This is 7th grade math: Equations and Inequalities word problems

The Total cost of a teapot and some teacups is $100. The teapot costs $40. Each teacup costs $10. Write an equation to find t, the total number of teacups bought.

Answer:

35% (decrease)

Step-by-step explanation:

V2-V1/V1 x 100

= 113.75-175/175 x 100

= -61.25/175 x 100

= -0.35 x 100

= -35% (change/decrease)

Answer:

x^3-18x^2+108x-216

Step-by-step explanation:

\(f(x)=x-6 \\\\g(x)=x^3 \\\\g(f(x))=(x-6)^3=x^3-18x^2+108x-216\)

Hope this helps!

The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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Answer:

Step-by-step explanation:

x + \(\frac{y}{3}\) = 0         ------    ( 1 )

6x - 2y = 6     ------    ( 2 )

6x + 2y = 0    ----- ( 3 )

6x - 2y = 6    ------ ( 4 )

Adding ( 3 ) and ( 4 ) ; we get ,

12x = 6

x = 1/2

putting value of x in (3) , we get ,

3 + 2y = 0

2y = -3

x + 2y = (1/2) - 3

= - 5/2

Marci can get 7 free comic books if she buys 68 comics. Therefore, option A, "7 free comic books" is the correct answer.

According to the question, the Comic Depot gives one free comic book to customers when they purchase 9 comic books. This means that a customer who buys 9 comic books gets one comic book for free. If a customer buys 18 comic books, he/she will get two comic books for free, and so on. We can find the relationship between the number of comic books a customer buys and the number of free comic books he/she gets by using a unitary method.

Let x be the number of comic books Marci buys and let y be the number of free comic books she gets. Since Marci gets one free comic book for every nine comic books she buys, we have that:

y = (1/9) x.

Rearranging the equation above to solve for x, we have that:

x = 9y

We are asked to find the number of free comic books Marci can get if she buys 68 comic books. Thus, we substitute x = 68 into the equation above to find the number of free comic books y:

y = (1/9)68 = 7.56

Thus, Marci can get 7 free comic books.

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The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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The hotel will need 32 feet of tiling in order to add this border.

The given figure represents a water fountain. A hotel needs to retile part of a water fountain. They plan to make a one -inch tile border around the edge of the pool. Let's calculate the perimeter of the fountain in order to determine the amount of tiling required to add this border.Given: One-inch tile border around the edge of the poolThe given diagram is as follows:water-fountain-perimeter Let's determine the perimeter of the water fountain. Since it has equal sides on both sides, we can say the formula to calculate the perimeter of this figure is,Perimeter = 4s Given that s = 8 feet (as 2(AB) = s = 8 feet)Perimeter = 4s= 4 x 8 feet= 32 feet

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Answer:

answer is b). y = 100+ 0.05x

Step-by-step explanation:

The Law of sines states:

Substituting with data, and solving for angle P, we get:

Step-by-step explanation:

write and say i am not understanding

Answer:

Ok ok, trust me this is not a scam nor hack

Step-by-step explanation:

I didn't no idea to explain in words so i edited the photo

The value of the double integral is zero.

To evaluate the double integral, we need to convert the Cartesian coordinates to polar coordinates since the region is a circle. Let's recall the formula for changing variables in double integrals:

\($\iint_R f(x,y) dA = \iint_S f(r\cos\theta, r\sin\theta) r dr d\theta$\)

where\($R$\) is the region in the \($xy$\)-plane and\($S$\) is the region in the \(r\theta$-\)plane.

In this case, the region \($D$\) is a circle with center at the origin and radius \($4$\), so we have:

\($\iint_D (6x-2y) dA = \int_0^{2\pi} \int_0^4 (6r\cos\theta - 2r\sin\theta) r dr d\theta$\)

\($= \int_0^{2\pi} \int_0^4 (6r^2\cos\theta - 2r^2\sin\theta) dr d\theta$\)

\($= \int_0^{2\pi} \left[3r^3\cos\theta - r^3\sin\theta\right]_0^4 d\theta$\)

\($= \int_0^{2\pi} (48\cos\theta - 64\sin\theta) d\theta$\)

\($= \left[48\sin\theta + 64\cos\theta\right]_0^{2\pi}$\)

\($= 0$\)

Therefore, the value of the double integral is zero.

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(complete question)

evaluate the double integral. (6x-2y)dA D is bounded by the circle with the center at the origin and radius 4. What to evaluate the integral for x and y.

