Riley is making slime. Her recipe calls for 1/4 cup
of glue for every 1 tbsp. of laundry detergent.
How much detergent will she need to use if
she uses 1 1/2cups of glue?

Answer:

45 cans

Step-by-step explanation:

To find the volume of a cylinder, we need to find the area of the cross section, which in this case is π(radius)², and multiply it with the height of the cylinder

This means the pot has a volume of:

- pot has radius of 7.5in. as diameter is 2 x radius

π x (15/2)² x 11 = 618.75π in.³

The soup can has a volume of:

- soup can has radius of 1.5in. as diameter is 2 x radius

π x (3/2))² x 6 = 13.5π in.³

Divide the volume of the pot by the volume of the can to get how many cans of soup will it take to fill the pot:

618.75π in.³ ÷ 13.5π in.³ = 45.833... cans

The question states you need to round to nearest can which would be 45 cans, but personally, I thought you would always round up as 45 cans won't fill up the whole pot, but it's up to the question.

Answer:

15.5

Step-by-step explanation:

Yes

Answer:

0 < x < 28

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of the triangle should be greater than the third side.

Therefore,

All the possible values of x are 26 < x < 28.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

So a triangle has three sides.

We have the triangle inequality theorem which states that,

The length of any side of the triangle is always less than the sum of the other two sides.

And the range of the possible measure of the third side is the sum and the difference of the other two sides.

So x < 27 + 1 = 28

and,

x > 27 - 1 = 26

So 26 < x < 28

Hence the measures of third side is 26 < x < 28.

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The equation that best represents this relationship is y = 1/35x. The best equation that represents the relationship between the number of miles traveled x, and the number of gallons of gas used y is y = 1/35x.

This is because the table shows that as the number of miles traveled increases, the number of gallons of gas used also increases, but not at a constant rate. The ratio of miles traveled to gallons used is not constant, meaning that the relationship is not directly proportional (y = kx). Instead, the data suggests that there is a constant "efficiency" rate of 1/35 gallons per mile.  

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Answer:

18:11

Step-by-step explanation:

33÷3=11

54÷3=18

so its 18:11

hope it helped! :D

\(\large\huge\green{\sf{Answer:-}}\)

ratio= 54 t shirt/33 sweatshirt

ratio= 54/33

ratio= 18/11

Jose should charge $0.65 for each bag if he intends to sell the bag for $0.15 more than he paid.

Mathematical problems dealing with word problems can be solved by arranging data given into variables and using the appropriate arithmetic operation to solve them.

From the given information:

If Jose bought a 750 bag of peanuts for $375.00. It means that he bought each bag(1 bag) for:

\(\mathbf{=\$\dfrac{375}{750}}\)

= $0.5

However, he intends to sell each bag for $0.15 more than he paid; Then the amount he should charge for each bag is:

=$0.5 + $0.15

=$0.65

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The solutions to the system of equations by using augmented matrices are:

x = (a + (3(5a + b))/7) / 4

y = -(5a + b)/7

The solution to the system of equations can be found using augmented matrices. By representing the coefficients and constants in matrix form, we can perform row operations to reduce the augmented matrix to row-echelon form. This will allow us to determine the values of x and y.

To solve the system using augmented matrices, we set up the augmented matrix as follows:

\(\begin{bmatrix}4 &3&|&a \\-5 &-4&|&b \\\end{bmatrix}\)

To eliminate the x coefficient in the second row, we can multiply the first row by 5 and add it to the second row:

\(\begin{bmatrix}4 &3&|&a \\0 &7&|&5a+b \\\end{bmatrix}\)

Now, we can solve for y by dividing the second row by -7:

\(\begin{bmatrix}4 &3&|&a \\0 &7&|&5a+b \\\end{bmatrix}\)

To eliminate the y coefficient in the first row, we can multiply the second row by -3 and add it to the first row:

\(\begin{bmatrix}4 &0&|&3(5a+b)/7 \\0 &1&|&(5a+b)/7 \\\end{bmatrix}\)

From the augmented matrix, we can see that x is equal to (a + (3(5a + b))/7) divided by 4, and y is equal to -(5a + b)/7.

Therefore, the solutions to the system of equations are:

x = (a + (3(5a + b))/7) / 4

y = -(5a + b)/7

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A prediction interval is an interval estimate of an individual y value, given values of the independent variables.

A prediction interval is an interval estimate that quantifies the uncertainty associated with a single future observation of the dependent variable (y), given a set of values for the independent variables.

The prediction interval takes into account both the error inherent in the model and the variability of the individual observations.

So, a prediction interval provides a range of plausible values for an individual observation, based on the model's prediction and the uncertainty associated with it.

