A store pays $842.00foracrystalsculptureandmarksthepriceupby29%.Whatistheamountofthemark-up?

Answer:

The graph would be shown as..you'll go 4 steps left and 6 steps upward. The inequality -4< x< 6

Step-by-step explanation:

The x axis is negative 4 so 4 steps to the left and y axis is positive 6 so from negative 4 you'll go 6 steps upward

Without specific data on the number of students who prefer each option, we cannot calculate the probability.

To determine the probability that a student prefers the zoo or the water park, we need to know the total number of students and the number of students who prefer each option. Without this information, it is not possible to calculate the probability accurately.

To calculate the probability, we would need to divide the number of students who prefer the zoo or the water park by the total number of students. For example, if there are 50 students in total and 30 prefer the zoo and 20 prefer the water park, the probability would be:

P(prefer zoo or water park) = (30 + 20) / 50 = 50 / 50 = 1

However, without specific data on the number of students who prefer each option, we cannot calculate the probability.

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Answer:

12.9 ft²

Step-by-step explanation:

sin = opp/hyp

sin 40 = height/ 5

5 * sin40 = height

h = 3.213938048432697

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

area = (1/2)bh

a = (1/2) * 8 * 3.213938048432697

a = 12.9 ft²

Answer:

Solution: x =5

Step-by-step explanation:

Solving Equations

Solve the following equation:

( 10 + 4 ) ( 5x - 22 ) = 3( 4x - 6 )

Operating:

14( 5x - 22 ) = 3( 4x - 6 )

Removing parentheses:

70x - 308 = 12x - 18

Subtracting 12x and adding 308:

70x -12x = 308 - 18

Operating:

58x = 290

Dividing by 58:

x = 290/58

x = 5

Solution: x =5

The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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61 matchsticks need to make 20 squares.

Given,

From the figure,

Matchsticks are used to make the pattern.

To make these 4 squares, you need 13 matchsticks.

To find the how many matchsticks do you need to make 20 squares?

Now, According to the question:

Let the need matchsticks be 'n'

The number of the squares to make 1 square , you need 4 matchsticks,

and when you need to add one square, you need three more matchsticks .

So , we have to make  n no. of squares you need

4 + 3(n - 1) matchsticks     (n \(\geq\) )

= 4 + 3n - 3

= 1 + 3n

When, n = 20

1 + 3 x 20

= 61

Hence, 61 matchsticks need to make 20 squares.

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B) 5x-4 = 3\(x^2\) has no real solution

To check real solution of a quadratic equation we have to check for discriminant value of each equation a\(x^2\) + bx +c is given by :

D =b^2 - 4ac.

if D<0 then equation have no solution.

now we need to check for each option the D value

Option A:

Therefore, the discriminant of the equation x^2 - 3x - 7 is (-3)^2 - 4(1)(-7) = 9 + 28 = 37.

Option B:

The discriminant of the quadratic equation 3x^2 - 5x + 4 is the value of b^2 - 4ac, which is (5)^2 - 4(3)(4) = 25 - 48 = -23. A negative discriminant (-23) would indicate that the equation has no real solutions, meaning it has no solutions in real numbers.

so option B  which is 5x-4 = 3\(x^2\) have no real solution.

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Complete question:

Which of the following equations has no real solutions?

A. \(x^2\) +3x=7

B. 5x-4 = 3\(x^2\)

C. \(x^2\) +1 = 3x

D. 2\(x^2\) +5x=3

Answer:

17.1 in2

Step-by-step explanation:

Resolviendo una simple ecuación con porcentajes, veremos que el número total de estudiantes es 17,727,273

Sabemos que en un dado año, 22% del numero total de estudiantes universitarios estaban matriculados a tiempo parcial, y hay un total de 3,900,000 estudiantes matriculados a tiempo parcial.

Sí definimos N como el numero total de estudiantes, entonces el 22% de N es igual a 3,900,000, entonces podemos escribir la ecuación:

(22%/100%)*N = 3,900,000

0.22*N = 3,900,000

N = 3,900,000/0.22 = 17,727,273

Ese es el numero total de estudiantes.

