, f(x) = (x-c)q(x)+f (c)

(x-c)q(x)+0 f(x) = (x-c)q (x)

Therefore, the polynomial f's factor (x-c) exists (x).

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Answer:

x=24.8

Step-by-step explanation:

24.8/4 = 6.2 and 6.2 times 4 is 24.8

Answer:

--------------------------

Given system:

Solve by substitution:

Find y:

The matching choice is A.

A rational expression that excludes the values 2 and -2 would be (any polynomial)/(x² - 4).

A rational expression is simply a fraction with polynomials as the numerator and denominator. When the denominator of a rational expression equals 0 (because division by 0 is undefined), you get excluded values.

The numerator can be any number. It could be 1, 10000x + x² or anything that comes to mind. Any polynomial in the numerator will not produce an excluded value. We get ( x - ( - 2 ) ) and ( x - 2 ) by excluding -2 and 2. We multiply them together: ( x + 2 ) ( x - 2 ) = x² - 4.

= (any polynomial)/(x² - 4)

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Finding the coordinates of an object in an image involves using image processing techniques such as object detection and image segmentation.

Object detection involves identifying the presence of an object in an image, while image segmentation involves isolating the object in the image.

Once the object is identified and isolated, its coordinates can be determined by using the position of the object's bounding box or contour.

Bounding box is a rectangular box that surrounds the object, its coordinates can be determined by the position of its top-left corner and bottom-right corner.

Contour is the boundary of the object, its coordinates can be determined by the points that are part of the boundary.

Computer Vision libraries such as OpenCV, Tensorflow or PyTorch can be used to perform object detection and image segmentation. They also provide pre-trained models which can be used for object detection and image segmentation without the need to train a model from scratch.

In conclusion, finding the coordinates of an object in an image requires using image processing techniques such as object detection and image segmentation to identify and isolate the object, and then determining its coordinates by using the position of the object's bounding box or contour.

This process can be aided by using Computer Vision libraries such as OpenCV, Tensorflow or PyTorch.

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5.33 trays must be sold to cover all costs including labor.

Cost means a price that must be paid for something or a sacrifice.

Given that,

Profit on each tray sold excluding labor cost = $35-$14 = $21

Thus, the Total labor cost for making a party tray for a day = Total labor hours * wages per hour* No. of labors = $7 * $8*2 = $112

The number of trays that must be sold to cover the cost will be = Total labor cost for making party tray for a day/ Profit on each tray sold excluding labor cost = $112/$21 = 5.33

Therefore, 5.33 trays must be sold to cover all costs including labor.

Complete question: Party trays which cost $14.00 to make not including labor are sold for $35.00. if two people work 8-hour shifts making the trays at $7.00 per hour, how many trays must be sold to cover all costs including labor?

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Mr. And Mr. Lopez will make a vegetable garden in their two rectangular plot. They decided to use 3/4 of one plot for peachy and the ret for lettuce. 3/2 part of the plot will be use for lettuce.

Rectangular plot:

To build a house, we are given a rectangular plot with length and façade dimensions. By law, there must be a minimum amount of space in front and back, as well as space on the other side.

Area can be defined as the amount of space covered by a plane of a particular shape. It is measured in "number" of square units (square centimeters, square inches, square feet, etc.). The area of ​​a rectangle is the number of unit squares that fit in the rectangle. Examples of rectangles are flat surfaces such as laptop monitors, chalkboards, and painting canvases. We can use the rectangle area formula to find the space occupied by these objects. For example, consider a rectangle that is 4 inches long and 3 inches wide.

According to the Question:

To find the number of garden plots planted with peachy, just multiply them.

Mathematical Sentence:

⇒ 2 × 3/4

⇒ 6/4 = 3/2 = 1.5

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Using equations, the number of small boxes shipped is 15 while the number of large boxes shipped is 7.

An equation is described as a mathematical statement of the equality of two or more mathematical expressions.

Equations use the equation sign (=) to show that the expressions are equivalent or equal.

The volume of each small box = 7 ft³

The volume of each large box = 20 ft³

The number of small boxes = x + 8

The number of large boxes = x

The total volume of all the boxes = 245 ft³

The total volume of the 8 additional small boxes = 56 ft³ (8 x 7 ft³)

The remaining volume of the boxes after subtracting the volume of the 8 additional small boxes = 189 ft³ (245 - 56)

7x + 56 + 20x = 245

7x + 20x = 189

27x = 189

x = 7 (189/27)

The number of small boxes shipped, x + 8 = 7 + 8 = 15 boxes

The number of large boxes shipped, x = 7 boxes

Check:

Small boxes = 15 x 7 ft³ = 105 ft³

Large boxes = 7 x 20 ft³ = 140 ft³

Total               22              245 ft³

Thus, the paper company shipped 15 small boxes with 7 large boxes.

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Answer:

75%

Step-by-step explanation:
part/whole(100)

360/489 = .75

.75(100) = 75%

The percent of [tex]\frac{480}{360}[/tex] equals to 75%

The probability of A or B would be 0.3269. Probability can be used to make predictions and make decisions based on uncertain information in fields such as finance, engineering, and science.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event will not occur and 1 indicating that an event will definitely occur. Events with probabilities closer to 1 are considered more likely to happen, while events with probabilities closer to 0 are considered less likely.

Since A and B are mutually exclusive events, they cannot occur at the same time. Therefore, the probability of A or B is the sum of their individual probabilities.

p(A or B) = p(A) + p(B) = 0.07692 + 0.25 = 0.32692

To four decimal places, the probability of A or B is 0.3269.

