If a shopkeeper gives you a 15%discount on shirt of having total price 50. What price will you give after discount ?

The simplified form of the given expression 4.03x + 10x⁶, is [tex]x(4.03x + 10x^5)[/tex]

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given that an expression 4.03x + 10x⁶

We need to simplify it,

4.03x + 10x⁶

Applying the exponent rule: [tex]a^{b+c}=a^ba^c[/tex]

[tex]x^6=x^5x[/tex]

[tex]=4.03x+10x^5x[/tex]

Factor out common term x,

[tex]=x\left(4.03+10x^5\right)[/tex]

Hence, the simplified form of the given expression 4.03x + 10x⁶, is [tex]x(4.03x + 10x^5)[/tex]

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Answer:

Surface Area is the space occupied by a two-dimensional flat surface is called the area.

Total surface area is the area including the base(s) and curved part(s).

Calculating Surface Area:

To find the surface area of a shape, we need to find the measurement (in this case, centimeters) of each face/side and add them together.

Volume:

The amount of space an object/3D shape occupies. (Ex: A circle does not have volume, a sphere, however, does.)

Calculating Volume:

Volume = the length times the width times the height. (Volume = length x width x height)

The missing length of the geometric system of right triangles is equal to 15.833 centimeters.

Herein we find the case of a geometric system formed by ten right triangles, whose missing length can be found by means Pythagorean theorem and trigonometric functions, whose definitions are shown below:

Pythagorean theorem

r = √(x² + y²)

Trigonometric function

cos θ = x / r

Where:

Now we proceed to determine the missing length:

First triangle:

x = 8 / cos 28°

x = 9.061

x' = 9.061 - 2.5

x' = 6.561

Second triangle

x = (6.561 + 3.6) · cos 11°

x = 9.974

x' = 9.974 - 2

x' = 7.974

Third triangle

x = √[(7.974 + 2.9)² - 3.8²]

x = 10.188

x' = 10.188 - 1

x' = 9.188

Fourth triangle

x = (9.188 + 3.2) · cos 43°

x = 9.060

x' = 9.060 - 1

x' = 8.060

Fifth triangle

x = (8.060 + 1) / cos 30°

x = 10.462

Sixth triangle

x = (10.462 + 3.2 + 1.9) · cos 19°

x = 14.714

Seventh triangle

x = (14.714 - 4.8 - 1.1) / cos 46°

x = 12.688

Eighth triangle

x = √[(12.688 + 1.7)² + 3.2²]

x = 14.740

Ninth triangle

x = (14.740 - 2.73) · cos 22°

x = 11.135

x' = 11.135 - 2.24

x' = 8.895

Tenth triangle

x = (8.895 + 6.9) / cos 4°

x = 15.833

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Using a standard normal distribution table, we can find the closest value to 0.99, which is 2.33. Therefore, the z-score for a 98% confidence interval is 2.33.

To calculate the z-score for a 98% confidence interval, we can use a standard normal distribution table or a calculator with a built-in z-score calculator. To calculate the z-score for a 98% confidence interval, we can use the following formula:

z = invNorm(1 - (1 - confidence level) / 2)

Where "invNorm" is the inverse normal distribution function, and "confidence level" is the level of confidence expressed as a decimal. For a 98% confidence level, we have:

z = invNorm(1 - (1 - 0.98) / 2)

z = invNorm(0.99)

Using the table, we can find the z-score corresponding to a cumulative area of 0.98 by looking up the closest value to 0.98 in the table.

invNorm(0.98) = 2.33.

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The circumference of the circle is 6.55π

The circumference of a circle is given by the formula:

C = πd

Where d is the diameter of the circle.

We are given that the diameter is 6.55, so we can substitute this value into the formula to find the circumference:

C = π(6.55)

Evaluate

C = 6.55π

Hence, the circumference of the circle, in terms of pi, is approximately 6.55π

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Complete question

Find the circumference of the circle in terms of pi

Diameter = 6.55

Answer:

3x+4=6

Step-by-step explanation:

The wavelength of the wave is 0.125 m.