Answer:

23%

Step-by-step explanation:

Step 1. Find increase of price amount

18.75 - 15.25 = 3.50

Step 2. Find the percentage increase

- Since we are finding the percent increase, we know that we need to find 3.50 is ____% of 15.25. We can simply do 3.50/15.25, which can be simplified to approximately 0.23.

- Note that percentage = 100 times decimal

100 x 0.23 = 23

The answer is 23%

Hope this helps :)

Have a nice day!

Answer:

194 yards

Step-by-step explanation:

Perimeter of the proposed parking lot

= 52 + 40 + 20 + (40 - x) + 24 + 10 + (52 - 20 - 24) + x

= 112 + (40 - x + x) + 34 + (52 - 44)

= 146 + 40 + 8

= 194 yards

Answer:

There are a total of 4 + 6 + 10 = 20 CDs in the case. Eric has a 10/20 = 1/2 chance of picking a pop CD since there are 10 pop CDs in the case.

Therefore, the answer is D) 1/2.

Answer:

Step-by-step explanation:

Eric has a total of 4 + 6 + 10 = 20 CDs in the case.

The probability of picking a pop CD is the number of pop CDs divided by the total number of CDs:

P(pick a pop CD) = 10/20 = 1/2 = 0.5

Therefore, the probability of Eric picking a pop CD is 0.5 or 50%.

Answer:

Below

Step-by-step explanation:

The end behavior of a function is how it grows when it reaches both plus and - infinity.

To do that we will calculate:

● lim h(x) x=> +infinity = lim-4x+4 x=> +inf = lim -4x x=> +inf

-4 is negative so the limit will be -infinity

● lim (-4x+4) x=> -inf = lim (-4x) x=> -inf

-4 is negative, x is negative then -4x is positive. So the limit will be + inf

To show that the function f(x) = 1/(1 + x) is integrable on [0, b] for any b > 0, we can use Riemann's Criterion for integrability. This criterion states that a function is integrable on a closed interval if and only if it is bounded and has a set of discontinuity points of measure zero. By analyzing the properties of f(x), we can conclude that it is bounded on [0, b] and its only point of discontinuity is at x = -1. Since the set of discontinuity points is a single point with measure zero, f(x) satisfies Riemann's Criterion for integrability on [0, b].

To apply Riemann's Criterion for integrability, we need to examine the properties of the function f(x) = 1/(1 + x) on the interval [0, b].

First, let's consider the boundedness of f(x). Since f(x) is a rational function, it is defined for all x except where the denominator equals zero. In this case, the denominator 1 + x is always positive on the interval [0, b] for any positive value of b. Therefore, f(x) is well-defined and bounded on [0, b].

Next, let's analyze the discontinuity points of f(x). The function f(x) is continuous for all x except where the denominator equals zero. The only point where the denominator is zero is at x = -1, which is outside the interval [0, b]. Thus, there are no discontinuity points within the interval [0, b], except possibly at the endpoints, and in this case, x = 0 and x = b are included in the interval.

Since the set of discontinuity points of f(x) within [0, b] is a single point (x = -1) with measure zero, f(x) satisfies Riemann's Criterion for integrability on [0, b]. Therefore, the function f(x) = 1/(1 + x) is integrable on [0, b] for any b > 0.

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Answer: ANSWERS BELOW

Step-by-step explanation:

Part A.

At time = 1 hour, k(x) = 6 and f(x) = 4.

At time = 2 hours, k(x) = 12 and f(x) = 8.

At time = 3 hours, k(x) = 18 and f(x) = 12.

At time = 4 hours, k(x) = 24 and f(x) = 16.

- - -

Part B.

Katherine travels farther within 4 hours. She travels 24 miles in 4 hours, which is 8 more than Julio travels.

- - -

Part C:

The function k(x) has a greater slope. It has a slope of 6, while k(x) has a slope of 4.

When the obtained value is greater than the critical value, the null hypothesis is rejected.

A null hypothesis is a statistical approach hypothesis that asserts that there is no statistical significance in a given set of observations. Using sample data, hypothesis testing is employed to evaluate the reliability of a hypothesis.

Some key features regarding the null hypothesis are-

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Answer:

1.5

Step-by-step explanation:

I think

The frequency distribution is shown below.

Frequency tables or charts are used to represent frequency distributions. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.

We have,

Two of the sectors say, "0 points," three say, "1 point," two say, "2 points," and one says, "5 points."