It is wider than a confidence interval because it includes the variability of the individual observations in addition to the uncertainty in the model.

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The given series is ∑n=1[infinity](-1)^nsin(4n). We can use the alternating series test to determine whether the series converges or diverges. Alternating series test: If ∑n=1[infinity](-1)^nb_n is an alternating series and b_n > b_{n+1} > 0 for all n, then the series converges.

Additionally, if lim n→∞ b_n = 0, then the series converges absolutely. To apply this test, let's first examine the sequence of terms b_n = sin(4n). We can observe that b_n is a decreasing sequence of positive numbers, which can be proved by calculating the derivative of sin(x) and showing it is negative on the interval (4n,4(n+1)).

We have shown that the terms of the sequence are decreasing, positive, and tend towards zero. So, the series converges absolutely. Therefore, the answer is C) Convergence.

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Answer: 4 hours

Step-by-step explanation:

322.58 - 200.14 = 122.44

122.44 divided by 30.61 = 4

Answer and Step-by-step explanation:

1. We can see that this kite-shape has 4 triangles in it.

The area of a triangle is as follows:

\(A = \frac{bh}{2}\)

Where:

b = Base (length)

h = Height

Top Right Triangle Area:

b = 9

h = 3

A = \(\frac{3 * 9}{2}\)

A = \(\frac{27}{2}\)

Bottom Right Triangle Area:

b = 9

h = 3

A = \(\frac{3 * 9}{2}\)

A = \(\frac{27}{2}\)

Top Left Triangle Area:

b = 4

h = 3

\(A = \frac{4*3}{2}\)

A = \(\frac{12}{2}\)

A = 6

Bottom Left Triangle Area:

b = 4

h = 3

\(A = \frac{4*3}{2}\)

A = \(\frac{12}{2}\)

A = 6

Now, we add all the areas together to get the area of the kite figure.

A = \(\frac{27}{2}\) +

A = 27 + 12

A = 39

The area of the kite figure is 39 \(m^{2}\).

2. We have to find the area of the trapezoid.

(I'm not sure if the 9 is for the entire bottom side length)

A = \(\frac{a + b}{2} h\)

to find the area of the entire trapezoid.

A = \(\frac{2.4 + 9}{9}\) × 8.2

A ≈ 46.74 \(mi^{2}\)

#teamtrees #PAW (Plant And Water)

Answer:

99π/4 sq ft

Step-by-step explanation:

Area = (110/360)\(\pi 9^{2}\)

        =  99π/4

a) 2338 ≡ 42 • 55 + 28 ≡ 28 (mod 55)

b) We want to find a such that

23a ≡ 1 (mod 55)

Use the Euclidean algorithm:

55 = 2 • 23 + 9

23 = 2 • 9 + 4

9 = 2 • 4 + 1

⇒   1 = 9 - 2 • 4

⇒   1 = 9 - 2 • (23 - 2 • 9) = 5 • 9 - 2 • 23

⇒   1 = 5 • (55 - 2 • 23) - 2 • 23 = 5 • 55 - 12 • 23

Solve for a :

5 • 55 - 12 • 23 ≡ 1 (mod 55)

⇒   -12 • 23 ≡ 1 (mod 55)

⇒   a ≡ -12 ≡ 43 (mod 55)

Answer: i don't get it

Step-by-step explanation:

Answer:

The model would be 42 inches long

Step-by-step explanation:

5.25 inches long times scale factor of 8

5.25 * 8 = 42

Answer:

The model would be 42 inches long.

The cost of equity for Chelsea Fashions is approximately 9.86%. This is calculated using the dividend discount model, taking into account the expected dividend, the stock price, and the growth rate.

The cost of equity for Chelsea Fashions can be determined using the dividend discount model (DDM). The DDM formula is as follows: Cost of Equity = Dividend / Stock Price + Growth Rate.

Given that the expected dividend is $1.10 and the market price of the stock is $21.80, we can substitute these values into the formula: Cost of Equity = $1.10 / $21.80 + 4.5%.

First, we divide $1.10 by $21.80 to get 0.0505 (rounded to four decimal places). Then, we add the growth rate of 4.5% (expressed as a decimal, 0.045). Finally, we sum these values: Cost of Equity = 0.0505 + 0.045 = 0.0955.

Converting this decimal to a percentage, we find that the cost of equity for Chelsea Fashions is approximately 9.55%. Therefore, the firm's cost of equity is approximately 9.86% when rounded to two decimal places.

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The correlation between the property damage due to earthquakes in Denton and Argyle, and the number of severe pest infestations in Corn Farm X and Corn Farm Y is **zero correlation**.

The correlation coefficient measures the strength and direction of the linear relationship between two random variables. A correlation coefficient of 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.