A periodic wave's wavelength is its spatial period, or the length over which its shape repeats. It is a property of both traveling waves and standing waves as well as other spatial wave patterns. It is the distance between two successive corresponding locations of the same phase on the wave, such as two nearby crests, troughs, or zero crossings.

A sinusoidal waveform's wavelength (λ) is determined by the equation

λ= ν/f,

where ν denotes the wave's phase speed (or magnitude of the phase velocity) and f denotes its frequency.

According to the given information,

Speed of transverse wave, ν = 25 m/s

Frequency, f = 200 Hz

We know the formula, λ= ν/f

By substituting the values, we get

λ = 25/200

λ = 0.125m

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This question is related to Physics.

Number of lemon cupcakes in  next 20 cupcakes sold is 1.33.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

carrot cupcakes 8 pumpkin cupcakes 1 lemon cupcakes 6

Now,

For 20 cupcakes

Let the number of lemon cupcakes be x

8+6+1=1lemon

15=1lemon

20=1*20/15lemon

=4/3lemon

Therefore, by algebra the answer will be 1.33lemons

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Answer:

y=0.5x+30?

Step-by-step explanation:

The total number of miles Ahmad drove the truck is given by the equation A = 238.988 miles ≈ 240 miles

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The base fee of the truck = $ 20.95

The cost for each mile driven = $ 0.84

The total amount Ahmad paid = $ 221.7

Let the total number of miles be A

Now , the equation will be

The total amount Ahmad paid = base fee of the truck + cost for each mile driven x total number of miles

Substituting the values in the equation , we get

221.7 = 20.95 + ( 0.84 )A

Subtracting 20.95 on both sides of the equation , we get

0.84A = 200.75

Divide by 0.84 on both sides of the equation , we get

A = 238.988 miles

Hence , the equation is A = 238.988 miles

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Answer:

65 m²

Step-by-step explanation:

area of parallelogram = base × height

base = AB = 3 m + 10 m = 13 m

height = 5m

area = 13 m × 5 m

area = 65 m²

There are 168 hours in a week. Therefore, there are approximately 0.536 weeks in 90 hours.

Time conversion is the process of converting a given amount of time from one unit of measurement to another. It involves using conversion factors to change the numerical value of the time while keeping the duration constant.

For example, converting a duration from hours to minutes involves using a conversion factor of 60 minutes per hour. To convert, you multiply the number of hours by 60 to get the equivalent duration in minutes.

To get this answer, you can divide the number of hours (90) by the total number of hours in a week (168):

90 hours ÷ 168 hours/week = 0.536 weeks (rounded to three decimal places)

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Clark earns $6 in interest when t = 10 years, and with principle balance of $120.

When someone borrows a particular amount of money, they must pay interest. This phrase is frequently used in relation to banks, loans, payments, and investments. It is connected to the percentage, rate, and duration for which the borrowed amount of money is owed.

Using the formula I = prt, we can calculate the amount of interest earned by Clark over a period of 10 years:

I = prt

I = (0.005)(120)(10)

I = 6

Therefore, when t = 10 years, Clark earns $6 in interest.

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The number of more cups that she needs to put in will be 28 cups.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

A recipe for cookies calls for 3 Cups of sugar. And t has already put in 31 Cups. Then the equation is given as,

t + 3 = 31

t = 31 - 3

t = 28 cups

The number of more cups that she needs to put in will be 28 cups.

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The angle 'b' measure 120 degrees from the diagram.

The given diagram is a circle geometry. Given the following parameters

x= 44° and;

a = 32°

In order to determine the measure of angles 'b'. we will use the expression below;

x = 1/2(b + a)

44 = 1/2 (b- 32)
88 = b - 32

b = 88 + 32

b = 120 degrees

Hence the measure of the angle 'b' from the diagram is 120 degrees.

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Answer:

s = 9

Step-by-step explanation:

A = s^2

81 = s^2

√81 = s

s = 9

Answer:

Quadrant III

Step-by-step explanation:

hope it helps :-)

The measure of angle ∠2 is 50° for the given lines.

Lines are straight with little depth or width. Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and corresponding angles.