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Answer:

p = 6

Step-by-step explanation:

All you have to do is use distributive property of the left side. Then, add like terms until you get p on one side and a constant on the other. Then just divide both sides by the number that is with the p. In the end you will reach the p = 6 answer.

Answer:

You would DIVIDE to solve this problem.

each runner will

get 1/6 gallon of apple juice

Step-by-step explanation:

Answer:

180-108=72   72/2=36 degrees

Step-by-step explanation:

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The equation that should be used to determine sales in 2025 is S = 0.0654x^(2) - 0.807x + 9.64, and the predicted sales for that year are 30.565 million.

To determine sales in 2025, we need to find the value of x that corresponds to that year. Since x = 0 represents the year 2000, we need to find the value of x that is 25 years after 2000. That value is x = 25.

Now we can substitute x = 25 into the equation S = 0.0654x^(2) - 0.807x + 9.64 to find the sales in millions for 2025.

S = 0.0654(25)^(2) - 0.807(25) + 9.64

S = 41.1 - 20.175 + 9.64

S = 30.565 million

Therefore, the equation that should be used to determine sales in 2025 is S = 0.0654x^(2) - 0.807x + 9.64, and the predicted sales for that year are 30.565 million. It's important to note that this is just a prediction based on the given model and may not necessarily reflect actual sales in 2025.

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Using trigonometric identities and algebraic manipulation, the solution to the equation sin(2x) = -3sin(x) + 4  is x = kπ, where k is any integer.

To solve the equation sin(2x) = -3sin(x) + 4:

1. Start by using the double-angle identity for sine:

  2sin(x)cos(x) = -3sin(x) + 4

2. Rearrange the equation:

  2sin(x)cos(x) + 3sin(x) - 4 = 0

3. Factor out sin(x):

  sin(x)(2cos(x) + 3) - 4 = 0

4. Set each factor equal to zero:

  sin(x) = 0    or    2cos(x) + 3 = 0

5. Solve the first equation sin(x) = 0:

  The solutions for sin(x) = 0 are x = 0 + kπ, where k is an integer.

6. Solve the second equation 2cos(x) + 3 = 0:

  Subtract 3 from both sides: 2cos(x) = -3

  Divide by 2: cos(x) = -3/2

Since the cosine function has a range of [-1, 1], there are no real solutions for cos(x) = -3/2. Thus, there are no solutions for this part of the equation.

Therefore, the solutions to the equation sin(2x) = -3sin(x) + 4 is x = kπ, where k is any integer.

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\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)

➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]

➝ -4 × (-2) [2 × (-6) + 3 × (4) ]

➝ -4 × (-2) [2 × (-6) + 12 ]

➝ -4 × (-2) [(-12) + 12 ]

➝ -4 × (-2) [0]

➝ -4 × 0

➝ 0

Answer:

-4*-2

Step-by-step explanation:

the multiple of both side is 4*2*,26+*32*--=6 44

Answer:

x=2.5

Step-by-step explanation:

Solve for x in this systems of equations, we already have two values which equal y so half the work is finished for us.

Starting with the equation:

\(x+12=17-x\)

Add x to both sides to remove the negative x on the right side of the equation:

\(2x+12=17\)

Subtract 12 from both sides to remove the 12 on the left side of the equation:

\(2x=5\)

Divide both sides by 2 to cancel out the x coefficient

\(x=2.5\)

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Number of bowls that Laura can make with 10lbs of clay is 16

To find out how many bowls Laura can make, we need to divide the amount of clay she has by the amount of clay needed to make one bowl.

Let's start by converting the fraction 3/5 into a decimal:

3/5 = 0.6

This means that Laura needs 0.6 lbs of clay to make one bowl.

Now we can divide the total amount of clay Laura has by the amount of clay needed for one bowl:

10 ÷ 0.6 = 16.67

Laura can make 16 complete bowls with 10 lbs of clay, and she will have some clay left over (0.07 lbs to be exact) that is not enough to make another full bowl.

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Thus, the length of the other side of Ross's garden is 18 feet.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

To find the length of the other side of Ross's garden, we can use the Pythagorean theorem.

In this case, let's assume the length of the other side of Ross's garden x.