So, the frequency distribution is

Outcome       0 pts  1 pts  2 pts  5 pts

Probability     2/8      3/8    1/8      1/8

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Answer:

0, 5, 7

Step-by-step explanation:

You just follow the rule written at the top, if the left column is x, the right column is x/6. For example, if the right column is 0, the left would be 0/6, which is 0.

The perimeter of the field is 100 feet.

The length of the field is 32 feet, and the width is 6 yards.

Since 1 yard is equivalent to 3 feet, the width is 18 feet.

To find the perimeter, add the lengths of all sides.

There are two lengths and two widths in a rectangle like this field.

Therefore, we have to multiply each length by two and each width by two and add them together.

Perimeter = 2(32 ft) + 2(18 ft)

Perimeter = 64 ft + 36 ftPerimeter = 100 ft

Therefore, the perimeter of the field is 100 feet.

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Answer:

x = - 2, y = - 8

Step-by-step explanation:

13x - 6y = 22 → (1)

x = y + 6 → (2)

substitute x = y + 6 into (1)

13(y + 6) - 6y = 22

13y + 78 - 6y = 22

7y + 78 = 22 ( subtract 78 from both sides )

7y = - 56 ( divide both sides by 7 )

y = - 8

substitute y = - 8 into (2)

x = y + 6 = - 8 + 6 = - 2

then x = - 2 and y = - 8

Answer:

2\(\sqrt{2}\) x

Step-by-step explanation:

The diagonal divides the square into 2 right angles with legs s and hypotenuse x

Using Pythagoras' identity on one of the right triangles, then

s² + s² = x²

2s² = x² ( divide both sides by 2 )

s² = \(\frac{x^2}{2}\) ( take the square root of both sides )

s = \(\sqrt{\frac{x^2}{2} }\) = \(\frac{x}{\sqrt{2} }\)

Thus

perimeter = 4s = 4 × \(\frac{x}{\sqrt{2} }\) = \(\frac{4x}{\sqrt{2} }\)

Multiply numerator/ denominator by \(\sqrt{2}\)

perimeter = \(\frac{4x\sqrt{2} }{2}\) = 2\(\sqrt{2}\) x

False. While it may be tempting to round the optimal solution of a linear programming model down to the nearest integer value to solve a mixed integer programming problem, this approach is not always guaranteed to produce an optimal solution.

In fact, mixed integer programming problems require specialized algorithms and techniques that are specifically designed to handle integer variables in the objective function and constraints. These methods search for feasible solutions within the space of integer values, which can be more computationally intensive than solving a linear programming model.

So, while rounding the optimal solution of a linear programming model may sometimes provide a good approximate solution to a mixed integer programming problem, it is not always the best or most reliable way to solve these types of problems.

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Answer:

Divide 52.8 by 9 = 5.866 ounces per bag

Step-by-step explanation:

Divide 52.8 by 9

52.8/9 = 5.866 ounces per bag

The probability that in a random sample of 100 TCS employees, the monthly expenditure lies between Rs. 38000 and Rs. 39000 is 0.1359 or approximately 13.59%.

To solve this problem, we need to standardize the random variable using the z-score formula:

z = (x - μ) / (σ / sqrt(n))

where:

x = 38000 and 39000

μ = 40000

σ = 20000

n = 100

For x = 38000:

z = (38000 - 40000) / (20000 / sqrt(100)) = -1

For x = 39000:

z = (39000 - 40000) / (20000 / sqrt(100)) = -0.5

Now, we need to find the probability that the z-score falls between -1 and -0.5. We can use a standard normal distribution table or calculator to find this probability.

Using a standard normal distribution table, we find that the probability of z falling between -1 and -0.5 is 0.1359.

Therefore, the probability that in a random sample of 100 TCS employees, the monthly expenditure lies between Rs. 38000 and Rs. 39000 is 0.1359 or approximately 13.59%.

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Question:

A fair die is tossed.

Find the probability of obtaining an even number

Answer:

sample space=(1,2,3,4,5,6)

number of favourable outcomes=3

Event A= (outcome is even)

             = (2,4,6)

Total number of outcomes=6

Thus, P(even number)=3/6

                                      =1/2

Question 2:

A drawer contains 10 identical handkerchiefs of which 2 are white, 5 are blue, and 3 are pink. A handkerchief is drawn at random. what is the probability that it is white or pink?

Answer:

total number of outcomes=10

P(the handkerchief is white or pink)=2+3/10

                                                          =5/10

                                                          =1/2