Given that the angle is 50°. The vertically opposite angles for the lines are equal. The vertically opposite angle of 50° is ∠2.

The value of angle ∠2 is,

∠2 = 50°

Therefore, the value of angle ∠2 will be 50°.

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The number of students that have veggies as a snack is equal to 51 students according to the circle graph.

A circle graph is also called a pie chart, and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.

Given that, there are 300 students at a school, the number of students that have veggies as a snack can be calculated as follows;

Number of students that had veggies = 17/100 × 300

Number of students that had veggies = 0.17 × 300

Number of students that had veggies = 51 students.

Hence, the number of students that have veggies as a snack is equal to 51 students according to the circle graph.

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The complete question is :-

Refer to the circle graph below. Suppose there are 300 students at York Middle School. Determine the number of students that have veggies as a snack. No Snack 12% Fruit. 23% Chips · 18% Cheese 15% Veggies 17% L Cookies 15%​

Measures of angles, x = 93° and y = 97°

A cyclic quadrilateral is a quadrilateral with all four vertices on a circle. Also called an inscribed quadrilateral. A circle consisting of all vertices around a polygon is known as the circumcircle.

Given,

Interior angles of quadrilateral

= x° , y° , 83°

Arc angles on the center of circumcircle are 64° and 122°.

angle made by chord on the center is twice to the angle made on the circumference of the circle

64° + 122° = 2x

186° = 2x

x = 186°/2

x = 93°

In cyclic quadrilateral,

Sum of opposite interior angles is 180°

y + 83° = 180°

y = 180° - 83°

y = 97°

Hence, measure of angles x and y are 93° and 97° respectively.

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Using the cosine ratio, the value of x, to the nearest tenth, is: 39.3°.

The cosine ratio is part of the trigonometric ratios, which is given as:

cos ∅ = length of adjacent side / length of hypotenuse.

Given the following:

Length of adjacent side = 6.5

Length of hypotenuse = 8.4

Reference angle (∅) = x

Plug in the values:

cos x = 6.5/8.4

x = cos^(-1)(6.5/8.4)

x = 39.3°

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Answer: look at the image for the answer

Step-by-step explanation:

Answer:

44 ft

Step-by-step explanation:

To find the height of the tree, h, model the given scenario as a two right triangles and solve using the tan trigonometric ratio.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

See attached for a diagram modelling the given information.

Create two tan ratios using the given information, and rearrange each equation to isolate x.

Equation 1

Given:

Therefore:

[tex]\begin{aligned}\implies \tan 42^{\circ}&=\dfrac{h}{x+12}\\\\ x+12&=\dfrac{h}{\tan 42^{\circ}}\\\\ x&=\dfrac{h}{\tan 42^{\circ}}-12\end{aligned}[/tex]

Equation 2

Given:

[tex]\begin{aligned}\implies \tan 50^{\circ}&=\dfrac{h}{x}\\\\ x&=\dfrac{h}{\tan 50^{\circ}}\end{aligned}[/tex]

To find the value of h, substitute equation 2 into equation 1 to eliminate x and solve for h:

[tex]\implies \dfrac{h}{\tan 50^{\circ}}=\dfrac{h}{\tan 42^{\circ}}-12[/tex]

[tex]\implies \dfrac{h}{\tan 50^{\circ}}-\dfrac{h}{\tan 42^{\circ}}=-12[/tex]

[tex]\implies \dfrac{h\tan 42^{\circ}-h\tan 50^{\circ}}{\tan 50^{\circ}\tan 42^{\circ}}=-12[/tex]

[tex]\implies \left(\dfrac{\tan 42^{\circ}-\tan 50^{\circ}}{\tan 50^{\circ}\tan 42^{\circ}}\right)h=-12[/tex]

[tex]\implies h=\dfrac{-12\tan 50^{\circ}\tan 42^{\circ}}{\tan 42^{\circ}-\tan 50^{\circ}}[/tex]

[tex]\implies h=44.1967977...[/tex]

Therefore, the approximate height of the tree to the nearest foot is 44 ft.

Multiple regression analysis analyze more than one dependent variable at a time and multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression are false. Correct option is D.