For Pair 1, the property damage due to earthquakes in Denton and Argyle, we cannot establish a direct cause-and-effect relationship between the two locations.

While Argyle is only 7 miles away from Denton, the property damage in each location can be influenced by various factors such as building structures, soil composition, and local geological conditions.

These factors may vary significantly within a small geographical distance, leading to different levels of property damage. Therefore, the correlation between the property damage in Denton and Argyle is likely to be close to zero.

For Pair 2, the number of severe pest infestations in Corn Farm X and Corn Farm Y, the distance of 2000 miles between the two farms suggests that they are located in different regions with potentially different climate conditions, soil types, and pest populations. As a result, the occurrence of severe pest infestations in one farm may not directly influence the occurrence in the other.

The independent factors affecting pest infestations, such as agricultural practices, pest control measures, and environmental factors, are likely to contribute to the absence of a significant correlation between the two farms.

In both cases, without a direct and consistent relationship between the variables, the correlation is expected to be close to zero.

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Answer:

908.967

Step-by-step explanation:

i hope this helps :)

The required real proportion's 95% confidence interval is (0.301; 0.359).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

So, the sample size is 1000.

Phat = 0.33

(1 - phat) = 1 - 0.33 = 0.67

Zcritical = 1.96 at 95%

The confidence range is as follows:

Phat ± margin of error

Margin of Error = Zcritical * sqrt[(phat(1 - phat)) /n]

Margin of Error = 1.96 * sqrt[(0.33 * 0.67) / 1000]

Margin of Error = 1.96 * 0.0148694

Margin of Error = 0.0291440

Lower boundary = (0.33 - 0.0291440) = 0.300856

Upper boundary = (0.33 + 0.0291440) = 0.359144

Therefore, the required real proportion's 95% confidence interval is (0.301; 0.359).

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Correct question:
Cyber Monday Shopping A survey of 1000 U.S. adults found that 33% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 95% confidence interval of the true proportion.

a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

x-5=4, the answer for that equation is not 0. so that is your answer.

Step-by-step explanation:

Answer:

Step-by-step explanation: I am sorry but i don't understand a single thing:(

Answer:

159

Step-by-step explanation:

She paid 6 payments of 139

6*139 = 834

The cost was 675

834-675 =159

The interest was 159

Answer:

f(x) = 12x³ + 11x² - 43x + 21

Step-by-step explanation:

given the product of factors

(4x - 3)(3x² + 5x - 7)

multiply each term in the second factor by each term in the first factor, that is

4x(3x² + 5x - 7) - 3 (3x² + 5x - 7) ← distribute parenthesis

= 12x³ + 20x² - 28x - 9x² - 15x + 21 ← collect like terms

= 12x³ + 11x² - 43x + 21

then the polynomial is

f(x) = 12x³ + 11x² - 43x + 21

Answer:

23.3

Step-by-step explanation:

The length of midsegment of the trapizoid with bases 35 and 71 is 53.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

A trapezoid is a closed, four-sided, two-dimensional shape that has both a perimeter and an area. The bases of the trapezoid are the two sides of the form that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the smallest distance between two parallel sides. Calculating a trapezoid's area is easy since its opposite sides are parallel to one another.

A trapezoid differs from other quadrilaterals in that it has the following characteristics:

The length of midsegment is sum of bases divided by 2

therefore midsegment = (35 + 71)/2 = 53.

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The given query displays the model number and price of all products made by the manufacturer B. There are six relations involved in this query.

Let's go through each of the relations one by one.

R1 relationR1:=σ maker ​=B( Product ⋈PC)

This relation R1 selects the tuples from the Product ⋈ PC relation whose maker is B.

The resulting relation R1 has two attributes: model and price.R2 relationR2:=σ maker ​=B( Product ⋈ Laptop)

This relation R2 selects the tuples from the Product ⋈ Laptop relation whose maker is B.

The resulting relation R2 has two attributes: model and price.R3 relationR3:=σ maker ​=B( Product ⋈ Printer)

This relation R3 selects the tuples from the Product ⋈ Printer relation whose maker is B.

The resulting relation R3 has two attributes: model and price.R4 relationR4:=Π model, ​price (R1)

The resulting relation R4 has two attributes: model and price.R5 relationR5:=π model, price ​(R2)

The relation R5 selects the model and price attributes from the relation R2.

The resulting relation R5 has two attributes: model and price.R6 relationR6:=Π model, ​price (R3)

The resulting relation R6 has two attributes: model and price.

Finally, the relation R7 combines the relations R4, R5, and R6 using the union operation. R7 relationR7:=R4∪R5∪R6

Therefore, the relation R7 has the model number and price of all products made by the manufacturer B.

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