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Solving provided question, we can say that the correlation coefficient for data shown will be as [tex]\sqrt{x} =\sqrt{y} = > \sqrt{x^2} = \sqrt{y^2}[/tex]

In statistics, the Pearson's correlation coefficient, often known as Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a metric for the linear correlation between two data sets. A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another variable's value. The values rise or fall jointly for variables with positive correlation. When evaluating the strength and direction of linear relationships between two sets of variables, correlation coefficients are used. If both variables are regularly distributed, use Pearson's correlation coefficient; if not, use Spearman's.

here,

the correlation coefficient for data shown will be as

[tex]\sqrt{x} =\sqrt{y} \\\sqrt{x^2} = \sqrt{y^2}[/tex]

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The sum of the first six terms of the given series is 31.99.

A list of elements or objects that have been arranged sequentially is referred to as a sequence.

The total of all the terms in a sequence can be used to very broadly define a series. All of the terms in the sequence must, however, clearly relate to one another.

The given sequence is 4, 10, 2.5, 0.625, . . .

Every successive term in given series is divided by 4, and the so the first six terms of the series are:

[tex]\frac{40}{4} = 10\\ \\ \frac{10}{4} = 2.5 \\\\\frac{2.5}{4}= 0.625\\ \\\frac{0.625}{4} = 0.156\\\\\frac{0.156}{4}= 0.039\\\\\frac{0.039}{4}= 0.0097[/tex]

Also, every even term in the series is subtracted from the previous term.

Adding all the given terms we have:

[tex]40-10+2.5-0.625+0.156-0.039 = 31.99[/tex]

Hence the sum of the first six terms of the series is 31.99.

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The amount of money Company B charge for x miles than Company A when Company A charges $35.50 and 11cent per mile. Company B charges $60.50 and 12cent per mile is $40 and 1 x cents.

The concept that will be used is the concept of substraction and unit conversion.

Company A  =$35.50 and 11 cent per mile

Company B  =  $60.50 and 12 cent per mile

(Amount of money from Company B -Amount of money from Company A)

($75.50 and 12 cent - $35.50 and 11 cent )

= $40.00 and 1 cents per mile.

Then to know the amount the Company B charge for x miles than Company A which is  x miles, we multiply $40.00 and 1 cents by x miles.

Since $1 =100

Then we can convert dollars to cents by multiply it by 100

which is (7562 - 3561 cents) = 4001 cents.

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Answer:

The result can be shown in multiple forms.

Exact Form: m = 49/2  

Decimal Form: m = 24.5

Mixed Number Form: m = 24 1/2 (twenty-four and a half as a fraction)

Step-by-step explanation:

1. Divide each term in 2 m = 49 by 2:

2m/2 = 49/2

2. Simplify the left side.

m = 49/2

The result can be shown in multiple forms.

Exact Form: m = 49/2  

Decimal Form: m = 24.5

Mixed Number Form: m = 24 1/2 (twenty-four and a half as a fraction)

The 49 increased by twice a number m is 49+2m

Given data :

49+2m

Increase means “go up” which is another way to say addition

Twice means “two times” or “doubled”

A number would be a variable since it’s unknown

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The volume of air in the spherical ball is [tex]\frac{4}{3}\cdot \pi\cdot 3^3\cdot 10^6[/tex]. So the option A is correct.

In the given question, we have to find the volume of air in the spherical ball.

A sphere's capacity is measured by its volume. It is the area the sphere calls home. Cubic units are used to express the volume of a sphere. The sphere has a three-dimensional, rounded shape. Its shape is defined by its three axes, which are the x, y, and z axes.

Since the cross-section of the sphere is a circle, the volume in this situation is dependent on the radius's diameter. A sphere's surface area is the area or region of its outside. The following formula can be used to determine the volume of a sphere whose radius is "r":

V = [tex]\frac{4}{3}\pi r^{3}[/tex]

As given r = 3·10^2. So,

V = [tex]\frac{4}{3}\pi (3\cdot 10^2)^{3}[/tex]

V = [tex]\frac{4}{3}\cdot \pi\cdot 3^3\cdot 10^6[/tex]

V = [tex]4\cdot \pi\cdot 3^2\cdot 10^6[/tex] cm^3

Hence, the option A is correct.

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The complete question is given below:

The pair in the solution of the equation 2x-3y = 7 is (5,1).

The set of all values that, when substituted for unknowns, make an equation true is known as the solution.

A specific location on the graph is the solution of a linear equation in two variables, where ax+by = c, meaning that when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values equals c. There are essentially an endless number of solutions to a linear equation with two variables.

Now in the question,

To find the pair of solutions of equation 2x - 3y = 7, we satisfy all the pairs one by one in the given equation

1. Putting the value of (x, y) as (0,2) in the equation we get-

2*0 - 3*2 = 7 ⇒ -6 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

2. Putting the value of (x, y) as (2,-3) in the equation we get-

2*2 - 3*-3 = 7 ⇒ 13 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

3. Putting the value of (x, y) as (5,1) in the equation we get-

2*5 - 3*1 = 7 ⇒ 7 = 7

Therefore LHS = RHS

Hence it is the solution to the equation.

4. Putting the value of (x, y) as (1,5) in the equation we get-

2*1 - 3*5 = 7 ⇒ -13 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

Thus (5,1) is the solution of the equation.

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The value of the third side of the triangle, that is x is 24.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

The given triangle is a right- angles triangle.

Use the Pythagorean theorem to find the third side of the triangle.

The Pythagorean theorem is given by the following formula:

a^2 + b^2 = c^2

10^2 + b^2 = 26 ^2

100 + b^2 = 676

b^2 = 676 - 100

b^2 = 576

b = 24

Hence, the value of the third side of the triangle, that is x is 24.

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