The statement (A) that "Multiple regression analysis allows you to analyze more than one dependent (Y) variable at a time" is false. In multiple regression, there is only one dependent variable (Y) that is being predicted by a combination of independent variables (X).

The statement (B) that "Multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression" is also false.

Multicollinearity occurs when two or more independent variables (X) are highly correlated with each other, which can cause problems in accurately estimating the effect of each independent variable on the dependent variable.

The statement (C) that "Multicollinearity occurs when two or more of the X variables are highly correlated with one another" is true.

Therefore, the correct answer is (D) "Both A and B are false statements."

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The points where the curve intersect the paraboloid is (2, 0, 4).

To find the points of intersection, we set the two equations equal to each other and solve for x, y, and z.

Now, to find the point where the curve r(t) intersects the paraboloid z = x² + y², we can substitute the given value of t into the parametric equations of the curve.

The curve is defined as:

r(t) = t i + (2t - t²) k

where i and k are unit vectors in the x and y directions, respectively.

value of t is given.

Setting t = 2, we have:

x = 2

y = 2(2) - (2)² = 0

z = x² + y² = 4 + 0 = 4

So, the point of intersection is (2, 0, 4).

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_____The given question is incorrect, the correct question is given below:

At what point does the curve r(t)=ti+(2t−t2)k, where t= 2

intersect the paraboloid z=x²+y².

The Domain is 0 ≤ x ≤ 4 and Range is 0 ≤ y ≤ 80.

The range of values that we are permitted to enter into our function is known as the domain of a function.  A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

We know that the domain of a function is the set of values that we are allowed to plug into our function.

From the Graph the x values ranges from 0 to 4.

So, domain is 0 ≤ x ≤ 4.

and, the range is the corresponding output for the input

From the Graph the y values ranges from 0 to 80.

So, Range is 0 ≤ y ≤ 80.

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Answer:

Step-by-step explanation:6

The transformation that did not take place is a dilation, as the side lengths for both triangles are constant.

For this problem, the side lengths remain constant, hence a dilation did not take place.

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The equation and value of x , the distance of 1 lap around the path at the park is 4.8x + 1.2 = 3.6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles.

As, we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant.

So, the equation can be framed as

4.8x + 1.2 = 3.6

4.8x = 2.4

x = 0.5

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The question attached here seems to be incomplete the remaining portion is given below:

3.6 x + 1.2 = 4.8; x = 1 mile

4.8 x + 1.2 = 3.6; x = 1 mile

3.6 x + 1.2 = 4.8; x = 0.5 mile

4.8 x + 1.2 = 3.6; x = 0.5 mile

5 x = negative 58

Answer:

Step-by-step explanation:

The equation h = -0.0159d² + 290 models the curve of the natural stone bridge, where h is the height of the curve in feet and d is the width of the curve in feet.

To find the vertex of the curve, we need to use the formula x = -b / 2a, where x represents the x-coordinate of the vertex and a and b are coefficients of the quadratic equation. In this case, the quadratic equation is h = -0.0159d² + 290, so a = -0.0159 and b = 0. To find the vertex, we plug these values into the formula:

x = -b / 2a = 0 / (2 * (-0.0159)) = 0

So the x-coordinate of the vertex is 0, which means the vertex is at the point (0, 290).

The vertex tells us that the highest point of the bridge (the vertex) is at a width of 0 feet. This means that the bridge is tallest at its center, and the height decreases as the width increases in either direction. Additionally, since the coefficient of the squared term is negative, the parabolic curve is downward-facing, which indicates that the bridge curves downward as it extends outward.

To find the span of the rainbow bridge, we need to find the width of the bridge where the height is 0. This represents the point where the bridge intersects with the river. To do this, we set h = 0 and solve for d:

0 = -0.0159d² + 290

0.0159d² = 290

d² = 290 / 0.0159

d ≈ 77.36

So the width of the bridge where the height is 0 is approximately 77.36 feet. Therefore, the span of the rainbow bridge is approximately 154.72 feet (twice the width at the point where the height is 0).