We can set up the following equation:

x² + 30² = 33²

Solving for x, we get:

x² = 33² - 30²

x² = 1089 - 900

x² = 289

x = √289

x = 17.

Thus, the length of the other side of Ross's garden is 18 feet.

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Answer:

x = 6

Step-by-step explanation:

Here it's sayin that Q is a point in between the end-points P & R. If we join P & R , it forms a line segment & Q is in the line segment PR. Hence PQ & QR are also line segments which combine to form line segment PR. So ,

PR = PQ + QR

Putting the given values of PQ ,QR & PR

=> 4x - 12 + 2x + 7 = 31

=> 6x - 5 = 31

=> 6x = 31 + 5

         = 36

=> x = 36/6 = 6

We can be 95% confident that the true population mean TV viewing time is between 3.812 and 4.388 hours.

To calculate the 95% confidence interval, we use the formula:

CI = x' ± Zα/2 * (σ/√n)

Where:

x' = sample mean

Zα/2 = the Z-score associated with the desired confidence level (in this case, 95%, so Zα/2 = 1.96)

σ = population standard deviation

n = sample size

Substituting the given values, we get:

CI = 4.1 ± 1.96 * (1.3/√78)

Calculating the standard error (SE) first:

SE = σ/√n

SE = 1.3/√78

SE ≈ 0.147

Then we substitute the SE value in the CI formula:

CI = 4.1 ± 1.96 * 0.147

CI = 4.1 ± 0.288

CI = (3.812, 4.388)

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If both the corresponding angles and sides are congruent and proportional, respectively, you can state that the triangles are similar.

To determine if two triangles are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.

To state if the triangles in each pair are similar, follow these steps:

1. Identify the corresponding angles: Compare the angles of one triangle to the angles of the other triangle. If all the corresponding angles are congruent, then the triangles are similar.

2. Check for proportional sides: Compare the lengths of the corresponding sides of the two triangles. If the ratios of the corresponding sides are equal, then the triangles are similar.

3. If both the corresponding angles and sides are congruent and proportional, respectively, you can state that the triangles are similar.

For example, consider two triangles with angles A, B, and C, and sides a, b, and c. If you find that angle A of one triangle is congruent to angle A of the other triangle, angle B is congruent to angle B, and angle C is congruent to angle C, and the ratios a/b, b/c, and a/c are all equal, then you can conclude that the two triangles are similar.

Remember, similarity is not the same as congruence. Similar triangles have the same shape but can differ in size.

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The permutation combination is 120 for 3 different topping pizzas are available.

Permutation Combination:

A variety of ways to select objects from a set, usually forming a subset without replacement. The selection of this subset is called a permutation if the order of selection is a factor, and a combination if the order is not a factor. The French mathematicians Blaise Pascal and Pierre de Fermat, in the 17th century, used many chances in his game of combinatorics and probability by considering the ratio of the number of required subsets to the number of all possible subsets stimulated the development of the theory.

The concepts of permutations and combinations and their differences can be illustrated by examining all the different ways of selecting pairs of objects from five identifiable objects such as the letters A, B, C, D and E.

According to the Question:

Given that :

Number of different toppings = 10

Number of Pizzas = 03

therefore,

The permutation  combination are :

                = 10!/7! 3!

                = 15 × 8

                = 120.

Therefore, there are 120 different combinations of toppings.

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The expression that represents the number of inches the plant grew this week is,

⇒ 8 - x

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

A plant measured x inches tall last week, and 8 inches tall this week.

Here, We have;

A plant measured x inches tall last week, and 8 inches tall this week.

Hence, The number of inches the plant grew this week is,

⇒ 8 - x

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The expression that uses the GCF and the Distributive Property to express the sum as a product of the expression given as 30 + 10 is 10(3 + 1)

The expression is given as:

30 + 10

Express the terms of the expression as the product of their GCF.

So, we have:

30 + 10 = 3 * 10 + 1 * 10

Factor out 10

30 + 10 = 10(3 + 1)

Hence, the expression that uses the GCF and the Distributive Property to express the sum as a product of the expression given as 30 + 10 is 10(3 + 1)

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Answer:

B

Step-by-step explanation:

the x values repeat so its not a function